• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.127-132
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• 1995

[1] Show that ∫$\_$0/$\^$1/ [∫$\_$0/$\^$1/ f($\chi$,y)dy] d$\chi$ = ∫$\_$0/$\^$1/[∫$\_$0/$\^$1/ f($\chi$,y)d$\chi$] Counterexample: If pk denotes the k-th prime number, let S(pk) = (equation omitted), let S = ∪$\_$k=1/$\^$$\infty$/ S(pk), and let Q = [0, 1]${\times}$[0, 1]. Define f on Q as follows; f($\chi$, y) = 0 ($\chi$, y)$\in$S, f($\chi$, y) = 1 ($\chi$, y)$\in$Q - S.(omitted)

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.205-213
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• 2022

In this paper we give a simple and direct proof of an Euler integral representation for a special class of _q+1F_q,k k-hypergeometric functions for q ≥ 2. The values of certain ₃F_2,k and ₄F_3,k functions at $x=\frac{1}{k}$, some of which can be derived using other methods. We may conclude that for k = 1 the results are reduced to [3].

• Korean Journal of Mathematics
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• 제6권2호
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• pp.299-302
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• 1998

In this paper, we will determine all the totally positive integers which cannot be represented by the sum of $k$ nonvanishing integral squares when $k{\geq}4$.

• 충청수학회지
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• 제18권2호
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• pp.131-143
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• 2005

We give bibasic expansion for basic Appell functions ${\Phi}^{(1)}$ and ${\Phi}^{(2)}$, and their integral representations. We also give a continued fraction representation for ${\Phi}^{(2)}$.

• 대한수학회지
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• 제55권1호
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• pp.29-42
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• 2018

We construct bounded linear integral operators that giving solutions to the ${\bar{\partial}}$-equation in $L^p$-spaces and with compact supports on a q-convex intersection ($q{\geq}1$) with ${\mathcal{C}}^3$ boundary in $K{\ddot{a}}hler$ manifolds, and we apply it to obtain a Hartogs-like extension theorems for ${\bar{\partial}}$-closed forms for some bidegree.

• 대한수학회보
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• 제42권4호
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• pp.889-900
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• 2005

We consider the second order mock theta functions defined by McIntosh and define generalized functions. We give integral representation and multibasic expansion of these functions. We also show that they are $F_q$-functions.

• 대한수학회지
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• 제34권3호
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• pp.707-717
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• 1997

The square of Brownian density process $Q^\lambda$ is defined where $\lambda$ is a parameter. Applying limit theorems of stochastic integrals w.r.t. martingale measure, we prove a weak limit theorem for $Q^\lambda$ in $D_{S'(R^d)}[0,1]$.

• 한국가스학회지
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• 제25권6호
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• pp.14-21
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• 2021

-162℃ 초저온 상태의 LNG를 저장하는 저장탱크의 내조는 균열과 같은 결함에 대한 구조 건전성 평가가 필요하다. 전통적인 파괴역학 관점에서는 응력확대계수 K, J-적분 그리고 CTOD를 이용한 단일 매개변수 평가가 주로 수행되어왔다. 그러나 실제 구조에서 발생되는 균열선단은 구조물의 크기, 시편형상 그리고 인장과 굽힘과 같은 하중의 형태에 따라 구속효과의 차이로 인한 영향이 발생하게 된다. 단일 매개변수 파괴역학을 보완하기 위해 다양한 시도가 있었고, 대표적으로 Q-응력법이 있다. 본 논문에서는 비선형 탄성영역의 균열선단 응력장 평가에 적합한 J적분에 Q응력을 유도하여 2 매개변수 접근법을 사용하고자 한다. SENB 시편의 균열비 0.1~0.7 그리고 광폭시편 균열비 0.2~0.6에 시편 균열선단의 응력을 J-Q 평가법을 이용하여 구속효과를 정량적으로 평가 하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.285-291
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• 2003

An experimental method to measure Q-parameter in-situ is described. The basic idea comes from the fact that the side necking near a crack tip indicates the loss of stress triaxiality, which can be scaled by Q. From the out-of-plane displacement and the in-plane strain near the surface of side necking, stress field averaged through the thickness is calculated and then Q is determined from the difference between the stress field and the HRR field corresponding to the identical J-integral. To prove the validity, three-dimensional finite element analysis has been performed for a CT configuration with side-groove. Q-value which was calculated directly from the near-tip stress field is compared with that determined by simulating the experimental procedure according to the proposed method, that is, the Q-value determined from the lateral displacement and the inplane strain. Also, the effect of location where the displacement and strain are measured is explored.

• 대한수학회지
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• 제35권1호
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• pp.177-189
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• 1998

In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.