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97,800 | Studying chalcogen interactions gives access to radical cations, which are used in mainstream synthetic chemistry. Metallic redox centers of biological importance are tunable by interactions of ligands containing chalcogens, such as methionine and selenocysteine. Also, chalcogen through-bonds can provide insight about ... | Oxygen family | 0.77758 |
97,801 | These compounds also feature into ligand chemistry and biochemistry. One application of chalcogens themselves is to manipulate redox couples in supramolar chemistry (chemistry involving non-covalent bond interactions). This application leads on to such applications as crystal packing, assembly of large molecules, and b... | Oxygen family | 0.77758 |
97,802 | In mathematics graph theory, a single-entry single-exit (SESE) region in a given graph is an ordered edge pair. For example, with the ordered edge pair, (a, b) of distinct control-flow edges a and b where: a dominates b b postdominates a Every cycle containing a also contains b and vice versa.where a node x is said to ... | Single-entry single-exit | 0.777577 |
97,803 | The Szegő kernel is defined by S ( z , ζ ) = k z ( ζ ) ¯ , z ∈ Ω , ζ ∈ ∂ Ω . {\displaystyle S(z,\zeta )={\overline {k_{z}(\zeta )}},\quad z\in \Omega ,\zeta \in \partial \Omega .} Like its close cousin, the Bergman kernel, the Szegő kernel is holomorphic in z. In fact, if φi is an orthonormal basis of H2(∂Ω) consisting... | Szegő kernel | 0.777575 |
97,804 | The Poisson integral implies that each element ƒ of H2(∂Ω) extends to a holomorphic function Pƒ in Ω. Furthermore, for each z ∈ Ω, the map f ↦ P f ( z ) {\displaystyle f\mapsto Pf(z)} defines a continuous linear functional on H2(∂Ω). By the Riesz representation theorem, this linear functional is represented by a kernel... | Szegő kernel | 0.777575 |
97,805 | The weight assigned to each property, w i {\displaystyle w_{i}} , are free parameters that can be chosen to emphasize certain characteristics over others or to obtain desired index thresholds or rankings. The webpage also ranks what it describes as the habitability of planets and moons according to three criteria: the ... | Earth Similarity Index | 0.777572 |
97,806 | For example, while surface temperature is influenced by a variety of factors including irradiance, tidal heating, albedo, insolation and greenhouse warming, as these factors are not known for any exoplanet, quoted ESI values use planetary equilibrium temperature as a stand-in.A webpage maintained by one of the authors ... | Earth Similarity Index | 0.777572 |
97,807 | The ESI, as proposed in 2011 by Schulze-Makuch et al. in the journal Astrobiology, incorporates a planet's radius, density, escape velocity, and surface temperature into the index. Thus the authors describe the index as having two components: (1) associated with the interior which is associated with the mean radius and... | Earth Similarity Index | 0.777572 |
97,808 | This was formulated by means of results in class field theory, such as Hasse's norm theorem. In the case of elliptic curves, it led to the key definition of the Tate–Shafarevich group in the Selmer group, which is the obstruction to the success of a local-global principle. | Galois cohomology | 0.777572 |
97,809 | Numerous direct calculations were done, and the proof of the Mordell–Weil theorem had to proceed by some surrogate of a finiteness proof for a particular H1 group. The 'twisted' nature of objects over fields that are not algebraically closed, which are not isomorphic but become so over the algebraic closure, was also k... | Galois cohomology | 0.777572 |
97,810 | In fact, for a while the multiplicative case of a 1-cocycle for groups that are not necessarily cyclic was formulated as the solubility of Noether's equations, named for Emmy Noether; they appear under this name in Emil Artin's treatment of Galois theory, and may have been folklore in the 1920s. The case of 2-cocycles ... | Galois cohomology | 0.777572 |
97,811 | The normal basis theorem implies that the first cohomology group of the additive group of L will vanish; this is a result on general field extensions, but was known in some form to Richard Dedekind. The corresponding result for the multiplicative group is known as Hilbert's Theorem 90, and was known before 1900. Kummer... | Galois cohomology | 0.777572 |
