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28,800 | Hence, there is always a basis for the eigenvalues of X where the action of P on any wavefunction is known: and the Hamiltonian in this basis is a linear differential operator on the state-vector components, Thus, the equation of motion for the state vector is but a celebrated differential equation, Since D is a differ... | Matrix Mechanics | 0.805857 |
28,801 | Quantum mechanics had been developing by two paths, one led by Einstein, who emphasized the wave–particle duality he proposed for photons, and the other led by Bohr, that emphasized the discrete energy states and quantum jumps that Bohr discovered. De Broglie had reproduced the discrete energy states within Einstein's ... | Matrix Mechanics | 0.805857 |
28,802 | On November 25, 1933, Born received a letter from Heisenberg in which he said he had been delayed in writing due to a "bad conscience" that he alone had received the Prize "for work done in Göttingen in collaboration – you, Jordan and I." Heisenberg went on to say that Born and Jordan's contribution to quantum mechanic... | Matrix Mechanics | 0.805857 |
28,803 | Jordan's Party affiliations and Jordan's links to Born may well have affected Born's chance at the Prize at that time. Bernstein further notes that when Born finally won the Prize in 1954, Jordan was still alive, while the Prize was awarded for the statistical interpretation of quantum mechanics, attributable to Born a... | Matrix Mechanics | 0.805857 |
28,804 | In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application... | Matrix Mechanics | 0.805857 |
28,805 | In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. | Matrix Mechanics | 0.805857 |
28,806 | For the time-independent operators X and P, ∂A/∂t = 0 so the Heisenberg equation above reduces to: where the square brackets denote the commutator. For a Hamiltonian which is p 2 / 2 m + V ( x ) {\displaystyle p^{2}/2m+V(x)} , the X and P operators satisfy: where the first is classically the velocity, and second is cl... | Matrix Mechanics | 0.805857 |
28,807 | Under this multiplication rule, the product depends on the order: XP is different from PX. The X matrix is a complete description of the motion of a quantum mechanical particle. Because the frequencies in the quantum motion are not multiples of a common frequency, the matrix elements cannot be interpreted as the Fourie... | Matrix Mechanics | 0.805857 |
28,808 | Matrix mechanics rapidly developed into modern quantum mechanics, and gave interesting physical results on the spectra of atoms. | Matrix Mechanics | 0.805857 |
28,809 | It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation. In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom ... | Matrix Mechanics | 0.805857 |
28,810 | Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreti... | Matrix Mechanics | 0.805857 |
28,811 | Even if the particles can only be in just two positions, the wavefunction for N particles requires 2N complex numbers, one for each total configuration of positions. This is exponentially many numbers in N, so simulating quantum mechanics on a computer requires exponential resources. Conversely, this suggests that it m... | Matrix Mechanics | 0.805857 |
28,812 | In particular, this means that a system of N interacting particles in 3 dimensions is described by one vector whose components in a basis where all the X are diagonal is a mathematical function of 3N-dimensional space describing all their possible positions, effectively a much bigger collection of values than the mere ... | Matrix Mechanics | 0.805857 |
28,813 | By one NASA estimate, for each year that astronauts spend in deep space, about one-third of their DNA will be hit directly by heavy ions.In increasing knowledge of the effects of cosmic radiation, NSRL studies may expand the understanding of the link between ionizing radiation and aging or neuro-degeneration, as well a... | NASA Space Radiation Laboratory | 0.805855 |
28,814 | Jointly managed by the U.S. Department of Energy's Office of Science and NASA's Johnson Space Center, the facility employs beams of heavy ions that simulate the cosmic rays found in space. NSRL also features its own beam line dedicated to radiobiology research, as well as specimen-preparation areas. Although Brookhaven... | NASA Space Radiation Laboratory | 0.805855 |
28,815 | Through its meetings CCPN provides a forum for the discussion of computational and experimental NMR techniques. The aim is to debate and spread best practice in the determination of macromolecular information, including structure, dynamics and biological chemistry. CCPN continues to arrange annual conferences for the U... | Collaborative Computing Project for NMR | 0.805854 |
