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14,900 | The production of many man-made chemicals such as drugs, plastics, food additives, fabrics depend on organic reactions. The oldest organic reactions are combustion of organic fuels and saponification of fats to make soap. Modern organic chemistry starts with the Wöhler synthesis in 1828. In the history of the Nobel Pri... | Organic chemical reaction | 0.814759 |
14,901 | Organic reactions are chemical reactions involving organic compounds. The basic organic chemistry reaction types are addition reactions, elimination reactions, substitution reactions, pericyclic reactions, rearrangement reactions, photochemical reactions and redox reactions. In organic synthesis, organic reactions are ... | Organic chemical reaction | 0.814759 |
14,902 | As stated earlier, there is significant confusion with regards to these two conventions. As a general rule, the engineering, quantum physics, and radio astronomy communities use the first convention, in which the wave is observed from the point of view of the source. In many physics textbooks dealing with optics, the s... | Circular Polarization | 0.814759 |
14,903 | In the quantum mechanical view, light is composed of photons. Polarization is a manifestation of the spin angular momentum of light. More specifically, in quantum mechanics, the direction of spin of a photon is tied to the handedness of the circularly polarized light, and the spin of a beam of photons is similar to the... | Circular Polarization | 0.814759 |
14,904 | In Greek and Latin grammar, combining bases usually require a thematic or stem-forming vowel. In biography, from Greek, the thematic is -o-; in agriculture, from Latin, it is -i-. In English morphology, this vowel can be considered as an interfix: in biology, the interfix -o-; in miniskirt, the interfix -i-. | Neoclassical compound | 0.814758 |
14,905 | Unlike this one, some of Barnes's coinages caught on, such as foreword, Barnes's replacement for the preface of a book. Later, Poul Anderson wrote a jocular piece called Uncleftish Beholding in a constructed language based on English which others have called "Ander-Saxon"; this attempted to create a pure English vocabu... | Neoclassical compound | 0.814758 |
14,906 | Prefixes include: aero- air, crypto- hidden, demo- people, geo- earth, odonto- tooth, ornitho- bird, thalasso- sea. Many have both a traditional simple meaning and a modern telescopic meaning: in biology, bio- means 'life', but in bio-degradable it telescopes 'biologically'; although hypno- basically means 'sleep' (hyp... | Neoclassical compound | 0.814758 |
14,907 | In the later 20th century, many forms have cut loose from ancient moorings: crypto- as in preposed Crypto-Fascist and pseudo- as in pseudoradical; postposed -meter in speedometer, clapometer. Processes of analogy have created coinages like petrodollar, psycho-warfare, microwave on such models as petrochemical, psycholo... | Neoclassical compound | 0.814758 |
14,908 | Many such words, such as thermometer, dinosaur, rhinoceros, and rhododendron, are thoroughly incorporated into the English lexicon and are the ordinary words for their referents. Some are prone to colloquial shortening; rhinoceros often becomes rhino. The binomial nomenclature of taxonomy and biology is a major source ... | Neoclassical compound | 0.814758 |
14,909 | In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping shapes is an independent set in the intersection graph of the shapes. Therefore, the MDS problem is a special case of the maximum indep... | Maximum disjoint set | 0.814756 |
14,910 | Several divide-and-conquer algorithms are based on a certain geometric separator theorem. A geometric separator is a line or shape that separates a given set of shapes to two smaller subsets, such that the number of shapes lost during the division is relatively small. This allows both PTASs and sub-exponential exact al... | Maximum disjoint set | 0.814756 |
14,911 | This separator theorem allows to build the following PTAS: Select a constant b. Check all possible combinations of up to b + 1 labels. If |MDS(C)| has a size of at most b (i.e. all sets of b + 1 labels are not disjoint) then just return that MDS and exit. This step takes nO(b) time. | Maximum disjoint set | 0.814756 |
14,912 | Let C be a set of n fat objects, such as squares or circles, of arbitrary sizes. Chan described an algorithm finds a disjoint set with a size of at least (1 − O(√b))·|MDS(C)| in time nO(b), for every constant b > 1. The algorithm is based on the following geometric separator theorem, which can be proved similarly to th... | Maximum disjoint set | 0.814756 |
