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https://en.wikipedia.org/wiki/Biositemap
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A Biositemap is a way for a biomedical research institution of organisation to show how biological information is distributed throughout their Information Technology systems and networks. This information may be shared with other organisations and researchers.
The Biositemap enables web browsers, crawlers and robots to easily access and process the information to use in other systems, media and computational formats. Biositemaps protocols provide clues for the Biositemap web harvesters, allowing them to find resources and content across the whole interlink of the Biositemap system. This means that human or machine users can access any relevant information on any topic across all organisations throughout the Biositemap system and bring it to their own systems for assimilation or analysis.
File framework
The information is normally stored in a biositemap.rdf or biositemap.xml file which contains lists of information about the data, software, tools material and services provided or held by that organisation. Information is presented in metafields and can be created online through sites such as the biositemaps online editor.
The information is a blend of sitemaps and RSS feeds and is created using the Information Model (IM) and Biomedical Resource Ontology (BRO). The IM is responsible for defining the data held in the metafields and the BRO controls the terminology of the data held in the resource_type field. The BRO is critical in aiding the interactivity of both the other organisations and third parties to search and refine those searches.
Data formats
The Biositemaps Protocol allows scientists, engineers, centers and institutions engaged in modeling, software tool development and analysis of biomedical and informatics data to broadcast and disseminate to the world the information about their latest computational biology resources (data, software tools and web services). The biositemap concept is based on ideas from Efficient, Automated Web Resource Harvesting an
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https://en.wikipedia.org/wiki/Cantor%27s%20diagonal%20argument
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In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. Such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which Cantor began.
The diagonal argument was not Cantor's first proof of the uncountability of the real numbers, which appeared in 1874.
However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the Entscheidungsproblem. Diagonalization arguments are often also the source of contradictions like Russell's paradox and Richard's paradox.
Uncountable set
Cantor considered the set T of all infinite sequences of binary digits (i.e. each digit is zero or one).
He begins with a constructive proof of the following lemma:
If s1, s2, ... , sn, ... is any enumeration of elements from T, then an element s of T can be constructed that doesn't correspond to any sn in the enumeration.
The proof starts with an enumeration of elements from T, for example
{|
|-
| s1 = || (0, || 0, || 0, || 0, || 0, || 0, || 0, || ...)
|-
| s2 = || (1, || 1, || 1, || 1, || 1, || 1, || 1, || ...)
|-
| s3 = || (0, || 1, || 0, || 1, || 0, || 1, || 0, || ...)
|-
| s4 = || (1, || 0, || 1, || 0, || 1, || 0, || 1, || ...)
|-
| s5 = || (1, || 1, || 0, || 1, || 0, || 1, || 1, || ...)
|-
| s6 = || (0, || 0, || 1, || 1, || 0, || 1, || 1, || ...)
|-
| s7 = || (1, || 0, || 0, || 0, || 1, || 0, || 0, || ...)
|-
| ...
|}
Next, a sequence s is constructed by choosing the 1st digit as complementary to the 1st digit of s1 (swapping 0s for 1s and vice versa), the 2nd digit as complementary to the 2nd dig
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https://en.wikipedia.org/wiki/Biological%20network
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A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. In general, networks or graphs are used to capture relationships between entities or objects. A typical graphing representation consists of a set of nodes connected by edges.
History of networks
As early as 1736 Leonhard Euler analyzed a real-world issue known as the Seven Bridges of Königsberg, which established the foundation of graph theory. From the 1930's-1950's the study of random graphs were developed. During the mid 1990's, it was discovered that many different types of "real" networks have structural properties quite different from random networks. In the late 2000's, scale-free and small-world networks began shaping the emergence of systems biology, network biology, and network medicine. In 2014, graph theoretical methods were used by Frank Emmert-Streib to analyze biological networks.
In the 1980s, researchers started viewing DNA or genomes as the dynamic storage of a language system with precise computable finite states represented as a finite state machine. Recent complex systems research has also suggested some far-reaching commonality in the organization of information in problems from biology, computer science, and physics.
Networks in biology
Protein–protein interaction networks
Protein-protein interaction networks (PINs) represent the physical relationship among proteins present in a cell, where proteins are nodes, and their interactions are undirected edges. Due to their undirected nature, it is difficult to identify all the proteins involved in an interaction. Protein–protein interactions (PPIs) are essential to the cellular processes and also the most intensely analyzed networks in biology. PPIs could be discovered by various experimental techniques, among which the yeast two-hybrid system is a commonly used technique for the study of binary interactions. Recently, high-throughput studies using
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https://en.wikipedia.org/wiki/Indefinite%20product
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In mathematics, the indefinite product operator is the inverse operator of . It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Some authors use term discrete multiplicative integration.
Thus
More explicitly, if , then
If F(x) is a solution of this functional equation for a given f(x), then so is CF(x) for any constant C. Therefore, each indefinite product actually represents a family of functions, differing by a multiplicative constant.
Period rule
If is a period of function then
Connection to indefinite sum
Indefinite product can be expressed in terms of indefinite sum:
Alternative usage
Some authors use the phrase "indefinite product" in a slightly different but related way to describe a product in which the numerical value of the upper limit is not given. e.g.
.
Rules
List of indefinite products
This is a list of indefinite products . Not all functions have an indefinite product which can be expressed in elementary functions.
(see K-function)
(see Barnes G-function)
(see super-exponential function)
See also
Indefinite sum
Product integral
List of derivatives and integrals in alternative calculi
Fractal derivative
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https://en.wikipedia.org/wiki/BIBO%20stability
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In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded.
A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is
For discrete-time signals:
For continuous-time signals:
Time-domain condition for linear time-invariant systems
Continuous-time necessary and sufficient condition
For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, , be absolutely integrable, i.e., its L1 norm exists.
Discrete-time sufficient condition
For a discrete time LTI system, the condition for BIBO stability is that the impulse response be absolutely summable, i.e., its norm exists.
Proof of sufficiency
Given a discrete time LTI system with impulse response the relationship between the input and the output is
where denotes convolution. Then it follows by the definition of convolution
Let be the maximum value of , i.e., the -norm.
(by the triangle inequality)
If is absolutely summable, then and
So if is absolutely summable and is bounded, then is bounded as well because .
The proof for continuous-time follows the same arguments.
Frequency-domain condition for linear time-invariant systems
Continuous-time signals
For a rational and continuous-time system, the condition for stability is that the region of convergence (ROC) of the Laplace transform includes the imaginary axis. When the system is causal, the ROC is the open region to the right of a vertical line whose abscissa is the real part of the "largest pole", or the pole that has the greatest real part of any pole in the system. The real part of the largest pole defining the ROC is called the abscissa of convergence. Therefore, all poles of the system must be in the strict left half of the s
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https://en.wikipedia.org/wiki/Allometry
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Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in On Growth and Form and by Julian Huxley in 1932.
Overview
Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body. One application is in the study of various insect species (e.g., Hercules beetles), where a small change in overall body size can lead to an enormous and disproportionate increase in the dimensions of appendages such as legs, antennae, or horns The relationship between the two measured quantities is often expressed as a power law equation (allometric equation) which expresses a remarkable scale symmetry:
or in a logarithmic form,
or similarly,
where is the scaling exponent of the law. Methods for estimating this exponent from data can use type-2 regressions, such as major axis regression or reduced major axis regression, as these account for the variation in both variables, contrary to least-squares regression, which does not account for error variance in the independent variable (e.g., log body mass). Other methods include measurement-error models and a particular kind of principal component analysis.
The allometric equation can also be acquired as a solution of the differential equation
Allometry often studies shape differences in terms of ratios of the objects' dimensions. Two objects of different size, but common shape, have their dimensions in the same ratio. Take, for example, a biological object that grows as it matures. Its size changes with age, but the shapes are similar. Studies of ontogenetic allometry often use lizards or snakes as model organisms both because they lack parental care after birth or hatching and because they exhibit a large range of body sizes between the juv
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https://en.wikipedia.org/wiki/Rice%20University%20Electrical%20and%20Computer%20Engineering
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The Rice University Department of Electrical and Computer Engineering is one of nine academic departments at the George R. Brown School of Engineering at Rice University. Ashutosh Sabharwal is the Department Chair. Originally the Rice Department of Electrical Engineering, it was renamed in 1984 to Electrical and Computer Engineering.
Research
Rice ECE Faculty perform research in the following areas: Computer Engineering; Data Science, Neuroengineering; Photonics, Electronics and Nano-devices, and Systems. Rice has a long history in digital signal processing (DSP) dating back to its inception in the late 1960s.
Computer Engineering faculty have a research focus in analog and mixed-signal design, VLSI signal processing, computer architecture and embedded systems, biosensors and computer vision, and hardware security and storage systems, including applications to education. Biosensors and mobile wireless healthcare are growing application areas in embedded systems research. Smartphones with imaging devices are leading to new areas in computer vision and sensing. In the area of computer architecture, research interests include parallel computing, large-scale storage systems, and resource scheduling for performance and power.
Data Science faculty integrate the foundations, tools and techniques involving data acquisition (sensors and systems), data analytics (machine learning, statistics), data storage and computing infrastructure (GPU/CPU computing, FPGAs, cloud computing, security and privacy) in order to enable meaningful extraction of actionable information from diverse and potentially massive data sources.
Neuroengineering faculty are members of the Rice Center for Neuroengineering, a collaborative effort with Texas Medical Center researchers. They develop technology for treating and diagnosing neural diseases. Current research areas include interrogating neural circuits at the cellular level, analyzing neuronal data in real-time, and manipulating healthy or dise
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https://en.wikipedia.org/wiki/Network%20virtualization%20platform
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A network virtualization platform decouples the hardware plane from the software plane such that the host hardware plane can be administratively programmed to assign its resources to the software plane. This allows for the virtualization of CPU, memory, disk and most importantly network IO. Upon such virtualization of hardware resources, the platform can accommodate multiple virtual network applications such as firewalls, routers, Web filters, and intrusion prevention systems, all functioning much like standalone hardware appliances, but contained within a single hardware appliance. The key benefit to such technology is doing all of this while maintaining the network performance typically seen with that of standalone network appliances as well as enabling the ability to administratively or dynamically program resources at will.
Server virtualization history
Server virtualization, a technology that has become mainstream, originally gained popularity when VMware entered the market in 2001 with its GSX server software. This technology gave IT organizations the ability to reduce the amount of rack space required to accommodate multiple servers and reduced the cost of powering and cooling data centers by consolidating server based applications onto a single piece of hardware. One of the problems with server virtualization is in how applications are networked together. Within a server virtualization environment, applications are interconnected by what is referred to as a virtual switch, which is very different from high-performing hardware-based network switches offered by the likes of Juniper Networks and Cisco Systems. Virtual switches are software-based switches and rely on the movement of packets up and down a software stack which relies on the same CPUs which are being used to drive the applications. Because of this software approach to switching, networking applications such as firewalls and routers, which require high levels of throughput and low levels of latenc
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https://en.wikipedia.org/wiki/Counting%20rods
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Counting rods () are small bars, typically 3–14 cm (1" to 6") long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
The written forms based on them are called rod numerals. They are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period (circa 475 BCE) to the 16th century.
History
Chinese arithmeticians used counting rods well over two thousand years ago.
In 1954 forty-odd counting rods of the Warring States period (5th century BCE to 221 BCE) were found in Zuǒjiāgōngshān (左家公山) Chu Grave No.15 in Changsha, Hunan.
In 1973 archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty (206 BCE to 220 CE). On one of the wooden scripts was written: "当利二月定算𝍥". This is one of the earliest examples of using counting-rod numerals in writing.
A square lacquer box, dating from c. 168 BCE, containing a square chess board with the TLV patterns, chessmen, counting rods, and other items, was excavated in 1972, from Mawangdui M3, Changsha, Hunan Province.
In 1976 a bundle of Western Han-era (202 BCE to 9 CE) counting rods made of bones was unearthed from Qianyang County in Shaanxi. The use of counting rods must predate it; Sunzi ( 544 to 496 BCE), a military strategist at the end of Spring and Autumn period of 771 BCE to 5th century BCE, mentions their use to make calculations to win wars before going into the battle; Laozi (died 531 BCE), writing in the Warring States period, said "a good calculator doesn't use counting rods". The Book of Han (finished 111 CE) recorded: "they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces".
At first, calculating rods were round in cross-section, but by the time of the Sui dynasty (581 to 618 CE) mathematicians used triangular rods to represent po
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https://en.wikipedia.org/wiki/Blue%20ice%20%28aviation%29
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In aviation, blue ice is frozen sewage material that has leaked mid-flight from commercial aircraft lavatory waste systems. It is a mixture of human biowaste and liquid disinfectant that freezes at high altitude. The name comes from the blue color of the disinfectant. Airlines are not allowed to dump their waste tanks mid-flight, and pilots have no mechanism by which to do so; however, leaks sometimes do occur from a plane's septic tank.
Danger of ground impact
There were at least 27 documented incidents of blue ice impacts in the United States between 1979 and 2003. These incidents typically happen under airport landing paths as the mass warms sufficiently to detach from the plane during its descent. A rare incident of falling blue ice causing damage to the roof of a home was reported on October 20, 2006 in Chino, California. A similar incident was reported in Leicester, UK, in 2007.
In 1971, a chunk of ice from an aircraft tore a large hole in the roof of the Essex Street Chapel in Kensington, London, and was one trigger for the demolition of the building.
In November 2011, a chunk of ice, the size of an orange, broke through the roof of a private house in Ratingen-Hösel, Germany.
In February 2013, a "football sized" ball of blue ice smashed through a conservatory roof in Clanfield, Hampshire, causing around £10,000 worth of damage.
In October 2016, a chunk of ice tore a hole in a private house in Amstelveen, The Netherlands.
In two incidents in May 2018, chunks of blue ice fell onto residents in Kelowna, British Columbia.
In November 2018, a chunk of ice fell from the sky and crashed through the roof of a home in Bristol, England.
Danger to aircraft
Blue ice can also be dangerous to the aircraft the National Transportation Safety Board has recorded three very similar incidents where waste from lavatories caused damage to the leaking aircraft, all involving Boeing 727s. In all three cases, waste from a leaking lavatory hit one (or the other) of the three
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https://en.wikipedia.org/wiki/Label%20switching
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Label switching is a technique of network relaying to overcome the problems perceived by traditional IP-table switching (also known as traditional layer 3 hop-by-hop routing). Here, the switching of network packets occurs at a lower level, namely the data link layer rather than the traditional network layer.
Each packet is assigned a label number and the switching takes place after examination of the label assigned to each packet. The switching is much faster than IP-routing. New technologies such as Multiprotocol Label Switching (MPLS) use label switching. The established ATM protocol also uses label switching at its core.
According to (An Architecture for Differentiated Services, December 1998):
"Examples of the label switching (or virtual circuit) model include Frame Relay, ATM, and MPLS. In this model path forwarding state and traffic management or quality of service (QoS) state is established for traffic streams on each hop along a network path. Traffic aggregates of varying granularity are associated with a label switched path at an ingress node, and packets/cells within each label switched path are marked with a forwarding label that is used to look up the next-hop node, the per-hop forwarding behavior, and the replacement label at each hop. This model permits finer granularity resource allocation to traffic streams, since label values are not globally significant but are only significant on a single link; therefore resources can be reserved for the aggregate of packets/cells received on a link with a particular label, and the label switching semantics govern the next-hop selection, allowing a traffic stream to follow a specially engineered path through the network."
A related topic is "Multilayer Switching," which discusses silicon-based wire-speed routing devices that examine not only layer 3 packet information, but also layer 4 (transport) and layer 7 (application) information.
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https://en.wikipedia.org/wiki/Adesto%20Technologies
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Adesto Technologies is an American corporation founded in 2006 and based in Santa Clara, California. The company provides application-specific semiconductors and embedded systems for the Internet of Things (IoT), and sells its products directly to original equipment manufacturers (OEMs) and original design manufacturers (ODMs) that manufacture products for its end customers. In 2020, Adesto was bought by Dialog Semiconductor.
History
Adesto Technologies was founded by Narbeh Derhacobian, Shane Hollmer, and Ishai Naveh in 2006. Derhacobian formerly served in senior technical and managerial roles at AMD, Virage Logic, and Cswitch Corporations. The company developed a non-volatile memory based on the movement of copper ions in a programmable metallization cell technology licensed from Axon Technologies Corp., a spinoff of Arizona State University.