97,812 | Firstly, Galois cohomology appeared as the foundational layer of étale cohomology theory (roughly speaking, the theory as it applies to zero-dimensional schemes). Secondly, non-abelian class field theory was launched as part of the Langlands philosophy. The earliest results identifiable as Galois cohomology had been kn... | Galois cohomology | 0.777572 |
97,813 | The current theory of Galois cohomology came together around 1950, when it was realised that the Galois cohomology of ideal class groups in algebraic number theory was one way to formulate class field theory, at the time it was in the process of ridding itself of connections to L-functions. Galois cohomology makes no a... | Galois cohomology | 0.777572 |
97,814 | In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L/K acts in a natural way on some abelian groups, for example those constructed directly from L, but al... | Galois cohomology | 0.777572 |
97,815 | Since the international adoption of the MKS standard in the 1940s and the SI standard in the 1960s, the technical use of CGS units has gradually declined worldwide. SI units are predominantly used in engineering applications and physics education, while Gaussian CGS units are commonly used in theoretical physics, descr... | CGS Units | 0.777571 |
97,816 | These correlations are the mass transfer analogies to heat transfer correlations of the Nusselt number in terms of the Reynolds number and Prandtl number. For a correlation for a given geometry (e.g. spheres, plates, cylinders, etc.), a heat transfer correlation (often more readily available from literature and experim... | Sherwood number | 0.777571 |
97,817 | It is similar to maximum likelihood method as the optimization tool used is similar. Assumption The output obtained from the sensors is a wide sense stationary random process with zero mean. P C ( K o x , w o ) = E = 1 ∑ α = 0 N − 1 ∑ β = 0 M − 1 ∑ l = 0 N − 1 ∑ m = 0 M − 1 ψ e ( l , α ; m , β ) {\displaystyle P_{C}\l... | Multidimensional spectral estimation | 0.77757 |
97,818 | The max entropy is of the form: P M E = 1 ∑ l ∑ m λ ( l , m ) e x p ( j k x l − j w m ) {\displaystyle P_{ME}={\frac {1}{\sum _{l}\sum _{m}\lambda \left(l,m\right)exp\left(jk_{x}l-jwm\right)}}} λ(l,m) must be chosen such that known autocorrelation coefficients are matched. LimitationsIt has constrained optimization. It... | Multidimensional spectral estimation | 0.77757 |
97,819 | The bows of these machines already featured a winched pull back system and could apparently throw two missiles at once.Philo of Byzantium provides probably the most detailed account on the establishment of a theory of belopoietics (belos = "projectile"; poietike = "(art) of making") circa 200 BC. The central principle ... | Catapult | 0.777569 |
97,820 | In microbiology, methyl red is used in the methyl red test (MR test), used to identify bacteria producing stable acids by mechanisms of mixed acid fermentation of glucose (cf. Voges–Proskauer test). The MR test, the "M" portion of the four IMViC tests, is used to identify enteric bacteria based on their pattern of gluc... | Methyl red | 0.777566 |
97,821 | In October 2022, Lineage announced the establishment of a new R&D facility in Carlsbad, California, as well as an expansion to the company’s existing GMP manufacturing facility in Israel. The new facility in Carlsbad will broaden Lineage’s R&D capabilities in the U.S. and support the development of current and future a... | Lineage Cell Therapeutics | 0.777566 |
97,822 | Lineage is a clinical-stage biotechnology company developing novel cell therapies for unmet medical needs. The company changed its name from BioTime Inc. to Lineage Cell Therapeutics less than one year following its appointment of a new CEO, Brian Culley, in August 2018 and completing a series of corporate transactions... | Lineage Cell Therapeutics | 0.777566 |
97,823 | Lineage Cell Therapeutics, Inc. is a clinical-stage biotechnology company developing novel cell therapies for unmet medical needs. Lineage’s programs are based on its robust proprietary cell-based therapy platform and associated in-house development and manufacturing capabilities. With this platform Lineage develops an... | Lineage Cell Therapeutics | 0.777566 |
97,824 | RepRap was founded in 2005 by Dr Adrian Bowyer, a Senior Lecturer in mechanical engineering at the University of Bath in England. Funding was obtained from the Engineering and Physical Sciences Research Council. On 13 September 2006, the RepRap 0.2 prototype printed the first part identical to its own, which was then s... | RepRap | 0.777565 |
