id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
87,700 | Xiao-Gang Wen, Yong-Shi Wu and Y. Hatsugai., Chiral operator product algebra and edge excitations of a FQH droplet (pdf),Nucl. Phys. | Topological phase transition | 0.781975 |
87,701 | Non-Abelian Quantum Algebraic Topology (NAQAT) 20 Nov. (2008),87 pages, Baianu, I.C. Levin A. and Olshanetsky M., Hamiltonian Algebroids and deformations of complex structures on Riemann curves, hep-th/0301078v1. | Topological phase transition | 0.781975 |
87,702 | Conf. on Groupoids in Physics, Analysis and Geometry(Boulder CO, 1999)', Editors J. Kaminker et al.,159{192 Contemp. Math. | Topological phase transition | 0.781975 |
87,703 | 2 (1): 113–123. doi:10.1142/s0218216593000076. Landsman N. P. and Ramazan B., Quantization of Poisson algebras associated to Lie algebroids, in Proc. | Topological phase transition | 0.781975 |
87,704 | PL/Perl (Procedural Language/Perl) is a procedural language supported by the PostgreSQL RDBMS. PL/Perl, as an imperative programming language, allows more control than the relational algebra of SQL. Programs created in the PL/Perl language are called functions and can use most of the features that the Perl programming ... | PL/Perl | 0.781974 |
87,705 | Schoenbach at Stevens Institute of Technology in Hoboken, New Jersey. The third international workshop was coordinated by the Institute of Low Temperature Plasma Physics alongside the Institute of Physics of Ernst-Moitz-Arndt-University in Greifswald, Germany, May 2006 (K.D. Weltmann). | Microplasma | 0.781973 |
87,706 | At the University of Southern California, Parish Sedghizadeh, Director of the USC Center for Biofilms and Chunqi Jiang, assistant research professor in the Ming Hsieh Department of Electrical Engineering-Electrophysics, work with researchers from Viterbi School of Engineering searching for new ways to fight off these b... | Microplasma | 0.781973 |
87,707 | Furthermore, specific energies approaching 10 J cm−3 are required to achieve a comparable destruction efficiency in the cross-flow reactor. This indicates that optimization of the reactor geometry is a critical aspect of achieving maximum destruction efficiencies. | Microplasma | 0.781973 |
87,708 | Methylcyclopentadiene is any of three isomeric cyclic dialkenes with the formula C5MeH5 (Me = CH3). These isomers are the organic precursor to the methylcyclopentadienyl ligand (C5H4Me, often denoted as Cp′), commonly found in organometallic chemistry. As with cyclopentadiene, methylcyclopentadiene is prepared by therm... | Methylcyclopentadiene | 0.781969 |
87,709 | It is possible for a dive computer to malfunction during a dive. Manufacturers are not obliged to publish reliability statistics, and generally only include a warning in the user manual that they are used at the diver's own risk. Reliability has markedly improved over time, particularly for the hardware. | Dive computers | 0.781968 |
87,710 | The Nexter group is divided in several smaller entities, with the main one being Nexter Systems. The sub-companies are: Nexter Munitions Nexter Mechanics Nexter Electronics Nexter Robotics Nexter Training OptSys NBC Sys Euro-Shelter Mecar Simmel Difesa | Nexter Systems | 0.781966 |
87,711 | (Sand dollars are a separate order in the sea urchin class Echinoidea.) The animals have been studied since the 19th century as model organisms in developmental biology, as their embryos were easy to observe. | Sea urchin | 0.781966 |
87,712 | Renewable thermal energy is the technology of gathering thermal energy from a renewable energy source for immediate use or for storage in a thermal battery for later use. The most popular form of renewable thermal energy is the sun and the solar energy is harvested by solar collectors to heat water, buildings, pools an... | Renewable thermal energy | 0.781965 |
87,713 | The results of these experiments led directly to the "one gene, one enzyme" hypothesis that specific genes code for specific proteins. This concept launched molecular biology. Sexual fruiting bodies (perithecia) can only be formed when two cells of different mating type come together (see Figure). | Mating in fungi | 0.781965 |
87,714 | Finally, the fungus causing witches' broom in cacao, Moniliophthora perniciosa, has a primarily homothallic biology despite having A and B mating type-like genes in its genome.Among the 250 known species of aspergilli, about 36% have an identified sexual state Among those Aspergillus species that exhibit a sexual cycle... | Mating in fungi | 0.781965 |
87,715 | SIMes (or H2Imes) is an N-heterocyclic carbene. It is a white solid that dissolves in organic solvents. The compound is used as a ligand in organometallic chemistry. It is structurally related to the more common ligand IMes but with a saturated backbone (the S of SIMes indicates a saturated backbone). | SIMes | 0.781964 |
