• 충청수학회지
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• 제7권1호
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• pp.227-236
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• 1994

• Structural Engineering and Mechanics
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• 제53권1호
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• pp.27-40
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• 2015

The rational analytical solutions are presented for functionally graded beams subjected to arbitrary tractions on the upper and lower surfaces. The Young's modulus is assumed to vary exponentially along the thickness direction while the Poisson's ratio keeps unaltered. Within the framework of symplectic elasticity, zero eigensolutions along with general eigensolutions are investigated to derive the homogeneous solutions of functionally graded beams with no body force and traction-free lateral surfaces. Zero eigensolutions are proved to compose the basic solutions of the Saint-Venant problem, while general eigensolutions which vary exponentially with the axial coordinate have a significant influence on the local behavior. The complete elasticity solutions presented here include homogeneous solutions and particular solutions which satisfy the loading conditions on the lateral surfaces. Numerical examples are considered and compared with established results, illustrating the effects of material inhomogeneity on the localized stress distributions.

• 대한수학회보
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• 제48권6호
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• pp.1303-1314
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• 2011

We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.460-465
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• 2009

This paper presents a new algorithm that includes a mechanism to avoid local solutions in a motion vector detection method that uses the steepest descent method. Two different implementations of the algorithm are demonstrated using two major search methods for tree structures, depth first search and breadth first search. Furthermore, it is shown that by avoiding local solutions, both of these implementations are able to obtain smaller prediction errors compared to conventional motion vector detection methods using the steepest descent method, and are able to perform motion vector detection within an arbitrary upper limit on the number of computations. The effects that differences in the search order have on the effectiveness of avoiding local solutions are also presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.57-68
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• 2015

When a straight channel formed by two parallel porous plates, through which two immiscible liquids occupying different heights are flowing a secondary motion is set up. The motion is caused by moving the upper plate with a uniform velocity about an axis perpendicular to the plates. The solutions are exact solutions. Here we discuss the effect of suction parameter and the position of interface on the flow phenomena in case of Couette flow. The velocity distributions for the primary and secondary flows have been discussed and presented graphically. The skin-friction amplitude at the upper and lower plates has been discussed for various physical parameters.

• 대한수학회논문집
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• 제35권4호
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• pp.1143-1158
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• 2020

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source u_t - △u - △u_t = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ ℝⁿ (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.475-487
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• 2009

This paper studies the iteration method of solving a type of second-order three-point boundary value problem with non-linear term f, which depends on the first order derivative. By using the upper and lower method, we obtain the sufficient conditions of the existence and uniqueness of solutions. Furthermore, the monotone iterative sequences generated by the method contribute to the minimum solution and the maximum solution. And the error estimate formula is also given under the condition of unique solution. We apply the solving process to a special boundary value problem, and the result is interesting.

• Journal of Mechanical Science and Technology
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• 제20권6호
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• pp.882-895
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• 2006

Surface and interfacial waves in two superposed horizontal inviscid fluids of finite depths are studied. The flow is induced by translating a vertical rigid plate with a prescribed velocity. Analytical solutions that accurately predict the motion of the free surface and the interface are obtained by using a small-Froude-number approximation. Three different velocities of the plate are considered, while flows induced by any arbitrary motion of the plate can be easily analyzed by a linear superposition of the solutions obtained. It is shown that pinching of the upper layer can occur for a sufficiently thin upper layer, which leads to its rupture into small segments. Other interesting phenomena, such as primary and secondary wiggles generated on the interface near the wavemaker, are discussed.

• 한국멀티미디어학회논문지
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• 제11권12호
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• pp.1688-1696
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• 2008

We propose a hierarchical service management method using Bloom filters for large MANETs. In this paper, a MANET is comprised of logical grid hierarchy, and each mobile node within the lowest service region multicasts the Attenuated Bloom Filter (ABF) for services itself to other nodes within the region. To advertise and discovery a service efficiently, the server node of the lowest server region sends the Summary Bloom Filter (SBF) for the ABFs to the server node of upper server region. Each upper server has the set of SBFs for lower vicinity service regions. The traffic load of the proposed method is evaluated by an analytical model, and is compared with that of two alternative advertisement solutions: complete advertisement and no advertisement. As a result, we identify that the traffic load of the proposed method is much lower than that of two alternative advertisement solutions.

• 한국전산유체공학회지
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• 제21권1호
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.