• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.984-987
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• 2003

This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Even if the solution of Bessel's function exists. as Bessel function is a series function, we must get the solution by numerical method, Hereof the author proposes the solution of the matrix method by Ritz's method, and proposes a new deflection shape

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.277-298
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• 2021

In this paper, we propose an extension of the classical Bessel function by means of our ℓ-hypergeometric function [2]. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schläfli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.8
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• pp.877-882
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• 2005

This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Enen if the solution of Bessel's function exists. as Bessel function is a series function. we must got the solution by numerical method Hereby the author Proposes the ununiform beam solution of the matrix method by Ritz's method. and Proposes a new deflection shape function.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.109-136
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• 2012

We aim at presenting certain unexpected functional relations among various hypergeometric functions of one or several variables (for example, see the identities in Corollary 5) by making use of Carlson's method employed in his work (Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2)(1970), 232-242).

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.591-608
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• 2005

Some new reverses of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces are pointed out. Applications for some Gruss type inequalities and for determinantal integral inequalities are given as well.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.207-222
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• 2008

A new counterpart of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces is obtained. Applications for some Gr$\"{u}$ss inequality for determinantal integral inequalities are also provided.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04d
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• pp.70-72
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• 2003

전자계 산란의 시간영역 신호는 대응하는 주파수 영역 응답에 대해서도 동시에 효율적인 방법으로 나타낼 수 있는 이유는 다항식의 직교하는 성질 때문이다. 직교 다항식을 이용함으로써, 이른 시간과 낮은 주파수 영역을 동시에 추정할 수 있다 그 접근법은 CGM(Conjugate Gradient Method)방법과 간단한 DFT(Discrete Fourier transform)에 의거한다. 본 논문에서는 Bessel-Chebyshev 함수를 이용한 이른 시간과 낮은 주파수영역 응답을 동시에 추정하기 위한 접근의 방법을 제시하고, 구현하였다. 오직 이른 시간과 낮은 주파수 정보를 필요로 하기 때문에 이 방법으로 계산시 반복계산의 수렴속도가 무척 빠르다는 이점이 있어, 신속한 정보를 얻을 수 있다.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.349-361
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• 2017

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

• Journal of the Institute of Convergence Signal Processing
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• v.10 no.1
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• pp.60-65
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• 2009

In this paper, we propose a new exponential pulse shaping function based on Chebychev identity equation and Bessel coefficients. The proposed pulse shaping function can produce various pulses with the different characteristics in the time and frequency domain by changing its two parameters. By differentiating the exponential pulse shaping function, we obtain new different pulse functions, in which the even order derivatives of the exponential pulse shaping function are orthogonal to its odd order derivatives. To find the efficiency of the proposed exponential pulse shaping function we analyze its essential characteristics and compare them with those of the conventional Gaussian pulses. We can choose the most suitable exponential pulse waveform according to the design criteria of communication systems.