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78,500 | Therefore, Ran(T) = T(Ker(F)) + T(Ker(F)⊥) is closed, and this proves the theorem. A more complete treatment of Atkinson's Theorem is in the reference by Arveson: it shows that if B is a Banach space, an operator is Fredholm iff it is invertible modulo a finite rank operator (and that the latter is equivalent to being ... | Atkinson's theorem | 0.785718 |
78,501 | Extend this inverse by 0 on Ran(T)⊥ = Ker(T*) to an operator S defined on all of H. Then I − TS is the finite-rank projection onto Ker(T*), and I − ST is the projection onto Ker(T). This proves the only if part of the theorem. For the converse, suppose now that ST = I + C2 for some compact operator C2. | Atkinson's theorem | 0.785718 |
78,502 | The outline of a proof is as follows. For the ⇒ implication, express H as the orthogonal direct sum H = Ker ( T ) ⊥ ⊕ Ker ( T ) . {\displaystyle H=\operatorname {Ker} (T)^{\perp }\oplus \operatorname {Ker} (T).} The restriction T: Ker(T)⊥ → Ran(T) is a bijection, and therefore invertible by the open mapping theorem... | Atkinson's theorem | 0.785718 |
78,503 | In operator theory, Atkinson's theorem (named for Frederick Valentine Atkinson) gives a characterization of Fredholm operators. | Atkinson's theorem | 0.785718 |
78,504 | Simulations are not primarily methods for optimization. To optimize the geometry of a building or the procedure with respect to evacuation time, a target function has to be specified and minimized. Accordingly, one or several variables must be identified which are subject to variation. | Evacuation simulation | 0.785717 |
78,505 | There exist general models with spatial aspects of pedestrian steps Social Force Model: continuous, microscopic model, based on equations from physics Queuing models: macroscopic models which are based on the graphical representation of the geometry. The movement of the persons is represented as a flow on this graph. P... | Evacuation simulation | 0.785717 |
78,506 | Since 1998, there has been an ascendancy in the value of interdisciplinary research and teaching and a growth in the number of bachelor's degrees awarded at U.S. universities classified as multi- or interdisciplinary studies. The number of interdisciplinary bachelor's degrees awarded annually rose from 7,000 in 1973 to... | Interdisciplinary studies | 0.785717 |
78,507 | Search involves a neural network in the brain for processing motion and location, and controlling saccades. This neural network is sensitive to color and to change; color and flash-coding (temporally-varying brightness) can complement each other to enhance search speed, without mutual interference.If there are N items ... | Color coding in data visualization | 0.785716 |
78,508 | Salient colors might be used, for example, to highlight patterns or to enable rapid search: Another application of color coding is to show symmetries in visualized data. Color coding can connect and untangle, e.g., trends on a plot, or the continuity of axons in the neural connectome. New applications of the innate ski... | Color coding in data visualization | 0.785716 |
78,509 | The optimization method has been extended to alternative objective functions. It has been applied to complex display situations and to small symbols. Technical color measurement and optimized color difference can generate several alternative equally-effective codes that exploit the full gamut of the display and human c... | Color coding in data visualization | 0.785716 |
78,510 | Because the smallest color differences interfere with search while large-enough color differences do not interfere (see Figure 3), the optimization objective is to maximize the minimum calculated color-difference, among the n(n-1)/2 color differences in an n-color code, in order to derive a large number (n) of distinct... | Color coding in data visualization | 0.785716 |
78,511 | Origins of color coding include rubrics, the Four Color Theorem of cartography and Jacques Bertin's 1967 book, Sémiologie Graphique (Semiology of Graphics). Contemporary color coding for data visualization is enabled by four technologies: statistics, color technology, displays and computing. Visualization of data was p... | Color coding in data visualization | 0.785716 |
