latex 演示文档模板

\documentclass{article}\usepackage{graphicx}\usepackage[round]{natbib}\bibliographystyle{plainnat}\usepackage[pdfstartview=FitH,%bookmarksnumbered=true,bookmarksopen=true,%colorlinks=true,pdfborder=001,citecolor=blue,%linkcolor=blue,urlcolor=blue]{hyperref}\begin{document}\title{Research plan under the Post-doctorate program at xx University}%\subtitle{aa}\author{Robert He}\date{2008/04/23}\maketitle\section{Research Title}~~~~Crustal seismic anisotropy in the xx using Moho P-to-S converted phases.\section{Research Background \& Purposes}~~~~Shear-wave splitting analyses provide us a new way to study the seismic structure and mantle dynamics in the crust and mantle. The crustal anisotropy is developed due to various reasons including lattice-preferred orientation (LPO) of mineral crystals and oriented cracks.\newlineTraditionally, the earthquakes occurring in the curst and the subducting plates are selected to determine the seismic anisotropy of the crust. However, none of these methods can help us to assess the anisotropy in the whole crust. Because crustal earthquakes mostly are located in the upper crust, they do not provide information of lower crust. On the other hand, earthquakes in the subducting plates provide information of the whole crust but combined with upper mantle. However, it’s difficult to extract the sole contri bution of the crust from the measurement. Fortunately P-to-S converted waves (Ps) at the Moho are ideal for investigation of crustal seismic anisotropy since they are influenced only by the medium above the Moho.Moho. Figure \ref{crustalspliting}~schematically shows the effects of shear wave splitting on Moho Ps phases. Initially, a near-vertically incident P wave generates a radially polarized converted shear wave at the crust-mantle boundary. The phases, polarized into fast and slow directions, progressively split in time as they propagate through the anisotropic media. Here, the Ps waves can be obtained from teleseismic receiver function analysis.%%\begin{figure}[htbp]\begin{center}\includegraphics[width=0.47\textwidth]{crustalsplit.png}\caption{The effects of shear wave splitting in the Moho P to S converted phase. Top shows a schematic seismogram in the fast/slow coordinate system with split horizontal Ps components.(cited from: McNamara and Owens, 1993)}\label{crustalspliting}\end{center}\end{figure}%%The Korean Peninsula is composed of three major Precambrian massifs, the Nangrim, Gyeongii, and Yeongnam massifs(Fig.\ref{geomap}). The Pyeongbuk-Gaema Massif forms the southern part of Liao-Gaema Massif of southern Manchuria, and the Gyeonggi and Mt. Sobaeksan massifs of the peninsula are correlated with the Shandong and Fujian Massifs of China.%\begin{figure}[htbp]\begin{center}\includegraphics[width=0.755\textwidth]{geo.png}\caption{Simplified geologic map. NCB: North China block; SCB: South China block.(cited from: Choi et al., 2006)}\label{geomap}\end{center}\end{figure}%Our purpose of the study is to measure the shear wave splitting parameters in the crust of the Korean Peninsula. The shear wave splitting parameters include the splitting time of shear energybetween the fast and slow directions, as well as fast-axis azimuthal direction in the Korean Peninsula. These two parameters provide us constraints on the mechanism causing the crustal anisotropy. From the splitting time, the layer thickness of anisotropy will be estimated. Whether crustal anisotropy mainly contributed by upper or lower crustal or both will be determined. Based on the fast-axis azimuthal direction, the tectonic relation between northeastern China and the Korean peninsula will be discussed.\section{Research Methods}~~~~Several methods have been introduced for calculation of receiver functions. An iterative deconvolution technique may be useful for this study since it produces more stable receiver function results than others. The foundation of the iterative deconvolution approach is aleast-squares minimization of the difference between the observed horizontal seismogram and a predicted signal generated by the convolution of an iteratively updated spike train with the vertical-component seismogram. First, the vertical component is cross-correlated with the radial component to estimate the lag of the first and largest spike in the receiver function (the optimal time is that of the largest peak in the absolute sense in the cross-correlation signal). Then the convolution of the current estimate of the receiver function with the vertical-component seismogram is subtracted from the radial-component seismogram, and the procedure is repeated to estimate other spike lags and amplitudes. With each additional spike in the receiver function, the misfit between the vertical and receiver-function convolution and the radial component seismogram is reduced, and the iteration halts when the reduction in misfit with additional spikes becomes insignificant.\newlineFor all measurement methods of shear-wave splitting, time window of waveform should be selected. Conventionally the shear-wave analysis window is picked manually. However, manual window selection is laborious and also very subjective; in many cases different windows give very different results.\newlineIn our study, the automated S-wave splitting technique will be used, which improves the quality of shear-wave splitting measurement and removes the subjectivity in window selection. First, the splitting analysis is performed for a range of window lengths. Then a cluster analysis isapplied in order to find the window range in which the measurements are stable. Once clusters of stable results are found, the measurement with the lowest error in the cluster with the lowest variance is presented for the analysis result.\section{Expected results \& their contributions}~~~~First, the teleseismic receiver functions(RFs) of all stations including radial and transverse RFs can be gained. Based on the analysis of RFs, the crustal thickness can be estimated in the Korean Peninsula. Then most of the expected results are the shear-wave splitting parameters from RFs analysis in the crust beneath the Korean Peninsula. The thickness of anisotropic layer will be estimated in the region when the observed anisotropy is assumed from a layer of lower crustal material.All the results will help us to understand the crustal anisotropy source.\newlineCrustal anisotropy can be interpreted as an indicator of the crustal stress/strain regime. In addition, since SKS splitting can offer the anisotropy information contributed by the upper mantle but combined with the crust, the sole anisotropy of the upper mantle can be attracted from the measurement of SKS splitting based on the crustal splitting result.%\cite{frogge2007}%%%\citep{frogge2008}%%%\citep{s-frogge2007}% 5. References\begin{thebibliography}{99}\item Burdick, L. J. and C. A. Langston, 1977, Modeling crustal structure through the use of converted phases in teleseismic body waveforms, \textit{Bull. Seismol. Soc. Am.}, 67:677-691.\item Cho, H-M. et al., 2006, Crustal velocity structure across the southern Korean Peninsula from seismic refraction survey, \textit{Geophy. Res. Lett.} 33, doi:10.1029/2005GL025145.\item Cho, K. H. et al., 2007, Imaging the upper crust of the Korean peninsula by surface-wave tomography, \textit{Bull. Seismol. Soc. Am.}, 97:198-207.\item Choi, S. et al., 2006, Tectonic relation between northeastern China and the Korean peninsula revealed by interpretation of GRACE satellite gravity data, \textit{Gondwana Research}, 9:62-67.\item Chough, S. K. et al., 2000, Tectonic and sedimentary evolution of the Korean peninsula: a review and new view, \textit{Earth-Science Reviews}, 52:175-235.\item Crampin, S., 1981, A review of wave motion in anisotropic and cracked elastic-medium, \textit{Wave Motion}, 3:343-391.\item Fouch, M. J. and S. Rondenay, 2006, Seismic anisotropy beneath stable continental interiors, \textit{Phys. Earth Planet. Int.}, 158:292-320.\item Herquel, G. et al., 1995, Anisotropy and crustal thickness of Northern-Tibet. New constraints for tectonic modeling, \textit{Geophys. Res. Lett.}, 22(14):1 925-1 928.\item Iidaka, T. and F. Niu, 2001, Mantle and crust anisotropy in the eastern China region inferred from waveform splitting of SKS and PpSms, \textit{Earth Planets Space}, 53:159-168.\item Kaneshima, S., 1990, Original of crustal anisotropy: Shear wave splitting studies in Japan, \textit{J. Geophys. Res.}, 95:11 121-11 133.\item Kim, K. et al., 2007, Crustal structure of the Southern Korean Peninsula from seismic wave generated by large explosions in 2002 and 2004, \textit{Pure appl. Geophys.}, 164:97-113.\item Kosarev, G. L. et al., 1984, Anisotropy of the mantle inferred from observations of P to S converted waves, \textit{Geophys. J. Roy. Astron. Soc.}, 76:209-220.\item Levin, V. and J. Park, 1997, Crustal anisotropy in the Ural Mountains foredeep from teleseismic receiver functions, \textit{Geophys. Res. Lett.}, 24(11):1 283 1286.\item Ligorria, J. P. and C. J. Ammon, 1995, Iterative deconvolution and receiver-function estimation. \textit{Bull. Seismol. Soc. Am.}, 89:1 395-1 400.\item Mcnamara, D. E. and T. J. Owens, 1993, Azimuthal shear wave velocity anisotropy in the basin and range province using Moho Ps converted phases, \textit{J. Geophys. Res.}, 98:12003-12 017.\item Peng, X. and E. D. Humphreys, 1997, Moho dip and crustal anisotropy in northwestern Nevada from teleseismic receiver functions, \textit{Bull. Seismol. Soc. Am.}, 87(3):745-754.\item Sadidkhouy, A. et al., 2006, Crustal seismic anisotropy in the south-central Alborz region using Moho Ps converted phases, \textit{J. Earth \& Space Physics}, 32(3):23-32.\item Silver, P. G. and W. W. Chan, 1991, Shear wave splitting and subcontinental mantle deformation, \textit{J. Geophys. Res.},96:16 429-16454.\item Teanby, N. A. et al., 2004, Automation of shear wave splitting measurement using cluster analysis, \textit{Bull. Seismol. Soc. Am.}, 94:453-463.\item Vinnik, L. and J-P. Montagner, 1996, Shear wave splitting in the mantle Ps phases,\textit{Geophys. Res. Lett.}, 23(18):2 449- 2 452.\item Yoo, H. J. et al., 2007, Imaging the three-dimensional crust of the Korean peninsula by joint inversion of surface-wave dispersion of teleseismic receiver functions, \textit{Bull. Seismol. Soc. Am.}, 97(3):1 002-1 011.\item Zhu, L., and H. Kanamori, 2000, Moho depth variation in Southern California from teleseismic receiver functions, \textit{J. Geophys. Res.}, doi :10.1029/1999JB900322, 105:2 969-2 980.%%%%\end{document}。

（完整版）latex初学者模板% a4paper - A4 纸 11pt - 字体 twoside - 双面 openany - 新章节可在偶数页开始\documentclass[a4paper,11pt,twoside,openany]{article} % ----------------------------- 纸张大小 ------------------------------------- % 定义转换成 pdf 文档的纸张大小，应与 \paperwidth \paperheight 一致 %\special{pdf: pagesize width 20cm height 30cm}% true 的含义是保持尺寸不会随一些参数的变化而变化，具体可见 Knuth 的 TeXbook % 纸张宽% 纸张高页面布局 --------% 正文宽%\textheight 20 true cm %\headheight 14pt %\headsep 16pt%\footskip27pt%\marginparsep 10pt %\marginparwidth 100pt % --------------------------- 页边空白调整\setlength{\evensidemargin}{0mm} % 置 0 \iffalse % 如果考虑右侧（书外侧）的边注区则改为\iftrue \addtolength{\evensidemargin}{\marginparsep}\addtolength{\evensidemargin}{\marginparwidth} \fi% \paperwidth = h + \oddsidemargin+\textwidth+\evensidemargin + h\setlength{\hoffset}{\paperwidth} \addtolength{\hoffset}{-\oddsidemargin} \addtolength{\hoffset}{-\textwidth} \addtolength{\hoffset}{-\evensidemargin}\setlength{\hoffset}{0.5\hoffset} \addtolength{\hoffset}{-1in}\setlength{\voffset}{-1in}\setlength{\topmargin}{\paperheight}%\paperwidth 20 true cm %\paperheight 30 true cm % ------------------------ %\textwidth 10 true cm % 正文高% 页眉高 % 页眉距离% 页脚距离 % 边注区距离 % 边注区宽\def\marginset#1#2{ \marginset{left}{top}\setlength{\oddsidemargin}{#1} \iffalse \iftrue\reversemarginpar\addtolength{\oddsidemargin}{\marginparsep}\addtolength{\oddsidemargin}{\marginparwidth} \fi% 页边设置% 左边（书内侧）装订预留空白距离% 如果考虑左侧（书内侧）的边注区则改为% h = \hoffset + 1in% 0 = \voffset + 1in\iffalse % 将这里改为 \iftrue 即可使用\ifx\pdfoutput\undefined % Not run pdftex % \ifx % \usepackage[dvips]{hyperref} % \else\addtolength{\topmargin}{-\headheight}\addtolength{\topmargin}{-\headsep}\addtolength{\topmargin}{-\textheight}\addtolength{\topmargin}{-\footskip}\addtolength{\topmargin}{#2}\setlength{\topmargin}{0.5\topmargin}% 上边预留装订空白距离}% 调整页边空白使内容居中，两参数分别为纸的左边和上边预留装订空白距离 \marginset{10mm}{12mm} % --------------------------- 字体支持 -------------------------\usepackage{times}字体% 使用 Times New Roman\usepackage{CJK,CJKnumb,CJKulem} % 中文支持宏包%\usepackage{ccmap} % 使pdfLatex 生成的文件支持复制等 %\usepackage[mtbold,mtpluscal,mtplusscr]{mathtime}% 数学环境用 Times New Roman% ---------------------------\usepackage{fancyhdr} \pagestyle{fancy}% --------------------------- \usepackage{color}\usepackage{indentfirst}%\setlength{\parindent}{2em}页眉页脚 -------------------------% 页眉页脚相关宏包 % 页眉页脚风格段落字体格式 ----% 支持彩色 % 首行缩进宏包% 段落缩进\setlength{\parskip}{0.7ex plus0.3ex minus0.3ex} %%\linespread{1.2}\renewcommand{\baselinestretch}{1.2} 段落间距% 行距倍数% 行距倍数（同上）\newcommand{\hei}{\CJKfamily{hei}}%黑体 \newcommand{\fs}{\CJKfamily{fs}}% 仿宋\newcommand{\kai}{\CJKfamily{kai}}%楷体 \newcommand{\li}{\CJKfamily{li}}% 隶书\newcommand{\you}{\CJKfamily{you}} %幼圆\newcommand{\wuhao}{\fontsize{10.5pt}{12.6pt}\selectfont} \newcommand{\xiaosi}{\fontsize{12pt}{14pt}\selectfont} \newcommand{\sihao}{\fontsize{14pt}{\baselineskip}\selectf ont} % %\marginparpush% 五号字体 % 小四字体四号字体%% --------------------------- 超链接和标签 ----------------------- %\renewcommand{\CJKglue}{\hskip 0pt plus 0.08\baselineskip} % 汉字字距% 自定义文字块例子%\newcommand{\aaa}{ 这是测试 }\newcommand{\song}{\CJKfamily{song}} % 宋体\usepackage[dvipdfm]{hyperref}% \fi \AtBeginDvi{\special{pdf:tounicode GBK-EUC-UCS2}} % GBK -> Unicode \else \usepackage[pdftex]{hyperref} \fi \hypersetup{CJKbookmarks,% bookmarksnumbered,% colorlinks,% linkcolor=blue,% citecolor=blue,% hyperindex,% plainpages=false,% pdfstartview=FitH} \fi% ------------------------------- 注释 --------------------------------------- \iffalse % 将这里改为 \iftrue 即可使用 %注释掉一段内容\usepackage{verbatim} \begin{comment}This is a comment example. \end{comment}\fi %\makeatletter % @ is now a normal "letter" for Tex%\makeatother % @ is restored as a "non-letter" for Tex % ------------------------------- 其他宏包------------------------ %\usepackage{amsmath,amsthm,amsfonts,amssymb,bm} % 数学宏包 %\usepackage{graphicx,psfrag} %\usepackage{makeidx} 包%\usepackage{listings} % ------------------------------- \begin{document} % 开始正文 % song- 宋体 hei- 黑体 fs- 仿宋 kai- 楷体 li- 隶书 you- 幼圆 com 为 song+hei\begin{CJK*}{GBK}{com}% 开始中文环境\CJKtilde % 重定义 ~代表的空白距离 \CJKindent首缩进\CJKcaption{GB} 节标题 \author{ceo}\title{ 一个 latex 例子 } \maketitle成标题%\thispagestyle{empty} % 设置首页的页眉页脚风格%\setlength{\baselineskip}{3ex plus1ex minus1ex} % 调整行距\TeX{}~ 是由图灵奖得主\index{Knuth, Donald E.}~Donald E. Knuth\cite{texbook}~ 编写的计算机程序，用于文章和数学公式的排版。

