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80,500 | Europe is regarded as a malaria-free region. Historically, the parasite and its disease had been most well known in Europe. But medical programmes since the early 20th century, such as insecticide spraying, drug therapy and environmental engineering, resulted in complete eradication in the 1970s. It is estimated that a... | Subtelomeric regions of the Plasmodium falciparum genome | 0.784941 |
80,501 | Oleg R. Musin proved several generalizations of the KKM lemma and KKMS theorem, with boundary conditions on the coverings. The boundary conditions are related to homotopy. | Knaster–Kuratowski–Mazurkiewicz lemma | 0.78494 |
80,502 | The application of De Morgan's theorem to conjunction is very similar to its application to a disjunction both in form and rationale. Consider the following claim: "it is false that A and B are both true", which is written as: ¬ ( A ∧ B ) . {\displaystyle \neg (A\land B).} | De Morgan duality | 0.78494 |
80,503 | In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purel... | De Morgan duality | 0.78494 |
80,504 | In some European countries a common form of set square combines a 90-45-45 triangle, a ruler and a protractor into a single tool made of stiff or slightly flexible transparent plastic. Being a mandatory tool used by pupils in middle school and higher in German-speaking and neighbouring countries, this specific design i... | Navigation protractor triangle | 0.784939 |
80,505 | The newforms are defined as a vector subspace of the modular forms of level N, complementary to the space spanned by the oldforms, i.e. the orthogonal space with respect to the Petersson inner product. The Hecke operators, which act on the space of all cusp forms, preserve the subspace of newforms and are self-adjoint ... | Atkin–Lehner involution | 0.784936 |
80,506 | One feature of M-theory that has drawn great interest is that it naturally predicts the existence of the graviton, a spin-2 particle hypothesized to mediate the gravitational force. Furthermore, M-theory naturally predicts a phenomenon that resembles black hole evaporation. Competing unification theories such as asympt... | Introduction to M-theory | 0.784934 |
80,507 | In the 1980s, a new mathematical model of theoretical physics, called string theory, emerged. It showed how all the different subatomic particles known to science could be constructed by hypothetical one-dimensional "strings", infinitesimal building-blocks that have only the dimension of length, but not height or width... | Introduction to M-theory | 0.784934 |
80,508 | M-theory brought all of the string theories together. It did this by asserting that strings are really one-dimensional slices of a two-dimensional membrane vibrating in 11-dimensional spacetime. Vibrations of higher-dimensional objects (as in three-dimensional vibrating blob or sphere or even more possible dimensions) ... | Introduction to M-theory | 0.784934 |
80,509 | In non-technical terms, M-theory presents an idea about the basic substance of the universe. As of 2023, science has produced no experimental evidence to support the conclusion that M-theory is a description of the real world. Although a complete mathematical formulation of M-theory is not known, the general approach i... | Introduction to M-theory | 0.784934 |
80,510 | In semiconductor physics, the band gap of a semiconductor can be of two basic types, a direct band gap or an indirect band gap. The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k... | Direct bandgap | 0.784933 |
80,511 | It can be proved by dividing the triangle into two right ones and using the above definition of sine. The law of sines is useful for computing the lengths of the unknown sides in a triangle if two angles and one side are known. This is a common situation occurring in triangulation, a technique to determine unknown dist... | Sin (trigonometry) | 0.784932 |
80,512 | In trigonometry, a unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system. Let a line through the origin intersect the unit circle, making an angle of θ with the positive half of the x-axis. The x- and y-coordinates of this point of intersection are equal to cos(θ) and ... | Sin (trigonometry) | 0.784932 |
80,513 | Researchers found that if the tail has been exposed to a cooler temperatures before the test, then the critical temperature decreases.Through use of the tail flick test, researchers have found that genetics play a role in pain sensation and the effectiveness of analgesics. A mouse of one genetic line may be more or les... | Tail flick test | 0.784932 |
80,514 | Ennis provides a comprehensive account of the derivation of Thurstonian models for a wide variety of behavioral tasks including preferential choice, ratings, triads, tetrads, dual pair, same-different and degree of difference, ranks, first-last choice, and applicability scoring. In Chapter 7 of this book, a closed form... | Thurstonian model | 0.784931 |
80,515 | This makes synchrotron radiation sources the most brilliant known sources of X-rays. The planar acceleration geometry makes the radiation linearly polarized when observed in the orbital plane, and circularly polarized when observed at a small angle to that plane.The advantages of using synchrotron radiation for spectro... | Synchrotron light sources | 0.78493 |
80,516 | Synchrotron radiation may occur in accelerators either as a nuisance, causing undesired energy loss in particle physics contexts, or as a deliberately produced radiation source for numerous laboratory applications. Electrons are accelerated to high speeds in several stages to achieve a final energy that is typically in... | Synchrotron light sources | 0.78493 |
80,517 | Synchrotron light is an ideal tool for many types of research in materials science, physics, and chemistry and is used by researchers from academic, industrial, and government laboratories. Several methods take advantage of the high intensity, tunable wavelength, collimation, and polarization of synchrotron radiation a... | Synchrotron light sources | 0.78493 |
80,518 | The timescale of thermal back-isomerization is important for applications, and may be molecularly engineered. Photochromic compounds considered to be "thermally stable" include some diarylethenes, which do not back isomerize even after heating at 80 C for 3 months. Since photochromic chromophores are dyes, and operate ... | Photochromism | 0.784929 |
80,519 | Photochromism does not have a rigorous definition, but is usually used to describe compounds that undergo a reversible photochemical reaction where an absorption band in the visible part of the electromagnetic spectrum changes dramatically in strength or wavelength. In many cases, an absorbance band is present in only ... | Photochromism | 0.784929 |
80,520 | Researchers at the Center for Exploitation of Solar Energy at the University of Copenhagen Department of Chemistry are studying, the photochromic dihydroazulene–vinylheptafulvene system, for possible application to harvest solar energy and store it for significant amounts of time. Although storage lifetimes are attract... | Photochromism | 0.784929 |
80,521 | GIZMO is a flexible, massively parallel, multi-physics simulation code, written in ANSI C by Philip F. Hopkins. The code offers diverse methods to solve fluid equations. It also introduces novel methods, which optimize the resolution of simulations and minimize common errors found in previous methods that limited the a... | List of cosmological computation software | 0.784929 |
80,522 | StePS, which stands for "STEreographically Projected cosmological Simulations" is a freely available code that implements a novel N-body simulation method that models an infinite universe within a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Unlike traditional m... | List of cosmological computation software | 0.784929 |
80,523 | The package is used by cosmological boltzmann codes (CMBFast, CAMB etc.) TOAST — Time Ordered Astrophysics Scalable Tools, developed and designed by Theodore Kisner, Reijo Keskitalo, Jullian Borrill et al. It "generalizing the problem of CMB map-making to the reduction of any pointed time-domain data, and ensuring that... | List of cosmological computation software | 0.784929 |
80,524 | Once t and ν {\displaystyle \nu } have been computed, these statistics can be used with the t-distribution to test one of two possible null hypotheses: that the two population means are equal, in which a two-tailed test is applied; or that one of the population means is greater than or equal to the other, in which a on... | Welch's t-test | 0.784929 |
