Content-Type: multipart/mixed; boundary="-------------0609182236645" This is a multi-part message in MIME format. ---------------0609182236645 Content-Type: text/plain; name="06-265.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-265.comments" Submitted to Phys. Rev. A ---------------0609182236645 Content-Type: text/plain; name="06-265.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-265.keywords" adiabatic invariants, separatrix crossing, nonlinear Landau-Zener tunneling ---------------0609182236645 Content-Type: application/postscript; name="Fcomment2.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Fcomment2.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: Fcomment2.dvi %%CreationDate: Tue Sep 19 12:17:50 2006 %%Pages: 5 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR10 CMR7 CMMI7 CMR6 CMTI9 CMR9 CMBX9 CMMI9 %%+ CMSY9 CMMI6 CMSY10 CMMI10 CMEX10 CMSY7 CMSY5 CMBX10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: DVIPS.EXE -P pdf -p1 -l5 Fcomment2 %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2006.09.19:1153 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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%%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 164 /asteriskmath put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueXX 5000815 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6784decd2fb36dec8f 7478da853762e00bc9c52ba86ef50d222ff142abc18e4fb95b86b3e57d9390ca 86e8de6347bf7f48f93322a372c5d7830521b14e8fa0771961b027c81365426d d95d16b950e216a90f28ce806244ff28dd969cb512a23e05045e7b2bcaf7d6f0 ca8b51494f2ec0681bdfde60420628d9bce98a0ca1ecca9140f452a88db19a30 ed46ae881b098c843a51d06f9a153489357fd24de6a0c36cb5a9eb9b3b64dd75 18f83018ae7cefa1c12fd205df6880a705e28457af7b869a6dd28f6b37d82cc3 e51cba348dcdb34efb119b8ce5a996f15492b0f5d34538850a2c1b6a509fe5fa 015eceaf28b787e54f5f78aa5a89e3ed380237c85d8bf04e237c596b7121c2b8 991c77ac8ff218d9e8bf0fdc11d19c5b06fc70dd7646b0e08768a406ea03b0fc dfc899c5c85914bd365a8f057eefc0b6a35e89debb6b54e7a7af7802afd568e6 0a8dafbd660a71e83396f034a361f71499692ab78df3c7dfe63608b5e00b6ca0 553dc4342abcb9047f5295a7a8409d46d18cb8527370eec456894c66d17a71e2 157ed47a53e09dd75d1b1d50d4501c911fcb6d770e60e86493a66083939c0692 3fdd80dc5e24eb187719b6a995bf425c65838e027c02a1ef6e71455d6fb62a6f dcb43b6c8ae00276adfec4e467b3729e22566479de3a499302b645164fb2826a 6aae6a7a5c25feacbdf6e9dd38553476124a72bbf48248fa0a2776046df2689b 058b6d11e1e0fb0e69a7cfa307caef22df2f667a39279a559275e07c4e740a6f 359f858bff306555d7752401c9753271a587bb5d6cdda682c8675028248070db eebab5483343eb4806d450f55f0c518f11e494e66eb519e53a3f2f18 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 164 /asteriskmath put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueXX 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b873912be368f3f300b584a7c5dcdc5e3f796d62bd191959cd043bc0a0 108ac1860e97e05173d3b979ffeaa815405d9db68a72c102cca8b3becc60437a 946131e0670abd3348ce6dcbd3bdd4797f83472f944778fbeb0a0b93d8a4d083 b01af5d0375175776132e925abf0d55900d5c4e077a7f1f3241798bd78cafb12 ff0909bc5c14ff1a1e8fe01488fe80788e8ac942fb61a682e771e819ffa932f9 048443d253d2fc3943f23a478429df0d08f342a3b9db69e8dae6813cc378e6e0 9d46c60925bfaab629e1b5efb00cf55cff363c686e0f4c8078dc9bdad4f87dc6 e8a4ee1f1cf95aaef83fae8d3a0263785734c7626aa72870887f4cf98b9484a3 230b39fe2e87a1ad32a2b4d2400d2c6c49d83d503b69ffe9a2070081b9ad6daf c0b51161bd35c5222d5b54ebab90cb25d4183652d0600759f27a5f91ae8281f6 aeac97f4ee762d887b29b467db6eee86f413128efd225d64d3ede82933c9bf65 91b2c1e323e3551d4f58fa8790145ddeb782ac9c174af6b850bc6b6c7f62c44f 8c4f4e506596ebed4c68d46c82d1c0c15c1b7546d703e046960d3fce81ea1aaf 755546ba253aa0dbb5c6df 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /parenleftbig put dup 164 /bracketrightbig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 90 /integraldisplay put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fbb931da9ee6ade43de532d888f4d9aeca091a3d519db29d75b39638cef311 18f347e943c5f7d9dc857d8bfa368dbed4f6e9578c9e0a4c49381162973615cc 57c8029fba2ff27b1fdaa46ae2bbb49b95fea2b7f53f97e19448f0003cf92a2a e30c2d7494ce3893aa3d5e307441f56a9b7f52708be852c06f0d0e4462c64f15 a0a1fcfdd1946fdb9a597d38ca52c6b11038535040d5a110fc6e851474b56401 6452eade41992543a047e49c6425dc91a266bbbcfb6930e773ae5daa483fbf27 0dccd8124459ec8a7cf4b92fd2e24eb0c529ef7180312ef003c0951e7e136d3c e467c45b9440ecfad4afc642bf5f8ade504cd89e27fc2e5dc700e44524d82e00 56ea9a820a0da5fa71a2d711225b79b295540e890c56a5888a186805cabbc903 5a2f4a0f4f2a1a6d46ac99d33f693704be783ce12981788fedafa9146baa0ce1 380d9ba49fa1e77d4fdfd54ee60123cf2047f159f22c6cb4a451853e02069e2a cccf29a969de133b5c5db1a4717ebc143535415a30280388a3094d84322571dd 7a5590436bfca0f207942a7af14e4b8f5f76966ce661a7ac4306332f94a9767e 44ae2075050a48f8576350957b2c931b5ccc6f2138c842d6a9c6985dcc2e4b68 3edfe34b1dc1eb317dd7c04822bb5a2590ec0fe9cf0ce9b0f6275e06f094748f 06d7df0f9b04b4dc4b9e0ca759ca835e0e7db600a96cd899f9de3e54ea8d70c2 2b1ecdcde0b92198f1f96891abb84938e1a05c550000162d4d8b098ee84bf091 24430790612d13700ffe6ad3a53867c4b30580ef4c302a2596c390b1d20f4554 edfc785a359b2280fa89abc8bb60d5e7032c99fdaed48665358de8b29946d48c c0bf3c14c29858941ec01ed5e74b1a418966dbafa74703a75f71bdeb6e148ce1 12e42858962143a6377a19b9b1a6d9b60b92d8143e43231a4130b38ca5b92010 87def3327d878ea497ff5df8ad995cde316a946afbf39577bf87725a62cefbb4 4db8185e87e41321b6f9dd6ffa3907559cd4ad9ea4c84b2cf10e72f3a1659976 862f8ec64b03a4aa7d2f20f2be5481ca1b42a35fc09d142b612d9460a9f582db ffdc66bc3f91b4f77a8ba69e93a3ab56ed754460bbef045821a15dab29ec7aa8 8c477962ef45635b7cd2cc4c34b646e69d9278dfc2807b1c4a3eafe6d86bd13d 1cde35ca5591cca275009ee07da6ba7039a77a9d35eafd9da7d3c31aa9fd3f6b db84ccfac8732ef0361769096d04b57bbbe61e564d1fc1cebcce361e7a749ea1 9418493b01ced1f2456e517bc34583b5d550e64469bd0675349676d7bbe976d6 642ae7c41b0fcbe23f4e1da2be1fd7db6608650a786cb0777dc365e06a20bc45 2b29dc042334c77852ef2044d7e7786505decba59deff14a268f1c7c35e816cd a137e4186df1a351b42d5f3bf5e57c12a45cff25a2aa1709ece793c0d90a8409 bf1d76d62f10dc27d62d7865f671ae55 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 164 /Lambda put dup 174 /alpha put dup 177 /delta put dup 178 /epsilon1 put dup 181 /theta put dup 182 /iota put dup 187 /xi put dup 188 /pi put dup 191 /tau put dup 193 /phi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 78 /N put dup 83 /S put dup 84 /T put dup 86 /V put dup 100 /d put dup 102 /f put dup 104 /h put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6 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8cea661f73f20f0f4ef03836698d59ade18a7d3d06573b9710eb409978642bb1 d9fa10601e701a728b62e7ba1d2db92d869f071e0346e0619d792122af166da4 26fb5bc2902765188450f293767fcd10dae6ba4368c92744c2dbd7bad3555c36 700b25db522894d04a95ca3d51c202d666661ed19a9566a8b21746594b9aead7 3c196f5496e29b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 164 /asteriskmath put dup 174 /circledivide put dup 177 /openbullet put dup 178 /bullet put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 187 /similar put dup 188 /approxequal put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 33 /arrowright put dup 106 /bar put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 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d3e16182038497cb4fbe875b1f72d1e45ec9f1d13ccfe8e4f3f1396f8e99b41d c945050924d10e44e7d9a4da90d0b1bf300462c89bde14a1968c2af70a71ab03 be29fd07c0761c0cd5d7fb4f0f9521753cfdf0502f3296bf312fd23a3e77d0eb b7b3be81b676e85a4869b473ec03e4d8822f1c822218ea842700e2a1a8d89f6f fa53f2001fd3b4dba1d637952e0c09029a3121fefbc17ceec0d84d34eb48b75b 41b6120c5c8e9fc61a5155f778c84130d6b0ef49a6b3f92faff9cc624f8eb02e 626c2e153da835426d8e50dfb6b793c90c3719c5ecc9f72fa4edf925e37d7f8e b4e10b6ad04834134d1e6ae1f680592c98d8b988106c8c3607a34c5445800356 558898450636320c083e4b6347bb867f7d82609f691da1896fcd3d715b7a5688 ac46b7aa1274fcc571490dc93da37b8da8cd1cc8ecbc3448195c32bbbdae9890 f2e9eb6bf33f4245f95bc1d656716c7747e10f578efbeeca685e979555bacf7f c506779003747cd2a9c3db9c61d82f1c246eb568a7e99c71392e958b990a5808 0fa1954a4f954d4088db63eeb5f2270e096fb82a6b9b979c155eb0d0c64fc206 746320a86114f0e06109ae3104c16d143fa1c0ea7c6887a732d50f61c43c1a1d e3b339ccff1f4fe4dee28373bebb087bd72085c1f3707b6840dd14a086013ff3 164455933298efd0917a880dc95fb9bc3725d1cf005f141dc8bbea644ac291cb 42ac5d36508f9e7e5b19854f97befa8d718ede472ff0badc26008d21d90fedb2 f3d3f6abff4d003c40f4378f099d44163443d2156ea7cea1af5473f4f6a146db 1c9e7570803b008655ead6533529aaf47fe82561bc4e4480a6895efd36facc0f 808c10f0ac6757e4318bc6f9a83bbb379c61eaaab524a90108a01dc5e837ed08 6fd3f67d8f27b4f6c332c31a02aac7c5973f06c213be7f9f475bbb1c5a975b43 01fe1fcfb9194c9245d28d9f001f42b8436f976f10c395c02c4e0a5e1d8614fe f00fca0cd5cf19cd03f41dae48e26d368df66581633c242bacba9b31f5a49f61 4cb6b95e328232c75fa7a6d4dfe40f1b75d846af8ee7e96c1fd048558816807c 06cd907d22d20fabe728d1f2e9e2297bd1ab123048106ca79ab3244779f38f25 d2dde1cad98f4719d88b1eae3db751821b9b8d777c8d96f6ee8df868a581fb94 5ec4b53f25901818e0f76c420b1f5c0352c6ea2899d3b6c9c54c8ff62b131ba5 f00e89faa7f17635741b27224bf17a0eea3a50ad708de77c2928485e1ffd7c1b fe2b20bc35beadfaacdede981c67cd3cf580489a56ff0d327f06793402a48827 bba7376637f596c0762561057c1df2c89caf838bf21e8941bd7f9f295dcf633f 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2c50cd16753e14cf2411a6ae85216a055b63055f03073509c72cb558aa27705c ebb653a3d4e17315e18eac2131c56c5500db4b56cd3215d059908587db2260d4 153adf6aa22356a7ada1e0497b6f1006edb1078fc3b869490e2ffb9464272357 77b911aac8765d9f9e1b380d8a4537cbbe643465b8f6fe6e4688a6dcb24eb7af 2958e415e91e40a4240646e3ed76a33955c0051fd0ac748e0f7fa056aa941250 0fd068b98914d5bcae5335f1318635828d6a857f04fdce77f501c9a93e57e309 ac105ef2dde426eca12516f1d2fa5ce7b2c17f7df1441e727334d98f1c64cbfb 28d1b2005ce06b9a8a67988a68235afbdaa0c2635d73ca39c0778253bcff96f5 7c6682708b1af0623ad071193da121116b72d7e3b76d6c8a06ffbcbc8104a0dc 26ef0811c61ca3c12fe0e310fc008ad1d85000abd3c3abee1e14845fab458f68 a0e1b5706d49930b13f9d043a98ed7d368530439dc1eefd28b1c2868ed56b7d6 b6b0954dec25ff5878fbd3e9de97c48914f25407515941b6d49d5d1e80e721e8 d12a35ee24c7cdd604542ba5e22794c37c741961f13393823deee51c9d344e23 b8d8874d4dbe82ad533a968cd4300fb85662ec2e81760de62ebc320009af4466 ee6763499b6acdbf7ce16dca0c16275da579c2b173a2a974506af24c1b03af37 eae004704e40bf61e81096735fae40b655731bb4f629eadf957ec2823a5e8b41 778e47c89fbe4d327bacb8f5179e81f9868b0d0e86b8bdf21ff9b6eea44c2da4 a857b6e7dcdcffd7905246800e4b0923667e17ced5ef8ec852708c371d35bf3c 7e323688cf7b39e682cd8d1796ce05b34671933df90416b76378fab0b85bc5a4 0c521776852866367ef43dbf485852ca400dd8a3bee3676963c6e04f2a82b873 a11bd980024072b09608930640513066ca348c4eb56ea8cffeaa99b1c3affdd0 b8ec6e08a610d5a1793ebea89380fee16ab32fc3dc9b9f80ecbfcd6475c52c44 e492ca9b9c54cf6676f0353a802d4f353b8f798d7122f74e1740029d752b508e c8ba1394b27a6b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 164 /Lambda put dup 174 /alpha put dup 177 /delta put dup 178 /epsilon1 put dup 181 /theta put dup 182 /iota put dup 187 /xi put dup 188 /pi put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 61 /slash put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff 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602f964514422a05808636d74ffbf7bc77349f68d654bfec2b750b4b3bce0e35 a2ee5daf40337e0029855fa314706af464550309f4673f1a731b28afcc448c9c dc041ae38c9657836a31014ad5bc61eb3adb66a50807ef4daf21b6d83b662c13 603c146139124428491f3d77c6e33ef3a2c55243e3f2b6d5d58408fa051bae3e d5c9f9c8d6d29cf084e96b7736bcd65b3efeaa27320d8f8064ff8029cb037c51 1b1f01e6a6cc5841f5d7bd0f76622d11051836d420ddc211a8c32c8943375201 87e6d8f52ef78e5bcba170094e3a25001f7a128de552621219c9c7568fcfe5ca f612c7515fc57a77d3bb51da0483af550959b1997021fc9fc64ccd3552e71a76 7eab5a0935a4a5e2a93b28f053deaca122c460551de55702ae4851a988db67da b329ad18bd7d148cdce439312322a13a3eb7a4cd4d5bc41ebe19daefa3b9b7c3 9471feb98e2c8961eab06c7276633a2a31e288caab59870f96ec40f2cb028917 e62a888e27d94d98f3f87827e8ae55ab0628099a5819d090c086e0322fb9fbf2 f90077f15e499d7b892a4c2143dd165706548b639fdc77cf47929e9712d5f9ca b5914447348b6af32e7007420e0ec5dd3461273d30835679c80751be77a79a86 e5c57f570801a93f39883cb9963e48285def40a1784f445679794a3af135d2cf 7935b88256d178a8638def9224216ee87806ae280bfd37a3b3e8d29d1b1b9eae 909fdb864fa0f4dd7a18ba7ea384fbd1754bb01453593219e191ceb7bc5dd086 098ae15c0d5af106c09053f7d85382a4e76c23127dcbab18e303c888e24f6219 a78da58e4fb15456785d46a298a01696b0d829fac3c04df5c2e7989046fdae69 ab7238ed749fe6e1459872fe9bcf51bfe20a353e4130601dc0f4cefce0971e99 bc7aa0c6c7b5891d097905b0bc82a127aab6f9e8ccbfb0bf3db62b8c74a86300 884021f40c2ddba8d3972862586e3824205c9f1833e1cd16f2519f7f86e94d20 a3d3b219f0773896e17d7387caafab11be680273bb179220b23541155c05013a 424015013000ab6742c89295f0a31c6c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 164 /asteriskmath put dup 174 /circledivide put dup 177 /openbullet put dup 178 /bullet put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 187 /similar put dup 188 /approxequal put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 112 /radical put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueXX 5000819 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 164 /Lambda put dup 174 /alpha put dup 177 /delta put dup 178 /epsilon1 put dup 181 /theta put dup 182 /iota put dup 187 /xi put dup 188 /pi put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 59 /comma put dup 61 /slash put dup 73 /I put dup 117 /u put dup 118 /v put dup 119 /w put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueXX 5087384 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b33ae3d31bfe98efe259f07f7950237bbaee4f7b64ffea83a 757fa717d50c3298392891bfd60e34a056b0d6021da3fd9b8b01bf78b0b23dc4 ea3b0605150d20b27ff9ea5f2524661019d982a2e47cd7c21ee5ca9ed9227821 f8d07119397de26838c11d7b35bcedc43e011626e300f8249ed846d7b5ccbd89 02550cda17ddf113df658fb13f8162681013766863784efac128e01ef997e1a4 