Topological properties of the efficient point set. II

Point-Set Topological Spatial Relations

Practical needs in the realm of Geographic Information Systems (GISs) have driven the efforts to investigate formal and sound methods to describe spatial relations. After an introduction of the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and inter...

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Point-Set Topology II

Structure of the Efficient Point Set

Let C be a nontrivial cone and Y be a set in the «-dimensional Euclidean space. Denote by E( Y|C) the set of all efficient points of X with respect to C. It will be proven that under some adequate assumptions E(Y|C) is homeomorphic to a simplex while n = 2, and for n > 2 it is a contractible set. Furthermore, the set of all weak efficient points of X with respect to C is arcwise connected and i...