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0705.2609.txt |@word partial:1 gr:3 results:1 four:2 scalar:1 grateful:1 edu:1 follow:1 consider:2 inverse:3 calculate:4 ac02:1 technique:1 tr:1 factoring:1 charge:1 th:5 under:3 alberta:1 divergent:1 conjecture:1 straightforward:1 exact:2 4n2:2 evaluation:1 zupan:1 aachen:3 upper:2 sin2:2 sign:1 fold:1 ter:1 odd:1 theory:1 even:1 sum:1 expressed:3 version:1 poles:1 tarasov:1 3d:4 here:3 obtained:3 remark:1 institute:1 products:1 procedure:1 suggestion:1 cancellation:1 departement:1 via:4 onshell:1 summation:1 use:1 λms:1 usa:1 commun:1 next:1 few:1 nucl:2 therefore:1 until:1 diagrams:5 more:2 fractions:1 nkl:1 particular:2 known:3 ward:1 calculability:1 work:2 values:5 closing:1 trans:1 example:1 proof:2 renormalization:2 figure:1 calculation:1 expanding:1 smirnov:6 broadhurst:4 high:6 axis:1 regularization:1 means:2 write:1 instead:1 czakon:1 parameter:1 sin:3 snf:1 express:3 communicating:1 may:2 advice:1 after:4 derived:3 respective:1 applications:1 plane:1 physik:3 lat:1 representations:1 forschungsgemeinschaft:1 vermaseren:1 effective:1 computations:1 deutsche:1 su:1 ones:1 subsequently:1 order:5 indeed:1 its:4 uwer:1 style:1 group:1 solving:2 davydychev:2 parts:3 fig:1 omitted:1 might:1 eur:1 them:1 combination:1 integral:13 introduce:1 mention:1 they:1 half:5 rotation:1 now:1 yu:3 pak:3 4f3:6 term:5 finite:1 university:2 irreducible:1 found:3 2n:18 2k:1 heavy:2 square:1 clausen:1 accelerator:1 series:1 hqet:5 hypergeometric:8 related:1 bradley:2 loops:2 eq:9 special:1 out:1 canada:1 factors:2 rwth:2 algebra:1 re:5 rational:1 conjectured:1 formula:1 wick:1 ref:7 correct:1 math:4 i2:8 linear:1 automatized:1 pub:1 quark:2 indices:1 completely:1 hep:14 r5:1 maˆıtre:2 correctness:1 massive:2 first:3 knots:1 simplifies:1 xl:9 jhep:1 relate:1 nested:1 least:1 another:1 electronic:1 given:1 needed:1 eqs:1 theoretische:2 relations:2 their:1 master:5 identity:1 calculations:1 zagier:2 exponents:1 shell:3 exactly:1 part:1 borwein:2 x2:2 x1:9 coefficients:1 2f1:3 preparation:1 classes:1 russia:1 p20:1 pre:1 motivation:1 comput:1 strengthen:1 argument:1 chetyrkin:1 orders:1 k2:3 k1:9 k0:1 multiple:2 shall:2 any:1 germany:1 an1:1 analytically:1 sfb:1 teilchenphysik:1 constructed:1 kalmykov:3 calculated:2 kl:9 feynman:5 exp:2 physics:2 hyper:1 supported:2 keywords:1 find:1 nlo:1 parameters:3 analytic:1 only:1 bases:3 transcendental:1 do:1 his:1 get:1 dd:3 de:2 obner:3 dz:1 dy:1 arxiv:1 method:5 analytical:5 2p0:1 requirement:1 set:2 yost:1 result:5 nuclear:1 diverge:1 written:1 various:1 progress:1 terms:8 budker:1 however:2 vanishing:1 both:1 cos:8 last:1 contract:2 multiloop:1 expression:3 weinzierl:2 simple:1 continuation:2 ca:2 harmonic:1 dimensional:1 grozin:3 cancel:1 zeta:1 polylogarithms:1 decoupling:1 due:1 been:5 reduction:4 ph:8 digits:1 corresponding:1 am:1 precision:1 czarnecki:1 2n3:11 2n2:24 2n1:3 general:1 those:1 p2:1 p0:8 loop:9 reads:1 im:1 subdiagram:1 different:1 containing:1 perform:1 barnes:2 problems:1 enumeration:1 slac:2 complex:1 several:1 higher:1 independent:1 used:1 i0:3 numerical:1 expand:3 compendium:1 gauss:2 center:1 well:1 without:1 solve:1 arising:1 construct:1 decimal:1 edmonton:1 obtain:4 transforms:1 using:4 rn1:3 yet:2 preprint:1 guaranteed:1 parametrization:1 lett:1 theorem:1 iπ:2 remaining:2 euler:2 real:1 tests:1 around:1 outermost:1 sums:15 know:1 vacuum:1 integer:8 mod:1 like:1 tkachov:2 integrals:7 arbitrary:1 pitha:1 reduced:1 methods:1 some:5 xn1:1 provided:1 quarks:1 integration:4 does:1 inserting:3 energy:6 huber:2 agreement:1 expansion:16 binomial:3 mellin:3 about:1 would:1 pe0:1 o:7 xnl:1 soc:1 nsk:1 into:1 numerically:1 76sf00515:1 three:6 appropriate:1 references:1 novosibirsk:1 qed:1 institut:1 additional:1 combinatorics:1 there:1 propagator:3 function:4 multiscale:1 epsilon:2 jun:1 but:1 applying:1 stanford:4 up:2 us:2 ur:1 converted:1 limit:2 similar:3 agree:1 int:1 certain:1 abstract:1 contribute:1 inp:1 convergent:1 single:2 typeset:1 check:2 physical:1 functions:11 nk:2 nl:1 acknowledgments:1 valid:1 department:1 moch:1 calculating:2 separate:1 3f2:10 in1:8 algorithm:4 required:1 mass:2 n1:45 n2:74 n3:36
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0705.2610.txt |@word measurements:2 partial:1 consider:1 maximum:5 mahadevan:1 stoehr:1 lack:2 results:16 leads:2 roy:2 scalar:4 code:1 entropy:2 squarks:4 ga:1 edu:1 consists:1 sci:1 l13:1 contributions:2 cases:7 issues:1 content:1 certainly:1 inverse:1 terms:4 calculate:1 aug:1 iii:1 pierce:1 θw:9 does:4 promoting:1 contours:2 determinations:1 under:2 tf:2 inwards:1 γa:1 include:6 cm2:1 di2:1 me:1 supported:1 mpc:1 very:3 bergstrom:3 rise:1 ρc:1 choice:1 denoted:2 wishes:1 fall:1 mixing:2 uncertain:4 nχ:2 bringing:1 condition:1 four:1 indicate:2 magic:4 level:1 did:2 cause:1 joel:1 applicable:3 fewer:1 correct:2 large:11 discrete:2 vector:1 quinn:2 affect:4 gut:2 small:2 relation:3 noted:3 gb:1 upper:16 strongly:2 fitting:1 computation:1 findings:2 appearance:1 consistent:7 lightest:4 discover:1 breaks:1 mh:2 blue:1 go:1 likely:1 today:1 enhancement:2 remainder:1 incidentally:1 odd:5 tev:40 wmap:9 spectral:1 neutralino:30 mlsp:1 tsuchiya:1 appear:2 rate:1 branchini:1 sun:1 section:27 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0705.2611.txt |@word represent:1 gt:1 consider:4 rev:8 edi:2 results:1 leads:1 gf:1 scalar:2 hennig:1 iζ2:1 edu:6 expressions:1 contributions:1 gr:1 replacements:1 calculate:1 caldwell:1 equivalence:9 contained:2 unanswered:1 kζ:10 th:13 under:1 kξ:13 divergent:9 case:1 preserved:1 orthogonal:1 gravitate:1 ed2:2 ed1:2 fall:1 entire:1 2κa:1 eds:1 ref:1 solution:1 integrated:1 large:3 enclosing:1 small:2 equation:4 force:27 grateful:1 deutsch:1 renormalized:2 mi:3 consistent:1 milano:1 literature:1 cosh:2 