14,913 | Let C be a set of n disks, such that the ratio between the largest radius and the smallest radius is at most r. The following algorithm finds MDS(C) exactly in time 2 O ( r ⋅ n ) {\displaystyle 2^{O(r\cdot {\sqrt {n}})}} .The algorithm is based on a width-bounded geometric separator on the set Q of the centers of all d... | Maximum disjoint set | 0.814756 |
14,914 | The idea of creating the International Physics Olympiad was conceived in Eastern Bloc countries, inspired by the 1959 established International Mathematical Olympiad. Poland seemed to offer the best conditions at the time, and so the first IPhO was held in Warsaw in 1967, organized by Czesław Ścisłowski. Some months pr... | International Physics Olympiad | 0.814752 |
14,915 | The International Physics Olympiad (IPhO) is an annual physics competition for high school students. It is one of the International Science Olympiads. The first IPhO was held in Warsaw, Poland in 1967.Each national delegation is made up of at most five student competitors plus two leaders, selected on a national level.... | International Physics Olympiad | 0.814752 |
14,916 | Some approaches to point set registration use algorithms that solve the more general graph matching problem. However, the computational complexity of such methods tend to be high and they are limited to rigid registrations. In this article, we will only consider algorithms for rigid registration, where the transformati... | Point set registration | 0.81475 |
14,917 | This algorithm was introduced in 2013 by H. Assalih to accommodate sonar image registration. These types of images tend to have high amounts of noise, so it is expected to have many outliers in the point sets to match. SCS delivers high robustness against outliers and can surpass ICP and CPD performance in the presence... | Point set registration | 0.81475 |
14,918 | The iterative closest point (ICP) algorithm was introduced by Besl and McKay. The algorithm performs rigid registration in an iterative fashion by alternating in (i) given the transformation, finding the closest point in S {\displaystyle {\mathcal {S}}} for every point in M {\displaystyle {\mathcal {M}}} ; and (ii) giv... | Point set registration | 0.81475 |
14,919 | The EM algorithm consists of two steps. First, in the E-step or estimation step, it guesses the values of parameters ("old" parameter values) and then uses Bayes' theorem to compute the posterior probability distributions P old ( i , s j ) {\displaystyle P^{\text{old}}(i,s_{j})} of mixture components. Second, in the M-... | Point set registration | 0.81475 |
14,920 | TEASER adopts the following truncated least squares (TLS) estimator: which is obtained by choosing the TLS robust cost function ρ ( x ) = min ( x 2 , c ¯ 2 ) {\displaystyle \rho (x)=\min(x^{2},{\bar {c}}^{2})} , where c ¯ 2 {\displaystyle {\bar {c}}^{2}} is a pre-defined constant that determines the maximum allowed res... | Point set registration | 0.81475 |
14,921 | Popular robust cost functions include ℓ 1 {\displaystyle \ell _{1}} -norm loss, Huber loss, Geman-McClure loss and truncated least squares loss. M-estimation has been one of the most popular paradigms for robust estimation in robotics and computer vision. Because robust objective functions are typically non-convex (e.g... | Point set registration | 0.81475 |
14,922 | In the simplest case, one can assume that all the correspondences are correct, meaning that the points m i , s i ∈ R 3 {\displaystyle m_{i},s_{i}\in \mathbb {R} ^{3}} are generated as follows: where l > 0 {\displaystyle l>0} is a uniform scaling factor (in many cases l = 1 {\displaystyle l=1} is assumed), R ∈ SO ( 3 ) ... | Point set registration | 0.81475 |
14,923 | Abduction is then the process that picks out some member of E {\displaystyle E} . Criteria for picking out a member representing "the best" explanation include the simplicity, the prior probability, or the explanatory power of the explanation. A proof-theoretical abduction method for first order classical logic based o... | Abductive validation | 0.814749 |
14,924 | Abductive conclusions do not eliminate uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely". One can understand abductive reasoning as inference to the best explanation, although not all usages of the terms abduction and inference to the best explanation are equivalent.In ... | Abductive validation | 0.814749 |
14,925 | {\displaystyle {\begin{aligned}\omega _{Y\,{\widetilde {\|}}\,X}&=\omega _{X\mid Y}\;{\widetilde {\circledcirc }}\;\omega _{X}\\&=(\omega _{X\mid Y}\;{\widetilde {\phi \,}}\;a_{Y})\;\circledcirc \;\omega _{X}\\&=\omega _{Y{\widetilde {|}}X}\;\circledcirc \;\omega _{X}\;.\end{aligned}}} The symbolic notation for subject... | Abductive validation | 0.814749 |
