• 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 of Magnetics
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• v.4 no.1
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• pp.13-16
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• 1999

Magnetic viscosities of a commercialized metal evaporated tape were measured as a function of sweeping rate in VSM at room temperature. Within several seconds in the viscosity measurement, curves are downward concave and more concave with increasing sweeping rate when magnetization were plotted as a logarithmic function of time. However, magnetization varied as a logarithmic function of time after several seconds. Magetic viscosity coefficient gradually increased with increasing sweeping rate and then kept a constant value at a rate faster than 61.5 Oe/s. It was supposed that magnetic viscosity occurs during field sweeping, which was in good agreement with Sharrock's model qualitatively. Activation volume decreased with increasing sweeping rate, which was due to the fact that magnetic viscosity coefficients increased with sweeping rate while irreversible susceptibilities were not affected by sweeping rate.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• 한국기계연구소 소보
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• s.15
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• pp.105-115
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• 1985

For the application of factory automation, a 3-axis numerical control system with personal computer and KM3701 function generator LSI chip, which has liner, circular, parabolic, logarithmic, and exponential interpolations, is developed. The developed system also has 2 control function to stabilize tooling speed and 1/1000mm step sizes.

• The Korean Journal of Applied Statistics
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• v.33 no.4
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• pp.357-364
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• 2020

We review the characteristics of a geometric mean and statistical inferences based on geometric means. We also show that the statistical results obtained by the logarithmic transform and back-transformation are related to geometric means and explain how to interpret the results produced in this process.

• Journal of the Korean Institute of Telematics and Electronics
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• v.6 no.1
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• pp.19-22
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• 1969

Detailed analysis has been developed concerning the transfer function and stability condition of the logarithmic amplifier using a common emitter transistor as a feed-back element. The analysis shows that input current vs output voltage transfer characteristics is accurately ogarithmic through entire operating current, and the time constant depends on input capcitance and collector-emitter equivalent resistance. Also the minimum value of imput capacitance required to stabilize the system is derived.

• East Asian mathematical journal
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• v.35 no.5
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• pp.597-612
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• 2019

In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.6
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• pp.1638-1658
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• 2024

As a crucial development direction for the sixth generation of mobile communication networks (6G), Low Earth Orbit (LEO) satellite networks exhibit characteristics such as low latency, seamless coverage, and high bandwidth. However, the frequent changes in the topology of LEO satellite networks complicate communication between satellites, and satellite power resources are limited. To fully utilize resources on satellites, it is essential to determine the association between satellites before power allocation. To effectively address the satellite association problem in LEO satellite networks, this paper proposes a satellite association-based resource allocation algorithm. The algorithm comprehensively considers the throughput of the satellite network and the fairness associated with satellite correlation. It formulates an objective function with logarithmic utility by taking the logarithm and summing the satellite channel capacities. This aims to maximize the sum of logarithmic utility while promoting the selection of fewer associated satellites for forwarding satellites, thereby enhancing the fairness of satellite association. The problems of satellite association and power allocation are solved under constraints on resources and transmission rates, maximizing the logarithmic utility function. The paper employs an improved Kuhn-Munkres (KM) algorithm to solve the satellite association problem and determine the correlation between satellites. Based on the satellite association results, the paper uses the Lagrangian dual method to solve the power allocation problem. Simulation results demonstrate that the proposed algorithm enhances the fairness of satellite association, optimizes resource utilization, and effectively improves the throughput of LEO satellite networks.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.6 no.1
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• pp.27-31
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• 1981

This paper deals with the variation of the effective detectability factor fo logarithmic receiver in noise interference environment. The computed results as a function of maximum detection range and jamming range were compared with the effective detectability factor for linear receiver. Even though the logarithmic receiver has a wide dynamic characteristics, it is found that the effective detectability factor being reduced about 15% than the linear receiver at 100 KM range.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1335-1352
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• 2019

In this article, a new family of lifetime distributions by adding two additional parameters is introduced. The new family is called, the logarithmic Kumaraswamy family of distributions. For the proposed family, explicit expressions for some mathematical properties are derived. Maximum likelihood estimates of the model parameters are also obtained. This method is applied to develop a new lifetime model, called the logarithmic Kumaraswamy Weibull distribution. The proposed model is very flexible and capable of modeling data with increasing, decreasing, unimodal or modified unimodal shaped hazard rates. To access the behavior of the model parameters, a simulation study has been carried out. Finally, the potentiality of the new method is proved via analyzing two real data sets.