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31,700 | Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include Moran's I {\displaystyle I} , Geary's C {\displaystyle C} , Getis's G {\displaystyle G} and the standard deviational ellipse. These statistics requ... | Spatial analyses | 0.804317 |
31,701 | Spatial interaction or "gravity models" estimate the flow of people, material or information between locations in geographic space. Factors can include origin propulsive variables such as the number of commuters in residential areas, destination attractiveness variables such as the amount of office space in employment ... | Spatial analyses | 0.804317 |
31,702 | A singular point is said to be movable if its location depends on the particular solution we have chosen, rather than being fixed by the equation itself. For example the equation d y d x = 1 2 y {\displaystyle {\frac {dy}{dx}}={\frac {1}{2y}}} has solution y = x − c {\displaystyle y={\sqrt {x-c}}} for any constant c. T... | Movable singularity | 0.804317 |
31,703 | In the theory of ordinary differential equations, a movable singularity is a point where the solution of the equation behaves badly and which is "movable" in the sense that its location depends on the initial conditions of the differential equation. Suppose we have an ordinary differential equation in the complex domai... | Movable singularity | 0.804317 |
31,704 | A dot product function is included in: BLAS level 1 real SDOT, DDOT; complex CDOTU, ZDOTU = X^T * Y, CDOTC, ZDOTC = X^H * Y Fortran as dot_product(A,B) or sum(conjg(A) * B) Julia as A' * B or standard library LinearAlgebra as dot(A, B) Matlab as A' * B or conj(transpose(A)) * B or sum(conj(A) . * B) or dot(A, B) Python... | Norm squared | 0.804317 |
31,705 | The Molecular Modelling Toolkit (MMTK) is an open-source software package written in Python, which performs common tasks in molecular modelling. The Molecular Modeling Toolkit is a library that implements common molecular simulation techniques, with an emphasis on biomolecular simulations. It uses modern software engin... | Molecular Modelling Toolkit | 0.804315 |
31,706 | Other findings from the statistics are that most installations are done via DVD images. The dominant architecture is x64. | OpenSUSE | 0.804315 |
31,707 | Linux at the time, the number 42 refers to the question about "life, the universe and everything" in the Hitchhiker's Guide to the Galaxy book series. After that, the basis packages are received from the SUSE Linux Enterprise, while applications and desktops come from Tumbleweed.At the openSUSE conference held in Nurem... | OpenSUSE | 0.804315 |
31,708 | The Hiyama coupling is a palladium-catalyzed cross-coupling reaction of organosilanes with organic halides used in organic chemistry to form carbon–carbon bonds (C-C bonds). This reaction was discovered in 1988 by Tamejiro Hiyama and Yasuo Hatanaka as a method to form carbon-carbon bonds synthetically with chemo- and r... | Hiyama-Denmark coupling | 0.804312 |
31,709 | Strategies for improving platinum-based anticancer drugs usually involve changes in the neutral spectator ligands, changes in the nature of the anions (halides vs various carboxylates), or changes in the oxidation state of the metal (Pt(II) vs Pt(IV)). Nanotechnology has been explored to deliver platinum more efficient... | Platinum-based antineoplastic | 0.804311 |
31,710 | Whereas the idea of JITs reaches back to the 1960s, tracing JITs have become used more often only recently. The first mention of an idea that is similar to today's idea of tracing JITs was in 1970. It was observed that compiled code could be derived from an interpreter at run-time by simply storing the actions performe... | Tracing just-in-time compilation | 0.804308 |
31,711 | Traces are easy to optimize, since they represent only one execution path, which means that no control flow exists and needs no handling. Typical optimizations include constant-subexpression elimination, dead code elimination, register allocation, invariant-code motion, constant folding, and escape analysis.After the o... | Tracing just-in-time compilation | 0.804308 |
