**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1163

# Search results for: singular equation.

##### 1163 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 1162 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation

**Authors:**
Xiguang Li

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

**Keywords:**
Singular differential equation,
boundary value problem,
coin,
fixed point theory.

##### 1161 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation.

##### 1160 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation.

##### 1159 Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation

**Authors:**
Mohammad Najafi,
Ali Jamshidi

**Abstract:**

We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

**Keywords:**
Hirota bilinear method,
potential Kadomtsev-Petviashvili equation,
multiple soliton solutions,
multiple singular soliton solutions.

##### 1158 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 1157 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 1156 Positive Solutions of Second-order Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular equation.

##### 1155 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type

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

**Abstract:**

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

**Keywords:**
Singular integral equations,
Cauchy kernel,
Chebyshev polynomials,
interpolation.

##### 1154 Contact Problem for an Elastic Layered Composite Resting on Rigid Flat Supports

**Authors:**
T. S. Ozsahin,
V. Kahya,
A. Birinci,
A. O. Cakiroglu

**Abstract:**

**Keywords:**
Frictionless contact,
Layered composite,
Singularintegral equation,
The theory of elasticity.

##### 1153 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.

##### 1152 Frictionless Contact Problem Between Two Orthotropic Elastic Layers

**Authors:**
V. Kahya,
A. Birinci,
R. Erdol

**Abstract:**

**Keywords:**
Frictionless contact,
Initial separation,
Orthotropicmaterial,
Singular integral equation.

##### 1151 Singular Value Decomposition Based Optimisation of Design Parameters of a Gearbox

**Authors:**
Mehmet Bozca

**Abstract:**

**Keywords:**
Singular value,
optimisation,
gearbox,
torsional
vibration.

##### 1150 Analytical Solution of Time-Harmonic Torsional Vibration of a Cylindrical Cavity in a Half-Space

**Authors:**
M.Eskandari-Ghadi,
M.Mahmoodian

**Abstract:**

**Keywords:**
Cosine transform,
Half space,
Isotropic,
Singular
integral equation,
Torsion

##### 1149 On Certain Estimates Of Rough Oscillatory Singular Integrals

**Authors:**
H. M. Al-Qassem

**Abstract:**

We obtain appropriate sharp estimates for rough oscillatory integrals. Our results represent significant improvements as well as natural extensions of what was known previously.

**Keywords:**
Oscillatory singular integral,
Rough kernel,
Singular integral,
L^{p} boundedness.

##### 1148 Semiconvergence of Alternating Iterative Methods for Singular Linear Systems

**Authors:**
Jing Wu

**Abstract:**

In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.

**Keywords:**
Alternating iterative method,
Semiconvergence,
Singular
matrix.

##### 1147 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Singular curve,
elliptic curve,
rational points.

##### 1146 Intensity of Singular Stress Field at the Corner of Adhesive Layer in Bonded Plate

**Authors:**
Nao-Aki Noda,
Yu Zhang,
Ken-Tarou Takaishi,
Hiroyuki Shibahara

**Abstract:**

**Keywords:**
Adhesive,
Adherent,
Intensity of singular stress,
Bonded strip

##### 1145 Enhancement of Low Contrast Satellite Images using Discrete Cosine Transform and Singular Value Decomposition

**Authors:**
A. K. Bhandari,
A. Kumar,
P. K. Padhy

**Abstract:**

**Keywords:**
Singular Value Decomposition (SVD),
discretecosine transforms (DCT),
image equalization and satellite imagecontrast enhancement.

##### 1144 LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case

**Authors:**
Salim Ibrir

**Abstract:**

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.

**Keywords:**
Singular systems,
Discrete-time systems,
Regularization,
LMIs

##### 1143 Analysis of a Singular Perturbed Synchronous Generator with a Bond Graph Approach

**Authors:**
Gilberto Gonzalez-A,
Noe Barrera-G

**Abstract:**

**Keywords:**
Bond graph modelling,
synchronous generator,
singular perturbations

##### 1142 Effects of Geometry on Intensity of Singular Stress Fields at the Corner of Single-Lap Joints

**Authors:**
Yu Zhang,
Nao-Aki Noda,
Kentaro Takaishi

**Abstract:**

**Keywords:**
Adhesive thickness,
Overlap length,
Intensity ofsingular stress,
Single-lap joint

##### 1141 Parallel Multisplitting Methods for Singular Linear Systems

**Authors:**
Guangbin Wang,
Fuping Tan

**Abstract:**

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

**Keywords:**
Singular H-matrix,
linear systems,
extrapolated iterative method,
GMAOR method,
convergence.

##### 1140 Numerical Solution for Elliptical Crack with Developing Cusps Subject to Shear Loading

**Authors:**
Nik Mohd Asri Nik Long,
Koo Lee Feng,
Zainidin K. Eshkuvatov,
A. A. Khaldjigitov

**Abstract:**

This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.

**Keywords:**
Elliptical crack,
stress intensity factors,
hyper singular integral equation,
shear loading,
conformal mapping.

##### 1139 Elliptic Divisibility Sequences over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic divisibility sequences,
singular elliptic divisibilitysequences,
elliptic curves,
singular curves.

##### 1138 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 1137 Encryption Image via Mutual Singular Value Decomposition

**Authors:**
Adil Al-Rammahi

**Abstract:**

Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.

**Keywords:**
Image cryptography,
Singular values decomposition.

##### 1136 Principal Component Analysis using Singular Value Decomposition of Microarray Data

**Authors:**
Dong Hoon Lim

**Abstract:**

A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented via a singular value decomposition(SVD), is useful for analysis of microarray data. For application of PCA using SVD we use the DNA microarray data for the small round blue cell tumors(SRBCT) of childhood by Khan et al.(2001). To decide the number of components which account for sufficient amount of information we draw scree plot. Biplot, a graphic display associated with PCA, reveals important features that exhibit relationship between variables and also the relationship of variables with observations.

**Keywords:**
Principal component analysis,
singular value decomposition,
microarray data,
SRBCT

##### 1135 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 1134 Robust Fuzzy Control of Nonlinear Fuzzy Impulsive Singular Perturbed Systems with Time-varying Delay

**Authors:**
Caigen Zhou,
Haibo Jiang

**Abstract:**

**Keywords:**
T–S fuzzy model,
singular perturbed systems,
time-varying delay,
robust control.