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8,200 | More precisely if the lattice has order n then the von Neumann regular ring can be taken to be an n by n matrix ring Mn(R) over another von Neumann regular ring R. Here a complemented modular lattice has order n if it has a homogeneous basis of n elements, where a basis is n elements a1, ..., an such that ai ∧ aj = 0 i... | Continuous geometry | 0.821727 |
8,201 | In mathematics, continuous geometry is an analogue of complex projective geometry introduced by von Neumann (1936, 1998), where instead of the dimension of a subspace being in a discrete set 0 , 1 , … , n {\displaystyle 0,1,\dots ,{\textit {n}}} , it can be an element of the unit interval {\displaystyle } . Von Neuman... | Continuous geometry | 0.821727 |
8,202 | Menger and Birkhoff gave axioms for projective geometry in terms of the lattice of linear subspaces of projective space. Von Neumann's axioms for continuous geometry are a weakened form of these axioms. A continuous geometry is a lattice L with the following properties L is modular. | Continuous geometry | 0.821727 |
8,203 | In projective geometry, the Veblen–Young theorem states that a projective geometry of dimension at least 3 is isomorphic to the projective geometry of a vector space over a division ring. This can be restated as saying that the subspaces in the projective geometry correspond to the principal right ideals of a matrix al... | Continuous geometry | 0.821727 |
8,204 | International Federation for the Promotion of Mechanism and Machine Science (IFToMM) is an organization that supports international exchange of researchers and engineers from the wide range of discipline related to Mechanical Engineering. | Mechanism and Machine Theory | 0.821718 |
8,205 | Microsoft's paper on machine learning with ML.NET demonstrated it is capable of training sentiment analysis models using large datasets while achieving high accuracy. Its results showed 95% accuracy on Amazon's 9GB review dataset. | ML.NET | 0.821718 |
8,206 | Microsoft acknowledged that the Python programming language is popular with Data Scientists, so it has introduced NimbusML the experimental Python bindings for ML.NET. This enables users to train and use machine learning models in Python. It was made open source similar to Infer.NET. | ML.NET | 0.821718 |
8,207 | Microsoft Research announced the popular Infer.NET model-based machine learning framework used for research in academic institutions since 2008 has been released open source and is now part of the ML.NET framework. The Infer.NET framework utilises probabilistic programming to describe probabilistic models which has the... | ML.NET | 0.821718 |
8,208 | ML.NET is a free software machine learning library for the C# and F# programming languages. It also supports Python models when used together with NimbusML. The preview release of ML.NET included transforms for feature engineering like n-gram creation, and learners to handle binary classification, multi-class classific... | ML.NET | 0.821718 |
8,209 | A full roadmap of planned features have been made available on the official GitHub repo.The first stable 1.0 release of the framework was announced at Build (developer conference) 2019. It included the addition of a Model Builder tool and AutoML (Automated Machine Learning) capabilities. Build 1.3.1 introduced a previe... | ML.NET | 0.821718 |
8,210 | ML.NET was derived from the TLC library and has largely surpassed its parent says Dr. James McCaffrey, Microsoft Research.Developers can train a Machine Learning Model or reuse an existing Model by a 3rd party and run it on any environment offline. This means developers do not need to have a background in Data Science ... | ML.NET | 0.821718 |
8,211 | ML.NET brings model-based Machine Learning analytic and prediction capabilities to existing .NET developers. The framework is built upon .NET Core and .NET Standard inheriting the ability to run cross-platform on Linux, Windows and macOS. Although the ML.NET framework is new, its origins began in 2002 as a Microsoft Re... | ML.NET | 0.821718 |
8,212 | ML.NET allows users to export trained models to the Open Neural Network Exchange (ONNX) format. This establishes an opportunity to use models in different environments that don't use ML.NET. It would be possible to run these models in the client side of a browser using ONNX.js, a javascript client-side framework for de... | ML.NET | 0.821718 |
8,213 | AI fairness and explainability has been an area of debate for AI Ethicists in recent years. A major issue for Machine Learning applications is the black box effect where end users and the developers of an application are unsure of how an algorithm came to a decision or whether the dataset contains bias. Build 0.8 inclu... | ML.NET | 0.821717 |
