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79,500 | Its Lie algebra is a Cartan subalgebra. For disconnected compact Lie groups there are several inequivalent definitions of a Cartan subgroup. The most common seems to be the one given by David Vogan, who defines a Cartan subgroup to be the group of elements that normalize a fixed maximal torus and fix the fundamental We... | Cartan algebra | 0.785341 |
79,501 | A Cartan subgroup of a Lie group is one of the subgroups whose Lie algebra is a Cartan subalgebra. The identity component of a subgroup has the same Lie algebra. There is no standard convention for which one of the subgroups with this property is called the Cartan subgroup, especially in the case of disconnected groups... | Cartan algebra | 0.785341 |
79,502 | In a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero (e.g., C {\displaystyle \mathbb {C} } ), a Cartan subalgebra is the same thing as a maximal abelian subalgebra consisting of elements x such that the adjoint endomorphism ad ( x ): g → g {\displaystyle \operatorna... | Cartan algebra | 0.785341 |
79,503 | In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra h {\displaystyle {\mathfrak {h}}} of a Lie algebra g {\displaystyle {\mathfrak {g}}} that is self-normalising (if ∈ h {\displaystyle \in {\mathfrak {h}}} for all X ∈ h {\displaystyle X\in {\mathfrak {h}}} , then Y ∈ h {\displaysty... | Cartan algebra | 0.785341 |
79,504 | In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules. | Cellular homology | 0.785341 |
79,505 | The Summary for Policymakers concludes that there was a high level of agreement and much evidence that "there is substantial economic potential for the mitigation of global greenhouse gas emissions over the coming decades, that could offset the projected growth of global emissions or reduce emissions below current leve... | Fourth assessment report | 0.785339 |
79,506 | Modern evolutionary developmental biology (evo-devo) follows von Baer, rather than Darwin, in pointing to active evolution of embryonic development as a significant means of changing the morphology of adult bodies. Two of the key principles of evo-devo, namely that changes in the timing (heterochrony) and positioning (... | Ontogeny recapitulates phylogeny | 0.785337 |
79,507 | The Strong Star Property is an alternative to the *-Property, in which subjects may write to objects with only a matching security level. Thus, the write-up operation permitted in the usual *-Property is not present, only a write-to-same operation. The Strong Star Property is usually discussed in the context of multile... | Bell–LaPadula model | 0.785336 |
79,508 | In mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. These properties are particularly considered in topology and graph theory, but also in set theory. | Induced-hereditary property | 0.785335 |
79,509 | There is no consensus for the meaning of "monotone property" in graph theory. Examples of definitions are: Preserved by the removal of edges. Preserved by the removal of edges and vertices (i.e., the property should hold for all subgraphs). Preserved by the addition of edges and vertices (i.e., the property should hold... | Induced-hereditary property | 0.785335 |
79,510 | In topology, a topological property is said to be hereditary if whenever a topological space has that property, then so does every subspace of it. If the latter is true only for closed subspaces, then the property is called weakly hereditary or closed-hereditary. For example, second countability and metrisability are h... | Induced-hereditary property | 0.785335 |
79,511 | In theoretical computer science, the log-rank conjecture states that the deterministic communication complexity of a two-party Boolean function is polynomially related to the logarithm of the rank of its input matrix.Let D ( f ) {\displaystyle D(f)} denote the deterministic communication complexity of a function, and l... | Log-rank conjecture | 0.785331 |
79,512 | The Society for Mathematical Biology is governed by its Officers and Board of Directors, elected by the membership. Current SMB President is Heiko Enderling (Moffitt Cancer Center), and Past-President serving as vice president is Alexander R.A. Anderson (Moffitt Cancer Center). SMB secretary is Gibin Powathil (Swansea ... | Society for Mathematical Biology | 0.78533 |