% a4paper - A4 纸 11pt - 字体 twoside - 双面 openany - 新章节可在偶数页开始 \documentclass[a4paper,11pt,twoside,openany]{article}% ----------------------------- 纸张大小 ------------------------------------- % 定义转换成 pdf 文档的纸张大小，应与 \paperwidth \paperheight 一致 %\special{pdf: pagesize width 20cm height 30cm}% true 的含义是保持尺寸不会随一些参数的变化而变化，具体可见 Knuth 的 TeXbook % 纸张宽% 纸张高页面布局 --------% 正文宽%\textheight 20 true cm %\headheight 14pt %\headsep 16pt%\footskip27pt%\marginparsep 10pt %\marginparwidth 100pt % --------------------------- 页边空白调整\setlength{\evensidemargin}{0mm} % 置 0 \iffalse % 如果考虑右侧（书外侧）的边注区则改为 \iftrue \addtolength{\evensidemargin}{\marginparsep} \addtolength{\evensidemargin}{\marginparwidth} \fi% \paperwidth = h + \oddsidemargin+\textwidth+\evensidemargin + h\setlength{\hoffset}{\paperwidth} \addtolength{\hoffset}{-\oddsidemargin} \addtolength{\hoffset}{-\textwidth} \addtolength{\hoffset}{-\evensidemargin} \setlength{\hoffset}{0.5\hoffset} \addtolength{\hoffset}{-1in}\setlength{\voffset}{-1in}\setlength{\topmargin}{\paperheight}%\paperwidth 20 true cm %\paperheight 30 true cm % ------------------------ %\textwidth 10 true cm % 正文高% 页眉高 % 页眉距离% 页脚距离 % 边注区距离 % 边注区宽\def\marginset#1#2{ \marginset{left}{top}\setlength{\oddsidemargin}{#1} \iffalse \iftrue\reversemarginpar\addtolength{\oddsidemargin}{\marginparsep} \addtolength{\oddsidemargin}{\marginparwidth} \fi% 页边设置% 左边（书内侧）装订预留空白距离% 如果考虑左侧（书内侧）的边注区则改为% h = \hoffset + 1in% 0 = \voffset + 1in\iffalse % 将这里改为 \iftrue 即可使用\ifx\pdfoutput\undefined % Not run pdftex % \ifx % \usepackage[dvips]{hyperref} % \else\addtolength{\topmargin}{-\headheight} \addtolength{\topmargin}{-\headsep} \addtolength{\topmargin}{-\textheight} \addtolength{\topmargin}{-\footskip} \addtolength{\topmargin}{#2} \setlength{\topmargin}{0.5\topmargin}% 上边预留装订空白距离}% 调整页边空白使内容居中，两参数分别为纸的左边和上边预留装订空白距离 \marginset{10mm}{12mm} % --------------------------- 字体支持 -------------------------\usepackage{times}字体% 使用 Times New Roman\usepackage{CJK,CJKnumb,CJKulem} % 中文支持宏包 %\usepackage{ccmap} % 使 pdfLatex 生成的文件 支持复制等 %\usepackage[mtbold,mtpluscal,mtplusscr]{mathtime}%数学环境用 Times New Roman% ---------------------------\usepackage{fancyhdr} \pagestyle{fancy}% --------------------------- \usepackage{color}\usepackage{indentfirst}%\setlength{\parindent}{2em}页眉页脚 -------------------------% 页眉页脚相关宏包 % 页眉页脚风格 段落字体格式 ----% 支持彩色 % 首行缩进宏包% 段落缩进\setlength{\parskip}{0.7ex plus0.3ex minus0.3ex} %%\linespread{1.2}\renewcommand{\baselinestretch}{1.2} 段落间距% 行距倍数% 行距倍数（同上）\newcommand{\hei}{\CJKfamily{hei}}%黑体 \newcommand{\fs}{\CJKfamily{fs}}% 仿宋\newcommand{\kai}{\CJKfamily{kai}}%楷体 \newcommand{\li}{\CJKfamily{li}}% 隶书\newcommand{\you}{\CJKfamily{you}} %幼圆\newcommand{\wuhao}{\fontsize{10.5pt}{12.6pt}\selectfont} \newcommand{\xiaosi}{\fontsize{12pt}{14pt}\selectfont}\newcommand{\sihao}{\fontsize{14pt}{\baselineskip}\selectfont} % %\marginparpush% 五号字体 % 小四字体四号字体%% --------------------------- 超链接和标签 ----------------------- %\renewcommand{\CJKglue}{\hskip 0pt plus 0.08\baselineskip} % 汉字字距% 自定义文字块例子%\newcommand{\aaa}{ 这是测试 }\newcommand{\song}{\CJKfamily{song}} % 宋体\usepackage[dvipdfm]{hyperref}% \fi \AtBeginDvi{\special{pdf:tounicode GBK-EUC-UCS2}} % GBK -> Unicode \else \usepackage[pdftex]{hyperref} \fi\hypersetup{CJKbookmarks,% bookmarksnumbered,% colorlinks,% linkcolor=blue,% citecolor=blue,% hyperindex,% plainpages=false,% pdfstartview=FitH} \fi% ------------------------------- 注释 --------------------------------------- \iffalse % 将这里改为 \iftrue 即可使用 %注释掉一段内容 \usepackage{verbatim} \begin{comment}This is a comment example. \end{comment}\fi %\makeatletter % @ is now a normal "letter" for Tex%\makeatother % @ is restored as a "non-letter" for Tex % ------------------------------- 其他宏包 ------------------------ %\usepackage{amsmath,amsthm,amsfonts,amssymb,bm} % 数学宏包 %\usepackage{graphicx,psfrag} %\usepackage{makeidx}包%\usepackage{listings} % ------------------------------- \begin{document} % 开始正文 % song- 宋体 hei- 黑体 fs- 仿宋 kai- 楷体 li- 隶书 you- 幼圆 com 为 song+hei\begin{CJK*}{GBK}{com}% 开始中文环境\CJKtilde % 重 定义 ~代表的空白距离 \CJKindent首缩进\CJKcaption{GB} 节标题 \author{ceo}\title{ 一个 latex 例子 } \maketitle成标题%\thispagestyle{empty} % 设置首页的 页眉页脚风格%\setlength{\baselineskip}{3ex plus1ex minus1ex} % 调整行距\TeX{}~ 是由图灵奖得主 \index{Knuth, Donald E.}~Donald E. Knuth\cite{texbook}~ 编写的计算机程序，用于文章和数学公式的排版。

