• Journal of Korean Society for Quality Management
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• v.16 no.1
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• pp.23-31
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• 1988

This paper studies the handling of significant digits and rounding off methods in domestic industries. ANOVA tables made by six well-known big companies are selected and analyzed. There exist various mistakes in handling of significant digits and rounding off methods such as: * too many significant digits in the Sum of Squares values in comparison to the original data * too many significant digits in the variance ratio in comparison to the F table values. * no consistancy in the number of significant digits * no consideration for the number of significant digits in computations * ignoring the KS A 0021 in rounding off methods etc. Such mistakes are caused from the characteristics of the personal computers rather than the misunderstandings about the significant digits conception. A subroutine is developed for PC in BASIC language to help the handling of significant digits and rounding off.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.16 no.28
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• pp.103-107
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• 1993

This paper studies computer programming for the analysis of data obtained by experiments using Orthogonal Arrays. The following items are considered in the computer programming : * significant digits in the computation of Sum of Squares, Mean Squares and Variance Ratios * containing the necessary F-distribution values in the program. * matching the rules of KS A 0021 and 3251 in the digit treatments etc. The running results of ANOVA Table and Pooled ANOVA Table of a fictitious example is added with the parts of a program. It should be mentioned that the main purpose of this paper is in the arousing of the discussion about significant digits concept in the computer programming for various kinds of Statistical Methods.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.419-428
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• 2018

Let us think of adding each digit of a natural number, in bases b, that are e-powered. By studying for a number becoming greater than or equal to oneself, we will consider values of ${\lim}_{b{\rightarrow}{\infty}}{\frac{N(e,b)}{b^e}}$.

• Journal of Korean Society for Quality Management
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• v.19 no.1
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• pp.163-169
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• 1991

This paper studies computer programming for Two-Way Layout with Multiple Observations - Fixed Model using the subroutines of the former paper. The following items are considered in the PC computer programming: * significant digits in the computation of Sum of Squares * containing the necessary F-distribution values in the program * including the necessary estimation after the Analysis of Variance * following the rules of KS A 0021 in rounding off digits etc. The running results of Analysis of Variation Table and Estimations of a fictitious example is added with the parts of PC program. It should be mentioned that the main purpose of this paper is in the arousing of the discussion about significant digits concept in the PC computer programming for various kinds of Statistical Methods.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.2
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• pp.107-112
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• 2011

It is very difficult to factorize composite number, $n=pq$ to integer factorization, p and q that is almost similar length of digits. Integer factorization algorithms, for the most part, find ($a,b$) that is congruence of squares ($a^2{\equiv}b^2$ (mod $n$)) with using factoring(factor base, B) and get the result, $p=GCD(a-b,n)$, $q=GCD(a+b,n)$ with taking the greatest common divisor of Euclid based on the formula $a^2-b^2=(a-b)(a+b)$. The efficiency of these algorithms hangs on finding ($a,b$) and deciding factor base, B. This paper proposes a efficient algorithm. The proposed algorithm extracts B from integer factorization with 3 digits prime numbers of $n+1$ and decides f, the combination of B. And then it obtains $x$(this is, $a=fxy$, $\sqrt{n}$ < $a$ < $\sqrt{2n}$) from integer factorization of $n-2$ and gets $y=\frac{a}{fx}$, $y_1$={1,3,7,9}. Our algorithm is much more effective in comparison with the conventional Fermat algorithm that sequentially finds $\sqrt{n}$ < $a$.

• Journal of KIISE:Software and Applications
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• v.28 no.9
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• pp.603-611
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• 2001

This paper proposes a novel fast layer-by-layer algorithm that has better generalization capability. In the proposed algorithm, the weights of the hidden layer are updated by the target vector of the hidden layer obtained by least squares method. The proposed algorithm improves the learning speed that can occur due to the small magnitude of the gradient vector in the hidden layer. This algorithm was tested in a handwritten digits recognition problem. The learning speed of the proposed algorithm was faster than those of error back propagation algorithm and modified error function algorithm, and similar to those of Ooyen's method and layer-by-layer algorithm. Moreover, the simulation results showed that the proposed algorithm had the best generalization capability among them regardless of the number of hidden nodes. The proposed algorithm has the advantages of the learning speed of layer-by-layer algorithm and the generalization capability of error back propagation algorithm and modified error function algorithm.

• Journal of the Korea Society of Computer and Information
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• v.19 no.7
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• pp.71-76
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• 2014

There is to be virtually impossible to solve the very large digits of prime number p and q from composite number n=pq using integer factorization in typical public-key cryptosystems, RSA. When the public key e and the composite number n are known but the private key d remains unknown in an asymmetric-key RSA, message decryption is carried out by first obtaining ${\phi}(n)=(p-1)(q-1)=n+1-(p+q)$ and then using a reverse function of $d=e^{-1}(mod{\phi}(n))$. Integer factorization from n to p,q is most widely used to produce ${\phi}(n)$, which has been regarded as mathematically hard. Among various integer factorization methods, the most popularly used is the congruence of squares of $a^2{\equiv}b^2(mod\;n)$, a=(p+q)/2,b=(q-p)/2 which is more commonly used then n/p=q trial division. Despite the availability of a number of congruence of scares methods, however, many of the RSA numbers remain unfactorable. This paper thus proposes an algorithm that directly and immediately obtains ${\phi}(n)$. The proposed algorithm computes $2^k{\beta}_j{\equiv}2^i(mod\;n)$, $0{\leq}i{\leq}{\gamma}-1$, $k=1,2,{\ldots}$ or $2^k{\beta}_j=2{\beta}_j$ for $2^j{\equiv}{\beta}_j(mod\;n)$, $2^{{\gamma}-1}$ < n < $2^{\gamma}$, $j={\gamma}-1,{\gamma},{\gamma}+1$ to obtain the solution. It has been found to be capable of finding an arbitrarily located ${\phi}(n)$ in a range of $n-10{\lfloor}{\sqrt{n}}{\rfloor}$ < ${\phi}(n){\leq}n-2{\lfloor}{\sqrt{n}}{\rfloor}$ much more efficiently than conventional algorithms.