In October 2010, Adesto acquired intellectual property and patents related to Conductive Bridging Random Access Memory (CBRAM) technology from Qimonda AG, and their first CBRAM product began production in 2011.
In 2015, the company held an initial public offering under the symbol IOTS, which entered the market at $5 per share. Underwriters included Needham & Company, Oppenheimer & Co. Inc., and Roth Capital Partners. The entire offering was valued at $28.75 million.
Between May and September 2018, Adesto completed two acquisitions of S3 Semiconductors and Echelon Corporation. In May, the company acquired S3 Semiconductors, a provider of analog and mixed-signal ASICs and Intellectual Property (IP) cores. In June, the company announced its intention to buy Echelon Corporation, a home and industrial automation company, for $45 million. The acquisition was completed three months later. The company's offerings were expanded to include ASICs and IP from S3 Semiconductors and embedded systems from Echelon Corporation, in addition to its original non-volatile memory (NVM) products.
In 2020, Adesto was acquired by Dialog Semicon
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https://en.wikipedia.org/wiki/Census%20of%20Marine%20Zooplankton
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The Census of Marine Zooplankton is a field project of the Census of Marine Life that has aimed to produce a global assessment of the species diversity, biomass, biogeographic distribution, and genetic diversity of more than 7,000 described species of zooplankton that drift the ocean currents throughout their lives. CMarZ focuses on the deep sea, under-sampled regions, and biodiversity hotspots. From 2004 until 2011, Ann Bucklin was the lead scientist for the project.
Technology plays a great role in CMarZ's research, including the use of integrated morphological and molecular sampling through DNA Barcoding. CMarZ makes its datasets available via the CMarZ Database.
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https://en.wikipedia.org/wiki/Altos%20586
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The Altos 586 was a multi-user microcomputer intended for the business market. It was introduced by Altos Computer Systems in 1983. A configuration with 512 kB of RAM, an Intel 8086 processor, Microsoft Xenix, and 10 MB hard drive cost about US$8,000. 3Com offered this Altos 586 product as a file server for their IBM PC networking solution in spring 1983. The network was 10BASE2 (thin-net) based, with an Ethernet AUI port on the Altos 586.
Reception
BYTE in August 1984 called the Altos 586 "an excellent multiuser UNIX system", with "the best performance" for the price among small Unix systems. The magazine reported that a Altos with 512 kB RAM and 40 MB hard drive "under moderate load approaches DEC VAX performance for most tasks that a user would normally invoke". A longer review in March 1985 stated that "despite some bugs, it's a good product". It criticized the documentation and lack of customer service for developers, but praised the multiuser performance. The author reported that his 586 had run a multiuser bulletin board system 24 hours a day for more than two years with no hardware failures. He concluded that "Very few UNIX or XENIX computers can provide all of the features of the 586 for $8990", especially for multiuser turnkey business users.
See also
Fortune XP 20
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https://en.wikipedia.org/wiki/Copurification
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Copurification in a chemical or biochemical context is the physical separation by chromatography or other purification technique of two or more substances of interest from other contaminating substances. For substances to co-purify usually implies that these substances attract each other to form a non-covalent complex such as in a protein complex.
However, when fractionating mixtures, especially mixtures containing large numbers of components (for example a cell lysate), it is possible by chance that some components may copurify even though they don't form complexes. In this context the term copurification is sometimes used to denote when two biochemical activities or some other property are isolated together after purification but it is not certain if the sample has been purified to homogeneity (i.e., contains only one molecular species or one molecular complex). Hence these activities or properties are likely but not guaranteed to reside on the same molecule or in the same molecular complex.
Applications
Copurification procedures, such as co-immunoprecipitation, are commonly used to analyze interactions between proteins. Copurification is one method used to map the interactome of living organisms.
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https://en.wikipedia.org/wiki/Phase%20vocoder
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A phase vocoder is a type of vocoder-purposed algorithm which can interpolate information present in the frequency and time domains of audio signals by using phase information extracted from a frequency transform. The computer algorithm allows frequency-domain modifications to a digital sound file (typically time expansion/compression and pitch shifting).
At the heart of the phase vocoder is the short-time Fourier transform (STFT), typically coded using fast Fourier transforms. The STFT converts a time domain representation of sound into a time-frequency representation (the "analysis" phase), allowing modifications to the amplitudes or phases of specific frequency components of the sound, before resynthesis of the time-frequency domain representation into the time domain by the inverse STFT. The time evolution of the resynthesized sound can be changed by means of modifying the time position of the STFT frames prior to the resynthesis operation
allowing for time-scale modification of the original sound file.
Phase coherence problem
The main problem that has to be solved for all cases of manipulation of the STFT is the fact that individual signal components (sinusoids, impulses) will be spread over multiple frames and multiple STFT frequency locations (bins). This is because the STFT analysis is done using overlapping analysis windows. The windowing results in spectral leakage such that the information of individual sinusoidal components is spread over adjacent STFT bins. To avoid border effects of tapering of the analysis windows, STFT analysis windows overlap in time. This time overlap results in the fact that adjacent STFT analyses are strongly correlated (a sinusoid present in analysis frame at time "t" will be present in the subsequent frames as well). The problem of signal transformation with the phase vocoder is related to the problem that all modifications that are done in the STFT representation need to preserve the appropriate correlation between adja
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https://en.wikipedia.org/wiki/Collision%20avoidance%20%28networking%29
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In computer networking and telecommunication, collision-avoidance methods try to avoid resource contention by attempting to avoid simultaneous attempts to access the same resource.
Collision-avoidance methods include prior scheduling of timeslots, carrier-detection schemes, randomized access times, and exponential backoff after collision detection.
See also
Carrier sense multiple access with collision avoidance
Polling
Collision domain
External links
Channel access methods
Computer networking
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https://en.wikipedia.org/wiki/Decapping
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Decapping (decapsulation) or delidding of an integrated circuit is the process of removing the protective cover or integrated heat spreader (IHS) of an integrated circuit so that the contained die is revealed for visual inspection of the micro circuitry imprinted on the die. This process is typically done in order to debug a manufacturing problem with the chip, or possibly to copy information from the device, to check for counterfeit chips or to reverse engineer it. Companies such as TechInsights and ChipRebel decap, take die shots of, and reverse engineer chips for customers. Modern integrated circuits can be encapsulated in plastic, ceramic, or epoxy packages.
Delidding may also be done in an effort to reduce the operating temperatures of an integrated circuit such as a processor, by replacing the thermal interface material (TIM) between the die and the IHS with a higher-quality TIM. With care, it's possible to decap a device and still leave it functional.
Method
Decapping is usually carried out by chemical etching of the covering, laser cutting, laser evaporation of the covering, plasma etching or mechanical removal of the cover using a milling machine, saw blade or by desoldering and cutting. The process can be either destructive or non-destructive of the internal die.
Chemical etching usually involves subjecting the (if made of plastic) IC package to concentrated or fuming nitric acid, heated concentrated sulfuric acid, white fuming nitric acid or a mixture of the two for some time, possibly while applying heat externally with a hot plate or hot air gun, which dissolve the package while leaving the die intact. The acids are dangerous, so protective equipment such as appropriate gloves, full face respirator with appropriate acid cartridges, a lab coat and a fume hood are required.
Laser decapping scans a high power laser beam across the plastic IC package to vaporize it, while avoiding the actual silicon die.
In a common version of non-destructive, mechani
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https://en.wikipedia.org/wiki/Computer%20engineering%20compendium
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This is a list of the individual topics in Electronics, Mathematics, and Integrated Circuits that together make up the Computer Engineering field. The organization is by topic to create an effective Study Guide for this field. The contents match the full body of topics and detail information expected of a person identifying themselves as a Computer Engineering expert as laid out by the National Council of Examiners for Engineering and Surveying. It is a comprehensive list and superset of the computer engineering topics generally dealt with at any one time.
Part 1 - Basics
Character Encoding
Character (computing)
Universal Character Set
IEEE 1394
ASCII
Math
Bitwise operation
Signed number representations
IEEE floating point
Operators in C and C++
De Morgan's laws
Booth's multiplication algorithm
Binary multiplier
Wallace tree
Dadda multiplier
Multiply–accumulate operation
Big O notation
Euler's identity
Basic Electronics
Series and parallel circuits
RLC circuit
Transistor
Operational amplifier applications
Signal Processing
Signal processing
Digital filter
Fast Fourier transform
Cooley–Tukey FFT algorithm
Modified discrete cosine transform
Digital signal processing
Analog-to-digital converter
Error Detection/Correction
Parity bit
Error detection and correction
Cyclic redundancy check
Hamming code
Hamming(7,4)
Convolutional code
Forward error correction
Noisy-channel coding theorem
Modulation
Signal-to-noise ratio
Linear code
Noise (electronics)
Part 2 - Hardware
Hardware
Logic family
Multi-level cell
Flip-flop (electronics)
Race condition
Binary decision diagram
Circuit minimization for Boolean functions
Karnaugh map
Quine–McCluskey algorithm
Integrated circuit design
Programmable Logic
Standard cell
Programmable logic device
Field-programmable gate array
Complex programmable logic device
Application-specific integrated circuit
Logic optimization
Register-transfer level
Floorplan (microelectronics)
Hardware description language
VHDL
Verilog
Electronic des
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https://en.wikipedia.org/wiki/IEEE%20P1906.1
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The IEEE P1906.1 - Recommended Practice for Nanoscale and Molecular Communication Framework is a standards working group sponsored by the IEEE Communications Society Standards Development Board whose goal is to develop a common framework for nanoscale and molecular communication. Because this is an emerging technology, the standard is designed to encourage innovation by reaching consensus on a common definition, terminology, framework, goals, metrics, and use-cases that encourage innovation and enable the technology to advance at a faster rate. The draft passed an initial sponsor balloting with comments on January 2, 2015. The comments were addressed by the working group and the resulting draft ballot passed again on August 17, 2015. Finally, additional material regarding SBML was contributed and the final draft passed again on October 15, 2015. The draft standard was approved by IEEE RevCom in the final quarter of 2015.
Membership
Working group membership includes experts in industry and academia with strong backgrounds in mathematical modeling, engineering, physics, economics and biological sciences.
Content
Electronic components such as transistors, or electrical/electromagnetic message carriers whose operation is similar at the macroscale and nanoscale are excluded from the definition. A human-engineered, synthetic component must form part of the system because it is important to avoid standardizing nature or physical processes. The definition of communication, particularly in the area of cell-surface interactions as viewed by biologists versus non-biologists has been a topic of debate. The interface is viewed as a communication channel, whereas the 'receptor-signaling-gene expression' events are the network.
The draft currently comprises: definition, terminology, framework, metrics, use-cases, and reference code (ns-3).
The standard provides a very broad foundation and encompasses all approaches to nanoscale communication. While there have been many su
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https://en.wikipedia.org/wiki/Vibration%20theory%20of%20olfaction
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The vibration theory of smell proposes that a molecule's smell character is due to its vibrational frequency in the infrared range. This controversial theory is an alternative to the more widely accepted docking theory of olfaction (formerly termed the shape theory of olfaction), which proposes that a molecule's smell character is due to a range of weak non-covalent interactions between its protein odorant receptor (found in the nasal epithelium), such as electrostatic and Van der Waals interactions as well as H-bonding, dipole attraction, pi-stacking, metal ion, Cation–pi interaction, and hydrophobic effects, in addition to the molecule's conformation.
Introduction
The current vibration theory has recently been called the "swipe card" model, in contrast with "lock and key" models based on shape theory. As proposed by Luca Turin, the odorant molecule must first fit in the receptor's binding site. Then it must have a vibrational energy mode compatible with the difference in energies between two energy levels on the receptor, so electrons can travel through the molecule via inelastic electron tunneling, triggering the signal transduction pathway. The vibration theory is discussed in a popular but controversial book by Chandler Burr.
The odor character is encoded in the ratio of activities of receptors tuned to different vibration frequencies, in the same way that color is encoded in the ratio of activities of cone cell receptors tuned to different frequencies of light. An important difference, though, is that the odorant has to be able to become resident in the receptor for a response to be generated. The time an odorant resides in a receptor depends on how strongly it binds, which in turn determines the strength of the response; the odor intensity is thus governed by a similar mechanism to the "lock and key" model. For a pure vibrational theory, the differing odors of enantiomers, which possess identical vibrations, cannot be explained. However, once the link betwe
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https://en.wikipedia.org/wiki/List%20of%20Mersenne%20primes%20and%20perfect%20numbers
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Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as for some positive integer . For example, is a Mersenne prime as it is a prime number and is expressible as . The numbers corresponding to Mersenne primes must themselves be prime, although not all primes lead to Mersenne primes—for example, . Meanwhile, perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, is a perfect number because the proper divisors of are , and , and .
There is a one-to-one correspondence between the Mersenne primes and the even perfect numbers. This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by Leonhard Euler: even numbers are perfect if and only if they can be expressed in the form , where is a Mersenne prime. In other words, all numbers that fit that expression are perfect, while all even perfect numbers fit that form. For instance, in the case of , is prime, and is perfect.
It is currently an open problem as to whether there are an infinite number of Mersenne primes and even perfect numbers. The frequency of Mersenne primes is the subject of the Lenstra–Pomerance–Wagstaff conjecture, which states that the expected number of Mersenne primes less than some given is , where is Euler's number, is Euler's constant, and is the natural logarithm. It is also not known if any odd perfect numbers exist; various conditions on possible odd perfect numbers have been proven, including a lower bound of .
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents . , there are 51 known Mersenne primes (and therefore perfect numbers), the largest 17 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or G
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https://en.wikipedia.org/wiki/MERMOZ
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MERMOZ (also, MERMOZ project and Monitoring planEtary suRfaces with Modern pOlarimetric characteriZation) is an astrobiology project designed to remotely detect biosignatures of life. Detection is based on molecular homochirality, a characteristic property of the biochemicals of life. The aim of the project is to remotely identify and characterize life on the planet Earth from space, and to extend this technology to other solar system bodies and exoplanets. The project began in 2018, and is a collaboration of the University of Bern, University of Leiden and Delft University of Technology.
According to a member of the research team, “When light is reflected by biological matter, a part of the light’s electromagnetic waves will travel in either clockwise or counterclockwise spirals ... This phenomenon is called circular polarization and is caused by the biological matter’s homochirality.” These unique spirals of light indicate living materials; whereas, non-living materials do not reflect such unique spirals of light, according to the researchers.
The research team conducted feasibility studies, using a newly designed detection instrument, based on circular spectropolarimetry, and named FlyPol+ (an upgrade from the original FlyPol), by flying in a helicopter at an altitude of and velocity of for 25 minutes. The results were successful in remotely detecting living material, and quickly (within seconds) distinguishing living material from non-living material. The researchers concluded: "Circular spectropolarimetry can be a powerful technique to detect life beyond Earth, and we emphasize the potential of utilizing circular spectropolarimetry as a remote sensing tool to characterize and monitor in detail the vegetation physiology and terrain features of Earth itself."
The researchers next expect to scan the Earth from the International Space Station (ISS) with their detection instruments. One consequence of further successful studies is a possible pathfinder space m
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https://en.wikipedia.org/wiki/Free%20variables%20and%20bound%20variables
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In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. The terms are opposites. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.
In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.
An instance of a variable symbol is bound, in contrast, if the value of that variable symbol has been bound to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifiers, variable-binding operators, or an explicit statement of allowed values for the variable (such as, "...where is a positive integer".) A variable symbol overall is bound if at least one occurrence of it is bound.pp.142--143 Since the same variable symbol may appear in multiple places in an expression, some occurrences of the variable symbol may be free while others are bound,p.78 hence "free" and "bound" are at first defined for occurrences and then generalized over all occurrences of said variable symbol in the expression. However it is done, the variable ceases to be an independent variable on which the value of the expression depends, whether that value be a truth value or the numerical result of a calculation, or, more generally, an element of an image set of a function.
While the domain of discourse in many contexts is understood, when an explicit range of values for the bou
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https://en.wikipedia.org/wiki/Phenology
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Phenology is the study of periodic events in biological life cycles and how these are influenced by seasonal and interannual variations in climate, as well as habitat factors (such as elevation).
