id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
31,800 | A problem in solving partial differential equations using previous methods is that the grid is constructed and the points are distributed in the physical domain before details of the solution is known. So the grid may or may not be the best for the given problem.Adaptive methods are used to improve the accuracy of the ... | Grid generation | 0.804277 |
31,801 | Meshes are created by computer algorithms, often with human guidance through a GUI , depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make ... | Grid generation | 0.804277 |
31,802 | The grid generation by algebraic methods is based on mathematical interpolation function. It is done by using known functions in one, two or three dimensions taking arbitrary shaped regions. The computational domain might not be rectangular, but for the sake of simplicity, the domain is taken to be rectangular. | Grid generation | 0.804277 |
31,803 | (Conferences whose primary topic is meshing are in bold.) Aerospace Sciences Meeting AIAA (15 meshing talks/papers) Canadian Conference on Computational Geometry CCCG CompIMAGE: International Symposium Computational Modeling of Objects Represented in Images Computational Fluid Dynamics Conference AIAA Computational Flu... | Grid generation | 0.804277 |
31,804 | Chapter 16: "Plenary Debate: Quantum Effects in Biology: Trivial or Not?" For panel: Paul C. W. Davies, Stuart Hameroff, Anton Zeilinger, Derek Abbott; Against panel: Jens Eisert, Howard M. Wiseman, Sergey M. Bezrukov, Hans Frauenfelder; Debate chair: Julio Gea-Banacloche; Transcript Editor: Derek Abbott. Chapter 17: "... | Quantum Aspects of Life | 0.804277 |
31,805 | Foreword by Roger PenroseSection 1: Emergence and Complexity Chapter 1: "A Quantum Origin of Life?" by Paul C. W. Davies Chapter 2: "Quantum Mechanics and Emergence" by Seth LloydSection 2: Quantum Mechanisms in Biology Chapter 3: "Quantum Coherence and the Search for the First Replicator" by Jim Al-Khalili and Johnjoe... | Quantum Aspects of Life | 0.804277 |
31,806 | Quantum Aspects of Life, a book published in 2008 with a foreword by Roger Penrose, explores the open question of the role of quantum mechanics at molecular scales of relevance to biology. The book contains chapters written by various world-experts from a 2003 symposium and includes two debates from 2003 to 2004; givin... | Quantum Aspects of Life | 0.804276 |
31,807 | The Many-worlds interpretation, also known as the Everett interpretation, is deterministic and has local dynamics, consisting of the unitary part of quantum mechanics without collapse. Bell's theorem does not apply because of an implicit assumption that measurements have a single outcome. | Bell test | 0.804276 |
31,808 | MP Materials focuses its production on Neodymium-Praseodymium (NdPr), a rare earth material used in high-strength permanent magnets that power the traction motors found in electric vehicles, robotics, wind turbines, drones and other advanced motion technologies. MP Materials is listed on the New York Stock Exchange und... | MP Materials | 0.804271 |
31,809 | Serine racemase (SR, EC 5.1.1.18) is the first racemase enzyme in human biology to be identified. This enzyme converts L-serine to its enantiomer form, D-serine. D-serine acts as a neuronal signaling molecule by activating NMDA receptors in the brain. Since NMDA receptors Dysfunction has been suggested as one of the pr... | Serine racemase | 0.804271 |
31,810 | Two intersecting planes meet in a line in three-space, and so, determine the axis and hence all of the planes in the pencil. The four-space of quaternions can be seen as an axial pencil of complex planes all sharing the same real line. In fact, quaternions contain a sphere of imaginary units, and a pair of antipodal po... | Pencil of circles | 0.80427 |
31,811 | Second, is a more complex model better? Third, what contribution do individual predictors make to the model? In order to assess models, different model fit statistics would be examined. | Multilevel model | 0.804267 |
31,812 | The documentary is about artificial intelligence and the biases that can be embedded into this technology. MIT media researcher Joy Buolamwini's computer science studies uncovered that her face was unrecognizable in many facial recognition systems and she worked to find out why these systems failed. She later found tha... | Coded Bias | 0.804265 |
31,813 | It says that some algorithms and artificial intelligence technologies discriminate by race and gender statuses in domains such as housing, career opportunities, healthcare, credit, education, and legalities. Buolamwini and her colleagues were later asked to testify in front of the US Congress about artificial intellige... | Coded Bias | 0.804265 |
