The limiting mass of cold white dwarfs was first calculated by E. Stoner in an approximate model a uniform star and soon reduced ~20% papers S. Chandrasekhar L. D. Landau based on exact solution the equations for stellar equilibrium. Here we examine models taking general relativity effects influence finite temperature into account. Solutions are obtained form analytic formulas and, masses diffe...

One of the most important quantities of the exact Markovian SIS epidemic process is the time-dependent prevalence, which is the average fraction of infected nodes. Unfortunately, the Markovian SIS epidemic model features an exponentially increasing computational complexity with growing network size N . In this paper, we evaluate a recently proposed analytic approximate prevalence function intro...

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

Fragment molecular orbital molecular dynamics (FMO-MD) with periodic boundary conditions is performed on liquid water using the analytic energy gradient, the electrostatic potential point charge approximation, and the electrostatic dimer approximation. Compared to previous FMO-MD simulations of water that used an approximate energy gradient, inclusion of the response terms to provide a fully an...

We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the to Smoluchowski coagulation equation with multiplicative kernel which an analytic solution exists. Our approach is then used approximate non-stationary 3-wave corresponding acoustic systems. validate neural network compare decay rate of to...

The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries ; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave r...

We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqueness of the exact solution in a neighborhood of a numerically computed approximate solution. Our method is based on a fixed-point formulation using the evolution operator, an iterative numerical verification scheme t...