79,513 | The Society for Mathematical Biology emerged and grew from the earlier school of mathematical biophysics, initiated and supported by the Founder of Mathematical Biology, Nicolas Rashevsky. Thus, the roots of SMB go back to the publication in 1939 of the first international journal of mathematical biology, previously en... | Society for Mathematical Biology | 0.78533 |
79,514 | The Society for Mathematical Biology (SMB) is an international association co-founded in 1972 in the United States by George Karreman, Herbert Daniel Landahl and (initially chaired) by Anthony Bartholomay for the furtherance of joint scientific activities between Mathematics and Biology research communities. The societ... | Society for Mathematical Biology | 0.78533 |
79,515 | In addition to its research and news publications, the society supports education in: mathematical biology, mathematical biophysics, complex systems biology and theoretical biology through sponsorship of several topic-focused graduate and postdoctoral courses. To encourage and stimulate young researchers in this relati... | Society for Mathematical Biology | 0.78533 |
79,516 | Heinz and Shen adsorbed monolayers of laser dye rhodamine to a planar fused silica surface; the coated surface was then pumped by a nanosecond ultra-fast laser. SH light with characteristic spectra of the adsorbed molecule and its electronic transitions were measured as reflection from the surface and demonstrated a qu... | Second-harmonic generation | 0.78533 |
79,517 | In theoretical computer science, the Krivine machine is an abstract machine (sometimes called virtual machine). As an abstract machine, it shares features with Turing machines and the SECD machine. The Krivine machine explains how to compute a recursive function. More specifically it aims to define rigorously head norm... | Krivine machine | 0.785328 |
79,518 | However, it can enter an infinite sequence of transitions, which means that the term it attempts reducing has no head normal form and corresponds to a non terminating computation. It has been proved that the Krivine machine implements correctly the call by name head normal form reduction in the lambda-calculus. Moreove... | Krivine machine | 0.785328 |
79,519 | A redex (one says also β-redex) is a term of the lambda calculus of the form (λ x. t) u. If a term has the shape (λ x. t) u1 ... un it is said to be a head redex. A head normal form is a term of the lambda calculus which is not a head redex. A head reduction is a (non empty) sequence of contractions of a term which con... | Krivine machine | 0.785328 |
79,520 | The Krivine machine, like the CEK machine, does not only functionally correspond to a meta-circular evaluator, it also syntactically corresponds to the λ ρ ^ {\displaystyle \lambda {\widehat {\rho }}} calculus -- a version of Pierre-Louis Curien's λ ρ ^ {\displaystyle \lambda {\widehat {\rho }}} calculus of explicit su... | Krivine machine | 0.785328 |
79,521 | The Krivine machine is based on two concepts related to lambda calculus, namely head reduction and call by name. | Krivine machine | 0.785328 |
79,522 | The Standard Model of particle physics contains three fundamental forces, the electromagnetic force, the weak force and the strong force. Shortly after the Big Bang, the extremely high temperatures may have modified the character of these forces. While these three forces act differently today, it has been conjectured t... | Cosmological phase transition | 0.785327 |
79,523 | Pauli and Jung's approach to dual-aspect monism has a very specific further feature, namely that different aspects may show a complementarity in a quantum physical sense. That is, the Pauli-Jung conjecture implies that with regard to mental and physical states there may be incompatible descriptions of different parts t... | Double-aspect theory | 0.785326 |
79,524 | The history of the Hubble Space Telescope can be traced back to 1946, when the astronomer Lyman Spitzer wrote the paper Astronomical advantages of an extraterrestrial observatory. Spitzer devoted much of his career to pushing for a space telescope. The 1966–1972 Orbiting Astronomical Observatory missions demonstrated t... | Great Observatories program | 0.785326 |
