text
stringlengths 0
190k
|
|---|
0705.1611.txt |@word represent:1 gu:5 2nπ:1 sci:1 chinese:1 rev:30 oss:1 results:12 leads:1 grateful:1 edu:1 consists:1 expressions:3 localized:1 ots:1 chain:1 γs:1 irrelevant:2 shanghai:3 ts:4 gu2:1 charge:10 critical:5 γc:1 divergent:1 alternating:1 eiq:1 conjecture:2 supported:1 straightforward:1 very:3 macris:2 wave:8 electron:1 fan:1 voit:2 difference:5 rapidities:1 condition:2 impressive:1 hamiltonian:11 large:8 solved:1 small:11 mn:1 mila:1 unpolarized:2 approximation:1 πc2:2 zero:1 dynamics:1 quite:1 canonical:1 even:2 will:3 appear:3 luchini:1 section:3 brief:1 expressed:1 new:2 net:1 method:10 edited:3 condensed:1 full:1 degree:1 respectively:5 never:1 equals:1 here:6 atoms:1 following:1 china:2 ansatz:1 separation:11 2kc:1 strong:1 observing:1 appears:1 superconductor:1 calculate:1 obtained:7 convert:1 institute:1 study:3 studied:3 approaches:1 suggests:2 loop:1 stiffness:1 hospitality:1 york:1 named:1 tosatti:1 term:4 figure:1 scales:1 understanding:1 φs:5 highly:1 excellently:2 use:1 νs:1 assaad:1 contains:1 lemberger:1 finally:1 giamarchi:1 process:1 therefore:1 until:2 hahm:1 clearly:3 becomes:7 operators:4 excellent:1 known:2 foundations:1 cases:1 lema:2 iii:2 fermionic:1 high:1 equation:1 work:5 modified:1 theories:1 vs:12 obvious:1 shelton:1 believed:1 example:1 decoupled:2 ions:4 compare:1 indicated:1 give:3 calculation:1 organized:1 δv2:6 sample:2 indicates:1 chin:1 numbers:1 νc:1 sense:1 interpreted:1 species:1 get:2 occur:1 how:1 nontrivial:2 coleman:1 parameter:1 sin:28 shiba:1 de:1 mat:2 may:2 max:1 after:1 hong:2 diagram:4 plane:1 fd:1 evaluations:1 cuhk:2 data:1 response:2 constants:1 liquid:2 ss:4 spectra:1 korepin:2 sj:1 hfk:1 hfm:1 correlation:13 ohmann:1 gagliano:1 nersesyan:1 order:3 carmelo:1 pointed:1 move:1 displayed:1 kong:2 produced:1 paper:1 committee:1 dw:1 its:4 diagonalized:2 derive:1 thank:1 decay:1 exact:5 boson:1 li:1 degrees:3 systems:1 schmidt:1 might:1 them:2 greater:1 jiaotong:1 universality:1 introduce:1 band:3 half:8 souza:1 now:1 discuss:1 nos:1 february:1 always:2 university:3 filling:11 mode:1 each:1 instability:3 heavy:1 el:1 directly:1 energy:3 bosonization:12 investigated:1 static:2 quantum:7 our:6 happen:1 transitions:3 eq:2 out:1 shown:2 dominates:1 factors:1 rep:1 since:4 crucial:2 denotes:2 cabra:1 suggesting:1 got:1 dominate:1 ri:2 math:1 theory:2 state:7 divergence:2 given:3 standard:4 clarify:1 completely:1 falicov:4 ocdw:1 onsite:1 interaction:7 transition:9 phy:1 ath:2 vc2:3 hence:1 essler:1 first:3 symmetry:1 reveals:1 third:1 variables:1 municipality:1 number:1 dominating:1 another:1 umklapp:4 size:2 πc:2 differ:1 temperature:4 πs:2 introduction:1 behaves:1 πn:2 system:10 their:4 wonderful:1 fermions:5 exponents:6 1d:10 asymmetric:4 exactly:1 larger:1 optical:2 than:1 ogata:2 kind:1 effective:2 showed:1 acknowledgement:1 limiting:1 annihilation:1 matter:3 states:1 classes:1 str:1 bosonize:1 olyom:1 correction:1 lin:7 say:1 seen:1 concentration:6 apparently:1 tσ:3 viewed:1 relatively:1 strength:1 umper:1 min:1 convenient:1 chessboard:1 online:3 so:4 ueltschi:2 singlet:1 algebraic:1 condens:2 timonen:1 phase:36 luttinger:2 cazalilla:1 kc:16 kf:36 αss:1 later:1 physica:1 kl:1 ks:16 definitely:1 electrons:14 exp:4 schulz:1 velocity:1 effect:2 physics:9 review:1 fact:4 ho:1 nsfc:1 bosonized:3 show:3 nσ:1 cdw:7 relation:1 find:3 ground:4 based:1 knowledge:1 itinerant:1 parrinello:1 enough:3 analytic:1 going:1 factor:4 constant:1 local:1 mixture:2 means:1 dependent:1 simplest:1 freezing:1 dx:8 lattices:1 years:1 baeriswyl:2 densities:2 tsvelik:1 πs2:2 approach:2 arxiv:2 summary:3 europhys:1 predicted:2 analytical:3 compressibility:1 view:1 ignored:2 exists:1 undergoes:1 see:3 discussions:1 close:1 phases:1 interacting:1 away:6 sites:1 µs:3 written:1 between:7 αi:4 limit:2 boundary:3 conditions:5 email:1 µc:3 triplet:1 terms:5 doma:2 attention:1 focus:1 wj:2 however:1 incommensurate:1 vanishing:1 comm:1 jk:1 bose:4 configuration:2 problem:2 suggested:1 both:3 hypercubic:1 last:2 many:2 region:6 according:1 propagation:3 figures:1 dated:1 drut:1 tll:3 cj:4 ch:2 fields:3 point:4 color:3 dimensional:6 decreases:1 cancel:1 proved:2 ps:8 pp:1 devreese:1 described:1 decoupling:1 tomonaga:2 due:2 been:7 strategy:1 varma:1 rgc:1 interpret:1 interest:1 penc:2 empty:1 fig:5 chen1:1 corresponding:3 montorsi:1 gas:1 cos:3 deep:1 denote:1 spin:20 present:1 case:8 pacs:1 solid:4 nski:4 aim:1 while:1 behavior:3 procedure:1 kimball:3 vc:13 hoping:2 site:4 iv:2 ii:2 reads:3 fluctuating:1 cond:2 dual:1 different:8 hubbard:8 fkm:8 grant:3 suggest:1 belong:1 any:1 shifts:3 φc:5 diagonalize:1 largest:1 modification:1 δv1:6 finite:5 development:1 used:2 http:1 αts:1 singapore:1 numerical:9 nj:6 counterparts:1 hand:2 v2:3 delicate:1 infinite:2 sorella:3 macedo:1 recent:2 lower:1 modes:7 hopping:3 framework:3 nevertheless:2 well:2 analysis:1 evrard:1 solids:1 studying:1 quantitative:1 model:15 dimension:1 unified:1 reprint:1 captures:1 obtain:4 rest:1 vanishes:1 segregate:1 identify:1 world:1 campbell:2 useful:1 density:8 haldane:1 had:1 lattice:6 wu:1 other:2 lett:12 theorem:1 diagonalization:5 momentum:2 gave:1 finitetemperature:1 spinless:2 around:1 frahm:2 breaks:1 possible:1 plenum:2 increases:1 press:1 using:1 part:1 intersection:1 mod:1 fradkin:1 like:1 particle:1 kennedy:1 δv:22 follows:1 collective:4 velocities:3 freericks:7 integrals:2 clay:1 valence:1 mathematical:1 www:1 susceptibilities:1 whenever:2 creation:2 some:3 manifest:1 scale:1 dimensions:1 cσ:1 tongji:1 extensively:1 instantaneous:1 does:1 assuming:1 prog:2 vs2:4 scientific:1 celled:1 equivalent:1 jl:1 agreement:1 negatives:1 although:1 accompanied:1 conducting:1 oi:2 most:1 freedom:4 scdw:1 wang1:1 introduced:1 lieb:3 homogeneous:1 cambridge:1 final:1 presence:1 orders:1 into:1 integral:3 ahm:10 down:9 determine:2 doren:1 proportional:1 screened:1 bosonic:1 analytically:1 van:1 there:3 low:4 way:1 analyze:1 was:2 naturally:1 function:4 gubernatis:1 sdw:5 form:5 phenomena:1 hq:1 extended:1 volume:1 hk:1 neutral:1 segregation:1 hm:12 hb:2 line:6 true:1 temp:1 2πi:4 up:5 us:2 theoretical:1 url:1 model13:1 fermi:2 fluctuations:4 distribution:1 agree:2 regimes:1 diverges:1 ordered:2 halffilling:1 defined:2 describe:2 proven:2 general:2 conserved:1 exist:1 together:1 controlled:1 ramirez:1 gruber:2 physical:1 ni:3 functions:11 beyond:1 nl:1 dotted:2 no:4 when:4 ne:3 invalid:1 field:3 points:3 role:1 spatial:1 department:3 tech:1 theor:1 deviate:1 stat:1 superconductivity:2 models:1 important:1 kivelson:1 structure:7 brandt:2 regime:1 happening:2 coulomb:1 deng:2 pseudo:1 emery:3 governed:1 mass:1 bethe:1 parola:2 |
0705.1612.txt |@word represent:1 code:8 consider:2 particular:3 results:7 leads:2 eds:1 consists:1 expressions:3 devoted:1 whose:4 depend:1 graph:6 technique:2 presents:1 monotonically:1 th:3 under:13 nodes:6 ptimal:2 applied:4 belonging:1 supported:1 worse:1 advantage:2 far:1 p0:1 geometrical:1 suggesting:1 corollary:6 lecture:1 exact:2 condition:22 presented:5 transmission:1 positions:1 notes:1 solution:2 large:1 solved:1 science:1 small:1 referred:2 upper:3 smaller:2 occurrence:1 ten:1 sign:6 rate:13 design:3 ǫm:1 concludes:1 linear:1 even:7 onclusion:1 section:10 expressed:5 decoding:8 version:2 resilient:1 new:2 increasing:1 ˆl:2 coefficient:1 relationships:3 degree:44 respectively:2 never:1 residual:1 tangent:3 possibility:3 represented:4 table:4 appears:1 knowledge:1 obtained:8 derivable:1 search:3 trans:3 study:1 studied:1 substituted:1 usually:3 adopting:1 fourier:5 changes:6 limx:1 via:1 useful:2 family:11 apr:1 tools:3 readily:1 plot:1 permitted:7 feb:1 usa:1 commun:1 positive:64 negative:4 optimize:2 depicted:3 associated:1 achieving:9 more:4 zeroes:1 introducing:1 becomes:1 berlin:1 everywhere:1 varying:1 known:10 cases:8 hold:1 iii:2 must:1 none:1 crosses:1 permits:1 recall:2 equation:3 work:1 values:13 following:10 bipartite:1 root:1 example:1 proof:4 control:1 practical:1 indicated:1 process:1 allowed:1 organized:1 states:3 minimum:10 performed:5 sense:2 verlag:2 information:1 discussion:1 holds:4 feature:1 regions:1 very:4 optimal:7 parameter:3 ensemble:5 express:1 algebra:1 may:1 after:1 diagram:2 fc:1 develop:1 choice:1 compatibility:1 third:3 sept:2 inform:3 fp6:1 so:1 decreasing:1 playing:1 developed:4 thresholds:8 satisfied:1 stability:1 paper:6 mentioned:1 existence:1 still:1 ieee:5 its:1 roots:11 xl:4 chosen:2 fix:1 exhibits:1 according:3 degrees:3 fig:6 derivative:3 main:1 correspondence:3 them:1 good:4 greater:3 numerically:1 enrico:1 they:3 symposium:1 univocally:1 represents:1 several:4 equality:4 name:1 fully:1 university:2 ashikhmin:1 sufficiently:1 inequality:2 transmitted:1 each:1 xℓ:5 identifies:1 european:1 characterized:2 constraints:11 subset:3 int:2 differential:4 ew:1 special:2 really:1 shown:9 acknowledgment:1 discrete:4 restricted:1 furthermore:1 since:1 denotes:1 looking:1 modulation:1 investigation:1 rational:1 denoted:1 formula:3 plotting:1 theory:5 free:1 quite:1 admits:3 besides:2 put:1 definition:2 pairs:1 spielman:1 could:2 iterative:1 ist:1 length:3 heck:1 leading:1 hence:5 approaching:1 first:9 xk:1 xi:7 ntroduction:1 probability:3 number:18 channels:1 directly:2 venezia:1 message:2 open:1 given:14 necessarily:1 reference:1 bologna:2 least:2 their:2 statement:1 vehicular:1 structures:2 tangency:2 ptimization:1 tool:3 continuous:1 proving:1 plane:2 part:1 authors:2 x2:6 x1:5 than:7 coefficients:6 bec:11 iteration:1 second:5 project:1 sweden:1 contrary:1 were:1 exhibit:4 michele:1 curves:2 unavailability:1 null:1 any:12 zero:1 depending:2 efficient:1 lin:1 able:1 note:1 instance:1 recognizing:1 without:6 channel:6 allerton:1 formulas:1 shokrollahi:4 chart:1 most:1 regular:31 germany:1 codeword:2 extremely:2 class:10 observation:2 considered:2 sometimes:1 coincides:1 order:3 looked:1 barbeau:1 points:4 principle:2 chiani:2 fact:6 manipulation:1 solutions:2 threshold:46 substituting:1 find:1 o:3 based:3 ensembles:6 parameters:1 outside:1 luby:1 analytic:8 only:10 explicitly:1 summarizing:1 over:1 achieve:4 erasure:10 xdc:2 means:1 de:8 brink:1 dc:79 mitzenmacher:1 xdv:1 ones:1 despite:1 dv:6 during:1 reveal:1 evolution:5 approach:3 arxiv:1 imposed:2 wish:1 fixed:13 valid:2 view:1 set:14 fossorier:1 exists:2 achieved:3 imposing:1 bounds:1 detection:1 differs:2 depends:1 computer:1 close:3 optimum:1 best:10 exploited:3 capacity:12 inequalities:4 currently:1 segment:2 symmetric:1 written:2 closed:13 between:17 αi:2 boundary:1 λl:33 conditions:2 email:1 x4:1 available:1 however:1 hypothesis:1 key:1 problem:6 thank:1 both:2 lass:1 last:2 irregular:2 region:8 annual:1 equal:6 admit:2 expression:13 arbitrarily:1 among:2 point:19 simple:5 paolini:2 pos:6 eferences:1 active:3 simply:1 iterations:1 sequences:6 polynomial:12 moreover:3 poli:1 pp:5 described:1 trajectory:6 three:2 been:10 commission:1 recognize:1 pj:1 pk:2 pi:3 pl:2 define:1 corresponding:6 sufficient:5 observe:1 general:6 those:1 case:7 exception:1 p1:1 developing:1 appearance:1 twenty:1 value:6 will:4 invoking:1 while:1 optimization:14 suppose:3 error:1 property:2 maximal:4 vol:3 vi:2 thus:2 non:2 iv:3 ii:5 optimizations:1 conf:2 technology:1 binary:4 different:2 constrained:4 italy:2 perform:1 belong:3 same:5 highlighted:1 finite:1 difficult:1 infinity:1 numerical:4 monticello:1 functions:3 counterparts:1 running:1 infinite:1 totally:1 gallager:1 cycle:1 lower:1 min:1 well:4 analysis:1 edge:2 sets:1 exploits:1 proposed:6 being:1 nd:4 kramer:1 obtain:6 ninth:1 λk:7 λi:15 previous:2 letting:1 oriented:3 intersection:1 density:6 except:1 counted:1 unambiguously:1 theorem:15 real:15 marco:1 evaluate:1 showing:1 possible:5 unibo:1 corresponds:1 afore:1 ldpc:10 using:5 bit:2 unique:1 correcting:1 loss:2 necessary:12 follows:5 admitted:1 specific:2 communications:1 always:7 recalls:1 parity:5 because:2 methods:3 namely:2 sequence:5 spring:1 some:23 springer:2 cs:1 examples:3 respect:2 matching:2 provided:1 ǫmin:6 does:2 exit:3 provides:1 tends:1 prof:1 proc:5 run:1 huber:1 equivalent:2 binomial:6 found:3 properties:5 about:2 constraint:4 dependence:1 recognized:1 compatible:1 involving:1 introduced:2 slightly:2 other:2 acm:1 into:1 within:6 obtaining:1 bound:3 due:1 right:1 determine:2 next:5 additional:4 removing:2 specifically:5 low:5 symp:2 was:4 function:5 form:17 differences:1 denoting:1 independently:1 but:3 true:1 he:2 made:1 applying:1 multiplicity:3 maximum:8 us:2 ωi:9 limit:2 ωl:2 distribution:54 similar:2 called:4 proved:2 computing:2 defined:6 certain:1 abstract:1 denote:2 exist:4 imai:1 distributions:44 check:45 constructed:1 again:1 mutual:1 codes:13 no:3 when:3 detail:1 application:1 priori:1 role:1 2dc:2 conclusion:1 node:3 phoenix:1 june:2 polynomials:5 develops:1 urbanke:2 variable:19 structure:1 algebraic:2 longer:1 algorithm:3 abscissa:1 assume:1 interval:1 together:1 equivalently:2 time:1 richardson:2 starting:1 |
0705.1613.txt |@word limited:3 gu:1 concept:1 partial:5 consider:7 madsen:2 global:9 focus:1 essai:1 gc:1 computation:1 gs:1 gm:9 gl:3 gk:24 gj:1 gi:1 devoted:1 certainly:1 inverse:1 graph:83 tn:1 present:1 under:1 undirected:29 applied:1 belonging:7 g1:5 g0:16 very:1 springer:2 results:1 glymour:1 corollary:5 condition:5 maxα:1 joined:1 fewer:1 solved:1 vector:9 independence:13 markov:21 upper:1 smaller:2 prediction:1 zero:2 estimated:2 will:8 sub:1 section:3 expressed:1 networks:2 intersect:1 new:4 coefficient:1 multivariate:3 full:8 simultaneously:1 degree:11 respectively:3 learn:3 component:3 here:1 separation:4 xβ:17 path:6 xα:25 obtained:2 search:2 items:1 vectors:2 allows:1 contradiction:1 published:1 cardinality:8 ekp:9 composed:1 useful:2 family:1 marginal:2 logical:1 univ:1 unit:1 independencies:5 use:1 proceed:3 prove:9 distinct:1 likelihood:1 whittaker:2 contains:3 next:1 pearl:2 m0:4 criteria:5 massam:3 scope:1 marginally:1 more:2 ecole:1 becomes:2 separates:12 known:1 iv:2 iii:4 pagination:1 ma:2 itself:1 values:1 starts:1 following:7 example:6 proof:11 figure:4 give:5 organized:1 high:1 indicates:1 sense:1 singletons:2 conversely:2 npcomplete:1 write:1 far:1 adjacent:10 parameter:2 product:2 drton:3 may:1 max:15 wiley:1 containing:2 connectivity:3 data:3 acyclic:1 lemmas:2 separations:1 correspond:1 st:1 cannot:1 so:37 subsequently:1 order:31 satisfied:3 paper:10 london:1 differs:1 existence:1 satisfies:2 its:3 before:1 perfect:10 le:1 outer:3 estimating:1 absence:5 mail:1 main:1 defining:1 variables:12 maximal:1 non:19 good:1 greater:1 than:6 wermuth:3 bernoulli:2 practice:1 separators:4 february:1 oxford:1 now:9 hall:1 represents:1 term:1 name:1 always:2 nationale:1 inequality:1 each:3 side:1 mean:1 subset:7 ek:17 series:1 revised:1 gaussian:7 carvalho:1 computable:1 geiger:2 loops:1 our:4 es:1 er:1 shown:1 matrix:3 space:2 res:2 furthermore:1 since:7 induces:1 looking:1 lauritzen:3 conjectured:1 denoted:5 induced:1 occurs:1 math:1 theory:1 conditioning:13 estimate:1 e1:8 e0:6 signaux:1 definition:7 pairs:1 applications:2 determining:6 could:2 v2:9 thing:1 isi:2 separator:19 hence:14 first:3 already:1 probability:15 xb:6 letac:2 xa:6 number:10 thereof:1 linking:1 another:1 xs:16 precisely:1 electronic:1 size:1 given:12 gpk:6 introduction:2 construct:1 needed:2 assumption:6 zeros:1 observations:1 statement:1 rajaratnam:2 perfectly:9 gives:1 relationship:1 exactly:3 part:1 uhlmann:2 separability:23 determined:3 pairwise:3 inferring:1 comput:1 ann:3 argument:1 chapman:1 say:3 disjoint:5 seen:4 concentration:19 any:24 emes:1 paths:1 min:7 efficient:1 latter:1 note:4 wishart:1 indexed:1 mit:1 continuous:1 multiple:1 friedman:2 nested:3 connected:22 pair:14 mach:3 doi:1 especially:1 clear:1 later:2 vertices:28 graphs:28 principle:1 joining:1 selection:3 show:3 random:12 purely:1 keywords:1 biometrics:1 d2:26 find:2 pe:1 based:1 should:1 jan:1 lemma:17 only:7 nachman:1 above:1 means:1 syst:1 de:1 subvectors:1 ones:1 altogether:1 applying:1 reprint:2 procedures:1 qp:1 arxiv:1 statist:3 contain:1 fixed:3 set:17 exists:9 see:18 justification:1 result:7 theoretic:1 said:1 kalisch:2 smallest:1 between:17 αi:2 tunis:2 αn:2 recently:1 missing:2 genet:1 however:1 york:3 article:1 problem:2 both:1 interpretations:1 last:1 cox:3 taking:1 according:1 estimation:3 expression:1 among:1 conclude:9 simple:2 corresponds:4 2nd:1 dimensional:1 represented:3 xγ:3 moreover:1 described:2 tremendous:1 due:2 been:1 pc:2 genetic:1 basic:1 flexible:1 wille:3 empty:14 define:6 graphical:16 corresponding:3 received:1 suppress:1 sufficient:1 covariance:12 modelling:1 assert:2 belvedere:1 bayesian:2 those:1 case:3 subsets:6 discrete:1 aim:2 suppose:6 property:15 procedure:4 studied:2 vol:1 vk:1 thus:4 equal:17 ii:5 vs:1 triple:3 different:2 belong:1 same:1 microarray:1 proved:3 finite:1 difficult:1 independent:3 used:1 infinity:1 markovianity:9 v1:1 intersects:2 edges:14 robust:1 well:2 analysis:1 obviously:1 edge:6 components:9 sets:1 model:12 decomposable:1 biometrika:1 immediately:1 inference:1 integer:1 tunisia:1 valid:4 easy:2 theorem:10 easily:6 typographic:1 spirtes:2 five:1 mol:1 press:2 using:16 rnu:1 follows:7 linial:1 either:4 stationary:1 because:1 methods:1 dempster:2 sequence:6 conditional:15 some:2 deduce:4 respect:4 chaudhuri:5 lead:1 connecting:1 assuming:2 minimal:9 illustrate:1 particular:1 algorithmic:1 equivalent:2 bi:5 bp:1 bs:2 properties:5 practical:1 remains:1 referred:1 consequently:1 em:9 cambridge:2 inclusion:1 causation:1 within:1 bound:1 three:3 references:1 determine:4 terminated:1 statistics:1 there:14 biol:2 accordingly:1 appl:1 low:9 ed:1 noncomplete:2 was:1 therefore:1 function:1 complete:15 subgraph:2 converse:2 analyse:1 but:2 msg:11 construction:1 larger:1 castello:5 true:1 directed:7 compute:1 wish:1 ancestral:1 maximum:5 us:12 below:2 diagrams:1 demonstrate:1 distribution:21 called:11 associated:7 defined:12 certain:2 influence:1 denote:1 eu:2 exist:1 ing:1 distributions:4 check:1 constructed:7 no:6 edwards:2 when:14 detail:1 other:4 test:1 conclusion:1 stat:1 models:15 vertex:7 precision:1 generated:1 important:1 variable:2 structure:1 network:1 implies:4 longer:1 algorithm:2 assume:4 richardson:3 quantity:2 starting:1 original:2 |
0705.1614.txt |@word gu:1 dist:4 consider:4 chinese:1 funct:1 brownian:6 results:5 leads:1 proposition:24 kulczycki:2 partial:2 γz:10 isometric:1 c0:10 depend:1 chain:1 γq:2 m2n:1 nonlocal:2 censored:12 uniqueness:1 γh:1 elliptic:8 stable:33 fronti:1 stochastic:4 2a8:5 ın:2 case:25 belonging:1 12k:1 g2:21 straightforward:2 song:10 regional:12 corollary:2 jacob:1 li:11 difference:1 condition:16 school:1 obvious:1 induction:3 vertex:1 singularly:1 convenience:1 vector:1 recall:3 small:4 markov:11 gruyter:1 martingale:2 still:3 zn:4 neighborhood:3 ga:1 estimates:20 measurable:2 jump:3 second:7 xτi:12 nonhomogeneous:3 follow:1 chen:11 further:3 dynamics:1 theory:5 aim:1 what:3 nonlinear:1 plays:1 sub:9 ere:1 giving:2 xσ:1 section:5 xτ:29 uniform:1 version:2 above:8 fractional:26 suppose:4 method:13 satisfy:4 garofalo:2 respectively:7 lipschitz:27 here:7 sinn:2 reported:1 objects:1 tangent:1 others:2 represented:1 studia:1 bogdan:12 equations:4 takeda:1 box:3 remark:12 relat:2 institute:1 involved:1 study:6 studied:2 contradiction:2 leaving:1 poisson:4 domains:5 fourier:1 y12:1 boundedness:2 formulated:1 classification:1 k5:2 gilbarg:1 replace:2 pxk:1 limk:2 feller:1 tp:2 tools:1 unit:3 derivatives:3 use:9 asymptotic:1 prove:36 positive:12 next:6 calculation:7 therefore:10 kumagai:2 2bk:10 associated:2 type:1 more:6 th:1 conclusions:1 operators:7 under:8 perturbed:1 berlin:1 appendix:1 particular:1 known:3 cases:2 hold:3 springer:3 ma:3 ρd:6 rβ:1 science:1 points:1 pour:1 mt:2 ey2:1 values:2 mr:1 following:20 example:6 proof:47 conference:1 f1:6 f2:2 omit:3 σli:4 give:7 process:20 sphere:1 assumptions:1 numbers:5 sense:1 sharp:4 yang:1 g1:1 pure:1 holds:10 principe:1 id:2 write:5 xσ1:4 get:11 csz:2 verlag:2 csq:3 sin:1 iberoamericana:1 r2n:1 mar:2 seoul:1 may:14 max:1 epsrc:2 applications:3 jumping:2 inst:1 coming:1 salsa:4 arch:1 constants:8 sets:14 lemmas:2 approximation:2 author:1 explicit:12 green:9 fundamental:1 definitions:4 op:1 order:10 nsfc:1 restriction:1 help:6 duke:1 l1u:3 mainly:1 choose:8 paper:14 through:1 y1:22 satisfies:8 y2:28 its:1 before:2 discontinuous:1 outer:3 τk:3 decay:5 ln:9 inward:1 adaption:1 τb:8 τa:3 better:1 systems:1 main:2 might:1 non:1 greater:1 yn:24 inductively:1 ye:1 noticing:14 introduce:2 reflected:16 scaling:7 they:1 half:2 yp:3 rotation:1 now:1 killed:2 bigger:2 term:1 dirac:1 2r:1 always:3 university:1 b3:1 orthonormal:2 inequality:36 l2:1 2a:4 l0:8 each:5 found:1 2n:7 ynp:4 side:1 mean:1 homogeneous:4 domain:13 differential:2 directly:1 simplicity:1 energy:1 related:3 γx0:2 used:6 ey:10 ex:16 measure:10 our:3 approximated:1 special:5 mat:3 space:1 xσk:12 furthermore:1 since:8 rev:2 acting:1 dominated:1 dxdy:3 conjectured:1 denoted:1 formula:8 rn:70 2k:4 ri:4 math:10 shows:4 bass:10 divergence:3 standard:3 york:1 dx:1 estimate:17 anal:6 nirenberg:1 definition:3 dirichlet:7 r0:29 r1:7 r2:7 r3:6 transition:1 phy:1 nonnegative:1 motion:6 xσ0:1 plane:2 place:1 hence:6 probab:5 generalizations:1 first:10 xk:27 xi:3 xn:19 probability:5 guan:5 primary:1 twisted:1 walter:1 2a4:1 multiplying:1 done:1 another:3 xs:2 xp:8 open:40 appl:3 xt:32 2k1:6 stochastics:1 given:9 perturbation:1 similarly:5 introduction:1 cc2:1 system:9 construct:3 their:3 perturbations:1 calculations:5 convention:2 jei:2 gives:8 eor:1 a34:1 academy:2 completed:1 continuous:5 proving:1 direct:3 erateur:1 assumption:2 part:1 cosα:1 x2:15 number:2 translation:2 x1:29 than:2 diffusion:2 distance:3 characterizations:1 sections:1 acknowledgement:1 dans:1 see:16 feathers:1 classes:1 were:2 bhi:19 generality:2 py2:1 argument:1 dθ1:2 zt:3 say:8 progr:1 harnack:40 need:7 any:12 seminar:1 relatively:4 6th:1 zero:8 depending:1 partly:1 studying:2 converges:1 k3:16 sciences:1 k1:101 potential:5 k7:2 take:6 ex0:6 jacobian:1 so:1 techniques:2 calculus:1 gδ:2 gγ:1 allow:1 normal:1 measures:2 birkh:1 simplify:3 beta:1 jul:1 significant:1 pair:1 analytically:1 probabilistic:3 class:1 observation:1 considered:1 clear:2 adopt:1 exk:4 tα:1 2nd:1 bracket:1 principle:7 li2:2 li3:2 subharmonic:3 nondivergence:1 show:5 supported:2 notations:4 spaces:3 relation:1 solutions:2 d2:1 find:13 d1:6 aρ:1 parameters:1 situations:1 enough:6 completes:4 lemma:51 only:9 generators:2 gb0:5 equilibrium:1 continuity:2 dk:6 notation:2 means:1 sup:32 aα:1 dz:10 aδ:2 words:1 dy:73 dw:3 dt:8 dr:15 ds:4 secondary:1 eme:1 processes:31 fields:4 arxiv:1 gbk:2 yield:1 2b0:2 cf:1 characteristic:3 including:1 fixed:2 kernel:14 set:37 exists:22 hα:5 comparable:1 j2:1 edition:2 depends:3 result:3 w1:1 y3:7 subject:1 satisfying:13 capacity:2 inequalities:10 fatou:2 uα:5 consequence:2 symmetric:21 outside:1 between:9 αi:3 boundary:34 conditions:10 email:1 available:1 notice:4 extend:1 importance:1 weak:1 however:1 wu:2 comm:2 ji:16 key:2 wp:22 distribution:1 improve:1 essentially:2 last:7 generator:2 σm:1 many:1 taking:8 τi:6 equal:1 dγq:2 oshima:1 otherwise:1 among:1 cn:1 point:9 cb:1 jk:13 harmonic:36 height:1 dimensional:3 bα:2 fukushima:1 moreover:2 throughout:2 pr:1 elliptique:1 strong:5 described:2 pw:5 equivalent:1 px:22 py:16 due:4 been:3 strategy:1 hitting:4 domaine:1 pa:3 xτ2:1 xτ1:7 xτ0:1 u10:5 ann:3 caffarelli:2 obtained:3 direction:1 corresponding:2 combing:3 cos:6 new:1 cones:1 generalization:1 univ:1 c3:15 c2:40 c1:34 general:8 former:1 present:1 applied:3 p0:6 τu:1 xτb:5 subordinate:4 xτk:3 rat:1 value:5 will:4 near:6 replaced:3 behavior:2 di:3 property:11 procedure:1 ix:2 characteristics:12 thus:10 vp:2 regularity:1 cone:4 ia:3 ib:2 k0:14 ig:4 different:2 verified:1 combining:1 began:2 same:16 check:6 ancona:2 parts:2 k2n:3 arguments:9 proved:10 finite:3 loughborough:1 independent:1 ball:1 i1:7 i0:6 i3:5 i2:8 upon:1 i4:5 hand:4 v1:4 v2:5 v3:2 auser:1 kim:5 dzdy:8 identity:1 recent:1 mech:1 reflection:3 older:5 x0:68 analysis:3 de:3 without:3 does:1 lim:11 coordinate:11 dimension:1 spherical:1 diffusions:2 τk0:2 obtain:1 λg:3 facts:1 letting:2 unique:1 preprint:2 lebesgue:2 k2:28 la:1 except:1 yt:4 s00:3 qx0:1 setting:3 extends:1 easy:1 theorem:35 τb0:2 formal:2 k6:3 identical:5 around:1 checking:1 big:3 showing:1 k4:14 dahlberg:2 boxes:1 know:2 destroy:1 integer:1 progresses:1 grenoble:1 amt:1 helpful:1 loss:2 k8:1 necessary:2 like:18 semi:1 follows:5 fabes:4 steps:1 because:10 functional:1 neumann:1 sequence:1 absolutely:1 some:41 ex1:3 a16:3 b0:16 examples:2 b2:3 respect:3 provided:3 a13:6 establish:1 cρ:1 shall:1 integration:2 critical:1 decomposition:1 refer:5 considering:3 power:1 kernels:1 uniformly:3 jumps:1 bk:4 references:1 approximating:1 super:12 properties:2 comparison:1 about:1 qing:1 extension:2 dθn:4 2h:2 theorems:1 discussed:1 yosida:1 pz:25 a2:3 a5:6 introduced:1 gb2:1 subset:5 generalized:1 h2:6 h1:14 integral:4 bound:1 remarks:1 right:1 cs0:4 laplacian:30 wα:1 operator:2 refined:1 methods:1 log:2 prepare:2 area:1 assumed:1 there:31 transform:4 u2:1 borel:1 way:2 was:11 function:60 trudinger:1 gρ:1 complete:1 form:6 hp:10 extended:3 heat:8 construction:1 schilling:1 indiana:1 convergence:1 burdzy:8 supy:2 made:1 applying:10 supp:1 levin:2 smooth:2 up:11 differentiable:1 below:8 un:2 limit:1 carleson:7 uk:1 ωn:3 continuously:5 problem:3 define:17 similar:12 called:4 b1:10 ac:3 later:6 constant:42 choosing:4 defined:9 abstract:1 describe:1 determinant:1 denote:18 exist:5 θn:5 inf:13 dγ:10 constructed:1 again:1 functions:31 compared:1 us:1 coefficient:1 no:14 when:24 vanishes:6 application:1 finish:1 other:5 role:1 details:2 glas:1 mathematics:3 px1:1 conclusion:5 a15:9 a14:6 px0:4 a11:3 a10:6 calculating:1 a12:3 sided:1 problems:3 includes:1 a1:4 a3:4 important:1 bounded:14 a4:4 a7:5 a6:7 a9:5 a8:20 structure:2 implies:7 assume:37 equivalently:1 fact:4 time:1 international:1 starting:2 original:1 |
0705.1615.txt |@word monte:1 code:1 consider:5 pointing:1 creminelli:2 results:4 exceeding:1 ciar:1 broader:1 talks:1 follow:1 excludes:1 depend:2 remarkable:1 paris:2 tt:1 finally:1 critical:1 spain:1 th:1 under:1 alberta:1 te:1 case:3 supported:1 very:3 difference:2 final:3 level:3 cmb:20 duquet:1 large:1 vector:2 team:2 dip:2 upper:1 sapienza:2 ifac:1 consistent:2 estimates:2 sign:1 astrophys:5 second:1 d69:1 estimated:3 carlo:1 wmap:10 spectral:1 what:2 errors:1 sub:1 section:4 selected:1 while:5 orski:4 wolfe:1 experiment:3 above:1 new:2 era:1 respectively:1 gathered:1 realizations:4 here:5 analysed:1 reported:2 tangent:1 groups:1 berkeley:3 represented:1 ratio:1 along:2 quite:1 galilei:1 obtained:4 search:1 canadian:1 institute:4 larger:3 mib:2 through:1 excursion:1 astrophysique:1 survey:2 usually:2 χ2b:8 conveniently:1 fourier:1 plotted:2 uniquely:1 via:1 scales:3 highly:3 apj:6 aimed:1 apc:1 total:4 asi:1 plot:2 use:6 usa:8 contains:1 suppl:1 france:1 comparing:1 m1:6 m0:5 m2:6 analysing:1 theoretical:3 more:2 flat:1 skewness:2 ti:7 about:1 bartolo:2 tested:2 transient:1 degrade:1 kurtosis:3 timestream:1 mf:2 ma:1 mc:13 work:1 mi:7 mj:4 reproduce:1 erf:1 marginalized:1 values:4 three:9 those:2 making:2 dec:1 latitudes:1 riotto:1 control:2 3yb:1 compare:2 weaker:2 cosmological:1 division:1 piacentini:2 neglected:1 purposes:1 high:7 assumptions:1 performed:1 want:1 sense:1 times:1 routines:1 conclude:1 provide:1 divided:1 get:2 csa:1 s4:4 regions:3 maps:24 hot:1 fourth:2 significance:1 instead:1 parameter:4 sim:1 map:22 rept:1 galactic:2 description:1 may:3 mjb:1 after:1 southern:1 mapping:1 demanding:1 plane:2 timelines:1 date:3 data:34 sz:1 vielva:2 third:1 sets:1 slightly:1 spectra:2 departure:1 ghz:6 cosmology:3 s3:5 so:4 block:1 order:7 help:1 indeed:1 thresholds:1 displayed:2 osservatorio:1 produced:4 course:1 experiments:2 including:2 statistical:1 cold:1 replicating:1 its:5 shallow:4 observational:1 huterer:1 style:1 derive:2 group:1 surviving:1 fit:6 la:2 chosen:1 better:1 detected:1 primordial:5 degrees:5 fig:10 inaf:1 wales:1 main:1 defining:1 pixel:7 non:8 good:1 pure:1 nside:1 effects:4 they:1 optimal:1 oxford:2 now:3 down:1 february:2 moscardini:1 fully:1 university:8 presented:1 realistic:1 theory:1 each:4 found:6 universit:4 higher:1 side:1 constraints:6 subset:1 square:5 significantly:1 devised:1 ee:1 density:1 mapmaking:1 gaussian:23 related:1 cf24:1 milan:1 frequency:1 expect:1 entering:1 year:1 laboratory:3 beyond:1 eq:4 borne:1 canada:4 montroy:2 matrix:3 space:10 restricted:1 3rh:1 rev:4 projected:1 research:1 rd:1 posteriori:1 dominated:2 ra:1 istituto:1 suggesting:1 forth:1 shows:5 foreground:2 linear:4 lawrence:1 derived:3 confidence:2 mechanisms:1 fisica:3 weakly:1 curto:2 completely:1 statistics:3 california:2 estimate:2 generate:1 gott:2 χ2i:1 pixelized:2 joint:6 could:1 cosmic:2 days:1 keep:1 counterpart:1 introduction:1 length:2 produce:3 gasperis:2 due:1 hence:3 retain:1 onto:1 top:2 first:5 spergel:4 features:2 probability:3 rms:2 distibution:1 number:4 references:1 restrict:1 fits:2 quality:2 angular:4 given:4 perturbation:2 temperature:2 jet:1 tor:2 dipartimento:1 realistically:1 their:4 perturbations:1 draft:2 linearities:1 starkman:1 esac:1 white:1 national:1 way:2 gls:2 centered:2 copi:2 task:1 binned:1 part:2 western:1 simulate:2 authors:1 than:6 toronto:4 observed:3 target:1 ipac:1 zero:1 submitted:2 smoothed:1 future:1 amplitude:1 tion:1 cabella:2 measure:2 spectrum:3 correspond:1 antarctica:1 headings:1 close:1 constrained:2 any:5 place:1 built:1 liguori:3 latter:3 agency:1 physique:1 polarization:5 sciences:1 potential:4 build:2 finding:5 negligible:1 detector:2 sect:1 even:2 hoover:1 trace:1 centre:1 simulated:7 effective:1 most:2 detect:1 connected:1 plan:1 significant:3 sophisticated:1 measured:2 quantify:1 probes:1 latex:1 deviations:1 observation:1 minimum:1 calculated:1 detectors:1 repeated:3 fluctuations:3 looked:1 principle:2 exp:1 cℓ:3 constrain:5 left:4 physics:7 reserve:1 spaced:1 show:5 text:2 random:1 degrades:1 threshold:1 degraded:1 trivial:1 find:2 impact:1 based:7 explain:1 ox1:1 controls:1 should:1 only:6 version:3 factor:2 sierra:1 employed:1 oct:1 do:1 lobo:1 correctly:1 di:8 beams:1 de:12 expectation:1 firenze:1 beam:1 cannot:1 procedures:1 gen:1 following:1 arxiv:1 paper:2 convolve:1 switzerland:1 london:1 fortunately:1 view:3 scanning:2 set:13 computed:3 robustness:1 sensitivity:5 correlations:2 statistic:2 detection:2 see:3 college:1 result:1 terms:1 contour:1 best:3 subject:1 archeops:1 propulsion:1 functionals:5 cambridge:2 µk:4 diamonds:1 crude:1 justified:1 across:1 recently:1 vertical:4 complementary:2 healpix:4 weak:2 however:4 wu:2 hypothesis:3 jointly:2 contamination:2 pixels:3 jb:3 thank:1 gaussianity:7 both:2 improved:2 limits:12 desired:1 region:11 conclusions:2 according:2 against:3 sensitive:3 tour:1 komatsu:5 figures:1 vergata:2 variance:1 contribution:2 fnl:41 con:1 among:2 ci:2 l27:1 cl:7 sky:6 ca:5 harmonic:1 sampling:1 dimensional:1 adding:1 respect:1 throughout:1 suppressing:1 locally:1 radiative:1 sachs:1 been:9 strategy:2 combined:1 expected:2 ph:4 define:5 contribute:1 flight:1 precision:1 epartement:1 systematic:2 astron:1 worked:1 evidence:1 spirit:1 present:1 applied:1 domon:1 subsets:1 empirical:5 value:4 will:1 dept:3 b03:19 behavior:2 error:2 couplings:1 procedure:3 release:1 identical:1 would:1 simulations:7 thus:3 them:1 eve:1 claimed:1 technology:3 elements:2 santos:2 natoli:2 italy:9 perform:2 balloon:1 radiation:1 cross:2 same:4 lbl:1 d70:1 φg:4 resulting:1 several:1 european:2 independent:1 used:2 effect:2 counterparts:1 hand:1 parametrized:1 constraining:1 moment:1 flown:1 purpose:1 multipoles:1 relies:1 genus:2 off:1 well:4 analysis:17 calibrated:1 residuals:2 frequentist:1 roma:7 firstly:1 model:2 maxima:1 stringent:2 moments:2 edmonton:1 sources:1 mfs:13 predicts:1 jcap:1 sampled:2 preprint:1 oliveira:1 regarded:1 point:2 smith:2 parametrization:1 bolometers:1 supercomputers:1 signals:5 instrument:1 pasadena:3 lett:1 stable:1 real:2 tests:5 increased:1 psb:2 bands:1 showing:1 astronomico:1 nersc:2 eorique:1 cruz:2 background:2 press:1 using:11 winitzki:2 follows:2 signal:12 alice:1 specific:1 keble:1 steps:1 sezione:3 reduced:3 grouping:1 draw:1 right:4 madrid:1 some:1 searching:1 vsa:1 towards:1 cleveland:1 ourselves:1 provided:1 flagging:1 cnr:1 bottom:2 though:1 integration:1 microwave:2 does:2 schmalzing:2 assuming:1 yields:1 noise:13 power:6 agreement:1 rue:1 shifting:1 although:1 explicitely:1 emulateapj:1 between:3 panel:7 stokes:1 pipeline:2 actual:1 working:1 extension:1 oh:2 dependence:1 simulation:2 compatible:1 estimator:9 plus:2 horizon:1 eight:1 efforts:1 mean:5 consequently:1 other:1 road:1 d63:1 computational:2 letter:1 into:1 nsf:1 dataset:5 assess:2 because:2 accounts:1 estimators:1 cardiff:2 ontario:2 institut:1 area:2 normalised:1 transfer:2 imperial:1 quadratic:3 low:2 kosowsky:2 astrophysics:2 analyze:1 was:2 function:3 tight:1 form:1 analyse:1 histogram:2 astro:4 cedex:1 properly:1 mnras:5 line:4 padova:3 infn:3 compute:3 embedded:1 minkowski:2 gravitational:3 systematics:1 up:1 us:1 different:1 projecting:1 limit:3 uk:4 boomerang:7 distribution:7 panels:3 similar:2 uc:1 ab:1 pin:1 defined:5 abstract:1 describe:1 deep:4 general:1 single:2 implement:1 goodness:5 our:15 nazionale:1 accounting:2 typeset:1 check:1 inc:1 again:1 functions:2 compared:2 no:5 when:1 mimic:1 ng:20 field:7 valid:1 statement:1 department:3 mathematics:1 deviation:1 briefly:1 over:1 covariance:5 generated:1 important:1 massachusetts:1 astronomy:2 jones:2 instrumental:1 correlated:1 coupling:4 algorithm:1 requires:1 interval:1 mask:1 masi:3 portion:1 nasa:1 time:1 far:1 matarrese:2 resolution:4 having:1 evenly:1 |