87,716 | In 2002, the University of Basel launched the Bachelor's and Master's degree programs in nanosciences. The annual Bacherlor's program cohort is between 20-40 students and includes biology, chemistry, physics and mathematics. In 2013 the SNI initiated a PhD School. Approximately 40 PhD are enrolled in the SNI PhD School... | Swiss Nanoscience Institute | 0.781963 |
87,717 | The Swiss Nanoscience Institute (SNI) at the University of Basel is a center of excellence for nanosciences and nanotechnology. It was founded in 2006 by the Canton of Aargau and the University of Basel . | Swiss Nanoscience Institute | 0.781963 |
87,718 | In molecular biology, Ornithine decarboxylase antizyme (ODC-AZ) is an ornithine decarboxylase inhibitor. It binds to, and destabilises, ornithine decarboxylase (ODC), a key enzyme in polyamine synthesis. ODC is then rapidly degraded. | Ornithine decarboxylase antizyme | 0.781962 |
87,719 | It uses the fact that the indefinite integrals of the functions gn in the given Cauchy sequence, namely converge uniformly on {\displaystyle } to some function G, continuous with bounded variation. The existence of the limit g ∈ L 2 {\displaystyle g\in L^{2}} for the Cauchy sequence is obtained by applying to G differ... | Riesz-Fischer theorem | 0.781961 |
87,720 | {\displaystyle \Omega .} Also, convergence to a limit in L 2 {\displaystyle L^{2}} –norm is called "convergence in the mean towards a function". Here is the statement, translated from French: Theorem. | Riesz-Fischer theorem | 0.781961 |
87,721 | 1023) states explicitly in a theorem (almost with modern words) that a Cauchy sequence in L 2 ( ) {\displaystyle L^{2}()} converges in L 2 {\displaystyle L^{2}} -norm to some function f ∈ L 2 ( ) . {\displaystyle f\in L^{2}().} In this Note, Cauchy sequences are called "sequences converging in the mean" and L 2 ( ) ... | Riesz-Fischer theorem | 0.781961 |
87,722 | In mathematics, the Riesz–Fischer theorem in real analysis is any of a number of closely related results concerning the properties of the space L2 of square integrable functions. The theorem was proven independently in 1907 by Frigyes Riesz and Ernst Sigismund Fischer. For many authors, the Riesz–Fischer theorem refers... | Riesz-Fischer theorem | 0.781961 |
87,723 | Economists debate whether various economic statistics, especially output, have a unit root or are trend-stationary. A unit root process with drift is given in the first-order case by y t = y t − 1 + c + e t {\displaystyle y_{t}=y_{t-1}+c+e_{t}} where c is a constant term referred to as the "drift" term, and e t {\displ... | Unit root | 0.781961 |
87,724 | In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-sta... | Unit root | 0.781961 |
87,725 | For p < ∞ , {\displaystyle p<\infty ,} the Minkowski inequality and the monotone convergence theorem imply that is defined μ {\displaystyle \mu } –almost everywhere and f ∈ L p ( μ ) . {\displaystyle f\in L^{p}(\mu ).} The dominated convergence theorem is then used to prove that the partial sums of the series converge ... | Riesz-Fischer theorem | 0.781961 |
87,726 | For some authors, notably Royden, the Riesz-Fischer Theorem is the result that L p {\displaystyle L^{p}} is complete: that every Cauchy sequence of functions in L p {\displaystyle L^{p}} converges to a function in L p , {\displaystyle L^{p},} under the metric induced by the p-norm. The proof below is based on the conve... | Riesz-Fischer theorem | 0.781961 |
87,727 | Kuhn's ideas influenced paleontologist Stephen Jay Gould, who introduced the idea of punctuated equilibrium in the field of evolutionary biology in 1972. Gould's initial work on punctuated equilibrium was coauthored with Niles Eldredge.Gould's model of punctuated equilibrium drew attention to episodic bursts of evoluti... | Critical juncture theory | 0.78196 |
87,728 | Moreover, the method further bolsters the link between DMD and the Koopman operator by demonstrating how the spectral content of the latter can be computed with verification and error control. Physics-informed DMD: Physics-informed DMD forms a Procrustes problem that restricts the family of admissible models to a matri... | Dynamic mode decomposition | 0.78196 |
87,729 | The Exact DMD algorithm removes this pre-processing step, and can produce DMD modes that cannot be written as the superposition of POD modes. Sparsity Promoting DMD: Sparsity promoting DMD is a post processing procedure for DMD mode and eigenvalue selection. Sparsity promoting DMD uses an ℓ 1 {\displaystyle \ell _{1}} ... | Dynamic mode decomposition | 0.78196 |
