• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.649-660
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• 2020

This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂_iu₁; ∂_ju₂; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊₃ := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

• Bulletin of the Korean Chemical Society
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• v.11 no.6
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• pp.560-563
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• 1990

A.c. susceptibility for $Bi_{1.4}Pb_{0.6}Sr_2Ca_2Cu_{3.6}O_x$ superconductor is measured as a function of temperature at different value of a.c. magnetic field amplitude. Two transition steps are attributed to the intergranular and intragranular properties. Based on Bean's critical state model, intergranular critical current density, $J_c^{gb}$ (11 $A/cm^2$ at 77 K) and intragranular critical current density, $J_c^g (7{\times}10^3\;A/cm^2$ at 100 K) are estimated. The low values of $J_c^{gb}$and $J_c^g$ reflect a poor nature of coupling between grains and the low pinning force density of intragrain in $Bi_{1.4}Pb_{0.6}Sr_2Ca_2Cu_{3.6}O_x$ superconductor.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.1073-1077
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• 1997

In this paper, we have studied internal quality including chemical compositions, microscopic structure and nonmetalic inclusion of test materials. We have analyzed machining characteristics including tensile strength value, impact value, hardness value etcs. Test materials are usd martensitic heat resisting steel, STR11 and STS420J2. The obtined results are as follows : 1. In analyzing internal quality, STR11 and STR420J2 have typical martensite structure and a minute needle-shaped structure. 2. Tensile strength and reduction of area and hardness value are large STR11 than STS420J2. But elongation impact are smaller STR11 than STS420J2. 3. Fracture surface of tensile speciman is ductile in STR11 and STS420J2.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.04a
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• pp.453-456
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• 2002

J2EE(Java 2 Enterprise Environment) 프레임워크는 확장성 있는 다단계(multi-tie.) 분산 어플리케이션을 만들기 위한 컴포넌트 소프트웨어 개발의 주요 기술로 자리를 잡고 있다. 따라서 컴포넌트 기반의 소프트웨어 개발 도구에서도 EJB 를 포함한 J2EE 프레임워크 개발을 필수적으로 지원하여야 한다. 본 논문에서는 J2EE 프레임워크 개발 및 적용에 있어서 모델링이나 개발 못지 않게 중요한 단계인 컴포넌트에 대한 표준 디스크립터 작성 및 어플리케이션 서버 탑재에 대한 확장성 있고 자동화된 방법을 제안한다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.5
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• pp.631-640
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• 2013

This paper provides a comparison of the J-integral estimation method under combined primary and secondary stress in the R6, RCC-MR A16 code. The comparisons of each code are based on finite element analysis using ABAQUS with regard to the crack shape, crack depth, and magnitude of secondary load. The estimate of the R6 code is conservative near $L_r=1$, and that of the RCC-MR A16 code is conservative near $L_r=0$. As a result, this paper proposes a modified method of J-integral estimation in the R6, RCC_MR A16 code. The J-integral using the modified method corresponds to the finite element analysis result.

• 대한핵의학회:학술대회논문집
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• 1999.11a
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• pp.41.2-41.2
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• 1999

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.3
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• pp.185-191
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• 2022

This paper proposed a division algorithm of performance complexity $O{\frac{n(n+1)}{2}}$ for a change-making problem(CMP) in which polynomial time algorithms are not known as NP-hard problem. CMP seeks to minimize the sum of the x_j number of coins exchanged when a given amount of money C is exchanged for c_j,j=1,2,⋯,n coins. Known polynomial algorithms for CMPs are greedy algorithms(GA), divide-and-conquer (DC), and dynamic programming(DP). The optimal solution can be obtained by DP of O(nC), and in general, when given C>2ⁿ, the performance complexity tends to increase exponentially, so it cannot be called a polynomial algorithm. This paper proposes a simple algorithm that calculates quotient by dividing upper triangular matrices and main diagonal for k×n matrices in which only j columns are placed in descending order of c_j of n for c_j ≤ C and i rows are placed k excluding all the dividers in c_j. The application of the proposed algorithm to 39 benchmarking experimental data of various types showed that the optimal solution could be obtained quickly and accurately with only a calculator.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.889-906
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• 2020

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.179-188
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• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.