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If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

The term "aliquot divisor" is commonly used to mean two distinct but related things. The first definition is a number that divides another exactly. For instance, 1, 2, 3, and ...

A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial P(x) with real coefficients. (1) Now write the original polynomial as ...