• The Mathematical Education
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• 제51권4호
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• pp.429-453
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• 2012

The purpose of the study were to analyze teaching models of arithmetic operations of integers in Korean middle school mathematics textbooks of the first grade and Americans', from which we compare and analyze standards for choice of models of middle school teachers and preservice mathematics teachers. We also analyze the effect of the choice of teaching models for students to understand and appreciate number systems as a coherent body of knowledge. On the basis of that, we would like to find the best model to help students understand and reason the process of formulate the arithmetic operations of natural numbers and integers into the operation of the real number system. Furthermore, we help these series of the study to be applied effectively in the middle school mathematics class in Korea.

• Honam Mathematical Journal
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• 제38권4호
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• pp.849-856
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• 2016

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.

• Journal of the Korea Society of Computer and Information
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• 제8권3호
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• pp.113-123
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• 2003

Many researches on the application of neural networks for making financial index prediction have proven their advantages over statistical and other methods. In this paper, a neural network model is proposed for the Buying, Holding or Selling timing prediction in stocks by the price index of stocks by inputting the closing price and volume of dealing in stocks and the technical indexes(MACD, Psychological Line). This model has an equalized multi-layer arithmetic function as well as the time series prediction function of backpropagation neural network algorithm. In the case that the numbers of learning data are unbalanced among the three categories (Buying, Holding or Selling), the neural network with conventional method has the problem that it tries to improve only the prediction accuracy of the most dominant category. Therefore, this paper, after describing the structure, working and learning algorithm of the neural network, shows the equalized multi-layer arithmetic method controlling the numbers of learning data by using information about the importance of each category for improving prediction accuracy of other category. Experimental results show that the financial index prediction using the equalized multi-layer arithmetic neural network has much higher correctness rate than the other conventional models.

• Structural Engineering and Mechanics
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• 제54권2호
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• pp.221-237
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• 2015

An integrated method is proposed for structural nonlinear damage detection based on time series analysis and the higher statistical moments of structural responses in this study. It combines the time series analysis, the higher statistical moments of AR model residual errors and the fuzzy c-means (FCM) clustering techniques. A few comprehensive damage indexes are developed in the arithmetic and geometric mean of the higher statistical moments, and are classified by using the FCM clustering method to achieve nonlinear damage detection. A series of the measured response data, downloaded from the web site of the Los Alamos National Laboratory (LANL) USA, from a three-storey building structure considering the environmental variety as well as different nonlinear damage cases, are analyzed and used to assess the performance of the new nonlinear damage detection method. The effectiveness and robustness of the new proposed method are finally analyzed and concluded.

• Journal of the Korean Mathematical Society
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• 제36권4호
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• pp.707-723
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• 1999

Since the modular curve $X(4)=\Gamma(4)/{\mathfrak{}}^*$ has genus 0, we have a field isomorphism K(X(4)){\approx}\mathcal{C}(j_{4})$ where $j_{4}(z)={\theta}_{3}(\frac{z}{2})/{\theta}_{4}(\frac{z}{2})$ is a quotient of Jacobi theta series ([9]). We derive recursion formulas for the Fourier coefficients of $j_4$ and $N(j_{4})$ (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.

• Industrial Engineering and Management Systems
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• 제1권1호
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• pp.87-92
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• 2002

A stochastic process {$A_n$, n = 1, 2, ...} is an arithmetic process (AP) if there exists some real number, d, so that {$A_n$ + (n-1)d, n =1, 2, ...} is a renewal process (RP). AP is a stochastically monotonic process and can be used for modeling a point process, i.e. point events occurring in a haphazard way in time (or space), especially with a trend. For example, the vents may be failures arising from a deteriorating machine; and such a series of failures id distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for an AP, similar to those for a geometric process (GP) proposed by Lam (1992). Two statistics are suggested for testing whether a given process is an AP. If this is so, we can estimate the parameters d, ${\mu}_{A1}$ and ${\sigma}^{2}_{A1}$ of the AP based on the techniques of simple linear regression, where ${\mu}_{A1}$ and ${\sigma}^2_{A1}$ are the mean and variance of the first random variable $A_1$ respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

• Bulletin of the Korean Mathematical Society
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• 제51권2호
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• pp.443-455
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• 2014

Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as $I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}$ and $R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}$ in [2] and [3]. Various properties of these functions have been investigated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of $PSL_2(\mathbb{Z})$, and studied some of the properties of these maps. In the present paper we generalize the previous work by introducing real moments and considering a larger class of maps. This allows us to explore new properties of these arithmetic functions.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제21권11호
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• pp.2750-2767
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• 1996

In this papr, a new lossless compression method is presented based on the Binary Adaptive Arithmetic Coder(BAAC). A simple unbalanced binary tree is created by recursively dividing the BAAC unit interval into two probability sub-inervals. On the tree the More Probable Predicted Value(MPPV) and Less Probable Predicated Value(LPPV) estimated by local statistics of the image pixels are arranged in decreasing order. The BAAC or Huffman coder is thus applied to the branches of the tree. The proposed method allows the coder be directly applied to the full bit-plane medical image without a decomposition of the full bit-planes into a series of binary bit-planes. The use of the full bit model template improves the compresion ratio. In addition, a fast computation for adjusting the interval is possible since a simple arithmetic operation based on probability interval estimation state machine is used for interval sub-division within the BAAC unit interval.

• Honam Mathematical Journal
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• 제39권2호
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• pp.297-305
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• 2017

Let ${\alpha}$ > 0 be a real number and $(s_{\alpha}(n))_{n{\geq}1}$ be the lexicographically greatest Sturmian word of slope ${\alpha}$. We investigate Dirichlet series of the form ${\sum}^{\infty}_{n=1}s_{\alpha}(n)n^{-s}$. To do this, a generalization of Euler's totient function is required. For a real ${\alpha}$ > 0 and a positive integer n, an arithmetic function ${\varphi}{\alpha}(n)$ is defined to be the number of positive integers m for which gcd(m, n) = 1 and 0 < m/n < ${\alpha}$. Under a condition Re(s) > 1, this paper establishes an identity ${\sum}^{\infty}_{n=1}s_{\alpha}(n)n^{-S}=1+{\sum}^{\infty}_{n=1}{\varphi}_{\alpha}(n)({\zeta}(s)-{\zeta}(s,1+n^{-1}))n^{-s}$.

• Journal for History of Mathematics
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• 제16권3호
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• pp.89-94
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• 2003

Though the concept of unique factorization was formulated in tile 19th century, Euclid already had considered the prime factorization of natural numbers, so called tile fundamental theorem of arithmetic. The unique factorization of algebraic integers was a crucial problem in solving elliptic equations and the Fermat Last Problem in tile 19th century On the other hand the unique factorization of the formal power series ring were a critical problem in the past century. Unique factorization is one of the idealistic condition in computation and prime elements and prime ideals are vital ingredients in thinking and solving problems.