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The vector field N_f(z)=-(f(z))/(f^'(z)) arising in the definition of the Newtonian graph of a complex univariate polynomial f (Smale 1985, Shub et al. 1988, Kozen and ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

A distribution which arises in the study of integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)-1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)-1) = ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...

Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

Regge calculus is a finite element method utilized in numerical relativity in attempts of describing spacetimes with few or no symmetries by way of producing numerical ...

Differential Equations

A system of equations is any set of simultaneous equations.

The system of ordinary differential equations u^' = A+u^2v-(B+1)u (1) v^' = Bu-u^2v (2) (Hairer et al. 1987, p. 112; Zwillinger 1997, p. 136). The so-called full Brusselator ...