Examples include the date of emergence of leaves and flowers, the first flight of butterflies, the first appearance of migratory birds, the date of leaf colouring and fall in deciduous trees, the dates of egg-laying of birds and amphibia, or the timing of the developmental cycles of temperate-zone honey bee colonies. In the scientific literature on ecology, the term is used more generally to indicate the time frame for any seasonal biological phenomena, including the dates of last appearance (e.g., the seasonal phenology of a species may be from April through September).
Because many such phenomena are very sensitive to small variations in climate, especially to temperature, phenological records can be a useful proxy for temperature in historical climatology, especially in the study of climate change and global warming. For example, viticultural records of grape harvests in Europe have been used to reconstruct a record of summer growing season temperatures going back more than 500 years.
In addition to providing a longer historical baseline than instrumental measurements, phenological observations provide high temporal resolution of ongoing changes related to global warming.
Etymology
The word is derived from the Greek φαίνω (phainō), "to show, to bring to light, make to appear" + λόγος (logos), amongst others "study, discourse, reasoning" and indicates that phenology has been principally concerned with the dates of first occurrence of biological events in their annual cycle.
The term was first used by Charles François Antoine Morren, a professor of botany at the University of Liège (Belgium). Morren was a student of Adolphe Quetelet. Quetelet made plant phenological observations at the Royal Observatory of Belgium in Brussels. He is considered "one of 19th century t
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https://en.wikipedia.org/wiki/Copulas%20in%20signal%20processing
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A copula is a mathematical function that provides a relationship between marginal distributions of random variables and their joint distributions. Copulas are important because it represents a dependence structure without using marginal distributions. Copulas have been widely used in the field of finance, but their use in signal processing is relatively new. Copulas have been employed in the field of wireless communication for classifying radar signals, change detection in remote sensing applications, and EEG signal processing in medicine. In this article, a short introduction to copulas is presented, followed by a mathematical derivation to obtain copula density functions, and then a section with a list of copula density functions with applications in signal processing.
Introduction
Using Sklar's theorem, a copula can be described as a cumulative distribution function (CDF) on a unit-space with uniform marginal distributions on the interval (0, 1). The CDF of a random variable X is the probability that X will take a value less than or equal to x when evaluated at x itself. A copula can represent a dependence structure without using marginal distributions. Therefore, it is simple to transform the uniformly distributed variables of copula (u, v, and so on) into the marginal variables (x, y, and so on) by the inverse marginal cumulative distribution function. Using the chain rule, copula distribution function can be partially differentiated with respect to the uniformly distributed variables of copula, and it is possible to express the multivariate probability density function (PDF) as a product of a multivariate copula density function and marginal PDF''s. The mathematics for converting a copula distribution function into a copula density function is shown for a bivariate case, and a family of copulas used in signal processing are listed in a TABLE 1.
Mathematical derivation
For any two random variables X and Y, the continuous joint probability distribution functi
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https://en.wikipedia.org/wiki/Klepton
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In biology, a klepton (abbr. kl.) and synklepton (abbr sk.) is a species that requires input from another biological taxon (normally from a species which is closely related to the kleptonic species) to complete its reproductive cycle. Specific types of kleptons are zygokleptons, which reproduce by zygogenesis; gynokleptons which reproduce by gynogenesis, and tychokleptons, which reproduce by a combination of both systems.
Kleptogenic reproduction results in three potential outcomes. A unisexual female may simply activate cell division in the egg through the presence of a male's sperm without incorporating any of his genetic material—this results in the production of clonal offspring. The female may also incorporate the male's sperm into her egg, but can do so without excising any of her genetic material. This results in increased ploidy levels that range from triploid to pentaploid in wild individuals. Finally, the female also has the option of replacing some of her genetic material with that of the male's, resulting in a "hybrid" of sorts without increasing ploidy.
Etymology
The term is derived from the (Ancient or Modern) Greek κλέπτ(ης) (klépt(ēs), “thief”) + -on, after taxon, or kleptein, "to steal". A klepton "steals" from an exemplar of another species in order to reproduce. In a paper entitled "Taxonomy of Parthenogenetic Species of Hybrid Origin", Charles J. Cole argues that the thief motif closely parallels the behaviour of certain reptiles.
Examples
Salamander species
In the wild, five species of Ambystoma salamanders contribute to a unisexual complex that reproduces via a combination of gynogenesis and kleptogenesis: A. tigrinum, A. barbouri, A. texanum, A. jeffersonium, and A. laterale. Over twenty genomic combinations have been found in nature, ranging from "LLJ" individuals (two A. laterale and an A. jeffersonium genome) to "LJTi" individuals (an A. laterale, A. jeffersonium, and an A. tigrinum genome). Every combination, however, contains the gen
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https://en.wikipedia.org/wiki/Pi%20%28art%20project%29
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Pi is the name of a multimedia installation in the vicinity of the Viennese Karlsplatz. Pi is located in the Opernpassage between the entrance to the subway and the subway stop in Secession near the Naschmarkt. The individual behind the project was the Canadian artist Ken Lum from Vancouver.
Pi, under construction from January 2005 to November 2006 and opened in December 2006, consists of statistical information and a representation of π to 478 decimal places. A more recent project is the calculation of the decimal places of π, indicating the importance of the eponymous media for installation of their number and infinity.
The exhibit is 130 meters long. In addition to the number pi, there is a total of 16 factoids of reflective display cases that convey a variety of statistical data in real time. Apart from the World population there are also topics such as the worldwide number of malnourished children and the growth of Sahara since the beginning of the year. Even less serious issues such as the number of eaten Wiener Schnitzels in Vienna of the given year and the current number of lovers in Vienna are represented.
In the middle of the passage standing there is a glass case with images, texts and books on the subjects of population and migration.
The scientific data were developed jointly by Ken Lum and the . "Pi" is to show that contemporary art is in a position to connect art to science, architecture and sociology. The aim of this project was to transform the Karlsplatz into a "vibrant place to meet, with communicative artistic brilliance."
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https://en.wikipedia.org/wiki/Integraph
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An Integraph is a mechanical analog computing device for plotting the integral of a graphically defined function.
History
Gaspard-Gustave de Coriolis first described the fundamental principal of a mechanical integraph in 1836 in the Journal de Mathématiques Pures et Appliquées. A full description of an integraph was published independently around 1880 by both British physicist Sir Charles Vernon Boys and Bruno Abdank-Abakanowicz, a Polish-Lithuanian mathematician/electrical engineer. Boys described a design for an integraph in 1881 in the Philosophical Magazine. Abakanowicz developed a practical working prototype in 1878, with improved versions of the prototype being manufactured by firms such as Coradi in Zürich, Switzerland. Customized and further improved versions of Abakanowicz's design were manufactured until well after 1900, with these later modifications being made by Abakanowicz in collaboration M. D. Napoli, the "principal inspector of the railroad Chemin de Fer de l’Est and head of its testing laboratory".
Description
The input to the integraph is a tracing point that is the guiding point that traces the differential curve. The output is defined by the path a disk that rolls along the paper without slipping takes. The mechanism sets the angle of the output disk based on the position of the input curve: if the input is zero, the disk is angled to roll straight, parallel to the x axis on the Cartesian plane. If the input is above zero the disk is angled slightly toward the positive y direction, such that the y value of its position increases as it rolls in that direction. If the input is below zero, the disk is angled the other way such that its y position decreases as it rolls.
The hardware consists of a rectangular carriage which moves left to right on rollers. Two sides of the carriage run parallel to the x axis. The other two sides are parallel to the y axis. Along the trailing vertical (y axis) rail slides a smaller carriage holding a tracing point.
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https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Tenenbaum%E2%80%93Ford%20constant
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The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. Named after mathematicians Paul Erdős, Gérald Tenenbaum, and Kevin Ford, it is defined as
where is the natural logarithm.
Following up on earlier work by Tenenbaum, Ford used this constant in analyzing the number of integers that are at most and that have a divisor in the range .
Multiplication table problem
For each positive integer , let be the number of distinct integers in an multiplication table. In 1960, Erdős studied the asymptotic behavior of and proved that
as .
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https://en.wikipedia.org/wiki/Power-line%20communication
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Power-line communication (also known as power-line carrier), abbreviated as PLC, carries data on a conductor that is also used simultaneously for AC electric power transmission or electric power distribution to consumers.
In the past, powerlines were solely used for transmitting electricity. But with the advent of advanced networking technologies, including broadband, there's a push for utility and service providers to find cost-effective and high-performance solutions. It's only recently that businesses have started to seriously consider using powerlines for data networking. The possibility of using powerlines as a universal medium to transmit not just electricity or control signals, but also high-speed data and multimedia, is now under investigation.
A wide range of power-line communication technologies are needed for different applications, ranging from home automation to Internet access which is often called broadband over power lines (BPL). Most PLC technologies limit themselves to one type of wires (such as premises wiring within a single building), but some can cross between two levels (for example, both the distribution network and premises wiring). Typically transformers prevent propagating the signal, which requires multiple technologies to form very large networks. Various data rates and frequencies are used in different situations.
A number of difficult technical problems are common between wireless and power-line communication, notably those of spread spectrum radio signals operating in a crowded environment. Radio interference, for example, has long been a concern of amateur radio groups.
Basics
Power-line communications systems operate by adding a modulated carrier signal to the wiring system. Different types of power-line communications use different frequency bands. Since the power distribution system was originally intended for transmission of AC power at typical frequencies of 50 or 60 Hz, power wire circuits have only a limited ability to
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https://en.wikipedia.org/wiki/Compact%20Model%20Coalition
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The Compact Model Coalition (formerly the Compact Model Council) is a working group in the Electronic Design Automation industry formed to choose, maintain and promote the use of standard semiconductor device models. Commercial and industrial analog simulators (such as SPICE) need to add device models as technology advances (see Moore's law) and earlier models become inaccurate. Before this group was formed, new transistor models were largely proprietary, which severely limited the choice of simulators that could be used.
It was formed in August, 1996, for the purpose developing and standardizing the use and implementation of SPICE models and the model interfaces. In May 2013, the Silicon Integration Initiative (Si2) and TechAmerica announced the transfer of the Compact Model Council to Si2 and a renaming to Compact Model Coalition.
New models are submitted to the Coalition, where their technical merits are discussed, and then potential standard models are voted on.
Some of the models supported by the Compact Modeling Coalition include:
BSIM3, a MOSFET model from UC Berkeley (see BSIM).
BSIM4, a more modern MOSFET model, also from UC Berkeley.
PSP, another MOSFET model. PSP originally stood for Penn State-Philips, but one author moved to ASU, and Philips spun off their semiconductor group as NXP Semiconductors. PSP is now developed and supported at CEA-Leti.
BSIMSOI, a model for silicon on insulator MOSFETs.
L-UTSOI, a model for fully-depleted silicon on insulator MOSFETs, developed and supported by CEA-Leti.
HICUM or HIgh CUrrent Model for bipolar transistors, from CEDIC, Dresden University of Technology, Germany, and UC San Diego, USA.
MEXTRAM, a compact model for bipolar transistors that aims to support the design of bipolar transistor circuits at high frequencies in Si and SiGe based process technologies. MEXTRAM was originally developed at NXP Semiconductors and is now developed and supported at Auburn University.
ASM-HEMT, and MVSG, the newest standard
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https://en.wikipedia.org/wiki/Host%20system
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Host system is any networked computer that provides services to other systems or users. These services may include printer, web or database access.
Host system is a computer on a network, which provides services to users or other computers on that network. Host system usually runs a multi-user operating system such as Unix, MVS or VMS, or at least an operating system with network services such as Windows.
Computer networking
fr:Système hôte
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https://en.wikipedia.org/wiki/Cognitive%20hearing%20science
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Cognitive hearing science is an interdisciplinary science field concerned with the physiological and cognitive basis of hearing and its interplay with signal processing in hearing aids. The field includes genetics, physiology, medical and technical audiology, cognitive neuroscience, cognitive psychology, linguistics and social psychology.
Theoretically the research in cognitive hearing science combines a physiological model for the information transfer from the outer auditory organ to the auditory cerebral cortex, and a cognitive model for how language comprehension is influenced by the interplay between the incoming language signal and the individual's cognitive skills, especially the long-term memory and the working memory.
Researchers examine the interplay between type of hearing impairment or deafness, type of signal processing in different hearing aids, type of listening environment and the individual's cognitive skills.
Research in cognitive hearing science has importance for the knowledge about different types of hearing impairment and its effects, as for the possibilities to determine which individuals can make use of certain type of signal processing in hearing aid or cochlear implant and thereby adapt hearing aid to the individual.
Cognitive hearing science has been introduced by researchers at the Linköping University research centre Linnaeus Centre HEAD (HEaring And Deafness) in Sweden, created in 2008 with a major 10-year grant from the Swedish Research Council.
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https://en.wikipedia.org/wiki/Unreasonable%20ineffectiveness%20of%20mathematics
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The unreasonable ineffectiveness of mathematics is a phrase that alludes to the article by physicist Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". This phrase is meant to suggest that mathematical analysis has not proved as valuable in other fields as it has in physics.
Life sciences
I. M. Gelfand, a mathematician who worked in biomathematics and molecular biology, as well as many other fields in applied mathematics, is quoted as stating,
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
An opposing view is given by Leonard Adleman, a theoretical computer scientist who pioneered the field of DNA computing. In Adleman's view, "Sciences reach a point where they become mathematized," starting at the fringes but eventually "the central issues in the field become sufficiently understood that they can be thought about mathematically. It occurred in physics about the time of the Renaissance; it began in chemistry after John Dalton developed atomic theory" and by the 1990s was taking place in biology. By the early 1990s, "Biology was no longer the science of things that smelled funny in refrigerators (my view from undergraduate days in the 1960s). The field was undergoing a revolution and was rapidly acquiring the depth and power previously associated exclusively with the physical sciences. Biology was now the study of information stored in DNA - strings of four letters: A, T, G, and C and the transformations that information undergoes in the cell. There was mathematics here!"
Economics and finance
K. Vela Velupillai wrote of The unreasonable ineffectiveness of mathematics in economics. To him "the headlong rush with which economists have equipped themselves with
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https://en.wikipedia.org/wiki/PHI-base
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https://canto.phi-base.org/
The Pathogen-Host Interactions database (PHI-base) is a biological database that contains curated information on genes experimentally proven to affect the outcome of pathogen-host interactions. The database is maintained by researchers at Rothamsted Research, together with external collaborators since 2005.
Since April 2017 PHI-base is part of ELIXIR, the European life-science infrastructure for biological information via its ELIXIR-UK node.
Background
The Pathogen-Host Interactions database was developed to utilise effectively the growing number of verified genes that mediate an organism's ability to cause disease and / or to trigger host responses.
The web-accessible database catalogues experimentally verified pathogenicity, virulence and effector genes from bacterial, fungal and oomycete pathogens which infect animal, plant and fungal hosts. PHI-base is the first on-line resource devoted to the identification and presentation of information on fungal and oomycete pathogenicity genes and their host interactions. As such, PHI-base aims to be a resource for the discovery of candidate targets in medically and agronomically important fungal and oomycete pathogens for intervention with synthetic chemistries and natural products (fungicides).
Each entry in PHI-base is curated by domain experts and supported by strong experimental evidence (gene disruption experiments) as well as literature references in which the experiments are described. Each gene in PHI-base is presented with its nucleotide and deduced amino acid sequence as well as a detailed structured description of the predicted protein's function during the host infection process. To facilitate data interoperability, genes are annotated using controlled vocabularies (Gene Ontology terms, EC Numbers, etc.), and links to other external data sources such as UniProt, EMBL and the NCBI taxonomy services.
Current developments
Version 4.15 (May 2, 2023) of PHI-base provides informa
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https://en.wikipedia.org/wiki/Molybdovanadate%20reagent
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The molybdovanadate reagent is a solution containing both the molybdate and vanadate ions. It is commonly used in the determination of phosphate ion content. The reagent used is ammonium molybdovanadate with the addition of 70% perchloric acid (sulfuric acid is also known to be used). It is used for purposes such as the analysis of wine, canned fruits and other fruit-based products such as jams and syrups.
Physical properties
The reagent appears as a clear, yellow liquid without odour. It is harmful if inhaled, a recognised carcinogen and can cause eye burns.
