• 대한수학회보
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• 제41권2호
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• pp.371-385
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• 2004

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.981-992
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• 2012

Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed to solving such equations. We introduce the NHPM for solving nonlinear integro-differential equations. Several examples for solving integro-differential equations are presented to illustrate the efficiency of the proposed NHPM.

• 대한수학회지
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• 제57권4호
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• pp.825-844
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• 2020

We obtain infinitely many solutions for a class of fractional Schrödinger equation, where the nonlinearity is superquadratic or involves a combination of superquadratic and subquadratic terms at infinity. By using some weaker conditions, our results extend and improve some existing results in the literature.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.547-552
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• 2007

In this note, we extends some of the results of Liu [Fuzzy Sets and systems 157 (2006) 869-878]. This extension consists of a simple proof involving weighted functions and their preference index. We also give an elementary simple proof of the maximum entropy weighting function problem with a given preference index value without using any advanced theory like variational principles or without using Lagrangian multiplier methods.

• 대한수학회논문집
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• 제31권4호
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권4호
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• pp.296-310
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• 2023

In this paper, we derive the Γ-limit of functionals pertaining to some optimal material distribution problems that involve a variable exponent, as the exponent goes to infinity. In addition, we prove a relaxation result for supremal optimal design functionals with respect to the weak-∗ L^∞(Ω; [0, 1])× W^1,p0 (Ω;ℝ^m) weak topology.

• Bulletin of the Korean Chemical Society
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• 제34권1호
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• pp.179-187
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• 2013

We describe newly developed software named KPACK for relativistic electronic structure computation of molecules containing heavy elements that enables the two-component ab initio calculations in Kramers restricted and unrestricted formalisms in the framework of the relativistic effective core potential (RECP). The spin-orbit coupling as relativistic effect enters into the calculation at the Hartree-Fock (HF) stage and hence, is treated in a variational manner to generate two-component molecular spinors as one-electron wavefunctions for use in the correlated methods. As correlated methods, KPACK currently provides the two-component second-order M${\o}$ller-Plesset perturbation theory (MP2), configuration interaction (CI) and complete-active-space self-consistent field (CASSCF) methods. Test calculations were performed for the ground states of group-14 elements, for which the spin-orbit coupling greatly influences the determination of term symbols. A categorization of three procedures is suggested for the two-component methods on the basis of spin-orbit coupling manifested in the HF level.

• 한국광학회지
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• 제13권1호
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• pp.51-57
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• 2002

Buried 채널 도파로의 필드 분포에 대한 analytic 표현식을 effective index method(EIM)와, variational method(VM) 사용하여 구한 뒤 angular spectrum방법을 적용하여 도파로 폭과 두께에 따른 최소의 반사율을 주는 코팅층의 최적 굴절율과 정규화된 최적 코팅 두께를 구하였고 이를 비교 검토하였다. 도파로 폭이 큰 영역에서는 두 방법으로 구한 코팅층의 파라메타가 비슷한 결과를 보였으나 도파로 폭이 작아질수록 VM을 사용하여 구한 코팅층의 최적 굴절율과 정규화된 최적 두께는 클래딩층만으로 구성된 물질과 공기사이에 존재하는 코팅층의 최적 굴절율과 정규화된 최적 두께로 접근한 반면에 EIM을 사용하여 구한 경우는 차이가 많이 발생하였다. Buried채널 도파로의 도파로 폭과 두께가 같을 때, 활성층과 클래딩층의 굴절율 차이의 비에 관계없이 VM을 사용하여 구한 quasi-TE모드와 quasi-TM모드의 공차지도는 거의 동일한 영역에 존재하였다. 반면에 free space radiation mode(FSRM) 방법의 경우는 활성층과 클래딩층의 굴절율 차이의 비가 10%일 때, quasi-TE 모드와 quasi-TM모드의 공차지도는 서로 다른 영역에 존재하였다. 따라서 VM과 angular spectrum방법을 사용하여 구한 공차지도가 FSRM 방법을 사용하여 구한 공차지도보다 정확함을 알 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권2호
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• pp.143-156
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• 2014

This paper aims to give a quick view on denoising without comprehensive details. Denoising can be understood as removing unwanted parts in signals and images. Noise incorporates intrinsic random fluctuations in the data. Since noise is ubiquitous, denoising methods and models are diverse. Starting from what noise means, we briefly discuss a denoising model as maximum a posteriori estimation and relate it with a variational form or energy model. After that we present a few major branches in image and signal processing; filtering, shrinkage or thresholding, regularization and data adapted methods, although it may not be a general way of classifying denoising methods.

• 대한수학회지
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• 제57권3호
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• pp.747-775
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• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).