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23,600 | Philosophical attempts to rationalize why different substances have different properties (color, density, smell), exist in different states (gaseous, liquid, and solid), and react in a different manner when exposed to environments, for example to water or fire or temperature changes, led ancient philosophers to postula... | History of chemistry | 0.808738 |
23,601 | 337). We have R+ = R if, and only if, R itself is transitive. Conversely, transitive reduction adduces a minimal relation S from a given relation R such that they have the same closure, that is, S+ = R+; however, many different S with this property may exist. Both transitive closure and transitive reduction are also us... | Transitive closure logic | 0.808737 |
23,602 | Keyword research and optimization Keyword research and optimization are fundamental aspects of search engine optimization (SEO) and play a vital role in improving website visibility and ranking on search engine results pages. Keyword research involves identifying specific words and phrases that users enter into search ... | Keyword research | 0.808735 |
23,603 | So the measure space associated to ν may have a larger σ-algebra than the measure space associated to μ. The restrictions of ν and μ to the smaller σ-algebra are identical. The elements of the larger σ-algebra which are not contained in the smaller σ-algebra have infinite ν-measure and finite μ-measure. From this persp... | Outer measure | 0.808733 |
23,604 | Suppose (X, d) is a metric space and φ an outer measure on X. If φ has the property that φ ( E ∪ F ) = φ ( E ) + φ ( F ) {\displaystyle \varphi (E\cup F)=\varphi (E)+\varphi (F)} whenever d ( E , F ) = inf { d ( x , y ): x ∈ E , y ∈ F } > 0 , {\displaystyle d(E,F)=\inf\{d(x,y):x\in E,y\in F\}>0,} then φ is called a met... | Outer measure | 0.808733 |
23,605 | Thus lim δ → 0 φ δ ( E ) = φ 0 ( E ) ∈ {\displaystyle \lim _{\delta \rightarrow 0}\varphi _{\delta }(E)=\varphi _{0}(E)\in } exists (possibly infinite). Theorem. φ0 is a metric outer measure on X. This is the construction used in the definition of Hausdorff measures for a metric space. | Outer measure | 0.808733 |
23,606 | Let X be a set, C a family of subsets of X which contains the empty set and p a non-negative extended real valued function on C which vanishes on the empty set. Theorem. Suppose the family C and the function p are as above and define φ ( E ) = inf { ∑ i = 0 ∞ p ( A i ) | E ⊆ ⋃ i = 0 ∞ A i , ∀ i ∈ N , A i ∈ C } . | Outer measure | 0.808733 |
23,607 | It is straightforward to use the above definition of μ {\displaystyle \mu } -measurability to see that if A ⊆ X {\displaystyle A\subseteq X} is μ {\displaystyle \mu } -measurable then its complement X ∖ A ⊆ X {\displaystyle X\setminus A\subseteq X} is also μ {\displaystyle \mu } -measurable.The following condition is k... | Outer measure | 0.808733 |
23,608 | In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstr... | Outer measure | 0.808733 |
23,609 | Towards the end of the 20th century, novel mathematical constructs such as fractal geometry and aperiodic tiling were seized upon by architects to provide interesting and attractive coverings for buildings. In 1913, the Modernist architect Adolf Loos had declared that "Ornament is a crime", influencing architectural th... | Mathematics and architecture | 0.808733 |
23,610 | 1650–1550 BC); this was first conjectured by historian Moritz Cantor in 1882. It is known that right angles were laid out accurately in ancient Egypt using knotted cords for measurement, that Plutarch recorded in Isis and Osiris (c. 100 AD) that the Egyptians admired the 3:4:5 triangle, and that a scroll from before 17... | Mathematics and architecture | 0.808733 |
23,611 | The pyramids of ancient Egypt are tombs constructed with mathematical proportions, but which these were, and whether the Pythagorean theorem was used, are debated. The ratio of the slant height to half the base length of the Great Pyramid of Giza is less than 1% from the golden ratio. If this was the design method, it ... | Mathematics and architecture | 0.808733 |
