• 호남수학학술지
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• 제41권2호
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• Bulletin of the Korean Chemical Society
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• 제30권11호
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• pp.2617-2620
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• 2009

Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${\psi}^{\alpha}$‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $\alpha$ = 1, 0, ‒1, ‒2,${\cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${\psi}^{\alpha}$‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.

• 소음진동
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• 제10권5호
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• pp.800-805
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• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• 전자공학회논문지A
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• 제30A권4호
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• pp.20-27
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• 1993

The E-polarized scattering problem by a resistive strip grating is analyzed by the method of moments in the spectral domain. For an E-polarized scattering, the induced current density is expected to blow up at both edges. Then the induced surface current density on the strip is expanded in a series of the multiplication of Ultraspherical polynomials with zeroth order and functions with appropriate edge condition. The expansion coefficients are calculated numerically in the spectral domain. When the resistivity of the strip becomes 0, the numerical results agree with those of a perfectly conducting strip srating. And the convergence of the moment-method solutions is very much improved using the basis functions proposed in this paper, compared with that of the existing exponential functions.

• 제어로봇시스템학회논문지
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• 제13권12호
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• pp.1153-1159
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• 2007

This paper presents the hardware implementation of nonlinear PID controllers for the ROBOKER humanoid robot arms. To design the nonlinear PID controller on an FPGA chip, nonlinear functions as well as the conventional PID control algorithm have to be implemented by the hardware description language. Therefore, nonlinear functions such as trigonometric or exponential functions are designed on an FPGA chip. Simulation studies of the position control of humanoid arms are conducted and results are compared. Superior performances by the nonlinear PID controllers are confirmed when disturbances are present. Experiments of humanoid robot arm control tasks are conducted to confirm the performance of our hardware design and the simulation results.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.725-742
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• 2021

The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the authors analyze these bounds in the special domains associated with exponential function and sine function. Further we obtain Fekete-Szegö inequalities for the defined subclasses of analytic functions defined through Poisson distribution series and Pascal distribution series.

• 대한수학회보
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• 제54권2호
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• pp.705-714
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• 2017

Let $A^2_{{\alpha},{\beta}}(\mathbb{B}_n)$ denote the space of holomorphic functions that are $L^2$ with respect to a weight of form ${\omega}_{{\alpha},{\beta}}(z)=(1-{\mid}z{\mid}^{\alpha}e^{-{\frac{\beta}{1-{\mid}z{\mid}}}}$, where ${\alpha}{\in}\mathbb{R}$ and ${\beta}$ > 0 on the unit ball $\mathbb{B}_n$. We obtain some results for the boundedness and compactness of $Ces{\grave{a}}ro$ operator on $A^2_{{\alpha},{\beta}(\mathbb{B}_n)$.

• 대한교통학회지
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• 제29권3호
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• pp.83-91
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• 2011

이 논문은 확률론적인 방법을 이용하여 동적 통행시간(dynamic travel time) 모형을 도출한다. 동적 통행시간 모형은 차량의 통행시간은 도로 공간상에서의 교통흐름 분포에 따라, 또는 통행구간 출발점에서 시간에 대한 교통흐름의 분포에 따라 결정된다고 가정하여 얻어진다. 이 모형들에서 교통흐름의 분포가 차량의 통행시간에 미치는 정도를 나타내는 확률밀도함수(probability density function)는 여러 가지 형태의 도입될 수 있으나 지수분포를 따른다고 가정한다.

• 대한기계학회논문집
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• 제6권3호
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• pp.247-255
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• 1982

The heat diffusion equation for an annular fin is analyzed by Laplace transformation. The fin has a uniform thickness, with its end insulated, and three different temperature profiles at the base such as step change, harmonic and exponential functions. The exact solutions for the temperature and heat flux of the fins are obtained with the infinite series. The series solutions converge rapidly for large values of dimensionless time, but slowly for small values. Therefore some approximate solutions are presented here to fine the temperature distribution and heat flux for small values of dimensionless time. Furthermore a simple approximate heat flux, .OMEGA.=1.13c.tau.$^{1}$2/ is found in the range of .tau. .leg. o.1/c for the exponential function at the base.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.125-134
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• 2014

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.