Extremal problems of distance geometry related to energy integrals

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Extremal problems in discrete geometry

In this paper, we establish several theorems involving configurations of points and lines in the Euclidean plane. Our results answer questions and settle conjectures of P. Erd6s, G. Purdy, and G. Dirac. The principal result is that there exists an absolute constant cl so that wlaen V'n<=t~_[T], the number of incidences between n points and t lines is less than c~n~/3t ""/3. Using this restllt, ...

متن کامل

Some Extremal Problems in Geometry

Continuing our work of [3] we obtain lower bounds on the number of simplices of different volumes and on the number of hyperplanes determined by n points in Ek , not all of which lie on an Ek-1 and no k of which lie on an Ek-2 . We also determine the minimum number of triangles t determined by n noncollinear points in the plane and discuss what values of t can be achieved . L . M . Kelly and 14...

متن کامل

Some Extremal Problems in Geometry Iv

1. Introduction plane, what is the We will be discussing some old and new problems and results in Combinatorial Geometry. We begin with some old problems. Some time ago the senior author conjectured that a convex polygon in the plane always has a vertex which does not have three vertices equidistant from it. In L3) it is mentioned that Danzer disproved this. It is stated there that Danzer also ...

متن کامل

On the Discretization of Distance Geometry Problems

Distance geometry consists of finding an embedding of a weighted undirected graph inR. Since some years, we are workingonsuitable discretizations for this problem. Because of the discretization, the search domain is reduced froma continuous to a discrete set which has the structure of a tree. Based on this combinatorial structure, we developed an efficient branch-and-prune (BP) algorithm for th...

متن کامل

Extremal Problems in Minkowski Space Related to Minimal Networks

We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan [FLM]: Is there an upper bound polynomial in n for the largest cardinality of a set S of unit vectors in an n-dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that |S| ≤ 2n and that equality holds iff the space is linearly isometric to l ∞ , the space with an n-c...

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

ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 1974

ISSN: 0002-9947

DOI: 10.1090/s0002-9947-1974-0350629-3