• 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.

• The Journal of the Acoustical Society of Korea
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• v.5 no.3
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• pp.13-20
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• 1986

본 논문은 신호처리가 가능한 2진 로가리즘 상수를 발생시키기 위한 programmable variable-rate up/down 계수기의 설계를 기술한다. 2진수에 대한 밑수가 2인 로가리즘 계승의 적용은 결 과적으로 오차가 발생한다. log\sub 2\(1+χ)-χ에 의해 정의된 것처럼 log\sub 2\(1+χ)에서의 오차는 직선의 집합으로 갖게된다. 계수기 rate는 직선의 기울기에 비례한다. 그러므로 신호처리가 가능한 2진 로가리즘 상수는 programmable 계수기를 사용함으로써 쉽게 발생될 수 있다.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.535-547
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• 2019

In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.

• Journal of Information Processing Systems
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• v.6 no.3
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• pp.335-346
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• 2010

The present study investigates the difficulty of solving the mathematical problem, namely the DLP (Discrete Logarithm Problem) for ephemeral keys. The DLP is the basis for many public key cryptosystems. The ephemeral keys are used in such systems to ensure security. The DLP defined on a prime field $Z^*_p of random prime is considered in the present study. The most effective method to solve the DLP is the ICM (Index Calculus Method). In the present study, an efficient way of computing the DLP for ephemeral keys by using a new variant of the ICM when the factors of p-1 are known and small is proposed. The ICM has two steps, a pre-computation and an individual logarithm computation. The pre-computation step is to compute the logarithms of a subset of a group and the individual logarithm step is to find the DLP using the precomputed logarithms. Since the ephemeral keys are dynamic and change for every session, once the logarithms of a subset of a group are known, the DLP for the ephemeral key can be obtained using the individual logarithm step. Therefore, an efficient way of solving the individual logarithm step based on the newly proposed precomputation method is presented and the performance is analyzed using a comprehensive set of experiments. The ephemeral keys are also solved by using other methods, which are efficient on random primes, such as the Pohlig-Hellman method, the Van Oorschot method and the traditional individual logarithm step. The results are compared with the newly proposed individual logarithm step of the ICM. Also, the DLP of ephemeral keys used in a popular password key exchange protocol known as Chang and Chang are computed and reported to launch key recovery attack.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.695-708
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• 2005

Certain observations about formal Dirichlet series whose coefficients are arithmetic functions are made. These include for example algebraic independence and representation as infinite series of logarithms.

• Journal of the Korean Society of Safety
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• v.30 no.1
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• pp.8-13
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• 2015

The experimental design methodology was applied in the drop tube furnace (DTF) to predict the various combustion properties according to the operating conditions and to assess the coal plant safety. Response surface method (RSM) was introduced as a design of experiment, and the database for RSM was set with the numerical simulation of DTF. The dependent variables such as burnout ratios (BOR) of coal and $CO/CO_2$ ratios were mathematically described as a function of three independent variables (coal particle size, carrier gas flow rate, wall temperature) being modeled by the use of the central composite design (CCD), and evaluated using a second-order polynomial multiple regression model. The prediction of BOR showed a high coefficient of determination (R2) value, thus ensuring a satisfactory adjustment of the second-order polynomial multiple regression model with the simulation data. However, $CO/CO_2$ ratio had a big difference between calculated values and predicted values using conventional RSM, which might be mainly due to the dependent variable increses or decrease very steeply, and hence the second order polynomial cannot follow the rates. To relax the increasing rate of dependent variable, $CO/CO_2$ ratio was taken as common logarithms and worked again with RSM. The application of logarithms in the transformation of dependent variables showed that the accuracy was highly enhanced and predicted the simulation data well.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.3
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• pp.3-12
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• 1999

The public key crytptosystem is represented by RSA based on the difficulty of integer factorization and ElGamal cryptosystem based on the intractability of the discrete logarithm problem in a cyclic group G. The index-calculus algorithm for discrete logarithms in GF${$q^n$}^+$ requires an polynomial factorization. The Niederreiter recently developed deterministic facorization algorithm for polynomial over GF$q^n$ In this paper we implemented the arithmetic of finite field with c-language and gibe an implementation of the Niederreiter's algorithm over GF$2^n$ using normal bases.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.105-121
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• 2009

In this paper we will be interested in characterizing and computing matrices $X\;{\in}\;C^{n{\times}n}$ that satisfy $e^X$ = A, that is logarithms of A. The study in this work goes through two lines. The first is concerned with a theoretical study of the solution set, S(A), of $e^X$ = A. Along the second line computational approaches are considered to compute the principal logarithm of A, LogA.

• Journal of Korean Society for Quality Management
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• v.21 no.2
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• pp.194-214
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• 1993

This paper purports to study on interactive fuzzy goal programming model which leads to the compromise solution which the decision maker satisfies through the interactive approach. We also attempted to calculate local proxy preference function from utility function of sum-of-logarithms in connection with marginal rate of substitution and interactive approach for the purpose of applying weight of multiobjective function. In an attempt to grasp compromise solution from fuzzy efficient solution, we decided to take the interactive method and presented stopping rule for this.