• 대한수학교육학회지:학교수학
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• 제18권1호
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• pp.159-173
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• 2016

실제 교육 현장에서는 구체적 맥락에서 추상화하는 과정과 반대로 추상화된 개념을 먼저 가르치고 구체적인 문제 상황을 도입하는 경우도 있다. 즉, 추상적 지식을 구체화 해야 하는 경우가 있는 것이다. Freudenthal은 이런 상황을 반교수학적인 전도라고 표현하며 부정적인 견해를 나타낸 바 있지만 모든 수업상황이 구체적 상황이나 구체물에서 출발하는 추상화로 진행될 수 있는지는 의문의 여지가 있다. 본 연구에서는 구체물을 추상화하여 추상적 개념을 형성하는 과정과 추상적 개념을 구체적인 상황으로 구체화하는 과정에서 나타나는 수학적 사고의 차이점을 비교 분석하여 그 교육적 시사점을 살펴보고자 한다. 이를위해 AiC의 분석틀을 활용하여 구체물의 추상화 과정에서의 수학적 사고를 분석하였고, AiC의 분석틀을 토대로 연구자가 구안한 방식으로 추상적 개념의 구체화 과정에서의 수학적 사고를 분석하였다. 두 과정을 비교 분석한 결과 구체물의 추상화 과정만큼이나 추상적 개념의 구체화 과정에서도 유의미한 수학적 사고를 유도할 수 있음을 확인할 수 있었다.

• 대한수학회지
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• 제42권5호
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• pp.959-973
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• 2005

In this paper, based on large deviation probabilities on Gaussian random vectors, we obtain Strassen's functional LIL for d-dimensional self-similar Gaussian process in Holder norm via estimating large deviation probabilities for d-dimensional self-similar Gaussian process in Holder norm.

• 대한수학회지
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• 제38권3호
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• pp.577-594
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• 2001

In this paper we establish limit theorems on the large and small increments of a two-parameter Gaussian random process on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter Gaussian random process.

• Korean Journal of Mathematics
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• 제27권4호
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• pp.929-947
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• 2019

In the present paper, we investigate the convergence, equivalence of convergence, rate of convergence and data dependence results using a three step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces. Also we give nontrivial examples for the rate of convergence and data dependence results to show effciency of three step iteration process. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.

• 대한수학회지
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• 제35권3호
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• pp.741-753
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• 1998

Let G(*) be a Borel function applied to a stationary long memory sequence {X$_{i}$} of standard Gaussian random variables. Focusing on the process {G(X$_{i}$)}, the present paper establishes the almost sure representation for the empirical quantile process, that is, Bahadur's representation, and for the empirical process with respect to sample mean. Statistical applications of the representations are also addressed.sed.

• 대한수학회논문집
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• 제18권3호
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.

• 대한수학회논문집
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• 제15권1호
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• pp.123-131
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• 2000

Let {X(t) : t $\geq$B 0} be a Symmetric $\alpha$ Stable and H-Self-similar process with stationary increments. We examine a.s. Holder unboundedness of S$\alpha$S H-sssi Chentsov processes and H-sssi Chentsov fields for order ${\gamma}$>H. Finally, we prove a.s. Holder continuity of S$\alpha$S H-sssi processes with ergodic seating transformations for the case of H>1/$\alpha$.

• 대한수학회논문집
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• 제21권4호
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• pp.787-794
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• 2006

Two main results are presented in relation to subordination, self-decomposability and semi-stability. One of the result is that strict semi-stability of subordinand process by selfdecomposable subordinator gives semi-selfdecomposability of the subordinated process. The second result is a sufficient condition for any subordinated process arising from a semi-stable subordinand and a semi-stable subordinator to be semi-selfdecomposable.

• 대한수학회지
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• 제47권6호
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.