latex模板Latex 实用例子通过实验本例子可以基本掌握科技排版的方法：\documentclass[twocolumn]{article}\usepackage{amsmath}\renewcommand{\rmdefault}{ptm}\begin{document}\title{ Measure the axes of nearby nitrogen-vacancy centers in diamond with polarized light}\author{ Jing-Ru Wang\\Department of physics,the Beijing University of Posts and Telecommunications}\date{November 17, 2015}\maketitle\begin{abstract}NV）center in diamond is an attractive The negatively charged nitrogen-vacancy（candidate because of their excellent spin and optical characteristics for quantum information and metrology. To research these characteristics,precise orientation of the NV axis in the lattice is essential.Here we show that the orientation of axes of two nearby NV in diamond can be efficiently measured through two beams of polarized light.\end{abstract}\section{text}The measurement of physical quantities is not only a main target but also an active impulsion for scientific research. Especially, it is important to image of nearby particles for modern science[1,2].The accuracy with which two nearby particles can beresolved is classically restricted because of the optical diffraction limit[3].During the last decade, the optical diffraction limit has been overcome with the introduction of several new concepts, pioneered by stimulated emission depletion[4], ground-state depletion[5], structured illumination microscopy[6,7],and image interference microscopy[8].Very recently, imaging methods that used distinguishing information based on photons emitted from different particles have been proposed to achieve precision beyond the diffraction limit. Phenomena from quantum mechanics have been applied to enhance the measurement and have been used to enhance the precision of measurement beyond the classical limit[9,10].So far, in quantum imaging sub-classical resolution has been achieved by using sources of entangled photons[11,13].They are fragile on account of quantum decoherence[14-16].The sub-P0issonian and temporal fluctuation have been applied to enhance the imaging resolution by N with an N th-order process. Until now, a quantum measurement method based on the quantum nature of antibunching photon emission had been developed to detect single particles without the restriction of the diffraction limit. Simultaneously, by counting the single-photon and two-photon signals with fluorescence microscopy, the images of nearby nitrogen-vacancy centers in diamond at distance of 4.25.8±nm had been successfully reconstructed [17]. In addition to imaging nearby NVS, the orientation of the axes of the NVCs is also very important. It is NV that is one of the most intensively studied atom-like solid-state systems in diamond.The NV center is a color defect in diamond consisting of a substituted nitrogen atom associated with an adjacent vacancy(Fig.1). Owing to υ3C symmetry, the NV defect can occur with fourdifferent orientations in the diamond matrix, along ]111[,]111[, ]111[, or ]111[crystallographic axes (Fig.1). In most diamond samples, the NV centers occupy these four orientations equally. The precision of measurement of axes of NV is important for various applications, including the development of hybrid quantum systems, where superconducting qubits are coupled to ensembles of NV defects [18, 19], high sensitivity magnetometry[20-22], and efficient coupling of NV defects to photonic waveguides or microcavities[23-25].For single NV centers, the method of determining the orientation of the NV axis had been published [26].However, there are many combinations of polarization for highly coincident two NVCs. Here, we use two beams of polarized light to measure the axes of highly coincident two NVCs.For this crystal orientation(see Fig.1), from four possible NV orientations, one of them ([111]) is normal to the sample surface. For the other orientations, they are located in the bottom of the directions.The spontaneous emission rates vary with the polarization of the pump beam according to different axes of NVCs and the luminescence intensities for the light polarized parallel (x I ) and perpendicular (y I ) to the laser polarization are [26]:% MathType!MTEF!2!1!+-%feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn %hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr %4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa %aaleaacaWG4baabeaakiabg2da9maalaaabaGaaGymaaqaaiaaikd a% aaGaamyqamaaBaaaleaacaWGWbaabeaakiaacUfaciGGZbGaaiyA ai%aac6gadaahaaWcbeqaaiaaikdaaaGccaGGOaGaeqy1dyMaaiykaia b% gUcaRmaalaaabaGaaGymaaqaaiaaiMdaaaGaci4yaiaac+gacaGGZ b% WaaWbaaSqabeaacaaIYaaaaOGaaiikaiabew9aMjaacMcacaGGDb aa% aa!4E79!${I_x} = \frac{1}{2}{A_p}[{\sin ^2}(\phi ) + \frac{1}{9}{\cos ^2}(\phi )]$% MathType!MTEF!2!1!+-%feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn %hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr %4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa %aaleaacaWG5baabeaakiabg2da9maalaaabaGaaGymaaqaaiaaikd a% aaGaamyqamaaBaaaleaacaWGWbaabeaakiaacUfaciGGJbGaai4B ai% aacohadaahaaWcbeqaaiaaikdaaaGccaGGOaGaeqy1dyMaaiykaia b% gUcaRmaalaaabaGaaGymaaqaaiaaiMdaaaGaci4CaiaacMgacaGG Ub% WaaWbaaSqabeaacaaIYaaaaOGaaiikaiabew9aMjaacMcacaGGDb aa% aa!4E7A!${I_y} = \frac{1}{2}{A_p}[{\cos ^2}(\phi ) + \frac{1}{9}{\sin ^2}(\phi )]$Where ? is angle between laser polarization and the projection of each NV axis ,p A is the total spontaneous emission rate.The photoluminescence minima occur when the projection of the NV axis onto the sample surface is parallel to the electric field of the optical excitation. With polarized optical pump for NV, the number of possible orientations of a given center is reduced from four to two, which are in the plane of ?=0?or ?=90?, as shown in Fig.1(b)(再添加进去投影图).With polarized optical pump for the NV toward one side, there will have intensity distribution of two kinds of shapes because of four orientations of axes of NV only have two kinds of polarization, as shown in Fig. 2. Next, we polarized optical pump for the NV toward other side and will get anotherset of intensity distribution. We only conserve ? from ?0to ?180. It have beenknown that intensity has the maximum when ? is ?90. We discuss four caseswhere the nitrogen atoms are likely to be located. We chose three edges to give the excitation light and the relationship between light intensity and angle is shown in Fig.4. (图4还未列出) Last, we simulated the intensity of the three experiments, it includes 6 combinations of possible axial direction for two nearby NVCs. We set that the first time to be excited is the edge of the number 1. From top to down in a counter clockwise direction, we excite the other two edges. (图5) Figure 5 shows the intensity that may appear after three experiments. If it occurs one of four kinds of condition in B, C, D, and E, we just need to excite two times. If the first two times the intensity is not distinguishable just as A and F, we need to excite third times.In summary, we proposed and demonstrated a measurement of axes of two nearby NVCs by spontaneous emission rates vary with the polarization of the pump beam. The orientation of crystallographic axes of two well-overlapping NVCs can be spatially resolved. This work is a significant step towards precision of physical characteristics of the NV for quantum information and sensing applications.[1] P. Alivisatos, Nat. Biotechnol. 22, 47 (2004).[2] G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, Annu. Rev. Phys. Chem. 61, 345 (2010).[3]Abbe E (1873) Conributions to the theory of the microscope and the microscopic perception (translated from German). Arch MikrAnat9:413–468.[4] Hell SW, Wichmann J (1994) Breaking the diffraction resolution limit by stimulated emission:Stimulated-emission-depletion fluorescence microscopy. OptLett19:780–782.[5] Hell SW, Kroug M (1995) Ground-state-depletion fluorescence microscopy: A concept for breaking the diffraction resolution limit. ApplPhys B Lasers Optics 60:495–497.[6] Gustafsson MGL (2000) Surpassing the lateral resolution limit by a factor of two using structuredillumination microscopy. J Microsc198:82–87.[7] Heintzmann R, Jovin TM, Cremer C (2002) Saturated patterned excitation microscopy: A concept for optical resolution improvement. J Opt Soc Am A 19:1599–1609.[8] Gustafsson MGL, Agard DA, Sedat JW (1999) (IM)-M-5: 3D wide-field light microscopy with better than100-nm axial resolution.J Microsc Oxford 195:10–16.[9] V. Giovannetti, S. Lloyd, and L. Maccone, Science 306,1330 (2004).[10] LIGO Scientific Collaboration, Nat. Phys. 7, 962 (2011).[11] M. D’Ang elo, C. V. Chekhova, Y. Shih, Phys. Rev. Lett.87, 013602 (2001).[12] P. R. Hemmer et al., Phys. Rev. Lett. 96, 163603 (2006).[13] A. Muthukrishnan, M. O. Scully, M. S. Zubairy, J. Opt. B 6,S575 (2004).[14] T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasak i, and S. Takeuchi, Science 316, 726 (2007).[15] F.W. Sun, B. H. Liu, Y. X. Gong, Y. F. Huang, Z.Y. Ou, and G.C. Guo, Europhys. Lett.82, 24 (2008).[16] G.Y. Xiang, B. L. D. Higgins, W. H. Berry, M.G. Wiseman, and J. Pryde, Nat. Photonics 5, 43 (2011).[17] Jin-Ming Cui, Fang-Wen Sun, Xiang-Dong Chen, Zhao-Jun Gong, and Guang-Can Guo, Phys. Rev. L 110,153901(2013).[18] Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N.Morishita, H. Abe, S. Onoda, T. Ohshimaet al., Phys. Rev. Lett. 107, 220501 (2011).[19] X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt,K. Nemoto et al., Nature 478, 221 (2011).[20] V. M. Acosta, E. Bauch, M. P. Ledbetter, C. Santori, K.-M.C. Fu, P. E. Barclay, R. G. Beausoleil, H. Linget,J. F. Roch, F. Treussart et al., Phys.Rev. B 80, 115202 (2009).[21] D. Le Sage, K. Arai, D. R. Glenn, S. J. DeVience, L. M. Pham, L. Rahn-Lee, M. D. Lukin, A. Yacoby, A.Komeili, and R. L. Walsworth, Nature 496, 486 (2013).[22] Y. Dumeige, M. Chipaux, V. Jacques, F. Treussart, J.-F. Roch, T. Debuisschert, V. M. Acosta, A. Jarmola, K.Jensen, P. Kehayias et al., Phys. Rev. B 87, 155202 (2013).[23] A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, Nat. Photonics 5, 301 (2011).[24] J. Riedrich-M€oller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly,F. M€ucklich, A. Baur, M. Wandt, S. Wolff,M. Fischer et al., Nat. Nanotechnol. 7, 69 (2011).[25] M. Loncar and A. Faraon, MRS Bull. 38, 144 (2013).[26] Thiago P. Mayer Alegre,Charles Santori,Gilberto Medeiros-Ribeiro,and Raymond G. Beausoleil，Phys. Rev. B 76, 165205 (2007)....\end{document}形成的PDF效果图：。

% a4paper - A4纸11pt -字体 twoside -双面 openany -新章节可在偶数页开始\documentclass[a4paper,11pt,twoside,openany]{article}%------------------------------纸张大小----------------------------------% 定义转换成pdf文档的纸张大小，应与\paperwidth \paperheight一致%\special{pdf: pagesize width 20cm height 30cm}% true的含义是保持尺寸不会随一些参数的变化而变化，具体可见Knuth的TeXbook%\paperwidth 20 true cm % 纸张宽%\paperheight 30 true cm % 纸张高%------------------------------页面布局----------------------------------%\textwidth 10 true cm % 正文宽%\textheight 20 true cm % 正文高%\headheight 14pt % 页眉高%\headsep 16pt % 页眉距离%\footskip 27pt % 页脚距离%\marginparsep 10pt % 边注区距离%\marginparwidth 100pt % 边注区宽%----------------------------页边空白调整-------------------------------\def\marginset#1#2{ % 页边设置\marginset{left}{top}\setlength{\oddsidemargin}{#1} % 左边（书内侧）装订预留空白距离\iffalse % 如果考虑左侧（书内侧）的边注区则改为\iftrue\reversemarginpar\addtolength{\oddsidemargin}{\marginparsep}\addtolength{\oddsidemargin}{\marginparwidth}\fi\setlength{\evensidemargin}{0mm} % 置0\iffalse % 如果考虑右侧（书外侧）的边注区则改为\iftrue\addtolength{\evensidemargin}{\marginparsep}\addtolength{\evensidemargin}{\marginparwidth}\fi% \paperwidth = h + \oddsidemargin+\textwidth+\evensidemargin + h\setlength{\hoffset}{\paperwidth}\addtolength{\hoffset}{-\oddsidemargin}\addtolength{\hoffset}{-\textwidth}\addtolength{\hoffset}{-\evensidemargin}\setlength{\hoffset}{0.5\hoffset}\addtolength{\hoffset}{-1in} % h = \hoffset + 1in\setlength{\voffset}{-1in} % 0 = \voffset + 1in\setlength{\topmargin}{\paperheight}\addtolength{\topmargin}{-\headheight}\addtolength{\topmargin}{-\headsep}\addtolength{\topmargin}{-\textheight}\addtolength{\topmargin}{-\footskip}\addtolength{\topmargin}{#2} % 上边预留装订空白距离\setlength{\topmargin}{0.5\topmargin}}% 调整页边空白使内容居中，两参数分别为纸的左边和上边预留装订空白距离\marginset{10mm}{12mm}%-----------------------------字体支持-----------------------------------\usepackage{times} % 使用 Times New Roman 字体\usepackage{CJK,CJKnumb,CJKulem} % 中文支持宏包%\usepackage{ccmap} % 使pdfLatex生成的文件支持复制等%\usepackage[mtbold,mtpluscal,mtplusscr]{mathtime}%数学环境用Times New Roman%-----------------------------页眉页脚-----------------------------------\usepackage{fancyhdr} % 页眉页脚相关宏包\pagestyle{fancy} % 页眉页脚风格%-----------------------------段落字体格式-------------------------------\usepackage{color} % 支持彩色\usepackage{indentfirst} % 首行缩进宏包%\setlength{\parindent}{2em} % 段落缩进\setlength{\parskip}{0.7ex plus0.3ex minus0.3ex} % 段落间距%\linespread{1.2} % 行距倍数\renewcommand{\baselinestretch}{1.2} % 行距倍数（同上）%\renewcommand{\CJKglue}{\hskip 0pt plus 0.08\baselineskip} % 汉字字距%\newcommand{\aaa}{这是测试} % 自定义文字块例子\newcommand{\song}{\CJKfamily{song}} % 宋体\newcommand{\hei}{\CJKfamily{hei}} % 黑体\newcommand{\fs}{\CJKfamily{fs}} % 仿宋\newcommand{\kai}{\CJKfamily{kai}} % 楷体\newcommand{\li}{\CJKfamily{li}} % 隶书\newcommand{\you}{\CJKfamily{you}} % 幼圆\newcommand{\wuhao}{\fontsize{10.5pt}{12.6pt}\selectfont} % 五号字体\newcommand{\xiaosi}{\fontsize{12pt}{14pt}\selectfont} % 小四字体\newcommand{\sihao}{\fontsize{14pt}{\baselineskip}\selectfont} % 四号字体%\marginparpush %%-----------------------------超链接和标签-------------------------------\iffalse % 将这里改为\iftrue即可使用\ifx\pdfoutput\undefined % Not run pdftex% \ifx% \usepackage[dvips]{hyperref}% \else\usepackage[dvipdfm]{hyperref}% \fi\AtBeginDvi{\special{pdf:tounicode GBK-EUC-UCS2}} % GBK -> Unicode\else\usepackage[pdftex]{hyperref}\fi\hypersetup{CJKbookmarks,%bookmarksnumbered,%colorlinks,%linkcolor=blue,%citecolor=blue,%hyperindex,%plainpages=false,%pdfstartview=FitH}\fi%--------------------------------注释------------------------------------\iffalse % 将这里改为\iftrue即可使用%注释掉一段内容\usepackage{verbatim}\begin{comment}This is a comment example.\end{comment}\fi%\makeatletter % @ is now a normal "letter" for Tex%\makeatother % @ is restored as a "non-letter" for Tex%--------------------------------其他宏包--------------------------------%\usepackage{amsmath,amsthm,amsfonts,amssymb,bm} % 数学宏包%\usepackage{graphicx,psfrag} % 图形宏包%\usepackage{makeidx} % 建立索引宏包%\usepackage{listings} % 源代码宏包%---------------------------------正文-----------------------------------\begin{document} % 开始正文% song-宋体 hei-黑体 fs-仿宋 kai-楷体 li-隶书 you-幼圆 com为 song+hei\begin{CJK*}{GBK}{com} % 开始中文环境\CJKtilde % 重定义~代表的空白距离\CJKindent % 段首缩进\CJKcaption{GB} % 中文章节标题\author{ceo} % 作者\title{一个latex例子} % 题目\maketitle % 生成标题%\thispagestyle{empty} % 设置首页的页眉页脚风格%\setlength{\baselineskip}{3ex plus1ex minus1ex} % 调整行距\TeX{}~是由图灵奖得主\index{Knuth, Donald E.}~Donald E. Knuth\cite{texbook}~编写的计算机程序，用于文章和数学公式的排版。