80,525 | A map from the Jacobi diagrams to the positive integers is called a weight system. The map extended to the space A(X) is also called the weight system. They have the following properties: Let g be a semisimple Lie algebra and ρ its representation. We obtain a weight system by "substituting" the invariant tensor of g in... | Kontsevich invariant | 0.784929 |
80,526 | Viewing A(S1) as the algebra with multiplication as connected sums, A(S1) is isomorphic to A(I). A Jacobi diagram can be viewed as abstraction of representations of the tensor algebra generated by Lie algebras, which allows us to define some operations analogous to coproducts, counits and antipodes of Hopf algebras. Si... | Kontsevich invariant | 0.784929 |
80,527 | The degree of a Jacobi diagram is defined to be the half of the sum of the number of its vertices with value 1 and one with value 3. It is the number of chords in the Chord diagram transformed from the Jacobi diagram. Just like for the tangles, the Jacobi diagrams form a monoidal category with the composition as the co... | Kontsevich invariant | 0.784929 |
80,528 | Jacobi diagrams were introduced as analogues of Feynman diagrams when Kontsevich defined knot invariants by iterated integrals in the first half of 1990s. He represented singular points of singular knots by chords, i.e. he treated only with chord diagrams. D. Bar-Natan later formulated them as the 1-3 valued graphs and... | Kontsevich invariant | 0.784928 |
80,529 | Alcoholism is associated with dampened activation in brain networks responsible for emotional processing (e.g. the amygdala and hippocampus). Evidence that the mental health disorders are often induced by alcohol misuse via distortion of brain neurochemistry is indicated by the improvement or disappearance of symptoms ... | Long-term effects of alcohol | 0.784927 |
80,530 | One study claims that "excessive alcohol consumption in Russia, particularly by men, has in recent years caused more than half of all the deaths at ages 15–54 years." However, there are some difficulties with this study. For instance, the same study also found a protective effect of heavy drinking on breast cancer mort... | Long-term effects of alcohol | 0.784927 |
80,531 | The original dish was built in 1967 under the umbrella of the National Radio Astronomy Observatory (NRAO). At that time, it was 36 feet (11 meters) in diameter and was known as the 36-foot Telescope. In 1984, it was renovated with a new backup structure and a slightly larger dish. | ARO 12m Radio Telescope | 0.784925 |
80,532 | In the almost 40 years since it was first built, the 12m Radio Telescope has been at the forefront of millimeter molecular astronomy: studying molecules in space through the use of molecular spectroscopy at millimeter wavelengths. Many of the molecules that have been discovered in the interstellar medium were discovere... | ARO 12m Radio Telescope | 0.784924 |
80,533 | When the measurement error is very low (ideal case), deconvolution collapses into a filter reversing. This kind of deconvolution can be performed in the Laplace domain. By computing the Fourier transform of the recorded signal h and the system response function g, you get H and G, with G as the transfer function. Using... | Deconvolution | 0.784924 |
80,534 | By the convolution theorem, this equation may be Fourier transformed to S ( ω ) = E ( ω ) W ( ω ) {\displaystyle S(\omega )=E(\omega )W(\omega )\,} in the frequency domain, where ω {\displaystyle \omega } is the frequency variable. By assuming that the reflectivity is white, we can assume that the power spectrum of the... | Deconvolution | 0.784924 |
80,535 | When performing image synthesis in radio interferometry, a specific kind of radio astronomy, one step consists of deconvolving the produced image with the "dirty beam", which is a different name for the point spread function. A commonly used method is the CLEAN algorithm. | Deconvolution | 0.784924 |
80,536 | Blind deconvolution is a well-established image restoration technique in astronomy, where the point nature of the objects photographed exposes the PSF thus making it more feasible. It is also used in fluorescence microscopy for image restoration, and in fluorescence spectral imaging for spectral separation of multiple ... | Deconvolution | 0.784924 |
80,537 | The theorem can be proved as an application of the law of cosines.Let θ be the angle between m and d and θ' the angle between n and d. Then θ' is the supplement of θ, and so cos θ' = −cos θ. Applying the law of cosines in the two small triangles using angles θ and θ' produces Multiplying the first equation by n and the... | Stewart's theorem | 0.784924 |
