• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.779-791
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• 2016

Transfer of homological properties under base change is a classical field of study. Let $R{\rightarrow}S$ be a ring homomorphism. The relations of Gorenstein projective (or Gorenstein injective) dimensions of unbounded complexes between $U{\otimes}^L_RX$(or $RHom_R(X,U)$) and X are considered, where X is an R-complex and U is an S-complex. In addition, some sufficient conditions are given under which the equalities $G-dim_S(U{\otimes}^L_RX)=G-dim_RX+pd_SU$ and $Gid_S(RHom_R(X,U))=G-dim_RX+id_SU$ hold.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1291-1302
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• 2012

In this paper, we introduce a new elliptic PDE: $$\{{\nabla}{\cdot}\(\frac{|{\gamma}^{\omega}(r)|^2}{\sigma}{\nabla}v_{\omega}(r)\)=0,\;r{\in}{\Omega},\\v_{\omega}(r)=f(r),\;r{\in}{\partial}{\Omega},$$ where ${\gamma}^{\omega}={\sigma}+i{\omega}{\epsilon}$ is the admittivity distribution of the conducting material ${\Omega}$ and it is shown that the introduced elliptic PDE can replace the standard elliptic PDE with conductivity coefficient in EIT imaging. Indeed, letting $v_0$ be the solution to the standard elliptic PDE with conductivity coefficient, the solution $v_{\omega}$ is quite close to the solution $v_0$ and can show spectroscopic properties of the conducting object ${\Omega}$ unlike $v_0$. In particular, the potential $v_{\omega}$ can be used in detecting a thin low-conducting anomaly located in ${\Omega}$ since the spectroscopic change of the Neumann data of $v_{\omega}$ is inversely proportional to thickness of the thin anomaly.

• East Asian mathematical journal
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• v.36 no.1
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• pp.81-90
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• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• East Asian mathematical journal
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• v.34 no.2
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• pp.155-176
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• 2018

The purpose of this article is to study the change of mathematics teaching efficacy of pre-service mathematics teachers in teaching practice course. For this purpose we collect data through questionnaire from 61 pre-service mathematics teachers. To make a questionnaire we rearrange Ryang's MTES items. The pre-service mathematics teachers fill out the questionnaire before and after teaching practice course. The data are analyzed by paired t-test using SPSS23. The result of paired t-test show that the difference between pre-test scores and post-test scores is significant statistically. So we can conclude that the mathematics teaching efficacy of pre-service mathematics teachers is changed and improved after teaching practice course.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.584-589
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• 1994

A time-varying nonlinear mathematical model was derived to consider the effect of change in roll radius on tension varation during winding and unwinding. A variable-gain PID controller was designed for tension control at start and stop in a multi-span continuous process system. The controller gains are updated at every control loop as roll radii continuously change. Computer simulation was carried out by using the mathematical model and the controller developed for a typical operating condition including acceleration and deceleration. When the variable-gain PID controller was used, the tension control performance was improved compared with that of existing control method during start-up and stop.

• Research in Mathematical Education
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• v.3 no.1
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• pp.1-8
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• 1999

The present study extends previous research in this area by investigating perceptions of change and reactions to reform efforts by pre-service and practicing secondary school mathematics teachers in the People's Republic of China (PRC) and the United States of America. Interviews were used to gather data about school experiences, teaching practices, and planned changes in mathematics programs. Analysis of the interview data supported earlier findings with respect to the well-planned nature of lessons by PRC teachers and the influence of mathematics contents and examination systems in the PRC. Findings also indicated a general agreement among teachers from both countries favoring less lecturing and more discussion and interactive activities. There were contrasts by nationality in descriptions of future teaching, ideal lessons, sources of teaching ideas, and preferences about school mathematics programs.

• Research in Mathematical Education
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• v.18 no.1
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• pp.41-54
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• 2014

This study investigated the visual-mental capability of pre-service and in-service mathematics teachers as well as academicians making a career change to mathematics teachers with regard to manipulations of two geometric shapes (from 2- to 3-dimensional). Moreover, it investigated whether there are differences between the visual-mental capability of these participant groups. Findings illustrate that most of the participants demonstrate an adequate visual capability relating to the task dealing with a cube. Conversely, very low percentage of participants manifested a visual-mental capability in a task requiring the identification of a solid resulting from rotation of a square page, whose diagonal serves as the rotation axis. The study indicates that learners' high visual view should be developed in order to enhance their visual-mental capability.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.33-46
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• 2007

In this Paper the change of trends over historical research of mathematics, that has been developed since 1970, is inquired. Most of all it deals with the controversy concerning so-called 'geometrical algebra'. It covers the contents of Euclid' work II. And the relation of the controversy with the change of direction over historical research of mathematics is examined.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.325-332
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• 1998

The use of air-supported membrane has considerable attention in recent years. There are, however, a number of problems in the behavior of these structures that have not been fully investigated. For example, the problem of local loafing on such membranes has not been analyzed yet. The paper presents an analysis of internal and external potential energy of a spherical air-supported membrane with vertical longitudinal axis, subjected to local loadings. An internal pressure value of the applied load is established at which tile potential of these structures change positive. During such change the loading portion of the membrane comes into work beyond stable state. The mathematical method is used throughout the paper in obtaining solution. For the mathematical modeling, two assumption are used. One is the theta's elimination and the other is the infinite condition. The paper is illustrating the examples of spherical air membrane dome subjected to local load.