01引言Chapter目的和背景目的背景适用范围和使用方法适用范围使用方法02 LaTeXChapterLaTeX概述LaTeX安装与配置编辑器选择及使用技巧03PPT制作要素与规范Chapter01020304统一使用相同的字体、字号、行间距等排版元素，确保整体风格一致。

保持一致性避免过多的文字和图片，突出关键信息，保持页面整洁。

简洁明了通过标题、副标题、正文等层次结构，使内容条理清晰，易于理解。

层次感合理安排页面元素的位置和大小，保持页面平衡和谐。

对齐与平衡页面布局与排版原则色彩搭配与视觉效果提升色彩选择对比度背景与前景图片与图标01020304图表类型选择简洁明了数据准确性数据可视化技巧图表制作及数据可视化方法04 LaTeXChapter主题突出背景简洁Logo 和标题030201封面设计目录结构设置层次分明导航清晰链接跳转正文内容编排技巧图文并茂文字简练结合图片、图表等可视化元素展示数据和信息，提高观众理解度。

突出重点图表插入与编辑方法选择合适图表类型根据数据特点选择合适的图表类型，如柱状图、折线图、饼图等。

数据编辑与格式化在LaTeX中编辑数据，设置图表标题、坐标轴标签等，使图表更加直观易懂。

图表美化调整图表颜色、线条粗细等样式，提升图表美观度。

05常见问题解决方案及优化建议Chapter编译错误处理策略确保LaTeX代码语法正确，特别是命令、环境、括号等。

编译错误时，查看LaTeX编译器提供的错误提示信息，定位问题所在。

将代码分块，逐步排查问题，缩小错误范围。

利用在线LaTeX编辑器或排错工具，检查并修正代码错误。

检查语法错误查看错误提示逐步排查使用在线工具保持一致性在整篇文档中保持字体、字号的一致性，避免过多的样式变化。

字体选择使用`usepackage{fontspec}`命令加载字体包，通过`setmainfont{FontName}`设置主字体。

字号调整使用`fontsize{size}{baselineskip}`命令设置字号和行间距，其中`size`为字号大小，`baselineskip`为行间距。

当您在撰写数学论文或报告时，使用LaTeX数学模板可以帮助您更轻松地组织和格式化数学内容。

以下是一个简单的LaTeX数学模板样例，用于演示如何使用LaTeX编写数学公式和符号。

首先，确保您已经安装了LaTeX软件包和相应的数学包。

然后，按照以下步骤创建数学模板文档：1. 创建一个新的LaTeX文档，并使用适合您的模板或新建一个空白文档。

2. 在文档中添加一个环境来包含您的数学公式和符号。

常用的环境是`equation`、`align`或`gather`等。

3. 在环境中，使用LaTeX数学命令来创建公式和符号。

以下是一些常用的命令示例：* `\frac{分子}{分母}`：用于分数。

* `\sqrt{x}`：用于平方根。

* `\lim_{x \rightarrow ∞}`：用于极限符号。

* `\oint_{x=a到b}`：用于积分符号。

* `\pm`、` \times`、` \div`等：基本的运算符。

4. 添加必要的上下文和说明。

例如，如果您要写一个数学定理的证明过程，请提供相关的定义、前提和结论。

5. 使用LaTeX文档类和数学包来正确显示公式和符号。

通常，LaTeX文档类提供了一些预设的样式和符号，而数学包提供了更多的符号和格式选项。

6. 在编译LaTeX文档时，确保正确设置了排版选项和格式化参数。

下面是一个简单的LaTeX数学模板样例，其中包含一些常见的数学公式和符号：```latex\documentclass{article} % 选择适合您的文档类，例如report或book\usepackage{amsmath} % 添加数学包以提供额外的符号和格式选项\begin{document}\begin{equation}\lim_{x \rightarrow \infty} \frac{x}{e^x} = 1\end{equation}\begin{align}a +b &=c \\x^2 + y^2 &= z^2 \\\frac{d}{dx} f(x) &= g(x)\end{align}\end{document}```这个样例包含了一个极限公式、一个加法公式和一个微分公式。

latex风格PPT模板目录•幻灯片整体风格设计•标题页设计•正文内容排版规则•目录页与过渡页设计•结尾部分设计•实例演示与操作指南幻灯片整体风格设计背景色与主题色选择背景色选择淡雅、柔和的颜色作为背景色，如浅灰、米白、淡蓝等，避免使用过于刺眼或深重的颜色。

主题色根据PPT的内容和目的，选择1-2种与背景色搭配协调的主题色，用于强调关键信息、突出重点。

字体类型与大小设置字体类型建议使用清晰易读的字体，如宋体、黑体、微软雅黑等，避免使用过于花哨或难以辨认的字体。

字体大小根据幻灯片的内容和布局，合理设置标题、正文、注释等不同层级的字体大小，确保观众能够清晰阅读。

图标、图片等素材搭配图标选择与PPT内容相关的图标，用于直观地表达关键信息或概念，注意图标的风格和色彩应与整体风格相协调。

图片选择与PPT内容相关的高质量图片，用于提升幻灯片的视觉效果和吸引力，注意图片的尺寸和分辨率应适合幻灯片布局。

标题页设计标题呈现方式居中放置标题应居中放置，突出主题，字体大小适中，醒目但不失庄重。

使用latex字体采用latex风格的字体，如ComputerModern或Latin Modern，保持学术风格的一致性。

适当使用粗体和斜体对于关键词或重要信息，可使用粗体或斜体进行强调，但不宜过多，以免显得杂乱。

在标题下方居中放置作者姓名，字体大小略小于标题，可使用较小字号以区分层次。

作者姓名单位名称和地址联系方式在作者姓名下方列出单位名称和地址，字体大小适中，保持清晰易读。

如有需要，可在单位信息下方提供作者的联系方式，如邮箱、电话等。

030201作者、单位信息展示在标题页底部注明报告或演示的日期，以便观众了解时间背景。

日期对于多次修改或更新的演示文稿，可在日期旁边注明版本号，方便观众了解内容的更新情况。

版本号根据实际需要，还可添加其他相关信息，如会议名称、地点等。

其他附加信息日期、版本号等附加信息正文内容排版规则文字段落格式设置字体选择01建议使用XeLaTeX或LuaLaTeX编译，以支持更多中文字体。

计算机辅助设计latex模板一、封面标题：计算机辅助设计系统研究作者：XXX日期：XXXX年XX月二、摘要本文主要研究了计算机辅助设计系统的关键技术和应用。

首先介绍了计算机辅助设计的基本概念和重要性，然后详细阐述了系统的算法描述、系统设计和实验分析。

最后，总结了本文的主要工作和未来研究方向。

三、前言随着科技的不断发展，计算机辅助设计已经成为工程领域中不可或缺的一部分。

计算机辅助设计系统能够提高设计效率、减少设计成本，并且能够实现更加精确的设计。

本文旨在研究计算机辅助设计系统的关键技术和应用，为相关领域的研究提供参考。

四、文献综述在文献综述部分，我们详细介绍了计算机辅助设计的历史、现状和发展趋势。

我们比较了不同计算机辅助设计系统的优缺点，并探讨了未来可能的研究方向。

通过文献综述，我们得出了计算机辅助设计系统在工程领域中的重要性和应用价值。

五、算法描述在算法描述部分，我们详细介绍了计算机辅助设计系统的算法原理和实现方法。

我们重点介绍了算法的输入、输出和处理过程，并给出了算法的时间复杂度和空间复杂度分析。

通过算法描述，我们得出了计算机辅助设计系统在算法层面的关键技术和实现方法。

六、系统设计在系统设计部分，我们详细介绍了计算机辅助设计系统的整体架构和模块设计。

我们重点介绍了系统的硬件和软件设计，并给出了系统设计的优缺点分析。

通过系统设计，我们得出了计算机辅助设计系统在整体架构和模块设计层面的关键技术和实现方法。

七、实验与分析在实验与分析部分，我们对计算机辅助设计系统进行了实验测试和性能分析。

我们比较了不同参数和不同场景下的实验结果，并给出了实验结果的分析和解释。

通过实验与分析，我们得出了计算机辅助设计系统在实际应用中的性能表现和适用范围。

八、结论本文主要研究了计算机辅助设计系统的关键技术和应用。

通过文献综述、算法描述、系统设计和实验分析，我们得出了计算机辅助设计系统在工程领域中的重要性和应用价值。

未来，我们将继续深入研究计算机辅助设计系统的关键技术和应用，为相关领域的研究提供更加深入的参考。

\documentclass[CJK,notheorems,mathserif,table]{beamer}\useoutertheme[height=0.1\textwidth,width=0.15\textwidth,hideothersubsections]{sidebar}\usecolortheme{whale} % Outer color themes, 其他选择: whale, seahorse, dolphin . 换一个编译看看有什么不同.\usecolortheme{orchid} % Inner color themes, 其他选择: lily, orchid\useinnertheme[shadow]{rounded} % 对box 的设置: 圆角、有阴影.\setbeamercolor{sidebar}{bg=blue!60} % sidebar的颜色, 50%的蓝色.\setbeamercolor{background canvas}{bg=blue!9} % 背景色, 9%的蓝色. 去掉下一行, 试一试这个.\setbeamertemplate{background canvas}[vertical shading][bottom=white,top=structure.fg!25] %%背景色, 上25%的蓝, 过渡到下白.\usefonttheme{serif} % 字体. 个人偏好有轮廓的字体. 去掉这个设置编译, 就看到不同了. \setbeamertemplate{navigation symbols}{} %% 去掉页面下方默认的导航条.%%------------------------常用宏包---------------------------------------------------------------------%%注意, beamer 会默认使用下列宏包: amsthm, graphicx, hyperref, color, xcolor, 等等\usepackage{CJK}\usepackage{amsmath,amsthm,amsfonts,amssymb,bm}%\usepackage{ntheorem}\usepackage{mathrsfs}\usepackage{subfigure} %%图形或表格并排排列\usepackage{xmpmulti} %%支持文中的\multiinclude 等命令, 使mp 文件逐帧出现. 具体讨论见beamer 手册.\usepackage{colortbl,dcolumn} %% 彩色表格\usepackage{graphicx}%\logo{\includegraphics[height=1in\textwidth]{ustc.eps}} %左上角科大logo %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%重定义字体、字号命令%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\newcommand{\songti}{\CJKfamily{song}} % 宋体\newcommand{\fangsong}{\CJKfamily{fs}} % 仿宋体\newcommand{\kaishu}{\CJKfamily{kai}} % 楷体\newcommand{\heiti}{\CJKfamily{hei}} % 黑体\newcommand{\lishu}{\CJKfamily{li}} % 隶书\newcommand{\youyuang}{\CJKfamily{you}} % 幼圆\newcommand{\sihao}{\fontsize{14pt}{\baselineskip}\selectfont} % 字号设置\newcommand{\xiaosihao}{\fontsize{12pt}{\baselineskip}\selectfont} % 字号设置\newcommand{\wuhao}{\fontsize{10.5pt}{\baselineskip}\selectfont} % 字号设置\newcommand{\xiaowuhao}{\fontsize{9pt}{\baselineskip}\selectfont} % 字号设置\newcommand{\liuhao}{\fontsize{7.875pt}{\baselineskip}\selectfont} % 字号设置\newcommand{\qihao}{\fontsize{5.25pt}{\baselineskip}\selectfont} % 字号设置\newcommand{\bahao}{\fontsize{4.5pt}{\baselineskip}\selectfont} % 字号设置%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{document}\begin{CJK*}{GBK}{kai}%%----------------------- Theorems ---------------------------------------------------------------------\newtheorem{theorem}{定理}\newtheorem{definition}{定义}\newtheorem{lemma}{引理}%%----------------------------------------------------------------------------------------------------\title{\heiti 题目}\author[\textcolor{white}{\songti 作者}]{{\songti 报告人~\textcolor{olive}{XXX}}\\{\songti 指导教师~~\textcolor{olive}{XXX}}}\institute{\wuhao \lishu \textcolor{violet}{XX实验室}}\date{12-26 2012}\frame{ \titlepage }%%---------------------------------------------------------------------------------------------------\section*{内容概览}\frame{\frametitle{目录}\tableofcontents}%%============================================================================ =======================\section{研究内容与方法}%任意两行单列线表示一张ppt%%---------------------------------------------------------------------------------------------------\begin{frame}\frametitle{西江月·顷在黄州}\begin{itemize}\item 顷在黄州，春夜行蕲水中，过酒家饮。

