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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|原子物理代写Atomic and Molecular Physics代考|ELECTRON-ION VECTOR CORRELATIONs

The common philosophy of the experiments discussed in this chapter relies on the use of velocity spectrometers [56,57] or reaction microscopes $[58,59]$ which give access to the complete MFPAD for each studied PI reaction, taking advantage of the occurrence of dissociative photoionization (DPI). The Vector Correlation (VC) method consists in measuring the nascent velocity vectors of the ionic fragments and the photoelectron $\mathrm{e}_{\mathrm{ph}}$ produced in each DPI event, therefore providing a full three-dimensional momentum imaging of the correlated photoelectron and photoion. In the investigation of inner shell photoionization dynamics, considering DPI processes does not constitute a limitation, since in most cases the ionic molecular state produced after the photoelectron ejection further decays by Auger electron emission leading to double, triple or multiple ionization of the target, and breakup induced by the Coulomb interaction. The multiple ionization and dissociative secondary decay reactions offer a number of opportunities to get access to combined photoionization and subsequent fragmentation dynamics diagnostics. For valence shell ionization, the method focuses on the study of the dynamics of PI into excited ionic molecular states lying above the first DPI limit and other strategies have to be considered to study molecular frame photoemission into the bound ionic states such as the ground state and/or lowest excited states of the molecular ion.

The VC method is most efficient when the axial recoil approximation is valid, i.e. when the fragmentation dynamics is such that the direction of the detection of fragments produced in dissociative ionization is identical to the orientation of the bond that breaks at the time of the ionization process $[60,61]$. This condition is fulfilled e.g. when the PI reaction populates the ionic molecular ion in a repulsive part of its potential energy curve or surface or when predissociation of a bound ionic state occurs on a time scale shorter than molecular rotation. Detailed discussion of examples of non-axial recoil dissociation dynamics and what can be learned in such conditions will be presented in sections VI-XI, based on the formalism presented in section III.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|Multi-Photon Ionization Induced by kHz Femtosecond Lasers

The experimental conditions attached to the study of multi-photon PI of linear and non-linear molecules are more challenging for the VC method due to the $\mathrm{kHz}$ repetition rate of the femtosecond lasers $[68,46,49]$. Indeed, performing coincidence measurements requires the occurrence of a maximum of one PI event per pulse, which imposes the constraint that the average number of PI event per pulse must be on the order of a few tenths. In the running conditions, an acquisition rate of a maximum of 50 coincidences/s ( $0.05$ coincident event/pulse) ensures a true-coincidence acquisition mode, whereas current acquisition conditions at the SR source may reach a few times $10^{3} \mathrm{c} / \mathrm{s}$ with an average number of $0.005 \mathrm{PI}$ event/pulse. Meanwhile, for a better efficiency the timing of the event acquisition may be chosen by using a logical signal synchronous with the 1 $\mathrm{kHz}$ laser pulse as the common start for the eight channels of the TDC stopped by the delay line signals. In the reported experiments the light signal also acts as a start for a Time-to-Amplitude Converter (TAC). When turning to XUV incident light, special care has to be given to the filtering of secondary electrons produced by the interaction of stray light with metal surfaces in order to preserve real coincidence conditions.

The experiments reported were carried out using femtosecond lasers of the Saclay Laser-matter Interaction Center (SLIC) facility of the Commissariat à l’Energie Atomique. These are Chirped Pulse Amplification titanium-sapphire (Ti:Sa) laser systems delivering few-mJ pulses at a carrier frequency corresponding to $\lambda_{\mathbb{R}} \sim 800 \mathrm{~nm}$ with a $1 \mathrm{kHz}$ repetition rate. The second or third harmonic pulses used $\left(\lambda_{\text {air }} \sim 400 \mathrm{~nm}\right.$ and $\sim 265 \mathrm{~nm}$ ) are obtained by type I frequency doubling in a BBO crystal. The pulse duration was on the order of $70 \mathrm{fs}$ and $120 \mathrm{fs}$, respectively.

# 原子物理代写

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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