• 대한수학회지
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• 제45권6호
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• pp.1647-1659
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• 2008

Let R be a ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. First, we investigate some connected conditions of the zero-divisor graph $\Gamma(R)$ of a noncommutative ring R as follows: (1) if $\Gamma(R)$ has no sources and no sinks, then $\Gamma(R)$ is connected and diameter of $\Gamma(R)$, denoted by diam($\Gamma(R)$) (resp. girth of $\Gamma(R)$, denoted by g($\Gamma(R)$)) is equal to or less than 3; (2) if X is a union of finite number of orbits under the left (resp. right) regular action on X by G, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3, in addition, if R is local, then there is a vertex of $\Gamma(R)$ which is adjacent to every other vertices in $\Gamma(R)$; (3) if R is unit-regular, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3. Next, we investigate the graph automorphisms group of $\Gamma(Mat_2(\mathbb{Z}_p))$ where $Mat_2(\mathbb{Z}_p)$ is the ring of 2 by 2 matrices over the galois field $\mathbb{Z}_p$ (p is any prime).

• Journal of electromagnetic engineering and science
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• 제4권3호
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• pp.113-118
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• 2004

As an application of ring filters, a new and simple method to determine an inherent-ring-resonance frequency is introduced. The ring filter consists of a ring and two short stubs. They are connected at 90$^{\circ}$ and 270$^{\circ}$ points of the ring and the ring filter may be seen in such way that two filters are connected in parallel. Therefore, if the two powers of the two filters are out-of-phase at the output, the power excited at the input can not be delivered. That can be done by making difference in length of the two short stubs, and when a certain condition is satisfied, a frequency exists where all the excited power is reflected. That is the very inherent-ring-resonance frequency. In the lossless case, the return loss with the condition reaches 0 dB at the inherent-ring-resonance frequency but does not with conductor, dielectric losses and so on. Therefore, the effective loss tangent at a frequency of interest may be obtained correctly. To verify the method, two ring filters have been fabricated in microstrip lines and the measured results show good agreement with the predicted ones.

• 대한수학회논문집
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• 제27권1호
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• pp.57-68
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• 2012

The commuting graph of an arbitrary ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of group ring $Z_nQ_8$. The main result is that $\Gamma(Z_nQ_8)$ is connected if and only if n is not a prime. If $\Gamma(Z_nQ_8)$ is connected, then diam($Z_nQ_8$)= 3, while $\Gamma(Z_nQ_8)$ is disconnected then every connected component of $\Gamma(Z_nQ_8)$ must be a complete graph with a same size. Further, we obtain the degree of every vertex in $\Gamma(Z_nQ_8)$, the maximum degree and the minimum degree of $\Gamma(Z_nQ_8)$.

• 한국가스학회:학술대회논문집
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• 한국가스학회 2004년도 추계학술발표회 논문집
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• pp.82-87
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• 2004

Compression ring is a part of LNG storage tank. The main function of the compression ring is connected the roof plate with concrete side wall. End of its one side is embedded in the side concrete wall and the other's connected with the roof plate by welding. It is designed to support stably for all the loads such as self weight of steel roof, inner pressure and concrete weight. We fulfill the FEM analysis to analysis the compression ring behavior during construction. Also we studied the effect of the change of design variables. On the basis of the results, we could introduce a more reasonable design method for compression ring.

• International Journal of Advanced Culture Technology
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• 제7권1호
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• pp.225-230
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• 2019

In order to improve performance for the size of the rat-race ring coupler, the CCL is used for the realization as the delay line. As realizing lower coupling coefficient, the ratio of the size-reduction for the CCL is enhanced. The CCL is alternated with ${\lambda}_g/4$ of the rat-race ring, and optimized two CCLs are inserted for the size-reduction. the coupling coefficient is 0.2, and electrical lengths of each CCL are $28.2^{\circ}$ and $21.7^{\circ}$. Designed rat-race ring using the CCL has the size of $18.76{\times}20.45mm^2$ and the size-reduction ratio of fabricated rat-race ring using the CCL has 76.8%. Also, fabricated rat-race ring is measured the insertion loss of 3.20dB at the center frequency of 2.45GHz and the 20dB bandwidth is 24.04%. Differenced magnitude and phase between threw port and coupled port are measured 0.1dB and $177.4^{\circ}$, respectively. These performances are almost same compared with the conventional rat-race ring. Suggested application of the CCL can be used various devices and circuits for the size-reduction.

• 충청수학회지
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• 제21권1호
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• pp.15-19
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• 2008

In this article, we investigate the functional inequalities concerned with a derivation and a generalized derivation.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.41-53
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• 2013

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto power-series rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of nil power-serieswise Armendariz rings. Finally, we study the nil-Armendariz property for Ore extensions and skew power series rings.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.611-619
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• 2014

We in this note study a ring theoretic property which unifies Armendariz and IFP. We call this new concept INFP. We first show that idempotents and nilpotents are connected by the Abelian ring property. Next the structure of INFP rings is studied in relation to several sorts of algebraic systems.

• 대한수학회보
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• 제58권6호
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• pp.1409-1418
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• 2021

In this paper, we study domination in the zero-divisor graph of a *-ring. We first determine the domination number, the total domination number, and the connected domination number for the zero-divisor graph of the product of two *-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart *-ring and relate it with the clique of the zero-divisor graph of a Rickart *-ring.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.613-627
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• 2019

Consider a connected molecular graph G = (V, E) where V is the set of vertices and E is the set of edges. In G, vertices represent the atoms and edges represent the covalent bonds between atoms. In graph G, every edge (say) e = uv will be connected by two atoms u and v. The edge Szeged index is a topological index which has been introduced by Ivan Gutman. In this paper, we have computed edge Szeged indices of a hydrocarbon family called Benzene ring and is denoted by $(BR)_{n{\times}n}$.