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The softmax function, also known as softargmax [1] : 184 or normalized exponential function, [2] : 198 converts a vector of K real numbers into a probability distribution of K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and used in multinomial logistic regression. The softmax function is often used ...
Ampère's circuital law. Bernoulli's equation. Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations. Bessel's differential equation. Boltzmann equation. Borda–Carnot equation. Burgers' equation. Darcy–Weisbach equation. Dirac equation.
Smoothstep. Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [4] The function depends on three parameters, the input x, the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
Lanchester's laws are mathematical formulae for calculating the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. [1] [2] In 1915 and 1916 during World War I, M. Osipov [3 ...
The Steinhart–Hart equation is a model relating the varying electrical resistance of a semiconductor to its varying temperatures. The equation is. where. are the Steinhart–Hart coefficients, which are characteristics specific to the bulk semiconductor material over a given temperature range of interest.
Ramberg–Osgood relationship. The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain —that is, the stress–strain curve —in materials near their yield points. It is especially applicable to metals that harden with plastic deformation (see work hardening ), showing a smooth elastic ...
PC-SAFT (perturbed chain SAFT) is an equation of state that is based on statistical associating fluid theory (SAFT). Like other SAFT equations of state, it makes use of chain and association terms developed by Chapman, et al from perturbation theory. [1] However, unlike earlier SAFT equations of state that used unbonded spherical particles as a ...
Root-finding algorithm. In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a function cannot ...
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