87,730 | Optimized DMD recasts the DMD procedure as an optimization problem where the identified linear operator has a fixed rank. Furthermore, unlike DMD which perfectly reproduces all of the snapshots except for the last, Optimized DMD allows the reconstruction errors to be distributed throughout the data set, which appears t... | Dynamic mode decomposition | 0.78196 |
87,731 | Each laboratory conceives and develops its own research projects in each field of interest. While most of the studies are coordinated and executed by biomedical researchers, the experimental equipment development and assembly falls to the Aerospace Engineering Lab, located within the School of Engineering. Commonplace ... | Microgravity Centre | 0.781959 |
87,732 | The centre is a multi-disciplinary unit that brings together researchers, professors and students from many different faculties within PUCRS, including medicine, engineering, aeronautical sciences, pharmacy, biosciences, physics, informatics, sports science, odontology, physiotherapy, nursing and nutrition. The centre ... | Microgravity Centre | 0.781959 |
87,733 | The American Society of Animal Science (ASAS) is a non-profit professional organization for the advancement of livestock, companion animals, exotic animals and meat science. Founded in 1908, ASAS is headquartered in Champaign, Illinois.ASAS members are involved in university research, education, and extension as well a... | American Society of Animal Science | 0.781956 |
87,734 | Both .X_T and .X_B are used for parts files. To use Parasolid effectively, software developers need knowledge of CAD in general, computational geometry and topology. Parasolid is available for Windows (32-bit, 64-bit and ARM64), Linux (64-bit), macOS (Intel and Apple Silicon), iOS, and Android. | Parasolid | 0.781956 |
87,735 | Parasolid is a geometric modeling kernel originally developed by Shape Data Limited, now owned and developed by Siemens Digital Industries Software. It can be licensed by other companies for use in their 3D computer graphics software products. Parasolid's capabilities include model creation and editing utilities such a... | Parasolid | 0.781956 |
87,736 | This is the fibered part of William Thurston's geometrization theorem for Haken manifolds, whose proof requires the Nielsen–Thurston classification for surface homeomorphisms as well as deep results in the theory of Kleinian groups. In geometric group theory the fundamental groups of such bundles give an important clas... | Surface bundle over the circle | 0.781955 |
87,737 | It is possible to show that the homeomorphism type of the bundle obtained depends only on the conjugacy class, in the mapping class group, of the gluing homeomorphism chosen. This construction is an important source of examples both in the field of low-dimensional topology as well as in geometric group theory. In the f... | Surface bundle over the circle | 0.781955 |
87,738 | James Daniel "BJ" Bjorken (born 1934) is an American theoretical physicist. He was a Putnam Fellow in 1954, received a BS in physics from MIT in 1956, and obtained his PhD from Stanford University in 1959. He was a visiting scholar at the Institute for Advanced Study in the fall of 1962. Bjorken is emeritus professor i... | Bjorken scaling | 0.781954 |
87,739 | J. D. Bjorken (1968). "Current Algebra at Small Distances", in Proceedings of the International School of Physics Enrico Fermi Course XLI, J. Steinberger, ed., Academic Press, New York, pp. 55–81. Online, SLAC-PUB-338 J.D. | Bjorken scaling | 0.781954 |
87,740 | Modern physics uses field theories to explain reality. These fields can be scalar, vectorial or tensorial. An example of a scalar field is the temperature field. An example of a vector field is the wind velocity field. An example of a tensor field is the stress tensor field in a stressed body, used in continuum mechani... | Scalar–tensor theory | 0.781952 |
87,741 | Modern physics tries to derive all physical theories from as few principles as possible. In this way, Newtonian mechanics as well as quantum mechanics are derived from Hamilton's principle of least action. In this approach, the behavior of a system is not described via forces, but by functions which describe the energy... | Scalar–tensor theory | 0.781952 |
87,742 | In physics, forces (as vectorial quantities) are given as the derivative (gradient) of scalar quantities named potentials. In classical physics before Einstein, gravitation was given in the same way, as consequence of a gravitational force (vectorial), given through a scalar potential field, dependent of the mass of th... | Scalar–tensor theory | 0.781952 |