28,816 | The Collaborative Computing project for NMR spectroscopy was set up in with three main aims; to create a common standard for representing NMR spectroscopy related data, to create a suite of new open-source NMR software packages and to arrange meetings for the NMR community, including conferences, workshops and courses ... | Collaborative Computing Project for NMR | 0.805854 |
28,817 | Nature versus nurture refers to the theory about how people are influenced. The nature mentality is around the idea that we are influenced by our genetics. This involves all of our physical characteristics and our personality. On the other hand, nurture revolves around the idea that we are influenced by the environment... | Information processing theory | 0.805854 |
28,818 | Information Processing Theory is currently being utilized in the study of computer or artificial intelligence. This theory has also been applied to systems beyond the individual, including families and business organizations. For example, Ariel (1987) applied Information Processing Theory to family systems, with sensin... | Information processing theory | 0.805854 |
28,819 | In high fidelity audio, an amplifier requires a flat frequency response of at least 20–20,000 Hz, with a tolerance as tight as ±0.1 dB in the mid-range frequencies around 1000 Hz; however, in telephony, a frequency response of 400–4,000 Hz, with a tolerance of ±1 dB is sufficient for intelligibility of speech.Once a fr... | Frequency function | 0.805852 |
28,820 | Calculus of voting refers to any mathematical model which predicts voting behaviour by an electorate, including such features as participation rate. A calculus of voting represents a hypothesized decision-making process. These models are used in political science in an attempt to capture the relative importance of vari... | Calculus of voting | 0.805849 |
28,821 | One such model was proposed by Anthony Downs (1957) and is adapted by William H. Riker and Peter Ordeshook, in “A Theory of the Calculus of Voting” (Riker and Ordeshook 1968) V = pB − C + Dwhere V = the proxy for the probability that the voter will turn out p = probability of vote “mattering” B = “utility” benefit of v... | Calculus of voting | 0.805849 |
28,822 | Systematic and Applied Microbiology is a peer-reviewed bimonthly journal deals with various aspects of microbial diversity and systematics of prokaryotes. It focuses on Bacteria and Archaea; eukaryotic microorganisms will only be considered in rare cases. According to the Journal Citation Reports, the journal has a 202... | Systematic and Applied Microbiology | 0.805846 |
28,823 | These are often original recordings that provide an example of the voice of the person concerned. Artificial intelligence can use this data to create an authentic voice, which can reproduce whatever is typed, called Text-To-Speech, or spoken, called Speech-To-Speech. This technology worries many because of its impact o... | Digital cloning | 0.805845 |
28,824 | Voice cloning is a case of the audio deepfake methods that uses artificial intelligence to generate a clone of a person's voice. Voice cloning involves deep learning algorithm that takes in voice recordings of an individual and can synthesize such a voice to the point where it can faithfully replicate a human voice wit... | Digital cloning | 0.805845 |
28,825 | Although digital cloning has already been in the entertainment and arts industry for a while, artificial intelligence can greatly expand the uses of these technology in the industry. The movie-industry can create even more hyper-realistic actors and actresses who have died. Additionally, movie-industry can also create ... | Digital cloning | 0.805845 |
28,826 | Intelligent Avatar Platform (IAP) can be defined as an online platform supported by artificial intelligence that allows one to create a clone of themselves. The individual must train his or her clone to act and speak like themselves by feeding the algorithm numerous voice recordings and videos of themselves. Essentiall... | Digital cloning | 0.805845 |
28,827 | Truby and Brown coined the term “digital thought clone” to refer to the evolution of digital cloning into a more advanced personalized digital clone that consists of “a replica of all known data and behavior on a specific living person, recording in real-time their choices, preferences, behavioral trends, and decision ... | Digital cloning | 0.805845 |