23,612 | The historian of Islamic art Antonio Fernandez-Puertas suggests that the Alhambra, like the Great Mosque of Cordoba, was designed using the Hispano-Muslim foot or codo of about 0.62 metres (2.0 ft). In the palace's Court of the Lions, the proportions follow a series of surds. A rectangle with sides 1 and √2 has (by Pyt... | Mathematics and architecture | 0.808733 |
23,613 | Alberti also documented Filippo Brunelleschi's discovery of linear perspective, developed to enable the design of buildings which would look beautifully proportioned when viewed from a convenient distance. The next major text was Sebastiano Serlio's Regole generali d'architettura (General Rules of Architecture); the fi... | Mathematics and architecture | 0.808733 |
23,614 | The early twentieth century movement Modern architecture, pioneered by Russian Constructivism, used rectilinear Euclidean (also called Cartesian) geometry. In the De Stijl movement, the horizontal and the vertical were seen as constituting the universal. The architectural form consists of putting these two directional ... | Mathematics and architecture | 0.808733 |
23,615 | Architects may also select the form of a building to meet environmental goals. For example, Foster and Partners' 30 St Mary Axe, London, known as "The Gherkin" for its cucumber-like shape, is a solid of revolution designed using parametric modelling. Its geometry was chosen not purely for aesthetic reasons, but to mini... | Mathematics and architecture | 0.808733 |
23,616 | The architecture of fortifications evolved from medieval fortresses, which had high masonry walls, to low, symmetrical star forts able to resist artillery bombardment between the mid-fifteenth and nineteenth centuries. The geometry of the star shapes was dictated by the need to avoid dead zones where attacking infantry... | Mathematics and architecture | 0.808733 |
23,617 | Firstly, they use geometry because it defines the spatial form of a building. Secondly, they use mathematics to design forms that are considered beautiful or harmonious. From the time of the Pythagoreans with their religious philosophy of number, architects in ancient Greece, ancient Rome, the Islamic world and the Ita... | Mathematics and architecture | 0.808733 |
23,618 | Equally, they note that in reactionary times such as the Italian Mannerism of about 1520 to 1580, or the 17th century Baroque and Palladian movements, mathematics was barely consulted. In contrast, the revolutionary early 20th-century movements such as Futurism and Constructivism actively rejected old ideas, embracing ... | Mathematics and architecture | 0.808733 |
23,619 | The emperor Justinian used two geometers, Isidore of Miletus and Anthemius of Tralles as architects; Isidore compiled the works of Archimedes on solid geometry, and was influenced by him. The importance of water baptism in Christianity was reflected in the scale of baptistry architecture. The oldest, the Lateran Baptis... | Mathematics and architecture | 0.808733 |
23,620 | Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms con... | Mathematics and architecture | 0.808733 |
23,621 | A master builder at the top of his profession was given the title of architect or engineer. In the Renaissance, the quadrivium of arithmetic, geometry, music and astronomy became an extra syllabus expected of the Renaissance man such as Leon Battista Alberti. | Mathematics and architecture | 0.808733 |
23,622 | The architects Michael Ostwald and Kim Williams, considering the relationships between architecture and mathematics, note that the fields as commonly understood might seem to be only weakly connected, since architecture is a profession concerned with the practical matter of making buildings, while mathematics is the pu... | Mathematics and architecture | 0.808733 |
23,623 | The property of being a G 2 {\displaystyle G_{2}} -manifold is much stronger than that of admitting a G 2 {\displaystyle G_{2}} -structure. Indeed, a G 2 {\displaystyle G_{2}} -manifold is a manifold with a G 2 {\displaystyle G_{2}} -structure which is torsion-free. The letter "G" occurring in the phrases "G-structure"... | G2-structure | 0.808733 |