0705.1616.txt |@word limited:1 since:1 evidence:1 consider:6 griggs:1 holman:1 interference:6 graham:1 global:13 bandgap:1 focus:4 leads:2 latter:1 broader:2 crete:3 follow:3 expressions:4 faster:4 gj:2 localized:1 phenomenon:1 whose:1 preserves:1 gases:3 depend:1 superpositions:1 attracted:1 tt:1 keeping:1 quasi:1 tm:6 those:2 under:13 ivanov:1 insights:1 presentation:2 worth:5 necessary:1 castin:1 interacting:9 lack:1 riou:1 advantage:1 orthogonal:1 far:6 frequencies:8 peaks:5 bilinear:2 none:2 seemingly:1 wave:2 ωz2:2 closeup:1 jack:2 kick:1 resonant:3 experimentally:2 associated:5 difference:3 exact:1 condition:6 inset:6 beating:2 decorrelation:3 exponential:1 level:2 opt:3 ref:1 solution:2 damped:1 large:8 discrete:4 unrelated:1 shenoy:1 small:4 relation:3 markov:7 dip:8 setup:3 upper:2 strongly:1 smaller:1 neighborhood:2 lewenstein:2 oscillation:2 consistent:2 strunz:2 direct:1 pulse:5 sign:1 approximation:4 consists:2 second:4 value:2 steadystate:1 further:5 dynamics:40 tweezers:2 substitute:1 linear:1 even:8 established:3 what:1 errors:1 ˆt:2 appear:1 rate:10 cˆi:1 section:6 transforms:1 illustration:1 expressed:2 uniform:1 ˆa:8 ˆb:54 experiment:2 ballagh:1 ˆf:2 view:2 new:2 d1:1 waveguide:2 consisting:2 movement:2 body:4 condensed:2 wavefunctions:9 simultaneously:1 κj:4 exchange:8 becs:26 error:1 component:1 κa:1 here:6 atoms:60 inverse:1 focused:4 eikz:1 separation:3 address:1 active:1 consideration:12 along:6 standard:3 equations:18 appears:2 z2:2 differential:2 box:2 solid:1 great:1 property:1 antisymmetric:5 noticeable:2 splitting:4 institute:1 involved:1 losses:2 allows:2 completely:1 kielpinski:1 recently:1 resulting:1 negative:1 action:1 advantages:1 narrow:5 studies:2 ratio:2 elongated:2 invalidate:1 orthonormality:1 followed:1 ratios:2 clark:1 scales:1 namely:4 integrations:1 brought:3 vice:1 achievable:1 issue:1 condensates:3 total:4 readily:3 choi:1 plot:2 use:3 proceed:2 working:1 dalibard:1 remains:4 give:4 finally:4 tightly:1 next:2 distinct:2 few:3 depicted:6 monotonically:2 estimated:1 therefore:4 unfortunately:1 means:2 stage:2 type:3 theoretical:4 more:12 separated:2 introducing:1 kgr:1 formally:1 said:1 comparison:2 becomes:3 operators:6 apparent:1 odinger:1 validity:1 transient:2 basically:3 studied:1 particular:14 known:5 cases:3 hold:1 keeps:1 must:2 involve:2 account:1 word:1 subject:1 science:1 challenge:1 work:14 oscillator:1 χk:5 ij:4 values:6 adiabaticity:1 starts:1 following:2 vt:4 closing:1 smerzi:1 example:1 vary:4 numbers:1 compare:4 persists:1 haine:1 figure:36 solved:1 process:5 sense:1 neglected:1 nielsen:1 states:28 application:1 performed:2 degenerate:1 allowed:1 david:1 bouyer:1 guarantee:1 united:1 end:8 varied:1 decaying:1 deserves:1 rather:6 verify:1 discussion:5 get:1 att:4 δk:1 write:1 how:3 duan:1 concerned:1 stemming:1 gati:1 fourth:1 holland:1 very:1 instead:1 absolute:1 profile:3 simplicity:2 rise:4 description:1 may:18 broad:3 earlier:4 santos:1 pfau:2 produce:1 induce:1 trapping:4 date:1 summarize:2 choice:1 response:8 period:1 realized:1 attempt:1 waist:1 effective:2 resemble:1 dot:1 lines:1 chikkatur:3 lζ:2 perform:1 ones:2 so:12 increasing:3 allow:2 decreasing:3 obvious:2 representation:1 subsequently:1 lasting:1 adams:1 equation:7 se:3 typical:5 interpretation:1 aforementioned:1 reservoir:4 correlation:5 leanhardt:1 indeed:1 over:6 lz2:1 mainly:5 satisfied:1 years:1 produced:2 experiments:2 scott:1 lasers:7 mentioned:1 minguzzi:1 still:1 excitations:2 its:3 before:2 lf:2 phillips:1 derive:1 longitudinal:4 thank:1 decay:4 chosen:2 dr:4 inclusion:4 exhibits:7 actually:3 better:1 shifts:1 lt:3 offers:1 degrees:2 systems:5 jε:1 covered:1 main:5 lz:6 overcome:1 ly:1 yi:1 non:42 resolve:1 motivated:2 combination:1 bay:3 material:1 processes:2 investigated:3 reflected:2 framework:5 walls:4 yz:1 repulsive:1 effects:7 they:2 oxford:1 feature:1 now:5 discuss:3 above:2 represents:2 term:2 gets:1 heisenberg:3 verlag:1 2s:1 always:2 university:3 hamiltonian:13 fluctuate:1 correspondence:1 applied:4 mode:31 reasonable:1 each:13 2m:4 soc:1 higher:5 2i:2 2j:1 mean:1 oscillatory:1 domain:1 schemes:1 transform:2 mωz2:1 populated:3 energy:1 barnett:2 reduce:6 gaussian:2 related:1 applicable:1 frequency:12 obtains:1 entering:2 ωy2:2 quantum:9 our:14 approximated:2 beyond:1 inverted:1 special:1 out:3 ketterle:1 cˆk:17 shown:2 gisin:2 literature:1 factors:1 quantify:1 rep:1 continua:4 crucial:2 research:1 increase:5 collisions:1 investigation:1 spacing:1 performs:1 denoted:1 dominate:1 forth:1 occurs:1 burnett:4 exactly:2 after:2 theory:6 normalized:6 interactions:16 destructive:2 gardiner:1 mechanisms:1 pumping:2 free:16 weakly:11 difficulty:1 approaches:1 complicated:1 york:1 besides:3 usual:2 estimate:1 lambropoulos:5 milburn:1 divergence:1 faller:1 horak:1 interaction:9 derivation:2 outcoupled:28 via:1 determining:1 could:1 transition:3 times:8 motion:5 turn:1 length:2 place:1 exponentially:1 signature:1 hence:10 approaching:1 distinguish:1 neglect:1 destruction:1 first:6 origin:1 initial:15 features:4 probability:1 ηmin:3 number:12 reaches:1 dˆ2:1 channels:3 temporarily:1 heraklion:2 directly:2 nikolopoulos:4 precisely:7 electronic:1 several:1 captions:1 purely:1 manuscript:1 given:5 perturbation:1 ten:1 similarly:1 introduction:1 condensate:17 structured:3 system:38 adopted:2 petruccione:2 their:3 intermediate:3 master:1 normalization:1 realization:3 brevity:1 scheme:2 eur:1 relations:2 gives:1 shifted:1 erfc:2 preserved:1 way:3 mostly:1 trapped:21 centered:1 completed:1 continuous:5 transverse:6 drψ:4 optical:7 hope:7 authors:3 x2:2 off:2 than:3 coefficients:2 population:29 distance:11 kind:1 hundred:1 determines:2 third:3 double:28 approximations:9 summary:1 zero:1 annihilation:3 determined:3 contrary:4 speaking:1 amplitude:1 onedimensional:1 identical:2 enables:1 treated:1 iωk:2 iωj:1 exhibit:3 function:7 addressing:1 modeled:2 unchanged:1 reduction:2 turned:1 spectrum:1 generalization:1 already:1 say:1 depleted:2 need:1 seem:1 unaffected:1 any:15 viewed:2 elsewhere:3 strength:6 thoroughly:1 self:2 responsible:1 able:2 isolated:1 mechanism:5 note:4 instance:5 ideal:3 potential:16 take:1 analogy:1 negligible:3 outlook:1 strengths:7 becoming:1 semiclass:1 raman:1 spectral:10 begin:2 towards:4 2lx:1 fundamental:2 investigations:1 measures:1 naraschewski:1 interatomic:8 wells:1 asymmetric:2 most:8 involving:4 experiences:2 but:9 significant:4 phase:7 cˆj:9 outcoupling:69 analytically:1 intrinsic:1 class:1 commutation:2 cause:1 χq:1 considered:2 clear:5 later:2 steady:9 order:9 part:2 formation:5 exp:3 justify:1 normally:1 fact:3 quantity:1 particularly:2 thorough:1 his:1 rotating:2 bring:3 corney:1 radio:1 dalton:1 participate:1 ground:10 partially:1 provided:1 based:1 knowledge:1 parameters:14 irreversible:3 less:1 savage:6 enough:3 spreeuw:1 analytic:5 only:29 stronger:1 replenishing:1 developed:2 evolve:1 hamiltonians:1 local:9 achieve:1 do:3 move:1 dj:1 dk:1 untrapped:3 di:1 dependent:4 beams:1 expectation:2 da:3 beam:1 cannot:2 ϕi:2 nearly:2 words:2 ϕj:5 combinations:1 during:3 respectively:6 ϕa:9 ϕb:8 adiabatically:2 evolution:14 exhibiting:1 continuum:23 approach:8 areas:1 arxiv:1 expansions:1 method:2 ρ1d:1 investigate:2 europhys:1 predicted:1 bec:55 nα:1 cˆq:1 gravitational:1 doublet:5 pitaevskii:2 satisfy:1 set:5 statistical:2 symmetrical:1 persist:1 frame:1 evolving:1 j2:1 transferred:2 relative:4 become:7 see:29 individual:1 sec:51 result:7 greece:2 close:3 forthcoming:1 observed:2 best:1 techniques:3 closer:4 integrands:1 axially:1 discretized:1 ways:1 away:1 currently:1 robins:3 symmetric:7 importance:1 state:32 difficulties:2 various:10 closed:4 between:33 affecting:1 noting:3 justified:1 reading:1 conditions:10 available:1 perfect:1 notice:1 terms:10 ωo:7 extend:1 complementary:1 initially:6 ikz:1 resonance:1 were:2 weak:11 however:9 quantitatively:1 ˆbˆ:2 petrosyan:1 ωx2:2 bose:3 suppressed:2 distribution:20 both:4 essentially:1 providing:2 instant:1 zoller:1 numerically:1 edwards:1 many:8 taking:1 uncertainty:1 gaebler:1 according:4 against:1 laplace:3 dkg:4 merging:16 figures:12 context:9 operating:1 regimes:1 safely:1 experimental:2 albeit:1 ck:2 minima:2 relevant:1 fields:2 point:2 simple:2 harmonic:5 dimensional:1 directions:3 pole:1 cirac:1 simply:2 decreases:2 giovanazzi:1 modeling:1 respect:2 throughout:8 considering:1 pp:1 strong:8 described:2 dum:1 capable:3 addition:2 arbitrary:1 absence:4 been:16 relying:1 faithfully:1 much:3 axis:1 change:1 interest:4 rates:7 expected:1 josse:1 ph:1 extreme:1 empty:3 choose:2 remedies:1 obtained:11 direction:3 enable:1 corresponding:9 versa:1 emerge:2 dashed:3 quantities:1 sufficient:1 formed:4 gas:4 gap:1 optics:1 coherent:4 confinement:1 understand:2 external:3 stems:1 last:1 despite:1 2ie:2 former:1 present:10 case:11 k2:1 laser:36 splits:1 josephson:12 pacs:1 contexts:1 might:1 expanded:1 appearance:3 profiles:3 rectangular:1 will:8 while:14 dense:1 lx:2 behavior:7 promising:1 situation:2 tunneling:3 guide:3 characterizing:1 va:6 vb:2 larger:6 attains:1 vf:6 coupled:7 almost:1 vanishes:1 refs:1 collisional:2 thus:19 them:1 ii:3 exchanging:1 reads:1 itself:2 confining:3 attributed:1 eberly:1 ie:1 ig:4 around:6 different:9 9qh:1 open:1 tweezer:2 perhaps:2 acknowledgments:1 make:1 disappearance:1 cross:1 same:3 clearly:2 shorter:1 read:2 stimulated:1 nonmarkovian:1 quant:2 schematic:1 mølmer:1 units:1 products:1 dimensionless:3 regime:25 prerequisite:1 difficult:2 independent:3 used:4 unconventional:2 olling:1 appreciably:1 effect:7 hand:12 occupies:1 moving:1 purpose:1 potentials:1 eigenenergies:1 protected:1 arb:1 expand:2 recent:2 relies:1 lower:1 task:2 schr:1 modes:10 scenario:2 band:2 nevertheless:3 expression:1 substantially:1 variety:1 well:44 analysis:2 without:1 edge:5 solve:1 involves:4 sets:1 eigenmode:1 position:2 model:20 otherwise:1 arising:1 whereas:1 left:4 distances:12 nc:8 fast:1 proposed:1 cj:2 guided:2 obtain:5 photonic:2 cˆ:9 press:1 shape:1 underlying:2 identify:1 atomic:24 aspect:1 xdirection:1 rest:1 scattering:1 eigenstates:3 λm:1 previous:1 like:2 opposite:1 density:12 passively:1 seems:4 source:2 other:15 corresponds:1 easy:1 role:1 wiseman:2 excited:1 momentum:3 iφ:1 kingdom:1 moy:4 aspects:3 forces:1 depends:3 easily:2 rules:1 evaluate:1 sussex:1 results:6 modifications:1 decorrelate:2 dark:4 increases:8 wright:1 sanpera:1 average:1 using:4 emergence:1 unique:1 apart:4 fantoni:1 guzman:1 populations:10 appearing:1 helpful:1 lost:1 follows:3 bn1:1 adiabatic:1 guerin:2 noted:1 reasons:1 yields:2 either:2 integrals:1 δi:1 output:6 inter:7 reduces:1 cooled:1 wilkens:1 mathematical:4 parity:1 right:5 2iκ:6 deal:1 some:4 springer:1 born:7 experienced:5 jeffers:1 moreover:4 oscillations:11 unless:1 indirect:1 neglecting:1 transport:3 absent:2 albiez:1 gross:2 gradually:2 scale:8 describing:1 carusotto:1 sufficiently:3 tasks:1 electromagnetic:2 though:1 overlap:7 decorrelating:1 does:8 prog:1 propagating:2 straightforward:1 demonstrated:3 trap:43 limitations:2 presented:3 varying:2 slight:2 radial:2 conventional:2 expansion:1 step:1 diosi:2 although:6 found:6 ostrovskaya:1 refers:1 originated:1 properties:3 brighton:1 sub:1 would:1 λt:2 dˆ:1 freedom:2 basis:2 discussed:8 dependence:3 o:3 side:3 collett:3 sake:6 range:1 ensure:2 obeys:1 mccann:1 importantly:1 introduced:1 enter:1 irreversibly:1 aˆ:6 discretization:11 rev:34 ηc:4 markovian:47 presence:6 previously:2 ωe:3 into:7 within:1 obtaining:2 bound:9 due:8 dissipation:2 inapplicability:1 references:1 einstein:3 operator:6 proportional:3 bosonic:8 significantly:1 proukakis:1 rely:2 traps:31 ωd:4 assumed:2 there:8 approximate:1 long:8 why:1 dispersion:3 start:3 accordingly:1 quadratic:2 low:2 fraction:1 irrespective:2 slowly:2 was:3 garraway:2 morrison:1 lowest:4 considerably:1 complete:2 form:10 offer:1 mind:1 phenomena:1 dips:1 three:1 overlapping:1 sophisticated:1 volume:2 atom:45 elimination:1 line:8 relatively:2 dissipative:1 considerable:1 rolston:1 longer:1 ωy:3 ωx:5 ωz:28 applying:2 evident:1 understood:1 whether:2 characteristic:6 inside:1 dω:2 smooth:2 up:2 us:10 until:1 perturbatively:1 ωk:5 ωj:13 limit:12 critical:1 utt:5 markus:1 ωa:1 highlight:1 problem:2 define:2 similar:3 called:2 nature:3 recalling:1 detailed:3 changes:1 diverges:2 constant:4 moore:1 interparticle:1 defined:1 certain:1 abstract:1 describe:2 am:1 javanainen:2 general:8 duration:3 single:6 reservoirs:1 governed:3 simulations:8 partly:1 exist:1 moves:3 distributions:9 internal:2 physical:2 vertical:1 again:1 functions:5 odkiewicz:1 expect:1 dotted:1 no:7 na:4 nb:3 wavefunction:4 when:1 detail:4 rewriting:1 field:6 valid:4 dt:10 details:1 spatial:1 department:2 shin:1 picture:1 briefly:4 coherence:1 superposition:2 pronounced:2 models:3 photon:2 quasicontinuous:1 time:43 problems:5 prepared:3 deriving:1 important:1 peak:10 cover:1 pertaining:2 jackson:1 martins:1 astronomy:1 structure:2 independently:5 oscillates:1 implies:1 coupling:20 magnified:1 practically:7 assume:7 physics:4 space:6 eigenfrequencies:2 together:2 breuer:2 broadband:1 depth:1 mass:1 lying:1 affects:4 kappler:1 meystre:3 lett:8 coherently:6 |
0705.1617.txt |@word represent:3 concept:2 consider:2 ceases:1 dynamic:1 results:1 indicates:2 computation:17 follow:2 pointing:2 concerned:3 technique:1 fundamentally:1 tm:23 th:1 must:8 indicating:2 activities:8 updated:2 confirmation:1 song:1 far:3 pictures:2 decide:1 difference:1 leads:1 school:1 presented:2 did:1 suffices:2 vector:18 noted:3 concluded:1 deutsch:1 second:11 dynamics:4 choices:1 machines:2 established:2 what:1 ˆs:22 ˆu:1 section:2 cell:12 above:2 ˆh:5 new:4 consisting:2 satisfy:2 evolving:1 full:6 led:1 respectively:1 never:1 represented:8 along:1 strong:1 observing:9 change:2 great:1 institute:1 involved:1 study:2 current:1 allows:1 contradiction:5 p2:20 describing:2 suggestion:1 makes:1 involves:7 emerge:1 followed:2 outcomes:1 total:1 unit:8 use:1 figure:2 would:7 prove:1 remains:1 contains:1 hilbert:5 calculation:1 examination:1 therefore:23 criteria:1 taken:1 type:1 theoretical:1 company:1 odinger:2 particular:14 cases:1 producing:1 insights:1 involve:1 evolution:15 effectively:1 science:1 setup:1 work:2 insists:1 london:2 examined:6 halts:9 following:9 example:8 indicated:3 stated:4 process:6 νy:1 νx:1 νz:1 states:4 sphere:5 kπ:1 performed:3 seoul:1 νh:2 axis:4 information:1 provide:2 discussion:3 machine:14 located:1 criterion:3 attachment:1 pure:2 answer:2 instead:1 intelligent:3 sin:10 description:14 undergoing:1 may:6 turing:13 after:4 different:3 halted:4 law:1 types:1 natural:2 conscious:34 counter:5 correspond:7 element:3 rather:3 so:2 fundamental:1 representation:3 subsequently:1 order:12 serving:4 ith:2 produces:1 satisfied:1 symbols:1 ended:1 paper:4 through:4 argued:3 satisfies:1 its:8 before:2 termed:1 undecidability:1 fig:4 into:5 non:12 incompleteness:1 halt:12 regarding:2 they:2 own:2 rotation:7 now:1 discuss:2 nor:2 eigenvalue:2 february:1 fully:3 university:1 level:3 applied:1 each:3 accompanied:1 went:1 cliffs:1 subsystem:1 status:12 just:1 directly:1 independent:1 principles:1 computable:25 measurement:14 quantum:51 operation:6 out:1 shown:11 network:2 space:6 since:2 research:1 re:1 performs:1 ancilla:1 denoted:5 issue:1 math:1 earlier:2 theory:15 approaches:9 york:1 additional:1 interaction:1 benioff:1 could:2 computers:1 conducted:2 first:13 initial:2 peculiar:2 number:1 reaches:1 done:1 another:1 illustrate:1 given:19 necessarily:12 reference:14 table:2 similarly:4 introduction:1 system:28 construct:1 their:2 assumption:8 observations:1 hypothetical:1 frame:11 gives:1 completed:2 exactly:1 simulate:1 schr:2 representing:6 than:4 specify:2 kind:1 penrose:3 instruction:3 roberts:1 outcome:9 solely:1 behaviors:2 modern:1 mind:1 argument:5 already:1 manner:2 need:1 seen:2 any:4 built:1 studying:1 self:1 able:1 note:1 sciences:1 internal:16 build:1 analogy:1 heisenberg:3 experienced:1 unless:2 object:1 involving:4 experiences:1 position:3 why:2 µx:2 forever:4 cause:1 observation:2 characterizes:2 considered:10 shortly:1 traditional:1 kr:1 mechanical:2 physics:2 notion:1 phenomenon:34 show:1 violation:1 halting:8 attempts:1 debate:1 completion:1 computability:18 based:4 simulating:1 writes:2 specified:1 state:28 should:8 only:10 tape:7 harvey:1 edelman:1 awareness:1 nj:1 do:2 predict:1 closed:2 notation:1 means:1 expectation:3 yielded:2 cannot:3 uy:14 subscript:1 processes:5 conditions:1 arxiv:1 yield:8 predicted:1 activity:16 including:1 discussing:1 view:1 set:6 computed:1 observer:45 observes:8 imitate:1 intelligence:4 configured:1 exists:2 operates:1 observed:4 edition:1 see:4 computer:11 result:3 discussions:1 violates:1 instance:1 visualize:1 µy:2 runs:2 µz:2 pattern:1 review:2 artificial:4 written:5 identification:1 µh:3 correctly:2 between:3 neither:1 approach:20 email:1 publishers:2 korea:2 terms:3 initially:3 however:7 distinguish:2 modeling:1 suggested:1 observable:30 cos:8 always:2 many:3 infinitely:1 equal:1 etc:2 σy:2 σx:2 logic:2 qubit:30 otherwise:2 reside:1 among:3 very:1 point:2 simple:1 corresponds:7 2nd:1 alone:1 simply:1 experiencing:1 constant:1 considering:1 invented:1 described:8 transformations:1 asks:1 addition:1 been:3 odel:3 describes:1 initiation:4 basic:1 ph:1 define:1 direction:4 corresponding:2 both:8 sufficient:1 observe:2 rephrased:1 spin:1 case:7 p3:15 p1:21 unlike:3 single:11 value:3 easier:2 will:20 while:8 suppose:2 applies:2 situation:1 property:4 identical:1 unitary:12 satisfying:1 almost:1 them:1 reads:4 itself:6 commonly:1 claimed:3 technology:1 containing:3 perhaps:1 σz:2 perform:1 make:2 same:9 complex:3 quant:1 physical:7 tononi:1 development:1 evolve:3 used:4 effect:2 prentice:2 levels:1 koch:1 entanglement:1 kias:1 explains:1 neural:2 well:2 evolves:2 thought:1 academic:1 without:1 components:1 coordinate:3 termination:3 model:21 left:2 consciousness:24 invalidate:1 being:8 ongoing:1 rotated:2 oxford:1 identify:1 transforms:2 aspect:2 previous:1 visualization:1 kluwer:1 density:1 except:4 hall:2 thermodynamics:1 other:6 transformed:4 association:1 theorem:2 input:38 transformation:3 real:2 represents:5 showing:1 possible:2 quest:1 entangled:1 press:1 using:10 moreover:2 advanced:1 phenomena:2 englewood:1 necessary:3 helpful:1 success:1 identifying:1 follows:11 unnecessary:1 serves:1 indication:3 either:9 arbitrary:2 output:1 works:1 mathematical:2 because:24 classical:10 successfully:1 some:2 examples:1 respect:8 proofs:1 recognition:1 provided:1 tms:2 proceeding:1 confirm:3 decision:1 does:3 provides:11 tmh:11 yields:6 generally:1 proc:2 demonstrated:5 equivalent:1 although:1 properties:3 russell:1 about:4 freedom:1 completing:1 discussed:9 slightly:1 bloch:3 soc:2 computational:28 previously:1 h0:5 h1:6 disentangled:2 included:1 right:2 references:1 determine:1 frames:2 next:1 devices:1 assumed:2 there:10 question:4 class:2 was:13 opposed:1 head:10 form:1 attempted:1 but:3 properly:1 larger:1 transforming:1 removed:2 made:2 applying:2 consist:1 instructive:1 whether:2 us:4 placed:2 below:1 problem:9 similar:3 called:4 associated:1 computing:7 defined:7 certain:2 abstract:2 describe:2 proven:1 peres:1 loops:4 examine:3 exist:2 moves:2 constructed:9 incorrect:2 functions:1 no:4 when:12 invalid:1 field:1 valid:4 role:2 conclusion:2 picture:5 stat:1 elements:1 symbol:9 ultimately:1 includes:1 important:1 vectors:5 variable:1 neuroscience:1 needed:3 matrix:1 assume:1 changed:6 time:6 observables:7 indirectly:2 |
0705.1618.txt |@word homomorphism:5 gr:1 roy:1 proposition:12 francesco:1 consider:3 whose:3 γn:5 th:3 under:1 alternating:1 transitively:2 corollary:10 every:1 irreducible:3 michael:1 deals:1 shows:2 der:2 miller:1 direct:3 second:1 further:10 zp:2 even:1 aim:2 richard:1 section:6 above:1 new:1 gl2:1 stabilizer:2 degree:1 mem:1 respectively:7 here:1 groups:40 others:1 z2:2 altn:1 remark:1 study:1 studied:3 quaternion:4 contradiction:5 action:13 projection:2 family:1 baer:1 prove:2 remains:1 contains:3 next:2 call:1 therefore:2 type:1 theoretical:1 aut:14 subcases:1 giovanni:1 company:1 particular:2 burnside:1 iii:2 springer:2 metabelian:1 recall:2 mo:3 publications:1 following:3 trans:1 example:2 stimulating:1 proof:13 claim:2 india:2 conversely:2 verlag:2 robinson:2 acts:3 american:1 write:1 nontrivial:9 divides:2 classify:4 lal:1 product:5 mat:1 may:1 after:2 derived:4 ronald:1 shukla:1 natural:6 sr:14 element:18 so:19 sect:1 jain:1 coprime:1 equation:1 jns:2 jnp:1 jnt:6 symbols:1 course:1 jna:21 paper:2 london:2 jnd:35 its:6 perfect:1 group:100 thank:1 fix:4 conjugation:4 h2:2 semisimple:15 maximal:3 non:5 indexing:1 newman:3 now:12 finite:34 2p:2 university:1 classified:1 identified:1 each:5 classifies:1 characterized:1 square:1 monolith:17 series:3 idea:1 society:1 out:26 shown:1 since:30 contained:6 daniel:1 suggesting:1 math:7 semidirect:2 theory:4 surveys:1 free:5 completely:2 york:1 monographs:1 nonnegative:4 length:2 hence:2 onto:2 xh:3 xi:2 lyons:1 xm:1 radical:4 number:3 xr:5 impossible:1 xt:1 given:1 liebeck:1 dedekind:39 introduction:1 least:1 their:1 1c:1 brevity:1 gives:1 akad:1 lists:1 x2:9 x1:4 cyclic:4 solomon:1 nonabelian:30 clearly:2 centerless:3 lie:1 odd:6 take:2 shall:1 most:1 automorphism:4 reducible:2 class:4 professor:1 order:27 mri:1 subgroup:32 dover:1 show:7 ugc:1 supported:1 notations:3 relation:2 trivial:2 struktur:1 title:1 q8:17 homomorphic:4 lemma:12 only:6 factor:2 abelian:14 means:1 de:1 allahabad:2 words:1 kurosh:1 prime:6 arxiv:1 fixes:2 contain:5 set:7 exists:12 edition:1 see:3 discussions:1 sporadic:1 gmail:1 jnn:3 smallest:4 email:1 terms:1 complement:1 key:1 outer:1 amer:3 many:1 com:1 rps:1 gxg:3 simple:14 coordinates:1 cr:4 pp:1 described:2 publishing:1 pt:3 copies:25 been:1 basic:2 pn:2 sufficient:1 observe:1 case:3 nonsolvable:8 will:5 suppose:7 situation:1 property:2 vol:1 thus:9 ii:8 ernet:1 trival:1 containing:2 noncentral:1 any:7 several:1 used:1 monolithic:7 running:1 infinite:1 subgroups:3 lower:1 center:3 acknowledgement:1 well:1 obviously:1 sets:1 coordinate:1 usual:3 just:9 rest:1 identify:1 michio:1 classification:3 nilpotent:5 lattice:1 praeger:1 easy:3 theorem:9 solvable:31 heidelberg:1 characteristically:3 government:1 possible:1 integer:4 unique:2 follows:2 either:2 multiplicative:1 mathematical:2 acad:1 sends:1 some:9 pacific:1 factorisations:1 table:1 images:3 normal:18 does:5 proc:3 minimal:1 ple:1 saxl:1 properties:3 injective:2 quotients:1 central:4 extension:1 meaning:2 o:3 transitive:6 soc:5 xyx:1 image:1 isomorphic:7 nothing:1 references:1 elementary:6 lastly:1 gruppe:1 there:18 normality:2 inner:1 suzuki:1 complete:1 but:18 hj:1 hi:2 msc:1 problem:1 more:1 chelsea:1 called:5 irish:1 defined:2 abstract:1 ao:6 denote:16 aq:1 proper:2 inn:19 proves:9 ax:3 ing:1 check:1 inc:1 ni:3 faithful:3 no:2 field:2 nat:1 department:1 mathematics:1 nr:1 elements:1 symbol:4 commutator:4 generated:1 structure:2 implies:7 assume:13 orbit:2 gorenstein:1 implied:1 n1:1 n2:1 |
0705.1619.txt |@word remarkable:1 wilkin:1 squared:3 magnetic:3 varying:1 leads:5 per:1 lll:16 wei:1 disk:2 displaying:1 reasoning:1 simon:1 number:7 zone:4 paris:1 finally:2 th:2 lore:1 case:2 global:1 advantage:1 zhang:1 very:3 morais:1 electron:5 experimentally:1 exact:5 conserved:1 magic:1 exponential:1 level:4 try:1 phase:9 relation:2 shows:1 noted:1 degeneracy:7 neighborhood:2 zi:14 zj:4 appearance:1 perspectives:1 fold:3 second:2 further:1 odd:5 cfs:5 yang:1 even:8 what:3 sud:1 stands:1 3p:2 expressed:1 3k:4 above:2 fractional:2 new:10 principal:1 filled:3 body:2 edited:2 lee:1 component:2 understanding:1 objects:1 ansatz:1 mes:1 based:1 along:1 greiter:1 change:2 obtained:3 shift:4 studied:1 trial:3 chang:1 narrow:1 studies:3 halperin:2 useful:2 projection:2 lederer:1 explained:1 total:2 unit:3 conventional:1 rises:1 takes:1 would:1 positive:7 contains:2 quasi:1 next:1 nucl:2 themselves:1 panel:2 ψf:2 theoretical:1 more:1 fractions:6 weakening:2 heinonen:1 composite:13 excellent:1 known:4 cases:1 account:1 quantized:1 zi1:1 reducing:1 equation:1 work:2 oller:1 values:2 following:1 making:1 example:3 figure:5 abelian:7 δv1:8 states:49 sphere:7 numbers:2 degenerate:5 ratio:4 practical:1 gcd:1 write:1 attachment:1 pure:6 instead:1 sin:1 product:1 ubiquitous:1 mat:2 may:13 thermodynamic:1 await:1 diagram:1 produce:1 incompressibility:1 realized:2 short:1 natural:2 effective:1 pseudopotential:3 parameterized:1 complexity:1 so:1 allow:1 decreasing:1 adams:1 brillouin:4 least:1 interpretation:1 help:2 hierarchy:4 indeed:2 pointed:2 displayed:1 expects:1 interpreted:1 stability:2 experiments:1 including:2 statistical:1 excitations:4 its:2 before:1 thank:1 fit:1 energies:1 ll:9 coordinates:3 destroyed:1 window:1 fig:11 decreased:1 main:2 antiholomorphic:1 tentatively:1 symmetrization:1 non:7 matches:1 propose:1 gunn:1 landau:7 band:1 repulsive:1 they:5 das:1 now:5 hall:8 jolicoeur:1 iϕi:1 assess:1 term:1 several:1 stabilize:1 b374:1 always:1 classified:1 filling:14 l0:1 2m:2 universit:1 statistiques:1 spinor:1 square:2 generation:1 series:15 energy:6 hard:2 idea:2 related:2 eb:1 extended:1 quantum:6 beyond:2 eq:8 adequately:1 special:2 out:3 living:1 shown:2 fluxes:1 rr:1 factors:5 open:1 since:4 rev:20 particles:5 print:1 ref:1 zj1:1 unifying:1 wiley:1 interactions:5 possibility:2 standard:5 formation:2 york:1 wanted:1 remainder:1 e2:4 plll:2 degeneracies:1 interaction:11 zjk:1 geometry:9 starts:2 transition:1 turn:1 explored:1 due:1 onto:1 first:2 exotic:1 already:1 symmetry:2 omitted:1 primary:1 b72:1 long:1 another:1 carry:1 array:1 clarity:1 electronic:3 angular:3 pfeiffer:2 wilczek:1 xia:1 given:1 temperature:1 needed:2 ordering:1 top:3 system:3 construct:2 1a:1 their:4 1c:1 1b:1 fermions:5 calculations:2 quanta:3 1d:1 relationship:1 favorably:1 relative:1 incompressible:5 immediate:1 part:1 elusive:1 translation:2 plausible:1 kind:1 polarized:1 liquid:5 φrr:3 divisible:1 lying:6 likely:3 contrary:1 precisely:1 function:2 symmetries:1 vicente:1 nonabelian:2 spectrum:7 clearly:1 viewed:1 lie:1 zero:1 convenient:1 physique:1 eles:1 generalized:1 online:1 xi:1 techniques:1 stormer:2 towards:1 jain:4 denominator:8 sequence:2 singlet:2 most:1 letter:1 nothing:1 appear:3 observation:1 clear:1 partition:1 neutral:2 hierarchical:2 electrons:15 ky:1 kx:1 tubes:2 fact:1 b44:1 b46:1 phenomenon:1 show:1 nφ:17 discovered:1 gauge:1 find:1 ground:18 cell:3 laughlin:4 written:2 topological:3 should:3 only:5 going:1 candidates:1 factor:12 nonzero:1 over:1 substitutions:1 do:5 2mp:1 means:2 de:1 stripes:1 nearly:1 kalmeyer:1 competing:1 arxiv:1 investigate:1 europhys:1 predicted:1 contain:1 through:1 doublet:3 view:3 reveals:1 set:2 computed:1 j1:1 observed:6 see:8 computer:1 sea:1 discussions:1 progress:1 quantizing:1 points:1 phases:2 nondegenerate:1 definite:1 b360:1 symmetric:1 state:49 between:6 limit:1 boundary:1 ings:1 recently:1 tsui:2 spacing:1 prior:1 rezayi:11 however:2 jk:1 bose:4 lopez:2 abruptly:1 suggested:2 both:1 cos:1 many:1 against:1 sensitive:1 finds:1 reside:1 destabilized:1 point:3 appeared:1 cb:2 cf:16 dimensional:3 exploit:1 simply:1 boson:1 quinn:1 sequences:4 yi:1 respect:2 smith:1 wavevector:1 unusual:1 described:2 tuning:1 basis:1 addition:2 west:2 three:2 been:7 quickly:1 expected:2 pm:1 dots:1 θi:3 corresponding:1 concerning:1 relevance:2 observe:1 wavevectors:3 general:1 spin:1 spirit:1 present:3 applied:1 subsets:1 pacs:1 iyi:1 quasiholes:2 value:3 rectangular:2 will:3 while:3 tweaking:1 involved:1 situation:1 weakens:1 correspondence:1 seven:2 larger:1 best:1 vi:3 vj:2 thus:2 vm:2 surface:1 ik:1 vs:2 cond:2 fermion:4 different:2 twofold:2 suggests:1 goerbig:1 large:1 belong:1 same:2 member:1 scarola:2 unity:1 ǫl0:1 units:1 φi:1 constructed:1 pan:6 higher:2 used:1 unconventional:3 singapore:1 i1:1 laboratoire:1 numerical:1 upon:1 effect:3 sarma:1 allocation:1 v1:11 levels:3 liquids:2 stripe:1 b66:1 robust:1 idris:1 recent:1 center:2 older:1 changes:2 well:3 physics:1 without:1 contact:1 components:1 model:1 spherical:3 unified:1 proposed:3 being:2 torus:8 transforms:1 aspect:4 world:1 baldwin:2 yet:1 sullivan:1 enters:1 candidate:6 haldane:4 character:1 wen:1 possibly:1 lattice:1 potential:3 lett:14 diagonalization:4 prominent:1 excited:2 momentum:4 b59:1 read:10 breaks:1 possible:7 eorique:1 confined:1 integer:3 color:1 mod:1 fradkin:2 appearing:1 like:3 particle:1 follows:1 collective:1 discarded:1 flux:25 lowlying:1 composites:1 ermi:2 polar:1 some:2 competition:2 happens:1 cooper:2 lead:1 bottom:1 overlap:6 does:1 refer:1 core:3 scientific:1 wavefunctions:5 use:2 notably:1 broken:1 step:1 although:1 instability:1 entirely:1 wealth:1 integers:1 fillings:1 o:1 compatible:1 range:4 repulsion:1 slightly:1 pinczuk:1 fqhe:8 previously:1 unbounded:1 into:2 within:1 numerically:1 bound:2 negative:11 down:1 pair:1 steven:1 operator:1 france:1 orsay:1 theoretically:1 clustering:5 there:19 gases:1 bosons:9 low:6 fraction:3 bubble:3 naturally:1 lowest:1 survives:1 form:6 compressible:2 but:2 cedex:1 construction:7 hc:1 made:1 applying:1 pseudomomentum:2 attached:2 up:1 zik:1 ui:3 ruling:1 uj:2 problem:2 define:1 similar:4 display:1 detailed:1 separated:1 constant:1 moore:1 defined:1 b69:2 describe:1 evidence:6 cbs:3 single:1 check:1 fill:2 mutual:1 pseudopotentials:1 weakened:2 no:2 wavefunction:6 when:2 pfaffian:2 field:2 other:2 branch:5 dipolar:2 mass:2 really:1 picture:2 emerges:1 symbol:1 jastrow:2 fermi:1 closeby:1 regime:1 longer:1 coulomb:13 4b:1 required:1 pseudo:2 uncovered:1 inset:2 compete:3 parafermionic:3 time:2 requires:2 original:1 4a:1 |
0705.1620.txt |@word concept:1 chain:4 kats:2 activated:2 illustrated:1 mild:1 clarification:1 environment:2 lore:1 anharmonic:2 very:3 choice:1 leads:1 incoherent:6 laying:1 solution:1 try:1 unrelated:1 small:1 reliable:1 dis:1 work:1 jump:1 rigorous:2 dynamics:4 folk:1 even:4 assisted:1 conduct:1 contrast:1 3d:2 loose:1 component:1 behaviour:1 relaxation:1 alone:1 change:1 conviction:1 study:1 exceptionally:1 contradiction:1 cogent:1 periodic:3 resulting:1 makes:1 explained:1 logical:1 qcs:3 use:1 would:5 contains:1 france:2 calculation:1 thermally:2 taken:1 today:1 more:1 ecole:1 postulated:1 cases:1 analogous:1 behalf:1 sample:1 account:1 room:1 des:1 temperatures:1 following:2 my:2 example:2 randomizing:1 figure:2 process:1 discussed:2 accept:1 high:2 assumptions:2 calvo:2 fibonacci:4 sense:1 unphysical:2 occur:2 discussion:2 how:1 methodology:1 animal:1 reject:1 mat:2 may:1 after:1 consequence:2 wrong:3 meaningful:1 refuse:1 frick:1 counter:2 correspond:1 so:1 typical:1 developed:1 years:1 paper:2 argued:1 still:1 birds:1 solving:1 palaiseau:1 compelling:1 factual:1 dubois:2 eur:2 thereby:1 introduce:1 they:6 structural:1 inversion:1 indeed:1 identified:1 possibilities:1 sufficiently:1 truth:1 found:1 lorentzian:3 heavy:1 energy:1 principles:1 ev:1 special:3 shown:1 factors:2 furthermore:1 since:1 rev:5 issue:2 shows:2 barrier:1 mechanisms:2 possibility:2 completely:2 could:3 hence:1 configurations:2 first:2 already:2 number:1 arrhenius:1 fast:5 another:1 temperature:1 monoatomic:1 least:1 their:4 assumption:2 too:1 calculations:1 molecular:1 low:1 statement:4 serve:1 artifact:1 authors:5 than:2 diffusion:4 showed:1 depends:1 matter:2 determined:1 were:1 exhibit:1 argument:1 concentration:1 clearly:3 anharmonicity:1 self:2 mechanism:2 potential:1 multiple:1 normal:1 eggs:1 howells:1 boltzmann:1 nothing:2 precludes:1 assisting:1 especially:1 tridimensional:1 clear:2 later:1 physica:1 occasion:1 assistance:1 fact:5 spaced:1 show:3 text:1 data:5 q2:1 lorentzians:3 proposed:2 explain:2 should:5 only:4 explicitly:1 factor:4 local:5 do:2 de:3 simplistic:1 cannot:2 arxiv:2 yield:1 experiments:1 implication:1 reference:6 physically:1 observed:3 intensity:1 result:1 close:1 said:1 phonons:1 away:1 sites:1 engel:4 identification:1 between:1 drawn:1 never:1 recently:2 importance:1 configuration:1 both:1 resides:1 according:2 against:1 dated:1 logic:1 distinction:1 argue:1 comes:1 otherwise:1 comment:4 relevant:1 co:1 point:1 reasons:1 harmonic:3 dimensional:1 respect:2 broadening:4 basis:2 due:1 been:1 define:1 mine:1 neighbour:1 coherent:1 irrelevant:1 present:1 case:3 plain:1 straight:1 value:2 aim:1 while:3 cond:4 claimed:1 author:1 perhaps:1 things:1 make:3 lett:1 same:1 any:2 randomization:3 muratov:1 several:1 neutron:1 higher:1 used:2 see:2 laboratoire:1 driven:1 potentials:1 totally:1 recent:1 lower:1 modes:1 scenario:1 nevertheless:1 well:2 obviously:1 solids:1 without:2 experimental:3 claims:1 model:2 justify:1 just:3 when:1 atomic:13 scattering:3 conclusions:3 had:1 other:3 deliberately:2 treatment:1 easy:1 warrant:1 real:3 trebin:1 possible:1 solides:1 adams:1 melting:1 pertinent:1 like:1 follows:1 signal:1 dishonest:1 unnecessary:1 polytechnique:1 arbitrary:1 page:1 terminology:1 because:4 people:1 some:4 gerrit:1 lipp:1 moreover:3 peter:1 provided:1 realistic:1 opposite:1 does:1 chains:1 biased:2 jumps:18 quasicrystalline:2 about:5 quasicrystals:6 certainty:1 introduces:2 range:2 quasielastic:1 introduced:2 equally:1 statements:2 presence:6 into:1 there:5 phason:2 long:1 width:2 futile:1 way:1 was:5 but:5 cedex:1 janot:2 atom:1 line:2 absent:1 rejection:1 vacancies:3 problem:2 certain:2 meaningless:1 general:1 single:1 exist:2 simulations:1 crystals:4 nn:1 no:2 claiming:2 book:1 es:1 papers:1 hpc:2 misinterpreted:1 draw:1 models:3 contradicted:1 important:1 structure:7 lang:1 space:1 barriers:1 phonon:7 time:1 |
0705.1622.txt |@word spherical:2 represent:1 katz:1 utticke:2 consider:2 softening:1 show:2 dettmar:2 astron:7 destroyed:1 results:1 murali:2 thanks:2 astrophys:4 japan:2 gm:5 disk:4 compared:1 previous:1 whose:2 patricio:1 ime:2 family:1 parameters:11 density:20 peanut:2 lateral:1 conclude:1 seems:1 coordinates:3 5r:2 initial:5 finally:1 other:2 precessing:1 subsection:4 mail:2 letelier:10 transformation:2 momentum:2 ellipses:1 identical:1 rescaled:4 non:5 references:1 depends:1 4πg:1 de:4 gonz:2 ak:1 obtain:1 yy:1 example:1 nearly:1 they:1 half:1 press:1 using:1 discuss:2 loss:1 february:1 bar:1 like:8 alez:2 presented:5 always:1 university:1 arxiv:1 mon:3 shapes:1 imposed:1 lemos:1 component:1 common:1 integrals:1 each:1 analytical:4 done:1 equation:9 view:2 characteristics:1 disks:1 financial:2 version:2 radial:4 sequence:1 variables:2 some:6 b22:5 b21:4 aplicada:1 approximation:1 see:1 used:3 having:1 nagai:14 zz:1 apply:1 qualitatively:1 dynamics:1 contour:2 brazil:1 large:1 shown:3 hernquist:2 lead:1 support:2 section:3 since:1 rev:8 fapesp:2 per:1 research:1 may:3 axial:1 daniel:1 flattening:1 above:1 respectively:2 yields:1 order:2 conditions:4 plotting:1 terms:1 exam:1 degree:1 singularities:4 planes:4 galaxies:11 bi:3 free:4 atica:1 ple:1 cartesian:3 them:1 departamento:1 br:2 zeeuw:2 along:1 equations:1 regular:1 takes:1 box:8 both:1 pairs:8 imecc:1 irregular:1 many:1 studied:2 discussed:1 so:2 display:1 vogt:6 bulges:6 levels:2 haloes:1 massive:1 poisson:1 system:1 axisymmetry:2 exhibited:1 first:2 soc:5 relevant:1 useful:2 although:1 symmetry:1 pfenniger:2 simple:4 triaxial:23 numerically:3 negative:5 dimensional:5 pair:4 xx:1 set:1 boxy:1 directly:1 respect:4 thick:1 total:1 angular:2 unit:1 plummer:1 diameters:1 use:1 statistics:1 transformations:1 their:1 introduction:1 data:1 top:1 there:3 three:6 long:2 ordinate:1 few:1 conservation:1 constants:1 time:4 astrophysics:1 ph:1 was:6 abstract:1 reflects:1 more:2 function:5 flat:1 almost:1 corresponding:1 form:1 b23:3 needle:1 obtained:3 plane:2 binney:1 astro:1 here:1 cylindrical:1 everywhere:2 curves:13 particular:1 x2:6 biˇc:1 cnpq:1 believe:1 present:1 case:5 made:1 applying:2 jaffe:2 versions:1 solid:4 gravitational:3 work:1 second:1 us:1 matter:2 determined:1 values:2 thin:1 morgan:4 were:7 following:3 about:1 distribution:8 monopole:2 similar:2 called:1 b1:6 bell:1 a33:1 compare:1 larger:2 constant:2 b2:9 figure:8 ai:2 relativistic:2 prolate:1 b3:6 matem:1 generalization:2 general:2 conserved:1 isodensity:3 exist:1 manner:1 tremaine:1 flatness:1 follows:1 miyamoto:14 satoh:8 universidade:1 viewed:1 axis:3 motion:5 different:2 recover:2 angle:1 no:1 rather:1 distributions:3 discussion:2 s0:1 when:2 axisymmetric:13 same:5 princeton:2 field:1 potential:30 generalized:1 energy:6 propose:1 before:1 resulting:1 several:2 start:1 allows:1 higher:2 polar:2 briefly:1 literature:1 galactic:5 estadual:1 models:14 unicamp:2 shaped:8 derived:2 orbits:9 campinas:2 publ:2 a1:14 pohlen:2 a3:12 a2:15 flattened:1 mechanical:1 infinite:1 revealed:1 types:1 recent:1 lynden:1 deviations:1 figures:5 constructed:1 calculated:5 orbit:2 original:2 nasa:1 mass:8 components:1 dashed:4 coordinate:7 model:4 plotted:1 whereas:1 oscillation:1 sd:1 |