31,814 | Kantayya previously directed a documentary titled Catching the Sun and also directed one episode of the National Geographic television series, Breakthrough. She is also an associate of UC Berkeley Graduate School of Journalism. Kantayya said an interview with 500 Global on August 17, 2021, that three years previously s... | Coded Bias | 0.804265 |
31,815 | IFAC Fellows Major Medals Giorgio Quazza Medal Nathaniel B. Nichols Medal Industrial Achievement Award Manfred Thoma MedalHigh Impact Paper Award Automatica Prize Paper Award Control Engineering Practice Prize Paper Award Journal of Process Control Prize Paper Award Engineering Applications of Artificial Intelligence P... | International Federation of Automatic Control | 0.804265 |
31,816 | IFAC pursues its purpose by organizing technical meetings, by publications, and by any other means consistent with its constitution and which will enhance the interchange and circulation of information on automatic control activities. International World Congresses are held every three years. Between congresses, IFAC s... | International Federation of Automatic Control | 0.804265 |
31,817 | ), the Doktoringenieur was not titled in Latin but German, and therefore written with dash (Dr.-Ing.). In the field of mathematics, computer science and natural sciences, some universities offer the choice between Dr.-Ing. and Dr. rer. | Doktoringenieur | 0.804264 |
31,818 | LifeWiki is a wiki dedicated to Conway's Game of Life. It hosts over 2000 articles on the subject and a large collection of Life patterns stored in a format based on run-length encoding that it uses to interoperate with other Life software such as Golly.LifeWiki was founded in 2009 by Nathaniel Johnston, a professor of... | LifeWiki | 0.80426 |
31,819 | From a practical view, an ontology is a representation of something we know about. "Ontologies" consist of representations of things that are detectable or directly observable, and the relationships between those things. There is no universal standard terminology in biology and related domains, and term usages may be s... | Gene Ontology | 0.804258 |
31,820 | As these annotations are not checked by a human, the GO Consortium considers them to be marginally less reliable and they are commonly to higher level, less detailed terms. Full annotation data sets can be downloaded from the GO website. To support the development of annotation, the GO Consortium provides workshops and... | Gene Ontology | 0.804258 |
31,821 | There is a significant body of literature on the development and use of the GO, and it has become a standard tool in the bioinformatics arsenal. Their objectives have three aspects: building gene ontology, assigning ontology to gene/gene products and developing software and databases for the first two objects. Several ... | Gene Ontology | 0.804258 |
31,822 | The Gene Ontology (GO) is a major bioinformatics initiative to unify the representation of gene and gene product attributes across all species. More specifically, the project aims to: 1) maintain and develop its controlled vocabulary of gene and gene product attributes; 2) annotate genes and gene products, and assimila... | Gene Ontology | 0.804258 |
31,823 | In mathematics, more precisely in differential geometry, a soldering (or sometimes solder form) of a fiber bundle to a smooth manifold is a manner of attaching the fibers to the manifold in such a way that they can be regarded as tangent. Intuitively, soldering expresses in abstract terms the idea that a manifold may h... | Solder form | 0.804254 |
31,824 | The reason for the name is that a solder form solders (or attaches) the abstract principal bundle to the manifold M by identifying an associated bundle with the tangent bundle. Solder forms provide a method for studying G-structures and are important in the theory of Cartan connections. The terminology and approach is ... | Solder form | 0.804254 |
31,825 | To register a new carbon mineral with the project, mineralogists are asked to adhere to the protocol outlined by the International Mineralogical Association Commission on New Minerals, Nomenclature and Classification. Once a carbon mineral is approved by that body, the team responsible for the mineral's discovery submi... | Carbon Mineral Challenge | 0.804252 |
31,826 | The research behind the Carbon Mineral Challenge is based on a type of analysis called Large Number of Rare Events (LNRE) modeling. To arrive at their total of 145 previously undescribed carbon minerals, Hazen and his colleagues, including mathematician Grethe Hystad of Purdue University-Calumet, focused on diversity-d... | Carbon Mineral Challenge | 0.804252 |
31,827 | Mineralogist Robert Hazen and his colleagues pioneered the concept of mineral evolution to explain how life and geology have intertwined throughout Earth's multi-billion year past. As part of that research, the group developed a model that combines the locations and distributions of known minerals to predict the number... | Carbon Mineral Challenge | 0.804252 |