14,926 | Assume the domains X {\displaystyle \mathbf {X} } and Y {\displaystyle \mathbf {Y} } with respective variables X {\displaystyle X} and Y {\displaystyle Y} , the set of conditional opinions ω X ∣ Y {\displaystyle \omega _{X\mid Y}} (i.e. one conditional opinion for each value y {\displaystyle y} ), and the base rate dis... | Abductive validation | 0.814749 |
14,927 | Trigonometry is useful in many physical sciences, including acoustics, and optics. In these areas, they are used to describe sound and light waves, and to solve boundary- and transmission-related problems. | Trigonometry | 0.814745 |
14,928 | Trigonometry has been noted for its many identities, that is, equations that are true for all possible inputs.Identities involving only angles are known as trigonometric identities. Other equations, known as triangle identities, relate both the sides and angles of a given triangle. | Trigonometry | 0.814745 |
14,929 | It was Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series. Also in the 18th century, Brook Taylor defined the general Taylo... | Trigonometry | 0.814745 |
14,930 | Trigonometry was still so little known in 16th-century northern Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts. Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major ... | Trigonometry | 0.814745 |
14,931 | Knowledge of trigonometric functions and methods reached Western Europe via Latin translations of Ptolemy's Greek Almagest as well as the works of Persian and Arab astronomers such as Al Battani and Nasir al-Din al-Tusi. One of the earliest works on trigonometry by a northern European mathematician is De Triangulis by ... | Trigonometry | 0.814745 |
14,932 | He also made important innovations in spherical trigonometry The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right. He was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spheric... | Trigonometry | 0.814745 |
14,933 | Centuries passed before more detailed tables were produced, and Ptolemy's treatise remained in use for performing trigonometric calculations in astronomy throughout the next 1200 years in the medieval Byzantine, Islamic, and, later, Western European worlds. The modern definition of the sine is first attested in the Sur... | Trigonometry | 0.814745 |
14,934 | Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They, and later the Babylonians, studied the ratios of the sides of similar triangles and discovered some properties of these ratios but did not turn that into a systematic method for finding sides and angles of triangles. The anc... | Trigonometry | 0.814745 |
14,935 | This Hartree–Fock model gives a reasonable description of H2 around the equilibrium geometry – about 0.735 Å for the bond length (compared to a 0.746 Å experimental value) and 350 kJ/mol (84 kcal/mol) for the bond energy (experimentally, 432 kJ/mol ). This is typical for the HF model, which usually describes closed-she... | Multi-configurational self-consistent field | 0.814745 |
14,936 | For the simplest single bond, found in the H2 molecule, molecular orbitals can always be written in terms of two functions χiA and χiB (which are atomic orbitals with small corrections) located at the two nuclei A and B: φ i = N i ( χ i A ± χ i B ) , {\displaystyle \varphi _{i}=N_{i}(\chi _{iA}\pm \chi _{iB}),} where N... | Multi-configurational self-consistent field | 0.814745 |
14,937 | Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states... | Multi-configurational self-consistent field | 0.814745 |
14,938 | Special theory of relativity imposes the condition for events related by cause and effect to be time-like separated, that is that causal efficacy propagates no faster than light. Maxwell's equations for electromagnetism are found to be in favor of this as electric and magnetic disturbances are found to travel at the sp... | Effective magnetic field | 0.814742 |
14,939 | A cell-free system is an in vitro tool widely used to study biological reactions that happen within cells apart from a full cell system, thus reducing the complex interactions typically found when working in a whole cell. Subcellular fractions can be isolated by ultracentrifugation to provide molecular machinery that c... | Cell-free system | 0.814738 |
14,940 | Thus, the defining characteristic of a structurally recursive function is that the argument to each recursive call is the content of a field of the original input. Structural recursion includes nearly all tree traversals, including XML processing, binary tree creation and search, etc. By considering the algebraic struc... | Recursion (computer science) | 0.814737 |