78,512 | An estimated 120,000 tons were produced in 2007". According to DuPont, the Bio-PDO process uses 40% less energy than conventional processes, Because of DuPont and Tate & Lyle's success in developing a renewable Bio-PDO process, the American Chemical Society awarded the Bio-PDO research teams the "2007 Heroes of Chemist... | Trimethylene glycol | 0.785715 |
78,513 | In organic chemistry, Wittig reagents are organophosphorus compounds of the formula R3P=CHR', where R is usually phenyl. They are used to convert ketones and aldehydes to alkenes: | Wittig reagents | 0.785715 |
78,514 | The dimension theory of commutative rings behaves poorly over non-Noetherian rings; the very fundamental theorem, Krull's principal ideal theorem, already relies on the "Noetherian" assumption. Here, in fact, the "Noetherian" assumption is often not enough and (Noetherian) universally catenary rings, those satisfying a... | Noetherian domain | 0.785715 |
78,515 | Over a commutative Noetherian ring, each ideal has a primary decomposition, meaning that it can be written as an intersection of finitely many primary ideals (whose radicals are all distinct) where an ideal Q is called primary if it is proper and whenever xy ∈ Q, either x ∈ Q or y n ∈ Q for some positive integer n. For... | Noetherian domain | 0.785715 |
78,516 | In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathed Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective special unitary groups over a finite field of odd order, depending on a certain c... | Alperin–Brauer–Gorenstein theorem | 0.785714 |
78,517 | Computational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realize financial models or systems.Computational fina... | Computational Finance | 0.785714 |
78,518 | Many of the new techniques came from signal processing and speech recognition rather than traditional fields of computational economics like optimization and time series analysis.By the end of the 1980s, the winding down of the Cold War brought a large group of displaced physicists and applied mathematicians, many from... | Computational Finance | 0.785714 |
78,519 | The birth of computational finance as a discipline can be traced to Harry Markowitz in the early 1950s. Markowitz conceived of the portfolio selection problem as an exercise in mean-variance optimization. This required more computer power than was available at the time, so he worked on useful algorithms for approximate... | Computational Finance | 0.785714 |
78,520 | The offset into the segment is the sum of the base offset and the contents of the index register.The software was modular based on the universal model of computation and the lambda calculus. Six Church instructions hide the details of a named function application using capability keys for the typed concepts of variable... | Plessey System 250 | 0.785713 |
78,521 | The laws of the lambda calculus are implemented by the Church instructions with micro-programmed access to the reserved (hidden) capability registers. The software is incrementally assembled as object-oriented machine-code linked by the capability keys. The structure of function abstractions, including those for memory... | Plessey System 250 | 0.785713 |
78,522 | Immutable capability keys represent named lambda calculus variables. This Church side is a lambda calculus meta-machine. The other side is an object-oriented machine of binary objects, programmed functions, capability lists defining function abstractions, storage for threads of computation (lambda calculus applications... | Plessey System 250 | 0.785713 |
78,523 | Instead, the pure object capability model of PP250 always requires a limited capability key to define the authority to operate. PP250 separated binary data from capability data to protect access rights, simplify the computer and speed garbage collection. The Church machine encapsulates and context limits the Turing mac... | Plessey System 250 | 0.785713 |
78,524 | A Church–Turing machine is a digital computer that encapsulates the symbols in a thread of computation as a chain of protected abstractions by enforcing the dynamic binding laws of Alonzo Church's lambda calculus Other capability based computers, which include CHERI and CAP computers, are hybrids. They retain default i... | Plessey System 250 | 0.785713 |