31,828 | This all has influences on the coordinate systems. There are however different coordinate systems for hyperbolic plane geometry. All are based on choosing a real (non ideal) point (the Origin) on a chosen directed line (the x-axis) and after that many choices exist. | Coordinate systems for the hyperbolic plane | 0.804252 |
31,829 | In hyperbolic geometry rectangles do not exist. The sum of the angles of a quadrilateral in hyperbolic geometry is always less than 4 right angles (see Lambert quadrilateral). Also in hyperbolic geometry there are no equidistant lines (see hypercycles). | Coordinate systems for the hyperbolic plane | 0.804252 |
31,830 | From Gyrovector space#Triangle centers The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both eucli... | Coordinate systems for the hyperbolic plane | 0.804252 |
31,831 | The Poincaré half-plane model is closely related to a model of the hyperbolic plane in the quadrant Q = {(x,y): x > 0, y > 0}. For such a point the geometric mean v = x y {\displaystyle v={\sqrt {xy}}} and the hyperbolic angle u = ln x / y {\displaystyle u=\ln {\sqrt {x/y}}} produce a point (u,v) in the upper half-pl... | Coordinate systems for the hyperbolic plane | 0.804252 |
31,832 | The Lobachevsky coordinates xℓ and yℓ are found by dropping a perpendicular onto the x-axis. xℓ is the distance from the foot of the perpendicular to the x-axis to the origin (positive on one side and negative on the other, the same as in axial coordinates).yℓ is the distance along the perpendicular of the given point ... | Coordinate systems for the hyperbolic plane | 0.804252 |
31,833 | Model-based coordinate systems use one of the models of hyperbolic geometry and take the Euclidean coordinates inside the model as the hyperbolic coordinates. | Coordinate systems for the hyperbolic plane | 0.804252 |
31,834 | In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of coordinatizing the plane in hyperbolic geometry are used. This article tries to give an overview of several coordinate systems in use for the two-dimensional hyperbolic ... | Coordinate systems for the hyperbolic plane | 0.804252 |
31,835 | The micrometer caliper was introduced to the mass market in anglophone countries by Brown & Sharpe in 1867, allowing the penetration of the instrument's use into the average machine shop. Brown & Sharpe were inspired by several earlier devices, one of them being Palmer's design. In 1888, Edward W. Morley added to the p... | Micrometer (device) | 0.804248 |
31,836 | A micrometer, sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for accurate measurement of components in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier, and digital calipers. Mic... | Micrometer (device) | 0.804248 |
31,837 | In number theory, the larger sieve is a sieve invented by Patrick X. Gallagher. The name denotes a heightening of the large sieve. Combinatorial sieves like the Selberg sieve are strongest, when only a few residue classes are removed, while the term large sieve means that this sieve can take advantage of the removal of... | Larger sieve | 0.804248 |
31,838 | The most common example is in measuring the pitch diameter of screw threads (which is also done with conical anvils or the 3-wire method, the latter of which uses similar geometry as the pair-of-balls approach). Bench micrometers are tools for inspection use whose accuracy and precision are around half a micrometre (20... | Micrometer (device) | 0.804248 |
31,839 | A vertex separator S in G is minimal if and only if the graph G – S, obtained by removing S from G, has two connected components C1 and C2 such that each vertex in S is both adjacent to some vertex in C1 and to some vertex in C2. The minimal (a,b)-separators also form an algebraic structure: For two fixed vertices a an... | Vertex cut | 0.804248 |
31,840 | These systems may be referred to as linear translation-invariant to give the terminology the most general reach. In the case of generic discrete-time (i.e., sampled) systems, linear shift-invariant is the corresponding term. LTI system theory is an area of applied mathematics which has direct applications in electrical... | Linear time invariant | 0.804247 |
31,841 | ), Paper Chemistry, 2nd Edition, London: Chapman & Hall, ISBN 978-0-7514-0236-0 Johnson, D. (2009), I. Thorn, C.O. Au (ed. ), Applications of Wet-End Paper Chemistry, 2nd Edition, Springer Netherlands, pp. 73–112, ISBN 978-1-4020-6037-3 == References == | Alkyl ketene dimer | 0.804246 |
31,842 | In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state (GHZ state) is a certain type of entangled quantum state that involves at least three subsystems (particle states, qubits, or qudits). The four-particle version was first studied by Daniel Greenberger, Michael Horne and Anton Zei... | GHZ state | 0.804238 |