setare:3 second:3 further:1 canonical:1 what:3 apparatus:5 diag:1 sum:1 uniform:6 consistently:1 3n:1 above:2 fiore:1 new:1 falling:1 change:1 consisting:2 ibid:1 respectively:1 component:1 here:10 conformation:1 cylindrical:1 cos2:1 sinh:1 address:4 represented:1 strong:3 equations:4 appears:1 z2:2 19b:1 obtained:1 contradiction:1 controversy:1 secs:1 karim:1 action:3 spacetime:2 via:1 useful:1 merely:1 total:1 unit:3 use:1 asymptotic:3 usa:2 remains:2 abbreviations:1 give:1 negative:3 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0705.2613.txt |@word code:2 remarkable:1 maximum:1 results:6 leads:2 concept:1 p06:1 computation:1 consists:1 remarkably:2 gk:9 gj:13 gi:13 whose:1 repetition:3 terms:1 graph:34 ıa:1 finally:1 moor:1 4na:1 protocols:1 under:3 stabilizing:3 ta:1 case:3 advantage:1 zhang:1 every:5 summarized:1 experimentally:1 matrices:9 condition:5 four:5 prefect:1 fewer:1 excellence:1 mn:1 zi:3 zj:2 zk:2 10b:1 10a:1 direct:1 fold:3 go:1 chen:1 greenberger:3 expressions:1 even:1 incompatible:1 near:1 reasoning:1 new:6 satisfy:7 supporting:1 simultaneously:3 mec:1 applies:1 hundreds:1 possibility:2 others:1 ver:1 equations:5 z1:1 z2:1 obtained:3 involved:1 inspired:1 allows:1 contradiction:1 simultaneous:2 products:5 permit:3 bob:16 andaluc:1 genuinely:1 uniquely:1 useful:1 classification:2 9a:1 requiring:2 9c:1 9b:1 9d:2 brought:1 contradictions:1 apply:1 total:1 establish:2 clifford:1 scarani:2 use:1 proceed:1 would:1 prove:2 distinct:2 positive:1 contains:1 eleven:1 therefore:12 more:3 separated:2 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0705.2616.txt |@word ibid:2 represent:3 logarithms:1 since:18 consider:11 pointing:1 priori:3 rev:6 results:2 integration:8 four:4 c3:2 scalar:10 per:1 computation:13 least:1 go:2 gn:1 expressions:6 faster:1 contributions:3 c1:2 giving:2 looking:4 certainly:2 c0:2 depend:5 remarkable:1 daleo:2 re:3 left:1 tn:15 finally:12 those:3 elliptic:3 under:6 connecting:1 analogous:3 te:1 passarino:5 divergent:1 case:14 belonging:2 supported:1 departament:1 g2:2 advantage:2 p3:7 very:1 radius:18 dell:2 semi:1 choice:2 calcolo:1 electron:1 novel:1 ultraviolet:4 difficult:1 specific:1 ln:3 converge:2 exact:3 condition:4 illustrated:2 partially:2 unlike:2 solves:1 level:1 t6:3 irreducible:2 t4:3 t5:2 t2:7 solution:49 t0:8 t1:2 large:9 solved:1 k6:1 unrelated:1 addition:1 wolfram:1 dealt:1 small:9 il:1 inspection:1 still:1 slow:1 sapienza:1 neighborhood:1 occurrence:2 wishes:1 semianalytical:1 estimates:1 direct:2 divergencies:1 split:1 approximation:1 zero:11 ecfa:1 value:2 denner:2 invariant:2 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0705.2620.txt |@word looped:15 homomorphism:6 consider:8 similarity:1 people:1 results:2 proposition:5 joachim:1 consists:2 follow:5 research:1 gi:30 sch:3 compact:1 whose:8 preserves:2 inverse:3 number:5 graph:120 equivalence:12 send:1 containing:1 finally:3 under:4 connecting:2 analogous:5 undirected:1 sent:1 kσ:1 applied:1 kρ:3 string:1 straightforward:1 implicitly:1 focussing:1 induce:2 choice:2 corollary:3 isomorphism:7 every:9 anonymous:1 exact:10 categories:1 subsets:1 turns:1 notes:1 large:3 discrete:1 convenience:2 commute:1 form:1 guiding:1 gi0:1 work:5 neighborhood:2 deutsch:1 folds:1 approximation:1 fold:2 second:2 further:2 odd:1 what:1 hn1:8 appear:2 anton:5 section:6 brief:1 version:4 above:9 referees:1 obvious:1 appeal:1 acknowledgments:1 notions:3 respectively:3 component:6 battelle:1 here:8 atoms:1 desired:2 identifications:1 objects:2 groups:36 represented:3 path:23 along:2 strong:4 cubical:4 morphisms:1 obtained:7 remark:1 study:1 studied:1 colourings:1 unproved:1 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0705.2621.txt |@word qiang:1 ron:1 qian:1 lack:2 results:5 juttner:1 scalar:2 gang:1 edu:1 gl:1 sung:1 calculate:2 effort:1 tr:1 finally:4 those:1 under:1 include:1 λqcd:3 very:2 wave:59 condition:4 erratum:1 guo:6 ryan:1 solved:1 vector:3 configurations:1 smaller:2 estimates:2 prediction:2 sign:2 reinders:1 chen:2 estimated:2 rough:1 letts:2 section:5 3p:4 3m:2 new:2 method:8 satisfy:1 full:7 lee:1 ibid:1 respectively:2 component:1 here:1 mev:19 focused:1 address:1 equations:9 change:1 obtained:2 institute:1 study:1 changed:2 usually:1 geng:1 chang:1 studies:1 b619:1 formulated:2 divide:1 analyzing:2 total:1 b349:1 propagators:1 unit:5 use:1 charge:6 takes:1 commun:1 steinhauser:1 predictions:8 few:1 nucl:3 m1:26 therefore:1 qcd:2 theoretical:2 more:1 introducing:1 penin:1 raynal:1 chuan:1 correspondingly:1 iii:4 md:1 λip:3 mc:1 mb:3 science:1 equation:9 work:1 mi:1 mu:1 values:5 ms:1 following:2 example:1 f1:13 f2:15 f3:12 f4:5 wang:7 give:7 calculation:1 relativistic:14 organized:1 states:35 lorentz:1 dominant:1 gev:8 thing:1 s2:1 discussion:2 s0:1 hot:1 d69:1 parameter:2 chou:1 may:1 after:2 data:7 constants:26 yaouanc:1 natural:1 third:1 light:3 spectra:12 si:1 so:5 λ2p:4 s1:2 nsfc:1 constituents:1 over:1 rolf:1 vary:2 years:1 including:1 argued:1 le:1 fit:2 decay:32 chosen:1 interesting:2 fix:1 solving:3 conjugation:6 li:8 estimating:1 pene:1 choose:5 stephen:1 ours:3 dae:1 them:4 good:1 integral:1 introduce:3 framework:4 they:2 2p:10 tandy:1 radial:4 found:3 constraints:3 heavy:19 veseli:1 ex:2 our:15 eq:2 flavor:1 shown:1 since:2 rev:10 m2i:1 mγ:1 reader:2 formula:3 ref:8 foundation:1 linear:1 pieter:1 quark:6 interaction:4 language:1 m21:1 m22:1 turn:2 b596:1 corrections:1 first:2 symmetry:2 kernel:3 variables:1 antiquark:1 adopted:1 dong:1 electronic:1 1p:8 little:1 rewritten:1 decrease:1 introduction:1 system:8 relations:2 stephan:1 mao:1 calculations:2 f1p:3 scheme:3 part:2 than:2 cheng:2 pagels:1 observed:1 roles:1 double:1 cvetic:1 roberts:1 minus:2 craig:1 topics:1 dunietz:1 b520:2 need:2 hsieh:1 min:1 fitting:2 potential:4 play:1 investigations:1 