0705.1624.txt |@word khalil:8 magnetic:5 contino:2 four:6 facilities:1 gabrielli:5 weiler:1 controversial:1 anticorrelated:1 violate:1 γs:4 under:2 chirally:1 figs:7 casas:1 govern:1 experimentally:2 ref:11 convenience:2 vector:1 jhep:10 semileptonic:1 estimates:4 direct:3 second:3 chen:1 estimated:1 goto:1 even:8 errors:4 selected:1 above:7 new:19 increasing:2 coefficient:3 simultaneously:3 κf:5 here:3 reported:2 asymmetry:4 q11:2 q10:1 q12:1 active:1 tevatron:1 obtained:11 study:9 brodsky:2 classification:1 misiak:3 neutrino:1 univ:1 linearly:3 plot:1 would:3 negative:6 discrepancies:1 call:1 therefore:9 buskulic:1 m2:2 type:4 successful:1 warn:1 separates:1 aligned:1 must:3 mg:6 room:1 mb:26 pursue:1 fµν:1 cancellations:1 mt:1 mw:1 mq:5 transparency:2 example:10 cottingham:1 renormalization:5 give:8 organized:1 santorelli:3 guarantee:2 end:1 provide:4 far:1 hou:1 chargino:1 answer:1 matias:1 after:1 confirmed:2 blanke:1 lat:1 summarize:4 constants:3 effective:12 gluino:5 green:1 correlation:6 order:20 over:6 expects:2 london:5 affect:1 before:2 fit:7 fix:1 expectations:1 fig:20 overcome:1 them:7 affected:1 combination:1 band:1 effects:15 they:24 eigenvalue:1 luca:1 reasonable:1 tributions:1 bona:6 side:3 independent:8 principles:4 literature:4 extract:3 rr:15 restricted:1 crucial:2 particles:7 re:9 rf:5 reader:5 rl:12 standard:3 carried:3 estimate:6 enormous:1 chiral:1 starts:2 fleischer:14 incorporated:1 corrections:16 stewart:5 features:1 channels:20 warped:1 nonperturbative:5 another:1 chakraverty:1 top:1 approximately:1 needed:1 too:3 murayama:1 urban:1 tool:3 zeroth:1 lower:6 barbieri:1 somewhat:1 peculiar:1 distance:4 last:5 tree:3 likely:1 collinear:3 dutta:1 perturbative:9 mannel:3 mind:3 hepex:17 seen:3 raz:5 relatively:1 strength:1 convenient:2 latter:4 fitting:1 absorbed:1 blue:4 shall:4 object:1 involving:5 phase:8 electroweak:5 observation:1 calculated:1 vertices:5 definitely:1 principle:1 section:9 fleming:1 kruger:1 gauge:1 solutions:1 calculable:5 d0:4 larson:1 spite:3 rich:2 hamiltonians:1 do:5 cheng:4 di:3 dg:2 dx:2 dy:1 report:5 unfortunately:2 runs:1 contributes:1 silvestrini:18 acknowledgments:1 gegenbauer:2 phenomenologically:1 testing:1 depends:1 result:2 discussions:1 best:1 subject:1 delphi:1 propagates:1 symmetric:1 babar:15 approach:11 terms:14 weak:7 however:6 wu:2 dø:2 suggested:2 cos:1 uncertainty:13 sudakov:3 contribution:11 burdman:1 con:1 2nd:1 factorize:1 represented:1 chromo:4 mssm:1 puts:1 basis:1 chirality:8 three:5 been:8 quickly:5 much:5 basic:7 expected:2 sρ0:2 supersymmetric:1 suppress:1 concerning:1 input:5 φbs:12 aip:1 aim:2 near:1 viii:2 procedure:1 played:1 phenomenological:2 λqcd:5 iv:4 ii:14 im:7 cone:3 conf:1 vectorlike:1 containing:3 perform:3 belle:9 make:1 complex:2 potentially:2 phenomenology:3 several:15 european:1 masiero:5 hand:4 kim:3 nir:4 weakly:1 kept:1 ope:1 rome:1 roma:2 left:4 unified:1 just:1 identify:3 thanks:1 facts:1 scattering:3 yet:1 previous:1 adding:1 enters:1 gluons:1 ψks:1 regarded:1 easy:1 polon:1 yukawa:2 possible:19 firmer:1 possibly:2 unification:1 specific:3 arbitrary:3 invaluable:1 rosiek:2 right:3 indirect:2 consensus:1 quarks:7 comments:2 chromomagnetic:4 okada:1 unit:1 leptons:1 post:1 super:1 t1j:1 plus:4 efforts:2 worah:2 presence:7 puzzle:1 bound:11 down:5 lies:1 abel:1 deshpande:1 support:3 way:6 m1:1 gim:11 was:2 questionable:1 form:5 denoting:2 fore:1 back:1 encoded:1 removed:1 inside:1 bounds:6 sπ0:10 computing:2 dξ:1 perez:2 check:1 physical:1 utfit:5 no:10 when:2 vanishes:1 handed:1 role:3 tii:3 np:55 picture:2 models:14 scale:19 variable:1 factorized:4 pion:1 assume:1 together:1 time:7 push:1 observables:1 huitu:2 remarkable:2 varying:1 focus:2 leads:2 computation:1 row:4 contributing:1 certainly:3 depend:5 finally:4 analogous:1 advantage:1 keeping:2 choice:1 bjorken:3 exact:1 impressive:1 level:3 turns:3 item:1 dip:1 upper:11 trend:3 prediction:1 sign:9 scet:20 appear:2 current:10 sequential:1 goes:1 shared:1 ms:2 understanding:2 along:2 q4:1 shift:1 usually:1 studies:1 qcdf:13 useful:2 extra:1 prefer:1 durham:1 gluon:5 2φm:3 wang:4 flavors:1 franco:10 positive:3 predictions:19 scenarios:1 encode:1 scope:1 theoretical:26 diagrams:1 baek:4 introducing:1 partons:1 nagashima:1 validity:1 cases:10 decay:18 modified:1 renders:1 following:10 making:1 completing:1 predict:4 topic:1 performed:4 allowed:8 conversely:1 tseng:1 discussion:3 s0:8 write:4 pure:8 ensure:1 parameter:4 dominance:2 product:2 may:2 iwasaki:1 produce:4 value:10 improving:1 data:21 sz:1 natural:1 dynamical:2 sectors:3 whenever:1 sq:1 sp:4 explicit:1 su:20 lebed:1 so:19 sm:39 sl:10 sg:2 sf:10 typical:1 hiller:5 indeed:4 mainly:1 course:1 experiments:1 still:4 vtb:4 group:6 how:1 sγ:8 interesting:7 sη:10 decreases:1 vts:4 decreased:1 main:4 decades:1 non:10 matches:1 introduce:1 scaling:1 now:9 discuss:7 nor:2 term:4 lunghi:2 advent:1 establishing:1 gabbiani:1 ei:1 ed:1 kane:1 squark:10 ex:16 entering:1 year:1 eu:1 eq:8 shown:9 factors:3 furthermore:7 interference:1 generation:1 looking:1 contained:3 investigation:1 formula:1 dominate:1 correct:2 shows:2 datta:1 theory:8 derived:1 zweig:3 fisica:1 possibility:2 quark:13 hfag:6 besides:1 sachrajda:4 e1:1 language:1 βs:6 isidori:4 hamel:1 turn:3 place:1 barberio:1 think:1 colliders:1 first:12 origin:3 symmetry:5 flipping:2 long:4 directly:3 xs:7 angular:2 size:1 given:17 necessarily:2 checked:1 unitarity:3 indicate:1 cope:1 kagan:3 transverse:6 than:7 coefficients:8 wide:1 hepph:25 third:1 require:1 fm1:2 future:3 were:2 bauer:5 pre:1 lowest:3 generality:1 correction:2 argument:3 say:2 any:5 martinelli:7 ideal:1 potential:1 take:3 channel:3 opposite:1 chankowski:1 remarks:2 probes:2 especially:1 considered:3 average:2 later:1 chiang:3 precise:1 show:6 timedependent:1 corner:1 nlo:1 gorbahn:1 state:4 only:20 explicitly:2 gev:1 contracts:1 guadagnoli:2 cannot:8 lighter:1 progress:3 neither:2 reveal:4 penguins:42 predicted:1 imposing:2 nardulli:3 namely:2 us:15 invalidating:1 reproduced:2 αs:5 ways:1 review:7 importance:1 behind:1 between:13 reading:1 notice:7 suppresses:1 hurth:1 concentrate:1 suppressed:15 motivations:1 vub:5 many:4 region:12 ballpark:1 vus:4 expression:4 comes:2 agashe:2 among:1 color:5 bm2:1 exploit:1 pqcd:15 come:5 workshop:1 combined:2 nonleptonic:10 observe:1 external:2 those:1 case:11 abulencia:1 situation:3 canceled:1 susy:24 motivated:2 different:9 chay:2 same:3 arguments:1 nnp:1 status:4 driven:1 constraining:2 delicate:2 changing:2 relies:2 modes:2 without:1 model:22 otherwise:1 wolfenstein:4 minima:1 being:1 generally:2 multiplet:1 flavor:33 grinstein:1 hint:3 except:1 greub:2 lett:52 π0k:3 shellness:1 eigenstate:1 momentum:3 aspects:6 around:2 spectacular:1 absorptive:1 dark:3 test:5 using:11 mod:1 particle:1 pokorski:1 either:6 always:1 reduced:3 specified:1 matching:1 nonzero:1 provided:1 dimensions:1 extensively:1 conservative:2 moderate:1 refer:2 considering:6 process:2 power:13 rohrer:1 each:2 khodjamirian:1 ratios:3 found:2 exciting:1 acc:1 comparison:1 central:1 oh:2 ach:1 discussed:6 acp:42 allowing:2 ηf:4 outlook:1 inclusion:2 unbounded:1 determine:1 elementary:1 ambrosio:1 theoretically:1 hep:137 assumed:2 there:11 dimopoulos:1 start:1 low:3 survives:1 complete:1 assl:2 applying:1 darker:1 detailed:4 ab:1 datadriven:1 ai:1 certain:1 sketched:1 am:2 uil:3 deep:1 general:22 cbs:10 scanned:1 lifetime:1 again:3 assessing:2 valid:1 parameterizations:2 papucci:2 sufficient:3 deviation:1 briefly:2 pseudoscalars:2 vertex:2 acosta:1 includes:2 a1:1 important:7 bounded:1 suited:1 insertions:12 perturbatively:1 mass:23 nelson:1 quantify:1 starting:1 abazov:4 consider:6 ali:3 forbidden:1 scalar:1 liao:1 referring:1 foster:2 ti:8 sound:1 kπ:8 amplitudes:15 very:14 soni:1 kω:1 paradisi:2 hamiltonian:7 issue:2 zupan:1 large:18 small:6 mishima:4 sapienza:1 grateful:1 rate:4 enhancement:3 further:2 tev:4 what:3 abe:3 witnessed:2 sum:2 method:2 full:2 tiii:1 directions:1 strong:10 table:8 search:3 colored:1 allows:1 invalidate:1 vii:5 establish:1 silva:1 contains:2 charge:2 comparing:1 nucl:25 moro:1 qcd:13 more:6 operators:23 emission:6 aleph:1 particular:6 known:2 factories:1 qc2:2 qc1:4 erratum:8 recall:2 remain:1 caveat:1 learn:1 compare:1 challenging:1 neglected:1 states:3 arise:4 information:12 needs:1 goal:1 rather:1 breaking:13 acta:1 singularities:1 gronau:6 plane:7 descotes:1 short:2 lhc:5 negligible:1 fundamental:1 isola:3 help:2 developed:1 resonant:1 through:1 suffer:1 avenue:1 its:1 absence:2 might:5 return:2 framework:1 yu:4 easily:1 2q:1 fully:2 factorizable:2 genon:1 inherent:1 heavy:6 england:1 aubert:14 hadronic:29 energy:4 hard:12 idea:6 harnik:1 obtains:1 measurement:2 beyond:8 really:1 solved:1 since:7 parametrizing:1 denotes:3 dominated:8 induced:8 evaluation:8 localization:1 put:3 morello:1 beginning:1 generate:4 asl:1 omit:1 rosner:6 grossman:3 probability:8 number:3 perturbation:2 jet:1 introduction:1 leading:10 generalities:1 least:2 ckmfitter:1 sℓ:5 calculations:2 scheme:4 kou:4 option:1 park:1 buchalla:4 sizable:5 part:2 authors:1 albeit:1 giudice:6 collaborations:1 double:2 annihilation:6 determined:5 contrary:2 doubly:4 wyler:1 conjugate:1 wilson:4 zero:4 depending:1 extracted:1 internal:1 generalized:2 analogy:1 eff:2 play:1 towards:1 electric:2 soares:1 measures:1 reach:3 singlet:1 most:3 charm:1 significant:1 extremely:3 branching:2 deviations:4 clear:1 ko:1 ks:31 exp:5 physics:11 sector:8 cdf:5 particularly:1 rtn:1 carefully:1 dictions:1 impact:2 parameters:33 less:1 factor:3 circle:1 triangle:3 spurious:1 express:1 pions:1 resolve:1 arxiv:179 factorization:28 obscure:1 ser:1 sez:1 see:12 sec:12 preparation:3 dipole:2 fcnc:4 various:1 neubert:8 available:8 vanishing:2 4gf:1 both:2 prospects:1 improved:1 opal:1 mrtn:3 sensitive:1 connection:2 context:2 experimental:42 point:7 simple:1 corresponds:3 parametrization:2 dimensional:1 kernels:4 pp:1 enhancements:2 due:5 pa:1 pj:1 ph:120 pi:5 firm:1 precision:2 schwab:5 deter:1 determination:3 systematic:1 nierste:1 p2:1 p3:1 pierce:1 p1:1 look:1 solid:1 reliable:1 evaluated:2 while:9 piai:1 error:7 couplings:2 loop:4 averaging:2 vanish:1 fermion:2 italy:1 carone:1 grand:1 neutron:1 higher:2 used:3 rescattering:1 moment:1 purpose:2 recent:2 subleading:6 task:1 analysis:10 competitive:1 reviewed:1 shape:1 λf:2 questions:2 alternative:3 tables:3 conclusions:1 signals:1 theorem:2 rgi:6 recksiegel:5 evaluate:1 showing:1 quest:1 helicity:1 bit:1 like:1 follows:4 shapes:1 collect:1 translated:1 methods:2 some:9 remarking:1 strongest:1 suprun:3 savage:1 φks:2 ackerstaff:1 measurements:1 bobeth:2 eliminate:2 tends:1 proc:2 cabibbo:7 minimal:2 bd:5 bl:8 agreement:1 step:2 br:56 bs:33 plots:4 constraint:7 dimuon:1 deserves:1 range:5 extensions:2 conserving:3 pierini:8 into:6 within:12 slawianowska:1 suppl:1 parton:1 uncertainties:5 measured:2 question:2 fast:1 bosons:1 koppenburg:1 forward:1 considerably:2 hoped:1 line:2 raising:1 penguin:52 infn:1 uta:2 intuitive:1 uv:2 up:6 barring:1 ui:1 marginally:1 boldface:1 similar:1 called:3 single:1 chau:1 formalism:4 fixing:1 yang:3 shimizu:1 elements:9 generates:1 accidental:1 problems:1 generated:4 sφks:12 suppression:8 lenz:1 sides:1 structure:4 correlated:3 required:1 romanino:1 requires:2 having:2 once:5 partial:1 gp:14 results:19 gf:1 ga:1 mesons:2 contributions:33 excluded:2 include:1 presently:1 wave:3 mescia:1 ishikawa:2 mixing:21 matrices:1 haisch:1 severely:1 smaller:3 imply:1 traveling:1 insertion:2 dynamics:4 plays:1 consistently:1 experiment:2 flowing:1 values:10 exercise:1 body:5 ibid:8 exchange:7 respectively:2 remark:1 involved:2 larger:4 chang:1 fourfold:1 formulated:1 jager:3 scales:6 apr:1 expect:2 meson:6 tools:2 imaginary:1 use:7 remains:2 next:3 few:9 buras:11 becomes:2 charming:5 iii:5 hints:2 account:2 decouples:1 averaged:5 reproduce:3 closing:1 averages:5 control:6 tarantino:1 theorems:1 calculation:5 high:3 assumptions:1 tab:2 dominant:11 tan:16 weaken:1 sit:1 six:1 fortunate:1 regions:3 dependent:9 instead:1 sin:6 afr:1 circular:1 tension:1 efficiently:1 realized:2 light:13 ciuchini:17 lines:2 correspond:5 element:1 allow:3 holds:1 saturated:1 produces:1 interpreted:1 including:3 yamaguchi:1 lepton:1 le:1 la:1 chosen:3 ll:20 li:12 lu:1 lr:18 okumura:3 eur:7 violating:4 fourth:1 mention:1 abreu:1 preclude:1 identified:1 magnitude:1 degrassi:2 constraints:20 qu1:3 qu2:2 sanda:3 related:4 operator:2 decays:64 computable:1 interplay:1 measure:1 our:4 meth:1 transitions:20 out:5 matrix:12 rev:85 asymmetries:22 postpone:1 suffices:1 integrated:1 math:1 interactions:4 diagonal:4 approaches:19 interaction:4 determining:1 could:1 instrum:1 rothstein:3 manuscript:1 powerful:3 improvements:2 strumia:2 precisely:2 revealed:1 system:1 their:2 fermions:1 perfectly:2 final:7 adopts:1 pirjol:6 lubicz:1 appealing:1 amplitude:17 eai:1 symmetries:1 tabs:1 cohen:1 reassuring:1 unlikely:1 need:4 constrained:2 clearly:1 angle:2 pursued:2 able:7 mechanism:2 heff:5 kaplan:1 schematically:2 accuracy:2 collaboration:38 connected:1 class:1 ckm:10 stronger:1 atwood:1 proceedings:1 constrain:7 emerging:1 violation:22 text:3 charles:1 sze:1 purely:1 nonfactorizable:1 melcher:1 decade:1 q1:3 o:13 q3:3 q2:1 based:4 knowledge:2 q7:2 q6:1 q9:1 q8:1 should:2 ambiguity:1 local:1 hope:1 handle:1 means:4 ones:7 legitimate:1 wise:1 processes:15 qr:4 qa:1 contain:1 qi:6 ql:9 view:3 predictive:1 computed:2 enhanced:3 violet:2 ligeti:1 acquires:1 phases:6 pattern:1 written:2 difficulties:1 unravel:1 invariant:1 boundary:1 luo:1 ability:1 gambino:4 emitted:1 interfere:1 reproduces:2 key:2 problem:5 endo:1 observable:1 acknowledge:1 equal:1 mixings:1 etc:1 safely:1 masses:14 grounds:6 strongly:2 ci:6 relevant:6 huang:3 conclude:4 cc:1 cs:1 respect:3 cp:51 ct:3 kolda:1 addition:3 yao:1 yan:1 enlarging:1 define:4 hernandez:2 describe:2 corresponding:5 leptonic:2 c2:2 c1:2 present:17 multi:1 harder:1 lepage:2 choices:1 will:8 reliability:1 untagged:1 vi:5 refs:8 thus:5 vs:2 φs:1 generic:1 ewerth:1 φb:2 parts:1 units:5 φm:3 difficult:4 ball:1 effect:1 infinite:6 tighter:1 off:2 nevertheless:1 ingredients:2 well:3 pham:2 spectator:5 arising:4 reintroduce:1 heavily:1 moments:2 kramer:1 obtain:2 sources:14 underlying:2 predicts:3 momenta:1 adv:1 generous:1 sπ:1 sks:4 density:6 lattice:2 combine:1 flavianet:1 ample:1 hisano:1 debatable:1 necessary:3 helpful:1 alternatively:1 become:1 soft:5 because:4 shen:1 righthanded:1 searching:1 zeppenfeld:1 neglecting:2 keum:2 lead:3 does:1 assuming:4 mined:1 expansion:6 although:5 analyses:3 hiding:1 about:2 rare:11 decoupling:1 introduces:1 dependence:7 compatible:1 statement:1 equally:1 contractions:7 roszkowski:2 ea1:1 additional:10 noticed:2 beneke:9 crucially:1 naturally:2 function:1 williamson:1 but:8 neutral:2 partially:1 compute:3 whether:2 variations:2 flip:2 below:5 frequency:1 limit:10 distribution:2 subdominant:1 universal:1 contribute:1 inp:1 denote:3 twist:1 functions:10 compared:1 variety:1 detail:1 other:13 details:4 quantities:1 zhou:1 variation:2 coupling:1 space:1 searched:1 indirectly:1 |
0705.1625.txt |@word nanocomposites:1 limited:1 monte:1 sci:1 results:10 illustrated:2 tensile:1 edu:1 contributions:2 layers:2 increase:6 calculate:2 description:1 technique:3 tr:1 environment:1 dereli:3 stable:6 tb:1 walled:5 very:1 amorphous:1 choice:1 ankara:1 electron:2 experimentally:1 difference:1 exact:1 deformations:1 4ev:1 solves:1 hamiltonian:1 positions:1 solution:1 large:1 discrete:1 pbc:1 enhance:1 loads:2 commented:1 locate:1 tem:1 trend:1 consistent:1 direct:1 literature:3 approximation:1 second:3 chen:1 further:1 dynamics:4 enthalpy:1 carlo:1 canonical:2 errors:1 plays:1 nano:1 while:1 melt:1 axial:1 above:6 contributes:1 method:15 temperatures:8 coefficient:8 processing:2 chose:1 degree:3 respectively:6 mei:1 here:3 atoms:18 reported:2 cylindrical:1 focused:1 possibility:1 groups:1 relaxation:1 based:2 along:2 restricts:1 equations:1 change:8 box:3 technical:4 study:5 larger:2 reports:1 nanoelectronic:1 periodic:2 usually:1 conveniently:1 studies:3 diameter:6 offs:1 adjustable:1 2000c:4 divide:1 increased:4 brought:2 outer:1 total:17 tn:1 use:1 figure:21 intensively:1 bundles:5 only:4 charlier:1 coalesce:1 call:1 therefore:1 vi:1 theoretical:1 more:3 introducing:1 muramatsu:1 successful:2 brings:1 under:4 odinger:2 unstable:1 long:1 swcnts:17 known:1 tearing:1 must:1 md:9 room:2 deformed:4 science:1 equation:2 work:2 mk:1 remain:1 values:5 emitters:1 detached:4 example:1 history:3 control:1 nearest:3 wang:3 indicated:2 give:3 process:2 thermally:1 hexagons:2 involve:1 assumptions:1 numbers:1 sharp:3 tan:2 rescaling:1 occur:1 information:1 miyamoto:2 discussion:1 breaking:4 chemical:1 varies:1 occasionally:1 adjacent:1 lamy:1 ensemble:2 fs:5 mat:1 may:2 after:6 treatments:1 applications:2 fg:1 parallel:1 bernier:1 effective:1 plateau:1 maintain:1 algorithms:5 vapor:1 order:5 pulsed:2 deform:1 laboratory:1 gradual:14 over:2 displayed:2 years:1 stability:22 thermal:56 experiments:2 decays:1 statistical:1 affect:1 kinetic:10 still:1 energetics:4 tendency:1 before:3 regions:1 group:1 decay:1 chosen:1 sakata:1 hot:1 decreases:2 li:2 absence:1 production:1 condition:1 derivative:1 deformation:1 non:1 good:1 affected:1 dac:2 propose:1 mvi:2 processes:2 scaling:2 band:6 walls:1 detachment:3 conquer:1 effects:3 they:10 thus:1 dielectric:1 structural:8 easily:1 2r:2 university:5 presented:1 kasuya:1 vibrations:1 each:9 found:7 2n:1 bond:21 subsystem:2 energy:43 reduce:1 related:1 used:3 sectional:1 our:8 ev:12 eq:2 repulsive:5 out:2 try:1 shown:1 matrix:2 space:2 since:1 rev:14 research:3 particles:1 investigation:1 1200k:7 suggesting:1 get:1 issue:1 integrated:1 shows:5 linear:1 interactions:1 swcnt:26 approaches:1 eigenvalues:1 sensors:1 rises:3 definition:1 takata:1 starts:1 times:1 motion:2 length:10 hence:1 retain:1 durable:1 first:7 there:2 features:1 withstand:1 third:4 thesis:1 number:4 restrict:1 done:2 defects:1 another:1 reached:1 electronic:1 size:5 xia:1 given:3 necessarily:1 temperature:65 indicate:1 introduction:1 leading:1 ultrathin:1 system:7 adopted:1 tou:1 their:4 chem:2 calculations:1 1k:3 molecular:4 structures:1 store:1 gives:1 shifted:1 trapped:1 alonso:1 yildiz:1 exactly:1 1500k:1 took:1 argon:1 simulate:1 authors:1 chapelle:1 constituent:1 fujiwara:2 than:2 diffusion:2 distance:5 determines:1 target:2 showed:5 accordance:3 approximations:2 acknowledgement:1 project:1 determined:3 were:2 verlet:2 college:1 enables:1 function:11 avoided:1 coalesced:1 fullerenes:2 conventional:1 curves:1 hexagonal:1 ray:1 strength:1 angle:9 newtonian:1 depending:1 xrd:1 able:1 mechanism:1 metallic:4 liu:1 high:8 materials:1 nanoscale:2 forces:1 techniques:1 accuracy:1 begin:1 sure:1 buffer:5 reach:1 impurities:1 most:1 optimized:4 involving:1 connected:1 sheets:1 position:2 phase:3 kb:1 especially:1 neighboring:2 average:10 broadened:2 flow:1 physica:1 traditional:1 principle:1 velocity:4 physics:2 fact:1 gold:1 show:3 supported:1 kwon:2 vacancy:1 bring:1 saito:1 mwnts:1 kar:1 slow:13 ratio:1 parameters:2 implementation:1 carbons:1 terrones:4 truncation:1 local:1 equilibrium:16 do:1 bonds:1 de:1 uniaxial:2 negative:1 during:3 evolution:1 increasing:5 aluminum:1 conditions:1 coalescence:3 arxiv:1 consisting:1 investigate:1 paper:1 through:4 fixed:2 600k:8 irradiation:1 computed:1 reference:1 900k:1 lett:8 observed:12 computer:1 radius:7 result:10 enhanced:1 conductivity:1 interacting:1 its:2 initially:1 state:2 smallest:1 various:1 between:9 consecutive:1 boundary:2 semiconductor:1 approach:2 available:3 accord:3 targeted:2 comp:1 attention:3 steady:1 however:2 yoon:1 rapidly:1 cut:1 comm:1 ji:1 huang:1 carbon:12 lopez:2 endo:1 both:4 improved:1 avoid:1 resistant:1 taking:1 barely:1 heating:30 energies:1 ung:2 whole:1 experimental:6 ajayan:2 point:2 wall:1 corresponds:1 vicinity:1 suematsu:1 respect:3 crystalline:1 turkey:3 ps:6 tuning:1 basis:1 chirality:1 due:2 been:7 quickly:1 much:1 slowly:1 rao:1 expected:1 ph:1 systems:1 obtained:2 direction:5 arises:1 corresponding:1 reaction:1 quantities:1 gas:2 requires:1 300k:16 hayashi:1 fund:1 observe:2 demand:1 careful:1 importance:1 equilibration:2 present:3 applied:8 laser:1 reciprocal:1 pacs:1 single:6 value:11 50a:1 will:1 near:2 ought:1 behavior:1 error:3 procedure:1 almost:1 characteristics:3 graphene:1 binding:3 equal:2 strain:1 examined:1 cond:1 yıldız:4 bandstructure:1 technology:1 situ:1 cuboidal:1 different:4 author:1 lengths:2 make:1 cross:1 same:11 check:1 shorter:1 several:1 schelling:3 higher:4 investigated:9 peaks:6 cubic:1 structurally:1 effect:3 hand:6 compared:3 kim:4 recent:1 eigenvectors:1 schr:2 largely:1 minimize:1 changes:3 motions:1 no:2 well:1 kept:1 patterns:1 without:1 solve:1 simulated:2 hamilton:1 left:2 kawai:2 distances:1 when:2 obtain:2 shape:1 atomic:3 followed:3 relaxations:2 previous:1 contradicting:1 rapid:2 density:1 parametrization:2 rubio:2 lattice:2 potential:4 transformed:1 treatment:4 theorem:2 diagonalization:1 role:1 coalescing:1 real:2 rescaled:1 nvt:2 around:4 disappearance:1 read:1 specimen:1 possible:2 increases:7 cnts:7 vacuum:1 press:1 using:15 disadvantage:1 atmospheres:1 melting:7 sugino:1 lost:1 sizes:1 iijima:2 velocities:2 benefit:1 indication:1 either:2 become:1 works:1 therein:1 because:1 methods:10 successfully:1 calculated:5 duration:1 diagonalizing:1 pronounced:1 cnt:1 scale:1 lead:2 affects:2 tube:14 measurements:1 integration:1 per:6 wong:1 provides:1 steps:3 averaging:1 equipartition:2 run:1 inaccurate:1 broadening:1 dangling:1 radial:18 lu:1 agreement:4 expansion:12 step:12 chiralities:2 properties:10 stage:1 about:1 carried:2 getting:1 dependence:1 o:24 simulation:24 dependency:4 range:4 chou:1 neighbor:4 ti:1 raised:1 letters:1 previously:2 into:3 within:1 functional:1 three:1 device:1 references:2 liew:2 heated:3 diameters:2 additional:1 elastic:1 initial:1 u1:1 transform:1 fast:13 imperial:1 start:3 accordingly:1 low:2 way:1 was:2 suzuki:1 nitride:1 form:1 metastable:1 but:4 dresselhaus:4 heat:5 nanotubes:8 atom:17 sustained:1 he:2 made:2 compute:1 mtrl:1 nanotube:3 up:6 devices:2 until:2 converted:1 graphite:4 distribution:16 called:2 ac:1 qin:1 proved:1 certain:1 abstract:1 measurement:1 proven:1 general:1 engineering:1 ar:1 exist:1 periods:2 simulations:14 controlled:1 proceeds:2 physical:7 functions:11 performed:5 nm:2 istanbul:2 locality:1 generally:1 zhao:2 tight:3 other:8 electrical:1 details:1 department:3 kira:1 conclusion:1 draw:1 la:1 sublimation:1 koga:1 variation:5 enlargement:3 bonding:2 important:4 peak:8 yields:4 structure:5 longer:2 algorithm:2 gan:3 tubes:4 chauvet:1 diffraction:1 time:10 starting:3 having:2 |
0705.1626.txt |@word gupta:1 both:2 trigonometric:6 abramo:2 ferreira:1 entropy:1 morphology:1 gm:7 denotes:3 removal:1 2004b:1 2004a:1 those:2 alphabetic:1 tegmark:3 tc:6 case:2 advantage:2 orthogonal:1 martinez:2 results:1 kℓm:4 difference:1 presented:1 anisotropy:1 sanz:1 cmb:10 sℓm:3 team:1 work:1 foundation:1 ubiquitous:1 sign:1 further:1 copenhagen:1 implemented:1 wmap:16 employ:1 what:1 heavens:1 section:1 while:1 expressed:1 orski:7 above:1 new:5 public:1 aℓm:15 coefficient:1 κm:4 full:18 multipole:2 respectively:2 dineen:4 here:1 understanding:1 pub:1 strong:1 box:1 institute:2 φℓm:9 fourier:11 studies:1 taipei:1 via:3 useful:3 divide:1 apj:11 plot:1 use:7 wealth:1 would:2 contains:1 next:1 szalay:1 therefore:2 hikage:2 taken:2 panel:1 more:3 sort:1 tojeiro:2 hivon:3 corrected:1 emission:1 known:2 account:1 avoiding:1 mn:1 tavakol:1 novikov:4 hansen:5 example:3 tap:1 wang:2 figure:4 process:2 zaldarriaga:1 bennett:5 high:3 weighting:3 imϕ:3 numbers:1 tan:2 information:4 needs:1 discontinuity:1 mpa:1 orthogonality:4 huterer:5 maps:3 significance:1 sin:2 map:24 galactic:12 after:1 derived:4 mapping:1 masks:3 reflect:1 plane:7 lay:1 data:6 vielva:3 light:2 register:1 lines:1 departure:3 cosmology:2 so:2 correlation:2 sc:2 order:1 serving:1 interpretation:1 closely:2 produces:1 developed:1 over:1 expects:1 paper:3 including:1 statistical:3 mentioned:1 still:2 its:3 galaxy:17 regions:5 style:1 derive:1 efstathiou:2 fit:1 how:1 jin:1 cleanest:1 fix:1 coordinates:1 writing:1 window:2 primordial:2 harmonics:3 latitude:13 defining:1 pixel:14 non:9 combination:3 largest:1 evolution:1 flipping:1 hamilton:3 they:1 now:1 easily:1 february:1 university:1 ensemble:1 theory:1 each:5 references:1 mean:18 heavy:1 domain:2 coles:14 significantly:1 series:1 gaussian:13 related:5 constitute:2 frequency:1 year:3 our:3 extract:1 shannon:1 standard:1 gonzalez:2 living:1 shown:1 space:1 doroshkevich:6 since:1 rev:11 research:1 imperative:1 wandelt:5 correct:1 foreground:5 christensen:1 linear:1 southern:1 mcewen:2 wℓm:4 free:2 diagnostic:2 release:1 surely:1 care:1 definition:1 sinica:1 cosmic:6 length:1 produce:2 signature:1 hence:1 lambda:1 spergel:2 vittorio:2 features:2 relate:1 variables:1 number:1 system:1 another:2 ring:7 angular:3 reboucas:1 temperature:4 needed:1 introduction:1 top:3 yih:1 adopted:1 their:1 observations:1 pavel:1 white:1 speaking:1 preserved:1 way:2 copi:5 park:2 part:2 coefficients:9 kind:1 was:1 see:9 submitted:7 providing:1 russia:1 function:2 cabella:3 correction:1 spectrum:4 correspond:1 qualitatively:1 seen:1 obviously:1 demonstration:1 any:4 lilje:3 angle:10 thorough:1 note:5 oliveira:4 internal:1 λcdm:1 shall:2 most:2 involving:1 importantly:1 printed:1 letter:4 phase:13 model:2 tikhonov:1 latex:1 xcut:3 pℓm:3 ways:1 proceedings:1 exp:8 chiang:18 incomplete:10 particularly:3 rayleigh:1 random:16 large:1 uniform:1 hobson:1 larson:2 based:6 implementation:1 ℓmax:8 distributed:2 outside:5 jap:1 should:1 only:5 nyquist:1 employed:1 continuity:1 legendre:3 dk:1 get:1 de:4 stripes:1 da:1 cannot:1 words:1 reconstruct:2 bardeen:2 earl:1 gray:5 processes:1 pearson:3 covering:1 denmark:1 arxiv:1 method:4 investigate:1 underlying:1 processed:1 contain:1 analytical:1 requirement:1 eriksen:6 starkman:5 testing:1 deconvolution:2 up:3 detection:1 namely:2 legacy:1 bernui:3 close:1 best:1 phases:45 mortlock:1 nℓm:6 federal:1 rings:11 verkhodanov:6 boundaries:1 written:1 boundary:5 approach:2 available:1 lasenby:1 terms:1 complementary:1 healpix:2 however:2 realization:6 hypothesis:1 key:1 contamination:1 probing:1 packages:1 pixels:1 gaussianity:7 received:1 cos:6 2003a:1 ilc:13 implementing:1 region:8 acknowledge:2 equal:7 against:1 komatsu:2 hinshaw:6 otherwise:1 magueijo:2 simple:1 harmonic:6 walk:1 dimensional:3 gorski:3 respect:1 conference:1 wright:1 barreiro:1 due:4 been:4 strategy:1 int:2 faithfully:1 combined:1 azimuthal:2 ph:7 fig:7 direction:3 resultant:1 cosmological:2 observable:1 θc:11 cayon:2 tapping:2 angles:10 astron:2 denote:1 present:3 applied:1 intriguing:1 castro:1 will:3 near:3 taking:1 mota:1 thus:1 apjs:4 according:1 apjl:7 l50:1 different:1 recover:1 acknowledgments:1 radiation:1 cross:2 same:1 emphasize:1 mukherjee:2 several:1 fairly:2 used:3 v2:1 purpose:1 dust:1 symmetric:1 normalization:1 costa:5 concordance:1 modes:2 nevertheless:1 well:4 analysis:11 bohr:1 without:2 residuals:1 coordinate:1 academia:1 dark:1 blegdamsvej:1 spherical:7 excessive:1 heavily:1 moments:6 when:1 obtain:1 imprint:1 intervals:1 localize:1 taiwan:1 mmax:3 wagg:2 cut:10 sky:28 cc:2 treatment:1 naselsky:21 details:1 real:1 around:1 lacking:1 devised:1 breaks:2 sums:1 caps:1 early:1 department:1 cruz:2 mon:1 background:7 using:7 accepted:3 pixelization:1 mod:2 like:1 alternatively:1 signal:7 isotropy:1 niels:1 specific:1 schwarz:4 follows:1 reduced:1 shed:1 methods:5 some:6 anisotropies:1 pagano:1 kaiser:1 bottom:3 microwave:7 polluted:3 decomposition:2 masked:1 assuming:1 eso:1 scientific:1 power:4 equivalent:1 illustration:1 broken:1 step:1 although:1 imaginary:1 properties:1 science:1 about:2 banday:4 package:2 universe:4 o:7 bond:3 software:1 soc:2 significant:3 into:2 within:1 θcut:3 down:1 lung:1 sheth:1 theoretically:1 area:6 artifacts:1 there:2 question:1 transform:2 fast:1 abovementioned:1 astrophysics:1 analyze:1 sections:1 synchrotron:1 interest:1 differences:1 jun:1 but:4 regularization:1 astro:8 mnras:11 deployed:2 longer:1 applying:1 whether:1 maximum:2 us:1 par:1 emissions:1 2003b:2 fluctuations:2 distribution:2 matsubara:2 called:1 cosmo:1 associated:1 pim:1 pin:1 defined:6 abstract:1 describe:1 covers:2 general:1 examine:3 exist:1 file:1 walks:2 archive:1 functions:1 compared:2 nl:1 dotted:1 no:1 eq:3 whereas:2 generally:2 wuensche:1 grf:4 field:1 other:1 special:1 nat:1 test:2 conclusion:1 polar:4 kinds:1 yℓm:4 uniformly:6 polynomials:4 scale:1 coverage:7 astronomy:1 structure:1 l65:1 land:2 coupling:1 mask:7 marinucci:2 equivalently:1 nasa:1 olesen:3 dϕ:1 resolution:1 lett:2 |
0705.1627.txt |@word limited:1 consider:1 chinese:2 caused:1 results:7 four:1 scalar:1 kc0:1 computation:1 anggi:1 localized:6 glimpse:1 inverse:1 terms:2 quasi:1 program:1 under:2 quasienergy:11 cm2:1 applied:1 jensen:2 advantage:1 very:2 frequencies:3 wave:6 electron:2 every:1 refractive:3 experimentally:1 difference:1 condition:1 cdt:6 cianci:1 level:1 steeply:1 solution:1 large:1 guiding:1 fourier:2 enhance:1 degeneracy:5 upper:1 force:7 oscillation:1 trend:1 discover:1 sign:1 approximation:4 fold:1 zero:2 enhancement:1 dynamics:1 index:4 nonlinear:40 appear:1 current:5 experiment:1 above:3 new:2 increasing:1 waveguide:13 contrast:1 coefficient:1 respectively:2 reported:1 china:3 address:1 strong:1 equations:5 appears:1 obtained:1 labs:2 laporta:1 institute:1 study:2 studied:2 zener:1 periodic:10 usually:1 narrow:1 plotted:3 appropriately:1 σeff:2 extra:1 aphy:1 condensates:1 unit:3 readily:2 aitchison:2 waveguides:23 remains:1 call:4 therefore:2 m2:1 taken:1 associated:1 type:1 theoretical:2 reflects:1 more:2 henneberger:1 initial:1 controlling:1 normalized:1 known:6 cases:2 high:4 tunnel:1 valle:1 equation:2 work:1 2πn2:3 obvious:1 example:1 control:1 beijing:1 want:1 figure:2 states:16 indicates:2 minimum:1 numbers:1 degenerate:2 occur:1 curving:1 rather:1 means:1 eigenenergies:1 write:1 how:1 opt:1 instead:1 parameter:2 sin:2 profile:1 staying:1 fu:1 modulation:3 max:1 after:2 derived:1 demonstrating:2 waves:1 horizontal:1 parallel:1 third:1 light:11 lines:4 correspond:2 so:2 eisenberg:1 order:1 our:8 morandotti:1 dx:2 pointed:1 eqs:9 experiments:3 through:1 still:1 ieee:1 its:5 before:1 jie:1 lc:2 directional:2 lm:1 li:1 offers:1 choose:1 guan:1 derivative:1 into:2 eventually:1 them:1 peskin:1 landau:1 mention:1 they:1 half:1 now:1 maxwellian:1 dielectric:2 term:1 finite:1 kerr:2 capability:2 magnitude:1 mode:6 reasonable:1 each:3 found:4 characterized:1 defocusing:1 populated:1 series:1 energy:2 gaussian:1 related:5 frequency:4 measure:2 quantum:7 laboratory:1 eq:4 witness:1 out:2 shown:2 rosenblum:1 driving:11 space:1 electronic:1 rep:1 since:1 rev:13 looking:1 may:4 wide:2 print:1 induced:2 ref:4 occurs:6 shows:2 linear:11 localization:8 free:2 standard:1 admits:1 completely:1 estimate:1 e0:3 shortest:1 kivshar:1 counterpart:1 length:1 neglect:1 first:5 simplifies:1 striking:1 relate:1 devices:1 open:1 πb:1 given:2 xie:1 similarly:1 condensate:2 system:14 expand:1 floquet:20 gives:1 academy:2 tool:1 zeroth:1 optical:8 packet:1 x2:1 crosssection:1 x0:3 than:2 coefficients:2 iωt:1 effective:6 double:4 intensity:4 project:1 grossmann:3 lowest:4 55µm:1 lin:1 ans:1 seen:4 clearly:3 strength:4 boyd:1 latter:1 able:1 isolated:5 note:3 sciences:2 ideal:1 potential:3 take:2 analogy:1 reversed:1 circles:2 electric:1 established:1 consistency:1 plugging:1 mimics:1 connected:1 letter:1 analytically:1 observation:2 surprising:1 clear:3 points:1 exp:5 oscillates:1 physics:1 dot:1 phenomenon:5 supported:1 discovered:2 focusing:2 shirley:1 corner:3 find:5 ratio:5 parameters:5 longhi:2 burak:1 should:1 only:6 silberberg:2 triangle:10 quantph:1 distance:3 define:3 dz:1 closely:2 evolution:1 substrate:1 arxiv:2 2b2:1 tuned:1 investigate:1 europhys:1 qe:1 view:1 reveals:1 set:5 computed:1 achieved:1 j0:4 quasienergies:16 observed:2 see:5 result:1 close:1 capacity:1 fang:1 state:4 between:10 approach:1 luo:1 available:2 notice:1 recently:2 ability:1 extend:1 initially:2 weak:1 focus:1 wi:1 wu:2 bose:3 suppressed:1 wz:4 improve:1 observable:2 cos:4 region:1 according:1 propagation:2 context:1 focused:1 experimental:5 solving:2 cn:1 point:5 appeared:1 period:2 leon:1 dimensional:3 2ns:2 respect:1 considers:1 oliver:1 described:1 second:1 lutions:1 due:1 been:2 much:1 ph:1 fig:21 firm:1 direction:1 corresponding:3 both:3 suppress:2 coherent:12 coherently:1 niu:1 c2:10 c1:14 c0:2 present:1 case:12 peres:1 novel:2 laser:1 pacs:1 solid:6 value:3 will:3 while:3 steinberg:1 tunneling:30 loop:1 della:1 bin:1 coupled:5 almost:1 averaging:1 thus:2 non:1 systems:1 biao:1 coupler:2 reads:1 examined:1 curved:5 n2s:1 ic:4 different:4 wang:1 radiation:1 cross:1 same:1 quant:1 schematic:1 visualized:1 units:1 regime:1 independent:1 used:2 numerical:5 effect:1 driven:2 levels:4 normalization:1 destruction:11 weakly:1 modes:1 scenario:1 well:15 metiu:1 moded:1 materials:2 solve:1 sets:1 model:9 drawing:1 left:1 bending:2 moiseyev:2 obtain:2 λb:1 love:1 speed:1 eigenstates:3 previous:1 liu:1 regarded:2 smith:1 mathematically:1 transformed:1 lett:11 input:2 sectional:1 transformation:3 real:1 showing:1 increases:3 2w:2 vacuum:1 orenstein:1 particle:1 grifoni:1 switching:1 reduced:1 because:2 classical:1 friberg:1 self:3 wider:1 extended:1 happens:1 scale:1 describing:1 demonstrates:1 does:1 linearly:1 bessel:1 demonstrated:2 2a:1 ruffo:1 power:2 binder:1 although:1 periodically:5 extension:2 discussed:1 simulation:1 2cm:1 range:8 plus:1 2iπ:1 cutoff:1 h0:3 within:3 numerically:4 nsf:1 three:4 hanggi:2 right:1 einstein:3 paradigmatic:1 theoretically:1 additional:3 iphy:1 area:1 transfer:1 there:10 u1:4 stark:1 u2:3 width:7 appl:3 kang:1 was:2 function:3 medium:2 elsewhere:1 form:3 triangular:3 but:4 link:3 line:8 compute:1 nonlinearity:11 villeneuve:1 us:1 placed:1 limit:1 demonstrate:1 2πz:2 similar:6 ac:1 constant:1 defined:2 certain:2 describe:1 dξ:1 single:1 wavelength:2 physical:1 functions:1 compared:1 no:4 dashed:5 when:5 field:3 other:3 details:1 ns:6 conclusion:1 briefly:1 excitation:1 dittrich:1 jung:1 prepared:1 important:1 peak:3 suppression:14 ballentine:1 structure:6 assume:2 values:1 stegeman:1 fact:2 time:3 far:1 n2:6 external:2 |
