• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.479-491
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• 2017

We investigate the zeros of Epstein zeta functions associated with positive definite quadratic forms with rational coefficients in the vertical strip ${\sigma}_1$ < ${\Re}s$ < ${\sigma}_2$, where 1/2 < ${\sigma}_1$ < ${\sigma}_2$ < 1. When the class number h of the quadratic form is bigger than 1, Voronin gave a lower bound and Lee gave an asymptotic formula for the number of zeros. Recently Gonek and Lee improved their results by providing a new upper bound for the error term when h > 3. In this paper, we consider the cases h = 2, 3 and provide an upper bound for the error term, smaller than the one for the case h > 3.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.293-307
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• 1997

In this paper we present the $L^2$-estimation for the kernel $K_n$ of the remaider term for the Gaussian quadrature with respect to one of four Chebyshev weight functions and the error bound of the type on the contour $$ $\mid$R_n(f)$\mid$ \leq \frac{2\pi}{\sqrt{l(\Gamma)}} max_{z\in\Gamma}$\mid$f(z)$\mid$ (\smallint_\Gamma $\mid$K_n(z)$\mid$^2$\mid$dz$\mid$)^\frac{2}{1}, $$ where $l(\Gamma)$ denotes the length of the contour $\Gamma$.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.6
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• pp.380-386
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• 2000

This paper presents the mathematical modelling analysis of Brushless Synchronous Motor(BLSM). The dynamic and the steady state characteristics of BLSM are simulated and analyzed : electromagnetic torque, speed, line voltage, and current. We used mathematical modelling to model of BLSM with sinusoidal back EMF, namely the shaft transformation referencing rotor frame from a, b, c three to produce constant torque like synchronous motor. The experiment result has already similar to compare with simulation result : torque error about 7%, speed error about 5%. The validity of proposed modelling and analysis was confirmed by the experimental result.

• 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.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.2
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• pp.48-55
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• 2001

An accumulator in hydraulic systems stores kinetic energy during braking action, and then that control hasty surge pres-sure. This study suggests a method to select the capacity of accumulator to control surge pressure to a desired degree. The selection method is based upon a trial and error approach and computer simulation. A mathematical dynamic model of the system was derived and the parameters in the model were identified from experimental data. A series of computer simulation were done for the brake action. The results of the simulation work were compared with those of experiments. These results of the computer simular-tion and experiments show that the proposed method can be applied effectively to control the surge pressure of the hydraulic regenerative brake systems.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.217-227
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• 2009

Assuming that a given nonlinear function f : $\mathbf{R}{\rightarrow}\mathbf{R}$ has a zero $\alpha$with integer multiplicity $m{\geq}1$ and is sufficiently smooth in a small neighborhood of $\alpha$, we define extended leap-frogging Newton's method. We investigate the order of convergence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1155-1175
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• 2014

We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost our semilocal convergence criteria can be weaker; the error bounds more precise and in the local case the convergence balls can be larger and the error bounds tighter than in earlier studies such as [1-3,7-14,16,20,21] at least for the cases of Newton's method and the secant method. Numerical examples are also presented to illustrate the theoretical results obtained in this study.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.401-414
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• 2020

It is computationally expensive to compute principal components from scratch at every update or downdate when new data arrive and existing data are truncated from the data matrix frequently. To overcome this limitations, incremental principal component analysis is considered. Specifically, we present a sliding window based efficient incremental principal component computation from a covariance matrix which comprises of two procedures; simultaneous update and downdate of principal components, followed by the rank-one matrix update. Additionally we track the accurate decomposition error and the adaptive numerical rank. Experiments show that the proposed algorithm enables a faster execution speed and no-meaningful decomposition error differences compared to typical incremental principal component analysis algorithms, thereby maintaining a good approximation for the principal components.

• East Asian mathematical journal
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• v.14 no.1
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.