latexPPT模板模板⼀%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % beamer template made by 李会% 2019-7-12 at Taiyuan,China% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%----------------------------------------------------------------------------------------% PACKAGES AND THEMES%----------------------------------------------------------------------------------------\documentclass{beamer}\mode<presentation> {% The Beamer class comes with a number of default slide themes% which change the colors and layouts of slides. 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Integer lectus nisl, ultricies in feugiat rutrum, porttitor sit amet augue. Aliquam ut tortor mauris. Sed volutpat ante purus, quis accumsan dolor.\end{columns}\end{frame}%------------------------------------------------\section{Second Section}%------------------------------------------------\begin{frame}\frametitle{Table}\begin{table}\begin{tabular}{l l l}\toprule\textbf{Treatments} & \textbf{Response 1} & \textbf{Response 2}\\\midruleTreatment 1 & 0.0003262 & 0.562 \\Treatment 2 & 0.0015681 & 0.910 \\Treatment 3 & 0.0009271 & 0.296 \\\bottomrule\end{tabular}\caption{Table caption}\end{table}\end{frame}%------------------------------------------------\begin{frame}\frametitle{Theorem}\begin{theorem}[Mass--energy equivalence]$E = mc^2$\end{theorem}\end{frame}%------------------------------------------------\begin{frame}[fragile] % Need to use the fragile option when verbatim is used in the slide\frametitle{Verbatim}\begin{example}[Theorem Slide Code]\begin{verbatim}\begin{frame}\frametitle{Theorem}\begin{theorem}[Mass--energy equivalence]$E = mc^2$\end{theorem}\end{frame}\end{verbatim}\end{example}\end{frame}%------------------------------------------------\begin{frame}\frametitle{Figure}Uncomment the code on this slide to include your own image from the same directory as the template .TeX file.%\begin{figure}%\includegraphics[width=0.8\linewidth]{test}%\end{figure}\end{frame}%------------------------------------------------\begin{frame}[fragile] % Need to use the fragile option when verbatim is used in the slide\frametitle{Citation}An example of the \verb|\cite| command to cite within the presentation:\\~This statement requires citation \cite{p1}.\end{frame}%------------------------------------------------\section{Third Section}%------------------------------------------------%------------------------------------------------\begin{frame}\frametitle{References}\footnotesize{\begin{thebibliography}{99} % Beamer does not support BibTeX so references must be inserted manually as below\bibitem[Smith, 2012]{p1} John Smith (2012)\newblock Title of the publication\newblock \emph{Journal Name} 12(3), 45 -- 678.\end{thebibliography}}\end{frame}%------------------------------------------------%\begin{frame}%\frametitle{Figure}%\begin{center}%\includegraphics[width=0.5\linewidth]{Fig10} %插⼊图⽚%\includegraphics[width=1.0\linewidth]{Fig10}%\end{center}%\end{frame}%------------------------------------------------\begin{frame}\Huge{\centerline{The End. Any advice?}}\end{frame}%----------------------------------------------------------------------------------------\end{document}--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------模板⼆% !Mode:: "TeX:UTF-8"%% 使⽤ XeLaTeX 编译.\documentclass[notheorems,mathserif,table]{beamer}\useoutertheme[height=0.1\textwidth,width=0.15\textwidth,hideothersubsections]{sidebar}\usecolortheme{dolphin} % Outer color themes, 其他选择: whale, seahorse, dolphin . 换⼀个编译看看有什么不同.\usecolortheme{lily} % Inner color themes, 其他选择: lily, orchid\useinnertheme[shadow]{rounded} % 对 box 的设置: 圆⾓、有阴影.\setbeamercolor{sidebar}{bg=blue!50} % sidebar的颜⾊, 50%的蓝⾊.\setbeamercolor{background canvas}{bg=cyan!9} % 背景⾊, 9%的蓝⾊. 去掉下⼀⾏, 试⼀试这个.\setbeamertemplate{background canvas}[vertical shading][bottom=white,top=structure.fg!25] %%背景⾊, 上25%的蓝, 过渡到下⽩. \usefonttheme{serif} % 字体. 个⼈偏好有轮廓的字体. 去掉这个设置编译, 就看到不同了.\setbeamertemplate{navigation symbols}{} %% 去掉页⾯下⽅默认的导航条.\usepackage{ragged2e}\justifying\let\raggedright\justifying%%------------------------常⽤宏包---------------------------------------------------------------------%%注意, beamer 会默认使⽤下列宏包: amsthm, graphicx, hyperref, color, xcolor, 等等\usepackage[UTF8]{ctex}\hypersetup{CJKbookmarks=true}\usepackage{subfigure} %%图形或表格并排排列\usepackage{colortbl,dcolumn} %% 彩⾊表格\usepackage{xcolor}\usepackage{lineno}% amsmath package, useful for mathematical formulas%\usepackage{multirow}\usepackage{amsmath}\usepackage{xcolor}\usepackage{bm}% amssymb package, useful for mathematical symbols\usepackage{amssymb}\usepackage{subfigure}% graphicx package, useful for including eps and pdf graphics% include graphics with the command \includegraphics\usepackage{graphicx}%\graphicspath{{note/figure/}{note/image}{./image/}}\graphicspath{{figures/}} %% 图⽚路径. 本⽂的图⽚都放在这个⽂件夹⾥了.%\usepackage{epstopdf}\usepackage{multirow}\usepackage{url}% cite package, to clean up citations in the main text. Do not remove.%\usepackage{cite}\usepackage{color}%\usepackage{lineno}% Use doublespacing - comment out for single spacing\usepackage{setspace}%\doublespacing\usepackage[square, comma, sort&compress, numbers]{natbib}%\usepackage{ulem}\usepackage{color}\usepackage{algorithm}\usepackage{algorithmicx}\usepackage{algpseudocode}\usepackage{amsmath}\floatname{algorithm}{Algorithm}\renewcommand{\algorithmicrequire}{\textbf{Input:}}\renewcommand{\algorithmicensure}{\textbf{Output:}}\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}% correct bad hyphenation here\hyphenation{op-tical net-works semi-conduc-tor}\logo{\includegraphics[height=0.09\textwidth]{SCUEC.png}}%% 民⼤校徽, MetaPost ⽂件.%\renewcommand{\raggedright}{\leftskip=0pt \rightskip=0pt plus 0cm}%\raggedright %% 中⽂对齐\def\hilite<#1>{\temporal<#1>{\color{blue!35}}{\color{magenta}}{\color{blue!75}}}%% ⾃定义命令, 源⾃ beamer_guide. item 逐步显⽰时, 使已经出现的item、正在显⽰的item、将要出现的item 呈现不同颜⾊.\newcolumntype{H}{>{\columncolor{blue!20}}c} %% 表格设置%==================================参考⽂献==============================================================\newcommand{\upcite}[1]{\textsuperscript{\cite{#1}}} %⾃定义命令\upcite, 使参考⽂献引⽤以上标出现\bibliographystyle{plain}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%重定义字体、字号命令%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document}%%----------------------- Theorems ---------------------------------------------------------------------\newtheorem{theorem}{定理}\newtheorem{definition}{定义}\newtheorem{lemma}{引理}\newtheorem{corollary}{推论}\newtheorem{proposition}{性质}\newtheorem{example}{例}\newtheorem{remark}{注}\renewcommand\figurename{\rm 图}\renewcommand\tablename{\bf 表}%%----------------------------------------------------------------------------------------------------\title{\heiti Latex制作ppt}\author[\textcolor{white}{\songti 作者~胡怀飞}]{\songti 作者~~\textcolor{olive}{胡怀飞}}\institute{\zihao{5} \lishu \textcolor{violet}{中南民族⼤学~~⽣物医学⼯程学院}}\date{\today}%%---------------------------------------------------------------------------------------------------\section*{⽬录}\frame{\frametitle{⽬录}\tableofcontents}%%===================================================================================================\section{简介}%%---------------------------------------------------------------------------------------------------\begin{frame}\frametitle{这是latex制作的ppt}latex与word，ppt是⽬前⽤得最多得排版⼯具。