78,525 | In general, constant-recursive sequences are closed under the following operations, where s = ( s n ) n ∈ N , t = ( t n ) n ∈ N {\displaystyle s=(s_{n})_{n\in \mathbb {N} },t=(t_{n})_{n\in \mathbb {N} }} denote constant-recursive sequences, f ( x ) , g ( x ) {\displaystyle f(x),g(x)} are their generating functions, and... | Linear recursive sequence | 0.785712 |
78,526 | In general, for sequences of integers or rationals, the closed formula will use algebraic numbers. The complex numbers r 1 , … , r n {\displaystyle r_{1},\ldots ,r_{n}} are the roots of the characteristic polynomial (or "auxiliary polynomial") of the recurrence: x d − c 1 x d − 1 − ⋯ − c d − 1 x − c d {\displaystyle x^... | Linear recursive sequence | 0.785712 |
78,527 | The d coefficients c 1 , c 2 , … , c d {\displaystyle c_{1},c_{2},\dots ,c_{d}} must be coefficients ranging over the same domain as the sequence (integers, rational numbers, algebraic numbers, real numbers, or complex numbers). For example for a rational constant-recursive sequence, s i {\displaystyle s_{i}} and c i {... | Linear recursive sequence | 0.785712 |
78,528 | A constant-recursive sequence is any sequence of integers, rational numbers, algebraic numbers, real numbers, or complex numbers s 0 , s 1 , s 2 , s 3 , … {\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } (written as ( s n ) n = 0 ∞ {\displaystyle (s_{n})_{n=0}^{\infty }} as a shorthand) satisfying a formula of the form ... | Linear recursive sequence | 0.785712 |
78,529 | S4000P - International specification for developing and continuously improving preventive maintenance is a specification developed jointly by a multinational team from the Aerospace and Defence Industries Association of Europe (ASD) and Aerospace Industries Association (AIA). S4000P is part of the S-Series of ILS speci... | S4000P | 0.785712 |
78,530 | A macroscopic quantum state is a state of matter in which macroscopic properties, such as mechanical motion, thermal conductivity, electrical conductivity and viscosity, can be described only by quantum mechanics rather than merely classical mechanics. This occurs primarily at low temperatures where little thermal moti... | Macroscopic quantum state | 0.78571 |
78,531 | Wilson's theorem can be expressed in general as ( n − 1 ) ! ( p − n ) ! ≡ ( − 1 ) n mod p {\displaystyle (n-1)! | Wilson prime | 0.785708 |
78,532 | + 1 {\displaystyle (p-1)!+1} . Both are named for 18th-century English mathematician John Wilson; in 1770, Edward Waring credited the theorem to Wilson, although it had been stated centuries earlier by Ibn al-Haytham.The only known Wilson primes are 5, 13, and 563 (sequence A007540 in the OEIS). | Wilson prime | 0.785708 |
78,533 | In number theory, a Wilson prime is a prime number p {\displaystyle p} such that p 2 {\displaystyle p^{2}} divides ( p − 1 ) ! + 1 {\displaystyle (p-1)!+1} , where " ! {\displaystyle !} " denotes the factorial function; compare this with Wilson's theorem, which states that every prime p {\displaystyle p} divides ( p − ... | Wilson prime | 0.785708 |
78,534 | However, if it is only required that α + β + γ ≤ π, it is possible to identify the triangle with the corresponding geodesic triangle in the hyperbolic plane with the Poincaré metric (or the Euclidean plane if equality holds). It is a classical result from hyperbolic geometry that the hyperbolic medians intersect in the... | Orbifold | 0.785707 |
78,535 | Historically one of the most important applications of orbifolds in geometric group theory has been to triangles of groups. This is the simplest 2-dimensional example generalising the 1-dimensional "interval of groups" discussed in Serre's lectures on trees, where amalgamated free products are studied in terms of actio... | Orbifold | 0.785707 |
78,536 | When the fields related with these twisted states acquire a non-zero vacuum expectation value, the singularity is deformed, i.e. the metric is changed and becomes regular at this point and around it. An example for a resulting geometry is the Eguchi–Hanson spacetime. From the point of view of D-branes in the vicinity o... | Orbifold | 0.785707 |
78,537 | In string theory, the word "orbifold" has a slightly new meaning. For mathematicians, an orbifold is a generalization of the notion of manifold that allows the presence of the points whose neighborhood is diffeomorphic to a quotient of Rn by a finite group, i.e. Rn/Γ. In physics, the notion of an orbifold usually descr... | Orbifold | 0.785707 |
