• The Pure and Applied Mathematics
• /
• v.24 no.1
• /
• pp.1-19
• /
• 2017

In this paper we obtain some integral inequalities by using Stieltjes derivatives, and we apply our results to the study of asymptotic behavior of a certain second-order integro-differential equation.

• Journal of Ocean Engineering and Technology
• /
• v.18 no.1
• /
• pp.7-9
• /
• 2004

Using the solution to th contour integral of the complex logarithmic function ${\oint}_cIn(z-z_{0})dz$, the following definite integral, derived from the formula to calculate the forces exerted to n circular cylinder by the discrete vortices shed from it, has been evaluated (equation omitted)

• The Transactions of the Korean Institute of Electrical Engineers C
• /
• v.53 no.12
• /
• pp.626-633
• /
• 2004

In this paper, we present a time domain combined field integral equation (TD-CFIE) formulation to analyze the transient electromagnetic response from three-dimensional dielectric objects. The solution method in this paper is based on the method of moments (MoM) that involves separate spatial and temporal testing procedures. A set of the RWG (Rao, Wilton, Glisson) functions Is used for spatial expansion of the equivalent electric and magnetic current densities and a combination of RWG and its orthogonal component is used as spatial testing. We also investigate spatial testing procedures for the TD-CFIE to select the proper testing functions that are derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable enables one to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are presented and compared with the solutions of the frequency domain combined field integral equation (FD-CFIE).

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.18 no.8
• /
• pp.1059-1068
• /
• 1993

We will put the emphasis on the analysis of arbitrarily shaped microstrip antennas. The most general and rigorous treatment of microstrip antennas is given by the electric field integral equation(EFIE), usally formulated in the spectral domain. In this paper, we use a modification of EFIE, called the mixed potential integral equation(MPIE) , and we solve it in the space domain. This technique uses Green's functions associated with the scalar and vector potential which are calculated by using stratified media theory and are expressed as Sommerfeld integrals. The integral equation is solved by a moment's method using rooftop subsectional basis function. Thus, microstrip patches of any shape can be analysed at any frequency and for any substrate. Numerical results for a rectangular patch and for a L-shaped patch are given and compared with measured values.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.39 no.10
• /
• pp.27-37
• /
• 2002

In this paper, we present various combined field integral equation (CFIE) formulations for the analysis of electromagnetic scattering from arbitrarily shaped three dimensional homogeneous dielectric body in the frequency domain. For the CFIE case, we propose eight separate formulations with different combinations of testing functions that result in sixteen different formulations of CFIE by neglecting one of testing terms. One of the objectives of this paper is to illustrate that not all CFIE are valid methodologies in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results involving far scattered fields and radar cross section (RCS) are presented for a dielectric sphere to illustrate which formulation works and which do not.

• Composites Research
• /
• v.23 no.4
• /
• pp.7-13
• /
• 2010

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solids containing interacting multiple anisotropic inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. Effects of the number of anisotropic inclusions and various fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy of the method is validated by solving the single inclusion problem for which solutions are available in the literature.

• Communications for Statistical Applications and Methods
• /
• v.12 no.2
• /
• pp.435-442
• /
• 2005

The mathematical properties of the sequentially operated systems are often described by integral equations. Reservoir system of a product and sequential probability ratio test (SPRT) are typical examples of sequentially operated systems. When the underlying random quantities follow Erlang distribution, a systematic method was developed to solve the integral equations. We extend the method to the cases having accrual functions of more general types. The solutions of the integral equations are represented as a linear combination of distribution functions, and the coefficients of the linear combination are obtained by solving linear system derived from the continuity condition of the solutions.

• Structural Engineering and Mechanics
• /
• v.43 no.5
• /
• pp.561-582
• /
• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.19 no.4
• /
• pp.427-435
• /
• 2008

In this paper, a stable marching-on in time(MOT) method with a time domain combined field integral equation(CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional conducting bodies. This formulation is based on a linear combination of the time domain electric field integral equation(EFIE) with the magnetic field integral equation(MFIE). The time derivatives in the EFIE and MFIE are approximated using a central finite difference scheme and other terms are averaged over time. This time domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. Numerical results with the proposed MOT scheme are presented and compared with those obtained from the conventional method and the inverse discrete Fourier transform(IDFT) of the frequency domain CFIE solution.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.9
• /
• pp.1284-1296
• /
• 2004

In order to investigate effects of anisotropic fiber packing on stresses in composites, a Volume Integral Equation Method is applied to calculate the elastostatic field in an unbounded isotropic elastic medium containing multiple orthotropic inclusions subject to remote loading, and a Mixed Volume and Boundary Integral Equation Method is introduced for the solution of elastostatic problems in unbounded isotropic materials containing multiple anisotropic inclusions as well as one void under uniform remote loading. A detailed analysis of stress fields at the interface between the isotropic matrix and the central orthotropic inclusion is carried out for square, hexagonal and random packing of orthotropic cylindrical inclusions, respectively. Also, an analysis of stress fields at the interface between the isotropic matrix and the central orthotropic inclusion is carried out, when it is assumed that a void is replaced with one inclusion adjacent to the central inclusion of square, hexagonal and random packing of orthotropic cylindrical inclusions, respectively, due to manufacturing and/or service induced defects. The effects of random orthotropic fiber packing on stresses at the interface between the isotropic matrix and the central orthotropic inclusion are compared with the influences of square and hexagonal orthotropic fiber packing on stresses. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with multiple orthotropic inclusions and one void, it will be established that these new methods are very accurate and effective for investigating effects of general anisotropic fiber packing on stresses in composites.