Exponential Stabilization of Euler-Bernoulli Beam with Input Time-Delay in the Boundary Control

The boundary control problem of a cantilever Euler-Bernoulli beam with input time delay is considered.In order to exponentially stabilize the system, a feedback controller is adopted.And we study the well-posedness and exponential stability of the closed-loop system.The approach used in this paper is done by several steps.Firstly, the well-posedness of this system is proved by semi-group theory.Secondly, the asymptotical expression of eigenvalue is investigated by spectral analysis.Thirdly, the exponential stability of the system is studied by multiplier technology.Finally, numerical simulations on the dynamical behavior of the system are given to support the results obtained.

A NON-TRIVIAL PRODUCT OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s ＋ 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s＋2ho（hmbn-1 -hnbm-1） ∈ ExtA^s＋6,t＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 7, n ≥ m ＋ 2 ≥ 5, q = 2（p- 1）, 0 ≤ s 〈 p - 2, t= （s ＋ 2 ＋ （s ＋ 2）p ＋ p^m ＋ p^n）q. The advantage of this method is to extend the range of s without much complicated argument as in [1].

EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p > 1) SPACES

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp（Γ） and lp（△）（p 〉1）. We first derive the representation of isometries between the unit spheres of complex Banach spaces lp（Γ） and lp（△）. Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp（Γ）and lp（△） can be extended to be a linear isometry on the whole space.

ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE

In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.

Effects of mushroom waste on improvement of reclaimed soil qualityin coal mining areas

Restoring soil quality is the main evaluation norm of the reclamation. In order to reveal the effects of mushroom waste on the quality improvement of reclaimed soil in coal mining areas, the physical, chemical and microbial characteristics of soil are studied. The results show clear improvement in the soil after using mushroom waste. Because of human cultivation and fertilization, cultivated soil after reclamation exhibits high comprehensive quality and the index of quality of surface soil reaches 0.64 and 0.73. The average index of surface soil quality is as high as 0.52 and 0.54. In comparison, the quality of reclaimed soil of forest land is low, with average index of 0.40. The effects of mushroom waste are mainly on the surface soil in the first 2 years after the application. After that period, with the decomposition of mushroom waste, soil quality index tends to be the same as the original soil. The quality of surface soil is higher than that of subsoil, especially after the application of mushroom waste, at which point the soil quality reaches a peak at about 15 cm. Cultivated soil after reclamation has great variance in quality, after the coefficient of 24.74%. Mushroom waste can reduce such variation, particularly with long-term use. The variance efficient falls to 3.59% after 3-year application.

Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean and fluc- tuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in the frequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance axe demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.

GLOBAL SOLUTIONS OF SYSTEMS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite. number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.

Analysis of Linear Triangular Elements for Convection-diffusion Problems by Streamline Diffusion Finite Element Methods

This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error estimate was obtained in L^2-norm. In the present paper, however, the same error estimate result is gained under the weaker condition that ε≤h.

Dynamics Evolution Investigation of Mack Mode Instability in a Hypersonic Boundary Layer by Bicoherence Spectrum Analysis

The instability of a hypersonic boundary layer on a cone is investigated by bicoherence spectrum analysis.The experiment is conducted at Mach number 6 in a hypersonic wind tunnel.The time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface along streamwise direction to investigate the development of the unstable disturbances.The bicoherence spectrum analysis based on wavelet transform is employed to investigate the nonlinear interactions of the instability of Mack modes in hypersonic laminar boundary layer transition.The results show that wavelet bicoherence is a powerful tool in studying the unstable mode nonlinear interaction of hypersonic laminar-turbulent transition.The first mode instability gives rise to frequency shifts to higher unstable modes at the early stage of hypersonic laminar-turbulent transition.The modulations subsequently lead to the second mode instability occurrence.The second mode instability governs the last stage of instability and final breakdown to turbulence with multi-scale disturbances growth.

GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR ACLASS OF NONLINEAR EVOLUTION EQUATIONSOF DISPERSIVE TYPE

The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.

On the Existence of Suprema of Infinite Many Elements in a Riesz Space

Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E for every x_i∈E (i∈I).

Riemann Boundary Value Problems on the Curve of Parabola

In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on the Curve of Parabola at infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Curve of Parabola as their jump curve and obtain the explicit form.

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical group L1, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L1, if so, the solution is given explicitly.

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space.The disjoint supercyclic properties of weighted translations on locally compact discrete groups,the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space ?~2(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.

Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.

COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

Let U^n be the unit polydisc of C^n and φ（φ,…,φ） a holomorphic selfmap of U^n. This paper shows that the composition operator Cφinduced by φis bounded on the little Bloch space β0＊（U^n） if and only if φ ∈β0＊（U^n） for every ι=1,2,... ,n, and also gives a sufficient and necessary condition for the composition operator Cφto be compact on the little Bloch space β0＊ （U^n）.

Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra

Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.

A Finite Volume Backward Euler Difference Method for Nonlinear Parabolic Integral-differential Equation

The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.