• Korean Journal of Mathematics
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• 제27권4호
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• pp.1005-1025
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• 2019

The paper is devoted to study local convergence of a continuation method under the assumption of majorant conditions. The method is used to approximate a zero of an operator in Banach space and is of third order. It is seen that the famous Kantorovich-type and Smale-type conditions are special cases of our majorant conditions. This infers that our result is a generalized one in comparison to results based on Kantorovich-type and Smale-type conditions. Finally a number of numerical examples have been computed to show applicability of the convergence analysis.

• 터널과지하공간
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• 제3권1호
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• pp.80-95
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• 1993

Convergence measurements play very important role in the assessment of stability of a tunnel and of the economics of rock reinforcements. The characteristics of convergences are both due to the face advance effect and the time-dependent behaviour of rocks. As the convergence law can be modeled as a specific function of two variables of distance and time, we can determine the type of function and the related parameters from the field measurements. By using the regression method based on the Levengberg-Marquardt algorithm, an analysis of convergence of two different tunnels and one numerical example is described. It is shown that the convergence can be modeled as following function, C(x)=a{1-exp(-bx)} or C(t)=a{1-exp(-bt)} in case of a tunnel excavated in elastic rocks, in case of elasto-plastic or over stressed rocks.

• 대한수학회지
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• 제51권1호
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• pp.137-162
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• 2014

In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < ${\lambda}$ < 2. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces. In fact, we obtain the recurrent sequence that majorizes the one given by the method and we characterize its convergence by a result that involves the relaxation parameter ${\lambda}$. We use a new technique that allows us on the one hand to generalize and on the other hand to extend the applicability of the result given initially by Kantorovich for ${\lambda}=1$.

• 대한수학회지
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• 제51권5호
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• pp.955-970
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• 2014

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.

• 통합자연과학논문집
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• 제1권3호
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• pp.216-220
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• 2008

In general the Banach space $L^1(T^1)$ doesn't admit convergence in norm. Thus the convergence in norm of the partial sums can not be characterized in terms of Fourier coefficients without additional assumptions about the sequence$\{^{\^}f(\xi)\}$. The problem of $L^1(T^1)$-convergence consists of finding the properties of Fourier coefficients such that the necessary and sufficient condition for (1.2) and (1.3). This paper showed that let $\{{\alpha}_{\kappa}\}{\in}BV$ and ${\xi}{\Delta}a_{\xi}=o(1),\;{\xi}{\rightarrow}{\infty}$. Then (1.1) is a Fourier series if and only if $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• 한국가시화정보학회지
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• 제17권3호
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• pp.19-23
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• 2019

The purpose of this research is to develop a facile measurement system for colorimetric analysis for zinc powder and size analyzer for zeolite particles in order to reduce the process time for their characteristic analysis. We present facile smartphone-based analysis methods to measure and estimate the size of zinc power by using colorimeteric method and the size of zeolite particles by using ImageJ program which is an open-source program. The results show a possibility of our methods to replace the previous professional analysis processes with them.

• East Asian mathematical journal
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• 제28권1호
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• pp.63-71
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• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.133-142
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• 2008

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

• Journal of Communications and Networks
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• 제14권2호
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• pp.206-212
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• 2012

In this paper, in order to effectively apply unitary space-time modulation to the direct-sequence spread-spectrum multiple-access (DSSS-MA) networks, we propose a low-rate, noncoherent, unitary, and space-time modulated DSSS system supporting any number of transmit antennas based on Walsh matrices. The proposed scheme simultaneously performs bandwidth spreading and space-time coding and outperforms those using high-rate, conventional unitary space-time constellations. Furthermore, the proposed scheme allows for a simple detector structure based on fast Walsh transforms.

• 한국융합학회논문지
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• 제12권1호
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• pp.89-97
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• 2021

최근 언택트(Untact) 시대에 강제적인 실내 생활의 중요성이 높아지면서 공간 환경들의 연계성과 관계성이 높아졌다. 즉, 다양한 공간에서의 서비스 제공을 위한 스마트 인터랙션 환경은 다양한 센서들을 통해 주변 정보를 수집 가공하여 필요한 장소와 시간에 맞게 사용자에게 정보들을 제공한다. 이러한 환경에서 사용자가 정보에 대한 선택과 집중을 위한 새로운 형태의 인터랙션 패러다임이 필요하다. 본 논문에서는 다양한 인터랙션 환경을 중심으로 인터랙션 공간 설계를 위한 패턴들에 대해서 연구한다. 즉, 인터랙션 모델기반의 기술을 통해 공간 중심으로 인터랙션 설계를 위한 가이드라인을 제공한다. 또한 다양한 사례를 기반으로 패턴과 템플릿 연구를 통해 이상적인 인터랙션 환경을 제안한다. 이를 통해 스마트 인터랙션 환경에 적합한 공간 중심 인터랙션 모델을 제공함으로써 사용자가 원하는 정보를 얻도록 한다.