**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**637

# Search results for: Integral methods

##### 637 On One Application of Hybrid Methods For Solving Volterra Integral Equations

**Authors:**
G.Mehdiyeva,
V.Ibrahimov,
M.Imanova

**Abstract:**

**Keywords:**
Volterra integral equation,
hybrid methods,
stability
and degree,
methods of quadrature

##### 636 Mechanical Quadrature Methods for Solving First Kind Boundary Integral Equations of Stationary Stokes Problem

**Authors:**
Xin Luo,
Jin Huang,
Pan Cheng

**Abstract:**

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

**Keywords:**
Stokes problem,
boundary integral equation,
mechanical
quadrature methods,
asymptotic expansions.

##### 635 Integral Methods in the Determination of Temperature Fields of Cooled Blades of Gas Turbines

**Authors:**
C. Ardil

**Abstract:**

**Keywords:**
Integral methods,
determination of temperature fields,
cooled blades,
gas turbines.

##### 634 Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation

**Authors:**
Xin Luo,
Jin Huang,
Chuan-Long Wang

**Abstract:**

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

**Keywords:**
Darcy's equation,
anisotropic,
mechanical quadrature methods,
extrapolation methods,
a posteriori error estimate.

##### 633 Monotonic and Cyclic J-integral Estimation for Through-Wall Cracked Straight Pipes

**Authors:**
Rohit,
S. Vishnuvardhan,
P. Gandhi,
Nagesh R. Iyer

**Abstract:**

**Keywords:**
304LN stainless steel,
cyclic J-integral,
Elastic-
Plastic Fracture Mechanics,
J-integral,
Through-wall crack

##### 632 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.

##### 631 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

##### 630 Order Reduction by Least-Squares Methods about General Point ''a''

**Authors:**
Integral square error,
Least-squares,
Markovparameters,
Moment matching,
Order reduction.

**Abstract:**

The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

**Keywords:**
Integral square error,
Least-squares,
Markovparameters,
Moment matching,
Order reduction.

##### 629 Integral Operators Related to Problems of Interface Dynamics

**Authors:**
Pa Pa Lin

**Abstract:**

This research work is concerned with the eigenvalue problem for the integral operators which are obtained by linearization of a nonlocal evolution equation. The purpose of section II.A is to describe the nature of the problem and the objective of the project. The problem is related to the “stable solution" of the evolution equation which is the so-called “instanton" that describe the interface between two stable phases. The analysis of the instanton and its asymptotic behavior are described in section II.C by imposing the Green function and making use of a probability kernel. As a result , a classical Theorem which is important for an instanton is proved. Section III devoted to a study of the integral operators related to interface dynamics which concern the analysis of the Cauchy problem for the evolution equation with initial data close to different phases and different regions of space.

**Keywords:**
Evolution,
Green function,
instanton,
integral operators.

##### 628 Response Time Behavior Trends of Proptional, Propotional Integral and Proportional Integral Derivative Mode on Lab Scale

**Authors:**
Syed Zohaib Javaid Zaidi,
W. Iqbal

**Abstract:**

The industrial automation is dependent upon pneumatic control systems. The industrial units are now controlled with digital control systems to tackle the process variables like Temperature, Pressure, Flow rates and Composition.

This research work produces an evaluation of the response time fluctuations for proportional mode, proportional integral and proportional integral derivative modes of automated chemical process control. The controller output is measured for different values of gain with respect to time in three modes (P, PI and PID). In case of P-mode for different values of gain the controller output has negligible change. When the controller output of PI-mode is checked for constant gain, it can be seen that by decreasing the integral time the controller output has showed more fluctuations. The PID mode results have found to be more interesting in a way that when rate minute has changed, the controller output has also showed fluctuations with respect to time. The controller output for integral mode and derivative mode are observed with lesser steady state error, minimum offset and larger response time to control the process variable. The tuning parameters in case of P-mode are only steady state gain with greater errors with respect to controller output. The integral mode showed controller outputs with intermediate responses during integral gain (ki). By increasing the rate minute the derivative gain (kd) also increased which showed the controlled oscillations in case of PID mode and lesser overshoot.

**Keywords:**
Controller Output,
P,
PI &PID modes,
Steady state gain.

##### 627 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.

##### 626 Spin Coherent State Path Integral for the Interaction of Two-Level System with Time Dependent Non-Uniform Magnetic Field

**Authors:**
Rekik Rima,
Aouachria Mekki

**Abstract:**

We study the movement of a two-level atom in interaction with time dependent nonuniform magnetic filed using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus the Rabi formula of the system are deduced.

**Keywords:**
Path integral,
Formalism,
Propagator,
Transition
probability.

##### 625 Modelling of Soil Structure Interaction of Integral Abutment Bridges

**Authors:**
Thevaneyan K. David,
John P. Forth

**Abstract:**

**Keywords:**
Constitutive Models,
FEM,
Integral AbutmentBridges,
Soil-structure Interactions

##### 624 Treatment of Spin-1/2 Particle in Interaction with a Time-Dependent Magnetic Field by the Fermionic Coherent-State Path-Integral Formalism

**Authors:**
Aouachria Mekki

**Abstract:**

We consider a spin-1/2 particle interacting with a time-dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form replacing the spin by two fermionic oscillators via the Schwinger model. The propagator is then exactly determined, thanks to a simple transformation, and the transition probability is deduced.

