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28,300 | Most modern evaluation functions make use of neural networks. The most common evaluation function in use today is the efficiently updatable neural network, which is a shallow neural network whose inputs are piece-square tables. Piece-square tables are a set of 64 values corresponding to the squares of the chessboard, a... | Chess-playing program | 0.80613 |
28,301 | In addition to points for pieces, most handcrafted evaluation functions take many factors into account, such as pawn structure, the fact that a pair of bishops are usually worth more, centralized pieces are worth more, and so on. The protection of kings is usually considered, as well as the phase of the game (opening, ... | Chess-playing program | 0.80613 |
28,302 | Within 40 years, in 1997, chess engines running on super-computers or specialized hardware were capable of defeating even the best human players. By 2006, programs running on desktop PCs had attained the same capability. In 2006, Monty Newborn, Professor of Computer Science at McGill University, declared: "the science ... | Chess-playing program | 0.80613 |
28,303 | Since then, chess enthusiasts and computer engineers have built, with increasing degrees of seriousness and success, chess-playing machines and computer programs. One of the few chess grandmasters to devote himself seriously to computer chess was former World Chess Champion Mikhail Botvinnik, who wrote several works on... | Chess-playing program | 0.80613 |
28,304 | Current research areas include interrogating neural circuits at the cellular level, analyzing neuronal data in real-time, and manipulating healthy or diseased neural circuit activity and connectivity using nano electronics, optics, and emerging photonics technologies. Photonics, Electronics and Nano-device researchers ... | Rice University Electrical and Computer Engineering | 0.806129 |
28,305 | 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 ac... | Rice University Electrical and Computer Engineering | 0.806129 |
28,306 | 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. | Rice University Electrical and Computer Engineering | 0.806129 |
28,307 | 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 fo... | Rice University Electrical and Computer Engineering | 0.806129 |
28,308 | 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 Comput... | Rice University Electrical and Computer Engineering | 0.806129 |
28,309 | This department is Space Plasma Group, which was founded in 1998 as the Department of Space Physics of the Institute of Atmospheric Physics. Primary investigations of this department are space plasma process which occur in solar-terrestrial interactions. Simulated and experimental data are applied in these studies. | Institute of Atmospheric Physics AS CR | 0.806129 |
28,310 | The Institute of Atmospheric Physics AS CR, also designated as the IAP, is part of the Academy of Sciences of the Czech Republic (AS CR). Within the IAP research institutions are combined in order to cover the whole field of science and humanities. The IAP was established in 1964, developed from a previously existing i... | Institute of Atmospheric Physics AS CR | 0.806129 |
28,311 | Other research is conducted that concerns the ozone, along with the previously mentioned ionosphere and magnetosphere. Regarding these upper atmosphere domains, the IAP conducts its own satellite experiments. Other research extends into space plasma physics and solar-terrestrial interactions. | Institute of Atmospheric Physics AS CR | 0.806129 |
28,312 | It primarily uses tools from biology and chemistry, with more recent approaches attempting a synthesis of many sciences. Life functions through the specialized chemistry of carbon and water, and builds largely upon four key families of chemicals: lipids for cell membranes, carbohydrates such as sugars, amino acids for ... | Prebiotic (chemistry) | 0.806126 |
28,313 | In biology, abiogenesis (from a- 'not' + Greek bios 'life' + genesis 'origin') or the origin of life is the natural process by which life has arisen from non-living matter, such as simple organic compounds. The prevailing scientific hypothesis is that the transition from non-living to living entities on Earth was not a... | Prebiotic (chemistry) | 0.806126 |
28,314 | The biochemist Nick Lane has proposed a possible scenario for the origin of life that integrates much of the available evidence from biochemistry, geology, phylogeny, and experimentation: | Prebiotic (chemistry) | 0.806126 |
28,315 | Russell has proposed that "the purpose of life is to hydrogenate carbon dioxide" (as part of a "metabolism-first," rather than a "genetics-first," scenario). The physicist Jeremy England has argued from general thermodynamic considerations that life was inevitable. | Prebiotic (chemistry) | 0.806126 |
