• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.19-30
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• 2011

In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

• 충청수학회지
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• 제27권1호
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• pp.17-27
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• 2014

In order to study the propagation of singularities for solutions to second order quasilinear strictly hyperbolic equations with boundary, we have to consider the regularity of solutions of first order nonlinear equations satisfied by a characteristic hyper-surface. In this paper, we study the regularity compositions of the form v(${\varphi}$(x), x) with v and ${\varphi}$ assumed to have limited Sobolev regularities and we use it to prove the regularity of solutions of the first order nonlinear equations.

• 호남수학학술지
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• 제39권4호
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• pp.465-473
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• 2017

In this paper, we define a totally umbilic hypersurface of first order and show that a totally umbilic hypersurface of first order in an Einstein manifold has a parallel second fundamental form. Furthermore we prove that a complete, simply connected and totally umbilic hypersurface of first order in a space of constant curvature is a Riemannian product of Einstein manifolds. Finally we show a proper example which is a totally umbilic hypersurface of first order but not a totally umbilic hypersurface.

• 대한수학회보
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• 제48권6호
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• pp.1157-1167
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• 2011

We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, a study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order 4 is provided to illustrate the result.

• 대한수학회지
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• 제54권1호
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• pp.87-99
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• 2017

To indicate the statistical complexity of dynamical systems, we introduce the notions of higher order irregular set and higher order maximal Birkhoff average oscillation in this paper. We prove that, in the setting of topologically mixing Markov chain, the set consisting of those points having maximal k-order Birkhoff average oscillation for all positive integers k is as large as the whole space from the topological point of view. As applications, we discuss the corresponding results on a repeller.

• 대한수학회논문집
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• 제20권1호
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• pp.1-14
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• 2005

The aim of this paper is to study order-congruences on a S-poset A and to characterize the order-congruences by the concepts of pseudooreders on A and quasi-chains module a congruence p. Some homomorphism theorems of S-posets are given which is similar to the one of ordered semigroups. Finally, It is shown that there exists the non-trivial order-congruence on a S-poset by an example.

• 대한수학회보
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• 제55권1호
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• pp.297-310
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• 2018

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

• 전기학회논문지
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• 제59권5호
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• pp.961-965
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• 2010

A reduced order observer with finite time convergence characteristics is proposed for linear time invariant systems. The proposed finite time reduced order observer(FTROO) is a dual observer scheme in which two reduced order Luenberger observers with asymptotic convergence characteristics and a finite time delay element are employed. The FTROO can be constructed so as to converge in the designer specified finite time independent of the eigenvalues of the reduced order observers. A numerical example is given to show the finite-time convergence characteristics of the proposed FTROO.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 춘계학술대회 논문요약집
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• pp.284-284
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• 2004

기존의 모빌리티 분석 방법은 크게 Grubler의 모빌리티 공식에 의한 zeroth-order 모빌리티 분석 방법, 관절 스크류를 활용한 일차 기구학 성질을 관절 스크류로서 활용한 first-order 모빌리티 분석 방법, 그리고 이차 기구학 특성을 활용하는 second-order 모빌리티 분석 방법으로 구분된다. 그러나, 많은 과다 구속 메커니즘의 경우 zeroth-order 또는 first-order 모빌리티 분석 방법에 의해서는 모빌리티의 분석이 불가능하며 현재까지 문헌에 소개된 second-order 모빌리티 분석 방법은 수치적인 방법에 의존하여 전체 메카니즘의 이차 기구학 특성을 분석하게 되므로 매우 복잡하여 활용하는데 매우 어려움이 있다.(중략)

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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• pp.289-295
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• 2012

We research the properties of solutions of general higher order non-homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.