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Bessel functions describe the radial part of vibrations of a circular membrane. Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation for an arbitrary complex number , which represents the order of the Bessel function.
In petroleum engineering, the Leverett J-function is a dimensionless function of water saturation describing the capillary pressure, [1] where is the water saturation measured as a fraction, is the capillary pressure (in pascal), is the permeability (measured in m²), is the porosity (0-1), is the surface tension (in N/m) and is the contact angle.
Functional analysis. One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with ...
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 as ...
The Journal of Functional Analysis is a mathematics journal published by Elsevier. Founded by Paul Malliavin, Ralph S. Phillips, and Irving Segal, [ 1] its editors-in-chief are, as of April 2024, Guido De Philippis, Alexandru D. Ionescu and Stefaan Vaes. [ 2]
Functional data analysis (FDA) is a branch of statistics that analyses data providing information about curves, surfaces or anything else varying over a continuum. In its most general form, under an FDA framework, each sample element of functional data is considered to be a random function. The physical continuum over which these functions are ...
Regression analysis. In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there is a non-zero amount of correlation between the residuals in the regression model. GLS is employed to improve statistical efficiency and reduce the risk of drawing erroneous ...
Gerard J. Murphy (November 1948 – 12 October 2006) MRIA was a prolific Irish mathematician. His textbooks are internationally acclaimed, and translated into different languages. His textbooks are internationally acclaimed, and translated into different languages.