Abstract This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expansion with deep learning-based algorithm. In particular, mathematical justification on is provided. Numerical examples Kolmogorov PDEs show effectiveness our method.

We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguousl...

the radar cross section of a target plays an important role in the detection of targets by radars‎. ‎this paper presents a new method to predict the bistatic and monostatic rcs of coated electrically large objects. ‎the bodies can be covered by lossy electric and/or magnetic radar absorbing materials (rams)‎. ‎these materials can be approximated by the fresnel reflection coefficients‎. ‎the pro...

The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...

Abstract In this paper, we study the rate of pointwise approximation for neural network operators Kantorovich type. This result is obtained proving a certain asymptotic expansion above and then by establishing Voronovskaja type formula. A central role in resuts played truncated algebraic moments density functions generated suitable sigmoidal functions. Furthermore, to improve convergence, consi...

Abstract We develop an asymptotic expansion for small time of the density solution a non-degenerate system stochastic differential equations with smooth coefficients, and apply this to stepwise approximation solutions. The expansion, which takes form multivariate Edgeworth-type is obtained from Kolmogorov forward equation using some standard PDE results. To generate one step solution, we use Co...

In this article, we present the analytical solution of the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenv...