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97,000 | The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formula... | Whittaker–Shannon interpolation formula | 0.777966 |
97,001 | The interpolation formula is derived in the Nyquist–Shannon sampling theorem article, which points out that it can also be expressed as the convolution of an infinite impulse train with a sinc function: x ( t ) = ( ∑ n = − ∞ ∞ T ⋅ x ( n T ) ⏟ x ⋅ δ ( t − n T ) ) ⊛ ( 1 T s i n c ( t T ) ) . {\displaystyle x(t)=\left(\s... | Whittaker–Shannon interpolation formula | 0.777965 |
97,002 | If the process mean is nonzero, then pairs of terms need to be considered to also show that the expected value of the truncated terms converges to zero. Since a random process does not have a Fourier transform, the condition under which the sum converges to the original function must also be different. A stationary ran... | Whittaker–Shannon interpolation formula | 0.777965 |
97,003 | (See Sampling theorem.) Otherwise, the frequency components above the Nyquist frequency "fold" into the sub-Nyquist region of X(f), resulting in distortion. (See Aliasing.) | Whittaker–Shannon interpolation formula | 0.777965 |
97,004 | However, Russell Mixter, another creationist writer, said that "One should not insist that "kind" means species. The word "kind" as used in the Bible may apply to any animal which may be distinguished in any way from another, or it may be applied to a large group of species distinguishable from another group there is ... | Created kind | 0.777963 |
97,005 | The methods of baraminology are not universally accepted among young-Earth creationists. Other creationists have criticized these methods as having the same problems as traditional cladistics, as well as for occasionally producing results that they feel contradict the Bible.Baraminology has been heavily criticized for ... | Created kind | 0.777963 |
97,006 | Consequently, in 2003 Wise and other creationists proposed a refined baramin concept in the hope of developing a broader creationist model of biology. Alan Gishlick, reviewing the work of baraminologists in 2006, found it to be surprisingly rigorous and internally consistent, but concluded that the methods did not work... | Created kind | 0.777963 |
97,007 | In statistics, reification is the use of an idealized model of a statistical process. The model is then used to make inferences connecting model results, which imperfectly represent the actual process, with experimental observations. Also, a process whereby model-derived quantities such as principal components, factors... | Reification (statistics) | 0.777962 |
97,008 | Riprap affects the amount of organic material in a waterbody by acting as a filter, catching wood and leaves before they can enter the water. Riprap also covers and prevents plants from growing through, which can reduce shade over the water. Introducing ripraps creates a rocky environment which can affect the ecology o... | Riprap | 0.77796 |
97,009 | Borel showed in 1909 that the exceptional set of real pairs (α,β) violating the statement of the conjecture is of Lebesgue measure zero. Manfred Einsiedler, Anatole Katok and Elon Lindenstrauss have shown that it must have Hausdorff dimension zero; and in fact is a union of countably many compact sets of box-counting d... | Littlewood conjecture | 0.777959 |
97,010 | It is known that this would follow from a result in the geometry of numbers, about the minimum on a non-zero lattice point of a product of three linear forms in three real variables: the implication was shown in 1955 by Cassels and Swinnerton-Dyer. This can be formulated another way, in group-theoretic terms. There is ... | Littlewood conjecture | 0.777959 |
97,011 | In computer science, pathological has a slightly different sense with regard to the study of algorithms. Here, an input (or set of inputs) is said to be pathological if it causes atypical behavior from the algorithm, such as a violation of its average case complexity, or even its correctness. For example, hash tables g... | Pathological (mathematics) | 0.777957 |
97,012 | For example, the exceptional Lie algebras are included in the theory of semisimple Lie algebras: the axioms are seen as good, the exceptional objects as unexpected but valid. By contrast, pathological examples are instead taken to point out a shortcoming in the axioms, requiring stronger axioms to rule them out. For ex... | Pathological (mathematics) | 0.777957 |
97,013 | A classic example of a pathology is the Weierstrass function, a function that is continuous everywhere but differentiable nowhere. The sum of a differentiable function and the Weierstrass function is again continuous but nowhere differentiable; so there are at least as many such functions as differentiable functions. I... | Pathological (mathematics) | 0.777957 |