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https://en.wikipedia.org/wiki/Hybrid%20%28biology%29
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In biology, a hybrid is the offspring resulting from combining the qualities of two organisms of different varieties, species or genera through sexual reproduction. Generally, it means that each cell has genetic material from two different organisms, whereas an individual where some cells are derived from a different organism is called a chimera. Hybrids are not always intermediates between their parents (such as in blending inheritance), but can show hybrid vigor, sometimes growing larger or taller than either parent. The concept of a hybrid is interpreted differently in animal and plant breeding, where there is interest in the individual parentage. In genetics, attention is focused on the numbers of chromosomes. In taxonomy, a key question is how closely related the parent species are.
Species are reproductively isolated by strong barriers to hybridization, which include genetic and morphological differences, differing times of fertility, mating behaviors and cues, and physiological rejection of sperm cells or the developing embryo. Some act before fertilization and others after it. Similar barriers exist in plants, with differences in flowering times, pollen vectors, inhibition of pollen tube growth, somatoplastic sterility, cytoplasmic-genic male sterility and the structure of the chromosomes. A few animal species and many plant species, however, are the result of hybrid speciation, including important crop plants such as wheat, where the number of chromosomes has been doubled.
Human impact on the environment has resulted in an increase in the interbreeding between regional species, and the proliferation of introduced species worldwide has also resulted in an increase in hybridization. This genetic mixing may threaten many species with extinction, while genetic erosion from monoculture in crop plants may be damaging the gene pools of many species for future breeding. A form of often intentional human-mediated hybridization is the crossing of wild and domestic
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https://en.wikipedia.org/wiki/Generalized%20inverse
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In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix .
A matrix is a generalized inverse of a matrix if A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse.
Motivation
Consider the linear system
where is an matrix and the column space of . If is nonsingular (which implies ) then will be the solution of the system. Note that, if is nonsingular, then
Now suppose is rectangular (), or square and singular. Then we need a right candidate of order such that for all
That is, is a solution of the linear system .
Equivalently, we need a matrix of order such that
Hence we can define the generalized inverse as follows: Given an matrix , an matrix is said to be a generalized inverse of if The matrix has been termed a regular inverse of by some authors.
Types
Important types of generalized inverse include:
One-sided inverse (right inverse or left inverse)
Right inverse: If the matrix has dimensions and , then there exists an matrix called the right inverse of such that , where is the identity matrix.
Left inverse: If the matrix has dimensions and , then there exists an matrix called the left inverse of such that , where is the identity matrix.
Bott–Duffin inverse
Drazin inverse
Moore–Penrose inverse
Some generalized inverses are defined and classified based on the Penrose conditions:
where denotes conjugate transpose
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https://en.wikipedia.org/wiki/Percentage%20point
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A percentage point or percent point is the unit for the arithmetic difference between two percentages. For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points (although it is a 10-percent increase in the quantity being measured, if the total amount remains the same). In written text, the unit (the percentage point) is usually either written out, or abbreviated as pp, p.p., or %pt. to avoid confusion with percentage increase or decrease in the actual quantity. After the first occurrence, some writers abbreviate by using just "point" or "points".
Differences between percentages and percentage points
Consider the following hypothetical example: In 1980, 50 percent of the population smoked, and in 1990 only 40 percent of the population smoked. One can thus say that from 1980 to 1990, the prevalence of smoking decreased by 10 percentage points (or by 10 percent of the population) or by 20 percent when talking about smokers only – percentages indicate proportionate part of a total.
Percentage-point differences are one way to express a risk or probability. Consider a drug that cures a given disease in 70 percent of all cases, while without the drug, the disease heals spontaneously in only 50 percent of cases. The drug reduces absolute risk by 20 percentage points. Alternatives may be more meaningful to consumers of statistics, such as the reciprocal, also known as the number needed to treat (NNT). In this case, the reciprocal transform of the percentage-point difference would be 1/(20pp) = 1/0.20 = 5. Thus if 5 patients are treated with the drug, one could expect to cure one more patient than would have occurred in the absence of the drug.
For measurements involving percentages as a unit, such as, growth, yield, or ejection fraction, statistical deviations and related descriptive statistics, including the standard deviation and root-mean-square error, the result should be expressed in units of percentage points instead of percentage
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https://en.wikipedia.org/wiki/Biological%20rules
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A biological rule or biological law is a generalized law, principle, or rule of thumb formulated to describe patterns observed in living organisms. Biological rules and laws are often developed as succinct, broadly applicable ways to explain complex phenomena or salient observations about the ecology and biogeographical distributions of plant and animal species around the world, though they have been proposed for or extended to all types of organisms. Many of these regularities of ecology and biogeography are named after the biologists who first described them.
From the birth of their science, biologists have sought to explain apparent regularities in observational data. In his biology, Aristotle inferred rules governing differences between live-bearing tetrapods (in modern terms, terrestrial placental mammals). Among his rules were that brood size decreases with adult body mass, while lifespan increases with gestation period and with body mass, and fecundity decreases with lifespan. Thus, for example, elephants have smaller and fewer broods than mice, but longer lifespan and gestation. Rules like these concisely organized the sum of knowledge obtained by early scientific measurements of the natural world, and could be used as models to predict future observations. Among the earliest biological rules in modern times are those of Karl Ernst von Baer (from 1828 onwards) on embryonic development, and of Constantin Wilhelm Lambert Gloger on animal pigmentation, in 1833.
There is some scepticism among biogeographers about the usefulness of general rules. For example, J.C. Briggs, in his 1987 book Biogeography and Plate Tectonics, comments that while Willi Hennig's rules on cladistics "have generally been helpful", his progression rule is "suspect".
List of biological rules
Allen's rule states that the body shapes and proportions of endotherms vary by climatic temperature by either minimizing exposed surface area to minimize heat loss in cold climates or maximizing ex
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https://en.wikipedia.org/wiki/Mathemagician
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A mathemagician is a mathematician who is also a magician. The term "mathemagic" is believed to have been introduced by Royal Vale Heath with his 1933 book "Mathemagic".
The name "mathemagician" was probably first applied to Martin Gardner, but has since been used to describe many mathematician/magicians, including Arthur T. Benjamin, Persi Diaconis, and Colm Mulcahy. Diaconis has suggested that the reason so many mathematicians are magicians is that "inventing a magic trick and inventing a theorem are very similar activities."
Mathemagician is a neologism, specifically a portmanteau, that combines mathematician and magician. A great number of self-working mentalism tricks rely on mathematical principles. Max Maven often utilizes this type of magic in his performance.
The Mathemagician is the name of a character in the 1961 children's book The Phantom Tollbooth. He is the ruler of Digitopolis, the kingdom of mathematics.
Notable mathemagicians
Arthur T. Benjamin
Jin Akiyama
Persi Diaconis
Richard Feynman
Karl Fulves
Martin Gardner
Ronald Graham
Royal Vale Heath
Colm Mulcahy
Raymond Smullyan
W. W. Rouse Ball
Alex Elmsley
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https://en.wikipedia.org/wiki/Glossary%20of%20power%20electronics
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This glossary of power electronics is a list of definitions of terms and concepts related to power electronics in general and power electronic capacitors in particular. For more definitions in electric engineering, see Glossary of electrical and electronics engineering. For terms related to engineering in general, see Glossary of engineering.
The glossary terms fit in the following categories in power electronics:
Electronic power converters; converters, rectifiers, inverters, filters.
Electronic power switches and electronic AC power converters; switches and controllers.
Essential components of electric power equipment; device, stack, assembly, reactor, capacitor, transformer, AC filter, DC filter, snubber circuit.
Circuits and circuit elements of power electronic equipment; arms and connections.
Operations within power electronic equipment; commutations, quenchings, controls, angles, factors, states, directions, intervals, periods, frequencies, voltages, breakthroughs and failures, breakdowns, blocking and flows.
Properties of power electronic equipment
Characteristic curves of power electronic equipment
Power supplies
A
B
C
D
E
F
H
I
J
L
M
N
O
P
Q
R
S
T
U
V
Overview of electronic power converters
See also
Glossary of engineering
Glossary of civil engineering
Glossary of mechanical engineering
Glossary of structural engineering
Notes
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https://en.wikipedia.org/wiki/Index%20set
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In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set may be indexed or labeled by means of the elements of a set , then is an index set. The indexing consists of a surjective function from onto , and the indexed collection is typically called an indexed family, often written as .
Examples
An enumeration of a set gives an index set , where is the particular enumeration of .
Any countably infinite set can be (injectively) indexed by the set of natural numbers .
For , the indicator function on is the function given by
The set of all such indicator functions, , is an uncountable set indexed by .
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm that can sample the set efficiently; e.g., on input , can efficiently select a poly(n)-bit long element from the set.
See also
Friendly-index set
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https://en.wikipedia.org/wiki/Phototroph
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Phototrophs () are organisms that carry out photon capture to produce complex organic compounds (e.g. carbohydrates) and acquire energy. They use the energy from light to carry out various cellular metabolic processes. It is a common misconception that phototrophs are obligatorily photosynthetic. Many, but not all, phototrophs often photosynthesize: they anabolically convert carbon dioxide into organic material to be utilized structurally, functionally, or as a source for later catabolic processes (e.g. in the form of starches, sugars and fats). All phototrophs either use electron transport chains or direct proton pumping to establish an electrochemical gradient which is utilized by ATP synthase, to provide the molecular energy currency for the cell. Phototrophs can be either autotrophs or heterotrophs. If their electron and hydrogen donors are inorganic compounds (e.g., , as in some purple sulfur bacteria, or , as in some green sulfur bacteria) they can be also called lithotrophs, and so, some photoautotrophs are also called photolithoautotrophs. Examples of phototroph organisms are Rhodobacter capsulatus, Chromatium, and Chlorobium.
History
Originally used with a different meaning, the term took its current definition after Lwoff and collaborators (1946).
Photoautotroph
Most of the well-recognized phototrophs are autotrophic, also known as photoautotrophs, and can fix carbon. They can be contrasted with chemotrophs that obtain their energy by the oxidation of electron donors in their environments. Photoautotrophs are capable of synthesizing their own food from inorganic substances using light as an energy source. Green plants and photosynthetic bacteria are photoautotrophs. Photoautotrophic organisms are sometimes referred to as holophytic.
Oxygenic photosynthetic organisms use chlorophyll for light-energy capture and oxidize water, "splitting" it into molecular oxygen.
Ecology
In an ecological context, phototrophs are often the food source for neighboring he
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https://en.wikipedia.org/wiki/Blue%20team%20%28computer%20security%29
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A blue team is a group of individuals who perform an analysis of information systems to ensure security, identify security flaws, verify the effectiveness of each security measure, and to make certain all security measures will continue to be effective after implementation.
History
As part of the United States computer security defense initiative, red teams were developed to exploit other malicious entities that would do them harm. As a result, blue teams were developed to design defensive measures against such red team activities.
Incident response
If an incident does occur within the organization, the blue team will perform the following six steps to handle the situation:
Preparation
Identification
Containment
Eradication
Recovery
Lessons learned
Operating system hardening
In preparation for a computer security incident, the blue team will perform hardening techniques on all operating systems throughout the organization.
Perimeter defense
The blue team must always be mindful of the network perimeter, including traffic flow, packet filtering, proxy firewalls, and intrusion detection systems.
Tools
Blue teams employ a wide range of tools allowing them to detect an attack, collect forensic data, perform data analysis and make changes to threat future attacks and mitigate threats. The tools include:
Log management and analysis
AlienVault
FortiSIEM (a.k.a. AccelOps)
Graylog
InTrust
LogRhythm
Microsoft Sentinel
NetWitness
Qradar (IBM)
Rapid7
SIEMonster
SolarWinds
Splunk
Security information and event management (SIEM) technology
SIEM software supports threat detection and security incident response by performing real-time data collection and analysis of security events. This type of software also uses data sources outside of the network including indicators of compromise (IoC) threat intelligence.
See also
List of digital forensics tools
Vulnerability management
White hat (computer security)
Red team
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https://en.wikipedia.org/wiki/List%20of%20eponyms%20of%20special%20functions
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This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym). Named symmetric functions, and other special polynomials, are included.
A
Niels Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomial
Sir George Biddell Airy: Airy function
Waleed Al-Salam (1926–1996): Al-Salam polynomial - Al Salam–Carlitz polynomial - Al Salam–Chihara polynomial
C. T. Anger: Anger–Weber function
Kazuhiko Aomoto: Aomoto–Gel'fand hypergeometric function - Aomoto integral
Paul Émile Appell (1855–1930): Appell hypergeometric series, Appell polynomial, Generalized Appell polynomials
Richard Askey: Askey–Wilson polynomial, Askey–Wilson function (with James A. Wilson)
B
Ernest William Barnes: Barnes G-function
E. T. Bell: Bell polynomials
Bender–Dunne polynomial
Jacob Bernoulli: Bernoulli polynomial
Friedrich Bessel: Bessel function, Bessel–Clifford function
H. Blasius: Blasius functions
R. P. Boas, R. C. Buck: Boas–Buck polynomial
Böhmer integral
Erland Samuel Bring: Bring radical
de Bruijn function
Buchstab function
Burchnall, Chaundy: Burchnall–Chaundy polynomial
C
Leonard Carlitz: Carlitz polynomial
Arthur Cayley, Capelli: Cayley–Capelli operator
Celine's polynomial
Charlier polynomial
Pafnuty Chebyshev: Chebyshev polynomials
Elwin Bruno Christoffel, Darboux: Christoffel–Darboux relation
Cyclotomic polynomials
D
H. G. Dawson: Dawson function
Charles F. Dunkl: Dunkl operator, Jacobi–Dunkl operator, Dunkl–Cherednik operator
Dickman–de Bruijn function
E
Engel: Engel expansion
Erdélyi Artúr: Erdelyi–Kober operator
Leonhard Euler: Euler polynomial, Eulerian integral, Euler hypergeometric integral
F
V. N. Faddeeva: Faddeeva function (also known as the complex error function; see error function)
G
C. F. Gauss: Gaussian polynomial, Gaussian distribution, etc.
Leopold Bernhar
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https://en.wikipedia.org/wiki/Representation%20theorem
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In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure.
Examples
Algebra
Cayley's theorem states that every group is isomorphic to a permutation group.
Representation theory studies properties of abstract groups via their representations as linear transformations of vector spaces.
Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets.
A variant, Stone's representation theorem for distributive lattices, states that every distributive lattice is isomorphic to a sublattice of the power set lattice of some set.
Another variant, Stone's duality, states that there exists a duality (in the sense of an arrow-reversing equivalence) between the categories of Boolean algebras and that of Stone spaces.
The Poincaré–Birkhoff–Witt theorem states that every Lie algebra embeds into the commutator Lie algebra of its universal enveloping algebra.
Ado's theorem states that every finite-dimensional Lie algebra over a field of characteristic zero embeds into the Lie algebra of endomorphisms of some finite-dimensional vector space.
Birkhoff's HSP theorem states that every model of an algebra A is the homomorphic image of a subalgebra of a direct product of copies of A.
In the study of semigroups, the Wagner–Preston theorem provides a representation of an inverse semigroup S, as a homomorphic image of the set of partial bijections on S, and the semigroup operation given by composition.
Category theory
The Yoneda lemma provides a full and faithful limit-preserving embedding of any category into a category of presheaves.
Mitchell's embedding theorem for abelian categories realises every small abelian category as a full (and exactly embedded) subcategory of a category of modules over some ring.
Mostowski's collapsing theorem states that every well-founded extensional structure is isomorphic t
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https://en.wikipedia.org/wiki/List%20of%20random%20number%20generators
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Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers).
This list includes many common types, regardless of quality or applicability to a given use case.
Pseudorandom number generators (PRNGs)
The following algorithms are pseudorandom number generators.
Cryptographic algorithms
Cipher algorithms and cryptographic hashes can be used as very high-quality pseudorandom number generators. However, generally they are considerably slower (typically by a factor 2–10) than fast, non-cryptographic random number generators.
These include:
Stream ciphers. Popular choices are Salsa20 or ChaCha (often with the number of rounds reduced to 8 for speed), ISAAC, HC-128 and RC4.
Block ciphers in counter mode. Common choices are AES (which is very fast on systems supporting it in hardware), TwoFish, Serpent and Camellia.
Cryptographic hash functions
A few cryptographically secure pseudorandom number generators do not rely on cipher algorithms but try to link mathematically the difficulty of distinguishing their output from a `true' random stream to a computationally difficult problem. These approaches are theoretically important but are too slow to be practical in most applications. They include:
Blum–Micali algorithm (1984)
Blum Blum Shub (1986)
Naor–Reingold pseudorandom function (1997)
Random number generators that use external entropy
These approaches combine a pseudo-random number generator (often in the form of a block or stream cipher) with an external source of randomness (e.g., mouse movements, delay between keyboard presses etc.).
