List of exponential topics
Encyclopedia
This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics.
- Accelerating changeAccelerating changeIn futures studies and the history of technology, accelerating change is a perceived increase in the rate of technological progress throughout history, which may suggest faster and more profound change in the future...
- Artin–Hasse exponential
- Bacterial growthBacterial growth250px|right|thumb|Growth is shown as L = log where numbers is the number of colony forming units per ml, versus T Bacterial growth is the division of one bacterium into two daughter cells in a process called binary fission. Providing no mutational event occurs the resulting daughter cells are...
- Baker–Campbell–Hausdorff formula
- Cell growthCell growthThe term cell growth is used in the contexts of cell development and cell division . When used in the context of cell division, it refers to growth of cell populations, where one cell grows and divides to produce two "daughter cells"...
- Barometric formulaBarometric formulaThe barometric formula, sometimes called the exponential atmosphere or isothermal atmosphere, is a formula used to model how the pressure of the air changes with altitude.-Pressure equations:...
- Basic infection number
- Beer–Lambert law
- Characterizations of the exponential functionCharacterizations of the exponential functionIn mathematics, the exponential function can be characterized in many ways. The following characterizations are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other...
- CatenaryCatenaryIn physics and geometry, the catenary is the curve that an idealised hanging chain or cable assumes when supported at its ends and acted on only by its own weight. The curve is the graph of the hyperbolic cosine function, and has a U-like shape, superficially similar in appearance to a parabola...
- Compound interestCompound interestCompound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
- De Moivre's formulaDe Moivre's formulaIn mathematics, de Moivre's formula , named after Abraham de Moivre, states that for any complex number x and integer n it holds that...
- Doléans-Dade exponentialDoléans-Dade exponentialIn stochastic calculus, the Doléans-Dade exponential, Doléans exponential, or stochastic exponential, of a semimartingale X is defined to be the solution to the stochastic differential equation with initial condition . The concept is named after Catherine Doléans-Dade...
- Elimination half-life
- Error exponentError exponentIn information theory, the error exponent of a channel code or source code over the block length of the code is the logarithm of the error probability. For example, if the probability of error of a decoder drops as e–nα, where n is the block length, the error exponent is α...
- Exponential factorialExponential factorialAn exponential factorial is a positive integer n raised to the power of n − 1, which in turn is raised to the power of n − 2, and so on and so forth, that is,...
- Euler's formulaEuler's formulaEuler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the deep relationship between the trigonometric functions and the complex exponential function...
- Euler's identity
- e (mathematical constant)E (mathematical constant)The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
- Exponent
- Exponent biasExponent biasIn IEEE 754 floating point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias....
- Exponential (disambiguation)
- Exponential backoffExponential backoffExponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate.-Binary exponential backoff / truncated exponential backoff:...
- Exponential decay
- Exponential dichotomy
- Exponential discounting
- Exponential diophantine equation
- Exponential dispersion modelExponential dispersion modelExponential dispersion models are statistical models in which the probability distribution is of a special form. This class of models represents a generalisation of the exponential family of models which themselves play an important role in statistical theory because they have a special structure...
- Exponential distributionExponential distributionIn probability theory and statistics, the exponential distribution is a family of continuous probability distributions. It describes the time between events in a Poisson process, i.e...
- Exponential errorExponential errorExponential error is an idea expressing how a very small error can compound itself over time. It can be characterized as the exponential growth of an error or the application of exponential growth in terms of an error.- See also :*Exponential growth...
- Exponential familyExponential familyIn probability and statistics, an exponential family is an important class of probability distributions sharing a certain form, specified below. This special form is chosen for mathematical convenience, on account of some useful algebraic properties, as well as for generality, as exponential...
- Exponential fieldExponential fieldIn mathematics, an exponential field is a field that has an extra operation on its elements which extends the usual idea of exponentiation.-Definition:...
- Exponential formulaExponential formulaIn combinatorial mathematics, the exponential formula states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.The exponential formula is a power-series version of a special case of Faà di...
- Exponential functionExponential functionIn mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
- Exponential generating function
- Exponential-Golomb codingExponential-Golomb codingAn exponential-Golomb code of order k is a type of universal code, parameterized by a nonnegative integer k. To encode a nonnegative integer in an order-k exp-Golomb code, one can use the following method:...
- Exponential growthExponential growthExponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
- Exponential hierarchy
- Exponential integralExponential integralIn mathematics, the exponential integral is a special function defined on the complex plane given the symbol Ei.-Definitions:For real, nonzero values of x, the exponential integral Ei can be defined as...
- Exponential mapExponential mapIn differential geometry, the exponential map is a generalization of the ordinary exponential function of mathematical analysis to all differentiable manifolds with an affine connection....
- Exponential notation
- Exponential objectExponential objectIn mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories...
