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85,500 | Pokorski, Stefan; Gauge Field Theories, Cambridge University Press (1987) ISBN 0-521-47816-2. 't Hooft, Gerard; The Glorious Days of Physics – Renormalization of Gauge theories, lecture given at Erice (August/September 1998) by the Nobel laureate 1999 . Full text available at: hep-th/9812203. | Renormalization | 0.782889 |
85,501 | for particle physics. Zee, Anthony; Quantum Field Theory in a Nutshell, Princeton University Press (2003) ISBN 0-691-01019-6. Another excellent textbook on Q.F.T. | Renormalization | 0.782889 |
85,502 | The coupling constants in the Standard Model of particle physics vary in different ways with increasing energy scale: the coupling of quantum chromodynamics and the weak isospin coupling of the electroweak force tend to decrease, and the weak hypercharge coupling of the electroweak force tends to increase. At the colos... | Renormalization | 0.782889 |
85,503 | Short-distance divergences in condensed matter physics do not present a philosophical problem since the field theory is only an effective, smoothed-out representation of the behavior of matter anyway; there are no infinities since the cutoff is always finite, and it makes perfect sense that the bare quantities are cuto... | Renormalization | 0.782889 |
85,504 | Beginning in the 1970s, however, inspired by work on the renormalization group and effective field theory, and despite the fact that Dirac and various others—all of whom belonged to the older generation—never withdrew their criticisms, attitudes began to change, especially among younger theorists. Kenneth G. Wilson and... | Renormalization | 0.782889 |
85,505 | A. N. Vasil'ev; The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Routledge Chapman & Hall 2004); ISBN 978-0-415-31002-4 Nigel Goldenfeld; Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics 85, Westview Press (June, 1992) ISBN 0-201-55409-7. Co... | Renormalization | 0.782889 |
85,506 | A deeper understanding of the physical meaning and generalization of the renormalization process, which goes beyond the dilatation group of conventional renormalizable theories, came from condensed matter physics. Leo P. Kadanoff's paper in 1966 proposed the "block-spin" renormalization group. The blocking idea is a wa... | Renormalization | 0.782889 |
85,507 | Connes, Alain; Symétries Galoisiennes & Renormalisation, Poincaré Seminar (Paris, Oct. 12, 2002), published in: Duplantier, Bertrand; Rivasseau, Vincent (Eds. ); Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003) ISBN 3-7643-0579-7. French mathematician Alain Connes (Fields medallist 1982) de... | Renormalization | 0.782889 |
85,508 | A large number of organoboron compounds are known and many are useful in organic synthesis. Many are produced from hydroboration, which employs diborane, B2H6, a simple borane chemical, or carboboration. Organoboron(III) compounds are usually tetrahedral or trigonal planar, for example, tetraphenylborate, − vs. triphen... | Boron-11 | 0.782887 |
85,509 | A special case of this theorem arises when X is an algebraic variety, in which case the conditions of the theorem imply that X is an affine variety. A similar result has stricter conditions on X but looser conditions on the cohomology: if X is a quasi-separated, quasi-compact scheme, and if H1(X, I) = 0 for any quasi-c... | Serre's theorem on affineness | 0.782886 |
85,510 | In the mathematical discipline of algebraic geometry, Serre's theorem on affineness (also called Serre's cohomological characterization of affineness or Serre's criterion on affineness) is a theorem due to Jean-Pierre Serre which gives sufficient conditions for a scheme to be affine. The theorem was first published by ... | Serre's theorem on affineness | 0.782886 |
85,511 | By varying U, we get an algebraic stack Shtukar of shtukas of rank r, a "universal" shtuka over Shtukar×X and a morphism (∞,0) from Shtukar to X×X which is smooth and of relative dimension 2r − 2. The stack Shtukar is not of finite type for r > 1. Drinfeld modules are in some sense special kinds of shtukas. | Drinfeld modules | 0.782886 |