0705.1628.txt |@word limited:1 since:2 consider:4 switched:1 rev:2 magnetic:15 lack:4 existing:2 leads:2 eds:2 ge:1 grateful:1 consists:1 causes:1 const:1 re:5 γr:8 tr:5 young:1 send:1 γt:9 tail:8 ucsb:1 perature:1 γb:12 luminosity:1 pacholczyk:2 advises:1 p2:1 conjecture:1 mpe:2 neuh:4 zhang:1 very:3 frequencies:4 wave:9 electron:3 p1:1 every:1 kϕ:6 braje:2 resonant:8 affect:1 parameter:3 condition:7 cool:1 entire:1 school:1 presented:4 turns:2 solution:1 large:2 becker:1 equation:6 cap:1 force:3 tem:1 miller:1 goldreich:4 second:3 summer:1 pass:1 further:1 estimated:2 spectral:6 intersection:1 appear:1 rate:3 uniform:2 erg:1 redistributes:1 above:5 flowing:1 order:3 contrast:1 condensed:3 led:1 fiz:1 respectively:2 nb0:2 component:3 here:1 magnetism:1 cylindrical:1 smearing:1 arons:2 along:4 standard:1 appears:1 obtained:1 receive:1 until:1 larger:2 reason:2 reports:1 periodic:1 domains:1 resonance:6 conveniently:1 blackbody:3 via:2 explained:1 δc2:1 highly:1 apj:7 earlier:2 total:2 use:4 takes:1 would:4 quasi:5 process:5 therefore:2 m2:2 means:2 planckian:3 achieving:2 ψd:1 more:1 3ev:1 pavlov:8 fb0:1 becomes:1 acceptable:1 postulated:1 emission:48 curvature:4 known:1 cases:1 aligned:2 effort:1 must:1 account:1 rotational:1 ma:1 mc:8 originally:1 work:1 theories:1 γr2:4 γr1:1 values:6 thin:2 following:3 nino:1 compare:3 bent:1 indicated:2 give:2 predict:1 relativistic:2 define:1 pons:3 high:3 lorentz:3 fulfillment:1 ψf:1 νm:4 orbits:1 hydrogen:2 occur:1 firmly:1 needs:1 rays:1 six:2 reject:1 instead:1 axis:2 explains:1 predehl:2 lai:4 may:2 max:1 reaction:1 derived:3 k2x:1 fb:1 produce:1 deviates:1 waves:12 ω2b:1 melikidze:4 data:5 umper:5 short:1 third:4 computations:1 light:1 spectra:8 lines:7 element:1 so:3 automatically:1 inhomogeneity:1 tbilisi:3 talk:1 typical:2 neglect:1 remnants:2 developed:1 over:2 eqs:1 produced:2 thermal:4 paper:4 pitch:6 mentioned:1 existence:2 kinetic:2 still:1 avenue:2 its:1 itp:1 before:1 observational:1 ginzburg:2 derive:1 outer:1 probability:1 fit:5 2e2:2 coordinates:1 detected:3 fig:10 mail:2 main:4 might:2 pce:1 freeman:1 non:2 propose:1 significance:1 2γr:1 primary:8 band:1 effects:1 they:2 half:1 rotation:3 yr:1 matched:1 2t:1 represents:1 february:1 gets:2 indeed:1 hereafter:1 always:1 university:1 level:1 drake:2 sufficiently:1 zavlin:7 magnitude:3 chandra:1 2a:1 2b:1 fields:1 instability:12 side:3 constraints:1 domain:6 ek:15 generation:4 energy:8 hard:1 related:2 eb:2 frequency:6 our:4 eq:26 out:3 shown:5 open:1 abastumani:1 rx:9 research:1 particles:25 modulation:2 u2x:3 doppler:2 linear:5 written:3 romani:3 mechanisms:1 quite:4 completely:1 term:3 org:1 estimate:3 beginning:1 generate:2 e2:4 ft0:1 interaction:3 r3:1 times:2 turn:1 length:2 leading:2 3km:1 interact:1 first:4 initial:2 features:3 manuscript:1 becher:1 assumptions:1 number:1 wash:1 l35:1 done:1 long:2 another:2 pulsar:15 miss:1 1s:2 temperature:4 introduction:1 unknown:1 top:1 behaves:1 system:1 reflectivity:2 assumption:4 too:1 1g:1 final:1 gives:1 way:1 explanation:3 acquire:5 transverse:3 rajagopal:2 resulted:1 haberl:1 optical:14 predictable:1 deceleration:1 than:6 diffusion:6 relative:1 observatory:1 effective:1 drift:1 see:8 αc:6 matter:2 absence:1 supposed:1 iron:1 lesch:2 providing:1 synchrotron:16 san:1 julian:4 spectrum:21 curves:1 substantial:1 any:2 relatively:2 lie:1 conversion:1 issue:1 angle:6 efficient:1 self:2 responsible:2 isolated:2 mechanism:7 k2:1 l33:1 take:9 forces:1 kaplan:1 adelsberg:1 lyutikov:2 3c2:1 sanwal:2 begin:2 continuous:1 ω2p:1 electric:1 though:3 object:2 reach:1 propagate:1 significant:2 acknowledgements:1 measured:8 why:1 kc:1 workshop:2 radiating:1 considered:1 average:2 malov:3 face:1 part:1 electrons:13 exp:1 kt:4 velocity:1 c2x:1 fact:3 quantity:2 slope:1 atmosphere:6 particularly:1 show:5 detection:1 supported:1 discovered:1 radio:12 substituting:2 find:5 finally:1 based:4 parameters:4 explain:4 enough:4 varenna:1 should:3 only:2 usov:3 factor:5 integrate:1 emitting:2 local:1 pointed:1 astrofizika:1 do:1 mixture:1 get:2 dependent:1 between:1 overall:3 beam:12 ionized:1 nearly:1 words:1 report:2 during:6 secondary:2 evolution:1 transversal:1 approach:1 arxiv:1 predicted:1 characteristic:1 ponents:1 explanations:1 view:1 reveals:1 observer:5 brinkman:1 maximum:4 observed:9 intensity:3 individual:1 radius:4 result:8 cyclotron:17 gmail:1 away:2 dipole:2 xray:1 state:3 unable:1 melrose:1 simplest:1 invariant:1 conditions:1 across:4 luo:1 available:1 multiplied:1 terms:4 nature:3 supernova:2 emitted:3 however:1 efficiency:1 key:1 modeling:1 come:3 distribution:19 suggested:1 received:1 burwitz:8 salpeter:2 density:6 resist:1 according:2 fulfilled:5 ln:1 receives:1 exceeds:1 requests:1 magnetosphere:6 com:2 finds:2 comes:1 nearby:1 cm:9 conclude:1 blandford:2 period:5 dimensional:2 kev:4 mc3:1 mc2:4 strong:3 described:1 pt:1 classic:1 due:2 been:7 pc:1 magnetized:1 describes:2 damping:1 anisotropic:1 ph:1 walter:3 γb2:1 direction:1 arises:4 corresponding:1 both:2 potekhin:1 argument:1 bulk:1 angles:6 c3:2 c2:2 plasmas:1 resultant:2 spin:4 former:1 present:2 case:10 p3:1 georgia:2 p5:1 straight:1 estimations:4 appearance:3 value:4 will:12 suppose:6 momentum:3 rotator:2 situation:1 region:2 vol:1 thus:1 surface:12 equal:1 cone:1 helium:1 different:2 grant:1 suggest:1 make:3 radiation:12 j1856:9 same:4 orders:2 parts:1 virtually:1 ray:24 grows:1 neutron:5 used:3 optic:2 effect:1 hand:6 moment:1 arose:1 ψ0t:2 contribution:1 recent:1 lower:1 nevertheless:1 expression:3 well:4 analysis:1 obviously:2 vladimirov:1 components:2 sets:1 coordinate:1 model:19 redistribution:1 whereas:2 left:1 distances:4 stringent:1 proposed:2 less:2 being:1 shape:2 ψ0b:2 momenta:2 yet:1 previous:1 now:4 letg:1 conclusions:2 absorption:2 auser:5 point:1 seems:1 source:2 bp3:1 vϕ:2 easy:1 mod:1 plasma:13 excited:5 match:1 easily:1 possible:3 corresponds:4 increases:1 rotate:1 five:1 using:5 accepted:1 ruled:1 atmospheres:1 effectiveness:2 lost:1 particle:1 γt2:1 follows:2 adiabatic:1 flux:4 imposes:2 unstable:1 mode:1 soft:2 essential:1 because:3 creation:1 play:1 strongest:1 growth:4 b0:4 sight:3 moskva:2 lead:1 confirm:3 kr2:2 γ2p:1 resonate:1 lattimer:1 does:4 esa:1 eso:1 propagating:1 proc:1 refer:1 limitations:1 noise:1 bb:5 convincing:1 rosat:1 perpendicular:2 stellar:1 found:3 cγ:1 after:5 stage:4 comparison:1 about:2 stationary:4 quasilinear:2 discussed:1 develops:1 range:2 larmor:1 wolk:1 mean:3 consequently:2 emissivity:1 primitive:1 prakash:1 into:2 obtaining:1 nsf:1 three:1 lies:1 turolla:2 right:5 references:1 chang:1 featureless:3 there:2 fast:1 u2:1 width:1 conservation:1 low:2 stars:4 astrophysics:3 was:3 function:12 medium:2 form:9 but:5 astro:2 ho:2 solar:1 filed:1 mnras:3 line:6 true:1 partially:1 azh:1 applying:1 ux:1 pulsars:3 variations:1 ωt:1 us:8 theoretical:2 below:2 astrophysical:1 pres:1 problem:2 ωb:5 similar:1 distance:5 hz:5 interval:1 constant:1 b2:2 introducing:1 defined:3 abstract:1 describe:2 covers:1 evidence:1 single:3 proves:1 pis:1 fizika:1 functions:1 no:4 zane:2 nb:3 when:3 nauka:2 power:1 field:15 other:4 role:1 papers:1 dipolar:1 ns:5 georgian:1 machabeli:21 polar:1 francisco:1 star:6 excitation:4 models:11 problems:3 helpful:1 generated:7 important:1 validity:1 astronomy:2 offprint:1 rxj:1 anomalous:1 practically:1 assume:6 nonmagnetic:1 age:1 required:2 fitted:3 time:6 requires:1 original:1 |
0705.1629.txt |@word proposition:23 villeurbanne:1 homomorphism:3 consider:30 remarkable:1 osp:43 results:5 leads:1 commute:2 ga:32 partial:1 expressions:1 gl:1 preserves:10 inverse:4 calculate:1 bivector:54 re:3 equivalence:3 list:3 finally:8 those:1 stable:2 rham:1 tb:1 ta:8 division:1 conjecture:1 summand:2 g1:4 g0:11 very:7 iτ2:1 choice:2 corollary:4 isomorphism:2 every:10 lecture:1 difference:1 exact:1 condition:10 tri:1 dim:5 chapoton:1 immediately:3 hamiltonian:15 turns:6 notes:1 t2:1 try:1 vector:67 conformally:1 superalgebras:7 equation:1 y0:2 computation:3 direct:8 sign:4 imply:2 further:1 reine:1 odd:56 substitute:1 linear:40 bilinear:8 appear:2 ξdξ:1 section:29 contracted:1 xτ:4 schwarzian:1 version:3 above:9 new:1 bn:3 satisfy:2 ξi:14 full:2 notions:5 degree:16 respectively:7 never:1 neveu:2 proc:1 here:4 κc:1 tangent:14 q12:1 represented:1 along:1 enveloping:2 z1:2 z2:15 obtained:5 sending:1 remark:8 study:4 studied:5 contradiction:1 p2:13 products:5 poisson:22 action:22 makes:4 quotient:1 inversed:2 beautiful:1 via:2 useful:2 projection:2 classification:15 belongs:8 proves:2 equivariant:1 viz:1 apply:1 univ:1 unit:11 use:3 projector:2 would:1 prove:16 remains:1 positive:1 h0:1 contains:15 uniqueness:1 france:1 few:1 xh1:4 call:11 therefore:13 endowed:1 conley:2 associated:1 type:28 kostant:1 more:11 pencil:3 operators:7 supergroup:1 k0:8 ip2:1 berlin:1 far:2 particular:9 known:6 projective:1 cases:1 calculus:1 r1:3 ρa:1 springer:1 valued:1 extension:28 viewed:4 recall:4 der:14 work:2 bivectors:3 infinitesimal:1 obvious:2 codimension:1 following:24 fh2:1 example:13 proof:37 f0:17 f1:8 compare:1 weaker:2 conf:1 give:3 calculation:1 dτ2:3 dτ1:3 preserving:10 respective:1 ready:2 degenerate:4 sense:7 standard:6 conversely:3 information:1 needs:1 end:14 straightforward:4 provide:2 discussion:1 acts:3 camille:1 how:3 parameter:1 classify:3 βa:1 map:22 product:9 mar:1 algebra:72 angew:1 after:1 singularities:2 different:5 inst:1 fg:1 multiplication:2 representations:24 summarize:2 compatibility:1 constants:3 realized:2 natural:2 outline:1 computations:1 explicit:2 correspond:1 element:29 darboux:1 cannot:2 so:20 allow:1 sl:1 representation:19 order:6 michel:1 typical:1 operations:1 restriction:1 commutator:4 holds:1 interpretation:1 words:4 developed:2 over:10 fλ:4 satisfied:3 abstract:1 course:5 paper:3 mentioned:1 existence:1 satisfies:3 its:5 le:1 group:2 τk:1 maps:4 τf:1 interesting:9 fix:3 affine:1 coordinates:7 actually:1 forms:17 complex:13 choose:6 jacobi:2 derivative:2 main:6 τr:3 into:4 lx:6 split:2 maximal:5 non:24 combination:2 introduce:7 functional:1 mention:1 they:1 half:2 now:11 realize:2 developments:1 structural:1 represents:1 inversion:2 gets:8 indeed:13 always:3 drop:1 identified:1 possibilities:2 2f:1 each:12 2n:4 2h:1 side:9 associative:9 homogeneous:25 differential:4 weight:2 density:2 commuting:3 ea:1 fr:1 related:3 eb:1 ξj:1 literature:1 obtains:18 iq2:1 our:2 operation:7 special:4 out:6 large:1 centerless:2 space:48 restricted:1 furthermore:6 since:19 semi:2 looking:1 reformulate:1 rational:2 reader:1 denoted:4 formula:16 math:8 shows:4 reformulation:2 theory:6 associate:4 possibility:1 quite:4 completely:1 bering:1 complicated:4 dx:1 intermediate:1 ovsienko:7 axioms:5 irreducible:2 asl:38 r4:11 definition:10 derivation:5 r2:10 geometry:9 omit:3 used:1 times:1 int:1 maximality:1 paire:2 derivations:14 δij:2 hence:2 βn:1 cc12:1 first:15 origin:1 xh:8 already:7 xn:9 symmetry:1 xm:1 number:2 rank:15 construct:3 another:3 fi:1 precisely:7 several:1 given:20 πa:10 checked:2 similarly:6 introduction:2 adjoint:4 πi:2 b2:2 twisted:1 least:1 fm:1 their:3 assumption:2 fn:3 statement:7 realization:1 recent:1 structures:4 supermanifolds:1 gives:2 lyon1:1 exactly:2 formulate:2 notices:2 part:29 jordan:5 x2:2 x0:10 x1:5 than:1 coefficients:3 aaf:3 fuchs:1 duval:2 iteration:1 see:20 preparation:2 determined:1 were:2 collecting:1 argument:1 say:2 xf0:4 intertwining:1 recover:1 any:12 contents:1 lie:223 zero:8 εr:6 εm:2 k2:9 ideal:14 εn:12 εi:21 take:1 εk:8 k4:5 xi:1 lhs:1 coincide:2 canonical:6 heisenberg:7 even:54 cnrs:1 rhs:1 algebraic:5 ker:9 eigenspaces:1 nothing:3 class:6 commutation:5 laurent:1 observation:1 characterizes:1 considered:3 chosen:2 later:1 coincides:8 χy:1 χx:2 χg:1 χf:4 bracket:16 χb:3 χa:4 left:3 physics:1 notion:13 fact:4 show:15 leibniz:4 tabachnikov:1 purely:9 relation:9 solutions:1 substituting:1 superalgebra:48 trivial:28 pleased:1 parmentier:1 q1:11 q2:10 ratio:1 dp2:2 dp1:2 eigenspace:1 explain:2 field1:1 should:1 lemma:16 only:13 explicitly:2 generators:2 equipped:8 integrate:1 constant:8 hamiltonians:3 axiom:4 do:2 his:1 means:4 df:1 dg:1 de:1 aα:3 famous:1 ones:1 aε:1 closely:2 combinations:2 dp:1 dq:1 symbols:1 densities:1 fields:37 arxiv:2 consisting:1 investigate:4 roger:1 contain:1 qi:2 kernel:3 set:7 exists:8 surjectivity:1 unpublished:1 fg0:1 ade:2 module:11 y1:2 namely:3 p21:1 result:7 p22:1 discussions:1 terms:11 λi:1 analog:7 clarifies:1 instance:6 lyon:1 satisfying:11 tensor:7 enlightening:1 nondegenerate:2 symmetric:11 written:3 αb:1 identification:2 between:4 invariant:8 geometric:4 conditions:4 checks:8 notice:2 recently:1 extend:2 however:8 submodule:1 κb:1 τj:3 amer:1 distribution:3 thank:1 both:7 essentially:1 universit:1 many:3 taking:1 τi:8 equal:1 voronov:1 quantization:1 summands:2 symplectic:22 embedding:1 casimir:1 whole:1 among:1 ci:1 cn:1 conclude:1 simple:32 cohomology:6 cf:5 dimensional:26 cz:1 taylor:1 simply:1 spans:2 polynomial:6 moreover:1 pr:1 equips:1 pq:4 abelian:7 commutative:34 second:8 basis:26 associativity:4 skew:5 copies:3 gd:2 ai:36 much:4 change:1 interest:1 basic:3 ph:1 algebras:26 ak:68 define:16 surjective:1 decomposed:1 relations:19 partly:1 commutes:1 am:1 subspace:8 lift:1 gak:1 c3:2 c2:6 c1:18 general:10 poncin:1 manifolds:2 case:43 p1:11 leites:1 look:1 aip:1 deformation:1 will:26 while:7 ar:2 suppose:1 τp:1 situation:2 skewsymmetric:1 property:4 conformal:19 correspondence:1 characteristics:1 ir:1 thus:5 them:2 according:1 ii:14 reads:1 itself:4 im:2 dual:7 susy:1 c0:7 vanish:5 superconformal:2 id:2 acknowledgments:1 par:1 classified:1 develop:2 etc:1 generic:1 suggest:1 cross:1 same:6 vaintrob:1 parts:1 k2n:2 arguments:3 survey:1 φj:1 finite:15 subalgebra:11 φn:1 independent:3 extended:2 again:12 hand:9 v0:2 v1:2 purpose:1 infinite:2 changing:1 invariance:1 genoud:3 identity:20 lxh:3 ckij:2 center:15 adα:4 expression:5 well:5 obviously:10 concrete:1 coboundary:4 contact:16 ae:1 dimension:4 dh1:1 usual:5 unified:1 manifold:1 graded:15 just:1 being:1 resp:1 identically:3 obtain:1 homogeneity:1 λc:5 λa:7 integer:2 alternative:1 λn:1 cocycle:12 note:15 intersection:1 preprint:1 family:1 generator:3 infinitely:2 nilpotent:7 seems:1 except:1 adx:2 discuss:1 appeared:1 setting:1 extends:3 δkℓ:1 easy:3 theorem:19 extensive:1 rk:3 euler:4 real:9 ample:8 easily:3 εj:4 spanned:2 corresponds:4 know:1 selects:1 21n:2 using:10 unique:10 complexification:1 formal:1 institut:1 degenerated:1 necessary:1 dq1:2 dq2:2 follows:20 ρb:1 intertwines:1 either:4 arbitrary:24 multiplicative:3 parity:8 right:7 methods:1 classical:1 sequence:1 iohara:1 φi:3 some:8 ideals:1 understood:3 q22:1 examples:11 choosing:1 respect:10 images:1 classes:1 provided:1 dense:1 presymplectic:5 morier:3 does:1 harmonic:4 provides:3 ff1:3 schwarz:2 ba:2 equivalent:8 bi:9 bj:4 bk:4 imaginary:1 super:2 properties:4 transformations:2 central:37 origins:1 most:2 pλ:1 generated:1 o:1 compatible:1 deserves:1 aℓ:5 a2:1 extensions:18 characterized:4 mixed:1 ah1:28 introduced:1 considerations:1 h2:2 image:1 h1:14 ahn:6 isomorphic:19 three:4 pair:5 square:2 references:1 inverting:2 operator:9 proportional:1 physical:1 span:1 additional:1 area:1 amazingly:2 suffice:1 there:23 antibracket:10 start:2 accordingly:1 quadratic:2 way:11 infinitedimensional:1 was:2 naturally:2 function:19 complete:6 form:36 miraculously:1 but:18 cedex:1 construction:4 link:1 functor:2 kravchenko:1 highest:1 longer:1 pi:2 applying:1 evident:1 characteristic:1 ωr:2 smooth:2 up:6 us:22 ωi:8 below:1 convince:1 sum:10 problem:4 similar:12 called:9 b1:3 changes:2 ab:3 proved:12 ad:5 defined:25 stronger:1 universal:2 aj:23 linearity:2 coadjoint:1 denote:10 associates:3 exist:1 rule:5 relates:1 corresponding:19 homotheties:1 formalism:1 identities:5 check:5 defines:8 grassmann:4 functions:37 integrability:1 no:15 generally:1 vanishes:6 field:30 other:15 details:4 bℓ:2 elements:19 symbol:1 polynomials:3 a1:70 a0:57 meaning:1 important:3 variable:3 structure:27 implies:16 anticommutator:8 assume:8 values:2 dτ:2 prequantization:1 modules:9 together:4 equivalently:2 lecomte:1 res:3 4f:1 understand:2 n2:2 lett:1 |
0705.1630.txt |@word consists:1 calculate:1 paris:3 presents:4 under:79 connects:4 every:19 convexity:5 school:1 solution:1 admissible:10 convenience:1 wulff:4 indices:1 markov:6 georgii:1 estimates:10 direct:1 second:15 rigorous:2 even:1 established:2 above:2 new:2 increasing:18 ˆn:7 notions:1 equals:11 here:9 path:19 shortness:1 logarithmic:4 derivable:2 study:8 permit:2 changes:1 diameter:18 divide:1 brn:6 rlw:2 would:1 inductive:3 negative:2 maes:2 noting:1 call:15 therefore:2 berlin:3 iv:4 must:4 springer:3 ma:1 permits:4 work:8 ωext:6 example:2 il:2 renormalization:11 give:3 end:2 provide:4 feature:1 nontrivial:1 adjacent:7 deuschel:1 config:1 description:6 after:6 diagram:1 law:6 types:1 third:2 summing:1 enter:2 order:13 restriction:8 interpretation:1 zej:3 over:17 satisfied:3 xi:23 london:1 satisfies:2 before:3 sciences:1 monotonicity:2 fix:13 edge:12 fig:6 maximal:1 them:7 pje:1 break:1 they:8 each:23 side:8 bond:23 series:1 principles:1 magnets:1 combining:3 logn:1 recognizable:2 crucial:1 iλn:29 adapt:2 mβ:5 rn:2 independence:1 turning:1 associate:2 given:34 free:5 standard:2 estimate:15 created:1 ordering:1 probab:7 already:3 rank:2 nhs:1 enumerate:1 similarly:2 top:34 xik:1 ordered:1 φsh:2 tool:2 convention:1 finitely:1 distance:5 preparation:2 classes:2 bodineau:6 tion:1 enables:1 stacey:2 mink:1 mind:1 minx:1 marstrand:2 seed:10 seen:4 60k35:1 tells:4 contents:1 maxx:1 strength:2 convenient:2 latter:1 responsible:1 isolated:1 indexes:1 uration:1 bovier:1 denominator:1 birkh:1 phase:31 partition:9 vertices:4 points:10 λln:5 notion:7 labels:2 subtle:1 d2:3 touches:9 t0l:1 do:4 dh:3 di:1 de:2 stop:1 dy:1 flour:2 covering:7 fields:3 twice:2 bad:1 34th:1 implication:3 ruins:1 reference:2 depends:7 result:9 discussions:1 techniques:5 said:1 µu:8 µt:3 µv:1 symmetric:1 µj:3 λl:4 paramagnetic:1 terms:2 nature:1 weak:1 however:2 adapting:1 facet:1 faces:14 exceeds:1 contribution:3 adapted:1 0l:2 thierry:1 height:6 directions:1 written:1 basis:2 union:1 three:2 been:2 much:4 interest:1 topics:1 quantities:2 concerning:1 θf:17 countably:2 spin:12 θw:13 suppose:1 property:2 elaborate:1 2βj:1 conditioned:1 ii:7 need:7 ik:1 ij:4 cone:1 exterior:2 wissenschaften:1 containing:1 dhk:5 make:1 several:3 independent:15 percolation:38 i1:4 laboratoire:1 hand:21 auser:1 ohlich:1 academic:1 contact:2 thk:1 jean:1 left:7 yej:10 just:6 thanks:24 facts:1 yet:14 previous:4 enters:1 instance:1 belongs:3 easy:3 εi:3 iλ:48 xs:1 possible:4 objective:3 boxes:2 ye1:1 unique:10 advanced:1 apart:1 appearing:1 bpi:2 steps:1 arbitrary:2 right:3 shapes:1 dense:2 bottom:14 normal:2 kupiainen:1 yields:8 illustration:4 properties:8 chapter:1 o:34 aεn:2 distinct:7 plus:3 eight:1 soc:1 statements:1 presence:1 bound:7 down:3 lies:2 φλn:1 methods:2 transform:1 way:4 gil:18 was:4 multiscale:1 form:10 converse:1 ψb:2 cedex:2 true:1 extremity:1 inside:1 crystal:3 anew:1 proved:7 abstract:1 covers:1 proves:1 exist:12 dλ:12 incursion:1 dβ:5 check:1 regime:3 nk:7 nl:2 no:14 whereas:2 generally:2 til:7 interested:1 role:3 models:13 uniformly:8 variable:11 assume:17 interval:1 together:8 dρ:2 time:3 neighbors:3 concept:1 remarkable:1 global:1 focus:3 leads:2 roy:1 extremities:1 lld:1 inverse:4 depend:2 graph:5 finally:3 di1:1 dokl:1 geometrical:8 dil:8 notations:3 din:1 turns:1 discrete:3 der:1 upper:2 prediction:1 cost:1 spectral:1 appear:2 uniform:14 goes:8 satisfy:5 abrupt:1 xκ:1 address:2 along:3 appears:3 change:2 box:6 studied:1 domains:1 conveniently:1 useful:1 griffiths:5 prove:20 sake:1 positive:4 predictions:1 france:2 associated:5 msc:1 introducing:2 clue:1 eλ:1 eκ:5 cases:4 logarithm:1 avoiding:2 modified:3 reviews:1 values:5 probabilit:1 believed:1 stimulating:1 claim:9 dedicated:1 figure:8 ωei:1 occur:4 verlag:3 s2:4 s1:4 means:2 write:3 criterion:4 pure:1 ensure:1 parameter:7 r2n:2 product:21 may:1 max:3 applications:5 designed:1 natural:1 whenever:5 lemmas:3 sp:46 their:4 sh:21 so:8 sn:14 sc:6 representation:4 typical:9 indeed:6 thresholds:4 course:1 statistical:3 still:2 disconnect:1 coordinates:4 forms:3 constitutes:4 main:8 djl:1 non:8 tjl:1 introduce:3 touching:2 half:2 nov:1 now:28 discuss:2 term:2 equality:6 pectation:1 establishing:1 possibilities:2 instability:1 entirely:3 domain:17 ei:52 eh:3 ek:34 ej:10 ee:2 ed:9 conventions:1 ex:6 es:1 er:3 ejl:2 shown:1 space:2 rounding:1 furthermore:4 atiment:1 dλ2:7 chevaleret:1 theory:5 rlf:2 e7:3 e1:7 e0:5 e3:1 e2:9 dλe:2 transition:6 turn:3 βc:11 βj:5 first:49 origin:1 xk:16 simplifies:1 xn:5 symmetry:1 striking:1 variables:5 xe:3 directly:1 impossible:1 open:26 xt:1 little:2 necessarily:1 crossings:1 realization:4 cite:1 gives:2 continuous:2 proving:4 x2:2 x3:1 x1:6 than:36 connections:5 schonmann:2 require:2 decompose:2 san:1 generality:1 ann:4 argument:4 generalization:2 say:16 recover:1 slab:25 any:97 efficient:1 note:9 martinelli:2 take:2 interior:2 coincide:3 begin:11 multiple:8 opposite:2 price:1 remarks:1 pages:2 hmax:3 considered:1 average:2 later:2 typically:1 laws:1 show:1 elat:3 obtains:1 threshold:5 ratio:1 outside:2 analytic:2 only:19 legendre:1 get:5 expectation:3 dyn:4 cannot:1 neither:1 regarding:1 yield:1 j0:2 j1:10 j2:4 relative:1 namely:3 y0:1 surgery:1 inequalities:3 definite:1 sites:1 enough:45 between:23 notice:1 vertical:8 jn:4 concentrate:1 comm:4 ji:1 jk:1 article:3 motivations:2 x2i:1 many:3 region:8 according:10 σy:6 σx:9 gibbsian:2 expression:1 among:3 characterization:1 overview:1 exploit:1 je:68 moreover:1 considering:1 marc:2 hardly:1 fk:19 direction:8 6d:8 external:1 former:4 those:3 countless:1 case:25 disconnected:2 eic:2 eil:23 orientation:1 cluster:86 aggstr:1 verified:1 author:1 media:29 same:15 poincar:1 arguments:2 intermediary:2 finish:1 closest:1 inbetween:1 edges:21 wired:2 eth:1 relies:2 sssr:1 roughly:1 components:1 coordinate:3 model:31 dimension:5 summer:1 being:3 when:11 resp:8 rest:2 aspect:1 touch:5 conclude:14 except:2 improvement:1 setting:1 lett:3 aspects:2 decomposed:1 coexistence:10 using:5 mod:1 either:4 dilution:2 conditional:7 deduce:1 provided:5 dimensions:1 confirm:2 pioneer:1 critical:4 decomposition:3 provides:6 refer:2 power:1 equivalent:4 notably:1 refers:1 2n:13 comparison:2 om:1 ferromagnetic:8 oh:3 stand:1 neighbor:1 mean:2 cambridge:3 inclusion:4 references:1 log:78 removing:1 strictly:3 there:74 hed:1 start:1 low:1 complete:2 applying:4 multiplicity:1 ωr:4 ωi:1 ωk:13 ωn:4 ωe:103 connect:5 detailed:1 ad:1 ai:2 describe:9 general:2 examine:1 formulation:5 again:5 field:4 mathematics:3 separate:1 vertex:4 includes:2 a1:2 important:5 ising:35 included:4 partitioned:2 original:4 consider:42 commute:2 generalize:2 follow:1 equivalence:1 tn:8 ti:1 stochastic:15 tc:1 jensen:1 straightforward:2 very:3 corollary:5 worst:4 difference:1 condition:24 randomness:4 t1:1 large:62 small:9 quicker:1 renormalized:1 design:1 perspective:1 infimum:3 pass:1 further:2 canonical:1 what:1 diam:1 sub:3 section:24 thickness:2 version:4 intersect:1 sup:26 acknowledgments:1 quenched:10 component:4 behaviour:1 relaxation:1 concluding:1 strong:3 uniquely:1 family:10 marginal:3 establish:3 select:1 proceed:3 probabilities:4 contains:3 ψj:11 h1l:2 ψl:2 taken:3 more:10 velenik:1 parallelepiped:2 domination:12 controlling:1 surface:6 particular:6 known:1 recall:11 equation:14 grundlehren:1 remain:1 dec:1 f0:10 compare:1 challenging:2 stated:1 states:1 contradicts:1 yκ:1 sense:1 lacks:2 information:7 respective:2 lexicographical:3 simplicity:1 fr:2 algebra:1 fx:8 fe:1 fi:12 horizontal:15 choice:4 fl:1 negligible:1 fundamental:5 fα:3 help:4 developed:1 soon:1 ferromagnets:2 held:1 paper:3 through:3 y1:2 existence:21 y3:1 y2:1 avenue:1 its:24 picard:1 lateral:3 actually:1 absence:3 microscopic:1 systems:8 finer:1 yi:10 yk:14 good:12 motivated:1 yn:3 propose:1 framework:3 always:2 events:11 2d:6 inequality:9 2c:1 2l:6 found:1 universit:2 characterized:1 another:4 weight:3 energy:1 positioned:2 expect:1 beyond:1 event:24 dominates:6 since:31 denotes:1 induced:2 occurs:5 reformulated:1 ast:1 reason:2 barsky:1 beginning:1 definition:22 omit:1 imry:1 consequence:13 reinforced:1 major:3 enlarges:1 probability:46 relate:1 number:1 linking:1 smaller:11 done:2 menshikov:1 passes:2 differ:1 heads:1 temperature:5 introduction:5 least:22 assumption:21 calculations:1 jei:1 elaboration:1 warmly:1 saint:2 akad:1 immediate:7 measurable:11 part:4 norms:1 believe:2 lebowitz:4 determines:1 double:5 determined:2 contrary:1 doubly:6 peierls:5 motivation:1 derivative:2 7l:4 elsevier:1 paths:7 generalizes:1 depending:1 lim:40 self:2 build:1 measurability:1 play:2 towards:5 measures:10 most:18 significant:1 probabilistic:3 stands:3 deviations:7 exn:1 clear:5 cover:1 kn:1 countable:4 h2l:1 exp:37 physics:1 joining:1 phenomenon:4 wehr:1 relation:2 find:1 parameters:5 distributed:2 betray:1 factor:1 notation:4 dependent:1 actions:1 closely:1 boils:1 bricmont:1 alexander:1 bˆ:1 2dβ:1 arxiv:1 exercise:2 set:25 ser:1 φei:4 see:24 close:2 chayes:7 minoration:1 fortuin:2 unions:1 smallest:2 intensities:1 hold:4 conditions:6 knowing:1 φe2:2 opposition:2 φe1:2 interface:10 ferromagnet:1 both:11 cubes:1 last:16 desired:1 connection:3 context:1 whole:1 arbitrarily:1 aizenman:5 point:14 simple:4 corresponds:5 whatever:1 coincidence:1 dimensional:8 simply:1 adaptation:13 ensures:1 described:4 b0l:1 z1:1 pc:8 describes:1 coarse:33 marginals:1 ph:1 pn:2 pl:8 generating:1 gap:1 lives:2 exponential:3 frozen:3 mli:5 while:15 behavior:6 couplings:8 loop:3 jpn:1 obstacle:1 foreword:1 belong:1 modification:8 used:1 moment:2 uses:1 necessity:1 lower:9 task:1 analysis:6 eles:1 λp:3 λe:11 alternative:2 λn:116 bi1:1 letting:3 ee1:4 ee2:5 theorem:52 remaining:2 bin:1 bil:42 additivity:1 modifications:4 imposed:1 follows:22 facets:4 separately:1 continue:2 eei:2 eek:1 translated:1 pointwise:1 disorder:7 essential:2 spins:1 mathematical:4 often:2 some:24 remarking:2 understood:1 b0:2 examples:1 scale:6 1g1:4 conditionally:3 connecting:9 tends:1 prof:1 proc:1 bl:1 bi:13 bj:1 step:8 br:4 bx:3 liggett:2 1gn:4 modal:1 consequently:1 block:3 cutoff:1 into:8 appropriate:2 statistics:1 placing:1 question:4 long:1 borel:5 δld:1 link:2 ioffe:1 line:1 up:2 us:18 sum:2 autocorrelation:2 fluctuations:3 similar:3 constant:1 defined:11 coincides:4 influence:3 warning:1 pˆ:3 analyticity:1 dashed:1 application:4 2dl:1 calculating:1 problems:1 shk:18 generated:1 fisher:2 mathematischen:1 structure:20 independently:2 suffers:1 implies:23 required:1 holes:1 graining:33 requires:1 having:2 issued:8 results:4 illustrated:2 proposition:37 stochastically:9 gj:2 gi:17 uniqueness:9 include:2 dramatically:1 random:40 presently:1 positions:3 notes:3 configurations:7 dilute:7 disordered:5 zk:2 zd:52 imply:1 dynamics:10 index:3 3i:1 3h:2 3n:2 3l:3 slabs:18 3d:4 led:1 degree:4 respectively:5 lek:1 following:20 objects:1 εn:3 cerf:6 remark:19 technical:1 larger:26 contradiction:1 makes:5 nearest:3 limp:1 limh:1 limn:1 liml:3 apply:1 use:11 links:1 remains:2 chl:2 next:1 few:4 usp:16 cram:3 rare:1 iii:10 integrating:1 averaged:32 ρl:11 obvious:1 proof:67 control:7 impedes:1 weaker:1 decorrelation:1 process:3 high:4 assumptions:3 holds:15 varies:1 instead:3 stoch:4 profile:1 tension:3 eatoires:1 collection:3 inst:1 efficiently:1 correspond:1 extremal:2 realizes:2 jussieu:1 nonequilibrium:1 including:2 ld:12 outer:3 la:1 ln:7 lk:10 li:18 cardinal:1 defining:2 lx:9 bernoulli:7 prevision:1 newman:3 mention:1 realize:1 february:1 university:1 l2:2 l1:8 crossing:41 constraints:1 subset:2 erisque:1 related:4 decays:1 measure:87 separating:1 blocks:12 transitions:2 out:2 develop:1 rev:4 ωe0:8 lecture:3 induction:2 math:8 statist:4 fluctuates:1 interactions:3 discontinuity:1 eck:1 supercritical:4 surely:3 interaction:2 geometry:2 could:5 keep:1 length:10 hence:33 hypercubes:1 1e1:3 precisely:1 bears:3 πk:1 πn:5 system:2 glauber:5 intermediate:2 πw:1 be2:1 potts:9 behaved:1 final:2 1ei:5 completed:1 exactly:1 1en:3 zλ:3 july:1 bei:1 submitted:1 disjoint:9 border:1 clearly:5 min:7 able:1 εl:8 concerns:2 pivotal:22 lectures:4 co2:5 connected:29 but:3 definitions:3 kasteleyn:2 volume:10 parametrize:1 stronger:1 face:17 fact:11 12d:1 ωce:3 trivial:3 sh1:1 sh2:1 sh3:1 based:2 basel:1 controls:2 should:3 lemma:34 candidates:1 attained:1 local:11 achieve:3 equilibrium:7 slows:1 handle:1 bonds:1 joint:9 ones:2 words:5 quantifies:1 processes:1 numerous:1 nauk:1 contain:2 fixed:1 pertains:1 view:11 hκ:3 requirement:2 exists:50 correlations:1 intensity:1 phases:2 struction:1 dln:1 dlr:14 state:6 closed:3 boundary:27 connectivities:1 counterexample:1 ends:2 hypothesis:3 key:2 configuration:10 restrictions:2 limits:2 taking:3 decay:1 equal:15 chosen:1 passing:1 ωf:4 otherwise:1 ck:1 ci:7 relevant:1 co:1 cn:5 cl:9 ca:1 cg:1 cf:8 ce:9 distinguish:1 cx:5 sequences:1 respect:2 define:16 cx2:4 corresponding:9 sufficient:2 clusters:25 c2:9 c1:16 present:15 multi:2 subsets:3 value:5 rectangular:2 will:13 owns:1 layer:2 almost:4 vi:1 thus:10 site:2 vn:9 dual:1 s2d:3 fkg:2 parts:2 φe:10 largest:1 φi:12 φj:114 finite:12 infer:3 difficult:2 reporting:2 v1:1 compared:2 urich:1 infinite:5 expand:2 center:1 disappears:1 well:8 sets:4 position:2 magnetization:4 less:3 obtain:5 preprint:1 density:19 lattice:2 other:17 extends:2 propositions:1 increases:1 know:3 press:2 intersection:3 necessary:2 grimmett:7 replacement:1 exceed:1 because:5 sequence:9 phenomena:2 choosing:1 convex:5 proofs:3 huse:2 happens:2 lead:1 does:17 assuming:5 chains:1 simpler:4 actual:1 extension:3 introduces:1 dependence:2 compatible:6 seeds:8 introduced:1 h1:4 sharpness:1 van:1 naturally:1 function:36 hs:16 sequel:1 overlapping:1 hj:2 hk:6 construction:10 hl:10 convergence:3 made:9 compute:1 whether:2 ωpn:1 below:9 limit:3 empty:2 distribution:2 mechanics:1 denote:28 our:15 undiluted:1 inf:54 diego:1 functions:2 hld:1 detail:1 book:1 conclusion:3 stat:1 αex:2 else:4 droplet:1 portion:2 |
0705.1631.txt |@word surrounded:1 consider:2 rev:13 magnetic:26 varying:7 dynamic:1 splitting:3 mx:6 illustrated:1 go:1 follow:1 expressions:1 contributions:2 weakly:1 devoted:1 whose:1 inverse:1 depend:1 calculate:1 attracted:1 eigenbasis:1 technique:1 ts:1 environment:21 those:3 include:1 applied:10 adiabatic:2 amplitudes:1 advantage:1 returning:1 very:5 equilateral:1 induce:1 focus:1 matsuda:1 orientations:2 stays:1 mixing:1 experimentally:1 bottleneck:2 condition:2 four:2 exponential:1 level:20 anisotropy:2 laue:1 magnet:8 vector:14 science:1 small:8 eigenvalues:2 barbara:2 noted:1 degeneracy:1 upper:1 smaller:2 zi:1 oscillation:2 direct:1 feasibility:1 fold:1 zero:9 displays:1 further:1 dynamics:12 theory:6 spectral:1 what:4 blum:1 chiorescu:1 section:1 while:1 current:1 experiment:3 above:2 new:2 contrast:1 splittings:1 compact:1 bi:2 full:1 chose:1 ibid:1 exchange:1 never:1 component:8 here:4 understanding:1 behaviour:1 corporation:1 objects:1 separation:1 relaxation:3 active:1 diagonalised:1 equations:1 excitations:1 fatter:1 great:1 dates:1 study:2 studied:1 allows:1 completely:1 zener:8 suggests:1 atom:1 periodic:2 suggestion:1 usually:2 resonance:1 sinusoidal:1 studies:2 involves:1 plotted:1 via:2 useful:5 scales:2 plenum:1 conditions:1 visible:5 rρ:2 total:3 manipulate:1 kerler:1 use:1 towards:1 asymptotic:4 would:7 probabilities:2 sowjetunion:1 give:3 predictions:1 flat:1 france:2 moriya:3 therefore:4 memory:2 taken:3 more:9 netic:1 jpn:3 molecules:1 05j:1 relax:1 clearly:1 remark:6 operators:2 apparent:2 distribution:1 validity:1 tested:1 berlin:1 transient:4 particular:5 known:2 cases:1 must:3 high:3 account:2 rotational:2 locked:1 recall:1 past:3 des:1 peeters:1 minimum:1 values:2 temperatures:4 choi:2 following:2 my:2 example:2 fe8:1 mz:12 control:2 ions:4 compare:1 transition:2 figure:8 chosen:1 calculation:3 purposes:1 saito:1 involve:2 villain:1 assumptions:1 attain:1 degenerate:5 yet:1 occur:5 axis:3 information:5 needs:1 rium:1 rather:1 purpose:1 six:1 write:1 pure:1 significance:1 hartmann:1 instead:1 absolute:1 parameter:1 profile:1 humboldt:1 staying:1 mat:1 beauty:1 may:14 oscillators:1 after:1 long:1 applications:4 modest:1 plane:2 designed:1 demonstrating:1 coming:1 law:1 response:5 included:1 sz:2 stress:1 short:1 dynamical:3 effective:3 vanadium:1 light:1 lines:1 correspond:2 st:1 ziman:1 complexity:1 luban:2 so:4 enter:1 taking:1 ostrovsky:1 order:6 stowe:1 pulsed:1 interpretation:1 correlation:1 indeed:1 vary:1 soc:4 cohen:1 course:1 thermal:2 experiments:9 including:2 statistical:2 argued:1 statements:1 avenue:1 its:4 spinger:1 before:1 strikingly:1 difference:3 longitudinal:6 manuscript:1 fit:1 decay:1 energies:3 interesting:1 redfield:2 boson:1 writing:2 degrees:2 choose:3 persist:1 rabi:2 decades:1 h0:14 ωkm:4 yi:1 non:6 greater:2 combination:1 propose:1 practice:2 fig:6 landau:8 break:1 couples:1 effects:7 they:6 acta:1 sweeping:1 now:5 discuss:1 worlds:1 february:1 several:4 even:1 fully:1 university:2 hamiltonian:8 sufficiently:6 each:4 crossing:16 found:2 2j:3 mean:2 em:1 kutta:1 ohmic:1 ei:1 primarily:1 ek:2 ej:1 generation:1 series:1 energy:9 frequency:3 principles:2 related:3 toda:1 used:4 static:3 ex:3 magnets:18 ez:8 eu:2 our:6 happen:1 transitions:4 eq:3 out:3 large:4 shown:4 matrix:11 borderline:1 space:2 furthermore:3 since:1 crucial:1 projected:1 looking:1 si:1 formula:2 machida:1 induced:2 issue:2 integrated:1 math:1 shows:1 occurs:1 wiley:1 inert:1 interactions:9 little:3 standard:2 difficulty:1 reason:1 markovian:1 term:3 put:1 region:1 hand:1 e1:1 finite:1 e2:2 barkhausen:1 degeneracies:1 interaction:1 chiral:5 geometry:1 could:3 computers:2 times:2 turn:2 conducted:1 period:1 isotropic:4 assumed:2 parallel:9 repeats:1 onto:1 first:6 initial:5 features:3 probability:4 wave:1 magnetizations:2 number:1 xx:1 improvements:1 done:1 ρtot:3 directly:1 impossible:1 precisely:1 open:3 causing:1 illustrate:3 timothy:1 given:3 necessarily:1 temperature:8 introduction:1 crossings:9 structured:1 system:17 least:5 raedt:2 needed:2 master:2 observations:2 passed:1 oldi:1 1k:1 molecular:20 structures:1 low:5 centred:1 calculations:2 wendell:1 1j:2 transverse:21 part:1 michielsen:1 mitamura:1 than:9 coefficients:1 sessoli:2 approximation:3 perfectly:1 determines:1 unfortunately:1 plateaux:1 edition:1 breuer:1 require:1 cimento:1 richer:1 seated:1 states:14 future:3 supposed:1 regions:1 were:2 perturbative:1 hz:13 formulated:1 symmetries:1 landauzener:1 spectrum:15 curves:1 say:1 rau:1 close:2 need:3 seen:6 egime:4 relatively:4 hypotheses:3 sandwiched:1 strength:1 helv:1 depending:1 studying:1 responsible:1 isolated:1 note:2 mix:1 ideal:1 potential:1 horowitz:1 build:1 analogy:1 online:5 xi:1 switching:2 hyperfine:1 heisenberg:1 blue:1 cnrs:1 added:1 unless:2 trace:1 shall:8 ıve:1 who:1 molecule:2 liouville:1 breaking:1 singlet:1 most:2 device:2 inserted:1 kb:1 especially:1 considered:4 calculated:3 h2v:1 differ:1 heat:2 physica:1 traditional:1 points:1 thesis:1 principle:1 exp:3 velocity:4 typically:1 sum:1 precise:2 thomas:1 phenomenon:1 show:4 probe:1 v15:6 perpendicular:11 fine:2 based:3 just:1 parameters:4 enough:1 should:4 being:1 only:5 explicitly:1 equation:5 rich:1 integrate:2 milton:1 interested:2 equilibrium:17 do:2 dm:14 triangle:3 di:1 dependent:3 βh0:1 de:2 hussain:1 dz:7 nearly:2 words:1 exchanges:2 during:1 lett:5 represented:1 gen:1 precession:1 heaviside:1 htot:1 fields:7 arxiv:1 yield:1 whether:2 paper:2 london:3 nβ:2 fixed:1 discussing:1 doublet:2 set:2 aspect:1 demkov:1 comparable:1 packet:1 ωt:2 opposite:1 see:2 individual:1 modelled:1 uller:1 discussions:1 sen:2 forthcoming:1 rettori:1 subject:3 coils:2 hilbert:2 compounds:1 phonons:1 nuclear:2 dipole:1 materials:1 symmetric:1 importance:1 state:6 determined:5 inset:1 closed:2 between:13 conceptual:1 probably:1 reading:1 approach:7 µb:1 available:1 relaxational:1 terms:3 anti:1 nature:4 qubits:1 attention:1 weak:7 however:4 jr:1 vanishing:1 ji:1 probing:1 article:1 maga:1 hashitsume:1 come:1 symmetry:7 thank:1 suggested:1 reaction:1 essentially:2 last:1 always:1 ill:2 conclusions:1 equal:1 against:2 etc:1 wernsdorfer:2 ramsey:1 figures:3 context:1 beyond:1 passing:1 argue:1 experimental:3 otherwise:1 detailed:2 ci:2 unclear:1 elser:1 timescale:1 characterization:1 simple:6 address:1 corresponds:2 2nd:1 dimensional:1 distinguish:2 dsz2:1 simply:1 written:1 along:1 second:1 chitra:2 described:5 leggett:1 leads:2 chirality:2 three:10 tiny:4 ai:2 much:4 slowly:1 interest:2 anisotropic:1 correction:1 systems:10 magnetisation:1 direction:6 contribute:1 both:4 concerning:1 photon:1 achiral:2 argument:1 understand:2 external:11 presented:2 spin:20 present:3 case:9 multi:2 look:4 josephson:1 pacs:1 defining:1 bω:3 value:3 will:10 near:1 behavior:1 applies:1 situation:1 tunneling:10 couplings:2 loop:4 identical:1 vectors:3 coupled:4 almost:1 formulation:1 thus:4 dalal:1 surface:1 ii:3 itself:2 cond:1 henv:2 different:10 righthand:1 sensitive:1 perform:1 make:4 renormalize:1 intrinsic:1 cross:3 same:1 any:1 shorter:1 unity:2 runge:1 units:13 dimensionless:1 physical:3 breaks:1 development:1 independent:2 literature:1 numerical:2 effect:2 hysteresis:11 doublets:1 kubo:2 levels:14 v4:1 appreciable:1 infinite:1 emphasised:1 recent:3 relies:1 lower:1 mech:1 nevertheless:1 changes:1 xkm:1 well:3 evolves:1 thought:1 solids:1 contact:1 epj:1 components:11 sets:1 quantitative:1 model:9 maxime:1 dimension:1 vogelsberger:1 restore:2 magnetization:34 generalization:1 moments:2 when:5 rotated:1 obtain:2 rest:1 oxford:1 shape:1 relevant:2 virtual:1 questions:2 multiplet:1 compared:1 previous:1 doctoral:1 rapid:1 density:10 extra:5 except:1 exclusively:1 nojiri:3 jules:1 color:5 internal:1 questioned:1 easy:1 5j:2 take:5 real:2 antiferromagnets:1 aspects:4 around:5 depends:1 represents:1 caldeira:1 showing:1 results:2 possible:1 harmonic:1 tunnelling:2 makes:1 background:1 press:1 using:1 makhlin:1 grenoble:2 mod:1 loss:1 martyrs:1 cu3:6 like:1 tomita:1 follows:1 velocities:1 extremely:3 informative:1 either:3 arbitrary:3 experimentalists:1 noncollinear:1 pereira:1 essential:2 spins:9 function:3 shed:1 because:6 old:1 often:1 classical:1 smoothly:1 phenomena:3 back:1 driving:1 another:1 elements:1 nonetheless:1 oscillations:28 multiple:1 eβω:1 anisotropies:5 scale:7 ajiro:1 lead:1 fourth:1 stronger:1 electromagnetic:1 measurements:3 langevin:1 integration:1 instantaneous:3 does:4 linearly:1 proc:1 majorana:1 measuring:1 object:1 nmr:1 power:1 seconds:1 wavefunctions:1 oscillating:2 analysed:2 rue:1 broken:1 step:1 chiralities:1 super:1 properties:2 panel:2 comparison:1 about:1 central:1 carried:1 freedom:2 dependence:2 o:1 reduced:4 range:2 repulsion:3 cos:2 loops:6 bloch:2 converging:1 mechanics:2 thinner:1 convergent:1 thermostat:1 presence:1 into:2 within:1 numerically:2 steady:1 bath:13 phase:3 appropriate:1 right:1 references:1 been:6 determine:3 operator:2 bosonic:1 approximately:1 institut:1 additional:5 featureless:1 transfer:1 suffice:1 there:12 question:1 fast:2 lags:1 tannoudji:1 editor:1 way:1 miyashita:3 lowest:4 hx:8 annals:1 form:6 some:4 differences:1 uckelberg:1 triangular:5 but:9 benedict:1 cedex:2 properly:1 might:1 larger:1 impedance:1 true:2 raising:1 longer:1 absent:1 garanin:1 instructive:1 mn12:1 characteristic:3 smooth:1 up:2 verlag:1 publishing:1 ωi:1 below:1 gaps:2 limit:3 planes:1 ey:1 problem:3 define:4 clear:2 strongly:1 later:1 constant:1 computing:1 defined:1 certain:1 abstract:1 describe:1 general:3 quantum:18 single:8 simulations:2 triangles:1 regime:6 avoided:14 ideally:1 no:2 na:1 whereas:1 storage:2 detail:3 nf:1 ballou:1 field:52 other:4 details:6 really:1 sufficient:1 conclude:1 politi:1 stat:1 repeat:1 calculating:1 time:24 vertex:1 variation:2 enlargement:1 generated:2 allowing:2 dissipation:3 gap:3 structure:1 building:1 implies:1 coupling:12 dω:2 physics:3 required:1 pseudo:1 together:1 phonon:2 memories:2 observables:2 decoherence:2 nuovo:1 |
