• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.455-460
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• 2000

This research is about the relationship of electroosmotic drainage and zeta potential. Two laboratory experiments were conducted, at first a constant 16 voltage was applied to the cylindrical consolidated specimen of 10cm in diameter, 16cm in length at the concentration of 0, 500, 3000ppm Pb(II) and electroosmotic flow was measured for 12days. Then, zeta potential of kaolinite suspension was measured at the same concentration of electroosmotic permeability experiments in the range of pH from 2 to 14. From the result of this study, it was shown that zeta potential was dependent on the concentration of electrolyte and pH, was proportional to coefficient of electroosmotic permeability. According to the compared result of electroosmotic drainage, as the concentration of Pb(II) was low, the negative value of zeta potential was high and electroosmotic total flow was much.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.303-311
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• 2017

In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.321-333
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• 2011

During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention by many authors. The functional determinant for the n-dimensional sphere $S^n$ with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on $S^n$ (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.

• Journal of Power Electronics
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• v.14 no.4
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• pp.649-660
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• 2014

A novel non-isolated bidirectional soft-switching SEPIC/ZETA converter with reduced ripple currents is proposed and characterized in this study. Two auxiliary switches and an inductor are added to the original bidirectional SEPIC/ZETA components to form a new direct power delivery path between input and output. The proposed converter can be operated in the forward SEPIC and reverse ZETA modes with reduced ripple currents and increased voltage gains attributed to the optimized selection of duty ratios. All switches in the proposed converter can be operated at zero-current-switching turn-on and/or turn-off through soft current commutation. Therefore, the switching and conduction losses of the proposed converter are considerably reduced compared with those of conventional bidirectional SEPIC/ZETA converters. The operation principles and characteristics of the proposed converter are analyzed in detail and verified by the simulation and experimental results.

• Journal of Power Electronics
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• v.6 no.2
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• pp.146-162
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• 2006

This paper deals with the analysis, design and implementation of an AC-DC Zeta converter in discontinuous current mode (DCM) of operation used for power quality improvement at AC mains in direct torque controlled (DTC) permanent magnet synchronous motor (PMSM) drives. The designed Zeta converter feeds a direct torque controlled PMSM drive system. Modeling and simulation is carried out in a standard PSIM software environment. Test results are obtained on the developed prototype Zeta converter using DSP ADMC401. The results obtained demonstrate the effectiveness of the Zeta converter in improving power quality at AC mains in the PMSM drive system.

• Bulletin of the Korean Chemical Society
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• v.3 no.3
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• pp.83-88
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• 1982

Viscosity and zeta-potential of 11.0 wt. % aqueous bentonite suspension containing various electrolytes and hydrogen-ion concentration were measured by using a Couette type automatic rotational viscometer and Zeta Meter, respectively. The effects of pH and elcctrolytes on the rheological properties of the suspension were investigated. A system, which has a large zeta-potcntial, has a small intrinsic relaxation time ${\beta}$ and a small intrinsic shear modulus $1/{\alpha}$ in the Ree-Eyring generalized viscosity equation, i.e., such a system has a small viscosity value, since ${\eta}={\beta}/{\alpha}$. In general, a stable suspension system has large zeta-potential. The stability condition of clay-water suspension can be estimated by viscometric method since stable suspension generally has small viscosity. The correlation between the stability, viscosity and zeta-potential has been explained by the Ree-Eyring theory of viscous flow.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.203-210
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• 1997

We give some interesting identities involving the Hurwitz and Riemann zeta functions.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.283-286
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• 2016

In this paper, we find a new recurrence formula of the Euler zeta functions.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.117-121
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• 2016

In this paper we give a determinant formula for the ratio of relative congruence zeta functions of cyclotomic function fields.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.