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87,800 | The need for National Astronomy Week (NAW) was first defined in the late 1970s. A group of both professional and amateur astronomers as well as teachers and educators was formed to define and run the first ever event. NAW was proposed in 1979 and a steering committee was set up in 1980. Since then a total of eight even... | National Astronomy Week | 0.781922 |
87,801 | During the week, astronomy societies, planetaria, schools, universities and other organisations from all over the UK organise events to promote interest in, and knowledge of, astronomy. The organisers promote the week using extensive contacts with the media and all the major UK astronomical organisations, many of whom ... | National Astronomy Week | 0.781922 |
87,802 | National Astronomy Week is sponsored (and funded) by a number of UK astronomy societies and actively supported by the Royal Astronomical Society. Other funds are sometimes obtained from science organisations in the UK, including the Science & Technology Facilities Council. | National Astronomy Week | 0.781922 |
87,803 | National Astronomy Week (NAW) is an event held every few years in the United Kingdom to promote public awareness of astronomy by celebrating notable astronomical events. The last NAW, Mars Encounter, was run during the week of 14–22 November 2020. | National Astronomy Week | 0.781922 |
87,804 | A sector instrument is a general term for a class of mass spectrometer that uses a static electric (E) or magnetic (B) sector or some combination of the two (separately in space) as a mass analyzer. Popular combinations of these sectors have been the EB, BE (of so-called reverse geometry), three-sector BEB and four-sec... | Sector mass spectrometer | 0.781921 |
87,805 | The Mattauch–Herzog geometry consists of a 31.82° ( π / 4 2 {\displaystyle \pi /4{\sqrt {2}}} radians) electric sector, a drift length which is followed by a 90° magnetic sector of opposite curvature direction. The entry of the ions sorted primarily by charge into the magnetic field produces an energy focussing effect ... | Sector mass spectrometer | 0.781921 |
87,806 | The Matsuda geometry consists of an 85° electric sector, a quadrupole lens and a 72.5° magnetic sector of the same curvature direction. This geometry is used in the SHRIMP and Panorama (gas source, high-resolution, multicollector to measure isotopologues in geochemistry). | Sector mass spectrometer | 0.781921 |
87,807 | At Siemens, his work was concerned with the acoustic properties of telephones. Between 1940 and 1945, he worked the Telecommunications Research Establishment being particularly responsible for developing the microwave radar After, Adams moved to the Atomic Energy Research Establishment until 1953. In 1953, he moved onc... | John Adams (physicist) | 0.78192 |
87,808 | The John Adams Institute for Accelerator Science (JAI), an accelerator physics research institute comprising researchers from Royal Holloway, University of London, University of Oxford and Imperial College London is named in his honour. A main road ("Route Adams") in CERN's Prevessin site is also named after him. | John Adams (physicist) | 0.78192 |
87,809 | Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. It is primarily used to generate detailed images conditioned on text descriptions, though it can also be applied to other tasks such as inpainting, outpainting, and generating image-to-image translations guided by a... | Stable Diffusion | 0.78192 |
87,810 | ControlNet is a neural network architecture designed to manage diffusion models by incorporating additional conditions. It duplicates the weights of neural network blocks into a "locked" copy and a "trainable" copy. The "trainable" copy learns the desired condition, while the "locked" copy preserves the original model.... | Stable Diffusion | 0.78192 |
87,811 | A "hypernetwork" is a small pretrained neural network that is applied to various points within a larger neural network, and refers to the technique created by NovelAI developer Kurumuz in 2021, originally intended for text-generation transformer models. Hypernetworks steer results towards a particular direction, allowi... | Stable Diffusion | 0.78192 |