78,538 | The orbihedron fundamental group can be naturally identified with the orbispace fundamental group of the associated orbispace. This follows by applying the simplicial approximation theorem to segments of an orbispace path lying in an orbispace chart: it is a straightforward variant of the classical proof that the funda... | Orbifold | 0.785707 |
78,539 | The time derivative of the differential variable, y ˙ {\displaystyle {\dot {y}}} , depends on itself, y {\displaystyle y} , on the algebraic variable, z {\displaystyle z} , and on the time, t {\displaystyle t} . The second equation can be seen as a constraint on differential variable, y {\displaystyle y} . Let us take ... | Segregated Runge–Kutta methods | 0.785706 |
78,540 | Consider an index 2 DAE defined as follows: y ˙ ( t ) = f ( y ( t ) , z ( t ) ) , 0 = g ( y ( t ) ) . {\displaystyle {\begin{aligned}{\dot {y}}(t)&=f(y(t),z(t)),\\0&=g(y(t)).\end{aligned}}} where y ( t ) ∈ R n {\displaystyle y(t)\in \mathbb {R} ^{n}} , z ( t ) ∈ R m {\displaystyle z(t)\in \mathbb {R} ^{m}} , f: R n + m... | Segregated Runge–Kutta methods | 0.785706 |
78,541 | The Segregated Runge–Kutta (SRK) method is a family of IMplicit–EXplicit (IMEX) Runge–Kutta methods that were developed to approximate the solution of differential algebraic equations (DAE) of index 2. The SRK method were motivated as a numerical method for the time integration of the incompressible Navier–Stokes equat... | Segregated Runge–Kutta methods | 0.785706 |
78,542 | R's capabilities are extended through user-created packages, which offer statistical techniques, graphical devices, import/export, reporting (RMarkdown, knitr, Sweave), etc. These packages and their easy installation and use has been cited as driving the language's widespread adoption in data science. The packaging sys... | R Statistics | 0.785705 |
78,543 | MPhil in Technology Policy at University of Cambridge, Judge Business School and Department of Engineering, University of Cambridge, United Kingdom (born out of the Cambridge–MIT Institute) MSc in Technology and Policy and Engineering and Systems Division at MIT Engineering and Public Policy at Carnegie Mellon Universi... | Technology policy | 0.785705 |
78,544 | The Bioconductor project provides packages for genomic data analysis, including object-oriented data handling and analysis tools for data from Affymetrix, cDNA microarray, and next-generation high-throughput sequencing methods.A group of packages called the Tidyverse, which can be considered a "dialect" of the R langua... | R Statistics | 0.785705 |
78,545 | With the prevalence of technology throughout the 2000s, its power in politics have raised concerns about the speed of technological change and difficulty in regulating it. In the 2016 U.S. presidential election, Neil Jenkins, the director in the Office of Cybersecurity and Communications at the Department of Homeland S... | Technology policy | 0.785705 |
78,546 | For example, with artificial intelligence gaining prominence throughout society, scientists fear that its potential of developing the cognitive skills of humans could force many individuals out of jobs and even put the lives of innocent people in danger. Most famously, scientist and entrepreneur Elon Musk has is very p... | Technology policy | 0.785705 |
78,547 | The DARPA initiative to support computing was the impetus for the Internet Protocol stack. In the same way that scientific consortiums like CERN for high-energy physics have a commitment to public knowledge, access to this public knowledge in physics led directly to CERN's sponsorship of development of the World Wide W... | Technology policy | 0.785705 |
78,548 | If K is a convex subset of Φ(A), the ultraweak closure of K (denoted by K−)coincides with the strong-operator, weak-operator closures of K in B(HΦ). The norm closure of K is Φ(A) ∩ K−. One can give a description of norm-closed left ideals in Φ(A) from the structure theory of ideals for von Neumann algebras, which is re... | Universal representation (C*-algebra) | 0.785705 |
78,549 | If π is a representation of A, there is a projection P in the center of Φ(A)− and a *-isomorphism α from the von Neumann algebra Φ(A)−P onto π(A)− such that π(a) = α(Φ(a)P) for each a in A. This can be conveniently captured in the commutative diagram below: Here ψ is the map that sends a to aP, α0 denotes the restricti... | Universal representation (C*-algebra) | 0.785705 |
