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The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

A principal vertex x_i of a simple polygon P is called a mouth if the diagonal [x_(i-1),x_(i+1)] is an extremal diagonal (i.e., the interior of [x_(i-1),x_(i+1)] lies in the ...

A necessary and sufficient condition that [alpha^'] should be comparable with [alpha] for all positive values of the a is that one of (alpha^') and (alpha) should be ...

A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

An arrangement of n>=3 points such that n-1 of them are collinear.

If m is an integer, then for every residue class r (mod m), there are infinitely many nonnegative integers n for which P(n)=r (mod m), where P(n) is the partition function P.

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...