87,812 | The International Computer Music Association (ICMA) is an international affiliation of individuals and institutions involved in the technical, creative, and performance aspects of computer music. It serves composers, engineers, researchers and musicians who are interested in the integration of music and technology. Are... | International Computer Music Association | 0.781919 |
87,813 | In mathematical representation theory, a minuscule representation of a semisimple Lie algebra or group is an irreducible representation such that the Weyl group acts transitively on the weights. Some authors exclude the trivial representation. A quasi-minuscule representation (also called a basic representation) is an ... | Minuscule representation | 0.781918 |
87,814 | The minuscule representations are indexed by the weight lattice modulo the root lattice, or equivalently by irreducible representations of the center of the simply connected compact group. For the simple Lie algebras, the dimensions of the minuscule representations are given as follows. | Minuscule representation | 0.781918 |
87,815 | The University has large departments in physics, chemistry, engineering, economics, and English. One of the largest departments is the Department of Materials Science and Engineering. The University has about 20,000 undergraduate students and about 2,000 PhD and graduate students. The Department of Materials Science an... | University of Science and Technology Beijing | 0.781918 |
87,816 | School of Civil and Resources Engineering School of Energy and Environment School of Metallurgical and Ecological Engineering School of Materials Science and Engineering School of Mechanical Engineering School of Automation and Electrical Engineering School of Computer and Communication Engineering Dongling School of E... | University of Science and Technology Beijing | 0.781918 |
87,817 | In addition, newly developed disciplines such as Computer Science, Information Technology, Environmental Engineering, and Civil Engineering are being proctored at the university. In December 2014, the total enrollment of 27,371 full-time students includes 13,393 undergraduates, 9,344 master candidates, 2,912 doctoral c... | University of Science and Technology Beijing | 0.781918 |
87,818 | USTB consists of 16 schools, provides 48 undergraduate programs, 121 master programs, 73 doctoral programs and 16 postdoctoral research fields. USTB attaches great importance to the establishment and development of its academic disciplines. As a result of many years of development, 12 national key disciplines such as F... | University of Science and Technology Beijing | 0.781918 |
87,819 | The University of Science and Technology Beijing (USTB; Chinese: 北京科技大学), formerly known as Beijing Steel and Iron Institute (北京钢铁学院) before 1988, is a national key university in Haidian District, Beijing, China. USTB's metallurgy and materials science programmes are highly regarded in China. It is a Chinese state Doub... | University of Science and Technology Beijing | 0.781918 |
87,820 | Some MMOGs have been designed to accurately simulate certain aspects of the real world. They tend to be very specific to industries or activities of very large risk and huge potential loss, such as rocket science, airplanes, trucks, battle tanks, submarines etc. Gradually as simulation technology is getting more mainst... | Massively multiplayer | 0.781918 |
87,821 | Modular provides value-added services, to help mines discover and address areas for improvement in various parts of mine operations and maintenance. The Modular Value Add Services (VAS) division specializes in design, implementation, and optimization of mine management systems, for both surface and underground mines. S... | Modular Mining Systems | 0.781917 |
87,822 | Modular provides software applications and hardware products designed to enhance mining operations’ productivity, safety, and equipment availability/utilization. The core Modular product line, the IntelliMine integrated asset management suite, includes the following products: Modular Mining's flagship product, the DISP... | Modular Mining Systems | 0.781917 |