80,538 | In geometry, Stewart's theorem yields a relation between the lengths of the sides and the length of a cevian in a triangle. Its name is in honour of the Scottish mathematician Matthew Stewart, who published the theorem in 1746. | Stewart's theorem | 0.784924 |
80,539 | Let a, b, c be the lengths of the sides of a triangle. Let d be the length of a cevian to the side of length a. If the cevian divides the side of length a into two segments of length m and n, with m adjacent to c and n adjacent to b, then Stewart's theorem states that A common mnemonic used by students to memorize this... | Stewart's theorem | 0.784924 |
80,540 | In microbiology, pleomorphism (from Ancient Greek πλέω-, pléō, "more", and -μορφή, morphḗ, form), also pleiomorphism, is the ability of some microorganisms to alter their morphology, biological functions or reproductive modes in response to environmental conditions. Pleomorphism has been observed in some members of the... | Pleomorphism (microbiology) | 0.784923 |
80,541 | In mathematics, the Drinfeld upper half plane is a rigid analytic space analogous to the usual upper half plane for function fields, introduced by Drinfeld (1976). It is defined to be P1(C)\P1(F∞), where F is a function field of a curve over a finite field, F∞ its completion at ∞, and C the completion of the algebraic ... | Drinfeld upper half plane | 0.784922 |
80,542 | Initially, let us assume that a thermodynamically large system is in thermal contact with the environment, with a temperature T, and both the volume of the system and the number of constituent particles are fixed. A collection of this kind of system comprises an ensemble called a canonical ensemble. The appropriate mat... | Grand partition function | 0.784922 |
80,543 | In organic chemistry, alkylimino-de-oxo-bisubstitution is the organic reaction of carbonyl compounds with amines to imines. The reaction name is based on the IUPAC Nomenclature for Transformations. The reaction is acid catalyzed and the reaction type is nucleophilic addition of the amine to the carbonyl compound follow... | Amine-carbonyl condensation | 0.784922 |
80,544 | The script tool mixes up algorithmics and geometry. Such scripting tools exist also in DrGeo, Kig and Cinderella (software). To run a script, one clicks over the icon representing a traffic light. A script can be attached to one or several points, so that any movement of one of these points runs the script. This allows... | CaRMetal | 0.784921 |
80,545 | A point can be made magnetic with a distance and a list of objects it is attracted to whenever the point is sufficiently near one or several of these objects (sufficiently near means that the distance between them is less than the minimal distance which is a property of the point, and is measured in pixel units). For e... | CaRMetal | 0.784921 |
80,546 | CaRMetal is an interactive geometry program which inherited the C.a.R. engine. The software has been created by Eric Hakenholz, in Java. | CaRMetal | 0.784921 |
80,547 | CaRMetal can also use the JavaScript objects like arrays, useful to make statistics on geometric figures; date object, useful to measure time; String and RegExp objects, which make it easy to implement L-systems; General JavaScript objects can be used to create new geometric objects like complex numbers, matrices etc. ... | CaRMetal | 0.784921 |
80,548 | CaRMetal allows the user to set some properties of the objects, like their color or the fact that they are visible or not, as conditional. Also each object can have a layer number. An important application of these features was the 2.5D mode of CaRMetal, emulating 3D geometry. | CaRMetal | 0.784921 |
80,549 | Introducing physical explanations for movement in space beyond just geometry, Kepler correctly defined the orbit of planets as follows:: 53–54 The planetary orbit is not a circle with epicycles, but an ellipse. The Sun is not at the center but at a focal point of the elliptical orbit. Neither the linear speed nor the a... | Kepler's Laws | 0.78492 |
80,550 | While all Hadamard codes are based on Hadamard matrices, the constructions differ in subtle ways for different scientific fields, authors, and uses. Engineers, who use the codes for data transmission, and coding theorists, who analyse extremal properties of codes, typically want the rate of the code to be as high as po... | Walsh code | 0.784919 |
