We calculate the fractal dimension d, , , of the shortest path I between two points on a percolation cluster, where 1 rd”n and r is the Pythagorean distance between the points. We find d , , ,= 1.130*0.002 for d = 2 and 1.34i0.01 for d =3 . What is the length 1 of the shortest path or ‘chemical distance’ between two points of a random material? In general, I is greater than r, the Pythagorean d...

a l t h o u g h m o s t c o m p a n i e s s p e n d l e s s o n p r o d u c t d e s i g n, e x p e r i e n c e s h o w s t h a t, t h e s e c o m p a n i e s h a v e t o p a y h i g h e r c o s t s d u e t o p r o d u c t i o n p r o b l e m s o r l o s s o f m a r k e t. l i t e r a t u r e s t u d i e s s h o w t h a t t h e d e s i g n f o r s i x s i g m a i s a p o w e r f u l a p p r o a ...

<abstract><p>In this paper we study infinite isoperimetric clusters. An cluster $ {\bf{E}} in \mathbb R^d is a sequence of disjoint measurable sets E_k\subset $, called regions the cluster, k = 1, 2, 3, \dots A natural question existence with given volumes a_k\ge 0 E_k having finite perimeter P({\bf{E}}) which minimal among all clusters same volumes. We prove that such exists planar...

A group-theoretic analysis is applied to nd the transformation of the homogeneous control points of k-dimensional B ezier simplices (such as two dimensional triangles and three dimensional tetrahedra) under a k-dimensional projective reparameterization. This transformation has applications in the perspective projection of textures represented as triangular spline intensity surfaces , in arbitra...

The locus of points where two non-concentric circles c1 and c2 are seen under equal angles is the equioptic circle e. The equioptic circles of the excircles of a triangle ∆ have a common radical axis r. Therefore the excircles of a triangle share up to two real points, i.e., the equioptic points of ∆ from which the circles can be seen under equal angles. The line r carries a lot of known triang...

g l o b a l c o m p e t i t i v e n e s s h a s r e c e n t l y b e c o m e a b i g c h a l l e n g e f o r m a n y c o m p a n i e s a r o u n d t h e w o r l d, w h i c h a r e f o r c e d t o s e e k l o w e r c o s t s a n d h i g h e r q u a l i t y f o r w h a t t h e y p r o d u c e. t h e p r o s p e r i t y o f m a n u f a c t u r i n g f i r m s d e p e n d s o n s e l e c t i n g a n...

Given a set of points in 2D, the problem of identifying the smallest rectangle of arbitrary orientation, and containing exactly points is studied in this paper. The worst case time and space complexities of the proposed algorithm are ! " # $ % and & respectively. The algorithm is then used to identify the smallest square of arbitrary orientation containing points in # ' ( ) * + ' time. , .0/21%...

Image content analysis has found many applications in various domains (such as in biomedical science) and plays an important role for adaptive multimedia retrieval. In order to effectively analyze the image contents, first we should be able to access and manipulate the images themselves (rather than staying with the metadata description of the images). Research effort has been made in this rega...

A p l a n calculus is presented which is being used to represent p r o g r a m s and a l i b ra ry of standard data and control abstractions in t h e p r o g r a m m e r ' s apprent ice . Important features of this formalism i n c l u d e : p rogramming language independence, additivity, v e r i f i a b i l i t y and mult ip le points of v iew. The logical foundations of t h e r e p r e s e n t...