8,214 | Sono-Seq (Sonication of Cross-linked Chromatin Sequencing) is a method in molecular biology used for determining the sequences of those DNA regions in the genome near regions of open chromatin of expressed genes. It is also known as "Input" in the Chip-Seq protocol, since it follows the same steps except it doesn't req... | Sono-Seq | 0.821715 |
8,215 | Another limitation is that some relevant proteins will likely be missed since no extraction condition is all encompassing. It is possible that proteins with low stoichiometry of phosphorylation, in very low abundance, or phosphorylated as a target for rapid degradation will be lost. Bioinformatics analyses of low-throu... | Phosphoproteomics | 0.8217 |
8,216 | The analysis of the entire complement of phosphorylated proteins in a cell is certainly a feasible option. This is due to the optimization of enrichment protocols for phosphoproteins and phosphopeptides, better fractionation techniques using chromatography, and improvement of methods to selectively visualize phosphoryl... | Phosphoproteomics | 0.8217 |
8,217 | "What the Tortoise Said to Achilles", written in 1895 by Lewis Carroll, was an attempt to reveal an analogous paradox in the realm of pure logic. If Carroll's argument is valid, the implication is that Zeno's paradoxes of motion are not essentially problems of space and time, but go right to the heart of reasoning itse... | Dichotomy paradox | 0.821698 |
8,218 | Omics is a term used informally to refer to branches of biology whose names end in the suffix -omics, such as genomics, proteomics, metabolomics, and glycomics. Marine Omics has recently emerged as a field of research of its own. Omics aims at collectively characterising and quantifying pools of biological molecules th... | Marine microbes | 0.821696 |
8,219 | Space weather is the environmental condition within the Solar System, including the solar wind. It is studied especially surrounding the Earth, including conditions from the magnetosphere to the ionosphere and thermosphere. Space weather is distinct from terrestrial weather of the troposphere and stratosphere. The term... | Solar phenomena | 0.821684 |
8,220 | Throughout history, observation technology and methodology advanced, and in the 20th century, interest in astrophysics surged. A number of new observatories were built with solar telescopes around the world. The 1931 invention of the coronagraph allowed the corona to be studied in full daylight. | Solar phenomena | 0.821684 |
8,221 | Molecular Membrane Biology is a peer-reviewed scientific journal that publishes review articles of biomembranes at the molecular level. It is published by Taylor & Francis. The editor-in-chief is Vincent Postis. | Molecular Membrane Biology | 0.82168 |
8,222 | Both binaries and source code are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as OpenBLAS, FLINT, GAP (computer algebra system), and NTL will be tuned and optimized for that computer, taking into account the number of processors, the size of ... | SageMath | 0.821674 |
8,223 | SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. The first version of SageMath was relea... | SageMath | 0.821674 |
8,224 | NNI (Neural Network Intelligence) is a free and open-source AutoML toolkit developed by Microsoft. It is used to automate feature engineering, model compression, neural architecture search, and hyper-parameter tuning.The source code is licensed under MIT License and available on GitHub. | Neural Network Intelligence | 0.821658 |
8,225 | Molecular cloning has led directly to the elucidation of the complete DNA sequence of the genomes of a very large number of species and to an exploration of genetic diversity within individual species, work that has been done mostly by determining the DNA sequence of large numbers of randomly cloned fragments of the ge... | Cloned DNA | 0.821658 |
8,226 | This is because multiples of the identity form a nontrivial normal subgroup, thus evading the definition. Equivalently, the corresponding Lie algebra has a degenerate Killing form, because multiples of the identity map to the zero element of the algebra. Thus, the corresponding Lie algebra is also neither simple nor se... | Exceptional groups | 0.821656 |
8,227 | It emerged in the course of classification of simple Lie groups that there exist also several exceptional possibilities not corresponding to any familiar geometry. These exceptional groups account for many special examples and configurations in other branches of mathematics, as well as contemporary theoretical physics.... | Exceptional groups | 0.821656 |