97,825 | COUPP (Chicagoland Observatory for Underground Particle Physics) was a similar project with members from Fermilab, University of Chicago, and Indiana University. Prototypes were tested in the MINOS experiment far hall, with a scaled-up experiment also operating at SNOLAB. It used trifluoroiodomethane (CF3I) as the medi... | PICASSO (dark matter) | 0.777564 |
97,826 | In the geometry of hyperbolic 3-space, the tetrahedral-square tiling honeycomb is a paracompact uniform honeycomb, constructed from tetrahedron, cuboctahedron and square tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. A geometric honey... | Tetrahedral-square tiling honeycomb | 0.777564 |
97,827 | Also, the stoichiometry of ternary oxide may be changed by varying the proportions of the two components and their oxidation states. For example, at least twenty ternary oxide phases are formed between strontium and vanadium including SrV2O6, Sr2V2O5, SrVO3 and Sr2VO4. The structural chemistry of ternary and more compl... | Surface properties of transition metal oxides | 0.777563 |
97,828 | Ec is the lowest energy of the conduction band, Ef is the Fermi energy (electrochemical energy of the electrons), Ev is the highest energy of the valence band, Nc is the effective mass and mobility of an electron in the conduction band (constant), and Nv is the effective mass and mobility of a valence band hole (consta... | Surface properties of transition metal oxides | 0.777563 |
97,829 | Simonkolleite is rhombohedral, space group R3m. There are two crystallographically distinct zinc sites in Simonkolleite, both of which are fully occupied by zinc. The Zn(1) site is coordinated by six hydroxyl (OH) groups in an octahedral geometry . The Zn(2) site is coordinated by three OH groups, and one Cl atom in a ... | Zinc chloride hydroxide monohydrate | 0.777562 |
97,830 | In molecular genetics, a repressor is a DNA- or RNA-binding protein that inhibits the expression of one or more genes by binding to the operator or associated silencers. A DNA-binding repressor blocks the attachment of RNA polymerase to the promoter, thus preventing transcription of the genes into messenger RNA. An RNA... | Repressor (genetics) | 0.77756 |
97,831 | Each positive sequence of type ℓ 1 {\displaystyle \ell ^{1}} in X {\displaystyle X} is order summable.In particular, if ( X , ≤ ) {\displaystyle (X,\leq )} is an Archimedean ordered vector space having an order unit then the order ≤ {\displaystyle \,\leq \,} is a regular order and X b = X + . {\displaystyle X_{b}=X^{+}... | Order topology (functional analysis) | 0.777559 |
97,832 | If ( X , ≤ ) {\displaystyle (X,\leq )} is an Archimedean ordered vector space over the real numbers having an order unit and let τ ≤ {\displaystyle \tau _{\leq }} denote the order topology on X . {\displaystyle X.} Then ( X , τ ≤ ) {\displaystyle \left(X,\tau _{\leq }\right)} is an ordered TVS that is normable, τ ≤ {\d... | Order topology (functional analysis) | 0.777559 |
97,833 | If the order of an ordered vector space X {\displaystyle X} is a regular order and if each positive sequence of type ℓ 1 {\displaystyle \ell ^{1}} in X {\displaystyle X} is order summable, then X {\displaystyle X} endowed with its order topology is a barreled space. If the order of an ordered vector space X {\displayst... | Order topology (functional analysis) | 0.777559 |
97,834 | If X b {\displaystyle X_{b}} separates points in X {\displaystyle X} (such as if ( X , ≤ ) {\displaystyle (X,\leq )} is regular) then ( X , τ ≤ ) {\displaystyle \left(X,\tau _{\leq }\right)} is a bornological locally convex TVS. Each positive linear operator between two ordered vector spaces is continuous for the respe... | Order topology (functional analysis) | 0.777559 |
97,835 | Throughout, ( X , ≤ ) {\displaystyle (X,\leq )} will be an ordered vector space and τ ≤ {\displaystyle \tau _{\leq }} will denote the order topology on X . {\displaystyle X.} The dual of ( X , τ ≤ ) {\displaystyle \left(X,\tau _{\leq }\right)} is the order bound dual X b {\displaystyle X_{b}} of X . {\displaystyle X.} | Order topology (functional analysis) | 0.777559 |
97,836 | The order topology of a finite product of ordered vector spaces (this product having its canonical order) is identical to the product topology of the topological product of the constituent ordered vector spaces (when each is given its order topology). | Order topology (functional analysis) | 0.777559 |