85,512 | In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism) such that P ∘ P = P {\displaystyle P\circ P=P} . That is, whenever P {\displaystyle P} is applied twice to any vector, it gives the same result as if it were applied onc... | Linear projection | 0.782886 |
85,513 | More generally, given a map between normed vector spaces T: V → W , {\displaystyle T\colon V\to W,} one can analogously ask for this map to be an isometry on the orthogonal complement of the kernel: that ( ker T ) ⊥ → W {\displaystyle (\ker T)^{\perp }\to W} be an isometry (compare Partial isometry); in particular it... | Linear projection | 0.782886 |
85,514 | In the theory of dynamical systems, a state variable in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable. In continuous time control theory, a system is unstable if any of the roots of its characteristic equation has ... | Instability | 0.782885 |
85,515 | Modifying the substrate structure and/or stereochemistry severely lowers the kinetic activity of the enzyme. This specificity occurs due to the high number of hydrogen bonds between substrate and enzyme; direct or water-facilitated hydrogen bonds exist, saturating both the four acceptor positions on the alpha carboxyla... | Arginase 1 | 0.782885 |
85,516 | This can lead to cost to benefits issues. The emergence of the DMN standard has mitigated this to some degree.Most BRMS vendors have evolved from rule engine vendors to provide business-usable software development lifecycle solutions, based on declarative definitions of business rules executed in their own rule engine.... | Business Rule Management System | 0.782884 |
85,517 | In that field, Cluster Theory (Porter, 1990 ) evolved in more environmentally sensitive theories, like Industrial Ecology (Frosh and Gallopoulos, 1989 ) and Industrial Symbiosis (Chertow, 2000). In 1994, Gunter Pauli and Heitor Gurgulino de Souza founded the research institute Zero Emission Research and Initiatives (ZE... | Systemic design | 0.782883 |
85,518 | For the same reason, a minimally imperfect graph whose complement has a 2-join cannot be Berge.A skew partition is a partition of a graph's vertices into two subsets, one of which induces a disconnected subgraph and the other of which has a disconnected complement; Chvátal (1985) had conjectured that no minimal counter... | Strong perfect graph conjecture | 0.782881 |
85,519 | The perfection of complements of bipartite graphs, and of complements of line graphs of bipartite graphs, are both equivalent to Kőnig's theorem relating the sizes of maximum matchings, maximum independent sets, and minimum vertex covers in bipartite graphs. The perfection of line graphs of bipartite graphs can be stat... | Strong perfect graph conjecture | 0.782881 |
85,520 | The proof of the strong perfect graph theorem by Chudnovsky et al. follows an outline conjectured in 2001 by Conforti, Cornuéjols, Robertson, Seymour, and Thomas, according to which every Berge graph either forms one of five types of basic building block (special classes of perfect graphs) or it has one of four differe... | Strong perfect graph conjecture | 0.782881 |
85,521 | The graphs having neither odd holes nor odd antiholes became known as the Berge graphs. Berge conjectured that every Berge graph is perfect, or equivalently that the perfect graphs and the Berge graphs define the same class of graphs. This became known as the strong perfect graph conjecture, until its proof in 2002, wh... | Strong perfect graph conjecture | 0.782881 |
85,522 | Equivalently, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} of dimension 4 n {\displaystyle 4n} whose holonomy group is contained in the compact symplectic group Sp(n).Indeed, if ( M , g , I , J , K ) {\displaystyle (M,g,I,J,K)} is a hyperkähler manifold, then the tangent space TxM is ... | Hyperkähler metric | 0.782881 |
85,523 | Compact hyperkähler manifolds have been extensively studied using techniques from algebraic geometry, sometimes under the name holomorphically symplectic manifolds. The holonomy group of any Calabi–Yau metric on a simply connected compact holomorphically symplectic manifold of complex dimension 2 n {\displaystyle 2n} w... | Hyperkähler metric | 0.782881 |