87,743 | There is a black diagonal on the sketch shown on the right. The length of the segment that runs perpendicularly from the intersection of this black diagonal with the red vertical axis to the point (1|0) should be called s. And the length of the section of the black diagonal from the coordinate origin point to the point... | Gauss lemniscate function | 0.78195 |
87,744 | If a {\displaystyle a} and p {\displaystyle p} are coprime, then there exist numbers p ′ ∈ Z {\displaystyle p'\in \mathbb {Z} } such that ( a p ) 4 = ∏ p ′ sl ( 2 ϖ a p ′ / p ) sl ( 2 ϖ p ′ / p ) . {\displaystyle \left({\frac {a}{p}}\right)_{4}=\prod _{p'}{\frac {\operatorname {sl} (2\varpi ap'/p)}{\operatorname {... | Gauss lemniscate function | 0.78195 |
87,745 | There are a number of causes for hard drives to fail including: human error, hardware failure, firmware corruption, media damage, heat, water damage, power issues and mishaps. Drive manufacturers typically specify a mean time between failures (MTBF) or an annualized failure rate (AFR) which are population statistics th... | Hard-disk failure | 0.78195 |
87,746 | Some early drives even had a table attached to a drive's case on which bad sectors were to be listed as they appeared. Later drives map out bad sectors automatically, in a way invisible to the user; a drive with remapped sectors may continue to be used, though performance may decrease as the drive must physically move ... | Hard-disk failure | 0.78195 |
87,747 | Hard drives with S.M.A.R.T.-reported average temperatures below 27 °C (81 °F) had higher failure rates than hard drives with the highest reported average temperature of 50 °C (122 °F), failure rates at least twice as high as the optimum S.M.A.R.T.-reported temperature range of 36 °C (97 °F) to 47 °C (117 °F). The corre... | Hard-disk failure | 0.78195 |
87,748 | Together with I 5 = e 123 E {\displaystyle I_{5}=e_{123}E} and 1 {\displaystyle 1} , these are the 32 basis blades of the algebra. The Flat Point Origin is written as an outer product because the geometric product is of mixed grade. ( E = e + e − {\displaystyle E=e_{+}e_{-}} ). | Conformal geometric algebra | 0.781949 |
87,749 | There is a vibrant and interdisciplinary community around Clifford and Geometric Algebras with a wide range of applications. The main conferences in this subject include the International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA) and Applications of Geometric Algebra in Compu... | Conformal geometric algebra | 0.781949 |
87,750 | Some intersection operations also acquire a tidy algebraic form: for example, for the Euclidean base space R3, applying the wedge product to the dual of the tetravectors representing two spheres produces the dual of the trivector representation of their circle of intersection. As this algebraic structure lends itself d... | Conformal geometric algebra | 0.781949 |
87,751 | Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space Rp,q to null vectors in Rp+1,q+1. This allows operations on the base space, including reflections, rotations and translations to be represented using versors of the geometr... | Conformal geometric algebra | 0.781949 |
87,752 | This motivates the subscripts o and ∞ for identifying the null basis vectors. The choice of the origin is arbitrary: any other point may be chosen, as the representation is of an affine space. The origin merely represents a reference point, and is algebraically equivalent to any other point. As with any translation, ch... | Conformal geometric algebra | 0.781949 |
87,753 | Algebraically, any nonzero null element of the homogeneous subspace will be used, with one element being referred to as normalized by some criterion. Boldface lowercase Latin letters are used to represent position vectors from the origin to a point in the base space. Italic symbols are used for other elements of the re... | Conformal geometric algebra | 0.781949 |
87,754 | In this article, the focus is on the algebra G ( 4 , 1 ) {\displaystyle {\mathcal {G}}(4,1)} as it is this particular algebra that has been the subject of most attention over time; other cases are briefly covered in a separate section. The space containing the objects being modelled is referred to here as the base spac... | Conformal geometric algebra | 0.781949 |
87,755 | This may result in failing to retrieve important or precedential cases. In some jurisdictions this may be especially problematic, as legal professionals are ethically obligated to be reasonably informed as to relevant legal documents.Legal Information Retrieval attempts to increase the effectiveness of legal searches b... | Legal information retrieval | 0.781948 |
