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E(a,b)/p denotes the elliptic group modulo p whose elements are 1 and infty together with the pairs of integers (x,y) with 0<=x,y<p satisfying y^2=x^3+ax+b (mod p) (1) with a ...

The second singular value k_2, corresponding to K^'(k_2)=sqrt(2)K(k_2), (1) is given by k_2 = tan(pi/8) (2) = sqrt(2)-1 (3) k_2^' = sqrt(2)(sqrt(2)-1). (4) For this modulus, ...

An odd Mathieu function se_r(z,q) with characteristic value a_r.

A catastrophe which can occur for three control factors and two behavior axes. The elliptical umbilic is catastrophe of codimension 3 that has the equation ...

The Elsasser function is defined by the integral E(y,u)=int_(-1/2)^(1/2)exp[-(2piyusinh(2piy))/(cosh(2piy)-cos(2pix))]dx. (1) Special values include E(0,u) = 1 (2) E(y,0) = ...

A knot K is an n-embeddable knot if it can be placed on a genus n standard embedded surface without crossings, but K cannot be placed on any standardly embedded surface of ...

The second-order ordinary differential equation (x^2y^')^'+x^2y^n=0.

An endogenous variable is an economic variable that is related to other economic variables and determines their equilibrium levels.

Given a module M over a unit ring R, the set End_R(M) of its module endomorphisms is a ring with respect to the addition of maps, (f+g)(x)=f(x)+g(x), for all x in M, and the ...

A modular form which is not allowed to have poles in the upper half-plane H or at iinfty.