87,823 | Collaborative combat aircraft (CCA), is a US program for unmanned combat air vehicles (UCAVs) and considered broadly equivalent to loyal wingman. CCAs are intended to operate in collaborative teams with the next generation of manned combat aircraft, including sixth-generation fighters and bombers such as the Northrop G... | Collaborative combat aircraft | 0.781916 |
87,824 | Air Force Secretary Frank Kendall envisions these uncrewed aircraft as performing parts of a larger mission; CCA development can be conducted in parallel with NGAD development, which has to take into account a larger set of requirements. Up to five autonomous CCAs would operate with an NGAD.Air Force Research Laborator... | Collaborative combat aircraft | 0.781916 |
87,825 | In Riemannian geometry, two Riemannian metrics g {\displaystyle g} and h {\displaystyle h} on a smooth manifold M {\displaystyle M} are called conformally equivalent if g = u h {\displaystyle g=uh} for some positive function u {\displaystyle u} on M {\displaystyle M} . The function u {\displaystyle u} is called the con... | Conformal mapping | 0.781916 |
87,826 | A classical theorem of Joseph Liouville shows that there are far fewer conformal maps in higher dimensions than in two dimensions. Any conformal map from an open subset of Euclidean space into the same Euclidean space of dimension three or greater can be composed from three types of transformations: a homothety, an iso... | Conformal mapping | 0.781916 |
87,827 | The normal-gamma distribution is a four-parameter exponential family with natural parameters α − 1 / 2 , − β − λ μ 2 / 2 , λ μ , − λ / 2 {\displaystyle \alpha -1/2,-\beta -\lambda \mu ^{2}/2,\lambda \mu ,-\lambda /2} and natural statistics ln τ , τ , τ x , τ x 2 {\displaystyle \ln \tau ,\tau ,\tau x,\tau x^{2}} . | Normal-gamma distribution | 0.781915 |
87,828 | The posterior distribution of μ {\displaystyle \mu } and τ {\displaystyle \tau } given this dataset X {\displaystyle \mathbb {X} } can be analytically determined by Bayes' theorem explicitly, P ( τ , μ ∣ X ) ∝ L ( X ∣ τ , μ ) π ( τ , μ ) , {\displaystyle \mathbf {P} (\tau ,\mu \mid \mathbf {X} )\propto \mathbf {L} (\ma... | Normal-gamma distribution | 0.781915 |
87,829 | In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision. | Normal-gamma distribution | 0.781915 |
87,830 | Given a task ( μ r e f , d ) {\displaystyle (\mu _{ref},d)} , the problem of training a DAE is the optimization problem:That is, the optimal DAE should take any noisy message and attempt to recover the original message without noise, thus the name "denoising". Usually, the noise process T {\displaystyle T} is applied o... | Denoising autoencoder | 0.781911 |
87,831 | An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning). An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation. The autoencode... | Denoising autoencoder | 0.781911 |
87,832 | Inspired by the sparse coding hypothesis in neuroscience, sparse autoencoders are variants of autoencoders, such that the codes E ϕ ( x ) {\displaystyle E_{\phi }(x)} for messages tend to be sparse codes, that is, E ϕ ( x ) {\displaystyle E_{\phi }(x)} is close to zero in most entries. Sparse autoencoders may include m... | Denoising autoencoder | 0.781911 |
87,833 | This was the first freeWAIS based on the wais-8-b5 codebase of TMC, with a wholly new software suite Isite based upon Z39.50:1992 using Isearch as its full-text search engine. Ulrich Pfeifer and Norbert Gövert of the computer science department of the University of Dortmund extended the CNIDR freeWAIS code to become fr... | Wide area information server | 0.781908 |
87,834 | Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems.Kernel methods (for instance, support vector machines or Gaussian processes) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplan... | Low-rank matrix approximations | 0.781908 |
87,835 | The (Lower Saxony) LBEG mining office (State Office for Mining, Energy and Geology) took the project lead. After the drilling project ended, the German Research Centre for Geosciences used the borehole to install a seismic deep observatory (Tiefenobservatorium) which was active from 1996 to 2001. The derrick used at th... | German Continental Deep Drilling Programme | 0.781908 |
87,836 | The von Neumann entropy is also strongly subadditive. Given three Hilbert spaces, A, B, C, S ( ρ A B C ) + S ( ρ B ) ≤ S ( ρ A B ) + S ( ρ B C ) . {\displaystyle S(\rho _{ABC})+S(\rho _{B})\leq S(\rho _{AB})+S(\rho _{BC}).} This is a more difficult theorem and was proved first by J. Kiefer in 1959 and independently by ... | Quantum entropy | 0.781906 |
