• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.1
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• pp.43-53
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• 2008

Surface edge crack in transversely isotropic piezoelectric material is analyzed. The concentrated antiplane mechanical and inplane electrical loadings are applied to an arbitrary point of the surface, where the impermeable crack boundary condition is imposed. Using Mellin transform the problem is formulated, from which Wiener-Hopf equations are derived. By solving the equations the solution is obtained in a closed form. Mechanical and electric intensity factors and energy release rate are obtained and discussed. This problem could be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.15-18
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• 2000

In this study, we improve the performance of a speech recognition system of visual information depending on lip movements. This paper focuses on the robustness of the word recognition system with the rotation, transition and scaling of the lip images. The different methods of lipreading have been used to estimate the stability of recognition performance. Especially, we work out the special system of the log-polar mapping, which is called Mellin transform with quasi RTS-invariant and related approaches to machine vision. The results of word recognition are reported with HMM (Hidden Markov Model) recognition system.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.403-414
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• 2015

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• Journal of the Institute of Electronics and Information Engineers
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• v.49 no.10
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• pp.91-101
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• 2012

DNA watermarking have been interested for both the security of private genetic information or huge DNA storage information and the copyright protection of GMO. Multimedia watermarking has been mainly designed on the basis of frequency domain, such as DCT, DWT, FMT, and so on, for the robustness and invisibility. But a frequency domain watermarking for coding DNA sequence has a considerable constraint for embedding the watermark because transform and inverse transform must be performed without completely changing the amino acid sequence. This paper presents a coding sequence watermarking on lifting based DWT domain and brings up the availability of frequency domain watermarking for DNA sequence. From experimental results, we verified that the proposed scheme has the robustness to until a combination of 10% point mutations, 5% insertion and deletion mutations and also the amino preservation and the security.