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19,200 | Curves of rank higher than 20 have been known since 1994, with lower bounds on their ranks ranging from 21 to 28, but their exact ranks are not known and in particular it is not proven which of them have higher rank than the others or which is the true "current champion".As for the groups constituting the torsion subgr... | Elliptic Curve | 0.811692 |
19,201 | Redoing the same with P1, that is to say P1 = 2P2 + Q2, then P2 = 2P3 + Q3, etc. finally expresses P as an integral linear combination of points Qi and of points whose height is bounded by a fixed constant chosen in advance: by the weak Mordell–Weil theorem and the second property of the height function P is thus expre... | Elliptic Curve | 0.811692 |
19,202 | The first part shows that for any integer m > 1, the quotient group E(Q)/mE(Q) is finite (this is the weak Mordell–Weil theorem). Second, introducing a height function h on the rational points E(Q) defined by h(P0) = 0 and h(P) = log max(|p|, |q|) if P (unequal to the point at infinity P0) has as abscissa the rational ... | Elliptic Curve | 0.811692 |
19,203 | Rational points can be constructed by the method of tangents and secants detailed above, starting with a finite number of rational points. More precisely the Mordell–Weil theorem states that the group E(Q) is a finitely generated (abelian) group. By the fundamental theorem of finitely generated abelian groups it is the... | Elliptic Curve | 0.811692 |
19,204 | Elliptic curves over finite fields are notably applied in cryptography and for the factorization of large integers. These algorithms often make use of the group structure on the points of E. Algorithms that are applicable to general groups, for example the group of invertible elements in finite fields, F*q, can thus be... | Elliptic Curve | 0.811692 |
19,205 | Let K = Fq be the finite field with q elements and E an elliptic curve defined over K. While the precise number of rational points of an elliptic curve E over K is in general difficult to compute, Hasse's theorem on elliptic curves gives the following inequality: | # E ( K ) − ( q + 1 ) | ≤ 2 q {\displaystyle |\#E(K)-(... | Elliptic Curve | 0.811692 |
19,206 | However in biochemical dynamic modeling and sensitivity analysis, N {\displaystyle {\bf {N}}} tends to be in more common use to indicate 'number'. In the chemistry domain, the symbol used for the stoichiometry matrix is highly variable though the symbols S and N have been used in the past. v {\displaystyle {\bf {v}}} i... | Biochemical systems equation | 0.811692 |
19,207 | The biochemical systems equation is a compact equation of nonlinear differential equations for describing a kinetic model for any network of coupled biochemical reactions and transport processes.The equation is expressed in the following form: d x d t = N v ( x ( p ) , p ) {\displaystyle {\dfrac {\bf {dx}}{dt}}={\bf {N... | Biochemical systems equation | 0.811692 |
19,208 | In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate f... | CKM matrix | 0.811687 |
19,209 | In 1963, Nicola Cabibbo introduced the Cabibbo angle (θc) to preserve the universality of the weak interaction. Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy, on the effectively rotated nonstrange and strange vector and axial weak currents, which he references.In light of current concepts (... | CKM matrix | 0.811687 |
19,210 | In theoretical computer science, chaos computing is the idea of using chaotic systems for computation. In particular, chaotic systems can be made to produce all types of logic gates and further allow them to be morphed into each other. | Chaos computing | 0.811682 |
19,211 | Strong and weak sampling are two sampling approach in Statistics, and are popular in computational cognitive science and language learning. In strong sampling, it is assumed that the data are intentionally generated as positive examples of a concept, while in weak sampling, it is assumed that the data are generated wit... | Strong and weak sampling | 0.811678 |
19,212 | The Hamiltonian for a hydrogen-like potential can be written in spherical coordinates as where V ( r ) = − Z e 2 / r {\displaystyle V(r)=-Ze^{2}/r} and p r {\displaystyle p_{r}} is the radial momentum which is real and self-conjugate. Suppose | n l ⟩ {\displaystyle |nl\rangle } is an eigenvector of the Hamiltonian wher... | Ladder operator | 0.811669 |
19,213 | An annihilation operator is used to remove a particle from the initial state and a creation operator is used to add a particle to the final state. The term "ladder operator" is also sometimes used in mathematics, in the context of the theory of Lie algebras and in particular the affine Lie algebras, to describe the su(... | Ladder operator | 0.811669 |
19,214 | In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raising operator is sometimes called the creation operator, and the lowering oper... | Ladder operator | 0.811669 |
