• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.365-383
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• 2001

We consider path integrals, more precisely projective systems of Fresnel distributions, associated with Sturm-Liouville boundary value problems.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-483
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• 2001

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.489-494
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• 2016

The purpose of this paper is to treat the generalized conditional Yeh-Wiener integral for the sample path-valued conditioning function. As a special case of our results, we obtain the results in [6].

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.62-69
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• 1996

In this study, an equivalent domain integral (EDI) method is presented to estimate the track-till integral parameter, J-value, for two dimensional cracked elastic bodies which may quantify the severity of the crack-tit) stress fields. The conventional J-integral method based on line integral has been converted to equivalent area or domain integrals by using the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of the domain integrals are readily available in a finite element analysis. The details and its implementation are extened to both h-version finite element model with 8-node isoparametric element and p-version finite element model with high order hierarchic element using Legendre type shape fuctions. The variations with respect to the different path of domain integrals from the crack-tip front and the choice of 5-function have been tested by several examples.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.279-287
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• 2000

A simple estimate of Feynman path-integration with general potential via its new definition is given and found to be very useful. This new method will help find the value of some Feynman path-integrals as precise as one wants.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.385-408
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• 2001

This is an introduction to a stochastic version of E. Cartan′s symplectic mechanics. A class of time-symmetric("Bernstein") diffusion processes is used to deform stochastically the exterior derivative of the Poincare-Cartan one-form on the extended phase space. The resulting symplectic tow-form is shown to contain the (a.e.) dynamical laws of the diffusions. This can be regarded as a geometrization of Feynman′s path integral approach to quantum theory; when Planck′s constant reduce to zero, we recover Cartan′s mechanics. The underlying strategy is the one of "Euclidean Quantum Mechanics".

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.319-332
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• 1996

Many authors have studied multiple stochastic integrals in pursuit of the existence of product processes in terms of multiple integrals. But there has not been much research into the structure of the product processes themselves. In this direction, a study which gives emphasis on sample path continuity and boundedness properties was initiated in Pyke[9]. For details of problem set-ups and necessary notations, see [9]. Recently the weak limits of U-processes are shown to be chaos processes, which is product of the same Brownian measures, see [2] and [7].

• Journal of Electrical Engineering and Technology
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• v.5 no.4
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• pp.511-521
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• 2010

This paper presents a new algorithm to determine accurate bus-wise transmission loss allocation utilizing path-integrals dictated by the transaction strategy. For any transaction strategy, the total sum of the allocated transmission losses of all buses is equal to the actual loss given by the AC power-flow calculation considering the distributed slack. In this paper, the bus-wise allocation of the transmission loss is calculated by integrating the differential loss along a path determined by the transaction strategy. The proposed algorithm is also compared with Galiana's method, which is the well-known transmission loss allocation algorithm based on integration. The performance of the proposed algorithm is evaluated by case studies carried out on the WSCC 9-bus, IEEE 14-bus, New England 39-bus, and IEEE 118-bus systems. The simulation results show that the proposed algorithm is fast and accurate with a large step size.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.2
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• pp.145-152
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• 2009

SGBEM(Symmetric Galerkin Boundary Element Method)-FEM alternating method has been proposed by Nikishkov, Park and Atluri. In the proposed method, arbitrarily shaped three-dimensional crack problems can be solved by alternating between the crack solution in an infinite body and the finite element solution without a crack. In the previous study, the SGBEM-FEM alternating method was extended further in order to solve elastic-plastic crack problems and to obtain elastic-plastic stress fields. For the elastic-plastic analysis the algorithm developed by Nikishkov et al. is used after modification. In the algorithm, the initial stress method is used to obtain elastic-plastic stress and strain fields. In this paper, elastic-plastic J integrals for three-dimensional cracks are obtained using the method. For that purpose, accurate values of displacement gradients and stresses are necessary on an integration path. In order to improve the accuracy of stress near crack surfaces, coordinate transformation and partitioning of integration domain are used. The coordinate transformation produces a transformation Jacobian, which cancels the singularity of the integrand. Using the developed program, simple three-dimensional crack problems are solved and elastic and elastic-plastic J integrals are obtained. The obtained J integrals are compared with the values obtained using a handbook solution. It is noted that J integrals obtained from the alternating method are close to the values from the handbook.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.9
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• pp.2433-2443
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• 1996

In this paper, a new technique is proposed for obtaining the error probabilities of the VSB(vestigial sideband modulation) signal in the presence of the cochannel interference and frequency-selective fading channel. For the receivers, a suboptimal matched filter receiver and the MLSE(maximum likelihood sequence estimation) receiver, which is known to be optimal on the fading channel, are considered. First, for the matched filter receiver, the distributions of the random variables, which determine the SER(symbol error rate) are obtained by decomposing the multi-path fading channel into Rayleigh distributed main path and Gaussian distributed remained path channels. the random variables mean the energy of the main path and subpath respecitively, and SER can be calculated from the distribution of them. Next, for the case of the MLSE receover, it is found that the random variables are expressed as a function of integrals. In order to obtain the distribution for the random variables, we expanded each element of integrals with the KL(Karhunen-Loeve) transformation. And it is derived that the distributions for the transformed random variables are given by a sum of chi-square distributions. Finally, we calculated the error rate derived formula on the two-ray fading channel, which is one of widely used models for the frequency-selective fading channel. From the numerical results, it is found that for the matched filer receiver, performance degradation is significant, while the performance degradation at the MLSE receiver is insignificant on the frequency-selective fading channel. However, in case of cochannel interference environment, the error rateis found to increase significantly both at the matched filter and at the MLSE receiver.