Probabilities of incidence between lines and a plane curve over finite fields

We study the probability for a random line to intersect a given plane curve, over a finite field, in a given number of points over the same field. In particular, we focus on the limits of these probabilities under successive finite field extensions. Supposing absolute irreducibility for the curve, we show how a variant of the Chebotarev density theorem for function fields can be used to prove the existence of these limits, and to compute them under a mildly stronger condition, known as simple tangency. Partial results have already appeared in the literature, and we propose this work as an introduction to the use of the Chebotarev theorem in the context of incidence geometry. Finally, Veronese maps allow us to compute similar probabilities of intersection between a given curve and random curves of given degree.     

Combined Spectroscopic and TD-DFT Analysis to Elucidate Substituent and Acidochromic Effects in Organic Dyes: A Case Study on Amino- versus Nitro-Substituted 2,4-Diphenylquinolines

A combined spectroscopic and TD-DFT case study was performed, to identify a robust method to calculate the complex near UV/Vis absorption spectra of various amino- vs. nitro-substituted 2,4-diphenylquinolines, which vary strongly under neutral and successively acidic conditions. For this, different DFT functionals were tested for geometry optimization and the TD part to calculate the neutral and different protonated species in a fast screening approach, i. e. using single point calculations in an implicit solvent. Offset-corrected M06HF, hitherto only applied to polymers, was identified as a suitable method to reproduce the absorption spectra in a reasonable fashion for all different substitution pattern and all different protonated species at different pH values; moreover, the method properly predicts the energetic ordering of low-lying n-π* and ππ* transitions, which is decisive for the non-/emissive nature of the different compounds. In all, this might provide a valuable tool for computer-aided design of related classes of compounds.     

Two classes of heterocycles—6,8‐dioxabicyclo[3.2.1]octanes and cyclopentenols from the same reagents: A quantum‐chemical comparison of mechanism

Most of the strategies for the synthesis of 6,8‐dioxabicyclo[3.2.1]octanes (BCO) and cyclopentenols (CP), which show high biological and pharmaceutical activity, are multistage and/or require hardly accessible starting materials and catalysts. The general method for BCO and CP preparation in a single preparative stage from two simple reagents, ketones and acetylene, under the action of an available super‐basic catalytic system KOH/DMSO becomes promising for the development of general approaches to the design of these classes of biologically active compounds. The mechanism of competing reactions yielding both 7‐methylene‐6.8‐dioxabicyclo[3.2.1]‐octanes and functionalized cyclopentenoles from their common intermediate 1,5‐diketones and acetylene in the KOH/DMSO superbasic media is investigated using the B2PLYP/6‐311++G**//B3LYP/6‐31+G* calculations with particular attention to the diastereoselectivity aspects of individual stages.     

Broadening-independent demodulation for wavelength modulation spectroscopy based on even-order harmonics

The line broadening of gas absorption spectrum is a significant but unknown factor in traditional demodulation of wavelength modulation spectroscopy, which is a kind of tunable diode laser absorption spectroscopy in weak absorption cases. In this paper, another signal demodulation method based on some simple algebraic operations with the amplitudes of the zero-, second-, and fourth-order harmonics was proposed. With this method the effect of spectrum broadening could be selfeliminated. That makes the amplitude of the demodulated signal is irrelevant to the broadening, and enables the direct and fast measurement without complex simulations and curve fittings in traditional method.     

Kernel regression estimation for continuous spatial processes

We investigate here a kernel estimate of the spatial regression function r(x) = E(Y _u | X _u = x), x ∈ ℝ^d, of a stationary multidimensional spatial process { Z _u = (X _u, Y _u), u ∈ ℝ ^N }. The weak and strong consistency of the estimate is shown under sufficient conditions on the mixing coefficients and the bandwidth, when the process is observed over a rectangular domain of ℝ^N. Special attention is paid to achieve optimal and suroptimal strong rates of convergence. It is also shown that this suroptimal rate is preserved by using a suitable spatial sampling scheme.      

Wavelength tuning in Er3+,Yb3+:glass microchip lasers

The paper presents the investigation results of laser generation around 1.5 μm at different wavelengths. The shifts of the wavelength were achieved by the change of pump power, transmission of an output mirror, and length of an active medium. Mathematical analysis and explanation of this phenomenon was curried out on the basis of the change in relation between the gain and loss lines.     

Cauchy problem for a quasilinear parabolic equation with a source term and an inhomogeneous density

The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered:

$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + u^p $

. The conditions on the parameters of the problem are found under which the solution to the Cauchy problem blows up in a finite time. A sharp universal (i.e., independent of the initial function) estimate of the solution near the blowup time is obtained.

     

相干激光雷达中最大似然离散谱峰值估计及Monte Carlo仿真

相干测风激光雷达中一个核心的问题是从微弱的气溶胶后向散射信号中估计出风速。基于零均值复高斯随机过程协方差矩阵统计模型的后向散射信号,首先讨论了最大似然（ML）离散谱峰值（DSP）风速估计算法的克拉美-罗下界（CRLB）与由Fisher信息矩阵论得到的精确CRLB之间的关系。其次,对于ML DSP估计应用于相干测风激光雷达中协方差矩阵统计模型的后向散射信号时,使用计算机Monte Carlo仿真的方法研究了风速估计的概率密度函数。分别讨论了信噪比、激光脉冲累积发数和发射激光脉冲宽度对ML DSP风速估计性能的影响。计算仿真结果表明：ML DSP风速估计的CRLB低于精确的CRLB;在信噪比为－20 dB,100发激光脉冲累积和信噪比为－30 dB,10 000发激光脉冲累积条件下,ML DSP风速估计中坏的估计值所占的比例都为0,好的估计值的标准差分别为0.62 m/s和0.50 m/s。     

XeCl准分子激光能量提取研究

在高功率准分子激光系统建设中,希望能获得较短的脉冲宽度和尽量多的激光能量。实验研究了不同注入水平下,脉冲时间间隔对脉冲链放大波形和放大器提取效率的影响;基于四能级速率方程和准分子反应动力学建立了准分子激光放大模型,计算了多种注入方式下种子光的放大过程,对关键参数给出了量化描述,得到与实验相符的计算结果。研究结果显示:脉冲序列间隔为9.3 ns时,可获得约95%的连续注入情形下放大能量;对该准分子激光系统来讲,9.3 ns是比较合适的脉冲间隔。     

MgnLa(n=2-6)掺杂团簇的密度泛函研究

采用密度泛函(DFT)中的B3LYP方法,选择CEP-31g基组,优化并得到了MgnLa(n=2- 6)小团簇的基态平衡结构,计算出了掺杂团簇的基态结构的平均键长、对称性、费米能级、能级间隙、束缚能、总能的二阶差分．结果表明,随着团簇原子数的增加,La原子更容易趋于团簇表面位置. 与未掺杂Mg团簇相比,La原子多采用取代其稳定基态结构的一个Mg原子形成掺杂团簇的稳定结构. 从有限的结果看,其中 Mg3La和 Mg6La的结构更为稳定．