• 대한수학회논문집
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• 제35권2호
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• pp.517-532
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• 2020

In this paper, we consider a class of nonlocal problems with indefinite weights in Orlicz-Sobolev space. Under some suitable conditions on the nonlinearities, we establish some existence results using variational techniques and Ekeland's variational principle.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.101-123
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• 2019

In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

• 대한수학회논문집
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• 제21권4호
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• pp.665-673
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• 2006

In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

• Korean Journal of Mathematics
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• 제25권1호
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• pp.19-35
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• 2017

In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.359-377
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• 2017

In this paper, we consider a system of generalized nonlinear ordered variational inclusions in real ordered Banach spaces and define an iterative algorithm for a solution of our problems. By using the resolvent operator techniques to prove an existence result for the solution of the system of generalized nonlinear ordered variational inclusions and discuss convergence of sequences suggested by the algorithms.

• Journal of Korean Society for Atmospheric Environment
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• 제19권E2호
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• pp.75-81
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• 2003

Variational data assimilation, which is recently introduced to the air quality modeling, is a promising tool for obtaining optimal estimates of initial conditions and other important parameters such as emission and deposition rates. In this paper. two advanced techniques for variational data assimilation, based on the adjoint and quasi-inverse methods, are tested for a simple air quality problem. The four-dimensional variational assimilation (4D-Var) requires to run an adjoint model to provide the gradient information in an iterative minimization process, whereas the inverse 3D-Var (I3D-Var) seeks for optimal initial conditions directly by running a quasi -inverse model. For a process with small dissipation, I3D-Vu outperforms 4D-Var in both computing time and accuracy. Hybrid application which combines I3D-Var and standard 4D-Var is also suggested for efficient data assimilation in air quality problems.

• Journal of Communications and Networks
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• 제18권3호
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• pp.397-410
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• 2016

This paper proposes a novel cooperative localization method for distributed wireless networks in 3-dimensional (3D) global positioning system (GPS) denied environments. The proposed method, which is referred to as hybrid ellipsoidal variational algorithm (HEVA), combines the use of non-parametric belief propagation (NBP) and variational Bayes (VB) to benefit from both the use of the rich information in NBP and compact communication size of a parametric form. InHEVA, two novel filters are also employed. The first one mitigates non-line-of-sight (NLoS) time-of-arrival (ToA) messages, permitting it to work well in high noise environments with NLoS bias while the second one decreases the number of calculations. Simulation results illustrate that HEVA significantly outperforms traditional NBP methods in localization while requires only 50% of their complexity. The superiority of VB over other clustering techniques is also shown.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.203-221
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• 2022

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

• 한국멀티미디어학회논문지
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• 제22권11호
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• pp.1251-1258
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• 2019

Intelligent tutoring system enables users to effectively learn by utilizing various artificial intelligence techniques. For instance, it can recommend a proper curriculum or learning method to individual users based on their learning history. To do this effectively, user's characteristics need to be analyzed and classified based on various aspects such as interest, learning ability, and personality. Even though data labeled by the characteristics are required for more accurate classification, it is not easy to acquire enough amount of labeled data due to the labeling cost. On the other hand, unlabeled data should not need labeling process to make a large number of unlabeled data be collected and utilized. In this paper, we propose a semi-supervised learning method based on feedback variational auto-encoder(FVAE), which uses both labeled data and unlabeled data. FVAE is a variation of variational auto-encoder(VAE), where a multi-layer perceptron is added for giving feedback. Using unlabeled data, we train FVAE and fetch the encoder of FVAE. And then, we extract features from labeled data by using the encoder and train classifiers with the extracted features. In the experiments, we proved that FVAE-based semi-supervised learning was superior to VAE-based method in terms with accuracy and F1 score.

• 대한수학회지
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• 제47권4호
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• pp.845-860
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• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.