30312afac8f3d948edecd7d5090ab5c864b91d7f6e80256f0e1fc99f1102b74c 61cc456e2e1bedf0e627d5f70f738f963a13666405c51ebf23ca077e97570a2f 1118536b92e585cf1dbd5fbf36a0a5d197538c05304e93a15f3c931168d91d42 483ef428b1a3f1b7e548fd1d23b80f5523c8b8bf450b02804fb689f915c86693 f7dfb1c43f681627c7f027021aa3a8179148f1819cd94b8890a9ac63dc1e8a68 f254b64f6f173c3d02e3ebc037da05074017c8b113e94f4e2d26b467ef9da07e afd7ea7c86e025af52c5ceeb835951e67e02a38daf1e9e698bd21996c1071e84 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 164 /Lambda put dup 174 /ff put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueXX 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 164 /Lambda put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 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%%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 164 /Lambda put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 74 /J put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put dup 122 /z put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueXX 5000827 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3036f2ed7bb65d cc883aff8d6350d6e8af1a9c1d2d7fcddc4c554c7e350f2420586f43e2124611 487cdb176d453854b51cb8f9100bf241899bbef87d57f1135e589813995c4d86 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f2ff4a0a13c75db940c7142ec546b14a79f0946635fab4493d2be1292b1a0289 ab5d99c2ee786ceee5496cbd27dfb5999af5da1dae5c1c128b25fb5b6c0aa088 8f028f3a93459e229c0f63c737f97e323e6ecf2d708b67 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 164 /Lambda put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615c31fa0dda3022e6c4280377 c7fc05d7171baf721953616aff57c215b922c58a7eadcefff122216df93857bb 5cf4fdbc70a42b604ec02620e28530f2896c96ef1f89f2054bc547825e74d22a 0e029f61a24352d29e63bc4d26ce4802e718056eef9d2c9ad5d4408449451702 3ce9ceaea284fdd5e8fc131b7b00dd39d9e30af990041c27d80e4486522fd16a a216f97a72eed9786d8e45e377d7a6e377a32a2cb5f213043e7bb79b93c22097 b70433969d2a36c8d56bb80b73e76cf0bf2d2091a6906cfbd7e2493af2b0f940 376739d9b08d4bb72c26d53fd4068327e4baec2d7b64568a104530d1239651ba 36ce9a2469f78ddff3d9ef048a9809628b4c2e3d1eb1ddd7631736f1bacccfc8 cb45319938d55ad69aba8e0b32d84e06bf1539188e5e9333c36aafefe838be61 3574b0e01433b35c20aa385bc1e0b3b6753a80681048ffd7ca473d8bc6879ba2 79b833e0cd1c8a280a4d770508a0dfb7be7d53d57e97e56766b67b51da775203 6a70523712c8f08f1dd5a0e5802482247da200b93f668ca20565f799cb18362b 761d516088cb4bfe0e52c43c916ac12d725290395d94cadde4e44b4eeda198d0 b25b5ffd67e075e5133252a1507489a25d0433e2fd22e65641684c413ead339d 66d0f5a8577f7934a6d2652a8791662e8fc2c46f00cdc7ef662930d8dc73420e 4b823cbd85781ee4740d61dd41f7f39bb78b42a0183fff635b7f8db4f1f653c6 57203d88c10a37774a4833269dcb52e279313dc6fe984f4576a04cc5020bf3ab 236b8f51652c9ff9a1c41e7a7cd12b7daadd9bab446b1c2f4d6f79678f681611 00e83ec5f5268ea45fc9c0b3657bf6bbb2d7f1168de45c6f40d34e40d57b6d23 614e539fbfaa0a32589e3edaff2bb94bb0da010c3691af60c99da06f5c64c9f1 6cf224df322f33918ea1d601772d07da1bf791ffd4198cd72897b0db7a8513be cb0e6c5d489c52cc800bcaade2b24c783935eb94cb2f8d8ca4f20079a556b8cf f5368c117b7b38c24ae3a77a521b7cf0ffb8033ba8ff0a607e2bb9d17dd42339 3946c8a05f28ffc5cd2ad5692117c87cb401e5989eb0b88c79fd41cf49852e56 a16e2cb7fd192528ad041e4b62f34c5a7b9010abd63b49a4d4578c5725bc62ed 8b30eeff9f373178075d584ef92294c30ad588ab25cdd66a89bd6fa428fe4321 e7907d319cfe2dad464f1c71a64ef93aeeb2012fe00be2875a8b23397ab0143a 887a69c74cdb16331f4bfa48908511cf034f22720b90d749e0e42777315e17b9 d5d664d04fe9a6601def751f87cd52a32aebe291a906c00d79a071e3a103080e f5cf8ad4966ed20faabe6068379500087e41abd3d8896a284a026aec55a6bc5c 048816a24540529f953bb7e8cadb7a81cfc418b4d2189a25a4064af16be36358 a43ad155fc535def5004f8bef6bee2b5d787379e3d166814edc09afff3d962f4 eb91f3c6cdb1100307aa3604f4efc2c40c33488de2b3947c39282cf4aeea86b9 967063cb01d02f195c3a3121feb500728711a7506acbef432861b0735ffdfb4c e3567e8d10a53af8b11879cc43a1b4ae15a61a528066eec1ab53a572aa76397e 7428b073040abfe28a8f8ffcb0ac0b261dbcd923645906ed8bded5f7f78b78d8 2f00c5a5a2009765fa1dc388624e90cd049df40d1b160a3b2cfbfd1e71740521 84593c7683c04348fffc394f5c748f43bf44592462ed1d3619685a0bf5351aee 4240a89caa3814bfe74918d6ded437d1f1e8b964fb1ba33a66f1f6850baca8a8 5eb0342d89bbe6bd40116fef00c8e1ede761a8a07de9e69b1bddf1ac7feecf3d 37a57b7b878d01dc23ccb3e3c9bde39df5dfe4d8d82a62186fc18924caeb65eb 31b63c3076d48ebba1b49154dc5fc651b198c8a38d3bf7d7d3bc8890c1b069b7 2be2d2af700a62281630e03088ce4e91055cc2f0f1c29df48a8650dae79bbe6d f137e15362a86af356d0f0c9aec4d71f7e73dd53e75abf7f2d1fb4f42f47e263 305ecf4a24d53ace9c6b6c5008d4333eb10ab88874b1b417e68c35f485bd91a2 e09080e809de9bfaef80e2e8f32d47ab7882a0302ea62999a59041d7e6897588 a33d7377cc8fb6ada5fd6593c56c563711227bfff480362388e6cb4bd4a1e672 dd3eb7a5e80cb42559fd2fee84d645f1a379be2b3ba7381d1f18847dedc988fd 074f2d895fd505ea17cb9d4349fed563f01855993a08306f86c643041ba7dbf3 3341e3562aeb39400e551977c50738c2bebd1e65e4fab49dbef6444a82cb5c44 f38949f26b5d3bd0db09aed8e96d6fe9c700fb9b6817b7c1beaa745384081859 f1dcf8a12b7d11963d49ca8fa802bdae609bcb32cd87fff66b04bde0cfaf4869 4db75187f9992f4611507da7ffecef64b5f42ffd810113a554935cd4704dd75e 5618d50fe6edf8f78818afeb1a48c4e55b9f072b44d7e9c96eac2faba580b70b b3db83897093723309f4dbbb8413573c3e50b8c81869a46059ef14970a80d212 899ed0f73a1a46f0fdcd686fdcf8e85f17ee5ee015458c58d108af0fbf743297 df2d00333076cffd56d1fa89d587f2c55e91adbef2197265796ad6d25b50209b 5b31a9b8efbab708279fcbcfe1fccf0163328acab3947e704a4cd41ebcce69b5 e6dddc80476daa100888f2c947aca0a43efdfebb8aefa42672a977ee78e98433 72ffbe9389d9bfc720d929979852d90ded723d8a3f0b01f272ca78f577abc982 74d94841972fa4101cf63f0edb53fc7b3518da080246c30e97872ad768b80aa7 ef3cad678c0ca8c6aa3445d43ee97fac52795a2877420d1317267fc9b8243ffa 342254d0878d20a56438ab65918695576be5243204e1bf8a666f39be175f0362 cb006a9dd4734a01011aba10addb3e3db557f06e416e8634f1f7ca58de0bb7cf dfb385015eb0236cdcdef5b766557e78443a9068583fa6320cedfee9a8e0d48c 3ad6f2c4a5af6cb4a32cf9e81a07602c1d2d2ad8977a52cd79e8f6ac08a47620 7dc2fcbac2327ee4792709b41a96dad683c43442f1fba2a0385266d423ef3a3e 8b9c79ffb2eb11be6dd03cf759ce078a3b4c2f10cbcd7b93657dd0097e5a4795 28eb3e0ac3e61eaec5aa78f361d6b820d05a09d1f8025f55180634d04fe0ae00 df8f2ff0984edc363cb27afcb8d5c8f0e178a13c2b1bb45e527cc072435b9ede 8dd473fcbdd0fe8f1ebb1757b2239e07dec3196732e37446fef965f2f9c5262b 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804c567d4a6f2f7dcff29372f3406eeb6e431c1b8ed6ff7c6d5035bcd6f4dbc2 3e1965f771651403a8d4402abc859c1edd4533fd69dc8c240a9d288cf4bb6d7c 9e380cf09ea547e465a51f0b7bdbc8b1d555a859945a5482a45346e4a8821e08 d4c41879f3ff585929601ad3f2422914e74b14a6a973a4d15a41d7bb61a38543 a49128fe29a3d107251efef0589eb91a2248a5899f8c410c1cf3986949932e38 ceb111b4dee8139d0eb07ad8d9f5f51988bb70486c0fcc3cfefe7abfbdf9ec45 658736247e7b94cb5cbc4c41b88c7dc22197d7fdd5670947ab66a0f3c92a4c4c 5b52bd460b0017bca53ef79944b2ea0ae84fcfb2a83a57bba650ca2fcc47797c d2072140a7f41bfe454dc48162850144832582937d4125e9858d3568e0985bcb 298a3b11da0ce003b7471bdb38b51a80014b4851c7bde8fa175a1da89d7f8689 