• Kyungpook Mathematical Journal
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• 제57권2호
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• pp.187-191
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• 2017

Let R be a domain with quotient field K and prime subring A. Then R is integral over each of its subrings having quotient field K if and only if (A, R) is a survival pair. This shows the redundancy of a condition involving going-down pairs in a earlier characterization of such rings. In characteristic 0, the domains being characterized are the rings R that are isomorphic to subrings of the ring of all algebraic integers. In positive (prime) characteristic, the domains R being characterized are of two kinds: either R = K is an algebraic field extension of A or precisely one valuation domain of K does not contain R.

• 한국생산제조학회지
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• 제9권5호
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• pp.47-57
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• 2000

In this study, a fundamental approach to make clear the mechanism of the mutual interference and coalescence of stress fields in the vicinity of two crack tips on the process of their slow growth, using boundary element method. Automatic generation of quadratic discontinuous elements along both of the crack boundaries which can be defined by an arbitrary piece-wise straight geometry. The direction of the crack-extension increment is predicted by the maximum principal stress criterion, corrected to account for the discreteness of the crack extension. Along the computed direction, the crack is extended one increment. Automatic incremental crack-extension analysis with no remeshing, computation of the stress intensity factors by J-integral. Numerical stress intensity factors for two growing cracks in plane-homogeneous regions were determined.

• 대한수학회보
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• 제40권3호
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• pp.509-520
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• 2003

Let p be a prime number, $Q_{p}$ the field of p-adic numbers, K a finite extension of $Q_{p}$, $\bar{K}}$ a fixed algebraic closure of K and $C_{p}$ the completion of K with respect to the p-adic valuation. Let E be a closed subfield of $C_{p}$, containing K. Given elements $t_1$...,$t_{r}$ $\in$ E for which the field K($t_1$...,$t_{r}$) is dense in E, we construct integral bases of E over K.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.457-463
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• 2008

In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert's integral inequality with a mixed kernel $k(x, y) = \frac {1}{A(x+y)+B{\mid}x-y{\mid}}$ and a best constant factors. As applications, some particular results with the best constant factors are considered.

• 대한수학회보
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• 제54권3호
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• pp.917-933
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• 2017

In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

• 충청수학회지
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• 제27권3호
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• pp.489-494
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• 2014

In this paper, we define the extension $f^*:[a,b]{\rightarrow}\mathbb{R}$ of a function $f:[a,b]_{\mathbb{T}}{\rightarrow}\mathbb{R}$ for a time scale $\mathbb{T}$ and investigate the properties of the Lebesgue delta integral of f on $[a,b]_{\mathbb{T}}$ by using the function $f^*$.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.55-60
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• 2002

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation $W^{(n)}$ of a Wiener process W, we prove that the multiple integral processes {${\int}_{0}^{t}{\cdots}{\int}_{0}^{t}f(t_{1},{\cdots},t_{m})W^{(n)}(t_{1}){\cdots}W^{(n)}(t_{m}),t{\in}[0,T]$} where f is a given symmetric function in the space $C([0,T]^{m})$, converge to the multiple Stratonovich integral of f in the uniform $L^{2}$-sense.

• 대한조선학회지
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• 제21권2호
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• pp.35-42
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• 1984

A line integral is exhibited which has the same value for all paths surrounding the tip of crack in a two dimensional strain field of elastic-plasticc material. Finite element method was used to determine Rice's J-integral value in centrally cracked plate. These numerical J-integral values were compared with corresponding values of reference with low hardening and high yield strength. The J-integral value was also computed for a crack extension and different load condition. For increasing crack length the value of J-integral also increases, this means that the crack is unstable. To prove path independent, three paths were used in the analysis and proved.

• 한국수학사학회지
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• 제22권4호
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• pp.145-160
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• 2009

20세기말 p-진 공간에서 p-진 q-적분의 개념이 김태균에 의해서 처음 도입 되었다([11]). 이러한 적분은 복소수 공간에서 잭슨의 q-적분을 p-진 공간으로 확장 시킨 것이며 또한 울트라 비 아르키메디언 적분의 존재성에 대한 질문의 답으로 볼 수 있다. 본 논문에서는 이러한 p-진 q-적분의 수학사적 배경을 살펴보고, 현재 어떠한 방향으로 연구가 진행되고 있는지를 고찰한다.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.53-69
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• 2020

Let (A, M) ⊂ (B, N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N. Suppose henceforth that M ⊆ N. If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A + N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite field.