8,228 | An equivalent definition of a simple Lie group follows from the Lie correspondence: A connected Lie group is simple if its Lie algebra is simple. An important technical point is that a simple Lie group may contain discrete normal subgroups. For this reason, the definition of a simple Lie group is not equivalent to the ... | Exceptional groups | 0.821656 |
8,229 | R , C , H , O {\displaystyle \mathbb {R,C,H,O} } stand for the real numbers, complex numbers, quaternions, and octonions. In the symbols such as E6−26 for the exceptional groups, the exponent −26 is the signature of an invariant symmetric bilinear form that is negative definite on the maximal compact subgroup. It is eq... | Exceptional groups | 0.821656 |
8,230 | In mechanical engineering, a parallel force system is a situation in which two forces of equal magnitude act in the same direction within the same plane, with the counter force in the middle. An example of this is a see saw. The children are applying the two forces at the ends, and the fulcrum in the middle gives the c... | Parallel force system | 0.821647 |
8,231 | In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures. These alternate meanings may or may not reduce to the same thing, depending on the context. | Zero vector | 0.821641 |
8,232 | Profiles like these are found for almost all proteins listed in Wikipedia. They are generated by organizations such as the Genomics Institute of the Novartis Research Foundation and the European Bioinformatics Institute. Additional information can be found by searching their databases (for an example of the GLUT4 trans... | Gene expression analysis | 0.821639 |
8,233 | For instance cumulative distribution functions are usually taken to be right continuous, as are functions integrated against in Lebesgue–Stieltjes integration. In this case H is the indicator function of a closed semi-infinite interval: The corresponding probability distribution is the degenerate distribution. H(0) = 0... | Unit step function | 0.821639 |
8,234 | The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. One author uses the terminology of the "Rule of Average Conditional Probabilities", while another refers to it as the "continuous law of al... | Law of total probability | 0.821637 |
8,235 | In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events, hence the name. | Law of total probability | 0.821637 |
8,236 | In 1990 the microbiologist Woese proposed the three-domain system that divided living things into bacteria, archaea and eukaryotes, and thereby split the prokaryote domain. Archaea differ from bacteria in both their genetics and biochemistry. For example, while bacterial cell membranes are made from phosphoglycerides w... | Microorganism | 0.821631 |
8,237 | There is evidence that 3.45-billion-year-old Australian rocks once contained microorganisms, the earliest direct evidence of life on Earth.Microbes are important in human culture and health in many ways, serving to ferment foods and treat sewage, and to produce fuel, enzymes, and other bioactive compounds. Microbes are... | Microorganism | 0.821631 |
8,238 | Codimension also has some clear meaning in geometric topology: on a manifold, codimension 1 is the dimension of topological disconnection by a submanifold, while codimension 2 is the dimension of ramification and knot theory. In fact, the theory of high-dimensional manifolds, which starts in dimension 5 and above, can ... | Dimension counting | 0.821622 |
8,239 | In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties. For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is ... | Dimension counting | 0.821622 |
8,240 | In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22×1019 GeV (the Planck energy, corresponding to the energy equivalent of the Planck mass, is 2.17645×10−8 kg) at which quantum effects of gravity become significant. At this scale, present descriptions and theories of sub-atomic p... | Planck volume | 0.821621 |
8,241 | Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds. | Arithmetic topology | 0.821621 |
8,242 | In the 1960s topological interpretations of class field theory were given by John Tate based on Galois cohomology, and also by Michael Artin and Jean-Louis Verdier based on Étale cohomology. Then David Mumford (and independently Yuri Manin) came up with an analogy between prime ideals and knots which was further explor... | Arithmetic topology | 0.821621 |
8,243 | Given a straight line segment called AB, could this be divided in three new equal segments and in many parts required by the use of intercept theorem. | Constructive geometry | 0.821621 |