31,712 | The guard is a quick check to determine whether the original condition is still true. If a guard fails, the execution of the trace is aborted. Since tracing is done during execution, the trace can be made to contain runtime information (e.g. type information). This information can later be used in the optimization phas... | Tracing just-in-time compilation | 0.804308 |
31,713 | We tell it to solve a mathematical problem, and it complies by turning all the matter in the solar system into a giant calculating device, in the process killing the person who asked the question. According to Eliezer Yudkowsky, a significant problem in AI safety is that unfriendly artificial intelligence is likely to ... | Seed AI | 0.804306 |
31,714 | AI researcher Hugo de Garis suggests that artificial intelligences may simply eliminate the human race for access to scarce resources, and humans would be powerless to stop them. Alternatively, AIs developed under evolutionary pressure to promote their own survival could outcompete humanity.Bostrom (2002) discusses hum... | Seed AI | 0.804306 |
31,715 | Unfortunately, it might also be the last, unless we learn how to avoid the risks." Hawking believed that in the coming decades, AI could offer "incalculable benefits and risks" such as "technology outsmarting financial markets, out-inventing human researchers, out-manipulating human leaders, and developing weapons we c... | Seed AI | 0.804306 |
31,716 | The term "technological singularity" reflects the idea that such change may happen suddenly, and that it is difficult to predict how the resulting new world would operate. It is unclear whether an intelligence explosion resulting in a singularity would be beneficial or harmful, or even an existential threat. Because AI... | Seed AI | 0.804306 |
31,717 | Between 1986 and 2007, machines' application-specific capacity to compute information per capita roughly doubled every 14 months; the per capita capacity of the world's general-purpose computers has doubled every 18 months; the global telecommunication capacity per capita doubled every 34 months; and the world's storag... | Seed AI | 0.804306 |
31,718 | The exponential growth in computing technology suggested by Moore's law is commonly cited as a reason to expect a singularity in the relatively near future, and a number of authors have proposed generalizations of Moore's law. Computer scientist and futurist Hans Moravec proposed in a 1998 book that the exponential gro... | Seed AI | 0.804306 |
31,719 | In 1965 I. J. Good predicted an ultraintelligent machine by 2000, Vinge (1993) predicted greater-than-human intelligence between 2005 and 2030, Yudkowsky (1996) predicted a singularity by 2021, and Kurzweil (2005) predicted human-level artificial intelligence by 2030. Moravec (1988) predicted human-level artificial int... | Seed AI | 0.804306 |
31,720 | Although technological progress has been accelerating in most areas, it has been limited by the basic intelligence of the human brain, which has not, according to Paul R. Ehrlich, changed significantly for millennia. However, with the increasing power of computers and other technologies, it might eventually be possible... | Seed AI | 0.804306 |
31,721 | Some writers use "the singularity" in a broader way to refer to any radical changes in society brought about by new technology (such as molecular nanotechnology), although Vinge and other writers specifically state that without superintelligence, such changes would not qualify as a true singularity. | Seed AI | 0.804306 |
31,722 | The former is predicted by Moore's Law and the forecasted improvements in hardware, and is comparatively similar to previous technological advances. But there are some AI researchers, who believe software is more important than hardware.A 2017 email survey of authors with publications at the 2015 NeurIPS and ICML machi... | Seed AI | 0.804306 |
31,723 | Finally, the laws of physics may eventually prevent further improvement. There are two logically independent, but mutually reinforcing, causes of intelligence improvements: increases in the speed of computation, and improvements to the algorithms used. | Seed AI | 0.804306 |
31,724 | Prominent technologists and academics dispute the plausibility of a technological singularity, including Paul Allen, Jeff Hawkins, John Holland, Jaron Lanier, Steven Pinker, Theodore Modis, and Gordon Moore, whose law is often cited in support of the concept.Most proposed methods for creating superhuman or transhuman m... | Seed AI | 0.804306 |