31,843 | This laboratory represents the organizational segment of the Institute which is dealing with genetic characterisation of DNA of human origin for the purpose of basic and applied research. We use molecular-genetics approach mainly PCR based in investigating the genetic structure. Main activities of the laboratory compri... | Institute for Genetic Engineering and Biotechnology | 0.804237 |
31,844 | In INGEB, there are following functional units: Laboratory for forensic genetics; Laboratory for human genetics; Laboratory for GMO and food biosafety; Laboratory for molecular genetics of natural resources; Laboratory for bioinformatics and biostatistics, and Laboratory for cytogenetics and genotoxicology. | Institute for Genetic Engineering and Biotechnology | 0.804237 |
31,845 | Research activities of the Laboratory for Cytogenetics and Genotoxicology are based on: Cytogenetic and genotoxicological analysis of bioactive potential of certain physical, chemical and biological agents, and Cytogenetic and genotoxicological monitoring of human populations in Bosnia and Herzegovina.Expert activity o... | Institute for Genetic Engineering and Biotechnology | 0.804237 |
31,846 | Laboratory for forensic genetics provides scientific approach to analysis of samples of different origin. In this laboratory DNA profiling is routinely done for skeletal remains, blood stains (on different materials), hair, semen, controversial traces on cigarette butts, controversial traces under fingernails, in urine... | Institute for Genetic Engineering and Biotechnology | 0.804237 |
31,847 | The laboratory scope includes wide array of activities mainly focused on the issues of food biosafety and plant biotechnology. It provides qualitative and quantitative analysis of specific DNA sequences in various food matrices, provides advice and correct interpretation of GMO related data to consumers and food safety... | Institute for Genetic Engineering and Biotechnology | 0.804237 |
31,848 | Institute for Genetic Engineering and Biotechnology (INGEB) is a Bosnian public research institute, member of Sarajevo University (UNSA), and affiliate center of International Centre for Genetic Engineering and Biotechnology (ICGEB). ICGEB was established as a special project of the United Nations Industrial Developmen... | Institute for Genetic Engineering and Biotechnology | 0.804237 |
31,849 | X-ray spectroelectrochemistry is a technique that studies the interaction of high-energy radiation with matter during an electrode process. X-rays can originate absorption, emission or scattering phenomena, allowing to perform both quantitative and qualitative analysis depending on the phenomenon taking place. All thes... | Spectroelectrochemistry | 0.804236 |
31,850 | Ultraviolet-visible(UV-Vis) absorption spectroelectrochemistry is a technique that studies the absorption of electromagnetic radiation in the UV-Vis regions of the spectrum, providing molecular information related to the electronic levels of molecules. It provides qualitative as well as quantitative information. UV-Vis... | Spectroelectrochemistry | 0.804236 |
31,851 | There are different spectroelectrochemical techniques based on the combination of spectroscopic and electrochemical techniques. Regarding electrochemistry, the most common techniques used are: Chronoamperometry, which measures current intensity as a function of time by applying a constant difference of potential to the... | Spectroelectrochemistry | 0.804236 |
31,852 | The versatility of spectroelectrochemistry is increasing due to the possibility of using several electrochemical techniques in different spectral regions depending on the purpose of the study and the information of interest.The main advantages of spectroelectrochemical techniques are: The simultaneous information is ob... | Spectroelectrochemistry | 0.804236 |
31,853 | The changes of the optical and electrical signal allow us to understand the evolution of the electrode process. The techniques on which the spectroelectrochemistry is based are: Electrochemistry, which studies the interaction between electrical energy and chemical changes. This technique allows us to analyse reactions ... | Spectroelectrochemistry | 0.804236 |
31,854 | Spectroelectrochemistry (SEC) is a set of multi-response analytical techniques in which complementary chemical information (electrochemical and spectroscopic) is obtained in a single experiment. Spectroelectrochemistry provides a whole vision of the phenomena that take place in the electrode process. The first spectroe... | Spectroelectrochemistry | 0.804236 |
31,855 | Raman spectroelectrochemistry is based on the inelastic scattering or Raman scattering of monochromatic light when strikes on a specific molecule, providing information about vibrational energy of that molecule. Raman spectrum provides highly specific information about the structure and composition of the molecules suc... | Spectroelectrochemistry | 0.804236 |
