• 대한수학회논문집
• /
• 제33권3호
• /
• pp.1013-1024
• /
• 2018

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

• 대한수학회지
• /
• 제50권2호
• /
• pp.259-274
• /
• 2013

In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제10권3호
• /
• pp.229-238
• /
• 2006

During World War II there was a statistical analysis conducted by the Allied analysts to estimate the German war productions, including their tank productions. This article revisits the analysis of the tank productions as a classroom activity format. Various reformed ideas are proposed in order to enhance students' perspectives of the point estimation. Comprehensive simulation works and actual classroom discussions will be provided along with the theoretical investigations.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.207-212
• /
• 2022

In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제20권4호
• /
• pp.233-242
• /
• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1994년도 가을 학술발표회 논문집
• /
• pp.38-45
• /
• 1994

P-version finite element model for the computation of stress intensity factors in two dimensional cracked panels by J-integral method is presented. The proposed model is based on high order theory and hierarchical shape function. The displacements fields are defined by integrals of Legendre polynomials which can be classified into three part such as basic mode, side mode, integral mode. The stress intensity factors are computed by J-integral method. The example models for validating the proposed p-version model are centrally cracked panel, single and double edged crack in a rectangular panel under pure Mode I. And the analysis results are compared with those by the h-version of FEM and empirical solutions in literatures. Very good agreement with the existing solution are shown.

• 콘크리트학회지
• /
• 제3권4호
• /
• pp.97-106
• /
• 1991

본 연구의 목적은 휨거동을 하는 철근콘크리트 부재의 변위를 해석적으로 정확하게 구하기 위해 평균 휨균열간격 및 휨모멘트-등가곡률 관계(M-$\Phi_eg$)의 해석법을 제안한 것이다. 제안식은 비균열 구간에서의 철근과 콘크리트 간의 부착특성 및 재료의 소성영역을 고려하여 정확한 곡률분포를 계산함으로써 구할 수 있다. 제안된 해석법의 타당성을 검증하기 위해 34개의 철근콘크리트 보 부재를 제작, 휨재하 실험을 실시하였으며 해석치와 비교검토하였다. 그 결과 실험치와 해석치는 매우 잘 일치하여 본 해석법의 실용성 및 정확성이 입증되었다.

• 한국전산구조공학회논문집
• /
• 제23권2호
• /
• pp.191-198
• /
• 2010

이 연구에서는 접착패치보강의 서로 다른 형태 즉, 패치와 접착제의 재료, 크기, 두께 뿐만 아니라 일면보강 또는 양면보강에 따른 일변균열판의 응력감소에 대한 연구가 수행되었다. 수치해석 도구로는 p-수렴 부분층별 모델이 사용되었다. 이 모델의 면내 변위는 구간별 연속인 선형변화로 가정하였고, 두께방향으로의 면외 변위는 일정한 상수로 가정하여 적용하였다. 변위장의 정의는 적분형 르장드르 다항식을 적용하였고, 수치적분은 별도의 외삽법 없이 각 층별의 절점에서 발생하는 적분값을 바로 얻을 수 있는 가우스-로바토 적분법을 사용 하였다. 또, 에너지 방출률법을 사용하여 응력확대계수를 산출하였다. 수치예제를 통해 제안된 모델의 정확도는 물론이고 접착패치 보강형태에 따라 변화되는 무차원 응력확대계수와 처짐의 항으로 응력감소 효과를 분석하였다.