• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권2호
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• pp.133-152
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• 2013

In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.337-343
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• 2006

In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ${\omega}$, the pointwise convergence and the uniform convergence of a sequence of ${\omega}$-bounded exponentially convex functions on S which are also continuous at the identity are equivalent.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.263-276
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• 2013

We discuss the effects of the ${\delta}^2$ and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even H$\ddot{o}$lder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.

• 대한수학회보
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• 제43권4호
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• pp.831-839
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• 2006

By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus ${\beta}(T^d)$ is constructed and studied. The space ${\beta}(T^d)$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from ${\beta}(T^d)$ onto a subspace of Schwartz distributions. The range of the Fourier transform is characterized. A necessary and sufficient condition for a sequence of Boehmians to converge is that the corresponding sequence of Fourier transforms converges in $D'({\mathbb{R}}^d)$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권1호
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• pp.1-15
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• 2016

The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator ${\nabla}_h$ with size h > 0, we verify that for an integer $m{\geq}0$ and a strictly decreasing sequence $h_n$ converging to zero, a continuous function f(x) satisfying $${\nabla}_{h_n}^{m+1}f(kh_n)=0,\text{ for every }n{\geq}1\text{ and }k{\in}{\mathbb{Z}}$$, turns to be a polynomial of degree ${\leq}m$. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.

• 공학논문집
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• 제3권1호
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• pp.65-73
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• 1998

영상복원법 중에는 복원하고자 하는 원 영상의 화소밝기분포가 부분적으로 평탄하다는 가정을 한 부가적인 Gibbs 사전정보를 포함하는 방법이 있다. 이 경우 Gibbs 사전정보를 표현하기 위해 원 영상의 화소밝기를 나타내는 실변수 뿐 아니라 경계를 정의하는 이진변수를 포함하는 에너지 함수를 정의하게 된다. 그러나, 이러한 실변수와 이진변수의 복합형태가 존재할 경우 이들을 동시에 추정하는 것은 매우 어려운 것으로 알려져 있다. 본 연구에서는 deterministic annealing 방법의 응용을 고찰하기로 한다. Deterministic annealing 방법은 다른 방법과 달리 실수 값을 취하는 변수 및 이진변수가 복합형태로 존재하는 문제를 다루는데 있어서 매우 원리적이고 효율적인 방법을 제공한다. 이 방법에서는 복합형태를 취하는 원 함수에 근접하도록 하는 일련의 함수들을 정의하게 되는데, 이때 새로운 일련의 함수들은 실변수만을 취하도록 변환된다. 일련의 함수 중 개개의 함수는 조종파라미터(냉각시 온도에 해당)에 의해 지정된다. 고온에서의 에너지 함수는 저온에서의 에너지와 유사하나 좀더 완만한 형태를 취하게 된다. 따라서, 온도를 서서히 낮추면서 고온에서의 에너지 함수를 저온에서의 에너지 함수로 변환시켜 감으로써 에너지 함수를 최소화하는 작업이 용이해 진다. 이것이 연속방법의 핵심이다. 본 논문에서는 이러한 연속방법을 Bayesian 영상복원 모델에 적용하여 그 성능을 실험을 통해 검증한다.

• 호남수학학술지
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• 제43권3호
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• pp.547-559
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• 2021

We first define the notions of filter continuous, filter sequentially continuous and filter strongly continuous in the framework of fuzzy normed space (FNS), and then we introduce the notion of filter slowly oscillating sequences in the setting of FNS and shows that this notion is stronger than slowly oscillating sequences. Further, we define the concept of filter slowly oscillating continuous functions, filter Cesàro slowly oscillating sequences as well as some other related notions in the aforementioned space and investigate several related results.

• 대한수학회지
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• 제55권1호
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• 대한수학회지
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• 제41권1호
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• pp.231-242
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• 2004

Let $A_b(B_E)$ be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball $B_E$ of a complex Banach space E, and holomorphic in the interior of $B_E$, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for $A_b(B_E)$ in case E belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in [6]. We also prove the non-existence of the Shilov boundary for $A_b(B_E)$ and give some examples of boundaries.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1133-1143
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• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.