(category theoryCategory theoryCategory theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
) - Exponential polynomials—see also Touchard polynomials (combinatoricsCombinatoricsCombinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
) - Exponential sheaf sequenceExponential sheaf sequenceIn mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry.Let M be a complex manifold, and write OM for the sheaf of holomorphic functions on M. Let OM* be the subsheaf consisting of the non-vanishing holomorphic functions. These are...
- Exponential smoothingExponential smoothingExponential smoothing is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random process, or it may be an...
- Exponential stability
- Exponential sumExponential sumIn mathematics, an exponential sum may be a finite Fourier series , or other finite sum formed using the exponential function, usually expressed by means of the functione = \exp.\,...
- Exponential time
- Sub-exponential time
- Exponential timeline
- Exponential treeExponential treeAn exponential tree is almost identical to a binary search tree, with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimension of 1, and has 2d children. In an exponential tree, the dimension equals the depth of the node,...
- Exponentially equivalent measuresExponentially equivalent measuresIn mathematics, the notion of exponential equivalence of measures is a concept that describes how two sequences or families of probability measures are “the same” from the point of view of large deviations theory.-Definition:...
- Exponentiating by squaring
- Gaussian function
- Gudermannian function
- Half-lifeHalf-lifeHalf-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...
- Hyperbolic functionHyperbolic functionIn mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" , and the hyperbolic cosine "cosh" , from which are derived the hyperbolic tangent "tanh" and so on.Just as the points form a...
- InflationInflationIn economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...
, inflation rateInflation rateIn economics, the inflation rate is a measure of inflation, the rate of increase of a price index . It is the percentage rate of change in price level over time. The rate of decrease in the purchasing power of money is approximately equal.The inflation rate is used to calculate the real interest...
- InterestInterestInterest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
- Lifetime (physics)
- Limiting factorLimiting factorA limiting factor or limiting resource is a factor that controls a process, such as organism growth or species population, size, or distribution. The availability of food, predation pressure, or availability of shelter are examples of factors that could be limiting for an organism...
- Lindemann–Weierstrass theoremLindemann–Weierstrass theoremIn mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if 1, ..., are algebraic numbers which are linearly independent over the rational numbers ', then 1, ..., are algebraically...
- List of integrals of exponential functions
- List of integrals of hyperbolic functions
- Lyapunov exponentLyapunov exponentIn mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories...
- Malthusian catastropheMalthusian catastropheA Malthusian catastrophe was originally foreseen to be a forced return to subsistence-level conditions once population growth had outpaced agricultural production...
- Malthusian growth modelMalthusian growth modelThe Malthusian growth model, sometimes called the simple exponential growth model, is essentially exponential growth based on a constant rate of compound interest...
- Matrix exponentialMatrix exponentialIn mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group....
- Moore's lawMoore's LawMoore's law describes a long-term trend in the history of computing hardware: the number of transistors that can be placed inexpensively on an integrated circuit doubles approximately every two years....
- Nachbin's theoremNachbin's theoremIn mathematics, in the area of complex analysis, Nachbin's theorem is commonly used to establish a bound on the growth rates for an analytic function. This article will provide a brief review of growth rates, including the idea of a function of exponential type...
- p-adic exponential functionP-adic exponential functionIn mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers...
- Power lawPower lawA power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
- Proof that e is irrationalProof that e is irrationalIn mathematics, the series representation of Euler's number ecan be used to prove that e is irrational. Of the many representations of e, this is the Taylor series for the exponential function evaluated at y = 1.-Summary of the proof:...
- Proof that e is transcendentalLindemann–Weierstrass theoremIn mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if 1, ..., are algebraic numbers which are linearly independent over the rational numbers ', then 1, ..., are algebraically...
- Q-exponential
- Radioactive decayRadioactive decayRadioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...
- Rule of 70, Rule of 72Rule of 72In finance, the rule of 72, the rule of 70 and the rule of 69 are methods for estimating an investment's doubling time. The rule number is divided by the interest percentage per period to obtain the approximate number of periods required for doubling...
- Six exponentials theoremSix exponentials theoremIn mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a set of exponentials.-Statement:...
- Spontaneous emissionSpontaneous emissionSpontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...
- Super-exponentiation
- TetrationTetrationIn mathematics, tetration is an iterated exponential and is the next hyper operator after exponentiation. The word tetration was coined by English mathematician Reuben Louis Goodstein from tetra- and iteration. Tetration is used for the notation of very large numbers...
- Versor
- Wilkie's theoremWilkie's theoremIn mathematics, Wilkie's theorem is a result by Alex Wilkie about the theory of ordered fields with an exponential function, or equivalently about the geometric nature of exponential varieties.-Formulations:...
- ZenzizenzizenzicZenzizenzizenzicZenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number , dating from a time when powers were written out in words rather than as superscript numbers...