• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1193-1208
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• 2021

Let 𝓐 be a von Neumann algebra with no central summands of type I₁. In this article, we study Lie n-derivation on von Neumann algebra and prove that every additive Lie n-derivation on a von Neumann algebra has standard form at zero product as well as at projection product.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.303-310
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• 2006

M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.443-447
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• 2001

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.

• Journal of KIISE:Software and Applications
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• v.41 no.7
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• pp.469-480
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• 2014

Software Product Line (SPL) is a software development paradigm that guarantees high productivity, reduced cost, and shorter time-to-market by systematically planning and reusing commonality and variability. In order to maximize the benefits of SPL engineering, testing should be integrated into the SPL engineering lifecycle processes that consist of domain engineering and application engineering and should be performed with as little test efforts as possible. This paper proposes a systematic software product line test cases derivation method using combinatorial test design. By applying combinatorial test design to product line test cases derivation and exploiting commonality between products at the same time, the number of generated test cases is dramatically reduced with the result that they can be effectively reused by the products of the given product line. Case studies conducted in this paper show the efficacy of our method compared with other methods that use only commonality or combinatorial design or neither of them in terms of the number of derived test cases.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1123-1132
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• 2015

In this paper, we investigate derivations on the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$. We then show that a derivation on $L^{\infty}_0({\omega})^*$ is continuous if and only if its restriction to rad($L^{\infty}_0({\omega})^*$) is continuous. We also prove that there is no nonzero centralizing derivation on $L^{\infty}_0({\omega})^*$. Finally, we prove that the space of all inner derivations of $L^{\infty}_0({\omega})^*$ is continuously homomorphic to the space $L^{\infty}_0({\omega})^*/L^1({\omega})$.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-485
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• 2023

Let 𝓐 be a unital Banach *-algebra and 𝓜 be a unital *-𝓐-bimodule. If W is a left separating point of 𝓜, we show that every *-derivable mapping at W is a Jordan derivation, and every *-left derivable mapping at W is a Jordan left derivation under the condition W𝓐 = 𝓐W. Moreover we give a complete description of linear mappings 𝛿 and 𝜏 from 𝓐 into 𝓜 satisfying 𝛿(A)B^* + A𝜏(B)^* = 0 for any A, B ∈ 𝓐 with AB^* = 0 or 𝛿(A)◦B^* + A◦𝜏(B)^* = 0 for any A, B ∈ 𝓐 with A◦B^* = 0, where A◦B = AB + BA is the Jordan product.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.2
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• pp.115-120
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• 2014

Many product line engineering methods use the feature model to structure commonality and variability among products in terms of features and to derive a product feature configuration, which is the set of features required for the development of a product. Features to be selected during product derivation are mainly determined based on the quality attributes required for a product. Most methods published so far derived an optimal product feature configuration through linear co-relationship between features and quality attributes. However, the co-relationship between features and quality attributes can be formulated as a non-linear function because of feature interactions. This paper proposes a method that derives an optimal product feature configuration considering feature interactions. Four product line cases are used to validate the proposed methods.

• Proceedings of the Korea Contents Association Conference
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• 2003.11a
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• pp.245-248
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• 2003

We construct a universal derivation module of an R-algebra which is constructed by means of a tensor product of three copies of the algebras.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.745-748
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• 1999

This paper propose the method to derive RM(Reed-Muller) expansion coefficients for Multiple-Valued function. The general method to obtain RM expansion coefficient for p valued n variable is derivation of single variable transform matrix and expand it n times using Kronecker product. The transform matrix used is p$^{n}$ $\times$ p$^{n}$ matrix. In this case the size of matrix increases depending on the augmentation of variables and the operation is complicated. Thus, to solving the problem, we propose derivation of RM expansion coefficients using p$\times$p transform matrix and Karnaugh-map.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.6
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• pp.274-283
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• 2005

This paper presents a new method to derive energy function based on vector product. Using this method, an energy function to consider transfer conductances and capacitors is derived. Then we recommend a voltage collapse criteria to predict the voltage collapse in power systems by using the energy margin derived by the proposed energy function. This energy function is applied to a 2-bus power system reflecting transfer conductances and capacitors. We show that the energy function derived based on vector product can be applied in order to analyze power system stability and the energy margin can be utilized as a criterion of voltage collapse by simulation for the 2-bus system.