58319bfbff2caad6f27720f63b05191b246e22d04c6e334e33b841cc0f704968 c1c3f031be5a7c063f33837dbcad83e60d69c4e40347006bfe68fd4fd88a755d ab1dc26484e30a1d44fb76ad3524e12fda47a90db9ae008ba61bb8123865fc6a f4638841655aa8799aca831b6099221ffd744c506dab10bd159891c59f3c199e 558555eb1b939e6dcd36dfbb5875a5aeac04ed616407b108a1ac187453c4909e 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 164 /Lambda put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 181 /theta put dup 182 /iota put dup 187 /xi put dup 188 /pi put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 59 /comma put dup 61 /slash put dup 84 /T put dup 102 /f put dup 105 /i put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueXX 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 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1337970a7f9c59a3d78f205f173492e45e9e15bd2000a491c90be2156df0db7b a10e29400a19f6562f86d76ddeb5d12caa10e483096630535ced6eb90e56185c 9a9dd4f94e5235846d62cc4cf4177a7d15180b864ebeabdf637018102b4387a4 2294f23be9df8fcb56eaf2c6f86abba4cef61e2e24e8085a4dae736912928c34 3b3a6f2b4222cafa5abdc3c83f6d40f0a18123e3eff48f94495be84a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 164 /Lambda put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueXX 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 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2a5c6561fe11e30d078edf74ae71cf4bd93982537ba258c49f3cba0ecbbb9999 f843e193429a3e7c482f1194a1c49ae525c39f9267cd2ba5cca67b396d520bb0 a9c024f462ab60a9b904f5e792c112c05c2eaf2befe9453a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 34 /quotedblright put dup 37 /percent put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 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CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 34 /quotedblright put dup 67 /C put dup 78 /N put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-53 -251 1139 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b(of)h(motion)g(\(1\)) g(restricted)f(to)g(surface)f(\(2\))i(are)e(equiv)-61 b(a-)-2000 50596 y(len)-31 b(t)295 b(to)g(equations)g(of)g(motion)h(in) e(a)h(Hamiltonian)j(system)c(with)-2000 51869 y(Hamiltonian)2823 55020 y Fe(H)398 b Fp(=)307 b Ff(\241)p Fe(\261)42 b Fp(\()p Fe(\277)125 b Fp(\))p Fe(w)277 b Fp(+)246 b(\(1)h Ff(\241)f Fe(w)30 b Fp(\))13938 54096 y Ff(p)p 14861 54096 2729 45 v 14861 55020 a Fp(1)247 b(+)f Fe(w)215 b Fp(cos)184 b Fe(\301;)3409 b Fp(\(4\))-2000 56898 y(where)641 b(canonically)j(conjugated)f(v)-61 b(ariables)642 b(are)f Fe(w)671 b Fp(and)641 b Fe(\301)p Fp(,)-2000 58171 y Fe(\301)601 b Fp(=)h(arctan)q(\()p Fe(v)40 b(=u)p Fp(\))546 b([see)f(Ref.)1022 b([1)q(];)635 b(there)545 b(is)h(a)g(misprin)-31 b(t)547 b(in)-2000 59444 y(the)369 b(form)-31 b(ula)371 b(for)f Fe(H)459 b Fp(there].)-893 60717 y(Consider)397 b(phase)g(p)31 b(ortraits)397 b(of)h(the)f(system)g(with)h(Hamilto-) -2000 61990 y(nian)293 b(\(4\))g(frozen)f(at)h(di\256eren)-31 b(t)293 b(v)-61 b(alues)292 b(of)g(parameter)h Fe(\261)334 b Fp([see)292 b(Fig.)-2000 63263 y(1].)487 b(In)348 b(these)h(p)31 b(ortraits,)354 b(p)31 b(oin)-31 b(ts)349 b(\(0,0,1\))j(and)d (\(0,0,-1\))j(are)d(rep-)-2000 64536 y(resen)-31 b(ted)286 b(as)g(segmen)-31 b(ts)287 b Fe(w)338 b Fp(=)307 b(1)287 b(and)f Fe(w)338 b Fp(=)307 b Ff(\241)p Fp(1)287 b(corresp)31 b(ondingly)-92 b(.)-2000 65809 y(P)-31 b(oin)g(t)341 b(\(0,0,1\))h(is)d(alw)-31 b(a)g(ys)342 b(a)d(stable)h(p)31 b(oin)-31 b(t)340 b(of)g(\(1\),)346 b(but)340 b(formally)-2000 67082 y(sp)31 b(eaking)479 b(this)f(is)g(not)h(true)f(for)g(the)g(p)31 b(oin)-31 b(ts)479 b(of)g(the)f(segmen)-31 b(t)-2000 68355 y Fe(w)509 b Fp(=)479 b(1)472 b(on)g(phase)g(p)31 b(ortraits)472 b(of)h(the)f(system)g(with)h(Hamilto-)-2000 69628 y(nian)392 b(\(4\).)562 b(If)392 b Fe(\261)433 b Fp(is)392 b(p)31 b(ositiv)-31 b(e)393 b(and)f Ff(j)p Fe(\261)42 b Ff(j)346 b Fe(>)14948 68712 y Ff(p)p 15871 68712 554 45 v 15871 69628 a Fp(2,)398 b(there)391 b(is)h(only)h(one) 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b(connecting)27224 54415 y(these)390 b(t)-31 b(w)g(o)393 b(saddles)d(corresp)31 b(onds)390 b(to)h(the)g(singular)h(tra)61 b(jectory)27224 55688 y(on)344 b(surface)h(\(2\).)485 b(On)345 b(the)f(phase)h(p)31 b(ortrait)345 b(of)g(the)g(system)g(with)27224 56961 y(Hamiltonian)266 b(\(4\))d(it)g(separates)f(rotations)i(and)e (oscillating)j(mo-)27224 58234 y(tions)411 b(and)g(w)-31 b(e)411 b(call)h(it)g(the)f(separatrix)g(of)g(the)g(frozen)g(system.) 27224 59508 y(Belo)-31 b(w,)303 b(w)-31 b(e)284 b(consider)f(the)h ("shifted")h(Hamiltonian)j Fe(E)371 b Fp(=)308 b Fe(H)165 b Fp(+)75 b Fe(\261)42 b Fp(;)27224 60781 y Fe(E)433 b Fp(equals)369 b(zero)g(on)h(the)f(separatrix.)28331 62599 y(A)-31 b(t)579 b Fe(\261)698 b Fp(=)656 b(0)579 b(the)g(singular)g(tra)61 b(jectory)580 b(on)f(\(2\))h(is)e(passing) 27224 63872 y(through)394 b(\(0,0,-1\),)404 b(and)394 b(corresp)31 b(ondingly)395 b(on)f(the)g(phase)f(p)31 b(or-)27224 65145 y(trait)345 b(the)f(segmen)-31 b(t)345 b Fe(w)338 b Fp(=)308 b Ff(\241)p Fp(1)344 b(b)31 b(elongs)345 b(to)f(the)h(separatrix)f([Fig.)27224 66536 y(1d].)544 b(A)-31 b(t)387 b(0)337 b Fe(>)e(\261)378 b(>)336 b Ff(\241)36180 65621 y(p)p 37103 65621 V 37103 66536 a Fp(2)386 b(the)h(phase)f(p)31 b(ortrait)387 b(lo)31 b(oks)387 b(as)f(sho)-31 b(wn)27224 67809 y(in)435 b(Fig.)690 b(1e.)f(Finally)-92 b(,)453 b(at)436 b(large)g(negativ)-31 b(e)436 b(v)-61 b(alues)435 b(of)h Fe(\261)42 b Fp(,)451 b(again)27224 69083 y(there)402 b(is)h(only)h(one)f(elliptic)i(stationary)g(p)31 b(oin)-31 b(t)403 b(at)h Fe(\301)363 b Fp(=)g Fe(\274)40 b Fp(,)412 b(and)27224 70356 y Fe(w)399 b Fp(close)370 b(to)g Ff(\241)p Fp(1.)28331 72174 y(Consider)456 b(no)-31 b(w)456 b(a)g(phase)g(tra)61 b(jectory)457 b(on)f(a)g(phase)g(p)31 b(ortrait)p eop %%Page: 3 3 3 2 bop 53901 -3985 a Fp(3)-2000 -1107 y(frozen)370 b(at)h(a)g(certain) g(v)-61 b(alue)370 b(of)h Fe(\261)42 b Fp(.)496 b(If)370 b(the)g(tra)61 b(jectory)372 b(is)e(closed,)-2000 166 y(the)257 b(area)f Fe(S)320 b Fp(inside)257 b(of)g(it)g(is)f(connected) h(with)h(the)e(action)i Fe(I)343 b Fp(of)257 b(the)-2000 1439 y(system)351 b(b)-31 b(y)350 b(a)h(simple)g(relation)h Fe(S)371 b Fp(=)307 b(2)p Fe(\274)40 b(I)87 b Fp(.)486 b(If)350 b(the)h(tra)61 b(jectory)352 b(is)-2000 2712 y(not)374 b(closed,)h(w)-31 b(e)374 b(de\257ne)f(the)g(action)i(as)e (follo)-31 b(ws.)508 b(If)373 b(the)g(area)h Fe(S)-2000 3985 y Fp(b)31 b(ounded)291 b(b)-31 b(y)291 b(the)g(tra)61 b(jectory)293 b(and)f(lines)f Fe(w)338 b Fp(=)307 b(1)p Fe(;)184 b(\301)309 b Fp(=)e(0)p Fe(;)184 b(\301)309 b Fp(=)e(2)p Fe(\274)-2000 5258 y Fp(is)402 b(smaller)i(than)f(2)p Fe(\274)40 b Fp(,)411 b(w)-31 b(e)403 b(still)h(ha)-31 b(v)g(e)403 b Fe(S)427 b Fp(=)362 b(2)p Fe(\274)40 b(I)87 b Fp(.)592 b(If)403 b Fe(S)465 b Fp(is)403 b(larger)-2000 6531 y(than)373 b(2)p Fe(\274)40 b Fp(,)374 b(w)-31 b(e)373 b(put)g(2)p Fe(\274)40 b(I)399 b Fp(=)313 b(4)p Fe(\274)288 b Ff(\241)248 b Fe(S)64 b Fp(.)502 b(De\257ned)372 b(in)h(this)f(w)-31 b(a)g(y)-92 b(,)375 b Fe(I)459 b Fp(is)-2000 7804 y(a)369 b(con)-31 b(tin)g(uous)371 b(function)g(of)f(the)f(co)31 b(ordinates.)