The purpose of the present paper is to study some results involving coefficient conditions, extreme points, distortion bounds, convolution conditions and convex combination for a new class of harmonic multivalent functions in the open unit disc. Relevant connections of the results presented here with various known results are briefly indicated.

Several interesting classes of k-uniformly close-to-convex functions and k-uniformly quasi-convex functions are defined here by using the DziokSrivastava operator. We provide necessary and sufficient coefficient conditions, extreme points, integral representations, and distortion bounds for functions belonging to each of these classes of k-uniformly close-to-convex functions and k-uniformly qua...

Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate coefficient estimates, distortion bounds and the results on integral transform. Further we investigate the neighbourhood results and partial sums. 2000 Mathematics Subject Classification: 30C45.

This paper investigates the problem of variable-length source coding with criteria normalized cumulant generating function codeword lengths and excess distortion probability. We analyze non-asymptotic fundamental limit under constraint that probability is allowed up to ϵ ∈ [0, 1). Our achievability converse bounds are characterized by quantity related Rényi entropy.

The M\"obius metric $\delta_G$ is studied in the cases where its domain $G$ an open sector of complex plane. We introduce upper and lower bounds for this terms hyperbolic angle sector, then use these results to find distortion under quasiregular mappings defined domains. Furthermore, we numerically study connection polygon

This paper provides lower bounds on the reconstruction error for transmission of two continuous correlated random vectors sent over both sum and parallel channels using the help of two causal feedback links from the decoder to the encoders connected to each sensor. This construction is considered for both uniformly and normally distributed sources with zero mean and unit variance. Additionally,...

We establish upper and lower bounds on the distortion bit-cost function for incremental firstorder Σ∆ ADC with constant input signal U that is uniformly distributed on (0, 1) and additive white Gaussian (AWG) input noise. It is shown, under mild conditions, that the mean squared-error distortion D scales with the number of index bits m roughly as 1/m. This is in sharp contrast to the 1/m scalin...

We initiate the study of low-distortion finite metric embeddings in multi-class (and multi-label) classification where (i) both the space of input instances and the space of output classes have combinatorial metric structure, and (ii) the concepts we wish to learn are low-distortion embeddings. We develop new geometric techniques and prove strong learning lower bounds. These provable limits hol...

In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy random projections of data. The problem has received significant interest in Compressed Sensing and Sensor Networks(SNETs) literature. Our goal here is two-fold: (a) analyze these problems in an information theoretic setting, namely, provide algorithm independent perform...

If we have found a ”good” clustering C of a data set, can we prove that C is not far from the (unknown) best clustering C of these data? Perhaps surprisingly, the answer to this question is sometimes yes. This paper proves spectral bounds on the distance d(C, C) for the case when “goodness” is measured by a quadratic cost, such as the squared distortion of K-means clustering, or the Normalized ...