79,525 | In 1979, a National Research Council of the National Academy of Sciences report, A Strategy for Space Astronomy and Astrophysics for the 1980s, identified a Shuttle Infrared Telescope Facility (SIRTF) as "one of two major astrophysics facilities for Spacelab," a Shuttle-borne platform. The launch of the Infrared Astro... | Great Observatories program | 0.785326 |
79,526 | All four telescopes have had a substantial impact on astronomy. The opening up of new wavebands to high resolution, high sensitivity observations by the Compton, Chandra and Spitzer has revolutionized our understanding of a wide range of astronomical objects, and has led to the detection of thousands of new, interestin... | Great Observatories program | 0.785326 |
79,527 | Gamma rays had been examined above the atmosphere by several early space missions. During its High Energy Astronomy Observatory Program in 1977, NASA announced plans to build a "great observatory" for gamma-ray astronomy. The Gamma Ray Observatory (GRO), renamed Compton Gamma-Ray Observatory (CGRO), was designed to tak... | Great Observatories program | 0.785326 |
79,528 | The concept of a Great Observatory program was first proposed in the 1979 NRC report "A Strategy for Space Astronomy and Astrophysics for the 1980s". This report laid the essential groundwork for the Great Observatories and was chaired by Peter Meyer (through June 1977) and then by Harlan J. Smith (through publication)... | Great Observatories program | 0.785326 |
79,529 | The Beyond Einstein program will seek to develop new areas of science. Constellation-X and the Laser Interferometer Space Antenna (LISA) have been referred to by NASA as the Einstein Great Observatories, to differentiate them from the current generation. However, they are not a part of the Great Observatories program.T... | Great Observatories program | 0.785326 |
79,530 | Occasionally it observes high-energy objects which happen to be in the view around the Sun.Another large, high-energy observatory is INTEGRAL, Europe's INTErnational Gamma Ray Astrophysics Laboratory, launched in 2002. It observes in similar frequencies to Compton. INTEGRAL uses a fundamentally different telescope tech... | Great Observatories program | 0.785326 |
79,531 | JWST will exceed Spitzer's performance in near-infrared, and the European Space Agency's Herschel Space Observatory, operational from 2009 to 2013, has exceeded Spitzer in the far-infrared. The SOFIA (Stratospheric Observatory for Infrared Astronomy) airborne platform observes in near- and mid-infrared. SOFIA has a lar... | Great Observatories program | 0.785326 |
79,532 | Educational Initiatives 2002-2003 Salon de l’Education Salon de l'Education is a large educational trade show held every year at the Palais De Congres in Montreal. Almost every high school in the Montreal area sends graduating students to the event. Team iSun was on hand with the car and the team to educate about renew... | McGill University Solarcar Team | 0.785326 |
79,533 | She spent some time discussing the project and the future of renewable energy technologies with the team. Clean Energy Awareness Promotions 2002-2003 During 2002-2003 The car was presented at these events as a special attraction. The 2002 Montreal International Auto Show The 2002 Montreal International Auto Show hosted... | McGill University Solarcar Team | 0.785325 |
79,534 | McGill University's Solar Car Team was composed of students from the faculties of Engineering and Computer Science. From 1990 - 2010, the team designed, built, tested and raced 3 generations of solar vehicles in international competitions. Under the brand Team iSun, the team placed 9th in the 2003 American Solar Challe... | McGill University Solarcar Team | 0.785325 |
79,535 | In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal tra... | Conformal manifold | 0.785325 |
79,536 | In statistics, shrinkage is the reduction in the effects of sampling variation. In regression analysis, a fitted relationship appears to perform less well on a new data set than on the data set used for fitting. In particular the value of the coefficient of determination 'shrinks'. This idea is complementary to overfit... | Shrinkage (statistics) | 0.785325 |
