• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.162-167
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• 1992

The effects of railway vibration on nearby structures or equipment become severe with increasing the train speed and they may be also sufficiently intense to annoy the recipients. Often, the cost of the postcautionary measures may be more expensive than that of the precautionary ones to eliminate potential problems. This paper presents the Boundary Element approach for the evaluation of the dynamic response (in the form of the compliance matrix) of sleeper which can be used to predict the change of the vibration level.

• Bulletin of the Korean Chemical Society
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• v.8 no.2
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• pp.83-88
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• 1987

The Smoluchowski equations with a linear and a parabolic potentials in one-dimensional case are solved for the reflecting boundary condition. Analytic expressions for the long-time behaviors of the remaining probabilities are obtained. These results, together with the previous result for a step potential, show the dependence of the desorption process on the form of potential. The effect of the radiation boundary condition is also investigated for three types of potentials.

• Korean Journal of Veterinary Research
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• v.26 no.2
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• pp.195-199
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• 1986

The papillary tubercles (PTs) developed on the splenic capsule of normal Landrace pigs were collected and their histological structures were observed with light microscope. The results were summarized as follows : 1. The external features of the PTs were smooth spherical or oval form protruded on the splenic capsules. On cross section of PTs, the shapes were predominantly round or elliptical single follicular form, and were often multifollicular and irregular form in some PTs. 2. The PTs were interposed into the splenic capsule. Therefore the peripheral boundary of PT was consisted of splenic capsular tissue and this tissue was covered with mesothelium, The basal tissues of PT were consisted of thick connective tissue and smooth muscle of splenic capsule, and capsular foramen for transport tract between splenic parenchyma and the PT was found at the center of the basal boundary of PT. 3. The basal region of PT was composed of parenchyma and this tissue was the splenic red pulp but the central and peripheral regions of PT contained much more erythrocytes than in the splenic parenchymae. 4. The splenic parenchymae adjoining to PT contained more erythrocytes than in other splenic parenchymal regions and parallel fixed cells directed to the capsular foramen.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.257-279
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• 2023

This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1273-1299
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• 2012

We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.985-994
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• 1994

Boundary value problems are common in nature. Here we restrict our attention to the second order differential equations of the form $$ (1.1) \frac{d^2 y}{dx^2} = P(x)y(x) + Q(x), 0 \leq x \leq 1, $$ $$ y(0) = \alpha, $$ $$ y(1) = \beta, $$ where P(x) and Q(x) are continuous functions with $P(x) \geq 0, x \in [0, 1]$.

• Journal of Korean Association for Spatial Structures
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• v.22 no.2
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• pp.57-64
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• 2022

In this paper, the physical model and governing equations of a shallow arch with a moving boundary were studied. A model with a moving boundary can be easily found in a long span retractable roof, and it corresponds to a problem of a non-cylindrical domain in which the boundary moves with time. In particular, a motion equation of a shallow arch having a moving boundary is expressed in the form of an integral-differential equation. This is expressed by the time-varying integration interval of the integral coefficient term in the arch equation with an un-movable boundary. Also, the change in internal force due to the moving boundary is also considered. Therefore, in this study, the governing equation was derived by transforming the equation of the non-cylindrical domain into the cylindrical domain to solve this problem. A governing equation for vertical vibration was derived from the transformed equation, where a sinusoidal function was used as the orthonormal basis. Terms that consider the effect of the moving boundary over time in the original equation were added in the equation of the transformed cylindrical problem. In addition, a solution was obtained using a numerical analysis technique in a symmetric mode arch system, and the result effectively reflected the effect of the moving boundary.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.59-71
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• 2018

We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at infinity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modified barrier for more general domain than an exterior domain.