• 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].

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1345-1356
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• 2013

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy $L_1G=f(G+C)$ for some constant vector $C{\in}\mathbb{E}^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.715-724
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• 2017

We study the Gauss map G of helicoidal surfaces in the 3-dimensional Euclidean space ${\mathbb{E}}^3$ with respect to the so called Cheng-Yau operator ${\square}$ acting on the functions defined on the surfaces. As a result, we completely classify the helicoidal surfaces with Gauss map G satisfying ${\square}G=AG$ for some $3{\times}3$ matrix A.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.733-741
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• 2008

Let T be Gauss transformation on the unit interval defined by T (x) = ${\frac{1}{x}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.229-237
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• 2012

In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that the right circular cones are the only rational kind GSCS's with pointwise 1-type Gauss map of the second kind.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.163-204
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• 2001

먼저 Erdos-Renyi의 새로운 강대수 법칙을 소개하고, 여러 가지 형태로 발전된 Erdos-Renyi 형의 법칙과 그 응용을 보여준다. 보다 더 일반적인 Erdos-Renyi형의 법칙과 그 응용을 보여준다. 보다 더 일반적인 Erdos-Renyi 형 법칙을 찾기 위해 Csorgo-Revesz 증분형태의 극한정리들을 소개하여 종속 mixing 조건이 주어진 정상 Gauss 확률변수들의 부분합에 대해 Csorgo-Revesz 증분형태의 새로운 극한정리들을 얻는다. 끝으로, 유한차원 벡터공간, ι(sup)p-공간, ι(sup)$\infty$-공간에서 각각 값을 갖는, 연속 Gauss 과정에 대해서 필자에 의해 최근에 발표된 몇 편의 논문을 소개한다.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.133-144
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• 2017

In this paper, we study ruled surfaces in 3-dimensional Euclidean and Minkowski space in terms of their Gauss map. We obtain classification theorems for these type of surfaces whose Gauss map G satisfying ${\Box}G=f(G+C)$ for a constant vector $C{\in}{\mathbb{E}}^3$ and a smooth function f, where ${\Box}$ denotes the Cheng-Yau operator.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.519-530
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• 2016

In this paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space. We classify surfaces of revolution generated by a non-isotropic curve in terms of the Gauss map and the Laplacian of the surface. Furthermore, we give the classification of surfaces of revolution generated by an isotropic curve satisfying pointwise 1-type Gauss map equation.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.865-878
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• 1996

We consider numerical methods for finding a solution to a nonlinear system of algebraic equations $$ (1) f(x) = 0, $$ where the function $f : R^n \to R^n$ is ain $x \in R^n$. In [10], a quasi-Gauss-Newton method is proposed and shown the computational efficiency over SQRT algorithm by numerical experiments. The convergence rate of the method has not been proved theoretically. In this paper, we show theoretically that the iterate $x_k$ obtained from the quasi-Gauss-Newton method for the problem (1) actually converges to a root by Kantorovich-type convergence analysis. We also show the rate of convergence of the method is superlinear.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.39 no.3
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• pp.181-188
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• 2003

The objects of this study were to discuss the performance of its using magnetic compass and to do a trial manufacture of the apparatus generating artificial magnetic field of 3-axis type to assess the performance of compass using terrestrial magnetism in the various magnetic field. The results obtained were summarized as follows: The magnetic field of each axis showed the linearly increase in accordance with the increase of electrical current. Average range difference between measured and calculated values was 0.33∼1.93μT and there were no big difference. The magnitude and direction of magnetic field showed some change in the edge of Helmholtz coil, but it appeared to stabilize in the center. In the horizontal magnetic force of 0.30gauss and 0.40gauss, the measured and calculated values of the damping characteristic of magnetic compass showed a good agreement. However, the confidence level was low at the horizontal magnetic force of 0.50gauss.