31,725 | If the vertices of a framework are in a motion, then that motion may be described over small scales of distance by its gradient, a vector for each vertex specifying its speed and direction. The gradient describes a linearized approximation to the actual motion of the points, in which each point moves at constant veloci... | Rigidity matroid | 0.804306 |
31,726 | A set of edges is independent, in the matroid, if it corresponds to a set of rows of the rigidity matrix that is linearly independent. A framework is called generic if the coordinates of its vertices are algebraically independent real numbers. Any two generic frameworks on the same graph G determine the same rigidity m... | Rigidity matroid | 0.804306 |
31,727 | The latest improvement to the bound on odd exponent is 101 obtained by Adian himself in 2015. The case of even exponent turned out to be considerably more difficult. It was only in 1994 that Sergei Vasilievich Ivanov was able to prove an analogue of Novikov–Adian theorem: for any m > 1 and an even n ≥ 248, n divisible ... | Burnside problem | 0.804306 |
31,728 | If G is a finitely generated, periodic group, then is G necessarily finite? This question was answered in the negative in 1964 by Evgeny Golod and Igor Shafarevich, who gave an example of an infinite p-group that is finitely generated (see Golod–Shafarevich theorem). However, the orders of the elements of this group ar... | Burnside problem | 0.804306 |
31,729 | (Later, in 1989, Efim Zelmanov was able to solve the restricted Burnside problem for an arbitrary exponent.) Issai Schur had shown in 1911 that any finitely generated periodic group that was a subgroup of the group of invertible n × n complex matrices was finite; he used this theorem to prove the Jordan–Schur theorem.N... | Burnside problem | 0.804306 |
31,730 | That July, Multiverse partnered with Bosch to integrate quantum algorithms into digital twin simulation workflow to scale simulations more efficiently and improve the accuracy of defect detection. Later that year, BASF used Multiverse’s Singularity to develop models for foreign exchange trading optimization between U.S... | Multiverse Computing | 0.804306 |
31,731 | Multiverse was co-founded in 2019 by Enrique Lizaso, Román Orús, Alfonso Rubio and Sam Mugel. Lizaso, treasurer and member of the governing board of the European Quantum Industry Consortium, and Orús, Ikerbasque Research Professor at DIPC and former Marie Curie Fellow at the Max Planck Institute of Quantum Optics, were... | Multiverse Computing | 0.804306 |
31,732 | Multiverse Computing’s algorithms have been implemented across verticals such as energy, manufacturing, logistics, finance, chemistry, space, and cybersecurity. On top of quantum machine learning and optimization algorithms, the company also uses quantum-inspired tensor networks to boost efficiency in solving industria... | Multiverse Computing | 0.804306 |
31,733 | Multiverse Computing is a Spanish quantum computing software company headquartered in San Sebastian, Spain, with offices in Paris, Munich, London, Toronto and Sherbrooke, Canada. The Spanish startup applies quantum and quantum-inspired algorithms to problems in energy, logistics, manufacturing, mobility, life sciences,... | Multiverse Computing | 0.804306 |
31,734 | This means that the particles were in inertial frames of reference. Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again. In a similar way, it is now common to describe that we exist in a four-dimensional geometry known as spacetime. In this picture, ... | Inertial observer | 0.804306 |
31,735 | As an example of why this is important, consider the geometry of an ellipsoid. In this geometry, a "free" particle is defined as one at rest or traveling at constant speed on a geodesic path. Two free particles may begin at the same point on the surface, traveling with the same constant speed in different directions. | Inertial observer | 0.804306 |
31,736 | The speed of light is considered to be the only true constant between moving frames of reference. The definition of inertial reference frame can also be extended beyond three-dimensional Euclidean space. Newton's assumed a Euclidean space, but general relativity uses a more general geometry. | Inertial observer | 0.804306 |