kai:1 maris:1 most:1 letter:3 qp2:1 chien:1 unequal:1 calculated:2 adopt:1 traditional:1 yang:4 usual:2 physics:1 sum:1 harbin:2 quantity:1 show:7 supported:1 notations:3 iǫ:2 d4:1 find:3 ground:3 q0:2 q2:6 based:1 knowledge:2 parameters:10 state:17 bernard:1 only:4 do:1 hit:1 dk:1 means:2 ϕp:10 wise:1 du:1 dq:11 qp:4 qt:1 d54:1 arxiv:1 predicted:2 fixed:1 saul:1 2p0:1 set:3 computed:1 national:1 relative:3 see:2 b560:1 contour:1 αs:4 qµ:2 review:1 definite:3 written:4 won:1 between:5 αi:2 invariant:1 approach:1 available:2 qt2:2 extend:1 2m:3 wu:1 come:2 both:1 d38:1 many:1 salpeter:23 equal:6 called:1 f2p:1 allton:1 china:2 contribution:1 hwang:2 experimental:7 cn:1 simple:1 dimensional:1 anti:2 table:11 pseudoscalar:2 pq:1 three:1 been:2 int:1 much:1 b420:1 ph:1 pi:1 pro:2 systems:1 corresponding:4 chua:1 chun:1 quantities:1 leptonic:2 χc1:1 χc0:1 careful:1 present:2 p2:4 p0:31 p1:75 value:2 while:1 behavior:1 narison:1 b633:1 a20:1 larger:1 coupled:1 almost:1 ip:8 iv:4 ii:4 characterize:1 vs:2 vv:2 vanish:1 technology:1 different:6 grant:1 same:4 parts:1 shao:1 higher:2 independent:1 numerical:7 v0:10 running:1 scale:2 kim:4 normalization:4 recent:2 lower:1 center:1 pµ:2 well:6 analysis:1 solve:2 components:4 model:4 stokar:1 left:1 mesons:13 obtain:6 yamada:1 momenta:1 previous:4 dqt:1 hai:2 dqp:1 cornell:1 wei:1 wen:1 isgur:1 lattice:1 other:5 lett:10 input:3 excited:5 momentum:3 aspects:1 read:1 decomposed:1 possible:6 using:2 xue:1 mod:2 appearing:1 bethesalpeter:1 follows:1 hung:1 become:1 parity:10 methods:1 some:1 pσ:1 peter:1 happens:1 meson:2 heinz:1 bottom:1 quarks:1 integration:1 instantaneous:6 b606:2 bf:1 sheng:1 hsi:1 agreement:2 oliver:1 bs:4 comparison:1 about:1 o:1 plus:1 evident:1 wang1:1 d65:1 d66:1 letters:1 jiao:1 into:1 splitting:3 bound:4 suppl:2 ηp:4 wan:1 jing:1 hep:1 log:1 comparing:1 there:5 long:1 b584:2 analyze:1 was:1 function:19 form:6 m2:26 but:3 hc:1 adler:1 compute:2 consist:1 up:2 us:1 bethe:6 ωi:4 un:1 zhi:2 agree:1 constant:10 defined:4 abstract:1 chao:2 general:4 rule:1 functions:15 no:1 nc:8 when:3 nf:1 interested:1 details:2 papers:1 department:1 theor:1 conclusion:1 node:2 briefly:1 models:1 a19:1 important:2 sides:1 coupling:6 d20:1 4p:3 mass:26
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0705.2622.txt |@word sector:1 gu:3 cincinnati:2 λu:10 show:1 aliev:1 jµ:1 vacuum:1 obtain:1 detail:1 leads:1 c3:4 scalar:3 edu:1 cp:1 d4:1 trivial:2 based:1 particles:1 adu:2 rapidly:1 sinθ:2 energies:3 wei:1 ali:1 ee2:1 finally:1 offers:1 fig:6 writen:1 renormalizable:1 cosθ:2 ca:1 non:2 gev:3 very:3 iε:3 introduce:1 scaling:9 electron:3 effects:2 qγµ:1 new:1 integer:1 du:20 condition:1 annihilate:1 qq:1 february:1 presented:1 fields:3 university:1 arxiv:8 colors:1 vector:5 li:1 ohio:1 fixed:1 reduced:1 bd:1 square:1 2k1:1 naveen:1 hadronic:1 energy:1 back:2 gaur:1 past:1 zero:2 extended:1 unparticle:11 chen:1 terms:2 beyond:1 eq:1 ee:7 tev:1 blue:1 scale:4 matrix:1 electronic:1 section:6 rev:1 µp:2 expressed:1 mesons:1 current:1 axial:2 above:2 fractional:1 invariant:1 email:1 red:1 luo:1 satisfy:1 outgoing:1 recently:1 positron:3 interactions:1 use:1 illustration:1 standard:1 broken:1 asymmetry:1 address:1 described:1 coupling:4 yan:1 bz:2 c22:2 both:1 search:1 c21:1 study:1 dependence:1 sensitive:2 range:1 acp:1 dated:1 done:1 geng:1 introduced:1 ding:1 jν:1 enegy:1 cm:1 greub:1 pcm:4 into:3 4m2p:1 number:1 reaches:1 georgi:2 anti:1 frame:1 operator:1 pairs:1 meson:1 bosonic:1 cv:1 unit:1 illustrate:1 given:1 hep:8 1t:2 introduction:1 assumed:1 been:3 pb:3 start:1 momenta:1 production:1 low:1 normalization:1 ph:8 cqq:2 propagator:1 fermions:2 function:1 obtained:2 form:2 c23:1 operators:1 factor:3 prospects:1 direct:1 transverse:1 part:1 purposes:1 qk2:1 c1:4 than:1 c2:3 fermionic:2 p2:12 ii:1 p1:10 zhu:1 effective:1 work:2 see:1 annihilation:11 below:1 amplitude:2 promising:1 similar:2 called:1 uc:1 process:1 abstract:1 ir:1 cee:3 high:3 converts:1 formalism:1 quark:3 2du:2 different:1 ev:2 rather:1 k2q:1 cross:6 k2:4 k1:6 es:1 department:1 mass:2 dimensionless:1 massless:2 used:1 centre:1 may:1 center:1 variation:3 diagram:1 explored:2 pair:1 invariance:2 constants:2 recent:1 unparticles:3 sectors:1 cornell:1 light:3 pseudo:3 analysis:1 element:2 feynman:1 green:1 sm:1 xeip:1 2sin:3 model:1 physics:8 dimension:7 restored:1
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0705.2623.txt |@word homomorphism:4 gr:1 results:1 lecture:2 proposition:19 consists:3 follow:1 consider:3 whose:2 inverse:2 paris:1 syntheses:1 restriction:1 th:1 under:2 applied:1 conjecture:1 string:2 pages:1 springer:1 choice:2 every:5 surprise:1 condition:2 school:1 roy:1 notes:2 discrete:9 commute:3 dealt:1 small:1 smaller:1 blacksburg:1 direct:1 sign:2 zero:6 pass:1 further:1 akbar:2 permutations:1 abh:1 section:1 shares:1 above:8 new:2 contrast:1 respectively:2 here:1 threads:2 possibility:1 groups:11 address:2 concluding:1 observing:1 appears:3 divisor:1 gln:1 shift:2 contradiction:2 resulting:1 pictorial:1 permutation:1 successors:1 patrick:2 via:1 apply:2 orderings:1 total:3 establish:1 use:2 additive:1 proceed:1 would:1 remains:1 positive:50 contains:6 negative:10 france:1 noting:3 call:1 therefore:7 candidates:1 associated:1 more:1 preserving:1 becomes:2 berlin:1 particular:1 known:3 cases:5 must:7 none:1 isomorphism:1 word:6 deformed:1 recall:2 det:2 ρn:6 obvious:1 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0705.2624.txt |@word consider:1 excellent:1 activated:1 results:3 leads:2 anggi:3 mccarthy:1 causes:2 row:2 γr:5 shanghai:4 program:2 γl:17 include:1 case:3 supported:1 amplitudes:7 very:1 than:1 electron:8 resonant:3 experimentally:1 little:1 condition:2 vibrational:3 level:1 notes:1 pacs:1 large:2 small:1 noted:1 smaller:1 approximation:1 rate:11 