• 대한수학회보
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• 제50권4호
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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.

• Kyungpook Mathematical Journal
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• 제57권1호
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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.

• 대한수학회지
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• 제33권4호
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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.

• 대한수학회논문집
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• 제30권2호
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• pp.81-92
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• 2015

In this paper, we aim at establishing a generalized fractional integral version of Gr$\ddot{u}$ss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.

• 호남수학학술지
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• 제31권2호
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• pp.167-176
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• 2009

The aim of this paper is to obtain three interesting results for reducibility of Kamp$\'{e}$ de $\'{e}$riet function. The results are derived with the help of contiguous Gauss's second summation formulas obtained earlier by Lavoie et al. The results obtained by Bailey, Rathie and Nagar follow special cases of our main findings.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.

• 한국안광학회지
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• 제2권1호
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• pp.17-24
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• 1997

Gauss 함수와 Lorentz 함수의 convolution인 Voight 함수를 혼합 알칼리 유리, 전이금속 산화물을 첨가시킨 유리 등의 MAS-NMR 스펙트럼의 시뮬레이션에 적용시켜 보았다. Gauss와 Lorentz의 convolution은 적분할 수 없으므로 어떤 형태를 갖는 Voight 함수는 없다. 그래서 컴퓨터를 이용한 개념적(원시적) 적분 방법으로 각 진동수에 대하여 Voight 함수 값을 얻었고, 그것은 MAS-NMR 스펙트럼과 매우 잘 일치하였다. 이 과정에서 MAS-NMR lineshape의 변화(Gauss에서 Lorentz lineshape으로의 변화 또는 그 반대)를 알 수 있다. 그러므로 다음과 같은 경우는 주의해야 할 것으로 생각된다. 유리의 구조, 전도 기구 또는 혼합 알칼리 효과 등을 연구하기 위해 NMR 스펙트럼을 컴퓨터 시뮬레이션 할 때 NMR 스펙트럼의 lineshape을 Gauss 함수 꼴로 가정해서 수행하는 경우가 대부분인데 이때 주의해야 할 것이다. 왜냐하면, NMR 스펙트럼 선 모양이 실제로는 Voight 함수 형태로 나타날 수 있기 때문이다.

• Advances in concrete construction
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• 제1권4호
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• pp.319-340
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• 2013

This paper presents a comparative study on the double-K fracture parameters of concrete obtained using four existing analytical methods such as Gauss-Chebyshev integral method, simplified Green's function method, weight function method and simplified equivalent cohesive force method. Two specimen geometries: three point bend test and compact tension specimen for sizes 100-500 mm at initial notch length to depth ratios 0.25 and 0.4 are used for the comparative study. The required input parameters for determining the double-K fracture parameters are derived from the developed fictitious crack model. It is found that the cohesive toughness and initial cracking toughness determined using weight function method and simplified equivalent cohesive force method agree well with those obtained using Gauss-Chebyshev integral method whereas these fracture parameters determined using simplified Green's function method deviates more than by 11% and 20% respectively as compared with those obtained using Gauss-Chebyshev integral method. It is also shown that all the fracture parameters related with double-K model are size dependent.

• 대한수학회지
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• 제54권2호
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• pp.381-397
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• 2017

In this paper, we study surfaces in 3-dimensional Minkowski space in terms of certain type of their Gauss map. We give several results on these surfaces whose Gauss map G satisfies ${\square}G=f(G+C)$ for a smooth function f and a constant vector C, where ${\square}$ denotes the ChengYau operator. In particular, we obtain classification theorems on the rotational surfaces in ${\mathbb{E}}^3_1$ with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.

• East Asian mathematical journal
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• 제17권1호
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• pp.147-158
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• 2001

The Gauss summation theorem plays a key role in the theory of(generalized) hypergeometric series. The authors study several proofs of the theorem and consider some applications of it.