latex科技文档排版"\documentclass[a4paper]{ctexart}\usepackage{amsmath}\usepackage{amssymb}\usepackage{mflogo}\usepackage{upgreek}\usepackage{paralist}\usepackage{chngpage}\usepackage{yhmath}\addtolength{\voffset}{-1cm}\addtolength{\textheight}{2cm}\addtolength{\hoffset}{-1.5cm}\addtolength{\textwidth}{3cm}\usepackage{color}\pagestyle{plain}\usepackage[dvipdfm]{hyperref}\hypersetup{colorlinks,linkcolor=blue, hyperindex,pdfstartview=FitH, CJKbookmarks,bookmarks, bookmarksnumbered,pdfauthor={aa},pdftitle={},pdfkeywords={},pdfsubject={}}\usepackage{makeidx}\usepackage{verbatim}\newcommand{\tex}{\TeX}\newcommand{\ltx}{\LaTeX}\newcommand{\ctex}{$\mathbb{C}$\TeX}\newcommand{\heitii}[1]{\textbf{#1}}\newcommand{\qdiao}[1]{\textbf{\large #1}}\newcommand{\zaogao}{\heitii{糟糕:}\quad}\newcommand{\gzaogao}{\heitii{更糟糕:}\quad} \newcommand{\cuowu}{\heitii{错误:}\quad}\newcommand{\zhengque}{\heitii{正确:}\quad} \newcommand{\zhushi}{\heitii{注释:}\quad}\newcommand{\lizi}[1]{\heitii{例~{#1}}\quad} \newcommand{\dkong}{\quad \quad \quad ~} \DeclareMathOperator{\arccot}{arccot}\DeclareMathOperator{\sh}{sh}\DeclareMathOperator{\arsinh}{arsinh}\DeclareMathOperator{\arcosh}{arcosh}\DeclareMathOperator{\arcoth}{arcosh}\DeclareMathOperator{\artanh}{artanh}\DeclareMathOperator{\arsech}{arsech}\DeclareMathOperator{\arcsch}{arcsch}\DeclareMathOperator{\arcsec}{arcsec}\DeclareMathOperator{\arccsc}{arccsc}\DeclareMathOperator{\csch}{csch}\DeclareMathOperator{\sech}{sech}\DeclareMathOperator{\shibu}{Re}\DeclareMathOperator{\xubu}{Im}\CTEXsetup[format={\large\bfseries}]{section} \makeindex\title{\LaTeX ~科技排版}\begin{document}\maketitle\tableofcontents\section{导言}在~\ctex~社区的努力下, 中国的~\ltx ~用户数量在过去几年中增长非常快速．虽然我们普遍认为~\tex ~内建的%排版机制是最好的, 但是每个用户实现的排版质量都可能不同．就像王垠博士（清华大学）所说的%:\!“世界上最漂亮的以及最难看的数学书都是用~\ltx ~排版的．”大体上来说, 有两种方法来“美化”你的文档：设计一个好看的页面样式（多少需要一些艺术素养）%或者精调文字和数学公式（这也正是这本小册子的内容）\!．在这本小册子中作者用例子来说明所有的点子．标有“糟糕”字样的例子或许可以生成所需要的效果%, 但是因为某些原因应该避免使用．标有“错误”字样的例子有非常大的问题所以在任何情况下%都不应该使用．标有“正确”字样的例子是你应该遵循的．这一小册子有两个版本, 分别叫做~CWS001-E~与~CWS001-C~．CWS001-E~是英文版的, 它介绍了排版只含有%英文的文档的规范．CWS001-C~则介绍了排版含有中文的文档的规范．\section{总体规则\index{总体规则}}\heitii{例~2.1}\quad 假设你想使用黑体而且更大一些的字体来表达强调\index{强调}的含义．\heitii{糟糕:}\quad \verb|The word \textbf{\large emphasis} is emphasized.|\heitii{正确:}\quad \verb|\renewcommand{emph}[1]{\textbf{\large #1}}|\quad \quad \quad ~\verb|The word \emph{emphasis} is emphasized.|\heitii{注释:}\quad 这里之所以对~\verb|\emph|~作重定义是因为如果你对用何字体表示%强调改变了主意, 所要做的只是简单的重定义 ~\verb|\emph|．\heitii{规则：总是使用~\textit{generic markup language}（通用标记）而非%~\textit{layout markup language}（附加标记）}\!．\heitii{例~2.2:}\quad $\mathbb{R}$\index{$\mathbb{R}$}~和~R\index{R}~都可以用来表示实数集\index{实数集}．假设你向一个出版社投稿, %而编辑没有告诉你使用那种字体, 你应该怎么做呢？聪明的做法是是定义一个新命令~\verb|rtn|, 即~\verb|newcommand{\rtn}{\mathbb{R}}|~并在%行文中使用它．这样, 如果出版社告诉你他们更喜欢~R, 你只需要重新定义~\verb|\rtn|~就好了．\heitii{例~2.3:}\heitii{糟糕:}\quad 正如上一节所说的……\quad \quad \quad ~参考上面的表格……\heitii{正确:}\quad 正如第~2~节所说的……\quad \quad \quad ~参考表2……\heitii{注释:}\quad 不排除你的文档被制作成电子版的可能性, 而交叉引用\index{交叉引用}可以被自动转换成%超链接．\heitii{规则：总是使用交叉引用功能}\heitii{例~2.4}\heitii{糟糕:}\quad 方程$x^2-2x+1=0$有2个解．\heitii{正确:}\quad 方程~$x^2-2x+1=0$有~2~个解．\heitii{注释:}\quad 使用~\textsf{CJK}~宏包时使用命令~\verb|CJKtidle|~会重定义~\verb|~|%~使其成为一个可断的橡皮长度．应该用它来隔开中文和英文、数字或数学公式．\section{标点符号}\index{标点符号}\heitii{例~3.1}\quad 半角和全角\index{半角和全角}\heitii{错误:}\quad 例如求解方程~$ x^3+ax+c=d$~的解, 在~$a$, $b$, $c$, 不是给定数值时%, 数值分析的方法是没有用的.\heitii{正确:}\quad 在只有中文而没有英文和数学公式的文档中, 全部使用全角标点万刚可以取得更好的%输出效果.但如果在文档中既有中文又有英文或者数学公式, 可以尝试遵循下面的规则：建议使用半角的标点：句号、顿号、括号、引号、书名号、间隔号建议使用全角的标点：逗号、分号、冒号、问号、感叹号一个基本的原则是尽可能减少与英文标点的区别.另外, 在科技文档中通常使用英文半角句点.在上面的例子中, 还要注意不要录入~\verb|$a, c, d$|, 而应该~\verb|$a$, $c$, $d$|.需要指出的是.使用全角括号和全角引号并非最好的主意, 我们不妨看这样一个例子：这样经过一番计算后（见上文）, 我们可以得到~$(a+b)+c=a+(b+c)$.相对较好的做法是定义如下一些命令：\begin{verbatim}\def\({\raisebox{0.25mm}{(}}\def\){\raisebox{0.25mm}{)}}\def\``{\raisebox{0.5mm}{``}}\def\"{\raisebox{0.5mm}{''}}\end{verbatim}然后在文中使用这些命令, 它们可以保证你全文标点的一致性, 但是多少麻烦了一些.我们期待更好的%解决方案.在本例中没有提及的标点符号会在接下来的例子中特别说明.\heitii{例~3.2:}\heitii{错误:}\quad 果汁说: “我很好喝. ”\heitii{正确:}\quad 果汁说:“我很好喝.”\heitii{注释:}\quad 在大多是半角标点之后应该加上一个空格, 但如果后面跟的是一个全角%标点情况就不同了！\heitii{例~3.3}\heitii{糟糕:}\quad 精调的文字和数学公式（这正是这本小册子的内容）.\heitii{正确:}\quad 精调的文字和数学公式（这正是这本小册子的内容）\!.\heitii{注释:}\quad 第二行的例子是用\verb|精调的文字和数学公式（这正是这本小册子的内容）\!.|获得的.注意其中~\verb|\!|~的使用.一般的, 在全角标点之后接一个半角标点时, 应该加上~\verb|\!|.\heitii{例~3.4}\quad 句点\index{句点}\heitii{错误:}\quad \verb|Prof. Duke|\quad \quad \quad ~\verb|This sentence ends with NASA. Go on to the next sentence.|\heitii{正确:}\quad \verb|Prof.\ Duke|\quad \quad \quad ~\verb|This sentence ends with NASA.\@ Go on to the next sentence.|\heitii{注释:}\quad Prof. Duke~中的句点并不代表句子的结束. 在这种情况下, 在句点之后%放上~\verb*|\ |~表示一般的空格.\ltx ~并不将大写字母之后的句点理解为句号, 而命令~\verb|\@|~可以告诉句点:“你表示%句子结束了.”\heitii{例~3.5}\quad 顿号与逗号\index{顿号与逗号}\heitii{错误:}\quad 10~以内的质数是~2、3、5、7.\quad \quad \quad ~宗教, 战争, 农业, 牧业和手工业\heitii{正确:}\quad 10~以内的质数是~2, 3, 5, 7.\quad \quad \quad ~宗教、战争、农业、牧业和手工业\heitii{注释:}\quad 外文、阿拉伯数字之间的并列关系并不用顿号, 而用逗号, 如~1, %2；如果并列词中有汉字, 则使用顿号. 注意不同层次的并列应以顿号、逗号区别, %不能一律用顿号.\heitii{例~3.6}\quad 连接号\index{连接号}\heitii{错误:}\quad 鲁迅（1881～1936)\quad \quad \quad ~物理-化学反应\heitii{正确:}\quad 鲁迅（1881~－~1936)\quad \quad \quad ~物理－化学反应\heitii{注释:}\quad 连接号有以下几种：（a）-（连字符号）:必要时表达公式号、图号、表号中的短横线；（b）－（连字符号）:用于时间、地点等的起止, 复合名词的短横线；（c)——（破折号）:中文的破折号. 我们衡量一个中文破折号是否“合格”的标准是它与汉字“一”%是否在一直线上. 按照这样的标准, 用~\verb|\raisebox{0.5mm}{------}|~获得的破折号是%比较美观的.\heitii{例~3.7}\quad 省略号\index{省略号}\heitii{糟糕:}\begin{displaymath}\begin{pmatrix}a_{11} & a_{12} & \cdots & a_{1n}\\a_{21} & a_{22} & \cdots & a_{2n}\\\cdots & \cdots & \cdots & \cdots \\a_{n1} & a_{n2} & \cdots & a_{nn}\\\end{pmatrix}\end{displaymath}\heitii{正确:}\begin{displaymath}\begin{pmatrix}a_{11} & a_{12} & \cdots & a_{1n}\\a_{21} & a_{22} & \cdots & a_{2n}\\\vdots & \vdots & \quad & \vdots \\a_{n1} & a_{n2} & \cdots & a_{nn}\\\end{pmatrix}\end{displaymath}\heitii{规则: 在矩阵中只是用三个竖点或者三个横点.} \heitii{例3.8}\quad 省略号\heitii{错误:}\quad 1, 2\,……\quad \quad \quad ~宗教, 战争, \ldots\heitii{正确:}\quad 1, 2,\ldots\quad \quad \quad ~宗教, 战争……\heitii{注释:}\quad 省略号有多种：（a）\ldots ~或~$\cdots$ ~用于外文、阿拉伯数字省略. 如果省略的是中间项, 前后标点均保留%; 如果省略的是后面所有项, 只保留省略号前面的标点. 使用~\verb|\ldots|~或~\verb|$\cdots$|~%生成.（b）……~用于汉语省略. 省略号前一般没有其他标点, 必要时也只保留句末点号, 省略号后不保%留任何标点. 也可以用于外文、阿拉伯数字整行及整段省略.（c）…………~用于汉语整行及整段省略.\heitii{例3.9}\quad 数学模式中的省略号后的标点\heitii{错误:}\quad $\uppi =3.141\,592\,6\ldots$,\heitii{正确:}\quad $\uppi =3.141\,592\,6\ldots \,$,\heitii{注释:}\quad 第二行的例子是这样生成的: \verb|$\uppi=3.141\,592\,6\ldots\,$,.|\footnote{因为用了~\textsf{upgreek}~宏包实现正体,在这里做了相应的改变.}省略号总是应该很仔细的来录入, 参考以下例子:\[x_1 + \cdots +x_n \]\[x_1=x_2= \cdots =x_n=0\]\[A_1 \times \cdots \times A_n\]\[f(x_1,\cdots ,x_n)\]\[x_1x_2\cdots x_n\]\[(1-x))(1-x^2)\ldots (1-x^n)\]\[n(n-1)\ldots (1)\]\section{数字}\index{数字}根据~GB/T~15835－1995《出版物上数字用法的规定》, 正确表达数字.\heitii{例~4.1}\heitii{错误:}\quad 123,456,789\heitii{正确:}\quad 123\,456\,789\heitii{注释:}\quad 专业性科技出版物的分节法是从小数点起, 向左和向右每三位数字一组%, 组间空四分之一个汉字的位置.\heitii{例~4.2}\quad 概数和约数\heitii{错误:}\quad 三、四天\heitii{糟糕:}\quad 1000~多种\heitii{正确:}\quad 三四天\quad \quad \quad ~一千多种\heitii{注释:}\quad 相邻的两个数字并列连用表示概数, 必须使用汉字, 连用的两个数字之间不得用%顿号隔开. 用“余”、“多”、“左右”、“上下”等表示的约数一般用汉字, 但如果文中出现一组%具有统计和比较意义的数字, 其中既有精确数字, 也有用“多”、“余”表示的概数, 为保持局部%体例上的一致, 其约数也可以使用阿拉伯数字. 例如: 某单位从机动财力拿出~1\,900~万元，调拨%钢材~3\,000~多吨、水泥~2~万多吨、柴油~1\,400~吨, 用于农田水利建设.\section{单位}\lizi{5.1}单位的字体\heitii{错误:}\quad 这把尺子长~100cm.\heitii{更糟糕:}这把尺子长~100~厘米.\heitii{正确:}\quad 这把尺子长~100\,cm.\heitii{注释:}\quad 单位符号置于数值之后并用一个四分之一汉字大小的空隙隔开.唯一的特例就是平面角的度、分、秒: $^\circ,\,',\,''$, 例如, $\alpha=360^\circ$, 而%非~$\alpha=360\,^\circ$. 不过, 摄氏度的符号前依然应该加上四分之一个汉字大小的空隙, 例如%, $t=25\,^\circ \textrm{C}$, 而非~$t=25^\circ \textrm{C}$.\heitii{例~5.2}\quad 单位的组合\heitii{糟糕:}\quad N\,m\quad \quad \quad ~m\,s$^{-1}$\zhengque N\,$\cdot$\,m\dkong m$\slash$s\zhushi 不过有一些出版社要求作者不使用点式的组合方式.\footnote{抄到这里才醒过来，可以把\heitii{错误:}这些很频繁的输入重定义以减少输入, 真是个大杯具. 留下记号, 作为经验教训.}你可以在《国际单位制》、\textit{ISO-31}、\textit{GB-3100}、\textit{GB-3101}~和~\textit{GB-3102}%~上找到完整的单位列表. 如果一个量又多个符号来表示, 总是使用第一个列出的. 作者在此列出一些%频繁用错的量和单位符号.\begin{inparaenum}\item 用符号~$\delta$~表示厚度, $d$~表示直径. 在国家标准中，厚度的首选符号是~$d\,$, 这样%就和直径的量符号产生了冲突.（我们的原则是一个量符号尽可能只赋予一个含义）. 考虑到~$d$~%被更普遍地用来表示直径, 我们推荐用~$\delta$~来表示厚度.\item 在向国际出版社投稿时, 不应该使用单位~n\,mile（海里）, 因为这一单位在国际上并不被认可.\item 虽然在中国,我们更普遍的使用~$S$~来表示面积, 但在国际数学界, 符号~$A$~用得更多.\item 公顷在国际上认可的符号式~ha（a~来自于单词~acre），但是, 中国国家标准将单位~a~作为%年的符号（来自单词~annus）, 例如, 1a~表示一年. 为了减少冲突, 我们使用~hm$^2$~表示公顷%, 也即~1\,hm$^2=10^4\,\textrm{m}^2\,$. 在任何情况下都不要使用~a~这一符号.\item 重量与质量是不同的概念, 例如, 如果一个物体的质量是~$m=10\,\textrm{kg}\,$, 则它的重量是%$W=98\,\textrm{N}$.\item 避免使用~bar, atm, Torr~和~mmHg~作为压力的单位, 总是使用~Pa.\item 使用~$\mu$~作为动摩擦因数的量符号, 而~$\mu _{\textrm{s}}$~作为静摩擦因数的量符号. %注意因数和系数两个词的区别.\item 使用~$T$~作为热力学温度的量符号, 而将~$t$~作为摄氏温度的量符号.\item 不可使用“比热”这一词, 使用“比热容”或者“质量热容”.\item 避免使用“内能”这一词, 使用“热力学能”代替.\item 不可使用“电流强度”这一词, 使用“电流”代替.\item 不可使用”电量“这一词, 使用“电荷量”或“电荷”代替.\item 使用~$V$~作为电势的量符号, $U$~作为电势差的量符号.\item 使用~$E$~作为电动势的量符号, 而非~$\varepsilon$.\item 使用~$\mathit{\Phi}$~作为磁通量.（\verb|$mathit{\Phi}$|）\item 不要将化学式作为下标, 例如, 记号~$c($H$_2$SO$_4)$是正确的, 而~$c_{\textrm{H}_2\textrm{SO}_4}$~是错误的.\item 使用上标~\begin{math}^\textrm{\textasteriskcentered}\end{math}~表示“纯的”%, 而~$^\ominus$~表示“标准的”, 例如, B~在气体混合物中的标准绝对活度由~$\lambda_{\textrm{B}}^{\ominus}$~表示.\item 术语“原子量”和“分子量”已被废止, 使用“相对原子质量”和“相对分子质量”代替%, 它们的量符号分别是~$A_\textrm{r}$~和~$M_\textrm{r}$.\item 使用~$N_\textrm{A}$~代表阿伏伽德罗常数, 而非~$N_A$.\item 术语“基本电荷”已被废止, 使用“元电荷”代替.\end{inparaenum}\section{数学}本节作为国家标准~GB 3012.11~或国际标准~ISO 31-11（物理科技和技术中常用数学符号）的补充文件. %对于本节没有提到的符号, 参照~GB 3012.11~或者~ISO 31-11~执行.\subsection{总体规则}作为总则, 如果标准中列出了两个或两个以上的符号, 则应使用第一个. 例如, 在~GB 3012.11~%中,“不属于”有两个符号: $\not\in$~和~$\bar{\in}$, 则应使用前者. 类似的, 我们应该%使用~$\bar{a}$~而不是~$\langle a \rangle$~来表达~$a$~的平均数.\lizi{6.1}符号的字体应用斜体表达的符号:－量的符号, 例如, $m$~是质量的符号;－物理常数, 例如, $N_{\textrm{A}}$~表示阿伏伽德罗常数;－变动附标与变量, 例如, $y=\sum_{i=1}^{m}x_iz_i,\,x^2=ay^2+bz^2$;－函数, 例如, $f,\,g$;－点~$A$, 线段~$AB$, 弧~$CD$.应用正体表示的符号:－单位, 例如, $\upmu$m, mL;－化学符号, 例如, O~表示氧, C~表示碳;－数学常数, 例如, $\textrm{i}^2=-1$，$\uppi=3.141\,592\,6\ldots\,$,$\textrm{e}=2.718\,281\,8\ldots\,$;－已定义的函数, 例如, $\sin x\,$,$\exp x\,$;－已定义的算子, 例如, $\updelta x\,$,$\textrm{d}f\slash \textrm{d}x\,$.应用黑斜体表达的符号:－向量; 例如, $\textbf{\textit{a}}=a_x\textbf{\textit{e}}_x+a_y\textbf{\textit{e}}_ y+a_z\textbf{\textit{e}}_z=(a_x,a_y,a_z)$;－矩阵, 例如, $\det \textbf{\textit{A}}\,$;应用~\textsf{sans serif}~斜体表达的符号－张量, 例如, $\textit{\textsf{T}}\,$.\zhushi \tex ~没有内建正体小写希腊字母, 但是有不少方法来得到他们. 抄写%者方法\footnote{~原作者的的方法在我看来太复杂了，这里用了~upgreek~宏包.}如下:安装~\textsf{upgreek}~宏包，通过~\verb|$\uppi$|~可以得到正体的~$\uppi\,$.\lizi{6.2} 下标的字体下标是量符号或变量时应使用斜体, 例如:$C_p$~中的~$p$~是压力的量符号, $q_m$~中的~$m$~是质量的量符号, $\omega_z$~中%的~$z$~是坐标.下标是描述性的信息时应使用正体, 例如:$C_{\textrm{g}}$~中的~g~表示气体, $\mu_{\textrm{r}}$~中的~r~表示相对, $E_{\textrm{k}}$~中的~k~表示动的.\lizi{6.3}\zaogao 考虑~$S_q\,$, $q < p\,$.\zhengque 考虑$S_q\,$, 其中~$q < p\,$.\zhushi 不同的公式最好用词语隔开.\lizi{6.4}\zaogao $x_n-a$ has $n$ distinct zeroes.\zhengque The polynomial $x_n-a$ has $n$ distinct zeroes.\zhushi 句子不应该用公式开头.\lizi{6.5} 行间的公式\zaogao 我们来看一个简单的分式~$\frac{1}{2}\,$.\gzaogao 我们来看一个简单的分式~$\displaystyle \frac{1}{2}\,$.\zhengque 我们来看一个简单的分式~$1\slash2 \,$.\zhushi 第一行的例子是糟糕的是因为分式的可读性大大降低了. 第二行的例子更糟糕是因为它破坏了%行距的统一性. 不过这一做法在中国颇为普遍, 这得“归功于”方正. 推荐的做法是使用~$1\slash2$~这样的样式.上、下标, 分式的分子和分母也应该视作行间模式, 例如:\[\textrm{e}^{1\slash2}\, , \quad \quad \frac{x\slash y}{z\slash y}\]一个类似的现象是过度使用~\verb|\limits|~命令. 我们推荐使用~\ltx~的缺省设置, 它们%往往给出更好的结果, 例如, 使用~$\lim_{x \rightarrow 3}x^2=9$~而非~$\lim \limits_{x \rightarrow 3}x^2=9\,$ , 使用~$\sum_{i=1}^{n} i$~而非~$\sum \limits_{i=1}^{n} i$~亦或者是~$\displaystyle \sum \limits_{i=1}^{n} i\,$.