• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.45-54
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• 1998

We study the space-times that have a unique terminal indecomposable past set or a unique terminal indecomposable future set and examine their causal boundary, and we investigate some conditions for the warped product space-times of the form (a, b) ${\times}_fF$ to have a unique terminal indecomposable past set or a unique terminal indecomposable future set.

• Korea Trade Review
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• v.42 no.1
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• pp.47-67
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• 2017

This paper analyzes industries of the Daegu-Gyeongbuk province of the Republic of Korea using the product space model that was developed mid 2000s on the basis of a network analysis framework. The study examines the structure of the product space for the 421 export items at HS 4-digit level after grouping them into 4 categories; classics, emerging champions, marginals and the disappearing products. The results suggest a significant structural transformation in the product space for the local industries and the scope and magnitude of such transformation was rather large. We were also able to confirm that the structural transformation of the product space differs from industry to industry and from group to group. While the approach used is not without shortcomings, our findings also indicate that information extracted from the world merchandise trade by way of product space indicators can be quite useful in identifying structural transformation of industries.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.687-704
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• 2017

Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman transform of the convolution product can be expressed in terms of the product of the conditional FourierFeynman transforms of each function. Finally we establish change of scale formulas for the generalized analytic conditional Fourier-Feynman transform and the conditional convolution product. In this evaluation formulas and change of scale formulas we use multivariate normal distributions so that the orthonormalization process of projection vectors which are essential to establish the conditional expectations, can be removed in the existing conditional Fourier-Feynman transforms, conditional convolution products and change of scale formulas.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-995
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• 2009

As warped product manifolds provide an excellent setting to model space time near black holes or bodies with large gravitational field, the study of these manifolds assumes significance in general. B. Y. Chen [4] initiated the study of CR-warped product submanifolds in a Kaehler manifold. He obtained a characterization for a CR-submanifold to be locally a CR-warped product and an estimate for the squared norm of the second fundamental form of CR-warped products in a complex space form (cf [6]). In the present paper, we have obtained a necessary and sufficient conditions in terms of the canonical structures P and F on a CR-submanifold of a nearly Kaehler manifold under which the submanifold reduces to a locally CR-warped product submanifold. Moreover, an estimate for the second fundamental form of the submanifold in a generalized complex space is obtained and thus extend the results of Chen to a more general setting.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.469-494
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• 2022

In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.707-723
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• 1996

We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.219-226
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• 2020

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

• Publications of The Korean Astronomical Society
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• v.24 no.1
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• pp.65-81
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• 2009

We present the performance test results of VLBI Correlation Subsystem (VCS) trial product which was being developed for 1 year from August 2007. It is a core component of Korea-Japan Joint VLBI Correlator (KJJVC). The aim for developing VCS trial product is to improve the performance of VCS main product to reduce the efforts and cost, and to solve the design problems by performing the preliminary test of the manufactured trial product. The function of VCS trial product is that it is able to process the 2 stations-1 baseline, 8 Gbps/station speed, 1.2 Gbps output speed with FX-type. VCS trial product consists of Read Data Control Board (RDC), Fourier Transform Board (FTB), and Correlation and Accumulation Board (CAB). Almost main functions are integrated in the FTB and CAB board. In order to confirm the performance of VCS trial product functions, the spectral analysis, delay compensation and correlation processing experiments were carried out by using simulation and real observation data. We found that the overflow problem of re-quantization after FFT processing was occurred in the delay compensation experiment. We confirmed that this problem was caused by valid bit-expression of the re-quantized data. To solve this problem, the novel method will be applied to VCS main product. The effectiveness of VCS trial product has been verified through the preliminary experimental results, but the overflow problem was occurred.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1039-1044
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• 2000

We investigate the projectively flat warped product manifolds and study the geometric structure of the base space and its fibre. Specifically we find the conditions that the scalar curvature of the base space (B,g) vanishes if and only if f is harmonic on (B,g) and the fibre (F,$\bar{g}$) is a space of constant curvature.

• Proceedings of the Korea Society of Design Studies Conference
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• 2004.05a
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• pp.42-43
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• 2004