We present the model theoretic concepts that allow mathematics to be developed with notion of potential infinite instead actual infinite. The is understood as a dynamic notion, being an indefinitely extensible finite. main adoption interpretation universal quantifier, which has implicit reflection principle. Each quantification refers large, but finite set. quantified sets may increase, so afte...

In this paper, time-domain dynamic analysis of dam - infinite reservoir is studied. A numerical method, discrete singular convolution (DSC), which seems to be efficient and simple, has been used to model the mixed boundary conditions. After a brief introduction, DSC is applied to model the equation of motion of fluid-structure with constant cross section subjected to El-Centro (1940) earthquake...

Dyson’s model in infinite dimensions is a system of Brownian particles interacting via logarithmic potential with an inverse temperature $$ \beta = 2$$ . The stochastic process given as solution to infinite-dimensional differential equation. Additionally, Dirichlet form the sine _2$$ point reference measure constructs functional associated configuration-valued diffusion process. In this paper, ...

In this article, we present a fractional order HIV-1 infection model of CD4+ T-cell. We analyze the effect of the changing the average number of the viral particle N with initial conditions of the presented model. The Laplace Adomian decomposition method is applying to check the analytical solution of the problem. We obtain the solutions of the fractional order HIV-1 model in the form of infini...

in this paper, convex semi-infinite programming is converted to an optimal control model of neural networks and the optimal control model is solved by iterative dynamic programming method. in final, numerical examples are provided for illustration of the purposed method.