Dimension and geometry of sets defined by polynomial inequalities

Computing the Top Betti Numbers of Semi-algebraic Sets Defined by Quadratic Inequalities in Polynomial Time

For any l > 0, we present an algorithm which takes as input a semi-algebraic set, S, defined by P1 ≤ 0, . . . , Ps ≤ 0, where each Pi ∈ R[X1, . . . ,Xk ] has degree ≤ 2, and computes the top l Betti numbers of S, bk−1(S), . . . , bk−l(S), in polynomial time. The complexity of the algorithm, stated more precisely, is ∑l+2 i=0 ( s i ) k2 O(min(l,s)) . For fixed l, the complexity of the algorithm ...

extensions of some polynomial inequalities to the polar derivative

توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی

Dimension of Cantor Sets with Complicated Geometry

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Multivariate Polynomial Inequalities via Pluripotential Theory and Subanalytic Geometry Methods

In this paper, we give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Ã Lojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for...