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94,500 | Let f ( t ) {\displaystyle f(t)} be a function defined whenever t ≥ 0. {\displaystyle t\geq 0.} Then its Laplace transform is given by if the integral exists.A property of the Laplace transform useful for evaluating improper integrals is provided lim t → 0 f ( t ) t {\displaystyle \lim _{t\to 0}{\frac {f(t)}{t}}} exist... | Dirichlet integral | 0.779111 |
94,501 | The continuity of f {\displaystyle f} can be justified by applying the dominated convergence theorem after integration by parts. Differentiate with respect to s > 0 {\displaystyle s>0} and apply the Leibniz rule for differentiating under the integral sign to obtain Now, using Euler's formula e i t = cos t + i sin t... | Dirichlet integral | 0.779111 |
94,502 | Consider As a function of the complex variable z , {\displaystyle z,} it has a simple pole at the origin, which prevents the application of Jordan's lemma, whose other hypotheses are satisfied. Define then a new function The pole has been moved to the negative imaginary axis, so g ( z ) {\displaystyle g(z)} can be inte... | Dirichlet integral | 0.779111 |
94,503 | In neuroscience, quantum brain dynamics (QBD) is a hypothesis to explain the function of the brain within the framework of quantum field theory.As described by Harald Atmanspacher, "Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quan... | Quantum consciousness | 0.779108 |
94,504 | In 2010, Lawrence Krauss was guarded in criticising Penrose's ideas. He said: "Roger Penrose has given lots of new-age crackpots ammunition... Many people are dubious that Penrose's suggestions are reasonable, because the brain is not an isolated quantum-mechanical system. To some extent it could be, because memories a... | Quantum consciousness | 0.779108 |
94,505 | I am claiming that the actions of consciousness are something different. I'm not saying that consciousness is beyond physics, either—although I'm saying that it's beyond the physics we know now.... My claim is that there has to be something in physics that we don't yet understand, which is very important, and which is ... | Quantum consciousness | 0.779108 |
94,506 | The proposed existence of gap junctions between neurons and glial cells was also falsified. Orch-OR predicted that microtubule coherence reaches the synapses through dendritic lamellar bodies (DLBs), but De Zeeuw et al. proved this impossible by showing that DLBs are micrometers away from gap junctions.In 2014, Hamerof... | Quantum consciousness | 0.779108 |
94,507 | He originally suggested that the tubulin-subunit electrons would form a Bose–Einstein condensate, but this was discredited. He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules, but this too was experimentally discredited.In other words, there is a missing link between physic... | Quantum consciousness | 0.779108 |
94,508 | He suggested each quantum superposition has its own piece of spacetime curvature and that when these become separated by more than one Planck length, they become unstable and collapse. Penrose suggested that objective reduction represents neither randomness nor algorithmic processing but instead a non-computable influe... | Quantum consciousness | 0.779108 |
94,509 | If this proves to be the case, then quantum mechanics will be significantly involved in brain activity. ": 400 Penrose determined that wave function collapse was the only possible physical basis for a non-computable process. Dissatisfied with its randomness, he proposed a new form of wave function collapse that occurs ... | Quantum consciousness | 0.779108 |
94,510 | Theoretical physicist Roger Penrose and anaesthesiologist Stuart Hameroff collaborated to produce the theory known as "orchestrated objective reduction" (Orch-OR). Penrose and Hameroff initially developed their ideas separately and later collaborated to produce Orch-OR in the early 1990s. They reviewed and updated thei... | Quantum consciousness | 0.779108 |
94,511 | He instead discusses how quantum mechanics may relate to dualistic consciousness. Chalmers is skeptical that any new physics can resolve the hard problem of consciousness. He argues that quantum theories of consciousness suffer from the same weakness as more conventional theories. Just as he argues that there is no par... | Quantum consciousness | 0.779108 |
