• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.161-171
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• 2013

Given an integer $n{\geq}1$ and a compact group G, we find some restrictions for the probability that two randomly picked elements $x^n$ and $y$ of G commute. In the case $n=1$ this notion was investigated by W. H. Gustafson in 1973 and its influence on the structure of the group has been studied in the researches of several authors in last years.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.2
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• pp.110-121
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• 1997

Stability issues of linear Takagi-Sugeno fuzzy modles are thoroughly investigated. At first, a systematic way of searching for a common symmetric positive definite P matrix (common P matrix in short), which is related to stability, is proposed for N subsystems which are under a pairwise commutativity assumption. Robustness issue under modeling uncertainty in each subsystem is then considered by proposing a quadratic stability criterion and a method of determining uncertainty bounds. Finally, it is shown that the pairwise commutative assumption can be in fact relaxed by interpreting the uncertainties as mismatch parts of non-commutative system matrices. Several examples show the validity of the proposed methods.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.177-183
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• 1997

Let ${\sigma}(X,x_0,G)$ be the fundamental group of a transformation group (X,G). Let $R({\varphi},{\psi})$) be the generalized Reidemeister number for an endomorphism $({\varphi},{\psi}):(X,G){\rightarrow}(X,G)$. In this paper, our main results are as follows ; we prove some sufficient conditions for $R({\varphi},{\psi})$ to be the cardinality of $Coker(1-({\varphi},{\psi})_{\bar{\sigma}})$, where 1 is the identity isomorphism and $({\varphi},{\psi})_{\bar{\sigma}}$ is the endomorphism of ${\bar{\sigma}}(X,x_0,G)$, the quotient group of ${\sigma}(X,x_0,G)$ by the commutator subgroup $C({\sigma}(X,x_0,G))$, induced by (${\varphi},{\psi}$). In particular, we prove $R({\varphi},{\psi})={\mid}Coker(1-({\varphi},{\psi})_{\bar{\sigma}}){\mid}$, provided that (${\varphi},{\psi}$) is eventually commutative.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.151-158
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• 1999

Let (X, G) be a transformation group and ${\sigma}(X,x_0,G)$ the fundamental group of (X, G). In this paper, we prove that the Reidemeister number $R(f_G)$ for an endomorphism $f_G:(X,G){\rightarrow}(X,G)$ is a homotopy invariant. In particular, when any self-map $f:X{\rightarrow}X$ is homotopic to the identity map, we give some calculation of the lower bound of $R(f_G)$. Finally, we discuss commutativity and product formula for the Reidemeister number $R(f_G)$.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.199-214
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• 2015

We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.12 no.3
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• pp.189-199
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• 1987

This paper describes a method to perform the conversion between two widely used multiplexing techniques in telephony. TDM and FDM. This method is based on the digitized Weaver modulator for single side-band modulation, and makes use of a PV digital filter which has commutativity with sinusoidal modulators and periodicity of coefficients. Thus we greatly reduce the complexity and multiplication rate of the system.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.417-428
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• 2016

We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying ${\varphi}$-contractive conditions or ${\psi}$-${\phi}$-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.565-571
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• 2013

In this paper, we investigate the commutativity of a semiprime ring R admitting a generalized derivation F with associated derivation D satisfying any one of the properties: (i) $F(x){\circ}D(y)=[x,y]$, (ii) $D(x){\circ}F(y)=F[x,y]$, (iii) $D(x){\circ}F(y)=xy$, (iv) $F(x{\circ}y)=[F(x) y]+[D(y),x]$, and (v) $F[x,y]=F(x){\circ}y-D(y){\circ}x$ for all x, y in some appropriate subsets of R.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.685-692
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• 2016

The aim of this paper is to investigate the differentials of the hypercomplex valued functions in Clifford analysis. Like as the differentials defined by the naïve approach in one complex variable analysis, we define the differentials of functions with values in ternary number functions by same ways. And we survey the properties of each differential with respect to a non-commutativity of the skew field.

• East Asian mathematical journal
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• v.29 no.1
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• pp.39-52
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• 2013

Let (X, S) be an association scheme where X is a finite set and S is a partition of $X{\times}X$. The size of X is called the order of (X, S). We define $\mathcal{C}$ to be the set of positive integers m such that each association scheme of order $m$ is commutative. It is known that each prime is belonged to $\mathcal{C}$ and it is conjectured that each prime square is belonged to $\mathcal{C}$. In this article we give a sufficient condition for a scheme of order pq to be commutative where $p$ and $q$ are primes, and obtain a partial answer for the conjecture in case where $p=q$.