87,837 | They were proved in 1970 by Huzihiro Araki and Elliott H. Lieb. While in Shannon's theory the entropy of a composite system can never be lower than the entropy of any of its parts, in quantum theory this is not the case, i.e., it is possible that S(ρAB) = 0, while S(ρA) = S(ρB) > 0. Intuitively, this can be understood ... | Quantum entropy | 0.781906 |
87,838 | John von Neumann established a rigorous mathematical framework for quantum mechanics in his 1932 work Mathematical Foundations of Quantum Mechanics. In it, he provided a theory of measurement, where the usual notion of wave-function collapse is described as an irreversible process (the so-called von Neumann or projecti... | Quantum entropy | 0.781906 |
87,839 | In planetary geology, a mensa (pl. mensae ) is a flat-topped prominence with cliff-like edges. The term is derived from the Latin word for table, and has the same root as the Spanish word for table, mesa. Mensa is used in the same manner as mesa is used in the Southwest United States. == References == | Mensa (geology) | 0.781905 |
87,840 | Sometimes the term "Hopf fibration" is restricted to the fibrations between spheres obtained above, which are S1 → S1 with fiber S0 S3 → S2 with fiber S1 S7 → S4 with fiber S3 S15 → S8 with fiber S7As a consequence of Adams's theorem, fiber bundles with spheres as total space, base space, and fiber can occur only in th... | Hopf bundle | 0.781905 |
87,841 | In particular, the Hopf fibration belongs to a family of four fiber bundles in which the total space, base space, and fiber space are all spheres: S 0 ↪ S 1 → S 1 , {\displaystyle S^{0}\hookrightarrow S^{1}\to S^{1},} S 1 ↪ S 3 → S 2 , {\displaystyle S^{1}\hookrightarrow S^{3}\to S^{2},} S 3 ↪ S 7 → S 4 , {\displaystyl... | Hopf bundle | 0.781905 |
87,842 | These tori are illustrated in the images at right. When R3 is compressed to the boundary of a ball, some geometric structure is lost although the topological structure is retained (see Topology and geometry). | Hopf bundle | 0.781905 |
87,843 | In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technicall... | Hopf bundle | 0.781905 |
87,844 | Primate cognition is the study of the intellectual and behavioral skills of non-human primates, particularly in the fields of psychology, behavioral biology, primatology, and anthropology.Primates are capable of high levels of cognition; some make tools and use them to acquire foods and for social displays; some have s... | Primate intelligence | 0.781904 |
87,845 | Statistica Sinica has been indexed and abstracted in Scopus, Science Citation Index Expanded, maintained by Institute for Scientific Information (ISI) and Current Contents (CC) from 1998. It is the first journal in statistics that is included in SCI in Asia. In 2000, it has been indexed in Current Index to Statistics (... | Statistica Sinica | 0.781902 |
87,846 | Statistica Sinica is an international journal publishing papers in all areas of statistics and data science, including theory, methods, and applications. First issued in 1991, this journal published semiannually in January and July from 1991 to 1995. From 1996 onward, it became quarterly in January, April, July, and Oc... | Statistica Sinica | 0.781902 |
87,847 | PathoPhenoDB is a biological database. The database connects pathogens to their phenotypes using multiple databases such as NCBI, Human Disease Ontology Human Phenotype Ontology, Mammalian Phenotype Ontology, PubChem, SIDER and CARD. Pathogen-disease associations were gathered mainly through the CDC and the List of Inf... | PathoPhenoDB | 0.781902 |
87,848 | This is a multistage stochastic programming problem, where stages are numbered from t = 0 {\displaystyle t=0} to t = T − 1 {\displaystyle t=T-1} . Optimization is performed over all implementable and feasible policies. | Stochastic linear program | 0.7819 |
87,849 | At the second stage, after a realization of ξ {\displaystyle \xi } becomes available, we optimize our behavior by solving an appropriate optimization problem. At the first stage we optimize (minimize in the above formulation) the cost c T x {\displaystyle c^{T}x} of the first-stage decision plus the expected cost of th... | Stochastic linear program | 0.7819 |
