• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1019-1028
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• 1997

The integral solution for a deterministic evolution equation was introduced by Benilan. Similarly, in this paper, we define the integral solution for a stochastic evolution equation with a state-dependent diffusion term and prove that there exists a unique integral solution of the stochastic evolution euation under some conditions for the coefficients. Moreover we prove that this solution is a unique strong solution.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.461-477
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• 2008

An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near crack tips. The domain integral technique, for which all relevant quantities are integrated over any arbitrary element areas around the crack tips, is utilized as the J-integral solution scheme with 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure onto a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Several benchmark problems are analyzed to evaluate the efficiency of the combined domain integral technique and the adaptive finite element method.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.709-717
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• 2005

Integral equations occur naturally in many fields of mechanics and mathematical physics. We consider the Fredholm integral equation of the first kind.In this paper we are interested in integral equation of convolution type. We give approximate solution by Meyer wavelets

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.869-881
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• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.4
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• pp.185-191
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• 2003

In this Paper, we propose an accurate and stable solution of the transient electromagnetic response from three-dimensional arbitrarily shaped conducting objects by using a time domain magnetic field integral equation. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of temporal expansion functions with decaying exponential functions and Laguerre·polynomials. Since these temporal expansion functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation and converges to zero unconditionally. To show the validity of the proposed method, we solve a time domain magnetic field integral equation for three closed conducting objects and compare the results of Mie solution and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• Structural Engineering and Mechanics
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• v.34 no.1
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• pp.85-95
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• 2010

In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

• East Asian mathematical journal
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• v.36 no.5
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• pp.605-612
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• 2020

We establish the existence of a positive solution to a semipositone system with integral boundary condition for the large value of the parameter involved in the system. We prove our results by using sub and super solution argument.

• International Journal of Highway Engineering
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• v.19 no.1
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• pp.53-62
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• 2017

PURPOSES : This research was a fundamental study on the application of an integral $TiO_2$ solution to asphalt concrete pavement. The integral $TiO_2$ solution was produced in pilot production equipment; application of the integral $TiO_2$ solution to asphalt pavement was conducted to examine the pollution-reducing capability of photocatalytic compounds such as $TiO_2$. The photocatalytic $TiO_2$ reacted with air pollutants, converting them into small amounts of relatively benign molecules. METHODS : In this study, laboratory experiments were conducted using five various testing methods. Tensile strength ratio (TSR) and British pendulum test (BPT) were conducted in order to evaluate the properties of asphalt pavement subsequent to the integral $TiO_2$ solution coating. In addition, methylene blue testing, a measurement of nitrate on the coated pavement, and nitrogen oxide (NOx) reduction testing were conducted in order to evaluate photocatalytic reaction. Lastly, a UV-A lamp was used as a light source for photocatalytic reactions. RESULTS : Test results indicated no change in the properties of asphalt pavement following the integral $TiO_2$ solution coating. In order to evaluate the performance of asphalt pavement as a function of $TiO_2$, the moisture susceptibility and skid resistance were investigated. The moisture susceptibility and skid resistance satisfied there quirements related to pavement quality and safety specification. Furthermore, the effects of reduction of air pollution were significantly improved as determined via the methylene blue test and NOx reduction test. The $TiO_2$-paved asphalt specimen exhibited approximately 43% reduction of NOx. CONCLUSIONS : This study has suggested that applying $TiO_2$ rarely impacts asphalt pavement performance measures such as moisture susceptibility and skid resistance, and that its application may be a better means of reducing air pollution. Further studies, such as proper $TiO_2$ dosage rates and compatibility with various pavement types, are required to broaden and generalize its application.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• East Asian mathematical journal
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• v.39 no.1
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• pp.43-50
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• 2023

This paper is concerned with the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. The fixed point index theorems are used for the main results.