• Journal of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.633-648
• /
• 1999

In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.111-125
• /
• 2009

The purpose of this paper is to study n-dimensional QR-submanifolds of (p-1) QR-dimension immersed in a quaternionic projective space $QP^{(n+p)/4}$ of constant Q-sectional curvature 4 and especially to determine such submanifolds under the additional condition concerning with shape operator.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.5-8
• /
• 2003

This paper we study the exact controllability for the nonlinear fuzzy control system in E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^{n}$ . fuzzy number of dimension n ; fuzzy control ; nonlinear fuzzy control system ; exact controllabilityty

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.1
• /
• pp.16-19
• /
• 2009

In this paper, we study the existence and uniqueness of solutions for the fuzzy differential equations in n-dimension fuzzy vector space $(E_N)^n$ using by Banach fixed point theorem.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.23-25
• /
• 2008

In this paper, we study the existence and uniqueness of solutions for the fuzzy differential equations in ${(E_N)^n}$ using by Banach fixed point theorem. ${(E_N)^n}$ is n-dimension fuzzy vector space.

• International Journal of Quality Innovation
• /
• v.2 no.2
• /
• pp.46-57
• /
• 2001

As the products which innovated usability have succeeded in the market, the usability of products is now considered as a new dimension of product design. This paper deals with the following questions: How has usability been embedded in the design and development of products? In the usability context, why have some breakthrough products succeeded commercially and others failed? What should be learned from the successes and the failures? For the purpose of discussing these questions, the photography industry was examined and the results were used as an illustration of the important points.

• Water Engineering Research
• /
• v.1 no.4
• /
• pp.279-291
• /
• 2000

A mathematical model using dynamic programming approach is applied to an optimal unit commitment problem. In this study, the units are treated as stages instead of as state dimension, and the time dimension corresponds to the state dimension instead of stages. A considerable amount of computer time is saved as compared to the normal approach if there are many units in the basin. A case study on the Lower Colorado River Basin System is presented to demonstrate the capabilities of the optimal scheduling of hydropower units.

• The Pure and Applied Mathematics
• /
• v.14 no.1 s.35
• /
• pp.1-5
• /
• 2007

We study the topological magnitude of a special subset from the distribution subsets in a self-similar Cantor set. The special subset whose every element has no accumulation point of a frequency sequence as some number related to the similarity dimension of the self-similar Cantor set is of the first category in the self-similar Cantor set.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.147-161
• /
• 2013

In this paper we determine certain class of $n$-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form, that is, a quaternionic K$\ddot{a}$hler manifold of constant Q-sectional curvature under the conditions (3.1) concerning with the second fundamental form and the induced almost contact 3-structure.

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.683-689
• /
• 2004

In this paper we define a Cantor-like set K with overlaps in R$^1$. We find the correlation dimension of the set K without two conditions: the control of placements of basic sets constructing K and the thickness of K being greater than 1.