A remark on a problem of Klee

A remark on the slicing problem

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I1(K,Z ◦ q (K)) = ∫ K ‖〈·, x〉‖Lq(K)dx. We show that an upper bound of the form I1(K,Z ◦ q (K)) 6 C1q snL2K , with 1/2 6 s 6 1, leads to the estimate Ln 6 C2 4 √ n logn q 1−s 2 , where Ln := max{LK : K is an isotropic convex body inR}.

A remark on the second neighborhood problem

Seymour’s second neighborhood conjecture states that every simple digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. Such a vertex is said to have the second neighborhood property (SNP). We define ”good” digraphs and prove a statement that implies that every feed vertex of a tournament has the SNP. In the case of digraphs missi...

A Remark on the Kramers Problem

1. Evolution of a physical system can be ordered in multi-timescales. Details of evolution on short-time-scale do not need for description in a closed form of a system evolution on long-time-scale and appears on this scale only in an average form. The prototype of such kind physical systems is dissipative Brownian motion of a particle in an external potential field. In this problem, with the ex...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

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...