Table of Content

30 June 2019, Volume 34 Issue 2

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Exponential Decay in a Timoshenko-type System of Thermoelasticity of Type III

QIN Yu-ming , LIU Zi-li

2019, 34(2):  111-125.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.001

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In this work, a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional, we establish the global existence and exponential decay of type-Ⅲ case. 

A Characterization of The Twisted Heisenberg-Virasoro Vertex Operator Algebra

CHENG Jun-fang, CHU Yan-jun

2019, 34(2):  126-137.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.002

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The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one. In this paper, we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra, which is a finite set consisting of two nontrivial elements. Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras. Moreover, associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra, we charaterized twisted Heisenberg-Virasoro vertex operator algebras. This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets. 

The Properties of Expected Scattering and Averaged Scattering and Their Applications to Texture Classication

WANG Juan, ZHAO Jie

2019, 34(2):  138-151.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.003

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In order to further improve the effectiveness of image processing, it is necessary that an efficient invariant representation is stable to deformation applied to images. This motivates the study of image representations defining an Euclidean metric stable to these deformation. This paper mainly focuses on two aspects. On the one hand, in this paper,two properties of expected scattering and averaged scattering, i.e., Lipschitz continuity and translation invariance, are proved in detail. These properties support that excepted scattering and averaged scattering are invariant, stable and informative representations. On the other hand, the issue of texture classification based on expected scattering and averaged scattering has been analyzed respectively in this study. Energy features, which are based on expected scattering and averaged scattering, are calculated and used for classification.Experimental results show that starting with the seventh feature, the two approaches can achieve good performance in texture image classification. 

Dyons of Unit Topological Charges in Gauged Skyrme Model

WU Zhong-lin, LI Dong-ya

2019, 34(2):  152-170.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.004

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Dyons are an important family of topological solitons carrying both electric and magnetic charges and the presence of a nontrivial temporal component of the gauge field essential for the existence of electricity often makes the analysis of the underlying nonlinear equations rather challenging since the governing action functional assumes an indefinite form. In this work, developing a constrained variational technique, We establish an existence theorem for the dyon solitons in a Skyrme model coupled with SO(3)-gauge fields, formulated by Brihaye, Kleihaus, and Tchrakian. These solutions carry unit monopole and Skyrme charges. 

Generalized Schwarzian Derivatives and Analytic Morrey Spaces

JIN Jian-jun, LI Hua-bing, TANG Shu-an

2019, 34(2):  171-187.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.005

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In this paper, we study univalent functions f for which log f’belongs to the analytic Morrey spaces. By using the characterization of higher order derivatives of functions in analytic Morrey spaces, we establish some new descriptions for the analytic Morrey domains in terms of two kinds of generalized Schwarzian derivatives. 

Stability Analysis of Fractional Nonlinear Dynamic Systems With Order Lying in (1,2)

QI Yong-fang, PENG You-hua

2019, 34(2):  188-195.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.006

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One new theorem for Caputo fractional derivative and two new theorems for Caputo fractional order systems, when 1 < a < 2, are proposed in this paper. The results have proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the instability and the stability of many fractional order systems,which can be nonlinear and time varying. 

n-tilting Torsion Classes and n-cotilting Torsion-free Classes

HE Dong-lin, LI Yu-yan

2019, 34(2):  196-203.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.007

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In this paper, we consider some generalizations of tilting torsion classes and cotilting torsion-free classes, give the definition and characterizations of n-tilting torsion classes and n-cotilting torsion-free classes, and study n-tilting preenvelopes and n-cotilting precovers. 

Two Geometric Inequalities in Spherical Space

ZHOU Yong-guo

2019, 34(2):  204-208.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.008

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In this paper, by using the theory and method of distance geometry, we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space. They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space. 

The Hamiltonian Structures and Algebro-geometric Solution of the Generalized Kaup-Newell Soliton Equations

WEI Han-yu, PI Guo-mei

2019, 34(2):  209-220.  doi:10.13371/j.cnki.chin.q.j.m.2019.02.009

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Staring from a new spectral problem, a hierarchy of the generalized Kaup-Newell soliton equations is derived. By employing the trace identity their Hamiltonian structures are also generated. Then, the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations. The Abel-Jacobi coordinates are introduced to straighten the flows, from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.