didnelpsun/math

考研数学，数学一，包括高等数学、线性代数、概率统计

Didnelpsun仓库说明

某不知名前端爱好者。全干工程师。

一个年老失修的个人博客。

欢迎朋友们加盟我的开源项目。在Tissue中留言即可，我每天都会查看相关内容并拉各位。

math's Issues

概率论中的小错误

在概率论的knowledge/law-of-large-numbers-and-central-limit-theorem.tex里面，有一个例题似乎有错误（应该是$n \ge 1$）

---

另外，在knowledge/2-random-variables-and-distribution/random-variables-and-distribution.tex有一个字打错了（性 →型）

在概率论的知识里面，第四章或是第五章缺少对应的标题

高数第一章，函数与极限小错误

你好，能加个好友吗？

Wechat: yzf880886

电脑上没有装tex，请问有pdf版本的吗？

。。。

请问作者使用的编辑器

我想知道作者您做笔记所用软件

VScode无法编译.tex

log 如下：

Initial Win CP for (console input, console output, system): (CP936, CP936, CP936)
I changed them all to CP936
Rc files read:
  NONE
Latexmk: This is Latexmk, John Collins, 4 Apr. 2023. Version 4.80.
No existing .aux file, so I'll make a simple one, and require run of *latex.
Latexmk: applying rule 'pdflatex'...
Rule 'pdflatex':  Reasons for rerun
Category 'other':
  Rerun of 'pdflatex' forced or previously required

------------
Run number 1 of rule 'pdflatex'
------------
------------
Running 'pdflatex  -synctex=1 -interaction=nonstopmode -file-line-error -recorder  "d:/Documents/Math-master/advanced-math/knowledge/0-perpare/perpare.tex"'
------------
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(d:/Documents/Math-master/advanced-math/knowledge/0-perpare/perpare.tex
LaTeX2e <2022-11-01> patch level 1
L3 programming layer <2023-02-22> (c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls (c:/texlive/2023/texmf-dist/tex/latex/ctex/config/ctexbackend.cfg) (c:/texlive/2023/texmf-dist/tex/latex/l3kernel/expl3.sty

c:/texlive/2023/texmf-dist/tex/latex/l3kernel/expl3.sty:78: LaTeX Error: Mismatched LaTeX support files detected.
(LaTeX)        Loading 'expl3.sty' aborted!
(LaTeX)        
(LaTeX)        The L3 programming layer in the LaTeX format
(LaTeX)        is dated 2023-02-22, but in your TeX tree the files require
(LaTeX)        at least 2023-08-11.

For immediate help type H <return>.
 ...                                              
                                                  
l.78      \ExplLoaderFileDate{expl3.sty}}
                                         %
)
Document Class: ctexart 2022/07/14 v2.5.10 Chinese adapter for class article (CTEX)
(c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexhook.sty) (c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexpatch.sty) (c:/texlive/2023/texmf-dist/tex/latex/base/fix-cm.sty (c:/texlive/2023/texmf-dist/tex/latex/base/ts1enc.def))
c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls:102: Undefined control sequence.
l.102 \sys_if_output_pdf:TF
                           

c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls:104: LaTeX Error: Control sequence \ifctexpdf already defined.

For immediate help type H <return>.
 ...                                              
                                                  
l.104   { \cs_new_eq:NN \ifctexpdf
                                   \if_false: }
(c:/texlive/2023/texmf-dist/tex/latex/ctex/config/ctexopts.cfg) (c:/texlive/2023/texmf-dist/tex/latex/base/article.cls
Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
(c:/texlive/2023/texmf-dist/tex/latex/base/size12.clo)) (c:/texlive/2023/texmf-dist/tex/latex/ctex/engine/ctex-engine-pdftex.def
c:/texlive/2023/texmf-dist/tex/latex/ctex/engine/ctex-engine-pdftex.def:97: Undefined control sequence.
l.97 \sys_if_output_pdf:T
                         