-893 9077 y(In)293 b(system)h(with)g(Hamiltonian)j(\(4\))e (with)g Fe(\277)432 b Fp(=)308 b Fe(\262t)p Fp(,)h(the)293 b(action)-2000 10350 y Fe(I)530 b Fp(is)443 b(an)h(adiabatic)i(in)-31 b(v)-61 b(arian)-31 b(t)445 b(of)f(motion)i(\(see,)463 b(for)443 b(example,)-2000 11623 y([3)q(]\).)490 b(F)-92 b(ar)359 b(from)h(the)g(separatrix,)j(it)e(undergo)31 b(es)359 b(oscillations)j(of)-2000 12896 y(order)428 b Fe(\262)p Fp(.)672 b(W)-92 b(e)428 b(in)-31 b(tro)31 b(duce)429 b(the)g(so)g(called)h(impro)-31 b(v)g(ed)430 b(adiabatic)-2000 14169 y(in)-31 b(v)-61 b(arian)-31 b(t)404 b Fe(J)469 b Fp(=)363 b Fe(I)354 b Fp(+)268 b Fe(\262f)119 b Fp(\()p Fe(w)30 b(;)184 b(\301;)g(\277)125 b Fp(\).)595 b(The)402 b(function)i Fe(f)521 b Fp(is)402 b(de\257ned)-2000 15442 y(as)369 b(follo)-31 b(ws)372 b([see,)d(for)g(example,)j([2)q(]]:)1758 18649 y Fe(f)427 b Fp(=)307 b Fe(f)119 b Fp(\()p Fe(w)30 b(;)184 b(\301;)g(\277)125 b Fp(\))311 b(=)10437 17900 y(1)p 10101 18394 1225 45 v 10101 19408 a(2)p Fe(\274)11643 17142 y Fd(Z)12750 17416 y Fn(T)12258 19657 y Fo(0)13631 17088 y Fd(\265)14579 17900 y Fe(T)p 14579 18394 801 45 v 14703 19408 a Fp(2)15759 18649 y Ff(\241)246 b Fe(t)17266 17088 y Fd(\266)18397 17900 y Fe(@)61 b(H)p 18397 18394 1660 45 v 18598 19408 a(@)g(\277)20190 18649 y(dt:)2344 b Fp(\(5\))-2000 21698 y(The)462 b(in)-31 b(tegral)464 b(in)e(\(5\))h(is)f(computed)h(along)g (the)f(unp)31 b(erturb)g(ed)-2000 22971 y(tra)61 b(jectory)443 b(passing)e(through)h(the)g(p)31 b(oin)-31 b(t)442 b(\()p Fe(w)30 b(;)184 b(\301)p Fp(\))443 b(at)e(the)h(time)-2000 24244 y(momen)-31 b(t)495 b Fe(t)515 b Fp(=)g(0;)556 b Fe(T)647 b Fp(is)494 b(the)g(p)31 b(erio)g(d)493 b(of)h(motion)i(on)e (this)g(tra-)-2000 25517 y(jectory)-92 b(.)988 b(If)533 b(the)i(tra)61 b(jectory)535 b(is)f(not)h(closed,)576 b Fe(T)688 b Fp(is)534 b(the)g(time)-2000 26790 y(necessary)482 b(for)h(a)g(phase)g(p)31 b(oin)-31 b(t)484 b(on)g(this)f(tra)61 b(jectory)485 b(to)e(co)-31 b(v)g(er)-2000 28063 y(the)330 b(distance)g(of)g(2)p Fe(\274)369 b Fp(along)331 b(the)f Fe(\301)p Fp(-axis.)480 b(F)-92 b(ar)328 b(from)i(the)g(separa-)-2000 29336 y(trices)394 b(v)-61 b(ariation)395 b(of)g Fe(J)499 b Fp(along)396 b(a)e(phase)f(tra)61 b(jectory)396 b(is)d(of)i(order) -2000 30609 y Fe(\262)-1551 30207 y Fo(2)-1054 30609 y Fp(.)647 b(As)421 b(the)g(slo)-31 b(w)421 b(time)h Fe(\277)546 b Fp(gro)-31 b(ws,)435 b(the)421 b(area)g(b)31 b(ounded)421 b(b)-31 b(y)421 b(the)-2000 31882 y(separatrix)448 b Fe(S)4030 31480 y Fc(\244)4539 31882 y Fp(\()p Fe(\277)125 b Fp(\))449 b(slo)-31 b(wly)449 b(c)-31 b(hanges.)729 b(On)448 b(the)g(other)g(hand,)468 b(a)-2000 33155 y(v)-61 b(alue)527 b(of)h(the)f(adiabatic)i(in)-31 b(v)-61 b(arian)-31 b(t)529 b(asso)31 b(ciated)528 b(with)g(a)f(cer-)-2000 34428 y(tain)416 b(phase)e(tra)61 b(jectory)416 b(sta)-31 b(ys)415 b(w)-31 b(ell-preserv)g(ed.)629 b(Accordingly)-92 b(,)-2000 35701 y(phase)506 b(tra)61 b(jectories)508 b(of)f(\(4\))h(can)e(cross)g(the)g(separatrix.)905 b(Let)-2000 36974 y(initially)478 b Fe(\261)516 b Fp(b)31 b(e)475 b(large)g(in)g(magnitude)i(and)e(p)31 b(ositivw,)503 b(so)475 b(that)-2000 38247 y(the)495 b(phase)g(p)31 b(ortrait)495 b(is)g(similar)h(to)g(one)f(sho)-31 b(wn)495 b(in)g(Fig.)870 b(1a.)-2000 39520 y(Consider)325 b(a)h(tra)61 b(jectory)326 b(rotating)i(close)d(to)h(the)f(singular)h(p)31 b(oin)-31 b(t)-2000 40793 y(on)356 b(\(2\).)489 b(Along)358 b(the)e(corresp)31 b(onding)356 b(phase)f(tra)61 b(jectory)358 b(on)e(the)-2000 42066 y(plane)303 b(\()p Fe(\301;)184 b(w)30 b Fp(\),)318 b(v)-61 b(alue)303 b(of)g Fe(w)332 b Fp(is)302 b(close)h(to)g(1.)471 b(W)-92 b(e)302 b(assume)g(1)112 b Ff(\241)g Fe(w)334 b Fp(on)-2000 43339 y(this)404 b(tra)61 b(jectory)406 b(to)f(b)31 b(e)403 b(small,)415 b(y)-31 b(et)404 b(\257nite.)598 b(Hence,)413 b(the)404 b(initial)-2000 44612 y(v)-61 b(alue)349 b Fe(J)1453 44778 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y(separatrix.)887 b(Calculating)503 b(c)-31 b(hange)502 b(in)e(the)h(impro)-31 b(v)g(ed)501 b(action)-2000 62434 y(due)467 b(to)h(the)f(separatrix)h (crossing)f(according)i(to)f(the)f(general)-2000 63707 y(metho)31 b(d,)371 b(w)-31 b(e)369 b(\257nd)3701 67652 y(2)p Fe(\274)40 b Fp(\242)p Fe(J)414 b Fp(=)308 b Ff(\241)p Fp(2)10958 66904 y Fe(\262)p Fp(\243)p 9591 67398 4044 45 v 9591 67619 a Fd(p)p 10698 67619 2937 45 v 943 x Fp(2)246 b Ff(\241)g Fe(\261)13138 68242 y Fo(2)13096 68835 y Fc(\244)13952 67652 y Fp(ln)q(\(2)184 b(sin)i Fe(\274)40 b(\273)51 b Fp(\))p Fe(;)4287 b Fp(\(6\))-893 70901 y(where)475 b Fe(\273)535 b Fp(=)485 b Ff(j)p Fe(h)5724 71067 y Fo(0)6220 70901 y Fe(=)p Fp(\()p Fe(\262)p Fp(\243\))p Ff(j)p Fp(,)505 b Fe(h)10700 71067 y Fo(0)11671 70901 y Fp(is)475 b(v)-61 b(alue)476 b(of)g(the)f(Hamiltonian)-2000 72174 y(at)492 b(the)f(time)h(of)g(the)f(last)h(crossing)f(of)g(the)g (v)-31 b(ertex)492 b(bisecting)27224 -2214 y 11796480 11796480 1315635 1315635 38416547 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/Ft2iYfW28Y@]m[UMRsUH.dU0fX0G`8Y/O\(]+oK=lrD]=YubD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@]m[UMRsUH.dU0fX0G`8Y/O\(]+oK=lrD]=YubD;`E eA5'm;(nO?&H6/Ft2iYfW28Y@ ]m[UMRsUH.dU0fX0G`8Y/O\(]+oK=lrD]=YubD;`EeA5'm;(nO?&H6/ Ft2iYfW28Y@]m[UMRsUH.dU0fX0G`8Y/O\(]+oK=lrD]=YubD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@]m[UMRsUH.dU 0fX0G`8Y/O\(]+oK=lrD]=YubD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@] m[UMRsUH.dU0fX0G`8Y/O\(]+oK=lrD]=YubD;`EeA5'm;(nalrD]=Y ubD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@]m[UMRsUH.dU0fX0G`8Y/O\( ]+oK=lrD]=YubD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@]m[UMRsUH.dU0 fX0G`8Y/O\(]+oK=lrD]=YubD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@]m[UMRsUH.dU0fX0G`8Y/O\(]+oK=lrD]=Yu bD;`EeA5'm;(nO?