• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• KSBB Journal
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• v.14 no.4
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• pp.495-502
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• 1999

The optimization of fed-batch yeast fermentation process has been performed using genetic algorithm(GA). Three strategies were designed and applied to obtain the optimal feed rate profiles. Genes in the chromosome (input variables for optimization) included feed rates on fixed time intervals (strategy I), or swiching times $t_s1\;and\;t_s2$, and feed rates on singular arc (strategy II), or feed rates and the length of time interval (strategy III). Strategy III showed the best results for all initial conditions due to efficient utilization of genetic information. Simulation results using GA showed similar or better performance compared with previous results by variational caculus and singular control approach.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1041-1061
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• 2015

The influence of hygrothermal effects on the vibration frequency and buckling load of a shear deformable composite plate with arbitrary initial stresses was investigated. The governing equations of the effects of humid, thermal and initial stresses are established using the variational method. The material properties of the composite plate are affected by both temperature and moisture. The initial stress is taken to be a combination of uniaxial load and pure bending in a hygrothermal environment. The influence of various parameters, such as the fiber volume fraction, temperature, moisture concentration, length/thickness ratios, initial stresses and bending stress ratio on the vibration and stability of the response of a laminated plate are studied in detail. The behavior of vibration and stability are sensitive to temperature, moisture concentration, fiber volume fraction and initial stresses.

• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.105-122
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• 2001

A new three-dimensional 13-node hexahedral element with rotational degrees of freedom, which is designated as MR-H13 element, is presented. The proposed element is established by adding five nodes to one of the six faces of basic 8-node hexahedral element. The new element can be effectively used in the connection between the refined mesh and the coarser mesh. The derivation of the current element in this paper is based on the variational principles in which the rotation and skew-symmetric stress are introduced as independent variables. Numerical examples show that the performance of the new element is satisfactory.

• Proceedings of the Korean Society of Computer Information Conference
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• 2021.07a
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• pp.57-60
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• 2021

본 논문에서는 기지 설비 중 주요 회전기기인 펌프의 이상탐지 알고리즘을 제안한다. 현재 인공지능을 활용하여 생산현장을 혁신하고자 하는 시도가 진행되고 있으나 외산 솔루션에 대한 의존도가 높은 것에 비해 국내 실정에 맞지 않는 경우가 많다. 이에 따라, 선행 연구를 통해 국내 실정에 맞는 인공지능 기술 도입이 필요하다. 본 연구에서는 VAE(Variational Auto Encoder) 알고리즘을 활용해 회전기기의 고장을 진단하는 알고리즘을 개발하였다. 본 연구 수행을 통한 회전기기의 고장 예지·진단 시스템 개발로 설비의 이상 징후 포착, 부품의 교환 시기 등 보수 일정을 예측하고 최종적으로 이를 통한 설비 가동의 효율 증대와 에너지 비용 감소의 효과를 기대한다.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.661-679
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• 2015

In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.695-709
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• 2013

Calcium is well known role for signal transduction in a neuron cell. Various processes and parameters modulate the intracellular calcium signaling process. A number of experimental and theoretical attempts are reported in the literature for study of calcium signaling in neuron cells. But still the role of various processes, components and parameters involved in calcium signaling is still not well understood. In this paper an attempt has been made to develop two dimensional finite element model to study calcium diffusion in neuron cells. The JRyR, JSERCA and JLeak, the exogenous buffers like EGTA and BAPTA, and diffusion coefficients have been incorporated in the model. Appropriate boundary conditions have been framed. Triangular ring elements have been employed to discretized the region. The effect of these parameters on calcium diffusion has been studied with the help of numerical results.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.423-438
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• 2017

The aim of this paper is to present two new viscosity rules for nonexpansive mappings in Hilbert spaces. Under some assumptions, the strong convergence theorems of the purposed new viscosity rules are proved. Some applications are also included.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1311-1326
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• 2012

We are concerned with the multiplicity of semiclassical solutions of the following Schr$\ddot{o}$dinger system involving critical nonlinearity and magnetic fields $$\{-({\varepsilon}{\nabla}+iA(x))^2u+V(x)u=H_u(u,v)+K(x)|u|^{2*-2}u,\;x{\in}\mathbb{R}^N,\\-({\varepsilon}{\nabla}+iB(x))^2v+V(x)v=H_v(u,v)+K(x)|v|^{2*-2}v,\;x{\in}\mathbb{R}^N,$$ where $2^*=2N/(N-2)$ is the Sobolev critical exponent and $i$ is the imaginary unit. Under proper conditions, we prove the existence and multiplicity of the nontrivial solutions to the perturbed system.

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.655-665
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• 2002

Two-dimensional elastic analysis of doubly periodic circular holes in an infinite plane is given in this paper. Two cases of loading, remote tension and remote shear, are considered. A rectangular cell is cut from the infinite plane. In both cases, the boundary value problem can be reduced to a complex mixed one. It is found that the eigenfunction expansion variational method is efficient to solve the problem. Based on the deformation response under certain loading, the notched medium could be modeled by an orthotropic medium without holes. Elastic properties for the equivalent orthotropic medium are investigated, and the stress concentration along the hole contour is studied. Finally, numerical examples and results are given.