87,756 | In order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. Adequate translation of both would allow accurate information retrieval without the high cost of human classification. These automatic systems... | Legal information retrieval | 0.781948 |
87,757 | The topology on V k ( F n ) {\displaystyle V_{k}(\mathbb {F} ^{n})} is the subspace topology inherited from F n × k . {\displaystyle \mathbb {F} ^{n\times k}.} With this topology V k ( F n ) {\displaystyle V_{k}(\mathbb {F} ^{n})} is a compact manifold whose dimension is given by dim V k ( R n ) = n k − 1 2 k ( k + 1... | Stiefel manifold | 0.781944 |
87,758 | The Stiefel manifold can be equipped with a uniform measure, i.e. a Borel measure that is invariant under the action of the groups noted above. For example, V 1 ( R 2 ) {\displaystyle V_{1}(\mathbb {R} ^{2})} which is isomorphic to the unit circle in the Euclidean plane, has as its uniform measure the obvious uniform m... | Stiefel manifold | 0.781944 |
87,759 | In probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another random vector. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar ra... | Cross-covariance matrix | 0.781941 |
87,760 | The Bethe–Salpeter equation (named after Hans Bethe and Edwin Salpeter) describes the bound states of a two-body (particles) quantum field theoretical system in a relativistically covariant formalism. The equation was actually first published in 1950 at the end of a paper by Yoichiro Nambu, but without derivation. Due ... | Bethe-Salpeter equation | 0.78194 |
87,761 | Smartphone: The networking of the self The internet of things: A planetary mesh of perception and response Augmented reality: An interactive overlay on the world Digital fabrication: Towards a political economy Cryptocurrency: The computational guarantee of value Blockchain beyond Bitcoin: A trellis for post-human inst... | Radical Technologies | 0.78194 |
87,762 | In the opening chapter on smartphones for example, whilst marvelling that the entire cartographic knowledge of the world and even our place in it is now available to us on a flat screen that we can hold in our hands, we are for the most part blissfully unaware of all of the interconnected technologies - the NAVSTAR sat... | Radical Technologies | 0.78194 |
87,763 | He did significant work in lead, oxygen and sulfur isotope geochemistry. He died in Canberra, Australia. == References == | Shen-su Sun | 0.781936 |
87,764 | Shen-su Sun (Chinese: 孫賢鉥; pinyin: Sūn Xiánshù; 27 October 1943 – 5 March 2005) was a Chinese-born Australian geochemist.Sun was born in Fuzhou, Fujian, China. He earned his bachelor's degree in geology from National Taiwan University, and obtained his Ph.D. from Columbia University in 1973. During 1981 to 1999, he was... | Shen-su Sun | 0.781936 |
87,765 | The James Webb Space Telescope is a space telescope operated by NASA and designed primarily to conduct infrared astronomy. Launched in December 2021, the spacecraft has been in a halo orbit around the second Sun–Earth Lagrange point (L2), about 1.5 million kilometers (900,000 mi) from Earth, since January 2022. At L2, ... | Webb's First Deep Field | 0.781934 |
87,766 | It has been reported that a reduction in loss of some post-translational modifications can be accomplished if IR MALDI is used instead of UV MALDIBesides proteins, MALDI-TOF has also been applied to study lipids. For example, it has been applied to study the catalytic reactions of phospholipases. In addition to lipids,... | Matrix-assisted laser desorption ionization-time of flight mass spectrometer | 0.781934 |
87,767 | In fantasy basketball, statistics are used in a formula as the measurement of a player's performance. | Basketball statistics | 0.781934 |
87,768 | Examples of tempo-free statistics including the following Pace: Possessions per game (typically ranges from 60 to 75) PPP: Points per possession, the points a team score for each possession regardless of a team's pace TO%: Turnover percentage, the measure of how often a team loses possession of the ball before creating... | Basketball statistics | 0.781934 |
87,769 | A player who makes double digits in a game in any two of the PTS, REB, AST, STL, and BLK statistics is said to make a double double; in three statistics, a triple double; in four statistics, a quadruple double. A quadruple double is extremely rare (and has only occurred four times in the NBA). There is also a 5x5, when... | Basketball statistics | 0.781934 |
87,770 | Examples of basketball statistics include: Averages per game are denoted by *PG (e.g. BLKPG or BPG, STPG or SPG, APG, RPG and MPG). Sometime the players statistics are divided by minutes played and multiplied by 48 minutes (had he played the entire game), denoted by * per 48 min. or *48M. | Basketball statistics | 0.781934 |
