Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure

In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions.     

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

One-dimensional non-nearest-neighbor random walks in the presence of traps

A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

小孔阵列衍射特性与应用

以单色标量波衍射理论为基础,研究了均匀平面波从不同角度入射小孔阵列的衍射特性。运用单孔衍射理论,同时考虑相邻小孔间衍射光强的相互影响,建立了小孔阵列衍射的理论模型和光强分布的数值积分式,小孔为硬边小孔。利用Matlab对500 nm波长的平面波入射微小方孔阵列衍射图样进行了计算机仿真,得到了不同几何参量下平面波从不同角度入射时的衍射图样的一维和二维光强分布图,并将仿真结果用于微型数字式太阳敏感器的光学系统中的结构参量设计和图像处理中的参量确定。太阳敏感器的成像实验结果表明,小孔阵列衍射光强分布图的仿真结果正确、太阳敏感器光学系统参量设计合理。小孔阵列衍射理论为太阳敏感器的光学系统设计和图像处理提供了可靠的理论基础。     

敏化光波长对(Fe,Ni):LiNbO3晶体全息记录性能的影响

分别采用514 nm绿光、488 nm蓝光和390 nm紫外光作为敏化光,633 nm红光作为记录光,详细研究了敏化光波长对氧化(Fe,Ni):LiNbO3晶体全息记录性能的影响.结果表明:随着敏化光波长的逐渐减小,氧化(Fe,Ni):LiNbO3晶体的非挥发全息记录性能逐渐优化,390 nm紫外光是这三种敏化光中最优的敏化光.考虑敏化光的吸收,为了在双中心全息记录中获得最优的性能,应当选择合适波长的敏化光:一方面短波长敏化光能有效地敏化深中心;另一方面短波长敏化光的吸收太强(如对光折变效应无用的基质吸收),不能沿厚度方向有效地敏化晶体,所以实际上需折衷考虑,并从理论上给予了解释.     

What is novel in quantum transport for mesoscopics?

The understanding of mesoscopic transport has now attained an ultimate simplicity. Indeed, orthodox quantum kinetics would seem to say little about mesoscopics that has not been revealed — nearly effortlessly — by more popular means. Such is far from the case, however. The fact that kinetic theory remains very much in charge is best appreciated through the physics of a quantum point contact. While discretization of its conductance is viewed as the exclusive result of coherent, single-electron-wave transmission, this does not begin to address the paramount feature of all metallic conduction: dissipation. A perfect quantum point contact still has finite resistance, so its ballistic carriers must dissipate the energy gained from the applied field. How do they manage that? The key is in standard many-body quantum theory, and its conservation principles.     

Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.