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A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most ...
In mathematics, an exponential field is a field with a further unary operation that is a homomorphism from the field's additive group to its multiplicative group. This generalizes the usual idea of exponentiation on the real numbers, where the base is a chosen positive real number.
Moore's law. Moore's law is the observation that the number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empirical relationship linked to gains from experience in production.
For example, the transition probabilities from 5 to 4 and 5 to 6 are both 0.5, and all other transition probabilities from 5 are 0. These probabilities are independent of whether the system was previously in 4 or 6. A series of independent states (for example, a series of coin flips) satisfies the formal definition of a Markov chain.
The exponential of X, denoted by eX or exp (X), is the n×n matrix given by the power series. where is defined to be the identity matrix with the same dimensions as . [1] The series always converges, so the exponential of X is well-defined. Equivalently, where I is the n×n identity matrix. When X is an n×n diagonal matrix then exp (X) will be ...
For example, the third equation above means: "For any function f(n) = O(1), there is some function g(n) = O(e n) such that n f(n) = g(n)." In terms of the "set notation" above, the meaning is that the class of functions represented by the left side is a subset of the class of functions represented by the right side.
Gompertz function. The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more ...
Definitions sinh, cosh and tanh csch, sech and coth. There are various equivalent ways to define the hyperbolic functions. Exponential definitions sinh x is half the difference of e x and e −x cosh x is the average of e x and e −x. In terms of the exponential function: Hyperbolic sine: the odd part of the exponential function, that is,