78,550 | Definition. Let A be a C*-algebra with state space S. The representation Φ := ∑ ρ ∈ S ⊕ π ρ {\displaystyle \Phi :=\sum _{\rho \in S}\oplus \;\pi _{\rho }} on the Hilbert space H Φ {\displaystyle H_{\Phi }} is known as the universal representation of A.As the universal representation is faithful, A is *-isomorphic to th... | Universal representation (C*-algebra) | 0.785705 |
78,551 | Let Φ(A)− denote the weak-operator closure of Φ(A) in B(HΦ). Each bounded linear functional ρ on Φ(A) is weak-operator continuous and extends uniquely preserving norm, to a weak-operator continuous linear functional ρ on the von Neumann algebra Φ(A)−. If ρ is hermitian, or positive, the same is true of ρ. The mapping ρ... | Universal representation (C*-algebra) | 0.785705 |
78,552 | Let f and g be continuous, real-valued functions on C4m and C4n, respectively, σ1, σ2, ..., σm be ultraweakly continuous, linear functionals on a von Neumann algebra R acting on the Hilbert space H, and ρ1, ρ2, ..., ρn be bounded linear functionals on R such that, for each a in R, f ( σ 1 ( a ) , σ 1 ( a ∗ ) , σ 1 ( a ... | Universal representation (C*-algebra) | 0.785705 |
78,553 | Let A be a C*-algebra acting on a Hilbert space H. For ρ in A* and S in Φ(A)−, let Sρ in A* be defined by Sρ(a) = ρ∘Φ−1(Φ(a)S) for all a in A. If P is the projection in the above commutative diagram when π:A → B(H) is the inclusion mapping, then ρ in A* is ultraweakly continuous if and only if ρ = Pρ. A functional ρ in... | Universal representation (C*-algebra) | 0.785705 |
78,554 | In the theory of C*-algebras, the universal representation of a C*-algebra is a faithful representation which is the direct sum of the GNS representations corresponding to the states of the C*-algebra. The various properties of the universal representation are used to obtain information about the ideals and quotients o... | Universal representation (C*-algebra) | 0.785705 |
78,555 | Issuers: They need HSMs for issuing cards, holding keys, and managing the cryptography associated with the cards. Issuers also need HSMs to authorize the cryptographic flow. Acquirers: According to the Four Corner Model, Acquirers must manage all financial terminal keys for the Merchants and process the cryptographic f... | Four Corners Model for Payment Security | 0.785704 |
78,556 | Cryptography is requested between all actors involved in the Four Corner Model. The many cryptographic keys and operations must be performed within a secure environment, such as a hardware security module (HSM). HSMs are a necessity in handling an increasing number of transactions and warding off attacks from skilled c... | Four Corners Model for Payment Security | 0.785704 |
78,557 | The Issuer is the bank or other financial institution that issues the payment card given to the Cardholder. There are typically three different types of payment cards: Debit card Credit card Prepaid cardThe Issuer provides the payment cards on behalf of a card payment network. Such networks include: Visa Mastercard Dis... | Four Corners Model for Payment Security | 0.785704 |
78,558 | TGF beta receptor 2 consists of a C-terminal protein kinase domain and an N-terminal ectodomain. The ectodomain consists of a compact fold containing nine beta-strands and a single helix stabilised by a network of six intra strand disulphide bonds. The folding topology includes a central five-stranded antiparallel beta... | TGF beta receptor 2 | 0.785704 |
78,559 | The following have received a medal: 2022: Michael Tarbutt, for pioneering experimental and theoretical work on the production of ultracold molecules by laser cooling, and the applications of those molecules to quantum science and tests of fundamental physics. 2021: Carla Faria, for distinguished contributions to the t... | Institute of Physics Joseph Thomson Medal and Prize | 0.785703 |
78,560 | The Thomson Medal and Prize is an award which has been made, originally only biennially in even-numbered years, since 2008 by the British Institute of Physics for "distinguished research in atomic (including quantum optics) or molecular physics". It is named after Nobel prizewinner Sir J. J. Thomson, the British physic... | Institute of Physics Joseph Thomson Medal and Prize | 0.785703 |
