• 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.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.467-484
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• 2022

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.382-383
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• 2013

Gate-controlled spin-orbit interaction parameter is a key factor for developing spin-Field Effect Transistor (Spin-FET) in a quantum well structure because the strength of the spin-orbit interaction parameter decides the spin precession angle [1]. Many researches show the control of spin-orbit interaction parameter in n-type quantum channels, however, for the complementary logic device p-type quantum channel should be also necessary. We have calculated the spin-orbit interaction parameter and the effective mass using the Shubnikov-de Haas (SdH) oscillation measurement in a GaSb two-dimensional hole gas (2DHG) structure as shown in Fig 1. The inset illustrates the device geometry. The spin-orbit interaction parameter of $1.71{\times}10^{11}$ eVm and effective mass of 0.98 $m^0$ are obtained at T=1.8 K, respectively. Fig. 2 shows the gate dependence of the spin-orbit interaction parameter and the hole concentration at 1.8 K, which indicates the spin-orbit interaction parameter increases with the carrier concentration in p-type channel. On the order hand, opposite gate dependence was found in n-type channel [1,2]. Therefore, the combined device of p- and n-type channel spin transistor would be a good candidate for the complimentary logic device.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.571-577
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• 2005

The aim of this paper is to establish the rate of convergence of Baskakov-Durrmeyer operators for bounded variation function. We have given the better estimate over the results due to Guo ([4]), Anial and Teberska ([1]) and Gupta and Srivastava ([8]).

• Journal of Korea Multimedia Society
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• v.21 no.11
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• pp.1333-1341
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• 2018

Recently, alleys, villages and traditional market spaces have been recreated as complex cultural spaces due to urban renewal or village community policies. However, previous studies only refer to buildings such as museums and libraries in dealing with complex cultural spaces. The purpose of this study is to suggest the recreated complex cultural space as a natural convergence type and analyze its characteristics. Therefore, this study aims to reestablish the concept and type of the newly created complex cultural space. For this study, Busan Bosu-dong Bookstores Alley, Daegu Kim Gwangseok-street, Andong Traditional Market and Andong Shin-sedong Mural Village were selected as research examples. As a result of the study, the natural convergence space reflects the locality of the contents constituting the space, and the various values are convergenced. And this type of space is being reborn as an advanced case of urban regeneration and serves as a representative tourist destination in the region. As a next study of this study, we proposed social studies such as quantitative research and qualitative research.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.679-688
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• 2019

In the present note, we study some approximation properties of the Szász type operators based on Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). We establish the rates of A-statistical convergence of these operators. Finally, we prove a Voronovskaja type approximation theorem and local approximation theorem via the concept of A-statistical convergence.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.359-373
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• 2017

In this paper, we propose the Stancu type generalization of a kind of modified q-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.887-898
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• 2011

In this paper, we first discuss the convergence of the continued fractions of generalized Rogers-Ramanujan type in the modified sense. Then we prove several equalities concerning these continued fractions. The proofs of our main results are mainly based on the Bauer-Muir transformation.

• Development and Reproduction
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• v.21 no.3
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• pp.259-267
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• 2017

Present study aimed to determine the effect of 'bitter melon', a popularly used fruit in Bangladesh and several other Asian countries, on high-fat-diet-induced type 2 diabetes. To investigate the effect, ethanol extract from bitter melon (BME) as a dietary supplement with mouse chow was used. BME was found to significantly attenuate the high-fat diet (HFD) -induced body weight and total fat mass. BME also effectively reduced the insulin resistance induced by the HFD. Furthermore, dietary supplementation of BME was highly effective in increasing insulin sensitivity and reducing hepatic fat and obesity. These results indicate that BME could be effective in attenuating type 2 diabetes and could therefore be a preventive measure against type 2 diabetes.