• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.242-242
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• 2000

Comparing to the conventional adaptive filters using LMS algorithm, the proposed adaptive filters can reduce the amounts of computation and have robustness to variance of characteristics of input signals. LMS algorithm is performed in the domain of Hadamard transform after a reference signal and input signal are transformed by fast Hadamard transformation. As a transformation from time domain to Hadamard transformed domain, the proposed filter not only maintains the performance of estimating an input signal but also greatly reduces the number of multiplication. Moreover, the effect of characteristic changes of input signal is decreased. Computer simulation shows the stability and robustness of the proposed filter.

• 폴리머
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• 제25권4호
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• pp.536-544
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• 2001

실험적 사실에 근거하여 고분자 유체의 점탄성 구성방정식에 빈번히 적용되어온 time-strain separability 가설의 타당성을 수학적 안정성 관점에서 분석한다. 안정성 조건으로는 방정식의 빠른 응답과 관련된 Hadamard 안정성과 소산 성질에 의하여 결정되는 소산 안정성이 있으며, asymptotic 분석을 이용한 결과 가설을 따르는 구성방정식은 Hadamard 또는 소산 불안정함이 증명되었다. 응력완화 실험에서 이미 관찰된 짧은 시간영역에서 time-strain separability의 가설이 적용되지 않는다는 사실은 본 결과와 일치한다. 따라서 separability를 구성방정식에 적용하는 것은 수학적 불안정뿐 아니라 열역학적 모순점을 나타내게 되며, 또한 실험에서도 그 타당성의 한계에 주의할 필요가 있다. 더욱이 damping 함수 역시 실제와는 무관한 가상적 값을 제공하므로 damping 함수의 사용은 긴 시간영역에서 응력완화 거동을 기술하기 위한 curve fitting 이상의 의미는 없다 하겠다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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• pp.1125-1128
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• 1993

We propose the new method about the neural-based pattern recognition by using Hadamard transform for the improvement of learning speed, stability and flexibility of network. We can obtain the spatial feature of pattern by Hadamard transformed pattern. We carried out an experiment to estimate the effect of Hadamard transform. We tried the learning of numeric patterns, and tried the pattern recognition with noisy pattern. As a result, the learning times of the network for the 'Hadamard' case is smaller than that of usual case. And the recognition rate of the network for the 'Hadamard' case is higher than that of usual case, too.

• Korea-Australia Rheology Journal
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• 제14권1호
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• pp.33-45
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• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.559-571
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• 2018

In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.

• Macromolecular Research
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• 제9권3호
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• pp.164-170
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• 2001

Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for the simplified differential version of these constitutive equations. It is proved that they are globally Hadamard stable except for the case of maximum constant backbone stretch (λ = q) with arm withdrawal s$\_$c/ neglected, as long as the orientation tensor remains positive definite or the smooth strain history in the now is previously given. However this model is dissipative unstable, since the steady shear How curves exhibit non-monotonic dependence on shear rate. This type of instability corresponds to the nonlinear instability in simple shear flow under finite amplitude disturbances. Additionally in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady now curves, the constitutive equations will possibly violate the positive definiteness of the orientation tensor and thus become Hadamard unstable.

• Korea-Australia Rheology Journal
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• 제15권3호
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• pp.131-150
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• 2003

A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 하계학술대회 논문집 D
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• pp.3115-3117
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• 2000

기존의 LMS 알고리듬을 이용한 적응필터에 비해 연산횟수를 줄이고 입력신호의 통계적 특성에 덜 민감한 적응필터를 제안한다. 입력 신호와 기준신호에 대한 고속 하다마드 변환을 수행한 후 하다마드 변환 영역에서 LMS 알고리듬을 적용한다 기존의 적응필터와 비교하여 필터의 입력신호 추정 성능은 유지하면서 고속 하다마드 변환으로 인해 적응과정에서의 곱셈연산이 크게 줄어드며 잡음의 분산값 변화와 같은 입력신호의 변화에 대한 필터의 안정도와 강인성이 크게 향상됨을 보인다.

• 한국수학사학회지
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• 제25권4호
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• pp.53-67
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• 2012

오늘날, 우주비행궤도의 정밀계산은 매우 실용적인 학문이 되었다. 프엥카레의 천체역학의 주요 키워드는 적분불변, 주기해, 점근해, 특성지수, 단일값을 갖는 새로운 적분의 불가능성등으로 볼 수 있다. 적분불변은 모든 시간에 걸쳐서 일정한 적분 값을 유지하는 것을 말한다. 곡선의 호상에서 취한 적분은 2, 3차원으로 확장하였다. 고유치는 궤적의 형식에 따라서 분류되는 바 매듭, 초점들, 말 안장점, 중심과 같은 것이다. 주기해에서는 고유값에 해당하는 특성지수에 따라서 주기해를 갖는다고 하였다. 주기해의 안정성은 특성지수의 성질을 조사하는 것과 동일한 것이다. 분지라고 불리는 천체궤도의 카오스적 존재 가능성을 프엥카레는 예외적 궤도의 존재로 주장하였고, 이는 아다마르의 견해대로 우연에 의한 확률적 궤도의 존재를 말하는 것이다. 호모크리닉점의 존재는 삼체문제의 이중 점근해를 말하고, 이것은 궤적이 카오적임을 말해주는 것이다. 주어진 조건에 따라서 엑스포넨셜 함수의 고유값인 특성지수가 계속 변함으로, 매우 작은 간격에서도 분지들은 얻게 되고, 원래의 주기와는 다소 멀어지는 것이다. 주기해의 안정성문제는 특성지수를 연구하는 것과 같다. 프엥카레는 궤적의 거동이 선형변환의 고유값 성질에 의존하고 이 고유값들과 서로 다른 특이점들 사이에 매우 밀접한 관련이 있음을 발견하였다. 뷔른스, 질덴, 순드만, 힐, 다윈, 벌코프, 하이테커, 아다마르등의 이론전개는 프엥카레의 이론과 불가분의 관계를 갖는다.