78,561 | PHOENIX includes a 2 track server configuration, one with an IMMKF and another with a 1MKF. Targets with different manoeuvrability have different statistics, which is expressed by the process noise of the motion model. The process noise is a mathematical description for the uncertainty of a future position and velocity... | Phoenix (ATC) | 0.785703 |
78,562 | Multi radar track servers (1MKF, IMMKF, MSDF; d-mrts) Track distribution services (d-trksend) Configuration and distribution servers (d-dis) Recording and replay servers (d-rdr) Message servers (d-msg) Flightplan and Linkage processing servers (d-fps) Persistence Servers (d-pds) Information Data Server for direction fi... | Phoenix (ATC) | 0.785703 |
78,563 | The Hitchin functional is analogous for six-manifold to the Yang-Mills functional for the four-manifolds. The Hitchin functional is manifestly invariant under the action of the group of orientation-preserving diffeomorphisms. Theorem. Suppose that M {\displaystyle M} is a three-dimensional complex manifold and Ω {\disp... | Hitchin functional | 0.785702 |
78,564 | The Hitchin functional is a mathematical concept with applications in string theory that was introduced by the British mathematician Nigel Hitchin. Hitchin (2000) and Hitchin (2001) are the original articles of the Hitchin functional. As with Hitchin's introduction of generalized complex manifolds, this is an example o... | Hitchin functional | 0.785702 |
78,565 | The Clostridiales-1 RNA motif is a conserved RNA structure identified by bioinformatics. It is a four-stem structure common in bacteria that inhabit the human gut and is also found in a variety of bacteria classified within the order Clostridiales. Its function is unknown. | Clostridiales-1 RNA motif | 0.785702 |
78,566 | In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. The result, proved by Alan Baker (1966, 1967a, 1967b), subsumed many earlier results in transcendental number theory and solved a problem pose... | Baker's method | 0.7857 |
78,567 | By this theory, the wing has a lift force smaller than that predicted by a purely two-dimensional theory using the Kutta–Joukowski theorem. This is due to the upstream effects of the trailing vortices' added downwash on the angle of attack of the wing. This reduces the wing's effective angle of attack, decreasing the a... | Kutta–Zhukovsky theorem | 0.785697 |
78,568 | This variation is compensated by the release of streamwise vortices, called trailing vortices, due to conservation of vorticity or Kelvin Theorem of Circulation Conservation. These streamwise vortices merge to two counter-rotating strong spirals separated by distance close to the wingspan and their cores may be visible... | Kutta–Zhukovsky theorem | 0.785697 |
78,569 | Various forms of integral approach are now available for unbounded domain and for artificially truncated domain. The Kutta Joukowski theorem can be recovered from these approaches when applied to a two-dimensional airfoil and when the flow is steady and unseparated. Lifting line theory for wings, wing-tip vortices and ... | Kutta–Zhukovsky theorem | 0.785697 |
78,570 | With this approach, an explicit and algebraic force formula, taking into account of all causes (inner singularities, outside vortices and bodies, motion of all singularities and bodies, and vortex production) holds individually for each body with the role of other bodies represented by additional singularities. Hence a... | Kutta–Zhukovsky theorem | 0.785697 |
78,571 | The motion of outside singularities also contributes to forces, and the force component due to this contribution is proportional to the speed of the singularity. Individual force of each body for multiple-body rotational flow When in addition to multiple free vortices and multiple bodies, there are bound vortices and v... | Kutta–Zhukovsky theorem | 0.785697 |
78,572 | When, however, there is vortex outside the body, there is a vortex induced drag, in a form similar to the induced lift. Generalized Lagally theorem For free vortices and other bodies outside one body without bound vorticity and without vortex production, a generalized Lagally theorem holds, with which the forces are ex... | Kutta–Zhukovsky theorem | 0.785697 |
78,573 | Lagally theorem When a (mass) source is fixed outside the body, a force correction due to this source can be expressed as the product of the strength of outside source and the induced velocity at this source by all the causes except this source. This is known as the Lagally theorem. For two-dimensional inviscid flow, t... | Kutta–Zhukovsky theorem | 0.785697 |
78,574 | The lift predicted by the Kutta-Joukowski theorem within the framework of inviscid potential flow theory is quite accurate, even for real viscous flow, provided the flow is steady and unseparated. In deriving the Kutta–Joukowski theorem, the assumption of irrotational flow was used. When there are free vortices outside... | Kutta–Zhukovsky theorem | 0.785697 |
78,575 | For a heuristic argument, consider a thin airfoil of chord c {\displaystyle c} and infinite span, moving through air of density ρ {\displaystyle \rho } . Let the airfoil be inclined to the oncoming flow to produce an air speed V {\displaystyle V} on one side of the airfoil, and an air speed V + v {\displaystyle V+v} on... | Kutta–Zhukovsky theorem | 0.785697 |
78,576 | This rotating flow is induced by the effects of camber, angle of attack and the sharp trailing edge of the airfoil. It should not be confused with a vortex like a tornado encircling the airfoil. At a large distance from the airfoil, the rotating flow may be regarded as induced by a line vortex (with the rotating line p... | Kutta–Zhukovsky theorem | 0.785697 |
78,577 | Kutta–Joukowski theorem is an inviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications.Kutta–Joukowski theorem relates lift to circulation much like the Magnus effect relates side force (called Magnus force) to rotation. However, the circulation here is not induced by ro... | Kutta–Zhukovsky theorem | 0.785697 |
78,578 | The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil (and any two-dimensional body including circular cylinders) translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. The the... | Kutta–Zhukovsky theorem | 0.785697 |
78,579 | The Strasbourg Institute of Material Physics and Chemistry (IPCMS—French: Institut de Physique et Chimie des Matériaux de Strasbourg) is a joint research unit between the French National Center for Scientific Research (CNRS) and the University of Strasbourg. It was founded in 1987 and is located in the district of Cron... | Strasbourg Institute of Material Physics and Chemistry | 0.785696 |
78,580 | The IPCMS was born from a reflection initiated in the early eighties on the need to refocus and coordinate research in the physics and chemistry of condensed matter and materials. In the context of the then emerging Materials Center in Strasbourg, a first reorganization project for condensed matter physics was formaliz... | Strasbourg Institute of Material Physics and Chemistry | 0.785696 |
78,581 | The IPCMS now employs a staff of 240 including about 80 researchers and teacher-researchers and 60 technical and administrative engineers, whose activities are divided into five departments: Department of Inorganic Materials Chemistry (DCMI) Department of Organic Materials (DMO) Department of Magnetism of NanoStructure... | Strasbourg Institute of Material Physics and Chemistry | 0.785696 |
78,582 | The projects LabEX NIE and EquipEX UNION and UTEM that the IPCMS directs reflect the recognized position of the laboratory. Located on the Campus of Cronenbourg, IPCMS is affiliated with the institutes of physics and chemistry of the CNRS as well as the Faculty of Physics and Engineering, it is also affiliated with the... | Strasbourg Institute of Material Physics and Chemistry | 0.785696 |
78,583 | An alternative formulation of the modularity, useful particularly in spectral optimization algorithms, is as follows. Define S v r {\displaystyle S_{vr}} to be 1 {\displaystyle 1} if vertex v {\displaystyle v} belongs to group r {\displaystyle r} and 0 {\displaystyle 0} otherwise. Then δ ( c v , c w ) = ∑ r S v r S w r... | Modularity (networks) | 0.785695 |
78,584 | Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules.... | Modularity (networks) | 0.785695 |
78,585 | So, even weakly interconnected complete graphs, which have the highest possible density of internal edges, and represent the best identifiable communities, would be merged by modularity optimization if the network were sufficiently large. For this reason, optimizing modularity in large networks would fail to resolve sm... | Modularity (networks) | 0.785695 |