23,624 | A manifold with holonomy G 2 {\displaystyle G_{2}} was first introduced by Edmond Bonan in 1966, who constructed the parallel 3-form, the parallel 4-form and showed that this manifold was Ricci-flat. The first complete, but noncompact 7-manifolds with holonomy G 2 {\displaystyle G_{2}} were constructed by Robert Bryant... | G2-structure | 0.808733 |
23,625 | Partitioning may be able assist the performance of bulk operations on a VLDB including backup and recovery., bulk movements due to information lifecycle management (ILM),: 3: 105–118 reducing contention: 327–329 as well as allowing optimization of some query processing. : 215–230 | Very large database | 0.808732 |
23,626 | In mathematics, the Denjoy theorem gives a sufficient condition for a diffeomorphism of the circle to be topologically conjugate to a diffeomorphism of a special kind, namely an irrational rotation. Denjoy (1932) proved the theorem in the course of his topological classification of homeomorphisms of the circle. He also... | Denjoy's theorem on rotation number | 0.808732 |
23,627 | Although it is still in its еarly stagеs, quantum computing holds еnormous potеntial for artificial intеlligеncе. Thе ability of qubits, oftеn rеfеrrеd to as quantum bits, to procеss many statеs at oncе has thе potеntial to rеvolutionizе AI tasks rеquiring complеx simulations and optimizations. | Hardware for artificial intelligence | 0.80873 |
23,628 | Specialized computer hardware is often used to execute artificial intelligence (AI) programs faster, and with less energy, such as Lisp machines, neuromorphic engineering, event cameras, and physical neural networks. As of 2023, the market for AI hardware is dominated by GPUs. | Hardware for artificial intelligence | 0.80873 |
23,629 | Since the 2010s, advances in computer hardware have led to more efficient methods for training deep neural networks that contain many layers of non-linear hidden units and a very large output layer. By 2019, graphics processing units (GPUs), often with AI-specific enhancements, had displaced central processing units (C... | Hardware for artificial intelligence | 0.80873 |
23,630 | Lisp machines were developed in the late 1970s and early 1980s to make Artificial intelligence programs written in the programming language Lisp run faster. | Hardware for artificial intelligence | 0.80873 |
23,631 | On December 14, 1900, Planck reported his findings to the German Physical Society, and introduced the idea of quantization for the first time as a part of his research on black-body radiation. As a result of his experiments, Planck deduced the numerical value of h, known as the Planck constant, and reported more precis... | Quantum | 0.808727 |
23,632 | For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only a... | Quantum | 0.808727 |
23,633 | In physics, a quantum (PL: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only d... | Quantum | 0.808727 |
23,634 | In mathematical physics the Knizhnik–Zamolodchikov equations, or KZ equations, are linear differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level. They form a system of complex partial differ... | KZ equation | 0.808726 |
23,635 | The action on V 1 ⊗ ⋯ ⊗ V n {\displaystyle V_{1}\otimes \dots \otimes V_{n}} by the analytic continuation of KZ equation is called monodromy representation of KZ equation. In particular, if all V i {\displaystyle V_{i}} 's have spin 1/2 representation then the linear representation obtained from KZ equation agrees with... | KZ equation | 0.808726 |
23,636 | Due to this analytic continuation, the holonomy of the KZ equation can be described by the braid group B n {\displaystyle B_{n}} introduced by Emil Artin. In general, A complex semi-simple Lie algebra g {\displaystyle {\mathfrak {g}}} and its representations ( ρ , V i ) {\displaystyle (\rho ,V_{i})} give the linear rep... | KZ equation | 0.808726 |