\lizi{6.6} A tricky one\zaogao 我们可以获得如下的结果: $f(x)=(4\slash\uppi)\sum_{k=1}^{\infty}\big(\sin(2k-1)x\slash(2k-1)\big)\,$.\zhengque 我们可以获得如下结果:\[f(x)=\frac{4}{\uppi}\sum_{k=1}^{\infty}\frac{\sin(2k-1)x}{2k-1}\,.\]\lizi{6.7} 分隔符的大小\zaogao \[\log_a\left(x\sqrt[4]{\frac{z^2}{y^2}}\right)\quad \quad \left(\sum_{k=1}^n A_k\right)\]\zhengque \[\log_a \bigg(x\sqrt[4]{\frac{z^2}{y^2}}\bigg)\quad \quad \bigg(\sum_{k=1}^n A_k\bigg)\]\zhushi 不要过度使用~ \verb|\left|~和~\verb|\right|~命令.\lizi{6.8} 分段函数\zaogao\begin{displaymath}p_{r-j}=\left\{\begin{array}{ll}0 & \text{if $r-j$ is old}\\r!(-1)^{(r-j)\slash2} & \text{if $r-j$ is even}\end{array}\right.\end{displaymath}\zhengque\begin{displaymath}p_{r-j}=\left\{\!\!\!\begin{array}{ll}0 & \text{if $r-j$ is old},\\r!(-1)^{(r-j)\slash2} & \text{if $r-j$ is even}.\end{array}\right.\end{displaymath}\zhushi 正确的例子是这样输入的,:\begin{verbatim}\begin{displaymath}p_{r-j}=\left\{\!\!\!\begin{array}{ll}0 & \text{if $r-j$ is old},\\r!(-1)^{(r-j)\slash2} & \text{if $r-j$ is even}.\end{array}\right.\end{displaymath}\end{verbatim}此处要注意两个主要的区别: \verb|\!\!\!|~的使用以及其中的标点符号.\lizi{6.9} 自变量\cuowu \verb|{\text{arccot}x|~输出的~$\text{arccot}x$\zhengque\verb|\DeclareMathOperator{\arccot}{arccot}|\quad\verb|$\arccot x$|~得到~$\arccot x\,$.\lizi{6.10} 自变量\cuowu $\sin (n\uppi)$\zhengque $\sin n\uppi$\zhushi 当函数的名子有两个或更多的字母组成且自变量不含~$+\,$, $-$~等运算时, 括号可以省略.\lizi{6.11} 公式的转行当一个表达式或方程须断开用两行或多行来表示时, 按照~Donald Knuth~的~\textit{The \tex book}中的规则:(a) 行间的公式在记号~$=$, $+$, $-$, $\pm $, $\mp $, $\times $, $\cdot $~或~$\div $~后断开, %而在下一行开头不再重复这一记号;(b) 如果是独立显示的大公式, 在紧靠其中记号~$=$, $+$, $-$, $\pm $, $\mp $, $\times $, $\cdot $~或~$\div $~前断开, 如：\begin{align*}x_{n}u_1 + \cdots + x_{n+t} u_t = & \,x_{n}u_{1}+(ax_{n}+c)u_2+\cdots \\&\, +\big(a^{t-1}x_n+c(at^{t-2}+\cdots+1)\big)\\= & \,(u_1+au_2+\cdots+a^{t-1})x_n+h(u_1,\cdots,u_t)\end{align*}\zhushi 国家标准~GB 3102.11~要求在所有情况下都将记号放在行末是考虑“第一行末尾的记号起着%像连字符号的作用, 告诉读者其后接着下一行乃至下一页”\!. 但根据统计, 国内外没有一份期刊、%杂志是这样做的. Springer~等知名出版社更是对如何断行有明确的条文规范, 考虑与国际接轨故作此调整.\lizi{6.12} 运算符号\zaogao\begin{eqnarray*}y & = & a+b+c+d\\& & +e+f+g\end{eqnarray*}\zhengque\begin{eqnarray*}y & = & a+b+c+d\\& & {}+e+f+g\end{eqnarray*}\zhushi 注意到~$1+2$~与~$+2$~中的~$+$~是不同的! 正确的例子是这样录入的:\begin{verbatim}\begin{eqnarray*}y & = & a+b+c+d\\& & {}+e+f+g\end{eqnarray*}\end{verbatim}\subsection{几何符号}\lizi{6.13} 线段\zaogao 线段~$\overline{AB}$~的长度为~$AB=4\,$cm.\zhengque 线段~$AB$~的长度为~$\mid AB\mid =4\,$cm.\zhushi 符号~$\overline{AB}$~由~$AB$~取代, 其长度使用“$\mid AB\mid$”表示. 我们还规定有向线段%~$\overrightarrow{AB}$~的数量也可以用~$AB$~表示. 一般的, “$\mid AB\mid=4$”表示线段~$AB$~的长%为~4, 而“$AB=4$”则表示向量线段~$\overline{AB}$~的数量为~4.\lizi{6.14} 弧\zaogao $\wideparen{AB}$~的长度为~4\,cm.\zhengque 弧~$AB$~的长度为~4\,cm.\zhushi 弧与平行四边形的符号没有形成国际统一的使用规范, 故不建议使用. 在可能的情况下, 还应该避免使用%三角形, 园, 相似, 全等这几个符号, 而代之以文字.\lizi{6.15} 平行\zaogao $a/\!\!/b$\zhengque $a\,\|\,b$\zhushi 使用~$\|$~而非~$/\!\!/$~的原因在于我们可以很容易的获得符号~$\nparallel\,$. 避免使用%“平行且全等”这一符号.\subsection{集合}\lizi{6.16} 集合\zaogao $\{x \mid 0<x\zhengque $\{\,x\in \mathbb{R} \mid 0<x<1\,\}$\zhushi 正确的例子是由~\verb|$\{\,x\in \mathbb{R} \mid 0<x 定义是“使命题~$p(x)$~为真的~$A$~中诸元素之集用记号~$\{\,x\in A \mid p(x)\,\}$~表示. 集合中%的空隙是一门艺术. 我们再来看一个例子:\[\bigl\{\,x\in A(n)\bigm|x\in B(n)\,\bigr\}\]是由~\verb~\[\bigl\{\,x\in A(n)\bigm|x\in B(n)\,\bigr\}\]~~生成的, 注意命令~\verb~\bigm|~~%的使用.\lizi{6.17} 集合~$A$~中诸元素的数目\cuowu $n(A)$\zhengque card$(A)$\lizi{6.18} 数集\cuowu $\textbf{N}=\{1,2,3\ldots\}$\zhengque $\mathbb{N}=\{0,1,2,\ldots\}$\zhushi 如果可能的话, 不要使用黑正体来表示数集. 如果你使用的是~Times New Roma</x</x<1\,\}$</xn, 使用~\textsf{amstex}~宏包的~\verb|\mathbb|~命令．如果你使用的是~Computer Nodern, 使用~\textsf{bbm}~宏包的~\verb|\mathbbm|~命令.注意自然数集是包含数字~0~的! 我们可以用下标~$+$~来表示取正, 上标~$\ast$~来排除~0. 例如: $\mathbb{R}_{+}$, $\mathbb{N}^{\ast}$~和~$\mathbb{N}^{+}$. 作者推荐第一种.\lizi{6.19}\zaogao 函数~$f(x)=\sqrt{x}$~的定义域是~$\mathbb{N}_{+}\cup\{{0}\}\,$.\zhengque 函数~$f(x)=\sqrt{x}$~的定义域是~$\left[0,+\infty\right)\,$.\lizi{6.20} 子集与真子集\zaogao 对于所有的~$x\in A$, 我们可以得到~$x\in B$, 那么~$A\subset B$.\zhengque 对于所有的~$x\in A$, 我们可以得到~$x\in B$, 那么~$A\subseteq B$.\zhushi 过去, 记号~$\subset$~意思是“真包含于”, 但是, 根据新的国际标准, 这一符号与~$\subseteq$~是等价的, 也即% ~$A\subset B$~与~$A\subseteq B$~相同. “真包含于”的新记号是~~$\subsetneqq$, 为了避免可能的误解, 我们%规定用~$A\subseteq B$~表示~“$A$~包含于~$B$”, 用~$A\subsetneqq B$~表示$A$~真包含于~$B$”. 因此, 直线~$l$~在平面~$\alpha$~内也可以用~$l\subsetneqq \alpha$~表示.\lizi{6.21} 集合之差\cuowu 集合~$A$~与~$B$~的差是~$A-B$.\zhengque 集合~$A$~与~$B$~的差是~$A\backslash B$.\lizi{6.22} 补集\cuowu 如果全集~$U=\mathbb{R}$, 则无理数集为~$\overline{\mathbb{Q}}\,$.\zhengque 果全集~$U=\mathbb{R}$, 则无理数集为~$\complement_{\mathbb{R}} \mathbb{Q}\,$.\zhushi 集合~$A$~中子集~$B$~的补集或余集用~$\complement_AB$~. 我们规定~$B'$~和~$B^C$~也可以接受.很多人更倾向于使用~$\overline{B}~$这一记号, 但是我们应该尽量避免给统同一符号赋予多种含义, 上划线%更普遍的被用以表示平均值. ~$B'$~和~$B^C$~为欧美的不少课本所用. 但是在可能的情况下, 尽量表达完整.\subsection{数理逻辑符号}\lizi{6.23} 数理逻辑符号\cuowu 对于~$\forall \varepsilon >0, \exists \, N\in \mathbb{N}_+$~使得当~$n>0$~时有~$| x_n-a|<\varepsilon$, 则~$lim_{n\rightarrow \infty} x_n=a\,$.\zhengque 如果对于任意的~$\varepsilon >0$, 存在一个正整数~$N$~使得当~$n>N$~时有~$| x_n-a|<\varepsilon$, 则~$lim_{n\rightarrow \infty} x_n=a\,$.\zhushi 行文中不应使用数理逻辑符号的规定在欧美国家为很多人赞同. Donald Knuth~教授也在他的~%Mathematical Writing~课程中谈及过. 但是在“真正的”逻辑推理过程中这些符号仍然可以使用%的! 另外在使用全称量词时, 最好不要将“对于”二字省略. 至于“$\because$”与“$\therefore$”这两个符号已经完全从国际标准和国家标准中消失了, 所以不再使用, 包括在逻辑推理过程中.\subsection{杂类符号}\lizi{6.24} 比例符号\cuowu $a$:$b$\zhengque $a:b$\zhushi 区分比例符号和冒号, 例如, 时间用~$12:15:18$~这样的形式表达是错误的, 应该是~12:15:18.\lizi{6.26} 无穷量\zaogao $(-\infty,+\infty)$\zhengque $(-\infty,\infty)$\zhushi 使用~$\infty$~更为普遍和简洁.\lizi{6.26} 数值范围\cuowu 2\,km $\sim$ 3\,km\zhengque 2\,km~至~3\,km\zhushi 符号~$\sim$~在国际标准中表示“正比例与”\!, 这与中国国家标准冲突. 另在国际标准中, 要求用%“2\,km to 3\,km”的形式来表达数值范围, 取代传统的~2－3\,km~的形式. 符号~$\sim$~应该被避免%使用, $a$~正比例与~$b$~应该用~$a\!\propto \!b$~来表达.\lizi{6.27}百分率\cuowu 2\% $\sim$ 3\%\zhengque 2\,\%~至~3\,\%\zhushi 正确的例子是用~\verb|\zhengque 2\,\%~至~3\,\%|~生成的. 注意百分率符号之前的小空隙, 这一做法%是国际标准所推荐的.\lizi{6.28} 括号\zaogao $f[g(x)]$\zhengque $f\big(g(x)\big)$\zhushi 不使用传统的圆括号外套中括号, 中括号外套大括号的习惯, 而是在圆括号外套更大的圆括号.Donald Knuth~语:“The world is short of delimiters.”另一个原因是不少人使用记号~$[a]$~来表示小于或等于~$a$~的最大整数, 这会导致不必要的误解.\subsection{运算符号}\lizi{6.29}二项式系数\zaogao $\big(_p^n\big)$\gzaogao $C_n^p$\zhengque $\textrm{C}_n^p$\zhushi 使用~$\textrm{C}_n^p$~表达二项式系数, 排列数则使用~$\textrm{P}_n^p$~表示,而非~$\textrm{A}_n^p$.事实上在国际数学界, $\big(_p^n\big)$~更为普遍, 但在解决排列、组合问题时将其与~$\textrm{P}_n^p$~并用显然不美观, 考虑一致性作此规定.注意字体!\lizi{6.31} 定积分\zaogao\[\int \limits _a^b f(x)\textrm{d}x\]\zhengque\[\int _a^b f(x)\,\textrm{d}x\]\zhushi 虽然糟糕的例子是国家标准中的首选, 但正确的例子在数学界更为普遍. 另外, 注意~$\textrm{d}x$~之前的空隙.\lizi{6.32} 以~e~为底的~$x$~的指数函数\zaogao $\textrm{e}^x$\zhengque $\exp x$\lizi{6.33}\zaogao $(\sin x)^2$\zhushi 类似的, 使用~$\lg^2$~而非$(\lg x)^2$, $f^2(x)$~而非~$\big(f(x)\big)^2$.\lizi{6.34}\cuowu $\sin^{-1}x$, $\sh x$, $\sinh^{-1}x$\zhengque $\arcsin x$, $\sinh x$, $\arsinh x$\zhushi $\sin^{-1}x$~很容易被误解成~$1/\sin x$~, 类似的, $\sinh^{-1}$~会被误解成~$1/\sinh x$.其它相关的记号是~$\arccos$, $\arctan$, $\arccot$, $\arcsec$, $\arccsc$, $\cosh$, $\tanh$,$\coth$, $\sech$, $\csch$, $\arcosh$, $\artanh$, $\arcoth$, $\arsech$, $\arcsch$.\subsection{复数记号}\lizi{6.35} 复数~$z$~的实部与虚部\cuowu $\Re (z)$, $\Im(z)$\zhengque $\shibu z$, $\xubu z$\lizi{6.36} 复数~$z$~的共轭\zaogao $\bar(z)$\zhushi 记号~$\bar z$~也是可以接受的. 但是应该记得我们尽量给同样的记号一个含义, 上划线更多的%被用来表示平均数.\subsection{矩阵的符号}\lizi{6.37} 单位矩阵\zaogao $\textbf{\textit{I}}$\zhengque $\textbf{\textit{E}}$\lizi{6.38} $\textbf{\textit{A}}$~的转置矩阵\cuowu $\textbf{\textit{A}}^T$\zhengque $\textbf{\textit{A}}^\textrm{T}$\lizi{6.39} 方阵的行列式\cuowu $|\textbf{\textit{A}}|$\zhengque $\det \textbf{\textit{A}}$\zhushi 如果不强调是方阵~$\textbf{\textit{A}}$~的矩阵, 一个斜体字母也可以接受, 例如~$\textbf{\textit{A}}$.\subsection{向量}\lizi{6.40} $\textbf{\textit{a}}$~方向的单位向量\cuowu $\textbf{\textit{a}}_0$\zhengque $\textbf{\textit{e}}_\textrm{a}$\lizi{6.41} 向量的坐标\cuowu $\vec{a}=\{a_x,a+y,a_z\}$\zhengque $a=\{a_x,a+y,a_z\}$\zhushi 上箭头的记法只在书写中使用.\section{几个精调过的例子}\lizi{7.1} 求证: 如果一个平面内有两条相交平面平行于另一个平面, 那么这两个平面平行.已知: $a\subsetneqq \beta$, $b\subsetneqq \beta$, $a\cap b=P$, $a\,\| \,\alpha$, $b\,\| \,\alpha$.求证: $\beta \,\| \,\alpha$证明: 假设~$\alpha \cap \beta= 直线 c$.因为~$a\,\|\,\alpha$, $a\subsetneqq \beta$,所以~$a\,\|\,c$.同理~$a\,\|\,c$.于是, 在平面~$\beta$~内, 过点~$P$~有两条直线~$a$, $b$~都平行于~$c$, 这与平行公理矛盾.所以~$\beta \,\| \,\alpha$.\lizi{7.2} 一工人维护甲、乙、丙~3~台机床, 在~1h~内, 甲、乙和丙需要维护的概率分别为~0.9, 0.8~和~0.85, 求~1h~内没有一台机床需要维护的概率.解: 设~$A$, $B$, $C$~分别表示甲、乙、丙~3~台机床需要维护的时间, 由于~$A$, $B$, $C$~互相独立, %因此他们各自的对立事件~$\complement_{\Omega}A$, $\complement_{\Omega}B$, $\complement_{\Omega}C$~ 也互相独立. 则没有一台机床需要维护的事件可以用~$\complement_{\Omega}A\cap\complement_{\Omega}B \cap\complement_{\Omega}C$~表示, 于是\begin{eqnarray*}P(\complement_{\Omega}A\cap\complement_{\Omega}B\c ap\complement_{\Omega}C) & = & P(\complement_{\Omega}A)\cdotP(\complement_{\Omega}B)\cdot (P\complement_{\Omega}C)\\ & = &\big(1-P(A)\big)\cdot \big(1-P(B)\big)\cdot \big(1-P(C)\big)\\& = &(1-0.9)(1-0.8)(1-0.85)\\& = &0.003\,.\end{eqnarray*}\lizi{7.3} 对于方阵\begin{equation}\textbf{\textit{A}}=\begin{pmatrix}1 &2 &3 \\2 & 2 & 1 \\3 &4 & 3\end{pmatrix},\nonumber\end{equation}我们可以得到~$\det \textbf{\textit{A}}=2\neq 0$, 所以~$\textbf{\textit{A}}$~有逆方阵. 求出~$\textbf{\textit{A}}$~% 的伴随方阵为\[\begin{pmatrix}2 & 6 & -4\\-3& -6& 5 \\2 & 2 & -2\\\end{pmatrix}\]因此\begin{equation}\textbf{\textit{A}}^{-1}=\frac{1}{2}\begin{pmatrix}2 & 6 & -4 \\-3 & -6 & 5 \\2 & 2 & -2\\\end{pmatrix}=\begin{pmatrix}1 & 3 & -2 \\-3/2& -3 & 5/2 \\1 & 1 & -14\\\end{pmatrix}\, .\nonumber\end{equation}\lizi{7.4} 对于连续函数~$f(x)$, 有算术平均值\begin{equation}\bar{f}=\frac{1}{b-a}\int_a^b f(x)\,\textrm{d}x\label{ssjz}\end{equation}和方根均值\begin{equation}\sqrt{\frac{1}{b-a}\int_a^b f^2(x)\,\textrm{d}x}\label{fjgz}\end{equation}候着可用于求交流电的有效值.交流电电压~$u(t)=U_{\textrm{m}}\sin \omega t$~经半波整流后, 求在一周期内的算术平均值与有效值.\textbf{解}\quad 交流电电压经半波整流后为\begin{displaymath}u(t)=\left\{\!\!\!\begin{array}{ll}U_{\textrm{m}} \sin \omega t & \text{当}~0\leqq t\leqq \uppi /\omega ,\\0 & \text{当}~\uppi /\omega \leqq t \leqq 2\uppi / \omega .\end{array}\right.\end{displaymath}由~(\ref{ssjz}), 得电压的算术平均值\begin{eqnarray*}\overline{U} & = & \frac{\omega}{2\uppi}\left(\int_0^{\uppi/\omega}U_{\textrm{m}} \sin\omega t\,\textrm{d}t+\int_{\uppi/\omega}^{2\uppi/\omega}0\,\textrm{d}t\right)\\ & = & \frac{\omega U_{\textrm{m}}}{2\uppi}\int_0^{\uppi/\omega}\sin \omega t\, \textrm{d}t\\& = & \frac{\omega U_{\textrm{m}}}{2\uppi}\left(-\frac{1}{\omega}\cos\omega t\right)\!\bigg|_0^{\uppi/\omega}\\& = & \frac{U_{\textrm{m}}}{\uppi}\\& \approx & 0.318U_{\textrm{m}}\,.\end{eqnarray*}由~(\ref{fjgz}), 得电压的有效值\begin{eqnarray*}U \!\!& = & \!\! \sqrt{\frac{1}{T}\int_0^T U^2(t)\,\textrm{d}t} \\& = & \!\! \sqrt{\frac{\omega}{2\uppi}\left(\int_0^{\uppi/\omega}U^2_\textrm{m}\sin ^2\omega t \,\textrm{d}t+\int_{\uppi/\omega}^{2\uppi/\omega}0\,\textrm{d}t\right) }\\& = & \!\!\sqrt{\frac{\omega}{2\uppi}U^2_\textrm{m}\int_0^{\uppi/\o mega}\sin ^2\omega t \,\textrm{d}t}\\& = & \!\!\sqrt{\frac{\omega}{4\uppi}U^2_\textrm{m}\frac{\uppi}{\ome ga}}\\& = & \!\!0.5U_\textrm{m}\end{eqnarray*}\section*{跋}\addcontentsline{toc}{section}{跋}用了一个星期的空闲时间终于把盖鹤麟先生的《\ltx~科技文档排版》抄写了一遍. 这要感谢中国网通无比糟糕的网络质量, 因为% 不能上网, 所以有了充足的时间来抄写, 在无事可做的时候总要做些什么打发时间啊. 总的来说, 遇到的困难远比想象的要多, % 对规则的认识远没有自己认为得多. 虽然难题都一一得到了解决, 但记住的也没多少.在抄写过程中基本上坚持原文的格式, 自然也是不能完全复制的, 就像镜像那样. 在代码的实现上肯定有很大的不同. 而且,由于原文用的是~Computer Modern~字体, 而我用的是~Times New Roman~，因此在一些细节上也有些差别. 我也很想抄写得和原文一样, %但是, 配置字体太难了, 只好放弃吧!Donald Knuth~教授的~\tex~配得上是“伟大”一词. 强大、灵。

