‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

‎In this paper‎, ‎we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells‎. ‎We study the effect of ‎the changing the average number of viral particles $N$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎The nonstandard finite difference (NSFD) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order HIV-1‎ ‎...

We show that in an ultraproduct of finite fields, the mod-n nonstandard size definable sets varies definably families. Moreover, if K is any pseudofinite field, then one can assign “nonstandard sizes mod n” to K. As n varies, these assemble into a strong Euler characteristic on K, taking values profinite completion \(\hat {\mathbb{Z}}\) integers. The not canonical, but depends choice Frobenius....

Introduction  The P300 test requires well-defined and unique criteria, in addition to training for the examiners, for a uniform analysis of studies and to avoid variations and errors in the interpretation of measurement results. Objectives  The objective of this study is to verify whether there are differences in P300 with and without subtraction of traces of standard and nonstandard stimuli. M...

I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a suitable expansion would imply that, assuming a one-way permutation exists, the computational class NP is not closed under complementation. Consider the foll...