• East Asian mathematical journal
• /
• v.23 no.3
• /
• pp.271-302
• /
• 2007

The purpose of this study is to study how effective teachers' self reflectiveness are on enhancing mathematics teaching activities. Researcher is the object of the study and relating preceding researches, establish some instruments for study. This research was examined for six times from fifth week of March to second week of May. In order to accomplish this study, one class of the first grade of high school in Ulsan was selected. In order to define the changes of teaching activity, the first lecture was practiced without analyzing or reflective activity. From the second lecture, analyze and reflect own teaching activity with recording. After finishing all lecture, distribute the recordings to observers and other teachers and then, get measured. Based on the results, self reflective teaching makes great effects on enhancing teachers' teaching activities. Through teachers' own reflective teaching, they can know their advantages and disadvantages, repeatable was of speaking, and the acknowledgement of objectives. And, finally, they can enhance their teaching activity by reflective teaching.

• East Asian mathematical journal
• /
• v.32 no.5
• /
• pp.659-675
• /
• 2016

In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history $$\large u_{tt}-M(x,t,{\tau},\;{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\\hspace{25}-{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{-{\infty}}}^t}\;k(t-{\tau}){\Delta}u(x,t)d{\tau}+{\mid}u{\mid}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

• East Asian mathematical journal
• /
• v.17 no.2
• /
• pp.367-374
• /
• 2001

Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[x]-module. Park generalized Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^S]$-module, where S is a submonoid of $\mathbb{N}$($\mathbb{N}$ is the set of all natural numbers). In this paper we extend the injective property to the Laurent power series module so that if R is a ring and E is an injective left R-module, then $E[[x^{-1},x]]$ is an injective left $R[x^S]$-module.

• East Asian mathematical journal
• /
• v.28 no.1
• /
• pp.63-71
• /
• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• East Asian mathematical journal
• /
• v.28 no.1
• /
• pp.25-36
• /
• 2012

We introduced a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$-metric $L({\alpha},{\beta})={\beta}\sum\limits_{k=0}^r\(\frac{\alpha}{\beta}\)^k$, where ${\alpha}<{\beta}$ and investigated it with respect to Berwald space ([12]) and Douglas space ([13]). The present paper is devoted to finding the condition that is projectively at on a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$)-metric above.

• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.9-23
• /
• 2010

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.

• East Asian mathematical journal
• /
• v.26 no.5
• /
• pp.627-639
• /
• 2010

In this paper, we introduce a new iterative sequence finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly-monotone mapping, the fixed point problem and the classical variational inequality problem. Our results improve and extend the corresponding results announced by many others.

• East Asian mathematical journal
• /
• v.23 no.2
• /
• pp.175-195
• /
• 2007

The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application, these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.

• East Asian mathematical journal
• /
• v.36 no.2
• /
• pp.273-289
• /
• 2020

This study introduces the process and results of developing an adaptive math learning program for self-directed learning. It presented the process and results of developing an adaptive math learning program that takes into account the level of learners using artificial intelligence. We wanted to get some suggestions on developing programs for artificial intelligence-based mathematics. The program was developed as Math4U, an application based on smart devices in the "character and expression" area for 7th grade. The Application Math4U may be used differently depending on its purpose. It is also expected to be a useful tool for providing self-directed learning to students as the basis for educational research using smart devices in a changing educational environment.

• East Asian mathematical journal
• /
• v.36 no.2
• /
• pp.147-172
• /
• 2020

The purpose of this study is to provide to understand correctly for teachers and pre-service teachers who have the wrong conception of mathematical modeling. We present the differences modeling problems and general application problems to identify between general application and modeling problems. We propose the entire process from modeling tasks development to solve the problems of mathematical modeling. Additionally, the entire process of the possible solutions was concluded for the presented modeling problems. We proposed what students and teachers should perform at each stage of each phase of the modeling cycle. The concrete tasks were suggested for teachers and students at each phase of modeling cycles, with the specific role of the teacher in the overall process for students' modeling activities.