• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.21-38
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• 2006

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권2호
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• pp.107-123
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• 2012

A group of twenty-nine high school student-teachers were given a set of mathematical propositions focusing on shape-to-shape transformations. Their task was to determine through hands-on manipulation and use of dynamic software that each shape be transformed into an area equivalent rectangular region. This paper reports on a classroom-based research.

• 대한수학회논문집
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• 제12권3호
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• pp.743-754
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• 1997

We introduce a class of finite and infinite moving average (MA) sequences of multivariate random vectors exponential marginals. The theory of dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain some probability bounds for the multivariate processes.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제8권3호
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• pp.145-155
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• 2004

Mathematics, by its nature, is a creative activity. Creativity can be developed either through considering its intrinsic beauty or by examining the role that it plays in applications to real world problems. Many of the great mathematicians have been vitally interested in applications and gained inspiration in developing new mathematics from the mathematical descriptions of physical phenomena. In this paper we will examine the processes of applying mathematics by looking at how mathematical models are formed and used. Applications from sport, the environment and populations are used as illustrations.

• 대한수학회보
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• 제53권1호
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• pp.39-48
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• 2016

In this paper we extend Takahashi's fixed point theorem on discrete semigroups to general semi-topological semigroups. Next we define the semi-asymptotic non-expansive action of semi-topological semi-groups to give a partial affirmative answer to an open problem raised by A.T-M. Lau.

• 대한수학회보
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• 제52권5호
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• pp.1649-1660
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• 2015

In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator $T{_{z{^N_1{\bar{z}}^M_2}}$ on the Bergman space $A^2(\mathbb{D}^2)$, where N and M are positive integers.

• 대한수학회보
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• 제48권6호
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• pp.1291-1302
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• 2011

We establish the local well-posedness for the Cauchy problem of the nonlinear Schr$\ddot{o}$odinger equation with harmonic potential in $H^s(\mathbb{R}^n)$, where $s{\in}\mathbb{R}$, s > 0.

• 대한수학회보
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• 제50권6호
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• pp.1841-1846
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• 2013

In this paper we establish some new results on sums of Hilbert space frames and Riesz bases. We also provide a correction to some recently established results in [2].

• 대한수학회보
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• 제54권2호
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• pp.359-373
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• 2017

In this paper, we propose the Stancu type generalization of a kind of modified q-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.

• 대한수학회보
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• 제41권2호
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• pp.359-369
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• 2004

The purpose of this paper is to compare the radicals of a left symmetric algebra considered in 〔1〕 when the associated Lie algebra is nilpotent. In this case, we show that all the radicals considered there are equal. We also consider some other radicals and show they are also equal.