31,737 | The motion of a body can only be described relative to something else—other bodies, observers, or a set of spacetime coordinates. These are called frames of reference. According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inerti... | Inertial observer | 0.804305 |
31,738 | A coherent algebra is an algebra of complex square matrices that is closed under ordinary matrix multiplication, Schur product, transposition, and contains both the identity matrix I {\displaystyle I} and the all-ones matrix J {\displaystyle J} . | Coherent algebra | 0.804301 |
31,739 | Dually, if A {\displaystyle {\mathcal {A}}} is a commutative coherent algebra (of order n {\displaystyle n} ), then E T , E ∗ ∈ Λ ( A ) {\displaystyle E^{T},E^{*}\in \Lambda ({\mathcal {A}})} for all E ∈ A {\displaystyle E\in {\mathcal {A}}} , 1 n J ∈ Λ ( A ) {\displaystyle {\frac {1}{n}}J\in \Lambda ({\mathcal {A}})} ... | Coherent algebra | 0.804301 |
31,740 | The intersection of a set of coherent algebras of order n {\displaystyle n} is a coherent algebra. The tensor product of coherent algebras is a coherent algebra, i.e. A ⊗ B := { M ⊗ N: M ∈ A and N ∈ B } {\displaystyle {\mathcal {A}}\otimes {\mathcal {B}}:=\{M\otimes N:M\in {\mathcal {A}}{\text{ and }}N\in {\mathcal {B}... | Coherent algebra | 0.804301 |
31,741 | It is isomorphic to the Minkowski plane M ( K ) {\displaystyle {\mathfrak {M}}(K)} with K = GF ( 2 ) {\displaystyle K=\operatorname {GF} (2)} (field { 0 , 1 } {\displaystyle \{0,1\}} ).An astonishing result is Theorem (Heise): Any Minkowski plane of even order is miquelian. Remark: A suitable stereographic projection... | Minkowski plane | 0.804301 |
31,742 | Theorem (Chen): Only a Minkowski plane M ( K ) {\displaystyle {\mathfrak {M}}(K)} satisfies the theorem of Miquel. Because of the last theorem M ( K ) {\displaystyle {\mathfrak {M}}(K)} is called a miquelian Minkowski plane. Remark: The minimal model of a Minkowski plane is miquelian. | Minkowski plane | 0.804301 |
31,743 | We get the most important examples of Minkowski planes by generalizing the classical real model: Just replace R {\displaystyle \mathbb {R} } by an arbitrary field K {\displaystyle K} then we get in any case a Minkowski plane M ( K ) = ( P , Z ; ∥ + , ∥ − , ∈ ) {\displaystyle {\mathfrak {M}}(K)=({\mathcal {P}},{\mathcal... | Minkowski plane | 0.804301 |
31,744 | From the definition above we find: Lemma: For any pair of non parallel points A , B {\displaystyle A,B} there is exactly one point C {\displaystyle C} with A ∥ + C ∥ − B {\displaystyle A\parallel _{+}C\parallel _{-}B} . For any point P {\displaystyle P} and any cycle z {\displaystyle z} there are exactly two points A ,... | Minkowski plane | 0.804301 |
31,745 | Applying the pseudo-euclidean distance d ( P 1 , P 2 ) = ( x 1 ′ − x 2 ′ ) 2 − ( y 1 ′ − y 2 ′ ) 2 {\displaystyle d(P_{1},P_{2})=(x'_{1}-x'_{2})^{2}-(y'_{1}-y'_{2})^{2}} on two points P i = ( x i ′ , y i ′ ) {\displaystyle P_{i}=(x'_{i},y'_{i})} (instead of the euclidean distance) we get the geometry of hyperbolas, bec... | Minkowski plane | 0.804301 |
31,746 | There is at least one cycle z {\displaystyle z} and a point P {\displaystyle P} not in z {\displaystyle z} .For investigations the following statements on parallel classes (equivalent to C1, C2 respectively) are advantageous. C1′: For any two points A , B {\displaystyle A,B} we have | A ¯ + ∩ B ¯ − | = 1 {\displaystyle... | Minkowski plane | 0.804301 |
31,747 | Given a Noetherian integral domain, if there are algorithms to solve the ideal membership problem and the syzygies problem for a single equation, then one may deduce from them algorithms for the similar problems concerning systems of equations.This theorem is useful to prove the existence of algorithms. However, in pra... | Linear equation over a ring | 0.804299 |
31,748 | The first problem becomes the submodule membership problem. The second one is also called the syzygy problem. A ring such that there are algorithms for the arithmetic operations (addition, subtraction, multiplication) and for the above problems may be called a computable ring, or effective ring. One may also say that l... | Linear equation over a ring | 0.804299 |
