A new method of determining eigenvalues and eigenfunctions

Eigenvalues and Eigenfunctions

The article describes the eigenvalue and eigenfunction problems. Basic properties, some applications and examples in system analysis are provided.

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has b...

solution of security constrained unit commitment problem by a new multi-objective optimization method

چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

Eigenvalues and Eigenfunctions of the Laplacian

The problem of determining the eigenvalues and eigenvectors for linear operators acting on finite dimensional vector spaces is a problem known to every student of linear algebra. This problem has a wide range of applications and is one of the main tools for dealing with such linear operators. Some of the results concerning these eigenvalues and eigenvectors can be extended to infinite dimension...