• 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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.483-492
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• 2008

The k-fold pseudo-Newton's method is proposed and its convergence behavior is investigated near a simple zero. The order of convergence is proven to be at least k + 2. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. High-precison numerical results are successfully implemented via Mathematica and illustrated for various examples.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.11-21
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• 2007

Given a nonlinear function f : $\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$, a new numerical method to be called k-fold pseudo- Halley's method is proposed and it's error analysis is under investigation to confirm the convergence behavior near ${\alpha}$. Under the assumption that f is sufficiently smooth in a small neighborhood of ${\alpha}$, the order of convergence is found to be at least k+3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, ${\alpha}$ and f as well as the derivatives of f. A zero-finding algorithm is written and has been successfully implemented for numerous examples with Mathematica.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.107-116
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• 2008

In this study the k-fold pseudo-Cauchy's method of order k+3 is proposed from the classical Cauchy's method defined by an iteration $x_{n+1}=x_n-{\frac{f^{\prime}(x_n)}{f^{{\prime}{\prime}}(x_n)}}{\cdot}(1-{\sqrt{1-2f(x_n)f^{{\prime}{\prime}}(x_n)/f^{\prime}(x_n)^2}})$. The convergence behavior of the asymptotic error constant is investigated near the corresponding simple zero. A root-finding algorithm with the k-fold pseudo-Cauchy's method is described and computational examples have successfully confirmed the current analysis.

• Journal of the Korean Magnetic Resonance Society
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• v.12 no.2
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• pp.103-110
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• 2008

Spin Hamiltonian for the paramagnetic center with a three-fold symmetry and high spin ($S{\geq}2$) multiplicity should contain the fourth order zero-field splitting (ZFS) terms. Electron magnetic resonance transition lines of the center with S = 5/2 are expected to split in a pair when the magnetic field is applied off the principal axes of ZFS, while they are superimposed when the magnetic field is applied parallel to the principal axes of ZFS. In this study we report that the transition lines of $Mn^{2+}$ centers at the three-fold symmetric sites in $LiNbO_3$, chemically equivalent but physically different, split in two due to the nonzero fourth order ZFS term.

• Proceedings of the KIEE Conference
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• 2006.10c
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• pp.285-287
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• 2006

The paper treats the nonlinear robust control of Chua's circuit having Chuar's diode as an element based on the internal model principle. The Chua's diode has unknown nonlinear parameters and the circuits parameters are alos assumend unknown. Nonlinear regulator equations are established to obtain 3-fold equilibrium equations on which the output error is zero. Also an internal model of the 3-fold exosystem is constructed for obtaining the control law. Pole Placement method is used for obtaining the feeback control law. Simulation results are presented for tracking the sinusoidal and constant reference input signal. Asymptotic trajectory control and the suppression of chaotic motion in spite of uncertainties in the system are accomplished.

• 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.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.455-465
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• 2022

We point out a flaw in a result proved by Singh and Shah [Kyungpook Math. J., 57(2017), 537-543] which was recently published in Kyungpook Mathematical Journal. Further, we point out an error in another result of the same paper which we correct and obtain integral extension of the corrected form.

• 한국초전도학회:학술대회논문집
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• v.10
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• pp.103-106
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• 2000

We have studied the magnetic properties in Bi$_2$Sr$_2$CaCu$_2$O$_8$ single crystal with columnar defects using micro Hall-probe array. We found that fold profiles inside sample were similar to the Bean's critical state model from the magnetic hysteresis measurement. In the magnetic relaxation measurement, the normalized relaxation rates were maximum near the center and decreased toward the edge of the sample expect zero gauss. The relaxation rates as a function of the temperature were maximum near the 40K and rapidly decreased both sides of the peak.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.2179-2184
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• 2012

Introduction and aim: To compare reproductive factor influence on patients with pathological diagnosed malignant and benign tumor in the Breast Department, The First Peoples' Hospital of Kunming in Yunnan province, China. Methods: A hospital-based case-control study was conducted on 263 breast cancer (BC) cases and 457 non-breast cancer controls from 2009 to 2011. The cases and controls information on demographics, medical history, and reproductive characteristics variables were collected using a self-administered questionnaire and routine medical records. Histology of breast cancer tissue and benign breast lesion were documented by pathology reports. Since some variables in data analysis had zero count in at least one category, binomial-response GLM using the bias-reduction method was applied to estimate OR's and their 95% confidence intervals (95% CI). To adjust for age and menopause status, a compound variable comprising age and menopausal status was retained in the statistical models. Results: multivariate model analysis revealed significant independent positive associations of BC with short menstrual cycle, old age at first live birth, never breastfeeding, history of oral contraception experience, increased number of abortion, postmenopausal status, and nulliparity. Categorised by age and menopausal status, perimenopausal women had about 3-fold and postmenopausal women had more than 5-fold increased risk of BC compared to premenopausal women. Discussion and Conclusion: This study has confirmed the significant association of BC and estrogen related risk factors of breast cancer including longer menstrual cycle, older age of first live birth, never breastfeeding, nulliparity, and number of abortions more than one. The findings suggest that female hormonal factors, especially the trend of menopause status play a significant role in the development of BC in Yunnan women.