For certain meromorphic function g and h, we study a class of functions f(z) = z−1 + ∑∞ n=1 fnz , (fn ≥ 0), defined in the punctured unit disk ∆∗, satisfying < ( (f ∗ g)(z) (f ∗ h)(z) ) > α (z ∈ ∆; 0 ≤ α < 1) . Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. Properties of an integral operator and its inverse defined on the new class is also...

A sufficient coefficient of this class is determined. It is shown that this coefficient bound is also necessary for the classM –– H n, λ, α if fn z h –– gn∈ MH n, λ, α , where h z z− ∑∞ k 2|ak|z, gn z −1 n ∑∞ k 1|bk|z and n ∈ N0. Coefficient conditions, such as distortion bounds, convolution conditions, convex combination, extreme points, and neighborhood for the class M –– H n, λ, α , are obta...

We give two-point distortion theorems for various subfamilies of analytic univalent functions. We also find the necessary and sufficient condition for these subclasses of analytic functions. 1. Introduction. Let Ω be the family of functions ω(z) regular in the unit disc D = {z | |z| < 1} and satisfying the conditions ω(0) = 0, |ω(z)| < 1 for z ∈ D. For arbitrary fixed numbers A, B, −1 ≤ B < A ≤...

We introduce a class TS p(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z) = z+ P∞ n=2 bnz , bn > 0, |z| < 1. We obtain the coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the class TS p(α).

This paper proposes five level diode clamped Z source Inverter. The existing PWM techniques used for ZSI are restricted for two level. The two level Z Source Inverter have high harmonic distortions which effects the performance of the grid connected PV system. To improve the performance of the system the number of voltage levels in the output waveform need to be increased. This paper presents c...

Analytical expressions are presented for relativistic corrections to the Kompaneets equation and the Sunyaev-Zel’dovich y-distortion. The latter provides a convenient method of inferring both the temperature and Thomson optical depth of the gas in clusters of galaxies using only observations of the spectrum of CMBR photons passing through the cluster. The relativistic correction gives an additi...

We study the Lp-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the lp-distortions of the groups C2 ≀Cn and Cpn ⋉Cn are in Θ((log n) 1/p), and that the lp-distortion of C2 n ⋉A Z, where A is the matrix (

We consider the distortion in the cosmic microwave background (CMB) due to galactic winds at high redshift. Winds outflowing from galaxies have been hypothesized to be possible sources of metals in the intergalactic medium, which is known to have been enriched to 10−2.5 Z⊙ at z ∼ 3. We model these winds as functions of mass of the parent galaxy and redshift, assuming they activate at a common i...