• 대한수학회보
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• 제35권4호
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• pp.689-700
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• 1998

We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.133-145
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• 2009

The purpose of this paper is to extend and globalize the Walrasian evolutionary cobweb model in an independent single local market of Brock and Hommes ([3]), to the case of the global market evolution over an infinite chain of many local markets interacting each other through a diffusion of prices between them. In the case of decreasing demands and increasing supplies with a weighted average of rational and naive predictors, we investigate, via the methods of Lattice Dynamical System, the spatial-temporal behaviors of global market dynamics and show that some kind of bounded dynamics of global market do exist and can be controlled by using the parameters in the model.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.427-441
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• 2009

The method of Lattice Dynamical System is used to establish a global model on an infinite chain of many local markets interacting each other through a diffusion of prices between them. This global model extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution. We assume that each local market has linear decreasing demands and quadratic supplies with naive predictors, and investigate the stationary behaviors of global price dynamics and show that their dynamics are conjugate to those of $H{\acute{e}}non$ maps and hence can exhibit complicated behaviors such as period-doubling bifurcations, chaos, and homoclic orbits etc.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.93-106
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• 2010

We employ the methods of Lattice Dynamical System to establish a global model extending the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution over an infinite chain of many local markets with interaction of each other through a diffusion of prices between them. For brevity of the model, we assume linear decreasing demands and logistic supplies with naive predictors, and investigate the traveling wave behaviors of global price dynamics and show that their dynamics are conjugate to those of H$\acute{e}$non maps and hence can exhibit complicated behaviors such as period-doubling bifurcations, chaos, and homoclic orbits etc.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.243-254
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• 2009

The main purpose of this paper is to use the methods of Lattice Dynamical System to establish a global model, which extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution over an infinite chain of many local markets interacting each other through a diffusion of prices between them. For brevity of the model, we assume linear decreasing demands and quadratic supplies with naive predictors, and investigate the spatially homogeneous global price dynamics and show that the dynamics is topologically conjugate to that of well-known logistic map and hence undergoes a period-doubling bifurcation route to chaos as a parameter varies through a critical value.

• Coupled systems mechanics
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• 제7권2호
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• pp.141-162
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• 2018

This work presents a novel model for analysis of the loading rate influence onto structure response. The model is based on the principles of nonlinear system dynamics, i.e., consists of a system of nonlinear differential equations. In contrast to classical linearized models, this one comprises mass and loading as integral parts of the model. Application of the Kelvin and the Maxwell material models relates the novel formulation to the existing material formulations. All the analysis is performed on a proprietary computer program based on Wolfram Mathematica. This work can be considered as an extended proof of concept for the application of the nonlinear solid model in material response to dynamic loading.

• Applied Microscopy
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• 제39권4호
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• pp.341-348
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• 2009

본 연구에서는 평균 입자크기가 100 nm인 $BaTiO_3$ 나노 결정체의 결정 구조를 전자회절을 이용하여 분석하였다. 전자회절을 이용하여 구조분석을 수행하기 위해 PED 장치의 실험인자를 보정한 후, PED와 일반적인 SAED를 이용하여 전자회절도형을 획득하여 비교 분석을 수행하였다. $BaTiO_3$ 나노 결정체에 대해 PED를 이용한 구조분석을 수행한 결과, $BaTiO_3$ 나노입자는 상온에서 입방정계와 정방정계의 구조가 혼합되어 존재함을 알 수 있었다. 또한 이론적 계산을 통해 두 상이 혼재된 $BaTiO_3$ 나노입자는 입방정계의 구조가 약 8.5nm의 표면을 형성하고 있는 coreshell 구조를 이루고 있음을 예측할 수 있었다. 이러한 $BaTiO_3$ 나노입자에 대한 입방정계와 정방정계 구조의 각각의 격자상수는 a=3.999${\AA}$과 a=3.999${\AA}$, c=4.022${\AA}$이었다. 이와 같이 일반적인 SAED에 비해 뛰어난 공간분해능과 다중산란 효과를 억제할 수 있는 PED 기법은 복합 나노 구조체의 결정구조분석에 보다 유용한 분석 기술로 활용할 수 있을 것으로 기대된다.