85,524 | Based on analysis of the molecular properties of the RecA system, Cox concluded that the data "provide compelling evidence that the primary mission of RecA protein is DNA repair." In a further essay on the function of the RecA protein, Cox summarized data demonstrating that "RecA protein evolved as the central componen... | RecA | 0.782879 |
85,525 | In Escherichia coli, homologous recombination events mediated by RecA can occur during the period after DNA replication when sister loci remain close. RecA can also mediate homology pairing, homologous recombination and DNA break repair between distant sister loci that had segregated to opposite halves of the E. coli c... | RecA | 0.782879 |
85,526 | Reductive carbonylation gives .The Rh-μ-Cl bonds are labile and cleave en route to a variety of adducts of the general formula Cp*RhCl2L. Treatment with silver ions in polar coordinating solvents causes precipitation of silver(I) chloride, leaving a solution containing dications of the form 2+ (L = H2O, MeCN). The chem... | Pentamethylcyclopentadienyl rhodium dichloride dimer | 0.782878 |
85,527 | Pentamethylcyclopentadienyl rhodium dichloride dimer is an organometallic compound with the formula 2, commonly abbreviated 2 This dark red air-stable diamagnetic solid is a reagent in organometallic chemistry. | Pentamethylcyclopentadienyl rhodium dichloride dimer | 0.782878 |
85,528 | "Reactions of Dienes Trienes and Tetraenes with Transition Metal Compounds". Organotransition Metal Chemistry: A Mechanistic Approach. Academic Press. | Pentamethylcyclopentadienyl rhodium dichloride dimer | 0.782878 |
85,529 | "Bis{(μ-chloro)} — {Rh(μ-Cl)Cl}2". In Herrmann, Wolfgang A.; Salzer, Albrecht (eds.). Synthetic Methods of Organometallic and Inorganic Chemistry – Volume 1: Literature, Laboratory Techniques, and Common Starting Materials. | Pentamethylcyclopentadienyl rhodium dichloride dimer | 0.782878 |
85,530 | Childhood cancer and cancer in adolescents is rare (about 150 cases per million yearly in the US). Leukemia (usually acute lymphoblastic leukemia) is the most common cancer in children aged 1–14 in the U.S., followed by the central nervous system cancers, neuroblastoma, Wilms' tumor, and non-Hodgkin's lymphoma. Statist... | Cancer epidemiology | 0.782878 |
85,531 | In the first year of life the incidence is about 230 cases per million in the U.S., with the most common being neuroblastoma. Data from 2004 to 2008 in the United States indicates that the overall age-adjusted incidence of cancer was approximately 460 per 100,000 men and women per year.Cancer is responsible for about 2... | Cancer epidemiology | 0.782878 |
85,532 | In samarium(II) iodide, the metal centers are seven-coordinate with a face-capped octahedral geometry. In its ether adducts, samarium remains heptacoordinate with five ether and two terminal iodide ligands. | SmI2 | 0.782877 |
85,533 | In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space. The homotopy extension property of cofibrations is dual to the homotopy lifting property that is used to define fibrations. | Homotopy extension property | 0.782877 |
85,534 | The product of the families B ∙ {\displaystyle {\mathcal {B}}_{\bullet }} is defined identically to how the basic open subsets of the product topology are defined (had all of these B i {\displaystyle {\mathcal {B}}_{i}} been topologies). That is, both the notations denote the family of all cylinder subsets ∏ i ∈ I S i ... | Filter base | 0.782876 |
85,535 | The preorder ≤ {\displaystyle \,\leq \,} that is defined below is of fundamental importance for the use of prefilters (and filters) in topology. For instance, this preorder is used to define the prefilter equivalent of "subsequence", where " F ≥ C {\displaystyle {\mathcal {F}}\geq {\mathcal {C}}} " can be interpreted a... | Filter base | 0.782876 |
85,536 | In the troposphere, ozone formation and destruction are no longer controlled by the ozone-oxygen cycle. Rather, tropospheric ozone chemistry is dominated today by industrial pollutants other gases of volcanic source. | Chapman cycle | 0.782876 |
