• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.269-286
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• 2015

In this paper, we extend the concept of the pseudo differential operators in the usual Schwartz's distribution spaces to the one of the generalized pseudo differential operators in the Beurling's generalized distribution spaces. And we shall investigate some properties of the generalized pseudo differential operators including the generalized pseudo local property. Finally, we will study the smoothness and properly supported property of these operators.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.747-761
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• 2017

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1249-1269
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• 2018

This paper provides a method to study the nonnegativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and nonnegative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be nonnegative and we will be able to study its powers. In particular, we have applied this method to Bessel-type operators.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.91-103
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• 2022

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.3
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• pp.15-34
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• 1994

This paper considers the genetic algorithms(GAs) for the mixed model assembly line sequencing(MMALS) in which the objective is to minimize the overall line length. To apply the GAs to the MMALS, the representation, selection, genetic sequencing operators, and genetic parameters are studied. Especially, the existing sequencing binary operators such as partially map crossover(PMX), cycle crossover(CX), and order crossover (OX) are modified to be suitable for the MMALS, and a new sequencing binary operator called immediate successor relationship crossover (ISR) is introduced. These binary operators mentioned above and/or unary operators such as swap, insertion, inversion, displacement, and splice are compared to find operators which work well in the MMALS. Experimental results indicate that 1) among the binary operators ISR operator is the best, followed by the modified OX, and the modified PMX, with the modified CX being the worst, 2) among the unary operators inversion operator is the best, followed by displacement, swap, and insertion, with splice being the worst, and 3) in general, the unary operators perform better than the binary operators for the MMALS.

• Proceedings of the IEEK Conference
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• 2000.11c
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• pp.13-16
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• 2000

This paper is to compare DTCNN(Discrete-time Cellular Neural Networks) applying the fuzzy morphology operators with the conventional FCNN(Fuzzy CNN) using the general morphology operators. These methods are to the image filtering, and are compared as MSE. Also the main goal of this paper is to compare the fuzzy morphology operators with the general morphology operators through image input. In a result of computer simulation, we could know that the error of DTCNN applying the fuzzy morphology operators is less about 6.1809 than FCNN using the general morphology operators in the image included 10% noise, also the error of the former is less about 5.5922 than the latter in the image included 20% noise. And the image of DTCNN applying the fuzzy morphology operators is superior to FCNN using the general morphology operators.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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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 ${\mathbf{Z}}_p$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.281-290
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• 2007

We deal with Bergman functions defined on the half-plane. We study integral operators, and some relationship between Berezin transforms and Toeplitz operators, and also show that some Berezin transforms are Mobius invariant.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.163-174
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• 2001

In this paper we introduce a notion of the $\chi-CLASS$ operators, which is a class including hyponormal operators and consider their spectral properties related to Weyl spectra.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.161-167
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• 2005

In this note we consider the projective property $\sigma(Re(T))\;=\;Re\;(\sigma$(T))$ of p-hyponormal operators and log-hyponormal operators.