28,828 | Furthermore, artificial intelligence will begin to appear in various aspects of society, which makes it important to have laws that protect humans rights as technology takes over. As the private sector gains more digital power over the public, it is important to set strict regulations and laws to prevent private corpor... | Digital cloning | 0.805845 |
28,829 | One way to prevent being a victim to any of the technology mentioned above is to develop artificial intelligence against these algorithms. There are already several companies that have developed artificial intelligence that can detect manipulated images by looking at the patterns in each pixel. By applying a similar lo... | Digital cloning | 0.805845 |
28,830 | The dimensions given are dimensions over C. Note that every complex Lie algebra can also be viewed as a real Lie algebra of twice the dimension. The Lie algebra of affine transformations of dimension two, in fact, exist for any field. An instance has already been listed in the first table for real Lie algebras. | Table of Lie groups | 0.805845 |
28,831 | Note that a "complex Lie group" is defined as a complex analytic manifold that is also a group whose multiplication and inversion are each given by a holomorphic map. The dimensions in the table below are dimensions over C. Note that every complex Lie group/algebra can also be viewed as a real Lie group/algebra of twic... | Table of Lie groups | 0.805845 |
28,832 | This article gives a table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness; compactness; the nature of the fundamental group; and whether or not they are simply connected) as well as on their algebraic properties (ab... | Table of Lie groups | 0.805845 |
28,833 | Improved results with respect to search engine optimization (SEO) is another side effect of a progressive enhancement-based Web design strategy. Because the basic content is always accessible to search engine spiders, pages built with progressive enhancement methods avoid problems that may hinder search engine indexing... | Progressive Enhancement | 0.805844 |
28,834 | David Artz, leader of the AOL Optimization team, developed a suite of Accessible Rendering Technologies, and invented a technique for disassembly of the "enhancement" on the fly, saving the user's preference. Chris Heilmann discussed the importance of targeted delivery of CSS so that each browser only gets the content ... | Progressive Enhancement | 0.805844 |
28,835 | Let a polynomial have degree n {\displaystyle n} . We derive the algorithm's complexity as follows: Due to the binomial theorem ( x − z ) k = ∑ i = 0 k ( k i ) ( − z ) k − i x i {\textstyle (x-z)^{k}=\sum \limits _{i=0}^{k}{\binom {k}{i}}(-z)^{k-i}x^{i}} , we may transition from f ( x ) {\displaystyle f(x)} to f ( x − ... | Berlekamp–Rabin algorithm | 0.805844 |
28,836 | In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials over a field Z p {\displaystyle \mathbb {Z} _{p}} . The method was discovered by Elwyn Berlekamp in 1970 as an auxiliary to the algorithm for polynomial factorizat... | Berlekamp–Rabin algorithm | 0.805844 |
28,837 | N is an elementary substructure or elementary submodel of M if N and M are structures of the same signature σ such that for all first-order σ-formulas φ(x1, …, xn) with free variables x1, …, xn, and all elements a1, …, an of N, φ(a1, …, an) holds in N if and only if it holds in M: This definition first appears in Tarsk... | Elementary equivalence | 0.805844 |
28,838 | A similar effect can be achieved by using template metaprogramming in C++. In both cases, work is moved to compile-time. The difference between C macros on one side, and Lisp-like macros and C++ template metaprogramming on the other side, is that the latter tools allow performing arbitrary computations at compile-time/... | System optimization | 0.805843 |
28,839 | Optimization during code development using macros takes on different forms in different languages. In some procedural languages, such as C and C++, macros are implemented using token substitution. Nowadays, inline functions can be used as a type safe alternative in many cases. In both cases, the inlined function body c... | System optimization | 0.805843 |
28,840 | In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonli... | Nonlinear differential equation | 0.805839 |
28,841 | In statistics, the Nemenyi test is a post-hoc test intended to find the groups of data that differ after a global statistical test (such as the Friedman test) has rejected the null hypothesis that the performance of the comparisons on the groups of data is similar. The test makes pair-wise tests of performance. The tes... | Nemenyi test | 0.805836 |