87,850 | Suppose the sample ξ 1 , … , ξ N {\displaystyle \xi ^{1},\dots ,\xi ^{N}} is i.i.d. and fix a point x ∈ X {\displaystyle x\in X} . Then the sample average estimator g ^ N ( x ) {\displaystyle {\hat {g}}_{N}(x)} , of g ( x ) {\displaystyle g(x)} , is unbiased and has variance 1 N σ 2 ( x ) {\displaystyle {\frac {1}{N}}\... | Stochastic linear program | 0.7819 |
87,851 | Stochastic dynamic programming is frequently used to model animal behaviour in such fields as behavioural ecology. Empirical tests of models of optimal foraging, life-history transitions such as fledging in birds and egg laying in parasitoid wasps have shown the value of this modelling technique in explaining the evolu... | Stochastic linear program | 0.7819 |
87,852 | Iodine-transfer polymerization (ITP, also called ITRP), developed by Tatemoto and coworkers in the 1970s gives relatively low polydispersities for fluoroolefin polymers. While it has received relatively little academic attention, this chemistry has served as the basis for several industrial patents and products and may... | Living free-radical polymerization | 0.7819 |
87,853 | Although the notation need not be taken literally, it is usually simpler than alternatives when the technique of separation of variables is used in the solution of differential equations. In physical applications, one may for example regard f(x) as measured in meters per second, and dx in seconds, so that f(x) dx is in... | Leibniz's notation | 0.781899 |
87,854 | Notations he used for the differential of y ranged successively from ω, l, and y/d until he finally settled on dy. His integral sign first appeared publicly in the article "De Geometria Recondita et analysi indivisibilium atque infinitorum" ("On a hidden geometry and analysis of indivisibles and infinites"), published ... | Leibniz's notation | 0.781899 |
87,855 | The Newton–Leibniz approach to infinitesimal calculus was introduced in the 17th century. While Newton worked with fluxions and fluents, Leibniz based his approach on generalizations of sums and differences. Leibniz was the first to use the ∫ {\displaystyle \textstyle \int } character. He based the character on the Lat... | Leibniz's notation | 0.781899 |
87,856 | The expression may also be thought of as the application of the differential operator d/dx (again, a single symbol) to y, regarded as a function of x. This operator is written D in Euler's notation. Leibniz did not use this form, but his use of the symbol d corresponds fairly closely to this modern concept. While there... | Leibniz's notation | 0.781899 |
87,857 | However, when solving differential equations, it is easy to think of the dys and dxs as separable. One of the simplest types of differential equations is M ( x ) + N ( y ) d y d x = 0 , {\displaystyle M(x)+N(y){\frac {dy}{dx}}=0,} where M and N are continuous functions. Solving (implicitly) such an equation can be done... | Leibniz's notation | 0.781899 |
87,858 | One reason that Leibniz's notations in calculus have endured so long is that they permit the easy recall of the appropriate formulas used for differentiation and integration. For instance, the chain rule—suppose that the function g is differentiable at x and y = f(u) is differentiable at u = g(x). Then the composite fu... | Leibniz's notation | 0.781899 |
87,859 | In the 1960s, building upon earlier work by Edwin Hewitt and Jerzy Łoś, Abraham Robinson developed mathematical explanations for Leibniz's infinitesimals that were acceptable by contemporary standards of rigor, and developed nonstandard analysis based on these ideas. Robinson's methods are used by only a minority of ma... | Leibniz's notation | 0.781899 |
87,860 | "Darwinism" soon came to stand for an entire range of evolutionary (and often revolutionary) philosophies about both biology and society. One of the more prominent approaches, summed in the 1864 phrase "survival of the fittest" by Herbert Spencer, later became emblematic of Darwinism even though Spencer's own understan... | Darwinian evolution | 0.781899 |
