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List Of Exponential Topics
{{Short description, none This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics. * Accelerating change * Approximating natural exponents (log base e) * Artin–Hasse exponential * Bacterial growth * Baker–Campbell–Hausdorff formula * Cell growth * Barometric formula * Beer–Lambert law * Characterizations of the exponential function * Catenary * Compound interest * De Moivre's formula * Derivative of the exponential map * Doléans-Dade exponential * Doubling time * ''e''-folding * Elimination half-life * Error exponent * Euler's formula * Euler's identity * e (mathematical constant) * Exponent * Exponent bias * Exponential (other) * Exponential backoff * Exponential decay * Exponential dichotomy * Exponential discounting * Exponential diophantine equation * Exponential dispersion model * Exponential distribution * Exponential error * Expone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Logarithm Topics
{{Short description, None This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics. * Acoustic power * Antilogarithm * Apparent magnitude * Baker's theorem * Bel (unit), Bel * Benford's law * Binary logarithm * Bode plot * Henry Briggs (mathematician), Henry Briggs * Bygrave slide rule * Cologarithm * Common logarithm * Complex logarithm * Discrete logarithm ** Discrete logarithm records * e (mathematical constant), e ** Representations of e * El Gamal discrete log cryptosystem * Harmonic series (mathematics), Harmonic series * History of logarithms * Hyperbolic sector * Iterated logarithm * Otis King * Law of the iterated logarithm * Linear form in logarithms * Linearithmic * List of integrals of logarithmic functions * Logarithmic growth * Logarithmic timeline * Log-likelihood ratio * Log-log, Log-log graph * Log-normal distribution * Log-periodic antenna * Log-Weibull distribution * Logarithmic algorithm * Logarithmic convolution * Logarithmic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E-folding
In science, ''e''-folding is the time interval in which an exponentially growing quantity increases by a factor of ''e''; it is the base-''e'' analog of doubling time. This term is often used in many areas of science, such as in atmospheric chemistry, medicine and theoretical physics, especially when cosmic inflation is investigated. Physicists and chemists often talk about the ''e''-folding time scale that is determined by the proper time in which the length of a patch of space or spacetime increases by the factor ''e'' mentioned above. In finance, the logarithmic return or continuously compounded return, also known as force of interest, is the reciprocal of the ''e''-folding time. The term ''e''-folding time is also sometimes used similarly in the case of exponential decay, to refer to the timescale for a quantity to decrease to 1/''e'' of its previous value. The process of evolving to equilibrium is often characterized by a time scale called the ''e''-folding time, '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Discounting
In economics exponential discounting is a specific form of the discount function, used in the analysis of choice over time (with or without uncertainty). Formally, exponential discounting occurs when total utility is given by :U(\_^)=\sum_^\delta^(u(c_t)), where ''c''''t'' is consumption at time ''t'', \delta is the exponential discount factor, and ''u'' is the instantaneous utility function. In continuous time, exponential discounting is given by :U(\_^)=\int_^ e^u(c(t))\,dt, Exponential discounting implies that the marginal rate of substitution between consumption at any pair of points in time depends only on how far apart those two points are. Exponential discounting is not dynamically inconsistent. A key aspect of the exponential discounting assumption is the property of dynamic consistency— preferences are constant over time. In other words, preferences do not change with the passage of time unless new information is presented. For example, consider an investment op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Dichotomy
In the mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity to non- autonomous systems. Definition If :\dot = A(t)\mathbf is a linear non-autonomous dynamical system in R''n'' with fundamental solution matrix Φ(''t''), Φ(0) = ''I'', then the equilibrium point 0 is said to have an ''exponential dichotomy'' if there exists a (constant) matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ... ''P'' such that ''P''2 = ''P'' and positive constants ''K'', ''L'', α, and β such that :, , \Phi(t) P \Phi^(s) , , \le Ke^\mboxs \le t -\infty. If furthermore, ''L'' = 1/''K'' and β = α, then 0 is said to have a ''uniform exponential dichotomy''. The constants α and β allow us to define the '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N. The solution to this equation (see derivation below) is: :N(t) = N_0 e^, where is the quantity at time , is the initial quantity, that is, the quantity at time . Measuring rates of decay Mean lifetime If the decaying quantity, ''N''(''t''), is the number of discrete elements in a certain set, it is possible to compute the average length of time that an element remains in the set. This is called the mean lifetime (or simply the lifetime), where the exponential time constant, \tau, relates to the decay rate constant, λ, in the following way: :\tau = \frac. The mean lifetime can be looked at as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Backoff
Exponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate. These algorithms find usage in a wide range of systems and processes, with radio networks and computer networks being particularly notable. Exponential backoff algorithm An exponential backoff algorithm is a form of closed-loop control system that reduces the rate of a controlled process in response to adverse events. Each time an adverse event is encountered, the rate of the process is reduced by some multiplicative factor. Examples of adverse events include collisions of network traffic, an error response from a service, or an explicit request to reduce the rate (i.e. "back off"). The rate reduction can be modelled as an exponential function: :t = b^c or :f = \frac Here, is the time delay applied between actions, is the multiplicative factor or "base", is the number of adverse events observed, and is the frequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential
Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exponential discounting, a specific form of the discount function, used in the analysis of choice over time *Exponential growth, where the growth rate of a mathematical function is proportional to the function's current value *Exponential map (Riemannian geometry), in Riemannian geometry * Exponential map (Lie theory), in Lie theory * Exponential notation, also known as scientific notation, or standard form *Exponential object, in category theory *Exponential time, in complexity theory *in probability and statistics: ** Exponential distribution, a family of continuous probability distributions **Exponentially modified Gaussian distribution, describes the sum of independent normal and exponential random variables **Exponential family, a paramet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential (other)
Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above *Exponential decay, decrease at a rate proportional to value *Exponential discounting, a specific form of the discount function, used in the analysis of choice over time *Exponential growth, where the growth rate of a mathematical function is proportional to the function's current value *Exponential map (Riemannian geometry), in Riemannian geometry *Exponential map (Lie theory), in Lie theory *Exponential notation, also known as scientific notation, or standard form *Exponential object, in category theory *Exponential time, in complexity theory *in probability and statistics: **Exponential distribution, a family of continuous probability distributions **Exponentially modified Gaussian distribution, describes the sum of independent normal and exponential random variables **Exponential family, a parametric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponent Bias
In IEEE 754 Floating-point arithmetic, floating-point numbers, the exponent is biased in the biasing, engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent. Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder. To solve this problem the exponent is stored as an unsigned value which is suitable for comparison, and when being interpreted it is converted into an exponent within a signed range by subtracting the bias. By arranging the fields such that the sign bit takes the most significant bit position, the biased exponent takes the middle position, then the significand will be the least significant bits and the resulting value will be ordered properly. This is the case whether or not it is interpreted as a floating-point or integer value. The pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponent
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E (mathematical Constant)
The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithms. It is the limit of as approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series e = \sum\limits_^ \frac = 1 + \frac + \frac + \frac + \cdots. It is also the unique positive number such that the graph of the function has a slope of 1 at . The (natural) exponential function is the unique function that equals its own derivative and satisfies the equation ; hence one can also define as . The natural logarithm, or logarithm to base , is the inverse function to the natural exponential function. The natural logarithm of a number can be defined directly as the area under the curve between and , in which case is the value of for which this area equals one (see image). There are various other characteriz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality e^ + 1 = 0 where : is Euler's number, the base of natural logarithms, : is the imaginary unit, which by definition satisfies , and : is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula e^ = \cos x + i\sin x when evaluated for . Euler's identity is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof that is transcendental, which implies the impossibility of squaring the circle. Mathematical beauty Euler's identity is often cited as an example of deep mathematical beauty. Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
