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List Of Mathematical Abbreviations
This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology. :''This list is limited to abbreviations of two or more letters. The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations.'' : * AC – Axiom of Choice, or set of absolutely continuous functions. * a.c. – absolutely continuous. * acrd – inverse chord function. * ad – adjoint representation (or adjoint action) of a Lie group. * adj – adjugate of a matrix. * a.e. – almost everywhere. * Ai – Airy function. * AL – Action limit. * Alt – alternating group (Alt(''n'') ''is also written as'' A''n''.) * A.M. – arithmetic mean. * arccos – inverse cosine function. * arccosec – inverse cosecant function. (''Also written as'' arccsc.) * arccot – inverse cotangent function. * arccsc – inverse cosecant function. (''Also written as'' arccosec.) * arcexc – inve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom Of Choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family (S_i)_ of nonempty sets, there exists an indexed set (x_i)_ such that x_i \in S_i for every i \in I. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. In many cases, a set arising from choosing elements arbitrarily can be made without invoking the axiom of choice; this is, in particular, the case if the number of sets from which to choose the elements is finite, or if a canonical rule on how to choose the elements is available – some distinguis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Hyperbolic Cosine
In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola , or twice the area of the corresponding sector of the unit hyperbola , just as a circular angle is twice the area of the circular sector of the unit circle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. It also occurs in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almost Surely
In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. The concept is analogous to the concept of "almost everywhere" in measure theory. In probability experiments on a finite sample space, there is no difference between ''almost surely'' and ''surely'' (since having a probability of 1 often entails including all the sample points). However, this distinction becomes important when the sample space is an infinite set, because an infinite set can have non-empty subsets of probability 0. Some examples of the use of this concept include the strong and uniform versions of the law of large numbers, and the continuity of the paths of Brownian motion. The terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Hyperbolic Tangent
In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola , or twice the area of the corresponding sector of the unit hyperbola , just as a circular angle is twice the area of the circular sector of the unit circle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. It also occurs in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Hyperbolic Sine
In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola , or twice the area of the corresponding sector of the unit hyperbola , just as a circular angle is twice the area of the circular sector of the unit circle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. It also occurs in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Hyperbolic Secant
In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola , or twice the area of the corresponding sector of the unit hyperbola , just as a circular angle is twice the area of the circular sector of the unit circle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. It also occurs in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arg Min
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized.For clarity, we refer to the input (''x'') as ''points'' and the output (''y'') as ''values;'' compare critical point and critical value. In contrast to global maxima, which refers to the largest ''outputs'' of a function, arg max refers to the ''inputs'', or arguments, at which the function outputs are as large as possible. Definition Given an arbitrary set a totally ordered set and a function, the \operatorname over some subset S of X is defined by :\operatorname_S f := \underset\, f(x) := \. If S = X or S is clear from the context, then S is often left out, as in \underset\, f(x) := \. In other words, \operatorname is the set of points x for which f(x) attains the function's largest value (if it exists). \operatorname may be the empty set, a singleton, or contain multiple elements. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arg Max
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized.For clarity, we refer to the input (''x'') as ''points'' and the output (''y'') as ''values;'' compare critical point and critical value. In contrast to global maxima, which refers to the largest ''outputs'' of a function, arg max refers to the ''inputs'', or arguments, at which the function outputs are as large as possible. Definition Given an arbitrary set a totally ordered set and a function, the \operatorname over some subset S of X is defined by :\operatorname_S f := \underset\, f(x) := \. If S = X or S is clear from the context, then S is often left out, as in \underset\, f(x) := \. In other words, \operatorname is the set of points x for which f(x) attains the function's largest value (if it exists). \operatorname may be the empty set, a singleton, or contain multiple elements. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arg (mathematics)
In mathematics (particularly in complex analysis), the argument of a complex number ''z'', denoted arg(''z''), is the angle between the positive real axis and the line joining the origin and ''z'', represented as a point in the complex plane, shown as \varphi in Figure 1. It is a multi-valued function operating on the nonzero complex numbers. To define a single-valued function, the principal value of the argument (sometimes denoted Arg ''z'') is used. It is often chosen to be the unique value of the argument that lies within the interval . Definition An argument of the complex number , denoted , is defined in two equivalent ways: #Geometrically, in the complex plane, as the 2D polar angle \varphi from the positive real axis to the vector representing . The numeric value is given by the angle in radians, and is positive if measured counterclockwise. #Algebraically, as any real quantity \varphi such that z = r (\cos \varphi + i \sin \varphi) = r e^ for some positive rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Tangent
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry. Notation Several notations for the inverse trigonometric functions exist. The most common convention is to name inverse trigonometric functions using an arc- prefix: , , , etc. (This convention is used throughout this article.) This notation arises from the following geometric relationships: when measuring in radians, an angle of ''θ'' radians will correspond to an arc whose length is ''rθ'', where ''r'' is the radius of the circle. Thus in the unit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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