**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1452

# Search results for: Generalized Laguerre functions

##### 1452 Lagrangian Method for Solving Unsteady Gas Equation

**Authors:**
Amir Taghavi,
kourosh Parand,
Hosein Fani

**Abstract:**

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

**Keywords:**
Unsteady gas equation,
Generalized Laguerre functions,
Lagrangian method,
Nonlinear ODE.

##### 1451 An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon

**Authors:**
Haniye Dehestani,
Yadollah Ordokhani

**Abstract:**

**Keywords:**
Collocation method,
fractional partial differential
equations,
Legendre-Laguerre functions,
pseudo-operational matrix
of integration.

##### 1450 Bilinear and Bilateral Generating Functions for the Gauss’ Hypergeometric Polynomials

**Authors:**
Manoj Singh,
Mumtaz Ahmad Khan,
Abdul Hakim Khan

**Abstract:**

The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials.

**Keywords:**
Appell’s functions,
Gauss hypergeometric functions,
Heat polynomials,
Kampe’ de Fe’riet function,
Laguerre polynomials,
Lauricella’s function,
Saran’s functions.

##### 1449 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin method,
Integral
equations,
Laguerre polynomial.

##### 1448 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

**Authors:**
Oleksandr Poliakov,
Yevgen Pashkov,
Marina Kolesova,
Olena Chepenyuk,
Mykhaylo Kalinin,
Vadym Kramar

**Abstract:**

**Keywords:**
Iterative method,
Laguerre's method,
Newton's
method,
polynomial equation,
system of equations

##### 1447 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

##### 1446 The Gerber-Shiu Functions of a Risk Model with Two Classes of Claims and Random Income

**Authors:**
Shan Gao

**Abstract:**

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

**Keywords:**
Poisson process,
generalized Erlang risk process,
Gerber-Shiu function,
generating function,
generalized Lundberg equation.

##### 1445 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.

##### 1444 Laplace Transformation on Ordered Linear Space of Generalized Functions

**Authors:**
K. V. Geetha,
N. R. Mangalambal

**Abstract:**

**Keywords:**
Laplace transformable generalized function,
positive cone,
topology of bounded convergence

##### 1443 On Fourier Type Integral Transform for a Class of Generalized Quotients

**Authors:**
A. S. Issa,
S. K. Q. AL-Omari

**Abstract:**

**Keywords:**
Fourier type integral,
Fourier integral,
generalized
quotient,
Boehmian,
distribution.

##### 1442 Complex-Valued Neural Network in Signal Processing: A Study on the Effectiveness of Complex Valued Generalized Mean Neuron Model

**Authors:**
Anupama Pande,
Ashok Kumar Thakur,
Swapnoneel Roy

**Abstract:**

**Keywords:**
Complex valued neural network,
Generalized Meanneuron model,
Signal processing.

##### 1441 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.

##### 1440 Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

**Authors:**
Yuli Hu,
Shaoquan Sun

**Abstract:**

**Keywords:**
BCI-algebras with operators,
generalized fuzzy subalgebras,
generalized fuzzy ideals,
generalized fuzzy quotient algebras.

##### 1439 Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models

**Authors:**
Ε. Giovanis

**Abstract:**

**Keywords:**
Forecast ,
Fuzzy membership functions,
Smoothingtransition,
Time-series

##### 1438 Influences of Thermal Relaxation Times on Generalized Thermoelastic Longitudinal Waves in Circular Cylinder

**Authors:**
Fatimah A. Alshaikh

**Abstract:**

This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.

**Keywords:**
Wave propagation,
longitudinal vibrations,
circular
cylinder,
generalized thermoelasticity,
Thermal relaxation times.

##### 1437 Transient Analysis of a Single-Server Queue with Fixed-Size Batch Arrivals

**Authors:**
Vitalice K. Oduol,
C. Ardil

**Abstract:**

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch size B as the generalizing parameter. Results for the case of single-packet arrivals are obtained first. The similarities between the two families of functions are then used to obtain results for the general case of batch arrival queue with a batch size larger than one.