displays:1 dynamics:1 canonical:1 even:2 established:1 assisted:5 current:14 schoeller:2 above:1 new:6 net:1 increasing:3 method:1 behavior:3 respectively:2 here:3 asymmetry:1 china:2 mes:1 relaxation:1 active:1 consideration:1 strong:4 equations:7 interpret:1 publisher:1 institute:1 larger:1 changes:1 der:3 examining:1 formulated:1 plenum:1 highly:1 unit:1 readily:1 plot:1 use:4 usa:1 probabilities:1 positive:4 ul0:1 century:1 negative:5 predict:1 therefore:1 characteristics:7 type:3 theoretical:1 more:2 becomes:2 under:4 correspondingly:2 rigid:1 particular:1 known:1 cases:1 tunnel:3 science:2 equation:1 mn:2 modified:1 remain:1 obvious:1 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0705.2625.txt |@word four:4 obstruction:10 whose:2 calculate:1 paris:1 presents:1 γi:6 edward:1 under:9 rise:2 every:6 school:1 solution:10 vector:7 indices:5 evaluating:3 consistent:1 estimates:1 direct:1 approximation:6 surrounding:1 second:45 tangential:15 even:20 established:1 above:19 new:25 notions:4 mem:1 here:17 represented:2 study:4 changed:1 suitable:1 spacetime:1 divide:2 brt:9 replace:7 patience:1 total:1 univ:1 unit:1 derivatives:62 would:7 inductive:4 negative:3 substitutions:3 call:3 therefore:9 indiana:1 type:1 until:1 brings:1 curvature:38 berlin:1 interaction:1 hold:3 must:14 springer:3 ma:1 ndimensional:1 work:7 theories:1 deficiencies:2 mr:23 root:5 example:4 renormalization:3 indicated:2 give:4 preserving:1 involve:1 indicates:1 cartan:1 degenerate:2 henningson:1 times:4 guarantee:1 end:2 provide:7 verify:3 how:15 replacing:1 after:5 types:1 third:10 bootstrap:7 summing:1 hypotheses:3 greek:1 enter:1 order:116 operations:1 restriction:2 satisfied:4 xi:12 london:1 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0705.2628.txt |@word customary:1 consider:14 similarity:5 crucial:1 child:1 results:12 invent:1 although:1 mild:1 proposition:16 grateful:1 edu:1 go:1 follow:5 research:7 rectangles:8 children:3 gi:5 compact:15 whose:3 academiae:1 cardinality:4 depend:4 ty:1 graph:4 equivalence:5 recurrence:1 answered:1 finally:4 present:1 ti:7 analogous:2 iij:2 overlaps:2 applied:1 conjecture:7 subcollection:3 mγ:8 orthogonal:6 very:7 desired:5 assuming:2 focus:2 falconer:2 sons:2 every:7 reordering:1 fall:1 resonant:18 affect:1 snk:5 exact:2 condition:11 dim:113 dominate:1 immediately:1 level:8 turns:2 kemeny:1 nostrand:1 occurs:3 large:7 discrete:6 vector:1 math:16 universal:1 small:12 markov:1 rk:1 correct:1 smaller:2 says:2 zi:6 among:1 direct:1 literature:1 approximation:1 morphology:1 zero:7 yoccoz:1 projecting:1 further:4 dynamics:3 estimated:1 linear:6 even:2 intersection:2 nonlinear:1 appear:1 iterating:5 contemp:1 sum:10 analogously:5 version:6 en:1 above:3 new:5 increasing:1 consisting:4 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0705.2629.txt |@word limited:2 magnetic:1 dynamic:1 four:21 facilities:1 consists:7 whose:4 calculate:1 presents:1 swap:1 under:3 worth:1 zachos:1 every:5 summarized:1 solution:1 admissible:28 vector:1 indices:2 10j:1 jhep:1 incremented:1 consistent:2 plaquette:65 direct:1 horn:1 likely:4 christensen:3 rigorous:1 qualitatively:1 implemented:1 even:4 errors:1 trapping:1 selected:5 above:9 new:4 contributes:2 consisting:1 simultaneously:2 evaluating:2 zach:3 here:14 reported:2 represented:1 path:1 quark:2 contraction:5 obtained:4 balance:3 study:6 changed:1 ignoring:2 changes:11 schur:1 projection:3 gluons:1 highly:2 brought:1 unit:6 would:4 negative:5 call:6 type:12 zeroes:1 successful:2 hold:1 must:6 fµν:2 theories:11 itself:1 example:6 transition:1 renormalization:1 indicated:1 give:8 organized:1 implementations:1 involve:2 times:3 absolute:2 verify:1 feature:2 revisit:1 how:7 adjacent:7 answer:2 thermodynamic:1 ladder:11 after:2 diagram:3 lat:3 parallel:1 constants:2 effective:1 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0705.2631.txt |@word sci:2 consider:1 caused:5 comparatively:2 dynamic:1 results:12 ferreira:1 hennig:10 gc:2 lebedev:1 remarkably:1 denotes:2 hole:1 causes:3 synthetic:1 increase:2 biol:1 const:2 integral:2 concerned:1 charge:7 does:3 tanaka:2 those:1 th:1 under:1 stochastic:10 fax:1 kats:2 amplitudes:1 zhang:1 very:2 springer:1 wave:5 electron:11 nichols:1 resonant:1 difference:2 exact:1 deformations:1 strand:3 randomness:1 europhys:1 vibrational:5 hamiltonian:4 positions:2 t2:2 applicable:2 large:2 vector:1 small:3 commented:1 lyra:2 zn:3 smaller:2 disordered:1 ten:1 sin2:1 ornstein:1 approximation:3 rate:14 displays:1 dominguez:1 zu:1 dynamics:5 estimated:1 subscripts:1 established:1 newtonstr:1 power:1 nano:1 section:4 brief:1 expressed:2 experiment:1 localized:4 above:1 expresses:2 consisting:2 3d:1 coefficient:2 behavior:14 ibid:2 respectively:6 even:1 berthelot:1 here:3 kayanuma:1 water:1 euro:1 address:1 active:2 depend:2 along:6 observing:1 change:1 extreme:1 obtained:4 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0705.2632.txt |@word extrapolated:1 saturating:2 squared:1 magnetic:55 dynamic:1 four:37 entropy:1 controversial:1 consists:1 localized:8 poorly:1 whose:14 calculate:2 γq:1 contained:1 presents:1 γi:1 under:16 divergent:2 iǫ:2 zachos:1 tantalizing:1 summarized:1 affect:1 brihaye:1 school:1 suffices:1 solution:9 convenience:2 vector:241 math:3 indices:3 jhep:8 force:1 consistent:7 estimates:9 direct:21 unpolarized:1 approximation:16 hata:3 second:8 me0:7 correlator:3 rigorous:1 qualitatively:2 estimated:1 expressions:1 even:11 established:6 ˆt:1 above:32 new:5 net:3 contributes:5 consisting:1 ˆn:2 coefficient:7 evolving:1 sugimoto:18 simultaneously:1 evaluating:1 gne:2 wrapping:2 equals:1 here:26 reported:1 asymmetry:4 mev:10 represented:3 quite:6 contraction:1 obtained:6 suitably:1 study:2 changed:1 completely:3 suitable:4 changes:1 astute:1 diameter:1 gluons:2 ground:2 explained:2 koji:1 