• Journal for History of Mathematics
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• v.31 no.6
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• pp.273-289
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• 2018

The KaiFangFa開方法 of traditional mathematics was completed in ${\ll}$JiuZhang SuanShu九章算術${\gg}$ originally, and further organized in Song宋 $Yu{\acute{a}}n$元 dinasities. The former is the ShiSuoKaiFangFa釋鎖開方法 using the coefficients of the polynomial expansion, and the latter is the ZengChengKaiFangFa增乘開方法 obtaining the solution only by some mechanical numerical manipulations. ${\ll}$SanHak JeongEui算學正義${\gg}$ basically used the latter and improved the estimate-value array by referring to the written-calculation in ${\ll}$ShuLi JingYun數理精蘊${\gg}$. As a result, ZengChengKaiFangFa was more refined so that the KaiFangFa algorithm is more consistent.

• Journal of Information Processing Systems
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• v.16 no.3
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• pp.639-647
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• 2020

In the vibration target localization algorithms based on time difference of arrival (TDOA), Fang algorithm is often used in practice because of its simple calculation. However, when the delay estimation error is large, the localization equation of Fang algorithm has no solution. In order to solve this problem, one dimensional search location algorithm based on TDOA is proposed in this paper. The concept of search is introduced in the algorithm. The distance d1 between any single sensor and the vibration target is considered as a search variable. The vibration target location is searched by changing the value of d1 in the two-dimensional plane. The experiment results show that the proposed algorithm is superior to traditional methods in localization accuracy.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.679-685
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• 2021

The target of this article is to modify the algorithm given by Fang and Huang [6]. The rate of convergence of our algorithm is faster than that of Fang and Huang [6]. A numerical example is given to justify our statement.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.285-297
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• 2004

The general scheme of an algorithm, called an ABS-FRE algorithm, for solving systems of fuzzy relation equations (systems of FRE) via the ABS algorithms is presented. As special cases, two particular algorithms for obtaining the greatest and minimal solutions of systems of FRE are described. Several new operations used in this scheme are given, for instance, operators $\veebar$ and $\underline{\wedge}$ called quasi-inverses of operators $\vee$ and $\wedge$, respectively, etc.

• ETRI Journal
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• v.34 no.5
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• pp.696-705
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• 2012

Accurate synthesis models based on artificial neural networks (ANNs) are proposed to directly obtain the physical dimensions of an asymmetric coplanar waveguide with conductor backing and substrate overlaying (ACPWCBSO). First, the ACPWCBSO is analyzed with the conformal mapping technique (CMT) to obtain the training data. Then, a modified genetic-algorithm-Levenberg-Marquardt (GA-LM) algorithm is adopted to train ANNs. In the algorithm, the maximal relative error (MRE) is used as the fitness function of the chromosomes to guarantee that the MRE is small, while the mean square error is used as the error function in LM training to ensure that the average relative error is small. The MRE of ANNs trained with the modified GA-LM algorithm is less than 8.1%, which is smaller than those trained with the existing GA-LM algorithm and the LM algorithm (greater than 15%). Lastly, the ANN synthesis models are validated by the CMT analysis, electromagnetic simulation, and measurements.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.489-499
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• 2004

In this paper, we introduce and study a new system of nonlinear variational inequalities. The existence and uniqueness of solution for this problem are proved and an iterative algorithm for approximating the solution of system of nonlinear variational inequalities is constructed.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.139-142
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• 2017

For the conventional computational methods for structural reliability analysis, the common limitations are long computational time, large number of iteration and low accuracy. Thus, a new novel method for structural reliability analysis has been proposed in this paper based on response surface method incorporated with an improved genetic algorithm. The genetic algorithm is first improved from the conventional genetic algorithm. Then, it is used to produce the response surface and the structural reliability is finally computed using the proposed method. The proposed method can be used to compute structural reliability easily whether the limit state function is explicit or implicit. It has been verified by two practical engineering cases that the algorithm is simple, robust, high accuracy and fast computation.

• Korean Journal of Radiology
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• v.19 no.6
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• pp.1147-1160
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• 2018

Soft-tissue calcification refers to a broad category of lesions. Calcifications are frequently identified by radiologists in daily practice. Using a simple algorithm based on the distribution pattern of the lesions and detailed clinical information, these calcified lesions can be systematically evaluated. The distribution pattern of the calcific deposits enables initial division into calcinosis circumscripta and calcinosis universalis. Using laboratory test results (serum calcium and phosphate levels) and clinical history, calcinosis circumscripta can be further categorized into four subtypes: dystrophic, iatrogenic, metastatic, and idiopathic calcification. This pictorial essay presents a systematic approach to the imaging features of soft-tissue calcifications and related diseases.

• Journal of Information Processing Systems
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• v.18 no.4
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• pp.500-509
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• 2022

With the rapid development of educational informatization, teaching methods become diversified characteristics, but a large number of information data restrict the evaluation on teaching subject and object in terms of the effect of English education. Therefore, this study adopts the concept of incremental learning and eigenvalue interval algorithm to improve the weighted decision tree, and builds an English education effect evaluation model based on association rules. According to the results, the average accuracy of information classification of the improved decision tree algorithm is 96.18%, the classification error rate can be as low as 0.02%, and the anti-fitting performance is good. The classification error rate between the improved decision tree algorithm and the original decision tree does not exceed 1%. The proposed educational evaluation method can effectively provide early warning of academic situation analysis, and improve the teachers' professional skills in an accelerated manner and perfect the education system.

• Wind and Structures
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• v.2 no.3
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• pp.189-200
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• 1999

In this paper, a new algorithm for active control design of structures is proposed and investigated. The algorithm preserves the decoupling property of the modal vibration equation and eliminates the spillover problem, which is the main shortcoming in the independent modal space control(IMSC) algorithm. With linear quadratic regulator(LQR) control law, the analytical solution of algebraic Riccati equation and the optimal actuator control force are obtained, and the control design procedure is significantly simplified. A numerical example for the control design of a tall building subjected to wind loads demonstrates the effectiveness of the proposed algorithm in reducing the acceleration and displacement responses of tall buildings under wind actions.