**Keywords:**
batch arrivals,
generalized Bessel functions,
queuetransient analysis,
time-varying probabilities.

##### 1436 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

**Authors:**
Xingping Sheng

**Abstract:**

**Keywords:**
Generalized inverse A(2)
T,
S,
Restricted inner product,
Iterative method,
Orthogonal projection.

##### 1435 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

**Authors:**
Chao Yuan,
Bao Guang Tian

**Abstract:**

**Keywords:**
Generalized linear model,
generalized relative coefficient,
least eigenvalue,
relative efficiency.

##### 1434 Generalized Chebyshev Collocation Method

**Authors:**
Junghan Kim,
Wonkyu Chung,
Sunyoung Bu,
Philsu Kim

**Abstract:**

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

**Keywords:**
Generalized Chebyshev Collocation method,
Generalized Chebyshev Polynomial,
Initial value problem.

##### 1433 (T1, T2)*- Semi Star Generalized Locally Closed Sets

**Authors:**
M. Sundararaman,
K. Chandrasekhara Rao

**Abstract:**

The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

**Keywords:**
(T1,
T2)*-semi star generalized locally closed sets,
T1T2-semi star generalized closed sets.

##### 1432 Rate of Convergence for Generalized Baskakov-Durrmeyer Operators

**Authors:**
Durvesh Kumar Verma,
P. N. Agrawal

**Abstract:**

In the present paper, we consider the generalized form of Baskakov Durrmeyer operators to study the rate of convergence, in simultaneous approximation for functions having derivatives of bounded variation.

**Keywords:**
Bounded variation,
Baskakov-Durrmeyer operators,
simultaneous approximation,
rate of convergence.

##### 1431 The Baer Radical of Rings in Term of Prime and Semiprime Generalized Bi-ideals

**Authors:**
Rattiya Boonruang,
Aiyared Iampan

**Abstract:**

**Keywords:**
ring,
prime and semiprime (generalized) bi-ideal,
Baer
radical.

##### 1430 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation

**Authors:**
Aziz Sezgin

**Abstract:**

**Keywords:**
Backstepping,
boundary control,
2-D,
3-D,
n-D heat
equation,
distributed parameter systems.

##### 1429 Convergence Analysis of the Generalized Alternating Two-Stage Method

**Authors:**
Guangbin Wang,
Liangliang Li,
Fuping Tan

**Abstract:**

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

**Keywords:**
Generalized alternating two-stage method,
linear system,
convergence.

##### 1428 Regular Generalized Star Star closed sets in Bitopological Spaces

**Authors:**
K. Kannan,
D. Narasimhan,
K. Chandrasekhara Rao,
R. Ravikumar

**Abstract:**

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.

**Keywords:**
τ1τ2-regular closed sets,
τ1τ2-regular open sets,
τ1τ2-regular generalized closed sets,
τ1τ2-regular generalized star
closed sets,
τ1τ2-regular generalized star star closed sets.

##### 1427 A Generalized Framework for Working with Multiagent Systems

**Authors:**
Debal Saha,
NirmalBaranHui

**Abstract:**

The present paper discusses the basic concepts and the underlying principles of Multi-Agent Systems (MAS) along with an interdisciplinary exploitation of these principles. It has been found that they have been utilized for lots of research and studies on various systems spanning across diverse engineering and scientific realms showing the need of development of a proper generalized framework. Such framework has been developed for the Multi-Agent Systems and it has been generalized keeping in mind the diverse areas where they find application. All the related aspects have been categorized and a general definition has been given where ever possible.

**Keywords:**
Generalized framework,
multiagent systems.

##### 1426 On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings

**Authors:**
Teerayut Chomchuen,
Aiyared Iampan

**Abstract:**

The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

**Keywords:**
Γ-semiring,
bi-Γ-ideal,
generalized bi-Γ-ideal.

##### 1425 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
Matrix equation,
Generalized inverse,
Generalized
singular-value decomposition.

##### 1424 The Bent and Hyper-Bent Properties of a Class of Boolean Functions

**Authors:**
Yu Lou,
Chunming Tang,
Yanfeng Qi,
Maozhi Xu

**Abstract:**

This paper considers the bent and hyper-bent properties of a class of Boolean functions. For one case, we present a detailed description for them to be hyper-bent functions, and give a necessary condition for them to be bent functions for another case.

**Keywords:**
Boolean functions,
bent functions,
hyper-bent functions,
character sums.

##### 1423 Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems

**Authors:**
Liping Zhou,
Liang Bao,
Yiqin Lin,
Yimin Wei,
Qinghua Wu

**Abstract:**

**Keywords:**
Quadratic eigenvalue problem,
Generalized secondorder Krylov subspace,
Generalized second-order Arnoldi process,
Projection technique,
Refined technique,
Restarting.