/dev/random – Unix-like systems
CryptGenRandom – Microsoft Windows
Fortuna
RDRAND instructions (called Intel Secure Key by Intel), available in Intel x86 CPUs since 2012. They use the AES generator built into the CPU, reseeding it periodically.
True Random Number Gen
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https://en.wikipedia.org/wiki/Complete%20set%20of%20invariants
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In mathematics, a complete set of invariants for a classification problem is a collection of maps
(where is the collection of objects being classified, up to some equivalence relation , and the are some sets), such that if and only if for all . In words, such that two objects are equivalent if and only if all invariants are equal.
Symbolically, a complete set of invariants is a collection of maps such that
is injective.
As invariants are, by definition, equal on equivalent objects, equality of invariants is a necessary condition for equivalence; a complete set of invariants is a set such that equality of these is also sufficient for equivalence. In the context of a group action, this may be stated as: invariants are functions of coinvariants (equivalence classes, orbits), and a complete set of invariants characterizes the coinvariants (is a set of defining equations for the coinvariants).
Examples
In the classification of two-dimensional closed manifolds, Euler characteristic (or genus) and orientability are a complete set of invariants.
Jordan normal form of a matrix is a complete invariant for matrices up to conjugation, but eigenvalues (with multiplicities) are not.
Realizability of invariants
A complete set of invariants does not immediately yield a classification theorem: not all combinations of invariants may be realized. Symbolically, one must also determine the image of
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https://en.wikipedia.org/wiki/Registered%20state%20change%20notification
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In Fibre Channel protocol, a registered state change notification (RSCN) is a Fibre Channel fabric's notification sent to all specified nodes in case of any major fabric changes. This allows nodes to immediately gain knowledge about the fabric and react accordingly.
Overview
Implementation of this function is obligatory for each Fibre Channel switch, but is optional for a node. This function belongs to a second level of the protocol, or FC2.
Some events that trigger notifications are:
Nodes joining or leaving the fabric (most common usage)
Switches joining or leaving the fabric
Changing the switch name
The nodes wishing to be notified in such way need to register themselves first at the Fabric Controller, which is a standardized FC virtual address present at each switch.
RSCN and zoning
If a fabric has some zones configured for additional security, notifications do not cross zone boundaries if not needed. Simply, there is no need to notify a node about a change that it cannot see anyway (because it happened in a separate zone).
Example
For example, let's assume there is a fabric with just one node, namely a server's FC-compatible HBA. First it registers itself for notifications. Then a human administrator connects another node, like a disk array, to the fabric. This event is known at first only to a single switch, the one that detected one of its ports going online. The switch, however, has a list of registered nodes (currently containing only the HBA node) and notifies every one of them. As the HBA receives the notification, it chooses to query the nearest switch about current list of nodes. It detects a new disk array and starts to communicate with it on a SCSI level, asking for a list of SCSI LUNs. Then it notifies a server's operating system, that there is a new SCSI target containing some LUNs. The operating system auto-configures those as new block devices, ready for use.
See also
Storage area network
Fibre Channel
Fibre Channel fabric
Fibre Chann
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https://en.wikipedia.org/wiki/List%20of%20plasma%20physics%20articles
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This is a list of plasma physics topics.
A
Ablation
Abradable coating
Abraham–Lorentz force
Absorption band
Accretion disk
Active galactic nucleus
Adiabatic invariant
ADITYA (tokamak)
Aeronomy
Afterglow plasma
Airglow
Air plasma, Corona treatment, Atmospheric-pressure plasma treatment
Ayaks, Novel "Magneto-plasmo-chemical engine"
Alcator C-Mod
Alfvén wave
Ambipolar diffusion
Aneutronic fusion
Anisothermal plasma
Anisotropy
Antiproton Decelerator
Appleton-Hartree equation
Arcing horns
Arc lamp
Arc suppression
ASDEX Upgrade, Axially Symmetric Divertor EXperiment
Astron (fusion reactor)
Astronomy
Astrophysical plasma
Astrophysical X-ray source
Atmospheric dynamo
Atmospheric escape
Atmospheric pressure discharge
Atmospheric-pressure plasma
Atom
Atomic emission spectroscopy
Atomic physics
Atomic-terrace low-angle shadowing
Auger electron spectroscopy
Aurora (astronomy)
B
Babcock Model
Ball lightning
Ball-pen probe
Ballooning instability
Baryon acoustic oscillations
Beam-powered propulsion
Beta (plasma physics)
Birkeland current
Blacklight Power
Blazar
Bohm diffusion
Bohr–van Leeuwen theorem
Boltzmann relation
Bow shock
Bremsstrahlung
Bussard ramjet
C
Capacitively coupled plasma
Carbon nanotube metal matrix composites
Cassini–Huygens, Cassini Plasma Spectrometer
Cathode ray
Cathodic arc deposition
Ceramic discharge metal-halide lamp
Charge carrier
Charged-device model
Charged particle
Chemical plasma
Chemical vapor deposition
Chemical vapor deposition of diamond
Chirikov criterion
Chirped pulse amplification
Chromatography detector
Chromo–Weibel instability
Classical-map hypernetted-chain method
Cnoidal wave
Colored-particle-in-cell
Coilgun
Cold plasma, Ozone generator
Collisionality
Colored-particle-in-cell
Columbia Non-neutral Torus
Comet tail
Compact toroid
Compressibility
Compton–Getting effect
Contact lithography
Coupling (physics)
Convection cell
Cooling flow
Corona
Corona di
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https://en.wikipedia.org/wiki/Law%20of%20large%20numbers
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In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed.
The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. Importantly, the law applies (as the name indicates) only when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be "balanced" by the others (see the gambler's fallacy).
The LLN only applies to the average. Therefore, while
other formulas that look similar are not verified, such as the raw deviation from "theoretical results":
not only does it not converge toward zero as n increases, but it tends to increase in absolute value as n increases.
Examples
For example, a single roll of a fair, six-sided die produces one of the numbers 1, 2, 3, 4, 5, or 6, each with equal probability. Therefore, the expected value of the average of the rolls is:
According to the law of large numbers, if a large number of six-sided dice are rolled, the average of their values (sometimes called the sample mean) will approach 3.5, with the precision increasing as more dice are rolled.
It follows from the law of large numbers that the empirical probability of success in a series of Bernoulli trials will converge to the theoretical probability. For a Bernoulli random variable, the expected value is the theoretical probability of success, a
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https://en.wikipedia.org/wiki/Isotricha
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Isotricha is a genus of protozoa (single-celled organisms) which are commensals of the rumen of ruminant animals. They are approximately long.
Species include:
Isotricha intestinalis Stein 1858
Isotricha prostoma Stein 1858
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https://en.wikipedia.org/wiki/2.5D%20integrated%20circuit
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A 2.5D integrated circuit (2.5D IC) is an advanced packaging technique that combines multiple integrated circuit dies in a single package without stacking them into a three-dimensional integrated circuit (3D-IC) with through-silicon vias (TSVs). The term "2.5D" originated when 3D-ICs with TSVs were quite new and still very difficult. Chip designers realized that many of the advantages of 3D integration could be approximated by placing bare dies side by side on an interposer instead of stacking them vertically. If the pitch is very fine and the interconnect very short, the assembly can be packaged as a single component with better size, weight, and power characteristics than a comparable 2D circuit board assembly. This half-way 3D integration was facetiously named "2.5D" and the name stuck.
Since then, 2.5D has proven to be far more than just "half-way to 3D."
Some benefits:
An interposer can support heterogeneous integration – that is, dies of different pitch, size, material, and process node.
Placing dies side by side instead of stacking them reduces heat buildup.
Upgrading or modifying a 2.5D assembly is as easy as swapping in a new component and revamping the interposer to suit; much faster and simpler than reworking an entire 3D-IC or System-on-Chip (SoC).
Some sophisticated 2.5D assemblies even incorporate TSVs and 3D components. Several foundries now support 2.5D packaging.
The success of 2.5D assembly has given rise to "chiplets" – small, functional circuit blocks designed to be combined in mix-and-match fashion on interposers. Several high-end products already take advantage of these LEGO-style chiplets; some experts predict the emergence of an industry-wide chiplet ecosystem.
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https://en.wikipedia.org/wiki/Symmetry%20%28physics%29
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In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.
A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group).
These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems.
Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of reference, which is described in special relativity by a group of transformations of the spacetime known as the Poincaré group. Another important example is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations, which is an important idea in general relativity.
As a kind of invariance
Invariance is specified mathematically by transformations that leave some property (e.g. quantity) unchanged. This idea can apply to basic real-world observations. For example, temperature may be homogeneous throughout a room. Since the temperature does not depend on the position of an observer within the room, we say that the temperature is invariant under a shift in an observer's position within the room.
Similarly, a uniform sphere rotated about its center will appear exactly as it did before the rotation. The sphere is said to exhibit spherical symmetry. A rotation about any axis of the sphere will preserve how the sphere "looks".
Invariance in force
The above
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https://en.wikipedia.org/wiki/List%20of%20rules%20of%20inference
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This is a list of rules of inference, logical laws that relate to mathematical formulae.
Introduction
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
Discharge rules permit inference from a subderivation based on a temporary assumption. Below, the notation
indicates such a subderivation from the temporary assumption to .
Rules for propositional calculus
Rules for negations
Reductio ad absurdum (or Negation Introduction)
Reductio ad absurdum (related to the law of excluded middle)
Ex contradictione quodlibet
Rules for conditionals
Deduction theorem (or Conditional Introduction)
Modus ponens (or Conditional Elimination)
Modus tollens
Rules for conjunctions
Adjunction (or Conjunction Introduction)
Simplification (or Conjunction Elimination)
Rules for disjunctions
Addition (or Disjunction Introduction)
Case analysis (or Proof by Cases or Argument by Cases or Disjunction elimination)
Disjunctive syllogism
Constructive dilemma
Rules for biconditionals
Biconditional introduction
Biconditional elimination
Rules of classical predicate calculus
In the following rules, is exactly like except for having the term wherever has the free variable .
Universal Generalization (or Universal Introduction)
Restriction 1: is a variable which does not occur in .
Restriction 2: is not mentioned in any hypothesis or undischarged assumptions.
Universal Instantiation (or Universal Elimination)
Restriction: No free occurrence of in falls within the scope of a quantifier quantifying a variable occurring in .
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https://en.wikipedia.org/wiki/Territory%20%28animal%29
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In ethology, territory is the sociographical area that an animal consistently defends against conspecific competition (or, occasionally, against animals of other species) using agonistic behaviors or (less commonly) real physical aggression. Animals that actively defend territories in this way are referred to as being territorial or displaying territorialism.
Territoriality is only shown by a minority of species. More commonly, an individual or a group of animals occupies an area that it habitually uses but does not necessarily defend; this is called its home range. The home ranges of different groups of animals often overlap, and in these overlap areas the groups tend to avoid each other rather than seeking to confront and expel each other. Within the home range there may be a core area that no other individual group uses, but, again, this is as a result of avoidance.
Function
The ultimate function of animals inhabiting and defending a territory is to increase the individual fitness or inclusive fitness of the animals expressing the behaviour. Fitness in this biological sense relates to the ability of an animal to survive and raise young. The proximate functions of territory defense vary. For some animals, the reason for such protective behaviour is to acquire and protect food sources, nesting sites, mating areas, or to attract a mate.
Types and size
Among birds, territories have been classified as six types.
Type A: An 'all-purpose territory' in which all activities occur, e.g. courtship, mating, nesting and foraging
Type B: A mating and nesting territory, not including most of the area used for foraging.
Type C: A nesting territory which includes the nest plus a small area around it. Common in colonial waterbirds.
Type D: A pairing and mating territory. The type of territory defended by males in lekking species.
Type E: Roosting territory.
Type F: Winter territory which typically includes foraging areas and roost sites. May be equivalent (in terms of locat
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https://en.wikipedia.org/wiki/Simple-As-Possible%20computer
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The Simple-As-Possible (SAP) computer is a simplified computer architecture designed for educational purposes and described in the book Digital Computer Electronics by Albert Paul Malvino and Jerald A. Brown. The SAP architecture serves as an example in Digital Computer Electronics for building and analyzing complex logical systems with digital electronics.
Digital Computer Electronics successively develops three versions of this computer, designated as SAP-1, SAP-2, and SAP-3. Each of the last two build upon the immediate previous version by adding additional computational, flow of control, and input/output capabilities. SAP-2 and SAP-3 are fully Turing-complete.
The instruction set architecture (ISA) that the computer final version (SAP-3) is designed to implement is patterned after and upward compatible with the ISA of the Intel 8080/8085 microprocessor family. Therefore, the instructions implemented in the three SAP computer variations are, in each case, a subset of the 8080/8085 instructions.
Variant
Ben Eater's Design
YouTuber and former Khan Academy employee Ben Eater created a tutorial building an 8-bit Turing-complete SAP computer on breadboards from logical chips (7400-series) capable of running simple programs such as computing the Fibonacci sequence. Eater's design consists of the following modules:
An adjustable-speed (upper limitation of a few hundred Hertz) clock module that can be put into a "manual mode" to step through the clock cycles.
Three register modules (Register A, Register B, and the Instruction Register) that "store small amounts of data that the CPU is processing."
An arithmetic logic unit (ALU) capable of adding and subtracting 8-bit 2's complement integers from registers A and B. This module also has a flags register with two possible flags (Z and C). Z stands for "zero," and is activated if the ALU outputs zero. C stands for "carry," and is activated if the ALU produces a carry-out bit.
A RAM module capable of storing 16 b
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https://en.wikipedia.org/wiki/Haplotype%20block
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In genetics, a haplotype block is a region of an organism's genome in which there is little evidence of a history of genetic recombination, and which contain only a small number of distinct haplotypes. According to the haplotype-block model, such blocks should show high levels of linkage disequilibrium and be separated from one another by numerous recombination events. The boundaries of haplotype blocks cannot be directly observed; they must instead be inferred indirectly through the use of algorithms. However, some evidence suggests that different algorithms for identifying haplotype blocks give very different results when used on the same data, though another study suggests that their results are generally consistent. The National Institutes of Health funded the HapMap project to catalog haplotype blocks throughout the human genome.
Definition
There are two main ways that the term "haplotype block" is defined: one based on whether a given genomic sequence displays higher linkage disequilibrium than a predetermined threshold, and one based on whether the sequence consists of a minimum number of single nucleotide polymorphisms (SNPs) that explain a majority of the common haplotypes in the sequence (or a lower-than-usual number of unique haplotypes). In 2001, Patil et al. proposed the following definition of the term: "Suppose we have a number of haplotypes consisting of a set of consecutive SNPs. A segment of consecutive SNPs is a block if at least α percent of haplotypes are represented more than once".
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https://en.wikipedia.org/wiki/Seshadri%20constant
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In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety. It was introduced by Demailly to measure a certain rate of growth, of the tensor powers of L, in terms of the jets of the sections of the Lk. The object was the study of the Fujita conjecture.
The name is in honour of the Indian mathematician C. S. Seshadri.
It is known that Nagata's conjecture on algebraic curves is equivalent to the assertion that for more than nine general points, the Seshadri constants of the projective plane are maximal. There is a general conjecture for algebraic surfaces, the Nagata–Biran conjecture.
Definition
Let be a smooth projective variety, an ample line bundle on it, a point of , = { all irreducible curves passing through }.
.
Here, denotes the intersection number of and , measures how many times passing through .
Definition: One says that is the Seshadri constant of at the point , a real number. When is an abelian variety, it can be shown that is independent of the point chosen, and it is written simply .
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https://en.wikipedia.org/wiki/Nullor
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A nullor is a theoretical two-port network consisting of a nullator at its input and a norator at its output. Nullors represent an ideal amplifier, having infinite current, voltage, transconductance and transimpedance gain. Its transmission parameters are all zero, that is, its input–output behavior is summarized with the matrix equation
In negative-feedback circuits, the circuit surrounding the nullor determines the nullor output in such a way as to force the nullor input to zero.
