• Korean Journal of Mathematics
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• v.27 no.4
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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.

• Tunnel and Underground Space
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• v.3 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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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 ${\lambda}=1$.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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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.

• Journal of Integrative Natural Science
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• v.1 no.3
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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 $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• Journal of the Korean Society of Visualization
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• v.17 no.3
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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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• v.28 no.1
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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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• v.48 no.1
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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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• v.14 no.2
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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.

• Journal of the Korea Convergence Society
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• v.12 no.1
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• pp.89-97
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• 2021

Recently, as the importance of forced indoor living has increased in the untact era, the connection and relationship between space environments is increasing. That is, the smart interaction environment for providing services in various spaces collects and processes a number of surrounding environment information through various sensors to provide desired information according to the required place and time. In this environment, a new type of interaction paradigm is needed for the user to select and focus on environmental information. In this paper, we provide guidelines based on models and patterns for designing various interactions around space. Through interaction model-based technology, we provide guidelines for space-oriented interaction design. We propose an ideal interaction environment through guideline-based patterns and templates. Finally, by providing a space-oriented interaction environment suitable for smart interaction, users can freely obtain desired information.