• 대한수학회논문집
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• 제35권4호
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.

• 소성∙가공
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• 제19권6호
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• pp.329-336
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• 2010

Ring forging process is more appropriate for high-length and thin walled ring, because it utilizes the forging press and hence does not require heavy-duty ring rolling mill. Although ring forging process is very simple and economic for facilities, the process is not efficient because of multi-forging-step and low material utilization. An effective ring forging process is developed using a hollow ingot. When a hollow ingot is used with a workpiece, the ingot can be forged into a final ring without multi-stage pre-forging process, such as, cogging, upsetting, and piercing, etc.. Finally it has advantages of the material utilization and process improvement because a few reheating and forging process are not necessary to make workpiece for ring forging. The important design variables are the applied plastic deformation energy to eliminate cast structure and make uniform properties. In this study, the mechanical properties after forging of hollow cast ingot were investigated from the experiment using circumferential sectional model. Also, the effects of process variables were studied by FEM simulation on the basis of thermo-visco-plastic constitutive equation. Applied strain is different at each position in length direction because diameter of hollow ingot is different in length direction. The different strain distribution become into a narrow gap by additional plastic deformation during diameter extension process.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 춘계학술대회 논문집
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• pp.459-466
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• 2005

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.

• International Journal of Contents
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• 제5권4호
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• pp.88-93
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• 2009

It is important for communication networks to possess the capability to overcome failures and provide survivable services. We address modeling and analysis of performability affected by both performance and availability of system components for a token ring network under failure and repair conditions. Stochastic reward nets (SRN) is an extension of stochastic Petri nets and provides compact modeling facilities for system analysis. In this paper, hierarchical SRN modeling techniques are used to overcome state largeness problem. The upper level model is used to compute availability and the lower level model captures the performance. And Normalized Throughput Loss (NTL) is obtained for the composite ring network for each node failures occurrence as a performability measure. One of the key contributions of this paper constitutes the Petri nets modeling techniques instead of complicate numerical analysis of Markov chains and easy way of performability analysis for a token ring network under SRN reward concepts.

• 대한수학회논문집
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• 제34권1호
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• pp.43-54
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• 2019

Let R be a ring with identity and J(R) denote the Jacobson radical of R, i.e., the intersection of all maximal left ideals of R. A ring R is called J-symmetric if for any $a,b,c{\in}R$, abc = 0 implies $bac{\in}J(R)$. We prove that some results of symmetric rings can be extended to the J-symmetric rings for this general setting. We give many characterizations of such rings. We show that the class of J-symmetric rings lies strictly between the class of symmetric rings and the class of directly finite rings.

• 대한수학회지
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• 제60권2호
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• pp.327-339
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• 2023

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce a new class of ring, called S-multiplication rings which are S-versions of multiplication rings. An R-module M is said to be S-multiplication if for each submodule N of M, sN ⊆ JM ⊆ N for some s ∈ S and ideal J of R (see for instance [4, Definition 1]). An ideal I of R is called S-multiplication if I is an S-multiplication R-module. A commutative ring R is called an S-multiplication ring if each ideal of R is S-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and S-P IR. Moreover, we generalize some properties of multiplication rings to S-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.

• 한국주조공학회지
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• 제35권2호
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• pp.29-35
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• 2015

In this study, potential defects of ring-type cast products during the mold-filling stage of the casting process were investigated using computer simulation. The main focus was on the effects of runner extension and ingates. During the mold filling the molten metal flowed from the bottom to the top of the mold in two curved paths along the ring-type cavity. The fluid fronts in the two paths did not show the identical velocity during the mold filling stage. This difference in the filling speeds may cause defects such as voids and local contractions. The present model contained virtual fluid detectors at various positions inside the mold. When the molten metal passed those points, the volume of fluid jumped up from zero to one. The moments were measured to compare the speeds of the fluid fronts. We attempted various combinations of runner extensions and ingates to stabilize the flow and then to optimize the casting mold design.

• East Asian mathematical journal
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• 제18권2호
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• Kyungpook Mathematical Journal
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• 제57권2호
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• pp.187-191
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• 2017

Let R be a domain with quotient field K and prime subring A. Then R is integral over each of its subrings having quotient field K if and only if (A, R) is a survival pair. This shows the redundancy of a condition involving going-down pairs in a earlier characterization of such rings. In characteristic 0, the domains being characterized are the rings R that are isomorphic to subrings of the ring of all algebraic integers. In positive (prime) characteristic, the domains R being characterized are of two kinds: either R = K is an algebraic field extension of A or precisely one valuation domain of K does not contain R.

• 대한수학회보
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• 제45권2호
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• pp.285-297
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• 2008

For an endomorphism ${\alpha}$ of a ring R, the endomorphism ${\alpha}$ is called semicommutative if ab=0 implies $aR{\alpha}(b)$=0 for a ${\in}$ R. A ring R is called ${\alpha}$-semicommutative if there exists a semicommutative endomorphism ${\alpha}$ of R. In this paper, various results of semicommutative rings are extended to ${\alpha}$-semicommutative rings. In addition, we introduce the notion of an ${\alpha}$-skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring $R[[x;\;{\alpha}]]$. We show that a number of interesting properties of a ring R transfer to its the skew power series ring $R[[x;\;{\alpha}]]$ and vice-versa such as the Baer property and the p.p.-property, when R is ${\alpha}$-skew power series Armendariz. Several known results relating to ${\alpha}$-rigid rings can be obtained as corollaries of our results.