14,941 | 170–181. 1958: Hannes Alfvén: Proceedings of the Second International Conference on Peaceful Uses of Atomic Energy (United Nations), 31, 3 1960: H Alfven, L Lindberg and P Mitlid, "Experiments with plasma rings" (1961) Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, Volume 1, Is... | Dense Plasma Focus | 0.814735 |
14,942 | {\displaystyle \delta _{\epsilon }\Phi =(\epsilon ^{*}Q+\epsilon Q^{\dagger })\Phi .} We can evaluate this variation using the action of Q on the superfields = ( ∂ ∂ θ − i θ ∗ ∂ ∂ t ) Φ = ψ + θ ∗ ( F − i ϕ ˙ ) + i θ θ ∗ ψ ˙ . {\displaystyle \left=\left({\frac {\partial }{\partial \theta }}\,-i\theta ^{*}{\frac {\parti... | Grassmann dimensions | 0.814733 |
14,943 | This means that a bracket may be defined between any two elements of this vector space, and that this bracket reduces to the commutator on two even coordinates and on one even and one odd coordinate while it is an anticommutator on two odd coordinates. This superspace is an abelian Lie superalgebra, which means that al... | Grassmann dimensions | 0.814733 |
14,944 | Supersymmetric quantum mechanics with N supercharges is often formulated in the superspace R1|2N, which contains one real direction t identified with time and N complex Grassmann directions which are spanned by Θi and Θ*i, where i runs from 1 to N. Consider the special case N = 1. The superspace R1|2 is a 3-dimensional... | Grassmann dimensions | 0.814733 |
14,945 | The difference here is that the Clifford algebra has a considerably richer and more subtle structure than the Grassmann numbers. So, the Grassmann numbers are elements of the exterior algebra, and the Clifford algebra has an isomorphism to the exterior algebra, but its relation to the orthogonal group and the spin grou... | Grassmann dimensions | 0.814733 |
14,946 | The four-dimensional examples take superspace to be super Minkowski space. Although similar to a vector space, this has many important differences: First of all, it is an affine space, having no special point denoting the origin. Next, the fermionic coordinates are taken to be anti-commuting Weyl spinors from the Cliff... | Grassmann dimensions | 0.814733 |
14,947 | In particular we may construct the supercharges Q = − ∂ ∂ θ ¯ + γ μ θ ∂ μ {\displaystyle Q=-{\frac {\partial }{\partial {\bar {\theta }}}}+\gamma ^{\mu }\theta \partial _{\mu }} which satisfy the supersymmetry algebra { Q , Q } = { Q ¯ , Q } C = 2 γ μ ∂ μ C = − 2 i γ μ P μ C {\displaystyle \left\{Q,Q\right\}=\left\{{\o... | Grassmann dimensions | 0.814733 |
14,948 | However, in this subsection we are considering the superspace with four fermionic components and so no Weyl spinors are consistent with the CPT theorem. Note: There are many sign conventions in use and this is only one of them. Therefore the four fermionic directions transform as a Majorana spinor θ α {\displaystyle \t... | Grassmann dimensions | 0.814733 |
14,949 | There is the Majorana spinor, the left-handed Weyl spinor and the right-handed Weyl spinor. The CPT theorem implies that in a unitary, Poincaré invariant theory, which is a theory in which the S-matrix is a unitary matrix and the same Poincaré generators act on the asymptotic in-states as on the asymptotic out-states, ... | Grassmann dimensions | 0.814733 |
14,950 | Perhaps the most studied concrete superspace in physics is d = 4 , N = 1 {\displaystyle d=4,{\mathcal {N}}=1} super Minkowski space R 4 | 4 {\displaystyle \mathbb {R} ^{4|4}} or sometimes written R 1 , 3 | 4 {\displaystyle \mathbb {R} ^{1,3|4}} , which is the direct sum of four real bosonic dimensions and four real Gra... | Grassmann dimensions | 0.814733 |
14,951 | Find the best similarity between small groups of terms, in a semantic way (i.e. in a context of a knowledge corpus), as for example in multi choice questions MCQ answering model. Expand the feature space of machine learning / text mining systems Analyze word association in text corpus Synonymy and polysemy are fundamen... | Latent semantic analysis | 0.814732 |
14,952 | Due to its cross-domain applications in Information Retrieval, Natural Language Processing (NLP), Cognitive Science and Computational Linguistics, LSA has been implemented to support many different kinds of applications. Sense Clusters, an Information Retrieval-oriented perl implementation of LSA S-Space Package, a Com... | Latent semantic analysis | 0.814732 |
14,953 | Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will ... | Latent semantic analysis | 0.814732 |