Inserting a nullor in a circuit schematic imposes mathematical constraints on how that circuit must behave, forcing the circuit itself to adopt whatever arrangements are needed to meet the conditions. For example, an ideal operational amplifier can be modeled using a nullor, and the textbook analysis of a feedback circuit using an ideal op-amp uses the mathematical conditions imposed by the nullor to analyze the circuit surrounding the op-amp.
Example: voltage-controlled current sink
Figure 1 shows a voltage-controlled current sink. The sink is intended to draw the same current iOUT regardless of the applied voltage VCC at the output. The value of current drawn is to be set by the input voltage vIN. Here the sink is to be analyzed by idealizing the op amp as a nullor.
Using properties of the input nullator portion of the nullor, the input voltage across the op amp input terminals is zero. Consequently, the voltage across reference resistor RR is the applied voltage vIN, making the current in RR simply vIN/RR. Again using the nullator properties, the input current to the nullor is zero. Consequently, Kirchhoff's current law at the emitter provides an emitter current of vIN/RR. Using properties of the norator output portion of the nullor, the nullor provides whatever current is demanded of it, regardless of the voltage at its output. In this case, it provides the transistor base current iB. Thus, Kirchhoff's current law applied to the transistor as a whole provides the output current
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https://en.wikipedia.org/wiki/Heterotroph
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A heterotroph (; ) is an organism that cannot produce its own food, instead taking nutrition from other sources of organic carbon, mainly plant or animal matter. In the food chain, heterotrophs are primary, secondary and tertiary consumers, but not producers. Living organisms that are heterotrophic include all animals and fungi, some bacteria and protists, and many parasitic plants. The term heterotroph arose in microbiology in 1946 as part of a classification of microorganisms based on their type of nutrition. The term is now used in many fields, such as ecology in describing the food chain.
Heterotrophs may be subdivided according to their energy source. If the heterotroph uses chemical energy, it is a chemoheterotroph (e.g., humans and mushrooms). If it uses light for energy, then it is a photoheterotroph (e.g., green non-sulfur bacteria).
Heterotrophs represent one of the two mechanisms of nutrition (trophic levels), the other being autotrophs (auto = self, troph = nutrition). Autotrophs use energy from sunlight (photoautotrophs) or oxidation of inorganic compounds (lithoautotrophs) to convert inorganic carbon dioxide to organic carbon compounds and energy to sustain their life. Comparing the two in basic terms, heterotrophs (such as animals) eat either autotrophs (such as plants) or other heterotrophs, or both.
Detritivores are heterotrophs which obtain nutrients by consuming detritus (decomposing plant and animal parts as well as feces). Saprotrophs (also called lysotrophs) are chemoheterotrophs that use extracellular digestion in processing decayed organic matter. The process is most often facilitated through the active transport of such materials through endocytosis within the internal mycelium and its constituent hyphae.
Types
Heterotrophs can be organotrophs or lithotrophs. Organotrophs exploit reduced carbon compounds as electron sources, like carbohydrates, fats, and proteins from plants and animals. On the other hand, lithoheterotrophs use inorgan
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https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation
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Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that frequently come up in quantum mechanics. Its use in quantum mechanics is quite widespread.
Bra-ket notation was created by Paul Dirac in his 1939 publication A New Notation for Quantum Mechanics. The notation was introduced as an easier way to write quantum mechanical expressions. The name comes from the English word "Bracket".
Quantum mechanics
In quantum mechanics, bra–ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets".
A ket is of the form . Mathematically it denotes a vector, , in an abstract (complex) vector space , and physically it represents a state of some quantum system.
A bra is of the form . Mathematically it denotes a linear form , i.e. a linear map that maps each vector in to a number in the complex plane . Letting the linear functional act on a vector is written as .
Assume that on there exists an inner product with antilinear first argument, which makes an inner product space. Then with this inner product each vector can be identified with a corresponding linear form, by placing the vector in the anti-linear first slot of the inner product: . The correspondence between these notations is then . The linear form is a covector to , and the set of all covectors form a subspace of the dual vector space , to the initial vector space . The purpose of this linear form can now be understood in terms of making projections on the state , to find how linearly dependent two states are, etc.
For the vector space , kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted using matrix multiplic
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https://en.wikipedia.org/wiki/List%20of%20lemmas
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This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.
Algebra
Abhyankar's lemma
Aubin–Lions lemma
Bergman's diamond lemma
Fitting lemma
Injective test lemma
Hua's lemma (exponential sums)
Krull's separation lemma
Schanuel's lemma (projective modules)
Schwartz–Zippel lemma
Shapiro's lemma
Stewart–Walker lemma (tensors)
Whitehead's lemma (Lie algebras)
Zariski's lemma
Algebraic geometry
Abhyankar's lemma
Fundamental lemma (Langlands program)
Category theory
Five lemma
Horseshoe lemma
Nine lemma
Short five lemma
Snake lemma
Splitting lemma
Linear algebra
Matrix determinant lemma
Matrix inversion lemma
Group theory
Burnside's lemma also known as the Cauchy–Frobenius lemma
Frattini's lemma (finite groups)
Goursat's lemma
Mautner's lemma (representation theory)
Ping-pong lemma (geometric group theory)
Schreier's subgroup lemma
Schur's lemma (representation theory)
Zassenhaus lemma
Polynomials
Gauss's lemma (polynomials)
Schwartz–Zippel lemma
Ring theory and commutative algebra
Artin–Rees lemma
Hensel's lemma (commutative rings)
Nakayama lemma
Noether's normalization lemma
Prime avoidance lemma
Universal algebra
Jónsson's lemma
Analysis
Fekete's lemma
Fundamental lemma of calculus of variations
Hopf lemma
Sard's lemma (singularity theory)
Stechkin's lemma (functional and numerical analysis)
Vitali covering lemma (real analysis)
Watson's lemma
Complex analysis
Estimation lemma (contour integrals)
Hartogs's lemma (several complex variables)
Jordan's lemma
Lemma on the Logarithmic derivative
Schwarz lemma
Fourier analysis
Riemann–Lebesgue lemma
Differential equations
Borel's lemma (partial differential equations)
Grönwall's lemma
Lax–Milgram lemma
Pugh's closing lemma
Weyl's lemma (Laplace equation) (partial differential equations)
Differential forms
Poincaré lemma of closed and exa
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https://en.wikipedia.org/wiki/List%20of%20prime%20knots
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In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes.
Table of prime knots
Six or fewer crossings
Seven crossings
Eight crossings
Nine crossings
Ten crossings
Higher
Conway knot 11n34
Kinoshita–Terasaka knot 11n42
Table of prime links
Seven or fewer crossings
Higher
See also
List of knots
List of mathematical knots and links
Knot tabulation
(−2,3,7) pretzel knot
Notes
External links
"KnotInfo", Indiana.edu.
Knot theory
Mathematics-related lists
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https://en.wikipedia.org/wiki/Of%20the%20form
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In mathematics, the phrase "of the form" indicates that a mathematical object, or (more frequently) a collection of objects, follows a certain pattern of expression. It is frequently used to reduce the formality of mathematical proofs.
Example of use
Here is a proof which should be appreciable with limited mathematical background:
Statement:
The product of any two even natural numbers is also even.
Proof:
Any even natural number is of the form 2n, where n is a natural number. Therefore, let us assume that we have two even numbers which we will denote by 2k and 2l. Their product is (2k)(2l) = 4(kl) = 2(2kl). Since 2kl is also a natural number, the product is even.
Note:
In this case, both exhaustivity and exclusivity were needed. That is, it was not only necessary that every even number is of the form 2n (exhaustivity), but also that every expression of the form 2n is an even number (exclusivity). This will not be the case in every proof, but normally, at least exhaustivity is implied by the phrase of the form.
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https://en.wikipedia.org/wiki/Iddq%20testing
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Iddq testing is a method for testing CMOS integrated circuits for the presence of manufacturing faults. It relies on measuring the supply current (Idd) in the quiescent state (when the circuit is not switching and inputs are held at static values). The current consumed in the state is commonly called Iddq for Idd (quiescent) and hence the name.
Iddq testing uses the principle that in a correctly operating quiescent CMOS digital circuit, there is no static current path between the power supply and ground, except for a small amount of leakage. Many common semiconductor manufacturing faults will cause the current to increase by orders of magnitude, which can be easily detected. This has the advantage of checking the chip for many possible faults with one measurement. Another advantage is that it may catch faults that are not found by conventional stuck-at fault test vectors.
Iddq testing is somewhat more complex than just measuring the supply current. If a line is shorted to Vdd, for example, it will still draw no extra current if the gate driving the signal is attempting to set it to '1'. However, a different input that attempts to set the signal to 0 will show a large increase in quiescent current, signalling a bad part. Typical Iddq tests may use 20 or so inputs. Note that Iddq test inputs require only controllability, and not observability. This is because the observability is through the shared power supply connection.
Advantages and disadvantages
Iddq testing has many advantages:
It is a simple and direct test that can identify physical defects.
The area and design time overhead are very low.
Test generation is fast.
Test application time is fast since the vector sets are small.
It catches some defects that other tests, particularly stuck-at logic tests, do not.
Drawback:
Compared to scan chain testing, Iddq testing is time consuming, and thus more expensive, as is achieved by current measurements that take much more time than reading digital pins i
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https://en.wikipedia.org/wiki/Landau%E2%80%93Ramanujan%20constant
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In mathematics and the field of number theory, the Landau–Ramanujan constant is the positive real number b that occurs in a theorem proved by Edmund Landau in 1908, stating that for large , the number of positive integers below that are the sum of two square numbers behaves asymptotically as
This constant b was rediscovered in 1913 by Srinivasa Ramanujan, in the first letter he wrote to G.H. Hardy.
Sums of two squares
By the sum of two squares theorem, the numbers that can be expressed as a sum of two squares of integers are the ones for which each prime number congruent to 3 mod 4 appears with an even exponent in their prime factorization. For instance, 45 = 9 + 36 is a sum of two squares; in its prime factorization, 32 × 5, the prime 3 appears with an even exponent, and the prime 5 is congruent to 1 mod 4, so its exponent can be odd.
Landau's theorem states that if is the number of positive integers less than that are the sum of two squares, then
,
where is the Landau–Ramanujan constant.
The Landau-Ramanujan constant can also be written as an infinite product:
History
This constant was stated by Landau in the limit form above; Ramanujan instead approximated as an integral, with the same constant of proportionality, and with a slowly growing error term.
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https://en.wikipedia.org/wiki/Orthomorphism
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In abstract algebra, an orthomorphism is a certain kind of mapping from a group into itself. Let G be a group, and let θ be a permutation of G. Then θ is an orthomorphism of G if the mapping f defined by f(x) = x−1 θ(x) is also a permutation of G. A permutation φ of G is a complete mapping if the mapping g defined by g(x) = xφ(x) is also a permutation of G. Orthomorphisms and complete mappings are closely related.
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https://en.wikipedia.org/wiki/Intraguild%20predation
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Intraguild predation, or IGP, is the killing and sometimes eating of a potential competitor of a different species. This interaction represents a combination of predation and competition, because both species rely on the same prey resources and also benefit from preying upon one another. Intraguild predation is common in nature and can be asymmetrical, in which one species feeds upon the other, or symmetrical, in which both species prey upon each other. Because the dominant intraguild predator gains the dual benefits of feeding and eliminating a potential competitor, IGP interactions can have considerable effects on the structure of ecological communities.
Types
Intraguild predation can be classified as asymmetrical or symmetrical. In asymmetrical interactions one species consistently preys upon the other, while in symmetrical interactions both species prey equally upon each other. Intraguild predation can also be age structured, in which case the vulnerability of a species to predation is dependent on age and size, so only juveniles or smaller individuals of one of the predators are fed upon by the other. A wide variety of predatory relationships are possible depending on the symmetry of the interaction and the importance of age structure. IGP interactions can range from predators incidentally eating parasites attached to their prey to direct predation between two apex predators.
Ecology of intraguild predation
Intraguild predation is common in nature and widespread across communities and ecosystems. Intraguild predators must share at least one prey species and usually occupy the same trophic guild, and the degree of IGP depends on factors such as the size, growth, and population density of the predators, as well as the population density and behavior of their shared prey. When creating theoretical models for intraguild predation, the competing species are classified as the "top predator" or the "intermediate predator," (the species more likely to be pre
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https://en.wikipedia.org/wiki/Electronic%20design%20automation
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Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing electronic systems such as integrated circuits and printed circuit boards. The tools work together in a design flow that chip designers use to design and analyze entire semiconductor chips. Since a modern semiconductor chip can have billions of components, EDA tools are essential for their design; this article in particular describes EDA specifically with respect to integrated circuits (ICs).
History
Early days
The earliest electronic design automation is attributed to IBM with the documentation of its 700 series computers in the 1950s.
Prior to the development of EDA, integrated circuits were designed by hand and manually laid out. Some advanced shops used geometric software to generate tapes for a Gerber photoplotter, responsible for generating a monochromatic exposure image, but even those copied digital recordings of mechanically drawn components. The process was fundamentally graphic, with the translation from electronics to graphics done manually; the best-known company from this era was Calma, whose GDSII format is still in use today. By the mid-1970s, developers started to automate circuit design in addition to drafting and the first placement and routing tools were developed; as this occurred, the proceedings of the Design Automation Conference catalogued the large majority of the developments of the time.
The next era began following the publication of "Introduction to VLSI Systems" by Carver Mead and Lynn Conway in 1980; considered the standard textbook for chip design. The result was an increase in the complexity of the chips that could be designed, with improved access to design verification tools that used logic simulation. The chips were easier to lay out and more likely to function correctly, since their designs could be simulated more thoroughly prior to construction. Although the languages and tools h
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https://en.wikipedia.org/wiki/Variance%20Adaptive%20Quantization
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Variance Adaptive Quantization (VAQ) is a video encoding algorithm that was first introduced in the open source video encoder x264. According to Xvid Builds FAQ: "It's an algorithm that tries to optimally choose a quantizer for each macroblock using advanced math algorithms." It was later ported to programs which encode video content in other video standards, like MPEG-4 ASP or MPEG-2.
In the case of Xvid, the algorithm is intended to make up for the earlier limitations in its Adaptive Quantization mode. The first Xvid library containing this improvement was released in February 2008.
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https://en.wikipedia.org/wiki/Terrainability
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The terrainability of a machine or robot is defined as its ability to negotiate terrain irregularities.
Terrainability is a term coined in the research community and related to locomotion in the field of mobile robotics. Its various definitions generically describe the ability of the robot to handle various terrains in terms of their ground support, obstacle sizes and spacing, passive/dynamic stability, etc.
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https://en.wikipedia.org/wiki/Woody%20plant
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A woody plant is a plant that produces wood as its structural tissue and thus has a hard stem. In cold climates, woody plants further survive winter or dry season above ground, as opposed to herbaceous plants that die back to the ground until spring.
Characteristics
Woody plants are usually trees, shrubs, or lianas. These are usually perennial plants whose stems and larger roots are reinforced with wood produced from secondary xylem. The main stem, larger branches, and roots of these plants are usually covered by a layer of bark. Wood is a structural tissue that allows woody plants to grow from above ground stems year after year, thus making some woody plants the largest and tallest terrestrial plants.
Woody plants, like herbaceous perennials, typically have a dormant period of the year when growth does not take place, in colder climates due to freezing temperatures and lack of daylight during the winter months, in subtropical and tropical climates due to the dry season when precipitation becomes minimal. The dormant period will be accompanied by shedding of leaves if the plant is deciduous. Evergreen plants do not lose all their leaves at once (they instead shed them gradually over the growing season), however growth virtually halts during the dormant season. Many woody plants native to subtropical regions and nearly all native to the tropics are evergreen due to year-round warm temperatures.
During the fall months, each stem in a deciduous plant cuts off the flow of nutrients and water to the leaves. This causes them to change colors as the chlorophyll in the leaves breaks down. Special cells are formed that sever the connection between the leaf and stem, so that it will easily detach. Evergreen plants do not shed their leaves and merely go into a state of low activity during the dormant season. During spring, the roots begin sending nutrients back up to the canopy.
When the growing season resumes, either with warm weather or the wet season, the plant will
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https://en.wikipedia.org/wiki/Parametric%20family
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In mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters.
Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc.
In probability and its applications
For example, the probability density function of a random variable may depend on a parameter . In that case, the function may be denoted to indicate the dependence on the parameter . is not a formal argument of the function as it is considered to be fixed. However, each different value of the parameter gives a different probability density function. Then the parametric family of densities is the set of functions , where denotes the parameter space, the set of all possible values that the parameter can take. As an example, the normal distribution is a family of similarly-shaped distributions parametrized by their mean and their variance.