79,537 | TRA has also been used to study consumer attitudes towards renewable energy. In 2000, Bang, et al. found that people who cared about environmental issues like pollution were more willing to spend more for renewable energy. Similarly, a 2008 study of Swedish consumers by Hansla et al. showed that those who with a positi... | Theory of reasoned action | 0.785323 |
79,538 | Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating ... | Maxwell's demon | 0.785322 |
79,539 | Real-life versions of Maxwellian demons occur, but all such "real demons" or molecular demons have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology. Single-atom... | Maxwell's demon | 0.785322 |
79,540 | The concept of Maxwell's demon has provoked substantial debate in the philosophy of science and theoretical physics, which continues to the present day. It stimulated work on the relationship between thermodynamics and information theory. Most scientists argue that, on theoretical grounds, no practical device can viola... | Maxwell's demon | 0.785322 |
79,541 | Marcus separates the inner sphere (reactant + tightly bound solvent molecules, in complexes + ligands) and the outer sphere (free solvent ) In this model Marcus confines himself to calculating the outer sphere energy of the non-equilibrium polarization of the "transition state". The outer sphere energy is often much la... | Reorganization energy | 0.785321 |
79,542 | A. Marcus received the Nobel Prize in Chemistry in 1992 for this theory. Marcus theory is used to describe a number of important processes in chemistry and biology, including photosynthesis, corrosion, certain types of chemiluminescence, charge separation in some types of solar cells and more. Besides the inner and out... | Reorganization energy | 0.785321 |
79,543 | In theoretical chemistry, Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). It was or... | Reorganization energy | 0.785321 |
79,544 | Littlewood's three principles are quoted in several real analysis texts, for example Royden, Bressoud, and Stein & Shakarchi.Royden gives the bounded convergence theorem as an application of the third principle. The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integra... | Littlewood's three principles of real analysis | 0.785318 |
79,545 | Littlewood stated the principles in his 1944 Lectures on the Theory of Functions as: There are three principles, roughly expressible in the following terms: Every (measurable) set is nearly a finite sum of intervals; every function (of class Lp) is nearly continuous; every convergent sequence of functions is nearly uni... | Littlewood's three principles of real analysis | 0.785318 |
79,546 | An example from linear algebra is the multiplicative monoid of real square matrices of order n (called the full linear monoid). The map which sends a matrix to its transpose is an involution because the transpose is well defined for any matrix and obeys the law (AB)T = BTAT, which has the same form of interaction with ... | Free semigroup with involution | 0.785318 |
79,547 | In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation ... | Free semigroup with involution | 0.785318 |
79,548 | Penicillium species, Aspergillus niger and Candida albicans are used in the pharmaceutical industry for microbial limit testing, bioburden assessment, method validation, antimicrobial challenge tests, and quality control testing. When used in this capacity, Penicillium and A. niger are compendial mold indicator organis... | Helminth eggs | 0.785318 |
79,549 | Much debate surrounds the topic of human enhancement and the means used to achieve one's enhancement goals. Ethical attitudes toward human enhancement can depend on many factors such as religious affiliation, age, gender, ethnicity, culture of origin, and nationality.In some circles the expression "human enhancement" i... | Human augmentation | 0.785318 |
79,550 | W. T. Tutte conjectured that every snark has the Petersen graph as a minor. That is, he conjectured that the smallest snark, the Petersen graph, may be formed from any other snark by contracting some edges and deleting others. Equivalently (because the Petersen graph has maximum degree three) every snark has a subgraph... | Snark (graph theory) | 0.785317 |