0705.1632.txt |@word hº:1 ωpi:2 h3:1 plasm:1 ωce:2 ωei:2 ωcs:9 vs:5 b0:2 ex:1 b2:1 ωpe:2 vx:1 ivy:1 n0s:1 iey:1 ps:2 αe0:1 ωps:10 γs:3 ee0:1 sµ:1 k2:1 ze:1 m2e:1 ph:1 ns:4 sin:1 kc:1 ms:3 v02:4 may:1 ikz:1 cos:1 zº:1 c3:1 c2:11 bx:1 e0:8 c5:1 he:1 me:2 iωt:1 qs:4 b0z:4 cmi:1 qs2:1 0z:2 physics:1 arxiv:1 ωt:2 iqs:1 iby:1 mv:1 qe:1 kv:1 exp:1 ωp:4 kz:2 n2:5 btot:1 ωe:1 e2:1 |
0705.1633.txt |@word slope:2 abundances:1 code:2 consider:1 represent:1 hamburg:1 results:7 bc:1 integration:1 four:2 stronger:1 gm:2 abundant:1 assembled:1 increase:4 calculate:1 does:3 th:1 under:6 cm3:1 mpc:1 very:8 ostriker:4 every:1 difficult:1 uncertain:1 cool:1 tran:1 fhi:1 level:1 e230m:2 t4:1 shock:2 list:3 applicable:2 correct:1 large:5 detected:3 small:2 inspection:1 ryd:1 favoured:1 bd:1 smaller:1 zh:1 zi:1 zd:1 ze:1 zg:1 za:1 literature:1 modified:3 metagalactic:2 rate:5 doppler:10 pasp:1 spectrograph:3 chen:2 estimated:4 observatories:2 λcdm:1 spectral:1 index:1 errors:4 hernquist:1 bb:1 section:2 selected:2 near:2 expressed:2 current:4 3i:1 obvious:1 contributes:1 l1:1 method:2 temperatures:10 coefficient:2 condensed:1 oegerle:3 degree:1 whose:1 galaxies:1 error:6 component:3 here:1 bi:1 behaviour:1 reported:3 l23:1 objects:2 others:1 giroux:1 path:5 along:1 table:4 change:4 obtained:2 search:5 dividing:1 study:3 studied:2 completely:1 hydrostatic:2 significantly:1 amount:3 resulting:7 sternwarte:1 prochaska:2 adopting:1 narrow:2 makes:1 nmax:3 absorbers:25 scales:1 explained:1 marked:5 highly:2 apj:18 decrease:1 total:20 research:1 unit:3 eye:1 would:12 contains:2 dnh:2 sample:19 songaila:1 therefore:2 taken:5 associated:1 pipeline:1 until:1 more:5 flat:1 treated:1 excluded:3 corrected:1 emission:3 warm:3 normalized:1 particular:3 known:2 cases:3 blocking:1 clumps:1 had:2 abundance:2 comoving:4 ρc:3 sightline:1 equation:1 work:2 oscillator:1 mh:1 reproduce:1 λcut:1 hardest:1 values:2 thin:2 universe:5 believed:1 gravitationally:1 hamburger:1 rodriguez:1 neglected:1 high:13 indicates:2 slit:3 minimum:1 numbers:1 interpreted:1 hydrogen:15 korista:1 absolute:1 rays:1 distinguishable:1 divided:2 uves:7 regions:4 far:1 hot:5 burles:1 forest:3 pure:4 significance:1 l9:1 parameter:16 stis:9 profile:2 galactic:1 substructure:2 may:3 wakker:1 derived:2 catalog:1 produce:1 noise:7 fg:8 fits:2 law:1 data:24 sorted:1 effective:1 light:1 spectra:7 lines:13 element:2 green:2 sect:4 decreasing:1 sb:1 sg:4 order:1 typical:2 our:2 wavelengths:1 katz:2 saturated:1 dx:1 bracketed:1 considerations:1 minimising:1 indeed:1 over:5 mainly:2 undetected:1 σww:1 years:1 thermal:9 paper:1 including:3 statistical:1 signs:2 mentioned:1 cold:1 still:2 its:7 galaxy:1 observational:1 silk:1 efstathiou:1 fit:3 varies:1 ionised:5 better:1 ricotti:2 absence:1 primordial:1 systems:2 clusters:2 schmidt:2 might:5 into:4 non:7 good:5 influences:1 combination:1 cen:5 fig:2 investigated:1 fion:3 dav:6 effects:4 they:4 clouds:1 now:2 continuum:8 represents:1 february:2 several:1 miralda:1 oxygen:4 brightness:1 even:2 traced:3 zb:1 possibilities:1 kpc:1 mode:1 each:11 found:14 beneath:1 higher:17 traces:1 constraints:1 whim:33 telescope:4 populated:1 colder:1 energy:2 hard:2 gaussian:4 photoionised:12 weinberg:3 ex:1 combining:1 assumption:6 approximated:2 transitions:1 eq:12 out:1 shown:1 ferland:4 space:3 quality:5 furthermore:4 since:17 danforth:2 denotes:1 content:6 asymmetries:1 bla:17 integrated:2 shows:5 ionisation:14 linear:1 written:1 mechanisms:1 possibility:1 quite:1 approaches:1 formation:1 imaging:1 estimate:2 additional:1 hubble:5 created:5 could:13 transition:1 cosmic:1 times:1 turn:1 length:6 corrections:1 major:1 spergel:2 features:8 manuscript:1 nhi:4 number:6 done:1 directly:2 impossible:2 sutherland:2 size:1 given:2 temperature:22 service:1 strict:2 introduction:1 unknown:3 system:1 least:6 sargent:1 their:1 cooling:1 intermediate:2 wisotzki:3 observations:3 calculations:4 rates:1 trend:1 hundred:1 final:1 gives:3 shifted:1 fraction:23 discussion:1 baryon:36 relative:1 shallow:4 resulted:3 part:2 nh1:1 too:3 apjs:5 zc:1 than:3 wide:2 showed:1 approximations:1 largely:1 imply:1 aims:1 matter:9 determined:6 supposed:2 recombination:1 tion:1 exposures:1 solely:1 shrinks:1 hagen:1 correction:1 anh:1 spectrum:4 valageas:2 astrophysical:1 inherit:1 close:1 quasars:7 cosmology:2 clearly:3 relatively:3 lie:1 absorber:12 studying:1 nucleosynthesis:1 able:2 note:2 empirically:1 without:1 2006a:5 2006b:10 new:1 strengths:1 tool:1 echelle:1 play:1 towards:1 multiple:1 trace:3 though:3 barycentric:1 most:8 boltzmann:1 intergalactic:6 connected:1 phase:2 baryons:18 future:1 measured:1 model:1 nagamine:1 volume:2 cause:1 placement:2 incomplete:1 calculated:2 broadened:2 flow:1 repeated:1 km:13 gnedin:1 bade:1 verde:1 sources:2 american:1 velocity:1 physics:1 bulletin:1 nmin:3 precise:1 selection:1 simultaneously:1 show:1 blended:1 detection:4 supported:1 vizier:1 l117:1 relation:1 substituting:1 impact:2 photoionisation:13 ratio:5 knowledge:2 parameters:4 baryonic:7 sembach:8 state:1 should:9 ed:1 only:4 smallest:1 candidates:1 factor:2 inhabit:2 local:6 astronomical:1 equilibrium:5 dn:1 do:1 his:1 dominant:2 lyα:6 zcut:1 get:1 dependent:3 vary:1 preferred:1 yielded:2 ωdm:1 dz:2 nearly:1 words:1 propagated:1 during:1 averaged:1 collisional:3 blends:2 following:2 evolution:6 densities:2 turbulence:1 covering:2 arxiv:1 yield:1 summary:1 dopita:2 shull:4 instrument:1 contain:5 mcintosh:1 2kt:1 set:2 often:1 hν:1 sensitivity:2 blend:1 observed:4 opposite:1 intensity:4 individual:1 result:7 madau:4 bth:1 best:1 awaits:1 phases:3 detect:4 fang:1 macroscopic:2 currently:1 symmetric:1 originated:1 enough:1 classes:1 various:1 between:2 αh:2 approach:4 tent:6 available:3 terms:2 extend:1 missing:2 baade:1 were:21 weak:1 however:9 incident:1 add:1 key:1 fluctuations:2 distribution:3 received:1 cos:1 last:2 missions:1 resides:1 many:2 region:1 uncertainty:3 according:3 sensitive:2 contribution:2 estimation:3 whole:5 reside:2 detailed:2 co:1 cm:7 bell:2 overview:1 jeans:1 corresponds:1 polynomial:2 hotter:1 throughout:1 mission:1 lies:2 escude:1 broadening:10 lyman:16 basis:1 addition:1 equations:1 create:3 lehner:6 due:4 been:6 lopez:2 reduction:1 describes:1 pg:5 interest:4 expected:8 ph:2 universal:3 treatment:1 tytler:2 corresponding:3 both:1 gas:34 great:1 neumann:1 determination:5 systematic:1 covered:2 suspected:5 plasmas:1 careful:1 diffuse:11 present:1 case:1 multi:3 main:1 atmospheric:2 limits:2 reliable:4 value:8 pixel:2 will:9 while:5 pressed:1 promising:3 richter:13 inherits:1 schaeffer:1 vi:1 blas:5 simulations:1 thus:18 surface:1 ii:3 ij:1 seen:2 limit:10 helium:2 different:8 theuns:1 make:3 radiation:6 cross:1 same:4 unity:1 parts:1 underestimate:2 widely:1 largest:1 survey:1 ray:4 residing:1 care:2 used:16 slightly:1 again:3 effect:2 ion:2 christlieb:1 discernable:2 lower:12 off:4 penton:2 programs:1 studies:1 tentative:8 well:5 remain:1 analysis:5 edge:2 solve:1 mathews:2 simulated:1 ionising:5 left:1 just:8 quasar:8 proximity:1 sizes:1 forests:2 proposes:1 shape:11 intervals:2 summed:2 speed:1 previous:2 cut:2 density:62 absorption:15 seems:3 except:1 source:2 haardt:4 other:1 board:1 collapse:1 grating:2 reason:2 plasma:2 servicing:1 real:2 usable:2 around:1 depends:2 bryan:1 big:2 online:1 possible:1 dark:2 possibly:3 increases:3 five:4 background:10 vacuum:1 average:2 using:15 accepted:1 like:1 particle:1 shaped:1 verner:1 signal:5 velocities:2 shapes:1 flux:1 detections:13 yields:1 page:5 opacity:1 another:1 methods:1 some:3 added:1 sight:3 redshifts:9 neglecting:1 savage:11 scale:1 confirm:1 detecting:1 broad:17 avoid:2 measurements:3 fivefold:1 per:6 planck:1 nonthermal:1 when:1 critical:1 assuming:1 eso:4 installed:1 ba:1 schaye:6 ωbm:2 power:1 slight:1 remembered:1 equivalent:1 pose:1 bh:1 analysed:6 pascual:1 offset:1 plots:1 properties:5 stage:1 about:6 origins:1 column:16 tracing:1 discussed:3 o:7 range:20 σw:1 determinable:1 reimers:6 mean:3 consequently:1 µmh:2 jν:3 metallicities:3 redshift:33 instruments:4 h0:4 within:4 bound:1 three:1 included:2 because:2 references:1 determine:2 heated:2 reworked:1 log:17 assumed:1 there:2 overestimate:1 width:6 restricts:1 much:4 low:16 stars:1 series:1 astrophysics:1 fechner:3 was:23 function:1 medium:4 complete:6 forming:1 collapsed:1 but:1 astro:2 neutral:8 hi:1 rauch:1 satisfactorily:1 solar:4 hm:2 mnras:1 line:16 highest:3 considerable:3 he:22 made:1 applying:1 evident:1 society:1 characteristic:1 gravitational:1 uv:6 up:6 frequency:1 ωm:1 hs:1 detectable:5 problem:3 ωb:21 called:1 tripp:14 distance:1 strongly:4 required:1 constant:6 defined:2 cover:1 abstract:1 contribute:4 influence:2 metals:1 general:3 single:1 dν:1 bg:3 wavelength:7 archive:1 nh:20 ni:1 functions:1 compared:1 no:2 amounts:3 infall:1 nb:6 percent:1 ne:1 tumlinson:1 field:1 valid:1 role:1 jenkins:1 igm:22 hydrodynamical:1 observable:1 optically:2 internally:1 provided:1 models:1 qso:1 stocke:2 variation:1 metallicity:2 important:5 additionally:1 variable:1 astronomy:1 agn:1 algorithm:1 assume:1 requires:1 proposed:1 interval:6 governed:1 mass:5 fitted:1 n1:1 resolution:7 peiris:1 once:1 |
0705.1634.txt |@word represent:1 quarks:6 gs:2 consider:5 remarkable:3 rev:21 magnetic:1 people:2 results:5 four:3 scalar:2 gd:3 generalize:1 york:1 go:4 sci:1 expressions:1 contributions:5 cases:1 sch:2 compact:2 increase:1 inverse:5 depend:1 calculate:4 tr:6 charge:3 does:6 indicate:1 under:3 regal:1 rischke:1 include:5 tc:57 iνn:1 applied:2 g0:45 far:1 frequencies:1 decreases:1 differently:1 induce:1 wave:3 prog:1 ultraviolet:2 dispersions:2 literatures:1 difference:7 matrices:3 condition:10 leads:3 nonrenormalizable:1 unlike:1 presented:1 crossovers:2 t2:1 solution:1 trg:1 occurs:1 large:9 solid:7 shuryak:2 small:9 ǫb:2 kitazawa:1 upper:1 strongly:5 approximately:3 pekalski:1 renormalized:1 consistent:4 coefficient:4 behave:1 approximation:14 zero:20 evaluated:3 chen:7 iσ2:1 remarkably:1 canonical:3 even:4 employ:2 kinetic:2 appear:1 brackets:1 deeply:1 section:11 feedback:2 ǫq:3 expressed:4 uniform:1 current:3 consistently:1 version:2 melo:2 above:19 new:2 net:1 increasing:1 method:1 contrast:1 temperatures:1 body:1 edited:1 condensed:13 full:3 ibid:1 respectively:3 diagramatic:1 modify:1 residual:1 here:1 haber:1 following:1 mev:21 china:1 b32:1 quark:24 equations:13 auxiliary:1 superconductor:3 obtained:3 great:1 ultra:5 lasinio:1 loktev:1 study:14 larger:2 allows:2 completely:1 significantly:3 calculations:4 action:1 bob:1 changes:1 ξk:79 plotted:1 via:3 jin:1 explained:1 σsc:9 replace:1 scaled:3 gluon:1 summation:2 apply:3 total:9 wang:1 flavors:1 derivatives:1 use:1 mb:13 d76:1 asymptotic:1 would:1 d75:2 kunihiro:1 contains:4 quasi:1 next:1 calculation:4 linear:2 program:1 therefore:2 m3:3 qcd:5 taken:1 eagles:1 associated:2 panel:2 type:1 tell:2 reflects:1 more:1 sharapov:1 introducing:1 almost:2 formally:1 composite:4 neglected:7 naive:4 factor:1 βv:1 levin:6 introduces:1 berlin:1 appendix:6 known:5 ward:1 iii:3 βq:1 high:7 account:1 pieri:1 rβ:1 integrating:1 equation:14 nozieres:2 reads:1 values:1 thin:1 believed:1 modifies:1 arrive:1 spontaneous:1 example:1 dropped:1 beijing:1 compare:1 renormalization:1 predict:1 relativistic:42 boseeinstein:1 rapp:1 organized:1 near:4 states:5 indicates:1 numbers:3 degenerate:3 zhuang:4 handle:1 standard:7 νn:1 6m2:1 tan:1 simple:3 verlag:1 needs:2 end:1 turn:1 rather:1 discussion:1 breaking:12 iz2:1 recovers:3 chemical:18 located:3 varies:2 relativistically:1 disappear:2 pure:1 significance:2 answer:1 acta:1 parameter:14 ensemble:3 b70:1 rept:3 blocks:2 b75:1 algebra:1 may:11 thermodynamic:5 npg:3 after:1 derived:1 regularization:4 diagram:1 hence:2 stars:2 deviates:3 lat:1 righthand:1 summarize:1 choice:1 parallel:1 constants:1 realized:4 short:1 natural:4 effective:6 gauge:2 lines:5 correspond:2 su:3 element:3 fortunately:1 green:4 expression:2 keeps:1 sc:39 representation:1 sa:2 order:29 help:1 cutoff:4 constituents:1 over:1 mainly:1 choose:1 2sc:12 thermal:1 paper:3 including:4 looks:1 thesis:1 omitting:1 mentioned:1 satisfies:5 still:6 excitations:3 its:6 perfect:1 lg:1 derive:1 rapidly:1 thank:1 how:2 ln:12 solving:1 tsc:6 boson:33 li:3 forms:1 ǫ2k:10 degrees:4 systems:8 derivative:3 setting:1 huang:3 non:22 good:4 pauli:2 combination:1 numerically:1 greiner:1 bound:6 break:2 framework:1 tsinghua:1 they:1 feature:1 now:8 discuss:3 entropy:2 chromodynamics:1 susceptibility:12 february:1 e2η:1 dirac:4 chien:1 university:3 drop:1 2ek:17 2f:22 mode:1 2z1:1 2c:1 found:3 2n:1 side:2 characterized:1 mean:30 heavy:1 int:2 square:2 another:2 ek:107 there:8 energy:27 hard:1 idea:1 related:4 pengfei:1 buballa:1 investigated:3 static:1 expect:2 combining:1 loops:1 our:6 approximated:2 beyond:7 explicit:3 brings:1 out:5 shown:6 dominates:9 matrix:3 space:4 since:18 lagrangian:2 investigate:2 research:2 particles:1 similarly:1 rf:2 conclusions:1 dominated:1 rb:4 dominate:1 integrated:1 red:3 shows:1 wiley:1 theory:60 alford:2 divergence:2 diagonal:6 free:3 quite:3 quick:1 approaches:3 toy:1 complicated:2 term:4 checked:1 phd:1 rewritten:1 ek2:4 definition:1 pairs:29 interaction:4 chiral:6 starts:2 transition:8 βx:1 hong:1 diquark:17 iz1:1 length:4 βg:1 massive:4 βc:1 consequence:2 δseff:1 undergo:2 hadrons:1 neglect:2 first:8 major:1 already:2 diagrammatically:1 symmetry:20 afer:2 number:21 removed:1 smaller:1 simplified:1 long:3 rink:2 q02:4 reached:4 thick:1 size:1 wilczek:2 given:4 law:3 bracket:1 temperature:108 likely:1 strict:1 introduction:1 condensate:12 behaves:1 system:14 construct:2 2ωq:2 their:5 cooling:1 quadratic:3 fermions:13 πt:1 leggett:4 listed:1 kf2:2 kf3:1 asymmetric:1 baryon:13 exactly:1 rajagopal:2 weakly:1 favorable:2 somewhat:2 x2:6 than:6 coefficients:4 peaked:1 wide:2 scheme:7 determines:1 liquid:1 bec:37 approximations:1 namely:3 modified:1 limiting:1 superfluid:3 determined:2 100mev:1 velkovsky:1 iωn:8 treated:2 isospin:1 generality:1 fluctuation:2 ann:1 modern:1 kao:1 generalization:4 crossover:31 medium:1 astrophysical:2 zappala:1 further:1 need:1 seen:1 recover:2 any:4 strength:6 castorina:1 convenient:1 self:10 gχ:4 instance:2 z1:33 potential:26 generalized:5 so:6 channel:2 gψ:1 blue:3 play:1 trace:1 normal:2 enter:3 molecule:7 what:1 z2:25 simplify:1 connected:1 significant:6 phase:19 analytically:2 why:1 stands:1 thermally:3 kf:16 gorkov:2 considered:5 τi:1 clear:2 partition:2 drawing:1 vanishingly:1 βek:4 uncondensed:21 principle:2 sun:2 velocity:1 physics:1 width:1 fact:4 quantity:2 superfluidity:5 phenomenon:1 show:13 supported:1 bring:5 colors:2 minimizing:1 relation:8 participate:1 carefully:1 nemoto:1 especially:1 longer:4 d3:33 ground:1 kadanoff:1 q0:13 q2:5 careful:1 parameters:3 explain:1 produces:1 state:18 controls:1 should:8 only:22 explicitly:2 molecules:6 developed:1 nucl:5 do:4 dominant:6 get:1 chicago:1 engelbrecht:2 de:2 rµ:2 2a:3 2mb:3 define:1 nearly:4 progress:2 dr:1 suffers:1 qq:1 contributes:1 fields:2 karsch:1 arxiv:1 summary:1 ωq:9 qc:1 contain:1 analytical:1 through:3 fixed:6 gell:1 diquarks:1 ignored:1 requirement:1 set:1 exists:3 sep:1 nardulli:1 see:3 bare:3 result:5 recently:3 yes:1 close:1 matter:7 review:2 2gd:1 ciγ:2 d59:1 written:5 between:10 limit:19 approach:7 µb:4 multiplied:1 nambu:3 attention:1 terms:6 adding:1 mei:1 suppresses:1 weak:13 however:5 vanishing:1 2pg:15 bose:6 kosztin:3 wx:1 both:6 essentially:1 4πas:1 many:2 region:44 iγ0:1 equal:4 iγ5:10 energies:1 dated:1 expand:3 contribution:9 estimation:1 safely:6 mann:1 among:3 4gd:1 point:6 color:32 son:2 corresponds:1 pol:1 grants:1 anti:11 conjugation:1 respect:3 considers:1 considering:2 wetzorke:1 strong:8 stajic:1 second:4 lattice:1 z0:5 ωmf:3 eβx:1 due:8 been:4 appears:1 pc:2 much:3 treat:2 interest:1 basic:1 expected:4 ph:5 fig:18 field:37 4t3:1 contribute:1 corresponding:2 d65:1 coherence:1 gas:13 σi:1 gap:13 2ǫf:1 external:1 c3:1 c2:4 general:1 spin:1 former:1 present:5 2ǫk:5 case:11 k2:10 ǫf:5 exponential:1 pacs:1 ǫk:12 plasma:1 means:3 value:4 transformation:1 will:11 while:14 euler:1 behavior:5 property:1 taking:3 identical:1 ξk2:2 unitary:1 3nb:1 find:1 coupled:7 2nπt:1 vi:2 binding:7 them:2 iv:2 ii:3 superconducting:2 cond:1 vanish:2 fermion:50 ig:2 different:2 hubbard:1 develop:2 perform:1 powers:2 koide:1 lett:4 same:3 clearly:1 selfconsistent:1 φa:3 strange:1 widely:3 grand:1 dimensionless:2 finite:19 breaks:2 used:7 infinity:1 numerical:5 effect:12 randeria:2 hand:5 usually:3 zwierlein:1 infinite:1 symmetric:1 identity:1 strinati:1 lower:1 task:1 off:2 scenario:1 acknowledgement:1 gaps:1 reobtain:1 well:4 ωnr:1 obviously:2 directly:4 without:2 solve:2 dashed:6 very:6 position:1 model:11 latter:1 subgroup:1 d72:2 cuprates:1 just:4 less:3 being:3 generally:3 ultrarelativistic:1 superconductors:3 obtain:4 competitive:1 λa:4 nonfermi:1 atomic:2 predicts:1 janko:2 flavor:12 scattering:3 yet:2 stratonovich:1 previous:1 proven:1 note:3 babaev:1 dissociation:2 density:27 regarded:3 nonrelativistic:2 seems:1 ideal:5 ther:1 thermodynamics:9 other:4 attractive:5 channels:1 b422:1 confirmed:1 excited:6 momentum:9 take:4 real:1 b58:1 around:7 depends:2 easily:1 evaluate:1 iγ:5 decomposed:1 possible:1 b55:1 pisani:1 increases:4 ψiγ:2 seff:3 press:1 using:3 part:5 mod:2 loss:1 necessary:4 like:3 particle:1 follows:1 qualitative:1 schmitt:3 specific:8 arbitrary:3 a16:1 become:3 stationary:1 reduced:4 spins:1 replacement:1 performing:1 methods:1 laermann:1 smoothly:3 some:3 begin:1 competition:2 njl:3 2ξk:2 calculated:1 trends:1 selfconsistently:1 suppl:1 statistic:1 proper:3 extended:1 happens:1 provided:1 meson:1 cooper:1 illustrated:1 sufficiently:3 though:1 integration:1 critical:38 disappears:2 assuming:1 gapless:3 nishida:1 moderate:12 proc:1 2z2:1 reflect:1 process:1 reasonable:1 power:2 reach:1 martin:1 expansion:6 2m:12 imaginary:1 properties:1 takes:3 about:3 extension:1 saddle:2 freedom:4 completing:2 discussed:1 dependence:2 o:4 hot:1 range:2 restoration:1 obeys:1 e14:1 cos:1 observation:1 projectors:1 automatically:1 d62:1 goldstone:1 mechanics:1 cambridge:2 ηc:2 presence:1 into:2 nsc:4 integral:3 functional:3 three:2 down:2 pair:49 right:1 determine:2 einstein:6 elementary:3 proportional:9 nsr:9 theoretically:1 often:3 hep:6 kapusta:2 comparing:1 springer:1 pairing:4 question:3 approximate:1 gases:1 dispersion:13 start:2 petreczky:1 conservation:1 bosons:16 low:15 way:1 shovkovy:1 sections:3 propagator:26 a2:1 naturally:1 function:8 tpg:17 ef:5 weldon:1 form:7 enough:3 adjusting:2 m2:4 agrees:1 but:12 σpg:6 change:5 heat:5 properly:2 pg:37 line:8 eb:9 themselves:1 he:5 consequences:2 temp:1 understood:1 whether:2 characteristic:1 mat:1 smooth:1 up:1 us:7 work:1 below:2 frequency:3 fermi:13 ωn:2 fluctuations:19 distribution:3 matsubara:2 similar:3 called:5 obtains:1 detailed:2 b61:1 developing:1 constant:7 pseudogap:50 defined:11 universal:1 describe:5 direction:1 deep:1 denote:2 quantum:1 lived:1 exist:6 wavelength:2 controlled:2 formalism:14 200mev:1 check:1 constructed:1 reexpress:1 again:1 functions:7 dotted:4 no:8 fixing:1 nb:22 nc:3 when:4 vanishes:3 nf:3 application:4 jona:1 valid:7 role:1 becomes:9 department:1 nq:1 massless:4 conclusion:1 conclude:1 elements:3 conventionally:1 excitation:1 superconductivity:27 models:1 ξq:12 abuki:2 includes:1 a1:1 a3:1 important:3 a5:1 a4:1 a7:1 a6:1 included:3 a8:1 needed:1 fraction:5 condensation:10 implies:2 coupling:42 pion:2 assume:1 deng:1 dτ:2 d24:1 together:1 equivalently:1 ren:1 mass:11 time:1 restored:2 bcs:62 |
0705.1635.txt |@word limited:1 partial:1 represent:1 magnetic:2 particular:1 results:5 leads:1 ge:1 disc:1 grateful:1 covalent:1 gl:1 voids:1 centers:1 depend:3 technique:2 environment:1 charge:6 disappearence:1 those:3 stable:1 flattening:1 case:2 amplitudes:1 very:2 frequencies:2 activation:1 electron:8 ical:1 summarized:1 experimentally:1 al2:5 induced:1 exponential:1 vibrational:2 luetkens:1 supports:1 large:5 setup:3 smaller:1 occurrence:1 thin:4 trend:1 consistent:1 direct:1 gmbh:1 displays:1 qualitatively:1 even:2 established:1 errors:1 trapping:2 neh:4 sum:1 oxide:2 find:1 experiment:2 dukes:1 above:2 waals:2 new:2 increasing:9 acknowledged:1 contrast:3 µsr:11 pioneering:1 edited:2 condensed:1 exchange:3 respectively:2 pushing:1 atoms:3 ionization:6 deposition:2 mev:5 free:3 separation:1 excess:10 undoped:2 strong:1 appears:1 change:1 acceptor:1 obtained:4 inefficiently:1 institute:2 involved:2 studied:3 allows:2 commonly:1 leaving:1 amount:2 products:1 neugebauer:1 studies:4 diamagnetic:11 diameter:3 followed:1 family:1 semiconductors:14 explained:1 visible:1 addressed:1 decrease:1 total:2 granular:1 conventional:1 eye:4 positive:3 lichti:1 negative:1 few:2 sample:6 foster:1 therefore:4 films:5 robertson:1 type:2 theoretical:2 reflects:3 more:2 fractions:3 binding:1 glass:1 unresolved:1 discrepancy:1 varying:2 hole:6 iii:3 states:23 mm:6 der:3 work:3 mu:50 mt:16 remain:1 mp:1 starts:1 making:1 scherrer:3 thicknesses:2 address:1 numbers:2 ions:1 prompt:2 figure:2 escapes:1 process:1 thermally:2 high:4 indicates:2 minimum:1 performed:2 david:1 hydrogen:10 axis:1 influenced:1 rather:1 acts:1 mµ:1 how:4 native:1 simplicity:1 mat:1 information:1 may:4 fz:1 after:3 derived:1 different:5 cation:1 reflect:1 davis:1 stars:1 fd:6 physik:1 fits:1 drastic:1 data:9 insitute:1 polarities:1 pereira:1 recombination:4 spectra:1 zno:2 hfi:4 si:17 so:3 fundamental:1 decreasing:5 order:5 typical:3 help:1 move:1 vary:1 interpreted:1 course:1 thermal:2 experiments:5 london:1 unobserved:1 still:1 its:3 observational:1 le:3 thank:2 decay:1 energies:7 interesting:1 exhibits:2 labor:1 forms:1 detected:1 fig:10 mail:1 main:1 weber:1 non:1 walle:2 material:2 band:2 rotation:1 now:1 discuss:1 easily:1 february:1 vidal:1 cases:1 fully:1 presented:1 identified:1 merge:1 morris:1 magnitude:1 stopped:1 2b:1 found:1 universit:1 difficult:1 characterized:1 bond:2 ei:17 significantly:1 generation:1 energy:28 idea:1 related:2 used:5 measure:1 our:4 transitions:1 shown:3 reducing:1 impurity:9 51a:1 open:2 rev:12 increase:2 collisions:2 investigation:1 asymmetries:2 venables:1 squares:2 ref:1 shows:6 sio2:12 isotope:2 formation:27 york:1 lmn:1 institut:2 estimate:1 generate:1 pairs:5 interaction:1 created:2 determining:2 could:1 times:2 silicon:1 length:1 isotropic:4 incorporated:2 consequence:2 first:1 origin:1 there:1 demonstrating:1 probability:2 number:7 reaches:1 xe:7 ranges:1 thick:4 electronic:2 size:1 temperature:5 indicate:1 behaves:1 parallel:2 1a:2 their:4 1b:1 ulich:2 too:2 recent:1 final:3 fraction:12 mostly:1 relative:2 shallow:5 transverse:1 sizable:1 optical:1 differentiate:1 than:6 distance:2 kind:1 polarized:1 require:2 measured:2 see:2 eeh:2 determined:1 contrary:1 light:1 providing:1 russia:1 resistivity:1 ev:3 san:1 lines:6 unchanged:1 mind:1 spectrum:1 curves:1 ras:1 further:3 seen:1 orders:1 depending:1 isolated:5 polarization:1 instance:1 without:2 donor:2 channel:1 hyperfine:3 circles:2 electric:3 trace:1 normal:3 track:13 impurities:4 extending:1 germany:1 channeling:1 significant:1 preliminary:1 phase:1 inserted:2 released:1 average:1 saturate:1 villigen:3 part:1 electrons:1 lying:1 khasanov:1 thomas:1 insulators:13 show:3 supported:1 discovered:1 availability:4 slow:1 explain:1 heavily:1 should:1 technologically:1 only:4 various:1 hope:1 equilibrium:1 klein:1 means:1 dependent:2 beams:2 de:2 stop:1 beam:1 ionized:1 nearly:3 during:3 dr:1 processes:3 precession:7 fields:3 arxiv:1 yield:1 tuned:2 investigate:3 predicted:1 activity:1 switzerland:4 shi:1 cycles:2 exists:1 sensitivity:1 observed:5 depends:2 discussions:1 close:1 techniques:1 surfaces:1 mut:3 detect:1 compounds:1 away:1 nature:1 µs:3 boundaries:1 pressures:3 state:5 smallest:1 identification:1 between:11 probably:1 paramagnetic:2 wide:1 available:1 triplet:3 recently:2 spectroscopy:2 missing:1 importance:1 were:4 however:1 spectroscopic:1 gratefully:1 incident:1 kev:23 suppressed:2 suggested:1 both:1 interpretations:1 last:1 mu0:6 cox:5 asymmetry:7 display:1 grain:3 dated:1 mean:3 experimental:4 ch:4 brewer:1 characterization:1 relaxation:1 decreases:2 path:1 respect:1 crystalline:2 implanted:1 fused:3 source:1 addition:1 due:8 been:5 reduction:1 interest:1 anisotropic:1 muons:3 prototype:1 anomaly:1 muonium:3 life:1 arises:1 corresponding:3 observable:3 suppress:1 thousand:4 formed:3 gas:2 requires:1 gap:2 bulk:5 deep:1 spin:5 present:5 applied:3 exception:1 novel:1 splits:1 kazan:2 pacs:1 solid:4 single:1 value:1 will:1 technical:1 while:1 superposed:1 behavior:6 unlikely:1 layer:4 sizeable:2 concomitant:1 orientation:1 played:1 vol:3 vi:2 thus:1 site:2 surface:2 ii:3 obstacle:1 cond:3 epithermal:2 grown:2 capture:3 confirmed:1 same:2 clearly:1 niedermayer:1 triangles:2 several:3 infer:1 higher:3 investigated:4 diego:1 cottrell:1 ion:1 levels:1 urich:2 fabrication:1 nm:13 lower:2 weakly:1 kept:1 center:1 changes:1 nitrides:1 academic:2 solids:2 materials:2 components:1 swiss:1 morenzoni:4 muon:6 less:2 generally:1 valuable:1 identify:1 atomic:2 paul:3 guides:4 alignment:1 previous:1 oriented:1 interstitial:2 had:1 theoret:1 signals:1 lattice:1 combine:1 lett:8 samples:4 technological:1 role:3 kiefl:1 mod:1 resolved:1 psi:4 around:1 thermalized:1 showing:1 disagreement:1 possible:1 five:1 vacuum:1 press:1 using:1 amu:8 apart:1 necessary:1 like:6 particle:1 sizes:1 signal:8 chow:1 agreement:1 mhz:4 either:1 conclusion:1 technologie:1 essential:1 therein:1 creation:1 growth:1 examples:1 moreover:1 oscillations:1 sufficient:1 patterson:1 pronounced:1 scale:1 per:2 does:1 o3:5 refer:1 measuring:1 perpendicular:1 onset:2 host:1 losing:1 approximating:1 singlet:1 properties:5 comparison:1 about:4 energetically:1 rare:1 anomalous:1 dependence:6 range:1 sµs:1 larmor:1 concentrations:1 introduced:2 letter:1 presence:2 implantation:15 into:3 within:1 bound:3 down:2 pair:1 references:1 capped:1 proportional:1 tetrahedral:1 statistics:1 van:3 additional:1 elastic:2 area:1 intrinsic:3 support:3 initial:2 question:2 gases:1 window:1 low:7 way:3 gil:1 was:4 function:9 delayed:14 atot:3 neutral:1 larger:3 convergence:1 line:1 highest:1 semimetals:1 faster:1 absent:1 whether:1 up:2 ur:1 crystal:5 below:3 frequency:1 sapphire:4 similar:1 called:1 strongly:2 ad:27 universal:1 escape:5 influence:1 direction:1 slowing:2 general:2 inn:1 ar:17 physica:3 intra:2 film:2 again:1 compared:1 spectroscopically:1 no:2 whereas:4 when:1 ne:11 field:7 other:4 electrical:2 details:1 becomes:2 hpa:6 concerning:1 4k:1 quartz:4 energetic:2 temperatures:2 matt:2 generated:4 important:1 suppression:3 variable:1 structure:1 implies:1 coupling:1 wafer:1 thermalization:1 emery:1 together:2 depth:4 correspondingly:1 correlates:1 fitted:2 time:6 far:2 appl:2 n2:9 resolution:1 |