85,537 | Klystrons can produce far higher microwave power outputs than solid state microwave devices such as Gunn diodes. In modern systems, they are used from UHF (hundreds of megahertz) up to hundreds of gigahertz (as in the Extended Interaction Klystrons in the CloudSat satellite). Klystrons can be found at work in radar, sa... | Klystron | 0.782875 |
85,538 | The Markov condition, sometimes called the Markov assumption, is an assumption made in Bayesian probability theory, that every node in a Bayesian network is conditionally independent of its nondescendants, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it.... | Causal Markov condition | 0.782874 |
85,539 | Pocket calculators became mass-market devices in 1970, starting in Japan. Programmable calculators followed in the late 1970s, being somewhat more general-purpose computers. The HP-01 algebraic calculator watch by Hewlett-Packard was released in 1977.A camera-to-tactile vest for the blind, launched by C.C. Collins in 1... | Wearable electronics | 0.782874 |
85,540 | The Asia-Pacific Journal of Chemical Engineering is a peer-reviewed scientific journal published by John Wiley & Sons on behalf of Curtin University of Technology. Until 2006 it was known as Developments in Chemical Engineering and Mineral Processing and published (in print only) by Curtin University of Technology. The... | Asia-Pacific Journal of Chemical Engineering | 0.782874 |
85,541 | "Cosmology tutorial and FAQ". Division of Astronomy & Astrophysics, UCLA. George Musser (February 2004). | Cosmological models | 0.782873 |
85,542 | Tyler, Pat, and Phil Newman "Beyond Einstein". Laboratory for High Energy Astrophysics (LHEA) NASA Goddard Space Flight Center. Wright, Ned. | Cosmological models | 0.782873 |
85,543 | Gale, George, "Cosmology: Methodological Debates in the 1930s and 1940s", The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.) Madore, Barry F., "Level 5: A Knowledgebase for Extragalactic Astronomy and Cosmology". Caltech and Carnegie. Pasadena, California. | Cosmological models | 0.782873 |
85,544 | During the earliest moments of the universe, the average energy density was very high, making knowledge of particle physics critical to understanding this environment. Hence, scattering processes and decay of unstable elementary particles are important for cosmological models of this period. As a rule of thumb, a scatt... | Cosmological models | 0.782873 |
85,545 | Cambridge Cosmology – from Cambridge University (public home page) Cosmology 101 – from the NASA WMAP group Center for Cosmological Physics. University of Chicago, Chicago. Origins, Nova Online – Provided by PBS. | Cosmological models | 0.782873 |
85,546 | His equations describe the Friedmann–Lemaître–Robertson–Walker universe, which may expand or contract, and whose geometry may be open, flat, or closed. In the 1910s, Vesto Slipher (and later Carl Wilhelm Wirtz) interpreted the red shift of spiral nebulae as a Doppler shift that indicated they were receding from Earth. ... | Cosmological models | 0.782873 |
85,547 | The assessment of audible magnetic noise in electrical machines can be done using three methods: using dedicated electromagnetic and vibro-acoustic simulation software (e.g. MANATEE ) using electromagnetic (e.g. Flux, Jmag, Maxwell, Opera), structural (e.g. Ansys Mechanical, Nastran, Optistruct) and acoustic (e.g. Actr... | Coil whine | 0.782872 |
85,548 | Given these definitions, continuous functions can be shown to preserve compactness:Theorem. If V , W {\displaystyle V,\ W} are topological spaces, f: V → W {\displaystyle f:V\to W} is a continuous function, and K ⊂ V {\displaystyle K\subset V} is compact, then f ( K ) ⊂ W {\displaystyle f(K)\subset W} is also compact. ... | Extreme value theorem | 0.782872 |
85,549 | The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum va... | Extreme value theorem | 0.782872 |
85,550 | By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics.Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources: ... | Malthusian parameter | 0.782872 |
85,551 | A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of... | Malthusian parameter | 0.782872 |