79,551 | Research on snarks originated in Peter G. Tait's work on the four color theorem in 1880, but their name is much newer, given to them by Martin Gardner in 1976. Beyond coloring, snarks also have connections to other hard problems in graph theory: writing in the Electronic Journal of Combinatorics, Miroslav Chladný and M... | Snark (graph theory) | 0.785317 |
79,552 | In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three colors. In order to avoid trivial cases, snarks are often restricted to have additional requirements on their connectivity and on the length of their cycles. Infini... | Snark (graph theory) | 0.785317 |
79,553 | In organic chemistry a methylthiomethyl (MTM) ether is a protective group for hydroxyl groups. Hydroxyl groups are present in many chemical compounds and they must be protected during oxidation, acylation, halogenation, dehydration and other reactions to which they are susceptible. Many kinds of protective groups for h... | Methylthiomethyl ether | 0.785317 |
79,554 | ROMeoRigorous Online Modelling and Equation Based Optimization is an advanced online chemical process optimizer of SimSci, a brand of Aveva software It is mainly used by process engineers in the chemical, petroleum and natural gas industries. It includes a chemical component library, thermodynamic property prediction m... | ROMeo (process optimizer) | 0.785317 |
79,555 | In physics, the mathematical description of any physical situation usually contains excess degrees of freedom; the same physical situation is equally well described by many equivalent mathematical configurations. For instance, in Newtonian dynamics, if two configurations are related by a Galilean transformation (an ine... | Gauge Transformation | 0.785316 |
79,556 | In statistics, a Yates analysis is an approach to analyzing data obtained from a designed experiment, where a factorial design has been used. Full- and fractional-factorial designs are common in designed experiments for engineering and scientific applications. In these designs, each factor is assigned two levels, typic... | Yates analysis | 0.785316 |
79,557 | In organometallic chemistry, a metal–ligand multiple bond describes the interaction of certain ligands with a metal with a bond order greater than one. Coordination complexes featuring multiply bonded ligands are of both scholarly and practical interest. Transition metal carbene complexes catalyze the olefin metathesis... | Pi-donor ligands | 0.785315 |
79,558 | The European Astrobiology Network Association (EANA) coordinates and facilities research expertise in astrobiology in Europe. EANA was created in 2001 to coordinate the different European centers in astrobiology and the related fields previously organized in paleontology, geology, atmospheric physics, planetary science... | European Astrobiology Network Association | 0.785313 |
79,559 | The specific objectives of EANA are to: bring together active European researchers and link their research programs fund exchange visits between laboratories optimize the sharing of information and resources facilities for research promote this field of research to European funding agencies and politicians promote rese... | European Astrobiology Network Association | 0.785313 |
79,560 | The American College of Medical Genetics recommends obstetric ultrasonography at 18–20 weeks gestation in cases of advanced paternal age to evaluate fetal development, but it notes that this procedure "is unlikely to detect many of the conditions of interest." They also note that there is no standard definition of adva... | Paternal age effect | 0.785313 |
79,561 | Reinforcement is a process within speciation where natural selection increases the reproductive isolation between two populations of species by reducing the production of hybrids. Evidence for speciation by reinforcement has been gathered since the 1990s, and along with data from comparative studies and laboratory expe... | Evidence of speciation by reinforcement | 0.785313 |
79,562 | We can also extend the usual p {\displaystyle p} -adic order functions to supernatural numbers by defining v p ( ω ) = n p {\displaystyle v_{p}(\omega )=n_{p}} for each p {\displaystyle p} . Supernatural numbers are used to define orders and indices of profinite groups and subgroups, in which case many of the theorems ... | Supernatural number | 0.785312 |