0705.1636.txt |@word beckers:2 limited:4 sco:1 consider:1 represent:1 observatorio:1 results:2 month:1 switches:1 bellingham:2 issues:4 inverse:1 new:2 removal:2 finally:2 tracker:1 under:6 friendly:1 summarizes:1 mpg:1 very:10 lopez:1 50ms:2 difference:2 founded:1 level:1 solution:3 damped:1 large:2 solved:1 min:1 oaa:1 enhance:2 optics:3 work:2 illustrating:1 direct:1 spectrograph:2 dynamics:1 air:1 targets:2 quite:1 calibrators:1 spectral:11 synthesis:1 what:2 errors:3 adds:1 while:1 current:11 sinc:1 version:2 values:1 net:1 edited:1 full:1 systematic:1 respectively:1 gilles:1 behaviour:4 tracks:1 objects:2 operating:1 arcetri:2 ratio:1 strong:2 observing:10 appears:1 change:1 box:1 technical:1 study:3 changed:1 allows:1 experience:1 example:1 astrophysique:2 amount:1 simultaneous:2 resulting:3 published:1 engineers:1 makes:1 plotted:1 useful:1 problematic:2 photometric:1 highly:3 brought:1 wit:1 decrease:2 achievable:2 resolutions:1 planck:2 unit:2 plot:1 use:6 would:1 may:2 faint:1 next:2 few:1 estimated:2 therefore:7 centre:1 taken:4 today:5 more:2 successful:1 oscar:1 corrected:1 limitation:1 visibility:6 instrumental:3 tested:1 domination:1 train:1 known:1 effort:1 must:1 kraus:1 account:5 room:1 effectively:1 science:3 averaged:1 degrees:1 snr2:1 9µm:1 mr:1 following:1 strategies:2 scatter:5 compare:1 mirrors:1 process:4 azur:1 high:6 unbiased:1 slit:1 way:2 performed:1 absolute:1 information:1 monitoring:1 goal:1 provide:1 get:2 feature:1 how:1 frontiers:1 instead:1 universitaire:1 fr:1 description:2 huge:2 specifications:1 max:2 perrin:2 after:1 southern:2 lab:1 applications:1 plane:1 snr:3 structure:1 coming:1 improving:1 drastic:1 data:32 efficiently:1 short:4 effective:1 manpower:1 recombination:1 documentation:1 obs:1 algorithms:1 correlation:2 order:3 wind:1 typical:4 astronomical:1 move:1 mainly:1 soon:1 osservatorio:1 installed:2 stability:1 held:1 already:5 looks:1 still:3 fwhm:1 its:3 lc:5 la:1 personal:1 fix:1 blurring:1 li:4 better:3 lr:2 fig:14 workable:2 freely:1 into:7 a92:1 lowell:1 non:2 affected:1 practice:3 introduce:1 band:1 effects:2 optimal:2 souza:2 now:1 articles:2 term:1 presented:1 identified:2 realistic:1 vibrations:8 visibilities:16 bonn:2 each:1 found:3 difficult:2 side:4 malbet:3 development:1 arxiv:1 significantly:1 hopefully:1 series:3 hard:2 gaussian:5 related:1 society:2 meilland:4 used:3 expect:1 calibrate:2 measurement:2 laboratory:3 operation:3 extract:1 special:2 try:1 opened:2 rep:1 since:5 squared:3 re:1 seriously:2 investigation:2 dominated:1 romain:1 electronics:1 induced:2 issue:4 correct:2 shows:1 occurs:1 unexpected:1 overheads:3 standard:4 base:6 imaging:1 members:1 put:1 estimate:1 beginning:1 telescopes:5 so:1 times:2 creates:1 length:2 ats:1 unknown:1 benisty:1 first:4 feed:1 behaves:1 features:2 probability:1 number:4 improvements:3 specifically:1 reached:2 open:1 idea:1 driebe:2 given:2 natta:1 their:1 introduction:1 leading:5 night:5 adopted:1 needed:3 observations:4 wrapped:1 1h:1 white:1 scheme:2 final:1 too:1 lot:3 releases:1 fabien:1 iau:1 2007a:3 optical:6 authors:1 july:1 than:3 center:1 observatory:6 showed:1 measured:1 submitted:1 limiting:2 project:1 future:3 were:2 aime:1 exposures:1 acquisition:1 result:1 courtesy:1 cleaner:1 rad:2 shrinks:1 spectrum:3 raw:1 commissioning:1 seen:1 linked:3 gives:1 instrumentation:1 nights:1 depending:2 able:1 ideas:1 provokes:1 note:1 extracted:1 fitting:1 internal:3 take:3 negligible:1 detector:10 channel:1 accuracy:7 even:1 tatulli:5 added:4 normal:1 object:1 reach:3 petrov:6 gauss:1 phase:8 plays:1 acknowledgements:1 intrinsic:1 volume:1 performances:5 average:2 proceedings:2 regards:1 tech:1 principle:1 dispersed:1 bulletin:1 slope:1 atmosphere:1 selection:1 show:1 chances:1 please:1 infrared:1 isella:1 purely:1 bright:5 solutions:1 find:1 principal:1 µm:1 based:2 knowledge:1 vakili:1 hrs:1 should:1 colloq:1 only:2 black:2 about:3 factor:2 traub:2 achieve:1 do:1 di:2 spurious:1 beams:1 de:7 firenze:1 beam:2 cannot:3 probably:2 report:1 during:6 closure:6 gray:1 conclusion:1 numerous:1 differential:5 paper:1 prevents:3 view:1 arrival:1 bars:5 achieved:1 acquired:1 problem:4 frame:3 millour:12 observed:2 mporzio:1 see:9 individual:2 descriptions:1 exoplanets:1 best:1 techniques:2 closer:1 phases:5 mpifr:2 pattern:2 currently:1 bias:4 artificial:1 symmetric:1 case:1 state:4 between:8 affecting:1 piston:2 geometric:1 conditions:5 available:3 multiplied:1 infrastructure:5 terms:2 wa:2 however:6 killing:1 erard:1 here:5 interface:1 article:1 pixels:1 improve:5 paranal:4 observable:2 recherche:1 limits:1 many:1 taking:1 etc:1 cylindrical:1 figures:3 ote:1 vlti:16 antoniucci:1 estimation:1 comes:1 filtering:2 jitter:4 overview:1 ca:1 corresponds:1 community:1 scientifique:1 inbetween:1 comprehension:1 maximize:1 table:4 san:1 consuming:1 combiner:1 puts:1 source:2 chesneau:5 three:4 been:5 strategy:1 reduction:10 much:3 basic:1 expected:6 restrain:1 ph:1 prototype:1 meeting:1 website:1 direction:1 offered:1 coherence:3 precision:5 weigelt:5 coherent:1 external:1 chile:2 spie:1 careful:1 present:4 p2:1 p3:1 p1:1 atmospheric:2 solid:2 reliable:1 engineering:1 evaluated:1 easier:1 will:2 institute:1 near:3 error:9 situation:2 region:1 procedure:1 interpolating:1 site:1 hardware:2 itself:1 fibers:3 same:1 check:1 finito:4 complex:1 evaluate:1 proved:1 several:3 european:2 status:1 investigated:1 http:3 diego:1 laboratoire:2 effect:5 driven:2 v2:5 edges:1 user:1 lower:1 modes:2 programs:1 changes:2 no:3 well:2 roughly:1 without:2 patterns:1 rome:1 solve:1 sets:1 calibrated:3 ujf:1 left:1 proposed:1 less:1 being:1 photo:1 consortium:1 coud:1 alpes:1 web:1 french:2 photons:2 except:1 instrument:21 potential:1 baselines:1 real:1 tests:1 around:1 bands:1 showing:2 digital:1 dark:1 facing:1 indicative:2 gianluca:1 using:5 grenoble:4 radioastronomie:2 vapour:1 loss:1 like:3 lost:1 signal:6 translates:1 specific:4 flux:8 2007b:5 either:1 martin:1 output:2 inter:1 page:1 www:1 right:1 schematics:1 successfully:1 some:1 cnrs:1 imaged:1 accelerate:1 specified:2 piezo:1 lagarde:2 shutter:1 affects:3 measurements:8 integration:3 per:1 instantaneous:1 domiciano:2 does:3 provides:1 eso:6 moderate:1 mode:5 limitations:1 biased:1 noise:7 stee:2 processing:13 bi:1 stellar:1 wesley:1 biases:2 interferometric:6 subtract:1 noisy:1 pipeline:3 working:2 fringe:3 introduces:1 dependence:3 o:5 nardetto:1 estimator:3 other:1 software:8 amber:49 seeing:2 dubois:4 mardones:2 due:2 references:1 national:1 frames:5 institut:1 log:1 transfer:7 there:3 long:4 dispersion:1 quadratic:1 low:13 stars:2 ed:3 was:1 interferometry:2 function:8 medium:5 complete:2 but:5 histogram:4 astro:2 magnitude:3 gain:1 chelli:1 line:6 hd:1 auxiliary:1 made:1 compute:2 ut:1 inside:1 up:2 us:1 ur:2 international:1 uts:4 gaps:1 distribution:6 strongly:4 associated:1 general:2 single:2 fringes:9 sourceforge:1 eric:1 interferences:4 radians:5 again:1 dotted:1 calibration:10 dashed:3 image:3 water:1 cˆ:1 preventing:1 points:1 role:1 investigations:1 spatial:2 sufficient:1 nice:1 0µm:2 elements:1 star:9 astrofisico:1 time:12 problems:2 spectrally:1 important:2 allowing:2 included:1 provence:1 transfert:1 exposure:6 correlated:2 regime:1 longer:1 algorithm:1 hofmann:2 together:2 mass:1 pupil:1 electromagnetic:3 observables:4 resolution:12 original:1 |
0705.1637.txt |@word luminosities:1 four:3 consists:1 oldest:1 poorly:1 whose:1 auf:1 charnley:9 under:3 spec:1 tafalla:1 figs:2 schilke:7 affect:1 vibrational:7 frozen:2 degeneracy:1 consistent:1 estimates:5 approximation:3 surrounding:2 second:1 street:1 estimated:4 even:8 errors:2 selected:2 above:2 new:1 increasing:2 coefficient:2 simultaneously:2 hern:1 atoms:1 reported:1 arcetri:1 obtained:17 daughter:2 study:6 adopting:1 diameter:8 yamada:2 9c:1 highly:1 moran:2 welch:2 opacities:1 total:27 univ:1 plot:4 would:1 therefore:11 type:5 separated:3 berlin:1 warm:1 garrod:3 abundance:23 kumar:1 springer:2 ma:1 mb:16 mm:25 work:5 temperatures:25 zams:1 example:2 indicated:3 give:6 involve:1 indicates:4 orion:19 provide:1 feature:1 hot:72 symposium:2 thermodynamic:1 after:2 confirmed:2 diagram:4 law:2 hpbw:1 types:1 recombination:1 complexity:1 g19:20 correlation:9 order:8 g10:54 over:2 vary:1 undetected:2 linewidth:1 fit:9 personal:1 exhibits:1 better:1 cesaroni:17 production:1 differently:1 inaf:3 haschick:4 them:11 affected:3 band:5 they:17 πd2:1 represents:2 oxygen:1 bonn:1 reasonable:1 each:20 telescope:9 displacement:2 used:13 laboratory:1 network:1 gradient:2 xu:2 arizona:4 linear:7 free:4 standard:1 formation:8 estimate:7 telescopes:1 steward:1 filter:1 ism:2 bologna:1 corrections:1 wobbling:2 onto:3 already:3 another:1 thick:2 similarly:1 top:5 approximately:3 compromise:1 observations:30 collapse:1 centered:1 albert:3 nh3:12 nh2:4 peculiar:1 begins:1 distance:2 showed:3 likely:5 pasp:1 evaporated:3 predicts:3 mind:1 spectrum:5 seen:9 seem:1 contents:1 strength:2 habing:1 latter:2 isolated:1 fitting:2 causing:1 circles:2 though:5 dθs:1 boltzmann:3 involving:4 germany:2 phase:16 acknowledgements:1 torsional:1 genzel:4 calculated:1 brackets:1 inferred:2 points:1 sum:1 fitted:1 dickey:1 probe:1 radio:3 hasegawa:1 d2:11 ıguez:6 spite:1 explain:2 rich:3 do:3 tracers:11 di:2 de:15 firenze:1 despite:1 dv:16 saturn:1 runs:2 pearson:9 bar:1 wavelenghts:1 l49:1 transforms:1 reference:1 detection:1 depends:1 decided:2 w3:6 result:4 discussions:1 best:4 away:1 symmetric:1 catalogue:3 ira:1 spectrometers:1 terms:1 weak:6 however:5 neverthless:2 boss:1 harvard:1 reipurth:2 suggested:2 received:1 irregular:1 against:4 receiver:3 requests:1 compilations:1 col:13 esis:1 blending:2 ether:1 nomura:2 basis:1 union:1 three:8 been:26 confident:1 much:6 interest:3 expected:7 quantities:3 irvine:1 wyrowski:7 θs:4 spin:1 applied:2 exception:3 heidelberg:1 near:1 suppose:1 property:2 procedure:4 iv:1 ii:3 conf:1 comparative:1 garay:9 containing:1 suggest:6 complex:67 split:1 several:8 fairly:2 satellite:2 peaks:1 hand:6 opportunity:1 interferometers:1 scenario:2 left:3 bandwidth:1 identify:2 thanks:1 yet:1 previous:3 mckee:3 beuther:5 had:2 macdonald:4 wright:4 east:1 baselines:1 elevation:1 bands:8 disagreement:1 possible:4 birth:2 radioastronomia:1 radioastronomie:1 advanced:2 g31:25 g34:27 cooler:1 caselli:16 detections:1 dissociative:1 night:1 signposts:1 right:7 j2000:5 jupiter:1 debye:1 statistic:1 fot:1 cnr:1 bottom:2 microwave:1 icy:1 core:20 yorke:2 properties:7 anomalous:1 o:39 slightly:1 considerations:1 mantle:2 1990b:2 1990a:2 obtaining:1 stutzki:2 often:2 intrinsic:1 initial:2 width:3 anderson:8 way:1 astrophysics:3 was:9 medium:1 form:4 offer:1 forming:1 differences:5 analyse:2 wobbler:1 heat:1 magnitude:3 underestimates:1 solar:1 hmcs:30 born:1 inside:1 maximum:6 tucson:4 mgas:7 stages:2 hotter:2 computing:1 abstract:1 evidence:1 check:2 triangles:1 physical:12 no:5 nb:4 when:8 ny:1 pasadena:1 ns:5 nu:2 optically:7 models:9 interferometric:8 dense:4 younger:1 assume:1 spectr:1 together:1 time:1 focus:4 leads:1 comments:1 grateful:1 morphology:1 abundant:3 rot:1 devoted:1 depend:1 environment:3 summarised:2 methyl:1 zhang:3 frequencies:5 looney:1 presented:1 turns:1 upper:14 plummer:3 prediction:2 spectral:1 appear:1 assistance:1 g29:22 international:1 filled:1 water:1 change:1 unidentified:2 studied:2 usually:1 studies:1 plotted:4 spatially:1 marked:2 planck:1 franco:1 predictions:8 france:1 theoretical:6 diagrams:5 greenhill:1 envelope:1 validity:1 appendix:6 serendipitously:1 effort:1 clumps:6 insights:1 rotational:28 sastry:4 foci:1 values:21 following:7 modifies:1 reflector:1 figure:6 predict:2 menten:2 sample:13 isotopologues:4 remijan:3 performed:3 verlag:1 discussion:3 chemical:22 submillimeter:1 map:1 may:6 max:1 date:2 revealed:3 stress:3 correlate:1 ss:2 ghz:2 condensations:2 so:3 typical:2 wavelengths:1 indeed:3 pointed:1 mainly:2 cols:9 osservatorio:1 course:1 lsr:1 statistical:2 cold:2 still:1 observational:5 derive:19 thank:2 presence:4 methanol:2 coordinates:1 forms:2 mail:1 main:12 processes:1 half:7 discuss:2 nor:1 inversion:6 name:3 corners:2 el:12 weighted:1 scheme:1 gaussian:7 eu:6 eq:5 hcs:2 shown:10 jackson:1 furthermore:1 increase:2 suggesting:6 hcn:4 correct:2 shows:5 theory:2 protonated:1 diameters:11 possibility:1 quite:2 vinyl:2 hc3:5 derivation:1 widths:9 collapsing:1 transition:8 massive:7 friedel:1 first:4 dimethyl:1 directly:1 open:2 angular:22 size:6 given:18 checked:5 indicate:5 1e:1 iau:1 mostly:1 asymmetric:1 released:2 representing:2 than:29 coefficients:2 population:1 l43:1 l41:1 require:1 crossroads:1 future:1 were:7 pre:1 san:1 correction:1 allen:2 turner:2 any:3 note:2 phillips:4 take:1 destroy:2 switching:2 hyperfine:2 cnrs:1 trace:10 opposite:1 decreasing:1 molecule:27 evaporate:1 pair:4 analytically:1 sutton:3 surprising:1 considered:3 average:22 typically:2 quantity:2 show:14 herbst:21 bright:2 southwestern:2 corner:1 trot:3 ratio:19 carral:2 only:14 wood:6 thompson:1 get:1 ionized:3 nearly:2 secondary:2 reveal:3 summary:1 predicted:2 mapped:1 hatchell:8 discussing:1 relative:5 insitut:1 surfaces:2 invoked:1 subsequent:1 between:45 fermi:1 justified:1 multiplied:1 august:3 parent:2 receivers:5 concentrate:1 virial:3 originates:1 reaction:2 panels:1 outflows:1 many:6 tmax:1 according:1 expression:1 among:4 associated:8 prototype:1 fig:63 6d:1 thousand:1 formed:7 those:28 case:2 klaus:1 bania:4 cannot:2 region:28 discrepancy:1 cluster:1 unblended:11 different:23 proto:1 same:24 html:2 grain:6 pan:2 extended:1 jorgensen:1 motions:1 ccn:2 solve:2 components:6 fixing:1 model:8 l107:1 being:3 rest:5 differentiation:7 ethyl:1 hofner:9 products:1 seems:1 except:3 multiplets:1 early:2 mol:1 using:4 accepted:1 correcting:1 nanda:1 velocities:11 reduced:1 densest:1 deduce:1 pascucci:1 table:41 confirm:1 extensively:1 critical:1 hjalmarson:2 toroidal:1 power:3 linewidths:7 ratios:5 throw:1 comparison:4 central:7 package:2 discussed:2 ob:1 cambridge:1 communication:2 references:1 einstein:1 assumed:1 there:4 generation:1 henning:1 low:5 stars:6 mannings:1 energy:4 gibb:4 applying:1 embedded:5 emissions:1 agree:5 detailed:1 describe:2 general:2 neri:2 ap:2 planets:5 mundy:2 gradients:1 az:1 russel:1 again:1 declination:1 masers:1 spatial:6 ign:1 opacity:1 separate:1 deriving:1 arcmin:1 important:1 peak:7 offprint:1 curve:1 mass:4 cores:72 resolution:20 veleta:1 represent:2 abundances:31 consider:1 pointing:1 follow:1 disk:1 program:1 present:6 th:1 mpg:1 very:7 fall:2 difference:17 gov:2 alma:1 list:4 devided:1 large:2 small:3 largo:1 rate:1 timescales:1 masson:1 further:2 sub:2 clock:2 section:2 version:1 fractional:9 method:4 full:1 iram:8 compilation:1 component:2 ranges:2 strong:4 observing:16 allows:2 pico:1 published:1 goss:1 via:2 mookerjea:5 marginal:1 distinct:3 comparing:3 taken:7 vlsr:15 more:8 emission:17 mehringer:1 vn:18 particular:3 known:4 none:1 middle:2 science:1 dem:1 den:1 dec:2 ions:1 compare:2 suggestions:1 states:1 minimum:1 numbers:4 νc:1 sharp:1 robinson:2 species:32 axis:2 maps:7 crowther:1 explains:1 galactic:1 derived:23 reflect:2 plane:2 coming:1 horizontal:1 keil:2 spectra:11 negligible:2 sect:13 fundamental:2 banks:1 help:1 paper:1 through:11 existence:1 suffer:1 its:2 energies:3 l71:1 actually:1 peng:1 detected:12 might:2 misalignment:1 good:4 return:1 yr:1 growing:1 hereafter:2 always:1 level:9 micro:1 found:20 characterized:2 reactions:14 weight:1 catalogues:3 colder:1 fish:2 idea:1 bima:1 since:6 nummelin:7 flattening:1 asp:2 reason:1 earliest:1 beginning:1 wachter:1 cyanide:3 clump:7 number:7 done:1 occurrence:1 temperature:33 introduction:1 least:2 assumption:6 molecular:38 listed:11 olmi:7 immediate:1 optical:6 authors:2 believe:3 churchwell:14 aims:1 determined:2 7b:1 ages:7 substantial:2 cometary:4 orders:2 zero:1 without:1 square:2 finding:1 towards:26 millimeter:3 react:1 most:5 significant:3 autocorrelator:1 measured:2 equatorial:1 clear:2 broadened:1 coincides:1 km:25 exp:1 azimuth:1 velocity:8 physics:1 thomas:1 somewhat:1 blended:6 v11:1 winnewisser:1 v15:1 relation:2 astrophys:1 find:11 wilner:3 parameters:13 surveyed:1 factor:9 his:1 observatory:1 during:16 continuum:12 arxiv:1 investigate:2 common:1 hinder:1 bars:1 ser:1 geoff:1 individual:2 sec:1 close:1 fontani:61 dipole:2 various:1 conditions:4 available:2 recently:1 missing:1 distinguish:2 both:24 whole:2 rodgers:2 point:4 reasons:1 simply:1 described:2 due:12 pc:6 reduction:1 ph:3 partly:2 gas:33 systematic:3 formate:1 uncertain:1 grains:6 solid:4 mh2:2 reliable:1 while:7 error:3 computed:5 jpl:4 apjs:16 ultracompact:2 italy:2 shorter:1 resulting:2 composition:2 higher:13 literature:1 moment:2 levels:1 lower:11 analysis:1 vibrationally:13 chemistry:4 distances:4 observed:55 alignment:1 tables:3 conclusions:3 source:48 location:1 excited:14 showing:2 like:4 follows:1 interestingly:2 separately:1 flux:1 physrefdata:1 whittet:1 methods:2 some:9 understood:1 experienced:1 30m:5 b2:4 mirror:1 scale:1 annu:1 measurements:3 saas:1 run:14 agreement:8 plots:3 depths:1 tracing:3 range:4 into:6 within:4 uncertainties:4 arrow:2 statistics:1 few:4 mantles:1 fragmented:1 sewilo:2 line:41 up:4 us:6 marginally:3 similar:8 called:2 uc:16 partition:3 constant:1 millar:5 cover:1 specified:2 influence:2 single:4 parsec:1 dashed:1 revision:1 akeson:4 excitation:4 astrofisico:1 kt:1 problems:1 lucia:14 allowing:1 structure:5 correlated:4 age:2 depth:5 nasa:1 weights:2 95a:1 gobetti:1 gu:2 code:2 results:18 eds:1 ammonia:2 compact:7 young:1 send:1 protostars:3 lodato:1 indicating:4 g5:1 garden:1 g1:1 vla:3 g9:1 avalos:3 clemens:1 evaporation:2 positions:2 danchi:1 optics:1 keene:1 concluded:1 hcooch3:22 smaller:7 carefully:1 surface:2 notwithstanding:1 plambeck:2 hourly:1 giving:1 bergman:5 3k:1 consistently:1 3a:1 led:1 lee:1 50th:1 respectively:16 youngest:1 och3:160 objects:4 separation:8 extrema:1 northern:1 larger:7 survey:1 makes:1 kurtz:6 sgr:3 private:1 apj:36 decrease:1 xclass:7 cloud:2 use:8 fee:1 usa:2 next:1 hnco:2 themselves:1 stage:3 becomes:1 normalized:1 account:1 oh:3 reproduce:1 ch2:1 ch3:181 thin:5 process:2 high:16 assumptions:3 bend:2 tab:11 ascension:1 tan:3 rodr:6 six:1 regions:13 located:1 galli:1 instead:1 goldsmith:2 profile:2 insu:1 fits:8 lines:75 correspond:3 allow:1 divided:1 evolutionary:5 saturated:1 astronomical:1 interpreted:3 report:2 mentioned:1 blake:6 ln:1 masses:8 clusters:1 greater:2 front:1 rotation:9 february:1 university:3 traced:6 identified:15 kpc:2 mode:2 accounts:1 traces:2 homogeneous:1 heated:2 frequency:10 our:42 transitions:47 out:9 rev:1 istituto:1 integrated:8 8m:1 8c:1 york:1 ridge:5 compositions:1 interaction:1 organic:1 could:3 times:4 errorbars:2 lte:4 hence:3 manuscript:1 reaches:1 publication:1 data:16 system:1 their:26 g45:1 scans:2 lot:1 exactly:1 july:4 tielens:1 see:38 comito:2 providing:2 hz:2 cohen:1 curves:1 unlikely:1 need:1 1988b:2 1988a:2 pickett:4 accuracy:1 centre:6 who:2 but:14 cases:1 class:1 astro:3 stronger:1 proceedings:3 constrain:2 fact:9 gain:1 supported:2 rotating:2 agrees:3 staff:1 highest:1 based:3 fuer:1 kuchar:3 should:1 surroundings:1 molecules:91 local:2 equilibrium:3 sagittarius:1 bear:1 beam:13 ones:1 bandwith:1 words:1 drawn:1 averaged:13 collisional:1 evolution:1 densities:34 beltr:5 lizano:3 reid:3 fixed:1 nist:1 view:1 multiplying:1 nitrogen:2 correlations:1 turbulent:1 freeze:1 intensity:7 nuclear:1 identification:5 neither:1 comparable:12 key:1 distribution:2 observable:2 keto:6 limits:3 equal:5 figures:1 otherwise:1 strongly:2 cn:486 cm:33 conclude:2 ca:1 bisschop:14 respect:4 kinematic:1 arises:1 corresponding:4 sufficient:4 astron:1 c3:1 c2:475 spain:1 hmc:20 value:2 will:7 sandell:1 thus:5 walmsley:10 vo:17 sity:1 jewitt:2 radiation:1 cross:2 largest:3 difficult:2 http:2 nfit:1 ion:2 v2:1 v6:1 v7:1 dust:6 destruction:1 center:3 nevertheless:1 well:10 thought:3 sets:1 firstly:1 position:7 arising:1 spherical:1 less:4 accurate:5 obtain:3 sources:23 distant:1 casper:1 uller:1 density:29 absorption:2 combine:1 halo:1 c13:2 c17:3 resolved:2 smithsonian:1 increases:1 five:1 denser:5 press:5 loss:1 helpful:1 sizes:1 mhz:24 works:1 poor:4 because:6 francisco:1 peter:1 broad:1 overlap:1 meier:1 does:4 assuming:7 eso:1 demonstrated:1 limitations:1 tmin:1 analysed:1 stellar:1 although:1 offset:2 panel:12 about:6 carried:2 column:55 langer:2 andez:1 software:4 h2:35 h3:152 interstellar:1 h4:1 h5:322 weather:1 van:1 additional:1 snyder:1 ed:5 yrs:7 function:1 overlapping:2 volume:2 ho:5 hc:9 ha:1 made:3 compute:1 whether:2 hosting:1 belov:1 limit:3 demonstrate:1 problem:2 bearing:34 ysos:1 carlstrom:4 functions:2 compared:3 calibration:1 detail:1 other:22 details:1 dishoeck:1 zheng:1 star:10 additionally:1 astronomy:1 portion:1 searched:1 4d:1 |
0705.1638.txt |@word managed:1 magnetic:3 activated:1 results:4 four:1 eds:3 remarkably:1 contributions:4 terms:1 concerned:1 technique:3 tn:1 ρsf:4 nonsuperconducting:1 tc:7 probe:1 7mev:2 far:2 wave:1 electron:19 sons:1 kittel:1 experimentally:1 ωsf:8 positions:1 unexpected:1 force:1 estimates:2 pulse:1 200nm:1 zero:1 enhancement:1 further:1 dynamics:1 quite:2 even:1 current:1 above:3 vishik:1 method:1 lee:2 respectively:3 residual:3 here:1 atoms:2 deposition:2 alone:1 strong:3 superconductor:1 noticeable:1 institute:1 larger:2 resulting:1 hamza:1 diamagnetic:1 fournier:3 anomalies:2 conventional:1 lemberger:1 few:1 thermally:1 films:13 type:1 theoretical:1 more:2 pcco:1 particular:1 kulkarni:1 pieces:1 sample:2 account:2 ρe:6 taguchi:1 motoyama:1 oscillator:1 ronning:1 values:2 thin:8 following:1 giannetta:2 attribute:1 desenvolvimento:1 high:4 lorentz:1 numbers:1 tan:1 attract:1 afm:3 rather:1 discussion:1 very:3 pure:1 parameter:1 80k:1 lao:3 mat:1 may:1 fy:1 after:1 fits:2 data:4 response:1 effective:1 sp:1 supercond:1 si:1 sm:5 typical:2 pulsed:2 characteristic:1 produced:2 engenharia:1 experiments:1 through:4 ρres:7 ce0:4 mentioned:1 22k:2 1mev:3 excitations:1 fit:1 acknowledge:1 tsf:9 interesting:1 li:1 lu:1 degrees:1 fig:6 lawrie:2 evolution:1 penetration:1 effects:3 bogoliubov:1 inelastic:2 yu:2 structural:2 february:1 drop:1 2ev:2 reasonable:3 found:6 carlos:2 mean:1 square:1 successively:1 chung:1 kang:2 energy:10 ef:4 displacement:2 24k:1 frequency:4 our:8 drude:1 extract:1 special:1 impurity:3 quality:2 since:2 rev:11 research:1 increase:1 hill:1 induced:6 ref:2 shows:1 wiley:1 linear:1 mechanisms:1 departamento:1 standard:1 dependencies:2 york:1 besides:1 bao:1 dubna:1 temperature:18 interaction:2 r0:1 r2:1 damascelli:1 sm3:4 sm2:1 sm1:5 impure:1 varshney:1 substrates:1 symmetry:1 armitage:1 specifically:1 thick:1 u2:2 electronic:1 size:2 dispersive:1 given:2 publication:1 introduction:2 greven:1 their:5 john:1 ranging:1 para:1 moscow:1 manifestation:6 injected:1 than:4 showed:1 rate:4 were:2 russia:1 exhibit:1 laalo3:1 fluctuation:3 spectrum:4 crossover:1 neel:1 alike:1 seen:2 linked:1 ray:3 wilson:1 prozorov:2 singh:1 hun:1 accuracy:2 electronphonon:1 normal:3 any:1 rhs:1 centro:1 impurities:1 letter:1 measured:4 kb:6 especially:1 average:1 stronger:2 points:1 kt:1 physics:2 fitted:4 ho:1 araujo:2 show:1 doped:6 cnpq:1 feng:1 based:1 seung:1 should:3 being:1 screening:1 jae:1 equilibrium:1 do:1 lobo:2 vajk:1 renaud:1 de:4 freezing:1 dc:1 pengcheng:2 joint:1 despite:1 10mev:1 qazilbash:1 choudhary:1 processes:1 substrate:2 numerous:1 arxiv:1 thermal:4 microscopy:1 summary:1 greene:5 optimally:5 ωp:3 peltier:1 including:1 lavrov:1 permittivity:1 scanning:1 barr:1 physically:1 sensitivity:1 correlations:1 kink:6 observed:7 intensity:2 close:1 best:4 brazil:1 federal:1 nuclear:1 state:4 reproducible:1 boundary:1 paramagnetic:2 across:1 notice:1 recently:1 nature:1 attention:2 agencies:1 naito:1 gratefully:1 jetp:1 both:3 tangible:1 many:2 region:1 theoreticians:1 according:2 attributed:5 dated:1 mang:1 contribution:7 expression:2 experimental:2 con:1 ch:1 cm:1 resistivity:8 ce:1 dimensional:1 moreover:1 cu:1 210k:1 broadening:2 unusual:2 second:1 addition:3 due:3 much:1 change:2 interest:1 expected:2 ph:3 corresponding:2 moreira:1 new:1 gap:1 inductance:1 spin:9 present:1 paying:1 homes:2 laser:2 pacs:1 solid:3 5mev:1 appearance:1 profiles:1 harmonic:1 behavior:7 cond:1 crystals:2 plcco:2 grown:2 different:2 verified:1 suggest:1 same:1 clearly:2 several:1 neutron:2 used:1 see:2 dai:2 ion:2 moment:1 kim:2 lowenergy:1 demarcates:1 recent:1 well:2 kurita:1 materials:1 comes:1 tokura:1 latest:1 moments:3 superconductors:1 voltage:1 scattering:9 wei:1 lett:8 samples:3 cex:3 around:4 dagan:2 possible:2 cf:1 vacuum:1 using:4 accepted:1 cu2:2 like:4 specific:1 continue:1 experimentalists:1 spins:1 therein:1 onose:1 shen:2 successfully:1 some:1 dinesh:1 home:1 pronounced:3 gapped:1 avoid:1 measurements:1 fapesp:1 assuming:1 nd2:1 demonstrated:1 ısica:2 ando:2 bt:2 step:4 joule:1 properties:4 bz:1 gauthier:1 about:1 anomalous:1 dependence:6 o:2 range:3 stand:1 cutoff:1 letters:1 presence:1 lies:1 references:1 financial:1 nodal:1 support:1 pairing:1 long:3 noticed:1 ωp2:3 width:2 quadratic:1 low:4 liang:1 brazilian:1 was:9 suzuki:1 cuo4:8 heat:1 related:1 line:2 trying:1 lynn:1 bontemps:1 made:1 antiferromagnetic:1 supr:1 antiferromagnet:1 below:1 fermi:3 spectroscopy:1 fluctuations:7 similar:2 constant:4 abstract:1 ao:2 single:1 laboratory:1 accounting:2 universidade:1 film:1 physical:2 mutual:1 no:1 eq:3 nd:1 phonon:7 field:1 other:2 electrical:1 details:1 investigations:1 node:1 excitation:1 yoichi:1 accounts:1 grupo:1 sides:1 komiya:2 coupling:3 dω:1 assume:1 diffraction:3 together:1 depth:1 correlates:1 plasmon:3 |
0705.1640.txt |@word four:63 gausterer:1 whose:1 replacements:9 calculate:1 auf:1 under:13 rise:2 summarized:1 manin:10 ref:21 vector:20 indices:48 degeneracy:1 jhep:1 consistent:7 direct:5 second:19 above:20 new:3 coefficient:2 applies:2 here:3 represented:1 contraction:3 obtained:9 changed:1 changes:1 orthonormality:2 explained:1 replace:6 would:9 substitutions:5 recommend:2 type:1 tell:2 qdb:1 qdc:1 schroeder:1 remark:1 curvature:1 aware:1 berlin:2 hold:11 must:1 springer:2 rα:1 rβ:1 work:3 theories:1 example:8 indicated:1 give:12 relativistic:2 organized:1 want:2 end:5 thing:1 provide:1 verify:3 feature:3 how:9 nontrivial:3 wolfram:1 fourdimensional:3 description:1 transforming:1 after:3 lay:1 righthand:2 constants:2 effective:1 order:3 interpretation:1 over:5 expects:2 thesis:2 satisfies:1 before:2 symmetry:8 fix:3 comprises:1 better:1 differently:1 schmidt:5 them:3 combination:1 they:17 sixteen:1 comodules:1 invariants:1 reasonable:3 each:14 side:7 mean:1 financial:1 series:1 braiding:19 contracting:4 literature:2 poincare:1 combining:1 extract:1 gol:1 jimbo:1 rs:2 restricted:1 reader:5 mθ:1 linear:3 free:4 standard:3 wanted:1 r4:70 ange:1 lorentzinvariant:1 r1:70 r2:70 r3:70 εabc:4 δik:1 onto:7 already:4 features:2 idempotency:1 another:5 udgen:1 antisymmetrizer:3 rewritten:1 top:1 twisted:1 antisymmetrized:18 too:1 ordered:2 fierz:20 serve:1 princeton:2 project:1 matter:3 enables:3 minus:4 mink:34 schladming:1 manner:13 seen:1 tells:4 contents:1 strength:2 thoroughly:1 responsible:1 forces:1 shall:5 object:1 simplify:1 involving:1 germany:2 plenty:1 phase:2 acknowledgements:1 cellular:1 preˇsnajder:1 observation:3 yang:3 principle:1 sum:2 incorporate:1 labels:3 attempts:1 gauge:1 solutions:1 substituting:1 analogue:1 make:9 x1:40 specify:1 ematiques:1 do:7 establishes:1 de:3 dc:1 da:1 bar:5 textbooks:1 fields:1 coproduct:1 drinfeld:2 explanations:1 dobrev:1 depends:2 result:5 subject:7 instance:1 µx:1 supergravity:2 symmetric:9 simplest:1 approach:1 terms:8 however:9 essentially:1 0x:1 0a:9 und:3 uni:2 adapted:1 con:137 commutative:3 basis:8 simplification:1 three:24 been:1 clifford:2 much:3 interest:1 algebras:6 θj:2 θk:5 θi:8 supersymmetric:1 deeper:2 θl:2 concerning:11 spin:43 applied:2 exception:1 slq:32 aim:5 euclidean:63 aii:2 aij:2 property:1 procedure:1 majid:4 played:1 iv:2 ii:7 ik:4 ij:36 perform:1 things:1 realizing:1 linked:2 εlj:2 several:1 vvv:1 counterparts:8 hand:11 normalization:6 possesses:1 left:10 σ0a:3 proposes:1 identify:1 transforms:4 tilde:7 facts:1 previous:3 decomposing:1 character:1 qx2:8 qx1:5 transformed:2 gρ:1 possible:4 spanned:1 unique:1 apart:2 performing:3 remind:2 steps:2 arbitrary:2 heisenberg:2 right:7 deal:7 begin:2 proceeding:2 comments:1 scholl:4 core:1 substitution:1 properties:11 westview:1 proceed:2 o:5 nonvanishing:1 considerations:10 soc:1 publishing:1 undeformed:7 maxwell:1 ferm:136 soq:9 lies:3 hermitian:1 podle:1 sov:3 prefactors:2 support:2 qca:1 demichev:2 way:20 was:9 gij:2 form:34 epsilon:18 denoting:1 coactions:11 removed:1 true:3 versions:9 prevents:1 computing:1 implications:1 abstract:1 proven:2 exist:2 regularisation:1 commuting:2 physical:4 dotted:3 no:5 whereas:3 reality:4 zeidler:1 setting:1 role:3 longer:1 assume:5 governed:1 χi:1 remarked:2 moreover:6 serious:1 remarkable:2 equalities:2 global:2 leads:6 computation:4 remarkably:2 row:1 devoted:1 inverse:33 depend:4 finally:16 ıi:5 ık:2 ıj:38 string:1 advantage:2 dokl:1 unchen:3 entries:7 presented:1 irreducible:3 discrete:2 εkl:14 εkj:2 εki:1 equation:4 upper:2 fµν:1 sign:4 substitute:5 stands:7 contracted:1 international:1 satisfy:2 understanding:2 gggg:1 groups:11 xβ:3 q5:2 xα:24 institute:2 vectors:2 hospitality:1 montreal:1 useful:5 raise:3 muenchen:2 ls:1 modifying:1 planck:2 projector:23 prove:5 sake:2 rasing:1 explicitly:2 opposed:1 meyer:1 reorder:1 introducing:2 apparent:1 appendix:2 cases:1 fermionic:11 eberhard:1 deformed:136 values:10 following:22 making:1 arrive:3 ihre:1 dedicated:1 qdeformed:7 arise:1 allowed:2 verlag:3 requirements:1 discussion:2 orthogonality:5 write:11 fourth:1 product:23 mat:1 may:2 max:1 applications:2 representations:13 natural:1 remember:1 explicit:12 su:16 st:3 switch:2 so:34 representation:17 ogievetsky:1 subsections:1 indeed:1 mainly:3 raised:3 differs:2 derive:4 group:31 thank:2 summands:1 interesting:1 coordinates:49 εjl:5 εji:4 εjk:2 mail:2 main:3 non:12 qs:1 introduce:4 flint:1 now:29 discuss:3 down:14 term:2 drop:1 possibilities:2 realistic:1 fabian:1 qx:5 spinor:50 ed:2 conventions:3 eq:12 living:1 shown:1 space:134 furthermore:3 nishijima:1 replacing:5 contained:2 formula:8 shows:2 theory:13 variant:1 possibility:2 remainder:2 axioms:2 care:1 derivation:1 βr:5 transition:2 turn:3 invitation:1 βl:21 first:26 xj:22 xk:6 xi:35 xl:4 omitted:1 variables:1 xa:1 transform:3 xx:4 carry:2 interchange:2 given:18 checked:1 types:6 convention:4 structures:4 1l:15 gives:5 takhtadzhyan:1 x2:33 copy:2 than:4 coefficients:15 require:1 were:4 ann:2 argument:1 say:4 exchanging:1 saw:1 any:2 symmetrized:15 conversion:5 pseudogroups:1 note:1 sciences:1 take:17 symmetrizer:3 simplifications:1 theoretischen:1 gleason:1 commonplace:1 trace:15 normal:1 algebraic:3 formulae:45 remarks:5 undotted:1 xµ:3 especially:1 later:4 steady:1 drastically:1 show:5 symmetrizers:1 notations:1 spaces:22 decompositions:2 counit:2 written:13 only:6 anticommutes:1 normalizations:1 get:15 rept:1 aα:4 conjunction:1 yield:2 nowicki:1 braidings:3 namely:1 euclid:34 concern:1 commutation:27 ways:1 review:6 functionals:1 bialgebras:1 between:41 geometric:1 slabospitsky:1 checks:1 multiplied:1 notice:25 εii:3 εik:9 εij:29 jl:2 concentrate:3 jj:2 jk:9 article:2 jetp:1 come:11 σm:1 σb:2 σa:1 σf:2 contract:2 called:8 expression:5 comes:1 constant:2 invert:1 wess:8 defined:3 enable:3 noncommutative:5 covers:1 efficients:1 former:1 those:13 case:24 arnold:1 lukierski:1 promising:1 situation:4 conformal:1 metric:39 according:6 different:22 insofar:2 same:32 poincar:5 arguments:2 ludwig:2 singapore:1 akademie:1 invariance:1 peculiarities:1 without:5 components:15 grounds:4 being:9 correspondences:1 generator:2 verse:1 lett:5 versa:4 momentum:1 real:3 aspects:1 read:9 decomposed:3 harmonic:1 using:7 decomposes:2 mod:3 reshetikhin:1 reduces:1 serves:2 either:2 detq:13 topologie:1 reduced:1 comodule:5 leningrad:1 deduce:2 specified:1 provided:1 dimensions:9 confirm:1 footing:1 decomposition:15 provides:1 refer:6 faddeev:1 scientific:1 equivalent:5 ratios:1 refers:3 repeating:1 comparison:1 central:1 discussed:1 generated:1 convenient:3 obeys:1 act:2 cambridge:2 references:1 determine:3 elementary:4 gσλ:2 lastly:2 spinors:62 hep:11 assumed:1 there:17 start:7 complete:5 terminus:4 arranged:1 minkowski:59 internationale:1 organize:1 ansaetze:3 detailed:1 ac:2 ab:31 ad:3 taste:1 certain:2 aj:4 general:6 examine:1 arises:1 together:13 formulation:1 again:16 completeness:10 mathematica:2 graduate:1 field:12 valid:4 mathematics:1 congress:1 time:14 a0:9 important:7 included:1 starting:5 fredenhagen:1 consider:8 alg:1 lack:1 scalar:1 commute:8 follow:6 expressions:12 als:1 referring:1 subjected:2 tr:8 th:10 presentation:2 straightforward:1 very:8 mpi:1 difference:3 deformations:2 condition:4 list:5 inversions:1 grateful:1 σa0:3 zero:4 further:8 canonical:1 bilinear:3 what:5 abc:3 section:13 version:4 suq:16 method:4 bailin:1 modify:1 ansatz:7 σab:6 equations:7 antisymmetric:9 inspired:1 action:3 options:2 via:8 requiring:1 establish:1 readily:1 takes:3 distinct:3 universelle:1 comparing:7 nucl:1 taken:2 minor:1 more:7 lowering:8 israel:1 known:5 foundations:4 analogous:1 quantized:2 recall:4 der:5 remain:3 compare:1 dual:6 stated:3 neglected:1 numbers:1 sense:6 mn:1 simple:3 goal:2 rather:7 enlarge:1 maps:1 algebra:33 derived:3 reflect:1 fa:1 plane:38 choice:9 transposed:1 short:4 fundamental:4 fα:2 help:7 hierarchy:1 developed:1 paper:8 through:1 existence:1 kinetic:2 its:33 discretizing:1 style:1 matrices:189 conjugation:6 deformation:3 supersymmetry:1 good:1 peskin:1 seeking:1 tureanu:1 framework:1 yu:3 sinegordon:1 easily:4 finite:1 2q:3 always:2 2x:1 iff:1 die:2 found:6 universit:4 characterized:1 referred:1 as1:1 formulate:1 reduce:1 idea:1 antiself:3 quantum:148 operation:1 braided:7 really:2 nuovo:1 since:13 vectorial:9 denotes:8 acting:1 hill:1 tαβ:1 denoted:2 reason:6 ask:1 definition:6 wachter:5 omit:2 round:1 consequence:8 eqs:8 number:1 done:6 construct:1 differ:2 grimm:1 introduction:4 leading:1 least:4 calculations:1 listed:2 relationship:2 luckily:1 part:10 consult:2 kind:5 determines:1 double:2 contravariant:1 determined:2 contrary:1 electrodynamics:3 qps:1 lie:3 self:3 ruegg:1 k3:28 k2:61 k1:70 build:5 k5:2 k4:21 analogs:18 play:1 towards:4 reach:1 most:9 nothing:4 kb:16 kf:10 kk:12 clear:2 sometimes:2 kl:56 ks:3 qba:1 barred:1 physics:2 relation:11 carefully:1 find:13 parameters:1 assertion:1 generators:30 subsection:1 factor:4 columns:1 his:3 notation:1 express:5 famous:1 combinations:2 hartmut:2 alexander:1 arxiv:1 common:1 bars:1 set:7 achieved:1 see:20 sec:16 theoretic:2 analog:6 fand:1 qλ2:1 conditions:2 attention:6 isoq:1 vanishing:8 maximilians:2 distinguish:4 both:12 recherche:1 last:12 reverse:2 quantization:2 point:5 reasons:1 corresponds:3 dimensional:73 fashion:1 simply:2 throughout:2 ps:11 pp:1 described:6 transformations:2 pt:1 due:2 pa:76 symmetrizing:2 kronecker:2 combine:2 ph:5 treatment:1 generating:1 schmidke:3 convert:3 demand:4 σcd:1 gab:5 p0:6 look:5 expanded:1 while:6 replaced:2 behavior:2 couplings:1 bos:136 vol:1 reads:3 itself:1 rij:1 vanish:2 twofold:1 rules:7 emphasize:1 resulting:2 higher:5 used:5 moment:2 purpose:3 koch:1 recent:1 lower:6 task:1 concrete:1 consistency:1 stating:1 λx:2 world:1 love:1 λi:1 bin:1 analogy:8 stein:1 oeckl:1 projects:5 like:12 modifications:1 follows:13 ignore:1 collect:2 yields:5 alternatively:6 rearrangement:2 essential:2 often:4 some:21 understood:5 examples:1 gνρ:2 ourselves:3 scale:1 describing:2 behave:4 eliminate:1 tends:1 inserting:2 carow:3 run:1 ba:1 bc:6 cgg:1 step:2 hilbert:1 concretely:4 covariant:9 restrict:5 into:23 within:1 isomorphic:1 unbarred:1 rows:1 span:2 few:4 twodimensional:1 question:2 long:1 analyze:1 sections:1 delta:2 line:1 raising:8 characteristic:1 uq:28 up:11 us:43 ur:3 planes:25 similar:7 ki:4 uber:2 associated:1 shortcuts:1 likewise:4 influence:1 lehrbuch:1 formalism:1 superanalysis:1 kr:1 kq:6 elements:6 calculating:1 girardi:1 prepared:1 meaning:1 sides:4 structure:15 σba:1 implies:5 vice:5 far:2 requires:4 having:1 once:7 results:11 gg:4 eds:1 compact:3 λij:1 include:1 wave:2 antipode:1 continued:2 fakult:2 categories:1 arrange:1 notes:1 trq:27 inspection:1 noted:1 imply:2 insertion:1 index:11 3x:1 plays:1 analogously:1 expressed:3 fiore:1 deduces:1 respectively:11 identifications:4 objects:10 consideration:7 deduced:1 great:2 involved:1 products:15 composed:1 app:7 conjugated:39 summation:1 apply:7 use:10 commun:6 remains:3 next:16 calculation:1 ust:1 themselves:1 becomes:8 carrying:1 iii:2 account:3 chaichian:3 obvious:1 fulfill:5 process:1 effectively:1 lorentz:31 gcc:3 gcd:1 holds:5 theresienstr:1 reducible:1 instead:7 stand:2 sommerfeld:1 specifications:3 collection:1 physik:5 multiplication:8 doplicher:1 kulish:2 correspond:4 element:3 dilatation:1 realizes:1 allow:1 gµν:10 mathematicians:1 including:1 mentioned:9 converting:3 chosen:2 ll:6 li:1 lect:1 degrees:1 choose:3 defining:3 eur:3 outlined:1 watamura:6 landau:1 mention:1 das:1 realize:4 coaction:6 university:3 identified:1 l2:4 l1:5 accompanied:1 monomials:1 baxter:2 weyl:1 doing:7 related:2 constitute:1 our:23 special:3 out:2 category:1 matrix:57 rev:4 geom:1 suffices:1 math:20 completely:2 corepresentation:2 geometry:2 could:4 counterpart:1 hence:1 klimyk:1 confuse:1 redefine:1 ordering:1 unknown:1 behaves:1 system:3 relations:102 their:37 final:1 reversed:1 exactly:2 theorie:2 cimento:1 roberts:1 symmetries:2 unchanged:2 enforces:1 need:1 clearly:2 viewed:4 mappings:2 εt:4 able:10 gravity:1 εl:3 εi:3 εk:2 εj:2 calculus:7 centre:1 gλ:1 rearrange:2 connected:1 definitions:4 tensor:46 teilchenphysik:1 takeuchi:1 proceedings:2 construction:5 normally:2 fact:9 trivial:2 q3:10 q2:19 based:4 q4:1 should:25 constituents:4 hopf:11 achieve:1 means:5 kk1:1 ones:16 words:6 applying:9 processes:1 gbb:2 numerous:4 differential:1 qa:2 stuff:1 contain:2 fixed:1 pertains:1 traceless:1 view:4 requirement:2 exists:1 notational:1 respect:8 module:2 grosse:2 edition:1 computer:1 λkl:1 pattern:1 state:1 importance:1 amer:1 tensors:3 undetermined:2 qft:1 taking:5 equal:4 bristol:1 otherwise:3 relevant:2 co:1 conclude:4 cb:1 leipzig:2 cf:14 cd:5 table:33 forms:3 addition:4 copies:6 treat:2 define:6 determinant:3 describe:6 corresponding:12 reasonings:10 scalars:1 listing:1 subspace:1 present:6 noncommuting:1 splits:2 choices:3 will:10 dieter:1 vi:2 refs:9 thus:13 examined:1 vv:2 pauli:125 φi:1 castellani:1 gets:1 difficult:1 zumino:2 grassmann:1 student:1 spinorial:16 identity:30 compendium:1 off:3 center:1 well:16 sets:2 position:1 schm:1 arising:1 usual:3 less:1 obtain:10 uller:1 paul:1 conjugates:4 preprint:1 etruy:1 lattice:1 book:1 extends:1 identical:2 know:5 press:4 variants:3 insert:3 helpful:1 exploiting:4 become:9 works:1 replacement:1 therein:1 because:1 classical:5 algebraically:1 neglecting:1 kern:1 lead:6 does:1 summand:3 obey:3 expansion:2 simpler:1 about:9 getting:1 column:1 freedom:1 recognized:3 compatible:1 carries:3 woronowicz:2 introduced:7 projectors:15 subset:2 equally:1 own:1 bosonic:15 additional:5 snyder:1 describes:2 bd:1 but:13 repeated:1 lowered:3 bagger:1 made:2 compute:5 instructive:2 whether:2 wish:3 converted:2 problem:2 interchanges:6 int:4 recognize:1 denote:6 twist:1 interchanged:1 ink:1 ing:1 identities:31 ina:1 compared:1 qλ:89 detail:5 other:17 details:2 theor:1 regularizing:1 repeat:1 covariance:1 additionally:3 rqn:1 lifschitz:1 factors:7 rule:3 |
