• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1251-1258
• /
• 2020

This paper establishes a formula changing the ring from a Noetherian local ring A of dimension d > 0 containing the residue field k to the polynomial ring in d variables k[X₁, X₂, …, X_d] for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of A by highest dimensional associated prime ideals of A.

• Korean Journal of Mathematics
• /
• v.21 no.1
• /
• pp.23-28
• /
• 2013

The structures of finite local rings of order ${\leq}$ 16 with nonzero Jacobson radical are investigated. The whole shape of non-commutative local rings of minimal order is completely determined up to isomorphism.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.387-391
• /
• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.747-755
• /
• 2013

This paper deals with the unit groups of the endomorphism rings of projective modules over polynomial rings and further over formal power series rings. A normal subgroup of the unit group is defined and discussed. The local splitting properties of element of endomorphism rings of projective modules over polynomial rings are given.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.6
• /
• pp.1479-1489
• /
• 1995

In this study, tensile strength and modulus were evaluated for a filament wound ring specimen by split disk test and compared with the theoretical values obtained by the rule of mixtures. The circumferentially wound ring specimens were prepared from 4 types of material systems. The results showed that the measured strengths of the composite systems were considerably lower than the theoretical values due to the local bending stresses around the split disk edges. for the measurement of elastic moduli of the filament wound ring specimens, the effect of friction on the strain of the ring must be taken into account. But the effect of friction between the split disk fixture and the ring specimen can be eliminated by averaging the moduli for loading and unloading state with maintaining the same crosshead rates. The measured elastic moduli of ring specimens showed very good agreement with the theoretical values.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1629-1643
• /
• 2016

Let R be a ring with identity, X be the set of all nonzero, nonunits of R and G be the group of all units of R. A ring R is called unit-duo ring if $[x]_{\ell}=[x]_r$ for all $x{\in}X$ where $[x]_{\ell}=\{ux{\mid}u{\in}G\}$ (resp. $[x]_r=\{xu{\mid}u{\in}G\}$) which are equivalence classes on X. It is shown that for a semisimple unit-duo ring R (for example, a strongly regular ring), there exist a finite number of equivalence classes on X if and only if R is artinian. By considering the zero divisor graph (denoted ${\tilde{\Gamma}}(R)$) determined by equivalence classes of zero divisors of a unit-duo ring R, it is shown that for a unit-duo ring R such that ${\tilde{\Gamma}}(R)$ is a finite graph, R is local if and only if diam(${\tilde{\Gamma}}(R)$) = 2.

• Tribology and Lubricants
• /
• v.14 no.3
• /
• pp.59-64
• /
• 1998

This paper presents the deformation characteristics of cam ring in a balanced type vane pump. Cam ring is operated in the high-pressure condition. Therefore the local deformation of cam ring affects the characteristics of compression, vane motion and noise and vibration. We analyzed the deformation of cam ring for the three types by using the finite element method. The deformed shape of cam ring and the effects of deformation on the compression are presented. As a result of analysis, we know that the right hole of the cam ring has advantage for reducing the pressure overshoot.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.479-484
• /
• 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 $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.10 no.6
• /
• pp.711-729
• /
• 2018

This paper reports on the experimental investigations on the failure modes of ring-stiffened cylinder models subjected to external hydrostatic pressure. Nine models were welded from general structural steel. The shells were initially formed by cold-rolling, and flat-bar ring frames were welded to the shell. The hydrostatic pressure tests were conducted by using water as the medium in pressure chambers. The details of the preparation and main test were briefly explained. The investigation identified the consequence of the structural failure modes, including: shell yielding, local shell buckling between ring stiffeners, overall buckling of the shell together with the stiffeners, and interactive buckling mode combining local and overall buckling. In addition, the ultimate strengths were predicted by using existing design codes. Non-linear numerical computations were also conducted by employing the actual imperfection coordinates. Finally, accuracy and reliability of the predictions of design formulae and numerical were substantiated with the test results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2009.04a
• /
• pp.359-360
• /
• 2009

In this study, we propose a practical method to improve the clarity and the period of the beat in a Korean bell. Proper beating in vibration and sound is very important feature in Korean bell. An equivalent ring theory is applied and finite element analysis is performed to determine the condition of the asymmetry of the bell. The clearity and the period of the beat are improved by attaching a counter mass or decreasing local thickness. This paper shows that the improved the attaching a counter mass or decreasing local thickness. This paper of the beat are improved by attaching a counter mass or decreasing local thickness. This paper shows that the amount and position of the local variation for the required beat condition can be predicted by using the equivalent model, The predicted results are verified by the experiment.