• KIEE International Transactions on Power Engineering
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• 제4A권2호
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• pp.73-78
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• 2004

This paper proposes a framework for determining the minimum load shedding for restoring solvability. The framework includes a continuation power flow (CPF) and an optimal power flow (OPF). The CPF parameterizes a specified outage from a set of multiple contingencies causing unsolvable cases, and it traces the path of solutions with respect to the parameter variation. At the nose point of the path, sensitivity analysis is performed in order to achieve the most effective control location for load shedding. Using the control location information, the OPF for locating the minimum load shedding is executed in order to restore power flow solvability. It is highlighted that the framework systematically determines control locations and the proper amount of load shedding. In a numerical simulation, an illustrative example of the proposed framework is shown by applying it to the New England 39 bus system.

• 대한수학회보
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• 제30권1호
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• pp.29-34
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• 1993

J. Leray [7] proposed a sufficient condition ofr the solvability of the Cauchy problem on the initial hyperplane x$_{1}$=0 with Cauchy data which are holomorphic with respect to the variables parallel to some analytic subvariety S of the initial hyperplane. Limiting the problem to the case of operators with constant coefficients, A. Kaneko [2] proposed a new sharper sufficient condition. Later we generalized this condition and showed that it is necessary and sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data and the distribution Cauchy data which contain variables parallel to S as holomorphic parameters in [5, 6]. In this paper, we extend the results in [6] to the case of operators with variable coefficients and show that it is sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data. Our main theorem can be considered as an example of a deep theorem on micro-hyperbolic systems by Kashiwara-Schapira [4] and we give a direct proof based on an elementary sweeping out procedure developed in Kaneko [3].

• 충청수학회지
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• 제25권3호
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• pp.425-443
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• 2012

Sufficient conditions for the existence of at least one solution of a class of multi-point boundary value problems of the fractional differential equations at resonance are established. The main theorem generalizes and improves those ones in [Liu, B., Solvability of multi-point boundary value problems at resonance(II), Appl. Math. Comput., 136(2003)353-377], see Remark 2.3. An example is presented to illustrate the main results.

• East Asian mathematical journal
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• 제27권1호
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• pp.51-65
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• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• 대한수학회보
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• 제54권1호
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• pp.145-158
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• 2017

We present a finite difference method for solving the Ohta-Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta-Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.

• 대한수학회지
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• 제43권1호
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• pp.87-98
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• 2006

In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권3호
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• pp.208-214
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• 2013

Bandler and Kohout investigated the solvability of fuzzy relation equations with inf-implication compositions in complete lattices. Perfilieva and Noskova investigated the solvability of fuzzy relation equations with inf-implication compositions in BL-algebras. In this paper, we investigate various solutions of fuzzy relation equations with inf-implication compositions in pseudo BL-algebras.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.145-161
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• 2020

In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.565-575
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• 2001

나는 대학원생인 여명환군과의 공동연구를 통해 결함 없는(perfect) 원판의 비선형 비대칭진동에 관한 Sridhar, Mook, Nayfeh에 의한 기존연구[1]에서 구한 가해조건(solvability conditions： 해를 asymptotic expansion으로 근사하는 과정에서 해가 유한하기 위해 응답특성이 만족해야 하는 조건)에 오류가 있음을 발견하고 수정하게 되었다. (중략)

• 대한수학회보
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• 제49권1호
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• pp.1-10
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• 2012

Let ${\Omega}$ be a bounded subset of $\mathbb{R}^n$ with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.