Given a weighted graph G = (V,E,w) with a set of k terminals T ⊂ V , the Steiner Point Removal problem seeks for a minor of the graph with vertex set T , such that the distance between every pair of terminals is preserved within a small multiplicative distortion. Kamma, Krauthgamer and Nguyen (SODA 2014, SICOMP 2015) used a ball-growing algorithm to show that the distortion is at most O(log k) ...

Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. It is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end-to-end distortion decays to zero exponentially fast as a function of the overall transmission rate, and is achieved by choosing ...

The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly ...

In this paper we introduce new classes of analytic functions with varying argument of coefficients defined by subordination. Several properties like the coefficients inequalities, distortion bounds, subordination theorems and integral means inequalities are investigated. Some consequences of our main results for new or well-known classes of functions are also pointed out. Mathematics subject cl...

In this paper we introduce new subclasses of k-uniformly convex and starlike functions with respect to other points. We provide necessary and sufficient conditions, coefficient estimates, distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for these classes. We also obtain integral means inequalities with the extremal functions for these classes.

Making use of Srivastava-Wright operator we introduced a new class of complexvalued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, convex combination. Mathematics subject classification (2010): 30C45.

Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

Bounds on the distortion derived in [1] are adapted to the case where two continuous random variables are sent over a multiple access channel with phase shifts using the help of two feedback channels. The first source is defined to be uniformly distributed and the second source is defined as the sum of the first source and an auxiliary random variable which is also uniform. Additionally, using ...

Lossy source coding under the mean-squared error fidelity criterion is considered. The rate-distortion function can be expressed in closed form only for very special cases, including Gaussian sources. The classical upper and lower bounds look exactly alike, except that the upper bound has the source power (variance) whereas the lower bound has the source entropypower. This pleasing duality of p...

In this paper, we define a generalized class of starlike functions with negative coefficients and obtain coefficient estimates, distortion bounds, closure theorems and extreme points. Further we obtain modified Hadamard product, radii of close-to-convex, starlikeness and convexity for functions belonging to this class. Furthermore neighborhood results are discussed.