**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**15

# Search results for: Analytic function

##### 15 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

**Authors:**
Rashidah Omar,
Suzeini Abdul Halim,
Aini Janteng

**Abstract:**

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function *f *ϵ* A *is said to be bi-univalent in the open unit disk *D* if both *f *and *f ^{-1}* are univalent in

*D*. The symbol

*A*denotes the class of all analytic functions

*f*in

*D*and it is normalized by the conditions

*f*(0) =

*f’*(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function

*f*is subordinate to an analytic function

*g*if there is an analytic function

*w*defined on

*D*with

*w*(0) = 0 and |

*w*(z)| < 1 satisfying

*f*(

*z*) =

*g*[

*w*(

*z*)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

**Keywords:**
Analytic functions,
bi-univalent functions,
Hohlov operator,
subordination.

##### 14 Modeling and System Identification of a Variable Excited Linear Direct Drive

**Authors:**
Heiko Weiß,
Andreas Meister,
Christoph Ament,
Nils Dreifke

**Abstract:**

**Keywords:**
Force variations,
linear direct drive,
modeling and system identification,
variable excitation flux.

##### 13 Matrix Valued Difference Equations with Spectral Singularities

**Authors:**
Serifenur Cebesoy,
Yelda Aygar,
Elgiz Bairamov

**Abstract:**

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

**Keywords:**
Difference Equations,
Jost Functions,
Asymptotics,
Eigenvalues,
Continuous Spectrum,
Spectral Singularities.

##### 12 Fekete-Szeg¨o Problem for Subclasses of Analytic Functions Defined by New Integral Operator

**Authors:**
Khalifa AlShaqsi

**Abstract:**

The author introduced the integral operator , by using this operator a new subclasses of analytic functions are introduced. For these classes, several Fekete-Szeg¨ type coefficient inequalities are obtained.

**Keywords:**
Integral operator,
Fekete-Szeg¨ inequalities,
Analytic
functions.

##### 11 Zeros of Bargmann Analytic Representation in the Complex Plane

**Authors:**
Muna Tabuni

**Abstract:**

The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.

**Keywords:**
Bargmann functions,
Husimi functions,
zeros.

##### 10 Open Problems on Zeros of Analytic Functions in Finite Quantum Systems

**Authors:**
Muna Tabuni

**Abstract:**

The paper contains an investigation on basic problems about the zeros of analytic theta functions. A brief introduction to analytic representation of finite quantum systems is given. The zeros of this function and there evolution time are discussed. Two open problems are introduced. The first problem discusses the cases when the zeros follow the same path. As the basis change the quantum state |f transforms into different quantum state. The second problem is to define a map between two toruses where the domain and the range of this map are the analytic functions on toruses.

**Keywords:**
open problems,
constraint,
change of basis.

##### 9 Winding Numbers of Paths of Analytic Functions Zeros in Finite Quantum Systems

**Authors:**
Muna Tabuni

**Abstract:**

The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

**Keywords:**
Winding numbers,
period,
paths of zeros.

##### 8 Univalence of an Integral Operator Defined by Generalized Operators

**Authors:**
Salma Faraj Ramadan,
Maslina Darus

**Abstract:**

In this paper we define generalized differential operators from some well-known operators on the class A of analytic functions in the unit disk U = {z ∈ C : |z| < 1}. New classes containing these operators are investigated. Also univalence of integral operator is considered.

**Keywords:**
Univalent functions,
integral operators,
differential operators.

##### 7 Certain Conditions for Strongly Starlike and Strongly Convex Functions

**Authors:**
Sukhwinder Singh Billing,
Sushma Gupta,
Sukhjit Singh Dhaliwal

**Abstract:**

**Keywords:**
Analytic function,
Multiplier transformation,
Strongly starlike function,
Strongly convex function.

##### 6 Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates

**Authors:**
Rana Khalid Naeem,
Asif Mansoor,
Waseem Ahmed Khan,
Aurangzaib

**Abstract:**

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating that the flow equations possess an infinite set of solutions.

**Keywords:**
Exact solutions,
Fluid of variable viscosity,
Navier-Stokes equations,
Steady plane flows

##### 5 A Sandwich-type Theorem with Applications to Univalent Functions

**Authors:**
Sukhwinder Singh Billing,
Sushma Gupta,
Sukhjit Singh Dhaliwal

**Abstract:**

**Keywords:**
Univalent function,
Starlike function,
Differential subordination,
Differential superordination.

##### 4 An Application of Differential Subordination to Analytic Functions

**Authors:**
Sukhwinder Singh Billing,
Sushma Gupta,
Sukhjit Singh Dhaliwal

**Abstract:**

the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction

**Keywords:**
function,
Differential subordination,
Multiplier transformation.

##### 3 Certain Subordination Results For A Class Of Analytic Functions Defined By The Generalized Integral Operator

**Authors:**
C. Selvaraj,
K. R. Karthikeyan

**Abstract:**

**Keywords:**
Analytic functions,
Hadamard product,
Subordinating factor sequence

##### 2 Differential Sandwich Theorems with Generalised Derivative Operator

**Authors:**
Maslina Darus,
Khalifa Al-Shaqsi

**Abstract:**

**Keywords:**
Analytic functions,
Univalent functions,
Derivative operator,
Differential subordination,
Differential superordination.

##### 1 An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes

**Authors:**
İnci M. Erhan

**Abstract:**

**Keywords:**
Bessel functions,
Eigenfunction expansion,
Quantum billiard,
Schrödinger equation,
Spherical harmonics