97,837 | If M {\displaystyle M} is a solid vector subspace of a vector lattice X , {\displaystyle X,} then the order topology of X / M {\displaystyle X/M} is the quotient of the order topology on X . {\displaystyle X.} | Order topology (functional analysis) | 0.777559 |
97,838 | If in addition X {\displaystyle X} is order complete then X {\displaystyle X} with the order topology is a barreled space and every band decomposition of X {\displaystyle X} is a topological direct sum for this topology. In particular, if the order of a vector lattice X {\displaystyle X} is regular then the order topol... | Order topology (functional analysis) | 0.777559 |
97,839 | {\displaystyle (X,\tau ).} If X {\displaystyle X} is a regularly ordered vector lattice then the ordered topology is the finest locally convex TVS topology on X {\displaystyle X} making X {\displaystyle X} into a locally convex vector lattice. | Order topology (functional analysis) | 0.777559 |
97,840 | For every a ≥ 0 , {\displaystyle a\geq 0,} let X a = ⋃ n = 1 ∞ n {\displaystyle X_{a}=\bigcup _{n=1}^{\infty }n} and endow X a {\displaystyle X_{a}} with its order topology (which makes it into a normable space). The set of all X a {\displaystyle X_{a}} 's is directed under inclusion and if X a ⊆ X b {\displaystyle X_... | Order topology (functional analysis) | 0.777559 |
97,841 | The family of all locally convex topologies on X {\displaystyle X} for which every order interval is bounded is non-empty (since it contains the coarsest possible topology on X {\displaystyle X} ) and the order topology is the upper bound of this family.A subset of X {\displaystyle X} is a neighborhood of the origin in... | Order topology (functional analysis) | 0.777559 |
97,842 | This allows for establishing intimate connections between this topology and the algebraic and order theoretic properties of ( X , ≤ ) . {\displaystyle (X,\leq ).} For many ordered topological vector spaces that occur in analysis, their topologies are identical to the order topology. | Order topology (functional analysis) | 0.777559 |
97,843 | In mathematics, specifically in order theory and functional analysis, the order topology of an ordered vector space ( X , ≤ ) {\displaystyle (X,\leq )} is the finest locally convex topological vector space (TVS) topology on X {\displaystyle X} for which every order interval is bounded, where an order interval in X {\di... | Order topology (functional analysis) | 0.777559 |
97,844 | These resolved sub-filter scales must be modeled using filter reconstruction. Sub-grid scales are any scales that are smaller than the cutoff filter width Δ {\displaystyle \Delta } . The form of the SGS model depends on the filter implementation. As mentioned in the Numerical methods for LES section, if implicit LES is... | Large eddy simulation | 0.777555 |
97,845 | One shortcoming of the DLM(+) model was that it did not describe backscatter which is known to be a real "thing" from analyzing DNS data. Two approaches were developed to address this. In one approach due to Carati et al. a fluctuating force with amplitude determined by the fluctuation-dissipation theorem is added in a... | Large eddy simulation | 0.777555 |
97,846 | )}}=C{\widehat {(.)}}} making E i j {\displaystyle E_{ij}} an algebraic function of C {\displaystyle C} which is then determined by requiring that E i j E i j {\displaystyle E_{ij}E_{ij}} considered as a function of C have the least possible value. However, since the C {\displaystyle C} thus obtained turns out to be ju... | Large eddy simulation | 0.777555 |
97,847 | Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is currently applied in a wide variety of engineering applications, including... | Large eddy simulation | 0.777555 |
97,848 | Inlet boundary conditions affect the accuracy of LES significantly, and the treatment of inlet conditions for LES is a complicated problem. Theoretically, a good boundary condition for LES should contain the following features:(1) providing accurate information of flow characteristics, i.e. velocity and turbulence; (2)... | Large eddy simulation | 0.777555 |
97,849 | Slooh is a robotic telescope service that can be viewed live through a web browser. It was not the first robotic telescope, but it was the first that offered "live" viewing through a telescope via the web. Other online telescopes traditionally email a picture to the recipient. The site has a patent on their live image ... | Slooh | 0.777553 |