8,244 | By the above paragraph, one can show that any constructible point can be obtained by such a sequence of extensions. As a corollary of this, one finds that the degree of the minimal polynomial for a constructible point (and therefore of any constructible length) is a power of 2. In particular, any constructible point (o... | Constructive geometry | 0.821621 |
8,245 | One can associate an algebra to our geometry using a Cartesian coordinate system made of two lines, and represent points of our plane by vectors. Finally we can write these vectors as complex numbers. Using the equations for lines and circles, one can show that the points at which they intersect lie in a quadratic exte... | Constructive geometry | 0.821621 |
8,246 | The line shapes and parameters p 0 {\displaystyle p_{0}} and w {\displaystyle w} of the individual component curves have been obtained experimentally. In this case the curve may be decomposed using a linear least squares process simply to determine the concentrations of the components. This process is used in analytica... | Spectroscopic line shape | 0.821617 |
8,247 | The Riemannian manifolds of constant curvature can be classified into the following three cases: elliptic geometry – constant positive sectional curvature Euclidean geometry – constant vanishing sectional curvature hyperbolic geometry – constant negative sectional curvature. | Constant curvature | 0.821614 |
8,248 | The quadratic identities can be proved in a finite-dimensional Jordan algebra over R or C following Max Koecher, who used an invertible element. They are also easy to prove in a Jordan algebra defined by a unital associative algebra (a "special" Jordan algebra) since in that case Q(a)b = aba. They are valid in any Jord... | Quadratic Jordan algebra | 0.821614 |
8,249 | On the other hand the bracketed terms can be simplified by the third displayed identity. It implies that both sides are equal to ½ L(a)R(b,a)L(b). For finite-dimensional unital Jordan algebras, the shift identity can be seen more directly using mutations. | Quadratic Jordan algebra | 0.821614 |
8,250 | In a unital linear Jordan algebra the shift identity asserts that Following Meyberg (1972), it can be established as a direct consequence of polarized forms of the fundamental identity and the commutation or homotopy identity. It is also a consequence of Macdonald's theorem since it is an operator identity involving on... | Quadratic Jordan algebra | 0.821614 |
8,251 | A quadratic Jordan algebra consists of a vector space A over a field K with a distinguished element 1 and a quadratic map of A into the K-endomorphisms of A, a ↦ Q(a), satisfying the conditions: Q(1) = id; Q(Q(a)b) = Q(a)Q(b)Q(a) ("fundamental identity"); Q(a)R(b,a) = R(a,b)Q(a) ("commutation identity"), where R(a,b)c ... | Quadratic Jordan algebra | 0.821614 |
8,252 | Omitting ± subscripts, these must satisfythe fundamental identity Q ( Q ( a ) b ) = Q ( a ) Q ( b ) Q ( a ) , {\displaystyle \displaystyle {Q(Q(a)b)=Q(a)Q(b)Q(a),}} the commutation or homotopy identity R ( a , b ) Q ( a ) = Q ( a ) R ( b , a ) = 2 Q ( Q ( a ) b , a ) , {\displaystyle \displaystyle {R(a,b)Q(a)=Q(a)R(b,a... | Quadratic Jordan algebra | 0.821614 |
8,253 | A linear unital Jordan algebra gives rise to a quadratic mapping Q and associated mapping R satisfying the fundamental identity, the commutation of homotopy identity and the shift identity. A Jordan pair (V+,V−) consists of two vector space V± and two quadratic mappings Q± from V± to V∓. These determine bilinear mappin... | Quadratic Jordan algebra | 0.821614 |
8,254 | Replacing c by b and b by a gives Also, since the right hand side is symmetric in b and 'c, interchanging b and c on the left and subtracting , it follows that the commutators are derivations of the Jordan algebra. Let Q ( a ) = 2 L ( a ) 2 − L ( a 2 ) . {\displaystyle \displaystyle {Q(a)=2L(a)^{2}-L(a^{2}).}} | Quadratic Jordan algebra | 0.821614 |
8,255 | Let B be a subspace of A. Define B to be a quadratic ideal or an inner ideal if the image of Q(b) is contained in B for all b in B; define B to be an outer ideal if B is mapped into itself by every Q(a) for all a in A. An ideal of A is a subspace which is both an inner and an outer ideal. A quadratic Jordan algebra is ... | Quadratic Jordan algebra | 0.821614 |
8,256 | Let A be a quadratic Jordan algebra over R or C. Following Jacobson (1969), a linear Jordan algebra structure can be associated with A such that, if L(a) is Jordan multiplication, then the quadratic structure is given by Q(a) = 2L(a)2 − L(a2). Firstly the axiom Q(a)R(b,a) = R (a,b)Q(a) can be strengthened to Q ( a ) R ... | Quadratic Jordan algebra | 0.821614 |
8,257 | Koecher's arguments apply for finite-dimensional Jordan algebras over the real or complex numbers. | Quadratic Jordan algebra | 0.821614 |