87,771 | Statistics in basketball are kept to evaluate a player's or a team's performance. | Basketball statistics | 0.781934 |
87,772 | The Berkeley Lower Extremity Exoskeleton (BLEEX) is a robotic device that attaches to the lower body. Its purpose is to complement the user's strength by adding extra force to the user's lower extremity bodily movements. The BLEEX was funded by the Defense Advanced Research Projects Agency (DARPA), and developed by the... | Berkeley Lower Extremity Exoskeleton | 0.781933 |
87,773 | Being one-to-one and holomorphic implies having a non-zero derivative. However, the exponential function is a holomorphic function with a nonzero derivative, but is not one-to-one since it is periodic.The Riemann mapping theorem, one of the profound results of complex analysis, states that any non-empty open simply con... | Conformal transformation | 0.781931 |
87,774 | If U {\displaystyle U} is an open subset of the complex plane C {\displaystyle \mathbb {C} } , then a function f: U → C {\displaystyle f:U\to \mathbb {C} } is conformal if and only if it is holomorphic and its derivative is everywhere non-zero on U {\displaystyle U} . If f {\displaystyle f} is antiholomorphic (conjugat... | Conformal transformation | 0.781931 |
87,775 | Applications of conformal mapping exist in aerospace engineering, in biomedical sciences (including brain mapping and genetic mapping), in applied math (for geodesics and in geometry), in earth sciences (including geophysics, geography, and cartography), in engineering, and in electronics. | Conformal transformation | 0.781931 |
87,776 | The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-r... | Conformal transformation | 0.781931 |
87,777 | The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-called Standard-Model Extension. This general framework has allowed experimental searches b... | Faster-than-light travel | 0.781931 |
87,778 | In physics, the Casimir–Polder force is a physical force exerted between separate objects due to resonance of vacuum energy in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, owing to the mathematical form of one possible way of calculat... | Faster-than-light travel | 0.781931 |
87,779 | In the unramified case the order of DPj is f and IPj is trivial, so the Frobenius element is in this case an element of DPj, and thus also an element of G. For varying j, the groups DPj are conjugate subgroups inside G: Recalling that G acts transitively on the Pj, one checks that if σ {\displaystyle \sigma } maps Pj t... | Inert prime | 0.781931 |
87,780 | In the following, the extension L/K is assumed to be a Galois extension. Then the prime avoidance lemma can be used to show the Galois group G = Gal ( L / K ) {\displaystyle G=\operatorname {Gal} (L/K)} acts transitively on the Pj. That is, the prime ideal factors of p in L form a single orbit under the automorphisms... | Inert prime | 0.781931 |
87,781 | In other words, it was believed that each electron contributed to the specific heat an amount on the order of the Boltzmann constant kB. This problem remained unsolved until the development of Fermi–Dirac statistics. Fermi–Dirac statistics was first published in 1926 by Enrico Fermi and Paul Dirac. | Fermi distribution | 0.781929 |
87,782 | Before the introduction of Fermi–Dirac statistics in 1926, understanding some aspects of electron behavior was difficult due to seemingly contradictory phenomena. For example, the electronic heat capacity of a metal at room temperature seemed to come from 100 times fewer electrons than were in the electric current. It ... | Fermi distribution | 0.781929 |
87,783 | According to Max Born, Pascual Jordan developed in 1925 the same statistics, which he called Pauli statistics, but it was not published in a timely manner. According to Dirac, it was first studied by Fermi, and Dirac called it "Fermi statistics" and the corresponding particles "fermions".Fermi–Dirac statistics was appl... | Fermi distribution | 0.781928 |
87,784 | It is also possible to derive Fermi–Dirac statistics in the canonical ensemble. Consider a many-particle system composed of N identical fermions that have negligible mutual interaction and are in thermal equilibrium. Since there is negligible interaction between the fermions, the energy E R {\displaystyle E_{R}} of a s... | Fermi distribution | 0.781928 |
87,785 | The IAMG Distinguished Lectureship is a special lecture series established in the year 2002 by the International Association for Mathematical Geosciences (IAMG). Each year IAMG selects IAMG Distinguished Lecturer, who is an outstanding individual with (i) demonstrated ability to communicate mathematical concepts to gen... | IAMG Distinguished Lectureship | 0.781928 |