80,551 | The Hadamard code is an error-correcting code named after Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels. In 1971, the code was used to transmit photos of Mars back to Earth from the NASA space probe Mariner 9. Because of its unique mat... | Walsh code | 0.784919 |
80,552 | In geology, the depositional resolution is the age span of objects that are contained within a stratum. In most cases the objects of interest are grains or fossils. | Depositional resolution | 0.784919 |
80,553 | Scarponi, Daniele (2012). "Sequence stratigraphy and the resolution of the fossil record". Geology. The Paleontological Society. | Depositional resolution | 0.784919 |
80,554 | The single-particle state is reduced to its wave function | 1 α ⟩ = ψ α {\displaystyle |1_{\alpha }\rangle =\psi _{\alpha }} . Other single-mode many-body (boson) states are just the tensor product of the wave function of that mode, such as | 2 α ⟩ = ψ α ⊗ ψ α {\displaystyle |2_{\alpha }\rangle =\psi _{\alpha }\otimes ... | Second quantization | 0.784918 |
80,555 | The starting point of the second quantization formalism is the notion of indistinguishability of particles in quantum mechanics. Unlike in classical mechanics, where each particle is labeled by a distinct position vector r i {\displaystyle \mathbf {r} _{i}} and different configurations of the set of r i {\displaystyle ... | Second quantization | 0.784918 |
80,556 | The creation and annihilation operators are Hermitian conjugate to each other, but neither of them are Hermitian operators ( c α ≠ c α † {\displaystyle c_{\alpha }\neq c_{\alpha }^{\dagger }} ). The Hermitian combination of the fermion creation and annihilation operators χ α , Re = ( c α + c α † ) / 2 , χ α , Im = ( c ... | Second quantization | 0.784918 |
80,557 | The following operator identities follow from the action of the fermion creation and annihilation operators on the Fock state, { c α † , c β † } = { c α , c β } = 0 , { c α , c β † } = δ α β . {\displaystyle \{c_{\alpha }^{\dagger },c_{\beta }^{\dagger }\}=\{c_{\alpha },c_{\beta }\}=0,\quad \{c_{\alpha },c_{\beta }^{\d... | Second quantization | 0.784918 |
80,558 | The following operator identities follow from the action of the boson creation and annihilation operators on the Fock state, = = 0 , = δ α β . {\displaystyle ==0,\quad =\delta _{\alpha \beta }.} These commutation relations can be considered as the algebraic definition of the boson creation and annihilation operators... | Second quantization | 0.784918 |
80,559 | The fermion creation (annihilation) operator is a linear operator, whose action on a N-particle first-quantized wave function Ψ {\displaystyle \Psi } is defined as c α † Ψ = 1 N + 1 ψ α ⊗ − Ψ , {\displaystyle c_{\alpha }^{\dagger }\Psi ={\frac {1}{\sqrt {N+1}}}\psi _{\alpha }\otimes _{-}\Psi ,} c α Ψ = 1 N ψ α ⊘ − Ψ , ... | Second quantization | 0.784918 |
80,560 | The creation and annihilation operators are introduced to add or remove a particle from the many-body system. These operators lie at the core of the second quantization formalism, bridging the gap between the first- and the second-quantized states. Applying the creation (annihilation) operator to a first-quantized many... | Second quantization | 0.784918 |
80,561 | The creation and annihilation of a particle is implemented by the insertion and deletion of the single-particle state from the first quantized wave function in an either symmetric or anti-symmetric manner. Let ψ α {\displaystyle \psi _{\alpha }} be a single-particle state, let 1 be the tensor identity (it is the genera... | Second quantization | 0.784918 |
80,562 | If the utilities of all agents are homogeneous functions, then the equilibrium conditions in the Fisher model can be written as solutions to a convex optimization program called the Eisenberg-Gale convex program. This program finds an allocation that maximizes the weighted geometric mean of the buyers' utilities, where... | Market equilibrium computation | 0.784918 |
80,563 | Cell decomposition is a process of partitioning the space of possible prices R + m {\displaystyle \mathbb {R} _{+}^{m}} into small "cells", either by hyperplanes or, more generally, by polynomial surfaces. A cell is defined by specifying on which side of each of these surfaces it lies (with polynomial surfaces, the cel... | Market equilibrium computation | 0.784918 |