23,637 | Let g ^ k {\displaystyle {\hat {\mathfrak {g}}}_{k}} denote the affine Lie algebra with level k and dual Coxeter number h. Let v be a vector from a zero mode representation of g ^ k {\displaystyle {\hat {\mathfrak {g}}}_{k}} and Φ ( v , z ) {\displaystyle \Phi (v,z)} the primary field associated with it. Let t a {\disp... | KZ equation | 0.808726 |
23,638 | It is also possible to deduce the Knizhnik–Zamodchikov equations without explicit use of vertex algebras. The termΦ(vi, zi) may be replaced in the correlation function by its commutator with Lr where r = 0, ±1. The result can be expressed in terms of the derivative with respect to zi. On the other hand, Lr is also give... | KZ equation | 0.808726 |
23,639 | In physics, chemistry and related fields, a kinetic scheme is a network of states and connections between them representing the scheme of a dynamical process. Usually a kinetic scheme represents a Markovian process, while for non-Markovian processes generalized kinetic schemes are used. Figure 1 shows an illustration o... | Kinetic scheme | 0.808724 |
23,640 | In mathematics and computer science, the middle-square method is a method of generating pseudorandom numbers. In practice it is a highly flawed method for many practical purposes, since its period is usually very short and it has some severe weaknesses; repeated enough times, the middle-square method will either begin ... | Middle-square method | 0.808722 |
23,641 | The cross chess board geometry has the same features as hexagon-based chessboards; however, diagonals and ranks are defined differently in cross chess from Gliński's and Shafran's hexagonal variants, resulting in move possibilities more akin to standard chess. (E.g., a bishop has six diagonal move directions in Glinski... | Cross chess | 0.80872 |
23,642 | In number theory, the Gaussian moat problem asks whether it is possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded. More colorfully, if one imagines the Gaussian primes to be stepping stones in a sea of complex numbers,... | Gaussian moat | 0.808719 |
23,643 | Oligo Primer Analysis Software by Molecular Biology Insights | OLIGO Primer Analysis Software | 0.808714 |
23,644 | In essence this algorithm shows how the presence of a cyclic structure in a DNA code reduces the complexity of the problem of testing the codewords for secondary structures. Novel constructions of such codes include using cyclic reversible extended generalized Hadamard matrices, and a binary approach. Before diving int... | DNA code construction | 0.808711 |
23,645 | The theorems that follow present conditions that ensure M-invariance. In conjunction with a certain uniformity property of polynomial coefficients, these conditions yield a simple method by which complex Hadamard matrices with cyclic core can be constructed. The goal here is to find cyclic matrix E = E c {\displaystyle... | DNA code construction | 0.808711 |
23,646 | Paradox is a relational database management system currently published by Corel Corporation. It was originally released for MS-DOS by Ansa Software, and then updated by Borland after it bought the company. In mid 1991 Borland began the process to acquire Ashton-Tate and its competing dBase product line; A Windows versi... | Paradox database | 0.808709 |
23,647 | The features that distinguished Paradox/DOS were: An enhanced design and implementation of visual Query by Example that was supported by an AI engine for heuristic, dynamic query optimization. Effective use of conventional, extended, and expanded memory – caching data tables and particularly indexes, which caused Parad... | Paradox database | 0.808709 |
23,648 | Paradox for DOS was a relational database management system originally written by Richard Schwartz and Robert Shostak, and released by their Belmont, California-based company Ansa Software in 1985.The New York Times described it as "among the first of an emerging generation of software making extensive use of artificia... | Paradox database | 0.808709 |
23,649 | Proteins of the general three-finger fold are widely distributed among metazoans. A 2008 bioinformatics study identified about 45 examples of such proteins, containing up to three three-finger domains, represented in the human genome. A more recent profile of the Ly6/uPAR gene family identified 35 human and at least 61... | Three-finger protein | 0.808704 |
