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1 #LyX file created by tex2lyx 2.2
2 \lyxformat 495
3 \begin_document
4 \begin_header
5 \origin roundtrip
6 \textclass book
7 \begin_preamble
8 %% Do not edit unless you really know what you are doing.
9
10
11
12
13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
14
15 \AtBeginDocument{\providecommand\partref[1]{\ref{part:#1}}}
16 \AtBeginDocument{\providecommand\chapref[1]{\ref{chap:#1}}}
17 \AtBeginDocument{\providecommand\secref[1]{\ref{sec:#1}}}
18 \AtBeginDocument{\providecommand\subsecref[1]{\ref{subsec:#1}}}
19 \AtBeginDocument{\providecommand\parref[1]{\ref{par:#1}}}
20 \AtBeginDocument{\providecommand\figref[1]{\ref{fig:#1}}}
21 \AtBeginDocument{\providecommand\tabref[1]{\ref{tab:#1}}}
22 \AtBeginDocument{\providecommand\algref[1]{\ref{alg:#1}}}
23 \AtBeginDocument{\providecommand\fnref[1]{\ref{fn:#1}}}
24 \AtBeginDocument{\providecommand\enuref[1]{\ref{enu:#1}}}
25 \AtBeginDocument{\providecommand\eqref[1]{\ref{eq:#1}}}
26 \AtBeginDocument{\providecommand\lemref[1]{\ref{lem:#1}}}
27 \AtBeginDocument{\providecommand\thmref[1]{\ref{thm:#1}}}
28 \AtBeginDocument{\providecommand\corref[1]{\ref{cor:#1}}}
29 \AtBeginDocument{\providecommand\propref[1]{\ref{prop:#1}}}
30 \floatstyle{ruled}
31 \newfloat{algorithm}{tbp}{loa}[chapter]
32 \providecommand{\algorithmname}{Algorithm}
33 \floatname{algorithm}{\protect\algorithmname}
34 \RS@ifundefined{subsecref}{\newref{subsec}{name = \RSsectxt}}{}
35 \RS@ifundefined{thmref}{\def\RSthmtxt{theorem~}\newref{thm}{name = \RSthmtxt}}{}
36 \RS@ifundefined{lemref}{\def\RSlemtxt{lemma~}\newref{lem}{name = \RSlemtxt}}{}
37
38
39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
40 \theoremstyle{plain}
41 \newtheorem{lem}[thm]{\protect\lemmaname}\theoremstyle{plain}
42 \newtheorem{cor}[thm]{\protect\corollaryname}\theoremstyle{plain}
43 \newtheorem{prop}[thm]{\protect\propositionname}\theoremstyle{plain}
44 \newtheorem{conjecture}[thm]{\protect\conjecturename}\theoremstyle{plain}
45 \newtheorem{fact}[thm]{\protect\factname}\theoremstyle{definition}
46 \newtheorem{defn}[thm]{\protect\definitionname}\theoremstyle{definition}
47 \newtheorem{example}[thm]{\protect\examplename}\theoremstyle{definition}
48 \newtheorem{problem}[thm]{\protect\problemname}\theoremstyle{definition}
49 \newtheorem{xca}[thm]{\protect\exercisename}\theoremstyle{remark}
50 \newtheorem{rem}[thm]{\protect\remarkname}\theoremstyle{remark}
51 \newtheorem{claim}[thm]{\protect\claimname}\ifx\proof\undefined
52 \newenvironment{proof}[1][\protect\proofname]{\par
53 \normalfont\topsep6\p@\@plus6\p@\relax
54 \trivlist
55 \itemindent\parindent
56 \item[\hskip\labelsep\scshape #1]\ignorespaces
57 }{%
58 \endtrivlist\@endpefalse
59 }
60 \providecommand{\proofname}{Proof}
61 \fi
62
63
64
65 \usepackage{babel}
66 \providecommand{\claimname}{Claim}
67 \providecommand{\conjecturename}{Conjecture}
68 \providecommand{\corollaryname}{Corollary}
69 \providecommand{\definitionname}{Definition}
70 \providecommand{\examplename}{Example}
71 \providecommand{\exercisename}{Exercise}
72 \providecommand{\factname}{Fact}
73 \providecommand{\lemmaname}{Lemma}
74 \providecommand{\problemname}{Problem}
75 \providecommand{\propositionname}{Proposition}
76 \providecommand{\remarkname}{Remark}
77 \providecommand{\theoremname}{Theorem}
78
79
80 \end_preamble
