• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.847-865
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• 2017

For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.

• Journal of Korea Multimedia Society
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• v.4 no.4
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• pp.356-362
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• 2001

In this paper, we show the behaviors of all states in C and the states in C', where C' is a complemented cellular automata whose the complemented vector is a nonzero state in the 0-tree of a linear TPMACA C. Also we show that if we know a path in the state-transition graph of C, then we can know the behavior of all states in C.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1031-1051
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• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.

• Journal of Korea Multimedia Society
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• v.6 no.3
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• pp.549-555
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• 2003

CA is cost-effective to generate pseudorandom patterns than LFSR. Based on the effectiveness of a CA based pseudorandom pattern generator, CA have been employed successfully in several applications. Especially Nongroup CA is applied to efficient hash function generation, cryptography and image compression. In this paper we analyze the properties of TPNCA and by using basic paths in the 0-tree of a linear TPNCA we analyze the structure of the state-transition graph. Also by showing the structure of the complemented CA which have the acyclic state of the 0-tree as the complement vector is isomorphic to the structure of the original TPNCA, we reduce the time in analyzing the CA-states.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.6
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• pp.811-821
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• 1998

A new scheduling algorithm for large scale semiconductor processes is addressed. The difficulties of scheduling for semiconductor fabrication processes are mainly due from repeating production of wafers that experience reentrant flows. Sequence branch algorithm (SBA) is proposed for large real scheduling problems when all processing times are deterministic. The SBA is based on the reachability graph of Petri net of which the several defects such as memory consumption and system deadlock are complemented. Though the SBA shows the solution deviating a little from the optimal solution of mixed integer programming, it is adjustable for large size scheduling problems. Especially, it shows a potential that is capable of handling commercial size problems that are intractable with mathematical programming.