• The Research Journal of the Costume Culture
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• v.5 no.2
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• pp.269-284
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• 1997

Followings are the analysis of the two areas'costumes, the Renaissance and Baroque, as the analytic and synthetic structures. From the analytic structure of the costumes, the analytic body and of the Renaissant man's outer garments is manteau, pourpoint, trousses, bas du chausses, and codpiece of the hat is toque. And the analyic body of the Baroque, man's costume is pourpoint and rhingrave, of the under garments is chemise, of the hat is felt, of the shoes is shoes. In the analytic structure of woman's costume, the analytic body of the Renaissant outer garments is robe, of the under garments is corps-pique, chemise, and vertugadin, of the hat is french hood. And the analytic body of the Baroque outer garments is skirt and overdress, of the undergarments is corps-baleine. The results we have got from the analysis of the synthetic structures of the costumes is that other analytic elements are chosen and united as the component features of the major analytic elements among the analytic elements in the tables of 3-1, 3-2, 3-3, and 3-4. If we compare the two analytic bodies of the two areas, we can see that the names of the costumes were changed and the component features about the names were changed according to an area, too. And we can see the synthetic structures were changed according to the analytic body in the analytic structures were changed according to the analytic body in the analytic structures with the synthetic structures.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.231-246
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• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.903-924
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• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.217-231
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• 2013

In this paper we establish a Fubini theorem for generalized analytic Feynman integral and $L_1$ generalized analytic Fourier-Feynman transform for the functional of the form $$F(x)=f({\langle}{\alpha}_1,\;x{\rangle},\;{\cdots},\;{\langle}{{\alpha}_m,\;x{\rangle}),$$ where {${\alpha}_1$, ${\cdots}$, ${\alpha}_m$} is an orthonormal set of functions from $L_{a,b}^2[0,T]$. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.1
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• pp.27-35
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• 2005

Due to the importance of lead time demand in the design of inventory management systems, researchers and practitioners have paid continuous attention and a few analytic models using the compound distribution approach have been reported. However, since the nature of compound distributions is hardly amenable, the analytic models have been done by non‐recognition of the compound nature of some components to reduce the analytic task. This study concerns some of the important aspects in the analytic models. Through the theoretic examination of the analytic model approach and the comparison with the rigid compound stochastic process approach, this study clarifies the assumptions implicitly made by the analytic models and provides some precautions in using the analytic models. Illustrative examples are also presented.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.1042-1047
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• 2003

Due to the Importance of lead time demand in the design of Inventory management systems. researchers and practitioners have paid continuous attention and a few analytic models using the compound distribution approach have been reported. However, since the nature or compound distributions is hardly amenable. the analytic models have been done by non-recognition of the compound nature or some components to reduce the analytic task. This study concerns some of the important aspects in the analytic models. Through the theoretic examination of the analytic model approach and the comparison with the rigid compound stochastic process approach. this study clarifies the assumptions implicitly made by the analytic models and provides some precautions in using the analytic models.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.411-421
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• 2015

This paper investigates the issue of analytic travelling wave solutions for some important coupled models of fractional order. Analytic travelling wave solutions of the considered model are found by means of the Q-function method. The results give us that the Q-function method is very simple, reliable and effective for searching analytic exact solutions of complex nonlinear partial differential equations.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1027-1041
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• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.47-66
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• 1998

In this paper, we introduce an $L_p$ analytic Fourier-Feynman transformation, show the existence of the $L_p$ analytic Fourier-Feynman transforms for a certain class of cylinder functionals on an abstract Wiener space, and investigate its interesting properties. Moreover, we define a convolution product for two functionals on the abstract Wiener space and establish the relationships between the Fourier-Feynman transform for the convolution product of two cylinder functionals and the Fourier-Feynman transform for each functional.