• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.2
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• pp.595-609
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• 2020

In this study, we propose a decentralized mathematical model for predictive control of a system of multi-autonomous unmanned aerial vehicles (UAVs), also known as drones. Being decentralized and autonomous implies that all members make their own decisions and fly depending on the dynamic information received from other unmanned aircraft in the area. We consider a variety of realistic characteristics, including time delay and communication locality. For this flocking flight, we do not possess control for central data processing or control over each UAV, as each UAV runs its collision avoidance algorithm by itself. The main contribution of this work is a mathematical model for stable group flight even in adverse weather conditions (e.g., heavy wind, rain, etc.) by adding Gaussian noise. Two of our proposed variance control algorithms are presented in this work. One is based on a simple biological imitation from statistical physical modeling, which mimics animal group behavior; the other is an algorithm for cooperatively tracking an object, which aligns the velocities of neighboring agents corresponding to each other. We demonstrate the stability of the control algorithm and its applicability in autonomous multi-drone systems using numerical simulations.

• Computers and Concrete
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• v.4 no.1
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• pp.1-18
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• 2007

Over the past decades, an enormous amount of effort has been expended in laboratory and field studies on concrete durability estimation. The results of this research are still either widely scattered in the journal literature or mentioned briefly in the standard textbooks. Moreover, the theoretical approaches of deterioration mechanisms with a predictive character are limited to some complicated mathematical models not widespread in practice. A significant step forward could be the development of appropriate software for computer-based estimation of concrete service life, including reliable mathematical models and adequate experimental data. In the present work, the basis for the development of a computer estimation of the concrete service life is presented. After the definition of concrete mix design and structure characteristics, as well as the consideration regarding the environmental conditions where the structure will be found, the concrete service life can be reliably predicted using fundamental mathematical models that simulate the deterioration mechanisms. The prediction is focused on the basic deterioration phenomena of reinforced concrete, such as carbonation and chloride penetration, that initiate the reinforcing bars corrosion. Aspects on concrete strength and the production cost are also considered. Field observations and data collection from existing structures are compared with predictions of service life using the above model. A first attempt to develop a database of service lives of different types of reinforced concrete structure exposed to varying environments is finally included.

• International Journal of Reliability and Applications
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• v.4 no.1
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• pp.1-12
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• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.

• Communications of Mathematical Education
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• v.35 no.1
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• pp.119-136
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• 2021

We performed the research and education programs using engineering tools such as Mathematica, Microsoft Excel and GeoGebra for the students in mathematics mentorship program of the institute of science education for the gifted. We used the engineering tools to solve the problems and found the rules by observing the solutions. Then we generalized the rules to theorems by proving the rules. Mathematica, the professional mathematical computation program, was used to calculate and find the length of the repeating portion of the repeating decimal. Microsoft Excel, the spreadsheet software, was used to investigate the Beatty sequences. Also GeoGebra, the dynamic geometric software, was used to investigate the Voronoi diagram and develop the Voronoi game. Using GeoGebra, we designed the Voronoi game plate for the game. In this program, using engineering tools improved the mathematical creativity and the logical thinking of the gifted students in mathematics mentorship program.

• Journal of Technologic Dentistry
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• v.45 no.1
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• pp.21-29
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• 2023

Purpose: This study attempted to collect basic data to improve the basic repair ability of university freshmen in a world where the usage of advanced medical devices related to computer programs is now common. Methods: The collected data from 280 university freshmen enrolled in nursing, dental, and health degrees or computer and engineering degrees at K university of Gangwon-do were analyzed using the t-test, ANOVA, correlation analysis, and linear regression analysis using the IBM SPSS Statistics ver. 21.0 (IBM). Results: The mathematical learning status and the detailed factors of basic mathematical ability had a positive (+) correlation. The factors of basic mathematical ability, psychology of learning (p<0.001), method of learning (p<0.001), and propensity to learn (p<0.05) were found to be statistically significant, and the model's explanatory power was 40.0%. Conclusion: As a result of this study and considering that advanced medical devices such as computer-aided design/computer-aided manufacturing and three-dimensional printers are becoming more common and up-to-date in clinical settings, it is determined that nursing and dental health students require education to improve their repair skills.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.434-437
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• 1999

The primary aim of this paper is to introduce and illustrate a radial basis function (RBF) modeling approach fur software module characterization, as an alternative to current techniques. The RBF model has been known to provide a rich analytical framework fur a broad class of so-called pattern recognition problems. Especially, it features both nonlinearity and linearity which in general are treated separately by its learning algorithm, leading to offer conceptual and computational advantages. Furthermore, our new modeling methodology fer determining model parameters has a sound mathematical basis and showed very interesting results in terms of model consistency as well as performance.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.133-143
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• 2001

In this paper, we characterize some semi-invariant submanifolds of codimension 3 with almost contact metric structure (${\phi}$, ${\xi}$, g) satisfying 𝔏_ξ∇ = 0 in a nonflat complex space form, where ${\nabla}$ denotes the Riemannian connection induced on the submanifold, and 𝔏_ξ is the operator of the Lie derivative with respect to the structure vector field ${\xi}$.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.85-96
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• 2003

An efficient algorithm for the multiplication in a binary finite filed using a normal basis representation of $F_{2^m}$ is discussed and proposed for software implementation of elliptic curve cryptography. The algorithm is developed by using the storage scheme of sparse matrices.

• The Mathematical Education
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• v.38 no.2
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• pp.189-197
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• 1999

Discrete mathematics allows students to examine and explore unique, special problem situations which were not used to solve problems by paper-and-pencil procedures or applying common formulas. The use and integration of accessible computer-related technologies such as 'Mathematics' or 'Maple' software programs enables students to explore problem situation dramatically. This study shows that it is possible to introduce computer-based discrete mathematics focused on the Leslie matrix model as modeling age-specific population growth to high school students.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.623-643
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• 2016

In this paper, we study piecewise Noetherian (resp., piecewise w-Noetherian) properties in several settings including flat (resp., t-flat) overrings, Nagata rings, integral domains of finite character (resp., w-finite character), pullbacks of a certain type, polynomial rings, and D + XK[X] constructions.