Pseudoconvex functionIn convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex. Informally, a differentiable function is pseudoconvex if it is increasing in any direction where it has a positive directional derivative. The property must hold in all of the function domain, and not only for nearby points.
Outer measureIn the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.
Electromagnetic fieldAn electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by moving electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified as light) and interacts with charges and currents.
Magnetic fieldA magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.
Media biasMedia bias is the bias of journalists and news producers within the mass media in the selection of many events and stories that are reported and how they are covered. The term "media bias" implies a pervasive or widespread bias contravening of the standards of journalism, rather than the perspective of an individual journalist or article. The direction and degree of media bias in various countries is widely disputed.
Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
Convex hullIn geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact.
Field (physics)In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.
Chebyshev's inequalityIn probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution's values can be k or more standard deviations away from the mean (or equivalently, at least 1 − 1/k2 of the distribution's values are less than k standard deviations away from the mean).
Old mediaOld media, or legacy media, are the mass media institutions that dominated prior to the Information Age; particularly print media, film studios, music studios, advertising agencies, radio broadcasting, and television. Old media institutions are centralized and communicate with one-way technologies to a generally anonymous mass audience. By definition, it is often dichotomized with New media, more often computer technologies that are interactive and comparatively decentralized; they enable people to telecommunicate with one another, due to their mass use and availability, namely through internet.
Complete measureIn mathematics, a complete measure (or, more precisely, a complete measure space) is a measure space in which every subset of every null set is measurable (having measure zero). More formally, a measure space (X, Σ, μ) is complete if and only if The need to consider questions of completeness can be illustrated by considering the problem of product spaces. Suppose that we have already constructed Lebesgue measure on the real line: denote this measure space by We now wish to construct some two-dimensional Lebesgue measure on the plane as a product measure.
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.
