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

The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...

A self-adjoint elliptic differential operator defined somewhat technically as Delta=ddelta+deltad, where d is the exterior derivative and d and delta are adjoint to each ...

In two-dimensional bipolar coordinates, Laplace's equation is ((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0, which simplifies to ...

A submodule L of a module M such that for any other nonzero submodule K of M, the intersection L intersection K is not the zero module. L is also called an essential ...

The statistical index P_L=(sump_nq_0)/(sump_0q_0), where p_n is the price per unit in period n and q_0 is the quantity produced in the initial period.

A generalization of the concept of set unions and intersections.

A distinct (including reflections and rotations) arrangement of adjacent squares on a grid, also called a fixed polyomino.

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.

A lattice embedding is a one-to-one lattice homomorphism.