(c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/CJKutf8.sty (c:/texlive/2023/texmf-dist/tex/generic/iftex/ifpdf.sty (c:/texlive/2023/texmf-dist/tex/generic/iftex/iftex.sty)) (c:/texlive/2023/texmf-dist/tex/latex/base/inputenc.sty) (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/CJK.sty (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/mule/MULEenc.sty) (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/CJK.enc)) (c:/texlive/2023/texmf-dist/tex/latex/base/fontenc.sty)) (c:/texlive/2023/texmf-dist/tex/latex/cjkpunct/CJKpunct.sty (c:/texlive/2023/texmf-dist/tex/latex/cjkpunct/CJKpunct.spa)) (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/CJKspace.sty) (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/UTF8/UTF8.bdg) (c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexspa.def)) (c:/texlive/2023/texmf-dist/tex/latex/zhnumber/zhnumber.sty (c:/texlive/2023/texmf-dist/tex/latex/zhnumber/zhnumber-utf8.cfg)) (c:/texlive/2023/texmf-dist/tex/latex/ctex/scheme/ctex-scheme-chinese-article.def (c:/texlive/2023/texmf-dist/tex/latex/ctex/config/ctex-name-utf8.cfg))
c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls:1471: Undefined control sequence.
<argument> \sys_if_output_pdf:TF 
                                 {##1}{##2}
l.1471       { \sys_if_engine_uptex:TF {#3} {#4} }
                                                  
