最大占据数为任意整数的统计

用拉格朗日乘子法推导了各个量子态上粒子最大占据数是任意整数的统计分布。     

The multielectron dissociative ionization dynamics of N2 molecule in intense femtosecond laser fields with arbitrary polarization

The field-ionization Coulomb explosion model is extended to investigate the multielectron dissociative ionization process of N₂ molecule irradiated by an intense femtosecond laser field with an arbitrary polarization. The ionization process of N₂ molecule is found to be optimal at the critical internuclear distance R_c=7a.u., which is independent of the laser polarization state, the molecular explosion channel and the angle between the molecular axis and the direction of laser electric field. The kinetic energies of the ion fragments are identical in the cases of linear and circular polarizations at the same incident laser intensity. However,the probability of electron ionization is very sensitive to the above three parameters. At the critical distance R_c=7a.u. the angular dependence of the threshold intensity for the over-the-barrier ionization leads to the geometric alignment of molecules in the case of linear polarization. The threshold intensity in the case of circular polarization is apparently higher than that in the case of linear polarization, which can well explain the significant decrease of ionization in the case of circular polarization. The numerical calculations are compared with the experimental measurements.     

Probabilistic teleportation of an arbitrary three-particle state

A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements, and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.     

A full-field approach for the elastic characterization of anisotropic materials

In the paper a procedure is described whereby the characterization of isotropic and anisotropic laminae is carried out by full-field measurement of the surface rotations under proper flexural loads. The analytic formulation does not necessarily imply a numerical calibration and the elastic constants are determined by integrating the whole experimental data on the surface of the specimen. Measurements were carried out by phase-stepped speckle interferometry using a shearometer based on Michelson design. The experimental instrumentation, including the loading device, and the procedures for the manipulation of experimental data are detailedly described; experimental results obtained on a steel specimen and a composite laminate are also reported.     

实Banach空间中渐近半压缩映射的强收敛性

利用新的分析技巧,建立了任意实Banach空间中具随机误差的Ishikawa迭代法生成的序列{xn}强收敛于渐近半压缩映射的不动点的一些充要条件.作为应用,证明了Oslike和Aniagbosor最近的q-一致光滑实Banach空间中渐近半压缩映射的不动点的迭代逼近的一主要结果(它本身主要是1998年Osilike的一定理的一般化)能被延拓至任意实Banach空间上,并给出了Ishikawa迭代序列的误差估计,且所用证明方法比已有的简单.     

Proper efficiency and duality for a class of constrained multiobjective fractional optimal control problems containing arbitrary norms

We establish necessary and sufficient conditions for properly efficient solutions of a class of nonsmooth nonconvex optimal control problems with multiple fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Subsequently, we utilize these proper efficiency criteria to construct two multiobjective dual problems and prove appropriate duality theorems. Also, we specialize and discuss these results for a particular case of our principal problem which contains square roots of positivesemidefinite quadratic forms. As special cases of the main proper efficiency and duality results, this paper also contains similar results for control problems with multiple, fractional, and ordinary objective functions.     

任意信源的一类Shannon-Mcmillan逼近定理

该文通过概率空间上的任意分布与另一任意分布相比较,研究任意随机序列相对熵密度的小偏差定理.并由此得出若干任意信源,m阶马氏信源的Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广.     

任意基数集上的拟阵的圈及连通性

通过研究任意基数集上的拟阵圈的性质,继而得出当此拟阵连通时,它可由含任一给定元素的圈集唯一确定的结论.     

Reliability in reconstruction of the axisymmetric refractive index profiles from transverse interferograms. Accurate versus approximate methods: A comparative study

A mathematical formalism related to the approximate as well as the accurate interferometric data reduction schemes is briefly outlined and subsequently applied in the reconstruction of the assumed (Luneburg) axisymmetric refractive index distribution. The presented comparative analysis confirms the generally held opinion that the approximate methods (“straight-line” and Kokubun-Iga approaches) may provide quite reasonable results in the examination of refractively inhomogeneous disturbances characterized by weak gradient and moderate index variation. On the other hand, the accurate scheme for transverse interferometric data interpretation and reduction, based on the close-form correlation between the fringe shift and the deflection function, [1] remains the only method for reliable reconstruction of strongly refracting index profiles, independently of magnitude of refraction and ambiguity of the fringes. This fact is of considerable importance for transverse interferometry of fibers (preform rods) and/or GRIN-rod lenses characterized by high numerical apertures.