97,850 | Rendering is practically exclusively concerned with the particle aspect of light physics – known as geometrical optics. Treating light, at its basic level, as particles bouncing around is a simplification, but appropriate: the wave aspects of light are negligible in most scenes, and are significantly more difficult to ... | Rendering engine | 0.777552 |
97,851 | One problem that any rendering system must deal with, no matter which approach it takes, is the sampling problem. Essentially, the rendering process tries to depict a continuous function from image space to colors by using a finite number of pixels. As a consequence of the Nyquist–Shannon sampling theorem (or Kotelniko... | Rendering engine | 0.777552 |
97,852 | On the 16 January 2023, the EU Parliament and Council adopted the 2022/2555 of the European Parliament and of the Council of 14 December 2022 on measures for a high common level of cybersecurity across the Union, amending Regulation (EU) No 910/2014 and Directive (EU) 2018/1972, and repealing Directive (EU) 2016/1148 (... | NIS Directive | 0.777552 |
97,853 | Bruce Schneier, the founder of Cupertino's Counterpane Internet Security, argues that companies will not make sufficient investments in cybersecurity unless the government forces them to do so. He also states that successful cyberattacks on government systems still occur despite government efforts.It has been suggested... | NIS Directive | 0.777552 |
97,854 | However, the regulations do not address numerous computer-related industries, such as Internet Service Providers (ISPs) and software companies. Furthermore, the regulations do not specify what cybersecurity measures must be implemented and require only a "reasonable" level of security. The vague language of these regul... | NIS Directive | 0.777552 |
97,855 | There are few federal cybersecurity regulations and the ones that exist focus on specific industries. The three main cybersecurity regulations are the 1996 Health Insurance Portability and Accountability Act (HIPAA), the 1999 Gramm-Leach-Bliley Act, and the 2002 Homeland Security Act, which included the Federal Informa... | NIS Directive | 0.777552 |
97,856 | A cybersecurity regulation comprises directives that safeguard information technology and computer systems with the purpose of forcing companies and organizations to protect their systems and information from cyberattacks like viruses, worms, Trojan horses, phishing, denial of service (DOS) attacks, unauthorized access... | NIS Directive | 0.777552 |
97,857 | The goal of this is to create a Commission that consists of a diverse group of thinkers with perspectives that can contribute to make recommendations on how to create a stronger cybersecurity for the public and private sector. The second highlight of the plan is to change Government IT. The new Government IT will make ... | NIS Directive | 0.777552 |
97,858 | The plan was made to create long-term actions and strategies in an effort to protect the US against cyber threats. The focus of the plan was to inform the public about the growing threat of cyber crimes, improve cybersecurity protections, protects personal information of Americans, and to inform Americans on how to con... | NIS Directive | 0.777552 |
97,859 | Another goal of the effort is to place cyber crimes prosecutable. The last major effort of the legislative proposal was to require businesses to report data breaching to consumers if their personal information had been sacrificed. By requiring companies to do so, consumers are aware of when they are in danger of identi... | NIS Directive | 0.777552 |
97,860 | The proposal was made in an effort to prepare the US from the expanding number of cyber crimes. In the proposal, Obama outlined three main efforts to work towards a more secure cyberspace for the US. The first main effort emphasized the importance of enabling cybersecurity information sharing. | NIS Directive | 0.777552 |
97,861 | It also tasks DHS with improving the process to expedite security clearance processes for applicable public and private sector entities to enable the federal government to share this information at the appropriate sensitive and classified levels. It directs the development of a framework to reduce cyber risks, incorpor... | NIS Directive | 0.777552 |