79,563 | In molecular biology, insertional mutagenesis is the creation of mutations in DNA by the addition of one or more base pairs. Such insertional mutations can occur naturally, mediated by viruses or transposons, or can be artificially created for research purposes in the lab. | Insertional mutagenesis | 0.785311 |
79,564 | Jordan superalgebras were introduced by Kac, Kantor and Kaplansky; these are Z / 2 {\displaystyle \mathbb {Z} /2} -graded algebras J 0 ⊕ J 1 {\displaystyle J_{0}\oplus J_{1}} where J 0 {\displaystyle J_{0}} is a Jordan algebra and J 1 {\displaystyle J_{1}} has a "Lie-like" product with values in J 0 {\displaystyle J_{0... | Jordan superalgebra | 0.785311 |
79,565 | To understand the relative risk of each contributing factor, consider that the rate of deaths totally attributed to the patient's health is 1:870. Compare that to the rate of deaths totally attributed to surgical factors (1:2860) or anesthesia alone (1:185,056) illustrating that the single greatest factor in anesthetic... | Anesthetic agents | 0.785309 |
79,566 | A Compton telescope (also known as Compton camera or Compton imager) is a gamma-ray detector which utilizes Compton scattering to determine the origin of the observed gamma rays. Compton cameras are usually applied to detect gamma rays in the energy range where Compton scattering is the dominating interaction process, ... | Compton telescope | 0.785309 |
79,567 | In functional analysis, a reflexive operator algebra A is an operator algebra that has enough invariant subspaces to characterize it. Formally, A is reflexive if it is equal to the algebra of bounded operators which leave invariant each subspace left invariant by every operator in A. This should not be confused with a ... | Reflexive operator algebra | 0.785309 |
79,568 | Every finite-dimensional reflexive algebra is hyper-reflexive. However, there are examples of infinite-dimensional reflexive operator algebras which are not hyper-reflexive. The distance constant for a one-dimensional algebra is 1. Nest algebras are hyper-reflexive with distance constant 1. Many von Neumann algebras ar... | Reflexive operator algebra | 0.785309 |
79,569 | {\displaystyle \left\{{\begin{pmatrix}a&b\\0&a\end{pmatrix}}\ :\ a,b\in \mathbb {C} \right\}.} This algebra is smaller than the Nest algebra { ( a b 0 c ): a , b , c ∈ C } {\displaystyle \left\{{\begin{pmatrix}a&b\\0&c\end{pmatrix}}\ :\ a,b,c\in \mathbb {C} \right\}} but has the same invariant subspaces, so it is not r... | Reflexive operator algebra | 0.785309 |
79,570 | Nest algebras are examples of reflexive operator algebras. In finite dimensions, these are simply algebras of all matrices of a given size whose nonzero entries lie in an upper-triangular pattern. In fact if we fix any pattern of entries in an n by n matrix containing the diagonal, then the set of all n by n matrices w... | Reflexive operator algebra | 0.785309 |
79,571 | The smallest such K is called the distance constant for A {\displaystyle {\mathcal {A}}} . A hyper-reflexive operator algebra is automatically reflexive. In the case of a reflexive algebra of matrices with nonzero entries specified by a given pattern, the problem of finding the distance constant can be rephrased as a m... | Reflexive operator algebra | 0.785309 |
79,572 | Here dist ( T , A ) {\displaystyle {\mbox{dist}}(T,{\mathcal {A}})} is the distance of T from the algebra, namely the smallest norm of an operator T-A where A runs over the algebra. We call A {\displaystyle {\mathcal {A}}} hyperreflexive if there is a constant K such that for every operator T in B(H), dist ( T , A ) ≤ ... | Reflexive operator algebra | 0.785309 |
79,573 | Let A {\displaystyle {\mathcal {A}}} be a weak*-closed operator algebra contained in B(H), the set of all bounded operators on a Hilbert space H and for T any operator in B(H), let β ( T , A ) = sup { ‖ P ⊥ T P ‖: P is a projection and P ⊥ A P = ( 0 ) } . {\displaystyle \beta (T,{\mathcal {A}})=\sup \left\{\left\|P^{\p... | Reflexive operator algebra | 0.785309 |
79,574 | Krohn–Rhodes theory, sometimes also called algebraic automata theory, gives powerful decomposition results for finite transformation semigroups by cascading simpler components. | Semigroup action | 0.785307 |
