• Communications of Mathematical Education
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• v.25 no.3
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• pp.557-575
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• 2011

The purpose of this paper is to analyze the way of teaching and learning logarithm in high school mathematics and provide practical suggestions for teaching logarithms. For such purpose, it reviewed John Napier's life and his ideas, the effect of logarithms on seventeenth century science, and a logarithmic scale and its methods of calculation. With this reviews, introduction of logarithms with function concept, logarithmic calculation with common logarithms, and the formula of converting to other logarithmic bases were reviewed for finding a new perspective of teaching and learning logarithms in high school mathematics. Through such historical and pedagogical reviews, this paper presented practical suggestions and comments about the way of teaching and learning logarithms in high school mathematics.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.409-419
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• 2014

In school mathematics, the logarithmic function is defined as the inverse function of an exponential function. And the natural logarithm is defined by the integral of the fractional function 1/x. But historically, Napier had already used the concept of logarithm in 1614 before the use of exponential function or integral. The calculation of the logarithm was a hard work. So mathematicians with arithmetic ability made the tables of values of logarithms and people used the tables for the estimation of data. In this paper, we first take a look at the mathematicians and mathematical principles related to the appearance and the developments of the logarithmic tables. And then we deal with the confusions between mathematicians, raised by the estimation data which were known as proportional parts or mean differences in common logarithmic tables.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.3
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• pp.411-418
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• 2000

By calculating the location and size of the relative eddy formed in the rotating impellers with the logarithmic spiral vanes, a new simple but accurate slip factor is analytically derived. The proposed slip factor depends on only one parameter that is a function of the number of vanes and the vane exit angle. Predicted slip factor for various cases are compared with those estimated by a number of previous slip factors as well as a recent theoretical calculation by Visser et al. ( JFM, Vol. 268, pp. 107-141, 1994). It is found that the present slip factor yields almost similar results to Wiesner's which has been empirically formulated based on the theoretical calculation of Busemann.

• Journal of the Korean Ceramic Society
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• v.40 no.4
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• pp.371-374
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• 2003

Various types of equation for mixing rule on permittivity of mixture have been proposed, but none of these is not perfect because of the inconsistency between the actual geometrical configuration and the basic model for calculation. Serial model and parallel model are lower and upper extremes of mixing manner, the apparent permittivity of any other type of mixture stay between these two extreme states. For the random mixture of the stumpy fine particles, customarily the logarithmic mixing rule has been applied. But, the logarithmic mixing rule does not give the proper value of permittivity in low or high mixing rate of constituent. The author proposed the new mixing rule that gives better consistency with measured value in whole mixing range compared to the logarithmic rule. In this paper, a desirable refinement on the equation proposed in the previous paper is made to adapt to thr configuration image of actual compound and then the equation has been expanded to the complex permittivity to apply the mixing rule on the dissipative materials cases.

• Journal of Ocean Engineering and Technology
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• v.34 no.2
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• pp.89-96
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• 2020

In this study, the Norbury-Fraenkel family of vortex rings is analyzed using a contour dynamics method for the stream function, which significantly reduces the numerical burden in the calculation. The stream function is formulated as the integral along the contour of the vorticity core. The integration over the logarithmic-singular segment is evaluated analytically, and the positions of the nodal points of the contour are calculated directly. The shapes of the cores and the dividing stream surfaces are found based on the mean core radius. Compared with other studies, the proposed method is verified and found to be more efficient.

• Bulletin of the Korean Chemical Society
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• v.8 no.5
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• pp.406-408
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• 1987

It has been shown that the distribution of relaxation times, H(ln $\tau$), in semi-logarithmic time scale can easily be calculated numerically from the derivative of the relaxation function in semilogarithmic scale. In that, ln$\tau$, the abscissa, is divided into N different segments of equal size, then H is considered to be a linear function of ln $\tau$within each segment. The technique has been applied to a Williams-Watts function as well as to the relaxation function obtained by photon correlation spectroscopy from atactic polystyrene glass. It has been demonstrated that the relaxation functions can be precisely reproduced from the calculated distribution functions.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.967-987
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• 2020

A numerical analysis is carried out for the marine propellers in open water conditions to investigate the effect of the wall treatments in model and full scale. The standard wall function to apply the low of the wall and the two layer zonal model to calculate the whole boundary layer for a transition phenomenon are used with one turbulence model. To determine an appropriate distance of the first grid point from the wall when using the wall function, a formula based on Reynolds number is suggested, which can estimate the maximum y+ satisfying the logarithmic law. In the model scale, it is confirmed that a transition calculation is required for a model scale propeller with low Reynolds number that the transient region appears widely. While in the full scale, the wall function calculation is recommended for efficient calculations due to the turbulence dominant flow for large Reynolds number.

• Journal of KSNVE
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• v.7 no.4
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• pp.645-653
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• 1997

For high performance rotating machinery, unstable vibrations may occur caused by hydrodynamic forces such as oil film forces, clearance excitation forces generated by the working fluid, and etc. In order to improve the availability one has to take into account the vibrations very accurately. When designing a rotating machinery, the stability behavior and the resonance response can be obtained by calculation of the complex eigenvalues. A suitable modifications of seal and/or bearing design may effectively improve the stability and the response of a rotor system. This paper deals with the optimum length and clearance of seals and bearings to minimize the resonance response(Q factor) and to maximize the logarithmic decrement in the operating speed under the constraints of design variables. Also, for an avoidance of resonance region from the operating speed, an optimization technique has been used to yield the critical speeds as far from the operating speed as possible. The optimization method is used by the genetic algorithm, which is a search algorithm based on the mechanics of natural selection and natural genetics. The results show that the optimum design of seals and bearings can significantly improve the resonance and the stability of the pump rotor system.

• Journal of the Institute of Convergence Signal Processing
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• v.14 no.2
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• pp.95-98
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• 2013

The LMS(Least Mean Square) algorithm, one of the most famous, is generally used because of tenacity and high mating spots and simplicity of realization, But it has trade-off between nonuniform collection and EMSE(Excess mean square error). To overcome this weakness, a variable step size is used widely, but it needs a lot of calculation loads. In this paper, we suggest changed algorithm in case of environment changes of cars and reduce amount of calculation as it uses original signal and noise signal of IGC(Instantaneous Gain Control) algorithm. In this paper, logarithmic function is removed because of real-time processing IGC. The performance of proposed algorithm is tested to adaptive noise canceller in automobile.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.71-90
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• 2016

In this paper, the normalized variable V=(log N-B)(log ${\Delta}{\sigma}-C$-C), as derived from the probabilistic S-N field of Castillo and Canteli, is taken as a reference for calculation of damage accumulation and probability of failure using the Miner number in scenarios of variable amplitude loading. Alternative damage measures, such as the classical Miner and logarithmic Miner, are also considered for comparison between theoretical lifetime prediction and experimental data. The suitability of this approach is confirmed for it provides safe lifetime prediction when applied to fatigue data obtained for riveted joints made of a puddle iron original from the Fao bridge, as well as for data from experimental programs published elsewhere carried out for different materials (aluminium and concrete specimens) under distinct variable loading histories.