Abstract: In this article an isotropic linear elastic half-space with
a cylindrical cavity of finite length is considered to be under the
effect of a ring shape time-harmonic torsion force applied at an
arbitrary depth on the surface of the cavity. The equation of
equilibrium has been written in a cylindrical coordinate system. By
means of Fourier cosine integral transform, the non-zero
displacement component is obtained in the transformed domain. With
the aid of the inversion theorem of the Fourier cosine integral
transform, the displacement is obtained in the real domain. With the
aid of boundary conditions, the involved boundary value problem for
the fundamental solution is reduced to a generalized Cauchy singular
integral equation. Integral representation of the stress and
displacement are obtained, and it is shown that their degenerated
form to the static problem coincides with existing solutions in the
literature.
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.
Abstract: These paper, we approximate the average run length
(ARL) for CUSUM chart when observation are an exponential first
order moving average sequence (EMA1). We used Gauss-Legendre
numerical scheme for integral equations (IE) method for approximate
ARL0 and ARL1, where ARL in control and out of control,
respectively. We compared the results from IE method and exact
solution such that the two methods perform good agreement.
Abstract: The paper considers a single-server queue with fixedsize
batch Poisson arrivals and exponential service times, a model
that is useful for a buffer that accepts messages arriving as fixed size
batches of packets and releases them one packet at time. Transient
performance measures for queues have long been recognized as
being complementary to the steady-state analysis. 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. The paper exploits
practical modelling to obtain a solution to the integral equation
encountered in the analysis. Results obtained indicate that under
heavy load conditions, there is significant disparity in the statistics
between the transient and steady state values.
Abstract: In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To
this purpose, we consider two stages of approximation.
First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems
and optimal control problems. Finally numerical examples is
proposed.
Abstract: A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.
Abstract: The effect of a chiral bianisotropic substrate on the
complex resonant frequency of a rectangular microstrip resonator has
been studied on the basis of the integral equation formulation. The
analysis is based on numerical resolution of the integral equation
using Galerkin procedure for moment method in the spectral domain.
This work aim first to study the effect of the chirality of a
bianisotopic substrate upon the resonant frequency and the half
power bandwidth, second the effect of a magnetic anisotropy via an
asymptotic approach for very weak substrate upon the resonant
frequency and the half power bandwidth has been investigated. The
obtained results are compared with previously published work [11-9],
they were in good agreement.
Abstract: In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.
Abstract: In this paper, growth and collapse of a vapour bubble
generated due to a local energy input inside a rigid cylinder and in
the absence of buoyancy forces is investigated using Boundary
Integral Equation Method and Finite Difference Method .The fluid is
treated as potential flow and Boundary Integral Equation Method is
used to solve Laplace-s equation for velocity potential. Different
ratios of the diameter of the rigid cylinder to the maximum radius of
the bubble are considered. Results show that during the collapse
phase of the bubble inside a vertical rigid cylinder, two liquid micro
jets are developed on the top and bottom sides of the vapour bubble
and are directed inward. It is found that by increasing the ratio of the
cylinder diameter to the maximum radius of the bubble, the rate of
the growth and collapse phases of the bubble increases and the life
time of the bubble decreases.
Abstract: As is known, one of the priority directions of research
works of natural sciences is introduction of applied section of
contemporary mathematics as approximate and numerical methods to
solving integral equation into practice. We fare with the solving of
integral equation while studying many phenomena of nature to whose
numerically solving by the methods of quadrature are mainly applied.
Taking into account some deficiency of methods of quadrature for
finding the solution of integral equation some sciences suggested of
the multistep methods with constant coefficients. Unlike these papers,
here we consider application of hybrid methods to the numerical
solution of Volterra integral equation. The efficiency of the suggested
method is proved and a concrete method with accuracy order p = 4
is constructed. This method in more precise than the corresponding
known methods.
Abstract: In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasi-stationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.
Abstract: In this study, the contact problem of a layered composite which consists of two materials with different elastic constants and heights resting on two rigid flat supports with sharp edges is considered. The effect of gravity is neglected. While friction between the layers is taken into account, it is assumed that there is no friction between the supports and the layered composite so that only compressive tractions can be transmitted across the interface. The layered composite is subjected to a uniform clamping pressure over a finite portion of its top surface. The problem is reduced to a singular integral equation in which the contact pressure is the unknown function. The singular integral equation is evaluated numerically and the results for various dimensionless quantities are presented in graphical forms.
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.
Abstract: The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL0). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL1) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL0) and (ARL1) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL1).
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.
Abstract: In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner?s hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.
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.