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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 ...

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 ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

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, ...

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...

A chord which is a normal at each end. A centrosymmetric set K subset R^d has d double normals through the center (Croft et al. 1991). For a curve of constant width, all ...

Down arrow notation is an inverse of the Knuth up-arrow notation defined by evn = lnn (1) evvn = ln^*n (2) evvvn = ln^(**)n, (3) where ln^*n is the number of times the ...

A term in social choice theory meaning each alternative receives equal weight for a single vote.