28,842 | In 1996 Joshua M. Epstein and Robert Axtell wrote the book Growing Artificial Societies which proposes a set of automaton rules and a system called Sugarscape which models a population dependent on resources (called sugar). Artificial neural networks attempt to solve problems in the same way that the human brain would,... | Generative sciences | 0.805836 |
28,843 | Continuous flow photochemistry offers multiple advantages over batch photochemistry. Photochemical reactions are driven by the number of photons that are able to activate molecules causing the desired reaction. The large surface area to volume ratio of a microreactor maximizes the illumination, and at the same time all... | Photochemistry | 0.805832 |
28,844 | Photoexcitation is the first step in a photochemical process where the reactant is elevated to a state of higher energy, an excited state. The first law of photochemistry, known as the Grotthuss–Draper law (for chemists Theodor Grotthuss and John W. Draper), states that light must be absorbed by a chemical substance in... | Photochemistry | 0.805832 |
28,845 | KOBIC was designated as the National Center for Biological Research Resource Information in 2010. KOBIC is affiliated with the Korea Research Institute of Bioscience and Biotechnology (KRIBB).As a national bioinformation management centre, KOBIC manages biological data from a number of different sources, with an emphas... | Korean Bioinformation Center | 0.805831 |
28,846 | The Korean Bioinformation Center (KOBIC) is the Korean national research centre in bioinformatics, based in Daejeon, South Korea. The centre is comparable to the National Center for Biotechnology Information (NCBI) in the United States and the European Bioinformatics Institute (EBI) in Europe and plays a key role in va... | Korean Bioinformation Center | 0.805831 |
28,847 | Partial algebra generalizes the notion of universal algebra to partial operations. An example would be a field, in which the multiplicative inversion is the only proper partial operation (because division by zero is not defined).The set of all partial functions (partial transformations) on a given base set, X , {\displ... | Partial functions | 0.80583 |
28,848 | This is the case in calculus, where, for example, the quotient of two functions is a partial function whose domain of definition cannot contain the zeros of the denominator. For this reason, in calculus, and more generally in mathematical analysis, a partial function is generally called simply a function. | Partial functions | 0.80583 |
28,849 | There is no need to differ between raising and lowering indices, and in this context and applications to physics and engineering the indices are usually all subscripted to remove confusion for exponents. All indices will be lowered in the remainder of this article. One can determine the actual raised and lowered indice... | Euclidean tensor | 0.805829 |
28,850 | This geometrically has the interpretation that a rectangular coordinate system is mapped to another rectangular coordinate system, in which the norm of the vector x is preserved (and distances are preserved). The determinant of L is det(L) = ±1, which corresponds to two types of orthogonal transformation: (+1) for rota... | Euclidean tensor | 0.805829 |
28,851 | The position vector x in R n {\displaystyle \mathbb {R} ^{n}} is a simple and common example of a vector, and can be represented in any coordinate system. Consider the case of rectangular coordinate systems with orthonormal bases only. It is possible to have a coordinate system with rectangular geometry if the basis ve... | Euclidean tensor | 0.805829 |
28,852 | Cartesian tensors may be used with any Euclidean space, or more technically, any finite-dimensional vector space over the field of real numbers that has an inner product. Use of Cartesian tensors occurs in physics and engineering, such as with the Cauchy stress tensor and the moment of inertia tensor in rigid body dyna... | Euclidean tensor | 0.805829 |
28,853 | In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is done through an orthogonal transformation. The most familiar coordinate systems are the two-dimensional an... | Euclidean tensor | 0.805829 |
28,854 | In 3D Euclidean space, R 3 {\displaystyle \mathbb {R} ^{3}} , the standard basis is ex, ey, ez. Each basis vector points along the x-, y-, and z-axes, and the vectors are all unit vectors (or normalized), so the basis is orthonormal. Throughout, when referring to Cartesian coordinates in three dimensions, a right-hande... | Euclidean tensor | 0.805829 |
