• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.293-304
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• 2007

In this paper, we present a Krylov subspace based projection method for reduced-order modeling of large scale bilinear multi-input multi-output (MIMO) systems. The reduced-order bilinear system is constructed in such a way that it can match a desired number of moments of multi-variable transfer functions corresponding to the kernels of Volterra series representation of the original system. Numerical examples report the effectiveness of this method.

• Research in Mathematical Education
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• v.26 no.3
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• pp.235-252
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• 2023

We investigated the classification of learner groups for students' mathematical modeling competency and analyzed the characteristics in each profile group for each country and variable using PISA 2012 data from six countries. With a perspective on measuring sub-competency, we applied the latent profile analysis method to student achievement for mathematical modeling variables - Formulate, Employ, Interpret. The findings showed the presence of 4-6 profile groups, with the variables exhibiting high and low achievement within each profile group varying by country, and a hierarchical structure was observed in the profile group distribution in all countries, interestingly, the Formulate variable showed the largest difference between high-achieving and low-achieving profile groups. These results have significant implications. Comparison by country, variable, and profile group can provide valuable insights into understanding the various characteristics of students' mathematical modeling competency. The Formulate variable could serve as the most suitable predictor of a student's profile group and the score range of other variables. We suggest further studies to gain more detailed insights into mathematical modeling competency with different cultural contexts.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.79-87
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• 2023

This paper considers some functional identities related to derivations of a ring R and their action on the centre of R/P where P is a prime ideal of R. It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.507-516
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• 2000

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.13.1-13
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• 2003

The Markovian arrival process with marked transitions (MMAP) is useful in modeling input processes of stochastic system with several types. Especially, the MMAP can be used to model the phenomena where the correlation of different types is considered. In this talk we discuss modeling issues for the queue with three types of customers; ordinary customers, negative customers and disasters which are correlated by using MMAP. We also present the recent results and further studies.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1295-1302
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• 2011

We present an analytic model of an unslotted opportunistic spectrum access (OSA) network and evaluate its performance such as interruption probability, service completion time, and throughput of secondary users. Numerical examples are given to show the performance of secondary users in cognitive networks. The developed modeling and analysis method can be used to evaluate the performance of various OSA networks.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.291-303
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• 2024

In this paper, we consider a feedforward network of overloaded multiclass processor sharing queues and we give a fluid model solution under the condition that the system is initially empty. The main theorem of the paper provides sufficient conditions for a fluid model solution to be linear with time. The results are illustrated through examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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• pp.83-106
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• 2016

This paper reviews and compares three different methods for modeling incompressible and immiscible ternary fluid flows: the immersed boundary, level set, and phase-field methods. The immersed boundary method represents the moving interface by tracking the Lagrangian particles. In the level set method, an interface is defined implicitly by using the signed distance function, and its evolution is governed by a transport equation. In the phase-field method, the advective Cahn-Hilliard equation is used as the evolution equation, and its order parameter also implicitly defines an interface. Each method has its merits and demerits. We perform the several simulations under different conditions to examine the merits and demerits of each method. Based on the results, we determine the most suitable method depending on the specific modeling needs of different situations.

• 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.

• Research in Mathematical Education
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• v.11 no.4
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• pp.235-246
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• 2007

The background and the existing problems in teaching of mathematics application were analyzed. Based on the mathematics knowledge which from the simple application, complicate application, and synthetically application to the mathematics modeling, the ability level test questions of mathematics application was worded out to help the teaching and learning in mathematics application.