• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1925-1932
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• 2000

Damage detection methods using vibration modes are investigated on ring structures and. modal behavior of the slightly asymmetric rings is examined. Mode shapes changes, MSER(modal strain energy ratio) and MCR(modal curvature ratio) are applied to identify the locations of faults or damages. Parameters are calculated and compared by finite element analysis on rings with designed local damages. Damages are modeled as reduced stiffness in the analysis. The results show MSER and MCR can be proper factors to detect local damages in ring structures.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.571-583
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• 2020

The Galois ring R of characteristic pⁿ having p^mn elements is a finite extension of the ring of integers modulo pⁿ, where p is a prime number and n, m are positive integers. In this paper, we develop the concepts of Jacobi sums over R and under the assumption that the generating additive character of R is trivial on maximal ideal of R, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.659-666
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• 2019

In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution ${\star}$ and if $a{\in}D^*=D{\setminus}\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at a are radical over the center F of D for every $x{\in}D^*$ with $x^{\star}=x$, then either $a{\in}F$ or ${\dim}_F\;D=4$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.559-571
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• 2017

We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.

• Journal of Advanced Marine Engineering and Technology
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• v.15 no.4
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• pp.29-45
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• 1991

Lip type stern tube sealing systems have used in almost all the middle or large ships which are being constructed in these days. It seems that the pressure fluctuation of the seal ring interspace, the cross-section profile and the materials quality of the seal rings have great effects on the sealing fuction of this sealing system. In this paper, the mechanical movement of lip seal ring which plays the most important role in stern tube sealing system and the possibility of leakage caused by pressure fluctuation are studied by theory and experiment. Using the finite element method for the axi-symetric object which receives the torsional load, the displacement and stress analysis of the seal rings, and also the possibility of crack occurance is checked by theoretical analysis. If the force which seal ring lip periphery receives is too small, there will be the possibility of leakage caused by the pressure fluctuation of the seal ring interspace, and if this force is too large, the frictional force between the seal ring and the liner will become problematical. The possibility of leakage caused by hardening of seal ring materials and creep phenomena of tested seal rings are also examined. The trial seal rings were designed and manufactured using the program of displacement and stress analysis developed in this study and the experimental apparatus to test the trial seal rings was also designed and manufactured. This trial seal rings were fitted in the experimental apparatus which was made in the same form as an actual stern tube. The one side of this apparatus was filled with sea water and the other side of it was filled with the lubricating oil. The leakage of oil and sea water was checked and the temperature was measured, rotating the propeller shaft at the constant velocity by D.C. motor. It was proved that the trial seal rings made in Viton rubber functioned excellenty but the trial seal rings made in N.B.R. rubber had problem in its durability.

• 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.

• Tribology and Lubricants
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• v.19 no.1
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• pp.9-14
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• 2003

The sealing performance of an elastomeric O-ring using the double layered material has been analyzed fer the contact stress behaviors that develop between the O-ring seal and the surfaces with which it comes into contact. The leakage of an O-ring will occur when the pressure differential across the seal Just exceeds the initial (or static) peak contact stress. The contact stress behaviors that develop in compressed O-rings, in common case of dovetail grooved geometry, are investigated using the finite element method. The FE analysis includes material hyperelasticity and axisymmetry. The computed FEM results show that the contact stress behaviors are related to the ratio of diameter between the inner ring and the outer ring, and the temperature of vacuum chamber.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2107-2117
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• 2017

We study the quasi-commutativity in relation with powers of coefficients of polynomials. In the procedure we introduce the concept of ${\pi}$-quasi-commutative ring as a generalization of quasi-commutative rings. We show first that every ${\pi}$-quasi-commutative ring is Abelian and that a locally finite Abelian ring is ${\pi}$-quasi-commutative. The role of these facts are essential to our study in this note. The structures of various sorts of ${\pi}$-quasi-commutative rings are investigated to answer the questions raised naturally in the process, in relation to the structure of Jacobson and nil radicals.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.35 no.1
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• pp.50-53
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• 1999

In this paper, the mechanical movement of lip seal-ring which plays the most important function in stern-tube sealing system and the possibility of leakage caused by pressure fluctuation are studied by theory and experiment. By the finite element method for axial symmetry object which receives the torsional bending load, the displacement and stress analysis of the seal-rings are executed for products of several representative manufacturers of seal-rings, and also the possibility of crack occurance are checked by theoretical analysis. A sample seal-ring id designed and manufactured using the program of displacement and stress analysis developed in this study and made an experimental apparatus to test the sampling seal-ring. The sampling seal-ring functioned excellently, but it had its durability and this problem may be solved by using the Viton instead of NBR.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.809-823
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• 2015

This paper is devoted to presenting a MacWilliams type identity for m-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the m-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.