94,512 | Eugene Wigner developed the idea that quantum mechanics has something to do with the workings of the mind. He proposed that the wave function collapses due to its interaction with consciousness. Freeman Dyson argued that "mind, as manifested by the capacity to make choices, is to some extent inherent in every electron"... | Quantum consciousness | 0.779108 |
94,513 | Karl Pribram's holonomic brain theory (quantum holography) invoked quantum mechanics to explain higher-order processing by the mind. He argued that his holonomic model solved the binding problem. Pribram collaborated with Bohm in his work on quantum approaches to mind and he provided evidence on how much of the process... | Quantum consciousness | 0.779108 |
94,514 | Mari Jibu and Kunio Yasue later popularized these results and discussed the implications towards consciousness.Umezawa emphasizes that macroscopic and microscopic ordered states are both of quantum origin according to quantum field theory and points out the shortcomings of classical neuronal models in describing them. ... | Quantum consciousness | 0.779108 |
94,515 | Historically, the Kodaira embedding theorem was derived with the help of the vanishing theorem. With application of Serre duality, the vanishing of various sheaf cohomology groups (usually related to the canonical line bundle) of curves and surfaces help with the classification of complex manifolds, e.g. Enriques–Kodai... | Kodaira vanishing theorem | 0.779105 |
94,516 | Until 1987 the only known proof in characteristic zero was however based on the complex analytic proof and the GAGA comparison theorems. However, in 1987 Pierre Deligne and Luc Illusie gave a purely algebraic proof of the vanishing theorem in (Deligne & Illusie 1987). Their proof is based on showing that the Hodge–de R... | Kodaira vanishing theorem | 0.779105 |
94,517 | The Kodaira vanishing theorem can be formulated within the language of algebraic geometry without any reference to transcendental methods such as Kähler metrics. Positivity of the line bundle L translates into the corresponding invertible sheaf being ample (i.e., some tensor power gives a projective embedding). The alg... | Kodaira vanishing theorem | 0.779105 |
94,518 | In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the group with index q = 0 is usually that its dimension — the numb... | Kodaira vanishing theorem | 0.779105 |
94,519 | Jumping Off the Planet, novel by David Gerrold The Last Theorem (2008), novel by Arthur C. Clarke and Frederik Pohl Limit (2009), novel by Frank Schätzing. Used for transporting nuclear fuel between Moon and Earth. The Long Mars (2014), novel by Stephen Baxter and Terry Pratchett. | Space elevators in fiction | 0.779105 |
94,520 | In molecular biology, an exonic splicing enhancer (ESE) is a DNA sequence motif consisting of 6 bases within an exon that directs, or enhances, accurate splicing of heterogeneous nuclear RNA (hnRNA) or pre-mRNA into messenger RNA (mRNA). | Exonic splicing enhancers | 0.779104 |
94,521 | First Statistics Bulletin published. 1986-87 - "Research Clubs" established to match DoE funds for projects. BEMS (Building Energy Management Systems) Centre established as autonomous centre of expertise. | BSRIA | 0.779102 |
94,522 | In number theory, Brocard's conjecture is the conjecture that there are at least four prime numbers between (pn)2 and (pn+1)2, where pn is the nth prime number, for every n ≥ 2. The conjecture is named after Henri Brocard. It is widely believed that this conjecture is true. | Brocard's conjecture | 0.779101 |
94,523 | In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables). | Univariate distribution | 0.779101 |
94,524 | The Canada Revenue Agency reported a theft of social insurance numbers belonging to 900 taxpayers, and said that they were accessed through an exploit of the bug during a 6-hour period on 8 April 2014. After the discovery of the attack, the agency shut down its website and extended the taxpayer filing deadline from 30 ... | Heartbleed bug | 0.7791 |
