• Korean Journal of Mathematics
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• v.14 no.1
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• pp.1-5
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• 2006

We will introduce tensor product spectrums on the tensor product spaces. And we will show that ${\sigma}[P(T_1,T_2,{\ldots},T_n)]=P[({\sigma}(T_1),{\sigma}(T_2){\ldots},{\sigma}(T_n)]={\sigma}(T_1,T_2{\ldots},T_n)$.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.43-50
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• 2005

We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.239-247
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• 2022

Let C₀[0, T] denote the Wiener space, the space of continuous functions x(t) on [0, T] such that x(0) = 0. Define a random vector $Z_{\vec{e},k}:C_0[0,\;T] {\rightarrow}{\mathbb{R}}^k$ by $$Z_{\vec{e},k}(x)=({\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;e_1(t)dx(t),\;{\ldots},\;{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;ek(t)dx(t))$$ where e_j ∈ L₂[0, T] with e_j ≠ 0 a.e., j = 1, …, k. In this paper we study the conditional Fourier-Feynman transform and a conditional convolution product for a cylinder type functionals defined on C0[0, T] with a general vector valued conditioning functions $Z_{\vec{e},k}$ above which need not depend upon the values of x at only finitely many points in (0, T] rather than a conditioning function X(x) = (x(t₁), …, x(t_n)) where 0 < t₁ < … < t_n = T. In particular we show that the conditional Fourier-Feynman transform of the conditional convolution product is the product of conditional Fourier-Feynman transforms.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.80-82
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• 1998

we introduce the concept of coverings, direct products, cascade products and wreath products of T-fuzzy finite state machines and investigate their algebraic structures.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.863-881
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• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• Fashion & Textile Research Journal
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• v.15 no.5
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• pp.722-732
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• 2013

The purposes of this study were to investigate the needs for eco t-shirts of the new elderly consumers and to suggest strategies for eco t-shirts product development and marketing. Quantitative research was employed for research method. The data was collected from men and women in their age of 50-65, who lived in Busan, Ulsan, and Kyungnam province, during October, 2011. Respondents were selected by convenience sampling. A total of 307 responses among 350 were analyzed. Factor analysis, frequency analysis, t-test, chi-square, and regression were used for analysis. SPSS 20.0 was used for data analysis. Characteristics of the new elderly (lifestyle and environmental concern), consumption status of eco t-shirts (possession status and reasons of purchase/non-purchase), purchase intention for eco tshirts, consumer needs for t-shirts (usage situation, benefits sought, and dissatisfaction with t-shirts), preference for eco t-shirts (color, pattern, material, and shape), and demographics were surveyed. Based on the results, the vision of eco tshirts market for the new elderly consumers was positively prospected. In conclusion, specific strategies for eco t-shirts products development and marketing were suggested. Product development focused on practicality and material, design development reflecting consumers' preference, multipurpose product development, building up the product recognition, and moderate price strategy were suggested.

• Journal of The Korean Society of Grassland and Forage Science
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• v.28 no.1
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• pp.41-48
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• 2008

This study was carried out investigate the effects of dietary supplementation of agricultural by-product feed(persimmon-pell+barley bran+fermented rice bran+activated carbon) on calves disease, growth and carcass characteristics of Korean native steer. A total of twenty Korean native steer were allocated into four feeding group and assigned to four dietary treatments: Control(normal concentrate as a basal diet), T1(1% addition of by-product feeds), T2(3% addition of by-product feeds) and T3(5% addition of by-product feeds). The calf diarrhea was the highest at Control, while T3 was the lowest. The breath disease was the lowest at T2, occurrence with diarrhea and breath disease was the highest at Control. The daily gain was orderly ranked as T2(0.76kg)>T1(0.7kg), T3(0.70kg)>Control(0.67kg). The back fat thickness was orderly ranked as T2>T3>Control>T1, eye muscle area was orderly ranked as T3>T1>Control>T2. Grade of meat quantity was the highest at T1(2.3), but fat color, firmness and maturity tends to have a similar result. The marbling score and quality grade of T2 were the highest at 5.0 and 3.5, respectively. Based on the study, agricultural by-product feeds are able to many used for various purposes at disease reduce, increment of meat quantity and improvement of quality grade.