79,575 | If S is a semigroup or monoid, then a set X on which S acts as above (on the left, say) is also known as a (left) S-act, S-set, S-action, S-operand, or left act over S. Some authors do not distinguish between semigroup and monoid actions, by regarding the identity axiom (e • x = x) as empty when there is no identity el... | Semigroup action | 0.785307 |
79,576 | This concept is linked to the more general notion of a semigroup by an analogue of Cayley's theorem. (A note on terminology: the terminology used in this area varies, sometimes significantly, from one author to another. See the article for details.) | Semigroup action | 0.785307 |
79,577 | In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corres... | Semigroup action | 0.785307 |
79,578 | Stated another way, the orientation of the coffee cup has become entangled with the orientation of the surrounding walls. Clearly the geometry of spatial vectors alone is insufficient to express the orientation entanglement (the twist of the rubber bands). Consider drawing a vector across the cup. | Orientation entanglement | 0.785307 |
79,579 | In mathematics and physics, the notion of orientation entanglement is sometimes used to develop intuition relating to the geometry of spinors or alternatively as a concrete realization of the failure of the special orthogonal groups to be simply connected. | Orientation entanglement | 0.785307 |
79,580 | In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility. Electron and hol... | Semiconductor carrier mobility | 0.785306 |
79,581 | Srinivasa Ramanujan gave the identity 1 ψ 1 = ∑ n = − ∞ ∞ ( a ; q ) n ( b ; q ) n z n = ( b / a , q , q / a z , a z ; q ) ∞ ( b , b / a z , q / a , z ; q ) ∞ {\displaystyle \;_{1}\psi _{1}\left=\sum _{n=-\infty }^{\infty }{\frac {(a;q)_{n}}{(b;q)_{n}}}z^{n}={\frac {(b/a,q,q/az,az;q)_{\infty }}{(b,b/az,q/a,z;q)_{\infty... | Basic hypergeometric function | 0.785306 |
79,582 | Conceptual concerns about the interpretation of quantum mechanics and the meaning of probability have motivated technical work. A quantum version of the de Finetti theorem, introduced by Caves, Fuchs, and Schack (independently reproving a result found using different means by Størmer) to provide a Bayesian understandin... | Quantum Bayesianism | 0.785301 |
79,583 | On occasion, the proposals of Bub and Pitowsky are also called "quantum Bayesianism".Zeilinger and Brukner have also proposed an interpretation of quantum mechanics in which "information" is a fundamental concept, and in which quantum states are epistemic quantities. Unlike QBism, the Brukner–Zeilinger interpretation t... | Quantum Bayesianism | 0.785301 |
79,584 | According to QBism, quantum theory is a tool which an agent may use to help manage his or her expectations, more like probability theory than a conventional physical theory. Quantum theory, QBism claims, is fundamentally a guide for decision making which has been shaped by some aspects of physical reality. Chief among ... | Quantum Bayesianism | 0.785301 |
79,585 | QBism should be distinguished from other applications of Bayesian inference in quantum physics, and from quantum analogues of Bayesian inference. For example, some in the field of computer science have introduced a kind of quantum Bayesian network, which they argue could have applications in "medical diagnosis, monitor... | Quantum Bayesianism | 0.785301 |
79,586 | Fuchs and Schack replied to these concerns in a later article. Mermin advocated QBism in a 2012 Physics Today article, which prompted considerable discussion. Several further critiques of QBism which arose in response to Mermin's article, and Mermin's replies to these comments, may be found in the Physics Today readers... | Quantum Bayesianism | 0.785301 |
79,587 | A critical article by Nauenberg in the American Journal of Physics prompted a reply by Fuchs, Mermin, and Schack. Some assert that there may be inconsistencies; for example, Stairs argues that when a probability assignment equals one, it cannot be a degree of belief as QBists say. Further, while also raising concerns a... | Quantum Bayesianism | 0.785301 |
79,588 | In physics and the philosophy of physics, quantum Bayesianism is a collection of related approaches to the interpretation of quantum mechanics, the most prominent of which is QBism (pronounced "cubism"). QBism is an interpretation that takes an agent's actions and experiences as the central concerns of the theory. QBis... | Quantum Bayesianism | 0.785301 |
