Solution of a Diophantine problem

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...

A Solution to a Problem of Cassels and Diophantine Properties of Cubics

We prove that almost any pair of real numbers α, β, satisfies the following inhomogeneous uniform version of Littlewood’s conjecture: For any real γ, δ, lim inf |n|→∞ n〈nα− γ〉〈nβ − δ〉 = 0, (0.1) where 〈·〉 denotes the distance from the nearest integer. The existence of even a single pair that satisfies (0.1), solves an open problem of Cassels [Ca] from the 50’s. We then prove that if 1, α, β spa...

A Solution to a Problem of Cassels and Diophantine Properties of Cubic Numbers

We prove that almost any pair of real numbers α, β, satisfies the following inhomogeneous uniform version of Littlewood’s conjecture: ∀γ, δ ∈ R, lim inf |n|→∞ |n| 〈nα− γ〉〈nβ − δ〉 = 0, (0.1) where 〈·〉 denotes the distance from the nearest integer. The existence of even a single pair that satisfies (0.1), solves a problem of Cassels [Ca] from the 50’s. We then prove that if 1, α, β span a totally...

The Diophantine Frobenius Problem

On a Linear Diophantine Problem of Frobenius

Let a1, a2, . . . , ak be positive and pairwise coprime integers with product P . For each i, 1 ≤ i ≤ k, set Ai = P/ai. We find closed form expressions for the functions g(A1, A2, . . . , Ak) and n(A1, A2, . . . , Ak) that denote the largest (respectively, the number of) N such that the equation A1x1 + A2x2 + · · · + Akxk = N has no solution in nonnegative integers xi. This is a special case of...