28,316 | In the 1980s, Wächtershäuser and Karl Popper postulated the iron–sulfur world hypothesis for the evolution of pre-biotic chemical pathways. It traces today's biochemistry to primordial reactions which synthesize organic building blocks from gases. Wächtershäuser systems have a built-in source of energy: iron sulfides s... | Prebiotic (chemistry) | 0.806126 |
28,317 | The observations show that the cloud is asymmetrical and matches the pattern of X-ray binaries (binary star systems containing black holes or neutron stars), mostly on one side of the Galactic Center. While the mechanism is not fully understood, it is likely to involve the production of electron–positron pairs, as ordi... | Anti matter | 0.806125 |
28,318 | The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for coll... | Probabilistic independence | 0.806125 |
28,319 | Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivale... | Probabilistic independence | 0.806125 |
28,320 | Major categories of software systems include those based on application software development, programming software, and system software although the distinction can sometimes be difficult. Examples of software systems include operating systems, computer reservations systems, air traffic control systems, military comman... | Software systems | 0.806125 |
28,321 | The nuclei of antihelium have been artificially produced, albeit with difficulty, and are the most complex anti-nuclei so far observed. Physical principles indicate that complex antimatter atomic nuclei are possible, as well as anti-atoms corresponding to the known chemical elements. There is strong evidence that the o... | Anti matter | 0.806125 |
28,322 | In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter, and can be thought of as matter with reversed charge, parity, and time, known as CPT reversal. Antimatter occurs in natural processes like cosmic ray collisions and some ... | Anti matter | 0.806125 |
28,323 | Software systems are an active area of research for groups interested in software engineering in particular and systems engineering in general. Academic journals like the Journal of Systems and Software (published by Elsevier) are dedicated to the subject.The ACM Software System Award is an annual award that honors peo... | Software systems | 0.806125 |
28,324 | A software system is a system of intercommunicating components based on software forming part of a computer system (a combination of hardware and software). It "consists of a number of separate programs, configuration files, which are used to set up these programs, system documentation, which describes the structure of... | Software systems | 0.806125 |
28,325 | Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne primes. Many of the largest known primes are Mersenne primes because Mersenne numbers are easier to check for primality. ... | Mersenne numbers | 0.806123 |
28,326 | Specifically, it can be shown that for prime p > 2, Mp = 2p − 1 is prime if and only if Mp divides Sp − 2, where S0 = 4 and Sk = (Sk − 1)2 − 2 for k > 0. During the era of manual calculation, all the exponents up to and including 257 were tested with the Lucas–Lehmer test and found to be composite. A notable contributi... | Mersenne numbers | 0.806123 |
28,327 | Mersenne primes Mp are closely connected to perfect numbers. In the 4th century BC, Euclid proved that if 2p − 1 is prime, then 2p − 1(2p − 1) is a perfect number. In the 18th century, Leonhard Euler proved that, conversely, all even perfect numbers have this form. This is known as the Euclid–Euler theorem. It is unkno... | Mersenne numbers | 0.806123 |
28,328 | This model provided a relation between the deviatoric stress and the strain rate for an incompressible Bingham solid However, the application of these theories did not begin before 1950, where limit theorems were discovered. In 1960, the first IUTAM Symposium “Creep in Structures” organized by Hoff provided a major dev... | Zerilli-Armstrong plasticity model | 0.806121 |
28,329 | In mathematics, specifically in topology, the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure... | Interior points | 0.806115 |
28,330 | If T {\displaystyle T} is open in X {\displaystyle X} then T ⊆ S {\displaystyle T\subseteq S} if and only if T ⊆ int S . {\displaystyle T\subseteq \operatorname {int} S.} int S {\displaystyle \operatorname {int} S} is an open subset of S {\displaystyle S} when S {\displaystyle S} is given the subspace topology. | Interior points | 0.806115 |