In decision theory, two-moment decision models can be applied when the decision-maker is faced with random variables drawn from a location-scale family of probability distributions.
In algebra and its applications
In economics, the Cobb–Douglas production function is a family of production functions parametrized by the elasticities of output with respect to the various factors of production.
In algebra, the quadratic equation, for example, is actually a family of equations parametrized by the coefficients of the variable and of its square and by the constant term.
See also
Indexed family
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https://en.wikipedia.org/wiki/Intrinsic%20motivation%20%28artificial%20intelligence%29
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Intrinsic motivation in the study of artificial intelligence and robotics is a mechanism for enabling artificial agents (including robots) to exhibit inherently rewarding behaviours such as exploration and curiosity, grouped under the same term in the study of psychology. Psychologists consider intrinsic motivation in humans to be the drive to perform an activity for inherent satisfaction – just for the fun or challenge of it.
Definition
An intelligent agent is intrinsically motivated to act if the information content alone, or the experience resulting from the action, is the motivating factor.
Information content in this context is measured in the information-theoretic sense of quantifying uncertainty. A typical intrinsic motivation is to search for unusual, surprising situations (exploration), in contrast to a typical extrinsic motivation such as the search for food (homeostasis). Extrinsic motivations are typically described in artificial intelligence as task-dependent or goal-directed.
Origins in psychology
The study of intrinsic motivation in psychology and neuroscience began in the 1950s with some psychologists explaining exploration through drives to manipulate and explore, however, this homeostatic view was criticised by White. An alternative explanation from Berlyne in 1960 was the pursuit of an optimal balance between novelty and familiarity. Festinger described the difference between internal and external view of the world as dissonance that organisms are motivated to reduce. A similar view was expressed in the '70s by Kagan as the desire to reduce the incompatibility between cognitive structure and experience. In contrast to the idea of optimal incongruity, Deci and Ryan identified in the mid 80's an intrinsic motivation based on competence and self-determination.
Computational models
An influential early computational approach to implement artificial curiosity in the early 1990s by Schmidhuber, has since been developed into a "Formal theory of cr
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https://en.wikipedia.org/wiki/Cobalt%20in%20biology
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Cobalt is essential to the metabolism of all animals. It is a key constituent of cobalamin, also known as vitamin B, the primary biological reservoir of cobalt as an ultratrace element. Bacteria in the stomachs of ruminant animals convert cobalt salts into vitamin B, a compound which can only be produced by bacteria or archaea. A minimal presence of cobalt in soils therefore markedly improves the health of grazing animals, and an uptake of 0.20 mg/kg a day is recommended because they have no other source of vitamin B.
Proteins based on cobalamin use corrin to hold the cobalt. Coenzyme B12 features a reactive C-Co bond that participates in the reactions. In humans, B12 has two types of alkyl ligand: methyl and adenosyl. MeB12 promotes methyl (−CH3) group transfers. The adenosyl version of B12 catalyzes rearrangements in which a hydrogen atom is directly transferred between two adjacent atoms with concomitant exchange of the second substituent, X, which may be a carbon atom with substituents, an oxygen atom of an alcohol, or an amine. Methylmalonyl coenzyme A mutase (MUT) converts MMl-CoA to Su-CoA, an important step in the extraction of energy from proteins and fats.
Although far less common than other metalloproteins (e.g. those of zinc and iron), other cobaltoproteins are known besides B12. These proteins include methionine aminopeptidase 2, an enzyme that occurs in humans and other mammals that does not use the corrin ring of B12, but binds cobalt directly. Another non-corrin cobalt enzyme is nitrile hydratase, an enzyme in bacteria that metabolizes nitriles.
Cobalt deficiency
In humans, consumption of cobalt-containing vitamin B12 meets all needs for cobalt. For cattle and sheep, which meet vitamin B12 needs via synthesis by resident bacteria in the rumen, there is a function for inorganic cobalt. In the early 20th century, during the development of farming on the North Island Volcanic Plateau of New Zealand, cattle suffered from what was termed "bush sickne
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https://en.wikipedia.org/wiki/Interplanetary%20contamination
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Interplanetary contamination refers to biological contamination of a planetary body by a space probe or spacecraft, either deliberate or unintentional.
There are two types of interplanetary contamination:
Forward contamination is the transfer of life and other forms of contamination from Earth to another celestial body.
Back contamination is the introduction of extraterrestrial organisms and other forms of contamination into Earth's biosphere. It also covers infection of humans and human habitats in space and on other celestial bodies by extraterrestrial organisms, if such organisms exist.
The main focus is on microbial life and on potentially invasive species. Non-biological forms of contamination have also been considered, including contamination of sensitive deposits (such as lunar polar ice deposits) of scientific interest. In the case of back contamination, multicellular life is thought unlikely but has not been ruled out. In the case of forward contamination, contamination by multicellular life (e.g. lichens) is unlikely to occur for robotic missions, but it becomes a consideration in crewed missions to Mars.
Current space missions are governed by the Outer Space Treaty and the COSPAR guidelines for planetary protection. Forward contamination is prevented primarily by sterilizing the spacecraft. In the case of sample-return missions, the aim of the mission is to return extraterrestrial samples to Earth, and sterilization of the samples would make them of much less interest. So, back contamination would be prevented mainly by containment, and breaking the chain of contact between the planet of origin and Earth. It would also require quarantine procedures for the materials and for anyone who comes into contact with them.
Overview
Most of the Solar System appears hostile to life as we know it. No extraterrestrial life has ever been discovered. But if extraterrestrial life exists, it may be vulnerable to interplanetary contamination by foreign microorganism
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https://en.wikipedia.org/wiki/Monogastric
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A monogastric organism has a simple single-chambered stomach (one stomach). Examples of monogastric herbivores are horses and rabbits. Examples of monogastric omnivores include humans, pigs, hamsters and rats. Furthermore, there are monogastric carnivores such as cats. A monogastric organism is comparable to ruminant organisms (which has a four-chambered complex stomach), such as cattle, goats, or sheep. Herbivores with monogastric digestion can digest cellulose in their diets by way of symbiotic gut bacteria. However, their ability to extract energy from cellulose digestion is less efficient than in ruminants.
Herbivores digest cellulose by microbial fermentation. Monogastric herbivores which can digest cellulose nearly as well as ruminants are called hindgut fermenters, while ruminants are called foregut fermenters. These are subdivided into two groups based on the relative size of various digestive organs in relationship to the rest of the system: colonic fermenters tend to be larger species such as horses and rhinos, and cecal fermenters are smaller animals such as rabbits and rodents. Great apes derive significant amounts of phytanic acid from the hindgut fermentation of plant materials.
Monogastrics cannot digest the fiber molecule cellulose as efficiently as ruminants, though the ability to digest cellulose varies amongst species.
A monogastric digestive system works as soon as the food enters the mouth. Saliva moistens the food and begins the digestive process. (Note that horses have no (or negligible amounts of) amylase in their saliva). After being swallowed, the food passes from the esophagus into the stomach, where stomach acid and enzymes help to break down the food. Once food leaves the stomach and enters the small intestine, the pancreas secretes enzymes and alkali to neutralize the stomach acid.
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https://en.wikipedia.org/wiki/Jarman%E2%80%93Bell%20principle
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The Jarman–Bell principle is a concept in ecology that the food quality of a herbivore's intake decreases as the size of the herbivore increases, but the amount of such food increases to counteract the low quality foods. It operates by observing the allometric (non- linear scaling) properties of herbivores. The principle was coined by P.J Jarman (1968.) and R.H.V Bell (1971).
Large herbivores can subsist on low quality food. Their gut size is larger than smaller herbivores. The increased size allows for better digestive efficiency, and thus allow viable consumption of low quality food. Small herbivores require more energy per unit of body mass compared to large herbivores. A smaller size, thus smaller gut size and lower efficiency, imply that these animals need to select high quality food to function. Their small gut limits the amount of space for food, so they eat low quantities of high quality diet. Some animals practice coprophagy, where they ingest fecal matter to recycle untapped/ undigested nutrients.
However, the Jarman–Bell principle is not without exception. Small herbivorous members of mammals, birds and reptiles were observed to be inconsistent with the trend of small body mass being linked with high-quality food. There have also been disputes over the mechanism behind the Jarman–Bell principle; that larger body sizes does not increase digestive efficiency.
The implications of larger herbivores ably subsisting on poor quality food compared smaller herbivores mean that the Jarman–Bell principle may contribute evidence for Cope's rule. Furthermore, the Jarman–Bell principle is also important by providing evidence for the ecological framework of "resource partitioning, competition, habitat use and species packing in environments" and has been applied in several studies.
Links with allometry
Allometry refers to the non-linear scaling factor of one variable with respect to another. The relationship between such variables is expressed as a power law, wher
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https://en.wikipedia.org/wiki/Wigner%20distribution%20function
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The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis.
The WDF was first proposed in physics to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, and it is of importance in quantum mechanics in phase space (see, by way of comparison: Wigner quasi-probability distribution, also called the Wigner function or the Wigner–Ville distribution).
Given the shared algebraic structure between position-momentum and time-frequency conjugate pairs, it also usefully serves in signal processing, as a transform in time-frequency analysis, the subject of this article. Compared to a short-time Fourier transform, such as the Gabor transform, the Wigner distribution function provides the highest possible temporal vs frequency resolution which is mathematically possible within the limitations of the uncertainty principle. The downside is the introduction of large cross terms between every pair of signal components and between positive and negative frequencies, which makes the original formulation of the function a poor fit for most analysis applications. Subsequent modifications have been proposed which preserve the sharpness of the Wigner distribution function but largely suppress cross terms.
Mathematical definition
There are several different definitions for the Wigner distribution function. The definition given here is specific to time-frequency analysis. Given the time series , its non-stationary auto-covariance function is given by
where denotes the average over all possible realizations of the process and is the mean, which may or may not be a function of time. The Wigner function is then given by first expressing the autocorrelation function in terms of the average time and time lag , and then Fourier transforming the lag.
So for a single (mean-zero) time series, the Wigner function is simply given by
The motivation for the Wigner function is that it reduces to
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https://en.wikipedia.org/wiki/Hawkboard
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The Hawkboard is a low-power, low-cost Single-board computer based on the Texas Instruments OMAP-L138. Along with the usage of the OMAP ARM9 processor, it also has a floating point DSP. It is a community supported development platform.
As of date, Hawkboard project is closed because of common hardware issue.
External links
An Open community portal for Texas Instruments AM1808 / OMAPL138 platform — hawkboard.org
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https://en.wikipedia.org/wiki/Quadrature%20%28geometry%29
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In mathematics, particularly in geometry, quadrature (also called squaring) is a historical process of drawing a square with the same area as a given plane figure or computing the numerical value of that area. A classical example is the quadrature of the circle (or squaring the circle).
Quadrature problems served as one of the main sources of problems in the development of calculus. They introduce important topics in mathematical analysis.
History
Antiquity
Greek mathematicians understood the determination of an area of a figure as the process of geometrically constructing a square having the same area (squaring), thus the name quadrature for this process. The Greek geometers were not always successful (see squaring the circle), but they did carry out quadratures of some figures whose sides were not simply line segments, such as the lune of Hippocrates and the parabola. By a certain Greek tradition, these constructions had to be performed using only a compass and straightedge, though not all Greek mathematicians adhered to this dictum.
For a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side (the geometric mean of a and b). For this purpose it is possible to use the following: if one draws the circle with diameter made from joining line segments of lengths a and b, then the height (BH in the diagram) of the line segment drawn perpendicular to the diameter, from the point of their connection to the point where it crosses the circle, equals the geometric mean of a and b. A similar geometrical construction solves the problems of quadrature of a parallelogram and of a triangle.
Problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge was proved in the 19th century to be impossible. Nevertheless, for some figures a quadrature can be performed. The quadratures of the surface of a sphere and a parabola segment discovered by Archimedes became the
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https://en.wikipedia.org/wiki/Aperture%20%28computer%20memory%29
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In computing, an aperture is a portion of physical address space (i.e. physical memory) that is associated with a particular peripheral device or a memory unit. Apertures may reach external devices such as ROM or RAM chips, or internal memory on the CPU itself.
Typically, a memory device attached to a computer accepts addresses starting at zero, and so a system with more than one such device would have ambiguous addressing. To resolve this, the memory logic will contain several aperture selectors, each containing a range selector and an interface to one of the memory devices.
The set of selector address ranges of the apertures are disjoint. When the CPU presents a physical address within the range recognized by an aperture, the aperture unit routes the request (with the address remapped to a zero base) to the attached device. Thus, apertures form a layer of address translation below the level of the usual virtual-to-physical mapping.
See also
Address bus
AGP aperture
Memory-mapped I/O
External links
Flash Memory Solutions
Computer memory
Computer architecture
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https://en.wikipedia.org/wiki/Heath-Brown%E2%80%93Moroz%20constant
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The Heath-Brown–Moroz constant C, named for Roger Heath-Brown and Boris Moroz, is defined as
where p runs over the primes.
Application
This constant is part of an asymptotic estimate for the distribution of rational points of bounded height on the cubic surface X03=X1X2X3. Let H be a positive real number and N(H) the number of solutions to the equation X03=X1X2X3 with all the Xi non-negative integers less than or equal to H and their greatest common divisor equal to 1. Then
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https://en.wikipedia.org/wiki/Nutritional%20science
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Nutritional science (also nutrition science, sometimes short nutrition, dated trophology) is the science that studies the physiological process of nutrition (primarily human nutrition), interpreting the nutrients and other substances in food in relation to maintenance, growth, reproduction, health and disease of an organism.
History
Before nutritional science emerged as an independent study disciplines, mainly chemists worked in this area. The chemical composition of food was examined. Macronutrients, especially protein, fat and carbohydrates, have been the focus components of the study of (human) nutrition since the 19th century. Until the discovery of vitamins and vital substances, the quality of nutrition was measured exclusively by the intake of nutritional energy.
The early years of the 20th century were summarized by Kenneth John Carpenter in his Short History of Nutritional Science as "the vitamin era". The first vitamin was isolated and chemically defined in 1926 (thiamine). The isolation of vitamin C followed in 1932 and its effects on health, the protection against scurvy, was scientifically documented for the first time.
At the instigation of the British physiologist John Yudkin at the University of London, the degrees Bachelor of Science and Master of Science in nutritional science were established in the 1950s.
Nutritional science as a separate discipline was institutionalized in Germany in November 1956 when Hans-Diedrich Cremer was appointed to the chair for human nutrition in Giessen. The Institute for Nutritional Science was initially located at the Academy for Medical Research and Further Education, which was transferred to the Faculty of Human Medicine when the Justus Liebig University was reopened. Over time, seven other universities with similar institutions followed in Germany.
From the 1950s to 1970s, a focus of nutritional science was on dietary fat and sugar. From the 1970s to the 1990s, attention was put on diet-related chronic diseas
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https://en.wikipedia.org/wiki/List%20of%20group%20theory%20topics
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In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
Structures and operations
Central extension
Direct product of groups
Direct sum of groups
Extension problem
Free abelian group
Free group
Free product
Generating set of a group
Group cohomology
Group extension
Presentation of a group
Product of group subsets
Schur multiplier
Semidirect product
Sylow theorems
Hall subgroup
Wreath product
Basic properties of groups
Butterfly lemma
Center of a group
Centralizer and normalizer
Characteristic subgroup
Commutator
Composition series
Conjugacy class
Conjugate closure
Conjugation of isometries in Euclidean space
Core (group)
Coset
Derived group
Euler's theorem
Fitting subgroup
Generalized Fitting subgroup
Hamiltonian group
Identity element
Lagrange's theorem
Multiplicative inverse
Normal subgroup
Perfect group
p-core
Schreier refinement theorem
Subgroup
Transversal (combinatorics)
Torsion subgroup
Zassenhaus lemma
Group homomorphisms
Automorphism
Automorphism group
Factor group
Fundamental theorem on homomorphisms
Group homomorphism
Group isomorphism
Homomorphism
Isomorphism theorem
Inner automorphism
Order auto
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https://en.wikipedia.org/wiki/Sociome
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The Sociome is a concept used by scientists in Biology and Sociology referring to the dimensions of existence that are social. The term is also an indication of the convergence of systems biology and the study of society as a complex system that has begun to occur among early 21st Century scientists. Just as the phenome is typically thought of as the set of expressed phenotypes of an organism, the sociome can be thought of as the set of observed characteristics of societies. For example, while all societies consisting of humans might be thought of as having the potential to become egalitarian social democracies, not all observed societies are egalitarian or social democracies. Thus, the sociome can also be thought of indirectly as an ideal type of the unrealized potential of any given organization of social beings.