97,014 | For example, in statistics, the Cauchy distribution does not satisfy the central limit theorem, even though its symmetric bell-shape appears similar to many distributions which do; it fails the requirement to have a mean and standard deviation which exist and that are finite. Some of the best-known paradoxes, such as B... | Pathological (mathematics) | 0.777957 |
97,015 | For example, the Dirichlet function is Lebesgue integrable, and convolution with test functions is used to approximate any locally integrable function by smooth functions.Whether a behavior is pathological is by definition subject to personal intuition. Pathologies depend on context, training, and experience, and what ... | Pathological (mathematics) | 0.777957 |
97,016 | Yet it does not: it fails to be simply connected. For the underlying theory, see Jordan–Schönflies theorem. Counterexamples in Topology is a whole book of such counterexamples. | Pathological (mathematics) | 0.777957 |
97,017 | Fields are better-behaved than skew fields or general rings. Separable field extensions are better-behaved than non-separable ones. Normed division algebras are better-behaved than general composition algebras. | Pathological (mathematics) | 0.777957 |
97,018 | The Stieglitz rearrangement is a rearrangement reaction in organic chemistry which is named after the American chemist Julius Stieglitz (1867–1937) and was first investigated by him and Paul Nicholas Leech in 1913. It describes the 1,2-rearrangement of trityl amine derivatives to triaryl imines. It is comparable to a B... | Stieglitz rearrangement | 0.777957 |
97,019 | One famous counterexample in topology is the Alexander horned sphere, showing that topologically embedding the sphere S2 in R3 may fail to separate the space cleanly. As a counterexample, it motivated mathematicians to define the tameness property, which suppresses the kind of wild behavior exhibited by the horned sphe... | Pathological (mathematics) | 0.777957 |
97,020 | Spaces with integer dimension are better-behaved than spaces with fractal dimension. In abstract algebra: Groups are better-behaved than magmas and semigroups. Abelian groups are better-behaved than non-Abelian groups. | Pathological (mathematics) | 0.777957 |
97,021 | Attractive fixed points are better-behaved than repulsive fixed points. Hausdorff topologies are better-behaved than those in arbitrary general topology. Borel sets are better-behaved than arbitrary sets of real numbers. | Pathological (mathematics) | 0.777957 |
97,022 | Lebesgue-integrable functions are better-behaved than general functions. In topology, continuous functions are better-behaved than discontinuous ones. Euclidean space is better-behaved than non-Euclidean geometry. | Pathological (mathematics) | 0.777957 |
97,023 | In probability, events contained in the probability space's corresponding sigma-algebra are well-behaved, as are measurable functions.Unusually, the term could also be applied in a comparative sense: In calculus: Analytic functions are better-behaved than general smooth functions. Smooth functions are better-behaved th... | Pathological (mathematics) | 0.777957 |
97,024 | In Bézout's theorem, two polynomials are well-behaved, and thus the formula given by the theorem for the number of their intersections is valid, if their polynomial greatest common divisor is a constant. A meromorphic function is a ratio of two well-behaved functions, in the sense of those two functions being holomorph... | Pathological (mathematics) | 0.777957 |
97,025 | This has the benefit of making analysis easier, but produces a loss of generality of any conclusions reached. In both pure and applied mathematics (e.g., optimization, numerical integration, mathematical physics), well-behaved also means not violating any assumptions needed to successfully apply whatever analysis is be... | Pathological (mathematics) | 0.777957 |
97,026 | Organobromine chemistry is the study of the synthesis and properties of organobromine compounds, also called organobromides, which are organic compounds that contain carbon bonded to bromine. The most pervasive is the naturally produced bromomethane. One prominent application of synthetic organobromine compounds is the... | Organobromine chemistry | 0.777955 |
97,027 | Many dyes contain carbon-bromine bonds. The naturally occurring Tyrian purple (6,6’-dibromoindigo) was a valued dye before the development of the synthetic dye industry in the late 19th century. Several brominated anthroquinone derivatives are used commercially. Bromothymol blue is a popular indicator in analytical che... | Organobromine chemistry | 0.777955 |
