• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.2
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• pp.121-134
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• 2013

The transverse cylindrical projection has been used in Korea since 1910s when the nationwide geodetic network was firstly established. However, the projection has a number of different types of functions according to a way of its mathematical derivation as well as a section of its coefficients and terms, for instance Gauss- Schreiber(GS) and Gauss-Kruger(GK) types. Although the transverse cylindrical projection itself is assigned to a system, projected coordinates would be diverse with respect to the function used in the actual calculation. In order to investigate impact of functions used in the computation, five different equations (i.e., 2 GS and 3 GK) were implemented in this study by using MATLAB. A series of numerical simulation tests has been carried out to compare and characterize them in terms of projection accuracy, difference of projected coordinates and distortion. Furthermore, a comparison between GS and GK function was made under the Korean gridding system, consisting of four zones. Results from the numerical computations were qualitatively analyzed and summarized in this paper.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.95-98
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• 1997

The Gaussian diffraction pattern initially assumed in the diffraction inverse problem is further sharply defined by multiplying $e^{-q{\omega}_0$\mid${\chi}$\mid$}$. The modified pupil function is obtained and the diffraction intensity distribution for the finite aperture ($-{\omega}_0~{\times}{\omega}_0$ is obtained, and then the OTF is derived analytically. It is found the OTF is equal to or less than the $(OTF)_{q=0}$, namely the modulation is not useful. It is shown that the narrowing down the initial Gaussian diffraction pattern does not give the anticipated improvement in OTF and the reason is clarified.

• Current Optics and Photonics
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• v.7 no.2
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• pp.127-135
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• 2023

Radially polarized beams with the ability to generate a sub-wavelength sized spot in a longitudinal field provides significant applications in microscopic imaging, optical tweezers, lithography and so on. However, this excellent property can also be achieved based on conventional circularly polarized beams. Here, we demonstrate its ability to create a strong longitudinal field by comparing the tight focusing characteristics of fractional-order vortex modulated radial polarized and left-handed circular polarized Bessel-Gauss beams. Additionally, the possibility of generating arbitrary fractional-order vortex modulated Bessel-Gauss beams with a strong longitudinal field is demonstrated. A special modulation method of left-handed circularly polarized Bessel-Gauss beams modulated by a fractional-order vortex is adopted creatively and a series of regulation laws are obtained. Specifically, the fractional-order phase modulation parameter n can accurately control the number of optical lobes. The ratio of the pupil radius to the incident beam waist β₁ can control the radius of the optical lobes. The first-order Bessel function amplitude modulation parameter β₂ can control the number of layers of optical lobes. This work not only adds a new modulation method for optical micromanipulation and optical communication, but also enriches the research on fractional vortex beams which has very important academic significance.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.223-228
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• 2005

In 2001, Choi, Harsh & Rathie [Some summation formulas for the Appell's function $F_1$. East Asian Math. J. 17 (2001), 233-237] have obtained 11 results for the Appell's function $F_1$ with the help of Gauss's summation theorem and generalized Kummer's summation theorem. We aim at presenting 22 more results for $F_1$ with the help of the generalized Gauss's second summation theorem and generalized Bailey's theorem obtained by Lavoie, Grondin & Rathie [Generalizations of Whipple's theorem on the sum of a $_3F_2$. J. Comput. Appl. Math. 72 (1996), 293-300]. Two interesting (presumably) new special cases of our results for $F_1$ are also explicitly pointed out.

• East Asian mathematical journal
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• v.22 no.2
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• pp.223-238
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• 2006

• Honam Mathematical Journal
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• v.41 no.1
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• pp.1-17
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• 2019

The aim of this paper is to establish certain integrals involving product of the Aleph function with exponential function and multi Gauss's hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, twelve corollaries are also recorded here as special case of our main results.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.65-94
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• 2016

In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620.629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting q-contiguous functions relations. These q-contiguous functions relations have wide applications.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.135-145
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• 1995

A new algorithm was given to successively fit the multiexponential function/nonlinear function to data by a weighted least squares method, using Gauss-Newton, Marquardt, gradient and DUD methods for convergence. This study also considers the problem of linear-nonlimear weighted least squares estimation which is based upon the usual Taylor's formula process.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.621-633
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• 2012

By establishing a new summation formula for the series $_3F_2(\frac{1}{2})$, recently Rathie and Pogany have obtained an interesting result known as Kummer type II transformation for the generalized hypergeometric function $_2F_2$. Here we aim at deriving their result by using a very elementary method and presenting two elegant results for certain terminating series $_3F_2(2)$. Furthermore two interesting applications of our new results are demonstrated.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.885-900
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• 2015

This paper introduces Romberg-Richardson's method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson's method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.