97,862 | "On May 12, 2011, US president Barack Obama proposed a package of cybersecurity legislative reforms to improve the security of US persons, the federal government, and critical infrastructure. A year of public debate and Congress hearings followed, resulting in the House of Representative passing an information sharing ... | NIS Directive | 0.777552 |
97,863 | The US Congress has proposed numerous bills that expand upon cybersecurity regulation. The Consumer Data Security and Notification Act amends the Gramm-Leach-Bliley Act to require disclosure of security breaches by financial institutions. Congressmen have also proposed "expanding Gramm-Leach-Bliley to all industries th... | NIS Directive | 0.777552 |
97,864 | The focus of their operations are on three factors: Recommendations to member states on the course of action for security breaches Policy making and implementation support for all members states of the EU Direct support with ENISA taking a hands-on approach to working with operational teams in the EUENISA is made up of... | NIS Directive | 0.777552 |
97,865 | The European Union Agency for Cybersecurity (ENISA) is a governing agency that was originally set up by the Regulation (EC) No 460/2004 of the European Parliament and of the Council of 10 March 2004 for the Purpose of Raising Network and Information Security (NIS) for all internetwork operations in the EU. ENISA curren... | NIS Directive | 0.777552 |
97,866 | The Cyber Resilience Act (CRA) is a regulation proposed on 15 September 2022 by the European Commission which outlines common cybersecurity standards for hardware and software products in the EU. | NIS Directive | 0.777552 |
97,867 | Cybersecurity standards have been of great prominence in today's technology driven businesses. To maximize their profits, corporations leverage technology by running most of their operations by the internet. Since there are a large number of risks that entail internetwork operations, such operations must be protected b... | NIS Directive | 0.777552 |
97,868 | Critics of the bill included the US Chamber of Commerce, advocacy groups like the American Civil Liberties Union and the Electronic Frontier Foundation, cybersecurity expert Jody Westby, and The Heritage Foundation, both of whom argued that although the government must act on cybersecurity, the bill was flawed in its a... | NIS Directive | 0.777552 |
97,869 | According to The Washington Post, experts said that the failure to pass the act may leave the United States "vulnerable to widespread hacking or a serious cyberattack." The act was opposed by Republican senators like John McCain who was concerned that the act would introduce regulations that would not be effective and ... | NIS Directive | 0.777552 |
97,870 | The Information Protection and Security Act requires that data brokers "ensure data accuracy and confidentiality, authenticate and track users, detect and prevent unauthorized activity, and mitigate potential harm to individuals. "In addition to requiring companies to improve cybersecurity, Congress is also considering... | NIS Directive | 0.777552 |
97,871 | All significant incidents must be notified to the CSIRTs. Significant cybersecurity incidents are determined by the number of users affected by the security breach as well as the longevity of the incident and the geographical reach of the incident. A NIS 2 is in the making.Only 23 Member States have fully implemented t... | NIS Directive | 0.777552 |
97,872 | Such resources are given the responsibility of handling cybersecurity breaches in a way that minimizes impact. In addition, all member states of the EU are encouraged to share cyber security information.Security requirements include technical measures that manage the risks of cybersecurity breaches in a preventative ma... | NIS Directive | 0.777552 |
97,873 | On July 6, 2016, the European Parliament set into policy the Directive on Security of Network and Information Systems (the NIS Directive).The directive went into effect in August 2016, and all member states of the European Union were given 21 months to incorporate the directive's regulations into their own national law... | NIS Directive | 0.777552 |
97,874 | In mathematics, a Hecke algebra is classically the algebra of Hecke operators studied by Erich Hecke. It may also refer to one of several algebras (some of which are related to the classical Hecke algebra): Iwahori–Hecke algebra of a Coxeter group. Hecke algebra of a pair (g,K) where g is the Lie algebra of a Lie group... | Hecke algebra (disambiguation) | 0.777551 |
