Wedemonstrate that a comprehensive nonstandard set theory can be developed in the standard ∈-language. As an illustration, a nonstandard Law of Large Numbers is obtained.

Vop\v{e}nka's Alternative Set Theory can be viewed both as an evolution and a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem's construction of model arithmetic, its inception has been explicitly mentioned attempt to axiomatize Robinson's Nonstandard Analysis. Vop\v{e}nka preferred working in axiomatic theory investigating individual models; he ...

A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the lin...

The obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand,...

We prove some fundamental properties of mu-differentiable functions. A new notion of local minimizer and maximizer is introduced and several extremum conditions are formulated using the language of nonstandard analysis.

BACKGROUND Empirical evidence has demonstrated adverse associations between parental nonstandard work schedules (i.e., evenings, nights, or weekends) and child developmental outcomes. However, there are mixed findings concerning the relationship between parental nonstandard employment and children’s body mass index (BMI), and few studies have incorporated information on paternal work schedules....

The French interrogative system, which allows for variation among several distinct syntactic structures, constitutes a domain in which normative prescription and actual usage differ greatly (Elsig, 2009). Although many sociolinguistic studies have examined this variation (e.g., Ashby, 1977; Behnstedt, 1973; Coveney, 1989, 2002; Fox, 1989; Myers, 2007; Quillard, 2000), most can be characterized ...

In this note, we make two nonstandard group-theoretic observations. First, we give a short nonstandard proof of a well-known result in group theory concerning locally nilpotent groups. Second, we outline a nonstandard way of viewing the projective limit of an projective family of groups. (We are unsure if this second observation, in some form, has already been discovered, although we would not ...

There has been a lot of interest and activity along the general lines of “analysis on metric spaces” recently, as in [2], [3], [26], [40], [41], [46], [48], [49], [51], [82], [83], [89], for instance. Of course this is closely related to and involves ideas concerning “spaces of homogeneous type”, as in [18], [19], [66], [67], [92], as well as subRiemannian spaces, e.g., [8], [9], [34], [47], [5...