Only one pair of distinct positive integers satisfy the equation m^n = n^m
Points: 526 | Comments: 157 | Author: keithmcnulty
Points: 526 | Comments: 157 | Author: keithmcnulty
This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive…
Conditional value-at-risk (CVaR) and value-at-risk, also called the superquantile and quantile, are frequently used to characterize the tails of probability distributions and are popular measures of risk in applications where the distribution represents the magnitude of a potenti…
In 1999 the author suggested an equation to describe the rate and temporal distribution of battle casualties. This equation was proposed as a replacement for the Lanchester equation. Unlike Lanchester's equation, the author's equation is based on a...
The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator equation are gi...
We concern in this paper the graph Kazdan-Warner equation \begin{equation*} Δf=g-he^f \end{equation*} on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational metho...
Characteristic equation may refer to: Characteristic equation (calculus), used to solve linear differential equations Characteristic equation, the equation obtained
This paper examines the properties of the homentropic Euler equations when the characteristics of the equations have been spatially averaged. The new equations are referred to as the characteristically averaged homentropic Euler (CAHE) equations. A...
Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations…
We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations an...
We examine by singularity analysis an equation derived by reduction using Lie point symmetries from the Euler--Bernoulli Beam equation which is the Painlevé--Ince Equation with additional terms. The equation possesses the same leading-order behaviou...
\noindent It is find a non-linear partial differential equation which we show contains the first Heavenly equation of Self-dual gravity and generalize the second one. This differential equation we call "Weak Heavenly Equation" (${\cal WH}$-equation...
In this article we find the solution of the Burger equation with viscosity applying the boundary layer theory. In addition, we will observe that the solution of Burger equation with viscosity converge to the solution of Burger stationary equation in...
This work concerns linearization methods for efficiently solving the Richards` equation,a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media.The discretization of Richards` equation is based on backward Eul...
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the Klein-Gordon equation...
This paper presents a new narrow-stencil finite difference method for approximating the viscosity solution of second order fully nonlinear elliptic partial differential equations including Hamilton-Jacobi-Bellman equations. The proposed finite differ...
We have seen many developments in Marchenko equation-based methods for internal multiple attenuation in the past years. Starting from a wave-equation based method that required a smooth velocity model, there are now Marchenko equation-based methods t...
In this paper, we consider the equivalence of the $p$th moment exponential stability for stochastic differential equations (SDEs), stochastic differential equations with piecewise continuous arguments (SDEPCAs) and the corresponding Euler-Maruyama me...
A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation under Newt...
We show how to reduce the nonlinear Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, to a hierarchy of matrix Riccati equations using the cominuscule induction. The construction works for...