• Journal of the Korea Society for Simulation
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• v.19 no.4
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• pp.67-75
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• 2010

Deadlock usually appears in contain subsystem which is run in parallel and resources share modules. Siphons and traps have been well introduced to characterize deadlocks of Petri nets. Siphon concept be well used for proposing the detect and prevent deadlock by the pleasure researchers. But it's need many times and efforts to detect all siphon sub-nets in the Petri model. Since transitive matrix could explain all relations between the place and transitions in Petri nets, we propose an algorithm to detect all siphon sub-nets after analyzed the transitive matrix's properties. Examples are givens to illustrate the method.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.259-267
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• 2016

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. Recently, the authors introduced the classes of QTAG-modules namely as socle-regular and strongly socle-regular QTAG-modules which properly contain the classes of transitive and fully transitive QTAG-modules respectively. Here we define strongly and quasi transitivities and study the inter relations between various type of transitivities.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.643-653
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• 2012

Let $f\;:\;M\;{\rightarrow}\;M$ be a diffeomorphism on a closed $C^{\infty}$ manifold. Let $\Lambda$ be a transitive set. In this paper, we show that (i) $C^1$-generically, $f$ has the shadowing property on a locally maximal $\Lambda$ if and only if $\Lambda$ is hyperbolic, (ii) f has the $C^1$-stably shadowing property on $\Lambda$ if and only if $\Lambda$ is hyperbolic.

• Journal of the Korea Society for Simulation
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• v.12 no.2
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• pp.13-24
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• 2003

In this study, we propose a scheduling analysis method of the Flexible management system using the transitive matrix. The Scheduling problem is a combination-optimization problem basically, and a complexity is increased exponentially for a size of the problem. To reduce an increase of a complexity, we define that the basic unit of concurrency (short BUC) is a set of control flows based on behavioral properties in the net. And we propose an algorithm to divide original system into some BUC. To sum up, we divide a petri net model of the Flexible management system Into the basic unit of concurrency through the division algorithm using the transitive matrix. Then we apply it to the division-scheduling algorithm to find an efficient scheduling. Finally, we verify its efficiency with an example.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.163-181
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• 2005

We study some properties of intuitionistic fuzzy equivalence relations. Also we introduce the concepts of intuitionistic fuzzy transitive closures and level sets of an intuitionistic fuzzy relation and we investigate some of their properties.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.97-104
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• 2010

The article is devoted to exhibit some general properties of strong chain recurrent set and strong chain transitive components for a continuous map f on a compact metric space X. We investigate the relation between the weak shadowing property and strong chain transitivity. It is shown that a continuous map f from a compact metric space X onto itself with the average shadowing property is strong chain transitive.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1683-1709
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• 2015

Let (${\Omega}$, S) be an association scheme where ${\Omega}$ is a non-empty finite set and S is a partition of ${\Omega}{\times}{\Omega}$. For a positive integer k we say that (${\Omega}$, S) is k-equivalenced if each non-diagonal element of S has valency k. In this paper we focus on 4-equivalenced association schemes, and prove that they are transitive.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.363-370
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• 2002

We show that G(x) = $e^{(x}$(1-x))/ -1 is the exponential generating function for the labeled digraphs whose weak components are transitive tournaments and derive both a recursive formula and an explicit formula for the number of them on n vertices. Moreover, we investigate the asymptotic behavior for the coefficients of G(x) using Hayman's method.d.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.485-491
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• 2004

We shall discuss irreducible and primitive S-automata. A variety of properties of transitive and primitive semigroups associated with them have been obtained. Also a classification of primitive semi groups will be given with S-automata.