highly:1 neutrons:2 remnant:1 total:3 unit:9 plot:1 would:41 call:1 therefore:5 seriously:1 type:8 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0705.2634.txt |@word neighbors:3 magnetically:1 partial:11 consider:1 chain:24 rev:5 magnetic:15 iib:1 results:2 steve:1 eds:1 generalize:1 grateful:1 follow:1 gi:9 particles:2 21st:1 uneven:1 dα2:3 advantage:1 irrelevant:1 technique:1 vs:1 tp:6 spirit:1 supported:1 charge:3 bjornsson:1 present:4 th:22 under:3 divergent:1 case:4 conjecture:4 global:2 deforming:1 string:29 g1:2 very:3 rise:2 springer:1 choice:4 witten:1 summarized:1 mixing:6 affect:1 matrices:1 deformations:1 condition:3 hamiltonian:6 supports:1 anisotropy:5 t2:10 applicable:2 2κi:2 large:4 discrete:1 differential:2 decouples:1 indices:1 relation:3 round:1 configurations:1 jhep:5 holography:1 force:3 nthu:1 sin2:8 direct:1 past:1 integrability:5 complicates:1 j22:2 zz:1 further:2 cft:2 melvin:1 tempted:2 goto:2 spectral:1 established:1 what:1 nonlinear:2 g22:2 ct2:1 cµ0:2 trivial:1 section:5 near:1 lunin:1 localized:1 goes:1 lifshitz:6 new:2 satisfy:1 full:2 κi:7 κj:2 relates:1 respectively:2 neveu:1 here:11 diagonal:2 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0705.2635.txt |@word sector:1 since:2 vorticity:4 consider:2 gq:2 being:1 rev:7 magnetic:11 out:1 means:1 rotating:1 known:1 gauge:8 12v:4 world:2 d4:4 seal:1 its:1 depend:1 chandrasekhar:1 field:10 irrelevant:1 lake:1 coordinates:1 writing:1 eµν:2 only:2 does:1 originally:1 condition:3 factor:1 stable:1 include:1 into:1 momentum:2 real:1 do:1 them:1 string:7 parametrizes:1 demands:1 davis:1 dam:2 couple:3 hµνρ:3 dφdφ:1 guarantees:1 cannot:1 reads:1 lett:5 background:1 invariant:1 confined:2 using:3 aλ:1 now:4 aν:2 ǫab:1 above:2 easily:1 finite:1 dirac:4 presented:1 fields:2 arxiv:1 kharagpur:1 4πg:1 flux:16 vector:2 euro:1 dae:1 radial:1 become:1 4πk:1 inside:1 configurations:1 parity:2 set:1 allowed:1 directly:1 achieved:1 strominger:1 national:1 nambu:2 related:1 balachandran:1 cremmer:1 daµ:1 see:4 result:1 escape:1 dµ:2 eq:1 techniques:1 ignore:1 what:1 aeµ:3 tensor:3 2e:1 stuck:1 tube:5 quarks:1 lagrangian:2 integration:1 per:2 mesons:1 current:8 µl:1 axial:3 2g:1 am:8 regge:1 replaced:1 integrated:1 akhmedov:1 ends:7 terms:1 theory:7 energy:4 found:1 however:1 here:3 quark:1 jm:6 chatterjee:3 marino:1 dualize:2 jd:1 bose:1 therefore:1 standard:1 equations:1 transformation:2 change:3 mathur:1 providing:1 antisymmetric:1 would:1 study:1 monopole:6 anomalous:1 must:2 motion:2 stabilized:1 length:4 bνρ:1 rewrite:1 massive:3 trajectory:1 action:3 dec:1 spacetime:1 lahiri:3 block:1 first:1 bowick:1 new:1 contains:1 presence:1 h2:1 maxwell:2 variables:3 xν:1 functional:3 closed:1 infinite:1 references:1 another:1 cancel:1 constant:2 open:2 angular:3 unit:2 2nπ:1 given:2 toy:1 hep:1 singular:3 second:1 start:1 introduction:1 17th:1 there:1 physics:1 least:1 fully:1 attach:1 nucl:1 conservation:2 scherk:1 fermions:4 sealed:2 basic:1 ph:1 xµ:2 anomaly:1 consistent:1 gives:2 function:5 introducing:1 generating:1 coupled:3 collapse:1 form:1 bµν:5 becomes:2 dxµ:3 m2:2 photon:5 but:1 back:1 effect:1 confinement:4 aµ:4 shellard:1 θr:1 θs:1 iii:1 than:1 fermionic:7 monopoles:9 unlike:1 integrating:2 was:1 equation:4 fµν:5 modified:2 london:1 2πn:2 will:1 minimize:1 absence:3 limit:1 thin:2 cancelled:1 suggestively:1 india:1 endpoints:1 similar:1 decompose:1 rename:1 due:1 ae:2 dual:1 eg:3 abelian:4 abstract:1 measure:1 thus:2 surface:1 high:1 dualization:1 conserved:2 dθ:1 sheet:2 allen:1 mod:1 quantization:1 species:3 currents:2 g2:1 containing:1 strength:1 escapes:1 minimally:3 polchinski:1 no:3 get:4 feature:1 conserve:1 write:2 sciences:1 other:1 take:2 opposite:1 jacobian:1 kolkata:1 symposium:1 massless:1 sharatchandra:1 dd:1 consequence:1 ev:1 brns:1 over:2 unless:1 intended:1 centre:1 may:1 eae:1 after:1 charge:1 dimensions:1 v2:1 regular:1 mass:2 linearization:1 invariance:1 electroweak:1 interacting:1 lee:1 implies:1 higgs:3 charges:1 salt:1 partition:4 well:1 dσ:2 order:2 part:2 so:5 exp:4 time:1 ud:1 model:5 tubes:5 strings:4 gµν:2 usual:1
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0705.2640.txt |@word replacing:1 represent:2 concept:1 maximum:5 skip:1 magnetic:2 results:5 roy:2 entropy:2 lll:4 go:1 whose:1 c0:10 depend:1 calculate:3 paris:2 concerned:2 equivalence:5 young:1 finally:1 monotonically:1 th:5 under:2 must:1 worth:1 indicating:1 provides:2 straightforward:1 sitting:1 far:2 implicitly:2 rise:1 primed:1 difference:6 exact:6 special:1 partitions:19 treating:1 exponential:1 level:4 turns:5 solution:3 large:30 generalises:1 small:3 zeitschr:1 originally:1 configurations:4 upper:2 employing:1 ze:4 direct:1 likely:1 evaluated:1 rigorous:2 further:1 zp:6 substitute:1 canonical:9 even:2 established:1 sud:1 const:1 deeply:1 sum:3 near:1 expressed:1 above:1 fractional:3 nonuniversal:2 new:5 unrestricted:4 increasing:2 method:4 contrast:4 body:4 pictorially:1 full:1 complex:2 ibid:6 exchange:1 respectively:2 shankar:1 here:4 behaviour:2 explore:1 inverse:3 andrews:2 address:1 based:1 along:3 strong:1 equations:1 appears:1 change:2 extreme:3 obtained:4 shift:1 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0705.2641.txt |@word consider:4 ceases:1 excepting:1 retain:1 stops:1 go:1 expressions:1 denotes:1 row:1 whose:1 depend:2 calculate:6 finally:1 program:1 cm3:1 conjecture:4 confirmation:1 2ri:2 wave:17 trouble:5 condition:1 riemann:1 hamiltonian:2 turns:3 t2:3 applicable:1 t0:11 t1:5 large:3 vector:8 small:5 divides:1 sin2:2 consists:1 second:4 even:1 what:1 section:11 analogously:3 find:1 above:4 expresses:1 movement:2 respectively:1 equals:1 here:7 heitler:1 eikx:2 based:1 along:2 eikr:2 change:1 schiff:1 obtained:2 institute:1 shift:2 allows:2 spheres:1 resulting:1 usually:3 fourier:4 