**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1092

# Search results for: Bessel functions

##### 1092 Analytical Modeling of Globular Protein-Ferritin in α-Helical Conformation: A White Noise Functional Approach

**Authors:**
Vernie C. Convicto,
Henry P. Aringa,
Wilson I. Barredo

**Abstract:**

**Keywords:**
Globular protein,
modulating function,
white noise,
winding probability.

##### 1091 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.

##### 1090 An Extension of the Kratzel Function and Associated Inverse Gaussian Probability Distribution Occurring in Reliability Theory

**Authors:**
R. K. Saxena,
Ravi Saxena

**Abstract:**

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

**Keywords:**
Fox-Wright function,
Inverse Gaussian distribution,
Krtzel function & Bessel function of the third kind.

##### 1089 Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation

**Authors:**
Anupma Bansal

**Abstract:**

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

**Keywords:**
Klein-Gordon-Schödinger Equation,
Lie Classical Method,
Exact Solutions

##### 1088 Spectral Investigation for Boundary Layer Flow over a Permeable Wall in the Presence of Transverse Magnetic Field

**Authors:**
Saeed Sarabadan,
Mehran Nikarya,
Kouroah Parand

**Abstract:**

**Keywords:**
MHD Falkner-Skan,
nonlinear ODE,
spectral
collocation method,
Bessel functions,
skin friction,
velocity.

##### 1087 Transient Analysis of a Single-Server Queue with Batch Arrivals Using Modeling and Functions Akin to the Modified Bessel Functions

**Authors:**
Vitalice K. Oduol

**Abstract:**

**Keywords:**
batch arrivals,
modelling,
single-server queue,
time-varying probabilities,
transient analysis.

##### 1086 Impedance of an Encircling Coil due to a Cylindrical Tube with Varying Properties

**Authors:**
Valentina Koliskina

**Abstract:**

**Keywords:**
Eddy currents,
magnetic permeability,
Besselfunctions

##### 1085 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

##### 1084 Modeling Bessel Beams and Their Discrete Superpositions from the Generalized Lorenz-Mie Theory to Calculate Optical Forces over Spherical Dielectric Particles

**Authors:**
Leonardo A. Ambrosio,
Carlos. H. Silva Santos,
Ivan E. L. Rodrigues,
Ayumi K. de Campos,
Leandro A. Machado

**Abstract:**

**Keywords:**
Bessel Beams and Frozen Waves,
Generalized Lorenz-Mie Theory,
Numerical Methods,
Optical Forces.

##### 1083 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.

##### 1082 Closed Form Solution to problem of Calcium Diffusion in Cylindrical Shaped Neuron Cell

**Authors:**
Amrita Tripathi,
Neeru Adlakha

**Abstract:**

**Keywords:**
Laplace Transform,
Modified Bessel function,
reaction diffusion equation,
diffusion coefficient,
excess buffer,
calcium influx

##### 1081 New Classes of Salagean type Meromorphic Harmonic Functions

**Authors:**
Hakan Bostancı,
Metin Öztürk

**Abstract:**

In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + g using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained.

**Keywords:**
Harmonic mappings,
Meromorphic functions,
Salagean
operator.

##### 1080 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.

##### 1079 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.

##### 1078 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.

##### 1077 Geometrically Non-Linear Axisymmetric Free Vibrations of Thin Isotropic Annular Plates

**Authors:**
Boutahar Lhoucine,
El Bikri Khalid,
Benamar Rhali

**Abstract:**

The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted *ا*here to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

**Keywords:**
Non-linear vibrations,
Annular plates,
Large vibration amplitudes.

##### 1076 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.

##### 1075 Unconventional Calculus Spreadsheet Functions

**Authors:**
Chahid K. Ghaddar

**Abstract:**

**Keywords:**
Calculus functions,
nonlinear systems,
differential algebraic equations,
solvers,
spreadsheet.

##### 1074 Geometric Properties and Neighborhood for Certain Subclasses of Multivalent Functions

**Authors:**
Hesam Mahzoon

**Abstract:**

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

**Keywords:**
Coefficient inequalities,
extreme points,
integral means,
multivalent functions,
Al-Oboudi operator,
and Sãlãgean operator.