8,258 | In mathematics, quadratic Jordan algebras are a generalization of Jordan algebras introduced by Kevin McCrimmon (1966). The fundamental identities of the quadratic representation of a linear Jordan algebra are used as axioms to define a quadratic Jordan algebra over a field of arbitrary characteristic. There is a unifo... | Quadratic Jordan algebra | 0.821614 |
8,259 | An element a is invertible if Q(a) is invertible and there exists b such that Q(b) is the inverse of Q(a) and Q(a)b = a: such b is unique and we say that b is the inverse of a. A Jordan division algebra is one in which every non-zero element is invertible. | Quadratic Jordan algebra | 0.821614 |
8,260 | Let A be a vector space over K with a quadratic form q and associated symmetric bilinear form q(x,y) = q(x+y) - q(x) - q(y). Let e be a "basepoint" of A, that is, an element with q(e) = 1. Define a linear functional T(y) = q(y,e) and a "reflection" y∗ = T(y)e - y. For each x we define Q(x) by Q(x): y ↦ q(x,y∗)x − q(x) ... | Quadratic Jordan algebra | 0.821614 |
8,261 | Let A be a unital Jordan algebra over a field K of characteristic not equal to 2. For a in A, let L denote the left multiplication map in the associative enveloping algebra L ( a ): x ↦ a x {\displaystyle L(a):x\mapsto ax\ } and define a K-endomorphism of A, called the quadratic representation, by Q ( a ) = 2 L ( a ) 2... | Quadratic Jordan algebra | 0.821614 |
8,262 | In particular these equations hold for x = ab. On the other hand if T = then D(z) = Tz is a derivation of the Jordan algebra, so that = R ( D c , d ) + R ( c , D d ) . {\displaystyle \displaystyle {=R(Dc,d)+R(c,Dd).}} | Quadratic Jordan algebra | 0.821614 |
8,263 | If A is a unital associative algebra over K with multiplication × then a quadratic map Q can be defined from A to EndK(A) by Q(a): b ↦ a × b × a. This defines a quadratic Jordan algebra structure on A. A quadratic Jordan algebra is special if it is isomorphic to a subalgebra of such an algebra, otherwise exceptional. | Quadratic Jordan algebra | 0.821614 |
8,264 | In mathematics, constant curvature is a concept from differential geometry. Here, curvature refers to the sectional curvature of a space (more precisely a manifold) and is a single number determining its local geometry. The sectional curvature is said to be constant if it has the same value at every point and for every... | Constant curvature | 0.821614 |
8,265 | Over GF(2) the AOP has many interesting properties, including: The Hamming weight of the AOP is m + 1, the maximum possible for its degree The AOP is irreducible if and only if m + 1 is prime and 2 is a primitive root modulo m + 1 (over GF(p) with prime p, it is irreducible if and only if m + 1 is prime and p is a prim... | All one polynomial | 0.821612 |
8,266 | A Siamese neural network (sometimes called a twin neural network) is an artificial neural network that uses the same weights while working in tandem on two different input vectors to compute comparable output vectors. Often one of the output vectors is precomputed, thus forming a baseline against which the other output... | Siamese neural networks | 0.821611 |
8,267 | In this role, these games are of particular importance in finite model theory and its applications in computer science (specifically computer aided verification and database theory), since Ehrenfeucht–Fraïssé games are one of the few techniques from model theory that remain valid in the context of finite models. Other ... | Ehrenfeucht–Fraïssé game | 0.821608 |
8,268 | In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the drawing of a single sample. For example, in simple random sampling the probabi... | Inclusion probability | 0.821597 |
8,269 | The Hayden–Preskill thought experiment implies that information that falls into a black hole can be recovered via the Hawking radiation, which raises the question: does the information that falls into a black hole fall in or radiate out? One approach to this is the concept of black hole complementarity, which claims th... | Hayden–Preskill thought experiment | 0.821594 |
8,270 | The Bioinformatics Resource Centers (BRCs) are a group of five Internet-based research centers established in 2004 and funded by NIAID (the National Institute of Allergy and Infectious Diseases.) The BRCs were formed in response to the threats posed by emerging and re-emerging pathogens, particularly Centers for Diseas... | Bioinformatics Resource Centers | 0.821591 |
8,271 | Some in the software engineering prefer to describe "legacy code" without the connotation of being obsolete. Among the most prevalent neutral conceptions are source code inherited from someone else and source code inherited from an older version of the software. Eli Lopian, CEO of Typemock, has defined it as "code that... | Legacy system | 0.821589 |
