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0705.0025.txt |@word cs:1 hc:1 arxiv:1 may:1 |
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0705.0035.txt |@word sector:1 logarithms:1 evidence:1 consider:3 represent:1 varying:1 results:31 existing:1 gg:1 scalar:9 squarks:1 houches:1 edu:2 go:1 cteq6l1:6 remarkably:2 denotes:1 contributions:2 mandelstam:4 issues:1 looking:2 ac02:1 γs:2 graph:1 finally:3 present:2 stable:1 discovering:1 details:2 include:5 nason:2 p2:3 1pi:2 outside:1 very:4 rise:2 account:2 focus:2 figs:2 mixing:1 difference:4 exact:1 condition:1 tri:1 four:1 gov:2 level:13 cause:1 p5:1 t2:4 haber:2 correct:3 large:15 c33:2 small:8 mangano:1 equation:1 application:1 expanded:2 consistent:6 lightest:2 prediction:4 sign:1 zero:2 evaluated:2 follow:1 further:3 dynamics:3 estimated:1 odd:2 expressions:3 reina:5 required:1 even:8 what:1 essence:1 appear:1 cµ1:4 laenen:1 giving:1 section:44 labeled:1 find:4 current:3 d0:3 above:4 new:2 acknowledgments:1 prefactor:1 coefficient:1 partonic:4 full:5 caveat:1 respectively:7 residual:3 here:2 agreement:1 lep:6 les:1 nnnlo:21 web:1 represented:2 based:1 entire:1 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0705.0036.txt |@word sci:1 consider:6 chain:1 results:5 leads:1 amplified:1 contributions:2 fontannaz:1 γx:1 calculate:4 γk:1 present:5 te:1 case:3 focus:2 experimentally:1 rapidities:3 bondarenko:1 jha:1 gg:6 die:1 solution:4 large:4 small:10 kolhinen:2 probably:1 dis:1 upper:1 smaller:1 ingelman:2 among:1 direct:3 cosh:1 second:1 enhancement:23 further:1 dynamics:2 estimated:2 quite:2 what:1 nonlinear:20 rate:1 section:14 virtualities:1 brief:1 above:1 new:1 contributes:1 cgc:2 unintegrated:2 full:1 ibid:2 kowalski:2 hera:4 component:2 here:2 ratio:11 tevatron:1 equations:6 instituto:1 incoming:1 cern:1 involved:1 study:4 studied:2 dy1:1 vogt:3 amount:1 resulting:2 usually:2 glr:5 enberg:2 via:3 followed:2 gluons:4 scales:3 orginos:1 weigert:3 gluon:19 medium:1 a692:1 takes:1 would:2 distinct:2 predictions:3 process:4 nucl:13 qcd:7 theoretical:1 diagrams:1 more:5 fractions:1 partons:3 initiated:2 b463:1 validity:2 glass:1 particular:6 kumar:2 account:1 decouples:1 equation:8 work:2 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0705.0040.txt |@word sci:1 consider:5 global:1 results:4 proposition:4 kato:3 expressions:1 whose:2 c0:6 re:1 uniqueness:1 preserved:1 under:2 norm:3 ingredient:1 applied:1 frequencies:5 choice:1 putting:1 microlocal:1 bounding:1 condition:2 solves:1 did:1 notes:1 solution:22 large:2 science:2 βx1:1 barbara:3 commented:1 edu:3 estimates:7 second:2 l2t:2 l2x:7 even:1 established:1 what:1 nonlinear:1 sum:3 version:1 above:8 sup:14 ˆh:1 new:2 increasing:1 method:1 coefficient:3 respectively:1 here:1 desired:3 tǫ1:5 strong:2 equations:16 contraction:3 obtained:2 sobolev:1 studied:2 allows:1 reports:1 fourier:1 studies:2 via:1 projection:3 classification:1 apr:1 hardy:1 sgn:1 apply:1 establish:3 rω:1 derivatives:1 use:5 prove:7 positive:7 negative:6 strauss:1 next:1 derivation:1 therefore:8 iteratively:1 type:3 tk:2 formally:4 becomes:1 operators:7 odinger:12 appendix:3 particular:1 hold:1 iii:3 must:1 integrating:2 recall:1 equation:26 mk:2 vega:3 following:9 ivp:3 proof:9 involve:1 assumptions:2 regularization:1 decaying:2 holds:3 kenig:3 write:2 paley:1 tǫ:2 pure:3 parameter:1 priori:3 simplicity:1 singular:1 may:1 earlier:1 needs:1 dx1:32 hence:1 multiplication:1 data:8 parallel:1 realized:1 third:1 hypotheses:1 so:5 sn:1 every:2 order:5 words:1 schwartz:2 symbols:2 helena:1 existence:8 satisfies:4 still:1 its:1 group:1 decay:3 fix:1 solving:2 lp:1 mail:3 main:1 lx:1 split:1 maximal:1 duhamel:1 eiθ2:1 integral:1 noticing:1 dxα:5 geodesic:1 effects:2 dxβ:2 term:1 university:3 inequality:11 l2:33 l1:1 repeating:1 2i:4 kappeler:1 2k:8 weighted:2 ei:1 energy:6 related:3 frequency:2 combining:2 our:3 rt:7 space:4 res:1 since:8 denotes:2 fellowship:1 ajk:1 dxdt:6 formula:1 rn:4 suffices:4 math:11 shows:3 benjamin:1 linear:3 free:2 standard:2 difficulty:1 calder:2 california:3 ask:1 e4:3 estimate:14 e2:2 definition:3 qj:1 r1:1 r2:2 omit:1 βx:2 int:1 place:2 exponentially:2 consequence:1 