We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square ...

Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the non-uniform point, as well as between the standard point and the nonstandard point, is showed. A new kind of equations, which differ essentially from those in ex...

Longitudinal data from the New Hope Project--an experimental evaluation of a work-based antipoverty program in Milwaukee, Wisconsin--was used to explore concurrent and lagged associations of nonstandard schedules and variable shifts with parental psychological well-being, regularity of family mealtimes, and child well-being among low-income families. Working a combination of variable shifts and...

Much of the world's nonstandard data resides in specialized data sources. This data must often be queried together with data from other sources to give users the information they desire. Queries that can span several specialized sources with diverse search capabilities pose new challenges for query optimization. This paper describes the design and illustrates the use of a general purpose optimi...

and, of course, the zero ideal. Such ideals are referred to as standard ideals. Any other closed ideals are denoted nonstandard ideals. It has been an open question for some time whether there exists any algebra weight {w(n)} such that ^(^(n)) contains a nonstandard ideal [6, p. 189], and the problem seems to go back to Silov (a proposed solution appearing in the literature [6, p. 205] is in er...

Data from the National Institute for Child Health and Human Development (NICHD) Study of Early Child Care (Phase I) and propensity score techniques were used to determine if working fulltime in a nonstandard schedule job during the child's first year predicted parenting practices over 3 years. Results indicated that women who worked fulltime in a nonstandard schedule job during the first year h...

A Riemannian Einstein solvmanifold is called standard, if the orthogonal complement to the nilradical of its Lie algebra is abelian. No examples of nonstandard solvmanifolds are known. We show that the standardness of an Einstein metric solvable Lie algebra is completely detected by its nilradical and prove that many classes of nilpotent Lie algebras (Einstein nilradicals, algebras with less th...

Smarandache (2003) introduced a new set-valued fuzzy logic called (nonstandard) neutrosophic by using Robinson’s nonstandard analysis. However, its definition involved many errors including the illegal use of In this paper, we provide rigorous logic. All in original are addressed. We then point out some paradoxes Finally formulate with no

We show that the supersymmetric nonlinear Schrödinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they con...