• Title, Summary, Keyword: elementary operators

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SOME PROPERTIES OF TOEPLITZ OPERATORS WITH SYMBOL μ

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.3
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    • pp.471-479
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    • 2010
  • For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

A Load Balancing Problem among Operators in a Nonidentical Parallel Machine Shop Considering Operator Sharing (작업자 공유가 가능한 이기종 병렬기계 작업장에서 작업자 부하균형 문제)

  • 문덕희;김대경
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.22 no.51
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    • pp.41-52
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    • 1999
  • In this paper, a load balancing problem among operators is considered, when one or more machines can be assigned to an operator. The machines are grouped into two types and there are more than one machines in each group. The type of machine in which a job can be processed, is determined. However, an operator can handle both types of machine. The elementary operations of a job are classified into three classes : machine-controlled elements, operator-controlled elements and machine/operator- controlled elements. The objective is to balance the workloads among operators under the constraints of available machine-time and operator-time. A heuristic solution procedure is suggested for allocating jobs to machines and allocating machines to operators. The performance of the algorithm is evaluated with various data set.

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SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS

  • Mejjaoli, Hatem
    • Korean Journal of Mathematics
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    • v.24 no.4
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    • pp.693-722
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    • 2016
  • In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

WEYL@S THEOREMS FOR POSINORMAL OPERATORS

  • DUGGAL BHAGWATI PRASHAD;KUBRUSLY CARLOS
    • Journal of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.529-541
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    • 2005
  • An operator T belonging to the algebra B(H) of bounded linear transformations on a Hilbert H into itself is said to be posinormal if there exists a positive operator $P{\in}B(H)$ such that $TT^*\;=\;T^*PT$. A posinormal operator T is said to be conditionally totally posinormal (resp., totally posinormal), shortened to $T{\in}CTP(resp.,\;T{\in}TP)$, if to each complex number, $\lambda$ there corresponds a positive operator $P_\lambda$ such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P_{\lambda}^{\frac{1}{2}}(T-{\lambda}I)|^{2}$ (resp., if there exists a positive operator P such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P^{\frac{1}{2}}(T-{\lambda}I)|^{2}\;for\;all\;\lambda)$. This paper proves Weyl's theorem type results for TP and CTP operators. If $A\;{\in}\;TP$, if $B^*\;{\in}\;CTP$ is isoloid and if $d_{AB}\;{\in}\;B(B(H))$ denotes either of the elementary operators $\delta_{AB}(X)\;=\;AX\;-\;XB\;and\;\Delta_{AB}(X)\;=\;AXB\;-\;X$, then it is proved that $d_{AB}$ satisfies Weyl's theorem and $d^{\ast}_{AB}\;satisfies\;\alpha-Weyl's$ theorem.

Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments

  • Srivastava, Hari Mohan
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.73-116
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    • 2020
  • The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.

THE EXTENSION OF SOLUTIONS FOR THE CAUCHY PROBLEM IN THE COMPLEX DOMAIN II

  • Lee, Eun-Gu;Kim, Dohan
    • 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].

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Efficiency of Rotational Operators for Geometric Manipulation of Chain Molecules

  • Seok, Chaok;Coutsias, Evangelos A.
    • Bulletin of the Korean Chemical Society
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    • v.28 no.10
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    • pp.1705-1708
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    • 2007
  • Geometric manipulation of molecules is an essential elementary component in computational modeling programs for molecular structure, stability, dynamics, and design. The computational complexity of transformation of internal coordinates to Cartesian coordinates was discussed before.1 The use of rotation matrices was found to be slightly more efficient than that of quaternion although quaternion operators have been widely advertised for rotational operations, especially in molecular dynamics simulations of liquids where the orientation is a dynamical variable.2 The discussion on computational efficiency is extended here to a more general case in which bond angles and sidechain torsion angles are allowed to vary. The algorithm of Thompson3 is derived again in terms of quaternions as well as rotation matrices, and an algorithm with optimal efficiency is described. The algorithm based on rotation matrices is again found to be slightly more efficient than that based on quaternions.

The Stream Environmental Education u-Learning Contents Development for Elementary School Students (초등학생을 위한 실개천 체험 유러닝 콘텐츠 개발)

  • Seo, Woo-Seok;Jyung, Chyul-Young;Lee, Jae-Ho;Kim, Jae-Ho;Lee, Yoon-Jo
    • Hwankyungkyoyuk
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    • v.22 no.4
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    • pp.95-110
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    • 2009
  • The purpose of the study was to develop The Stream Environmental education u-learning contents for elementary school students. For the development of content, the researchers commissioned detailed examination to experts to confirm validity, did a literature review and hosted expert forums. In addition, to enhance accessibility, they asked fairytale writers to develop easier and more valid scenarios and narrations of u-learning contents for elementary school students. The development content is for 18 hours of education and has three sections: i) Preparation, ii) Exploration, and iii) Arrangement. Since the content has been developed based on SCROM, it is expected to have re-usability, accessibility, compatibility and durability. Based on evaluation criteria of u-learning contents suggested in the research methods, the research group commissioned evaluation to ten experts in environmental education of each school level. Recommendations for applying the content developed in this study and further research are as follows: First, the developed content should be actively promoted and provided both online and offline so that elementary school students can fully utilize them. To this end, the website of the Ministry of Environment and u-learning training centers of universities of education should be used. Since content requires interaction not only between learners of the content but also between learners and operators, additional administrative and financial support should be provided. Second, this study focuses on the development of u-learning contents for elementary school students. Further studies are needed to develop content for secondary school students.

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Implementation of the noise eliminating operators of binary image (이진화상 잡음제거 연산자에 관한 연구)

  • Hong, Hee-Kyung;Cho, Dung-Sub
    • Proceedings of the KIEE Conference
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    • pp.636-639
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    • 1988
  • This paper suggests the operation performing the noise elimination of binary image. The image is read by the scanner. And operand is selected according to the size of input image. Through the Dilation and Erosion, elementary vector operation with selected operand, the noise of input image is eliminated.

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