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

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.765-771
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• 2014

Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.203-219
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• 2007

We estimate the stable rank and connected stable rank of group $C^*$-algebra of certain disconnected solvable Lie groups such as semi-direct products of connected solvable Lie groups by the integers.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.525-533
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• 1997

We analysis spectral subspaces of $C^*$-algebras for a compacr group action. And we prove the condition that the fixed point algebra of the product action is the tensor product of the fixed point algebras.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.529-539
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• 2023

In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying C^*-algebra.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.213-223
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• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.189-212
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• 2006

Let $F^{\alpha}G$ be a twisted group algebra with basis ${{\mu}g|g\;{\in}\;G}$ and $P\;=\;{C_g|g\;{\in}\;G}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $F^{\alpha}G$ generated by all class sums $\sum\limits{_{x{\in}C_g}}\;{\mu}_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^{\alpha}G$ and in $F^{\alpha}H$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $\alpha-spherical$ functions as characters of projective class algebras.

• 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.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].

• International Journal of Computer Science & Network Security
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• v.22 no.5
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• pp.149-153
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• 2022

This study examines the effect of using interactive electronic models to teach mathematical concepts on students' achievement in the linear algebra course at university. The field sample consisted of 200 students divided into two equal groups, an experimental group of 100 students and a control group of 100 students. The researcher used an achievement test in some mathematical concepts related to linear algebra. The results of the study showed that there were statistically significant differences (0.05) between the average achievement scores of the experimental and control groups in the post application of the achievement test, in favor of the experimental group. The size of the influence of the independent factor on the results of the study, which is "interactive electronic forms", on the dependent factor, which is the students' academic achievement in the prepared test, had a very large effect. Also, the results of the study showed that there were statistically significant differences (0.05) between the mean scores of the experimental group in the pre and post applications of the achievement test, in favor of the post application. The researcher recommended the use of interactive electronic models in teaching mathematical concepts at the university level and diversifying the strategies of teaching mathematics, using technology to attract learners and raise their academic achievement.