81 \use_default_options false
82 \begin_modules
83 theorems-ams
84 \end_modules
85 \maintain_unincluded_children false
86 \language english
87 \language_package default
88 \inputencoding iso8859-15
89 \fontencoding T1
90 \font_roman default
91 \font_sans default
92 \font_typewriter default
93 \font_math auto
94 \font_default_family default
95 \use_non_tex_fonts false
96 \font_sc false
97 \font_osf false
98 \font_sf_scale 100
99 \font_tt_scale 100
100 \graphics default
101 \default_output_format default
102 \output_sync 0
103 \bibtex_command default
104 \index_command default
105 \paperfontsize default
106 \spacing single
107 \use_hyperref false
108 \papersize default
109 \use_geometry false
110 \use_package amsmath 1
111 \use_package amssymb 0
112 \use_package cancel 0
113 \use_package esint 1
114 \use_package mathdots 0
115 \use_package mathtools 0
116 \use_package mhchem 0
117 \use_package stackrel 0
118 \use_package stmaryrd 0
119 \use_package undertilde 0
120 \cite_engine basic
121 \cite_engine_type default
122 \biblio_style plain
123 \use_bibtopic false
124 \use_indices false
125 \paperorientation portrait
126 \suppress_date false
127 \justification true
128 \use_refstyle 1
129 \index Index
130 \shortcut idx
131 \color #008000
132 \end_index
133 \secnumdepth 3
134 \tocdepth 3
135 \paragraph_separation indent
136 \paragraph_indentation default
137 \quotes_language english
138 \papercolumns 1
139 \papersides 2
140 \paperpagestyle default
141 \tracking_changes false
142 \output_changes false
143 \html_math_output 0
144 \html_css_as_file 0
145 \html_be_strict false
146 \end_header
147
148 \begin_body
149
150 \begin_layout Part
151 part
152 \begin_inset CommandInset label
153 LatexCommand label
154 name "part:part"
155
156 \end_inset
157
158
159 \end_layout
160
161 \begin_layout Standard
162
163 \begin_inset CommandInset ref
164 LatexCommand formatted
165 reference "part:part"
166
167 \end_inset
168
169
170 \end_layout
171
172 \begin_layout Chapter
173 chapter
174 \begin_inset CommandInset label
175 LatexCommand label
176 name "chap:chapter"
177
178 \end_inset
179
180
181 \end_layout
182
183 \begin_layout Standard
184
185 \begin_inset CommandInset ref
186 LatexCommand formatted
187 reference "chap:chapter"
188
189 \end_inset
190
191
192 \end_layout
193
194 \begin_layout Section
195 Section
196 \begin_inset CommandInset label
197 LatexCommand label
198 name "sec:Section"
199
200 \end_inset
201
202
203 \end_layout
204
205 \begin_layout Standard
206
207 \begin_inset CommandInset ref
208 LatexCommand formatted
209 reference "sec:Section"
210
211 \end_inset
212
213
214 \end_layout
215
216 \begin_layout Subsection
217 Subsection
218 \begin_inset CommandInset label
219 LatexCommand label
220 name "subsec:subsection"
221
222 \end_inset
223
224
225 \end_layout
226
227 \begin_layout Standard
228 Ref to 
229 \begin_inset CommandInset ref
230 LatexCommand formatted
231 reference "subsec:subsection"
232
233 \end_inset
234
235 .
236 \end_layout
237
238 \begin_layout Subsubsection
239 Subsubsection
240 \begin_inset CommandInset label
241 LatexCommand label
242 name "subsec:Subsubsection"
243
244 \end_inset
245
246
247 \end_layout
248
249 \begin_layout Standard
250 Ref to 
251 \begin_inset CommandInset ref
252 LatexCommand formatted
253 reference "subsec:Subsubsection"
254
255 \end_inset
256
257 .
