On the Theory of Coconvex Bodies
نویسندگان
چکیده
Coconvex sets (complements in a convex cone of convex subsets coinciding with the cone far enough from its apex) appear in singularity theory (as Newton diagrams) and in commutative algebra. Such invariants of coconvex sets as volumes, mixed volumes, number of integer points, etc., play an important role. This paper aims at extending various results from the theory of convex bodies to the coconvex setting. These include the Aleksandrov–Fenchel inequality and the Ehrhart duality.
منابع مشابه
Numerical Simulation of Partial Cavitation over Axisymmetric Bodies: VOF Method vs. Potential Flow Theory
A computational study of partial cavitation over axisymmetric bodies is presented using two numerical methods. The first method is based on the VOF technique where transient 2D Navier-Stokes equations are solved along with an equation to track the cavity interface. Next, the steady boundary element method (BEM) based on potential flow theory is presented. The results of the two methods for a di...
متن کاملCoconvex polynomial approximation
Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson type estimates and summarize the positive and negative...
متن کاملNikolskii-type estimates for coconvex approximation of functions with one inflection point∗
For each r ∈ N we prove the Nikolskii type pointwise estimate for coconvex approximation of functions f ∈ W , the subspace of all functions f ∈ C[−1, 1], possessing an absolutely continuous (r−1)st derivative on (−1, 1) and satisfying f (r) ∈ L∞[−1, 1], that change their convexity once on [−1, 1].
متن کاملCoconvex pointwise approximation
There are two kinds of estimates of the degree of approximation of continuous functions on [−1, 1] by algebraic polynomials, Nikolskii-type pointwise estimates and Jackson-type uniform estimates, involving either ordinary moduli of smoothness, or the DitzianTotik (DT) ones, or the recent estimates involving the weighted DTmoduli of smoothness. The purpose of this paper is to complete the table ...
متن کاملCoconvex Approximation
Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials which are coconvex with it, namely, polynomials that change their convexity exactly at the points where f does. We discuss some Jackson type estimates where the constants involved depend on the location of the points of change of c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 52 شماره
صفحات -
تاریخ انتشار 2014