28,331 | Analytic geometry was developped from the Cartesian coordinate system introduced by René Descartes. It implicitly assumed this axiom by blending the distinct concepts of real numbers and points on a line, sometimes referred to as the real number line. Artin's proof, not only makes this blend explicity, but also that an... | Cantor–Dedekind axiom | 0.806112 |
28,332 | In mathematical logic, the Cantor–Dedekind axiom is the thesis that the real numbers are order-isomorphic to the linear continuum of geometry. In other words, the axiom states that there is a one-to-one correspondence between real numbers and points on a line. This axiom became a theorem proved by Emil Artin in his boo... | Cantor–Dedekind axiom | 0.806112 |
28,333 | In fluid flow around a body with a sharp corner, the Kutta condition refers to the flow pattern in which fluid approaches the corner from above and below, meets at the corner, and then flows away from the body. None of the fluid flows around the sharp corner. The Kutta condition is significant when using the Kutta–Jouk... | Kutta condition | 0.80611 |
28,334 | The high airspeed around the trailing edge causes strong viscous forces to act on the air adjacent to the trailing edge of the airfoil and the result is that a strong vortex accumulates on the topside of the airfoil, near the trailing edge. As the airfoil begins to move it carries this vortex, known as the starting vor... | Kutta condition | 0.80611 |
28,335 | The airfoil is generating lift, and the magnitude of the lift is given by the Kutta–Joukowski theorem. : § 4.5 One of the consequences of the Kutta condition is that the airflow over the topside of the airfoil travels much faster than the airflow under the underside. A parcel of air which approaches the airfoil along t... | Kutta condition | 0.80611 |
28,336 | This algorithm can be used to sample from the area under any curve, regardless of whether the function integrates to 1. In fact, scaling a function by a constant has no effect on the sampled x-positions. This means that the algorithm can be used to sample from a distribution whose probability density function is only k... | Slice sampling | 0.806108 |
28,337 | In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be achiral. A chiral object and its mirror image are said to be enantiomorp... | Chirality (mathematics) | 0.806107 |
28,338 | A figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. (In Euclidean geometry any isometry can be written as v ↦ A v + b {\displaystyle v\mapsto Av+b} with an orthogonal matrix A {\displaystyle A} and a vector b {\displaystyle b} . The determinant of A {\displaystyle... | Chirality (mathematics) | 0.806107 |
28,339 | Thus, one can consider a probability distribution P I {\displaystyle P_{I}} induced by the group's action on images I {\displaystyle I} ( g I {\displaystyle gI} can be seen as a realization of a random variable). This probability distribution P I {\displaystyle P_{I}} can be almost uniquely characterized by K {\display... | M-Theory (learning framework) | 0.806106 |
28,340 | In machine learning and computer vision, M-theory is a learning framework inspired by feed-forward processing in the ventral stream of visual cortex and originally developed for recognition and classification of objects in visual scenes. M-theory was later applied to other areas, such as speech recognition. On certain ... | M-Theory (learning framework) | 0.806106 |
28,341 | This allows recognition from very few labeled examples – in the limit, just one. Neuroscience suggests that natural functionals for a neuron to compute is a high-dimensional dot product between an "image patch" and another image patch (called template) which is stored in terms of synaptic weights (synapses per neuron). | M-Theory (learning framework) | 0.806106 |
28,342 | No real attention has been given to biologically plausible features of higher complexity. While mainstream computer vision has always been inspired and challenged by human vision, it seems to have never advanced past the very first stages of processing in the simple cells in V1 and V2. Although some of the systems insp... | M-Theory (learning framework) | 0.806106 |
28,343 | M-theory is based on a quantitative theory of the ventral stream of visual cortex. Understanding how visual cortex works in object recognition is still a challenging task for neuroscience. Humans and primates are able to memorize and recognize objects after seeing just couple of examples unlike any state-of-the art mac... | M-Theory (learning framework) | 0.806106 |
28,344 | It can be proven that if for a transformation g ′ {\displaystyle g^{\prime }} , support set will also lie within g ′ G 0 {\displaystyle g^{\prime }G_{0}} , then signature of I {\displaystyle I} is invariant with respect to g ′ {\displaystyle g^{\prime }} . This theorem determines the range of transformations for which ... | M-Theory (learning framework) | 0.806106 |
