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Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior. It also describes the ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...

Using disk point picking, x = sqrt(r)costheta (1) y = sqrt(r)sintheta (2) for r in [0,1], theta in [0,2pi), choose two points at random in a unit disk and find the ...

The W polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. (The corresponding w polynomials are called Lucas polynomials.) They have explicit ...

A bridge of a connected graph is a graph edge whose removal disconnects the graph (Chartrand 1985, p. 45; Skiena 1990, p. 177). More generally, a bridge is an edge of a ...