19,215 | "Computing Machinery and Intelligence" is a seminal paper written by Alan Turing on the topic of artificial intelligence. The paper, published in 1950 in Mind, was the first to introduce his concept of what is now known as the Turing test to the general public. Turing's paper considers the question "Can machines think?... | Computing Machinery and Intelligence | 0.811669 |
19,216 | An examination of the development in artificial intelligence that has followed reveals that the learning machine did take the abstract path suggested by Turing as in the case of Deep Blue, a chess playing computer developed by IBM and one which defeated the world champion Garry Kasparov (though, this too is controversi... | Computing Machinery and Intelligence | 0.811669 |
19,217 | This more complex system is explained by Turing as "..would be such that the machines store would be largely occupied with definitions and propositions. The propositions would have various kinds of status, e.g., well-established facts, conjectures, mathematically proved theorems, statements given by an authority, expre... | Computing Machinery and Intelligence | 0.811669 |
19,218 | More recent AI research in robotics and computational intelligence attempts to find the complex rules that govern our "informal" and unconscious skills of perception, mobility and pattern matching. See Dreyfus' critique of AI). This rejoinder also includes the Turing's Wager argument. Extra-sensory perception: In 1950,... | Computing Machinery and Intelligence | 0.811669 |
19,219 | The Mathematical Objection: This objection uses mathematical theorems, such as Gödel's incompleteness theorem, to show that there are limits to what questions a computer system based on logic can answer. Turing suggests that humans are too often wrong themselves and pleased at the fallibility of a machine. (This argume... | Computing Machinery and Intelligence | 0.811669 |
19,220 | Having clarified the question, Turing turned to answering it: he considered the following nine common objections, which include all the major arguments against artificial intelligence raised in the years since his paper was first published. Religious Objection: This states that thinking is a function of man's immortal ... | Computing Machinery and Intelligence | 0.811669 |
19,221 | The International Journal of Mathematics and Computer Science (online: ISSN 1814-0432, print: ISSN 1814-0424) is a quarterly peer-reviewed scientific journal which was established in 2006 and publishes original papers in the broad subjects of mathematics and computer science. It is abstracted and indexed by Clarivate A... | International Journal of Mathematics and Computer Science | 0.811665 |
19,222 | From its origins as a language for children of all ages, standard Smalltalk syntax uses punctuation in a manner more like English than mainstream coding languages. The remainder of the language, including control structures for conditional evaluation and iteration, is implemented on top of the built-in constructs by th... | Smalltalk | 0.811664 |
19,223 | The formula states that if Π {\displaystyle \Pi } is an irreducible representation with highest weight λ {\displaystyle \lambda } , then the character X {\displaystyle \mathrm {X} } of Π {\displaystyle \Pi } satisfies: X ( e H ) = ∑ w ∈ W det ( w ) e i ⟨ w ⋅ ( λ + ρ ) , H ⟩ ∑ w ∈ W det ( w ) e i ⟨ w ⋅ ρ , H ⟩ {\display... | Compact group | 0.811662 |
19,224 | The classification of compact, simply connected Lie groups is the same as the classification of complex semisimple Lie algebras. Indeed, if K is a simply connected compact Lie group, then the complexification of the Lie algebra of K is semisimple. Conversely, every complex semisimple Lie algebra has a compact real form... | Compact group | 0.811662 |
19,225 | And by the Peter–Weyl theorem, the characters of the irreducible representations form an orthonormal basis for the space of square integrable class functions. If there were some λ {\displaystyle \lambda } that is not the highest weight of a representation, then the corresponding Φ λ {\displaystyle \Phi _{\lambda }} wou... | Compact group | 0.811661 |
19,226 | The Weyl integral formula. The Peter–Weyl theorem for class functions, which states that the characters of the irreducible representations form an orthonormal basis for the space of square integrable class functions on K {\displaystyle K} .With these tools in hand, we proceed with the proof. The first major step in the... | Compact group | 0.811661 |
19,227 | {\displaystyle 1\to G_{0}\to G\to \pi _{0}(G)\to 1.} Meanwhile, for connected compact Lie groups, we have the following result: Theorem: Every connected compact Lie group is the quotient by a finite central subgroup of a product of a simply connected compact Lie group and a torus.Thus, the classification of connected c... | Compact group | 0.811661 |
