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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. ...

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 ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

A map f:R^n|->R which assigns each x a scalar function f(x).

Take K a number field and L an Abelian extension, then form a prime divisor m that is divided by all ramified primes of the extension L/K. Now define a map phi_(L/K) from the ...

The field F^_ is called an algebraic closure of F if F^_ is algebraic over F and if every polynomial f(x) in F[x] splits completely over F^_, so that F^_ can be said to ...