Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...

In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference ...

The power supply of a space satellite is by means of a radioisotope. The power output, in watts, is given by \({w_t} = {w_o}{e^{kt}}\) where \(t\) is the time in days. The power output at launch is 60 ...

Consider solving the Dirichlet problem $$\Delta u(P) = 0, P \in \mathbb R^2\backslash S,$$ $$u(P) = h(P),\quad P \in S,$$ $$\sup|u(P)| < \infty,$$ $$P \in \Bbb{R}^2 ...

Abstract: We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of Itô stochastic differential equations (SDEs) with ...

Abstract: Lichtenecker's logarithmic mixture formula for dielectrics has proven to be a useful practical formulation for determining the effective permittivity of homogenized dielectric mixtures.