31,749 | In algebra, linear equations and systems of linear equations over a field are widely studied. "Over a field" means that the coefficients of the equations and the solutions that one is looking for belong to a given field, commonly the real or the complex numbers. This article is devoted to the same problems where "field... | Linear equation over a ring | 0.804299 |
31,750 | Let R be an effective commutative ring. There is an algorithm for testing if an element a is a zero divisor: this amounts to solving the linear equation ax = 0. There is an algorithm for testing if an element a is a unit, and if it is, computing its inverse: this amounts to solving the linear equation ax = 1. Given an ... | Linear equation over a ring | 0.804299 |
31,751 | There are algorithms to solve all the problems addressed in this article over the integers. In other words, linear algebra is effective over the integers; see Linear Diophantine system for details. More generally, linear algebra is effective on a principal ideal domain if there are algorithms for addition, subtraction ... | Linear equation over a ring | 0.804299 |
31,752 | Linear algebra is effective on a polynomial ring k {\displaystyle k} over a field k. This has been first proved in 1926 by Grete Hermann. The algorithms resulting from Hermann's results are only of historical interest, as their computational complexity is too high for allowing effective computer computation. Proofs th... | Linear equation over a ring | 0.804299 |
31,753 | Linear algebra is effective on the polynomial ring R {\displaystyle R} if and only if one has an algorithm that computes an upper bound of the degree of the polynomials that may occur when solving linear systems of equations: if one has solving algorithms, their outputs give the degrees. Conversely, if one knows an up... | Linear equation over a ring | 0.804299 |
31,754 | When Hall's condition does not hold, the original theorem tells us only that a perfect matching does not exist, but does not tell what is the largest matching that does exist. To learn this information, we need the notion of deficiency of a graph. Given a bipartite graph G = (X+Y, E), the deficiency of G w.r.t. X is th... | Marriage Theorem | 0.804296 |
31,755 | The graph theoretic formulation of Marshal Hall's extension of the marriage theorem can be stated as follows: Given a bipartite graph with sides A and B, we say that a subset C of B is smaller than or equal in size to a subset D of A in the graph if there exists an injection in the graph (namely, using only edges of th... | Marriage Theorem | 0.804296 |
31,756 | By examining Philip Hall's original proof carefully, Marshall Hall Jr. (no relation to Philip Hall) was able to tweak the result in a way that permitted the proof to work for infinite F {\displaystyle {\mathcal {F}}} . This variant extends Philip Hall's Marriage theorem. Suppose that F = { A i } i ∈ I {\displaystyle {\... | Marriage Theorem | 0.804296 |
31,757 | Let G = ( X , Y , E ) {\displaystyle G=(X,Y,E)} be a finite bipartite graph with bipartite sets X {\displaystyle X} and Y {\displaystyle Y} and edge set E {\displaystyle E} . An X {\displaystyle X} -perfect matching (also called an X {\displaystyle X} -saturating matching) is a matching, a set of disjoint edges, which ... | Marriage Theorem | 0.804296 |
31,758 | This theorem is part of a collection of remarkably powerful theorems in combinatorics, all of which are related to each other in an informal sense in that it is more straightforward to prove one of these theorems from another of them than from first principles. These include: The König–Egerváry theorem (1931) (Dénes Kő... | Marriage Theorem | 0.804295 |
31,759 | The theorem has many applications. For example, for a standard deck of cards, dealt into 13 piles of 4 cards each, the marriage theorem implies that it is possible to select one card from each pile so that the selected cards contain exactly one card of each rank (Ace, 2, 3, ..., Queen, King). More generally, any regula... | Marriage Theorem | 0.804295 |
31,760 | An alternative term for transversal is system of distinct representatives. The collection F {\displaystyle {\mathcal {F}}} satisfies the marriage condition when each subfamily of F {\displaystyle {\mathcal {F}}} contains at least as many distinct members as its number of sets. That is, for all G ⊆ F {\displaystyle {\ma... | Marriage Theorem | 0.804295 |
31,761 | A good example of application of the boundary element method is efficient calculation of natural frequencies of liquid sloshing in tanks. Boundary element method is one of the most effective methods for numerical simulation of contact problems, in particular for simulation of adhesive contacts.Boundary element formulat... | Boundary Element Method | 0.804295 |
31,762 | Among pnictogen group Lewis acidic compounds, unusual lewis acidity of Lewis acidic antimony compounds have long been exploited as both stable conjugate acids of non-coordinating anions (SbF−6 and Sb2F−11), and strong Lewis acid counterparts of well-known superacids (magic acids, fluoroantimonic acid). Also, Lewis-acid... | Lewis acidic antimony compounds | 0.804295 |
31,763 | In detail, the LUMO can be assigned to as localized orbital on stiborafluorene moiety with larger nodes at the 9-position (Sb). Thus, Lewis bases bind towards trans to biphenylene and its fluoride adducts are asymmetric: 8·F− has two enantiomers and 7·F− has two diastereomers and four enantiomers. A bisantimony complex... | Lewis acidic antimony compounds | 0.804295 |
31,764 | In plasma physics, the magnetic topology of a plasma is the structure and linkage of its magnetic field.The magnetic topology of a plasma can be changed through magnetic diffusion and reconnection. In the limit of a large magnetic Reynolds number, however, diffusion and reconnection of the magnetic field cannot occur, ... | Magnetic topology | 0.804291 |
31,765 | Semi-biotic systems are systems that incorporate biologically derived components/modules – which could range from multi-protein complexes through DNA constructs to multi-cellular assemblies – and integrate them with synthetic components (e.g. microfabricated systems) to produce hybrid devices. One of the potential attr... | Semi-biotic systems | 0.804289 |
31,766 | But it is not yet possible to combine components in a systematic way to build larger, more complex systems. Principles of physics and examples from nature both suggest that it will be possible to extend atomically precise fabrication to more complex products of larger size, involving a wider range of materials. An exam... | Productive nanosystems | 0.804289 |
31,767 | Mihail Roco, one of the architects of the USA's National Nanotechnology Initiative, has proposed four states of nanotechnology that seem to parallel the technical progress of the Industrial Revolution, of which productive nanosystems is the most advanced.1. Passive nanostructures - nanoparticles and nanotubes that prov... | Productive nanosystems | 0.804289 |
31,768 | Among the topics covered by environmental engineering are pollutant transport, water purification, waste water treatment, air pollution, solid waste treatment, recycling, and hazardous waste management. Environmental engineers administer pollution reduction, green engineering, and industrial ecology. Environmental engi... | Civil engineering | 0.804289 |
31,769 | Environmental engineering is the contemporary term for sanitary engineering, though sanitary engineering traditionally had not included much of the hazardous waste management and environmental remediation work covered by environmental engineering. Public health engineering and environmental health engineering are other... | Civil engineering | 0.804289 |
31,770 | Civil engineers typically possess an academic degree in civil engineering. The length of study is three to five years, and the completed degree is designated as a bachelor of technology, or a bachelor of engineering. The curriculum generally includes classes in physics, mathematics, project management, design and speci... | Civil engineering | 0.804289 |
31,771 | Civil engineering systems is a discipline that promotes the use of systems thinking to manage complexity and change in civil engineering within its wider public context. It posits that the proper development of civil engineering infrastructure requires a holistic, coherent understanding of the relationships between all... | Civil engineering | 0.804289 |
31,772 | Civil engineering is the application of physical and scientific principles for solving the problems of society, and its history is intricately linked to advances in the understanding of physics and mathematics throughout history. Because civil engineering is a broad profession, including several specialized sub-discipl... | Civil engineering | 0.804289 |