named:1 ipa:10 namely:1 vice:1 ipx:4 total:7 unit:13 use:2 contains:4 only:3 ψk:7 chs:1 kinematics:1 therefore:8 averaging:1 type:3 theoretical:1 more:1 company:2 fixed:1 everywhere:1 known:6 given:1 iii:2 must:3 quantized:1 equation:2 macroscopically:1 values:1 ρv:1 following:5 example:2 proof:1 compare:1 renormalization:1 give:2 process:3 relativistic:3 cited:1 preserving:1 neglected:2 collision:3 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0705.2642.txt |@word landecker:8 toth:1 bull:1 results:4 comments:2 grateful:1 go:2 l75:1 research:2 compact:5 wendker:1 dougherty:1 removal:3 citing:1 foster:2 those:2 include:3 supported:1 zhang:2 very:1 frequencies:15 presented:2 did:2 cause:1 cavendish:1 shock:1 bright:5 large:3 reich:7 enclosing:1 small:1 noted:5 concluded:1 too:1 consistent:1 direct:1 likely:6 masson:1 spectral:7 index:4 what:1 errors:7 appear:1 giving:1 sun:1 section:9 urst:6 version:1 above:4 new:1 purton:1 contributes:1 unsurprisingly:1 here:4 mnras:5 reported:10 them:1 represented:1 iras:3 gigahertz:2 change:1 canadian:3 involved:1 larger:2 reports:1 suggests:1 survey:12 published:10 makes:1 goss:2 useful:1 scales:2 private:4 scaled:2 remnant:18 apply:1 resolutions:1 total:1 use:4 would:1 brighter:1 give:4 durand:1 few:2 snrs:4 noting:1 therefore:1 taken:1 astr:1 more:3 conclusions:1 apparent:1 corrected:1 limitation:1 curvature:1 labelled:2 cases:1 iii:1 sample:1 integrating:1 cas:1 work:1 cao:2 thin:2 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0705.2643.txt |@word essay:2 limited:1 logarithms:1 consider:2 remarkable:1 similarity:1 depends:1 rev:3 particular:4 results:3 baby:1 go:1 localized:2 gh:2 compact:3 whose:2 certainly:1 ihes:1 depend:2 superspace:4 mutatis:1 equivalence:1 acting:1 quasi:1 th:1 stable:1 hermann:1 details:2 analogous:1 fermionic:2 ingredient:1 mpg:1 belonging:1 string:1 very:9 continues:1 wave:5 electron:3 summarized:1 affect:1 matrices:1 hamiltonian:6 turns:1 large:3 involution:1 vector:1 guiding:1 small:1 khalatnikov:3 barbara:1 challenge:2 upper:2 unexpected:1 neighborhood:1 cce:1 ten:3 approximation:1 zero:1 dynamics:14 canonical:4 bilinear:2 established:3 what:2 waa:2 sub:2 geometrodynamical:1 deeply:1 section:1 while:2 version:1 axel:1 sur:1 above:3 lifshitz:3 new:5 satisfy:1 layers:1 outgoing:1 full:1 led:1 notions:1 implying:1 respectively:1 here:10 understanding:3 behaviour:1 modular:1 smearing:1 groups:3 cab:1 consideration:2 disappeared:1 equations:1 appears:1 logarithmic:2 bojowald:1 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0705.2644.txt |@word sector:1 operations:1 manifold:1 being:1 equality:1 eds:1 scalar:5 using:2 satisfies:4 reality:1 find:6 submodule:1 preprint:1 calculate:1 sciences:1 commutators:1 field1:1 lake:1 forms:1 leibniz:2 only:1 under:1 jacobi:1 derivative:15 include:1 resolved:1 dae:2 them:1 l81:1 press:1 interior:2 know:1 new:1 oxford:1 17th:1 discuss:1 identity:1 term:1 dαp:4 like:2 fields:8 university:1 differential:1 kharagpur:1 identified:1 grav:2 vector:15 esi:1 lv:20 div:1 side:1 arxiv:1 sparling:3 national:1 idea:2 module:1 zero:1 w1:8 w0:4 delivered:1 operation:1 lw1:2 es:1 twistor:1 bilinear:1 αp:22 what:1 space:2 µw:1 since:1 thank:1 mason:1 written:1 various:1 formula:2 geometric:1 organisers:1 math:1 nurowski:3 linear:2 degree:1 however:1 here:1 how:1 chatterjee:3 jd:1 bose:1 contraction:4 definition:1 improved:1 βq:5 algebra:1 v1:9 geometry:1 vectors:1 allows:1 etc:2 resulting:1 invitation:1 action:1 introduced:1 spacetime:1 lahiri:2 block:1 first:1 extra:1 problematic:1 xg:2 modifying:1 multiplication:2 right:1 references:1 respect:4 perj:1 derivatives:2 pp:1 lv1:9 lv0:1 would:2 lw:2 introduction:1 together:1 eqs:1 negative:1 therefore:2 basic:1 ph:1 was:2 energy:2 tod:1 define:6 iit:2 form:9 schwarzschild:1 equipped:1 took:1 but:1 iw:6 demand:1 antisymmetric:1 iii:1 guha:1 present:1 applied:1 vienna:1 expanded:1 modified:1 us:2 will:1 following:2 problem:1 dec:1 wedge:1 ordered:3 kv0:5 defined:6 abstract:3 india:1 correction:1 iv:8 high:2 itself:1 cartan:1 exterior:2 our:1 work:1 robinson:3 clearly:1 lie:15 develop:1 no:1 holds:1 when:1 virtual:1 any:2 field:8 quant:2 generalized:26 kolkata:1 symposium:2 ordinary:10 dv0:1 brns:2 product:3 used:1 centre:1 may:1 hand:1 v0:10 commutator:5 moment:1 iv1:3 pair:3 class:2 structure:2 physics:3 rule:2 complexity:1 add:1 salt:1 talk:1 usual:1
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0705.2645.txt |@word limited:1 lindfors:1 sci:3 consider:2 remarkable:2 illustrates:1 rev:3 magnetic:1 excellent:1 results:5 yellow:2 avalanche:1 follow:2 yaish:1 contributions:1 layers:46 increase:2 guerrero:1 depend:1 calculate:1 re:1 iii:1 technique:1 german:1 finally:1 does:1 device:1 present:1 under:1 include:1 silicon:1 sent:1 anisotropic:1 impinges:1 zhang:4 very:4 wave:5 leverhulme:1 electron:4 every:5 difficult:1 refractive:11 experimentally:1 difference:3 expectations:1 condition:9 mauri:2 splitter:3 school:2 accompanying:1 transmission:3 bright:1 ioannina:1 large:8 convenience:1 reich:1 ozyilmaz:1 quick:3 enhance:2 dubonos:2 optics:2 der:1 9pl:1 configurations:1 schultz:2 quicker:1 force:1 trend:1 folds:1 direct:3 nair:8 sign:4 approximation:2 second:3 enhancement:1 spectrograph:1 chen:2 further:2 chem:6 quite:2 seyller:1 even:1 index:15 what:2 eng:1 nano:4 giving:1 600nm:1 section:1 selected:1 near:2 thickness:19 access:1 consistently:1 experiment:4 goes:2 hecht:1 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0705.2648.txt |@word ibid:1 reparametrize:1 customary:1 gr:1 pointing:1 focus:4 generalize:1 computation:3 sci:1 remarkably:1 consider:3 inverse:1 depend:1 aug:1 paris:2 passage:1 quasi:1 behave:1 th:2 stochastic:1 indicating:1 activities:1 very:1 results:4 fall:1 experimentally:2 exact:1 condition:1 harlow:1 rigourous:1 