19,228 | In mathematics, a compact (topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group). Compact groups are a natural generalization of finite groups with the discrete topology and have properties t... | Compact group | 0.811661 |
19,229 | We now outline the proof of the theorem of the highest weight, following the original argument of Hermann Weyl. We continue to let K {\displaystyle K} be a connected compact Lie group and T {\displaystyle T} a fixed maximal torus in K {\displaystyle K} . We focus on the most difficult part of the theorem, showing that ... | Compact group | 0.811661 |
19,230 | Every analytically integral element is integral in the Lie algebra sense, but not the other way around. (This phenomenon reflects that, in general, not every representation of the Lie algebra k {\displaystyle {\mathfrak {k}}} comes from a representation of the group K.) On the other hand, if K is simply connected, the ... | Compact group | 0.811661 |
19,231 | The irreducible finite-dimensional representations of K are then classified by a theorem of the highest weight, which is closely related to the analogous theorem classifying representations of a semisimple Lie algebra. The result says that: every irreducible representation has highest weight, the highest weight is alwa... | Compact group | 0.811661 |
19,232 | Specifically, the weights are the nonzero weights for the adjoint action of T on the complexified Lie algebra of K. The root system R has all the usual properties of a root system, except that the elements of R may not span t {\displaystyle {\mathfrak {t}}} . We then choose a base Δ {\displaystyle \Delta } for R and we... | Compact group | 0.811661 |
19,233 | We now briefly describe the structures needed to formulate the theorem; more details can be found in the article on weights in representation theory. We need the notion of a root system for K (relative to a given maximal torus T). The construction of this root system R ⊂ t {\displaystyle R\subset {\mathfrak {t}}} is ve... | Compact group | 0.811661 |
19,234 | Here the fact that in the limit a faithful representation of G is found is another consequence of the Peter–Weyl theorem. The unknown part of the representation theory of compact groups is thereby, roughly speaking, thrown back onto the complex representations of finite groups. This theory is rather rich in detail, but... | Compact group | 0.811661 |
19,235 | A combination of Weyl's work and Cartan's theorem gives a survey of the whole representation theory of compact groups G. That is, by the Peter–Weyl theorem the irreducible unitary representations ρ of G are into a unitary group (of finite dimension) and the image will be a closed subgroup of the unitary group by compac... | Compact group | 0.811661 |
19,236 | The representation theory of compact groups (not necessarily Lie groups and not necessarily connected) was founded by the Peter–Weyl theorem. Hermann Weyl went on to give the detailed character theory of the compact connected Lie groups, based on maximal torus theory. The resulting Weyl character formula was one of the... | Compact group | 0.811661 |
19,237 | Certain simple examples of the representation theory of compact Lie groups can be worked out by hand, such as the representations of the rotation group SO(3), the special unitary group SU(2), and the special unitary group SU(3). We focus here on the general theory. See also the parallel theory of representations of a s... | Compact group | 0.811661 |
19,238 | Amongst groups that are not Lie groups, and so do not carry the structure of a manifold, examples are the additive group Zp of p-adic integers, and constructions from it. In fact any profinite group is a compact group. This means that Galois groups are compact groups, a basic fact for the theory of algebraic extensions... | Compact group | 0.811661 |
19,239 | Lie groups form a class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups include the circle group T and the torus groups Tn, the orthogonal group O(n), the special orthogonal group SO(n) and its covering spin group Spin(n), the unitary gro... | Compact group | 0.811661 |
19,240 | The Ambrose–Singer theorem makes explicit this relationship between the curvature and holonomy. Other notions of connection come equipped with their own parallel transportation systems as well. | Parallel transport | 0.81166 |
19,241 | In geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold ... | Parallel transport | 0.81166 |
19,242 | In (pseudo) Riemannian geometry, a metric connection is any connection whose parallel transport mappings preserve the metric tensor. Thus a metric connection is any connection Γ such that, for any two vectors X, Y ∈ Tγ(s) ⟨ Γ ( γ ) s t X , Γ ( γ ) s t Y ⟩ γ ( t ) = ⟨ X , Y ⟩ γ ( s ) . {\displaystyle \langle \Gamma (\ga... | Parallel transport | 0.81166 |
19,243 | If ∇ is a metric connection, then the affine geodesics are the usual geodesics of Riemannian geometry and are the locally distance minimizing curves. More precisely, first note that if γ: I → M, where I is an open interval, is a geodesic, then the norm of γ ˙ {\displaystyle {\dot {\gamma }}} is constant on I. Indeed, d... | Parallel transport | 0.81166 |