97,028 | The initial stages of the deposition process can be described with the rate equation d Γ d t = k c {\displaystyle {d\Gamma \over dt}=kc} where Γ {\displaystyle \Gamma } ; is the number density of deposited particles, t {\displaystyle t} is the time, c {\displaystyle c} the particle number concentration, and k {\display... | Particle deposition | 0.777955 |
97,029 | This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations.Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects. Sin... | Inflation model | 0.777954 |
97,030 | If X is a vector random variable: Theorem. If a is (possibly) an atom of X (in the univariate case this means a point of discontinuity of FX ) then If X is scalar: If X is a vector random variable: Theorem (Gil-Pelaez). | Characteristic function (probability) | 0.777953 |
97,031 | There is a one-to-one correspondence between cumulative distribution functions and characteristic functions, so it is possible to find one of these functions if we know the other. The formula in the definition of characteristic function allows us to compute φ when we know the distribution function F (or density f). If,... | Characteristic function (probability) | 0.777953 |
97,032 | If the characteristic function φX of a random variable X is integrable, then FX is absolutely continuous, and therefore X has a probability density function. In the univariate case (i.e. when X is scalar-valued) the density function is given by In the multivariate case it is where t ⋅ x {\textstyle t\cdot x} is the dot... | Characteristic function (probability) | 0.777953 |
97,033 | Mathias’ theorem. A real-valued, even, continuous, absolutely integrable function φ, with φ(0) = 1, is a characteristic function if and only if ( − 1 ) n ( ∫ R φ ( p t ) e − t 2 / 2 H 2 n ( t ) d t ) ≥ 0 {\displaystyle (-1)^{n}\left(\int _{\mathbf {R} }\varphi (pt)e^{-t^{2}/2}H_{2n}(t)\,dt\right)\geq 0} for n = 0,1,2,.... | Characteristic function (probability) | 0.777953 |
97,034 | Pólya’s theorem, on the other hand, provides a very simple convexity condition which is sufficient but not necessary. Characteristic functions which satisfy this condition are called Pólya-type.Bochner’s theorem. An arbitrary function φ: Rn → C is the characteristic function of some random variable if and only if φ is ... | Characteristic function (probability) | 0.777953 |
97,035 | There is also interest in finding similar simple criteria for when a given function φ could be the characteristic function of some random variable. The central result here is Bochner’s theorem, although its usefulness is limited because the main condition of the theorem, non-negative definiteness, is very hard to verif... | Characteristic function (probability) | 0.777953 |
97,036 | Because of the continuity theorem, characteristic functions are used in the most frequently seen proof of the central limit theorem. The main technique involved in making calculations with a characteristic function is recognizing the function as the characteristic function of a particular distribution. | Characteristic function (probability) | 0.777953 |
97,037 | If a random variable has a moment-generating function M X ( t ) {\displaystyle M_{X}(t)} , then the domain of the characteristic function can be extended to the complex plane, and φ X ( − i t ) = M X ( t ) . {\displaystyle \varphi _{X}(-it)=M_{X}(t).} Note however that the characteristic function of a distribution alwa... | Characteristic function (probability) | 0.777953 |
97,038 | The bijection stated above between probability distributions and characteristic functions is sequentially continuous. That is, whenever a sequence of distribution functions Fj(x) converges (weakly) to some distribution F(x), the corresponding sequence of characteristic functions φj(t) will also converge, and the limit ... | Characteristic function (probability) | 0.777953 |
97,039 | In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provide... | Characteristic function (probability) | 0.777953 |
97,040 | The bunker is built to deflect a 30 megaton nuclear explosion as close as 1.2 miles. Within a mountain tunnel are sets of 25-ton blast doors and another for the civil engineering department. The doors were built so that they can always be opened when needed. Should a nuclear blast hit the building, they are designed to... | NORAD Computer System | 0.777952 |
97,041 | Electronic Systems Division Detachment 10 at Ent AFB became the Cheyenne Mountain Complex Management Office (CMCMO) in 1963, the year the Chidlaw Combined Operations Center began operations; and on February 15, 1980, ESD Detachment 2 was established at the "Cheyenne Mountain Complex" (Det 2 became the AFSC focal point ... | NORAD Computer System | 0.777952 |
97,042 | "Classical Language Toolkit Archived 24 May 2016 at the Wayback Machine" (CLTK). A Natural language processing toolkit for Python offering a variety of functionality for Latin and other classical languages. "Collatinus web". Online lemmatizer and morphological analysis for Latin texts. | Latin Language | 0.777951 |
