• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1829-1839
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• 2017

In this paper, we show some results on the vanishing and the finiteness of local cohomology modules with respect to a pair of ideals. We also prove that Supp($H^{dim\;M-1}_{I,J}(M)/JH^{dim\;M-1}_{I,J}(M)$) is a finite set.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.803-813
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• 2020

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂_R M^∗ → Hom_R(Hom_R(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and Extⁱ_R(M, M) = 0 (i ⩾ 1), then M is projective.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.243-249
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• 2003

We consider weighted Bergman spaces and radial derivatives on the spaces. We also prove that for each element f in B$\^$p, r/ there is a unique f in B$\^$p, r/ such that f is the radial derivative of f and for each f$\in$B$\^$r/(i), f is the radial derivative of some element of B$\^$r/(i) if and only if, lim f(tz)= 0 for all z$\in$H.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.33-39
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• 1994

The purpose of this paper prove the following property; Suppose A has many units (local global ring) and |A/m| > 5 for every maximal ideal $m{\subseteq}A$. Let(E, q) ${\in}$ Q(A) and $E=E_1{\bot}{\cdots}{\bot}E_t$ be an orthogonl decomposition of E with $t{\geq}2$ and $rk(E_i){\geq}1$, for $i=1,{\cdots},t$. Let $x{\in}E$ be a primitive vector. Then there exists ${\sigma}{\in}O(q)$ such that ${\sigma}(x)$ is transversal to this decomposition.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.23-29
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• 2007

Let X and Y be vector spaces. In this paper we prove that a mapping $f:X{\rightarrow}Y$ satisfies the following functional equation $${\large}\sum_{1{\leq}k<l{\leq}n}\;(f(x_k+x_l)+f(x_k-x_l))-2(n-1){\large}\sum_{i=1}^{n}f(x_i)=0$$ if and only if the mapping f is quadratic. In addition we investigate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.

• Journal of the Korean Society of Safety
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• v.10 no.2
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• pp.3-9
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• 1995

Several piping material test methods have been developed as a result of advances in elastic-plastic fracture mechanics. It's known that, crack propagation of the materials strongly governed by the $J_{Ic}$ value. But the value is still difficult to be obtained because of it's complicate and troble-some determination process. In this paper, to prove the validity of the developed test procedure a series of tests were peformed at various temperatures and for different material directions. directions.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.651-662
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• 2014

The main goal of this study is to extend the domain of influence result to cover the micropolar thermoelastic diffusion. So, we prove that for a finite time t>0 the displacement field $u_i$, the microrotation vector ${\varphi}_i$, the temperature ${\theta}$ and the chemical potential P generate no disturbance outside a bounded domain $B_t$.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.85-95
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• 2019

In this paper, we define near-minimal shadow and study the existence problem of extremal Type I binary self-dual codes with near-minimal shadow. We prove that there is no such codes of length n = 24m + 2($m{\geq}0$), n = 24m + 4($m{\geq}9$), n = 24m + 6($m{\geq}21$), and n = 24m + 10($m{\geq}87$).

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.729-740
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• 2018

In this paper, we define near-minimal shadow and study the existence problem of extremal Type I additive self-dual codes over GF(4) with near-minimal shadow. We prove that there is no such codes if the code length n = 6m+1($m{\geq}0$), $n=6m+5(m{\geq}1)$.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.359-379
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• 2023

In the present paper, we study translation hypersurfaces in E⁴. In this context, firstly we obtain first, second and third Laplace-Beltrami (LB^I, LB^II and LB^III) operators of the translation hypersurfaces in E⁴. By solving second and third order nonlinear ordinary differential equations, we prove theorems that contain LB^I-minimal, LB^II-minimal and LB^III-minimal translation hypersurfaces in E⁴.