23,650 | The definitions and results in this section are taken from the 1913 text Plane and Solid Geometry by George Wentworth and David Eugene Smith (Wentworth & Smith 1913). A cylindrical surface is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane ... | Cylinder | 0.808704 |
23,651 | A cylinder (from Ancient Greek κύλινδρος (kúlindros) 'roller, tumbler') has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface i... | Cylinder | 0.808704 |
23,652 | Tensor networks have been adapted for supervised learning, taking advantage of similar mathematical structure in variational studies in quantum mechanics and large-scale machine learning. This crossover has spurred collaboration between researchers in artificial intelligence and quantum information science. In June 201... | Tensor network | 0.808704 |
23,653 | This result is due to Eilenberg. For h and k multiplicatively independent, a sequence is both h-automatic and k-automatic if and only if it is ultimately periodic. This result is due to Cobham also known as Cobham's theorem, with a multidimensional generalisation due to Semenov. If u(n) is a k-automatic sequence over a... | Automatic sequence | 0.808702 |
23,654 | Let φ {\displaystyle \varphi } be a k-uniform morphism of a free monoid Σ ∗ {\displaystyle \Sigma ^{*}} and let τ {\displaystyle \tau } be a coding (that is, a 1 {\displaystyle 1} -uniform morphism), as in the automata-theoretic case. If w {\displaystyle w} is a fixed point of φ {\displaystyle \varphi } —that is, if w ... | Automatic sequence | 0.808702 |
23,655 | Let u(n) be a sequence over an alphabet Σ and suppose that there is an injective function β from Σ to the finite field Fq, where q = pn for some prime p. The associated formal power series is ∑ i ≥ 0 β ( u ( i ) ) X i . {\displaystyle \sum _{i\geq 0}\beta (u(i))X^{i}.} Then the sequence u is q-automatic if and only if ... | Automatic sequence | 0.808702 |
23,656 | In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is k) is an infinite sequence of terms characterized by a finite automaton. The n-th term of an automatic sequence a(n) is... | Automatic sequence | 0.808702 |
23,657 | In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube. There are 6 truncations for the 7-cube. Vertices of the truncated 7-cube are located as pairs on the edge of the 7-cube. | Bitruncated 7-cube | 0.8087 |
23,658 | Lee, Peter M. Bayesian Statistics: An Introduction. Fourth Edition (2012), John Wiley ISBN 978-1-1183-3257-3 Carlin, Bradley P. & Louis, Thomas A. | Bayesian methods | 0.808699 |
23,659 | (2007) Introduction to Bayesian Statistics: Second Edition, John Wiley ISBN 0-471-27020-2 Winkler, Robert L (2003). Introduction to Bayesian Inference and Decision (2nd ed.). Probabilistic. | Bayesian methods | 0.808699 |
23,660 | ISBN 978-0-534-23476-8. Morris H. DeGroot & Mark J. Schervish (2002). Probability and Statistics (third ed.). | Bayesian methods | 0.808699 |
23,661 | (1996). Statistics: A Bayesian Perspective. Duxbury. | Bayesian methods | 0.808699 |
23,662 | If P ( M ) = 0 {\displaystyle P(M)=0} then P ( M ∣ E ) = 0 {\displaystyle P(M\mid E)=0} . If P ( M ) = 1 {\displaystyle P(M)=1} , then P ( M | E ) = 1 {\displaystyle P(M|E)=1} . This can be interpreted to mean that hard convictions are insensitive to counter-evidence. The former follows directly from Bayes' theorem. Th... | Bayesian methods | 0.808699 |
23,663 | However, if the random variable has an infinite but countable probability space (i.e., corresponding to a die with infinite many faces) the 1965 paper demonstrates that for a dense subset of priors the Bernstein-von Mises theorem is not applicable. In this case there is almost surely no asymptotic convergence. Later in... | Bayesian methods | 0.808699 |
