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In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

A bilinear basis is a basis, which satisfies the conditions (ax+by)·z=a(x·z)+b(y·z) z·(ax+by)=a(z·x)+b(z·y).

Find necessary and sufficient conditions that determine when the integral curve of two periodic functions kappa(s) and tau(s) with the same period L is a closed curve.

One out of a set of identical observations in a given experiment under identical conditions.

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...

A partial differential diffusion equation of the form (partialU)/(partialt)=kappadel ^2U. (1) Physically, the equation commonly arises in situations where kappa is the ...

In two-dimensional Cartesian coordinates, attempt separation of variables by writing F(x,y)=X(x)Y(y), (1) then the Helmholtz differential equation becomes ...

Let X be an infinite set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A,B in V(X) be finitary algebras with finitely many operations, and ...

The moment problem, also called "Hausdorff's moment problem" or the "little moment problem," may be stated as follows. Given a sequence of numbers {mu_n}_(n=0)^infty, under ...