• 대한수학회논문집
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• 제32권1호
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• pp.29-38
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• 2017

The main objective of this paper is to establish certain unified integral formula involving the product of the generalized Mittag-Leffler type function $E^{({\gamma}_j),(l_j)}_{({\rho}_j),{\lambda}}[z_1,{\ldots},z_r]$ and the Srivastava's polynomials $S^m_n[x]$. We also show how the main result here is general by demonstrating some interesting special cases.

• Structural Engineering and Mechanics
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• 제64권1호
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• pp.71-79
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• 2017

In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.347-354
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• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• 대한수학회논문집
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• 제27권2호
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• Coupled systems mechanics
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• 제6권1호
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• pp.75-96
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• 2017

As electron donor/acceptor materials for organic photovoltaic cells, small-molecules donors/acceptor are attracting more and more attention. In this work, we investigated the electronic structures, electrochemical properties, and charge carrier transport properties of four recently-synthesized small-molecule donors/acceptor, namely, DPDCPB (A), DPDCTB (B), DTDCPB (A1), and DTDCTB (B1), by a series of ab initio calculations. The calculations look into the electronic structure of singly oxidized and reduced molecules, the first anodic and cathodic potentials, and the electrochemical gaps. Results of our calculations were in accord with those from experiments. Using Marcus theory, we also computed the reorganization energies of hole/electron hoppings, as well as hole/electron transfer integrals of multiple possible molecular dimer configurations. Our calculations indicated that the electron/hole transport properties are very sensitive to the relative separations/orientations between neighboring molecules. Due to high reorganization energies for electron hopping, the hole mobilities in the molecular crystals are at least an order of magnitude higher than the electron mobilities.

• 한국전산구조공학회논문집
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• 제22권3호
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• pp.267-275
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• 2009

이 논문에서는 복합재료 적층판 해석을 위해 등가단층요소와 부분-선형 층별 적층요소를 서로 연계시킨 결합요소를 제안하였다. 등가단층요소는 퇴화 쉘요소에 의해 정식화되었으며, 반면에 부분-선형 층별요소의 경우 면내변위는 부분적 선형변화로, 두께방향으로의 면외변위는 일정하다고 가정하였다. 제안된 유한요소모델은 p-수렴방식에 기초를 두고 있다. 변위장 보간을 위해 적분형 르장드르 다항식이, 수치적분을 수행하기 위해서는 가우스-로바토 적분을 각각 채택하였다. 이 연구에서는 주로 p-수렴 결합요소의 검증을 위해 다양한 형태의 유한요소 다중모델에 대해 안정된 수치해석값을 보여주는 지에 초점을 두었다. 채택한 예제는 정해를 쉽게 알고 있는 단순한 문제로 인장력을 받는 평판 또는 연직하중을 받는 캔틸레버보에 적용하여 제안된 요소의 성능을 평가하였다.

• 한국해양공학회지
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• 제24권5호
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• pp.16-21
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• 2010

During the loading/offloading operation of a liquefied natural gas carrier (LNGC) that is moored in a side-by-side configuration with an offshore plant, sloshing that occurs due to the partially filled LNG tank and the interactive effect between the two floating bodies are important factors that affect safety and operability. Therefore, a time-domain software program, called CHARM3D, was developed to consider the interactions between sloshing and the motion of a floating body, as well as the interactions between multiple bodies using the potential-viscous hybrid method. For the simulation of a floating body in the time domain, hydrodynamic coefficients and wave forces were calculated in the frequency domain using the 3D radiation/diffraction panel program based on potential theory. The calculated values were used for the simulation of a floating body in the time domain by convolution integrals. The liquid sloshing in the inner tanks is solved by the 3D-FDM Navier-Stokes solver that includes the consideration of free-surface non-linearity through the SURF scheme. The computed sloshing forces and moments were fed into the time integration of the ship's motion, and the updated motion was, in turn, used as the excitation force for liquid sloshing, which is repeated for the ensuing time steps. For comparison, a sloshing motion coupled analysis program based on linear potential theory in the frequency domain was developed. The computer programs that were developed were applied to the side-by-side offloading operation between the offshore plant and the LNGC. The frequency-domain results reproduced the coupling effects qualitatively, but, in general, the peaks were over-predicted compared to experimental and time-domain results. The interactive effects between the sloshing liquid and the motion of the vessel can be intensified further in the case of multiple floating bodies.