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The Sombor index of a graph is defined as half the sum of the matrix elements of its Sombor matrix.

Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...

V_t=e^(-ytau)S_tN(d_1)-e^(-rtau)KN(d_2), where N is the cumulative normal distribution and d_1,d_2=(log((S_t)/K)+(r-y+/-1/2sigma^2)tau)/(sigmasqrt(tau)). If y=0, this is the ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally ...

The apodization function A(x)=cos((pix)/(2a)). Its full width at half maximum is 4a/3. Its instrument function is I(k)=(4acos(2piak))/(pi(1-16a^2k^2)), which has a maximum of ...

A polybe is a polyform formed from a polycubes by removing of half of each cube such that at least half of the original join between cubes is retained. The numbers of polybes ...

There are several definitions of a ray. When viewed as a vector, a ray is a vector AB^-> from a point A to a point B. In geometry, a ray is usually taken as a half-infinite ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...