• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.1
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• pp.23-32
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• 1982

Herein the motion of a freely-floating sphere in a water of finite depth is analysed within the framework of a linear potential theory. A velocity potential describing fluid motion is generated by distributing pulsating sources and dipoles on the immersed surface of the sphere, without introducing an inner flow model. The potential becomes the solution of an integral equation of Fredholm's second type. In the light of the vertical axisymmetry of the flow, surface integrals reduce to line integrals, which are approximated by summation of the products of the integrand and the length of segments along the contour. Following this computational scheme the diffraction potential and the radiation potential are determined from the same algorithm of solving a set of simultaneous linear equations. Upon knowing values of the potentials hydrodynamic forces such as added mass, hydrodynamic damping and wave exciting forces are evaluated by the integrating pressure over the immersed surface of the sphere. It is found in the case of finite water depth that the hydrodynamic forces are much different from the corresponding ones in deep water. Accordingly motion response of the sphere in a water of finite depth displays a particular behavior both in a amplitude and phase.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.28-31
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• 2003

In the present work, a main purpose is to propose a fuzzy integral-based aggregation framework to complementarily combine partial information due to lack of completeness. Based on Choquet integral (CI) viewed as monotone expectation, we take into account complementary, non-interactive, and substitutive aggregations of different sources of defective information. A CI-based system representing upper, conventional, and lower expectations is designed far handling three aggregation attitudes towards uncertain information. In particular, based on Choquet integrals for belief measure, probability measure, and plausibility measure, CI$\_$bi/-, CI$\_$pr/ and CI$\_$pl/-aggregator are constructed, respectively. To illustrate a validity of proposed aggregation framework, multiple matching systems are developed by combining three simple individual template-matching systems and tested under various image variations. Finally, compared to individual matchers as well as other traditional multiple matchers in terms of an accuracy rate, it is shown that a proposed CI-aggregator system, {CI$\_$bl/-aggregator, CI$\_$pl/-aggregator, Cl$\_$pl/-aggregator}, is likely to offer a potential framework for either enhancing completeness or for resolving conflict or for reducing uncertainty of partial information.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.375-382
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• 2008

The particular integral formulation for two(2D) and three(3D) dimensional inelastic transient dynamic stress analysis is presented. The elastostatic equation is used for the complementary solution. Using the concept of global shape function, the particular integrals for displacement and traction rates are obtained to approximate acceleration of the inhomogeneous equation. The Houbolt time integration scheme is used for the time-marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. Numerical results of four example problems are given to demonstrate the validity and accuracy of the present formulation.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.283-295
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• 1997

This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using $2^N$ algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

• East Asian mathematical journal
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• v.34 no.3
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• pp.295-303
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• 2018

Gautam et al. [9] introduced the multivariable A-function, which is very general, reduces to yield a number of special functions, in particular, the multivariable H-function. Here, first, we aim to establish two very general integral formulas involving product of the general class of Srivastava multivariable polynomials and the multivariable A-function. Then, using those integrals, we find a solution of partial differential equations of heat conduction at zero temperature with radiation at the ends in medium without source of thermal energy. The results presented here, being very general, are also pointed out to yield a number of relatively simple results, one of which is demonstrated to be connected with a known solution of the above-mentioned equation.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1017-1031
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• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1527-1575
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• 2017

In a spirit of Givental's constructions Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested Landau-Ginzburg models for smooth Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau-Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.597-612
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• 2021

Several useful and interesting extensions of the various special functions have been introduced by many authors during the last few decades. Various integral formulas associated with Wright function have been studied and a noteworthy amount of work have found in literature. The principal object of the present paper is to evaluate finite integral formulas containing the product of orthogonal polynomials with generalized Wright function. These integral formulas are expressed in terms of Srivastava and Daoust function. Some interesting particular cases are obtained from the main results by specialising the suitable values of the parameters involved.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.481-486
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• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.