• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-69
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• 2000

For a permutation ${\mu}$ in S$\sub$b/, the limit algebra A${\mu}$ of the stationary system given by ${\mu}$ is isomorphic to a refinement limit algebra if and only if its exponent set E(${\mu}$) is the set {0}. In the current paper, we prove a sufficient condition under which E(${\mu}$)={0} when the order of ${\mu}$ is a power of p, where p is a prime number dividing b.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.65-73
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• 2005

Let g = g(A) = (equation omitted) + be a symmetrizable Kac-Moody Lie algebra of type D/sub l//sup (1) with W as its Weyl group. We construct a sequence of root spaces with certain conditions. We also find the number of terms of this sequence is less then or equal to the hight of θ, the highest root.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1111-1120
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• 2005

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.210-214
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• 1994

The purpose of this paper is to investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring g $r_{I}$(R) of an ideal I in a local ring (R,m) of dim(R) > 0. The relationship between the Cohen-Macaulayness of these two rings has been studied extensively. Let (R, m) be a local ring and I an ideal of R. An ideal J contained in I is called a reduction of I if J $I^{n}$ = $I^{n+1}$ for some integer n.geq.0. A reduction J of I is called a minimal reduction of I. The reduction number of I with respect to J is defined by (Fig.) S. Goto and Y.Shimoda characterized the Cohen-Macaulay property of the Rees algebra of the maximal ideal of a Cohen-Macaulay local ring in terms of the Cohen-Macaulay property of the associated graded ring of the maximal ideal and the reduction number of that maximal ideal. Let us state their theorem.m.m.

• Journal of Internet Computing and Services
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• v.20 no.6
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• pp.21-28
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• 2019

Process mining is state-of-the-art technology in the workflow field. Recently, process mining becomes more important because of the fact that it shows the status of the actual behavior of the workflow model. However, as the process mining get focused and developed, the material of the process mining - workflow event log - also grows fast. Thus, the process mining algorithms cannot operate with some data because it is too large. To solve this problem, there should be a lightweight process mining algorithm, or the event log must be divided and processed partly. In this paper, we suggest a set of operations that control and edit XES based event logs for process mining. They are designed based on relational algebra, which is used in database management systems. We designed three operations for tailoring XES event logs. Select operation is an operation that gets specific attributes and excludes others. Thus, the output file has the same structure and contents of the original file, but each element has only the attributes user selected. Union operation makes two input XES files into one XES file. Two input files must be from the same process. As a result, the contents of the two files are integrated into one file. The final operation is a slice. It divides anXES file into several files by the number of traces. We will show the design methods and details below.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.187-198
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• 2022

In this paper, we introduce a new concept in number theory called ζ-factors associated with a positive integer n. Applications of ζ-factors are in the arrangement of the defining polynomials in cyclic n-roots algebraic system and are thoroughly investigated. More precisely, ζ-factors arise in the proofs of vanishing theorems in regard to associated prime factors of the system. Exact computations through concrete examples of positive dimensions for n = 16, 18 support the results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.2
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• pp.659-679
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• 2015

Distributed applications are composed of multiple nodes, which exchange information with individual nodes through message passing. Compared with traditional applications, distributed applications have more complex behavior patterns because a large number of interactions and concurrent behaviors exist among their distributed nodes. Thus, it is difficult to detect anomalous behaviors and determine the location and scope of abnormal nodes, and some attacks and misuse cannot be detected. To address this problem, we introduce a method for detecting anomalous behaviors based on process algebra. We specify the architecture of the behavior detection model and the detection algorithm. The anomalous behavior detection and analysis demonstrate that our method is a good discriminator between normal and anomalous behavior characteristics of distributed applications. Performance evaluation shows that the proposed method enhances efficiency without security degradation.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.193-207
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• 2004

In this expository article we survey some recent developments on the construction of a holomorphic functional calculus for an infinite number of elements in a commutative unital Banach algebra.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.1
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• pp.15-28
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• 2018

Recently Machine Learning algorithms are widely used to process Big Data in various applications and a lot of these applications are executed in run time. Therefore the speed of Machine Learning algorithms is a critical issue in these applications. However the most of modern iteration Machine Learning algorithms use a successive iteration technique well-known in Numerical Linear Algebra. But this technique has a very low convergence, needs a lot of iterations to get solution of considering problems and therefore a lot of time for processing even on modern multi-core computers and clusters. Tchebychev iteration technique is well-known in Numerical Linear Algebra as an attractive candidate to decrease the number of iterations in Machine Learning iteration algorithms and also to decrease the running time of these algorithms those is very important especially in run time applications. In this paper we consider the usage of Tchebychev iterations for acceleration of well-known K-Means and SVM (Support Vector Machine) clustering algorithms in Machine Leaning. Some examples of usage of our approach on modern multi-core computers under Apache Spark framework will be considered and discussed.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.255-265
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• 2023

The purpose of this article is to construct a unital 8 dimensional hypercomplex number system H^*₈ that is neither alternative nor commutative unlike the octonions by means of the unital 4 dimensional, commutative, and nonassociative hypercomplex number system H^*. We also establish some algebraic properties related to H^*₈ and compare to those of octonions.