97,043 | In the late 19th century, the metaphysical term "planes" was popularized by H. P. Blavatsky, who propounded a complex cosmology consisting of seven "planes". The term aether ("ether") was adopted from Ancient Greek via Victorian physics that would later be discredited. The term "ether" was then incorporated into the wr... | Interdimensional UFO hypothesis | 0.777949 |
97,044 | In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of convex uniform 6-polytopes has not been determined, but most can be made as Wythoff constructions from a small set of symmetry gr... | Uniform polypeton | 0.777948 |
97,045 | Strings are further classified into open and closed. The topology of the worldsheet of an open string is R × I {\displaystyle \mathbb {R} \times I} , where I := {\displaystyle I:=} , a closed interval, and admits a global coordinate chart ( τ , σ ) {\displaystyle (\tau ,\sigma )} with − ∞ < τ < ∞ {\displaystyle -\inft... | World sheet | 0.777946 |
97,046 | In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in w... | World sheet | 0.777946 |
97,047 | Felix Klein (1883) and Henri Poincaré (1882) conjectured the uniformization theorem for (the Riemann surfaces of) algebraic curves. Henri Poincaré (1883) extended this to arbitrary multivalued analytic functions and gave informal arguments in its favor. The first rigorous proofs of the general uniformization theorem we... | Uniformization theorem | 0.777945 |
97,048 | Richard S. Hamilton showed that the normalized Ricci flow on a closed surface uniformizes the metric (i.e., the flow converges to a constant curvature metric). However, his proof relied on the uniformization theorem. The missing step involved Ricci flow on the 2-sphere: a method for avoiding an appeal to the uniformiza... | Uniformization theorem | 0.777945 |
97,049 | (2006), Teichmüller theory and applications to geometry, topology, and dynamics. Vol. 1. | Uniformization theorem | 0.777945 |
97,050 | Rado's theorem shows that every Riemann surface is automatically second-countable. Although Rado's theorem is often used in proofs of the uniformization theorem, some proofs have been formulated so that Rado's theorem becomes a consequence. Second countability is automatic for compact Riemann surfaces. | Uniformization theorem | 0.777945 |
97,051 | Many classical proofs of the uniformization theorem rely on constructing a real-valued harmonic function on the simply connected Riemann surface, possibly with a singularity at one or two points and often corresponding to a form of Green's function. Four methods of constructing the harmonic function are widely employed... | Uniformization theorem | 0.777945 |
97,052 | It further follows that every Riemann surface admits a Riemannian metric of constant curvature, where the curvature can be taken to be 1 in the elliptic, 0 in the parabolic and -1 in the hyperbolic case. The uniformization theorem also yields a similar classification of closed orientable Riemannian 2-manifolds into ell... | Uniformization theorem | 0.777945 |
97,053 | In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the p... | Uniformization theorem | 0.777945 |
97,054 | In 1965, Moore’s law forever changed the world of technology. That seminal prediction developed its roots within the Society. ECS has included numerous Nobel laureates among its members, most recently the three co-winners of the 2019 Nobel Prize in Chemistry. John B. Goodenough, M. Stanley Whittingham, and Akira Yoshin... | ECS Transactions | 0.777944 |
97,055 | Bridging the gap between electrical engineering and chemistry led innovative young people in industrial and academic circles to search for a new forum to discuss developments in the burgeoning field of electrochemistry. The original constitution of the Society called for holding meetings and publishing papers presented... | ECS Transactions | 0.777944 |
97,056 | Among the significant talent recognized at an early age by this award is Nobel laureate, M. Stanley Whittingham, who received it in 1970. The Olin Palladium Award (formerly the Palladium Medal Award), established in 1950, is presented in odd-numbered years to recognize "distinguished contributions to the field of elect... | ECS Transactions | 0.777944 |
97,057 | Battery (BATT) Topical Interest Area (TIA): Batteries and Energy Storage (established 1947) High-Temperature Energy, Materials, & Processes (H-TEMP) TIA: Fuel Cells, Electrolyzers, and Energy Conversion (established 1921) Corrosion (CORR) TIA: Corrosion Science and Technology (established 1942) Industrial Electrochemis... | ECS Transactions | 0.777944 |
97,058 | A nephroid is an algebraic curve of degree 6. an epicycloid with two cusps a plane simple closed curve = a Jordan curve | Nephroid caustic | 0.777943 |