19,244 | The isomorphisms between fibers obtained in this way will, in general, depend on the choice of the curve: if they do not, then parallel transport along every curve can be used to define parallel sections of E over all of M. This is only possible if the curvature of ∇ is zero. In particular, parallel transport around a ... | Parallel transport | 0.81166 |
19,245 | Thus the Picard–Lindelöf theorem guarantees the existence and uniqueness of the solution. Thus the connection ∇ defines a way of moving elements of the fibers along a curve, and this provides linear isomorphisms between the fibers at points along the curve: Γ ( γ ) s t: E γ ( s ) → E γ ( t ) {\displaystyle \Gamma (\gam... | Parallel transport | 0.81166 |
19,246 | In organic chemistry, a methylene bridge, methylene spacer, or methanediyl group is any part of a molecule with formula −CH2−; namely, a carbon atom bound to two hydrogen atoms and connected by single bonds to two other distinct atoms in the rest of the molecule. It is the repeating unit in the skeleton of the unbranch... | Active methylene compound | 0.811653 |
19,247 | A multi-level converter (MLC) is a method of generating high-voltage wave-forms from lower-voltage components. MLC origins go back over a hundred years, when in the 1880s, the advantages of DC long-distance transmission became evident.Modular multi-level converters (MMC) were investigated by Tricoli et al in 2017. Alth... | Multi-level converter | 0.811647 |
19,248 | Because the relationship pKb = pKw − pKa holds only in aqueous solutions (though analogous relationships apply for other amphoteric solvents), subdisciplines of chemistry like organic chemistry that usually deal with nonaqueous solutions generally do not use pKb as a measure of basicity. Instead, the pKa of the conjuga... | Acidity constant | 0.811647 |
19,249 | This permits a technique called isoelectric focusing, which is used for separation of proteins by 2-D gel polyacrylamide gel electrophoresis. Buffer solutions also play a key role in analytical chemistry. They are used whenever there is a need to fix the pH of a solution at a particular value. | Acidity constant | 0.811647 |
19,250 | A knowledge of pKa values is important for the quantitative treatment of systems involving acid–base equilibria in solution. Many applications exist in biochemistry; for example, the pKa values of proteins and amino acid side chains are of major importance for the activity of enzymes and the stability of proteins. Prot... | Acidity constant | 0.811647 |
19,251 | Much of the theory of nuclear spaces was developed by Alexander Grothendieck while investigating the Schwartz kernel theorem and published in (Grothendieck 1955). We have the following generalization of the theorem. Schwartz kernel theorem: Suppose that X {\displaystyle X} is nuclear, Y {\displaystyle Y} is locally con... | Nuclear spaces | 0.811641 |
19,252 | A continuous functional C {\displaystyle C} on a nuclear space A {\displaystyle A} is called a characteristic functional if C ( 0 ) = 1 , {\displaystyle C(0)=1,} and for any complex z j and x j ∈ A , {\displaystyle z_{j}{\text{ and }}x_{j}\in A,} j , k = 1 , … , n , {\displaystyle j,k=1,\ldots ,n,} Given a characterist... | Nuclear spaces | 0.811641 |
19,253 | In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite dimensional Euclidean spaces and share many of their desirable properties. Nuclear spaces are however quite different from Hilbert spaces, another generalization of finite dimensional Euclidean spaces. They wer... | Nuclear spaces | 0.811641 |
19,254 | The pseudo-code can be summarized as: Objective function: f ( x ) , x = ( x 1 , x 2 , … , x d ) ; {\displaystyle f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},\dots ,x_{d});\,} Generate an initial population of n {\displaystyle n} host nests; While (t F j {\displaystyle F_{i}>F_{j}} ), Replace j by the new solution; ... | Cuckoo search | 0.811639 |
19,255 | In operations research, cuckoo search is an optimization algorithm developed by Xin-She Yang and Suash Deb in 2009. It was inspired by the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of host birds of other species. Some host birds can engage direct conflict with the intruding cuck... | Cuckoo search | 0.811639 |
19,256 | Some cuckoo species such as the New World brood-parasitic Tapera have evolved in such a way that female parasitic cuckoos are often very specialized in the mimicry in colors and pattern of the eggs of a few chosen host species. Cuckoo search idealized such breeding behavior, and thus can be applied for various optimiza... | Cuckoo search | 0.811639 |
19,257 | Research balloons are balloons that are used for scientific research. They are usually unmanned, filled with a lighter-than-air gas like helium, and fly at high altitudes. Meteorology, atmospheric research, astronomy, and military research may be conducted from a research balloon. Weather balloons are a type of researc... | Research balloon | 0.811638 |
