• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.291-304
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• 2005

We introduce a concept of Cauchy complete Csaszar frames and construct Cauchy completions of Csaszar frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.173-182
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• 2007

In this paper, we prove the Cauchy-Rassias stability of derivations on quasi-Banach algebras associated to the Cauchy functional equation and the Jensen functional equation. We use the Cauchy-Rassias inequality that was first introduced by Th. M. Rassias in the paper "On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300".

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1427-1437
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• 2016

Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. D. S. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. T. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function $e^t$. Recently J. Jeong, S. H. Rim and B. M. Kim studied on finite times degenerate Cauchy numbers and polynomials. In this paper we consider finite times degenerate higher-order Cauchy numbers and polynomials, and give some identities and properties of these polynomials.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.29-34
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• 1993

J. Leray [7] proposed a sufficient condition ofr the solvability of the Cauchy problem on the initial hyperplane x$_{1}$=0 with Cauchy data which are holomorphic with respect to the variables parallel to some analytic subvariety S of the initial hyperplane. Limiting the problem to the case of operators with constant coefficients, A. Kaneko [2] proposed a new sharper sufficient condition. Later we generalized this condition and showed that it is necessary and sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data and the distribution Cauchy data which contain variables parallel to S as holomorphic parameters in [5, 6]. In this paper, we extend the results in [6] to the case of operators with variable coefficients and show that it is sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data. Our main theorem can be considered as an example of a deep theorem on micro-hyperbolic systems by Kashiwara-Schapira [4] and we give a direct proof based on an elementary sweeping out procedure developed in Kaneko [3].

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.1-16
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• 2005

This paper presents a fast factorization algorithm for confluent Cauchy-like matrices. The algorithm consists of two parts. First. a confluent Cauchy-like matrix is transformed into a Cauchy-like matrix available to pivot without changing its structure. Second. a fast partial pivoting factorization algorithm for the Cauchy-like matrix is presented. A new displacement structure cannot possibly generate all entries of a transformed matrix, which is called by 'partially reconstructible'. This paper also discusses how the proposed factorization algorithm can be generally applied to partially reconstructive matrices.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.481-493
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• 2007

This paper deals with, by employing the relation between Cauchy representation and the Fourier transform and properties of the former in $L_1$-space, the investigation of the Cauchy representation of integrable Boehmians as a natural extension of tempered distributions, we have investigated Cauchy representation of tempered Boehmians. An inversion formula is also proved.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.621-629
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• 2021

The idea of C^*-algebra valued metric spaces was given by Ma, Jiang and Sun. In this paper we have studied the ideas of I-Cauchy and I^*-Cauchy sequences and their properties in such spaces and also we give the idea of C^*-algebra valued normed spaces.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.929-937
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• 2019

The main purpose of this paper is to establish $H{\ddot{o}}lder$ estimates for the Cauchy transform in a class of finite/infinite type convex domains in $\mathbb{C}^2$.

• East Asian mathematical journal
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• v.14 no.1
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• pp.141-148
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• 1998

• The KIPS Transactions:PartB
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• v.8B no.3
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• pp.237-242
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• 2001

고전적인 GLA 알고리즘과 마찬가지로 Kohonen 학습법은 경도 강하법으로 오차함수의 해에 접근해 나간다. 따라서 KLA의 이러한 문제를 극복하기 위해 모의 담금질법의 일종인 Cauchy 학습법을 응용을 제안한다. 그러나 이 방법은 학습시간이 느리다고 하는 단점이 있다. 본 논문 이 점을 개선시키기 위해 Cauchy 학습법과 Kohonen 학습법을 순차 결합시킨 또 다른 학습법을 제안한다. 그 결과 코시 학습법과 마찬가지로 국부최적 문제를 극복하면서도 삭습시간을 단축할 수 있었다.