##### 1073 Design of MBMS Client Functions in the Mobile

**Authors:**
Jaewook Shin,
Aesoon Park

**Abstract:**

**Keywords:**
BM-SC,
Broadcast,
MBMS,
Mobile,
Multicast.

##### 1072 Performance Evaluation of Complex Valued Neural Networks Using Various Error Functions

**Authors:**
Anita S. Gangal,
P. K. Kalra,
D. S. Chauhan

**Abstract:**

**Keywords:**
Complex backpropagation algorithm,
complex errorfunctions,
complex valued neural network,
split activation function.

##### 1071 Performance Evaluation of Popular Hash Functions

**Authors:**
Sheena Mathew,
K. Poulose Jacob

**Abstract:**

**Keywords:**
Cryptography,
Hash function,
JERIM-320,
Messageintegrity

##### 1070 Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals

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

**Abstract:**

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.

**Keywords:**
Fractional Derivatives and Integrals,
Hypergeometric
functions.

##### 1069 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method

**Authors:**
Changqing Yang,
Jianhua Hou,
Beibo Qin

**Abstract:**

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

**Keywords:**
Hybrid functions,
Riccati differential equation,
Blockpulse,
Chebyshev polynomials,
Tau method,
operational matrix.

##### 1068 Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models

**Authors:**
Ε. Giovanis

**Abstract:**

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

##### 1067 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.

##### 1066 Orthogonal Functions Approach to LQG Control

**Authors:**
B. M. Mohan,
Sanjeeb Kumar Kar

**Abstract:**

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

**Keywords:**
Linear quadratic Gaussian control,
linear quadratic estimator,
linear quadratic regulator,
time-invariant systems,
orthogonal functions,
block-pulse functions,
shifted legendre polynomials.

##### 1065 Screened Potential in a Reverse Monte Carlo (RMC) Simulation

**Authors:**
M. Habchi,
S. M. Mesli,
M. Kotbi

**Abstract:**

**Keywords:**
RMC simulation; Screened potential; partial and pair
distribution functions; glassy and liquid state

##### 1064 A Computational Model of Minimal Consciousness Functions

**Authors:**
Nabila Charkaoui

**Abstract:**

Interest in Human Consciousness has been revived in the late 20th century from different scientific disciplines. Consciousness studies involve both its understanding and its application. In this paper, a computational model of the minimum consciousness functions necessary in my point of view for Artificial Intelligence applications is presented with the aim of improving the way computations will be made in the future. In section I, human consciousness is briefly described according to the scope of this paper. In section II, a minimum set of consciousness functions is defined - based on the literature reviewed - to be modelled, and then a computational model of these functions is presented in section III. In section IV, an analysis of the model is carried out to describe its functioning in detail.

**Keywords:**
Consciousness,
perception,
attention.

##### 1063 Multi-Objective Optimal Threshold Selection for Similarity Functions in Siamese Networks for Semantic Textual Similarity Tasks

**Authors:**
Kriuk Boris,
Kriuk Fedor

**Abstract:**

This paper presents a comparative study of fundamental similarity functions for Siamese networks in semantic textual similarity (STS) tasks. We evaluate various similarity functions using the STS Benchmark dataset, analyzing their performance and stability. Additionally, we present a multi-objective approach for optimal threshold selection. Our findings provide insights into the effectiveness of different similarity functions and offer a straightforward method for threshold selection optimization, contributing to the advancement of Siamese network architectures in STS applications.

**Keywords:**
Siamese networks,
Semantic textual similarity,
Similarity functions,
STS Benchmark dataset,
Threshold selection.