19,258 | The data exchange format (spML) is also under development.Mass spectrometry and mass spectrometry informatics documents have been published as recommendations by the mass spectrometry working group. The working group has released several data exchange format: the mzML, for the capture of data generated by a mass spectr... | Proteomics Standards Initiative | 0.811637 |
19,259 | As said in the introduction, dimensional homogeneity is the quality of an equation having quantities of same units on both sides. A valid equation in physics must be homogeneous, since equality cannot apply between quantities of different nature. This can be used to spot errors in formula or calculations. | Homogeneity (physics) | 0.811631 |
19,260 | In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all points experience the same physics). A material constructed wit... | Homogeneity (physics) | 0.811631 |
19,261 | Numerous fields require the use of estimation theory. Some of these fields include: Interpretation of scientific experiments Signal processing Clinical trials Opinion polls Quality control Telecommunications Project management Software engineering Control theory (in particular Adaptive control) Network intrusion detect... | Estimating parameters | 0.81163 |
19,262 | The above examples show the potential reactivity and specificity of these molecules. The binding cavity between the side arms of the tweezer can evolve to bind to an appropriate guest with high specificity, depending on the configuration of the tweezer. That makes this overall class of macromolecule truly synthetic mol... | Molecular tweezer | 0.811629 |
19,263 | The maximum sectional curvature (4) is attained at a holomorphic 2-plane — one for which J(σ) ⊂ σ — while the minimum sectional curvature (1) is attained at a 2-plane for which J(σ) is orthogonal to σ. For this reason, the Fubini–Study metric is often said to have "constant holomorphic sectional curvature" equal to 4. ... | Fubini-Study metric | 0.811624 |
19,264 | The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James W. L. Glaisher to give a formula for the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equiv... | Sideways sum | 0.811618 |
19,265 | In mathematics, the Skolem problem is the problem of determining whether the values of a constant-recursive sequence include the number zero. The problem can be formulated for recurrences over different types of numbers, including integers, rational numbers, and algebraic numbers. It is not known whether there exists a... | Skolem problem | 0.811618 |
19,266 | There does exist an algorithm to test whether a constant-recursive sequence has infinitely many zeros, and if so to construct a decomposition of the positions of those zeros into periodic subsequences, based on the algebraic properties of the roots of the characteristic polynomial of the given recurrence. The remaining... | Skolem problem | 0.811618 |
19,267 | This theorem states that, if such a sequence has zeros, then with finitely many exceptions the positions of the zeros repeat regularly. Skolem proved this for recurrences over the rational numbers, and Mahler and Lech extended it to other systems of numbers. However, the proofs of the theorem do not show how to test wh... | Skolem problem | 0.811618 |
19,268 | : p. 19f. However, it lacks many (if not most) of the properties that make Bayes' rule intuitively desirable, leading some to argue that it cannot be considered a generalization in any meaningful sense. For example, DS theory violates the requirements for Cox's theorem, which implies that it cannot be considered a cohe... | Dempster–Shafer theory | 0.811617 |
19,269 | Kłopotek and Wierzchoń proposed to interpret the Dempster–Shafer theory in terms of statistics of decision tables (of the rough set theory), whereby the operator of combining evidence should be seen as relational joining of decision tables. In another interpretation M. A. Kłopotek and S. T. Wierzchoń propose to view th... | Dempster–Shafer theory | 0.811617 |
19,270 | The conjugate gradient method can be derived from several different perspectives, including specialization of the conjugate direction method for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. Despite differences in their approaches, these derivations share a common topic—proving t... | Conjugate gradient | 0.811616 |
19,271 | This follows from the Chinese remainder theorem and the fact that a ring of the form Z / k Z {\displaystyle \mathbb {Z} /k\mathbb {Z} } is a field if and only if k {\displaystyle k} is prime. For every positive integer n {\displaystyle n} , the set of all positive divisors of n {\displaystyle n} becomes a partially ord... | Square-free integer | 0.811616 |
