• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.4
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• pp.24-36
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• 2011

In this paper, we verify the channel synthesis and decomposition of polar codes using successive cancellation decoding algorithm over binary discrete memoryless symmetric channel by modifying Arikan's algebraic formular on encoding and decoding of polar codes. In addition, we found that information bits are sent by efficiently consisting of polar codes with their size $2^n$ through polarizing matrix ${G_2}^{{\otimes}n}$ over binary discrete memoryless symmetric channel W. Expecially, if $N{\geq}2$, the complexity of Arikan's encoding and decoding for polar codes is O($Nlog_2N$). Furthermore, we found that polar codes are one of the solution to the challenging problems for the multipoint communication.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1509-1517
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• 1993

The purpose of this study is to develop a program for the automatic derivation of the symbolic equations necessary for the kinematic and dynamic analyses of the spatial mechanism. For this purpose, a symbolic manipulation package called MCSYMA is used. Every symbolic equation is formulated using relative joint coordinate to obtain the numerically efficient system equations. These equations are produced in FORTRAN statements and linked to a FORTRAN program for numerical analysis. Several examples are taken for comparison with the commercial package called DADS which is using Cartesian coordinate approach. Also, this symbolic formulation approach is compared with a conventional numerical approach for an example. The results show that this symbolic approach with relative joint coordinate system is most efficient in computational time among three and is recommended for the derivation of macro elements frequently used.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1384-1390
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• 2001

This paper deals with the forward kinematics of the 6-6 Stewart platform of planar base and moving platform using one extra linear sensor. Based on algebraic elimination method, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretic alone, a correction method is also used in this paper. The overall procedure requires so little computation time that it can be efficiently used for real-time applications. In addition, unlike the iterative scheme e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.4
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• pp.266-273
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• 2019

The efficiency and effectiveness of mission performance can be greatly changed according to the operating conditions such as the number of manned aircraft, flight altitude, and so on, in performing search and reconnaissance missions using a large number of small reconnaissance unmanned aerial vehicles. However, it is not easy to determine which operating conditions are most reasonable. Therefore, in this study, we developed an unmanned airplane flight simulation that can detect and identify the target while avoiding collision according to autonomous flight, suggesting a way to derive operating conditions when operating a large number of unmanned aerial vehicles.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.10
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• pp.153-162
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• 2017

Weapon systems have been developed with high technology electronic equipment due to technology growth. In addition, the capital, operational and maintenance costs of weapon systems have all increased. However, cost of operation and maintenance for weapon systems has been decreased relatively compared to the increased capital cost of weapon systems. Therefore, the defense industry needs to research the life cycle cost of weapon systems that have high operational and maintenance costs. This paper focuses on maintenance equipment for the operation and maintenance of weapon systems. Recently, it seems that the weapon systems that have periodic calibration with maintenance equipment are valid. The equipment requires periodic calibration by the manufacturer to check its own validation. Basically, customers demand high reliability devices from foreign companies that have qualified in the global market. Therefore, the tools need to be calibrated overseas. In other words, weapon systems are not available when the equipment has to be calibrated overseas because the systems require validation with valid maintenance equipment. A purpose of this paper is to compare the loss costs that arise from the calibration of the equipment overseas and the purchasing cost of the tools. Finally, the research shows the number of equipment that customers need to minimize the cost. This research will help to improve the efficiency of operation of weapon systems and solve the problems associated with the need for maintenance overseas.