94,525 | Heartbleed is a security bug in some outdated versions of the OpenSSL cryptography library, which is a widely used implementation of the Transport Layer Security (TLS) protocol. It was introduced into the software in 2012 and publicly disclosed in April 2014. Heartbleed could be exploited regardless of whether the vuln... | Heartbleed bug | 0.7791 |
94,526 | In mathematics, the Manin–Drinfeld theorem, proved by Manin (1972) and Drinfeld (1973), states that the difference of two cusps of a modular curve has finite order in the Jacobian variety. | Manin–Drinfeld theorem | 0.7791 |
94,527 | Neurophotonics is a quarterly, peer-reviewed scientific journal covering optical technology applicable to study of the brain and their impact on basic and clinical neuroscience applications, published by SPIE. The editor-in-chief is Anna Devor (Boston University, USA). | Neurophotonics | 0.779098 |
94,528 | A basic question is the following: if two closed manifolds are homotopy equivalent, are they homeomorphic? This is not true in general: there are homotopy equivalent lens spaces which are not homeomorphic. Nevertheless, there are classes of manifolds for which homotopy equivalences between them can be homotoped to home... | Borel conjecture | 0.779096 |
94,529 | In mathematics, specifically geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of equivalence (namely, homotopy equivalence) should... | Borel conjecture | 0.779096 |
94,530 | A lighting ballast is a device to provide proper starting and operating electrical conditions to light one or more fluorescent lamps, while also limiting the amount of current. A familiar and widely used example is the traditional inductive ballast used in fluorescent lamps, to limit the current through the tube, which... | Lighting ballast capacitor | 0.779095 |
94,531 | The chemical has received attention due to litigation from the PFOA-contaminated community around DuPont's Washington Works facility in Washington, West Virginia, along with EPA focus. In 2004, ChemRisk—an "industry risk assessor" that had been contracted by Dupont, reported that over 1.7 million pounds of C8 had been ... | Perfluorooctanoic acid | 0.779095 |
94,532 | The scope of the workshop includes the following topics: Shannon Theory: including Complexity theory, Information theoretic security, Multi-terminal information theory and Quantum information theory Communication Theory: including Cognitive radio systems, Cooperative communications, Network resource sharing and schedul... | Iran Workshop on Communication and Information Theory | 0.779094 |
94,533 | The 2nd IWCIT took place at Sharif University of Technology, Tehran, Iran from Wednesday May 7 to Thursday May 8, 2014. Distinguished Keynote Speakers at IWCIT 2014 were Prof. Behnaam Aazhang (Department of Electrical and Computer Engineering, Rice University), Prof. David Tse (Department of Electrical Engineering and ... | Iran Workshop on Communication and Information Theory | 0.779094 |
94,534 | OpenCell is primarily used for work related to biochemical and biomolecular activities such as DNA sequencing. It opened to the public in June 2018. The space uses shipping containers to house biotechnology laboratories. The laboratories contain biotechnology equipment including real-time PCR instruments, Plate reader,... | OpenCell | 0.779093 |
94,535 | Individual B-cells in lymphoid tissue possess either kappa or lambda light chains, but never both together. Using immunohistochemistry, it is possible to determine the relative abundance of B-cells expressing kappa and lambda light chains. If the lymph node or similar tissue is reactive, or otherwise benign, it should ... | Immunoglobulin light chain | 0.779091 |
94,536 | Michael Eaton Gage is a mathematician who works as a professor of mathematics at the University of Rochester. He is known for his work on the curve-shortening flow, and in particular for the Gage–Hamilton–Grayson theorem, proved by Gage with Richard S. Hamilton and Matthew Grayson, which describes the behavior of any s... | Michael Gage (mathematician) | 0.779091 |
94,537 | The Brauer group was generalized from fields to commutative rings by Auslander and Goldman. Grothendieck went further by defining the Brauer group of any scheme. There are two ways of defining the Brauer group of a scheme X, using either Azumaya algebras over X or projective bundles over X. The second definition involv... | Brauer group | 0.779091 |
