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TWO INEQUALITIES INVOLVING HADAMARD PRODUCTS OF POSITIVE SEMI-DEFINITE HERMITIAN MATRICES

  • Cao, Chong-Guang;Yang, Zhong-Peng;Xian Zhang
    • Journal of applied mathematics & informatics
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    • v.10 no.1_2
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    • pp.101-109
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    • 2002
  • We extend two inequalities involving Hadamard Products of Positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods we different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458-463(2000)] and B.-Y Wang et al in [Lin. Alg. Appl. 302-303: 163-172(1999)] .

COMPREHENSIVE ASSESSMENT MODEL OF ECOLOGICAL RIPARIAN ZONE

  • Xia, Ji-Hong;Wu, Wei;Yan, Zhong-Min
    • Water Engineering Research
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    • v.6 no.4
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    • pp.169-178
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    • 2005
  • Comprehensive assessment of ecological riparian zone is to analyze and evaluate the status of riparian zone ecosystem. The existing problem of the ecosystem can be found through the assessment. The AHP-FUZZY method used in the assessment is based on the hierarchy model of index, grade model of object, and attribution degree of index. Accordingly, the four models have been discussed and presented from the aspect of the stability, landscape, eco-health and eco-safety of riparian zone.

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VALUE DISTRIBUTION OF SOME q-DIFFERENCE POLYNOMIALS

  • Xu, Na;Zhong, Chun-Ping
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.29-38
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    • 2016
  • For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN THE WEIGHTED BERGMAN SPACES AND THE WEIGHTED BLOCH SPACES

  • Tong, Ce-Zhong;Zhou, Ze-Hua
    • Journal of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.125-135
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    • 2014
  • We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

GRADED POST-LIE ALGEBRA STRUCTURES, ROTA-BAXTER OPERATORS AND YANG-BAXTER EQUATIONS ON THE W-ALGEBRA W(2, 2)

  • Tang, Xiaomin;Zhong, Yongyue
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1727-1748
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    • 2018
  • In this paper, we characterize the graded post-Lie algebra structures on the W-algebra W(2, 2). Furthermore, as applications, the homogeneous Rota-Baxter operators on W(2, 2) and solutions of the formal classical Yang-Baxter equation on $W(2,2){\ltimes}_{ad^*} W(2,2)^*$ are studied.

NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION

  • FANG ZHONG BO;KWAK, MIN-KYU
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.829-836
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    • 2005
  • In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

NEW CHARACTERIZATIONS OF COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

  • Fang, Zhong-Shan;Zhou, Ze-Hua
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.751-759
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    • 2015
  • In this paper, we give new characterizations of the boundedness and compactness of composition operators $C_{\varphi}$ between Bloch type spaces in the unit ball $\mathbb{B}^n$, in terms of the power of the components of ${\varphi}$, where ${\varphi}$ is a holomorphic self-map of $\mathbb{B}^n$.