• 대한수학회논문집
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• 제32권4호
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• pp.851-864
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• 2017

The problems of global and local exponential stability analysis of a class of nonlinear non-autonomous difference equations in Banach spaces are studied in this paper. By a novel comparison technique, new explicit exponential stability conditions are derived. Numerical examples are given to illustrate the effectiveness of the obtained results.

• 대한수학회논문집
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• 제24권1호
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• pp.85-97
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• 2009

In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].

• 충청수학회지
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• 제37권1호
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• pp.41-55
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• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• 대한지리학회지
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• 제45권4호
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• pp.478-501
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• 2010

이 연구의 목적은 경제공간의 역동성을 이끄는 세계화, 지식기반경제, 정보사회, 서비스세계의 4대 글로벌 메가트랜드를 통해 국가간 및 지역간에 나타나는 공간경제의 불균형을 이해하는 것이다. 동아시아를 대상으로 국가간 불균형과 일본, 한국, 태국을 사례 로 국가 내에서 지역간 불균형을 분석하였다. 4대 메가트랜드와 관련된 변수들을 모두 고려할 때, 4대 글로벌 메가트랜드는 국제적인 차원과 국가내의 지역적인 차원에서 불균형의 변이를 설명해주고 있다. 그러나 개별변수들이 공간적 불균형에 미치는 영향은 분석의 공간적 규모와 국가적 특성에 따라 달리 나타난다. 대체로 동아시아국가들간에 1인당 GNI는 수렴하는 경향을 보이고, 한 국가내의 지역차원에서는 불균형이 줄어드는 경향과 확대하는 경향이 함께 나타나고 있다. 1970년대의 두 차례의 석유파동과 1990년대 말경의 동아시아 금융위기는 일반적인 불균형완화경향의 연속성을 단절시키는 결과를 초래했고, 경제활동의 지역간 국제간 불균형을 증가시켰다. 이는 세계적인 위기의 영향이 국가에 따라 다르지만 일반적으로 주변국가와 주변지역의 경제는 세계적 경제위기상황에서 더욱 취약하다는 점을 시사한다.

• 한국사회복지학
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• 제65권4호
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• pp.295-315
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• 2013

이 연구는 유력한 지구시민권구상인 Rawls의 자유주의적 접근과 코즈모폴리턴 공화주의구상에 대해 지구적 정의론으로서의 윤리학적 기초를 연구하는 것이 목적이다. 의무론측면에서 자유주의적 국제주의에 경도된 Rawls의 견해는 국제관계의 불평등이 구조화된 경제의 세계화시대의 호혜성의 의무와 시민적 권리에 관한 의무를 반영하지 못하는 한계가 있지만, 코즈모폴리턴 공화주의는 지구적 차원의 반지배원칙의 구현을 주창해 의무론적 정당화의 기반을 갖추고 있다. 공리주의 면에서 Rawls는 자유주의적 국제주의에 입각해 개별국가들 간의 재분배를 거부하는 논리에 대해 정당화를 시도하고 있지만, 코즈모폴리턴 공화주의는 개도국시민들의 구조적 희생을 극복해 지구적 차원의 해악을 줄이고 효용수준을 획기적으로 개선할 가능성이 있다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.43-55
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• 2011

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1395-1407
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• 2011

When a Sequential Quadratic Programming (SQP) method is used to solve the nonlinear programming problems, one of the main difficulties is that the Quadratic Programming (QP) subproblem may be incompatible. In this paper, an SQP algorithm is given by modifying the traditional QP subproblem and applying a class of $l_{\infty}$ penalty function whose penalty parameters can be adjusted automatically. The new QP subproblem is compatible. Under the extended Mangasarian-Fromovitz constraint qualification condition and the boundedness of the iterates, the algorithm is showed to be globally convergent to a KKT point of the non-linear programming problem.

• Journal of Electrical Engineering and Technology
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• 제12권4호
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• pp.1417-1426
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• 2017

Power system analysis, Non-Convex Economic Dispatch (NED) is considered as an open and demanding optimization problem. Despite the fact that realistic ED problems have non-convex cost functions with equality and inequality constraints, conventional search methods have not been able to effectively find the global answers. Considering the great potential of meta-heuristic optimization techniques, many researchers have started applying these techniques in order to solve NED problems. In this paper, a new and efficient approach is proposed based on imperialist competitive algorithm (ICA). The proposed algorithm which is named multi-operator ICA (MuICA) merges three operators with the original ICA in order to simultaneously avoid the premature convergence and achieve the global optimum answer. In this study, the proposed algorithm has been applied to different test systems and the results have been compared with other optimization methods, tending to study the performance of the MuICA. Simulation results are the confirmation of superior performance of MuICA in solving NED problems.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.961-972
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• 2008

In this paper, we consider the global exponential stability of cellular neural networks with time-varying delays. Based on the Lyapunov function method and convex optimization approach, a novel delay-dependent criterion of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, the interior point algorithm is utilized in this work. Two numerical examples are given to show the effectiveness of our results.

• 대한수학회보
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• 제58권5호
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.