94,538 | The Brauer group Br(K) fits into an exact sequence constructed by Hasse: 0 → Br ( K ) → ⨁ v ∈ S Br ( K v ) → Q / Z → 0 , {\displaystyle 0\rightarrow {\textrm {Br}}(K)\rightarrow \bigoplus _{v\in S}{\textrm {Br}}(K_{v})\rightarrow \mathbf {Q} /\mathbf {Z} \rightarrow 0,} where S is the set of all places of K and the rig... | Brauer group | 0.779091 |
94,539 | Artin conjectured that every proper scheme over the integers has finite Brauer group. This is far from known even in the special case of a smooth projective variety X over a finite field. Indeed, the finiteness of the Brauer group for surfaces in that case is equivalent to the Tate conjecture for divisors on X, one of ... | Brauer group | 0.779091 |
94,540 | The Brauer group plays an important role in the modern formulation of class field theory. If Kv is a non-Archimedean local field, local class field theory gives a canonical isomorphism invv: Br(Kv) → Q/Z, the Hasse invariant.The case of a global field K (such as a number field) is addressed by global class field theory... | Brauer group | 0.779091 |
94,541 | The Brauer group Br(R) of the field R of real numbers is the cyclic group of order two. There are just two non-isomorphic real division algebras with center R: R itself and the quaternion algebra H. Since H ⊗ H ≅ M(4, R), the class of H has order two in the Brauer group. Let K be a non-Archimedean local field, meaning ... | Brauer group | 0.779091 |
94,542 | K is the function field of an algebraic curve over an algebraically closed field (Tsen's theorem). More generally, the Brauer group vanishes for any C1 field. K is an algebraic extension of Q containing all roots of unity. | Brauer group | 0.779091 |
94,543 | In the following cases, every finite-dimensional central division algebra over a field K is K itself, so that the Brauer group Br(K) is trivial: K is an algebraically closed field. K is a finite field (Wedderburn's theorem). Equivalently, every finite division ring is commutative. | Brauer group | 0.779091 |
94,544 | In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer. The Brauer group arose out of attempts to classify division algebras ... | Brauer group | 0.779091 |
94,545 | Usually in cryptography the notion of malleability is not seen as an "advantage," but under certain applications such as secure electronic voting and threshold cryptosystems, this property may indeed be necessary. Paillier and Pointcheval however went on to propose an improved cryptosystem that incorporates the combine... | Paillier cryptosystem | 0.779091 |
94,546 | The Paillier cryptosystem, invented by and named after Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography. The problem of computing n-th residue classes is believed to be computationally difficult. The decisional composite residuosity assumption is the intractability hypothesis... | Paillier cryptosystem | 0.779091 |
94,547 | Paillier cryptosystem exploits the fact that certain discrete logarithms can be computed easily. For example, by binomial theorem, ( 1 + n ) x = ∑ k = 0 x ( x k ) n k = 1 + n x + ( x 2 ) n 2 + higher powers of n {\displaystyle (1+n)^{x}=\sum _{k=0}^{x}{x \choose k}n^{k}=1+nx+{x \choose 2}n^{2}+{\text{higher powers of }... | Paillier cryptosystem | 0.779091 |
94,548 | 2020 Kenneth T. Gillen - Sandia National Labs researcher noted for contributions to service life prediction methods for elastomers 2021 Howard Colvin - Organic chemist and consultant to the tire and rubber industries noted for developments to rubber chemicals and polymers 2022 Anil K. Bhowmick - University of Houston p... | Melvin Mooney Distinguished Technology Award | 0.77909 |
94,549 | 1990 Gerard Kraus - Phillips Petroleum Scientist known for developing testing standard for carbon black surface area 1991 Charles S. Schollenberger - B. F. Goodrich chemist who invented Estane 1992 Robert W. Layer - B. F. Goodrich chemist noted for contributions to chemistry of imines 1993 John R. Dunn - Polysar synthe... | Melvin Mooney Distinguished Technology Award | 0.77909 |
