Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

微光成像系统的阈值探测理论和视距探测方程的研究

研究目前文献中常见的１８种微光成像系统探测方程之间的内在联系和异同之处，分析论证各种阈值探测理论和探测方程存在的问题和不足。在此基础上，从人眼的视觉理论和阈值特性出发，建立微光成像系统新的阈值探测理论模型，并分别导出微光直视系统和微光电视系统的视距探测方程。应用所导出的理论公式计算的数据与各种实际系统的实测数据进行了比较，证明新的阈值探测理论和视距探测方程是正确可靠的，且具有很高的精度。     

Equilibrium theory for the hard-core systems

It is found that the density expansion in the argument of the exponential function gives a fine convergence on the equation of state of the hard-sphere system. The pair distribution function and the equation of state is constructed by an intuitive kinetic theoretical method. The equation of state of the hard-core system with attractive potential is constructed semiempirically with the aid of this simple analytical result, and Kamerling-Onnes' constant of the critical point is obtained analytically.     

半线性椭圆方程的正解

本文用特征理论及上下解方法,证明了一类半线性椭圆方程边值问题的正解的存在性,同时给出了解的估计.     

Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint

We compute the cyclic homology of the coordinate ring A(SL_q(2)) of the quantum algebraic group SL _q (2). We observe a degeneration of the noncommutative de Rham complex. The results are also verified from the point of view of Connes' noncommutative differential geometry.     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

Value functions,domination cones and proper efficiency in multicriteria optimization

In the absence of a clear objective value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications potential optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.     

Information amount and higher-order efficiency in estimation

By means of second-order asymptotic approximation, the paper clarifies the relationship between the Fisher information of first-order asymptotically efficient estimators and their decision-theoretic performance. It shows that if the estimators are modified so that they have the same asymptotic bias, the information amount can be connected with the risk based on convex loss functions in such a way that the greater information loss of an estimator implies its greater risk. The information loss of the maximum likelihood estimator is shown to be minimal in a general set-up. A multinomial model is used for illustration.