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Eigenvalue problem of a class of fourth-order Hamiltonian operators

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Applied Mathematics(A Journal of Chinese Universities) 2013年第1期28卷 101-115页

作者： wang hua huaNG Jun-jie Alatancang College of Sciences Inner Mongolia University of Technology School of Mathematical Sciences Inner Mongolia University

The eigenvalue problem of a class of fourth-order Hamiltonian operators is studied. We first obtain the geometric multiplicity, the algebraic index and the algebraic multiplicity of each eigenvalue of the Hamiltonian operators. Then, some necessary and sufficient conditions for the completeness of the eigen or root vector system of the Hamiltonian operators are given, which is characterized by that of the vector system consisting of the first components of all eigenvectors. Moreover, the results are applied to the plate bending problem.

关键词： Hamiltonian operator eigenvalue multiplicity completeness.

Symmetry of the Point Spectrum of Infinite Dimensional Hamiltonian Operators and Its Applications

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Acta Mathematicae Applicatae Sinica 2012年第1期28卷 149-156页

作者： hua wang Alatancang Jun-jie huaNG School of Mathematical Sciences Inner Mongolia UniversityHohhot 010021China College of Sciences Inner Mongolia University of TechnologyHohhot 010051China

This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.

关键词： infinite dimensional Hamiltonian operator point spectrum symmetry thin plate on elasticfoundation plane elasticity problem harmonic equation

The prediction method of similar cycles

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Research in Astronomy and Astrophysics 2011年第12期11卷 1482-1492页

作者： Zhan-Le Du hua-Ning wang Key Laboratory of Solar Activity National Astronomical Observatories Chinese Academy of Sciences Beijing 100012 China

The concept of degree of similarity （η）, is proposed to quantitatively describe the similarity of a parameter （e.g. the maximum amplitude Rmax） of a solar cycle relative to a referenced one, and the prediction method of similar cycles is further developed. For two parameters, the solar minimum （Rmin） and rising rate （βa）, which can be directly measured a few months after the minimum, a synthesis degree of similarity （ηs） is defined as the weighted-average of the η values around Rmin and βa, with the weights given by the coefficients of determination of Rmax with Rmin and βa, respectively. The monthly values of the whole referenced cycle can be predicted by averaging the corresponding values in the most similar cycles with the weights given by the ηs values. As an application, Cycle 24 is predicted to peak around January 2013 i8 （month） with a size of about Rmax = 84 ± 17 and to end around September 2019.

关键词： Sun: activity -- Sun: general -- sunspots

The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1361-1376页

作者： Xing hua wang Shi Jun YANG Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China College of Mathematics and Information Science Wenzhou University Zheiianq 325200 P R China Department of Mathematics Hangzhou Normal College Hangzhou 310012 P. R. China

In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.

关键词： Iyengar inequality Chebyshev center Best quadrature formula Best interpolation Nikol-skii type estimations

Fuzzy Stability of Quadratic-cubic Functional Equations

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2191-2204页

作者： Zhi hua wang Wan Xiong ZHANG Department of Mathematics Sichuan University Chengdu 610064 P. R. China School of Science Hubei University of Technology Wuhan 430068 P. R. China College of Mathematics and Statistics Chongqing University Chongqing 401331 P. R. China

In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.

关键词： Fuzzy normed space quadratic-cubic functional equation fixed point alternative method Hyers-Ulam-Rassias stability

On Realization of Fusion Rings from Generalized Cartan Matrices

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Acta Mathematica Sinica,English Series 2017年第3期33卷 362-376页

作者： Zhi hua wang Li Bin LI Department of Mathematical Sciences Taizhou University(Jiangsu) School of Mathematical Science Yangzhou University

The Casimir element of a fusion ring （R, B） gives rise to the so called Casimir matrix C of （R,B）. This enables us to construct a generalized Cartan matrix D - C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D - C of finite （resp. affine） type. It turns out that there exists a fusion ring with D - C being of finite （resp. affine） type if and only if D - C has only the form A2 （resp. A1^（1）））. We also realize all fusion rings with D - C being a particular generalized Cartan matrix of indefinite type.

关键词： Fusion ring Casimir matrix generalized Cartan matrix

Extension of Isometries Between the Unit Spheres of Normed Space E and C(Ω)

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1819-1824页

作者： Xi Nian FANG Jian hua wang Department of Applied Mathematics Nanjing Audit University Nanjing 210029 P. R. China Department of Mathematics Anhui Normal University Wuhu 241000 P. R. China

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.

关键词： isometric mapping isometric extension Tingley's problem

The relationships of solar flares with both sunspot and geomagnetic activity

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Research in Astronomy and Astrophysics 2012年第4期12卷 400-410页

作者： Zhan-Le Du hua-Ning wang Key Laboratory of Solar Activity National Astronomical ObservatoriesChinese Academy of SciencesBeijing 100012China

The relationships between solar flare parameters （total importance, time duration, flare index, and flux） and sunspot activity （R z ） as well as those between geomagnetic activity （aa index） and the flare parameters can be well described by an integral response model with the response time scales of about 8 and 13 months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with R z , of aa with the flare parameters, and of aa with R z based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays between the flare parameters with respect to R z , aa to the flare parameters, and aa to R z at their peaks in a solar cycle can be predicted in part by this model （82%, 47%, and 78%, respectively）. These results may be further improved when using a cosine filter with a wider window. It implies that solar flares are related to the accumulation of solar magnetic energy in the past through a time decay factor. The above results may help us to understand the mechanism of solar flares and to improve the prediction of the solar flares.

关键词： Sun: activity -- Sun: sunspots -- Sun: flares -- geomagnetic activity

Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates

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Communications in Theoretical Physics 2009年第12期52卷 1087-1092页

作者： wang hua Alatancang huaNG Jun-Jie School of Mathematical Sciences Inner Mongolia University Hohhot 010021 China Department of Mathematics College of Science Inner Mongolia University of Technology Hohhot 010051 China

The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.

关键词： free vibration of rectangular thin plate double symplectic eigenfunction expansion method upper triangular matrix differential system general solution