Convex and Discrete Geometry: Ideas, Problems and Results

نویسنده

  • Peter M. Gruber
چکیده

Convex geometry is an area of mathematics between geometry, analysis and discrete mathematics. Classical discrete geometry is a close relative of convex geometry with strong ties to the geometry of numbers, a branch of number theory. Both areas have numerous relations to other fields of mathematics and its applications. While it is out of reach to describe on one or two dozen pages the main features of convex and discrete geometry, it is well possible to show the flavor of these areas by describing typical ideas, problems and results. This will be done in the following. In particular, we consider

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

SIZE AND GEOMETRY OPTIMIZATION OF TRUSS STRUCTURES USING THE COMBINATION OF DNA COMPUTING ALGORITHM AND GENERALIZED CONVEX APPROXIMATION METHOD

In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...

متن کامل

Sweep Line Algorithm for Convex Hull Revisited

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

متن کامل

Non-homogeneous continuous and discrete gradient systems‎: ‎the quasi-convex case

‎In this paper‎, ‎first we study the weak and strong convergence of solutions to the‎ ‎following first order nonhomogeneous gradient system‎ ‎$$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\‎‎x(0)=x_0in Hend{cases}$$ to a critical point of $phi$‎, ‎where‎ ‎$phi$ is a $C^1$ quasi-convex function on a real Hilbert space‎ ‎$H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...

متن کامل

Extension Complexity and Realization Spaces of Hypersimplices

The (n, k)-hypersimplex is the convex hull of all 0/1-vectors of length n with coordinate sum k. We explicitly determine the extension complexity of all hypersimplices as well as of certain classes of combinatorial hypersimplices. To that end, we investigate the projective realization spaces of hypersimplices and their (refined) rectangle covering numbers. Our proofs combine ideas from geometry...

متن کامل

12 Discrete Aspects of Stochastic Geometry

Stochastic geometry studies randomly generated geometric objects. The present chapter deals with some discrete aspects of stochastic geometry. We describe work that has been done on familiar objects of discrete geometry, like finite point sets, their convex hulls, discrete point sets, arrangements of flats, tessellations of space, under various assumptions of randomness. Most of the results to ...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006