• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1013-1015
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• 2005

Liu[Fuzzy Optimization and Decision Making, 2(2003), 87-100] proved that convergence in credibility does not imply convergence a.s. and convergence in mean does not imply convergence a.s. by giving counter-examples. But these examples are not true. In this note, we prove that convergence in credibility implies convergence a.s. and convergence in mean implies convergence a.s.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.191-204
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• 2022

This paper introduces the statistical convergence concepts of double sequences of complex uncertain variables: statistical convergence almost surely(a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely(u.a.s.).

• Journal of Engineering Education Research
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• v.15 no.6
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• pp.92-97
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• 2012

This paper deals with the model of natural sciences and engineering's convergence education. Recently, convergence education's necessary is needed since the most of new products are designed and produced based on the convergence technology. But our country's education system is keeping existing education process. This make industrial world undurable to employ the current graduated students. Also in view of educational world, they have no proper convergence education model for their students. In this paper, to solve the non-existing convergence education model, we derive the a few convergence education model and list up their model each. This result will be helpful for the introducer of the convergence education system.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.133-139
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• 2006

By combining the classical Newton's method with the pseudo-secant method, pseudo-secant-Newton's method is constructed and its order and rate of convergence are investigated. Given a function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$ and is sufficiently smooth in a small neighborhood of ${\alpha}$, the convergence behavior is analyzed near ${\alpha}$ for pseudo-secant-Newton's method. The order of convergence is shown to be cubic and the rate of convergence is proven to be $\(\frac{f^{{\prime}{\prime}}(\alpha)}{2f^{\prime}(\alpha)}\)^2$. Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

• ETRI Journal
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• v.31 no.6
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• pp.765-769
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• 2009

In this paper, we present the fabrication of 40 Gb/s traveling-wave electroabsorption modulator-integrated laser (TW-EML) modules. A selective area growth method is first employed in 40 Gb/s EML fabrication to simultaneously provide active layers for lasers and modulators. The 3 dB bandwidth of a TW-EML module is measured to be 34 GHz, which is wider than that of a lumped EML module. The 40 Gb/s non-return-to-zero eye diagram shows clear openings with an average output power of +0.5 dBm.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.43-65
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• 2015

We present a new convergence analysis of popular Broyden's method in the Banach/Hilbert space setting which is applicable to non-smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying assumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden's iterations. To demonstrate practical merits of Broyden's method, we use it for numerical solution of three nontrivial infinite-dimensional problems.

• Journal of Families and Better Life
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• v.27 no.5
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• pp.25-42
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• 2009

This study examines the actual state of using digital convergence products by consumers, and analyzes the expectation that consumers have regarding digital convergence products and the actual satisfaction of the digital convergence products. In addition, it analyzes factors affecting the satisfaction with digital convergence products. First, mobile phones, which 99.4% of those surveyed had, cameras, which 90.6% had, and mp3s, which 71.8% had, were found to be necessities. Second, the ratio of owning digital convergence products was 79.5%, 48.1%, and 52.4%, respectively. In the case of a mobile phones, a digital convergence type is already common. Third, regarding the reason for purchasing digital convergence products, they chose convergence products because there was no product with a simple function that they wanted to have: 38.2% in terms of a mobile phone, 47.2% for a camera, and 28.2% for an mp3. This shows that a consumer's choice was infringed in a great deal at the back of remarkable quantitative growth in digital convergence products. Fourth, the analysis of the factor regarding the consumer's expectation on digital convergence products showed 3 kinds of factors, i.e., expectation of benefit, expectation of risk, and expectation of situation. Fifth, as a result of analyzing the structural model regarding the effect on satisfaction by a consumer's expectation and the outcome on digital convergence products, all the expectations and outcomes of benefit, risk, and situation did not have a direct effect on satisfaction. Only an indirect effect through inconsistency showed a statistical significance.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.49-56
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• 2006

A convergence behavior is under investigation near a simple real zero for the k-fold pseudo-Olver's method defined by extending the classical Olver's method. The order of convergence is shown to be at least k+3. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. Various numerical examples with a proposed zero-finding algorithm are successfully confirmed with the use of symbolic and computational ability of Mathematica.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.261-267
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• 2006

A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the $Fr\'{e}chet$-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].

• East Asian mathematical journal
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• v.25 no.2
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• pp.153-157
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• 2009

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.