28,855 | As for the curl of a vector field A, this can be defined as a pseudovector field by means of the ε symbol: which is only valid in three dimensions, or an antisymmetric tensor field of second order via antisymmetrization of indices, indicated by delimiting the antisymmetrized indices by square brackets (see Ricci calcul... | Euclidean tensor | 0.805829 |
28,856 | Following are the differential operators of vector calculus. Throughout, let Φ(r, t) be a scalar field, and be vector fields, in which all scalar and vector fields are functions of the position vector r and time t. The gradient operator in Cartesian coordinates is given by: and in index notation, this is usually abbrev... | Euclidean tensor | 0.805829 |
28,857 | ISBN 0-792-317-491. T. Dass; S. K. Sharma (1998). Mathematical Methods In Classical And Quantum Physics. | Euclidean tensor | 0.805829 |
28,858 | Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach. The Kluwer International Series in Engineering and Computer Science: Robotics: vision, manipulation and sensors. Vol. | Euclidean tensor | 0.805829 |
28,859 | Vectors, Pure and Applied: A General Introduction to Linear Algebra. Cambridge University Press. p. | Euclidean tensor | 0.805829 |
28,860 | Tensor Calculus. Courier Dover Publications. p. | Euclidean tensor | 0.805829 |
28,861 | Relativity and Geometry. Courier Dover Publications. p. | Euclidean tensor | 0.805829 |
28,862 | S. Lipcshutz; M. Lipson (2009). Linear Algebra. Schaum's Outlines (4th ed.). McGraw Hill. | Euclidean tensor | 0.805829 |
28,863 | A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics. However, a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily i... | Test statistic | 0.805828 |
28,864 | The null hypothesis is that two variances are the same – so the proposed grouping is not meaningful. In the table below, the symbols used are defined at the bottom of the table. Many other tests can be found in other articles. Proofs exist that the test statistics are appropriate. | Test statistic | 0.805828 |
28,865 | These types of models allow the coupling of different compartments of the earth, such as the atmosphere, the biosphere and the hydrosphere; allowing the users to analyze the complicated interactions between them. Some models are constructed by automatic code generators (e.g. Autochem or Kinetic PreProcessor). In this a... | Atmospheric chemist | 0.805828 |
28,866 | these models can be global (simulating the entire earth) or they can be regional (focused on only a specific region). The trade-off between the two approaches is their resolution as well as the amount of detail they can provide; global models usually have lower horizontal resolution and represent less complex chemical ... | Atmospheric chemist | 0.805828 |
28,867 | In order to synthesize and test theoretical understanding of atmospheric chemistry, computer models (such as chemical transport models) are used. Numerical models solve the differential equations governing the concentrations of chemicals in the atmosphere. They can be very simple or very complicated. One common trade o... | Atmospheric chemist | 0.805828 |
28,868 | Two particularly important examples of this were the explanation by Sydney Chapman and Gordon Dobson of how the ozone layer is created and maintained, and the explanation of photochemical smog by Arie Jan Haagen-Smit. Further studies on ozone issues led to the 1995 Nobel Prize in Chemistry award shared between Paul Cru... | Atmospheric chemist | 0.805828 |
28,869 | The ancient Greeks regarded air as one of the four elements. The first scientific studies of atmospheric composition began in the 18th century, as chemists such as Joseph Priestley, Antoine Lavoisier and Henry Cavendish made the first measurements of the composition of the atmosphere.In the late 19th and early 20th cen... | Atmospheric chemist | 0.805828 |
28,870 | This occurs because everything, all real processes, produce entropy and the destruction of exergy or the rate of 'Irreversibility' is proportional to this entropy production (Gouy-Stodola theorem). Where entropy production may be calculated as the net increase in entropy of the system together with its surroundings. En... | Available energy | 0.805825 |
28,871 | These benefits include the basis for determining energy quality (or exergy content), enhancing the understanding of fundamental physical phenomena, and improving design, performance evaluation and optimization efforts. In thermodynamics, the exergy of a system is the maximum useful work that can be produced as the syst... | Available energy | 0.805825 |