97,875 | The band explained that the first part of the trilogy would be centred on the rise of "artilects (artificial intellects) with mental capacities far above the human level of thought" and that "by the year 2030, one of the world's biggest industries will be 'artificial brains,' used to control artilects that will be genu... | Scar Symmetry | 0.777545 |
97,876 | Monogamy ( mə-NOG-ə-mee) is a dyadic relationship in which two members of a group form an exclusive intimate partnership. Having only one partner at any one time, whether that be for life or whether that be serial monogamy, contrasts with various forms of non-monogamy (e.g., polygamy or polyamory). More generally, the ... | Varieties of monogamy | 0.777545 |
97,877 | Here ( ⋅ ; ⋅ ) ∞ {\displaystyle (\cdot ;\cdot )_{\infty }} is the infinite q-Pochhammer symbol. The q {\displaystyle q} -gamma function satisfies the functional equation In addition, the q {\displaystyle q} -gamma function satisfies the q-analog of the Bohr–Mollerup theorem, which was found by Richard Askey (Askey (197... | Q-gamma function | 0.777543 |
97,878 | And our visual system adapts these statistics features in order to code information efficiently. However, there is not always a clear temporal analogue to spatial features. For example, spatial features have a key role in linking signals across space to get boundaries inference, while temporal signals may not play the ... | Visual tilt effects | 0.777541 |
97,879 | The simultaneous tilt illusion is generated due to spatial context, and the tilt aftereffect is due to temporal context; experimental data however show many similarities between them. Schwartz et al. (2007) reviewed the psychophysical and electrophysiological parallels between the TI and TAE, which are probably reveali... | Visual tilt effects | 0.777541 |
97,880 | Psychophysics experiments have shown that relative orientations between 0 deg and about 50 deg produce repulsion effects (the test line or grating tends to rotate away from the contextual stimulus), which is known as the direct form of the tilt effect; but larger relative orientations up to 90 deg produce attraction ef... | Visual tilt effects | 0.777541 |
97,881 | Schwartz et al. (2009) proposed that natural scene statistics could also effect changes on orientation tuning curves with the presence of context. The coordination between the surround and the center across segmentation boundaries is greatly reduced, and our visual system takes advantage of this natural statistics feat... | Visual tilt effects | 0.777541 |
97,882 | Sobolev's original proof of the Sobolev embedding theorem relied on the following, sometimes known as the Hardy–Littlewood–Sobolev fractional integration theorem. An equivalent statement is known as the Sobolev lemma in (Aubin 1982, Chapter 2). A proof is in (Stein 1970, Chapter V, §1.3). Let 0 < α < n and 1 < p < q < ... | Sobolev inequality | 0.77754 |
97,883 | The logarithmic Sobolev inequality says, roughly, that if a function is in L p {\displaystyle L^{p}} with respect to a Gaussian measure and has one derivative that is also in L p {\displaystyle L^{p}} , then f {\displaystyle f} is in " L p {\displaystyle L^{p}} -log", meaning that the integral of | f | p log | f | {\... | Sobolev inequality | 0.77754 |
97,884 | Thus, if the dimension n {\displaystyle n} of the space on which f {\displaystyle f} is defined is large, the improvement in the local behavior of f {\displaystyle f} from having a derivative in L p {\displaystyle L^{p}} is small ( p ∗ {\displaystyle p^{*}} is only slightly larger than p {\displaystyle p} ). In particu... | Sobolev inequality | 0.77754 |
97,885 | The simplest of the Sobolev embedding theorems, described above, states that if a function f {\displaystyle f} in L p ( R n ) {\displaystyle L^{p}(\mathbb {R} ^{n})} has one derivative in L p {\displaystyle L^{p}} , then f {\displaystyle f} itself is in L p ∗ {\displaystyle L^{p^{*}}} , where 1 / p ∗ = 1 / p − 1 / n . ... | Sobolev inequality | 0.77754 |
97,886 | The second part of the Sobolev embedding theorem applies to embeddings in Hölder spaces C r,α(Rn). If n < pk and 1 p − k n = − r + α n , or, equivalently, r + α = k − n p {\displaystyle {\frac {1}{p}}-{\frac {k}{n}}=-{\frac {r+\alpha }{n}},{\mbox{ or, equivalently, }}r+\alpha =k-{\frac {n}{p}}} with α ∈ (0, 1) then one... | Sobolev inequality | 0.77754 |