94,550 | 1982 J. Roger Beatty - Senior Research Fellow at B. F. Goodrich known for development of rubber testing instruments and methods 1983 Aubert Y. Coran - Monsanto researcher responsible for invention of thermoplastic elastomer Geolast 1984 Eli M. Dannenberg - Cabot scientist known for contributions to surface chemistry of... | Melvin Mooney Distinguished Technology Award | 0.77909 |
94,551 | 2000 Joseph Kuczkowski - Goodyear chemist who elucidated mechanisms of antioxidant function, resulting in the commercialization of several new antioxidant systems 2002 C. Michael Roland - Naval Research Lab scientist recognized for blast and impact protection using elastomers, and for diverse contributions to elastomer... | Melvin Mooney Distinguished Technology Award | 0.77909 |
94,552 | The theory behind noise analysis of photon statistics (sometimes called the forward Kolmogorov equation) starts from the Masters equation from Shimoda et al. where a {\displaystyle a} corresponds to the emission cross section and upper population number product σ e N 2 {\displaystyle \sigma _{e}N_{2}} , and the b {\dis... | Quantum noise | 0.77909 |
94,553 | We can take the equipartition theorem or the fact that in equilibrium the energy is equally shared among a molecule/atoms degrees of freedom in thermal equilibrium , i.e., In the classical autocorrelation, we have while in the quantum autocorrelation we have Where the fraction terms in parentheses is the zero-point ene... | Quantum noise | 0.77909 |
94,554 | The uncertainty principle requires any amplifier or detector to have noise.Macroscopic manifestations of quantum phenomena are easily disturbed, so quantum noise is mainly observed in systems where conventional sources of noise are suppressed. In general, noise is uncontrolled random variation from an expected value an... | Quantum noise | 0.77909 |
94,555 | Quantum noise is noise arising from the indeterminate state of matter in accordance with fundamental principles of quantum mechanics, specifically the uncertainty principle and via zero-point energy fluctuations. Quantum noise is due to the apparently discrete nature of the small quantum constituents such as electrons,... | Quantum noise | 0.77909 |
94,556 | Only the time difference matters. Noise is due to a very large number of fluctuating charge so that the central limit theorem applie, i.e., the noise is Gaussian or normally distributed. G v v {\displaystyle G_{vv}} decays to zero rapidly over some time τ c {\displaystyle \tau _{c}} . | Quantum noise | 0.77909 |
94,557 | The Wiener–Khinchin theorem generally states that a noise's power spectrum is given as the autocorrelation of a signal, i.e., The above relation is sometimes called the power spectrum or spectral density. In the above outline, we assumed that Our noise is stationary or the probability does not change over time. | Quantum noise | 0.77909 |
94,558 | Issues like space debris, radio and light pollution are increasing in magnitude and at the same time lack progress in national or international regulation. Space debris pose dangers to the spacecraft (including satellites) in or crossing geocentric orbits and have the potential to drive a Kessler syndrome which could p... | Earth satellite | 0.779089 |
94,559 | Hitachi Energy has stated that it has been using 100 percent renewable energy for its global operations since January 2022 and is furthermore aiming for carbon neutrality by 2030. == References == | Hitachi Energy | 0.779089 |
94,560 | Supplier for Changji-Guquan UHVDC transmission line in China, the world’s first transmission line operating at 1,100kV voltage (2018) Fluoronitrile-based gas replacement for the greenhouse gas sulphur hexafluoride for National Grid in Kent, UK (2021) HVDC converter stations for high-voltage direct current submarine pow... | Hitachi Energy | 0.779089 |
94,561 | Hitachi Energy Ltd is a global technology company headquartered in Zurich, Switzerland. The company provides sustainable energy solutions to buildings, utilities, industries, and infrastructure sectors. The company’s portfolio includes high-voltage equipment, transformers, grid integration and grid automation technolog... | Hitachi Energy | 0.779089 |
94,562 | In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research... | Peano axiom | 0.779088 |