19,272 | Some other researchers have suggested that learning in DDM tasks can be explained by a connectionist theory or connectionism. The connections between units, whose strength or weighing depend upon previous experience. Thus, the output of a given unit depends upon the output of the previous unit weighted by the strength ... | Dynamic decision-making | 0.811614 |
19,273 | General linear methods (GLMs) are a large class of numerical methods used to obtain numerical solutions to ordinary differential equations. They include multistage Runge–Kutta methods that use intermediate collocation points, as well as linear multistep methods that save a finite time history of the solution. John C. B... | General linear methods | 0.811613 |
19,274 | Numerical methods for first-order ordinary differential equations approximate solutions to initial value problems of the form y ′ = f ( t , y ) , y ( t 0 ) = y 0 . {\displaystyle y'=f(t,y),\quad y(t_{0})=y_{0}.} The result is approximations for the value of y ( t ) {\displaystyle y(t)} at discrete times t i {\displayst... | General linear methods | 0.811613 |
19,275 | Jess et al., 2016. Cover Article of Nature Physics, Volume 12 Issue 2, February 2016 Solar Multi-Conjugate Adaptive Optics at the Dunn Solar Telescope Rimmele, T., Hegwer, S., Richards, K., Woeger, F.. , 2008, Multi-Conjugate Adaptive Optics. Speckle interferometry with adaptive optics corrected solar data Wöger, F., v... | Dunn Solar Telescope | 0.811611 |
19,276 | This bearing allowing the entire 250 ton vacuum tube to be rotated, compensating for the apparent rotation of the image as the Sun rises into the sky. The tower telescope was originally dedicated on October 15, 1969, and renamed in 1998 after Richard B. Dunn. A plaque at the facility reads: "Named in honor of one of so... | Dunn Solar Telescope | 0.811611 |
19,277 | As such, it provides the ability to image multiple layers of the photosphere and chromosphere simultaneously. At its installation in 2010 it generated up to 12 TByte of data per day making it one of the largest data sets in ground-based solar astronomy at the time. In addition, some older instruments are available, alt... | Dunn Solar Telescope | 0.811611 |
19,278 | Inferring telescope polarization properties through spectral lines without linear polarization. Derks, A., Beck, C., Martínez Pillet, V., 2018. Astronomy and Astrophysics volume 615, A22 (2018) Adaptation of Dunn Solar Telescope for Jovian Doppler spectro imaging. Underwood, T.A., Voelz, D., Schmider, F.-X., Jackiewicz... | Dunn Solar Telescope | 0.811611 |
19,279 | A formal language is a language that is defined by a formal system. Like languages in linguistics, formal languages generally have two aspects: the syntax of a language is what the language looks like (more formally: the set of possible expressions that are valid utterances in the language) studied in formal language t... | Deductive system | 0.811608 |
19,280 | A deductive system, also called a deductive apparatus or a logic, consists of the axioms (or axiom schemata) and rules of inference that can be used to derive theorems of the system.Such deductive systems preserve deductive qualities in the formulas that are expressed in the system. Usually the quality we are concerned... | Deductive system | 0.811608 |
19,281 | Displacement shaders manipulate surface geometry independent of color. Deformation shaders transform the entire space. Only one RenderMan implementation, the AIR renderer by SiTex Graphics, implemented this shader type, supporting only a single linear transformation applied to the space. | Shading language | 0.811605 |
19,282 | "Key relevance" may also be applied to types of electronic locks when used to refer to similarities in magnetic signatures or radio codes, though truly digital-coded radio signals do not have key relevance ratings because they must have precise unlocking codes, with no degree of difference whatsoever in order to operat... | Key relevance | 0.811599 |
19,283 | The basis of materials science is studying the interplay between the structure of materials, the processing methods to make that material, and the resulting material properties. The complex combination of these produce the performance of a material in a specific application. Many features across many length scales impa... | Material Sciences | 0.811593 |
19,284 | "essential2" attempted to improve the industry's image by emphasizing the importance of chemical industry products – especially plastics – to everyday life, and by using the term "American Chemistry" rather than "chemical industry". ACC later shifted to a more directed lobbying and policy-shaping effort, including taki... | American Chemistry Council | 0.811593 |
19,285 | The mission of the American Chemistry Council is to promote the interests of corporations of the chemical industry. The trade group represents U.S. chemical companies as well as the plastics and chlorine industries, formerly known as the American Plastics Council, the Center for the Polyurethanes Industry and the Chlor... | American Chemistry Council | 0.811593 |