87,786 | A direct limit of the direct system ⟨ X i , f i j ⟩ {\displaystyle \langle X_{i},f_{ij}\rangle } is a universally repelling target ⟨ X , ϕ i ⟩ {\displaystyle \langle X,\phi _{i}\rangle } in the sense that ⟨ X , ϕ i ⟩ {\displaystyle \langle X,\phi _{i}\rangle } is a target and for each target ⟨ Y , ψ i ⟩ {\displaystyle ... | Inductive limit | 0.781928 |
87,787 | We will first give the definition for algebraic structures like groups and modules, and then the general definition, which can be used in any category. | Inductive limit | 0.781928 |
87,788 | Molecular Ecology expects that data supporting the results in the paper should be archived in an appropriate public archive, such as GenBank, Gene Expression Omnibus, TreeBASE, Dryad, the Knowledge Network for Biocomplexity, your own institutional or funder repository, or as Supporting Information on the Molecular Ecol... | Data repository | 0.781926 |
87,789 | In 1960, Russian researcher Rudolf Zaripov published worldwide first paper on algorithmic music composing using the "Ural-1" computer.In 1965, inventor Ray Kurzweil premiered a piano piece created by a computer that was capable of pattern recognition in various compositions. The computer was then able to analyze and us... | AI-generated music | 0.781925 |
87,790 | Artificial intelligence also drives interactive composition technology, wherein a computer composes music in response to a live performance. There are other AI applications in music that cover not only music composition, production, and performance but also how music is marketed and consumed. Several music player progr... | AI-generated music | 0.781925 |
87,791 | Artificial intelligence and music (AIM) is a common subject in the International Computer Music Conference, the Computing Society Conference and the International Joint Conference on Artificial Intelligence. The first International Computer Music Conference (ICMC) was held in 1974 at Michigan State University. Current ... | AI-generated music | 0.781925 |
87,792 | MorpheuS is a research project by Dorien Herremans and Elaine Chew at Queen Mary University of London, funded by a Marie Skłodowská-Curie EU project. The system uses an optimization approach based on a variable neighborhood search algorithm to morph existing template pieces into novel pieces with a set level of tonal t... | AI-generated music | 0.781925 |
87,793 | This function determines how much each subset of U {\displaystyle U} is worth to that partner. Let X {\displaystyle X} a partition of U {\displaystyle U} to k {\displaystyle k} measurable sets: U = X 1 ⊔ ⋯ ⊔ X k {\displaystyle U=X_{1}\sqcup \cdots \sqcup X_{k}} . Define the matrix M X {\displaystyle M_{X}} as the follo... | Dubins–Spanier theorems | 0.781924 |
87,794 | There is a set U {\displaystyle U} , and a set U {\displaystyle \mathbb {U} } which is a sigma-algebra of subsets of U {\displaystyle U} . There are n {\displaystyle n} partners. Every partner i {\displaystyle i} has a personal value measure V i: U → R {\displaystyle V_{i}:\mathbb {U} \to \mathbb {R} } . | Dubins–Spanier theorems | 0.781924 |
87,795 | The following statement is Dubins-Spanier Theorem on the existence of super-proportional division: 6 The hypothesis that the value measures V 1 , . . . | Dubins–Spanier theorems | 0.781924 |
87,796 | The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although the original motivation for these theorems is fair division, they are in fact general theorems in measure theory. | Dubins–Spanier theorems | 0.781924 |
87,797 | But the arrival of the coronavirus pandemic meant that conventional events could not be run, so instead the week was run "virtually" and involved streaming live events and observation sessions direct to homes. Most of the talks and observation sessions were run by the National Astronomy Week organising team, and these ... | National Astronomy Week | 0.781922 |
87,798 | Silver hexafluorophosphate is a commonly encountered reagent in inorganic and organometallic chemistry. It is commonly used to replace halide ligands with the weakly coordinating hexafluorophosphate anion; the abstraction of the halide is driven by the precipitation of the appropriate silver halide. Illustrative is the... | Silver hexafluorophosphate | 0.781922 |
87,799 | Participating organisations included astronomy societies, schools, universities, and Scouts/Guides. The details of the 2014 NAW are still available on the National Astronomy Week website. The event was widely announced in the UK, for example in Astronomy & Geophysics magazine, and there is also information on the NAW T... | National Astronomy Week | 0.781922 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.