• Journal of the Korean Society of Manufacturing Process Engineers
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• v.21 no.4
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• pp.53-59
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• 2022

In this study, an enhanced first-order shear deformation theory is proposed to efficiently and accurately predict the thermo-mechanical-viscoelastic coupled behavior of laminated composite structures. To this end, transverse shearstress and displacement fields are independently assumed, and the strain-energy relationship between these fields issystematically established using the mixed variational theorem (MVT). In MVT, the transverse shear stress fields are obtained from the third-order zigzag model, whereas the displacement fields of the conventional first-order model are considered to amplify the benefits of numerical efficiency. Additionally, a transverse displacement field with a smooth parabolic distribution is introduced to accurately predict the thermal behavior of composite structures. Furthermore, the concept of Laplace transformation is newly employed to simplify the viscoelastic problem, similar to the linear-elastic problem. To demonstrate the performance of the proposed theory, the numerical results obtained herein were compared with those available in the literature.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-949
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• 2011

In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when X and Y are convex sets in topological vector spaces, a new subclass of KKM(X, Y) different by any admissible class $\mathfrak{u}_c$(X, Y). For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.4
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• pp.202-208
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• 2015

In this study, we propose a new inference algorithm for a multiclass Gaussian process classification model using a variational EM framework and the Laplace approximation (LA) technique. This is performed in two steps, called expectation and maximization. First, in the expectation step (E-step), using Bayes' theorem and the LA technique, we derive the approximate posterior distribution of the latent function, indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. In the maximization step, we compute the maximum likelihood estimators for hyper-parameters of a covariance matrix necessary to define the prior distribution of the latent function by using the posterior distribution derived in the E-step. These steps iteratively repeat until a convergence condition is satisfied. Moreover, we conducted the experiments by using synthetic data and Iris data in order to verify the performance of the proposed algorithm. Experimental results reveal that the proposed algorithm shows good performance on these datasets.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.113-128
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• 2014

Consider a class of p(x)-Kirchhoff type equations of the form $$\left\{-M\left({\int}_{\Omega}\;\frac{1}{p(x)}{\mid}{\nabla}u{\mid}^{p(x)}\;dx\right)\;div\;({\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)={\lambda}V(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u=0\;on\;{\partial}{\Omega},$$ where p(x), $q(x){\in}C({\bar{\Omega}})$ with 1 < $p^-\;:=inf_{\Omega}\;p(x){\leq}p^+\;:=sup_{\Omega}p(x)$ < N, $M:{\mathbb{R}}^+{\rightarrow}{\mathbb{R}}^+$ is a continuous function that may be degenerate at zero, ${\lambda}$ is a positive parameter. Using variational method, we obtain some existence and multiplicity results for such problem in two cases when the weight function V (x) may change sign or not.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.703-709
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• 2012

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. Next, in [10], the first author considered a generalization of (GS) into a multi-valued circumstance called the multi-valued quasi-generalized system (in short, MQGS). In the current work, we provide an extension of (MQGS) into a system of (MQGS) in general settings. This system is called the generalized multi-valued quasi-generalized system (in short, GMQGS). Using the existence theorem for abstract economy by Kim [8], we prove the existence of solutions for (GMQGS) in the framework of Hausdorff topological vector spaces. As an application, an existence result of a system of generalized vector quasi-variational inequalities is derived.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.703-723
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• 2019

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.419-428
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• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.117-124
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• 2013

We investigate the existence of weak solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We get a theorem which shows the existence of nontrivial solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We obtain this result by reducing the biharmonic problem with nonlinear term to the biharmonic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced biharmonic problem with bounded nonlinear term.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.87-102
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• 2011

The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.