Origin of term
The first known usage of the term sociome was in 2001 by Daichi Kamiyama. The term has also been utilized by sociologist Adam Thomas Perzynski. The two scientists differ in their usage. Kamiyama's study describes a new scientific "era of the sociome (Sociology[+ome])" characterized by the study of the social activities of molecules. This usage is an anthropomorphism of social behavior, wherein molecules are described as having the ability to socialize. Perzynski's social scientific usage varies from this considerably. While Sociology is the study of society, behavior and social relationships, the sociome is the characterization and quantification of patterns, variables, activities, relationships and attributes across all societies that exist and can be studied. The suffix -ome has been used primarily in biology, as in genome, proteome, microbiome, metabolome and phenome. Basu and colleagues have used the term sociome to refer to a sort of standardized approach to the characterization of geocoded social attributes (e.g. neighborhood level). In 2014, Del Savio and colleagues discussed the blurring of the boundaries between disciplines, and
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https://en.wikipedia.org/wiki/Clarifying%20agent
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Clarifying agents are used to remove suspended solids from liquids by inducing flocculation, causing the solids to form larger aggregates that can be easily removed after they either float to the surface or sink to the bottom of the containment vessel.
Process
Particles finer than 0.1 µm (10−7m) in water remain continuously in motion due to electrostatic charge (often negative) which causes them to repel each other. Once their electrostatic charge is neutralized by the use of a coagulant chemical, the finer particles start to collide and agglomerate (collect together) under the influence of Van der Waals forces. These larger and heavier particles are called flocs.
Flocculants, or flocculating agents (also known as flocking agents), are chemicals that promote flocculation by causing colloids and other suspended particles in liquids to aggregate, forming a floc. Flocculants are used in water treatment processes to improve the sedimentation or filterability of small particles. For example, a flocculant may be used in swimming pool or drinking water filtration to aid removal of microscopic particles which would otherwise cause the water to be turbid (cloudy) and which would be difficult or impossible to remove by filtration alone.
Many flocculants are multivalent cations such as aluminium, iron, calcium or magnesium. These positively charged molecules interact with negatively charged particles and molecules to reduce the barriers to aggregation. In addition, many of these chemicals, under appropriate pH and other conditions such as temperature and salinity, react with water to form insoluble hydroxides which, upon precipitating, link together to form long chains or meshes, physically trapping small particles into the larger floc.
Long-chain polymer flocculants, such as modified polyacrylamides, are manufactured and sold by the flocculant producing business. These can be supplied in dry or liquid form for use in the flocculation process. The most common liquid polyac
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https://en.wikipedia.org/wiki/Sooraj%20Surendran
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Sooraj Surendran is an Indian technologist and electronic engineering graduate from Anna University. He has made significant contributions to motorized wheelchair deployment in Tamil Nadu.
Early life and education
Surendran was born in Kollam, Kerala, India. His mother Sudha was a housewife and his father was K Surendran Pillai.
He completed schooling in Sree Buddha, a Central Board of Secondary Education school in Karunagappalli, Kerala. He earned his degree from Anna University in electronic engineering.
Career
Surendran graduated from Anna University with a BTech in electronic engineering in 2011. He worked on motorized wheelchair design and nursing care bed electronic unit design, and developed an electronic system for nursing care beds that integrated Bluetooth technology to control the functions of a nursing care bed via an Android application. Surendran was invited to help develop electronic control units for lightweight motorized wheelchairs as a part of a Tamil Nadu program to distribute motorized wheelchairs to 2,000 people.
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https://en.wikipedia.org/wiki/Sums%20of%20powers
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In mathematics and statistics, sums of powers occur in a number of contexts:
Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
Faulhaber's formula expresses as a polynomial in , or alternatively in terms of a Bernoulli polynomial.
Fermat's right triangle theorem states that there is no solution in positive integers for and .
Fermat's Last Theorem states that is impossible in positive integers with .
The equation of a superellipse is . The squircle is the case , .
Euler's sum of powers conjecture (disproved) concerns situations in which the sum of integers, each a th power of an integer, equals another th power.
The Fermat-Catalan conjecture asks whether there are an infinitude of examples in which the sum of two coprime integers, each a power of an integer, with the powers not necessarily equal, can equal another integer that is a power, with the reciprocals of the three powers summing to less than 1.
Beal's conjecture concerns the question of whether the sum of two coprime integers, each a power greater than 2 of an integer, with the powers not necessarily equal, can equal another integer that is a power greater than 2.
The Jacobi–Madden equation is in integers.
The Prouhet–Tarry–Escott problem considers sums of two sets of th powers of integers that are equal for multiple values of .
A taxicab number is the smallest integer that can be expressed as a sum of two positive third powers in distinct ways.
The Riemann zeta function is the sum of the reciprocals of the positive integers each raised to the power , where is a complex number whose real part is greater than 1.
The Lander, Parkin, and Selfridge conjecture concerns the minimal value of in
Waring's problem asks whether for every natural number ther
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https://en.wikipedia.org/wiki/Anti-hijack%20system
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An anti-hijack system is an electronic system fitted to motor vehicles to deter criminals from hijacking them. Although these types of systems are becoming more common on newer cars, they have not caused a decrease in insurance premiums as they are not as widely known as other more common anti-theft systems such as alarms or steering locks. It can also be a part of an alarm or immobiliser system. An approved anti-hijacking system will achieve a safe, quick shutdown of the vehicle it is attached to. There are also mechanical anti-hijack devices.
Diversify Solutions, a company in South Africa, has announced its research and development at the Nelson Mandela University of a GSM based Anti hijacking system.
The system works off a verification process with added features such as alcohol sensors and signal jamming capabilities, this comes after increasing rates of hijackings in South Africa and alarming rates of accidents caused by driving under the influence and texting whilst driving.
Technology
There are three basic principles on which the systems work.
Lockout
A lockout system is armed when the driver turns the ignition key to the on position and carries out a specified action, usually flicking a hidden switch or depressing the brake pedal twice. It is activated when the vehicle drops below a certain speed or becomes stationary, and will cause all of the vehicle's doors to automatically lock, to prevent against thieves stealing the vehicle when it is stopped, for example at a traffic light or pedestrian crossing.
Transponder
A transponder system is a system which is always armed until a device, usually a small RFID transponder, enters the vehicle's transmitter radius. Since the device is carried by the driver, usually in their wallet or pocket, if the driver leaves the immediate vicinity of the vehicle, so will the transponder, causing the system to assume the vehicle has been hijacked and disable it.
As the transponder itself is concealed, the thief woul
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https://en.wikipedia.org/wiki/Brown%20measure
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In mathematics, the Brown measure of an operator in a finite factor is a probability measure on the complex plane which may be viewed as an analog of the spectral counting measure (based on algebraic multiplicity) of matrices.
It is named after Lawrence G. Brown.
Definition
Let be a finite factor with the canonical normalized trace and let be the identity operator. For every operator the function
is a subharmonic function and its Laplacian in the distributional sense is a probability measure on
which is called the Brown measure of Here the Laplace operator is complex.
The subharmonic function can also be written in terms of the Fuglede−Kadison determinant as follows
See also
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https://en.wikipedia.org/wiki/Colonel%20Meow
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Colonel Meow (October 11, 2011 – January 29, 2014) was an American Himalayan–Persian crossbreed cat, who temporarily held the 2014 Guinness world record for the longest fur on a cat (nine inches or about 23 cm). He became an Internet celebrity when his owners posted pictures of his scowling face to Facebook and Instagram. He was lovingly known by his hundreds of thousands of followers as an "adorable fearsome dictator", a "prodigious Scotch drinker" and "the angriest cat in the world".
Background
Colonel Meow was rescued by Seattle Persian and Himalayan Rescue and was later adopted at a Petco by his owner Anne Avey. He rose to internet fame after his owner posted a picture of his angry-looking scowl to Facebook and Instagram.
Health complications and death
In November 2013, Colonel Meow was hospitalized due to heart problems and underwent a difficult surgery and blood transfusion. On January 30, 2014, his owner announced on Facebook that Colonel Meow had died. She also expressed gratitude for the support of his more than 350,000 followers.
In July 2014, Friskies posted an ad entitled "Cat Summer" and announced that for each view they would donate one meal to needy cats in Colonel Meow's name. The video stars Grumpy Cat as well as other famous internet cats.
See also
Lil Bub
List of individual cats
Notes
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https://en.wikipedia.org/wiki/List%20of%20United%20States%20regional%20mathematics%20competitions
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Many math competitions in the United States have regional restrictions. Of these, most are statewide.
For a more complete list, please visit here .
The contests include:
Alabama
Alabama Statewide High School Mathematics Contest
Virgil Grissom High School Math Tournament
Vestavia Hills High School Math Tournament
Arizona
Great Plains Math League
AATM State High School Contest
California
Bay Area Math Olympiad
Lawrence Livermore National Laboratories Annual High School Math Challenge
Cal Poly Math Contest and Trimathlon
Polya Competition
Bay Area Math Meet
College of Creative Studies Math Competition
LA Math Cup
Math Day at the Beach hosted by CSULB
Math Field Day for San Diego Middle Schools
Mesa Day Math Contest at UC Berkeley
Santa Barbara County Math Superbowl
Pomona College Mathematical Talent Search
Redwood Empire Mathematics Tournament hosted by Humboldt State (middle and high school)
San Diego Math League and San Diego Math Olympiad hosted by the San Diego Math Circle
Santa Clara University High School Mathematics Contest
SC Mathematics Competition (SCMC) hosted by RSO@USC
Stanford Mathematics Tournament
UCSD/GSDMC High School Honors Mathematics Contest
Colorado
Colorado Mathematics Olympiad
District of Columbia
Moody's Mega Math
Florida
Florida-Stuyvesant Alumni Mathematics Competition
David Essner Mathematics Competition
James S. Rickards High School Fall Invitational
FAMAT Regional Competitions:
January Regional
February Regional
March Regional
FGCU Math Competition
Georgia
Central Math Meet(grades 9 - 12)
GA Council of Teachers of Mathematics State Varsity Math Tournament
STEM Olympiads Of America Math, Science & Cyber Olympiads (grades 3 - 8)
Valdosta State University Middle Grades Mathematics Competition
Illinois
ICTM math contest (grades 3–12)
Indiana
[IUPUI High School Math Contest] (grades 9–12)
Huntington University Math Competition (grades 6–12)
Indiana Math League
IASP Academic Super Bowl
Rose-Hulman H
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https://en.wikipedia.org/wiki/List%20of%20repunit%20primes
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This is a list of repunit primes.
Base 2 repunit primes
Base-2 repunit primes are called Mersenne primes.
Base 3 repunit primes
The first few base-3 repunit primes are
13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 ,
corresponding to of
3, 7, 13, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, 2215303, 2704981, 3598867, ... .
Base 4 repunit primes
The only base-4 repunit prime is 5 (). , and 3 always divides when n is odd and when n is even. For n greater than 2, both and are greater than 3, so removing the factor of 3 still leaves two factors greater than 1. Therefore, the number cannot be prime.
Base 5 repunit primes
The first few base-5 repunit primes are
31, 19531, 12207031, 305175781, 177635683940025046467781066894531, 14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531, 35032461608120426773093239582247903282006548546912894293926707097244777067146515037165954709053039550781, 815663058499815565838786763657068444462645532258620818469829556933715405574685778402862015856733535201783524826169013977050781 ,
corresponding to of
3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279, 3300593, ... .
Base 6 repunit primes
The first few base-6 repunit primes are
7, 43, 55987, 7369130657357778596659, 3546245297457217493590449191748546458005595187661976371, 133733063818254349335501779590081460423013416258060407531857720755181857441961908284738707408499507 ,
corresponding to of
2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019, 3360347, ... .
Base 7 repunit primes
The first few base-7 repunit primes are
2801, 16148168401, 85053461164796801949539541639542805770666392330682673302530819774105141531698707146930307290253537320447270457,1385022127101034087007743810331355039266633249933176317292277906573251633103418332277759454260526
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https://en.wikipedia.org/wiki/TI%20StarterWare
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StarterWare was initially developed by TI as a free software package catering to their arm A8 and A9 microprocessors. Its primary purpose was to offer drivers and libraries with a consistent API tailored for processors within these microprocessor families. The package encompassed utilities and illustrative use cases across various applications. Despite TI's diminished active backing, the software lingers in open-source repositories on GitHub, primarily upholding support for widely used beagle boards that make use of these processors.
This software collection closely aligns with what many chip manufacturers refer to as a HAL (Hardware Abstraction Layer). In TI's context, it's termed DAL (Device Abstraction Layer). Its role revolves around furnishing fundamental functionalities and an API that an operating system can conveniently adapt to. For those inclined to create baremetal programs by directly engaging with the starterware API, the package also offered documentation and assistance.
Texas Instruments
Embedded systems
System software
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https://en.wikipedia.org/wiki/Uniqueness%20theorem
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In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions. Examples of uniqueness theorems include:
Alexandrov's uniqueness theorem of three-dimensional polyhedra
Black hole uniqueness theorem
Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.
Cauchy–Kowalevski–Kashiwara theorem is a wide generalization of the Cauchy–Kowalevski theorem for systems of linear partial differential equations with analytic coefficients.
Division theorem, the uniqueness of quotient and remainder under Euclidean division.
Fundamental theorem of arithmetic, the uniqueness of prime factorization.
Holmgren's uniqueness theorem for linear partial differential equations with real analytic coefficients.
Picard–Lindelöf theorem, the uniqueness of solutions to first-order differential equations.
Thompson uniqueness theorem in finite group theory
Uniqueness theorem for Poisson's equation
Electromagnetism uniqueness theorem for the solution of Maxwell's equation
Uniqueness case in finite group theory
The word unique is sometimes replaced by essentially unique, whenever one wants to stress that the uniqueness is only referred to the underlying structure, whereas the form may vary in all ways that do not affect the mathematical content.
A uniqueness theorem (or its proof) is, at least within the mathematics of differential equations, often combined with an existence theorem (or its proof) to a combined existence and uniqueness theorem (e.g., existence and uniqueness of solution to first-order differential equations with boundary condition).
See also
Existence theorem
Rigidity (mathematics)
Uniqueness quantification
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https://en.wikipedia.org/wiki/Librem
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Librem is a line of computers manufactured by Purism, SPC featuring free (libre) software. The laptop line is designed to protect privacy and freedom by providing no non-free (proprietary) software in the operating system or kernel, avoiding the Intel Active Management Technology, and gradually freeing and securing firmware. Librem laptops feature hardware kill switches for the microphone, webcam, Bluetooth and Wi-Fi.
Models
Laptops
Librem 13, Librem 15 and Librem 14
In 2014, Purism launched a crowdfunding campaign on Crowd Supply to fund the creation and production of the Librem 15 laptop, conceived as a modern alternative to existing open-source hardware laptops, all of which used older hardware. The in the name refers to its 15-inch screen size. The campaign succeeded after extending the original campaign, and the laptops were shipped to backers. In a second revision of the laptop, hardware kill switches for the camera, microphone, Wi-Fi, and Bluetooth were added.
After the successful launch of the Librem 15, Purism created another campaign on Crowd Supply for a 13-inch laptop called the Librem 13, which also came with hardware kill switches similar to those on the Librem 15v2. The campaign was again successful and the laptops were shipped to customers.
Purism announced in December 2016 that it would start shipping from inventory rather than building to order with the new batches of Librem 15 and 13.
, Purism has one laptop model in production, the Librem 14 (version 1, US$1,370).
Comparison of laptops
Librem Mini
The Librem Mini is a small form factor desktop computer, which began shipping in June 2020.
Librem 5
On August 24, 2017, Purism started a crowdfunding campaign for the Librem 5, a smartphone aimed to run 100% free software, which would "[focus] on security by design and privacy protection by default". Purism claimed that the phone would become "the world's first ever IP-native mobile handset, using end-to-end encrypted decentralized communica
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