23,664 | Consider the behaviour of a belief distribution as it is updated a large number of times with independent and identically distributed trials. For sufficiently nice prior probabilities, the Bernstein-von Mises theorem gives that in the limit of infinite trials, the posterior converges to a Gaussian distribution independ... | Bayesian methods | 0.808699 |
23,665 | Let the vector θ {\displaystyle {\boldsymbol {\theta }}} span the parameter space. Let the initial prior distribution over θ {\displaystyle {\boldsymbol {\theta }}} be p ( θ ∣ α ) {\displaystyle p({\boldsymbol {\theta }}\mid {\boldsymbol {\alpha }})} , where α {\displaystyle {\boldsymbol {\alpha }}} is a set of paramet... | Bayesian methods | 0.808699 |
23,666 | Bayesian inference has been applied in different Bioinformatics applications, including differential gene expression analysis. Bayesian inference is also used in a general cancer risk model, called CIRI (Continuous Individualized Risk Index), where serial measurements are incorporated to update a Bayesian model which i... | Bayesian methods | 0.808699 |
23,667 | Bayes procedures with respect to more general prior distributions have played a very important role in the development of statistics, including its asymptotic theory." "There are many problems where a glance at posterior distributions, for suitable priors, yields immediately interesting information. Also, this techniqu... | Bayesian methods | 0.808699 |
23,668 | They are useful because the property of being Bayes is easier to analyze than admissibility." "In decision theory, a quite general method for proving admissibility consists in exhibiting a procedure as a unique Bayes solution." "In the first chapters of this work, prior distributions with finite support and the corresp... | Bayesian methods | 0.808699 |
23,669 | Laser science or laser physics is a branch of optics that describes the theory and practice of lasers.Laser science is principally concerned with quantum electronics, laser construction, optical cavity design, the physics of producing a population inversion in laser media, and the temporal evolution of the light field ... | Laser Physics | 0.808698 |
23,670 | The flux control summation theorem was discovered independently by the Kacser/Burns group and the Heinrich/Rapoport group in the early 1970s and late 1960s. The flux control summation theorem implies that metabolic fluxes are systemic properties and that their control is shared by all reactions in the system. When a si... | Metabolic Control Analysis | 0.808693 |
23,671 | Given the flux expression, it is possible to derive the flux control coefficients by differentiation and scaling of the flux expression. This can be done for the general case of n {\displaystyle n} steps: C i J = 1 k i ∏ j = i n q j ∑ j = 1 n 1 k j ∏ k = j n q k {\displaystyle C_{i}^{J}={\frac {{\frac {1}{k_{i}}}\prod ... | Metabolic Control Analysis | 0.808693 |
23,672 | s i − 1 {\displaystyle s_{i-1}} is the substrate and s i {\displaystyle s_{i}} the product. If we recall that the equilibrium constant for this simple reaction is: K e q = q i = k i k − i = s i s i − 1 {\displaystyle K_{eq}=q_{i}={\frac {k_{i}}{k_{-i}}}={\frac {s_{i}}{s_{i-1}}}} we can modify the mass-action kinetic eq... | Metabolic Control Analysis | 0.808693 |
23,673 | The connectivity theorems are specific relationships between elasticities and control coefficients. They are useful because they highlight the close relationship between the kinetic properties of individual reactions and the system properties of a pathway. Two basic sets of theorems exists, one for flux and another for... | Metabolic Control Analysis | 0.808693 |
23,674 | It is possible to combine the summation with the connectivity theorems to obtain closed expressions that relate the control coefficients to the elasticity coefficients. For example, consider the simplest non-trivial pathway: X o → S → X 1 {\displaystyle X_{o}\rightarrow S\rightarrow X_{1}} We assume that X o {\displays... | Metabolic Control Analysis | 0.808693 |
23,675 | It is a regularly updated online resource that contains >13,000 entries from ~1,000 distinct references. Examples of data include transcription and translation rates, organism and organelle sizes, metabolites concentrations and growth rates. Entries are provided with full reference and details such as measurement metho... | BioNumbers | 0.808693 |