85,552 | Thus, we have the following generalization of the extreme value theorem:Theorem. If K {\displaystyle K} is a compact set and f: K → R {\displaystyle f:K\to \mathbb {R} } is a continuous function, then f {\displaystyle f} is bounded and there exist p , q ∈ K {\displaystyle p,q\in K} such that f ( p ) = sup x ∈ K f ( x )... | Extreme value theorem | 0.782872 |
85,553 | When moving from the real line R {\displaystyle \mathbb {R} } to metric spaces and general topological spaces, the appropriate generalization of a closed bounded interval is a compact set. A set K {\displaystyle K} is said to be compact if it has the following property: from every collection of open sets U α {\displays... | Extreme value theorem | 0.782872 |
85,554 | In calculus, the extreme value theorem states that if a real-valued function f {\displaystyle f} is continuous on the closed interval {\displaystyle } , then f {\displaystyle f} must attain a maximum and a minimum, each at least once. That is, there exist numbers c {\displaystyle c} and d {\displaystyle d} in {\displ... | Extreme value theorem | 0.782872 |
85,555 | ∎ Applying this result to −f proves: Theorem: If a function f: → (–∞, ∞] is lower semi-continuous, meaning that for all x in , then f is bounded below and attains its infimum. A real-valued function is upper as well as lower semi-continuous, if and only if it is continuous in the usual sense. Hence these two theorems ... | Extreme value theorem | 0.782872 |
85,556 | In the proof of the boundedness theorem, the upper semi-continuity of f at x only implies that the limit superior of the subsequence {f(xnk)} is bounded above by f(x) < ∞, but that is enough to obtain the contradiction. In the proof of the extreme value theorem, upper semi-continuity of f at d implies that the limit su... | Extreme value theorem | 0.782872 |
85,557 | If the continuity of the function f is weakened to semi-continuity, then the corresponding half of the boundedness theorem and the extreme value theorem hold and the values –∞ or +∞, respectively, from the extended real number line can be allowed as possible values. More precisely: Theorem: If a function f: → , then f... | Extreme value theorem | 0.782872 |
85,558 | This defines a sequence {dn}. Since M is an upper bound for f, we have M – 1/n < f(dn) ≤ M for all n. Therefore, the sequence {f(dn)} converges to M. The Bolzano–Weierstrass theorem tells us that there exists a subsequence { d n k {\displaystyle d_{n_{k}}} }, which converges to some d and, as is closed, d is in . Sinc... | Extreme value theorem | 0.782872 |
85,559 | By the boundedness theorem, f is bounded from above, hence, by the Dedekind-completeness of the real numbers, the least upper bound (supremum) M of f exists. It is necessary to find a point d in such that M = f(d). Let n be a natural number. As M is the least upper bound, M – 1/n is not an upper bound for f. Therefore... | Extreme value theorem | 0.782872 |
85,560 | Because {\displaystyle } is bounded, the Bolzano–Weierstrass theorem implies that there exists a convergent subsequence ( x n k ) k ∈ N {\displaystyle (x_{n_{k}})_{k\in \mathbb {N} }} of ( x n ) {\displaystyle ({x_{n}})} . Denote its limit by x {\displaystyle x} . As {\displaystyle } is closed, it contains x {\displa... | Extreme value theorem | 0.782872 |
85,561 | In the setting of non-standard calculus, let N be an infinite hyperinteger. The interval has a natural hyperreal extension. Consider its partition into N subintervals of equal infinitesimal length 1/N, with partition points xi = i /N as i "runs" from 0 to N. The function ƒ is also naturally extended to a function ƒ* d... | Extreme value theorem | 0.782872 |
85,562 | Supramolecular electronics is the experimental field of supramolecular chemistry that bridges the gap between molecular electronics and bulk plastics in the construction of electronic circuitry at the nanoscale 1. In supramolecular electronics, assemblies of pi-conjugated systems on the 5 to 100 nanometer length scale ... | Supramolecular electronics | 0.782871 |
85,563 | This definition, as given in the introduction, is natural in classical terms, and is due to Helmut Hasse and Ernst Witt (1936). It provides a solution to the question of the p-rank of the Jacobian variety J of C; the p-rank is bounded by the rank of H, specifically it is the rank of the Frobenius mapping composed with ... | Hasse invariant of an elliptic curve | 0.782871 |
