• Proceedings of the SAREK Conference
• /
• 2009.06a
• /
• pp.955-960
• /
• 2009

In order to improve the efficiency of the main transformer in a tilting train, the optimal operation of a cooling system is necessary. Mathematical models of a main transformer cooling system were developed. These include models for the main transformer, the oil pump, the oil cooler, and the blower. The optimal oil temperature algorithm was also developed. This consists of the optimal setpoint algorithm and the control algorithm. A simulation program was developed by using mathematical models and the optimal oil temperature algorithm. Simulation results showed that the dynamic behavior of a main transformer cooling system was predicted well by mathematical models and a main transformer cooling system was controlled effectively by the optimal oil temperature algorithm.

• Journal of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.565-602
• /
• 2024

We study the collective behaviors of two second-order nonlinear consensus models with a bonding force, namely the Kuramoto model and the Cucker-Smale model with inter-particle bonding force. The proposed models contain feedback control terms which induce collision avoidance and emergent consensus dynamics in a suitable framework. Through the cooperative interplays between feedback controls, initial state configuration tends to an ordered configuration asymptotically under suitable frameworks which are formulated in terms of system parameters and initial configurations. For a two-particle system on the real line, we show that the relative state tends to the preassigned value asymptotically, and we also provide several numerical examples to analyze the possible nonlinear dynamics of the proposed models, and compare them with analytical results.

• Korean Journal of Radiology
• /
• v.22 no.7
• /
• pp.1194-1202
• /
• 2021

Objective: To investigate the age-dependent changes in regional cerebral blood flow (CBF) in healthy adults by fitting mathematical models to imaging data. Materials and Methods: In this prospective study, 90 healthy adults underwent pseudo-continuous arterial spin labeling imaging of the brain. Regional CBF values were extracted from the arterial spin labeling images of each subject. Multivariable regression with the Akaike information criterion, link test, and F test (Ramsey's regression equation specification error test) was performed for 7 models in every brain region to determine the best mathematical model for fitting the relationship between CBF and age. Results: Of all 87 brain regions, 68 brain regions were best fitted by cubic models, 9 brain regions were best fitted by quadratic models, and 10 brain regions were best fitted by linear models. In most brain regions (global gray matter and the other 65 brain regions), CBF decreased nonlinearly with aging, and the rate of CBF reduction decreased with aging, gradually approaching 0 after approximately 60. CBF in some regions of the frontal, parietal, and occipital lobes increased nonlinearly with aging before age 30, approximately, and decreased nonlinearly with aging for the rest of life. Conclusion: In adults, the age-related perfusion patterns in most brain regions were best fitted by the cubic models, and age-dependent CBF changes were nonlinear.

• Research in Mathematical Education
• /
• v.15 no.1
• /
• pp.93-104
• /
• 2011

Sixty-four EC-6 teacher candidates were asked to elaborate on the method they used when interrupting seven mathematical pictorial models. The instrument used was research designed but modeled after a 4th grade released state tests. This study was conducted in the southern part of the United States. A panel of experts worked with the researcher to determine the most appropriate initial approach to interrupting the mathematical pictorial model. The pictorial models examined such concepts as measurement, place value and time. Since the questions were on a 4th grade level, it was expected that the teacher candidates would score 100%, however, this was not the case. The results will be given in the paper as each question is discussed. The results of the survey are being used to develop teaching modules for teacher candidates in mathematics methodology classes.

• Journal of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.327-349
• /
• 2021

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.573-581
• /
• 1997

This paper is concerned with the strong consistency of the $L_1$-norm estimators for the nonlinear regression models when dependent variables are subject to censoring, and provides the sufficient conditions which ensure the strong consistency of $L_1$-norm estimators of the censored regression models.

• East Asian mathematical journal
• /
• v.34 no.2
• /
• pp.203-217
• /
• 2018

This study examined preservice elementary teachers' patterns and tendencies in thinking of drawn models of multiplication with fractions. In particular, it investigated preservice elementary teachers' work in a context where they were asked to select among drawn models for symbolic expressions illustrating multiplication with non-whole number fractions including a mixed number. Preservice teachers' interpretations of fraction multiplication used in interpreting different types of drawn models were analysed-both quantitatively and qualitatively. Findings and implications are discussed and further research is suggested.

• International Journal of Computer Science & Network Security
• /
• v.22 no.5
• /
• pp.149-153
• /
• 2022

This study examines the effect of using interactive electronic models to teach mathematical concepts on students' achievement in the linear algebra course at university. The field sample consisted of 200 students divided into two equal groups, an experimental group of 100 students and a control group of 100 students. The researcher used an achievement test in some mathematical concepts related to linear algebra. The results of the study showed that there were statistically significant differences (0.05) between the average achievement scores of the experimental and control groups in the post application of the achievement test, in favor of the experimental group. The size of the influence of the independent factor on the results of the study, which is "interactive electronic forms", on the dependent factor, which is the students' academic achievement in the prepared test, had a very large effect. Also, the results of the study showed that there were statistically significant differences (0.05) between the mean scores of the experimental group in the pre and post applications of the achievement test, in favor of the post application. The researcher recommended the use of interactive electronic models in teaching mathematical concepts at the university level and diversifying the strategies of teaching mathematics, using technology to attract learners and raise their academic achievement.

• Journal for History of Mathematics
• /
• v.25 no.1
• /
• pp.45-56
• /
• 2012

Mathematical biology has been recognized its importance recently and widely studied in the fields of mathematics, biology, medical sciences, and immunology. Mathematical ecology is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats. It was the earliest form of the research field of mathematical biology and has been providing its basis. This article deals with various form of interactions between two biological species in a common habitat. Mathematical models of predator-prey type, competitive type, and simbiotic type are investigated.

• The Mathematical Education
• /
• v.29 no.1
• /
• pp.51-54
• /
• 1990