28,872 | In 1848, William Thomson, 1st Baron Kelvin, asked (and immediately answered) the question Is there any principle on which an absolute thermometric scale can be founded? It appears to me that Carnot's theory of the motive power of heat enables us to give an affirmative answer.With the benefit of the hindsight contained ... | Available energy | 0.805825 |
28,873 | Carnot's focus on heat engines, equilibrium, and heat reservoirs is also the best entry point for understanding the closely related concept of exergy. Carnot believed in the incorrect caloric theory of heat that was popular during his time, but his thought experiment nevertheless described a fundamental limit of nature... | Available energy | 0.805825 |
28,874 | This circumstance is the re-establishing of equilibrium... Imagine two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies, to which we can give or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimit... | Available energy | 0.805825 |
28,875 | A common hypothesis in systems ecology is that the design engineer's observation that a greater capital investment is needed to create a process with increased exergy efficiency is actually the economic result of a fundamental law of nature. By this view, exergy is the analogue of economic currency in the natural world... | Available energy | 0.805825 |
28,876 | Some proponents of utilizing exergy concepts describe them as a biocentric or ecocentric alternative for terms like quality and value. The "deep ecology" movement views economic usage of these terms as an anthropocentric philosophy which should be discarded. A possible universal thermodynamic concept of value or utilit... | Available energy | 0.805825 |
28,877 | In recent decades, utilization of exergy has spread outside of physics and engineering to the fields of industrial ecology, ecological economics, systems ecology, and energetics. Defining where one field ends and the next begins is a matter of semantics, but applications of exergy can be placed into rigid categories. A... | Available energy | 0.805825 |
28,878 | Since March 2018, 100 VDL Citea articulated electric buses operated by Connexxion have served Schiphol airport. The buses have a battery capacity of 170 kWh and a range of 80 kilometres. They are charged during the day by Heliox 450 kW fast chargers, taking between 15 and 25 minutes. Overnight, 30 kW slow charges take ... | Electric bus | 0.805823 |
28,879 | Calcareous grassland - Calcareous - Calciorthid - Calcisols - Cambisols - Canada Land Inventory - Capacitance probe - Carbon cycle re-balancing - Casa Grande (soil) - Cation-exchange capacity - Cellular confinement - Cecil (soil) - Characterisation of pore space in soil - Charlottetown (soil series) - Chernozem - Clay ... | Index of soil-related articles | 0.805823 |
28,880 | Baer's law - Bama (soil) - Barren vegetation - Base-richness - Bay mud - Bearing capacity - Bentonite - Berkshire (soil) - Bevameter - Biochar - Biogeology - Blandford (soil) - Blue goo - Bog - Brickearth - Brown earth - Brown podzolic | Index of soil-related articles | 0.805823 |
28,881 | SahysMod - Saline seep - Salinity in Australia - Salt marsh - Salting the earth - SaltMod - San Joaquin (soil) - Sand - Sand boil - Sandbag - Scobey (soil) - Seitz (soil) - Serpentine soil - Shear strength (soil) - Shear strength test - Shrub swamp - Silt - Slope stability - Slump - Sodium adsorption ratio - Soil - Soi... | Index of soil-related articles | 0.805823 |
28,882 | Ecological land classification - Ecosystem ecology - Edaphic - Edaphology - Effective stress - Eluvium - Entisol - Environmental impact of irrigation - Erosion - European Soil Bureau Network - European Soil Database - Expansive clay | Index of soil-related articles | 0.805823 |
28,883 | Darcy (unit) - Darcy's law - Darcy–Weisbach equation - Dark earth - Dispersion (geology) - Downer (soil) - Downhill creep - Drainage research - Drilosphere - Drucker–Prager yield criterion - Drummer (soil) - Dry quicksand - Dryland salinity - Duricrust - Durisols - Dynamic compaction | Index of soil-related articles | 0.805823 |
28,884 | In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherica... | Spherical basis | 0.80582 |
28,885 | Analogously to how the spherical harmonics transform under a rotation, a general spherical tensor transforms as follows, when the states transform under the unitary Wigner D-matrix D ( R ) {\displaystyle {\mathcal {D}}(R)} , where R is a (3×3 rotation) group element in SO(3). That is, these matrices represent the rotat... | Spherical basis | 0.80582 |