87,861 | In the 2008 documentary film Expelled: No Intelligence Allowed, which promotes intelligent design (ID), American writer and actor Ben Stein refers to scientists as Darwinists. Reviewing the film for Scientific American, John Rennie says "The term is a curious throwback, because in modern biology almost no one relies so... | Darwinian evolution | 0.781898 |
87,862 | Twenty years hence naturalists may be in a position to say whether this is, or is not, the case; but in either event they will owe the author of "The Origin of Species" an immense debt of gratitude.... And viewed as a whole, we do not believe that, since the publication of Von Baer's "Researches on Development," thirty... | Darwinian evolution | 0.781898 |
87,863 | In molecular biology, the hyccin protein family is a family of proteins which may have a role in the beta-catenin-Tcf/Lef signaling pathway, as well as in the process of myelination of the central and peripheral nervous system. One member of this family is hyccin, encoded by the FAM126A gene. Defects in Hyccin are the ... | Hyccin protein family | 0.781898 |
87,864 | Hiroshi Ishiguro (石黒浩 Ishiguro Hiroshi) is director of the Intelligent Robotics Laboratory, part of the Department of Systems Innovation in the Graduate School of Engineering Science at Osaka University, Japan. A notable development of the laboratory is the Actroid, a humanoid robot with lifelike appearance and visible... | Geminoid | 0.781898 |
87,865 | Hiroshi also uses the android to teach his classes at Osaka University of Japan and likes to scare his students by making Geminoid do human-like movements like blinking, "breathing" and fidgeting with his hands. Ishiguro has been listed, in 2011, as one of the 15 Asian Scientists to Watch by Asian Scientist Magazine. I... | Geminoid | 0.781898 |
87,866 | The Finsler–Hadwiger theorem is statement in Euclidean plane geometry that describes a third square derived from any two squares that share a vertex. The theorem is named after Paul Finsler and Hugo Hadwiger, who published it in 1937 as part of the same paper in which they published the Hadwiger–Finsler inequality rela... | Finsler–Hadwiger theorem | 0.781898 |
87,867 | To state the theorem, suppose that ABCD and AB'C'D' are two squares with common vertex A. Let E and G be the midpoints of B'D and D'B respectively, and let F and H be the centers of the two squares. Then the theorem states that the quadrilateral EFGH is a square as well.The square EFGH is called the Finsler–Hadwiger sq... | Finsler–Hadwiger theorem | 0.781898 |
87,868 | Repeated application of the Finsler–Hadwiger theorem can be used to prove Van Aubel's theorem, on the congruence and perpendicularity of segments through centers of four squares constructed on the sides of an arbitrary quadrilateral. Each pair of consecutive squares forms an instance of the theorem, and the two pairs o... | Finsler–Hadwiger theorem | 0.781898 |
87,869 | The Hartle–Hawking state is a proposal in theoretical physics concerning the state of the Universe prior to the Planck epoch. It is named after James Hartle and Stephen Hawking. Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the Universe, we would note that quite near what... | Hartle–Hawking state | 0.781893 |
87,870 | Measurement of polyphenol and carotenoid content in food is not a straightforward process, as antioxidants collectively are a diverse group of compounds with different reactivities to various reactive oxygen species. In food science analyses in vitro, the oxygen radical absorbance capacity (ORAC) was once an industry s... | Antioxidant supplements | 0.781891 |
87,871 | "Vanishing Theorems for Weakly 1-Complete Manifolds II". Publications of the Research Institute for Mathematical Sciences. 10 (1): 101–110. doi:10.2977/prims/1195192175. === Secondary sources === | Nakano vanishing theorem | 0.78189 |
87,872 | "Vanishing theorems for weakly 1-complete manifolds". Number theory, algebraic geometry and commutative algebra — in honor of Yasuo Akizuki. Kinokuniya. | Nakano vanishing theorem | 0.78189 |
87,873 | Akizuki, Yasuo; Nakano, Shigeo (1954). "Note on Kodaira-Spencer's proof of Lefschetz theorems". Proceedings of the Japan Academy. 30 (4): 266–272. | Nakano vanishing theorem | 0.78189 |