97,059 | In geometry, a nephroid (from Ancient Greek ὁ νεφρός (ho nephros) 'kidney-shaped') is a specific plane curve. It is a type of epicycloid in which the smaller circle's radius differs from the larger one by a factor of one-half. | Nephroid caustic | 0.777943 |
97,060 | A Markush structure is a representation of chemical structure used to indicate a group of related chemical compounds. They are commonly used in chemistry texts and in patent claims. Markush structures are depicted with multiple independently variable groups, such as R groups in which a side chain can have varying struc... | Markush structure | 0.777941 |
97,061 | In organosulfur chemistry, thioacetals are the sulfur (thio-) analogues of acetals (R−CH(−OR)2). There are two classes: the less-common monothioacetals, with the formula R−CH(−OR')−SR", and the dithioacetals, with the formula R−CH(−SR')2 (symmetric dithioacetals) or R−CH(−SR')−SR" (asymmetric dithioacetals).The symmetr... | Thioacetal | 0.777941 |
97,062 | Platinum black is widely used as a thin film covering solid platinum metal, forming platinum electrodes for applications in electrochemistry. The process of covering platinum electrodes with such a layer of platinum black is called "platinization of platinum." The platinized platinum has a true surface area much higher... | Platinized platinum | 0.77794 |
97,063 | MediaWiki can use either the MySQL/MariaDB, PostgreSQL or SQLite relational database management system. Support for Oracle Database and Microsoft SQL Server has been dropped since MediaWiki 1.34. A MediaWiki database contains several dozen tables, including a page table that contains page titles, page ids, and other me... | MediaWiki extension | 0.77794 |
97,064 | In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed 1979 by W. H. Cunningham to defeat the deformed hypercube constructions by Klee and Minty et al. (see, e.g.... | Cunningham's rule | 0.77794 |
97,065 | Due to the water scarcity issue, the construction of coal-fired power plants in the west is hindered. Another issue is transmission efficiency. Using combined heat and power at the user end is more energy efficient than using power from long distance transmission lines. Economic issue: The total investment is estimated... | Ultra-high-voltage electricity transmission in China | 0.777938 |
97,066 | Older power plants along the coast will be retired. This will lower the total current amount of pollution, as well as the pollution felt by citizens within urban dwellings. The use of large central power plants providing electric heating are also less polluting than individual boilers used for winter heating in many no... | Ultra-high-voltage electricity transmission in China | 0.777938 |
97,067 | China's electricity consumption is expected to reach 6,800–6,900 TWh by 2018 from 4,690 TWh in 2011, with installed capacity reaching 1,463 GW from 1,056 GW in 2011, of which 342 GW is hydropower, 928 GW coal-fired, 100 GW wind, 43GW nuclear, and 40GW natural gas. China is the country with the largest consumption of el... | Ultra-high-voltage electricity transmission in China | 0.777938 |
97,068 | Bouncy Castle started when two colleagues were tired of having to re-invent a set of cryptography libraries each time they changed jobs working in server-side Java SE. One of the developers was active in Java ME (J2ME at that time) development as a hobby and a design consideration was to include the greatest range of J... | Bouncy Castle (cryptography) | 0.777934 |
97,069 | Bouncy Castle is a collection of APIs used in cryptography. It includes APIs for both the Java and the C# programming languages. The APIs are supported by a registered Australian charitable organization: Legion of the Bouncy Castle Inc. Bouncy Castle is Australian in origin and therefore American restrictions on the ex... | Bouncy Castle (cryptography) | 0.777934 |
97,070 | The intent is to use the low-level API in memory constrained devices (JavaME) or when easy access to the JCE libraries is not possible (such as distribution in an applet). As the light-weight API is just Java code, the Java virtual machine (JVM) does not impose any restrictions on the operation of the code, and at earl... | Bouncy Castle (cryptography) | 0.777934 |
97,071 | The Center of Excellence in Nanotechnology for Energy (CENE) officially started in April 2012, when the former Excellence Center ended. The former Center (October 2006 – March 2012) comprised three groups of the faculties from Pharmacy, Science and Engineering which had been doing research in drug delivery, multilayers... | Center of Excellence in Nanotechnology for Energy | 0.777934 |
97,072 | The Bouncy Castle architecture consists of two main components that support the base cryptographic capabilities. These are known as the 'light-weight' API, and the Java Cryptography Extension (JCE) provider. Further components built upon the JCE provider support additional functionality, such as PGP support, S/MIME, et... | Bouncy Castle (cryptography) | 0.777934 |