LaTeXBeamer笔记——用LaTeX做演示文稿文章目录简介Beamer主要功能itemizepause创建目录页突出当前章节标题突出当前副章节标题标题页目录页添加特效高亮自定义演示文稿字体大小字体类型字体主题从系统导入字体主题/颜色主题字体分栏显示中文LaTeX快速入门：Learn LaTeX in 30 minutes我的博客：LaTeX Beamer 笔记简介Beamer是一个功能强大且灵活的LaTeX类，可用于创建美观的演示文稿。

\documentclass{beamer}%Information to be included in the title page:\title{Sample title}\title{Sample title}\author{Anonymous}\institute{Overleaf}\date{2021}\begin{document}\frame{\titlepage}\begin{frame}\frametitle{Sample frame title}This is some text in the first frame. This is some text in the first frame. This is some text in the first frame. \end{frame}\end{document}用TeXStudio编译预览，可生成文档如下：编译后，将生成一个两页的PDF文件。

第一页是标题页，第二页包含示例内容。

\documentclass{Beamer} - 声明Beamer演示文稿\document - 文档\frame - 文档中的页变量以\为开头注释以%为开头单行内容 - \frame{xxx}多行内容 - \begin{frame} xxx \end{frame}可以通过\usetheme{xxx}指定使用的主题\begin{document}前的区域叫做导言区Beamer主要功能标题页标题页的选项比简介中提供的选项多。