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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 * Mental calculation, Approximating natural exponents (log base e) * Artin–Hasse exponential Talk:Artin–Hasse exponential, * Bacterial growth Talk:Bacterial growth, * Baker–Campbell–Hausdorff formula * Cell growth Talk:Cell growth, * Barometric formula Talk:Barometric formula, * Beer–Lambert law Talk:Beer–Lambert law, * Characterizations of the exponential function Talk:Characterizations of the exponential function, * Catenary Talk:Catenary, * Compound interest Talk:Compound interest, * De Moivre's formula Talk:de Moivre's formula, * Derivative of the exponential map Talk:Derivative of the exponential map, * Doléans-Dade exponential Talk:Doléans-Dade exponential, * Doubling time Talk:Doubling time, * e-folding, ''e''-folding Talk:e-folding, * Elimination half-life Talk:Elimination half-life, * Error expone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
List Of Logarithm Topics
A list is a set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of the list-maker, but lists are frequently written down on paper, or maintained electronically. Lists are "most frequently a tool", and "one does not ''read'' but only ''uses'' a list: one looks up the relevant information in it, but usually does not need to deal with it as a whole".Lucie Doležalová,The Potential and Limitations of Studying Lists, in Lucie Doležalová, ed., ''The Charm of a List: From the Sumerians to Computerised Data Processing'' (2009). Purpose It has been observed that, with a few exceptions, "the scholarship on lists remains fragmented". David Wallechinsky, a co-author of ''The Book of Lists'', described the attraction of lists as being "because we live in an era of overstimulation, especially in terms of information, and lists help us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
E-folding
In science, ''e''-folding is the time interval in which an exponentially growing quantity increases or decreases 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, theoretical physics, and cosmology. In cosmology the ''e''-folding time scale is the proper time in which the length of a patch of space or spacetime increases by the factor ''e''. In finance, the logarithmic return or continuously compounded return, also known as force of interest, is the reciprocal of the ''e''-folding time. The process of evolving to equilibrium is often characterized by a time scale called the ''e''-folding time, ''τ''. This time is used for processes which evolve exponentially toward a final state (equilibrium). In other words, if we examine an observable, ''X'', associated with a system, (temperature or density, for example) then after a time, ''τ'', the initial difference bet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 \Bigl(\_^ \Bigr) = \sum_^ \delta^(u(c_t)) where is consumption at time , is the exponential discount factor, and is the instantaneous utility function. In continuous time, exponential discounting is given by U \Bigl(\_^ \Bigl) = \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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Exponential Dichotomy
In the mathematics, mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolic equilibrium point, hyperbolicity to non-autonomous system (mathematics), autonomous systems. Definition If :\dot = A(t)\mathbf is a linear system, 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 (mathematics), matrix ''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 ''spectral window'' of the equilibrium point, (−α, β). Explanation The matrix ''P'' is a projection onto the stable subspace and ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 Lambda (; uppercase , lowercase ; , ''lám(b)da'') is the eleventh letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoen ...) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N(t). The solution to this equation (see #Solution_of_the_differential_equation, 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 (mathematics), se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. For example, if a smartphone app fails to connect to its server, it might try again 1 second later, then if it fails again, 2 seconds later, then 4, etc. Each time the pause is multiplied by a fixed amount (in this case 2). In this case, the adverse event is failing to connect to the server. Other 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 exponenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Exponent Bias
In 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, 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 purpose of this is to enable high sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Exponent
In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_.In particular, b^1=b. The exponent is usually shown as a superscript to the right of the base as or in computer code as b^n. This binary operation is often read as " to the power "; it may also be referred to as " raised to the th power", "the th power of ", or, most briefly, " to the ". The above definition of b^n immediately implies several properties, in particular the multiplication rule:There are three common notations for multiplication: x\times y is most commonly used for explicit numbers and at a very elementary level; xy is most common when variables are used; x\cdot y is used for emphasizing that one talks of multiplication or when omitting the multiplication sign would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
E (mathematical Constant)
The number is a mathematical constant approximately equal to 2.71828 that is the base of a logarithm, base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted \gamma. Alternatively, can be called Napier's constant after John Napier. The Swiss mathematician Jacob Bernoulli discovered the constant while studying compound interest. The number is of great importance in mathematics, alongside 0, 1, Pi, , and . All five appear in one formulation of Euler's identity e^+1=0 and play important and recurring roles across mathematics. Like the constant , is Irrational number, irrational, meaning that it cannot be represented as a ratio of integers, and moreover it is Transcendental number, transcendental, meaning that it is not a root of any non-zero polynomial with rational coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Euler's Identity
In mathematics, Euler's identity (also known as Euler's equation) is the Equality (mathematics), equality e^ + 1 = 0 where :e is E (mathematical constant), Euler's number, the base of natural logarithms, :i is the imaginary unit, which by definition satisfies i^2 = -1, and :\pi 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 x = \pi. Euler's identity is considered 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 Lindemann–Weierstrass theorem#Transcendence of e and π, a proof that is Transcendental number, 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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