28,886 | Molecular orbitals and, more specifically, the bonding orbital is a theory that is taught in all different areas of chemistry, from organic to physical and even analytical, because it is widely applicable. Organic chemists use molecular orbital theory in their thought rationale for reactions; analytical chemists use it... | Bonding orbital | 0.805819 |
28,887 | In theoretical chemistry, the bonding orbital is used in molecular orbital (MO) theory to describe the attractive interactions between the atomic orbitals of two or more atoms in a molecule. In MO theory, electrons are portrayed to move in waves. When more than one of these waves come close together, the in-phase combi... | Bonding orbital | 0.805819 |
28,888 | Communications in Mathematical Physics is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, statistical mechanics and quantum field theory, and in operator algebras, quantu... | Communications in Mathematical Physics | 0.805818 |
28,889 | Rudolf Haag conceived this journal with Res Jost, and Haag became the Founding Chief Editor. The first issue of Communications in Mathematical Physics appeared in 1965. Haag guided the journal for the next eight years. Then Klaus Hepp succeeded him for three years, followed by James Glimm, for another three years. | Communications in Mathematical Physics | 0.805818 |
28,890 | In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d, and a closed for... | Closed differential form | 0.805817 |
28,891 | This generalization is useful even for the study of fields – notably, many algebraic objects associated to a field are not themselves fields, but are instead rings, such as algebras over a field, as in representation theory. Just as one can extend scalars on vector spaces, one can also extend scalars on group algebras ... | Extension of scalars | 0.805816 |
28,892 | One of the simplest examples is complexification, which is extension of scalars from the real numbers to the complex numbers. More generally, given any field extension K < L, one can extend scalars from K to L. In the language of fields, a module over a field is called a vector space, and thus extension of scalars conv... | Extension of scalars | 0.805816 |
28,893 | In Euclidean geometry, AAA (angle-angle-angle) (or just AA, since in Euclidean geometry the angles of a triangle add up to 180°) does not provide information regarding the size of the two triangles and hence proves only similarity and not congruence in Euclidean space. However, in spherical geometry and hyperbolic geom... | Triangle congruence | 0.805816 |
28,894 | Where the angle is a right angle, also known as the hypotenuse-leg (HL) postulate or the right-angle-hypotenuse-side (RHS) condition, the third side can be calculated using the Pythagorean theorem thus allowing the SSS postulate to be applied. If two triangles satisfy the SSA condition and the corresponding angles are ... | Triangle congruence | 0.805816 |
28,895 | Quantum metrology is the use of quantum physics to aid the measurement of quantities that, generally, had meaning in classical physics, such as exploiting quantum effects to increase the precision with which a length can be measured. A celebrated example is the introduction of squeezed light into the LIGO experiment, w... | Measurement in quantum mechanics | 0.805815 |
28,896 | The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as a semi-classical approximation to modern quantum mech... | Measurement in quantum mechanics | 0.805815 |
28,897 | Leland Clark (Professor of Chemistry, Antioch College, Yellow Springs, Ohio, and Fels Research Institute, Yellow Springs, Ohio) had developed the first bubble oxygenator for use in cardiac surgery. However, when he came to publish his results, his article was refused by the editor since the oxygen tension in the blood ... | Clark electrode | 0.805813 |
28,898 | A widely reposted 2021 Facebook post claiming that the mRNA vaccines against COVID-19 could cause prion diseases was based on a paper by J. Bart Classen. The paper was published in Microbiology and Infectious Diseases, whose publisher, Scivision Publishers, is included in Beall's list of publishers of predatory journal... | COVID-19 vaccine misinformation and hesitancy | 0.805813 |
28,899 | A professor from the University of Warsaw in Poland, claimed that her research found that medical mistrust was higher in nations that had experienced Soviet-style communism in the past, and vaccine hesitancy could be seen if the countries introduced compulsory vaccination regulations. Medical mistrust is also seen in R... | COVID-19 vaccine misinformation and hesitancy | 0.805813 |
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