80,564 | Bogomolnaia and Moulin and Sandomirskiy and Yanovskaia studied the existence and properties of CE in a Fisher market with bads (items with negative utilities) and with a mixture of goods and bads. In contrast to the setting with goods, when the resources are bads the CE does not solve any convex optimization problem ev... | Market equilibrium computation | 0.784918 |
80,565 | Market equilibrium computation (also called competitive equilibrium computation or clearing-prices computation) is a computational problem in the intersection of economics and computer science. The input to this problem is a market, consisting of a set of resources and a set of agents. There are various kinds of market... | Market equilibrium computation | 0.784917 |
80,566 | The above equations can be expressed in matrix algebra, by considering a and b as two elements of a vector, and the transform itself as multiplication by a matrix of the form: H 1 = {\displaystyle H_{1}={\begin{bmatrix}2&1\\1&1\end{bmatrix}}} The inverse can then be derived by inverting the matrix. However, the matrix... | Pseudo-Hadamard transform | 0.784916 |
80,567 | Thus as the nuclear physics inputs can be found in the literature or data compilations, the Computational Infrastructure for Nuclear Astrophysics allows one to do post-processing calculations on various X-ray burst models, and define for oneself the criteria for the waiting point, as well as alter any nuclear parameter... | Nucleon drip line | 0.784915 |
80,568 | Nuclear stability is limited to those combinations of protons and neutrons described by the chart of the nuclides, also called the valley of stability. The boundaries of this valley are the neutron drip line on the neutron-rich side, and the proton drip line on the proton-rich side. These limits exist because of partic... | Nucleon drip line | 0.784915 |
80,569 | The Pegasus Toroidal Experiment is a plasma confinement experiment relevant to fusion power production, run by the Department of Engineering Physics of the University of Wisconsin–Madison. It is a spherical tokamak, a very low-aspect-ratio version of the tokamak configuration, i.e. the minor radius of the torus is comp... | Pegasus Toroidal Experiment | 0.784915 |
80,570 | FlexGen was a biotechnology company based in Leiden, Netherlands. FlexGen was a spin-off from Leiden University Medical Centre and Dutch Space (part of EADS) and had proprietary technologies for laser based in-situ synthesis of oligonucleotides and other biomolecules. On 21 December 2015, Flexgen Bv in Leiden (South Ho... | FlexGen B.V. | 0.784914 |
80,571 | FleXelect oligopools consist of custom oligonucleotides in solution and can be used for in solution target enrichment prior to next generation DNA sequencing. Target enrichment or In solution hybrid selection is a method for genomic selection in an increasing number of applications such as; Analysis of custom genomic r... | FlexGen B.V. | 0.784914 |
80,572 | The FlexArrayer is an in-house custom oligonucleotide synthesis instrument. The FlexArrayer facilitates high throughput synthesis of FleXelect oligopools for in-solution target enrichment as well as custom microarray production. The FlexArrayer is also applicable for array based re-sequencing.The FlexArrayer provides m... | FlexGen B.V. | 0.784914 |
80,573 | John Philoponus, also known as John the Grammarian, was an Alexandrian philologist, Aristotelian commentator and Christian theologian, and author of philosophical treatises and theological works. He was the first who criticized Aristotle and attacked Aristotle's theory of the free fall. His criticism of Aristotelian ph... | Byzantine astronomy | 0.784911 |
80,574 | In light of the COVID-19 pandemic, BAS organized many virtual talks and webinars in year 2020 to help keep enthusiasts engaged during the lockdown phases. The talks were recorded and uploaded to the official YouTube Channel.In September 2022, BAS joined hands with the Indian Institute of Astrophysics to organize a join... | Bangalore Astronomical Society | 0.784911 |
80,575 | BAS's activities broadly fall under Observing, Instrumentation, Outreach, Workshops and Meetings respectively. BAS Activities are normally open to one and all. BAS organizes, motivates and encourages its members to volunteer in Astronomy popularization and outreach initiatives. BAS Activities are normally announced and... | Bangalore Astronomical Society | 0.784911 |