14,954 | In semantic hashing documents are mapped to memory addresses by means of a neural network in such a way that semantically similar documents are located at nearby addresses. Deep neural network essentially builds a graphical model of the word-count vectors obtained from a large set of documents. Documents similar to a q... | Latent semantic analysis | 0.814732 |
14,955 | Several approaches to simulate NMR observables of carbohydrates has been reviewed. They include: Universal statistical database approaches (ACDLabs, Modgraph, etc.) Usage of neural networks to refine the predictions Regression based methods CHARGE Carbohydrate-optimized empirical schemes (CSDB/BIOPSEL, CASPER). Combine... | Carbohydrate NMR | 0.814731 |
14,956 | Symbolic Manipulation Program, usually called SMP, was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979. It was initially developed in the Caltech physics department with contributions from Geoffrey C. Fox, Jeffrey M. Greif, Eric D. Mjolsness, Larry J. Romans, Timothy Shaw, ... | SMP (computer algebra system) | 0.814728 |
14,957 | Applications include alteration of gene expression - both as inhibitor and promoter in different cases, antigene and antisense therapeutic agent, anticancer agent, antiviral, antibacterial and antiparasitic agent, molecular tools and probes of biosensor, detection of DNA sequences, and nanotechnology.PNAs can be used t... | Peptide nucleic acid | 0.814725 |
14,958 | Peptide nucleic acid (PNA) is an artificially synthesized polymer similar to DNA or RNA.Synthetic peptide nucleic acid oligomers have been used in recent years in molecular biology procedures, diagnostic assays, and antisense therapies. Due to their higher binding strength, it is not necessary to design long PNA oligom... | Peptide nucleic acid | 0.814725 |
14,959 | Gauss–Codazzi equations Darboux frame Hypersurface Induced metric Nash embedding theorem minimal surface Helicoid Catenoid Costa's minimal surface Hsiang–Lawson's conjecture | List of differential geometry topics | 0.814724 |
14,960 | Diffeomorphism Large diffeomorphism Orientability characteristic class Chern class Pontrjagin class spin structure differentiable map submersion immersion Embedding Whitney embedding theorem Critical value Sard's theorem Saddle point Morse theory Lie derivative Hairy ball theorem Poincaré–Hopf theorem Stokes' theorem D... | List of differential geometry topics | 0.814724 |
14,961 | Sheaf (mathematics) Pseudogroup G-structure synthetic differential geometry | List of differential geometry topics | 0.814724 |
14,962 | Non-Euclidean geometry Elliptic geometry Spherical geometry Sphere-world Angle excess hyperbolic geometry hyperbolic space hyperboloid model Poincaré disc model Poincaré half-plane model Poincaré metric Angle of parallelism | List of differential geometry topics | 0.814724 |
14,963 | Möbius transformation Conformal map conformal connection tractor bundle Weyl curvature Weyl–Schouten theorem ambient construction Willmore energy Willmore flow | List of differential geometry topics | 0.814724 |
14,964 | List of curves topics Frenet–Serret formulas Curves in differential geometry Line element Curvature Radius of curvature Osculating circle Curve Fenchel's theorem | List of differential geometry topics | 0.814724 |
14,965 | List of coordinate charts List of formulas in Riemannian geometry Christoffel symbols | List of differential geometry topics | 0.814724 |
14,966 | Klein geometry, Erlangen programme symmetric space space form Maurer–Cartan form Examples hyperbolic space Gauss–Bolyai–Lobachevsky space Grassmannian Complex projective space Real projective space Euclidean space Stiefel manifold Upper half-plane Sphere | List of differential geometry topics | 0.814724 |
14,967 | covariant derivative exterior covariant derivative Levi-Civita connection parallel transport Development (differential geometry) connection form Cartan connection affine connection conformal connection projective connection method of moving frames Cartan's equivalence method Vierbein, tetrad Cartan connection applicati... | List of differential geometry topics | 0.814723 |
14,968 | This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. | List of differential geometry topics | 0.814723 |
14,969 | Theorema egregium Gauss–Bonnet theorem First fundamental form Second fundamental form Gauss–Codazzi–Mainardi equations Dupin indicatrix Asymptotic curve Curvature Principal curvatures Mean curvature Gauss curvature Elliptic point Types of surfaces Minimal surface Ruled surface Conical surface Developable surface Nadira... | List of differential geometry topics | 0.814723 |
14,970 | Theorema Egregium Gauss–Bonnet theorem Chern–Gauss–Bonnet theorem Chern–Weil homomorphism Gauss map Second fundamental form Curvature form Riemann curvature tensor Geodesic curvature Scalar curvature Sectional curvature Ricci curvature, Ricci flat Ricci decomposition Schouten tensor Weyl curvature Ricci flow Einstein m... | List of differential geometry topics | 0.814723 |
