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The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

The Spearman rank correlation coefficient, also known as Spearman's rho, is a nonparametric (distribution-free) rank statistic proposed by Spearman in 1904 as a measure of ...

The Stieltjes integral is a generalization of the Riemann integral. Let f(x) and alpha(x) be real-valued bounded functions defined on a closed interval [a,b]. Take a ...

Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...

Integration by parts is a technique for performing indefinite integration intudv or definite integration int_a^budv by expanding the differential of a product of functions ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...