31,856 | Nuclear magnetic resonance (NMR) is a technique used to obtain physical, chemical, electronic and structural information about molecules due to the chemical shift of the resonance frequencies of nuclear spins in the sample. Its combination with electrochemical techniques can provide detailed and quantitative informatio... | Spectroelectrochemistry | 0.804236 |
31,857 | Infrared spectroscopy is based on the fact that molecules absorb electromagnetic radiation at characteristic frequencies related to their vibrational structure. Infrared (IR) spectroelectrochemistry is a technique that allows the characterization of molecules based on the resistance, stiffness and number of bonds prese... | Spectroelectrochemistry | 0.804236 |
31,858 | One case study with coral reef restoration was conducted on the island of Oahu in Hawaii. The University of Hawaii operates a Coral Reef Assessment and Monitoring Program to help relocate and restore coral reefs in Hawaii. A boat channel from the island of Oahu to the Hawaii Institute of Marine Biology on Coconut Islan... | Formation of coral reefs | 0.804234 |
31,859 | It is a Widlar mirror without an emitter degeneration resistor in the follower (output) transistor. This topology can only be done in an IC, as the matching has to be extremely close and cannot be achieved with discretes. Another topology is the Wilson current mirror. The Wilson mirror solves the Early effect voltage p... | Current mirror | 0.804226 |
31,860 | The current mirror is used to provide bias currents and active loads to circuits. It can also be used to model a more realistic current source (since ideal current sources don't exist). The circuit topology covered here is one that appears in many monolithic ICs. | Current mirror | 0.804226 |
31,861 | As a by-product, of Carleson's work, the Carleson measure was invented which itself is a very useful tool in modern function theory. It remains an open question whether there are versions of the corona theorem for every planar domain or for higher-dimensional domains. Note that if one assumes the continuity up to the b... | Corona theorem | 0.804225 |
31,862 | In 1979 Thomas Wolff gave a simplified (but unpublished) proof of the corona theorem, described in (Koosis 1980) and (Gamelin 1980). Cole later showed that this result cannot be extended to all open Riemann surfaces (Gamelin 1978). | Corona theorem | 0.804225 |
31,863 | In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by Kakutani (1941) and proved by Lennart Carleson (1962). The commutative Banach algebra and Hardy space H∞ consists of the bounded holomorphic functions on the open unit disc D. Its... | Corona theorem | 0.804225 |
31,864 | P.N. Vabishchevich, The Method of Fictitious Domains in Problems of Mathematical Physics, Izdatelstvo Moskovskogo Universiteta, Moskva, 1991. Smagulov S. Fictitious Domain Method for Navier–Stokes equation, Preprint CC SA USSR, 68, 1979. Bugrov A.N., Smagulov S. Fictitious Domain Method for Navier–Stokes equation, Math... | Fictitious domain method | 0.804222 |
31,865 | In mathematics, the Fictitious domain method is a method to find the solution of a partial differential equations on a complicated domain D {\displaystyle D} , by substituting a given problem posed on a domain D {\displaystyle D} , with a new problem posed on a simple domain Ω {\displaystyle \Omega } containing D {\dis... | Fictitious domain method | 0.804222 |
31,866 | Finally, we can approximate any loop by a sequence of geodesic segments, so the most general result (on or off the surface of the sphere) is that the net precession is equal to the enclosed solid angle. To put it in different words, there are no inertial forces that could make the pendulum precess, so the precession (r... | Berry phase | 0.804222 |
31,867 | Separation of proteins, for example, screening of protein abnormalities in clinical chemistry.Agarose gels are easily cast and handled compared to other matrices and nucleic acids are not chemically altered during electrophoresis. Samples are also easily recovered. After the experiment is finished, the resulting gel ca... | Agarose gel electrophoresis | 0.804221 |
31,868 | The rate at which the various forms move however can change using different electrophoresis conditions, and the mobility of larger circular DNA may be more strongly affected than linear DNA by the pore size of the gel.Ethidium bromide which intercalates into circular DNA can change the charge, length, as well as the su... | Agarose gel electrophoresis | 0.804221 |
31,869 | In additive and algebraic number theory, the Skolem–Mahler–Lech theorem states that if a sequence of numbers satisfies a linear difference equation, then with finitely many exceptions the positions at which the sequence is zero form a regularly repeating pattern. This result is named after Thoralf Skolem (who proved th... | Skolem–Mahler–Lech theorem | 0.804219 |
