Search Results for ""

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

The curve d(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u).

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

The metric g defined on a nonempty set X by g(x,x) = 0 (1) g(x,y) = 1 (2) if x!=y for all x,y in X. It follows that the open ball of radius r>0 and center at x_0 B(x_0,r)={x ...

A dynamical system in which the phase space volume contracts along a trajectory. This means that the generalized divergence is less than zero, (partialf_i)/(partialx_i)<0, ...

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

sum_(k=-n)^n(-1)^k(n+b; n+k)(n+c; c+k)(b+c; b+k)=(Gamma(b+c+n+1))/(n!Gamma(b+1)Gamma(c+1)), where (n; k) is a binomial coefficient and Gamma(x) is a gamma function.