80,576 | Some historians suspect that Copernicus or another European author had access to an Arabic astronomical text, resulting in the transmission of the Tusi couple, an astronomical model developed by Nasir al-Din al-Tusi that later appeared in the work of Nicolaus Copernicus. Byzantine scientists also became acquainted with... | Byzantine astronomy | 0.784911 |
80,577 | During the Middle Ages, there was frequently an exchange of works between Byzantine and Islamic science. The Byzantine Empire initially provided the medieval Islamic world with Ancient and early Medieval Greek texts on astronomy, mathematics and philosophy for translation into Arabic as the Byzantine Empire was the lea... | Byzantine astronomy | 0.784911 |
80,578 | Byzantine scientists preserved and continued the legacy of the great Ancient Greek mathematicians and put mathematics in practice. In early Byzantium (5th to 7th century) the architects and mathematicians Isidore of Miletus and Anthemius of Tralles developed mathematical formulas to construct the great Hagia Sophia chu... | Byzantine astronomy | 0.784911 |
80,579 | The Bangalore Astronomical Society (BAS) is a society of amateur astronomers and other interested individuals, headquartered in Bangalore. The primary objective of the BAS is to promote and popularize Astronomy as a hobby and science. | Bangalore Astronomical Society | 0.784911 |
80,580 | It can be used to relate molecular vibrations and intermolecular forces to equilibrium isotope effects.As the model is an approximation, many applications append corrections for improved accuracy. Some common, significant modifications to the equation include accounting for pressure effects, nuclear geometry, and corre... | Urey–Bigeleisen–Mayer equation | 0.784911 |
80,581 | In 1946, Urey delivered the Liversidge lecture at the then-Royal Institute of Chemistry, where he outlined his proposed model of stable isotope fractionation. Bigeleisen and Mayer had been working on similar work since at least 1944 and, in 1947, published their model independently from Urey. Their calculations were ma... | Urey–Bigeleisen–Mayer equation | 0.784911 |
80,582 | Initially used to approximate chemical reaction rates, models of isotope fractionation are used throughout the physical sciences. In chemistry, the Urey–Bigeleisen–Mayer equation has been used to predict equilibrium isotope effects and interpret the distributions of isotopes and isotopologues within systems, especially... | Urey–Bigeleisen–Mayer equation | 0.784911 |
80,583 | In stable isotope geochemistry, the Urey–Bigeleisen–Mayer equation, also known as the Bigeleisen–Mayer equation or the Urey model, is a model describing the approximate equilibrium isotope fractionation in an isotope exchange reaction. While the equation itself can be written in numerous forms, it is generally presente... | Urey–Bigeleisen–Mayer equation | 0.784911 |
80,584 | The maximal torus in a compact group plays a role analogous to that of the Cartan subalgebra in a complex semisimple Lie algebra. In particular, once a maximal torus T ⊂ K {\displaystyle T\subset K} has been chosen, one can define a root system and a Weyl group similar to what one has for semisimple Lie algebras. These... | Compact topological group | 0.78491 |
80,585 | A key idea in the study of a connected compact Lie group K is the concept of a maximal torus, that is a subgroup T of K that is isomorphic to a product of several copies of S 1 {\displaystyle S^{1}} and that is not contained in any larger subgroup of this type. A basic example is the case K = SU ( n ) {\displaystyle ... | Compact topological group | 0.78491 |
80,586 | From this last expression and the standard formula for the character in terms of the weights of the representation, we can read off that the weights of the representation are m , m − 2 , … , − ( m − 2 ) , − m , {\displaystyle m,m-2,\ldots ,-(m-2),-m,} each with multiplicity one. (The weights are the integers appearing ... | Compact topological group | 0.784909 |
80,587 | We now consider the case of the compact group SU(2). The representations are often considered from the Lie algebra point of view, but we here look at them from the group point of view. We take the maximal torus to be the set of matrices of the form ( e i θ 0 0 e − i θ ) . | Compact topological group | 0.784909 |