28,345 | In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless. Such a subset that contains all the useful information is called a Markov blanket. If a Markov blanket is minimal, meaning that it cannot drop any variable ... | Markov blanket | 0.806106 |
28,346 | For example, for the free group monad discussed above, a T {\displaystyle T} -algebra is a set X {\displaystyle X} together with a map from the free group generated by X {\displaystyle X} towards X {\displaystyle X} subject to associativity and unitality conditions. Such a structure is equivalent to saying that X {\dis... | Algebra over a monad | 0.806103 |
28,347 | Monads are used in functional programming to express types of sequential computation (sometimes with side-effects). See monads in functional programming, and the more mathematically oriented Wikibook module b:Haskell/Category theory. Monads are used in the denotational semantics of impure functional and imperative prog... | Algebra over a monad | 0.806103 |
28,348 | I would be identical to the axiom of extensionality in ZFC, except that the scope of I includes proper classes as well as sets. II. Classification (schema): An axiom results if in For each β {\displaystyle \beta } , β ∈ { α: A } {\displaystyle \beta \in \{\alpha :A\}} if and only if β {\displaystyle \beta } is a set an... | Morse–Kelley set theory | 0.806102 |
28,349 | The axioms and definitions in this section are, but for a few inessential details, taken from the Appendix to Kelley (1955). The explanatory remarks below are not his. The Appendix states 181 theorems and definitions, and warrants careful reading as an abbreviated exposition of axiomatic set theory by a working mathema... | Morse–Kelley set theory | 0.806102 |
28,350 | MK was first set out in Wang (1949) and popularized in an appendix to J. L. Kelley's (1955) General Topology, using the axioms given in the next section. The system of Anthony Morse's (1965) A Theory of Sets is equivalent to Kelley's, but formulated in an idiosyncratic formal language rather than, as is done here, in s... | Morse–Kelley set theory | 0.806102 |
28,351 | In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays... | Morse–Kelley set theory | 0.806102 |
28,352 | Without proper compensation or reward for traditional knowledge of natural resources, the sudden increase in commercial value of the species producing the active compound can make it now unaffordable for the native people. In some cases, a patent filed by the western company could prohibit the use or sell of the resour... | Biopiracy | 0.8061 |
28,353 | The "Gene Rush" is the new era of biotechnology that allows scientists to extract specific genes from living organisms as raw materials. With the introduction of deoxyribonucleic acid (DNA) research, Sri Lanka has been marked with imminent danger as a target of biopiracy. Spotted in the top 34 biodiversity hotspots, Sr... | Biopiracy | 0.8061 |
28,354 | India-based Research Foundation for Science, Technology, and Ecology (RFSTE) challenged the US patent with the claim that the qualities of the neem tree and their use had been known in India for over 2,000 years. The Congressional Research Service (CRS) reported to US Congress in justification of the patent claiming th... | Biopiracy | 0.8061 |
28,355 | The Wolfram Language was a part of the initial version of Mathematica in 1988.Symbolic aspects of the engine make it a computer algebra system. The language can perform integration, differentiation, matrix manipulations, and solve differential equations using a set of rules. Also, the initial version introduced the not... | Wolfram Language | 0.806097 |
28,356 | The reference book is open access.In the over three-decade-long existence of the Wolfram language, a number of open source third party implementations have also been developed. Richard Fateman's MockMMA from 1991 is of historical note, both for being the earliest reimplementation and for having received a cease-and-des... | Wolfram Language | 0.806097 |
28,357 | NBI is short for the Nanomaterial-Biological Interactions Knowledgebase at Oregon State University, a repository for annotated data on nanomaterials characterization (purity, size, shape, charge, composition, functionalization, agglomeration state), synthesis methods, and nanomaterial-biological interactions (beneficia... | NBI Knowledgebase | 0.806097 |
28,358 | A graph property H is semi-hereditary if there exists a hereditary graph property H such that any graph satisfying P satisfies H, and for every ε > 0 {\displaystyle \varepsilon >0} there is an M ( ε ) {\displaystyle M(\varepsilon )} such that every graph of size at least M ( ε ) {\displaystyle M(\varepsilon )} that is ... | Property testing | 0.806094 |