31,773 | Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage systems, pipelines, structural components of buildings, and railways.Civil e... | Civil engineering | 0.804289 |
31,774 | There are a number of sub-disciplines within the broad field of civil engineering. General civil engineers work closely with surveyors and specialized civil engineers to design grading, drainage, pavement, water supply, sewer service, dams, electric and communications supply. General civil engineering is also referred ... | Civil engineering | 0.804289 |
31,775 | Construction engineering involves planning and execution, transportation of materials, site development based on hydraulic, environmental, structural and geotechnical engineering. As construction firms tend to have higher business risk than other types of civil engineering firms do, construction engineers often engage ... | Civil engineering | 0.804289 |
31,776 | Municipal engineering is concerned with municipal infrastructure. This involves specifying, designing, constructing, and maintaining streets, sidewalks, water supply networks, sewers, street lighting, municipal solid waste management and disposal, storage depots for various bulk materials used for maintenance and publi... | Civil engineering | 0.804289 |
31,777 | 3). That is how much energy is donated to an energy transformation process. These methods are used in ecological physical chemistry, and ecosystem evaluation. | Energy quality | 0.804289 |
31,778 | Energy quality is a measure of the ease with which a form of energy can be converted to useful work or to another form of energy: i.e. its content of thermodynamic free energy. A high quality form of energy has a high content of thermodynamic free energy, and therefore a high proportion of it can be converted to work; ... | Energy quality | 0.804289 |
31,779 | Thus, discussions of energy quality can sometimes be found in the Humanities, such as dialectics, Marxism and postmodernism. This is effectively because disciplines such as economics failed to recognize the thermodynamic inputs into the economy (now recognized as thermoeconomics), while disciplines such as physics and ... | Energy quality | 0.804289 |
31,780 | The above example focused on the economic impacts of the exploitation of energy. A similar scenario plays out in nature and biology, where living organisms can extract energy of varying quality from nature, ultimately driven by solar energy as the primary driver of thermodynamic disequilibrium on Earth. The ecological ... | Energy quality | 0.804289 |
31,781 | We define the tautological bundle γn, k over G n ( R n + k ) {\displaystyle G_{n}(\mathbb {R} ^{n+k})} as follows. The total space of the bundle is the set of all pairs (V, v) consisting of a point V of the Grassmannian and a vector v in V; it is given the subspace topology of the Cartesian product G n ( R n + k ) × R ... | Tautological subbundle | 0.804288 |
31,782 | Since its tenth year of publication, the journal annually awards the $5000 PLOS Genetics Research Prize for the best paper published in the previous year based on nominations from members of the genetics community. | PLoS Genetics | 0.804285 |
31,783 | PLOS Genetics is a peer-reviewed open access scientific journal established in 2005 and published by the Public Library of Science. The founding editor-in-chief was Wayne N. Frankel (Columbia University Medical Center). The current editors-in-chief are Gregory S. Barsh (HudsonAlpha Institute of Biotechnology and Stanfo... | PLoS Genetics | 0.804285 |
31,784 | In mathematics, and in particular the necklace splitting problem, the Hobby–Rice theorem is a result that is useful in establishing the existence of certain solutions. It was proved in 1965 by Charles R. Hobby and John R. Rice; a simplified proof was given in 1976 by A. Pinkus. | Hobby–Rice theorem | 0.804284 |
31,785 | This fair-division challenge is sometimes referred to as the consensus-halving problem. The Hobby–Rice theorem implies that this can be done with n cuts. == References == | Hobby–Rice theorem | 0.804284 |