(c:/texlive/2023/texmf-dist/tex/latex/ctex/fontset/ctex-fontset-windows.def)) (c:/texlive/2023/texmf-dist/tex/latex/ctex/config/ctex.cfg) (c:/texlive/2023/texmf-dist/tex/latex/graphics/color.sty (c:/texlive/2023/texmf-dist/tex/latex/graphics-cfg/color.cfg) (c:/texlive/2023/texmf-dist/tex/latex/graphics-def/pdftex.def) (c:/texlive/2023/texmf-dist/tex/latex/graphics/mathcolor.ltx)) (c:/texlive/2023/texmf-dist/tex/latex/amsfonts/amssymb.sty (c:/texlive/2023/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) (c:/texlive/2023/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(c:/texlive/2023/texmf-dist/tex/latex/amsmath/amstext.sty (c:/texlive/2023/texmf-dist/tex/latex/amsmath/amsgen.sty)) (c:/texlive/2023/texmf-dist/tex/latex/amsmath/amsbsy.sty) (c:/texlive/2023/texmf-dist/tex/latex/amsmath/amsopn.sty)) (c:/texlive/2023/texmf-dist/tex/latex/geometry/geometry.sty (c:/texlive/2023/texmf-dist/tex/latex/graphics/keyval.sty) (c:/texlive/2023/texmf-dist/tex/generic/iftex/ifvtex.sty)) (c:/texlive/2023/texmf-dist/tex/latex/tools/indentfirst.sty) (c:/texlive/2023/texmf-dist/tex/latex/setspace/setspace.sty) (c:/texlive/2023/texmf-dist/tex/latex/hyperref/hyperref.sty (c:/texlive/2023/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty) (c:/texlive/2023/texmf-dist/tex/generic/pdftexcmds/pdftexcmds.sty (c:/texlive/2023/texmf-dist/tex/generic/infwarerr/infwarerr.sty)) (c:/texlive/2023/texmf-dist/tex/latex/kvsetkeys/kvsetkeys.sty) (c:/texlive/2023/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty) (c:/texlive/2023/texmf-dist/tex/generic/pdfescape/pdfescape.sty) (c:/texlive/2023/texmf-dist/tex/latex/hycolor/hycolor.sty) (c:/texlive/2023/texmf-dist/tex/latex/letltxmacro/letltxmacro.sty) (c:/texlive/2023/texmf-dist/tex/latex/auxhook/auxhook.sty) (c:/texlive/2023/texmf-dist/tex/latex/hyperref/nameref.sty (c:/texlive/2023/texmf-dist/tex/latex/refcount/refcount.sty) (c:/texlive/2023/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty (c:/texlive/2023/texmf-dist/tex/latex/kvoptions/kvoptions.sty))) (c:/texlive/2023/texmf-dist/tex/latex/etoolbox/etoolbox.sty) (c:/texlive/2023/texmf-dist/tex/latex/hyperref/pd1enc.def) (c:/texlive/2023/texmf-dist/tex/generic/intcalc/intcalc.sty) (c:/texlive/2023/texmf-dist/tex/latex/hyperref/puenc.def) (c:/texlive/2023/texmf-dist/tex/latex/url/url.sty) (c:/texlive/2023/texmf-dist/tex/generic/bitset/bitset.sty (c:/texlive/2023/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty)) (c:/texlive/2023/texmf-dist/tex/latex/base/atbegshi-ltx.sty)) (c:/texlive/2023/texmf-dist/tex/latex/hyperref/hpdftex.def (c:/texlive/2023/texmf-dist/tex/latex/base/atveryend-ltx.sty) (c:/texlive/2023/texmf-dist/tex/latex/rerunfilecheck/rerunfilecheck.sty (c:/texlive/2023/texmf-dist/tex/generic/uniquecounter/uniquecounter.sty))) (c:/texlive/2023/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty (c:/texlive/2023/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty (c:/texlive/2023/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def) (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex (c:/texlive/2023/texmf-dist/tex/generic/pgf/pgf.revision.tex))) (c:/texlive/2023/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty (c:/texlive/2023/texmf-dist/tex/latex/graphics/graphicx.sty (c:/texlive/2023/texmf-dist/tex/latex/graphics/graphics.sty (c:/texlive/2023/texmf-dist/tex/latex/graphics/trig.sty) (c:/texlive/2023/texmf-dist/tex/latex/graphics-cfg/graphics.cfg))) (c:/texlive/2023/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty (c:/texlive/2023/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.tex)) (c:/texlive/2023/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg) (c:/texlive/2023/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def (c:/texlive/2023/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def))) (c:/texlive/2023/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex)) (c:/texlive/2023/texmf-dist/tex/latex/xcolor/xcolor.sty (c:/texlive/2023/texmf-dist/tex/latex/graphics-cfg/color.cfg) (c:/texlive/2023/texmf-dist/tex/latex/graphics/mathcolor.ltx)) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex)) (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfint.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex))) (c:/texlive/2023/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex) (c:/texlive/2023/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty) (c:/texlive/2023/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty)) (c:/texlive/2023/texmf-dist/tex/latex/pgf/utilities/pgffor.sty (c:/texlive/2023/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex)) (c:/texlive/2023/texmf-dist/tex/latex/pgf/math/pgfmath.sty (c:/texlive/2023/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex)) (c:/texlive/2023/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex)) (c:/texlive/2023/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex (c:/texlive/2023/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex) (c:/texlive/2023/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex))) (c:/texlive/2023/texmf-dist/tex/latex/tools/array.sty) (c:/texlive/2023/texmf-dist/tex/latex/psnfss/pifont.sty (c:/texlive/2023/texmf-dist/tex/latex/psnfss/upzd.fd) (c:/texlive/2023/texmf-dist/tex/latex/psnfss/upsy.fd)) (c:/texlive/2023/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex) (c:/texlive/2023/texmf-dist/tex/latex/scalerel/scalerel.sty (c:/texlive/2023/texmf-dist/tex/latex/tools/calc.sty)) (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/UTF8/UTF8.enc) (c:/texlive/2023/texmf-dist/tex/latex/cjk/texinput/UTF8/UTF8.chr) (c:/texlive/2023/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def) (./perpare.aux) (c:/texlive/2023/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (c:/texlive/2023/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty (c:/texlive/2023/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg))
*geometry* driver: auto-detecting
*geometry* detected driver: pdftex
(c:/texlive/2023/texmf-dist/tex/latex/ctex/fd/c70rm.fd) (c:/texlive/2023/texmf-dist/tex/latex/amsfonts/umsa.fd) (c:/texlive/2023/texmf-dist/tex/latex/amsfonts/umsb.fd)
No file perpare.toc.
(c:/texlive/2023/texmf-dist/tex/generic/ctex/zhmap/ctex-zhmap-windows.tex) [1{c:/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
Underfull \hbox (badness 8038) in paragraph at lines 98--99
[]$\OML/cmm/m/it/12 u[]u[]:::u[]$\C70/rm/m/n/12/53 � \C70/rm/m/n/12/4e � \C70/rm/m/n/12/4f ^^? \C70/rm/m/n/12/75 ($[][] [] \OML/cmm/m/it/12 u[]$\C70/rm/m/n/12/67 e \C70/rm/m/n/12/78 ^^T