94,563 | Their difficulty was one of materials science and the lack of a suitable friction material, before asbestos clutch linings, that could handle the specific power / area at an elevated operating temperature. As the Hele-Shaw clutch did not rely on friction, it generated only a fraction of the heat of other designs and it... | Hele-Shaw clutch | 0.779087 |
94,564 | A cleanroom suit, clean room suit, or bunny suit, is an overall garment worn in a cleanroom, an environment with a controlled level of contamination. One common type is an all-in-one coverall worn by semiconductor and nanotechnology line production workers, technicians, and process / equipment engineers. Similar garmen... | Cleanroom suit | 0.779083 |
94,565 | Given a cylinder set {\displaystyle } , its measure is μ ( ) = ∏ i = 0 n p x i {\displaystyle \mu \left(\right)=\prod _{i=0}^{n}p_{x_{i}}} The equivalent expression, using the notation of probability theory, is μ ( ) = P r ( X 0 = x 0 , X 1 = x 1 , … , X n = x n ) {\displaystyle \mu \left(\right)=\mathrm {Pr} (X_{0}... | Ornstein's theorem | 0.779078 |
94,566 | The associated measure is called the Bernoulli measure μ = { p 1 , … , p N } Z {\displaystyle \mu =\{p_{1},\ldots ,p_{N}\}^{\mathbb {Z} }} The σ-algebra A {\displaystyle {\mathcal {A}}} on X is the product sigma algebra; that is, it is the (countable) direct product of the σ-algebras of the finite set {1, ..., N}. Thus... | Ornstein's theorem | 0.779078 |
94,567 | However, while in the beginning, technological investment involved little more than the time, efforts, and skills of one or a few men, today, such investment may involve the collective labor and skills of many millions. Most recently, because of the COVID-19 pandemic, the proportion of firms employing advanced digital ... | Technology and society | 0.779077 |
94,568 | According to the statistics, in the early beginnings of 1990s the use of Internet in schools was, on average, 2–3%. Continuously, by the end of 1990s the evolution of technology increases rapidly and reaches to 60%, and by the year of 2008 nearly 100% of schools use Internet on educational form. According to ISTE resea... | Technology and society | 0.779077 |
94,569 | Development and technologies' implicationsSome technologies are designed specifically with the environment in mind, but most are designed first for financial or economic effects such as the free market's profit motive. The effects of a specific technology is often not only dependent on how it is used – e.g. its usage c... | Technology and society | 0.779077 |
94,570 | Since the field of vision area can vary considerably between different microscopes, the exact area of the high power fields should be defined in order to compare results from different studies. Accordingly, one of the main problems of counting mitosis has been the reproducibility. Thus, the need for standardized method... | Proliferative index | 0.779076 |
94,571 | Of Babylonian astronomy, practically nothing was known to historians of science before the 1880s. Surviving ancient writings of Pliny had made bare mention of three astronomical schools in Mesopotamia – at Babylon, Uruk, and 'Hipparenum' (possibly 'Sippar'). But definite modern knowledge of any details only began when ... | Lunar theory | 0.779075 |
94,572 | In parallel with these developments, a new class of analytical lunar theory has also been developed in recent years, notably the Ephemeride Lunaire Parisienne by Jean Chapront and Michelle Chapront-Touzé from the Bureau des Longitudes. Using computer-assisted algebra, the analytical developments have been taken further... | Lunar theory | 0.779075 |
94,573 | The main aim of Newton's successors, from Leonhard Euler, Alexis Clairaut and Jean d'Alembert in the mid-eighteenth century, down to Ernest William Brown in the late nineteenth and early twentieth century, was to account completely and much more precisely for the moon's motions on the basis of Newton's laws, i.e. the l... | Lunar theory | 0.779075 |
94,574 | The Moon has been observed for millennia. Over these ages, various levels of care and precision have been possible, according to the techniques of observation available at any time. There is a correspondingly long history of lunar theories: it stretches from the times of the Babylonian and Greek astronomers, down to mo... | Lunar theory | 0.779075 |