&H6/Ft2iYfW28Y@]m[UMRsUH.dU0fX0G`8Y/O\(] +oK=lrD]=YubD;`EeA5'm;(n %%EOF %%EndDocument endTexFig 27224 19981 a Fk(FIG.)287 b(2:)428 b(The)287 b(surface)f Fi(u)36895 19557 y Fm(2)37475 19981 y Fk(+)118 b Fi(v)38922 19557 y Fm(2)39669 19981 y Fk(=)284 b(\()p Fi(w)145 b Fk(+)118 b(1\)\()p Fi(w)145 b Fh(\241)118 b Fk(1\))46951 19557 y Fm(2)47415 19981 y Fi(=)p Fk(2.)437 b(Action)287 b(v)-57 b(ari-)27224 21143 y(able)321 b(is)g(related)h(to)f(area)g (within)g(a)g(tra)57 b(jectory)321 b(on)f(the)i(hamiltonian)27224 22305 y(phase)350 b(p)28 b(ortrait,)352 b(not)e(on)g(\()p Fi(u;)171 b(v)36 b Fk(\))p Fh(\241)351 b Fk(plane.)482 b(Con)-28 b(trary)348 b(to)i(Ref.)482 b([1],)353 b(\241)27224 23468 y(is)359 b(not)g(prop)28 b(ortional)358 b(to)h(square)g(ro)28 b(ot)359 b(of)f(action)i(\(i.e.,)365 b(square)359 b(ro)28 b(ot)27224 24630 y(of)294 b(\242)p Fi(I)373 b Fk(in)294 b(the)i(case)e(initial)j(action)e(is)g(zero.)440 b(Note)295 b(that)f(w)-28 b(e)295 b(calculate)27224 25792 y(c)-28 b(hange)410 b(in)h(action)g(only)h(in)f(the)g(case)g(where)g(the)g (initial)h(action)g(is)27224 26954 y(not)341 b(v)-28 b(ery)342 b(small\).)27224 31207 y Fp(the)543 b(angle)i(b)31 b(et)-31 b(w)g(een)544 b(incoming)i(and)e(outgoing)i(separatrices)27224 32480 y(of)517 b(the)h(saddle)f(p)31 b(oin)-31 b(t)518 b Fe(C)597 b Fp(outside)518 b(the)f(separatrix)h(lo)31 b(op)518 b(\(see)27224 33753 y(Fig.)495 b(1c\))370 b(b)31 b(efore)370 b(crossing)g(the)g(separatrix;)h(\243)309 b(=)f Fe(dS)r(=d\277)125 b Ff(j)52042 33919 y Fn(\277)90 b Fo(=)p Fn(\277)53628 34030 y Fb(\244)54147 33753 y Fp(;)27224 35026 y Fe(\261)27716 35192 y Fc(\244)28557 35026 y Fp(=)332 b Fe(\261)42 b Fp(\()p Fe(\277)31198 35192 y Fc(\244)31708 35026 y Fp(\).)538 b(The)384 b(v)-61 b(alue)385 b Fe(\273)435 b Fp(strongly)385 b(dep)31 b(ends)383 b(on)i(initial)i(con-)27224 36299 y(ditions:)562 b(a)403 b(small)i(of)f(order)f Fe(\262)g Fp(v)-61 b(ariation)405 b(of)f(initial)i(conditions)27224 37572 y(results)384 b(generally)i(in)e(v)-61 b(ariation)387 b(of)e Fe(\273)435 b Fp(of)385 b(order)f(1.)539 b(Often,)389 b(this)27224 38845 y(v)-61 b(alue)505 b(can)h(b)31 b(e)504 b(considered)h(as)h(a)f (random)h(v)-61 b(ariable)506 b(\(in)g(par-)27224 40118 y(ticular,)415 b(when)406 b(one)f(considers)f(a)i(bunc)-31 b(h)404 b(of)i(tra)61 b(jectories)407 b(with)27224 41391 y(initial)j(conditions)g(distributed)f(in)f(certain)g(v)-31 b(olume)410 b(in)e(phase)27224 42664 y(space\).)762 b(As)458 b(a)h(result,)482 b(jump)459 b(of)h(the)f(adiabatic)i(in)-31 b(v)-61 b(arian)-31 b(t)461 b(at)27224 43937 y(separatrix)430 b(crossing)f(is)g(also)h(quasi-random)h(v)-61 b(alue)429 b(\(strongly)27224 45210 y(dep)31 b(enden)-31 b(t)506 b(on)h(initial)h(conditions\).)906 b(The)507 b(form)-31 b(ula)508 b(is)e(v)-61 b(alid)27224 46483 y(pro)-31 b(vided)536 b Fe(\273)586 b Fp(is)535 b(not)h(to)31 b(o)536 b(close)f(to)h(0)f(or)g (1)h(\(i.e.,)578 b(not)536 b(for)g(all)27224 47756 y(tra)61 b(jectories)413 b(from)f(the)g(bunc)-31 b(h,)423 b(but)412 b(only)h(for)f(most)g(of)h(them;)27224 49029 y(for)452 b(details,)476 b(see)452 b(Ref.)742 b([3)q(])453 b(\).)743 b(F)-92 b(or)452 b(large)h Ff(j)p Fe(\261)42 b Ff(j)p Fp(,)475 b(the)453 b(function)h Fe(f)27224 50302 y Fp(tends)351 b(to)i(zero,)i(and)d(action)i Fe(I)438 b Fp(coincides)352 b(with)h Fe(J)106 b Fp(.)487 b(Hence,)356 b(for-)27224 51575 y(m)-31 b(ula)391 b(\(6\))h(giv)-31 b(es)391 b(the)f(v)-61 b(ariation)392 b(in)e(action)i Fe(I)87 b Fp(.)555 b(As)389 b(w)-31 b(e)391 b(consider)27224 52848 y(slo)-31 b(w)518 b(c)-31 b(hange)518 b(of)g Fe(\261)558 b Fp(from)518 b(initial)i(large)e(p)31 b(ositiv)-31 b(e)518 b(v)-61 b(alue)518 b Fe(\261)42 b Fp(\()p Fe(t)53656 53014 y Fn(i)54024 52848 y Fp(\))27224 54121 y(to)388 b(\257nal)g(large)g (negativ)-31 b(e)390 b(v)-61 b(alue)388 b Fe(\261)42 b Fp(\()p Fe(t)42427 54287 y Fn(f)43001 54121 y Fp(\),)392 b(in)c(the)g(adiabatic)i(limit)27224 55394 y Fe(w)30 b Fp(\()p Fe(t)28876 55560 y Fn(f)29450 55394 y Fp(\))543 b(=)g Ff(\241)p Fe(w)30 b Fp(\()p Fe(t)34340 55560 y Fn(i)34709 55394 y Fp(\),)546 b(i.e.)917 b(sign)511 b(of)g Fe(w)540 b Fp(is)510 b(rev)-31 b(ersed)509 b(due)h(to)i(the)27224 56667 y(passage)350 b(through)h(resonance,)j(but)c(its)g(absolute)h(v) -61 b(alue)351 b(is)e(pre-)27224 57940 y(serv)-31 b(ed:)634 b(\242)p Ff(j)p Fe(w)30 b Ff(j)428 b Fp(=)e Fe(w)30 b Fp(\()p Fe(t)36913 58106 y Fn(f)37488 57940 y Fp(\))294 b(+)f Fe(w)30 b Fp(\()p Fe(t)41018 58106 y Fn(i)41387 57940 y Fp(\))427 b(=)f(0.)707 b(Small)442 b(nonadiabatic)27224 59213 y(correction)448 b(arise)f(due)g(to)h(quasi-random)h(jump)f(of)g (adiabatic)27224 60486 y(in)-31 b(v)-61 b(arian)-31 b(t)455 b(at)f(the)f(separatrix)h(crossing)f(as)g(describ)31 b(ed)452 b(ab)31 b(o)-31 b(v)g(e,)27224 61759 y(and)369 b(the)h(resulted)f(\242)p Ff(j)p Fe(w)30 b Ff(j)370 b Fp(is)g(equal)g(to)g(c)-31 b(hange)370 b(in)f(action)i(\242)p Fe(I)87 b Fp(.)28331 63263 y(W)-92 b(e)446 b(presen)-31 b(t)447 b(detailed)i(theoretical)h(calculations)g(in)e(a)f(sep-)27224 64536 y(arate)440 b(pap)31 b(er.)702 b(Note)441 b(that)f(similar)h (calculations)h(are)d(done)g(in)27224 65809 y(Ref.)663 b([7)q(].)g(Similar)428 b(form)-31 b(ulas)427 b(has)f(b)31 b(een)425 b(used)g(in)i(some)f(prob-)27224 67082 y(lems)502 b(of)g(plasma)h(ph)-31 b(ysics)502 b(and)g(h)-31 b(ydro)31 b(dynamics.)892 b(Although)27224 68355 y(they)484 b(do)g(not)g(relate)h (explicitly)h(the)e(c)-31 b(hange)484 b(in)g(action)i(with)27224 69628 y(initial)352 b(conditions,)j(they)350 b(are)f(useful)h(in)f (describing)h(dynamics)27224 70901 y(of)480 b(the)f(corresp)31 b(onding)480 b(systems,)507 b(esp)31 b(ecially)481 b(when)e(m)-31 b(ultiple)27224 72174 y(separatrix)370 b(crossings)e(o)31 b(ccur.)p eop %%Page: 4 4 4 3 bop 53901 -3985 a Fp(4)-893 -1107 y(Let)519 b(us)f(giv)-31 b(e)521 b(no)-31 b(w)520 b(sev)-31 b(eral)519 b(remarks)g(concerning)g (calcula-)-2000 166 y(tions)370 b(of)g(Ref.)492 b([1)q(].)-893 1559 y(In)444 b(these)h(pap)31 b(ers,)463 b(it)446 b(w)-31 b(as)446 b(correctly)f(established)h(that)g(the)-2000 2832 y(nonadiabatic)390 b(correction)e(b)31 b(eha)-31 b(v)g(es)388 b(as)f(a)h(p)31 b(o)-31 b(w)g(er)387 b(of)h(the)g(small) -2000 4105 y(parameter.)843 b(Ho)-31 b(w)g(ev)g(er,)517 b(there)486 b(are)g(some)g(inconsistencies)h(in)-2000 5378 y(deriv)-61 b(ation)435 b(of)e(this)h(p)31 b(o)-31 b(w)g(er)433 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Fe(\261)534 b Fp(in)493 b(the)g(Hamiltonian)j(\(4\))d(with)h(the)-2000 15682 y Ff(\241)p Fe(\261)42 b(w)568 b Fp(term)538 b(instead)h(of)f(+)p Fe(\261)42 b(w)30 b Fp(\).)1000 b(Main)538 b(phenomena)h(in)g(this) -2000 16955 y(problem)375 b(o)31 b(ccur)373 b(near)h(the)g(separatrix,) j(and)d(the)g(separatrix)h(is)-2000 18228 y(not)276 b(sho)-31 b(wn)275 b(at)h(all)h(in)e(Fig.6)h(of)g([1)q(].)461 b(There)275 b(are)g(no)g(stable)h(p)31 b(oin)-31 b(ts)-2000 19501 y(on)453 b(the)g(phase)f(p)31 b(ortrait)454 b(of)f(the)g(Hamiltonian)j (\(4\))e(at)f Fe(w)477 b Fp(=)447 b(1)-2000 20893 y(at)395 b Fe(\261)c(>)1470 19977 y Ff(p)p 2393 19977 554 45 v 2393 20893 a Fp(2.)567 b(A)-31 b(t)395 b Fe(\261)c Fp(=)7537 19977 y Ff(p)p 8459 19977 V 916 x Fp(2)q(,)400 b(t)-31 b(w)g(o)396 b(saddle)e(p)31 b(oin)-31 b(ts)395 b(and)g(one)f(ellip-) -2000 22166 y(tic)428 b(p)31 b(oin)-31 b(t)428 b(app)31 b(ear.)665 b(These)427 b(saddle)g(p)31 b(oin)-31 b(ts)427 b(are)g(not)g(sho)-31 b(wn)428 b(in)-2000 23439 y(Fig.6.)653 b(of)422 b(Ref.)652 b([1)q(])422 b(and)g(not)h(accoun)-31 b(ted)424 b(for)e(in)g(the)h(analysis)-2000 24712 y(\(corresp)31 b(ondingly)-92 b(,)373 b(the)f(curv)-31 b(e)371 b(structure)g(of)h (Fig.4)g(of)g(Ref.)499 b([1)q(])-2000 25985 y(seems)369 b(to)h(b)31 b(e)368 b(inadequate\).)