97,073 | When the canonical bundle K X {\displaystyle K_{X}} is not trivial, ample, or anti-ample, it is not possible to ask for a Kähler–Einstein metric, as the class c 1 ( X ) {\displaystyle c_{1}(X)} cannot contain a Kähler metric, and so the necessary topological condition can never be satisfied. This follows from the Kodai... | Kähler–Einstein metric | 0.777934 |
97,074 | The existence problem for Kähler–Einstein metrics can be split up into three distinct cases, dependent on the sign of the topological constant λ {\displaystyle \lambda } . Since the Kähler form ω {\displaystyle \omega } is always a positive differential form, the sign of λ {\displaystyle \lambda } depends on whether th... | Kähler–Einstein metric | 0.777934 |
97,075 | In differential geometry, a Kähler–Einstein metric on a complex manifold is a Riemannian metric that is both a Kähler metric and an Einstein metric. A manifold is said to be Kähler–Einstein if it admits a Kähler–Einstein metric. The most important special case of these are the Calabi–Yau manifolds, which are Kähler and... | Kähler–Einstein metric | 0.777934 |
97,076 | Suppose ( X , g ) {\displaystyle (X,g)} is a Riemannian manifold. In physics the Einstein field equations are a set of partial differential equations on the metric tensor g {\displaystyle g} which describe how the manifold X {\displaystyle X} should curve due to the existence of mass or energy, a quantity encapsulated ... | Kähler–Einstein metric | 0.777934 |
97,077 | In MPEG codecs, the full process consists of a discrete cosine transform, followed by quantization and entropy encoding. Because of this, rate-distortion optimization is much slower than most other block-matching metrics, such as the simple sum of absolute differences (SAD) and sum of absolute transformed differences (... | Rate–distortion optimization | 0.777933 |
97,078 | Rate-distortion optimization solves the aforementioned problem by acting as a video quality metric, measuring both the deviation from the source material and the bit cost for each possible decision outcome. The bits are mathematically measured by multiplying the bit cost by the Lagrangian, a value representing the rela... | Rate–distortion optimization | 0.777933 |
97,079 | The University of Kentucky, based in Lexington, has operated two satellite campuses at different times: In 1948, the university opened an extension campus in Covington known as the Northern Extension Center. In 1968, this campus was separated from UK, becoming the institution now known as Northern Kentucky University, ... | Satellite campuses | 0.777932 |
97,080 | OCLC 667041380. Beals, Richard; Greiner, Peter (1988). Calculus on Heisenberg manifolds. | Richard Beals (mathematician) | 0.777932 |
97,081 | Richard William Beals (28 May 1938, Erie, Pennsylvania) is an American mathematician who works on partial differential equations and functional analysis. He is known as the author or co-author of several mathematical textbooks. Beals studied at Yale University earning a B.A. | Richard Beals (mathematician) | 0.777932 |
97,082 | Therefore I can assume that this other person knows very little about chemistry." This assumption may be true in any number of specific cases, making inductive reasoning based on this assumption cogent, but is not applicable in the general case (there are many people who are very knowledgeable in the field of chemistry... | Psychologist's fallacy | 0.77793 |
97,083 | In this alternative form, the fallacy is described as a specific form of the "similar to me" stereotype: what is unknown about another person is assumed, for simplicity, using things the observer knows about themself. Such a bias leads the observer to presuppose knowledge or skills, or lack of such, possessed by anothe... | Psychologist's fallacy | 0.77793 |
97,084 | The explanation is that the Hamiltonian used in nonrelativistic quantum mechanics is only an approximation to the Hamiltonian from quantum field theory. The higher-energy electron states (2s, 2p, 3s, etc.) are stationary states according to the approximate Hamiltonian, but not stationary according to the true Hamiltoni... | Energy eigenfunction | 0.777929 |
97,085 | Spontaneous decay complicates the question of stationary states. For example, according to simple (nonrelativistic) quantum mechanics, the hydrogen atom has many stationary states: 1s, 2s, 2p, and so on, are all stationary states. But in reality, only the ground state 1s is truly "stationary": An electron in a higher e... | Energy eigenfunction | 0.777929 |
