• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.289-309
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• 2019

This paper is intended as a discussion of some generalizations of the notion of a reversible ring, which may be obtained by the restriction of the zero commutative property from the whole ring to some of its subsets. By the INCZ property we will mean the commutativity of idempotent elements of a ring with its nilpotent elements at zero, and by ICZ property we will mean the commutativity of idempotent elements of a ring at zero. We will prove that the INCZ property is equivalent to the abelianity even for nonunital rings. Thus the INCZ property implies the ICZ property. Under the assumption on the existence of unit, also the ICZ property implies the INCZ property. As we will see, in the case of nonunital rings, there are a few classes of rings separating the class of INCZ rings from the class of ICZ rings. We will prove that the classes of rings, that will be discussed in this note, are closed under extending to the rings of polynomials and formal power series.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.8 no.4
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• pp.257-262
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• 2015

In this paper, the split-ring DGS resonator is proposed and its equivalent circuit are analyzed to design the low pass filter. Compared with the conventional dumbell DGS cell, this structure has a flat fluctuation in low frequency range and a sharp slop at edge frequency. The out-band suppression of the SRR-DGS cell can be improved by placing the open stubs on the conductor line which operates as parallel capacitances. Making use of equivalent circuit analytical method, the characteristics of the improved SRR DGS cell are investigated and applied to design compact low pass filter, which has a low in-band loss, sharp slop and high suppression of more than 35dB within a wide out-band frequency range. The dependence of the transmission characteristic on the dimension of a split ring, such as side-length and split-gap, is analyzed in detail. In addition, an improved SRR DGS cell model with open stubs loaded on the conductor line is then presented to improve the out-band suppression. By using the equivalent-circuit analytical method, an S-band microstrip low-pass filter with perfect low-pass characteristic and high out-band suppression is designed and fabricated.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.457-466
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• 2005

We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.887-893
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• 1996

Let (R,m) be a Cohen-Macaulay local ring with an infinite residue field and let $J = (a_1, \cdots, a_l)$ be a minimal reduction of an equimultiple ideal I of R. In this paper we shall prove that the following conditions are equivalent: (1) $I^2 = JI$. (2) $gr_I(R)/mgr_I(R)$ is Cohen-Macaulay with minimal multiplicity at its maximal homogeneous ideal N. (3) $N^2 = (a'_1, \cdots, a'_l)N$, where $a'_i$ denotes the images of $a_i$ in I/mI for $i = 1, \cdots, l$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.23-33
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• 2011

Extending the notion of McCoy rings, we introduce the class of McCoy modules. Over a given ring R, it contains the class of Armendariz modules (over R). Some properties of this class of modules are established, and equivalent conditions for McCoy modules are given. Moreover, we study the relationship between a module and its polynomial module. Several known results relating to McCoy rings can be obtained as corollaries of our results.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.127-135
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m. Then we say that I is an equimultiple good ideal in A, if I contains a reduction Q = ( $a_1$, $a_2$,ㆍㆍㆍ, $a_{s}$ ) generated by s elements in A and G(I) =(equation omitted)$_{n 0}$ $I^{n}$ / $I^{n＋1}$ of I is a Gorenstein ring with a(G(I)) = 1 - s, where s = h $t_{A}$ I and a(G(I)) denotes the a-invariant of G(I). Let $X_{A}$$^{s}$ denote the set of equimultiple good ideals I in A with h $t_{A}$ I = s, R(I) = A [It] be the Rees algebra of I, and $K_{R(I)}$ denote the canonical module of R(I). Let a I such that $I^{n＋l}$ = a $I^{n}$ for some n$\geq$0 and $\mu$$_{A}$(I)$\geq$2, where $\mu$$_{A}$(I) denotes the number of elements in a minimal system of generators of I. Assume that A/I is a Cohen-Macaulay ring. We show that the following conditions are equivalent. (1) $K_{R(I)}$(equation omitted)R(I)＋as graded R(I)-modules. (2) $I^2$ = aI and aA : I$\in$ $X^1$$_{A}$._{A}$./.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.871-883
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• 2015

This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.

• Journal of the Korean Institute of Gas
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• v.16 no.6
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• pp.67-72
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• 2012

In this study, the leak-free performance and sealing endurance safety of CNG fueling nipple in which are related to the contact normal stress and equivalent true stress have been analyzed for CNG automobile using a finite element analysis. For the conventional circular o-rings and new double-lip o-rings with an initial compression rate of 15 percentages, the leak-free performance of double-lip o-rings with two contact sealing spots is 41% higher than that of the conventional circular o-rings with a contact sealing spot. The FEM computed results present that the leak-free endurance safety of double-lip o-rings with two contact sealing spots is 5% higher than that of the conventional circular o-rings for initial compression ratio of 15 percentages and a gas compression pressure of 8MPa. And, the maximum equivalent true stress of double-lip o-rings is 10.2% higher than that of the conventional circular o-rings for the leak-free endurance safety. This means that the double-lip o-ring may guarantee the extended sealing life compared to that of a conventional circular o-ring.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.4
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• pp.629-635
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• 2017

Free-Flooded Ring (FFR) transducer array for use in Sonar system can be driven with large amplitude in a wide frequency band due to its structural characteristics, in which two resonances of a ring mode (1st radial mode) and an inner cavity vibration mode occur in a low frequency band. Since its sound wave generation characteristics are not influenced by the water pressure, the FFR transducer array is widely used in the deep sea. So FFR has been recognized as a low-frequency active sound source and has received much attention ever since. In order to utilize the FFR transducer array for SONAR systems in military and industrial applications, its equivalent electric circuit model is necessary especially to design the matching circuit between the driving power amplifier and the FFR transducer array. Thus this paper proposes the equivalent electric circuit model of FFR transducer array by using measured values of parameter, and suggest the improved method of parameter identification. Finally it verifies the effectiveness of the proposed circuit model of FFR transducer array by experimental measurements.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.