• 한국학교수학회논문집
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• 제14권2호
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• pp.227-239
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• 2011

삼각형의 외심은 중학교 2학년에 처음 도입되는 논증기하의 부분에서 다루어진다. 증명을 통해 도형의 성질을 다루는 과정에 본질적으로 상당한 어려움이 내포되어 있긴 하나, 학생들 은 교과서에서 다루는 외심과 관련한 명제의 증명을 학습하는데 특히 많은 어려움을 겪는다. 따라서 본 연구에서는 우리나라 교과서에서 다루는 외심의 정의와 증명을 오랜기간 논증기 하의 교과서로 사용된 유클리드 원론 및 현행 미국 교과서의 방식과 비교함으로써 삼각형의 외심 지도에 관한 시사점을 끌어내고자 한다.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• East Asian mathematical journal
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• 제26권5호
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.471-497
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• 2022

In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.

• 대한수학회보
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• 제39권4호
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• 대한수학회보
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• 제57권2호
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• pp.311-330
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• 2020

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

• Ocean Systems Engineering
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• 제1권2호
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• pp.171-194
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• 2011

A method to design a boundary controller for global stabilization of three-dimensional nonlinear dynamics of flexible marine risers is presented in this paper. Equations of motion of the risers are first developed in a vector form. The boundary controller at the top end of the risers is then designed based on Lyapunov's direct method. Proof of existence and uniqueness of the solutions of the closed loop control system is carried out by using the Galerkin approximation method. It is shown that when there are no environmental disturbances, the proposed boundary controller is able to force the riser to be globally exponentially stable at its equilibrium position. When there are environmental disturbances, the riser is stabilized in the neighborhood of its equilibrium position by the proposed boundary controller.

• 대한수학회지
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• 제40권2호
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• pp.195-205
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• 2003

In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma ［16］, ［17］ as special cases.

• 대한수학회지
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• 제43권1호
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• pp.45-63
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• 2006

This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.

• 대한수학회보
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• 제57권1호
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• pp.219-244
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• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.