31,870 | The Skolem problem is the problem of determining whether a given recurrence sequence has a zero. There exist an algorithm to test whether there are infinitely many zeros, and if so to find the decomposition of these zeros into periodic sets guaranteed to exist by the Skolem–Mahler–Lech theorem. However, it is unknown w... | Skolem–Mahler–Lech theorem | 0.804219 |
31,871 | The index (the n) equals to the number of nodes in the diagram, the number of simple roots in a basis, the dimension of the root lattice and span of the root system, the number of generators of the Coxeter group, and the rank of the Lie algebra. However, n does not equal the dimension of the defining module (a fundamen... | Simply laced Dynkin diagram | 0.804219 |
31,872 | Dynkin diagrams can be interpreted as classifying many distinct, related objects, and the notation "An, Bn, ..." is used to refer to all such interpretations, depending on context; this ambiguity can be confusing. The central classification is that a simple Lie algebra has a root system, to which is associated an (orie... | Simply laced Dynkin diagram | 0.804219 |
31,873 | In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebras over algebraically closed fields, in the classification of Weyl groups and ... | Simply laced Dynkin diagram | 0.804219 |
31,874 | In physics, there are four observed fundamental interactions (also known as fundamental forces) that form the basis of all known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative theories have proposed a fifth force to explain various anomalous observation... | Fifth force | 0.804217 |
31,875 | Every ring with unity is a free module and hence is a projective as a module over itself, but it is rarer for a ring to be injective as a module over itself, (Lam 1999, §3B). If a ring is injective over itself as a right module, then it is called a right self-injective ring. Every Frobenius algebra is self-injective, b... | Injective dimension | 0.804214 |
31,876 | If M is an injective left R-module, then annI(M) is an injective left R/I-module. Applying this to R=Z, I=nZ and M=Q/Z, one gets the familiar fact that Z/nZ is injective as a module over itself. While it is easy to convert injective R-modules into injective R/I-modules, this process does not convert injective R-resolut... | Injective dimension | 0.804214 |
31,877 | For any Artinian ring, just as for commutative rings, there is a 1-1 correspondence between prime ideals and indecomposable injective modules. The correspondence in this case is perhaps even simpler: a prime ideal is an annihilator of a unique simple module, and the corresponding indecomposable injective module is its ... | Injective dimension | 0.804214 |
31,878 | Therefore, the finitely generated injective left A-modules are precisely the modules of the form Homk(P, k) where P is a finitely generated projective right A-module. For symmetric algebras, the duality is particularly well-behaved and projective modules and injective modules coincide. | Injective dimension | 0.804214 |
31,879 | If G is a finite group and k a field with characteristic 0, then one shows in the theory of group representations that any subrepresentation of a given one is already a direct summand of the given one. Translated into module language, this means that all modules over the group algebra kG are injective. If the character... | Injective dimension | 0.804214 |
31,880 | In relative homological algebra, the extension property of homomorphisms may be required only for certain submodules, rather than for all. For instance, a pure injective module is a module in which a homomorphism from a pure submodule can be extended to the whole module. | Injective dimension | 0.804214 |
31,881 | A strong violation oracle for K is an oracle that, given a vector c in Rn and a real number r, returns one of the following: Assert that c ⋅ x ≤ r {\displaystyle c\cdot x\leq r} for all x in K; Find a vector y in K with c ⋅ y > r {\displaystyle c\cdot y>r} .A weak violation oracle for K is an oracle that, given a vecto... | Separation oracle | 0.804214 |
31,882 | A separation oracle (also called a cutting-plane oracle) is a concept in the mathematical theory of convex optimization. It is a method to describe a convex set that is given as an input to an optimization algorithm. Separation oracles are used as input to ellipsoid methods. : 87, 96, 98 | Separation oracle | 0.804214 |
31,883 | An optimization oracle is an oracle which finds an optimal point in a given convex set. Formally, a strong optimization oracle for K is an oracle that, given a vector c in Rn, returns one of the following: Assert that K is empty. Find a vector y in K that maximizes c ⋅ y {\displaystyle c\cdot y} (that is, c ⋅ y ≥ c ⋅ x... | Separation oracle | 0.804214 |
31,884 | In some linear optimization problems, even though the number of constraints is exponential, one can still write a custom separation oracle that works in polynomial time. Some examples are: The minimum-cost arborescence problem: given a weighted directed graph and a vertex r in it, find a subgraph of minimum cost that c... | Separation oracle | 0.804214 |
