Discussions are presented by Morita and Sato on the problem of obtaining particular solution an inhomogeneous differential equation with polynomial coefficients in terms Green's function. In present paper, is given without using function, basis nonstandard analysis. It applied to hypergeometric, Hermite, a simple ordinary fractional equation.

OBJECTIVES The effect of employment insecurity on employee health is an important public health issue due to the recent effects of neoliberalism and the global financial crisis (2007-2008) on labor markets. This study aims to evaluate the differences in cardiovascular health status and the use of preventive screening services between standard and nonstandard workers. METHODS Waged employees (...

We use the insights of Robinson’s nonstandard analysis as a powerful tool to extend and simplify the construction of compactifications of regular spaces. In particular, we deal with the Stone-Čech compactification and compactifications formed from topological ends. For the nonstandard extension of a metric space, the monad of a standard point x is the set of all points infinitesimally close to ...

In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorical properties are well behaved under enlargements.

Previously, the authors used insights of Robinson's nonstandard analysis as a powerful tool to extend and simplify construction some compactifications regular spaces. They now show that any Hausdorff compactification is obtainable with their method.

Abstract. We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic L transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time evolution operator. The derivation will be for all self-adjoint nonvector potential Hamiltonians. For systems with potential that carries at most a finite num...

An important open problem in Reverse Mathematics ([16, 25]) is the reduction of the first-order strength of the base theory from IΣ1 to I∆0 + exp. The system ERNA, a version of Nonstandard Analysis based on the system I∆0 + exp, provides a partial solution to this problem. Indeed, Weak König’s lemma and many of its equivalent formulations from Reverse Mathematics can be ‘pushed down’ into ERNA,...

Abstract In functional analysis, there are different notions of limit for a bounded sequence $$L^1$$ L 1 functions. Besides the pointwise limit, that does not always exist, behaviour functions can be described in terms its weak- $$\star $$ ⋆ or by intro...

The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are absent either from mathematical elegance or from practical usefulness. The aim of this paper is to exhibit a not only mathematically elegant but also practic...