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Find necessary and sufficient conditions that determine when the integral curve of two periodic functions kappa(s) and tau(s) with the same period L is a closed curve.

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

A linear functional on a smooth differential form.

A power of 10.

The elliptic lambda function lambda(tau) is a lambda-modular function defined on the upper half-plane by lambda(tau)=(theta_2^4(0,q))/(theta_3^4(0,q)), (1) where tau is the ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

If (1+xsin^2alpha)sinbeta=(1+x)sinalpha, then (1+x)int_0^alpha(dphi)/(sqrt(1-x^2sin^2phi))=int_0^beta(dphi)/(sqrt(1-(4x)/((1+x)^2)sin^2phi)).

If a Sylow 2-subgroup T of G lies in a unique maximal 2-local P of G, then P is a "strongly embedded" subgroup of G, and G is known.

A circle-preserving transformation composed of an even number of inversions.

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the local discrepancy is defined as D(J,P)=|(number of x_n in J)/N-Vol(J)|, Vol(J) is the ...