• Journal of Korean Institute of Industrial Engineers
• /
• 제16권1호
• /
• pp.17-25
• /
• 1990

Most of the least cost transportation network design problems are frequently formulated as the minimum spanning arborescence problems in directed networks with bitype are costs. These costs are classified whether the arc is included in the path from the root to a specified node over a given spanning arborescence. We prove that this problem is NP-hard, and develop a polynomial time algorithm for acyclic networks. The probelm in acyclic networks is initially formulated as 0-1 integer programming. Next, we prove that the 0-1 relaxed linear programming has an integral optimum solution by complementary slackness conditions. In this paper, we present an $O(n^2)$ algorithm based on a shortest path algorithm.

• The Journal of the Acoustical Society of Korea
• /
• 제21권3호
• /
• pp.304-309
• /
• 2002

We propose the computation reduction method of real root method that is mainly used in the CELP (Code Excited Linear Prediction) vocoder. The real root method is that if polynomial equations have the real roots, we are able to find those and transform them into LSP. However, this method takes much time to compute, because the root searching is processed sequentially in frequency region. In this paper, to reduce the computation time of real root, we compare the real root method with two methods. In first method, we use the mal scale of searching frequency region that is linear below 1 kHz and logarithmic above. In second method, The searching frequency region and searching interval are ordered by each coefficient's distribution. In order to compare real root method with proposed methods, we measured the following two. First, we compared the position of transformed LSP (Line Spectrum Pairs) parameters in the proposed methods with these of real root method. Second, we measured how long computation time is reduced. The experimental results of both methods that the searching time was reduced by about 47% in average without the change of LSP parameters.

• Journal for History of Mathematics
• /
• 제15권3호
• /
• pp.25-34
• /
• 2002

This paper explains methods of numerical analysis which appear on Cardano's Ars Magna and Newton's Principia. Cardano's method is secant method, but its actual al]plication is severely limited by technical difficulties. Newton's method is what nowadays called Newton-Raphson's method. But mysteriously, Newton's explanation had been forgotten for two hundred years, until Adams rediscovered it. Newton had even explained finding the root using the second degree Taylor's polynomial, which shows Newton's greatness.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• 제7권4호
• /
• pp.73-80
• /
• 1997

유한체 위에서 다항식의 근을 구하는 문제는 수학의 오래된 문제중 하나이고 최근들어 암호학과 관련하여 유한체 위서의 다항식 연산과 성질등이 쓰이고 있다. 유한체 위에서 다항식의 최대공약수(greatest common divisor) 를 구하는데 많은 시간이 소요 된다. Rabin의 알고리즘에서 주어진 다항식의 근들의 곱(F(x), $x^{q}$ -x)를 구하는 과정을 c F(p), $f_{c}$ (x)=(F(x), $T_{r}$ (x)-c), de$gf_{c}$ (x)>0인 $f_{c}$(x) s로 대체한 효율적인 알고리즘 제안과 Mathematica를 이용한 프로그램의 실행 결과를 제시한다.

• Bulletin of the Korean Mathematical Society
• /
• 제53권1호
• /
• pp.21-28
• /
• 2016

It is known that no two of the roots of the polynomial equation (1) $$\prod\limits_{l=1}^{n}(x-r_l)+\prod\limits_{l=1}^{n}(x+r_l)=0$$, where 0 < $r_1{\leq}r_2{\leq}{\cdots}{\leq}r_n$, can be equal and all of its roots lie on the imaginary axis. In this paper we show that for 0 < h < $r_k$, the roots of $$(x-r_k+h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x-r_l)+(x+r_k-h)\prod\limits_{{l=1}\\{l{\neq}k}}^{n}(x+r_l)=0$$ and the roots of (1) in the upper half-plane lie alternatively on the imaginary axis.