258 \end_layout
259
260 \begin_layout Paragraph
261 paragraph
262 \begin_inset CommandInset label
263 LatexCommand label
264 name "par:paragraph"
265
266 \end_inset
267
268
269 \end_layout
270
271 \begin_layout Standard
272
273 \begin_inset CommandInset ref
274 LatexCommand formatted
275 reference "par:paragraph"
276
277 \end_inset
278
279
280 \end_layout
281
282 \begin_layout Subparagraph
283 subparagraph
284 \begin_inset CommandInset label
285 LatexCommand label
286 name "par:subparagraph"
287
288 \end_inset
289
290
291 \end_layout
292
293 \begin_layout Standard
294
295 \begin_inset CommandInset ref
296 LatexCommand formatted
297 reference "par:subparagraph"
298
299 \end_inset
300
301
302 \end_layout
303
304 \begin_layout Standard
305
306 \begin_inset Float figure
307 wide false
308 sideways false
309 status open
310
311
312 \begin_layout Standard
313
314 \begin_inset ERT
315 status collapsed
316
317 \begin_layout Plain Layout
318
319 \backslash
320 protect
321 \end_layout
322
323 \end_inset
324
325
326 \begin_inset Caption Standard
327
328 \begin_layout Plain Layout
329 figure
330 \begin_inset CommandInset label
331 LatexCommand label
332 name "fig:figure"
333
334 \end_inset
335
336
337 \end_layout
338
339 \end_inset
340
341
342 \end_layout
343
344 \end_inset
345
346
347 \end_layout
348
349 \begin_layout Standard
350
351 \begin_inset CommandInset ref
352 LatexCommand formatted
353 reference "fig:figure"
354
355 \end_inset
356
357
358 \end_layout
359
360 \begin_layout Standard
361
362 \begin_inset Float table
363 wide false
364 sideways false
365 status open
366
367
368 \begin_layout Standard
369
370 \begin_inset ERT
371 status collapsed
372
373 \begin_layout Plain Layout
374
375 \backslash
376 protect
377 \end_layout
378
379 \end_inset
380
381
382 \begin_inset Caption Standard
383
384 \begin_layout Plain Layout
385 table
386 \begin_inset CommandInset label
387 LatexCommand label
388 name "tab:table"
389
390 \end_inset
391
392
393 \end_layout
394
395 \end_inset
396
397
398 \end_layout
399
400 \end_inset
401
402
403 \end_layout
404
405 \begin_layout Standard
406
407 \begin_inset CommandInset ref
408 LatexCommand formatted
409 reference "tab:table"
410
411 \end_inset
412
413
414 \end_layout
415
416 \begin_layout Standard
417
418 \begin_inset Float algorithm
419 wide false
420 sideways false
421 status open
422
423
424 \begin_layout Standard
425
426 \begin_inset ERT
427 status collapsed
428
429 \begin_layout Plain Layout
430
431 \backslash
432 protect
433 \end_layout
434
435 \end_inset
436
437
438 \begin_inset Caption Standard
439
440 \begin_layout Plain Layout
441 algorithm
442 \begin_inset CommandInset label
443 LatexCommand label
444 name "alg:algorithm"
445
446 \end_inset
447
448
449 \end_layout
450
451 \end_inset
452
453
454 \end_layout
455
456 \end_inset
457
458
459 \end_layout
460
461 \begin_layout Standard
462
463 \begin_inset CommandInset ref
464 LatexCommand formatted
465 reference "alg:algorithm"
466
467 \end_inset
468
469
470 \end_layout
471
472 \begin_layout Standard
473
474 \begin_inset Foot
475 status collapsed
476
477
478 \begin_layout Standard
479 foot
480 \begin_inset CommandInset label
481 LatexCommand label
482 name "fn:foot"
483
484 \end_inset
485
486
487 \end_layout
488
489 \end_inset
490
491
492 \end_layout
493
494 \begin_layout Standard
495
496 \begin_inset CommandInset ref
497 LatexCommand formatted
498 reference "fn:foot"
499
500 \end_inset
501
502
503 \end_layout
504
505 \begin_layout Standard
506
507 \begin_inset Marginal
508 status collapsed
509
510
511 \begin_layout Standard
512 margin
513 \begin_inset CommandInset label
514 LatexCommand label
515 name "margin"
516
517 \end_inset
518
519
520 \end_layout
521
522 \end_inset
523
524
525 \end_layout
526
527 \begin_layout Standard
528
529 \begin_inset CommandInset ref
530 LatexCommand ref
531 reference "margin"
532
533 \end_inset
534
535  
536 \end_layout
537
538 \begin_layout Enumerate
539 item
540 \begin_inset CommandInset label
541 LatexCommand label
542 name "enu:item"
543
544 \end_inset
545
546  
547 \end_layout
548
549 \begin_layout Standard
550
551 \begin_inset CommandInset ref
552 LatexCommand formatted
553 reference "enu:item"
554
555 \end_inset
556
557
558 \end_layout
559
560 \begin_layout Standard
561
562 \begin_inset Formula \begin{equation}
563 A=B\label{eq:A=00003DB}
564 \end{equation}
565 \end_inset
566
567
568 \end_layout
569