28,359 | In computer science, a property testing algorithm for a decision problem is an algorithm whose query complexity to its input is much smaller than the instance size of the problem. Typically property testing algorithms are used to distinguish if some combinatorial structure S (such as a graph or a boolean function) sati... | Property testing | 0.806094 |
28,360 | In particular, note that constant h 0 {\displaystyle h_{0}} come up naturally as the size of the samples. Also, the query complexity using this regularity approach is large due to the tower function bound in Szemerédi regularity lemma. Theorem (Infinite graph removal lemma). For each (possibly infinite) set of graphs H... | Property testing | 0.806094 |
28,361 | Every hereditary graph property is testable with one-sided error. The proof relies on a version of the graph removal lemma for infinite families of induced subgraphs. We reproduce the theorem here without proof. | Property testing | 0.806094 |
28,362 | A graph property is hereditary if it is preserved under deletion of vertices, or equivalently, if it is preserved under taking induced subgraphs, hence the name hereditary. A few important hereditary properties are H-freeness (for some graph H), k-colorability, and planarity. All hereditary properties are testable. The... | Property testing | 0.806094 |
28,363 | Antimony was selected as the positive electrode due to its low cost and higher anticipated discharge voltage. In 2011, the researchers demonstrated a cell with a lithium anode and a lead–antimony cathode, which had higher ionic conductivity and lower melting points (350–430 °C). The drawback of the Li chemistry is high... | Liquid metal battery | 0.806092 |
28,364 | The next version of BioPAX, Level 4, is being developed by a community of researchers. Development is coordinated by the board of editors and facilitated by various BioPAX work groups. Systems Biology Pathway Exchange (SBPAX) is an extension for Level 3 and proposal for Level 4 to add quantitative data and systems biol... | BioPAX | 0.806091 |
28,365 | Software supporting BioPAX include: Paxtools, a Java API for handling BioPAX files Systems Biology Linker (Sybil), an application for visualizing BioPAX and converting BioPAX to SBML, as part of the Virtual Cell. ChiBE (Chisio BioPAX Editor), an application for visualizing and editing BioPAX. BioPAX Validator - syntax ... | BioPAX | 0.806091 |
28,366 | Since this property is invariant under homeomorphism, this proves that the Whitehead manifold is not homeomorphic to R3. However, it is a theorem of John R. Stallings that for n ≥ 5 {\displaystyle n\geq 5} , a contractible n-manifold is homeomorphic to Rn precisely when it is simply connected at infinity. == References... | Simply connected at infinity | 0.806091 |
28,367 | In topology, a branch of mathematics, a topological space X is said to be simply connected at infinity if for any compact subset C of X, there is a compact set D in X containing C so that the induced map π 1 ( X − D ) → π 1 ( X − C ) {\displaystyle \pi _{1}(X-D)\to \pi _{1}(X-C)} is the zero map. Intuitively, this is t... | Simply connected at infinity | 0.806091 |
28,368 | The active set at x 0 {\displaystyle x_{0}} is made up of those constraints g i ( x 0 ) {\displaystyle g_{i}(x_{0})} that are active at the current point (Nocedal & Wright 2006, p. 308). The active set is particularly important in optimization theory, as it determines which constraints will influence the final result o... | Active set | 0.806087 |
28,369 | In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem. An opt... | Active set | 0.806087 |
28,370 | As a product of compact Hausdorff spaces, the Hilbert cube is itself a compact Hausdorff space as a result of the Tychonoff theorem. The compactness of the Hilbert cube can also be proved without the axiom of choice by constructing a continuous function from the usual Cantor set onto the Hilbert cube. In ℓ 2 , {\displa... | Hilbert cube | 0.806086 |
28,371 | It is sometimes convenient to think of the Hilbert cube as a metric space, indeed as a specific subset of a separable Hilbert space (that is, a Hilbert space with a countably infinite Hilbert basis). For these purposes, it is best not to think of it as a product of copies of , {\displaystyle ,} but instead as as state... | Hilbert cube | 0.806086 |
28,372 | In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can be embedded in the Hilbert cube; that is, can be viewed as subspaces of the Hilbert cube (see below). | Hilbert cube | 0.806086 |
28,373 | The term exoplanetary system is sometimes used in reference to other planetary systems. As of 1 September 2023, there are 5,506 confirmed exoplanets in 4,065 planetary systems, with 878 systems having more than one planet. Debris disks are also known to be common, though other objects are more difficult to observe. Of ... | Solar systems | 0.806085 |