87,874 | In mathematics, specifically in the study of vector bundles over complex Kähler manifolds, the Nakano vanishing theorem, sometimes called the Akizuki–Nakano vanishing theorem, generalizes the Kodaira vanishing theorem. Given a compact complex manifold M with a holomorphic line bundle F over M, the Nakano vanishing theo... | Nakano vanishing theorem | 0.78189 |
87,875 | In molecular biology, an autotransporter domain is a structural domain found in some bacterial outer membrane proteins. The domain is always located at the C-terminal end of the protein and forms a beta-barrel structure. The barrel is oriented in the membrane such that the N-terminal portion of the protein, termed the ... | Autotransporter family | 0.781888 |
87,876 | This gives us the base case. Now, assume that the theorem holds for all polynomials in n − 1 variables. | Schwartz–Zippel lemma | 0.781887 |
87,877 | Theorem 1 (Schwartz, Zippel). Let P ∈ F {\displaystyle P\in F} be a non-zero polynomial of total degree d ≥ 0 over a field F. Let S be a finite subset of F and let r1, r2, ..., rn be selected at random independently and uniformly from S. Then Pr ≤ d | S | . {\displaystyle \Pr\leq {\frac {d}{|S|}}.} Equivalently, the ... | Schwartz–Zippel lemma | 0.781887 |
87,878 | The importance of the Schwartz–Zippel Theorem and Testing Polynomial Identities follows from algorithms which are obtained to problems that can be reduced to the problem of polynomial identity testing. | Schwartz–Zippel lemma | 0.781887 |
87,879 | Agrawal and Biswas use a more sophisticated technique, which divides P n {\displaystyle {\mathcal {P}}_{n}} by a random monic polynomial of small degree. Prime numbers are used in a number of applications such as hash table sizing, pseudorandom number generators and in key generation for cryptography. Therefore, findin... | Schwartz–Zippel lemma | 0.781887 |
87,880 | For example, is ( x 1 + 3 x 2 − x 3 ) ( 3 x 1 + x 4 − 1 ) ⋯ ( x 7 − x 2 ) ≡ 0 ? {\displaystyle (x_{1}+3x_{2}-x_{3})(3x_{1}+x_{4}-1)\cdots (x_{7}-x_{2})\equiv 0\ ?} To solve this, we can multiply it out and check that all the coefficients are 0. However, this takes exponential time. In general, a polynomial can be algeb... | Schwartz–Zippel lemma | 0.781887 |
87,881 | Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph of n vertices where n is even. Does G contain a perfect matching? Theorem 2 (Tutte 1947): A Tutte matrix determinant is not a 0-polynomial if and only if there exists a perfect matching. A subset D of E is called a matching if each vertex in V is incident with at mos... | Schwartz–Zippel lemma | 0.781887 |
87,882 | Condition of asymptotic completeness in the Delta-compactness theorem is satisfied by uniformly convex Banach spaces, and more generally, by uniformly rotund metric spaces as defined by J. Staples. | Delta-convergence | 0.781887 |
87,883 | The Delta-compactness theorem of T. C. Lim states that if ( X , d ) {\displaystyle (X,d)} is an asymptotically complete metric space, then every bounded sequence in X {\displaystyle X} has a Delta-convergent subsequence. The Delta-compactness theorem is similar to the Banach–Alaoglu theorem for weak convergence but, un... | Delta-convergence | 0.781887 |
87,884 | Often optimization is also used.Typically optics have refractive and reflective surfaces and light travels through media of different refractive indices as it crosses the optic. In those cases a quantity called optical path length (OPL) may be defined as S = ∑ i n i d i {\textstyle S=\sum _{i}n_{i}d_{i}} where index i ... | Non-imaging optics | 0.781883 |
87,885 | The journal was published by MAIK Nauka/Interperiodica from 1991 to 2005, by Springer Science+Business Media from 2006 to 2012, and since then by IOP Publishing. Its sister journal, Laser Physics Letters, was established in 2004. | Laser Physics (journal) | 0.781883 |
87,886 | The journal was established in 1990 with Alexander M. Prokhorov as founding editor-in-chief until 2002. The current editor-in-chief is Vanderlei S. Bagnato. It is a sister journal to Laser Physics Letters. | Laser Physics (journal) | 0.781883 |
87,887 | Laser Physics is a monthly peer-reviewed scientific journal covering research on the physics and technology of lasers and their applications. It is owned and editorially managed by Astro Ltd. and published on their behalf by IOP Publishing. | Laser Physics (journal) | 0.781883 |
