• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.377-392
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• 2008

Let X be a real reflexive Banach space with a uniformly $G\hat{a}teaux$ differentiable norm, C a nonempty closed convex subset of X, T : C $\rightarrow$ X a continuous pseudocontractive mapping, and A : C $\rightarrow$ C a continuous strongly pseudocontractive mapping. We show the existence of a path ${x_t}$ satisfying $x_t=tAx_t+(1- t)Tx_t$, t $\in$ (0,1) and prove that ${x_t}$ converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path ${x_t}$ defined by $x_t=tAx_t+(1-t)(2I-T)x_t$ to a fixed point of firmly pseudocontractive mapping T.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.933-957
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• 2017

In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

• Journal of Ship and Ocean Technology
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• v.12 no.2
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.263-271
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• 2006

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.

• Journal of The Korean Astronomical Society
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• v.31 no.2
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• pp.89-93
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• 1998

An attempt is made to find the boundary tangential components of potential magnetic fields without constructing solutions in the entire domain. In our procedure, the magnetic energy is expressed as a functional of tangential and normal magnetic fields at the boundary and is minimized by the variational principle. This paper reports a preliminary study on two dimensional potential fields above a plane.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.183-191
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• 2007

In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets.

• The Journal of the Convergence on Culture Technology
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• v.8 no.4
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• pp.91-98
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• 2022

Lifelog data continuously collected through a wearable device may contain many outliers, so in order to improve data quality, it is necessary to find and remove outliers. In general, since the number of outliers is less than the number of normal data, a class imbalance problem occurs. To solve this imbalance problem, we propose a method that applies Variational AutoEncoder to outliers. After preprocessing the outlier data with proposed method, it is verified through a number of machine learning models(classification). As a result of verification using body weight data, it was confirmed that the performance was improved in all classification models. Based on the experimental results, when analyzing lifelog body weight data, we propose to apply the LightGBM model with the best performance after preprocessing the data using the outlier processing method proposed in this study.

• Structural Engineering and Mechanics
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• v.27 no.4
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• pp.457-475
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• 2007

Analysis of transverse stresses at layer interfaces in a composite laminate has always been a challenging task. Composite structures possess highly irregular material properties at layer interfaces, which cause high shear stresses. Classical Plate Theory and First Order Shear Deformation Theory (FSDT) use post computing to calculate transverse stresses. This paper presents Reissner Mixed Variational Theorem (RMVT) based finite element model to carry out layer-wise analysis of composite laminates. Selective integration scheme has been used. The formulation has been validated by solving numerical examples and comparing the results with those published in the literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.411-432
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• 2021

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.