• Proceedings of the Korean Society of Agricultural Engineers Conference
• /
• 한국농공학회 2001년도 학술발표회 발표논문집
• /
• pp.65-68
• /
• 2001

This study was conducted to develop a soil moisture meter using capacitance probe. A parallel cylinder type capacitance probe (C-probe) was fabricated The 5 MHz of crystal oscillator was constructed to detect the capacitance change of the C-probe with moist soil. A third order polynomial regression model for volumetric water content having oscillation frequency changes at 5 MHz as independent variables presented the determination coefficient of 0.979 and root mean square error of $0.031\;cm^{3}cm^{3}$ for all soil samples. A prototype soil moisture meter consisting of the sample container, C-probe, oscillator, frequency counter and related signal procession units presented the correlation coefficient of 0.987 and the root mean square error of $0.032\;cm^{3}cm^{3}$ as compared with the oven drying method for unknown soil samples.

• Computers and Concrete
• /
• 제5권5호
• /
• pp.461-473
• /
• 2008

The paper explores the potential of Support Vector Machines (SVM) approach in predicting 28-day compressive strength and slump flow of self-compacting concrete. Total of 80 data collected from the exiting literature were used in present work. To compare the performance of the technique, prediction was also done using a back propagation neural network model. For this data-set, RBF kernel worked well in comparison to polynomial kernel based support vector machines and provide a root mean square error of 4.688 (MPa) (correlation coefficient=0.942) for 28-day compressive strength prediction and a root mean square error of 7.825 cm (correlation coefficient=0.931) for slump flow. Results obtained for RMSE and correlation coefficient suggested a comparable performance by Support Vector Machine approach to neural network approach for both 28-day compressive strength and slump flow prediction.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• 제8권3호
• /
• pp.563-568
• /
• 2007

We propose the computation reduction method of real root method that is used in the EVRC(Enhanced Variable Rate Codec) system. The real root method is that if polynomial equations have the real roots, we are able to find those and transform them into LSP. However, this method takes much time to compute, because the root searching is processed sequentially in frequency region. But, the important characteristic of LSP is that most of coefficients are occurred in specific frequency region. So, to reduce the computation time of real root, we used the met scale that is linear below 1kHz and logarithmic above. In order to compare real root method with proposed method, we measured the following two. First, we compared the position of transformed LSP(Line Spectrum Pairs) parameters in the proposed method with these of real root method. Second, we measured how long computation time is reduced. The experimental result is that the searching time was reduced by about 48% in average without the change of LSP parameters.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• 제8권5호
• /
• pp.1122-1127
• /
• 2007

We propose the complexity reduction algorithm of real root method that is mainly used in the Vocoder. The real root method is that if polynomial equations have the real roots, we are able to find those and transform them into LSP(Line Spectrum Pairs). However, this method takes much time to compute, because the root searching is processed sequentially in frequency region. The important characteristic of LSP is that most of coefficients are occurred in specific frequency region. So, the searching frequency region is ordered and adjusted by each coefficient's distribution in this paper. Transformation time can be reduced by proposed algorithm than the sequential searching method in frequency region. When we compare this proposed method with the conventional real root method, the experimental result is that the searching time was reduced about 48% in average.

• Tunnel and Underground Space
• /
• 제28권5호
• /
• pp.426-441
• /
• 2018

Recently, the generalized Hoek-Brown (GHB) failure criterion has been actively employed in various rock engineering calculations, but the analytical form of the corresponding Mohr failure envelope is not available, making it difficult to extend the application of the GHB criterion. In order to overcome this disadvantage, this study proposes a new method to express the tangential friction angle as an explicit function of normal stress by invoking the polynomial best-fitting to the relationship between normal stress and tangent friction angle implied in the GHB failure function. If this normal stress - tangential friction angle relationship is best-fitted with linear or quadratic polynomial function, it is possible to find the analytical root for tangential friction angle. Subsequently, incorporating the root into the relationship between shear stress and tangential friction angle accomplishes the derivation of the approximate Mohr envelope for the GHB criterion. It is demonstrated that the derived approximate Mohr failure envelopes are very accurate in the entire range of GSI value.