78,586 | Many scientifically important problems can be represented and empirically studied using networks. For example, biological and social patterns, the World Wide Web, metabolic networks, food webs, neural networks and pathological networks are real world problems that can be mathematically represented and topologically stu... | Modularity (networks) | 0.785695 |
78,587 | The toy model of Malliavin calculus is an irreducible Gaussian probability space X = ( Ω , F , P , H ) {\displaystyle X=(\Omega ,{\mathcal {F}},P,{\mathcal {H}})} . This is a (complete) probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} together with a closed subspace H ⊂ L 2 ( Ω , F , P ) {\dis... | Malliavin calculus | 0.785695 |
78,588 | Malliavin calculus is named after Paul Malliavin whose ideas led to a proof that Hörmander's condition implies the existence and smoothness of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. The calculus has been app... | Malliavin calculus | 0.785695 |
78,589 | P. Malliavin first initiated the calculus on infinite dimensional space. Then, the significant contributors such as S. Kusuoka, D. Stroock, J-M. Bismut, S. Watanabe, I. Shigekawa, and so on finally completed the foundations. | Malliavin calculus | 0.785695 |
78,590 | If X {\displaystyle X} is a Wiener process, the Girsanov theorem then yields the following analogue of the invariance principle: E ( F ( X + ε φ ) ) = E . {\displaystyle E(F(X+\varepsilon \varphi ))=E\left.} Differentiating with respect to ε on both sides and evaluating at ε=0, one obtains the following integration by... | Malliavin calculus | 0.785695 |
78,591 | The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications for example in stochastic filtering. | Malliavin calculus | 0.785695 |
78,592 | The Skorokhod integral operator which is conventionally denoted δ is defined as the adjoint of the Malliavin derivative in the white noise case when the Hilbert space is an L 2 {\displaystyle L^{2}} space, thus for u in the domain of the operator which is a subset of L 2 ( [ 0 , ∞ ) × Ω ) {\displaystyle L^{2}([0,\infty... | Malliavin calculus | 0.785695 |
78,593 | X {\displaystyle \lim _{\varepsilon \to 0}{\frac {1}{\varepsilon }}(F(X+\varepsilon \varphi )-F(X))=\int _{0}^{1}F'(X,dt)\varphi (t)\ \mathrm {a.e.} \ X} then F ( X ) = E ( F ( X ) ) + ∫ 0 1 H t d X t , {\displaystyle F(X)=E(F(X))+\int _{0}^{1}H_{t}\,dX_{t},} where H is the previsible projection of F'(x, (t,1]) which m... | Malliavin calculus | 0.785695 |
78,594 | One of the most useful results from Malliavin calculus is the Clark–Ocone theorem, which allows the process in the martingale representation theorem to be identified explicitly. A simplified version of this theorem is as follows: Consider the standard Wiener measure on the canonical space C {\displaystyle C} , equippe... | Malliavin calculus | 0.785695 |
78,595 | Malliavin introduced Malliavin calculus to provide a stochastic proof that Hörmander's condition implies the existence of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. His calculus enabled Malliavin to prove regula... | Malliavin calculus | 0.785695 |
78,596 | In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of derivatives of random variables. Malliavin calculus is... | Malliavin calculus | 0.785695 |
78,597 | The application to Hawking's problem was that by the equivalence principle, a stationary observer near the event horizon of a black hole carrying a particle detector would observe excitations in the detector as if it were accelerating at an enormous rate in an otherwise vacuum-state flat spacetime. This accounts for th... | History of the philosophy of field theory | 0.785693 |
78,598 | A more detailed understanding of the framework is obtained by studying the Lagrangian density of a field theory which encodes the information of its allowed particle interactions.But even in this framework for which there is no action-at-a-distance contention as with classical fields, quantum fields may be thought of a... | History of the philosophy of field theory | 0.785693 |
78,599 | Because this definition is very broad, it is unclear whether Kant had in mind for his "matter" the same sort of field Michael Faraday would discover. Kant himself was a proponent of the aether theory, which is mentioned in his Opus Postumum. But in whatever capacity Kant's metaphysics actually predicates the discoverie... | History of the philosophy of field theory | 0.785693 |
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