19,286 | American Chemistry Council (ACC), known as the Manufacturing Chemists' Association at its founding in 1872 then as the Chemical Manufacturers' Association (from 1978 until 2000), is an industry trade association for American chemical companies, based in Washington, D.C. | American Chemistry Council | 0.811593 |
19,287 | During the period leading up to the referendum vote the American Chemistry Council stepped into this local affair, ultimately spending some $1.4 million on their successful effort to thwart the proposed system of fully accounting for the cost of plastic bags. Seattle in 2012 overcame ACC objections and successfully ena... | American Chemistry Council | 0.811593 |
19,288 | They view campaigns like "essential2" as efforts to distract public attention away from products and practices that they view as harmful and dangerous. The American Chemistry Council's stance on chemical regulation was heavily criticized in the 2015 documentary Stink! available on Netflix. | American Chemistry Council | 0.811593 |
19,289 | The former is stochastic and discontinuous, writes von Neumann, and the latter deterministic and continuous. This dichotomy has set the tone for much later debate. Some interpretations of quantum mechanics find the reliance upon two different types of time evolution distasteful and regard the ambiguity of when to invok... | Quantum measurement | 0.811591 |
19,290 | Of primary interest is the seeming disparity between apparently distinct types of time evolution. Von Neumann declared that quantum mechanics contains "two fundamentally different types" of quantum-state change. : §V.1 First, there are those changes involving a measurement process, and second, there is unitary time evo... | Quantum measurement | 0.811591 |
19,291 | Despite the consensus among scientists that quantum physics is in practice a successful theory, disagreements persist on a more philosophical level. Many debates in the area known as quantum foundations concern the role of measurement in quantum mechanics. Recurring questions include which interpretation of probability... | Quantum measurement | 0.811591 |
19,292 | : 24 But the devices used to build the experimental apparatus are themselves physical systems, and so quantum mechanics should be applicable to them as well. Beginning in the 1950s, Rosenfeld, von Weizsäcker and others tried to develop consistency conditions that expressed when a quantum-mechanical system could be trea... | Quantum measurement | 0.811591 |
19,293 | The Robertson–Schrödinger uncertainty principle establishes that when two observables do not commute, there is a tradeoff in predictability between them. The Wigner–Araki–Yanase theorem demonstrates another consequence of non-commutativity: the presence of a conservation law limits the accuracy with which observables t... | Quantum measurement | 0.811591 |
19,294 | In materials science and engineering, one is often interested in understanding the forces or stresses involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law, which says that the force experienced by a spring is proportional to the distance... | Viscous forces | 0.811589 |
19,295 | Monolayers have a multitude of applications both at the air-water and at air-solid interphases. Nanoparticle monolayers can be used to create functional surfaces that have for instance anti-reflective or superhydrophobic properties.Monolayers are frequently encountered in biology. A micelle is a monolayer, and the phos... | Monolayer | 0.811588 |
19,296 | The concepts of plant perception, communication, and intelligence have parallels in other biological organisms for which such phenomena appear foreign to or incompatible with traditional understandings of biology, or have otherwise proven difficult to study or interpret. Similar mechanisms exist in bacterial cells, cho... | Plant neurobiology | 0.811587 |
19,297 | The BIPM – YouTube channel "The role of the Planck constant in physics" – presentation at 26th CGPM meeting at Versailles, France, November 2018 when voting on superseding the IPK took place on YouTube | Kilogram | 0.811586 |
19,298 | The principle of complementarity means that both systems have to be optimized. If you focus on one system and have bias over the other it will likely lead to the failure of the organization or jeopardize the success of a system. Although the above socio-technical system theory is focused on an organization, it is undou... | Science and technology studies | 0.811586 |
19,299 | This is what we call the sociotechnical systems. In socio-technical systems, there are two principles to internalize, that is joint optimization and complementarity. Joint optimization puts an emphasis on developing both systems in parallel and it is only in the interaction of both systems that the success of an organi... | Science and technology studies | 0.811586 |
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