• Honam Mathematical Journal
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• v.26 no.3
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• pp.341-353
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• 2004

We denote by ${{\mathcal{Q}}(A)}$ the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set ${\mathcal{S}}$ of sign patterns such that the set of sign patterns of vectors in the null-space of ${\tilde{A}}$ is ${\mathcal{S}}$, for each ${\tilde{A}}{\in}{{\mathcal{Q}}(A)}$. Some properties of matrices with signed null-spaces are investigated.

• School Mathematics
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• v.4 no.2
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• pp.297-316
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• 2002

In this paper, a teaching unit on series of number sentences with patterns is designed according to Wittmann's perspectives. In this paper, series of number sentences wish patterns means number sentences in which some patterns are contained. especially, seven kinds of number sentences wish patterns are offered as basic materials, and fifteen tasks based on these basic materials are offered. These tasks are for ninth grade students and higher grade students. These tasks heap students to recognize patterns, and to understand mechanism underlying in those patterns by looking for patterns and proving whether these patterns are generally hold. As working on these tasks, students can reinforce meaning of algebraic expression, its manipulation, and concept of number series. Students also can reinforce mathematical thinking such as analogical thinking, deductive thinking, etc. In this point, this teaching unit reveal important objectives, contents, and Principles of mathematics education. This teaching unit can also be rich sources for student's activities. Especially, for each task's level is different, each student's personal ability is considered fully. Since teachers can know mathematical facet, psychological facet, and didactical facet holistically, this teaching unit can offer broad possibilities for experimental studies. SD, this leaching unit can be said to be substantial. In this paper, this leaching unit is not applied in classroom directly. Actually such applying in classroom is suggested as follow-up studies. By appling this teaching unit in various classroom, some effective informations for teaching this teaching unit and some particular phenomenons in those teaching processes can be identified, and this teaching unit can be revised to be better one.

• East Asian mathematical journal
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• v.27 no.1
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• pp.83-89
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• 2011

We denote by $\mathcal{Q}(A)$ the set of all matrices with the same sign pattern as A. A matrix A has signed -space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the -space of e $\tilde{A}$ is S, for each e $\tilde{A}{\in}\mathcal{Q}(A)$. In this paper, we show that the number of sign patterns of elements in the row space of $\mathcal{S}^*$-matrix is $3^{m+1}-2^{m+2}+2$. Also the number of sign patterns of vectors in the -space of a totally L-matrix is obtained.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.305-318
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• 2019

A sign pattern is a matrix whose entries belong to the set {+, -, 0}. An n-by-n sign pattern ${\mathcal{A}}$ is said to allow an eventually positive matrix or be potentially eventually positive if there exist at least one real matrix A with the same sign pattern as ${\mathcal{A}}$ and a positive integer $k_0$ such that $A^k>0$ for all $k{\geq}k_0$. Identifying the necessary and sufficient conditions for an n-by-n sign pattern to be potentially eventually positive, and classifying the n-by-n sign patterns that allow an eventually positive matrix are two open problems. In this article, we focus on the potential eventual positivity of broom sign patterns. We identify all the minimal potentially eventually positive broom sign patterns. Consequently, we classify all the potentially eventually positive broom sign patterns.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• Research in Mathematical Education
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• v.26 no.3
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• pp.147-166
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• 2023

Mathematics is a science of pattern. Mathematics is a subject of inquiring which aims at discovering the models hidden behind the world. Pattern is abstraction and generalization of the model. Mathematical pattern is a higher level of mathematical model. Mathematics patterns are often hidden in pattern similarity. Creation of mathematics lies largely in discovering the pattern similarity among the various components of mathematics. Inquiring is the core and soul of mathematics teaching. It is very important for students to study mathematics like mathematicians' exploring and discovering mathematics based on pattern similarity. The author describes an example about how to guide students to carry out mathematics inquiring based on pattern similarity in classroom.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1113-1122
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• 2015

This paper is concerned with the pattern formation of a diffusive predator-prey model with two time delays. Based upon an analysis of Hopf bifurcation, we demonstrate that time delays can induce spatial patterns under some conditions. Moreover, by use of a series of numerical simulations, we show that the type of spatial patterns is the spiral wave. Finally, we demonstrate that the spiral wave is asymptotically stable.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.561-573
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• 1995

A matrix whose entries consist of the symbols +, - and 0 is called a sign pattern matrix. In [1], a graph theoretic characterization of sign idempotent pattern matrices was given. A question was given for the sign patterns which allow idempotence. We characterized the sign patterns which allow idempotence in the sign idempotent pattern matrices.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.659-670
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• 2008

We denote by $\mathcal{Q}$(A) the set of all real matrices with the same sign pattern as a real matrix A. A matrix A is an SN-matrix provided there exists a set S of sign pattern such that the set of sign patterns of vectors in the -space of $\tilde{A}$ is S, for each ${\tilde{A}}{\in}\mathcal{Q}(A)$. Some properties of SN-matrices arc investigated.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.615-624
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• 2014

We study special types of matrices. The involutary fuzzy matrices are important in various applications and have many interesting properties. Using the graphical method, we have the zero patterns of involutary fuzzy matrix, that is, involutary Boolean matrices. And we give the construction of all involutary fuzzy matrices for some dimensions and suggest the canonical form of involutary fuzzy matrix.