The nonlinear Wannier function in square Kronig-Penney model

The nonlinear Wannier functions in square Krnig-Penney potential are investigated with the help of a set of exact nonlinear Bloch solutions. The nonlinear interaction makes the Wannier functions fall off as non-exponential law with distance and enhances the tunneling coupling between the neighbor sites.     

《红楼梦》前80回与后40回某些文风差异的统计分析\,(两个独立二项总体等价性检验的一个应用)

本文以数据分析为基础,应用统计学中``两总体等价性检验'的理论和方法,提供了一个强有力的证据:《红楼梦》前80回与后40回在某些重要的情景描写上确实存在非常显著的差异,这一结论的可信概率不低于98\%.     

因子分析模型的改进与应用

本文针对迄今国际国内最流行的因子分析模型(正交因子模型)的缺点,提出了改进的因子分析模型L,论证了标准化主成分及其载荷阵和它们的旋转提供了因子分析模型L在某种最优意义上的精确解,并对因子分析模型L的应用步骤及注意事项进行了论述,还指出了一些待解决的问题。     

Unitary quasi-affine transforms of contractions

The unitary quasi-affine transforms of contractions are the cornerstone of the exact theory of irreversibility introduced by Misra, Prigogine and Courbage. This work shows that the class of contractions with unitary quasi-affine transforms is just C⋅1 and that every unitary quasi-affine transform of a contraction is unitarily equivalent to the residual part of its Sz.-Nagy-Foia? dilation. Some connections with the Grossmann theory of nested Hilbert spaces and generalized eigenvalues are established. These results are applied to the study of the baker map.     

Exact solutions of accelerated flows for a Burgers’ fluid II. The cases γ = λ2/4 and γ > λ2/4

The purpose of this study is to provide the exact analytic solutions of accelerated flows for a Burgers’ fluid when the relaxation times satisfy the conditions γ = λ²/4 and γ > λ²/4. The velocity field and the adequate tangential stress that is induced by the flow due to constantly accelerating plate and flow due to variable accelerating plate are determined by means of Laplace transform. All the solutions that have been obtained are presented in the form of simple or multiple integrals in terms of Bessel functions. A comparison between Burgers’ and Newtonian fluids for the velocity and the shear stress is also made through several graphs.     

Constructive approximation of solution for fourth‐order nonlinear boundary value problems

In this paper, we obtain a sequence of approximate solution converging uniformly to the exact solution of a class of fourth‐order nonlinear boundary value problems. Its exact solution is represented in the form of series in the reproducing kernel space. The n‐term approximation u_n(x) is proved to converge to the exact solution u(x). Moreover, the derivatives of u_n(x) are also convergent to the derivatives of u(x). Copyright © 2008 John Wiley & Sons, Ltd.     

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

We consider first order quasilinear hyperbolic systems with vertical characteristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on the equations corresponding to zero eigenvalues. In this paper, we will establish the exact controllability only by means of physically meaningfnl internal controls applied to the equations corresponding to non-zero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.     

Geometrically exact curved beam element using internal force field defined in deformed configuration

This paper presents a study on the development of high-performance finite elements for geometrically nonlinear analysis of frame structures with curved members. Based on the geometrically exact beam theory, a highly efficient and accurate mixed finite element is developed. A new approach is proposed for constructing the independent internal force field by including major terms satisfying equilibrium conditions in the deformed configuration. An element-level equilibrium iteration procedure is employed for the condensation of element internal degrees of freedom during the nonlinear solution. Numerical results are presented to demonstrate the excellent performance of the element developed, and it is shown that even when each structural member is modelled with just one element, accurate solutions can still be achieved.     

Smooth and Peaked Solitary Wave Solutions of the Broer-Kaup System Using the Approach of Dynamical System

The bifurcations of traveling wave solutions of the Broer-Kaup system are investigated and all possible exact parametric representations of the smooth and peaked solitary waves are presented.     

Analytical study of the two-dimensional time-fractional Navier-Stokes equations

In this paper, the two-dimensional (2D) Holf-Cole transformation with mass conservation in the frame of conformable derivative is developed, and then by introducing some exact solutions that satisfy linear differential equations and using the symbolic computation method, four exact solutions of 2D-nonlinear Navier-Stokes equations (NSEs) with the conformable time-fractional derivative are established. Some physical properties of the exact solutions are described preliminarily. Our results are the first ones on analytical study for the 2D time-fractional NSEs.