31,786 | The theorem was used by Noga Alon in the context of necklace splitting in 1987. Suppose the interval is a cake. There are n partners and each of the n functions is a value-density function of one partner. We want to divide the cake into two parts such that all partners agree that the parts have the same value. | Hobby–Rice theorem | 0.804284 |
31,787 | In mathematics, specifically algebraic geometry, the valuative criteria are a collection of results that make it possible to decide whether a morphism of algebraic varieties, or more generally schemes, is universally closed, separated, or proper. | Valuative criterion | 0.804283 |
31,788 | In software engineering, a circular dependency is a relation between two or more modules which either directly or indirectly depend on each other to function properly. Such modules are also known as mutually recursive. | Circular dependencies | 0.804282 |
31,789 | In mathematics you have a function, you write down the function, you calculate, or you add, or you multiply, or you can differentiate. You have something very concrete. In geometry the geometric situation is described by numbers, but you can change your numbers arbitrarily. So to handle this, you need the Ricci calculu... | Tensor calculus | 0.804281 |
31,790 | Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus:In our subject of differential geometry, where you talk about manifolds, one difficulty is that the geometry is described by coordinates, but the coordinates do not have ... | Tensor calculus | 0.804281 |
31,791 | In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of re... | Tensor calculus | 0.804281 |
31,792 | Tensor calculus provides a generalization to the gradient vector formula from standard calculus that works in all coordinate systems: ∇ F = ∇ i F Z → i {\displaystyle \nabla F=\nabla _{i}F{\vec {Z}}^{i}} Where: ∇ i F = ∂ F ∂ Z i {\displaystyle \nabla _{i}F={\frac {\partial F}{\partial Z^{i}}}} In contrast, for standard... | Tensor calculus | 0.804281 |
31,793 | Tensors notation allows a vector ( V → {\displaystyle {\vec {V}}} ) to be decomposed into an Einstein summation representing the tensor contraction of a basis vector ( Z → i {\displaystyle {\vec {Z}}_{i}} or Z → i {\displaystyle {\vec {Z}}^{i}} ) with a component vector ( V i {\displaystyle V_{i}} or V i {\displaystyle... | Tensor calculus | 0.804281 |
31,794 | In physics, the first law of thermodynamics is an expression of the conservation of total energy of a system. The increase of the energy of a system is equal to the sum of work done on the system and the heat added to that system: d E t = d Q + d W {\displaystyle dE_{t}=dQ+dW} where E t {\displaystyle E_{t}} is the tot... | First law of thermodynamics (fluid mechanics) | 0.80428 |
31,795 | In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics... | Independent identically-distributed random variables | 0.804279 |
31,796 | The International Journal of Algebra and Computation is published by World Scientific, and contains articles on general mathematics, as well as: Combinatorial group theory and semigroup theory Universal algebra Algorithmic and computational problems in algebra Theory of automata Formal language theory Theory of computa... | International Journal of Algebra and Computation | 0.804278 |
31,797 | A logical machine is a tool containing a set of parts that uses energy to perform formal logic operations. Early logical machines were mechanical devices that performed basic operations in Boolean logic. Contemporary logical machines are computer-based electronic programs that perform proof assistance with theorems in ... | Logical machine | 0.804277 |
31,798 | In finite elements, the highest-dimensional mesh entities are called "elements," "edges" are 1D and "nodes" are 0D. If the elements are 3D, then the 2D entities are "faces." In computational geometry, the 0D points are called vertices. Tetrahedra are often abbreviated as "tets"; triangles are "tris", quadrilaterals are... | Grid generation | 0.804277 |
31,799 | The problem is the connectivity hampers if mesh point movement is very large. Steady flow and the time-accurate flow calculation can be solved through this adaptive method. The grid is refined and after a predetermined number of iteration in order to adapt it in a steady flow problem. The grid will stop adjusting to th... | Grid generation | 0.804277 |
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