• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.531-542
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• 2014

In this paper, we apply some properties of reversible rings, Baerness of fixed rings, skew group rings and Morita Context rings to get conditions that shows fixed rings, skew group rings and Morita Context rings are reversible. Moreover, we investigate conditions in which Baer rings are reversible and reversible rings are Baer.

• Environmental Engineering Research
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• v.23 no.1
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• pp.70-75
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• 2018

A pilot scale anaerobic fixed-bed with a reactor volume of $2.8m^3$ was built to treat slaughterhouse wastewater. Bamboo rings were chosen as support media mainly because of their cheaper price in underdeveloped countries. Even with their lower porosity and specific surface, the reactor performance showed a maximum 95% COD removal efficiency at an organic loading rate (OLR) of $1kg\;COD/m^3-d$ with its corresponding hydraulic retention time (HRT) of 7.5 d. At a higher OLR of $4.0kg\;COD/m^3-d$, the COD removal efficiency of 75% was achieved with an HRT of 2 d. No big difference in COD removal efficiencies was found between the reactors operated in both upflow and downflow modes. Their operational behavior and effluent characteristics were similar. The effluent COD/TKN ratio of 6.67 at an OLR of $4.0kg\;COD/m^3-d$ was only marginal acceptable range for a subsequent biological denitrification process. Otherwise carbon supplementation is required at a lower OLR.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.455-468
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• 2020

An element in a ring R with identity is called invo-clean if it is the sum of an idempotent and an involution and R is called invoclean if every element of R is invo-clean. Let C(R) be the center of a ring R and g(x) be a fixed polynomial in C(R)[x]. We introduce the new notion of g(x)-invo clean. R is called g(x)-invo if every element in R is a sum of an involution and a root of g(x). In this paper, we investigate many properties and examples of g(x)-invo clean rings. Moreover, we characterize invo-clean as g(x)-invo clean rings where g(x) = (x-a)(x-b), a, b ∈ C(R) and b - a ∈ Inv(R). Finally, some classes of g(x)-invo clean rings are discussed.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.499-502
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• 2003

The aim of the present paper is to establish for commutativity of rings with unity 1 satisfying one of the properties $(xy)^{k+1}=x^ky^{k+1}x$ and $(xy)^{k+1}=yx^{k+1}y^k$, for all x, y in R, and the mapping $x{\rightarrow}x^k$ is an anti-homomorphism where $k{\geq}1$ is a fixed positive integer.

• Wind and Structures
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• v.25 no.5
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• pp.433-457
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• 2017

As a novel typical wind-sensitive structure, the wind load and wind-induced structural behaviors of super-large straight-cone cooling towers are in an urgent need to be addressed and studied. A super large straight-cone steel cooling tower (189 m high, the highest in Asia) that is under construction in Shanxi Power Plant in China was taken as an example, for which four finite element models corresponding to four structural types: the main drum; main drum + stiffening rings; main drum + stiffening rings + auxiliary rings (auxiliary rings are hinged with the main drum and the ground respectively); and main drum + stiffening rings + auxiliary rings (auxiliary rings are fixed onto the main drum and the ground respectively), were established to compare and analyze the dynamic properties and force transferring paths of different models. After that, CFD method was used to conduct numerical simulation of flow field and mean wind load around the cooling tower. Through field measurements and wind tunnel tests at home and abroad, the reliability of using CFD method for numerical simulation was confirmed. On the basis of this, the surface flow and trail characteristics of the tower at different heights were derived and the wind pressure distribution curves for the internal and external surfaces at different heights of the tower were studied. Finally, based on the calculation results of wind-induced responses of the four models, the effects of stiffening rings, auxiliary rings, and different connecting modes on the dynamic properties and wind-induced responses of the tower structure were derived and analyzed; meanwhile, the effect mechanism of internal suction on such kind of cooling tower was discussed. The study results could provide references to the structure selection and wind resistance design of such type of steel cooling towers.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.997-1005
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• 2009

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+$yd(x))^n$ = xy + yx for all x, y $\in$ I, then R is commutative. (ii) If char R $\neq$ = 2 and (d(x)y + xd(y) + d(y)x + $yd(x))^n$ - (xy + yx) is central for all x, y $\in$ I, then R is commutative. We also examine the case where R is a semiprime ring.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.95-107
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• 2023

Consider ℛ to be an associative prime ring and 𝒦 to be a nonzero dense ideal of ℛ. A mapping (need not be additive) ℱ : ℛ → 𝒬_mr associated with derivation d : ℛ → ℛ is called a multiplicative b-generalized derivation if ℱ(αδ) = ℱ(α)δ +bαd(δ) holds for all α, δ ∈ ℛ and for any fixed (0 ≠)b ∈ 𝒬_s ⊆ 𝒬_mr. In this manuscript, we study the commutativity of prime rings when the map b-generalized derivation satisfies the strong commutativity preserving condition and moreover, we investigate the commutativity of prime rings that admit multiplicative b-generalized derivation, which improves many results in the literature.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• International Journal of Air-Conditioning and Refrigeration
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• v.10 no.1
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• pp.40-49
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• 2002

Floating fixed scroll adopted for tip sealing enhancement in a scroll compressor is always under the influence of tipping moment produced by internal gas forces. Unless the tipping moment is property compensated by some restoring moment, the fired scroll would suffer tipping movement, degrading the compressor performance. The condition on which the tipping movement of the fixed scroll can be suppressed has been investigated analytically. For no tipping movement, the floating fixed scroll should be suspended on the main frame at proper level. The upper limit of the stable suspension is the axial location of the o-rings adopted for a back pressure chamber sealing on the rear side of the fixed scroll, and the lower limit is the mid-height of the scroll wrap.

• Tribology and Lubricants
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• v.23 no.4
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• pp.170-174
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• 2007

Wear and scuffing tests were conducted using friction and wear measurement of piston rings and cylinder blocks in low friction diesel engine. The frictional forces, wear amounts and cycles to scuffing in boundary lubricated sliding condition were measured using the reciprocating wear tester. The cylinder blocks were used as reciprocating specimens, and the piston rings with several coatings were used as fixed pin. Several coatings were used such as DLC, TiN, Cr-ceramic and TiAlN in order to improve the tribological characteristics. From the tests wear volume of piston ring surfaces applied various coatings were compared. During the tests coefficients of friction were monitored. Test results showed that DLC coatings showed good tribological properties. TiN and Cr-ceramic coated rings showed good wear resistance properties but produced high friction.