• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1327-1334
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• 2012

In this paper, using analytic method and the properties of the Legendre's symbol, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m{\geq}2$. This solves a conjecture of He and Zhang [On the 2k-th power mean value of the generalized quadratic Gauss sums, Bull. Korean Math. Soc. 48 (2011), no. 1, 9-15].

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.6
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• pp.1-8
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• 2007

In this paper, research on joint optimization of the image spatial registration and the exposure compensation is conducted. The exposure compensation is performed in a frame work of the intensity compensation based on the polynomial approximation of the relationship between images. This compensation is jointly combined with the registration problem employing the Gauss-Newton nonlinear optimization method. In this paper, to perform for a simple and stable optimization, the block-coordinate method is combined with the Gauss-Newton optimization and extensively compared with the traditional approaches. Furthermore, regression analysis is considered in the compensation part for a better stable performance. By combining the block-coordinate method with the Gauss-Newton optimization, we can obtain a compatible performance reducing the computational complexity and stabilizing the performance. In the numerical result for a particular image, we obtain a satisfactory result for 10 repeats of the iteration, which implies a 50% reduction of the computational complexity. The error is also further reduced by 1.5dB compared to the ordinary method.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.7
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• pp.3460-3467
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• 2013

The In this paper, we have made numerical experiments to compare 2D image reconstruction algorithm of earth model by electrical resistance tomograpy (ERT). Gauss-Newton, simultaneous iterative reconstruction technieque (SIRT) and truncated least squares (TLS) approaches for Wenner and Schlumberger electrode arrays are presented for the solution of the ERT image reconstruction. Computer simulations show that the Gauss-Newton and TLS approach in ERT are proper for 2D image reconstruction of an earth model.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.119-136
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• 2007

Block Jacobi and Gauss-Seidel iterative methods are studied for solving $n{\times}n$ fuzzy linear systems. A new splitting method is considered as well. These methods are accompanied with some convergence theorems. Numerical examples are presented to illustrate the theory.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3007-3019
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• 1993

For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

• 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 Journal of the Acoustical Society of Korea
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• v.9 no.2
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• pp.61-69
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• 1990

We have investigated the digital bit synchronization problem in baseband communication receiver systems using the Gauss-Markov estimation technique which is equivalent to the weighted least square method. The realized bit synchronizer, including the data detector, processes the input signal two dimensionally into the transition phase and data level under the white Gaussian noise environment. We have confirmed the relization of the bit synchronizer via computer simulation. In addition, we have compared and evaluated the estimation error performance of the proposed method with that of the conventional DTTL method and of the minimum likelihood method.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.93-98
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• 2001

An adaptive Cartesian grid method having the best elements of structured, unstructured, and Cartesian grids is developed to solve the steady two-dimensional Euler equations. The solver is based on a cell-centered finite-volume method with Roe's flux-difference splitting and implicit point Gauss-seidel time integration method. Calculations of several compressible flows are carried out to show the efficiency of the developed computer code. The results were generally in good agreements with existing data in the literature and the developed code has the good ability to capture important feature of the flows.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.7
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• pp.683-687
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• 2007

In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and Closed-Form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-Form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a Self-Tuning Weighted Least Square AOA algorithm that is a modified version of the conventional Closed-Form solution. In order to estimate the error covariance matrix as a weight, a two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.509-512
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• 2007

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.