28,374 | HTML Greek, in parallel with English translation: Fr. Kenny's collection (with Aquinas's commentary) HTML Greek, in parallel with French translation: P. Remacle's collection Thomas Aquinas's Commentary A 'Bigger' Physics – lecture at MIT on how Aristotle's natural philosophy complements modern science and the need for ... | Physics (Aristotle) | 0.806079 |
28,375 | Greek text of Physics, as edited by W.D. Ross Perseus edition of Physics in Greek Aristotle: Motion and its Place in Nature entry in the Internet Encyclopedia of Philosophy. Philosophical Powers (humor) Physics, English Translation by Thomas Taylor public domain audiobook at LibriVox Text of Physics, (in html, epub or ... | Physics (Aristotle) | 0.806079 |
28,376 | This is demonstrated by describing the celestial bodies thus: the first things to be moved must undergo an infinite, single and continuous movement, that is, circular. This is not caused by any contact but (integrating the view contained in the Metaphysics, bk. XII) by love and aspiration. | Physics (Aristotle) | 0.806079 |
28,377 | Book VIII (which occupies almost a fourth of the entire Physics, and probably constituted originally an independent course of lessons) discusses two main topics, though with a wide deployment of arguments: the time limits of the universe, and the existence of a Prime Mover — eternal, indivisible, without parts and with... | Physics (Aristotle) | 0.806079 |
28,378 | Bertrand Russell says of Physics and On the Heavens (which he believed was a continuation of Physics) that they were: ...extremely influential, and dominated science until the time of Galileo ... The historian of philosophy, accordingly, must study them, in spite of the fact that hardly a sentence in either can be acce... | Physics (Aristotle) | 0.806079 |
28,379 | The process of publishing them is slow and ongoing. Below is a brief representative bibliography of published commentaries on Aristotle's Physics available on or through the Internet. Like the topic itself, they are perforce multi-cultural, but English has been favored, as well as the original languages, ancient Greek ... | Physics (Aristotle) | 0.806079 |
28,380 | The Physics is composed of eight books, which are further divided into chapters. This system is of ancient origin, now obscure. In modern languages, books are referenced with Roman numerals, standing for ancient Greek capital letters (the Greeks represented numbers with letters, e.g. A for 1). Chapters are identified b... | Physics (Aristotle) | 0.806079 |
28,381 | The Physics (Greek: Φυσικὴ ἀκρόασις Phusike akroasis; Latin: Physica, or Naturales Auscultationes, possibly meaning "lectures on nature") is a named text, written in ancient Greek, collated from a collection of surviving manuscripts known as the Corpus Aristotelicum, attributed to the 4th-century BC philosopher Aristot... | Physics (Aristotle) | 0.806079 |
28,382 | Martin Heidegger writes: The Physics is a lecture in which he seeks to determine beings that arise on their own, τὰ φύσει ὄντα, with regard to their being. Aristotelian "physics" is different from what we mean today by this word, not only to the extent that it belongs to antiquity whereas the modern physical sciences b... | Physics (Aristotle) | 0.806079 |
28,383 | Italian theoretical physicist Carlo Rovelli writes: Aristotelian physics is a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton theory is an approximation of Einstein's theory. Aristotelian physics lasted long not because ... | Physics (Aristotle) | 0.806079 |
28,384 | Often one can also state constructions of orders, like the product order, in terms of categories. Further insights result when categories of orders are found categorically equivalent to other categories, for example of topological spaces. This line of research leads to various representation theorems, often collected u... | Order relation | 0.806077 |
28,385 | For a given mathematical result, one can just invert the order and replace all definitions by their duals and one obtains another valid theorem. This is important and useful, since one obtains two theorems for the price of one. Some more details and examples can be found in the article on duality in order theory. | Order relation | 0.806077 |
28,386 | This yields the so-called dual, inverse, or opposite order. Every order theoretic definition has its dual: it is the notion one obtains by applying the definition to the inverse order. Since all concepts are symmetric, this operation preserves the theorems of partial orders. | Order relation | 0.806077 |
