• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.487-497
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• 2006

The purpose of this paper is to describe the structure of the rings $\mathbb{Z}_{p^2}[X]/({\alpha}(X))$ with ${\alpha}(X)$ a monic polynomial and $\={X}^{\kappa}=0$ for some nonnegative integer ${\kappa}$. Especially we will see that any ideal of such rings can be generated by at most two elements of the special form and we will find the 'minimal' set of generators of the ideals. We indicate how to identify the isomorphism types of the ideals as $\mathbb{Z}_{p^2}-modules$ by finding the isomorphism types of the ideals of some particular ring. Also we will find the annihilators of the ideals by finding the most 'economical' way of annihilating the generators of the ideal.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.475-484
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• 2023

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.490-493
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• 2002

In this paper, the old Fourier-Motzkin method (abbreviated as the old FH method from now on) is first modified to the form which can derive all minimal vectors as well as all minimal support vectors of nonnegative integer homogeneous solutions (i.e., T-invariants) for a matrix equation $Ax=b=0^{m{\times}1}$, $A\epsilonZ^{m{\times}n}$ and $b\epsilonZ^{m{\times}1}$, of a given Petri net, where the old FM method is a well-known and direct method that can obtain at least all minimal support solutions for $Ax=0^{m{\times}1}$ from the incidence matrix . $A\epsilonZ^{m{\times}n}$, Secondly, for $Ax=b\ne0^{m{\times}n}$ a new extended FM method is given; i.e., all nonnegative integer minimal vectors which contain all minimal support vectors of not only homogeneous but also inhomogeneous solutions are systematically obtained by applying the above modified FH method to the augmented incidence matrix $\tilde{A}$ =〔A,-b〕$\epsilon$ $Z^{m{\times}(n＋1)}$ s.t. $\tilde{A}\tilde{x}$ = 0^{m{\times}1}$ However, note that for this extended FM method we need some criteria to obtain a minimal vector as well as a minimal support vector from both of nonnegative integer homogeneous and inhomogeneous solutions for Ax=b. Then those criteria are also discussed and given in this paper.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2009.11a
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• pp.181-184
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• 2009

A development of a composite solid propellant is carried out for an application to gas generators as an energy source of rocket system. With HTPB as a propellant binder which has 80% of particle loading ratio, a favorable rheology, and moderate curing properties at the range of $-50^{\circ}C{\sim}70^{\circ}C$, AN is selected as the first kind of oxidizer having the characteristics of a low flame temperature, minimal particle residual as well as nontoxic products. AP is the second oxidant for ballistic property control. A series of experiments for the improvement of physical properties were conducted and resulted in the propellant formulation having 30% of strain rate at 8 bar of max. stress.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.799-809
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• 2013

An ideal I of a local ring (R, m, k) is said to be m-full if there exists an element $x{\in}m$ such that Im : x = I. An ideal I of a local ring R is said to have the Rees property if ${\mu}$(I) > ${\mu}$(J) for any ideal J containing I. We study properties of m-full ideals and we characterize m-primary m-full ideals in terms of the minimal number of generators of the ideals. In particular, for a m-primary ideal I of a 2-dimensional regular local ring (R, m, k), we will show that the following conditions are equivalent. 1. I is m-full 2. I has the Rees property 3. ${\mu}$(I)=o(I)+1 In this paper, let (R, m, k) be a commutative Noetherian local ring with infinite residue field k = R/m.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.359-368
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• 2018

In this paper, we investigate quasi-cyclic codes over the ring $R={\mathbb{F}}_2+v{\mathbb{F}}_2$, where $v^2=v$. We investigate the structure of generators for one-generator quasi-cyclic codes over R and their minimal spanning sets. Moreover, we find the rank and a lower bound on minimum distances of free quasi-cyclic codes over R. Further, we find a relationship between cyclic codes over a different ring and quasi-cyclic codes of index 2 over R.

• Nuclear Engineering and Technology
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• v.56 no.4
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• pp.1454-1459
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• 2024

Researchers have applied theoretical and CFD models for years to analyze the fluidelastic instability (FEI) of tube arrays in steam generators and other heat exchangers. The accuracy of each approach has typically been evaluated using the discrepancy between the experimental critical flow velocity and the predicted value. In the best cases, the predicted critical flow velocity was within an order of magnitude comparable to the measured one. This paper revisits the quasi-steady approach for damping controlled FEI in a normal triangular array with a pitch ratio of P/d = 1.375. The method addresses the fluidelastic frequency at the stability threshold as an input parameter for the approach. The excellent agreement between the estimated stability thresholds and the equivalent experimental results suggests that the fluidelastic frequency must be included in the quasi-steady analysis, which requires minimal computing time and experimental data. In addition, the model allows a simple time delay analysis regarding flow convective and viscous effects.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.197-204
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• 2024

Let R = 𝕂[x] be a univariate polynomial ring over an algebraically closed field 𝕂 of characteristic zero. Let A ∈ M_m,m(R) be an m×m matrix over R with non-zero determinate det(A) ∈ R. In this paper, utilizing linear-algebraic techniques, we investigate the relationship between a basis for the syzygy module of f₁, . . . , f_m and a basis for the syzygy module of g₁, . . . , g_m, where [g₁, . . . , g_m] = [f₁, . . . , f_m]A.