• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.657-665
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• 2016

In this investigation we studied completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Some characterizations of completely quasi primary and weakly completely quasi primary ideals were obtained. Moreover, we investigated relationships between completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Finally, we obtained necessary and sufficient conditions for a weakly completely quasi primary ideal to be a completely quasi primary ideal.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.729-743
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• 2019

In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if $ab{\in}Q$ for $a,b{\in}R$ implies either $a^2{\in}Q$ or $b^n{\in}Q$ ($a^n{\in}Q$ or $b^2{\in}Q$) for some $n{\in}{\mathbb{N}}$. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph ${\Gamma}_I(R)$ and denote it by ${\Gamma}^*_I(R)$, where I is an ideal of R. We investigate the relations between ${\Gamma}^*_I(R)$ and ${\Gamma}_I(R)$. Further, we use strongly quasi primary ideals and ${\Gamma}^*_I(R)$ to characterize von Neumann regular rings.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.148-164
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• 2022

The main purpose of this paper is to apply the notion of hesitant fuzzy sets to an algebraic structure, so called a BCI-algebra. The primary goal of the study is to define hesitant fuzzy p-ideals and hesitant fuzzy quasi-associative ideals in BCI-algebras, and to investigate their properties and relations.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.93-104
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• 2024

Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a² ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2012.05a
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• pp.356-363
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• 2012

This paper addresses an analytical study on the gas-solid two phase flows in a nozzle. The primary purpose is to get recognition into the gas-solid suspension flows and to investigate the particle motion and its influence on the gas flow field. The present study is the primal step to comprehend the gas-solid suspension flow in the convergent-divergent nozzle. This paper try to made a development of an analytical model to study the back pressure ratio, particles loading and the particle diameter effect on gas-solid suspension flow. Mathematical model of gas-solid two phase flow was developed based on the single phase flow models to solve the quasi-one-dimensional mass, momentum equations to calculate the steady pressure field. The influence of particles loading and particle diameter is analyzed. The results obtained show that the suspension flow of smaller diameter particles has almost same trend as that of single phase flow using ideal gas as working fluid. And the presence of particles will weaken the strength of the shock wave; the bigger particle will have larger slip velocity with gas flow. The thrust coefficient is found to be higher for larger particles/gas loading or back pressure ratio, but it also depends on the ambient pressure.