570 \begin_layout Standard
571
572 \begin_inset CommandInset ref
573 LatexCommand formatted
574 reference "eq:A=00003DB"
575
576 \end_inset
577
578  
579 \end_layout
580
581 \begin_layout Lemma
582 lemma
583 \begin_inset CommandInset label
584 LatexCommand label
585 name "lem:lemma"
586
587 \end_inset
588
589
590 \end_layout
591
592 \begin_layout Lemma
593
594 \begin_inset CommandInset ref
595 LatexCommand formatted
596 reference "lem:lemma"
597
598 \end_inset
599
600
601 \end_layout
602
603 \begin_layout Theorem
604 theorem
605 \begin_inset CommandInset label
606 LatexCommand label
607 name "thm:theorem"
608
609 \end_inset
610
611
612 \end_layout
613
614 \begin_layout Theorem
615
616 \begin_inset CommandInset ref
617 LatexCommand formatted
618 reference "thm:theorem"
619
620 \end_inset
621
622
623 \end_layout
624
625 \begin_layout Corollary
626 corollary
627 \begin_inset CommandInset label
628 LatexCommand label
629 name "cor:corollary"
630
631 \end_inset
632
633
634 \end_layout
635
636 \begin_layout Corollary
637
638 \begin_inset CommandInset ref
639 LatexCommand formatted
640 reference "cor:corollary"
641
642 \end_inset
643
644
645 \end_layout
646
647 \begin_layout Proposition
648 proposition
649 \begin_inset CommandInset label
650 LatexCommand label
651 name "prop:proposition"
652
653 \end_inset
654
655
656 \end_layout
657
658 \begin_layout Proposition
659
660 \begin_inset CommandInset ref
661 LatexCommand formatted
662 reference "prop:proposition"
663
664 \end_inset
665
666
667 \end_layout
668
669 \begin_layout Conjecture
670 conjecture
671 \begin_inset CommandInset label
672 LatexCommand label
673 name "conjecture"
674
675 \end_inset
676
677
678 \end_layout
679
680 \begin_layout Conjecture
681
682 \begin_inset CommandInset ref
683 LatexCommand ref
684 reference "conjecture"
685
686 \end_inset
687
688
689 \end_layout
690
691 \begin_layout Fact
692 fact
693 \begin_inset CommandInset label
694 LatexCommand label
695 name "fact"
696
697 \end_inset
698
699
700 \end_layout
701
702 \begin_layout Fact
703
704 \begin_inset CommandInset ref
705 LatexCommand ref
706 reference "fact"
707
708 \end_inset
709
710
711 \end_layout
712
713 \begin_layout Definition
714 definition
715 \begin_inset CommandInset label
716 LatexCommand label
717 name "definition"
718
719 \end_inset
720
721
722 \end_layout
723
724 \begin_layout Definition
725
726 \begin_inset CommandInset ref
727 LatexCommand ref
728 reference "definition"
729
730 \end_inset
731
732
733 \end_layout
734
735 \begin_layout Example
736 example
737 \begin_inset CommandInset label
738 LatexCommand label
739 name "example"
740
741 \end_inset
742
743
744 \end_layout
745
746 \begin_layout Example
747
748 \begin_inset CommandInset ref
749 LatexCommand ref
750 reference "example"
751
752 \end_inset
753
754
755 \end_layout
756
757 \begin_layout Problem
758 problem
759 \begin_inset CommandInset label
760 LatexCommand label
761 name "problem"
762
763 \end_inset
764
765
766 \end_layout
767
768 \begin_layout Problem
769
770 \begin_inset CommandInset ref
771 LatexCommand ref
772 reference "problem"
773
774 \end_inset
775
776
777 \end_layout
778
779 \begin_layout Exercise
780 exercise
781 \begin_inset CommandInset label
782 LatexCommand label
783 name "exercise"
784
785 \end_inset
786
787
788 \end_layout
789
790 \begin_layout Exercise
791
792 \begin_inset CommandInset ref
793 LatexCommand ref
794 reference "exercise"
795
796 \end_inset
797
798
799 \end_layout
800
801 \begin_layout Remark
802 remark
803 \begin_inset CommandInset label
804 LatexCommand label
805 name "remark"
806
807 \end_inset
808
809
810 \end_layout
811
812 \begin_layout Remark
813
814 \begin_inset CommandInset ref
815 LatexCommand ref
816 reference "remark"
817
818 \end_inset
819
820
821 \end_layout
822
823 \begin_layout Claim
824 claim
825 \begin_inset CommandInset label
826 LatexCommand label
827 name "claim"
828
829 \end_inset
830
831
832 \end_layout
833
834 \begin_layout Claim
835
836 \begin_inset CommandInset ref
837 LatexCommand ref
838 reference "claim"
839
840 \end_inset
841
842
843 \end_layout
844
845 \begin_layout Proof
846 proof
847 \begin_inset CommandInset label
848 LatexCommand label
849 name "proof"
850
851 \end_inset
852
853
854 \end_layout
855
856 \begin_layout Proof
857
858 \begin_inset CommandInset ref
859 LatexCommand ref
860 reference "proof"
861
862 \end_inset
863
864
865 \end_layout
866
867 \end_body
868 \end_document