-893 27378 y Fa(2\))431 b Fp(The)f(most)h(imp)31 b(ortan)-31 b(t)433 b(issue)d(is)g (calculation)j(of)e(c)-31 b(hange)-2000 28651 y(of)447 b(the)g(action.)727 b(Ev)-61 b(aluation)450 b(of)d(in)-31 b(tegral)449 b(\(14\))f(in)f(Ref.)725 b([1)q(])447 b(is)-2000 29924 y(improp)31 b(er.)818 b(In)478 b(that)h(Ref.,)506 b(expression)477 b(\(16\))j(is)d(obtained)j(b)-31 b(y)-2000 31197 y(di\256eren)g(tiation)320 b(of)e(\(11\))i(and)e(describ)31 b(es)316 b(the)i(rate)g(of)g(motion)h(of)-2000 32470 y(elliptic)379 b(\257xed)d(p)31 b(oin)-31 b(ts)378 b(due)e(to)h(slo)-31 b(w)378 b(v)-61 b(ariation)379 b(of)e Fe(\261)42 b Fp(.)514 b(Ho)-31 b(w)g(ev)g(er,)-2000 33743 y(to)375 b(obtain)h(their)e(Eq.)508 b(\(18\),)377 b(the)e(authors)f(use)g(this)g(expression)-2000 35016 y(near)415 b Fe(w)f Fp(=)383 b(1,)427 b(i.e.)631 b(near)414 b(a)i(h)-31 b(yp)31 b(erb)g(olic)415 b(p)31 b(oin)-31 b(t)416 b(\(actually)-92 b(,)430 b(ev)-31 b(en)-2000 36289 y(in)518 b(case)g(the)g(expression)f(w)-31 b(ere)518 b(used)f(near)h(an)g(elliptic)i(\257xed)-2000 37562 y(p)31 b(oin)-31 b(t)384 b(as)f(in)-31 b(tended,)387 b(it)d(is)f(not)g(clear)h (wh)-31 b(y)383 b(the)g(rate)g(of)h(motion)-2000 38835 y(of)348 b(elliptic)j(\257xed)d(p)31 b(oin)-31 b(ts)348 b(should)h(b)31 b(e)347 b(related)i(to)g(the)f(c)-31 b(hange)349 b(in)-2000 40108 y(the)307 b(action)i(in)e(suc)-31 b(h)306 b(a)h(simple)h(w)-31 b(a)g(y)308 b(as)f(describ)31 b(ed)306 b(in)h(Section)h(4.)-2000 41381 y(Calculation)433 b(of)e(c)-31 b(hange)430 b(of)h(action)g(in)f(this)g(system)g(is)g(a)g (v)-31 b(ery)-2000 42654 y(di\261cult)397 b(mathematical)i(problem.)570 b(In)395 b(suc)-31 b(h)394 b(systems)h(c)-31 b(hange)-2000 43927 y(in)338 b(action)h(is)f(usually)h(related)f(to)h(motion)h(near)d (unstable)i(\257xed)-2000 45200 y(p)31 b(oin)-31 b(ts,)597 b(where)550 b(manipulations)j(with)e(linearization)j(around)-2000 46473 y(elliptic)371 b(\257xed)f(p)31 b(oin)-31 b(ts)370 b(do)f(not)h(help)f(m)-31 b(uc)g(h\).)-893 47867 y Fa(3\))436 b Fp(The)g(statemen)-31 b(t)437 b(\241)8915 47465 y Fo(2)9830 47867 y Fp(=)418 b(\242)p Fe(I)87 b(=)p Fp(2)436 b(\(where)g(\241)418 b(=)g(1)291 b Ff(\241)f Fe(w)30 b Fp(,)453 b(see)-2000 49140 y(Eq.14)475 b(of)f(Ref.)805 b([1)q(]\))475 b(is)e(also)h (incorrect.)806 b(Brie\260y)-92 b(,)500 b(for)473 b(a)h(non-)-2000 50413 y(hamiltonian)407 b(dynamical)e(system,)413 b(area)403 b(within)i(a)e(tra)61 b(jectory)-2000 51686 y(has)363 b(nothing)i(to)f(do)g(with)h(the)e(action)i(\(note)g(that)f(the)g (expres-)-2000 52959 y(sion)459 b(w)-31 b(as)459 b(related)g(to)g(the)f (case)g(of)h(zero)f(initial)j(action,)483 b(so)458 b(it)-2000 54232 y(means)425 b(\241)2136 53830 y Fo(2)3033 54232 y Fp(=)401 b Fe(I)87 b(=)p Fp(2,)440 b(where)425 b Fe(I)511 b Fp(is)425 b(the)g(action)i(obtained)g(during)-2000 55505 y(the)360 b(motion)h(near)f Fe(w)337 b Fp(=)308 b(1.)490 b(W)-92 b(e)358 b(do)i(not)g(consider)g(this)g(case)f(\(of) -2000 56778 y(zero)340 b(or)g(v)-31 b(ery)341 b(small)g(initial)i (action\))g(in)d(our)h(Commen)-31 b(t,)349 b(still)341 b(it)-2000 58051 y(is)415 b(imp)31 b(ortan)-31 b(t)417 b(to)f(establish)f(ho)-31 b(w)416 b(the)f(action)i(is)e(related)g(to)h Fe(w)-2000 59324 y Fp(in)369 b(the)h(system\).)-893 60717 y(Consider)460 b(\257rstly)f(the)g(system)h(in)f(the)h(Hamiltonian)j (form,)-2000 61990 y(with)594 b(Hamiltonian)i(function)e(\(4\))g(and)f (canonically)j(conju-)-2000 63263 y(gated)529 b(v)-61 b(ariables)529 b Fe(w)30 b(;)184 b(\301)p Fp(.)971 b(It)528 b(is)g(a)h(w)-31 b(ell-kno)g(wn)531 b(fact)e(that)h(the)-2000 64536 y(action)421 b(is)e(prop)31 b(ortional)422 b(to)e(the)g(area)f (on)h(the)g(phase)f(p)31 b(ortrait)-2000 65809 y(on)353 b(plane)g(\()p Fe(\301;)184 b(w)30 b Fp(\).)489 b(In)352 b(the)h(case)f(of)h(a)g(large)h Fe(\261)394 b Fp(and)353 b Fe(w)382 b Fp(close)353 b(to)h(1)-2000 67082 y([this)266 b(is)f(the)g(case)g(discussed)f(ab)31 b(o)-31 b(v)g(e)266 b(and)f(represen)-31 b(ted)264 b(in)i(Fig.3b)-2000 68355 y(in)358 b(Ref.)489 b([1)q(]],)361 b(the)d(area)g(b)31 b(et)-31 b(w)g(een)359 b(a)f(phase)f(tra)61 b(jectory)360 b(and)e(the)-2000 69628 y(line)289 b Fe(w)338 b Fp(=)307 b(1)289 b(is)g(prop)31 b(ortional)290 b(to)f(\(1)85 b Ff(\241)g Fe(w)30 b Fp(\),)306 b(i.e.,)h(\241)288 b([see)g(also)i (Fig.2)-2000 70901 y(in)282 b(our)f(pap)31 b(er].)464 b(Considering)283 b(this)e(question)i(using)f(the)g(system)-2000 72174 y(in)404 b(non-Hamiltonian)k(form)c(\(Eqs.)597 b(\(1\))405 b(\))f(is)g(a)g(little)i(bit)f(more)27224 -1107 y(complicated.)636 b(In)415 b(Section)i(IV)f(of)h(Ref.)633 b([1)q(])416 b(the)g(authors)h(con-)27224 166 y(sider)308 b(a)h(closed)h(tra)61 b(jectory)310 b(with)h Fe(w)339 b Fp(close)309 b(to)h(1)f(on)g(the)g(surfaces)27224 1439 y Fe(u)27858 1037 y Fo(2)28702 1439 y Fp(+)347 b Fe(v)30487 1037 y Fo(2)31545 1439 y Fp(=)562 b(1)348 b Ff(\241)g Fe(w)35900 1037 y Fo(2)36918 1439 y Fp([Blo)31 b(c)-31 b(h)523 b(sphere)e(of)i(a)f(t)-31 b(w)g(o-mo)31 b(de)524 b(Bose-)27224 2712 y(Josephson)357 b(system])i(and)f Fe(u)39210 2310 y Fo(2)39929 2712 y Fp(+)223 b Fe(v)41590 2310 y Fo(2)42393 2712 y Fp(=)308 b(\()p Fe(w)253 b Fp(+)223 b(1\)\()p Fe(w)255 b Ff(\241)223 b Fp(1\))50648 2310 y Fo(2)51146 2712 y Fe(=)p Fp(2)358 b([the)27224 3985 y(corresp)31 b(onding)398 b(surface)g(in)g(the)g(considered)g (problem].)580 b(They)27224 5258 y(state)329 b(that)h("the)g(surface)f (area)g(enclosed)g(within)h(this)g(p)31 b(erio)g(dic)27224 6531 y(tra)61 b(jectory)435 b(is)e(just)h(the)g(action)h(...)686 b(accum)-31 b(ulated)436 b(during)e(the)27224 7804 y(sw)-31 b(eep".)929 b(Ho)-31 b(w)g(ev)g(er,)553 b(it)515 b(is)f(not)h(so.)929 b(Action)516 b(v)-61 b(ariable)515 b(is)g(the)27224 9077 y(\257rst)328 b(in)-31 b(tegral)331 b(of)f(the)f(unp)31 b(erturb)g(ed)327 b(system.)480 b(Hence)329 b(it)g(should)27224 10350 y(b)31 b(e)533 b(preserv)-31 b(ed)532 b(b)-31 b(y)534 b(the)f(\260o)-31 b(w)535 b(of)e(system)h(\(1\))h([system)f(\(6\))g(in) 27224 11623 y([1)q(]])500 b(at)g(a)f(constan)-31 b(t)501 b(v)-61 b(alue)500 b(of)g(parameter)g Fe(\261)42 b Fp(.)882 b(Consider)500 b(mo-)27224 12896 y(tion)346 b(in)g(this)f(system)h(on)f (the)h(lev)-31 b(el)346 b(surface)f Fe(L)308 b Fp(=)f(0)346 b(of)f(function)27224 14169 y Fe(L)308 b Fp(=)f Fe(u)30087 13767 y Fo(2)30773 14169 y Fp(+)190 b Fe(v)32401 13767 y Fo(2)33086 14169 y Ff(\241)g Fp(\()p Fe(w)221 b Fp(+)189 b(1\)\()p Fe(w)222 b Ff(\241)189 b Fp(1\))41090 13767 y Fo(2)41588 14169 y Fe(=)p Fp(2.)484 b(In)341 b(order)f(to)i (understand)27224 15442 y(what)552 b(measure)g(on)f(this)h(surface)f (is)h(preserv)-31 b(ed,)596 b(consider)551 b(a)27224 16715 y(close)464 b(lev)-31 b(el)466 b(surface)e Fe(L)i Fp(=)g Fe(d;)651 b Ff(j)p Fe(d)p Ff(j)468 b(\277)e Fp(1.)778 b(Consider)465 b(a)f(surface)27224 17988 y(elemen)-31 b(t)459 b Fe(dS)522 b Fp(on)459 b(surface)e Fe(L)g Fp(=)e(0)k(and)f(an) h(elemen)-31 b(tary)460 b(cylin-)27224 19261 y(der)319 b(b)31 b(ounded)320 b(b)-31 b(y)320 b(this)g(surface)g(elemen)-31 b(t,)331 b(a)321 b(surface)e(comp)31 b(osed)27224 20534 y(of)440 b(normals)g(to)g Fe(L)426 b Fp(=)e(0)440 b(passing)g(through)g (the)g(b)31 b(order)439 b(of)h Fe(dS)64 b Fp(,)27224 21807 y(and)442 b(surface)f Fe(L)429 b Fp(=)g Fe(d)p Fp(.)711 b(In)441 b(the)h(limit)i(as)e Fe(d)429 b Ff(!)f Fp(0)443 b(w)-31 b(e)442 b(\257nd)g(that)27224 23080 y(the)333 b(v)-31 b(olume)336 b(of)e(this)g(elemen)-31 b(tary)335 b(cylinder)f(is)f Fe(dV)553 b Fp(=)308 b Fe(dS)r(=)p Ff(jr)p Fe(L)p Ff(j)p Fp(.)27224 24353 y(System)391 b(\(1\))g(is)f(v) -31 b(olume-preserving.)558 b(Hence)390 b(this)h(elemen)-31 b(tary)27224 25626 y(v)g(olume)321 b(is)e(in)-31 b(v)-61 b(arian)-31 b(t)321 b(under)e(the)h(\260o)-31 b(w)320 b(of)g(this)g(system.)476 b(There-)27224 26899 y(fore,)497 b(the)471 b(in)-31 b(tegral)473 b(of)e(the)g(unp)31 b(erturb)g(ed)470 b(system)h(is)g(not)h(the)27224 28172 y(area)423 b(on)h(the)f(surface)g Fe(L)398 b Fp(=)f(0)424 b(\(and,)438 b(of)423 b(course,)437 b(not)424 b(the)f(area)27224 29445 y(within)360 b(a)f(tra)61 b(jectory\),)364 b(but)359 b(the)g(area)g(on)g(the)f(surface)h(divided) 27224 30718 y(b)-31 b(y)491 b(magnitude)i(of)e(the)h(gradien)-31 b(t)492 b Ff(jr)p Fe(L)p Ff(j)p Fp(.)860 b(Near)491 b(the)g(singular) 27224 31991 y(p)31 b(oin)-31 b(t)392 b Fe(u)345 b Fp(=)f Fe(v)384 b Fp(=)345 b(0)p Fe(;)370 b(w)375 b Fp(=)345 b(1)391 b(the)h(surface)f(is)h(essen)-31 b(tially)393 b(conical)27224 33264 y(and)454 b(this)g(gradien)-31 b(t)456 b(is)e(prop)31 b(ortional)456 b(to)f(\(1)303 b Ff(\241)g Fe(w)30 b Fp(\).)747 b(Th)-31 b(us,)476 b(w)-31 b(e)27224 34537 y(\257nd)429 b(that)i(action)g(v)-61 b(ariable)431 b(is)f(prop)31 b(ortional)431 b(to)g(\(1)287 b Ff(\241)f Fe(w)30 b Fp(\))431 b(and)27224 35810 y(not)381 b(to)g(\(1)254 b Ff(\241)f Fe(w)30 b Fp(\))34170 35408 y Fo(2)35047 35810 y Fp(as)380 b(the)h(authors)f(of)h(Ref.)525 b([1)q(])381 b(state)g(\(see)f(also)27224 37083 y(Fig.2\).)28331 38716 y Fa(4\))545 b Fp(F)-92 b(rom)544 b(ph)-31 b(ysical)546 b(p)31 b(oin)-31 b(t)546 b(of)f(view,)590 b(it)546 b(should)f(b)31 b(e)544 b(noted)27224 39989 y(that)324 b(b)31 b(oth)324 b(Landau-Zener)f(mo)31 b(del)324 b(and)f(the)h(mo)31 b(del)324 b(of)f(Ref.)477 b([1)q(])27224 41262 y(predict)523 b(100\045)i(transfer)f(e\261ciency)g(in)f(the)h(adiabatic)i(limit.) 27224 42535 y(Nonadiabatic)399 b(corrections)d(discussed)e(ab)31 b(o)-31 b(v)g(e)397 b(in)-31 b(tro)31 b(duce)397 b(just)27224 43808 y(small)254 b(deviations)i(from)e(100\045)h(e\261ciency)-92 b(.)455 b(Ho)-31 b(w)g(ev)g(er,)278 b(the)254 b(c)-31 b(har-)27224 45081 y(acteristic)413 b(feature)g(of)g(the)f(exp)31 b(erimen)-31 b(tal)414 b(data)g(of)f(Ref.)621 b([9)q(])413 b(is)27224 46354 y(that)329 b(it)g(has)f(appro)-31 b(ximately)331 b(50\045)f(e\261ciency)e(in)h(the)f(adiabatic)27224 47627 y(limit.)775 b(The)463 b(exp)31 b(erimen)-31 b(tal)465 b(data)f(from)f(Ref.)773 b([9)q(])463 b(w)-31 b(as)463 b(repro-)27224 48900 y(duced)447 b(in)h(Fig.1)h(of)f(Ref.)727 b([1)q(],)468 b(but)448 b(only)g(for)g(the)g(case)f(of)h(not)27224 50173 y(v)-31 b(ery)404 b(slo)-31 b(w)405 b(ramp)g(sp)31 b(eeds.)597 b(This)404 b(mak)-31 b(es)405 b(Fig.)599 b(1)404 b(of)h(Ref.)598 b([1)q(])404 b(a)27224 51446 y(little)365 b(bit)e(confusing.)492 b(What)363 b(is)g(sho)-31 b(wn)363 b(in)g(the)g(Fig.)491 b(is)363 b(related)27224 52719 y(not)j(to)h(regime)f(of)g(exp)31 b(onen)-31 b(tially)369 b(small)e(fraction)h(of)e(remnan)-31 b(t)27224 53992 y(atoms)408 b(in)e(Landau-Zener)h(mo)31 b(del)408 b(\(or)f(p)31 b(o)-31 b(w)g(er-la)g(w)408 b(fraction)g(in)27224 55265 y(the)356 b(nonlinear)g(mo)31 b(del\),)361 b(but)355 b(to)i(the)e(regime)i(of)f(fast)g(ramping.)27224 56538 y(Ho)-31 b(w)g(ev)g(er,)418 b(theoretical)409 b(considerations)f(of)f (Ref.)605 b([1)q(])407 b(\(and)h(our)27224 57811 y(presen)-31 b(t)333 b(Commen)-31 b(t\))336 b(are)d(for)h(the)g(case)f(of)h(small)h (nonadiabatic)27224 59084 y(corrections.)28331 60717 y(T)-92 b(o)338 b(conclude,)346 b(from)338 b(our)g(p)31 b(oin)-31 b(t)340 b(of)e(view)h(the)g(main)g(result)f(of)27224 61990 y(the)276 b(commen)-31 b(ted)279 b(pap)31 b(er)276 b(is)g(v)-31 b(ery)277 b(in)-31 b(teresting)278 b(analogy)h(b)31 b(et)-31 b(w)g(een)27224 63263 y(dynamics)288 b(of)g(F)-92 b(esc)-31 b(h)g(bac)g(h)287 b(resonance)g(passage)g(and)h(fundamen-) 27224 64536 y(tal)408 b(issue)f(in)g(classical)h(mec)-31 b(hanics,)418 b(i.)607 b(e.)f(destruction)407 b(of)h(adi-)27224 65809 y(abatic)376 b(in)-31 b(v)-61 b(ariance)376 b(at)g(separatrix)g (crossings.)509 b(Unfortunately)-92 b(,)27224 67082 y(the)496 b(main)h(results)f(declared)g(in)g(this)g(Ref.)873 b(\(Eqs.)h(\(26\)) 498 b(and)27224 68355 y(\(20\))344 b(of)f(Ref.)483 b([1)q(]\))344 b(seems)d(to)j(b)31 b(e)342 b(incorrect)g(due)g(to)i(the)e(reasons) 27224 69628 y(discussed)463 b(ab)31 b(o)-31 b(v)g(e.)777 b(In)463 b(the)h(\257rst)g(part)g(of)g(the)g(Commen)-31 b(t,)490 b(w)-31 b(e)27224 70901 y(presen)g(ted)418 b(constructiv)-31 b(e)420 b(analysis)g(of)g(the)f(case)f(where)h(initial)27224 72174 y(molecular)406 b(fraction)g(is)f(not)g(v)-31 b(ery)405 b(small)h(\(1)271 b Ff(\241)f Fe(w)30 b Fp(\()p Fe(t)49022 72340 y Fn(i)49391 72174 y Fp(\))367 b Ff(\300)f Fp(1)p Fe(=)-61 b(N)121 b Fp(\).)p eop %%Page: 5 5 5 4 bop 53901 -3985 a Fp(5)-2000 -1107 y(W)-92 b(e)349 b(did)h(not)h(consider)e(here)g(the)i(case)e(with)i(v)-31 b(ery)350 b(small)h(initial)-2000 166 y(molecular)328 b(fraction)f(\(whic)-31 b(h)328 b(lead)f(to)g(inclusion)g(of)g("quan) -31 b(tum-)-2000 1439 y(noise")502 b(term)f(and)g(Eq.)889 b(\(26\))502 b(of)g(Ref.)888 b([1)q(],)534 b(\241)527 b Ff(\273)g Fe(\256)t Fp(\).)889 b(Ho)-31 b(w-)-2000 2712 y(ev)g(er,)296 b(w)-31 b(e)277 b(noted)h(that)g(statemen)-31 b(t)279 b(\241)13141 2310 y Fo(2)13945 2712 y Ff(\273)307 b Fp(\242)p Fe(I)364 b Fp(is)277 b(incorrect)g(whic)-31 b(h)-2000 3985 y(w)g(ould)428 b(mak)-31 b(e)427 b(Eq.\(26\))j(also)d (incorrect)g(in)f(case)h(\242)p Fe(I)513 b Fp(w)-31 b(ere)426 b(cal-)-2000 5258 y(culated)390 b(correctly)-92 b(.)553 b(Since)389 b(this)h(is)f(not)h(the)f(case,)395 b(the)389 b(Eq.\(26\))-2000 6531 y(migh)-31 b(t)496 b(b)31 b(e)494 b(true)h(b)-31 b(y)494 b(coincidence)i(\(in)f(case)g(sev)-31 b(eral)495 b(mistak)-31 b(es)-2000 7804 y(cancel)324 b(eac)-31 b(h)323 b(other\).)478 b(This)324 b(requires)e(more)h (detailed)i(consider-)-2000 9077 y(ation.)-893 10350 y(A.P)-92 b(.I.)397 b(is)e(supp)31 b(orted)395 b(b)-31 b(y)396 b(JSPS.)g(This)g(w)-31 b(ork)396 b(w)-31 b(as)396 b(also)h(sup-)27224 -1107 y(p)31 b(orted)465 b(in)h(part)g(b)-31 b(y)466 b(Gran)-31 b(ts-in-Aid)467 b(for)e(Scien)-31 b(ti\257c)467 b(Researc)-31 b(h)27224 166 y(No.)748 b(15540381)458 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y(BCAM2005)341 b(\(2005)h(Ban\256)f(Cold)h(A)-28 b(tom)341 b(meeting\).)27224 25646 y([9])443 b(K.E)299 b(Strec)-28 b(k)g(er,)307 b(G.B.)299 b(P)-28 b(artridge,)307 b(and)298 b(R.G.)h(Hulet,)308 b(Ph)-28 b(ys.)298 b(Rev.)28747 26808 y(Lett.)343 b Fj(91)p Fk(,)f(080406)g(\(2003\).)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0609182236645--