Any harmonic function in the open unit discD {z | |z| < 1} can be written as a sum of an analytic and antianalytic functions f h z g z , where h z and g z are analytic functions in D and are called the analytic part and the coanalytic part of f, respectively. Many important questions in the study of the classes of functions are related to bounds on the modulus of functions growth or the modulus...

In this study, we evaluated the image distortion of three magnetic resonance imaging (MRI) systems with magnetic field strengths of 0.4 T, 1.5 T and 3 T, during stereotactic irradiation of the brain. A quality assurance phantom for MRI image distortion in radiosurgery was used for these measurements of image distortion. Images were obtained from a 0.4-T MRI (APERTO Eterna, HITACHI), a 1.5-T MRI...

Let {(X,, Y,J}r= 1 be a sequence of independent drawings of a pair of dependent random variables X, Y. Let us say that X takes values in the finite set 6. It is desired to encode the sequence {X,} in blocks of length n into a binary stream*of rate R, which can in turn be decoded as a sequence { 2k}, where zk E %, the reproduct ion alphabet. The average distorjion level is (l/n) cl= 1 E[D(X,,z&,...

In the present investigation, the authors define a new class of meromorphic functions defined in the punctured unit disk Δ∗ := {z ∈ C : 0 < ∣z∣ < 1}. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also prove a Property using an integral operator and its inverse defined on the new class.

In this paper, we introduce two subclasses Ωp(α) and Λ ∗ p(α) of meromorphic pvalent functions in the punctured diskD = {z : 0 < |z| < 1}. Coefficient inequalities, distortion theorems, the radii of starlikeness and convexity, closure theorems and Hadamard product ( or convolution) of functions belonging to these classes are obtained.

Abstract -A complex-valued functions that are univalent and sense preserving in the unit disk U can be written in the form ( ) ( ) ( ) f z h z g z   , where U(z) and g(z) are analytic in. We will introduced the operator D which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(,, n) by generalized derivative operator of harmonic un...

Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...

Let A(ω) denote the class of functions of the form f(z) = (z−ω)+ a2(z−ω)+ ... normalized by f(ω) = 0 and f ′(ω)− 1 = 0 and which are anal;ytic in the unit disk E = {z : |z| < 1}. We define operators Lω,n : A(ω) → A(ω) using the convolution ∗ and we use this operators to define and study a refinement by way of new generalization of some subclasses of analytic and univalent functions and properti...

If K = Goφ Z where φ is a tame automorphism of the 1-relator group G, then the combinatorial area of loops in a Cayley graph of G is undistorted in a Cayley graph of K. Examples of distortion of area in fibres of fibrations over the circle are given and a notion of exponent of area distortion is introduced and studied. The inclusion of a finitely generated abelian subgroup in the fundamental gr...