• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.105-115
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• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.137-147
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• 2024

In the present paper, we introduce a new class of operators called p-demicompact operators between two lattice normed spaces X and Y. We study the basic properties of this class. Precisely, we give some conditions under which a p-bounded operator be p-demicompact. Also, a sufficient condition is given, under which each p-demicompact operator has a modulus which is p-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.

• East Asian mathematical journal
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• v.10 no.1
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• pp.35-45
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• 1994

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.169-178
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• 2007

We consider the set of $n{\times}n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

• Journal of Navigation and Port Research
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• v.40 no.5
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• pp.249-256
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• 2016

The International Association of Marine Aids to Navigation and Lighthouse Authorities(IALA) model course recommends specific aspects of basic curriculums for Vessel Traffic Services(VTS) operator education such as modules, course hours, contents, etc. Most domestic training programs for newly appointed VTS operators comply with such recommendations. The objective of this study is to determine whether such modules for VTS operator training recommended by the current IALA model course correspond to the actual opinions of VTS operators who are currently working in the field. To this end, the relative importance of basic modules for vessel traffic services operator training was analyzed using the Analytic Hierarchy Process(AHP) method. A questionnaire was designed to include 8 modules recommended by the IALA model course, and the survey results of 52 individuals working at 5 VTS centers were analyzed. The result showed that, unlike the assumption by the IALA, domestic VTS operators viewed Nautical Knowledge as the most important modules, followed by Emergency Situations, Traffic Management, Language, Equipment, VHF Radio, Communication Co-ordination, and Personal Attributes, in that order.

• Language and Information
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• v.1
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• pp.137-179
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• 1997

This paper discusses several basic issues of the 'focus' phenomenon. One of them is the issue of the nature of focus, i.e., what constituent of the sentences gets focused. Another is the issue of to what aspect of meaning the focus contributes. The other is the issue of the functions of focus-sensitive operators. As for the first issue, it is observed that the basic function of focus is to mark all and only the new information of the sentence. But for the cases in which this principle is not observed, it is proposed that the focus in these cases in general plays a secondary function of triggering an additional emphatic scalar meaning. And yet, in these cases, the state of the matter is different between free focus and bound focus. It is also shown that contrary to the general belief that free focus contributes to the meaning semantically. Concerning focus-sensitive operators, we classify them into two groups, i.e., quantificational and scalar operators, and try to formalize their meaning in the framework of Pulman's(1997) 'higher order unification theory'.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.573-597
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• 2005

A continuous linear operator T, on the space of entire functions in d variables, is PDE-preserving for a given set $\mathbb{P}\;\subseteq\;\mathbb{C}|\xi_{1},\ldots,\xi_{d}|$ of polynomials if it maps every kernel-set ker P(D), $P\;{\in}\;\mathbb{P}$, invariantly. It is clear that the set $\mathbb{O}({\mathbb{P}})$ of PDE-preserving operators for $\mathbb{P}$ forms an algebra under composition. We study and link properties and structures on the operator side $\mathbb{O}({\mathbb{P}})$ versus the corresponding family $\mathbb{P}$ of polynomials. For our purposes, we introduce notions such as the PDE-preserving hull and basic sets for a given set $\mathbb{P}$ which, roughly, is the largest, respectively a minimal, collection of polynomials that generate all the PDE-preserving operators for $\mathbb{P}$. We also describe PDE-preserving operators via a kernel theorem. We apply Hilbert's Nullstellensatz.

• East Asian mathematical journal
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• v.26 no.1
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• pp.95-103
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• 2010

In this paper using Lipschitz continuity of the resolvent operator associated with general H-maximal m-relaxed $\eta$-monotone operators, existence and uniqueness of the solution of a variational inclusion system is proved. Also, an iterative algorithm and its convergence analysis is given.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.743-756
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• 2022

We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.75-89
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• 2022

In this paper, we prove new fixed point theorems for single-valued and multi-valued weakly Picard operators in complete metric spaces and give several examples. As applications, we give several results to Fredholm integral equation.