85,564 | The case of elliptic curves was worked out by Hasse in 1934. Since the genus is 1, the only possibilities for the matrix H are: H is zero, Hasse invariant 0, p-rank 0, the supersingular case; or H non-zero, Hasse invariant 1, p-rank 1, the ordinary case. Here there is a congruence formula saying that H is congruent mod... | Hasse invariant of an elliptic curve | 0.782871 |
85,565 | It can be manufactured by oxidation of methanol or by the reaction of formaldehyde with methanol. In aqueous acid, it is hydrolyzed back to formaldehyde and methanol. Due to the anomeric effect, dimethoxymethane has a preference toward the gauche conformation with respect to each of the C–O bonds, instead of the anti c... | Dimethoxymethane | 0.78287 |
85,566 | Meat extracts have largely been supplanted by bouillon cubes and yeast extract. Some brands of meat extract, such as Oxo and Bovril, now contain yeast extract as well as meat extract. For example, the current formulation of Bovril contains 41% beef stock, 24% yeast extract, 1% dehydrated beef and salt (388 mg sodium pe... | Meat extract | 0.782869 |
85,567 | Meat extract is highly concentrated meat stock, usually made from beef or chicken. It is used to add meat flavour in cooking, and to make broth for soups and other liquid-based foods. Meat extract was invented by Baron Justus von Liebig, a German 19th-century organic chemist. Liebig specialised in chemistry and the cla... | Meat extract | 0.782869 |
85,568 | In mathematics, in particular linear algebra, the Bunch–Nielsen–Sorensen formula, named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen, expresses the eigenvectors of the sum of a symmetric matrix A {\displaystyle A} and the outer product, v v T {\displaystyle vv^{T}} , of vector v {\displaystyle v} ... | Bunch–Nielsen–Sorensen formula | 0.782868 |
85,569 | In 2007 the Human Genetics Unit formed a partnership with two neighbouring research centres on the Western General Hospital campus, the Centre for Genomic and Experimental Medicine (University of Edinburgh) and the Edinburgh Cancer Research Centre (Cancer Research UK), to create the Institute of Genetics and Molecular ... | MRC Human Genetics Unit | 0.782867 |
85,570 | The Medical Research Council (UK) Human Genetics Unit is situated at the Western General Hospital in Edinburgh. It is one of the largest MRC research establishments, housing over two hundred scientists, support staff, research fellows, PhD students, and visiting workers. | MRC Human Genetics Unit | 0.782867 |
85,571 | The Human Genetics Unit is divided into three sections: Biomedical Genomics -Research harnesses the power of large genome-size and population data to reveal the complex nature of disease processes. Section Head: Professor Chris Ponting Genome Regulation -Research focuses on mechanisms that maintain the stability of the... | MRC Human Genetics Unit | 0.782867 |
85,572 | While it may be difficult to decide on a standard 'textbook' description of the field of astroparticle physics, the field can be characterized by the topics of research that are actively being pursued. The journal Astroparticle Physics accepts papers that are focused on new developments in the following areas: High-ene... | Particle astrophysics | 0.782866 |
85,573 | Located within the Gran Sasso mountain, near L'Aquila (Italy). Its experimental halls are covered by 1400 m of rock, which protects experiments from cosmic rays. SNOLAB Aspera European Astroparticle network Started in July 2006 and is responsible for coordinating and funding national research efforts in Astroparticle P... | Particle astrophysics | 0.782866 |
85,574 | Facilities, experiments and laboratories involved in astroparticle physics include: IceCube (Antarctica). The longest particle detector in the world, was completed in December 2010. | Particle astrophysics | 0.782866 |
