The theoretical formulation of the variational bounds on scattering parameters is briefly reviewed. The upper and lower bounds on scattering parameters are realized by the manner in which the distortion of the target during the scattering is treated, in terms of the static and adiabatic pictures. The variational bounds are obtained by gradually improving the trial functions that describe the ta...

The class of univalent harmonic functions on the unit disc satisfying the condition ∑∞ k=2 (k m − αk)(|ak|+ |bk|) ≤ (1−α)(1−|b1|) is given. Sharp coefficient relations and distortion theorems are given for these functions. In this paper we find that many results of Özturk and Yalcin [5] are incorrect. Some of the results of this paper correct the theorems and examples of [5]. Further, sharp coe...

We derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the Gilbert-Varshamov or Tsfasman-Vll adut-Zink bounds. Formulas giving the high resolution vector quantizer distortion of these systems are also derived. In addition, we give bounds on how far below channel capacity the transmission rate should be for a given delay constraint.

Abstract: The aim of this paper is to introduce and study a new class [ ] * C A,B, δ α of Janowski QuasiConvex univalent functions of order alpha associated with Ruscheweyh derivative. Sharp coefficient bound, distortion result and some inclusion results are discussed. Invariance of [ ] * C A,B, δ α under convolution with convex functions has also been examined and some of its applications are ...

This paper contains bounds for the distortion in the spherical metric, that is to say, bounds for the constant of Hölder continuity of mappings f : (Rn, q) → (Rn, q) where q denotes the spherical metric. The mappings considered are K-quasiconformal (K ≥ 1) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as K → 1.

In this paper, we present upper bounds for the rate distortion function (RDF) of finite-length data blocks of Gaussian wide sense stationary (WSS) sources and we propose coding strategies to achieve such bounds. In order to obtain those bounds, we previously derive new results on the discrete Fourier transform (DFT) of WSS processes.

Deep convolutional networks are prominently used in object detection tasks due to their notable performances. These typically have pooling layers following the convolution, which effectively subsamples convolution output, potentially introducing aliasing. An aliased signal emerging earlier inevitably propagates throughout network and such distortion prevents getting best performance out of a ne...

By using q-convolution, we determine the coefficient bounds for certain symmetric subclasses of analytic functions complex order, which are introduced here by means a non-homogeneous Cauchy–Euler-type differential equation order m.

We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this problem, which takes the form of a linear program, by utilizing random binning and simultaneous decoding techniques [1] and compare it with the existing bounds....