• 충청수학회지
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• 제24권4호
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• pp.745-758
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• 2011

Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2008년도 추계종합학술대회 B
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• pp.49-52
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• 2008

In this letter, we derive a tight closed form formula for an ergodic rapacity of a multiple-input multiple-output (MIMO) for the application of wireless communications. The derived expression is a simple close-form formula to determine the ergodic capacity of MIMO systems. Assuming the channels are independent and identically distributed (i.i.d.) Rayleigh flat-fading between antenna pairs, the ergodic capacity can be expressed in a closed form as the finite sum of exponential integrals.

• 대한수학회논문집
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• 제33권1호
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• pp.179-196
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• 2018

In this paper we extend the two q-additions with powers in the umbrae, define a q-multinomial-coefficient, which implies a vector version of the q-binomial theorem, and an arbitrary complex power of a JHC power series is shown to be equivalent to a special case of the first q-Lauricella function. We then present several q-analogues of hypergeometric integral formulas from the two books by Exton and the paper by Choi and Rathie. We also find multiple q-analogues of hypergeometric integral formulas from the recent paper by Kim. Finally, we prove several multiple q-hypergeometric integral formulas emanating from a paper by Koschmieder, which are special cases of more general formulas by Exton.

• International Journal of Aeronautical and Space Sciences
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• 제11권1호
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• pp.10-18
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• 2010

The purpose of this paper deals with direct multiple-shooting method (DMS) to resolve helicopter maneuver problems of helicopters. The maneuver problem is transformed into nonlinear problems and solved DMS technique. The DMS method is easy in handling constraints and it has large convergence radius compared to other strategies. When parameterized with piecewise constant controls, the problems become most effectively tractable because the search direction is easily estimated by solving the structured Karush-Kuhn-Tucker (KKT) system. However, generally the computation of function, gradients and Hessian matrices has considerably time-consuming for complex system such as helicopter. This study focused on the approximation of the KKT system using the matrix exponential and its integrals. The propose method is validated by solving optimal control problems for the linear system where the KKT system is exactly expressed with the matrix exponential and its integrals. The trajectory tracking problem of various maneuvers like bob up, sidestep near hovering flight speed and hurdle hop, slalom, transient turn, acceleration and deceleration are analyzed to investigate the effects of algorithmic details. The results show the matrix exponential approach to compute gradients and the Hessian matrix is most efficient among the implemented methods when combined with the mixed time integration method for the system dynamics. The analyses with the proposed method show good convergence and capability of tracking the prescribed trajectory. Therefore, it can be used to solve critical areas of helicopter flight dynamic problems.

• Journal of information and communication convergence engineering
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• 제7권2호
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• pp.182-184
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• 2009

In this letter, we derive a tight closed-form formula for an ergodic capacity of a multiple-input multiple-output (MIMO) for the application of wireless communications. The derived expression is a simple closed-form formula to determine the ergodic capacity of MIMO systems. Assuming the channels are independent and identically distributed (i.i.d.) Rayleigh flat-fading between antenna pairs, the ergodic capacity can be expressed in a closed form as the finite sum of exponential integrals.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.25-31
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• 1984

A technique which has been used for the evaluation of certain kinds of multiple integrals, viz., the technique of imcomplete gamma function operators, is employed and extended to the case where the parameters and arguments are non-equal and non-integer for the probability integral of the inverted Dirichlet distribution. Several types of recurrence formulas have been developed for the tail probabilities and a subset selection procedure in ranking variances is discussed as an application.

• 자원환경지질
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• 제27권1호
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• pp.41-47
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• 1994

적분방정식을 사용한 3차원 전자기 모델링에 나오는 많은 텐서 그린 적분의 수치계산에 신속 한겔변환 (FHT) 아르고리즘 (Anderson, 1982)을 적용하였다. 한겔변환은 FHT에서 사용가능한 연관 및 지연 중합으로 효율적으로 계산할 수 있다. 먼저 수평 층서모형에 대한 텐서 그린 적분을 보여주고 난 다음 이들을 FHT로 신속하게 계산할 수 있도록 서로 연관된 형태의 함수로 고쳐쓴다. FHT로 연관된 한겔변환의 전행열이 단일 직접 중합과 거의 비슷한 계산시간으로 신속 정확하게 구해진다. 5층 수평 층서모형에 대한 컴퓨터실험의 결과, FHT는 직접 및 지연 중합법에 비하여 각각 117 및 4배 빠르다.

• International Journal of Automotive Technology
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• 제8권1호
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• pp.33-38
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• 2007

Since it is difficult to analytically express the Melnikov function when a dynamic system possesses multiple saddle fixed points with homoclinic and/or heteroclinic orbits, this paper investigates a vehicle model with nonlinear suspension spring and hysteretic damping element, which exhibits multiple heteroclinic orbits in the unperturbed system. First, an algorithm for Melnikov integrals is developed based on the Melnikov method. And then the amplitude threshold of road excitation at the onset of chaos is determined. By numerical simulation, the existence of chaos in the present system is verified via time history curves, phase portrait plots and $Poincar{\acute{e}}$ maps. Finally, in order to further identify the chaotic motion of the nonlinear system, the maximal Lyapunov exponent is also adopted. The results indicate that the numerical method of estimating chaotic threshold is an effective one to complicated vehicle systems.

• 호남수학학술지
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• 제32권3호
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• pp.389-397
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• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (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 $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• Communications for Statistical Applications and Methods
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• 제24권5호
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• pp.481-492
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• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.