• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.437-453
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• 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ~ on S defined by letting a ~ b if and only if ann_S(a) = ann_S(b), is an equivalence relation. The compressed zero-divisor graph 𝚪_E(S) of S is the undirected graph whose vertices are the equivalence classes induced by ~ on S other than [0]_S and [1]_S, in which two distinct vertices [a]_S and [b]_S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R₀[x] and the near-ring of the power series R₀[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam(𝚪_E(R₀[x])) and diam(𝚪_E(R₀[[x]])). As a corollary, it is shown that for a reduced ring R, diam(𝚪_E(R)) ≤ diam(𝚪_E(R₀[x])) ≤ diam(𝚪_E(R₀[[x]])).

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.301-309
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• 2011

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.60.2-60.2
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• 2014

The dust cloud around ${\lambda}$-Orionis is seen to be circular symmetric with the large angular extent (${\sim}8^{\circ}$). However, whether the three dimensional structure of the cloud is shell or torus ring is not yet fully resolved. We studied the structure of the dust cloud using a three-dimensional Monte-Carlo simulation code, MoCafe (Monte Carlo radiative transfer). The dust density structure of the cloud was inferred based on the star-count method. We assumed that the cloud is a spherical shell or a torus ring and calculated the radial profiles of scattered light originating from a central OB association. Comparison of the results with the S2/68 ultraviolet observations indicates that the cloud is a spherical shell. We also compared the Av map around ${\lambda}$-Orionis with the optical depth obtained based on the star-count.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.151-156
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• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.347-352
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• 2012

In this paper, we denote that $R$ is a near-ring and $G$ an $R$-group. We initiate the study of faithful $R$-group, the substructures of $R$ and $G$, also quotients of substructure relations between them. Next, we investigate some isomorphic properties of near-rings and $R$-groups.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.305-312
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• 2011

In this paper, we denote that R is a near-ring and G an R-group. We initiate the study of the substructures of R and G. Next, we investigate some properties of R-groups, d.g. near-rings and monogenic (R, S)-groups.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.343-347
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• 2010

In this paper we study the connection between 2-primal rings, (S,1)-rings and related conditions. And we investigate some condition which is the special case of pseudo symmetric. We also study the condition (KJ) which is given by J. Y. Kim and H. L. Jin. We introduce some condition and we prove that our condition is equivalent to the condition (KJ) when it is an (S,1)-ring.

• Journal of Communications and Networks
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• v.9 no.1
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• pp.93-104
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• 2007

Traffic grooming, in which low-rate circuits are multiplexed onto wavelengths, with the goal of minimizing the number of add-drop multiplexers (ADMs) and wavelengths has received much research attention from the optical networking community in recent years. While previous work has considered various traffic models and network architectures, protection requirements of the circuits have not been considered. In this paper, we consider survivable traffic grooming, or grooming traffic which contains a mix of circuits that need protection and that do not need protection. We assume a unidirectional ring network with all-to-all symmetric traffic with $t\geq1$ circuits between each node pair, of which s require protection. As it turns out, survivable traffic grooming presents a significant tradeoff between the number of wavelengths and the number of ADMs, which is almost non-existent in non-survivable traffic grooming for this type of traffic. We explore this tradeoff for some specific cases in this paper. We also present some new results and solution methods for solving certain non-survivable traffic grooming problems.

• International Journal of Fluid Machinery and Systems
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• v.4 no.1
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• pp.57-66
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• 2011

Radial-vaned air separators show a strong stall suppression effect in an axial flow fans. From a survey of existing literature on the effects and the author's data, a possible mechanism for the significant effects has been proposed here. The stall suppression is suggested to have been achieved by a combination of the following several effects; (1) suction of blade and casing boundary layers and elimination of embryos of stall, (2) separation and straightening of reversed swirling flow from the main flow, (3) induction of the fan main flow toward the casing wall and enhancement of the outward inclination of meridional streamlines across the rotor blade row, thus keeping the Euler head increase in the decrease in fan flow rate, and (4) reinforcement of axi-symmetric structure of the main flow. These phenomena have been induced and enhanced by a stable vortex-ring encasing the blade tips and the air separator. These integrated effects appear to have caused the great stall suppression effect that would have been impossible by other types of stall prevention devices. Thus the author would like to name the device "tip-vortex-ring assisted stall suppression device".