A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

关于折射率对散射光场分布影响的研究

根据Mie散射理论,采用理论计算和实验相结合的手法,研究了光散射现象以及散射介质的折射率对散射光场分布的影响.通过对空气中不同折射率的散射介质形成的散射光场光强的实验比较,论证了散射介质折射率的实部变化对散射光强的影响不大,其主要影响是通过对相位的变化来实现的,也即散射介质折射率的虚部变化对光强的影响很大,在实际应用中不可忽略.这一结论对以散射光场的分布为基础的各种研究具有一定的指导意义.     

锥形光纤的偏振特性

随着光通信技术的不断发展，光纤的应用越来越广泛，而锥形光纤以其独特的传光方式越来越多地应用于光纤连接、成像及测量等领域。实验测定了不同锥角和不同长度锥形光纤的偏振特性。理论上，根据麦克斯韦方程组以及边界条件给出了光在理想光纤中的场分布，阐明了实际光纤中光的传输特性。论证了锥形光纤长度与其偏振特性的关系，进而利用几何光学方法对锥形光纤锥角与其偏振特性的关系作了定性说明。并用具体数据进行了定量计算，得出偏振光经锥形光纤传输或耦合后再传输到其终端所得到均是椭圆偏振光的结论。     

相对论速调管放大器辐射频率可调性机理

 用场方法研究了相对论速调管放大器辐射频率的可调性。发现调制电流频率的可调性与一阶Bessel函数的周期相关，对应相同的一阶Bessel函数值，可以有多个不同数值的宗量，调制电流的频率与Bessel函数宗量数值包括中间腔与提取腔之间的距离和电子束的传输速度等因素相联系。理论估计的调制电流频率可调范围与实验测得的结果符合得很好。相对论速调管放大器辐射频率的可调性还取决于提取腔的设计。     

开关型霍尔传感器的原理与工程实现

介绍了开关型霍尔传感器的工作原理，设计了适用于工程测量的具体线路，并分析了该线路的特点。     

动态规划在教学管理中的应用

本将动态规划理论应用于高校教学管理当中，得出了教学管理中重要的环一排课的最优策略。     

Particle Size Analysis by Transmission Fluctuation Spectrometry: Experimental Results Obtained with a Gaussian Beam and Analog Signal Processing

Transmission fluctuation spectrometry (TFS) is a method for the analysis of particle size distributions based on the statistical fluctuations of a transmission signal. Complete information on the PSD and particle concentration can be retrieved by a special transformation of the transmission signal, whereby the expectancy of the transmission square (ETS) is determined after the signal has been subjected to a procedure of spatial and temporal averaging. By varying the averaging parameters over a wide range, a spectrum of ETSs is obtained and introduced into a linear equation system, which yields the PSD. In the experimental realization presented here, variable temporal averaging is realized in the frequency domain with a series of low pass filters at different cutoff frequencies while spatial averaging inevitably occurs as the particles pass through a focused Gaussian beam of finite cross section. Experimental results on spherical particles (glass beads) and non‐spherical particles (SiC) are presented. The PSDs are resolved in 30 intervals within a particle size range from 1–1000 μm, employing a modified Chahine inversion algorithm. So far, the measurements are limited to moderate particle concentrations. Some influences affecting the measurements, especially for higher particle concentrations, are discussed in detail.     

一种有交易费用的交互式组合证券投资方法

本基于乘积最大化准则，提出一种新的交互式组合证券投资方法，即将不可微的双目标规划问题转化为可微的单目标规划问题。该方法可以充分考虑投资的要求，在考虑交易费用的前提下，在整个投资方案达到投资要求底限的同时，实现收益和风险的权衡。     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.