85,575 | Since he did not observe a dip in ionization levels, Hess reasoned that the source had to be further away in space. For this discovery, Hess was one of the people awarded the Nobel Prize in Physics in 1936. In 1925, Robert Millikan confirmed Hess's findings and subsequently coined the term 'cosmic rays'.Many physicists... | Particle astrophysics | 0.782866 |
85,576 | Astroparticle physics, also called particle astrophysics, is a branch of particle physics that studies elementary particles of astronomical origin and their relation to astrophysics and cosmology. It is a relatively new field of research emerging at the intersection of particle physics, astronomy, astrophysics, detecto... | Particle astrophysics | 0.782866 |
85,577 | One main task for the future of the field is simply to thoroughly define itself beyond working definitions and clearly differentiate itself from astrophysics and other related topics.Current unsolved problems for the field of astroparticle physics include characterization of dark matter and dark energy. Observations of... | Particle astrophysics | 0.782866 |
85,578 | The field of astroparticle physics is evolved out of optical astronomy. With the growth of detector technology came the more mature astrophysics, which involved multiple physics subtopics, such as mechanics, electrodynamics, thermodynamics, plasma physics, nuclear physics, relativity, and particle physics. Particle phy... | Particle astrophysics | 0.782866 |
85,579 | Lead–acid cells consist of two plates of lead, which serve as electrodes, suspended in an electrolyte consisting of diluted sulfuric acid. VRLA cells have the same chemistry, except the electrolyte is immobilized. In AGM this is accomplished with a fiberglass mat; in gel batteries or "gel cells", the electrolyte is in ... | Sealed battery | 0.782866 |
85,580 | The nonlinear Schrödinger equation is a nonlinear partial differential equation, applicable to classical and quantum mechanics. | Nonlinear Schrödinger equations | 0.782866 |
85,581 | Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state. The 1D NLSE is an example of an integrable model. In quantum mechanics, the 1D NLSE is a special case of the classical nonlinear Schrödinger field, which in turn is a classical limit of a quantum Schrödinger field. | Nonlinear Schrödinger equations | 0.782866 |
85,582 | In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confi... | Nonlinear Schrödinger equations | 0.782866 |
85,583 | In physics, there are only three noble metals: copper, silver and gold. In dentistry, silver is not always counted as a noble metal since it is subject to corrosion when present in the mouth. In chemistry, the term noble metal is sometimes applied more broadly to any metallic or semimetallic element that does not react... | Noble metals | 0.782864 |
85,584 | Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole as a unit like the metre or the second have arisen: the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity that can be expressed simply as a number, not requiring a di... | Mole (unit) | 0.782863 |
85,585 | The Jacobus Kapteyn Telescope or JKT is a 1-metre optical telescope named for the Dutch astronomer Jacobus Kapteyn (1851-1922) of the Isaac Newton Group of Telescopes at the Roque de los Muchachos Observatory on La Palma in the Canary Islands, Spain. Funded jointly by the Netherlands and the United Kingdom with plannin... | Jacobus Kapteyn Telescope | 0.78286 |
85,586 | The Berkovich spectrum of a Banach k-algebra A is the set of multiplicative semi-norms on A that are bounded with respect to the given norm on k, and it has a topology induced by evaluating these semi-norms on elements of A. Since the topology is pulled back from the real line, Berkovich spectra have many nice properti... | Rigid analytic geometry | 0.78286 |
85,587 | Huber worked out a theory of adic spaces to resolve this, by taking a limit over all blow-ups. These spaces are quasi-compact, quasi-separated, and functorial in the rigid space, but lack a lot of nice topological properties. Vladimir Berkovich reformulated much of the theory of rigid analytic spaces in the late 1980s,... | Rigid analytic geometry | 0.78286 |
