• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.449-468
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• 2022

In this paper we determine explicitly the kernels 𝕜_α,β associated with new Bergman spaces A²_α,β(𝔻) considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when α ∈ ℕ where the zeros are given by the zeros of a real polynomial Q_α,β. Some numerical results are given throughout the paper.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.395-406
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• 2023

As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(𝜏). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

• The Mathematical Education
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• v.54 no.1
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• pp.31-47
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• 2015

School Math Field Trips(SMFT) for School Mathematics can be defined as teaching and learning activity of mathematics going into the field of Korean history, culture, science and technology. This is a literature analysis study to systemize teaching and learning method of mathematics based on literature analysis and real SMFT activity. First, SMFT was introduced to improve cognitive affective and cultural-mathematical teaching and learning method of mathematics. Second, SMFT has three purposes of cognitive, affective and cultural-mathematical. Third, to conduct mathematical education activity the direction of teaching was set. Forth, the progressing way of developing material and SMFT was researched. Fifth, developing the evaluation standard of SMFT and evaluation method was suggested.

• The Mathematical Education
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• v.47 no.3
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• pp.337-351
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• 2008

The intersection between mathematics and biology is rapidly expanding. The purpose of this paper is to develop college mathematics curriculum to improve the quantitative and mathematical skills of life & biological science students, and to help them better appreciate the importance and utility of mathematics. We deal with 4 questions. We first study how mathematics plays an important role in biological education and the history of biology. Secondly, we do a case study about partnership between mathematics and biology societies not only in university but in highschool of US, specially via Bio2010 and Math & Bio2010. We then investigate a way to enhance new mathematics curriculum as a service in biological science. Finally, we survey university students' basic background in order to determine the level of curriculum. From our investigation, we suggest some points to renew curriculum.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.421-436
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• 1997

In this paper we first give a simple proof of the analytic characterization theorems of the operator symbols by using the characterization theorem for white noise functionals. We next give a criterion for the convergence of operators on white noise functionals in terms of their symbols and then use this result to give a proof for the Fock expansion theorem of operators on white noise functionals.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.145-155
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• 1997

We present a couple of tools that can be used in the solution of nonsymmetric eigenvalue problems. The first one allows us to convert power iterates into Arnoldi's results so that a few eigenpairs are easily obtainable. The other converts Arnoldi's results into power iterates to simulate the power method and improve the result. Suggestions for application are also given.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.981-995
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• 1995

This paper first establishes some conditions for preconditioner under which PGCR does not break down. Next, VPGCR algorithm whose preconditioners can be easily obtained is introduced and then its breakdown and convergence properties are discussed. Lastly, implementation details of VPGCR are described and then numerical results of VPGCR with a certain criterion guaranteeing no breakdown are compared with those of restarted GMRES.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1035-1046
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• 2015

In this work we present some geometric properties (like star-likeness and convexity of order ${\alpha}$ and also close-to-convexity of order ($1+{\alpha}$)/2) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{{\mu},{\upsilon}}(z)$ to belong to the Hardy space $H^p$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.267-285
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• 2014

An upstream scheme based on the pseudostress-velocity mixed formulation is studied to solve convection-dominated Oseen equations. Lagrange multipliers are introduced to treat the trace-free constraint and the lowest order Raviart-Thomas finite element space on rectangular mesh is used. Error analysis for several quantities of interest is given. Particularly, first-order convergence in $L^2$ norm for the velocity is proved. Finally, numerical experiments for various cases are presented to show the efficiency of this method.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1209-1219
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• 2013

In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it's first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br$\ddot{u}$ck conjecture with the idea of sharing functions.