The straightforward algebraic method is to equate X(s) = Y(t) and solve for the parameters s and t. Observe that the vector equation yields two polynomial equations of degree max{n, m} in the two unknowns s and t. The method of elimination may be used to obtain a single polynomial ...
The Eikonal equation is defined as an equation on a computational domain where the gradient of a function is equal to a given function, with boundary values prescribed on the boundary of the domain. It is used to propagate information from the boundary to the rest of the domain through a se...
Let us then denote the unknown scalar function of the tensor equation \(\varphi _u\) (instead of \(\bar{\xi }\psi \)). Then let us choose any constant antisymmetric second-rank tensor \(v^{\mu \nu }\) satisfying the following conditions: $$\begin{aligned}{} & {} \left( v^{...
Full size table The residual part of the Helmholtz energy considers intermolecular forces that lead to non-ideal behavior. Therefore, the residual part describes the deviation from ideal-gas behavior. While the ideal part is physically based, the residual part is an empirical formulation. For THF,...
3, 85. Introduction to Plane and Solid Loci, as translated by Joseph Seidlin in David E. Smith(ed.)A Source Book in Mathematics (1959), 389. Alternate translation using Google Translate: “Whenever in a final equation there are two unknown quantities, there is a locus, the end of one ...
Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) ...
We then apply the fourth order Ronge-Kutta method to the closed moment system and the first-order and the second-order moments are solved. Results It is generally hard to determine the unknown rate constants of oligomer growth. For simplicity, we assume all the polymerization rates are ...
Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer’s update step. However, many such functions cannot be implemented by any master equation, even approxi
The statistical problem is one of estimating the unknown parameters in θ, and evaluating whether the population means μ and covariances Σ are consistent with the null hypothesis or whether μ≠μ(θ) and/or Σ≠Σ(θ). This notation can be made even more compact by arranging β = {μ...
To solve this equation for calculating surface free energy, there are three unknown parameters. So, at least the surface tension data of three liquids must be used. γL(1+cosθ)=2γLLWγSLW+2γL+γS−+2γL−γS+ Show moreView chapterExplore book A molecular dynamics study of ...