23,676 | BioNumbers is a free-access database of quantitative data in biology designed to provide the scientific community with access to the large amount of data now generated in the biological literature. This aims to make quantitative values more easily available, to aid fields such as systems biology. The BioNumbers project... | BioNumbers | 0.808693 |
23,677 | The database is a Wikipedia-format community collaborative initiative began in 2007 by Ron Milo, Paul Jorgensen and Mike Springer at the systems biology department at Harvard Medical School. It is currently managed and curated at the Milo lab from the Weizmann Institute of Science. BioNumbers was being supported by the... | BioNumbers | 0.808693 |
23,678 | Ocean Biology DAAC (OB.DAAC): ocean biology, ocean color, ocean biogeochemistry, sea surface temperature. Physical Oceanography DAAC (PO DAAC): sea surface temperature, ocean winds, circulation and currents, topography and gravity. Socioeconomic Data and Applications Data Center (SEDAC): human interactions, land use, e... | Distributed Active Archive Centers | 0.808692 |
23,679 | Level 1 Atmosphere Archive and Distribution System (LAADS) DAAC: radiance, atmosphere. National Snow and Ice Data Center (NSIDC DAAC): snow, ice, cryosphere, climate. Oak Ridge National Laboratory DAAC (ORNL DAAC): biogeochemical dynamics, terrestrial ecology, carbon and nitrogen cycle, environmental processes. | Distributed Active Archive Centers | 0.808692 |
23,680 | Atmospheric Science Data Center (ASDC): radiation budget, clouds, aerosols, tropospheric chemistry. Crustal Dynamics Data Information System (CDDIS): satellite geodesy. Global Hydrometeorology Resource Center (GHRC) DAAC: severe weather interactions, lightning, atmospheric convection. | Distributed Active Archive Centers | 0.808692 |
23,681 | A Distributed Active Archive Center (DAAC) is a part of EOSDIS. DAACs process, archive, document, and distribute data from NASA's past and current Earth Observing System (EOS) satellites and field measurement programs. Each of the twelve DAACs serves one or more specific Earth science disciplines and provides its user ... | Distributed Active Archive Centers | 0.808692 |
23,682 | In pseudo-Euclidean spaces and symplectic vector spaces, for example, orthogonal complements exist. However, these spaces may have null vectors that are orthogonal to themselves, and consequently there exist subspaces N {\displaystyle N} such that N ∩ N ⊥ ≠ { 0 } {\displaystyle N\cap N^{\perp }\neq \{0\}} . As a result... | Vector subspace | 0.808692 |
23,683 | In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. | Vector subspace | 0.808692 |
23,684 | In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. | Non-binding constraint | 0.808691 |
23,685 | WolframMathWorld has a page titled "Triangle conics" which gives a list of 42 items (not all of them are conics) without giving a definition of triangle conic. However, Paris Pamfilos in his extensive collection of topics in geometry and topics in other fields related to geometry defines a triangle conic as a "conic ci... | Triangle conic | 0.808684 |
23,686 | In triangle geometry, a triangle conic is a conic in the plane of the reference triangle and associated with it in some way. For example, the circumcircle and the incircle of the reference triangle are triangle conics. Other examples are the Steiner ellipse which is an ellipse passing through the vertices and having it... | Triangle conic | 0.808684 |
23,687 | In the cradle-to-cradle model, all materials used in industrial or commercial processes—such as metals, fibers, dyes—fall into one of two categories: "technical" or "biological" nutrients. Technical nutrients are strictly limited to non-toxic, non-harmful synthetic materials that have no negative effects on the natural... | Cradle-to-cradle design | 0.808682 |
23,688 | Building off the whole systems approach of John T. Lyle's regenerative design, the model in its broadest sense is not limited to industrial design and manufacturing; it can be applied to many aspects of human civilization such as urban environments, buildings, economics and social systems. The term "Cradle to Cradle" i... | Cradle-to-cradle design | 0.808682 |
23,689 | The Ford River Rouge Complex redevelopment, cleaning 20 billion US gallons (76,000,000 m3) of rainwater annually. The Netherlands Institute of Ecology (NIOO-KNAW) planned to make its laboratory and office complex completely cradle-to-cradle compliant. Several private houses and communal buildings in the Netherlands. Fa... | Cradle-to-cradle design | 0.808682 |
23,690 | The method uses the term 'risk' in the sense of hazard (as opposed to consequence and likelihood). Material reutilization, which is about recovery and recycling at the end of product life. Assessment of energy required for production, which for the highest level of certification needs to be based on at least 50% renewa... | Cradle-to-cradle design | 0.808682 |
23,691 | Characters also can be defined almost verbatim for weight modules over a Kac–Moody or generalized Kac–Moody Lie algebra. | Algebraic character | 0.808681 |
23,692 | The algebraic character of the Verma module M λ {\displaystyle M_{\lambda }} with the highest weight λ {\displaystyle \lambda } is given by the formula c h ( M λ ) = e λ ∏ α > 0 ( 1 − e − α ) , {\displaystyle ch(M_{\lambda })={\frac {e^{\lambda }}{\prod _{\alpha >0}(1-e^{-\alpha })}},} with the product taken over the s... | Algebraic character | 0.808681 |
23,693 | An algebraic character is a formal expression attached to a module in representation theory of semisimple Lie algebras that generalizes the character of a finite-dimensional representation and is analogous to the Harish-Chandra character of the representations of semisimple Lie groups. | Algebraic character | 0.808681 |
23,694 | Algebraic characters are defined for locally-finite weight modules and are additive, i.e. the character of a direct sum of modules is the sum of their characters. On the other hand, although one can define multiplication of the formal exponents by the formula e μ ⋅ e ν = e μ + ν {\displaystyle e^{\mu }\cdot e^{\nu }=e^... | Algebraic character | 0.808681 |
23,695 | Let g {\displaystyle {\mathfrak {g}}} be a semisimple Lie algebra with a fixed Cartan subalgebra h , {\displaystyle {\mathfrak {h}},} and let the abelian group A = Z ] {\displaystyle A=\mathbb {Z} ]} consist of the (possibly infinite) formal integral linear combinations of e μ {\displaystyle e^{\mu }} , where μ ∈ h ∗ ... | Algebraic character | 0.808681 |
23,696 | This can be proved using the Chinese remainder theorem. Carmichael's theorem explains how to compute λ of a prime power pr: for a power of an odd prime and for 2 and 4, λ(pr) is equal to the Euler totient φ(pr); for powers of 2 greater than 4 it is equal to half of the Euler totient: λ ( p r ) = { 1 2 φ ( p r ) if p = ... | Reduced totient | 0.80868 |
23,697 | By the unique factorization theorem, any n > 1 can be written in a unique way as n = p 1 r 1 p 2 r 2 ⋯ p k r k {\displaystyle n=p_{1}^{r_{1}}p_{2}^{r_{2}}\cdots p_{k}^{r_{k}}} where p1 < p2 < ... < pk are primes and r1, r2, ..., rk are positive integers. Then λ(n) is the least common multiple of the λ of each of its pr... | Reduced totient | 0.80868 |
23,698 | In number theory, a branch of mathematics, the Carmichael function λ(n) of a positive integer n is the smallest positive integer m such that a m ≡ 1 ( mod n ) {\displaystyle a^{m}\equiv 1{\pmod {n}}} holds for every integer a coprime to n. In algebraic terms, λ(n) is the exponent of the multiplicative group of integers... | Reduced totient | 0.80868 |
23,699 | The corresponding proper time is d τ 2 = − ( d x 0 ) 2 + 4 ( x 3 ) ( d x 0 ) ( d x 2 ) − 2 ( d x 1 ) ( d x 2 ) − 2 ( x 3 ) 2 ( d x 2 ) 2 − ( d x 3 ) 2 . {\displaystyle {d\tau }^{2}=-(dx^{0})^{2}+4(x^{3})(dx^{0})(dx^{2})-2(dx^{1})(dx^{2})-2(x^{3})^{2}(dx^{2})^{2}-(dx^{3})^{2}.} The Riemann tensor has only one algebraica... | Ozsváth–Schücking metric | 0.80868 |
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