turns:1 dif:1 solution:2 t1:1 large:24 unrelated:1 math:8 small:1 challenge:1 consistent:1 estimates:1 direct:1 sign:2 approximation:1 edelman:1 zero:13 correlator:8 further:1 linear:2 even:2 established:1 what:1 sud:2 plays:1 d2:1 diffusing:1 contributed:1 derrida:1 indian:1 goes:1 new:1 method:2 full:3 chose:1 degree:2 respectively:1 realizations:2 here:4 l1157:1 reported:1 appears:1 change:2 obtained:4 study:2 changed:1 allows:1 suggests:2 involves:1 plotted:1 useful:2 castin:1 highly:1 reverting:1 unit:2 plot:5 takes:1 remains:1 neighbours:1 france:2 few:2 therefore:1 egory:1 more:2 validity:1 tested:1 normalized:3 particular:2 known:1 dougherty:1 keeping:2 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0705.2649.txt |@word λs:20 λp:6 dx:7 xˆ:8 x1:2 vǫ:2 nτ:20 ux:2 λk:3 gn:5 λi:5 c1:3 d0:2 λl:15 q0:1 nǫ:5 vτ:1 aτ:4 tx:15 bx0:10 ll:1 γp:3 lj:18 b1:1 γj:1 tl:1 tj:2 oº:1 λis:2 kθ:2 jac:1 kσ:1 iθ:1 dk:1 kxn:3 kτ:3 df:1 eis:7 tjn:1 me:17 ϕn:11 dz:6 zº:1 dy:9 dw:25 dt:20 ds:1 dp:10 sτ:4 2s:9 kǫ:1 qx:10 arxiv:1 rº:1 t1:1 sǫ:19 fτ:3 rj:18 l1:3 λi1:2 2j:1 qn:9 cǫ:17 en:24 ei:7 zj:2 zk:4 eλs:4 n2:3 eλl:1 dº:2 eλj:4 b2:2 λj:45 eq:1 es:3 zs:3 αp:7 αs:6 rs:8 ˆx:15 rx:5 dpi:2 cτ:2 i1:7 mβ:1 αi:1 rm:1 αk:7 mθ:2 math:1 mτ:3 ms:22 wn:5 zl:1 bi:15 bj:6 hǫ:14 jn:8 q2s:2 eλ1:1 bx:2 z1:10 z2:4 e2:1 pβ:4 a1:2 pα:12 r0:9 r1:4 idx:12 cº:1 o:6 z1α1:1 nζ:2 uǫ:9 σs:16 2k:1 lº:1 βj:2 ck:20 2nǫ:3 v1:1 ψq:14 xn:11 cn:9 eǫ:4 fº:3 cf:4 ce:2 rτ:4 cx:1 limn:8 πl:1 ukj:1 ct:2 ei1:7 sº:1 ψx:8 feb:1 log:41 πs:14 πj:21 eτ:2 kσn:1 ej:1 eσ:3 dnt:11 m1:5 m0:12 kµ:1 pj:6 pk:18 pn:7 rǫ:68 θj:1 iº:1 θn:2 ii1:1 pγ:2 p1:1 sx:6 aµ:1 sxn:2 kº:7 x2:1 c2:4 x0:6 aº:2 eγ:3 supx:1 p0:3 wτ:4 ma:1 r2:1 ψf:1 rxn:32 ρm:1 mk:1 ωi:2 ek:2 nº:5 un:12 fˆ:2 ωn:5 iin:5 mx:3 ex:37 exˆ:6 ae:2 vj:4 b3:2 vl:1 e1:3 vn:7 dθ:1 vx:2 ax:23 inf:4 ckj:2 anx:3 tτ:3 maxz:1 φq:1 nk:5 fn:4 min:4 s3:1 s2:2 rl:10 maxv:1 lǫ:5 nxn:2 nx:11 k2:10 k1:13 fxn:12 lip:12 tǫ:14 m¹:6 mº:2 dǫ:12 nλ1:2 fx:28 max:7 dgn:1 ζn:8 xº:3 βl:9 a2:2 qτ:4 imθ:1 fm:1 cµ:1 man:1 βe:1 cpk:3 χs:1 rn:32 pº:1 kj:10 sp:2 kn:4 kl:2 dn:2 ψx0:1 sm:3 lim:2 n1:15 d1n:2 kx:58 χk:11 χi:2
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0705.2650.txt |@word fα:4 differentiability:2 λw:3 consider:1 show:5 indeed:6 converse:2 supported:1 choose:1 godefroy:1 scalar:1 paper:1 london:1 banach:27 differentiation:1 existence:1 satisfies:1 research:1 its:4 compact:2 mazur:1 preprint:2 ıguez:1 han:2 providence:1 fix:6 xm:10 no:5 topological:1 tn:9 lemma:1 only:5 tk:2 philos:1 theorem:16 jacobi:1 mail:1 main:1 operators:3 over:2 norm:30 real:5 case:3 ym:1 subspaces:1 phelps:1 get:7 results:1 song:1 functional:4 department:1 corollary:9 valued:1 every:16 polydisc:1 background:1 mathematics:1 using:2 respectively:1 unique:1 geometric:1 condition:1 well:1 δy:2 benyamini:1 university:1 arxiv:1 consisting:3 δn:4 proposition:6 either:2 each:11 references:1 anal:2 refer:1 view:2 subset:31 supx:1 zn:28 set:50 says:1 illinois:1 exposed:4 smooth:13 special:1 some:5 direct:1 pacific:1 observed:1 society:2 imply:1 gδ:18 radius:4 result:4 convex:11 funct:1 contains:2 zp:7 globevnik:1 ba:4 nonzero:2 αp:3 shown:11 said:8 dense:32 denseness:7 renorming:1 space:30 univ:1 since:4 uniform:1 boundaries:3 re:3 ǫp:8 cambridge:1 closed:5 sup:28 denoted:1 limit:1 boundary:5 order:3 proc:1 method:3 math:9 shows:9 foundation:1 notice:3 korea:1 λz:4 lee:8 ju:1 weak:1 dineen:1 acosta:1 ranges:1 norming:13 metrizable:4 subsequences:2 polynomials:4 put:3 equipped:1 studia:1 strong:40 bx:81 topology:1 definition:1 remark:2 αq:5 βp:3 βq:5 fa:1 choi:2 hull:2 studied:1 funded:1 ath:1 mathematical:2 american:2 rodr:1 colloquium:1 embedding:1 hence:10 introduced:1 krf:1 separable:5 xk:6 soc:1 locally:9 xn:10 ff:1 ri:1 point:13 cb:11 into:2 cf:1 dimensional:1 limk:2 limn:12 another:3 sequences:2 polynomial:3 moreover:1 precisely:1 open:3 unit:5 postech:1 use:1 xα:9 prove:2 addition:1 equations:1 there:31 finally:1 vol:1 echet:8 appl:2 therefore:1 deville:1 indiana:1 variational:4 was:1 metric:8 gives:2 function:17 holomorphic:6 israel:2 corresponding:2 complete:11 form:1 scalars:3 government:1 continuous:10 subspace:7 kim:1 issue:1 particular:3 known:1 nikod:1 moehrd:1 completes:3 ρa:12 exposes:2 springer:1 algebras:4 palacios:1 showed:1 recall:2 work:1 supt:1 see:1 differentiable:8 radon:1 subsequence:3 un:15 suppose:11 publications:1 shall:4 following:4 john:1 property:3 similar:1 called:1 proof:9 strongly:14 bourgain:2 dedicated:1 ab:6 attains:4 ad:1 defined:1 endowed:1 abstract:1 horv:1 thus:3 argument:1 ferrera:1 denote:5 convergent:3 sphere:3 say:5 proves:1 au:15 attain:2 dual:1 further:1 need:1 inf:12 mn:11 bishop:5 verlag:1 spaces:6 functions:29 any:2 grant:1 lim:5 holds:2 when:1 converges:10 polarization:1 field:1 complex:12 generalized:1 interior:2 so:3 korean:1 concerning:1 ac:1 principle:1 category:3 fr:8 elements:7 columbia:1 lindenstrauss:3 algebra:2 may:1 numerical:23 uniformly:16 mapping:2 ball:2 applications:2 satisfying:1 bounded:6 peak:45 necessity:1 infinite:3 homogeneous:2 nonlinear:1 identity:1 appear:1 sx:7 implies:9 zizler:1 whenever:4 optimization:1 linear:4 stronger:3 analysis:2 element:2 their:1 kr:1 baire:3 points:24 attaining:9 sn:7 sm:3 missouri:1 sc:2 hamilton:1 sa:3 dimensions:2 sequence:8 sf:3 minimal:1