Underfull \hbox (badness 10000) in paragraph at lines 121--122
[]\C70/rm/m/n/12/5b � \C70/rm/m/n/12/4e I \C70/rm/m/n/12/57 �|\C70/rm/m/n/12/ff ^^Z| $\OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 ^^@1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 +\OMS/cmsy/m/n/12 1\OT1/cmr/m/n/12 )$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 �|\C70/rm/m/n/12/ff ^^Z|

pdfTeX warning (ext4): destination with the same identifier (name{page.1}) has been already used, duplicate ignored
<to be read again> 
                   \relax 
l.128 \subparagraph
                   {对数函数} \leavevmode \medskip [1] [2] [3] [4] [5] [6]
Overfull \hbox (2.47614pt too wide) in paragraph at lines 477--478
[]$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/4e : \C70/rm/m/n/12/5b � \C70/rm/m/n/12/65 p|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/4e ^^M \C70/rm/m/n/12/8d � \C70/rm/m/n/12/8f �$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/76 � \C70/rm/m/n/12/67 ^^@ \C70/rm/m/n/12/59 ' \C70/rm/m/n/12/65 t p \C70/rm/m/n/12/79 � \C70/rm/m/n/12/4e : \C70/rm/m/n/12/51 v \C70/rm/m/n/12/65 t p \C70/rm/m/n/12/90 � \C70/rm/m/n/12/52 ^^F$\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ]$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/51 v \C70/rm/m/n/12/5b � \C70/rm/m/n/12/4e I \C70/rm/m/n/12/57 � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 R$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 Z$|\C70/rm/m/n/12/30 ^^B|

Underfull \hbox (badness 10000) in paragraph at lines 477--478


Underfull \hbox (badness 2057) in paragraph at lines 519--520
[]$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/6c �$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/8f t \C70/rm/m/n/12/5d � \C70/rm/m/n/12/79 �$\OML/cmm/m/it/12 x[]$\C70/rm/m/n/12/4e * \C70/rm/m/n/12/53 U \C70/rm/m/n/12/4f M \C70/rm/m/n/12/95 ^^?

Underfull \hbox (badness 8038) in paragraph at lines 519--520
\C70/rm/m/n/12/5e � \C70/rm/m/n/12/5f � \C70/rm/m/n/12/52 0$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x \OT1/cmr/m/n/12 + \OML/cmm/m/it/12 x[]\OT1/cmr/m/n/12 )$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/54 ^^Q \C70/rm/m/n/12/53 �

Underfull \hbox (badness 10000) in paragraph at lines 541--542
[]$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/6c �$\OML/cmm/m/it/12 y$\C70/rm/m/n/12/8f t \C70/rm/m/n/12/4e 
 \C70/rm/m/n/12/79 �$\OML/cmm/m/it/12 y[]$\C70/rm/m/n/12/4e * \C70/rm/m/n/12/53 U \C70/rm/m/n/12/4f M \C70/rm/m/n/12/95 ^^? \C70/rm/m/n/12/5e � \C70/rm/m/n/12/5f �
[7]
Underfull \hbox (badness 2253) in paragraph at lines 600--601
[]\C70/rm/m/n/12/5c ^^F$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e �$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/8f t$\OML/cmm/m/it/12 y$\C70/rm/m/n/12/8f t \C70/rm/m/n/12/53 s \C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/70 �
[8]
Underfull \hbox (badness 10000) in paragraph at lines 637--638
[]\C70/rm/m/n/12/4f � \C70/rm/m/n/12/75 Y$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 ($\OT1/cmr/m/n/12 [0\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 1\OT1/cmr/m/n/12 ]$\C70/rm/m/n/12/76 � \C70/rm/m/n/12/90 � \C70/rm/m/n/12/52 ^^F|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/5e v
[9] [10{c:/texlive/2023/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc}] [11] [12]
Overfull \hbox (5.74239pt too wide) in paragraph at lines 893--901
[]\C70/rm/m/n/12/4e � \C70/rm/m/n/12/57 ^^F \C70/rm/m/n/12/53 J \C70/rm/m/n/12/5f � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 r$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/64 F \C70/rm/m/n/12/70 � \C70/rm/m/n/12/4e ^^N \C70/rm/m/n/12/57 ^^F \C70/rm/m/n/12/5f � \C70/rm/m/n/12/62 @ ^^P \C70/rm/m/n/12/76 � \C70/rm/m/n/12/7e � \C70/rm/m/n/12/62 @ \C70/rm/m/n/12/8f l \C70/rm/m/n/12/52 � \C70/rm/m/n/12/59 9 \C70/rm/m/n/12/89 � \C70/rm/m/n/12/5b � \C70/rm/m/n/12/5e � \C70/rm/m/n/12/5f ' \C70/rm/m/n/12/5e � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 t$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/51 v \C70/rm/m/n/12/4e -$\OML/cmm/m/it/12 t \OMS/cmsy/m/n/12 2 \OT1/cmr/m/n/12 [0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 2\OML/cmm/m/it/12 ^^Y\OT1/cmr/m/n/12 ]$|\C70/rm/m/n/12/ff ^^L|
[13] [14] [15] [16]
Overfull \hbox (2.87325pt too wide) in paragraph at lines 1083--1084
[]\C70/rm/m/n/12/6b c \C70/rm/m/n/12/5f & \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p$\OML/cmm/m/it/12 y \OT1/cmr/m/n/12 = [] \OML/cmm/m/it/12 x$\C70/rm/m/n/12/57 ( \C70/rm/m/n/12/4e ; \C70/rm/m/n/12/50 < \C70/rm/m/n/12/53 : \C70/rm/m/n/12/95 �$[]$\C70/rm/m/n/12/4e 
 \C70/rm/m/n/12/76 � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/5c 1 \C70/rm/m/n/12/66 / \C70/rm/m/n/12/53 � \C70/rm/m/n/12/6b c \C70/rm/m/n/12/5f & \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/8b � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 y \OT1/cmr/m/n/12 =

Overfull \hbox (8.34384pt too wide) in paragraph at lines 1099--1100
[]\C70/rm/m/n/12/56 � \C70/rm/m/n/12/4e : \C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e �$[]$\C70/rm/m/n/12/5b � \C70/rm/m/n/12/79 �|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/82 �$\OML/cmm/m/it/12 x[]; x[] \OMS/cmsy/m/n/12 2 \OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1)$|\C70/rm/m/n/12/ff ^^L| $\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 ^^@\OML/cmm/m/it/12 x[]$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/52 ^^Y$[] \OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + [] \OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 =
[17]
Overfull \hbox (5.05315pt too wide) in paragraph at lines 1117--1118
[]\C70/rm/m/n/12/6b c \C70/rm/m/n/12/52 ^^G \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/66 / \C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/70 � \C70/rm/m/n/12/5b � \C70/rm/m/n/12/79 �|\C70/rm/m/n/12/30 ^^A| \C70/rm/m/n/12/4e % \C70/rm/m/n/12/68 < \C70/rm/m/n/12/53 U \C70/rm/m/n/12/8c ^^C \C70/rm/m/n/12/90 ^^R \C70/rm/m/n/12/58 �|\C70/rm/m/n/12/30 ^^A| \C70/rm/m/n/12/67 	 \C70/rm/m/n/12/75 L \C70/rm/m/n/12/76 � \C70/rm/m/n/12/59 G \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p|\C70/rm/m/n/12/30 ^^B| \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 � \C70/rm/m/n/12/4e :$[]$|\C70/rm/m/n/12/ff ^^L|
[18] [19] [20]
Overfull \hbox (23.49008pt too wide) in paragraph at lines 1299--1300
[]\C70/rm/m/n/12/63 � \C70/rm/m/n/12/5e ^^? \C70/rm/m/n/12/51 l \C70/rm/m/n/12/5f ^^O \C70/rm/m/n/12/4e ^^@ \C70/rm/m/n/12/52 0 \C70/rm/m/n/12/8f � \C70/rm/m/n/12/7e � \C70/rm/m/n/12/53 : \C70/rm/m/n/12/95 � \C70/rm/m/n/12/4e ^^T$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/57 ($\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 a; b\OT1/cmr/m/n/12 ](\OML/cmm/m/it/12 a < b\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/4e 
 \C70/rm/m/n/12/53 � \C70/rm/m/n/12/79 �|\C70/rm/m/n/12/ff ^^Z| $\OMS/cmsy/m/n/12 j [][] \OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )[]\OML/cmm/m/it/12 x\OMS/cmsy/m/n/12 j \U/msa/m/n/12 6 [][] \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 j[]\OML/cmm/m/it/12 x$|\C70/rm/m/n/12/30 ^^B|
[21]
Overfull \hbox (8.95349pt too wide) in paragraph at lines 1324--1325
[]$\U/msa/m/n/12 *$\C70/rm/m/n/12/97 ^^@ \C70/rm/m/n/12/89 � \C70/rm/m/n/12/8b � \C70/rm/m/n/12/66 ^^N \C70/rm/m/n/12/67 	 \C70/rm/m/n/12/75 L \C70/rm/m/n/12/60 '|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/4e � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/68 9 \C70/rm/m/n/12/53 � \C70/rm/m/n/12/4e ^^M \C70/rm/m/n/12/7b I \C70/rm/m/n/12/5f ^^O \C70/rm/m/n/12/4e � \C70/rm/m/n/12/97 ^^@ \C70/rm/m/n/12/89 � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/59 ' \C70/rm/m/n/12/4e �\OT1/cmr/m/n/12 0|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/62 @ \C70/rm/m/n/12/4e � \C70/rm/m/n/12/97 ^^@ \C70/rm/m/n/12/89 � \C70/rm/m/n/12/8b � \C70/rm/m/n/12/66 ^^N$\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 j \OT1/cmr/m/n/12 =
[22] [23] (./perpare.aux)name = unihei75, rootname = unihei, pointsize = 75
mktexmf: empty or non-existent rootfile!
Cannot find font unihei75 in map file(s).

