• Journal for History of Mathematics
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• v.15 no.3
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• pp.83-93
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• 2002

We investigate a history of reseahches of a nonlinear elliptic equation with jumping nonlinearity, under Dirichlet boundary condition. The investigation will be focussed on the researches by topological methods. We also add recent researches, relations between multiplicity of solutions and source terms of tile equation when the nonlinearity crosses two eigenvalues and the source term is generated by three eigenfunctions.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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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.

• Journal of Integrative Natural Science
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• v.6 no.3
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• pp.181-182
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• 2013

In this note, we are concerned with a class of semi-linear elliptic pdes with exponential nonlinearity in a bounded domain. Here, the nonlinearity is more or less growing exponentially with power p. We consider the problem under two types of Dirichlet boundary condition. We give existence and non-existence of solutions for those problems and some asymptotics.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1133-1148
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• 2016

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.

• ETRI Journal
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• v.43 no.1
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• pp.74-81
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• 2021

The mixture model is a very powerful and flexible tool in clustering analysis. Based on the Dirichlet process and parsimonious Gaussian distribution, we propose a new nonparametric mixture framework for solving challenging clustering problems. Meanwhile, the inference of the model depends on the efficient online variational Bayesian approach, which enhances the information exchange between the whole and the part to a certain extent and applies to scalable datasets. The experiments on the scene database indicate that the novel clustering framework, when combined with a convolutional neural network for feature extraction, has meaningful advantages over other models.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-44
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• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.15 no.6
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• pp.10-23
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• 2016

With requiring circumspections using big data, this study attempts to develop and apply the search method for audit issues relating to the ITS policy or program. For the foregoing, the auditing process of the board of audit and inspection was converged with the theoretical frame of boundary analysis proposed by William Dunn as an analysis tool for audit issues. Moreover, we apply the text mining technique in order to computerize the analysis tool, which is similar to the boundary analysis in the concept of approaching meta-problems. For the text mining analysis, specific model we applied the antisymmetry-symmetry compound lexeme-based LDA model based on the Latent Dirichlet Allocation(LDA) methodologies proposed by David Blei. The several prime issues were founded through a case analysis as follows: lack of collection of traffic information by the urban traffic information system, which is operated by the National Police Agency, the overlapping problems between the Ministry of Land, Infrastructure and Transport and the Advanced Traffic Management System and fabrication of the mileage on digital tachograph.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.3
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• pp.97-106
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• 1989

This paper is on the modeling of two-dimensional groundwater flow, which is the first step of the development of Dynamic System Model for groundwater flow and pollutant transport in subsurface porous media. The particular features of the model are its versatility and flexibility to deal with as many real-world problems as possible. Points as well as distributed sources/sinks are included to represent recharges/pumping and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Sources/sinks strength over each element and node, hydraulic head at each Dirichlet boundary node and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution methed for the matrix equation approximating the partial differential equation of groundwater flow. The model also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. The groundwater flow model shall be combined with the model of pollutant transport in subsurface porous media. Then the combined model, with the applications of the Eigenvalue technique and the Dynamic system theory, shall be improved to the Dynamic System Model which can simulate the real groundwater flow and the pollutant transport accurately and effectively for the analyses and predictions.

• Smart Media Journal
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• v.11 no.3
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• pp.9-17
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• 2022

Algorithmic trading, which uses algorithms to trade financial products, has a problem in that the results are not stable due to many factors in the market. To alleviate this problem, ensemble techniques that combine trading algorithms have been proposed. However, there are several problems with this ensemble method. First, the trading algorithm may not be selected so as to satisfy the minimum performance requirement (more than random) of the algorithm included in the ensemble, which is a necessary requirement of the ensemble. Second, there is no guarantee that an ensemble model that performed well in the past will perform well in the future. In order to solve these problems, a method for selecting trading algorithms included in the ensemble model is proposed as follows. Based on past data, we measure the contribution of the trading algorithms included in the ensemble models with high performance. However, for contributions based only on this historical data, since there are not enough past data and the uncertainty of the past data is not reflected, the contribution distribution is approximated using the Dirichlet distribution, and the contribution values are sampled from the contribution distribution to reflect the uncertainty. Based on the contribution distribution of the trading algorithm obtained from the past data, the Transformer is trained to predict the future contribution. Trading algorithms with high predicted future contribution are selected and included in the ensemble model. Through experiments, it was proved that the proposed ensemble method showed superior performance compared to the existing ensemble methods.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.