97,086 | Asteroid 14724 SNO is named in honour of SNO. In November 2006, the entire SNO team was awarded the inaugural John C. Polanyi Award for "a recent outstanding advance in any field of the natural sciences or engineering" conducted in Canada. SNO principal investigator Arthur B. McDonald won the 2015 Nobel Prize in Physic... | Sudbury Neutrino Observatory | 0.777926 |
97,087 | The Sudbury Neutrino Observatory (SNO) was a neutrino observatory located 2100 m underground in Vale's Creighton Mine in Sudbury, Ontario, Canada. The detector was designed to detect solar neutrinos through their interactions with a large tank of heavy water. The detector was turned on in May 1999, and was turned off o... | Sudbury Neutrino Observatory | 0.777926 |
97,088 | This was important to the standard solar model. In 2007, the Franklin Institute awarded the director of SNO Art McDonald with the Benjamin Franklin Medal in Physics. In 2015 the Nobel Prize for Physics was jointly awarded to Arthur B. McDonald, and Takaaki Kajita of the University of Tokyo, for the discovery of neutrin... | Sudbury Neutrino Observatory | 0.777926 |
97,089 | In physics, the weber ( VAY-, WEH-bər; symbol: Wb) is the unit of magnetic flux in the International System of Units (SI), whose units are volt-second. A magnetic flux density of one Wb/m2 (one weber per square metre) is one tesla. The weber is named after the German physicist Wilhelm Eduard Weber (1804–1891). | Weber (unit) | 0.777924 |
97,090 | Founded in 1952 with chemistry faculty inherited from Jiaotong University, AuroraUniversity, Utopia University, Soochou University and Jiangnan University. | East China University of Science and Technology | 0.77792 |
97,091 | East China University of Science and Technology (ECUST, simplified Chinese: 华东理工大学; traditional Chinese: 華東理工大學; pinyin: Huádōng Lǐgōng Dàxué) is a public research university with two campuses located in Shanghai, China. Established in 1952 as East China Institute of Chemical Technology, it has evolved from an institut... | East China University of Science and Technology | 0.77792 |
97,092 | Seven majors are distinguished as national key disciplines, those include: Chemical Engineering Chemical Technology Biochemical Engineering Applied Chemistry Industrial Catalysis Chemical Process Equipment Control Theory and Control Engineering Material ScienceEssential Science Indicators (ESI) Subject Ranking ECUST ha... | East China University of Science and Technology | 0.77792 |
97,093 | Long-term academic relationships have been established with more than 60 universities, enterprises, and research institutes all over the world. The following degrees are offered jointly with partner universities: MBA Program with the University of Canberra, Australia International Business Program with Wollongong Unive... | East China University of Science and Technology | 0.77792 |
97,094 | Library The Library of East China University of Science and Technology (ECUST) was established in 1952 and is placed under direct auspice of the Ministry of Education of People's Republic of China. Starting with the collections of the different departments that initially made up the foundation of the college, it has de... | East China University of Science and Technology | 0.77792 |
97,095 | {\displaystyle C^{\infty }(U).} With this definition of multiplication by a smooth function, the ordinary product rule of calculus remains valid. However, some unusual identities also arise. | Tempered distributions | 0.77792 |
97,096 | Operations on distributions and spaces of distributions are often defined using the transpose of a linear operator. This is because the transpose allows for a unified presentation of the many definitions in the theory of distributions and also because its properties are well-known in functional analysis. For instance, ... | Tempered distributions | 0.77792 |
97,097 | Many operations which are defined on smooth functions with compact support can also be defined for distributions. In general, if A: D ( U ) → D ( U ) {\displaystyle A:{\mathcal {D}}(U)\to {\mathcal {D}}(U)} is a linear map that is continuous with respect to the weak topology, then it is not always possible to extend A ... | Tempered distributions | 0.77792 |
97,098 | If F {\displaystyle F} is a submersion, then F # {\displaystyle F^{\#}} is defined on distributions by finding the transpose map. The uniqueness of this extension is guaranteed since F # {\displaystyle F^{\#}} is a continuous linear operator on D ( U ) . {\displaystyle {\mathcal {D}}(U).} Existence, however, requires u... | Tempered distributions | 0.77792 |
97,099 | A necessary (but not sufficient) condition for extending F # {\displaystyle F^{\#}} to distributions is that F {\displaystyle F} be an open mapping. The Inverse function theorem ensures that a submersion satisfies this condition. | Tempered distributions | 0.77792 |
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