94,575 | The topology on which the Kuramoto model is studied can be made adaptive by use of fitness model showing enhancement of synchronization and percolation in a self-organised way. A graph with the minimal degree at least d m i n ≥ 0.5 n {\displaystyle d_{min}\geq 0.5\ n} will be connected nevertheless for a graph to synch... | Kuramoto model | 0.779072 |
94,576 | Beside the original model, which has an all-to-all topology, a sufficiently dense complex network-like topology is amenable to the mean-field treatment used in the solution of the original model (see Transformation and Large N limit above for more info). Network topologies such as rings and coupled populations support ... | Kuramoto model | 0.779072 |
94,577 | The Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto (蔵本 由紀, Kuramoto Yoshiki), is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated by the behavior of systems of che... | Kuramoto model | 0.779072 |
94,578 | In the work from Dörfler and colleagues, several theorems provide rigorous conditions for phase and frequency synchronization of this model. Further studies, motivated by experimental observations in neuroscience, focus on deriving analytical conditions for cluster synchronization of heterogeneous Kuramoto oscillators ... | Kuramoto model | 0.779072 |
94,579 | The dithionite is the oxyanion with the formula 2−. It is commonly encountered as the salt sodium dithionite. For historical reasons, it is sometimes called hydrosulfite, but it contains no hydrogen and is not a sulfite. The dianion has a steric number of 4 and trigonal pyramidal geometry. | S2O42- | 0.779072 |
94,580 | In his joint work with M. Suzuki and G. Ricotta a new correspondence in number theory is proposed, between the arithmetic zeta functions and mean-periodic functions in the space of smooth functions on the real line of not more than exponential growth. This correspondence is related to the Langlands correspondence. Two ... | Arithmetic zeta function | 0.77907 |
94,581 | There are a number of conjectures concerning the behavior of the zeta function of a regular irreducible equidimensional scheme X (of finite type over the integers). Many (but not all) of these conjectures generalize the one-dimensional case of well known theorems about the Euler-Riemann-Dedekind zeta function. The sche... | Arithmetic zeta function | 0.779069 |
94,582 | If X is the spectrum of the ring of integers, then ζX (s) is the Riemann zeta function. More generally, if X is the spectrum of the ring of integers of an algebraic number field, then ζX (s) is the Dedekind zeta function. | Arithmetic zeta function | 0.779069 |
94,583 | In fact, this conjecture of Tate's is equivalent to a generalization of Birch and Swinnerton-Dyer. More generally, Soulé conjectured o r d s = n − m ζ X ( s ) = − ∑ i ( − 1 ) i r k K i ( X ) ( m ) {\displaystyle \mathrm {ord} _{s=n-m}\zeta _{X}(s)=-\sum _{i}(-1)^{i}rkK_{i}(X)^{(m)}} The right hand side denotes the Adam... | Arithmetic zeta function | 0.779069 |
94,584 | In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes the Riemann zeta function and Dedekind zeta function to higher dimensions. The arithmetic zeta function is one of the most-fundamental objects of number theory. | Arithmetic zeta function | 0.779069 |
94,585 | Although boundedness is the same as continuity for linear maps between normed spaces, the term "bounded" is more commonly used when dealing primarily with Banach spaces. If f: X → R {\displaystyle f:X\to \mathbb {R} } is a subadditive function (such as a norm, a sublinear function, or real linear functional), then f {\... | Banach norm | 0.779067 |
94,586 | When X {\displaystyle X} does not contain ℓ 1 , {\displaystyle \ell ^{1},} every element of B ′ ′ {\displaystyle B^{\prime \prime }} is weak*-limit of a sequence in the unit ball of X . {\displaystyle X.} When the Banach space X {\displaystyle X} is separable, the unit ball of the dual X ′ , {\displaystyle X^{\prime },... | Banach norm | 0.779067 |