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0705.2651.txt |@word limited:1 emerging:1 drastically:1 sch:10 fong:2 abundances:5 gx:1 sources:1 cambridge:1 radio:1 dish:3 patel:1 determined:1 fredrik:1 cases:1 compact:2 based:1 knowledge:1 fit:2 title:1 presence:1 editors:1 decreases:2 circumstellar:5 other:1 fig:2 molecules:1 acknowledge:1 local:1 indicating:1 equilibrium:4 case:3 non:5 australia:2 onsala:1 garden:1 loss:2 vla:2 2006b:2 smithsonian:1 results:1 increases:1 mon:1 atca:2 socorro:1 using:2 delgado:2 cool:1 atmospheres:1 easily:1 processes:2 irc:3 crt:2 alez:2 interestingly:1 arxiv:1 michael:1 suggested:1 large:1 cas:1 wong:2 l2:1 predicted:1 radial:1 found:1 photodissociation:3 university:1 csiro:1 indications:1 right:1 financial:1 methods:1 trend:1 series:1 consistent:4 estimates:2 freeze:1 observed:1 photospheric:2 full:1 radius:1 progress:2 enhanced:1 year:1 further:2 prep:2 best:1 out:2 still:1 excitation:1 space:1 requires:1 probed:1 magnitude:3 envelopes:1 fractional:3 ik:1 new:1 nsw:1 acknowledgments:1 sma:1 stockholm:1 asp:1 recently:1 albanova:1 reveal:1 importance:2 respectively:1 rudimentary:1 component:4 however:2 stellar:1 harvard:1 formation:1 carbon:5 interferometric:1 pup:1 properties:1 panel:1 obtained:3 usa:1 starts:1 region:3 larger:2 but:1 o:5 david:1 suggests:1 carries:1 objects:1 including:2 lte:3 adsorption:1 hya:1 onto:5 first:1 pre:1 there:3 cm:2 facility:1 simple:1 consequently:1 apj:1 dust:5 lundgren:1 references:1 names:1 iras:1 tony:1 moreover:1 research:1 telescope:1 conference:1 atmosphere:1 strong:1 publication:1 would:1 needed:1 introduction:1 transfer:2 support:1 initial:1 radiative:2 predictions:1 been:3 their:1 much:2 observations:5 stars:12 expected:3 inner:2 ph:1 type:5 national:2 more:2 box:2 samples:1 form:1 relative:1 addition:2 emission:4 modelling:1 volume:1 astrophysics:1 condensation:1 lindqvist:2 line:7 evidence:1 than:3 abundance:9 sample:1 multi:1 observatory:3 ma:1 grains:6 kerschbaum:2 solid:1 was:1 cherchneff:2 rate:1 po:2 sweden:2 street:1 were:1 distribution:1 steep:1 clear:1 depleted:1 detailed:4 tau:1 transition:1 figure:1 vol:1 abstract:1 epping:1 agb:8 high:6 effectively:1 single:4 performed:2 council:1 our:1 models:2 gradients:1 orders:2 gonz:2 relatively:1 swedish:1 information:1 initiated:1 initiate:1 cse:1 dashed:1 zhang:1 generally:1 freezes:1 chemical:5 complex:1 2006a:2 low:2 spatial:3 photosphere:2 additional:1 several:1 sio:16 higher:2 picture:1 extended:2 star:3 see:2 may:1 published:1 derived:2 hand:1 most:1 studies:1 hans:1 astronomy:1 data:3 recent:1 interferometers:1 lower:1 accreted:1 center:2 scenario:1 olofsson:5 typically:2 average:2 required:1 oier:10 analysis:2 astro:1 rather:1 nlte:1 mass:2 se:2 dor:1 model:3 chemistry:8 resolution:3 order:2 wind:2
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0705.2652.txt |@word consider:2 remarkable:1 switched:1 rev:10 magnetic:1 lack:2 results:1 gy:1 switches:1 scalar:1 drastically:1 kc1:1 gb:1 ecnu:1 inverse:1 re:3 shanghai:1 supported:1 γj:1 tl:1 program:1 those:1 under:5 tg:1 ωt0:1 applied:1 confirmation:1 orthogonal:1 very:6 frequencies:2 induce:2 wave:4 p1:2 resonant:1 condition:4 four:1 level:7 tanh:1 solution:6 t1:1 solved:1 vector:38 small:5 nos:1 optics:1 configurations:1 zl:1 upper:1 smaller:2 ten:1 pulse:1 sign:2 approximation:2 rate:1 fiber:1 design:1 chen:1 manipulating:2 petrosyan:1 established:1 nonlinear:11 g22:3 apparatus:2 g21:1 cundiff:1 near:2 cell:1 experiment:1 above:5 new:1 d1:6 method:2 cesium:1 led:1 exchange:1 respectively:7 component:2 here:8 atoms:2 china:3 active:4 based:1 strong:3 equations:3 z1:1 z2:2 obtained:4 great:1 balance:5 shift:1 study:2 allows:2 completely:1 prior:1 characterizing:2 stressed:1 t21:1 resonance:1 fourier:1 makes:1 composed:1 control:8 via:3 scales:1 δc2:4 δc1:5 electromagnetically:3 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0705.2653.txt |@word ηl:2 vl:1 2τd:1 eu:1 τff:2 lmin:7 mmax:1 vl2:2 τd:1 lmax:12 mmin:1 msol:1 ξl2:1 m1:1 εd:6 ph:1 ρsh:2 dl:11 dm:2 ba:1 lg:2 sfr:2 sf:1 astro:1 ξl:3 fe:8 yr:1 σl2:3 kb:2 mg:1 ml:1 arxiv:1 t2:1 ρl:4 o:7 mj:1 dl1:1 exp:2 τcoll:3 dec:1 ql:3 gyr:5
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0705.2654.txt |@word limited:5 abundances:1 code:1 eriksson:1 sch:28 isotropically:1 results:2 leads:1 known:1 per:2 ionize:1 intricate:2 abundant:2 fredrik:1 ryde:1 causes:1 increase:2 depend:2 subjected:1 editors:1 presents:1 present:2 marks:2 include:2 case:2 adiabatic:3 shielding:1 very:9 johansson:1 wave:1 ultraviolet:1 interpreting:1 predominately:1 continued:1 vast:1 cool:2 hya:1 ramstedt:5 presented:2 kerschbaum:2 large:7 small:3 equation:3 dis:1 concluded:2 upper:1 smaller:1 illustrating:2 tenuous:1 consistent:5 estimates:5 goldreich:4 approximation:1 winds:1 rate:50 compensates:1 profiles:1 download:1 further:2 estimated:3 rough:2 even:2 established:1 errors:3 plays:1 sub:1 complexities:1 section:1 brief:1 shares:1 thickness:1 current:1 bipolar:1 transfered:1 fractional:1 new:2 acknowledgments:1 contrast:1 full:2 degree:4 exchange:1 respectively:2 error:2 component:1 gilman:2 here:3 agreement:1 asymmetry:1 objects:5 clumpiness:2 ratio:7 trung:1 jura:2 change:1 obtained:5 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0705.2656.txt |@word myung:1 gr:39 chinese:1 both:2 liddle:1 results:7 leads:1 roy:1 scalar:18 entropy:4 edu:1 perturbations:14 expressions:2 relict:1 hole:6 issues:2 consider:4 certainly:2 remarkable:3 sahni:1 cobe:6 irrelevant:1 rel:1 must:1 does:4 promoting:1 th:11 under:4 include:1 lidsey:1 brown:1 attempts:1 supported:1 string:2 zhang:21 very:10 mpl:2 rise:4 wave:1 affect:1 difference:5 matrices:1 condition:23 four:1 annihilated:1 hamiltonian:16 ref:1 anisotropy:5 proposals:1 solution:5 terminating:1 large:1 discrete:6 convenience:2 math:2 science:2 indices:2 study:2 noted:2 possibility:1 jhep:2 smaller:3 zh:1 braneworld:2 folds:5 sin2:2 sign:1 approximation:2 located:1 rate:2 cyclic:1 evaluated:4 dynamics:20 theories:1 canonical:3 even:5 eia:1 what:9 plays:1 appear:3 giving:1 section:5 3w:1 labeled:2 expressed:5 reheating:7 version:1 turnaround:2 causes:1 reconstruction:1 basic:2 new:5 3a:1 increasing:2 acknowledgments:1 seeks:1 piao:7 crunch:1 iσi:1 focuses:1 led:2 behavior:7 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