8,272 | The interpretation of the latent spaces of machine learning models is an active field of study, but latent space interpretation is difficult to achieve. Due to the black-box nature of machine learning models, the latent space may be completely unintuitive. Additionally, the latent space may be high-dimensional, complex... | Latent space | 0.821587 |
8,273 | A latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge from the resemb... | Latent space | 0.821587 |
8,274 | GloVe embeddings are known for capturing both semantic and relational similarities between words. Siamese Networks: Siamese networks are a type of neural network architecture commonly used for similarity-based embedding. They consist of two identical subnetworks that process two input samples and produce their respecti... | Latent space | 0.821587 |
8,275 | Several embedding models have been developed to perform this transformation to create latent space embeddings given a set of data items and a similarity function. These models learn the embeddings by leveraging statistical techniques and machine learning algorithms. Here are some commonly used embedding models: Word2Ve... | Latent space | 0.821587 |
8,276 | In statistics, combinatorial data analysis (CDA) is the study of data sets where the order in which objects are arranged is important. CDA can be used either to determine how well a given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data. | Combinatorial data analysis | 0.821574 |
8,277 | The researchers estimated that a 1024-bit RSA modulus would take about 500 times as long.Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, for instance more th... | Factoring integers | 0.821569 |
8,278 | The presumed difficulty of this problem is important for the algorithms used in cryptography such as RSA public-key encryption and the RSA digital signature. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing... | Factoring integers | 0.821569 |
8,279 | In number theory, integer factorization is the decomposition, of a positive integer into a product of integers. If the factors are further restricted to be prime numbers, the process is called prime factorization, and includes the test whether the given integer is prime (in this case, one has a "product" of a single fa... | Factoring integers | 0.821569 |
8,280 | Once the vacuum levels are aligned it is possible to use the electron affinity and band gap values for each semiconductor to calculate the conduction band and valence band offsets. The electron affinity (usually given by the symbol χ {\displaystyle \chi } in solid state physics) gives the energy difference between the ... | Electron affinity rule | 0.821568 |
8,281 | Reciprocity in electrical networks is a property of a circuit that relates voltages and currents at two points. The reciprocity theorem states that the current at one point in a circuit due to a voltage at a second point is the same as the current at the second point due to the same voltage at the first. The reciprocit... | Reciprocity theorem (electrical circuits) | 0.821566 |
8,282 | The first-order theory of Abelian groups, established by Szmielew in 1955. The first-order theory of hyperbolic geometry, established by Schwabhäuser in 1959. Specific decidable sublanguages of set theory investigated in the 1980s through today. (Cantone et al., 2001) The monadic second-order theory of trees (see S2S).... | Decidability (logic) | 0.821564 |
8,283 | The first-order theory of algebraically closed fields of a given characteristic, established by Tarski in 1949. The first-order theory of real-closed ordered fields, established by Tarski in 1949 (see also Tarski's exponential function problem). The first-order theory of Euclidean geometry, established by Tarski in 194... | Decidability (logic) | 0.821564 |
8,284 | The completeness was established by Mojżesz Presburger in 1929. The first-order theory of the natural numbers in the signature with equality and multiplication, also called Skolem arithmetic. The first-order theory of Boolean algebras, established by Alfred Tarski in 1940 (found in 1940 but announced in 1949). | Decidability (logic) | 0.821564 |
8,285 | In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable if membership in their set of logically valid formulas (or th... | Decidability (logic) | 0.821564 |
8,286 | The validities of monadic predicate calculus with identity are decidable, however. This system is first-order logic restricted to those signatures that have no function symbols and whose relation symbols other than equality never take more than one argument. Some logical systems are not adequately represented by the se... | Decidability (logic) | 0.821564 |