onto:2 support:1 first:7 xj:7 xk:1 initial:4 ono:1 xl:6 xm:30 omitted:1 primary:1 u0:6 restrict:1 done:1 precisely:1 xt:2 size:1 dispersive:1 given:3 necessarily:1 reference:1 similarly:1 introduction:1 interact:1 system:8 construct:7 needed:1 1d:1 final:1 speaking:1 gives:1 centered:1 immediate:1 part:3 authors:1 norms:1 x3:1 coefficients:2 showed:1 double:1 zero:3 project:1 fˆ:1 were:1 projections:1 hz:3 generality:1 rewrite:1 craig:1 ann:1 argument:7 roughly:2 manner:1 need:1 clearly:1 gagliardo:1 ideas:1 note:3 instance:1 take:4 persistence:2 shall:3 viscosity:1 involving:2 class:3 doi:1 χr:2 consequences:1 considered:2 flow:1 principle:4 35b65:1 fact:3 show:2 supported:5 x2:10 spaces:1 postdoctoral:1 solutions:12 find:7 finally:2 escauriaza:1 aφ:17 commutators:1 enough:1 lemma:5 x4:2 parabolic:2 local:4 ied:1 do:2 strichartz:1 notation:2 ϕu:1 de:3 ωdr:1 dx:28 compute:2 dt:14 gen:1 secondary:1 evolution:2 arxiv:1 wish:1 qk:23 fixed:1 ql:1 satisfy:1 multiplying:2 exists:7 see:4 result:3 fail:1 dyadic:1 nonstandard:1 subject:1 hilbert:3 inequalities:1 artificial:1 µm:2 written:1 boundary:2 approach:1 notice:4 terms:1 extend:1 however:1 hypothesis:3 key:1 both:6 ill:1 comm:4 pde:1 finds:1 among:1 co:4 conclude:1 continuation:2 ca:13 address:3 dimensional:2 grants:1 constant:1 described:3 addition:1 eβx:8 three:1 been:2 molinet:1 cauchy:2 pk:14 define:7 corresponding:1 observe:4 general:1 case:8 eit:3 exponential:1 littlewood:2 eix:2 value:3 hdx:1 will:12 behavior:1 ǫt:4 property:1 taking:2 coupled:4 thus:3 iw:4 ii:2 regularity:1 im:1 author:1 belong:1 same:1 any:6 parts:1 arguments:1 proved:1 several:1 independent:2 lie:1 absorb:1 hand:3 arose:1 4ca:1 prescribed:1 lower:1 schr:12 onedimensional:1 page:1 well:4 posedness:3 academic:1 without:1 solve:3 left:2 cj:3 obtain:6 scattering:1 letting:3 family:1 character:1 except:1 other:1 combine:1 theorem:7 semigroup:2 guarantees:1 generalized:4 real:1 depends:1 advances:1 iβ:3 posed:2 know:2 press:2 using:10 unique:4 loss:1 necessary:1 follows:9 korteweg:3 arbitrary:1 works:1 essential:1 therein:1 right:1 some:4 back:1 supplementary:1 specified:2 kdv:3 ourselves:1 describing:1 extensively:1 ucsb:3 decomposition:2 provides:1 assuming:1 yields:2 proc:1 refer:1 run:1 equivalent:2 step:1 santa:3 properties:3 l1t:10 introduces:1 dependence:1 side:3 ensure:1 cutoff:1 into:4 obtaining:1 bound:1 nsf:2 ppl:1 lies:1 appropriate:1 acad:1 references:2 operator:2 schrodinger:7 nirenberg:1 strictly:1 there:7 transform:4 ponce:11 smoothing:3 appl:3 notices:1 was:5 assumes:1 function:9 complete:1 form:1 2iβ:5 differences:1 denoting:1 but:2 gain:1 removed:1 hf:1 hd:1 applying:3 supp:10 ut:2 supt:2 bounds:1 us:1 below:1 limit:1 uk:1 problem:5 more:1 similar:3 associated:4 computing:1 defined:2 abstract:1 proven:1 denote:2 ap:9 engineering:1 av:2 eralized:1 dawson:7 functions:4 qθ:1 nd:1 multipliers:1 interested:1 nat:1 department:3 mathematics:5 symbol:1 uniformly:2 commutator:4 bounded:1 variable:5 structure:1 uncoupled:2 assume:1 vries:3 dτ:4 interval:6 time:10 once:1 |
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0705.0042.txt |@word replacing:4 represent:2 logarithms:1 consider:4 illustrates:1 equalities:1 results:4 leads:1 eds:2 commute:1 edu:3 consists:2 follow:2 primes:1 research:2 children:1 gi:1 whose:8 preserves:1 inverse:8 calculate:1 graph:105 equivalence:8 lsa:1 uniqueness:1 preserved:1 th:1 under:3 γb:2 analogous:1 p2:57 labels:1 g1:9 rise:4 differently:1 splitting:1 corollary:12 every:13 additional:1 lecture:2 animals:3 difference:2 partitions:2 four:4 squares:1 exponential:4 immediately:2 roy:1 proc:1 notes:2 corneil:1 list:2 joined:1 discrete:2 proposition:4 recall:5 indices:4 prins:1 noted:1 still:1 zm:5 des:1 neighborhood:23 zf:4 zg:13 zb:4 zc:2 translating:1 second:3 quebec:2 gn:9 further:1 zp:11 zq:1 canonical:1 index:13 sum:4 expressed:7 agrees:1 above:3 new:9 construction:2 superimposition:18 contrast:1 coefficient:2 multivariate:1 sinks:1 degree:9 bergeron:1 join:5 like:1 component:3 here:2 analytiques:1 sink:1 groups:2 address:2 represented:2 november:1 strong:4 respect:1 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