kpathsea: Running mktexmf unihei75.mf

The command name is C:\texlive\2023\bin\windows\mktexmf
Cannot find unihei75.mf .
I try ps2pk --> gsftopk --> ttf2pk --> hbf2gf.
ps2pk cannot be used.
I try gsftopk.
gsftopk.exe unihei75 864
gsftopk cannot be used.
Next I try ttf2pk.
ttf2pk.exe -q unihei75 864
ttf2pk failed.
Finally I try hbf2gf.
hbf2gf.exe -q -p unihei75 864
All trials failed.

kpathsea: Running mktexpk --mfmode / --bdpi 600 --mag 1+264/600 --dpi 864 unihei75

The command name is C:\texlive\2023\bin\windows\mktexpk
kpathsea: Appending font creation commands to missfont.log.


Package rerunfilecheck Warning: File `perpare.out' has changed.
(rerunfilecheck)                Rerun to get outlines right
(rerunfilecheck)                or use package `bookmark'.

 )
(see the transcript file for additional information)
!pdfTeX error: pdflatex.exe (file unihei75): Font unihei75 at 864 not found
 ==> Fatal error occurred, no output PDF file produced!
Latexmk: Missing input file 'perpare.toc' (or dependence on it) from following:
  No file perpare.toc.
Latexmk: Getting log file 'perpare.log'
Latexmk: Examining 'perpare.fls'
Latexmk: Examining 'perpare.log'
Latexmk: References changed.
Latexmk: Errors, so I did not complete making targets
Collected error summary (may duplicate other messages):
  pdflatex: Command for 'pdflatex' gave return code 1
      Refer to 'perpare.log' and/or above output for details

Latexmk: If appropriate, the -f option can be used to get latexmk
  to try to force complete processing.
C:\texlive\2023\bin\windows\runscript.tlu:921: command failed with exit code 12:
perl.exe c:\texlive\2023\texmf-dist\scripts\latexmk\latexmk.pl -synctex=1 -interaction=nonstopmode -file-line-error -pdf -outdir=d:/Documents/Math-master/advanced-math/knowledge/0-perpare d:/Documents/Math-master/advanced-math/knowledge/0-perpare/perpare

期望

祝自己成功上岸 初试+复试