28,387 | An n-type p(x) is said to be realized in M {\displaystyle {\mathcal {M}}} if there is an element b ∈ Mn such that M ⊨ p ( b ) {\displaystyle {\mathcal {M}}\models p({\boldsymbol {b}})} . The existence of such a realization is guaranteed for any type by the compactness theorem, although the realization might take place ... | Omitting types theorem | 0.806076 |
28,388 | This constructs the Stone space associated to the Boolean algebra, which is a compact, Hausdorff, and totally disconnected space. Example. The complete theory of algebraically closed fields of characteristic 0 has quantifier elimination, which allows one to show that the possible complete 1-types (over the empty set) c... | Omitting types theorem | 0.806076 |
28,389 | The set of formulas in free variables x1,…,xn over A up to this equivalence relation is a Boolean algebra (and is canonically isomorphic to the set of A-definable subsets of Mn). The complete n-types correspond to ultrafilters of this Boolean algebra. The set of complete n-types can be made into a topological space by ... | Omitting types theorem | 0.806076 |
28,390 | This type is a point in the Stone space that is closed but not isolated.In other words, the 1-types correspond exactly to the prime ideals of the polynomial ring Q over the rationals Q: if r is an element of the model of type p, then the ideal corresponding to p is the set of polynomials with r as a root (which is only... | Omitting types theorem | 0.806076 |
28,391 | The Galois group Gal(QCM/Q) has a center generated by an element of order 2 (complex conjugation) and the quotient by its center is the group Gal(QR/Q). If V is a complex abelian variety of dimension n, then any abelian algebra F of endomorphisms of V has rank at most 2n over Z. If it has rank 2n and V is simple then F... | CM-field | 0.806072 |
28,392 | One feature of a CM-field is that complex conjugation on C {\displaystyle \mathbb {C} } induces an automorphism on the field which is independent of its embedding into C {\displaystyle \mathbb {C} } . In the notation given, it must change the sign of β. A number field K is a CM-field if and only if it has a "units defe... | CM-field | 0.806072 |
28,393 | Contrary, current and voltage sources can be connected to each other without any problems, and this technique is widely used in circuitry (e.g., in cascode circuits, differential amplifier stages with common emitter current source, etc.) Because no ideal sources of either variety exist (all real-world examples have fin... | Constant current source | 0.80607 |
28,394 | In physics a null is a point in a field where the field quantity is zero as the result of two or more opposing quantities completely cancelling each other. The field may be scalar, vector or tensor in nature. Common situations where nulls arise are in the polar patterns of microphones and antennae, and nulls caused by ... | Null (physics) | 0.80607 |
28,395 | These include the Bachelor of Computing (BComp) and Bachelor of Computer Science (BCompSc) degrees. Computer science is also offered as a major within most Bachelor of Science programs. The practically oriented degrees cover many disciplines from within the IT industry including software engineering, information system... | Baccalaureate degree | 0.80607 |
28,396 | In countries following British tradition (the University of Malta is an exception), medical students pursue an undergraduate medical education and receive bachelor's degrees in medicine and surgery (MBBChir, MBBS, BMBS, BM, MBChB, etc.). This was historically taken at the universities of Oxford, Cambridge, and Dublin a... | Baccalaureate degree | 0.80607 |
28,397 | In Nepal, the bachelor's degree was initially a three-year program for courses like Bachelor of Business Studies (BBS), Bachelor of Sciences (BSc), Bachelor of Education (BEd), Bachelor of Arts (BA) from Tribhuvan University, Pokhara University, Purbanchal University and Kathmandu University but now it is mostly a four... | Baccalaureate degree | 0.80607 |
28,398 | for Sarjana Ekonomi (literally translated as "Bachelor of Economy"), S.Kom. for Sarjana Ilmu Komputer (literally translated as "Bachelor of Computer Science"), S.S. for Sarjana Sastra (literally translated as "Bachelor of Literature") or S.Sos. for Sarjana Ilmu Sosial (literally translated as "Bachelor of Social Scienc... | Baccalaureate degree | 0.80607 |
28,399 | The Bachelor of Science and/with Education degree (BScEd) is a degree awarded to students who complete the four- to five-year course of study in the field of science (major and minor in general biology, chemistry, physics, and mathematics) and education. Although notionally BSc and BEd are two degrees, they must be tak... | Baccalaureate degree | 0.80607 |
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