85,588 | Around 1970, Michel Raynaud provided an interpretation of certain rigid analytic spaces as formal models, i.e., as generic fibers of formal schemes over the valuation ring R of k. In particular, he showed that the category of quasi-compact quasi-separated rigid spaces over k is equivalent to the localization of the cat... | Rigid analytic geometry | 0.78286 |
85,589 | This is analogous to the notion of manifolds being coverable by open subsets isomorphic to euclidean space, or schemes being coverable by affines. Schemes over k can be analytified functorially, much like varieties over the complex numbers can be viewed as complex analytic spaces, and there is an analogous formal GAGA ... | Rigid analytic geometry | 0.78286 |
85,590 | The topology on affinoids is subtle, using notions of affinoid subdomains (which satisfy a universality property with respect to maps of affinoid algebras) and admissible open sets (which satisfy a finiteness condition for covers by affinoid subdomains). In fact, the admissible opens in an affinoid do not in general en... | Rigid analytic geometry | 0.78286 |
85,591 | The basic rigid analytic object is the n-dimensional unit polydisc, whose ring of functions is the Tate algebra T n {\displaystyle T_{n}} , made of power series in n variables whose coefficients approach zero in some complete nonarchimedean field k. The Tate algebra is the completion of the polynomial ring in n variabl... | Rigid analytic geometry | 0.78286 |
85,592 | In the United States, the U.S. Geological Survey (USGS) is the principal federal agency tasked with maintaining records of natural resources. Within the USGS, the Water Resources Division carries the responsibility for monitoring water resources. To establish a stream gauge, USGS personnel first choose a site on a stre... | Stream gauge | 0.78286 |
85,593 | David Zuckerman is an American theoretical computer scientist whose work concerns randomness in computation. He is a professor of computer science at the University of Texas at Austin. | David Zuckerman (computer scientist) | 0.782858 |
85,594 | Most of Zuckerman's work concerns randomness in computation, and especially pseudorandomness. He has written over 80 papers on topics including randomness extractors, pseudorandom generators, coding theory, and cryptography. Zuckerman is best known for his work on randomness extractors. | David Zuckerman (computer scientist) | 0.782858 |
85,595 | Zuckerman received an A.B. in mathematics from Harvard University in 1987, where he was a Putnam Fellow in 1986. He went on to earn a Ph.D. in computer science from the University of California at Berkeley in 1991 advised by Umesh Vazirani. He then worked as a postdoctoral fellow at the Massachusetts Institute of Techn... | David Zuckerman (computer scientist) | 0.782858 |
85,596 | In population ecology and demography, the net reproduction rate, R0, is the average number of offspring (often specifically daughters) that would be born to a female if she passed through her lifetime conforming to the age-specific fertility and mortality rates of a given year. This rate is similar to the gross reprodu... | Net reproduction rate | 0.782857 |
85,597 | Suction vortices (or suction spots) are really substructures of many, perhaps all, tornadoes but are not always easily visible. These usually occur at the base of the tornado vortex where the tornado makes contact with the surface. Subvortices tend to form after vortex breakdown reaches the surface and are resultant fr... | Multiple-vortex tornado | 0.782857 |
85,598 | In mathematics, the Federer–Morse theorem, introduced by Federer and Morse (1943), states that if f is a surjective continuous map from a compact metric space X to a compact metric space Y, then there is a Borel subset Z of X such that f restricted to Z is a bijection from Z to Y. Moreover, the inverse of that restrict... | Federer–Morse theorem | 0.782857 |
85,599 | For example, the Inuit, Chukchi and Evenks all have a worldview based on their religious beliefs and have related traditions about astronomy. While differing traditions exist among groups, they overlap in the way the stars, weather, and folk tales assist in hunting, navigation and teaching their young about the world.T... | Inuit astronomy | 0.782854 |
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