80,588 | The Lie algebra is the set of purely imaginary numbers, H = i θ , θ ∈ R , {\displaystyle H=i\theta ,\,\theta \in \mathbb {R} ,} and the kernel of the (scaled) exponential map is the set of numbers of the form i n {\displaystyle in} where n {\displaystyle n} is an integer. A linear functional λ {\displaystyle \lambda } ... | Compact topological group | 0.784909 |
80,589 | Then for λ {\displaystyle \lambda } to give a well-defined map ρ {\displaystyle \rho } , λ {\displaystyle \lambda } must satisfy λ ( H ) ∈ Z , H ∈ Γ , {\displaystyle \lambda (H)\in \mathbb {Z} ,\quad H\in \Gamma ,} where Z {\displaystyle \mathbb {Z} } is the set of integers. A linear functional λ {\displaystyle \lambda... | Compact topological group | 0.784909 |
80,590 | To describe these representations concretely, we let t {\displaystyle {\mathfrak {t}}} be the Lie algebra of T and we write points h ∈ T {\displaystyle h\in T} as h = e H , H ∈ t . {\displaystyle h=e^{H},\quad H\in {\mathfrak {t}}.} In such coordinates, ρ {\displaystyle \rho } will have the form ρ ( e H ) = e i λ ( H )... | Compact topological group | 0.784909 |
80,591 | Robomow was originally named ‘Friendly Machines’ with the goal of constructing robots that will, as Udi Peless says in Space Daily, "move in and around the home, doing the mundane tasks that people do not like to do anymore".The Robomow Classic model debuted in the GLEE exhibition in Birmingham, UK in 1997 and was the ... | Robomow | 0.784907 |
80,592 | First, we will review spin for non-relativistic quantum mechanics. Spin, an intrinsic property similar to angular momentum, is defined by a spin operator S that plays a role on a system similar to the operator L for orbital angular momentum. The operators S 2 {\displaystyle S^{2}} and S z {\displaystyle S_{z}} whose ei... | Anti-symmetric operator | 0.784903 |
80,593 | A photon can become both a positron and electron and vice versa. Because of the anti-symmetric statistics, a particle of spin 1 2 {\displaystyle {\frac {1}{2}}} obeys the Pauli-Exclusion Rule. Two particles can exist in the same state if and only if the spin of the particle is opposite. | Anti-symmetric operator | 0.784903 |
80,594 | Characterized by their spin, a bosonic field can be scalar fields, vector fields and even tensor fields. To illustrate, the electromagnetic field quantized is the photon field, which can be quantized using conventional methods of canonical or path integral quantization. This has led to the theory of quantum electrodyna... | Anti-symmetric operator | 0.784903 |
80,595 | Another type of operator in quantum field theory, discovered in the early 1970s, is known as the anti-symmetric operator. This operator, similar to spin in non-relativistic quantum mechanics is a ladder operator that can create two fermions of opposite spin out of a boson or a boson from two fermions. A Fermion, named ... | Anti-symmetric operator | 0.784903 |
80,596 | In quantum mechanics, a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raising operator is sometimes called the creation operator, and the lowering operator the annihilation operator. Well-kno... | Anti-symmetric operator | 0.784903 |
80,597 | Most vertebrate species have a cerebellum and one or more cerebellum-like structures, brain areas that resemble the cerebellum in terms of cytoarchitecture and neurochemistry. The only cerebellum-like structure found in mammals is the dorsal cochlear nucleus (DCN), one of the two primary sensory nuclei that receive inp... | Granule cell layer | 0.784903 |
80,598 | Several other recipients of the J. Robert Oppenheimer Memorial Prize were later awarded the Nobel Prize in Physics (specifically, Sheldon Glashow, Yoichiro Nambu, Frederick Reines, Abdus Salam, and Steven Weinberg). The inaugural recipient, Paul Dirac, was already a Nobel laureate. | Center for Theoretical Studies, University of Miami | 0.784901 |
80,599 | These meetings had already begun in January 1964, and continued through December 2003. The original series has now been superseded by the annual Miami physics conferences on elementary particles, astrophysics, and cosmology.From 1969 onwards the Center awarded the J. Robert Oppenheimer Memorial Prize to recognize physi... | Center for Theoretical Studies, University of Miami | 0.784901 |
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