94,587 | ℓ 1 {\displaystyle \ell ^{1}} basis Weakly Cauchy sequences and the ℓ 1 {\displaystyle \ell ^{1}} basis are the opposite cases of the dichotomy established in the following deep result of H. P. Rosenthal. A complement to this result is due to Odell and Rosenthal (1975). By the Goldstine theorem, every element of the un... | Banach norm | 0.779067 |
94,588 | When two compact Hausdorff spaces K 1 {\displaystyle K_{1}} and K 2 {\displaystyle K_{2}} are homeomorphic, the Banach spaces C ( K 1 ) {\displaystyle C\left(K_{1}\right)} and C ( K 2 ) {\displaystyle C\left(K_{2}\right)} are isometric. Conversely, when K 1 {\displaystyle K_{1}} is not homeomorphic to K 2 , {\displayst... | Banach norm | 0.779067 |
94,589 | The normed space X {\displaystyle X} is called reflexive when the natural map is surjective. Reflexive normed spaces are Banach spaces. This is a consequence of the Hahn–Banach theorem. Further, by the open mapping theorem, if there is a bounded linear operator from the Banach space X {\displaystyle X} onto the Banach ... | Banach norm | 0.779067 |
94,590 | {\displaystyle X.} Thus, the vector space B ( X , Y ) {\displaystyle B(X,Y)} can be given the operator norm For Y {\displaystyle Y} a Banach space, the space B ( X , Y ) {\displaystyle B(X,Y)} is a Banach space with respect to this norm. In categorical contexts, it is sometimes convenient to restrict the function space... | Banach norm | 0.779067 |
94,591 | For every Banach space Y , {\displaystyle Y,} there is a natural norm 1 {\displaystyle 1} linear map obtained by extending the identity map of the algebraic tensor product. Grothendieck related the approximation problem to the question of whether this map is one-to-one when Y {\displaystyle Y} is the dual of X . {\disp... | Banach norm | 0.779067 |
94,592 | The Institute of Higher Nervous Activity and Neurophysiology is a research institute located in Moscow, Russia that specializes in neuroscience, and is a part of the Russian Academy of Sciences. | Institute of Higher Nervous Activity | 0.779062 |
94,593 | The 2020 Cloud Threat Report released by Unit 42 (the threat intelligence unit of cybersecurity provider Palo Alto Networks) identified around 200,000 potential vulnerabilities in infrastructure as code templates. | Infrastructure as Code | 0.77906 |
94,594 | There are also more refined statements. The Lang–Trotter conjecture (1976) of Serge Lang and Hale Trotter states the asymptotic number of primes p with a given value of ap, the trace of Frobenius that appears in the formula. For the typical case (no complex multiplication, trace ≠ 0) their formula states that the numbe... | Lang–Trotter conjecture | 0.779059 |
94,595 | {\sqrt {p}})\ } as p → ∞ {\displaystyle p\to \infty } , and the point of the conjecture is to predict how the O-term varies. The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008... | Lang–Trotter conjecture | 0.779059 |
94,596 | In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational numbers by reduction modulo almost all prime numbers p. Mikio Sato and John Tate independently posed the conjecture around 1960. If Np denotes the number of poin... | Lang–Trotter conjecture | 0.779059 |
94,597 | The chart below shows these differences for various colours:- Both ISO 13803 and ASTM E430 method B require a separate measurement of luminous reflectance, Y, to calculate compensated haze. The tri-stimulus value Y gives a measure of the lightness of the material as defined in ISO 7724-2 requiring a 45°/0° geometry to ... | Haze (optics) | 0.779058 |
94,598 | Gleason's theorem finds application in quantum logic, which makes heavy use of lattice theory. Quantum logic treats the outcome of a quantum measurement as a logical proposition and studies the relationships and structures formed by these logical propositions. They are organized into a lattice, in which the distributiv... | Gleason's theorem | 0.779057 |
94,599 | : §1 In the related no-hidden-variables result known as Bell's theorem, the assumption that the hidden-variable theory is noncontextual instead is replaced by the assumption that it is local. The same sets of rays used in Kochen–Specker constructions can also be employed to derive Bell-type proofs.Pitowsky uses Gleason... | Gleason's theorem | 0.779057 |
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