• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.107-119
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• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

• The Journal of the Acoustical Society of Korea
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• v.1 no.1
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• pp.92-96
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• 1982

In this paper, the interaction of electron and phonon in metals is expressed using Hamiltonian operator as follows. By excahnging phonon energy with in the vicinity of isotropical Fermi surface and using following electron and hole operators. We obtain the interaction of electron and phonon. And new Feynman Graphs are tried with the following conditions on. First, when state transfer state, phonon cannot be created. Second, when state transfer state, phonon cannot be destroyed. Third, when state transfer state, phonon can be created or destroyed. Fourth, when state transfer state, phonon can be created or destroyed.

• Electrical & Electronic Materials
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• v.17 no.4
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• pp.23-31
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• 2004

20세기 중반까지 과학을 통한 한 개의 전자 및 원자의 인위적으로 제어할 수 있는 장치의 제조는 어려울 것이라 예측되었고, 많은 사람들은 이러한 생각을 받아들였다. 그러나 1959년 Feynman은 그의 미래 지향적 언급에서 "There's plenty of room at the bottom." 이라 하여 당시에 불가능하다고 생각되던 단일 전자, 원자 및 분자의 제어가 20세기 안에 가능해질 것을 예시하였고, 실제로 그의 예상대로 1981년 Binnig와 Rohrer가 STM을 사용한 원자 및 분자 조작이 가능하다는 것을 밝혔으며, 1985년에 Likharev는 단일전자 트랜지스터(single electron transistor)를 통해 전자 한 개의 조작이 가능하다는 것을 보여주었다.(중략)

• Electrical & Electronic Materials
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• v.17 no.4
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• pp.40-46
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• 2004

나노테크놀러지(Nanotechnology)는 1965년도 노벨물리학상 수상자인 Richard P. Feynman이 1959년에 칼텍(CalTech)에서 했던 강연 "There's Plenty of Room at the bottom"에서 처음으로 예언되었다 그는 전 세계의 모든 정보를 2백분의 1인치 크기의 정육면체에 기록할 수 있는 날이 올 것이라고 예언하였다. 최근 기술 선진국들은 미래지식산업시대를 겨냥한 고부가가치 제품개발에 집중하고 있으며, 제품크기의 극소화를 통해 성능 고도화와 가격경쟁력 향상은 물론 에너지와 자원의 경제적 활용을 추구하고 있다.(중략)하고 있다.(중략)

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.181-195
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• 2020

This paper suggests the price of vulnerable European option under a constant elasticity of variance model by using asymptotic analysis technique and obtains the approximated solution of the option price. Finally, we illustrate an accuracy of the vulnerable option price so that the approximate solution is well-defined.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.

• Bulletin of the Korean Chemical Society
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• v.12 no.4
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• pp.383-387
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• 1991

A new perturbation theory called as star expansion method is used to obtain the nonlinear retarded solution of the Schlogl models with some kinds of external input. The approximate nonlinear solutions are compared with the exact solution, linear solutions, and those obtained by the Feynman method.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.63-80
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• 2006

Along with natural and algebraic languages, schema is a fundamental component of mathematical language. The principal purpose of this present study is to focus on this point in detail. Schema was already in use during Pythagoras' lifetime for making geometrical inferences. It was no different in the case of Oriental mathematics, where traces have been found from time to time in ancient Chinese documents. In schma an idea is transformed into something conceptual through the use of perceptive images. It's heuristic value lies in that it facilitates problem solution by appealing directly to intuition. Furthermore, introducing schema is very effective from an educational point of view. However we should keep in mind that proof is not replaceable by it. In this study, various schemata will be presented from a diachronic point of view, We will show with emaples from the theory of categories, Feynman's diagram, and argand's plane, that schema is an indispensable tool for constructing new knowledge.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.349-361
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• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.