14,971 | Hodge star operator Weitzenböck identity Laplacian operators in differential geometry | List of differential geometry topics | 0.814723 |
14,972 | Gauss–Bonnet theorem Hopf–Rinow theorem Cartan–Hadamard theorem Myers theorem Rauch comparison theorem Morse index theorem Synge theorem Weinstein theorem Toponogov theorem Sphere theorem Hodge theory Uniformization theorem Yamabe problem | List of differential geometry topics | 0.814723 |
14,973 | Atiyah–Singer index theorem de Rham cohomology Dolbeault cohomology elliptic complex Hodge theory pseudodifferential operator | List of differential geometry topics | 0.814723 |
14,974 | Symplectic topology Symplectic space Symplectic manifold Symplectic structure Symplectomorphism Contact structure Contact geometry Hamiltonian system Sasakian manifold Poisson manifold | List of differential geometry topics | 0.814723 |
14,975 | See also multivariable calculus, list of multivariable calculus topics Manifold Differentiable manifold Smooth manifold Banach manifold Fréchet manifold Tensor analysis Tangent vector Tangent space Tangent bundle Cotangent space Cotangent bundle Tensor Tensor bundle Vector field Tensor field Differential form Exterior ... | List of differential geometry topics | 0.814723 |
14,976 | Riemannian symmetric space Margulis lemma Space form Constant curvature taut submanifold Uniformization theorem Myers theorem Gromov's compactness theorem | List of differential geometry topics | 0.814723 |
14,977 | Riemann surface Complex projective space Kähler manifold Dolbeault operator CR manifold Stein manifold Almost complex structure Hermitian manifold Newlander–Nirenberg theorem Generalized complex manifold Calabi–Yau manifold Hyperkähler manifold K3 surface hypercomplex manifold Quaternion-Kähler manifold | List of differential geometry topics | 0.814723 |
14,978 | Prime geodesic Geodesic flow Exponential map (Lie theory) Exponential map (Riemannian geometry) Injectivity radius Geodesic deviation equation Jacobi field | List of differential geometry topics | 0.814723 |
14,979 | Intrinsic metric Pseudo-Riemannian manifold Sub-Riemannian manifold Finsler geometry General relativity G2 manifold Information geometry Fisher information metric | List of differential geometry topics | 0.814723 |
14,980 | Hence, the system can be assumed to follow the simpler σ ˙ = 0 {\displaystyle {\dot {\sigma }}=0} condition after some initial transient during the period while the system finds the sliding mode. The same motion is approximately maintained when the equality σ ( x ) = 0 {\displaystyle \sigma (\mathbf {x} )=\mathbf {0} }... | Sliding mode control | 0.814723 |
14,981 | The following theorems form the foundation of variable structure control. | Sliding mode control | 0.814723 |
14,982 | For the system given by Equation (1) and sliding surface given by Equation (2), the subspace for which the { x ∈ R n: σ ( x ) = 0 } {\displaystyle \{\mathbf {x} \in \mathbb {R} ^{n}:\sigma (\mathbf {x} )=\mathbf {0} \}} surface is reachable is given by { x ∈ R n: σ ⊺ ( x ) σ ˙ ( x ) < 0 } {\displaystyle \{\mathbf {x} \... | Sliding mode control | 0.814723 |
14,983 | One application of sliding mode controller is the control of electric drives operated by switching power converters. : "Introduction" Because of the discontinuous operating mode of those converters, a discontinuous sliding mode controller is a natural implementation choice over continuous controllers that may need to b... | Sliding mode control | 0.814723 |
14,984 | Note that because the control law is not continuous, it is certainly not locally Lipschitz continuous, and so existence and uniqueness of solutions to the closed-loop system is not guaranteed by the Picard–Lindelöf theorem. Thus the solutions are to be understood in the Filippov sense. Roughly speaking, the resulting c... | Sliding mode control | 0.814723 |
14,985 | Another goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Instead of using classical bits, quantum computers use qubits, which can be in superpositions of states. Quantum programmers are able to manipulate the superposi... | Applications of quantum mechanics | 0.814723 |
14,986 | Quantum mechanics can also provide quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are energetically favorable to which others and the magnitudes of the energies involved.Historically, the first applications of quantum mechanics to physical systems were the algebraic... | Applications of quantum mechanics | 0.814723 |
