Solution of a transcendental eigenvalue problem via interval analysis

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...

Numerical solution of a quadratic eigenvalue problem

We consider the quadratic eigenvalue problem (QEP) (λ2M + λG + K)x = 0, where M = MT is positive definite, K = KT is negative definite, and G = −GT . The eigenvalues of the QEP occur in quadruplets (λ, λ,−λ,−λ) or in real or purely imaginary pairs (λ,−λ). We show that all eigenvalues of the QEP can be found efficiently and with the correct symmetry, by finding a proper solvent X of the matrix e...

The Transcendental Eigenvalue Problem and Its Application in System Identification

Approximate solution of eigenvalue problem for modal analysis

The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures. The approach is based on transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculati...

An extremal graph problem with a transcendental solution

We prove that the number of multigraphs with vertex set {1, . . . , n} such that every four vertices span at most nine edges is a +o(n) where a is transcendental (assuming Schanuel’s conjecture from number theory). This is an easy consequence of the solution to a related problem about maximizing the product of the edge multiplicities in certain multigraphs, and appears to be the first explicit ...