87,888 | Flow chemistry is a well-established technique for use at a large scale when manufacturing large quantities of a given material. However, the term has only been coined recently for its application on a laboratory scale by chemists and describes small pilot plants, and lab-scale continuous plants. Often, microreactors a... | Continuous flow reactor | 0.781883 |
87,889 | In flow chemistry, also called reactor engineering, a chemical reaction is run in a continuously flowing stream rather than in batch production. In other words, pumps move fluid into a reactor, and where tubes join one another, the fluids contact one another. If these fluids are reactive, a reaction takes place. | Continuous flow reactor | 0.781883 |
87,890 | Recent developments in electrochemical flow-systems enabled the combination of reaction-oriented electrochemical flow systems with species-focused spectroscopy which allows a complete analysis of reactions involving multiple electron transfer steps, as well as unstable intermediates. These systems which are referred to... | Continuous flow reactor | 0.781883 |
87,891 | Continuous flow electrochemistry like continuous photochemistry offers many advantages over analogous batch conditions. Electrochemistry like Photochemical reactions can be considered as 'reagent-less' reactions. In an electrochemical reaction the reaction is facilitated by the number of electrons that are able to acti... | Continuous flow reactor | 0.781883 |
87,892 | Choosing to run a chemical reaction using flow chemistry, either in a microreactor or other mixing device offers a variety of pros and cons. | Continuous flow reactor | 0.781883 |
87,893 | Microwave reactors are frequently used for small-scale batch chemistry. However, due to the extremes of temperature and pressure reached in a microwave it is often difficult to transfer these reactions to conventional non-microwave apparatus for subsequent development, leading to difficulties with scaling studies. A fl... | Continuous flow reactor | 0.781883 |
87,894 | Reaction temperature can be raised above the solvent's boiling point as the volume of the laboratory devices is typically small. Typically, non-compressible fluids are used with no gas volume so that the expansion factor as a function of pressure is small. Mixing can be achieved within seconds at the smaller scales use... | Continuous flow reactor | 0.781882 |
87,895 | Alternatives to Darwinian evolution have been proposed by scholars investigating biology to explain signs of evolution and the relatedness of different groups of living things. The alternatives in question do not deny that evolutionary changes over time are the origin of the diversity of life, nor that the organisms al... | Non-Darwinian evolution | 0.781881 |
87,896 | Instead, the experimental work of the German biologist August Weismann resulted in the germ plasm theory of inheritance, which Weismann said made the inheritance of acquired characteristics impossible, since the Weismann barrier would prevent any changes that occurred to the body after birth from being inherited by the... | Non-Darwinian evolution | 0.781881 |
87,897 | In 2012, Gunda Georg (University of Minnesota) and Shaomeng Wang (University of Michigan) succeeded Portoghese (University of Minnesota). In 2021, Craig W. Lindsley (Vanderbilt University) became editor-in-chief. According to the Journal Citation Reports, the journal has a 2021 impact factor of 8.039, ranking it 1st ou... | Journal of Medicinal Chemistry | 0.781881 |
87,898 | The Journal of Medicinal Chemistry is a biweekly peer-reviewed medical journal covering research in medicinal chemistry. It is published by the American Chemical Society. It was established in 1959 as the Journal of Medicinal and Pharmaceutical Chemistry and obtained its current name in 1963. Philip S. Portoghese serve... | Journal of Medicinal Chemistry | 0.781881 |
87,899 | In mathematics, a coframe or coframe field on a smooth manifold M {\displaystyle M} is a system of one-forms or covectors which form a basis of the cotangent bundle at every point. In the exterior algebra of M {\displaystyle M} , one has a natural map from v k: ⨁ k T ∗ M → ⋀ k T ∗ M {\displaystyle v_{k}:\bigoplus ^{k}T... | Coframe | 0.78188 |
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