8,287 | Each logical system comes with both a syntactic component, which among other things determines the notion of provability, and a semantic component, which determines the notion of logical validity. The logically valid formulas of a system are sometimes called the theorems of the system, especially in the context of firs... | Decidability (logic) | 0.821564 |
8,288 | Decidability should not be confused with completeness. For example, the theory of algebraically closed fields is decidable but incomplete, whereas the set of all true first-order statements about nonnegative integers in the language with + and × is complete but undecidable. Unfortunately, as a terminological ambiguity,... | Decidability (logic) | 0.821564 |
8,289 | However, if the IGM was ionized at very early times when the universe was still denser, then there are two main effects on the CMB: Small scale anisotropies are erased. (Just as when looking at an object through fog, details of the object appear fuzzy.) The physics of how photons are scattered by free electrons (Thomso... | Cosmic Microwave Background | 0.821561 |
8,290 | An incidence structure C = ( P , L , I ) {\displaystyle C=(P,L,I)} consists of points P {\displaystyle P} , lines L {\displaystyle L} , and flags I ⊆ P × L {\displaystyle I\subseteq P\times L} where a point p {\displaystyle p} is said to be incident with a line l {\displaystyle l} if ( p , l ) ∈ I {\displaystyle (p,l)\... | Partial geometry | 0.82156 |
8,291 | A partial linear space S = ( P , L , I ) {\displaystyle S=(P,L,I)} of order s , t {\displaystyle s,t} is called a semipartial geometry if there are integers α ≥ 1 , μ {\displaystyle \alpha \geq 1,\mu } such that: If a point p {\displaystyle p} and a line ℓ {\displaystyle \ell } are not incident, there are either 0 {\di... | Partial geometry | 0.82156 |
8,292 | production, stockpiling, or use of biological weapons as well as outbreaks of newly emergent and epidemic disease".A number of nations have developed biological weapons for military use, and many civilian research projects in medicine have the potential to be used in military applications (dual-use research), so biosec... | Medical countermeasure | 0.821559 |
8,293 | The definition has sometimes been broadened to embrace other concepts, and it is used for different purposes in different contexts. A 2016 draft handbook on biosecurity education produced by the Bradford Disarmament Research Centre at Bradford University in the UK, where the focus is on the dangers of "dual-use" resear... | Medical countermeasure | 0.821559 |
8,294 | This result was popularized by Victor Weisskopf in a Physics Today article. For instance, for a small angular diameter, a moving sphere remains circular and is rotated. This kind of visual rotation effect is called Penrose-Terrell rotation. | Space contraction | 0.821556 |
8,295 | Every malnormal subgroup is a special type of C-group called a trivial intersection subgroup or TI subgroup.When G is finite, a malnormal subgroup H distinct from 1 and G is called a "Frobenius complement". The set N of elements of G which are, either equal to 1, or non-conjugate to any element of H, is a normal subgro... | Malnormal subgroup | 0.82155 |
8,296 | The temperature of a sample of a substance reflects the average kinetic energy of its constituent particles (atoms or molecules) relative to its center of mass. Quantum mechanics predicts that, at room temperature and ordinary pressures, an isolated atom in a gas cannot store any significant amount of energy except in ... | Molar heat capacity | 0.821543 |
8,297 | The SI unit of molar heat capacity heat is joule per kelvin per mole (J/(K⋅mol), J/(K mol), J K−1 mol−1, etc.). Since an increment of temperature of one degree Celsius is the same as an increment of one kelvin, that is the same as joule per degree Celsius per mole (J/(°C⋅mol)). In chemistry, heat amounts are still ofte... | Molar heat capacity | 0.821543 |
8,298 | In informal chemistry contexts, the molar heat capacity may be called just "heat capacity" or "specific heat". However, international standards now recommend that "specific heat capacity" always refer to capacity per unit of mass, to avoid possible confusion. Therefore, the word "molar", not "specific", should always b... | Molar heat capacity | 0.821543 |
8,299 | The ratio between the two, however, is the same heat capacity ratio obtained from the corresponding specific heat capacities. This property is most relevant in chemistry, when amounts of substances are often specified in moles rather than by mass or volume. | Molar heat capacity | 0.821543 |
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