• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.299-308
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• 1997

In this paper we show that the limit of a convergent in-vertible sequence in the set of invertible elements Inv(A) in a Banach algebra A under a certain conditions is invertible and we investigate some properties of the spectral radius of banach algebra with unit.

• 대한수학회지
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• 제50권6호
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• pp.1349-1367
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• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.

• 호남수학학술지
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• 제26권4호
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• pp.471-481
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• 2004

In this paper we introduce the notion of a (pre-)Coxeter algebra and show that a Coxeter algebra is equivalent to an abelian group all of whose elements have order 2, i.e., a Boolean group. Moreover, we prove that the class of Coxeter algebras and the class of B-algebras of odd order are Smarandache disjoint. Finally, we show that the class of pre-Coxeter algebras and the class of BCK-algebras are Smarandache disjoint.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.269-277
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• 2019

Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

• 대한수학회보
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• 제37권3호
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• pp.537-542
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• 2000

When A is a subalgebra of a $C^*$-algebra, the spatial numerical range of element of A can be described in terms of positive linear functionals on the $C^*$-algebra.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.481-489
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• 2005

We first show that any complete MV-algebra whose Boolean subalgebra of idempotent elements is atomic, called a complete MV-algebra with atomic center, is isomorphic to a product of unit interval MV-algebra 1's and finite linearly ordered MV-algebras of A(m)-type $(m{\in}{\mathbb{Z}}^+)$. Secondly, for a semi-simple MV-algebra A, we introduce a completion ${\delta}(A)$ of A which is a complete, MV-algebra with atomic center. Under their intrinsic topologies $(see\;{\S}3)$ A is densely embedded into ${\delta}(A)$. Moreover, ${\delta}(A)$ has the extension universal property so that complete MV-algebras with atomic centers are epireflective in semi-simple MV-algebras

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권5호
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• pp.2346-2361
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• 2017

A major challenge in cloud infrastructure is the efficient allocation of virtual network elements on top of substrate network elements. Path algebra is a mathematical framework which allows the validation and convergence analysis of the mono-constraint or multi-constraint routing problems independently of the network topology or size. The present study proposes a new heuristic approach based on mathematical framework "paths algebra" to map virtual nodes and links to substrate nodes and paths in cloud. In this approach, we define a measure criterion to rank the substrate nodes, and map the virtual nodes to substrate nodes according to their ranks by using a greedy algorithm. In addition, considering multi-constraint routing in virtual link mapping stage, the used paths algebra framework allows a more flexible and extendable embedding. Obtained results of simulations show appropriate improvement in acceptance ratio of virtual networks and cost incurred by the infrastructure networks.

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.529-543
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• 2008

It is shown that every almost linear mapping h : $A{\rightarrow}B$ of a unital PoissonC*-algebra A to a unital Poisson C*-algebra B is a Poisson C*-algebra homomorph when $h(2^nuy)\;=\;h(2^nu)h(y)$ or $h(3^nuy)\;=\;h(3^nu)h(y)$ for all $y\;\in\;A$, all unitary elements $u\;\in\;A$ and n = 0, 1, 2,$\codts$, and that every almost linear almost multiplicative mapping h : $A{\rightarrow}B$ is a Poisson C*-algebra homomorphism when h(2x) = 2h(x) or h(3x) = 3h(x for all $x\;\in\;A$. Here the numbers 2, 3 depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings. We prove the Cauchy-Rassias stability of Poisson C*-algebra homomorphisms in unital Poisson C*-algebras, and of homomorphisms in Poisson Banach modules over a unital Poisson C*-algebra.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.53-60
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• 2018

In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

• 대한수학회논문집
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• 제11권3호
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• pp.595-600
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• 1996

We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.