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Exponentiation occurs in many areas of mathematics and its inverse function is often referred to as the logarithm. For example, the logarithm of a matrix is the (multi-valued) inverse function of the matrix exponential. [97] Another example is the p-adic logarithm, the inverse function of the p-adic exponential.
The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.
In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object.A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.
State-transition tables are sometimes one-dimensional tables, also called characteristic tables. They are much more like truth tables than their two-dimensional form. The single dimension indicates inputs, current states, next states and (optionally) outputs associated with the state transitions.
The Bateman equation is a classical master equation where the transition rates are only allowed from one species (i) to the next (i+1) but never in the reverse sense (i+1 to i is forbidden). Bateman found a general explicit formula for the amounts by taking the Laplace transform of the variables.