• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1343-1359
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• 2009

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.661-680
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• 2013

The eigenvalue problems arise in the analysis of stability of traveling waves or rest state solutions are currently dealt with, using the Evans function method. In the literature, it had been shown that, use of this method is not straightforward even in very simple examples. Here an extended "variational" method to solve the eigenvalue problem for the higher order dierential equations is suggested. The extended method is matched to the well known variational iteration method. The criteria for validity of the eigenfunctions and eigenvalues obtained is presented. Attention is focused to find eigenvalue and eigenfunction solutions of the Kuramoto-Slivashinsky and (K[p,q]) equation.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.613-622
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• 2023

In this paper, finite element method is applied to solve boundary control problem governed by elliptic variational inequality with an infinite number of variables. First, we introduce some important features of the finite element method, boundary control problem governed by elliptic variational inequalities with an infinite number of variables in the case of the control and observation are on the boundary is introduced. We prove the existence of the solution by using the augmented Lagrangian multipliers method. A triangular type finite element method is used.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1311-1327
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• 2015

In this paper, we have applied a new class of approximate analytical methods called Variational Approach (VA) for high nonlinear vibration equations. Three examples have been introduced and discussed. The effects of important parameters on the response of the problems have been considered. Runge-Kutta's algorithm has been used to prepare numerical solutions. The results of variational approach are compared with energy balance method and numerical and exact solutions. It has been established that the method is an easy mathematical tool for solving conservative nonlinear problems. The method doesn't need small perturbation and with only one iteration achieve us to a high accurate solution.

• The Korean Journal of Applied Statistics
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• v.34 no.1
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• pp.9-23
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• 2021

In the following paper we introduce a variational Bayes method that approximates posterior distributions with mean-field method. In particular, we introduce automatic differentiation variation inference (ADVI), which approximates joint posterior distributions using the product of Gaussian distributions after transforming parameters into real coordinate space, and then apply it to pharmacokinetic models that are models for the study of the time course of drug absorption, distribution, metabolism and excretion. We analyze real data sets using ADVI and compare the results with those based on Markov chain Monte Carlo. We implement the algorithms using Stan.

• Journal of Internet Computing and Services
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• v.22 no.2
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• pp.1-9
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• 2021

Traditionally, most malicious codes have been analyzed using feature information extracted by domain experts. However, this feature-based analysis method depends on the analyst's capabilities and has limitations in detecting variant malicious codes that have modified existing malicious codes. In this study, we propose a ResNet-Variational AutoEncder-based variant malware classification method that can classify a family of variant malware without domain expert intervention. The Variational AutoEncoder network has the characteristics of creating new data within a normal distribution and understanding the characteristics of the data well in the learning process of training data provided as input values. In this study, important features of malicious code could be extracted by extracting latent variables in the learning process of Variational AutoEncoder. In addition, transfer learning was performed to better learn the characteristics of the training data and increase the efficiency of learning. The learning parameters of the ResNet-152 model pre-trained with the ImageNet Dataset were transferred to the learning parameters of the Encoder Network. The ResNet-Variational AutoEncoder that performed transfer learning showed higher performance than the existing Variational AutoEncoder and provided learning efficiency. Meanwhile, an ensemble model, Stacking Classifier, was used as a method for classifying variant malicious codes. As a result of learning the Stacking Classifier based on the characteristic data of the variant malware extracted by the Encoder Network of the ResNet-VAE model, an accuracy of 98.66% and an F1-Score of 98.68 were obtained.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.191-207
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• 2013

In this paper, we introduce the shrinking projection method for hemi-relatively nonexpansive mappings to find a common solution of variational inequality problems and equilibrium problems in uniformly convex and uniformly smooth Banach spaces and prove some strong convergence theorems to the common solution by using the proposed method.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.12
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• pp.36-42
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• 1993

By the variational method, the coplanar waveguide(C.P.W) shielded by two conducting plates has been analyzed. The particular potential solution has been obtained for the boundary conditions in C.P.W. The characteristic impedance and the effective dielectric constant in C.P.W. have been obtained by the variational method using the potential function and the assumed basis function for charge distributions. To consider the effect of the conducting plate in C.P.W. two cases, with and without the top plate, have been analyzed and compared respectively.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.469-481
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• 2017

In this paper, we established a general nonconvex split variational inequality problem, this is, an extension of general convex split variational inequality problems in two different Hilbert spaces. By using the concepts of prox-regularity, we proved the convergence of the iterative schemes for the general nonconvex split variational inequality problems. Further, we also discussed the iterative method for the general convex split variational inequality problems.

• Journal of Information Processing Systems
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• v.15 no.6
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• pp.1296-1305
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• 2019

To solve the problem of poor noise suppression capability and frequent loss of edge contour and detailed information in current fusion methods, an infrared and visible light image fusion method based on variational multiscale decomposition is proposed. Firstly, the fused images are separately processed through variational multiscale decomposition to obtain texture components and structural components. The method of guided filter is used to carry out the fusion of the texture components of the fused image. In the structural component fusion, a method is proposed to measure the fused weights with phase consistency, sharpness, and brightness comprehensive information. Finally, the texture components of the two images are fused. The structure components are added to obtain the final fused image. The experimental results show that the proposed method displays very good noise robustness, and it also helps realize better fusion quality.