Semidirect productIn mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: an inner semidirect product is a particular way in which a group can be made up of two subgroups, one of which is a normal subgroup. an outer semidirect product is a way to construct a new group from two given groups by using the Cartesian product as a set and a particular multiplication operation.
Dimension (vector space)In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension. For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say is if the dimension of is finite, and if its dimension is infinite.
Microsoft EdgeMicrosoft Edge (or simply Edge) is a proprietary, cross-platform web browser created by Microsoft. It was first released in 2015 as part of Windows 10 and Xbox One and later ported to other platforms as a fork of Google's Chromium open-source project: Android and iOS, macOS, older Windows versions (Windows 7, Windows Server 2008 R2 and later were supported until early 2023), and most recently Linux. Edge was created as the successor to Internet Explorer (IE).
Uniform isomorphismIn the mathematical field of topology a uniform isomorphism or is a special isomorphism between uniform spaces that respects uniform properties. Uniform spaces with uniform maps form a . An isomorphism between uniform spaces is called a uniform isomorphism. A function between two uniform spaces and is called a uniform isomorphism if it satisfies the following properties is a bijection is uniformly continuous the inverse function is uniformly continuous In other words, a uniform isomorphism is a uniformly continuous bijection between uniform spaces whose inverse is also uniformly continuous.
TheoryA theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
Superstring theorySuperstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity. Since the second superstring revolution, the five superstring theories (Type I, Type IIA, Type IIB, HO and HE) are regarded as different limits of a single theory tentatively called M-theory.
M-theoryM-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995 (M-Theory - Edward Witten (1995)). Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory.
Uniform continuityIn mathematics, a real function of real numbers is said to be uniformly continuous if there is a positive real number such that function values over any function domain interval of the size are as close to each other as we want. In other words, for a uniformly continuous real function of real numbers, if we want function value differences to be less than any positive real number , then there is a positive real number such that at any and in any function interval of the size .
Mehler kernelThe Mehler kernel is a complex-valued function found to be the propagator of the quantum harmonic oscillator. defined a function and showed, in modernized notation, that it can be expanded in terms of Hermite polynomials H(.) based on weight function exp(−x2) as This result is useful, in modified form, in quantum physics, probability theory, and harmonic analysis. In physics, the fundamental solution, (Green's function), or propagator of the Hamiltonian for the quantum harmonic oscillator is called the Mehler kernel.
String theoryIn physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string.
BeijingBeijing (beɪˈdʒɪŋ ; ; AUDBeijing pronunciation.oggbei3.jing1), alternatively romanized as Peking (piːˈkɪŋ ), is the capital of the People's Republic of China. With over 21 million residents, Beijing is the world's most populous national capital city as well as China's second largest city after Shanghai. It is located in Northern China, and is governed as a municipality under the direct administration of the State Council with 16 urban, suburban, and rural districts.
Critical theoryA critical theory is any approach to social philosophy that focuses on society and culture to attempt to reveal, critique, and challenge power structures. With roots in sociology and literary criticism, it argues that social problems stem more from social structures and cultural assumptions than from individuals. It argues that ideology is the principal obstacle to human liberation. Critical theory finds applications in various fields of study, including psychoanalysis, sociology, history, communication theory, philosophy and feminist theory.
