• Communications of the Korean Mathematical Society
• /
• v.12 no.1
• /
• pp.75-78
• /
• 1997

We show that if a simple $C^*$-algebra A satisfies certain $K_1$-group conditions, then two unitarily equivalent projections are homotopic. Also we show that the equivalence of projections determined by a dimension function is a homotopy.

• Proceedings of the KIEE Conference
• /
• 1998.07b
• /
• pp.468-470
• /
• 1998

We have studied system identification model reduction method, optimal control by orthogonal functions. This paper presents the easy method that solves algebra equations instead of differential equations using Walsh, Haar, Block pulse function of orthogonal functions in state equation. The proposed algorithm is verified through some examples.

• The Pure and Applied Mathematics
• /
• v.11 no.2
• /
• pp.149-154
• /
• 2004

We show that the Choquet boundary of the tensor product of two real function algebras is the product of their Choquet boundaries.

• Journal of the Korean Society for Precision Engineering
• /
• v.29 no.10
• /
• pp.1119-1127
• /
• 2012

In this paper, we present an inverse kinematics of a 7-dof Anthropomorphic robot arm using conformal geometric algebra. The inverse kinematics of a 7-dof Anthropomorphic robot arm using CGA can be computed in an easy way. The geometrically intuitive operations of CGA make it easy to compute the joint angles of a 7-dof Anthropomorphic robot arm which need to be set in order for the robot to reach its goal or the positions of a redundant robot arm's end-effector. In order to choose the best solution of the elbow position at an inverse kinematics, optimization techniques have been proposed to minimize an objective function while satisfying the euler-lagrange equation.

• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1159-1170
• /
• 2020

We consider the weighted spaces ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓ^p(𝕊, 𝜓) to be multiplier weighted-space of ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓ^p(ℤ,𝜓) is a convolutive algebra.

• Journal of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1537-1556
• /
• 2017

In this paper, we introduce the notion of generating index ${\mathcal{I}}_1(A)$ (2-generating index ${\mathcal{I}}_2(A)$, resp.) of a left-symmetric algebra A, which is the maximum of the dimensions of the subalgebras generated by any element (any two elements, resp.). We give a classification of left-symmetric algebras with ${\mathcal{I}}_1(A)=1$ and ${\mathcal{I}}_2(A)=2$, 3 resp., and show that all such algebras can be constructed by linear and bilinear functions. Such algebras can be regarded as a generalization of those relating to the integrable (generalized) Burgers equation.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.35 no.3
• /
• pp.155-162
• /
• 2012

This study proposes an integrated approach that uses both a fuzzy service FMEA (failure mode and effect analysis) and HOQ (house of quality) matrix algebra in designing and improving a service system. The fuzzy service FMEA methodology applies the customer satisfaction to the fuzzy RPN model. We fuzzify only the service satisfaction that consist in two failure factors, intangible service and tangible service, to more effectively assess the customer satisfactions on service encounters. Proposed fuzzy service satisfactions with triangle membership function are defuzzified by using the Fuzzy Inference System, and these are eventually identified the ranks on the potential fail points. HOQ matrices are constructed from cause-effect relationships. It is possible for these relationship matrix to find a linear approximation solution on the engineering attributes. Thus, in order to demonstrate how the proposed methods work, practical sample of the A/S part in S Electronic Co. provides for the ranking of the engineering attributes which has been successfully implemented.

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.93-111
• /
• 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 $S({L_{a,\;b}}^{2}[0, T])$.

• Journal for History of Mathematics
• /
• v.22 no.3
• /
• pp.45-60
• /
• 2009

Mathematical thinking can be symbolized by the external signs, and these signs determine in reverse the form of mathematical thinking. Each symbol - a symbol in algebra, a symbol in analysis, and a diagram which verifies syllogism - reflects the diverse characteristic of cogitation in mathematics and perfirms a heuristic function.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.405-411
• /
• 2003

We prove that 25 different Artinian O-Sequences of codimension 3 type 3 with length 7 among all possible 334 cases are not level.