• Journal of Korean Society of Transportation
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• v.17 no.1
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• pp.105-112
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• 1999

Image Processing Technique has been used as an efficient method to collect traffic information on the road such as vehicle counts, speed, queues, congestion and incidents. Most of the current methods which have been used to detect vehicles by the image processing are based on point processing, dealing with the local gray level of each pixel in the small window. However, these methods have some drawbacks. Firstly, detection is restricted by image quality. Secondly, they can not deal with occlusion and perspective projection problems, In this research, a new method which possibly deals with occlusion and perspective problems will be proposed. It extracts spatial information such as the position, the relationship of vehicles in 3-dimensional space, as well as vehicle detection in the image. The main algorithm used in this research is based on an extension of the Hough Transform. The Hough Transform which is proposed to estimates parameters of vertices and directed edges analytically on the Hough Space, is a valuable method for the 3-dimensional analysis of static scenes, motion detection and the estimation of viewing parameters.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.7
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• pp.607-615
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• 2020

The purpose of this study was to analyze the research status and trends related to the industrial mathematics based on text mining techniques with a sample of 4910 papers collected in the SIAM Journal on Applied Mathematics from 1970 to 2019. The R program was used to collect titles, abstracts, and key words from the papers and to analyze topic modeling techniques based on LDA algorithm. As a result of the coherence score on the collected papers, 20 topics were determined optimally using the Gibbs sampling methods. The main results were as follows. First, studies on industrial mathematics were conducted in a variety of mathematics fields, including computational mathematics, geometry, mathematical modeling, topology, discrete mathematics, probability and statistics, with a focus on analysis and algebra. Second, 5 hot topics (mathematical biology, nonlinear partial differential equation, discrete mathematics, statistics, topology) and 1 cold topic (probability theory) were found based on time series regression analysis. Third, among the fields that were not reflected in the 2015 revised mathematics curriculum, numeral system, matrix, vector in space, and complex numbers were extracted as the contents to be covered in the high school mathematical curriculum. Finally, this study suggested strategies to activate industrial mathematics in Korea, described the study limitations, and proposed directions for future research.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.2D
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• pp.233-239
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• 2006

Most research for until at now link travel time were research for mean link travel time calculate or estimate which uses the average of the individual vehicle. however, the link travel time distribution is divided caused by with the impact factor which is various traffic condition, signal operation condition and the road conditional etc. preceding study result for link travel time distribution characteristic showed that the patterns of going through traffic were divided up to 2 in the link travel times. therefore, it will be more accurate to divide up the link travel time into the one involving delay and the other without delay, rather than using the average link travel time in terms of assessing the traffic situation. this study is it analyzed transit hour distribution characteristic and a cause using examine to the variables which give an effect at link travel time distribute using simulation program and determinate link travel time distribute ratio estimation model. to assess the distribution of the link travel times, this research develops the regression model and the fuzzy model. the variables that have high level of correlations in both estimation models are the rest time of green ball and the delay vehicles. these variables were used to construct the methods in the estimation models. The comparison of the two estimation models-fuzzy and regression model- showed that fuzzy model out-competed the regression model in terms of reliability and applicability.

• Journal of Korean Society of Transportation
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• v.20 no.5
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• pp.113-130
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• 2002

In this paper, we developed DNL(Dynamic Network Loading) model based on Moving cell theory to analyze the dynamic characteristics of traffic flow in congested network. In this paper vehicles entered into link at same interval would construct one cell, and the cells moved according to Cell following rule. In the past researches relating to DNL model a continuous single link is separated into two sections such as running section and queuing section to describe physical queue so that various dynamic states generated in real link are only simplified by running and queuing state. However, the approach has some difficulties in simulating various dynamic flow characteristics. To overcome these problems, we present Moving cell theory which is developed by combining Car following theory and Lagrangian method mainly using for the analysis of air pollutants dispersion. In Moving cell theory platoons are represented by cells and each cell is processed by Cell following theory. This type of simulation model is firstly presented by Cremer et al(1999). However they did not develop merging and diverging model because their model was applied to basic freeway section. Moreover they set the number of vehicles which can be included in one cell in one interval so this formulation cant apply to signalized intersection in urban network. To solve these difficulties we develop new approach using Moving cell theory and simulate traffic flow dynamics continuously by movement and state transition of the cells. The developed model are played on simple network including merging and diverging section and it shows improved abilities to describe flow dynamics comparing past DNL models.