**Keywords:**
Path integral,
formalism,
Propagator.

##### 623 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays

**Authors:**
Longqiao Zhou,
Zixin Liu,
Shu Lü

**Abstract:**

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

**Keywords:**
Lur’e system,
Convex function,
Jensen integral inequality,
Triple-integral method,
Exponential stability.

##### 622 High Accuracy Eigensolutions in Elasticity for Boundary Integral Equations by Nyström Method

**Authors:**
Pan Cheng,
Jin Huang,
Guang Zeng

**Abstract:**

**Keywords:**
boundary integral equation,
extrapolation algorithm,
aposteriori error estimate,
elasticity.

##### 621 On the Existence and Global Attractivity of Solutions of a Functional Integral Equation

**Authors:**
Asadollah Aghajani,
Yaghoub Jalilian

**Abstract:**

Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

**Keywords:**
Functional integral equation,
fixed-point,
measure of noncompactness,
attractive solution,
asymptotic stability.

##### 620 On a Way for Constructing Numerical Methods on the Joint of Multistep and Hybrid Methods

**Authors:**
G.Mehdiyeva,
M.Imanova,
V.Ibrahimov

**Abstract:**

**Keywords:**
Multistep and hybrid methods,
initial value problem,
degree and stability of hybrid methods

##### 619 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind

**Authors:**
jianhua Hou,
Changqing Yang,
and Beibo Qin

**Abstract:**

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

**Keywords:**
Hybrid functions,
Fredholm integral equation,
Blockpulse,
Chebyshev polynomials,
product operational matrix.

##### 618 Review of Scouring on Integral Bridge and its Possible Protection

**Authors:**
Shatirah Akib,
Teuku K. Syamsura,
S.M. Shirazi,
Moatasem M. Fayyadh,
Budhi Primasari

**Abstract:**

**Keywords:**
bentonite,
integral bridge,
possible protection,
scouring

##### 617 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.

##### 616 Structure of Linkages and Cam Gear for Integral Steering of Vehicles

**Authors:**
Petre Alexandru,
Dragos Macaveiu,
Catalin Alexandru

**Abstract:**

**Keywords:**
Cam gear,
four wheel drive,
integral steering,
linkage.

##### 615 The First Integral Approach in Stability Problem of Large Scale Nonlinear Dynamical Systems

**Authors:**
M. Kidouche,
H. Habbi,
M. Zelmat,
S. Grouni

**Abstract:**

**Keywords:**
Comparison principle,
First integral,
Large scale
system,
Lyapunov stability.

##### 614 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.

##### 613 Efficient Mean Shift Clustering Using Exponential Integral Kernels

**Authors:**
S. Sutor,
R. Röhr,
G. Pujolle,
R. Reda

**Abstract:**

This paper presents a highly efficient algorithm for detecting and tracking humans and objects in video surveillance sequences. Mean shift clustering is applied on backgrounddifferenced image sequences. For efficiency, all calculations are performed on integral images. Novel corresponding exponential integral kernels are introduced to allow the application of nonuniform kernels for clustering, which dramatically increases robustness without giving up the efficiency of the integral data structures. Experimental results demonstrating the power of this approach are presented.

**Keywords:**
Clustering,
Integral Images,
Kernels,
Person Detection,
Person Tracking,
Intelligent Video Surveillance.

##### 612 Solution of First kind Fredholm Integral Equation by Sinc Function

**Authors:**
Khosrow Maleknejad,
Reza Mollapourasl,
Parvin Torabi,
Mahdiyeh Alizadeh,

**Abstract:**

**Keywords:**
Integral equation,
Fredholm type,
Collocation method,
Sinc approximation.

##### 611 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

**Authors:**
Akbar H. Borzabadi,
Omid S. Fard

**Abstract:**

**Keywords:**
Fredholm integral equation,
Optimization method,
Optimal control,
Nonlinear and linear programming

##### 610 Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications

**Authors:**
Zixin Liu,
Shu Lü,
Shouming Zhong,
Mao Ye

**Abstract:**

**Keywords:**
Gronwall-Bellman-Type integral inequalities,
integrodifferential equation,
p-exponentially stable,
mixed delays.

##### 609 Time Development of Local Scour around Semi Integral Bridge Piers and Piles in Malaysia

**Authors:**
Shatirah Akib,
Sadia Rahman

**Abstract:**

Scouring around a bridge pier is a complex phenomenon. More laboratory experiments are required to understand the scour mechanism. This paper focused on time development of local scour around piers and piles in semi integral bridges. Laboratory data collected at Hydraulics Laboratory, University of Malaya was analyzed for this purpose. Tests were performed with two different uniform sediment sizes and five ranges of flow velocities. Fine and coarse sediments were tested in the flume. Results showed that scour depths for both pier and piles increased with time up to certain levels and after that they became almost constant. It had been found that scour depths increased when discharges increased. Coarser sediment also produced lesser scouring at the piers and combined piles.

**Keywords:**
Pier,
pile,
scour,
semi integral bridge,
time.

##### 608 Flutter Analysis of Slender Beams with Variable Cross Sections Based on Integral Equation Formulation

**Authors:**
Z. El Felsoufi,
L. Azrar

**Abstract:**

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

**Keywords:**
Chimney,
BEM and integral equation formulation,
non uniform cross section,
vibration and Flutter.