14,987 | Quantum physics is a branch of modern physics in which energy and matter are described at their most fundamental level, that of energy quanta, elementary particles, and quantum fields. Quantum physics encompasses any discipline concerned with systems that exhibit notable quantum-mechanical effects, where waves have pro... | Applications of quantum mechanics | 0.814723 |
14,988 | Many scientists are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to more fully develop quantum cryptography, which will theoretically allow guaranteed secure transmission of information. An inherent advantage yielded by quantum cryptography when compared to classical ... | Applications of quantum mechanics | 0.814723 |
14,989 | Some negative differential resistance devices also utilize the quantum tunneling effect, such as resonant tunneling diodes. Unlike classical diodes, its current is carried by resonant tunneling through two or more potential barriers (see figure at right). Its negative resistance behavior can only be understood with qua... | Applications of quantum mechanics | 0.814723 |
14,990 | Many modern electronic devices are designed using quantum mechanics. Examples include lasers, electron microscopes, magnetic resonance imaging (MRI) devices and the components used in computing hardware. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable parts of m... | Applications of quantum mechanics | 0.814723 |
14,991 | While quantum mechanics primarily applies to the smaller atomic regimes of matter and energy, some systems exhibit quantum mechanical effects on a large scale. Superfluidity, the frictionless flow of a liquid at temperatures near absolute zero, is one well-known example. So is the closely related phenomenon of supercon... | Applications of quantum mechanics | 0.814722 |
14,992 | Quantum theory also provides accurate descriptions for many previously unexplained phenomena, such as black-body radiation and the stability of the orbitals of electrons in atoms. It has also given insight into the workings of many different biological systems, including smell receptors and protein structures. Recent w... | Applications of quantum mechanics | 0.814722 |
14,993 | Median salaries ranged from $70,450 for chemical engineers with fewer than three years of experience to $156,000 for those with more than 40 years in the workforce.In the UK, the IChemE 2016 Salary Survey reported a median salary of approximately £57,000, with a starting salary for a graduate averaging £28,350. Chemica... | Chemical engineer | 0.814721 |
14,994 | In the field of engineering, a chemical engineer is a professional, equipped with the knowledge of chemical engineering, who works principally in the chemical industry to convert basic raw materials into a variety of products and deals with the design and operation of plants and equipment. In general, a chemical engine... | Chemical engineer | 0.814721 |
14,995 | At the first General Meeting of the Society in 1882, some 15 of the 300 members described themselves as chemical engineers, but the Society's formation of a Chemical Engineering Group in 1918 attracted about 400 members.In 1905 a publication called The Chemical Engineer was founded in the US, and in 1908 the American I... | Chemical engineer | 0.814721 |
14,996 | The president of the Institution of Chemical Engineers said in his presidential address "I believe most of us would be willing to regard Edward Charles Howard (1774–1816) as the first chemical engineer of any eminence". Others have suggested Johann Rudolf Glauber (1604–1670) for his development of processes for the man... | Chemical engineer | 0.814721 |
14,997 | Examples include ultra-strong fibers, fabrics, adhesives and composites for vehicles, bio-compatible materials for implants and prosthetics, gels for medical applications, pharmaceuticals, and films with special dielectric, optical or spectroscopic properties for opto-electronic devices. Additionally, chemical engineer... | Chemical engineer | 0.814721 |
14,998 | Historically, the chemical engineer has been primarily concerned with process engineering, which can generally be divided into two complementary areas: chemical reaction engineering and separation processes. The modern discipline of chemical engineering, however, encompasses much more than just process engineering. Che... | Chemical engineer | 0.814721 |
14,999 | The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory. In reverse mathematics, one starts with a framework language and a base theory—a core axiom system—that is too weak to prove most of the theorems one might be interested ... | Proof theory | 0.814718 |
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