79,589 | The urgleichung, in contrast, is a relation between different contexts which finds its justification in the predictive success of quantum physics. The SIC representation of quantum states also provides a reformulation of quantum dynamics. Consider a quantum state ρ ^ {\displaystyle {\hat {\rho }}} with SIC representati... | Quantum Bayesianism | 0.785301 |
79,590 | Note that the urgleichung is structurally very similar to the law of total probability, which is the expressionThey functionally differ only by a dimension-dependent affine transformation of the SIC probability vector. As QBism says that quantum theory is an empirically-motivated normative addition to probability theor... | Quantum Bayesianism | 0.785301 |
79,591 | Similarly, Schlosshauer and Claringbold state that QBism is a consistent interpretation of quantum mechanics, but do not offer a verdict on whether it should be preferred. In addition, some agree with most, but perhaps not all, of the core tenets of QBism; Barnum's position, as well as Appleby's, are examples. Populari... | Quantum Bayesianism | 0.785301 |
79,592 | The phosphorus atom in phosphines has a formal oxidation state −3 (σ3λ3) and are the phosphorus analogues of amines. Like amines, phosphines have a trigonal pyramidal molecular geometry although often with smaller C-E-C angles (E = N, P), at least in the absence of steric effects. The C-P-C bond angle is 98.6° for trim... | Organophosphine | 0.785301 |
79,593 | Organophosphines, like phosphine itself, are pyramidal molecules with approximate C3v symmetry. The C–P–C bond angles are approximately 98.6°. The C–P–C bond angles are consistent with the notion that phosphorus predominantly uses the 3p orbitals for forming bonds and that there is little sp hybridization of the phosph... | Organophosphine | 0.785301 |
79,594 | Tertiary phosphines are often used as ligands in coordination chemistry. The binding of phosphines bind to metals, which serve as Lewis acids. For example, silver chloride reacts with triphenylphosphine to 1;1 and 1:2 complexes: PPh3 + AgCl → ClAgPPh3 PPh3 + ClAgPPh3 → ClAg(PPh3)2The adducts formed from phosphines and ... | Organophosphine | 0.785301 |
79,595 | The precise statement is as follows: if A is a small abelian category, then there exists a ring R (with 1, not necessarily commutative) and a full, faithful and exact functor F: A → R-Mod (where the latter denotes the category of all left R-modules). The functor F yields an equivalence between A and a full subcategory ... | Mitchell embedding theorem | 0.785301 |
79,596 | {\displaystyle G:{\mathcal {L}}\to R\operatorname {-Mod} .} The composition G H: A → R - M o d {\displaystyle GH:{\mathcal {A}}\to R\operatorname {-Mod} } is the desired covariant exact and fully faithful embedding. Note that the proof of the Gabriel–Quillen embedding theorem for exact categories is almost identical. =... | Mitchell embedding theorem | 0.785301 |
79,597 | In topology, a branch of mathematics, for i ≥ 2 {\displaystyle i\geq 2} , the i-th homotopy group with coefficients in an abelian group G of a based space X is the pointed set of homotopy classes of based maps from the Moore space of type ( G , i ) {\displaystyle (G,i)} to X, and is denoted by π i ( X ; G ) {\displayst... | Homotopy group with coefficients | 0.785299 |
79,598 | According to csrankings.org, for the combined subfields of computer graphics, HCI, and visualization the dgp is the number one research institution in the world.Since then, dgp has hosted many well known faculty and students in computer graphics, computer vision and HCI (e.g., Alain Fournier, Bill Reeves, Jos Stam, Dem... | Dynamic Graphics Project | 0.785298 |
79,599 | The Dynamic Graphics Project (commonly referred to as dgp) is an interdisciplinary research laboratory at the University of Toronto devoted to projects involving Computer Graphics, Computer Vision, Human Computer Interaction, and Visualization. The lab began as the computer graphics research group of Computer Science P... | Dynamic Graphics Project | 0.785298 |
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