• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.155-162
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• 1996

We will show that let X and Y be M -finite Banach spaces with canonical M-decompositions $X{\cong}{{\prod}^{{\gamma}_{\infty}}_{i=1}}{X^{n_i}}_{i}\;and\;Y{\cong}{{\prod}^{{\bar{\gamma}}_{\infty}}_{j=1}}{\tilde{Y}^{m_j}}_{j}$, respectively and M and N nonzero locally compact Hausdorff spaces. Then I : $C_{0}$(M,X) ${\longrightarrow}\;C_{0}$(N,Y) is an isometrical isomorphism if and only if r = $\bar{r}$ and there are permutation and homeomorphisms and continuous maps such that I = ${I^{-1}}_{N.Y}\;{\circ}I_{w}^{-1}{\circ}({{\prod}^{\gamma}}_{i=1}I_{t_i,u_i}){\circ}I_{M,X}$.

• The Mathematical Education
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• v.14 no.1
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• pp.22-26
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• 1975

In this paper, we define a differential module and study its properties. In section 2, as for propositions, Ive research some properties, directsum, isomorphism of factorization, exact sequence of derived modules. And then as for theorem, I try to present the following statement, if the sequence of homomorphisms of differential modules is exact. Then the sequence of homomorphisms of Z(X) is exact, also the sequence of homomorphisms of Z(X) is exact. According to the theorem, as for Lemma, we consider commutative diagram between exact sequence of Z(X) and exact sequence of Z'(X) . As an immediate consequence of this theorem, we obtain the following result. If M is an arbitrary module and the sequence of homomorphisms of the modules Z(X) is exact, then the sequence of their tensor products with the trivial endomorphism is semi-exact.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.69-76
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• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.

• Smart Media Journal
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• v.9 no.2
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• pp.33-38
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• 2020

Order preserving matching refers to the problem of reporting substrings of a given text where there exists order isomorphism with the pattern. In this paper, we propose a new algorithm based on filtering and evaluation. The proposed algorithm is simple and easy to implement, and runs in linear time on average. Experimental results show that it works efficiently with real world data.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.687-690
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• 1988

Algorithms that represent given pattern in the form of an ARG (Attributed relational graph) using not only structural relations but also symbolic or numerical attributes, and then recognize that pattern by graph matching process are presented in this paper. Based on definitions of pattern deformational models, algorithms that can find GPECI(Graph preserved error correcting isomorphism). SGECI(subgraph ECI) and DSECI(Double subgraph ECI) are proposed and comparisons among these algorithms are described. To be useful in performig practical tasks, efficient schemes for extraction of ARG representation fron raw image are needed. In this study, given patterns are restricted within objects having distinct skeleton, and then the information which is necessary for recognition and analysis is successfully extracted.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.661-681
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• 2004

We research properties of the space of measurable functions square integrable with weight exp$2\nu $\mid$x$\mid$$, and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the space of analytic functions extended to any strip in $C^n$ which are estimated with the aid of a special exponential function exp($\mu$｜x｜).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.569-581
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• 2011

Let a finite group R act smoothly on a closed manifold M. We assume that R acts freely on M except a union of closed submanifolds with codimension at least two. Then, we show that there exists an isomorphism between equivariant topological complex vector bundles over M and nonequivariant topological complex vector orbibundles over the orbifold M/R. By using this, we can classify nonequivariant vector orbibundles over the orbifold especially when the manifold is two-sphere because we have classified equivariant topological complex vector bundles over two sphere under a compact Lie group (not necessarily effective) action in [6]. This classification of orbibundles conversely explains for one of two exceptional cases of [6].

• Honam Mathematical Journal
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• v.41 no.3
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• pp.559-568
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• 2019

In this paper we introduce and study the concept of of (${\varphi}$, ${\psi}$)-am-enability of a locally compact group G, where ${\varphi}$ is a continuous homomorphism on G and ${\psi}:G{\rightarrow}{\mathbb{C}}$ multiplicative linear function. We prove that if the group algebra $L^1$ (G) is (${\tilde{\varphi}}$, ${\tilde{\psi}}$)-amenable then G is (${\varphi}$, ${\psi}$)-amenable, where ${\tilde{\varphi}}$ is the extension of ${\varphi}$ to M(G). In the case where ${\varphi}$ is an isomorphism on G it is shown that the converse is also valid.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.451-459
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• 2019

Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be two operator ${\ast}$-rings such that ${\mathcal{A}}$ is prime. In this paper, we show that if the map ${\Phi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves Jordan or ${\ast}$-Jordan triple product, then it is additive. Moreover, if ${\Phi}$ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of ${\Phi}$. Finally, we show that if ${\mathcal{A}}$ and ${\mathcal{B}}$ are two prime operator ${\ast}$-algebras, ${\Psi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves ${\ast}$-Jordan triple product, then ${\Psi}$ is a ${\mathbb{C}}$-linear or conjugate ${\mathbb{C}}$-linear ${\ast}$-isomorphism.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.201-217
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• 2019

Ricci curvature for locally finite graphs, as proposed by Lin, Lu and Yau, provides a useful isomorphism invariant. A Matching Condition was introduced as a key tool for computation of this Ricci curvature. The scope of the Matching Condition is quite broad, but it does not cover all cases. Thus the current paper introduces extended versions of the Matching Condition, and applies them to the computation of the Ricci curvature of a class of circulants determined by certain number-theoretic data. The classical Matching Condition is also applied to determine the Ricci curvature for other families of circulants, along with Cayley graphs of abelian groups that are generated by the complements of (unions of) subgroups.