0705.1641.txt |@word concept:1 partial:3 consider:18 equalities:3 four:2 scalar:9 proposition:1 ηi1:1 consists:2 follow:1 depend:1 tu:1 tr:29 finally:1 th:1 applied:1 vlm:5 abelian:1 ηik:1 isomorphism:2 every:4 commute:1 rm:1 1s:1 matrices:10 dim:4 presented:1 t2:2 involution:2 vector:8 τˆk:1 section:2 small:2 gauge:2 upper:1 mi:1 direct:1 sign:1 second:4 further:1 odd:23 linear:5 bilinear:1 index:5 what:1 brackets:2 diag:2 sum:4 abk:2 expressed:1 vb1:3 subspaces:2 new:4 method:1 satisfy:1 notions:1 respectively:1 here:1 groups:3 represented:2 invented:1 equations:4 contraction:3 eij:3 antisymmetric:3 institute:1 products:1 suitable:1 via:1 projection:2 vij:2 replace:2 summation:3 establish:1 clifford:90 use:5 prove:11 contains:3 comparing:2 therefore:6 type:4 more:1 initial:1 operators:3 validity:1 particular:5 known:5 cases:4 must:2 account:2 ibk:4 ers:1 equation:2 det:6 values:1 following:18 arrive:2 example:2 proof:16 claim:1 give:4 calculation:1 pieces:2 tetrads:1 numbers:5 evidently:2 get:16 write:3 maps:1 e2k:8 map:4 product:22 express:1 blocks:1 mat:14 algebra:75 ua1:18 derived:1 conjugations:1 multiplication:2 representations:14 types:1 e24:6 transposed:1 natural:1 e23:4 element:29 so:5 representation:18 order:1 operations:4 eigen:5 developed:1 over:4 paper:2 mentioned:1 satisfies:2 steklov:1 τn:4 τl:9 τm:1 group:4 τk:24 summands:1 ll:6 lk:8 conjugation:10 forms:1 complex:14 main:3 non:1 antihermitian:2 multiindices:1 now:6 discuss:1 establishes:2 february:1 equality:1 2r:3 2s:3 sobczyk:1 2et:3 orthonormal:14 iff:1 each:1 found:1 2n:3 2k:16 em:11 spinor:1 en:24 ei:2 ee:1 ea:69 related:2 eb:15 ea1:55 eu:1 operation:23 ep:18 ru:2 shown:3 matrix:28 space:13 nuovo:4 may:8 denoted:2 formula:27 induction:1 math:2 theory:1 rlk:1 diagonal:6 possibility:1 standard:4 indices:17 completely:2 lounesto:1 e5:3 e4:17 hand:6 e1:63 e3:14 e2:32 language:1 nonnegative:2 length:2 place:1 signature:8 hence:6 ej1:4 first:6 already:1 qkl:1 grade:2 number:5 rank:3 least:3 1p:1 given:1 relations:2 uτk:5 structures:2 gives:8 e25:2 moscow:1 part:4 qlk:2 authors:1 completes:5 coefficients:3 sections:1 bea:4 cimento:4 namely:1 were:2 symmetries:1 generality:1 rewrite:1 spectrum:3 say:3 ras:1 increment:1 need:1 idempotents:6 any:4 contents:1 lie:5 zero:4 min:1 mills:1 note:6 ideal:24 take:20 coincide:1 εa:1 tool:1 calculus:1 even:23 trace:2 normal:9 sequence:1 enumerates:2 connected:1 multiply:1 shirokov:2 hestenes:1 considered:5 sometimes:1 coincides:3 kn:4 kl:10 kq:1 kp:1 usual:1 physics:1 notion:2 fact:1 117b:2 signatures:3 show:1 notations:1 spaces:4 relation:1 trivial:1 pkm:1 addend:2 commutators:11 state:1 than:1 lemma:2 only:2 anticommutes:1 generators:20 indeed:1 enumerated:1 alternation:1 columns:1 do:1 dm:1 above:1 notation:2 means:5 between:1 words:1 e245:2 geometric:1 qr:1 bar:1 ie1:6 fields:1 ie3:6 arxiv:1 common:2 contain:5 cℓ:57 qk:2 riemannian:2 set:10 exists:2 j1:4 ebk:15 depends:1 ebr:3 said:1 tensor:3 written:2 αe:2 closed:2 ηba:1 neither:1 115b:1 conditions:2 vrs:1 terms:3 λb1:4 tut:1 jl:8 uω:5 eb1:27 eb2:3 multiplier:2 uτ:1 amer:1 both:2 last:3 reverse:1 equal:7 2e2:3 com:11 τd:2 ck:7 multiplies:1 conclude:1 cd:3 dimensional:6 cℓn:1 anti:5 2e4:2 respect:7 considering:1 ei3:13 ei2:21 ei4:5 leads:1 basis:37 three:2 belongs:1 evenness:1 ph:1 algebras:16 abstract:1 define:14 determinant:1 corresponding:1 commutes:2 sufficient:2 subspace:1 dirac:6 spin:2 present:3 case:11 multi:5 e45:2 value:4 euclidean:4 suppose:6 aid:9 eik:19 property:5 identical:1 unitary:15 thus:2 according:1 ik:23 itself:1 exterior:6 ia:4 different:3 suggest:2 same:9 parts:2 several:3 subalgebra:1 ωuv:1 independent:4 literature:1 see:10 i1:22 i3:10 i2:12 i4:7 possible:1 uses:1 identity:4 numbered:2 lower:2 center:3 expression:1 idempotent:12 well:5 without:2 sets:1 dimension:11 left:27 unified:1 λv:1 λu:2 obtain:1 oxford:1 λe:2 integer:4 previous:2 generator:6 elm:10 cl:13 except:2 other:4 conjugated:4 easy:1 theorem:22 generalized:1 real:4 rules:1 advances:1 decomposed:1 sums:1 term:2 press:2 using:5 variants:1 lost:1 follows:3 ηab:8 remind:1 eee:1 mathematical:3 reidel:1 right:6 classical:1 formulas:24 εa1:4 some:6 ideals:1 b1:11 b2:12 generates:1 dimensions:3 lead:1 univ:2 hodge:3 decomposition:2 summand:1 cnk:2 minimal:5 ei1:52 bl:8 equivalent:3 pp:7 bk:5 binomial:1 br:6 2m:1 nℓ:2 properties:5 publishing:1 column:3 theorems:1 mutually:1 block:3 primitive:2 cambridge:1 el:16 into:3 down:2 hermitian:31 square:1 references:1 operator:1 ea2:4 spinors:1 rows:1 span:1 transfer:1 there:6 u1:2 transform:1 physicists:1 was:1 eak:2 form:11 ean:4 δkl:2 sequel:1 volume:3 construction:2 ec:1 eas:3 ear:3 true:1 evident:1 ut:1 uw:2 uv:16 up:1 us:25 ωv:4 assume:1 utu:2 ue:4 ua:4 called:18 ub:1 ab:5 ordered:3 ub1:2 pin:2 defined:3 ak:59 doesn:2 denote:10 tˆ:2 ar:4 au:1 exist:1 identities:1 computational:1 defines:3 nm:1 nn:1 no:2 field:4 valid:7 details:1 papers:2 company:1 elements:56 superposition:1 a1:23 commutator:5 generated:3 a2:15 116b:1 structure:6 euclidian:1 ranks:6 pseudo:1 cℓk:7 |
0705.1642.txt |@word limited:1 partial:5 consider:7 caused:1 particular:8 results:25 existing:1 four:4 consists:1 follow:2 contributions:1 causes:1 iii:7 contained:2 γi:1 program:1 th:2 breach:1 must:1 case:8 amplitudes:1 far:1 p0:1 wave:7 advised:1 experimentally:1 condition:1 leads:1 presented:1 cause:1 large:7 progress:2 small:11 eigenvalues:2 employing:1 findings:2 consistent:3 direct:2 literature:2 threshold:2 second:1 go:1 further:1 dynamics:3 even:4 established:4 what:1 expressed:1 find:2 current:1 experiment:4 obvious:1 increasing:7 boost:2 method:1 satisfy:1 outgoing:7 led:1 exchange:4 respectively:4 compilation:1 component:1 here:5 reported:7 explore:1 mev:6 stancu:2 active:2 along:4 quite:3 appears:1 obtained:2 almost:1 incoming:6 noticeable:1 involved:1 study:5 studied:1 ravndal:3 amount:1 published:1 usually:1 resonance:7 studies:2 cancellation:2 capstick:6 useful:1 projection:1 dmfa:2 austria:2 gluon:2 apply:1 meson:4 covariant:7 wiped:1 predictions:16 few:3 nucl:3 m1:7 therefore:1 ψm:1 taken:3 themselves:1 type:2 theoretical:15 more:2 sponds:1 raynal:1 becomes:2 operators:1 apparent:1 emission:2 appendix:1 basically:1 varying:1 cases:6 producing:1 insights:1 majority:1 account:1 erratum:1 mm:1 science:1 work:2 mj:11 mt:14 remain:2 values:2 following:1 arrive:1 example:1 nected:1 compare:2 give:5 calculation:5 relativistic:22 states:5 indicates:1 lorentz:3 performed:3 magnitudes:1 lacks:1 evidently:1 decaying:2 rather:7 occur:1 necessary:1 influences:2 syst:2 either:1 inputs:1 description:1 may:6 earlier:1 variant:2 reflect:1 produce:1 physik:2 fi:4 data:12 types:2 profited:1 dynamical:1 third:1 light:2 correspond:1 element:2 provide:1 fwf:2 so:2 specifying:1 fundamental:2 decreasing:3 representation:2 acknowledges:1 order:2 nonstrange:7 serving:1 wigner:1 numbers:1 developed:1 mainly:1 produced:2 experiments:2 through:1 thesis:1 austrian:1 still:2 boosts:3 before:2 transitions:1 group:1 decay:58 krassnigg:2 masses:12 glozman:2 boson:1 pene:1 degrees:1 differently:1 might:1 refinements:1 underestimate:1 them:2 regarding:2 framework:1 effects:11 they:6 focus:1 2t:1 dirac:1 respectable:1 always:1 university:1 level:1 establishing:1 2e:2 magnitude:1 mode:1 each:2 found:10 universit:2 characterized:2 prevailing:1 goldstone:1 another:1 eg:1 operator:14 decays:28 isospin:1 obtains:1 geiger:1 quantum:3 our:7 beyond:2 eq:1 out:3 emerges:1 shown:1 rw:2 matrix:2 space:1 furthermore:1 since:1 rev:16 denotes:1 rd:5 misses:1 dominated:1 emerged:2 denoted:1 ref:7 occurs:1 theory:2 quark:15 approaches:1 york:1 care:1 derivation:1 widths:27 could:2 transition:4 turn:2 gordon:1 removing:1 consequence:1 hadrons:1 first:5 already:4 surviving:1 striking:3 number:2 channels:9 smaller:3 done:2 approximately:1 directly:3 atsplatz:1 reached:2 given:3 introduction:1 leading:2 theoretische:1 relations:1 their:2 too:2 calculations:7 2ωi:1 especially:1 relativized:2 observations:1 stars:1 mostly:1 baryon:28 acquire:1 obsolete:1 sizable:2 authors:2 oge:20 constituent:4 than:5 observed:2 kind:1 unfortunately:1 measured:1 namely:2 final:1 roberts:6 future:2 amplitude:2 were:3 mini:2 remained:1 close:1 seen:2 picks:1 any:3 karl:1 relatively:1 zero:3 latter:4 mechanism:1 canton:3 note:3 k2:9 k1:6 internal:1 generalized:2 simplified:1 finding:1 new:1 underestimating:1 play:1 regard:1 allow:1 investigations:5 quote:2 reach:1 most:4 formulae:1 pair:1 baryons:6 extremely:5 class:1 observation:1 surprising:1 considered:4 calculated:4 later:1 feynman:3 proceedings:2 velocity:3 physics:1 nogami:3 applied:1 2m1:1 supported:1 ki:11 keywords:1 d3:6 ground:1 q0:1 explain:1 state:1 fund:1 should:1 only:7 going:1 factor:1 employed:2 columns:4 gev:1 notation:1 get:1 familiar:1 yielded:1 congruent:3 ones:4 nearly:1 dy:1 report:1 graz:3 gbe:16 arxiv:1 summary:2 though:2 including:1 view:1 body:2 fair:1 observes:1 frame:3 wagenbrunn:4 up:1 relative:1 bled:2 see:3 result:4 corre:1 discussions:1 terms:7 keister:1 flavor:1 reproduced:1 project:1 qµ:2 ways:1 nature:1 yet:1 behind:1 µi:5 tendency:1 between:2 invariant:3 approach:6 available:1 various:2 recently:1 kaonic:1 extend:1 tables:4 importance:1 jp:1 attention:2 namical:1 however:5 vanishing:3 conthe:1 σk:6 received:1 σi:4 last:3 resides:1 according:2 attributed:2 figures:1 context:1 pdg:5 distinction:1 experimental:18 mechanics:3 nonrelativistic:17 cf:1 decreases:1 table:12 improvement:1 sensible:3 oliver:1 enhancements:1 cqm:20 basis:2 three:2 been:2 reduction:3 much:2 interest:1 expected:1 ph:1 pi:2 questioned:1 corresponding:6 kaon:3 essentially:2 ljubljana:2 general:3 spin:8 former:1 present:5 p2:3 p3:3 exception:3 p1:4 pacs:1 reliable:1 value:1 employ:2 while:5 replaced:1 behavior:4 promising:1 bhaduri:3 eur:2 couplings:1 larger:1 phenomenological:1 refs:1 thus:1 iv:1 ii:8 reads:1 vanish:1 different:12 barnes:1 lett:1 same:3 poincar:2 strange:11 2p20:1 contents:1 fkr:11 difficult:1 independent:1 used:4 reporting:1 effect:2 hand:1 parametrized:1 slovenia:2 4m:1 delicate:1 changing:1 least:1 supersede:1 largely:1 nevertheless:1 changes:1 well:4 obviously:1 spectator:3 entry:2 model:9 usual:2 quoted:4 among:1 being:2 when:5 obtain:1 rest:1 quotes:1 underlying:1 λk:5 ωm:2 momenta:2 eigenstates:1 previous:2 adv:1 k3:9 doctoral:1 conclusions:1 point:5 fitting:1 isgur:4 hyperons:1 treatment:1 reason:1 input:3 eigenstate:2 momentum:2 take:1 parametrisations:1 koniuk:4 phenomenology:2 possible:2 swanson:2 vacuum:1 using:4 projects:1 mod:1 pertinent:1 particle:1 sizes:1 eem:12 channel:3 fully:1 underestimation:1 become:1 works:1 essential:1 spins:1 parametrizations:2 truncated:1 creation:1 some:6 examples:1 cr:4 extended:1 employment:1 total:1 describing:1 both:6 lead:1 confirm:1 resonances:12 opposite:1 mesonic:3 refer:1 journal:1 notable:1 agreement:1 expansion:1 2m:1 properties:1 hadron:1 gained:1 comparison:5 about:1 central:1 extension:1 freedom:1 dependence:1 o:1 reduced:2 remains:1 2j:1 introduced:2 consequently:3 strangeness:12 inclusion:1 into:1 within:1 integral:1 due:1 phase:1 appropriate:1 elementary:2 valuable:1 often:1 uncertainties:2 rows:1 institut:1 additional:3 comparing:1 intrinsic:3 support:1 there:5 yao:1 width:5 workshop:2 conˆ:1 biggest:1 decisive:1 was:6 function:1 complete:1 form:6 differences:3 but:1 construction:1 desplanques:1 line:2 removed:1 considerable:1 truncation:2 made:4 evident:2 deficiency:1 variations:1 bounds:1 ur:1 ωi:4 below:5 limit:7 benchmarks:1 mtm:1 demonstrate:2 polyzou:1 similar:7 called:1 strongly:1 constant:1 defined:1 certain:2 denote:1 franzens:1 formalism:2 again:1 functions:7 nk:1 varga:1 neglecting:2 generally:4 acknowledgments:1 other:3 role:1 details:3 papers:1 nr:1 theussl:1 picture:2 suppl:2 models:8 preceding:1 primed:1 ξk:1 included:1 parities:1 plessas:9 implies:1 coupling:6 practically:2 dσ:1 governed:1 correspondingly:1 mass:11 nuclei:1 |
0705.1643.txt |@word neighbors:9 limited:2 monte:10 barone:1 transitions:2 consider:12 chain:5 switched:1 roman:2 magnetic:12 varying:1 results:10 existing:1 leads:1 eds:2 nanoparticle:1 higher:1 computation:10 maxima:2 consists:2 landau:1 bruinsma:1 gr:1 depend:3 calculate:4 kontos:2 description:2 illustrates:2 functions:1 environment:1 charge:2 does:1 device:1 present:3 th:2 under:4 analogous:1 include:3 tc:2 maximum:1 applied:3 digit:1 supported:1 straightforward:2 nearestneighbor:1 very:17 continues:1 curves:1 seemingly:1 choice:1 vertex:1 niskanen:1 kimura:1 fan:1 orientations:1 summarized:2 experimentally:2 ln:1 difference:2 exact:3 condition:1 squids:1 four:13 indicate:1 dominate:1 exponential:1 hamiltonian:3 ref:10 anisotropy:1 t2:2 applicable:3 damped:1 large:17 solved:2 convenience:1 unrelated:1 affect:1 science:1 small:12 entropy:5 unaware:1 pyrochlore:1 upper:1 smaller:1 disordered:9 foundation:1 plaquette:40 sign:3 go:1 zero:9 cost:1 design:2 superstructure:1 subtle:1 growing:2 further:3 implemented:2 carlo:10 even:6 transfer:1 rewritten:1 ubner:3 plays:1 appear:1 brackets:2 d2:2 sum:2 axes:2 while:1 brink:3 current:8 3j:4 version:1 en:1 above:5 flowing:1 new:2 d1:2 consisting:6 filled:5 3d:2 condensed:1 full:1 simultaneously:1 degree:2 exchange:1 respectively:6 loose:1 modify:2 tf2:1 here:10 agreement:2 following:6 them:5 possibility:5 sinh:1 aid:1 directions:2 consideration:1 along:2 quite:4 table:3 change:2 obtained:8 separating:1 dividing:1 institute:1 shift:4 study:4 studied:2 approaches:1 reports:1 napoli:1 simultaneous:1 light:5 rareearth:1 bd2:1 usually:2 complicated:10 demonstrates:3 della:1 changes:1 composed:1 named:1 formulated:2 spatially:1 namely:1 explained:1 layer:1 moessner:2 highly:2 modulated:2 decrease:2 clockwise:4 during:7 plot:7 use:8 wealth:2 working:3 remains:1 bondarenko:1 predictions:1 next:10 calculation:1 mation:1 going:2 therefore:5 memory:1 taken:2 bonds:4 meyer:4 type:14 theoretical:1 diagrams:2 more:7 smeared:1 flat:2 schematic:2 becomes:2 stable:2 om:1 tested:1 intermediate:3 particular:2 central:2 cases:1 iii:1 circle:2 must:1 high:3 account:3 left:5 quantized:1 coupler:1 car:1 der:4 work:3 modified:1 mk:1 ferro:1 reproduce:2 macroscopically:1 itself:1 values:13 temperatures:15 den:3 ishihara:1 already:3 meet:2 spontaneous:1 example:8 performed:2 control:3 nearest:25 compare:1 figure:3 give:2 process:3 numerator:1 sense:1 relaxation:1 smirnov:2 pieces:1 states:20 indicates:3 minimum:7 numbers:1 degenerate:2 arise:5 attract:1 occur:1 junctions:4 axis:1 end:1 notation:2 noises:1 fortunately:1 discussion:3 get:5 range:12 arrangement:2 write:2 located:1 nontrivial:2 numerous:3 thermodynamics:1 instead:2 widespread:1 strong:2 parameter:9 izmalkov:5 simplicity:1 rise:1 contribute:1 mat:3 staircase:2 manganites:1 may:33 selke:3 after:2 tien:2 scalable:2 diagram:17 fa:1 plane:7 ehs:2 demonstrating:1 waves:1 develop:1 summarize:1 data:2 response:1 types:10 curve:1 realized:5 amin:3 natural:2 effective:2 enhance:1 computations:12 maybe:1 counter:2 lines:1 correspond:5 element:1 quadrant:2 rather:8 si:2 frustrated:1 so:8 enter:2 region:4 order:11 figs:3 le11:1 help:1 correlation:1 indeed:4 over:1 despite:1 mainly:1 characteristic:4 course:4 thermal:3 experiments:3 including:1 enumeration:1 cuts:1 mentioned:1 converting:3 still:3 its:13 controllable:8 curly:2 how:3 energies:18 interesting:5 presence:1 vicinity:3 exhibits:3 shifts:1 according:1 meissner:1 systems:14 constitutes:1 clusters:20 travelling:2 main:4 decades:1 lx:1 eur:1 versus:7 non:1 good:2 junction:11 illustrate:2 combination:1 kirtley:3 method:2 fig:61 introduce:3 primary:1 mention:1 walls:3 cutting:1 they:5 rotation:1 now:9 implies:1 discuss:7 dielectric:1 2t:1 easily:7 february:1 finite:6 publication:1 always:1 university:1 presented:6 arrows:3 2z:1 2d:1 realistic:3 2f:1 magnitude:1 reasonable:1 each:13 crossing:4 found:5 2n:1 difficult:2 nori:1 characterized:3 mean:3 heavy:1 el:1 domain:21 square:44 directly:1 farhi:1 list:1 energy:36 ef:3 idea:2 related:6 solution:3 inhomogeneous:1 owing:1 expect:6 kusmartsev:5 loops:7 our:5 operation:1 beyond:1 salesman:3 array:10 intended:1 deals:1 shown:14 network:3 kieu:2 space:1 tosatti:2 since:1 rev:20 cuprate:1 research:2 increase:3 similarly:2 lundstr:1 wu:1 thermodynamic:1 induced:1 issue:2 plotting:1 inevitably:1 barrier:2 interactions:32 confidence:1 mechanisms:1 diagonal:31 free:4 standard:1 fractal:2 applications:3 formation:8 ecp:3 dopants:1 e4:7 boehm:1 e1:7 e3:6 e2:7 pairs:1 interaction:19 r2:1 created:1 geometry:3 could:14 transition:4 obstacle:1 insulating:1 ordering:8 produce:1 circuit:2 signature:1 hence:1 retain:1 santoro:2 configurations:16 onto:4 eqs:1 substrates:1 first:8 origin:1 initial:3 features:5 symmetry:2 variables:1 powerful:1 number:10 reaches:1 devices:1 glassy:10 done:1 defects:24 another:4 blank:1 ring:26 open:5 horizontal:18 size:4 passes:1 given:5 toy:4 temperature:23 quadrupolar:1 introduction:4 revealed:1 interact:1 behaves:2 franco:1 system:25 least:2 parallel:1 uchaikin:2 their:6 annni:8 constants:10 calculations:2 realization:1 perfectly:1 structures:8 final:7 listed:1 way:5 ratio:13 svedlindh:1 academy:1 moscow:1 exactly:1 studies:1 technique:1 favorable:8 manifestation:1 rijnders:1 broader:1 cosh:2 than:7 royal:1 observed:3 kind:4 analyze:4 impractical:1 lesueur:1 surrounding:2 double:1 roberto:1 see:29 tunable:2 cite:1 project:1 matter:2 determined:1 doubly:1 str:2 were:3 gives:2 treated:4 russia:1 traveling:1 lowest:4 close:2 electrodynamics:1 conventional:2 mind:1 defect:2 generalization:1 crossover:2 say:2 manner:1 distorted:1 need:1 obviously:1 demonstration:1 any:3 rocca:1 built:1 proliferation:10 sj:2 efficient:1 thoroughly:1 separate:1 therewith:1 able:2 isolated:2 note:8 sciences:1 checkerboard:12 take:2 forces:1 online:2 finding:1 algorithms:1 reversed:1 ishizaka:1 guichard:1 circles:4 formulas:1 towards:1 multiple:1 giuseppe:2 populate:1 opposite:1 serve:1 who:1 reach:1 mimics:1 most:5 boltzmann:1 involving:1 plan:1 phase:40 grateful:1 analytically:1 proliferate:3 trapping:1 picture:2 unequal:1 especially:2 considered:2 neighboring:2 clear:1 flop:1 physica:3 feynman:2 trapped:4 definitely:1 principle:1 mechanical:1 consisted:1 physics:3 section:4 fact:1 phenomenon:3 lundgren:1 show:3 circulating:1 labels:1 fs:1 sites:8 solutions:2 keywords:1 corner:7 trivial:1 find:15 ground:21 polygonal:1 slow:3 based:7 just:1 parameters:2 implementation:2 written:1 topological:13 should:3 knauf:1 being:4 only:9 experiment:1 various:4 constant:4 hamiltonians:1 local:1 alternation:1 hope:1 dn:4 do:4 mixture:1 plaquettes:6 viewpoint:2 means:2 grynberg:1 simplest:2 barriers:2 straightforwardly:1 kinks:1 cannot:1 negative:1 reversal:1 competing:17 lattices:1 dt:1 superstructures:4 differentiating:1 takahashi:1 adiabatically:3 evolution:19 exhibiting:1 substrate:2 consist:1 horizontally:1 conditions:1 arxiv:1 european:1 tuned:2 investigate:4 paper:5 schemes:1 architecture:1 forrester:2 mapped:1 analytical:1 through:1 fixed:4 bak:3 available:1 set:3 exists:4 achieved:1 bias:2 laad:1 j1:3 j2:3 operates:2 unexpectedly:1 depends:2 computer:5 result:11 enhanced:1 khomskii:2 discussions:1 terms:2 schematically:1 phases:17 exploited:1 capacity:16 interacting:1 compounds:2 ways:1 subsequent:1 review:1 currently:2 rings:47 dipole:10 label:1 boundaries:13 qubits:10 state:57 smallest:1 enumerated:3 correctly:2 between:36 without:1 boundary:21 reading:1 approach:4 knowing:1 sections:1 notice:1 recently:3 reproduced:1 vertical:15 nature:3 importance:1 attention:2 weak:1 however:7 reproduces:1 regime:1 no:1 key:1 analyzed:2 configuration:6 distribution:7 received:1 kataev:1 maassen:3 many:8 taking:2 zagoskin:4 equal:5 etc:1 connection:1 manifestations:1 dated:1 qubit:1 estimation:1 whole:2 comes:2 kugel:1 hilgenkamp:3 strongly:1 would:2 flexibility:1 point:11 simple:2 seems:1 others:1 dislocations:9 corresponds:9 nordblad:1 dimensional:14 represented:1 grajcar:5 simply:2 decreases:1 associated:13 dislocation:4 leave:1 considering:1 unusual:2 devil:2 described:10 tuning:1 topical:1 addition:3 locally:1 three:9 been:5 relying:1 underlying:1 int:1 much:4 deposited:3 superconductor:1 interest:1 basic:1 anisotropic:1 proposal:1 hardly:1 configurational:1 choose:2 field:4 direction:2 arises:5 controlled:3 both:3 quantities:2 occurs:2 formed:2 frustration:1 external:1 general:3 spin:31 those:3 case:9 multi:1 closed:1 processes:1 josephson:10 pacs:1 solid:2 plain:2 straight:1 value:17 will:20 contemp:1 near:2 tsuei:2 programme:1 april:1 behavior:5 error:2 cancelled:1 situation:8 gave:1 couplings:3 loop:6 alike:1 planar:19 changed:2 orientation:3 almost:1 vi:1 refs:1 sondhi:1 thus:9 site:30 surface:1 iv:1 ii:4 cluster:11 superconducting:6 arrangements:1 cond:3 il:5 lifetime:1 rid:1 currents:5 orbital:17 binary:4 different:29 verified:1 shorted:1 grant:1 generic:2 acknowledgments:1 lett:9 same:10 clearly:1 pass:1 kunert:1 quant:2 arguments:1 widely:1 largest:1 elliott:2 several:1 ichev:5 start:2 loughborough:1 evolve:1 used:8 peaks:5 cubic:2 stripy:1 numerical:2 effect:1 hand:1 domains:3 moment:5 levels:2 kock:1 stripe:14 characters:1 infinite:10 changing:1 dimensionless:1 contribution:2 recent:1 numbered:1 dark:5 lower:2 center:2 expression:2 degeneracy:4 well:8 remain:2 analysis:7 externally:1 patterns:2 solids:1 materials:1 solve:1 experimental:5 tokura:1 na:2 exponentials:3 position:1 model:42 arising:9 usual:5 ferroelectrics:1 proposed:2 less:2 moments:12 rogalla:1 superconductors:1 obtain:1 competitive:1 ideas:1 difficulties:1 via:3 positions:5 love:2 macroscopic:3 previous:6 oriented:3 candidate:1 density:1 yu:2 character:5 dc:1 sometimes:1 lattice:37 authors:1 aprili:2 developments:1 versa:1 theorem:2 wagner:2 build:1 supercurrent:1 customers:1 around:4 read:1 possible:21 early:2 department:1 increases:2 five:4 know:1 performance:1 using:5 color:2 occurring:1 vertically:1 bistable:1 promising:1 necessary:1 like:12 obvious:1 qualitative:2 adiabatic:43 addressed:1 specific:6 flux:8 indication:2 either:3 arbitrary:2 popular:2 become:1 london:2 conclusion:1 disorder:1 spins:13 sipser:1 therein:1 gutmann:1 performing:4 often:1 classical:2 vortices:1 frustrations:3 successfully:1 phenomena:1 draw:1 competition:2 separated:1 deduce:1 repeat:1 nonetheless:1 specified:1 proper:1 peter:2 squares:2 happens:1 provided:1 minima:3 illustrated:6 2e:4 broad:5 avoid:1 measurements:1 future:1 per:8 contrast:1 esf:1 critical:1 provides:1 wohlleben:1 yields:1 chains:2 demonstrated:2 inserting:1 denominator:1 resolve:1 indicated:1 retains:1 equivalent:2 electrically:1 perpendicular:2 illustration:1 binder:1 inherently:1 although:2 plots:4 properties:7 von:1 panel:11 about:1 goods:1 actual:2 ferromagnetic:4 discussed:8 dependence:3 o:2 simulation:2 distinct:2 carries:1 regular:2 2j:42 neighbor:17 mixed:2 shared:2 introduced:2 slightly:1 book:1 peak:3 goldstone:1 own:2 nonequivalent:1 plethora:1 into:17 within:3 numerically:2 due:8 down:2 included:1 odd:1 because:1 references:1 determine:2 proportional:1 gomez:1 significantly:3 20d:1 theor:1 fast:1 van:7 additional:6 paramagnetic:3 there:22 long:6 3tu:1 anderson:2 describes:2 low:14 lot:1 ed:1 slowly:1 pdni:1 was:13 hare:1 treat:1 function:11 alloys:1 creation:4 complete:1 form:13 enough:1 metastable:4 some:6 distortions:1 arima:1 but:6 erio:2 hk:1 heat:19 properly:1 link:1 gain:2 aqc:17 larger:8 russian:2 encoded:2 line:2 true:1 ph:2 faster:1 directed:1 made:3 portions:2 annihilate:1 evident:1 society:1 arrays:15 antiferromagnetic:28 cells:4 practically:1 up:5 us:15 lead:3 limit:4 today:1 uk:1 planes:3 utz:1 demonstrate:1 problem:10 panels:1 similar:12 called:1 distance:1 detailed:3 bearing:1 partition:9 ordered:3 computing:7 defined:1 certain:2 abstract:1 describe:2 influence:1 metals:1 denote:2 quantum:24 single:3 antivortices:1 right:6 simulations:6 corresponding:23 antiferromagnetism:3 nondegenerate:1 distributions:1 physical:6 again:2 perovskite:1 compared:1 polygon:1 nn:2 variety:1 eq:4 whereas:4 edwards:2 when:13 detail:1 sublattice:7 application:2 other:10 role:1 details:1 branch:2 dipolar:2 mass:1 out:2 spinels:1 nonzero:3 briefly:1 elements:1 kinds:2 calculating:4 pronounced:1 models:2 shintani:1 problems:4 variation:3 helpful:1 evolves:1 important:2 bounded:1 ising:36 variable:2 fisher:2 needed:1 structure:9 matrix:1 individual:1 coupling:26 algorithm:1 vice:1 holes:1 persistent:3 stripes:21 original:1 portion:8 4j:30 procedure:2 time:6 appl:1 decoherence:2 4e:8 having:7 once:1 |
0705.1644.txt |@word secondly:1 code:5 gs:1 consider:4 represent:1 rev:6 mackay:2 results:26 integration:2 four:1 entropy:20 overlap:19 moustakas:1 follow:1 manipulations:1 row:3 looking:1 dimensionality:2 calculate:1 integral:1 ǫr1:4 deterministic:2 send:1 striking:2 must:1 behave:1 tanaka:2 those:3 th:1 under:7 suffered:1 characterised:2 presentation:1 sent:2 overlaps:5 division:1 straightforward:1 very:4 decreases:1 rise:3 account:1 focus:1 electron:1 crosses:5 every:1 entries:1 affect:1 concatenating:1 exact:1 condition:1 generalised:1 coordinate:2 moderate:1 spinglass:1 level:22 transmission:3 evaluation:1 tanh:42 t2:3 solution:19 correct:1 large:11 discrete:2 insights:1 vector:6 rj:5 ndimensional:1 small:5 biological:1 exhibits:2 equation:9 configurations:1 upper:4 zn:4 averaged:2 disordered:1 29th:1 appearance:1 guidelines:1 direct:1 past:1 threshold:7 zero:16 sengupta:1 rigorous:1 further:1 dynamics:2 estimated:1 odd:1 linear:1 even:3 employ:1 errors:2 plays:1 sub:3 invertible:1 giving:1 section:8 decoding:20 current:3 above:4 crossed:1 poorly:1 john:1 method:2 quenched:2 focuses:1 simultaneously:1 degree:1 q0:3 respectively:10 realizations:1 component:1 here:7 agreement:1 behaviour:9 reported:2 simon:1 them:3 ansatz:8 directions:1 ratio:1 along:1 strong:1 equations:20 appears:1 obtained:21 sending:5 trans:4 sender:11 difficulty:1 oxford:2 study:9 studied:4 allows:1 experience:2 leaving:1 prior:2 maximising:1 simultaneous:1 graph:4 studies:2 helps:1 plotted:2 emerge:3 via:3 useful:1 cν:3 scales:1 marginal:1 explained:2 highly:4 expect:1 visible:1 boolean:1 decrease:2 aimed:1 achievable:1 sgn:6 apply:1 tools:1 senders:5 unit:3 readily:1 poor:1 plot:6 use:9 graphs:2 additive:1 figure:14 working:1 codewords:11 remains:3 continuous:4 negative:5 scenarios:1 few:1 depicted:5 noting:2 call:1 averaging:1 encode:2 means:2 iteratively:1 type:2 theoretical:27 reflects:1 more:10 introducing:1 sons:1 ˆl2:5 h1:2 becomes:6 ti:8 benchmark:1 cooperate:1 phone:1 final:1 appendix:6 far:2 particular:6 known:6 cases:12 ferromagnetic:15 logarithm:1 states:9 keeping:2 include:2 ma:1 r2:12 effectively:2 ρi:2 science:2 originally:1 work:1 det:1 dzi:3 values:17 thin:1 cam:1 following:4 making:1 metal:1 drops:1 averages:1 numbers:1 control:2 compare:2 onset:1 corrupted:3 indicated:4 give:4 process:2 iterative:1 ˆl1:1 high:1 indicates:3 imaging:1 performed:1 employs:1 unphysical:1 times:4 τi0:3 breaking:2 simple:7 axis:2 information:25 end:1 hoc:1 provide:2 clever:1 get:1 xˆ:5 feature:2 occur:1 write:2 necessary:3 βr1:2 fourth:1 migliorini:1 simplifies:1 optimal:3 2lr:1 parameter:2 ensemble:1 circular:1 profile:4 inputs:4 product:1 mpm:1 mat:1 stable:3 huge:1 may:6 thermodynamic:3 earlier:1 derived:2 mapping:1 constraint:1 reflect:1 mac:10 explored:1 cambridge:2 representations:1 choice:2 data:1 grow:1 types:1 examining:1 changes:4 ziµ:3 dynamical:34 third:2 ss:1 amount:1 lines:4 correspond:3 sj:9 si:3 fp6:1 algorithms:2 deterioration:3 enter:1 order:4 bins:3 typical:7 operations:1 atanh:26 interpretation:1 developed:1 over:11 insight:1 vary:1 paper:2 including:2 statistical:40 τia:12 differs:1 suffer:2 ieee:5 its:2 before:5 perfect:4 superior:1 τl:2 derive:1 group:1 xl:1 qˆ:4 τi:11 chosen:2 matrices:5 xm:6 suboptimal:1 τa:4 better:2 estimating:1 detected:1 complex:1 systems:8 relate:1 derivative:1 main:2 decades:1 easier:1 xl1:2 eventually:1 aston:1 good:1 affected:1 interdisciplinary:1 entire:3 powerful:1 amenable:1 cover:1 introduce:2 reflected:1 scaling:4 framework:5 transmissions:1 motivates:1 effects:3 they:4 symposium:2 ˆx:3 now:1 transparent:1 rµ:1 transmitter:15 finite:2 indeed:1 2r:1 rendering:1 always:4 university:3 presented:2 arrows:1 identified:3 transmitted:9 editor:1 each:16 crossing:1 accommodated:1 higher:5 decreasing:1 glasses:2 square:1 significantly:2 map:1 energy:24 hard:1 reduce:2 gaussian:21 related:2 used:5 obtains:1 encodings:1 eu:1 organised:1 sourlas:1 transitions:5 extract:1 thick:4 shannon:17 out:2 simplify:1 network:4 rs:11 vch:1 interference:48 convenience:1 tolerated:1 research:1 increase:12 combinatorial:1 sociological:1 conclusions:1 fountain:2 ra:1 reader:1 denoted:2 adaptive:1 receiving:1 sensor:3 ri:2 interchanging:2 shows:14 foundation:1 wiley:2 log2:5 theory:13 variant:1 contain:1 diagonal:1 free:18 lesser:1 indices:5 approaches:1 term:2 mi:7 franz:1 approach:2 estimate:2 likelihood:1 mimo:46 defining:2 diagram:1 interaction:1 r1:11 βr:12 could:3 transition:53 messages:13 david:1 ǫr2:2 βf:5 mitzenmacher:1 normalisation:3 derivations:1 hence:1 cdma:2 onto:2 first:15 origin:1 info:3 already:2 transmitters:15 features:1 probability:5 encoding:1 omitted:1 variables:12 coding:7 number:30 na:2 channels:43 instances:1 symmetry:2 unexpected:1 directly:1 message:14 quality:1 millions:1 equating:1 given:21 temperature:5 likely:1 introduction:3 meaningful:1 top:1 structured:1 system:17 relations:1 their:5 paramagnetic:1 brevity:1 constants:1 calculations:3 rates:1 white:1 scheme:1 bits:3 unpublished:1 paved:1 centred:2 q0i:2 mostly:1 asymmetric:16 kirkpatrick:2 exactly:2 interesting:1 extended:1 x2:2 x1:10 representing:2 population:4 peaked:1 observed:1 perfectly:2 determines:1 prevent:1 double:1 roberto:1 rate:3 modelled:1 replicas:2 virasoro:1 lim:2 future:1 contrary:1 represents:2 were:1 providing:1 ia1:1 takes:1 vicente:2 acknowledged:1 correction:1 modern:1 qˆ0:2 summing:1 randomly:1 replicated:2 delta:7 seen:1 seem:2 recover:2 linked:1 viewed:2 iba:1 constructions:3 inform:1 efficient:1 uncoded:1 responsible:1 consequentially:1 note:5 instance:3 kabashima:3 subjects:1 xi:14 performance:5 sherrington:2 clarifies:1 channel:45 beyond:1 added:1 multiple:12 allow:1 inference:1 established:1 contrasted:1 denoting:1 measures:1 exercised:1 most:2 regular:3 experiences:3 iterated:1 letter:1 codeword:2 phase:2 coded:2 interacting:1 volume:1 iterating:2 surprising:1 mobile:1 histograms:3 clear:2 partition:4 coincides:1 traditional:1 awgn:1 points:12 exp:21 multiplicative:1 left:3 physics:9 sum:2 fact:4 reserve:1 precise:1 thomas:1 particularly:2 show:3 random:7 solving:1 relation:1 solutions:6 tµ:2 carefully:1 trivial:2 networks:4 fifth:1 d1:1 access:7 indicator:1 based:3 spite:3 hawkes:1 distributed:2 outside:1 luby:2 should:5 2q0:1 being:4 only:6 explicitly:1 subsection:2 factor:1 attained:1 employed:2 constant:3 thresholds:1 achieve:1 ip:1 monotonically:1 dl:1 dominant:2 goes:1 notation:1 di:4 simplest:1 ration:2 processing:1 marks:6 joint:9 s21:2 ˆi:4 report:1 dr:2 areas:1 acm:1 increasing:3 resource:4 zecchina:1 fields:4 transposition:1 arxiv:1 comprising:1 doubled:1 investigate:1 europhys:1 mapped:2 analytical:4 identify:1 algebraic:1 reveals:1 art:1 achieved:1 undergoes:1 δjk:1 lett:4 up:3 detection:1 y1:1 see:7 computer:2 result:7 integrating:1 york:1 techniques:1 closer:1 practice:1 αr:1 capacity:9 probable:1 2l:3 currently:2 symmetric:18 wol:1 state:4 determined:1 various:6 correctly:1 between:15 xˆ1:1 limit:34 conditions:3 ire:1 available:5 gives:4 recently:1 boldface:1 vertical:2 receivers:32 complement:1 dˆ:2 kanter:1 however:5 rapidly:1 efficiency:1 vanishing:1 concentrate:1 jointly:5 2σj:4 jk:1 tˆi:1 come:2 distribution:11 abruptly:2 xˆi:8 both:18 enables:3 last:1 candidate:2 limits:5 gratefully:1 retrievable:1 many:1 region:1 termed:1 equal:5 against:2 emit:1 ln:43 improves:1 figures:1 context:1 receiver:27 moments:1 variance:3 mean:3 expression:1 guarantee:1 otherwise:1 minimises:1 generalisation:1 relevant:2 co:1 conclude:1 reasons:1 continuation:1 corresponds:2 exemplars:1 dimensional:4 represented:2 diverges:1 simply:1 adding:1 r43:1 leads:1 respect:8 dqd:2 publishing:1 second:15 would:1 suppressed:1 ai1:2 due:6 been:4 ai:8 difference:2 describes:1 slowly:2 interest:4 basic:1 expected:2 differently:1 generating:1 contribute:2 corresponding:7 optimally:1 received:6 quantities:3 new:2 gap:2 complements:1 σj2:10 c2:3 c1:3 denote:2 spin:6 former:1 present:2 xˆl:3 case:56 multi:2 mlf:1 irregular:2 exponential:1 pacs:1 solid:4 wellknown:1 tolerate:1 examine:3 value:7 will:14 technical:1 while:13 optimization:1 error:9 investigating:1 2k:3 taking:1 hartmann:1 identical:1 43rd:1 vectors:4 attains:1 iq:1 characteristics:1 t1:3 non:8 obeying:1 continues:1 sudden:1 cond:1 io:2 weakest:1 aspects:1 investigated:2 increased:1 binary:5 different:7 any:1 suggests:1 parisi:1 make:2 cross:1 same:15 clearly:1 another:2 sji:11 nishimori:5 units:3 several:2 infeasible:1 grows:2 difficult:3 independent:3 literature:2 http:1 solved:1 singapore:1 numerical:10 effect:2 average:9 phy:1 levels:9 user:5 internal:7 infinite:1 changing:1 gallager:3 identity:2 keep:2 relies:1 lower:2 mech:1 kept:1 scenario:4 neural:1 makes:1 simplicity:1 well:5 analysis:8 factorises:1 s22:2 academic:1 without:1 components:1 sets:1 firstly:1 model:3 leone:1 usual:1 load:2 world:1 nc:2 just:1 among:2 increasingly:2 accurate:1 obtain:8 sources:3 birmingham:1 integer:2 followed:1 λi:2 macroscopic:1 emergence:3 λm:1 previous:1 sampled:1 interestingly:1 generator:1 density:1 point:47 except:1 node:1 improvement:1 signals:1 thermodynamics:1 interested:1 treatment:1 relevance:2 input:2 occurring:1 ricci:1 transformation:1 scientific:1 real:1 conventional:1 around:1 easily:2 advances:1 showing:2 normalise:1 possible:4 increases:5 indicative:2 rescales:1 ldpc:11 press:3 using:16 bit:3 correcting:5 mod:4 counterintuitive:1 appearing:1 xli:2 systematically:1 follows:1 signal:1 isomorphism:1 serves:1 basics:1 either:1 sparse:1 arbitrary:5 βr2:4 output:2 factorise:1 disorder:2 essential:1 mathematical:1 parity:8 right:3 functional:2 methods:10 sends:2 affects:1 successfully:2 some:2 stat:1 multiuser:1 b4:1 tµi:1 zi:1 table:4 little:1 shokrollahi:2 monasson:1 provided:1 describing:1 lead:1 bottom:2 stronger:1 broad:1 transactions:1 fluids:1 per:4 whole:2 does:3 linearly:1 provides:1 saad:7 proc:2 refer:1 inserting:1 noise:40 obey:2 power:3 derivatives:1 s12:2 s11:2 instabilities:1 communicate:1 analysed:2 how:4 step:2 substituted:1 although:5 found:2 plots:2 refers:2 dictated:1 properties:4 noisy:1 comparison:4 about:1 carried:2 extension:2 saddle:11 column:10 discussed:1 dependence:1 o:62 mixes:1 practical:7 range:3 estimator:1 tersenghi:1 obeys:1 learning:1 underway:1 mixed:1 introduced:2 other:6 functions:3 converging:1 considerations:1 computational:2 significant:1 keeps:1 communication:11 into:4 within:3 numerically:1 bound:2 lies:1 appropriate:1 references:1 ezard:1 anderson:1 resilience:1 realisation:1 rely:2 acknowledgements:1 additional:3 comparing:1 support:1 there:2 fast:1 noticed:1 decode:1 accordingly:1 low:2 way:2 2m:1 sections:2 function:15 decoded:3 form:4 energies:3 metastable:10 becoming:1 differences:1 analyse:4 but:4 back:3 hj:3 taken:2 posterior:1 construction:1 repeatedly:1 larger:1 encoded:2 line:24 highest:1 weigt:1 extend:1 made:1 evident:1 understood:3 2πi:3 characteristic:2 bounds:2 us:3 stops:1 ωi:13 considered:6 below:7 gaps:1 maximiser:1 uk:3 spielman:1 problem:2 similar:5 called:2 yˆ1:2 regimes:1 mechanics:32 ac:1 later:1 proved:1 ad:1 ag:1 computing:2 defined:5 certain:1 abstract:1 measure:2 calculated:3 general:2 dashed:14 single:18 replica:11 initial:3 our:2 hamiltonian:3 distributions:5 check:8 constructed:1 again:1 marking:1 codes:12 thermodynamical:28 dotted:7 no:2 index:4 edwards:1 when:5 vanishes:1 field:2 setting:1 role:1 details:1 annual:2 ny:1 gaining:1 picture:1 briefly:1 elements:5 users:7 separate:3 models:1 montanari:1 resembles:1 problems:9 shown:3 a1:5 meaning:1 important:2 bounded:2 ising:1 suited:1 urbanke:2 variable:4 aggregated:1 matrix:19 independently:1 suffers:1 πi:2 glass:1 assume:2 requires:1 extraction:1 daily:1 4q:1 equivalently:1 inset:4 dot:2 introduces:1 time:5 qualitatively:1 richardson:2 starting:1 original:5 once:1 |