31,885 | Chemically, the equivalent to a snow avalanche is a spark causing a forest fire. In nuclear physics, a single stray neutron can result in a prompt critical event, which may finally be energetic enough for a nuclear reactor meltdown or (in a bomb) a nuclear explosion. Numerous chain reactions can be represented by a mat... | Chain reaction (chemistry) | 0.80421 |
31,886 | The Newton disc, also known as the disappearing colour disc, is a well-known physics experiment with a rotating disc with segments in different colours (usually Newton's primary colours: red, orange, yellow, green, blue, indigo, and violet or ROYGBIV) appearing as white (or off-white or grey) when it spun rapidy about ... | Newton disc | 0.80421 |
31,887 | Any node of a circuit that is available for connection to an external circuit is called a pole (or terminal if it is a physical object). The port condition is that a pair of poles of a circuit is considered a port if and only if the current flowing into one pole from outside the circuit is equal to the current flowing ... | Port (circuit theory) | 0.804208 |
31,888 | That is, by means of a pair of linear algebraic equations or a 2×2 transfer function matrix. However, the variables at the two ports will be different and the two-port parameters will be a mixture of two energy domains. For instance, in the actuator example, the z-parameters will include one electrical impedance, one m... | Port (circuit theory) | 0.804208 |
31,889 | The concept of ports can be extended into other energy domains. The generalised definition of a port is a place where energy can flow from one element or subsystem to another element or subsystem. This generalised view of the port concept helps to explain why the port condition is so defined in electrical analysis. If ... | Port (circuit theory) | 0.804208 |
31,890 | RF and microwave circuit topologies are commonly unbalanced circuit topologies such as coaxial or microstrip. In these formats, one pole of each port in a circuit is connected to a common node such as a ground plane. It is assumed in the circuit analysis that all these commoned poles are at the same potential and that ... | Port (circuit theory) | 0.804208 |
31,891 | MetaboLights is a data repository founded in 2012 for cross-species and cross-platform metabolomic studies that provides primary research data and meta data for metabolomic studies as well as a knowledge base for properties of individual metabolites. The database is maintained by the European Bioinformatics Institute (... | MetaboLights | 0.804208 |
31,892 | The decidability of GLP in polynomial space was proven by I. Shapirovsky, and the PSPACE-hardness of its variable-free fragment was proven by F. Pakhomov. Among the most notable applications of GLP has been its use in proof-theoretically analyzing Peano arithmetic, elaborating a canonical way for recovering ordinal not... | Japaridze's polymodal logic | 0.804207 |
31,893 | GLP, under the name GP, was introduced by Giorgi Japaridze in his PhD thesis "Modal Logical Means of Investigating Provability" (Moscow State University, 1986) and published two years later along with (a) the completeness theorem for GLP with respect to its provability interpretation (Beklemishev subsequently came up w... | Japaridze's polymodal logic | 0.804207 |
31,894 | Mathematical Notes 2012; 91:318–333. D. Fernandez-Duque and J.Joosten, "Well-orders in the transfinite Japaridze algebra". Logic Journal of the IGPL 22 (2014), pp. | Japaridze's polymodal logic | 0.804207 |
31,895 | L. Beklemishev, "A simplified proof of arithmetical completeness theorem for provability logic GLP". Proceedings of the Steklov Institute of Mathematics 274 (2011), pp. 25–33. | Japaridze's polymodal logic | 0.804207 |
31,896 | L. Beklemishev, "Ordinal completeness of bimodal provability logic GLB". Lecture Notes in Computer Science 6618 (2011), pp. 1–15. | Japaridze's polymodal logic | 0.804207 |
31,897 | L. Beklemishev, "Provability algebras and proof-theoretic ordinals, I". Annals of Pure and Applied Logic 128 (2004), pp. 103–123. L. Beklemishev, J. Joosten and M. Vervoort, "A finitary treatment of the closed fragment of Japaridze's provability logic". | Japaridze's polymodal logic | 0.804207 |
31,898 | Japaridze's polymodal logic (GLP) is a system of provability logic with infinitely many provability modalities. This system has played an important role in some applications of provability algebras in proof theory, and has been extensively studied since the late 1980s. It is named after Giorgi Japaridze. | Japaridze's polymodal logic | 0.804207 |
31,899 | The problem of being a theorem of GLP is PSPACE-complete. So is the same problem restricted to only variable-free formulas of GLP. | Japaridze's polymodal logic | 0.804207 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.