97,887 | Let W k,p(Rn) denote the Sobolev space consisting of all real-valued functions on Rn whose first k weak derivatives are functions in Lp. Here k is a non-negative integer and 1 ≤ p < ∞. The first part of the Sobolev embedding theorem states that if k > ℓ, p < n and 1 ≤ p < q < ∞ are two real numbers such that 1 p − k n ... | Sobolev inequality | 0.77754 |
97,888 | In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly stronger conditions... | Sobolev inequality | 0.77754 |
97,889 | Let (X, d) be a metric space and let Cl(X) denote the collection of all d-closed subsets of X. For a point x ∈ X and a set A ∈ Cl(X), set d ( x , A ) = inf a ∈ A d ( x , a ) . {\displaystyle d(x,A)=\inf _{a\in A}d(x,a).} A sequence (or net) of sets Ai ∈ Cl(X) is said to be Wijsman convergent to A ∈ Cl(X) if, for each x... | Levi–Lechicki theorem | 0.777538 |
97,890 | In theoretical physics, the BRST formalism is a method of implementing first class constraints. The letters BRST stand for Becchi, Rouet, Stora, and (independently) Tyutin who discovered this formalism. It is a sophisticated method to deal with quantum physical theories with gauge invariance. For example, the BRST meth... | BRST formalism | 0.777537 |
97,891 | The Journal of Civil Engineering and Management is a peer-reviewed scientific journal covering civil engineering published by Taylor & Francis on behalf of Vilnius Gediminas Technical University and the Lithuanian Academy of Sciences. It is an official journal of the International Council for Research and Innovation in... | Journal of Civil Engineering and Management | 0.777535 |
97,892 | The Therac-25 was a computer-controlled radiation therapy machine produced by Atomic Energy of Canada Limited (AECL) in 1982 after the Therac-6 and Therac-20 units (the earlier units had been produced in partnership with Compagnie générale de radiologie (CGR) of France). It was involved in at least six accidents betwee... | Therac-25 | 0.777534 |
97,893 | A back-illuminated sensor, also known as backside illumination (BI) sensor, is a type of digital image sensor that uses a novel arrangement of the imaging elements to increase the amount of light captured and thereby improve low-light performance. The technique was used for some time in specialized roles like low-light... | BSI CMOS | 0.777534 |
97,894 | The computational time required to diagonalize a matrix scales as N 3 {\displaystyle N^{3}} , where N {\displaystyle N} is the dimension of the matrix, so it is important to choose the smallest basis possible from which the relevant wavefunctions can be constructed. It is also convenient to choose a basis in which the ... | Berry–Tabor conjecture | 0.777533 |
97,895 | For conservative systems, the goal of quantum mechanics in non-perturbative regimes is to find the eigenvalues and eigenvectors of a Hamiltonian of the form H = H s + ε H n s , {\displaystyle H=H_{s}+\varepsilon H_{ns},\,} where H s {\displaystyle H_{s}} is separable in some coordinate system, H n s {\displaystyle H_{n... | Berry–Tabor conjecture | 0.777533 |
97,896 | During the first half of the twentieth century, chaotic behavior in mechanics was recognized (as in the three-body problem in celestial mechanics), but not well understood. The foundations of modern quantum mechanics were laid in that period, essentially leaving aside the issue of the quantum-classical correspondence i... | Berry–Tabor conjecture | 0.777533 |
97,897 | Many Hamiltonian systems which are classically integrable (non-chaotic) have been found to have quantum solutions that yield nearest neighbor distributions which follow the Poisson distributions. Similarly, many systems which exhibit classical chaos have been found with quantum solutions yielding a Wigner-Dyson distrib... | Berry–Tabor conjecture | 0.777533 |
97,898 | It is thought that regular classical dynamics is manifested by a Poisson distribution of energy levels: P ( s ) = e − s . {\displaystyle P(s)=e^{-s}.\ } In addition, systems which display chaotic classical motion are expected to be characterized by the statistics of random matrix eigenvalue ensembles. For systems invar... | Berry–Tabor conjecture | 0.777533 |
97,899 | Questions related to the correspondence principle arise in many different branches of physics, ranging from nuclear to atomic, molecular and solid-state physics, and even to acoustics, microwaves and optics. However, classical-quantum correspondence in chaos theory is not always possible. Thus, some versions of the cla... | Berry–Tabor conjecture | 0.777533 |
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