• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.209-227
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• 2021

In this paper, we deal with the question that what kind of properties does a ring gain when it satisfies symmetricity or reversibility by the way of nilpotent elements? By the motivation of this question, we approach to symmetric and reversible property of rings via nilpotents. For symmetricity, we call a ring R middle right-(resp. left-)nil symmetric (mr-nil (resp. ml-nil) symmetric, for short) if abc = 0 implies acb = 0 (resp. bac = 0) for a, c ∈ R and b ∈ nil(R) where nil(R) is the set of all nilpotent elements of R. It is proved that mr-nil symmetric rings are abelian and so directly finite. We show that the class of mr-nil symmetric rings strictly lies between the classes of symmetric rings and weak right nil-symmetric rings. For reversibility, we introduce left (resp. right) N-reversible ideal I of a ring R if for any a ∈ nil(R), b ∈ R, being ab ∈ I implies ba ∈ I (resp. b ∈ nil(R), a ∈ R, being ab ∈ I implies ba ∈ I). A ring R is called left (resp. right) N-reversible if the zero ideal is left (resp. right) N-reversible. Left N-reversibility is a generalization of mr-nil symmetricity. We exactly determine the place of the class of left N-reversible rings which is placed between the classes of reversible rings and CNZ rings. We also obtain that every left N-reversible ring is nil-Armendariz. It is observed that the polynomial ring over a left N-reversible Armendariz ring is also left N-reversible.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1174-1180
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• 2001

Various experimental data, including mixing areas, cross correlation factors, surface flow patterns on nozzle walls, and far field noise spectra, was used to draw a noise control mechanism in a supersonic jet. In the underexpanded case, mixing of the jet air with ambient air was significantly enhanced as presented before, and mixing noise was also dramatically reduced. Screech tones, in the overexpanded case, were effectively suppressed by trailing edge modifications, although mixing enhancement was not noticeable. From mixing and noise performance of nozzles with modified trailing edges, enhancing mixing through streamwise vortices seems an effective way to reduce mixing noise in the underexpanded flow regime. However, screech tones in the overespanded flow regime is well controlled or suppressed by making shock cells and/or spanwise large scale structures irregular and/or less organized by a proper selection of trailing edges. The noise field in the overexpanded flow regime was greatly affected by the symmetricity of the nozzle exit geometry. In the underexpanded flow regime, the effects of the symmetricity of the nozzle exit on mixing were negligible.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.63-72
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• 2002

An inverse interpolation problem for rational matrix functions with a certain type of symmetricity in zero-pole structure is studied.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.413-423
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• 2014

In this article we study different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like completeness, solidness, sequence algebra, symmetricity and convergence free.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.29 no.3
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• pp.175-180
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• 2016

In this study, we proposed an optical compensation method to improve the symmetricity of contrast ratio for wide viewing angle IPS (in-plane switching) LCD. First, the phase retardation depending on the thickness of compensation film is calculated, and then the phase change is presented at the $Poincar{\acute{e}}$ sphere. The phase retardation and the polarization state of the light passing through the optical elements are caculated by using the EJMM (extended Jones matrix method). In addition, the transmittance and the contrast countour are also calculated by using the Berremann's $4{\times}4$ matrix method. The simulation is carried out for a IPS LC cell with positive A/C/A compensation film. From the standard deviation of the contrast ratio, we confirmed the symmetricity at each viewing angle is inversely proportional to the standard deviation and calculated the optimum design condition of the uniaxial compensation film for the IPS LCD.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.565-574
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• 2010

In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.345-352
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• 2011

In this article we introduce the fuzzy real valued double sequence spaces $_2{\ell}^F$ (p) where p = ($p_{nk}$) is a double sequence of bounded strictly positive numbers. We study their different properties like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results also.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.321-332
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• 2014

In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.11-22
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• 2014

The sequence spaces $c^F$(M), $c^F_0$(M) and ${\ell}^F$(M) of fuzzy real numbers with fuzzy metric are introduced. Some properties of these sequence spaces like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving these sequence spaces.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.189-200
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• 2012

In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.