0705.1645.txt |@word magnetic:1 four:8 helices:4 nwo:1 whose:3 neighbours:2 under:4 worth:4 every:5 summarized:2 encounter:1 basics:1 specify:1 solution:4 vector:7 math:25 ups:2 degeneracy:3 jhep:6 heckman:1 hori:1 miller:1 consistent:2 miur:1 plaquette:28 direct:2 elegant:2 second:1 valiant:1 subquivers:2 even:12 contemp:1 zaslow:2 above:12 sheffield:1 new:7 net:7 increasing:1 consisting:4 coefficient:1 wrapping:2 equals:2 here:8 represented:9 path:18 interpret:8 obtained:11 endpoints:1 cachazo:1 leaves:1 changed:4 aki:1 changes:3 cancellation:1 appropriately:1 cohn:1 projection:2 elaborated:1 explained:2 plenum:1 replace:1 brought:2 counts:7 total:11 unit:5 flop:2 would:10 bundles:3 negative:9 call:1 therefore:10 m2:9 survive:3 care:1 type:6 decomposable:1 separated:1 alberto:1 solitons:1 naive:1 adjacency:8 correspondingly:1 hole:3 hold:1 must:13 morally:1 join:1 mn:2 mi:14 theories:13 concepts:1 root:1 example:23 quiver:75 renormalization:1 give:9 preserving:1 stressing:1 indicates:1 want:2 times:3 end:2 b185:1 provide:1 verify:2 recovers:2 how:5 holonomy:1 adjacent:6 config:1 description:2 arcs:2 after:7 diagram:14 summarize:4 arch:1 attempt:2 summing:1 complexity:2 green:2 keeps:1 order:7 interpretation:23 feedback:1 over:10 satisfied:1 pascal:1 london:1 poincaré:4 maxi:2 before:2 surviving:1 writing:1 better:1 distinguishing:1 fig:15 omitted:1 maximal:1 them:4 combination:7 pfaffians:2 they:21 singularity:3 represents:2 netherlands:2 alet:1 invariants:1 classified:1 arrow:10 each:49 side:7 mean:1 series:1 braiding:1 antiparticle:3 used:6 extract:1 gon:1 network:1 gradient:3 particles:1 re:6 reader:2 rn:1 ri:1 foundation:4 turning:1 linear:4 associate:5 parame:1 free:36 admits:1 nth:1 degeneracies:1 chiral:2 created:3 starts:1 creates:4 signature:2 corrections:2 already:7 features:1 grade:1 rank:1 clear:1 relations:11 another:15 sutherland:1 illustrate:4 top:4 rong:3 needed:2 too:1 ordered:3 variational:1 positively:1 showed:1 tree:2 matter:2 classes:4 tion:1 solely:1 minus:5 kuperberg:3 bridge:1 emphasizing:1 seen:18 contents:2 ray:2 convenient:3 latter:3 isolated:4 oriented:4 uration:1 reversed:5 blue:1 though:1 complexes:1 regular:1 phase:2 acknowledgements:1 singer:2 observation:1 partition:22 vertices:22 curie:1 points:10 principle:1 zaffaroni:1 sum:14 labels:2 kennaway:3 infrared:1 gauge:56 constituent:5 d3:2 topological:3 aspinwall:2 touched:1 oct:1 do:8 subspaces:3 di:2 yielded:1 runs:1 contributes:2 misguich:1 fields:3 twice:1 reference:5 clarified:1 generally:1 1960s:1 depends:2 result:11 fail:2 subject:1 c2p:10 birational:5 away:1 propagates:1 eigenstates:1 symmetric:2 propp:1 simplest:1 c2k:4 approach:2 preserve:4 terms:18 extend:2 nature:3 wk:1 consists:4 clues:1 bose:1 picking:1 topology:1 suggested:2 cos:13 cor:1 faces:3 genus:8 appeared:1 mutations:5 height:22 directions:6 theoret:1 polynomial:33 basis:7 union:1 three:2 been:5 quickly:2 much:6 interest:3 basic:4 expected:3 transformed:1 algebras:2 ann:1 supersymmetric:13 coherent:4 pezzo:2 berezin:1 worked:3 maximally:3 spin:6 manifolds:2 finset:1 explicitly:2 exception:1 euclidean:4 ain:8 aik:3 aij:3 property:1 study:2 della:1 cylinder:17 a26:1 ir:1 obeying:1 disjoint:4 cone:1 ramifications:1 ni0:8 containing:4 make:7 linked:1 complex:24 split:1 big:1 several:1 european:1 independent:1 i0:23 counterparts:1 hand:8 normalization:1 cycle:4 joos:1 contact:1 cern:1 left:20 graded:5 just:4 newton:15 assigned:1 identify:2 thanks:4 human:1 integer:3 yet:5 previous:3 adding:1 regarded:2 character:1 belongs:3 collections:15 easy:5 5b:1 spinoza:1 breaks:1 possible:18 unification:1 background:1 unique:3 melting:8 appearing:3 performing:1 specific:1 scheidegger:1 bps:6 steps:1 sezione:1 arbitrary:4 amoebae:2 right:16 deal:1 critique:1 icm:1 grading:8 comments:1 contributing:7 track:2 fom:1 deleted:3 rhombi:1 upward:3 super:2 properties:2 chapter:1 beilinson:2 counterclockwise:1 o:4 plus:3 eight:1 lieb:1 duke:2 raised:1 tutte:2 presence:1 22g:3 down:2 pair:3 dualities:20 raises:2 wrap:1 amsterdam:4 divisor:3 methods:2 combinatorics:3 topologies:1 initial:4 accordingly:1 way:6 m1:7 was:15 lowest:1 form:16 unoriented:1 attempted:1 δkl:2 converse:1 removes:1 δkk:1 failure:1 heat:1 encoded:2 true:1 prevents:1 attached:1 maximum:4 discretized:3 fermi:2 fulfills:1 digression:1 proved:2 semicolon:1 computing:2 proven:1 conserved:4 exist:2 nnz:2 simulations:1 face:2 physical:7 ni:6 nj:7 nk:17 no:28 na:12 nb:15 nc:11 nd:13 ne:1 handed:2 nz:4 interested:1 role:1 np:5 khovanov:6 schrader:1 nw:6 node:23 picture:3 superposition:2 models:4 sqm:7 variable:2 parities:1 jones:3 longer:2 χx:1 bottom:4 together:1 remarked:4 n1:2 n2:3 precise:3 concept:1 chain:18 global:2 primed:1 invent:1 leads:2 foundations:2 nkz:1 viceversa:1 depend:1 ıt:2 everything:1 aufgabe:1 graph:89 finally:4 analogous:1 string:6 forcella:1 seemingly:1 choice:8 orientations:11 entries:1 word:1 exact:2 partitions:1 dim:6 annihilated:4 tilings:5 riemann:6 level:5 turns:2 solved:1 annihilates:2 upper:1 work:4 sign:22 bondal:1 pmi:4 adds:1 appear:3 xπ:1 reminiscent:2 annals:2 goes:2 shared:2 satisfy:4 subdivided:1 pm0:5 pm1:8 pm2:7 pm3:1 understanding:2 tachyons:1 groups:14 alone:1 along:1 change:16 sending:1 incoming:2 institute:3 shift:1 vectors:1 usually:1 hospitality:1 y4:4 lowers:1 useful:4 extra:2 marked:1 franco:2 working:1 prove:2 positive:8 perm:2 anticommutation:4 live:1 going:4 opposed:1 scope:3 theoretical:1 diagrams:1 reducibility:1 introducing:3 ambiguity:2 clue:1 appendix:3 cases:2 capturing:1 fermionic:7 originally:1 modified:1 quivers:12 values:1 following:24 making:2 vegh:3 figure:23 expanding:4 permutations:12 performed:2 allowed:8 conversely:1 occur:1 regularization:1 domenico:1 fortunately:1 exceptional:30 write:2 zn0:1 pure:2 ensure:1 parameter:2 map:20 product:15 may:1 max:1 expectation:2 produce:1 representations:5 natural:4 whenever:1 explicit:3 yielding:2 si:4 so:14 sn:2 znz:1 prefactor:2 joins:1 indeed:10 pointed:2 soc:1 years:1 course:3 statistical:8 differs:1 still:4 supplemented:1 group:7 thank:3 interesting:4 2lπ:3 coordinates:5 forms:1 dxψ:1 correspondence:22 non:29 qs:16 introduce:6 chromatic:2 scaling:5 touching:1 sorted:3 nov:2 now:19 nor:1 term:8 equality:1 name:1 temperley:2 corners:3 arrows:34 spinor:1 weighted:2 ei:15 ek:3 gaussian:1 ec:1 inhomogeneous:1 113b:1 approximated:1 eq:25 living:9 shown:13 space:5 furthermore:5 looking:1 contained:2 investigation:1 suggesting:1 formula:2 squares:2 shows:1 theory:49 state:43 hull:1 alternatingly:1 complicated:1 e1:2 e2:2 training:1 cycles:16 language:1 impose:2 turn:5 hanany:4 place:2 massive:1 think:2 first:8 symmetry:4 zag:7 variables:3 directly:3 open:5 size:4 given:36 antiparticles:1 seiberg:22 convention:2 white:5 structures:5 speaking:1 gives:9 dolan:1 mostly:1 ch:1 continuous:1 62b:1 62a:1 representing:1 than:8 coefficients:1 were:1 decompose:1 topics:1 argument:2 generalization:2 winding:43 say:6 flatness:1 recover:5 any:15 functors:2 downwards:1 note:14 emphasis:1 potential:1 take:5 forming:1 interior:1 coincide:1 trace:5 opposite:11 probed:1 correlation:1 neutrinos:1 algebraic:2 exploited:1 connor:2 remarks:1 xµ:1 surprising:3 later:2 quantity:1 slope:3 show:7 fermionization:1 discovered:1 spaces:1 decompositions:1 corner:6 ground:9 homology:4 aπ:6 feng:1 enough:3 analytic:1 only:35 anticommutes:1 black:16 helix:10 get:1 straightforwardly:1 cannot:5 theta:2 enjoys:1 mapped:3 imposing:1 connections:2 b201:1 namely:1 surfaces:5 satisfying:2 enlightening:1 crystal:9 ways:2 review:2 label:2 outside:1 plaquettes:4 between:38 affecting:1 geometric:4 reading:1 notice:1 vertical:5 originated:1 concentrate:3 ji:2 jk:1 come:1 many:2 region:3 according:7 contract:2 embedding:5 expression:4 comes:2 among:1 caianiello:3 period:1 anti:1 moreover:5 fruitful:1 branes:27 specializing:3 amer:1 110b:1 110a:1 locally:1 attaching:1 cosine:1 direction:14 embeddable:1 qsj:1 qsi:5 qsn:1 stems:1 careful:1 those:6 case:23 grassmanian:3 might:2 cast:2 situation:1 eik:1 eij:1 planar:2 orientation:12 different:20 verified:1 same:35 adsorption:1 verifies:1 valckenierstraat:1 extended:1 foam:1 edges:23 arose:1 changing:4 invariance:2 modes:2 charges:2 severe:1 without:3 solve:1 components:2 coordinate:1 model:63 dimension:3 wavefunction:1 manifold:2 being:8 when:17 resp:3 actions:1 diagrammatic:7 correspondences:1 touch:1 captured:2 cn:1 blow:4 heuristic:1 except:3 treatment:3 versa:3 real:3 around:13 eigenvalue:1 read:6 decomposed:7 sums:1 vacuum:2 using:7 mod:6 bigraded:1 reshetikhin:2 particle:3 identifying:2 reduces:2 serves:1 wecht:1 either:6 fully:3 downward:3 inter:1 reduced:1 satisfactory:1 itfa:1 madrid:1 ct:1 hurst:1 respect:3 matching:35 dimensions:2 footing:1 critical:3 decomposition:4 provides:2 torsion:2 refer:1 considering:2 power:1 equivalent:8 y2k:3 island:1 discussed:2 generated:11 addition:1 act:2 2k:4 cambridge:2 accounts:2 operator:46 hep:20 removing:2 there:14 dispersion:1 start:2 low:1 complete:8 regard:2 elimination:1 attainable:1 divisors:4 arranged:1 annihilate:1 embedded:8 multiplicity:3 homotopy:2 b435:1 connect:1 strongly:1 definitions:2 ag:1 ai:3 certain:7 describe:2 moved:2 general:22 quantum:20 ar:1 moves:12 again:7 extending:1 deserve:1 pfaffian:11 field:6 mathematics:5 massless:11 oneself:2 time:17 vertex:7 important:1 bounded:2 ising:6 partitioned:1 mass:1 once:7 starting:6 strings:6 represent:2 monte:1 sci:1 consider:18 pointing:17 alg:1 commute:2 follow:1 expressions:2 causes:1 preserves:3 zmn:6 combinatorial:2 tv:1 equivalence:6 tr:12 program:2 c5:5 th:21 nodes:24 belonging:7 straightforward:1 very:6 fas:6 witten:5 interpreting:1 difference:3 condition:10 switches:1 wm0:1 t2:1 joined:4 large:2 programme:2 employing:1 tem:1 periodicity:2 zero:8 pass:2 further:4 canonical:1 bilinear:1 will:23 what:5 nonlinear:1 section:34 intersect:1 fractional:7 apply:1 method:5 outgoing:2 full:7 component:4 modular:5 concluding:1 strong:1 equations:1 search:1 colored:2 inspired:2 stretching:1 allows:3 periodic:2 permutation:16 action:13 specialize:1 anticommutators:1 uniquely:3 via:5 superpotential:4 requiring:1 thatcher:1 clifford:1 takes:5 distinct:1 contains:5 charge:11 nucl:4 taken:2 more:21 operators:23 basically:1 particular:13 known:4 projective:2 producing:1 ekµ:1 kenyon:5 science:1 equation:1 det:9 remain:4 del:2 learn:1 singularities:1 rudakov:2 f0:4 states:61 tensoring:1 numbers:12 sense:4 61b:1 61c:1 61a:1 information:7 rather:2 maps:22 explains:1 simplicity:1 algebra:6 derived:9 mapping:6 3y2:2 plane:11 coming:3 fi:13 horizontal:2 geometrical:3 concentrating:1 fn:1 short:1 vafa:6 fundamental:3 essence:1 paper:4 through:1 signs:9 y2:4 okounkov:4 its:27 roots:1 continued:6 actually:2 absence:1 systems:1 sheaves:16 yk:1 return:1 intriligator:1 fiol:1 evaded:1 association:1 easily:10 2p:4 always:11 2d:1 2g:2 found:5 2n:2 2h:2 2i:2 referred:2 weight:27 energy:9 idea:3 expect:1 loops:69 operation:1 beyond:3 yµ:1 since:23 research:3 acting:4 denoted:1 benjamin:1 ask:1 beginning:1 generate:4 definition:7 pairs:4 deleting:3 omit:1 american:2 assign:3 relate:3 number:62 done:1 least:1 differ:1 introduction:6 leading:1 construct:11 seminaire:1 expand:2 exponents:1 recovered:2 immediate:2 luckily:1 part:7 authors:1 inventing:1 translation:1 believe:1 cyclic:10 double:21 determined:2 2kπ:5 doubly:1 treated:1 aout:11 karp:1 comput:1 pasquier:1 nonabelian:1 hexagonal:1 pmn:1 paths:3 constructions:1 depending:1 mial:1 self:1 k2:1 internal:12 generalized:6 finding:2 honeycomb:1 towards:1 diatomic:1 plan:1 statistics:2 karowski:1 singled:1 soliton:1 constructed:8 torus:33 parafermion:1 coincides:3 kn:1 physica:1 ext:1 kw:16 kz:9 physics:14 lying:1 joining:3 sector:1 thomas:1 particularly:1 multiplicities:4 relation:14 ferroelectrics:1 find:8 parameters:1 subsection:1 factor:2 windings:2 abelian:2 his:1 triangle:1 notation:6 categorifications:2 rest:1 combinations:4 during:2 alexander:1 resolve:1 continuum:2 arxiv:1 common:1 becher:1 set:19 ser:1 achieved:2 throwing:1 calabi:9 see:27 arc:1 sec:14 descriptions:2 close:3 theoretic:2 permuted:1 unions:1 smallest:2 various:1 consecutive:1 conditions:8 missing:1 attention:2 untouched:1 vanishing:14 δaa:1 δab:2 distinguish:1 both:6 last:4 reverse:1 annihilators:1 mrtn:1 sensitive:1 connection:2 context:1 whole:3 finds:2 arbitrarily:2 point:26 simple:5 corresponds:27 community:1 subgraphs:4 carlo:1 simply:1 112b:1 pp:2 pq:1 described:5 raise:1 create:1 due:2 laplacian:1 strategy:1 describes:2 pf:6 coarse:1 collected:1 ph:3 pi:4 pm:7 generating:13 contractible:2 gas:6 remark:1 lives:4 assigning:2 p2:2 p0:1 p1:3 look:1 exponential:1 solid:2 expanded:1 evaluated:2 technical:1 while:15 loop:84 studied:1 vol:1 reads:4 itself:2 spond:1 ready:1 fermion:66 nielsen:2 italy:1 grant:1 categorification:17 deletion:1 products:1 relatively:1 composition:7 prerequisite:1 higher:5 literature:3 dimh:1 marie:1 sys:1 moving:2 homologies:1 rabin:1 task:1 spent:1 analysis:2 obviously:5 edge:15 machinery:1 consistency:5 reviewed:1 iqbal:1 world:2 λk:3 regardless:1 bi0:7 conclusions:2 shortcut:1 causing:1 theorem:1 transformation:5 euler:14 isomorphisms:6 evaluate:1 necessary:5 bit:1 follows:15 collect:1 yields:3 translated:1 mathematical:5 often:1 creation:3 some:8 back:1 understood:1 added:1 b0:1 sight:1 mirror:3 ourselves:3 electric:1 describing:2 integration:1 providence:1 behave:1 prod:1 minimal:4 ba:12 jumps:2 clay:2 bt:2 weil:1 bs:1 relating:1 zza:1 integers:2 constraint:1 deserves:1 involving:2 digraph:1 into:32 integral:6 isomorphic:1 baez:1 proportional:1 rows:1 span:7 question:2 long:1 sections:1 subgraph:4 collapsed:2 link:3 wnw:1 line:14 directed:2 infn:2 consist:1 fulfilling:1 characteristic:11 up:13 us:14 jacobsen:1 paired:10 exploration:1 similar:2 called:16 sometimes:1 associated:15 defined:18 specified:1 globally:1 single:1 formalism:6 duality:10 polygon:3 amounts:3 dashed:5 bracket:1 confine:1 draw:1 elements:4 generates:3 problems:1 polynomials:4 meaning:4 graphically:1 fisher:4 structure:7 independently:2 implies:1 vice:3 holes:6 equivalently:2 neighbouring:4 weights:11 xbd:2 nash:2 requires:2 having:3 normalized:1 katz:2 partial:6 results:12 eds:1 go:3 contributions:1 toric:21 compact:4 compose:1 concerned:1 random:3 expressing:1 electron:1 isomorphism:5 redefinition:1 ending:1 matrices:5 categories:2 zeit:1 eigenvalues:3 majorana:6 inspection:2 dimer:68 configurations:27 zn:4 smaller:3 zk:19 sin2:3 jump:3 fold:1 dynamics:1 zw:2 odd:5 index:6 giving:3 3q:1 labeled:1 lexicographic:1 consistently:1 crossed:2 susanne:1 3d:1 respectively:1 spacing:1 objects:5 108b:1 108a:1 others:5 luis:1 z1:2 z2:8 morphisms:1 great:1 scienza:1 receive:1 leaving:1 resulting:8 hexagon:4 makes:1 composed:2 transformations:2 herzog:3 summation:1 redefining:1 resolutions:2 clockwise:1 use:7 commun:2 remains:5 next:3 zig:7 depicted:5 doubling:2 simpler:1 sort:1 started:1 becomes:7 45a:1 labelled:4 iib:1 account:3 crosses:2 reproduce:1 obvious:6 fulfill:1 proof:2 control:1 xca:2 links:3 process:4 purposes:1 pieces:1 holds:1 superstrings:1 frontiers:1 instead:3 ferdinand:2 sin:1 singular:7 collection:19 multiplication:1 realized:3 acyclic:19 computations:1 light:2 lines:4 correspond:22 redundant:1 emanuel:1 allow:3 subsequently:1 bipartite:9 saturated:1 nekrasov:1 move:4 interpreted:5 mentioned:4 categorify:1 perfect:75 chemical:1 revived:1 ext2:3 ext1:3 decay:1 chosen:2 lh:2 li:8 lw:4 permanent:10 lr:2 choose:5 lz:9 parabola:1 polarizations:2 front:1 dirac:16 betti:1 university:3 identified:7 crossing:6 references:1 monomials:3 constraints:4 subset:1 illuminate:1 matchings:88 doing:1 related:4 ext1s:3 society:3 our:16 ext1x:1 special:2 out:13 category:11 matrix:27 rev:5 geom:1 playground:1 lecture:1 red:1 dictionary:3 interactions:2 diagonal:1 clarify:1 completely:1 york:1 monographs:1 compositions:1 ninomiya:2 geometry:8 could:5 keep:1 counterpart:1 bstract:1 università:1 hence:2 phrased:1 staggered:1 diagrammatically:3 manuscript:1 blown:3 reached:1 precisely:11 observer:1 hyperbolic:1 ordering:10 sep:1 system:27 πl:5 their:11 melnikov:1 fermions:9 b628:1 final:4 klemm:1 explanation:2 exactly:4 branches:1 45b:1 reverses:1 negatively:1 w2:3 function:53 symmetries:1 unchanged:4 curves:1 discussions:1 harnack:1 need:2 gradings:2 clearly:2 studying:1 able:1 gravity:1 polarization:8 combin:2 techniques:2 lectures:1 brane:6 anticommute:1 connected:2 representation:14 kähler:1 kasteleyn:26 parametrize:2 enumerating:1 neighboring:1 milano:3 χy:2 counted:3 graphs:9 proceedings:1 construction:8 mechanical:1 typical:2 fact:12 supported:5 chapters:1 bicocca:2 trivial:15 q1:10 q0:3 q2:1 based:3 knowledge:3 should:4 candidates:1 molecules:1 employed:1 partially:5 local:9 preliminaries:4 meant:1 xdc:2 means:11 familiar:1 overall:7 ones:7 words:2 applying:1 qp:1 evolution:5 qw:4 differential:6 qa:5 qz:4 contain:11 qh:5 fixed:6 qm:4 ql:2 view:5 computed:1 exists:3 computes:1 computer:2 geometrically:3 embeddings:1 packed:2 braid:1 pattern:1 written:7 closed:11 invariant:8 boundary:17 injectively:1 reproduces:1 probing:5 configuration:19 david:2 interpretations:1 freely:1 taking:9 ext0:1 equal:8 etc:1 admit:1 passing:4 otherwise:2 ck:3 detailed:1 uct:1 co:19 wq:4 triangular:2 superpartners:1 cohomology:5 cy:1 ab:8 sequences:4 table:12 cp:1 46a:1 46b:1 yau:9 aligning:1 responds:1 rhode:1 anomaly:4 domino:2 define:13 hernandez:1 determinant:21 arises:1 corresponding:15 commutes:1 sufficient:1 c3:7 c2:5 c1:9 c0:9 present:6 c4:5 multi:1 unlike:1 defining:1 appearance:1 value:4 rectangular:1 categorifying:1 monodromy:1 thus:6 site:3 surface:21 respected:1 thun:1 arrangements:1 dual:14 capture:1 wy2:1 generic:1 lett:3 s2r:1 units:2 finite:4 difficult:2 upon:2 effect:4 parametrized:3 infinite:7 susskind:1 identity:4 supercharges:2 tessellation:1 colour:2 well:2 thought:3 patterns:1 sets:5 position:2 polya:2 arising:4 drawing:1 usual:6 restore:1 vakil:1 less:2 monomial:1 obtain:4 underlying:1 web:1 unsigned:1 lattice:37 add:1 combine:2 c15:1 resolved:5 dimers:18 five:1 know:2 knot:5 press:1 exts:3 intersection:1 dimensional:6 δz:4 like:8 b105:1 vortex:2 become:12 soft:1 page:6 parity:3 because:8 classical:3 sequence:11 q21:1 choosing:8 convex:1 kdv:1 lead:2 avoid:1 reproducing:1 does:10 mutation:2 blowing:2 obey:1 selecting:1 journal:3 expansion:10 q2p:5 98b:1 98c:1 q2z:1 98a:1 identifies:1 stage:1 about:1 actual:1 carried:1 freedom:2 introduces:1 recognizes:1 introduced:5 pandharipande:1 massachusetts:1 discretization:2 own:1 previously:1 ai0:9 square:27 consecutively:1 bosonic:3 transfer:3 noticed:1 quadratic:2 inner:4 symmetrizing:1 inspiration:1 naturally:3 hz:10 hq:1 hw:12 but:8 volume:1 repeated:1 hi:1 highest:2 hf:3 davide:1 he:3 count:2 compute:1 whether:1 cells:1 signed:2 placed:2 below:1 convince:2 limit:13 problem:10 mechanics:12 interchanges:2 pik:1 universal:1 contribute:1 denote:1 rule:2 interchanged:3 relates:1 crystals:1 ing:1 identities:1 inc:1 functions:10 transitions:3 thermodynamical:1 detail:1 other:21 details:1 regularizing:1 homologically:1 bundle:1 upwards:1 ghost:1 ranks:4 resolution:6 factors:1 decategorification:1 original:2 |
0705.1646.txt |@word homomorphism:2 consider:8 chain:2 gp:4 alg:2 equalities:2 results:1 invent:1 scalar:1 proposition:23 sci:2 gm:1 excluded:2 reasoning:1 zink:1 compact:1 sga4:2 inverse:1 depend:1 combinatorial:1 paris:2 equivalence:1 extraneous:1 quasi:3 th:2 under:3 arranged:1 analogous:2 norm:1 conjecture:1 g2:3 g0:43 regional:2 choice:3 corollary:2 every:7 chooses:1 lecture:2 affect:1 exact:3 condition:8 dim:12 induced:1 did:1 irreducible:2 notes:2 applicable:1 t0:1 t1:3 vector:7 rj:3 indices:2 shows:2 deleting:4 zn:6 smaller:3 sℓ:3 direct:1 likely:1 irreducibility:1 pass:1 further:5 odd:2 expressions:2 eigenspaces:1 canonical:1 spectral:2 index:2 filtration:2 appear:1 section:3 cohomologie:2 uniform:1 above:3 sup:1 shared:1 method:2 satisfy:1 supporting:1 justification:1 gruppen:1 aten:2 never:2 smi:5 here:9 ranges:1 bourbaki:1 groups:14 address:2 sga1:4 along:1 quite:1 appears:2 change:2 obtained:6 remark:5 divisor:1 gln:3 wλ1:3 inspired:1 larger:1 bou:2 products:1 domains:14 makes:1 york:2 via:1 term:2 br:2 claim:2 app:1 wis:1 org:1 sga:2 apply:4 use:9 would:2 prove:7 remains:1 positive:6 contains:2 ej:3 finally:2 france:1 comparing:2 m1:4 therefore:1 reductive:3 postfach:1 care:1 type:22 theoretical:1 more:5 finitude:1 duality:4 integers:1 immersion:1 becomes:2 stable:2 corrected:1 ematiques:1 aware:1 flag:1 particular:1 known:2 projective:5 cases:8 iv:1 springer:4 isomorphism:1 left:1 frobenius:3 recall:5 der:3 des:1 mi:3 london:1 preliminaries:1 obvious:2 following:19 nonsingular:3 root:3 example:1 proof:18 factor:1 νt:1 affineness:1 f4:1 give:2 calculation:1 arise:1 updated:1 indicates:1 dropped:1 sense:4 νi:1 absolute:2 sis:1 etales:1 verify:1 aff:11 holds:2 berlin:4 feature:1 write:5 maps:1 nontrivial:1 criterion:7 variet:2 pure:1 verlag:2 fq:30 product:3 proc:1 fu:1 algebra:2 fx:6 suppose:3 after:1 derived:1 orbits:2 sni:2 santa:1 consequence:1 levi:1 adic:2 coming:1 date:1 representations:3 fn:2 tordu:1 sαi:1 induction:4 natural:1 varieties:22 imply:1 ss:12 sr:2 author:1 lines:1 element:16 en1:9 si:9 so:4 sn:8 fundamental:6 s2:7 representation:4 order:1 michel:2 enk:3 help:1 fθ:6 indeed:3 over:22 fν:2 interpreted:3 stability:1 course:1 mathematicians:1 paper:2 through:2 signs:4 still:1 vari:1 its:6 roots:3 before:4 du:2 group:19 thank:1 how:1 chosen:1 faltings:1 fix:1 affine:18 systems:1 bonnaf:1 covered:1 main:2 sheaves:1 image:1 s1:19 maximal:6 closure:1 non:5 within:1 affected:1 university:1 number:2 mathematik:2 oxford:1 formulating:1 now:9 smoothness:2 bigger:1 easily:1 february:1 gets:1 equality:2 always:1 reasonably:1 raynaud:1 2x:11 identified:3 iff:1 inequality:4 bonn:4 rℓ:10 each:4 xℓ:19 universit:1 side:1 ts1:1 homogeneous:2 domain:7 weyl:8 ei:6 map:2 series:2 leray:2 revised:1 reduce:2 society:2 expect:1 die:2 relates:1 happen:1 special:1 out:2 shown:2 monographs:2 factors:3 parabolics:1 since:18 denotes:3 may:11 contained:1 multiply:1 rational:2 hcj:1 ramified:1 get:2 hci:22 supports:1 ri:8 math:13 rk:1 fiber:2 belief:1 associate:1 standard:3 small:4 completely:1 base:3 e8:1 put:4 e4:2 e7:1 e6:1 e1:20 universally:11 xg0:27 e2:10 definition:2 hc1:1 r0:8 r1:2 r2:4 ion:1 geometry:1 determining:1 times:1 english:1 length:9 cbms:2 period:21 incarnation:1 avec:1 hence:14 retain:1 2xn:4 first:7 xk:6 xi:8 xn:73 features:1 xm:58 urich:1 conjugacy:19 xg:2 rank:5 twisted:1 clear:2 choose:2 soci:1 another:1 carry:1 xs:2 precisely:2 open:5 xw:6 bois:2 given:10 checked:1 annotated:1 similarly:3 introduction:3 xii:1 adjoint:8 system:3 construct:1 their:7 assumption:1 types:2 statement:13 convention:2 scheme:1 final:1 gives:1 calculations:1 exactly:1 proving:1 immediate:1 part:2 deligne:23 x2:35 x3:4 iwahori:1 believe:3 than:3 x4:1 e3:4 roles:1 functoriality:1 modelled:1 classes:5 treated:2 w2:7 exhibit:1 pointed:1 sees:1 close:1 sw:13 ann:2 curves:2 already:1 say:1 conjugate:2 disjoint:1 any:14 viewed:1 functors:2 lie:4 documents:1 zero:1 pursued:1 hyperplanes:2 en2:3 note:7 new:3 coincide:2 even:4 differences:1 unless:2 sm:6 normal:3 collaboration:1 sets:1 birkh:1 algebraic:5 connected:5 but:3 position:1 remarks:1 acknowledgements:1 class:14 inequalities:6 digne:2 mumford:1 observation:1 ebrique:2 introduced:1 torus:5 adopt:1 proceedings:1 verdier:1 reflections:6 subgroup:6 fact:6 directed:1 madison:1 cmin:2 show:6 converse:1 chapters:1 purely:1 trivial:5 find:3 x1:45 basel:1 assertion:3 should:1 lemma:24 only:7 em1:5 equipped:3 parabolic:4 identification:1 local:2 cocharacters:1 etrie:2 dl:33 his:2 notation:3 exceptional:1 de:7 ki:1 satisfied:7 cannot:1 rt1:1 3b:2 compute:3 reprint:2 αk:2 prime:10 covering:1 fields:4 arxiv:2 fixes:1 emk:5 fqe:3 geometrie:1 cℓ:1 identify:3 homeomorphic:11 groupe:1 set:22 pfeiffer:5 exists:4 smooth:18 relative:5 edition:1 depends:1 computer:1 merits:1 result:8 w1:11 discussions:1 recently:1 elliptic:1 august:1 mechanically:1 commutation:1 held:1 below:3 xvi:1 state:1 various:1 closed:4 between:1 αi:8 geometric:1 approach:3 checks:2 αn:7 commute:1 wf:3 restricting:2 embeddings:1 hecke:2 se1:2 complement:2 cit:1 however:2 wi:10 vanishing:14 succeed:1 hypothesis:4 wr:3 lectures:2 amer:1 wx:45 both:3 essentially:1 cor:4 last:3 la:1 patrick:1 equal:3 became:1 und:1 lusztig:25 uni:2 expression:4 sheaf:14 comes:3 among:2 qℓ:2 coxeter:13 point:2 simple:15 character:1 leipzig:3 cohomology:17 corresponds:5 eminaire:2 rouquier:3 associated:4 torsion:2 conference:2 pp:4 second:2 basis:1 union:1 locally:1 due:2 strategy:1 pgln:7 arbeit:1 treat:2 algebras:3 pn:1 universal:1 empty:2 define:1 surjective:1 corresponding:13 restrictions:1 concerning:1 informatik:1 gal:3 chevalley:1 mail:2 general:5 present:1 case:37 stalks:1 subsets:1 ǫk:5 ǫi:7 easier:1 will:4 steinberg:1 applies:1 situation:3 property:4 ix:1 vol:2 thus:5 clearly:2 dual:2 ia:3 qx:35 containing:3 fibers:1 generic:1 make:1 same:3 poincar:4 split:8 fakulta:1 proved:2 finite:7 φm:9 difficult:1 independent:1 used:2 http:1 see:1 ni:11 marie:2 hand:4 action:10 auser:1 kim:2 aℓ:12 totally:1 subgroups:1 characters:2 suffices:6 reflection:4 no:9 well:3 obviously:1 concrete:1 thm:8 gkp:2 entry:2 ωnf:3 dimension:4 usual:1 rapoport:11 revˆetements:1 being:1 when:12 resp:7 fondamental:1 obtain:3 actions:3 subcase:4 drinfeld:4 immediately:1 λk:3 λj:4 previous:4 adv:2 tables:2 conjugates:1 multiplication:1 candidate:1 application:3 stabilit:1 algebraischen:1 seems:2 except:9 add:1 treatment:1 easy:1 theorem:20 solvable:1 remaining:1 identical:1 checking:2 replaced:1 papers:1 possible:1 cf:16 cruz:1 press:2 integer:1 helpful:1 semi:2 follows:13 reduces:2 french:1 chamber:4 ai:3 either:1 alternatively:1 translated:1 simply:2 xviii:1 reduced:1 mathematical:2 www:1 acad:1 illusie:3 classical:5 sequence:5 absolutely:5 sympos:1 some:1 2x1:1 algebraically:1 deduce:4 sure:1 b0:1 examples:1 proper:3 multiple:1 ourselves:1 xn1:13 provided:1 euclidian:1 esp:1 shall:1 expository:1 prop:4 providence:2 does:2 decomposition:3 chains:1 numbers:3 minimal:16 refer:1 2b:1 power:1 wt:2 equivalent:1 arbitrary:1 bt:3 clarendon:1 although:1 become:1 comparison:1 about:1 extension:2 most:1 o:2 pν:1 addition:1 fibering:2 ensure:1 xni:4 germany:2 acyclic:1 morphism:2 subset:3 soc:1 own:1 real:2 computes:1 h2:3 into:2 h1:3 isomorphic:2 three:1 lies:2 schemes:2 references:1 elementary:1 successively:1 swf:4 wλ:14 αni:8 loc:1 serre:1 institut:1 springerverlag:1 strictly:1 there:20 question:1 long:2 strict:1 borel:2 milne:1 universita:2 way:2 αn1:2 form:8 enough:5 sequel:1 jul:1 repeated:2 etale:5 hc:4 line:2 removed:1 true:2 he:4 orlik:11 made:1 applying:1 attached:1 up:1 us:6 dℓ:9 international:1 dmr:4 αm:8 grothendieck:2 ωn:6 problem:1 similar:1 called:2 b1:3 uber:1 interval:1 constant:3 ad:1 ag:1 defined:4 inv:2 denote:3 xiii:2 exist:3 interchanged:1 our:4 em2:5 identities:1 check:3 defines:4 again:2 ematique:1 variety:17 galois:4 ecole:1 generally:1 field:3 other:8 es:1 bℓ:9 tamely:1 mathematics:4 nt:3 mathematisches:1 elements:20 congress:1 bundle:1 a1:10 a0:1 a3:1 geck:5 structure:1 implies:3 assume:7 starting:1 american:1 space:8 curve:1 orbit:2 eom:2 original:1 eℓ:1 time:1 n1:3 once:2 requires:1 furthermore:1 satz:2 |
0705.1647.txt |@word chain:3 lack:1 datum:1 results:4 illustrated:3 8e:1 particles:5 paris:1 unanswered:1 analogous:1 conjecture:1 global:1 presently:1 takes:1 very:5 giorgilli:4 dokl:1 choice:1 mixing:8 four:1 hamiltonian:4 did:1 large:5 quick:1 cerruti:1 estimates:1 zero:6 perspective:2 pass:1 further:2 estimated:1 quite:1 approached:1 even:1 what:1 nonlinear:1 appear:4 chicago:2 selected:2 near:1 expressed:1 saldini:1 increasing:6 method:2 3e:1 full:1 whose:1 respectively:3 here:3 understanding:1 behaviour:1 attainment:1 address:6 strong:1 equations:1 obtained:2 studied:2 dcds:1 suggests:2 opinion:1 suitable:4 studies:1 plotted:6 via:1 followed:1 scales:1 requiring:1 integrations:2 total:2 asymptotic:12 would:2 positive:4 coupled:1 frog:1 readability:1 eleven:2 call:1 taken:1 gauthier:1 type:1 livi:2 more:1 gaveau:1 schulman:1 relax:3 started:2 naive:1 tested:2 normalized:8 particular:1 known:3 cases:1 had:3 high:5 integrating:1 recall:2 ematiques:1 remain:1 values:20 following:1 europhysics:1 averages:3 example:1 numbers:2 figure:2 give:2 discussed:2 sample:1 performed:2 sense:2 unimi:4 decaying:1 rather:3 feature:1 fpu:13 far:1 nontrivial:1 instead:6 parameter:1 ensemble:4 mat:6 may:4 thermodynamic:6 orbits:3 φt:2 data:18 grow:1 natural:1 benettin:1 computations:1 lines:1 correspond:1 galgani:5 so:3 correlation:3 increase:1 order:3 ulam:1 over:4 interpreted:2 experiments:1 through:1 mentioned:1 still:3 its:1 fit:1 decay:7 energies:19 interesting:4 expectations:1 actually:6 better:1 tenenbaum:1 fig:15 persist:1 might:1 setting:1 versus:9 good:1 autocorrelations:6 arnold:1 now:3 day:1 february:1 explains:1 university:2 sufficiently:1 magnitude:1 mode:8 each:4 found:9 mean:2 domain:1 weighted:1 ek:1 ej:16 series:1 energy:11 reduce:1 related:1 frequency:5 obtains:1 measure:4 our:2 special:3 out:6 leave:1 shown:2 space:1 restricted:1 rev:2 chaos:5 looking:2 got:1 induced:1 occurs:4 math:2 shows:1 theory:2 standard:5 small:1 kantz:1 pairs:2 r2:1 persists:3 diminished:1 vulpiani:2 linearized:1 motion:1 exhibited:1 first:2 xk:3 major:2 there:1 xn:2 feel:1 number:7 disappearing:1 another:1 precisely:4 electronic:4 given:2 temperature:1 indicate:1 system:4 avez:1 their:1 1e:2 bambusi:1 final:1 collapse:2 took:1 mech:1 because:2 x0:1 x1:1 than:3 kind:1 see:6 smoothed:1 matter:1 were:8 verlet:1 perturbative:1 exhibit:1 shrinks:1 fluctuation:1 cohen:1 curves:6 seen:1 seem:1 any:3 emes:1 chirikov:3 lie:1 implemented:1 physique:1 extracted:1 concerns:2 play:2 towards:1 normal:2 decreasing:2 involving:1 letter:2 phase:1 class:1 parisi:1 especially:2 considered:2 later:3 flow:1 graphs:1 part:1 metastability:2 probl:1 celebrated:1 phenomenon:12 show:2 trivial:1 debate:1 parameters:1 enough:2 should:2 only:4 attained:2 integrable:1 pointed:1 equilibrium:5 do:1 viewpoint:1 exceptional:1 de:2 freezing:1 expectation:1 ones:4 report:1 lattices:1 arxiv:1 paper:1 common:1 analytical:1 fixed:1 valid:1 fucito:1 correlations:7 observed:7 namely:7 result:4 recently:1 analog:4 techniques:1 tend:1 state:1 between:1 invariant:2 approach:4 available:2 notice:3 terms:1 attention:1 points:2 however:2 p2k:1 sola:1 comm:1 come:1 distribution:1 improve:1 both:1 essentially:1 last:2 classique:1 reported:1 la:1 according:2 against:1 chosen:1 connection:1 dated:1 0e:2 passing:2 disappears:1 nearby:3 cj:14 relevant:1 16k:1 guaranteed:1 relaxation:2 dimensional:4 pol:1 springs:1 considers:1 considering:1 broadening:1 pp:1 thermodynamics:1 curve:6 quickly:1 montecarlo:2 much:2 interest:2 certain:1 expected:2 pk:1 pn:1 define:1 interparticle:1 ergodic:2 arises:1 corresponding:3 6e:1 quantities:4 concerning:2 spirit:1 present:3 statist:1 case:7 p1:1 look:1 pacs:2 frozen:1 straight:1 value:11 will:1 while:1 property:3 larger:1 played:1 vol:1 averaging:4 thus:1 equal:1 regularity:1 peliti:1 cond:2 different:2 italy:1 open:2 generic:2 suggest:2 same:8 gibbs:1 units:1 finite:1 infer:1 investigated:1 infinity:1 mih:1 numerical:3 monotonic:1 hand:1 moving:2 delicate:1 superpose:1 recent:1 weakly:1 modes:11 well:4 sets:1 position:1 model:1 left:8 just:1 among:1 being:3 when:2 shape:1 questions:2 stabilization:1 casetti:1 previous:1 sampled:3 villars:1 point:2 seems:2 ruffo:3 lattice:1 potential:1 conjugated:1 lett:1 theorem:2 relevance:1 occurring:1 remaining:1 momentum:1 rescaled:1 increased:1 press:2 moreover:1 apart:1 facchi:1 like:2 particle:1 follows:1 microcanonical:7 specific:6 indications:3 right:7 pettini:2 some:11 begin:1 evaluated:1 respect:1 dimensions:1 2e:2 franzosi:1 leap:1 does:3 tends:1 equipartition:4 step:1 carati:5 although:1 2m:1 pasta:1 plots:1 refers:1 properties:1 panel:11 constraint:1 anomalous:4 dependence:2 nonvanishing:1 nj:2 computational:1 letters:1 ecanique:1 within:4 numerically:1 three:1 variable:1 square:1 sov:1 proportional:2 initial:17 question:1 long:1 quadratic:1 low:9 way:1 was:6 function:5 survives:1 complete:1 phenomena:1 relaxed:1 but:2 collected:1 marinari:1 true:1 made:1 whether:8 characteristic:2 marchesoni:1 smooth:1 up:3 us:1 ωj:1 limit:7 autocorrelation:5 problem:4 panels:1 computing:3 defined:1 milano:2 ak:1 year:1 proven:2 denote:1 single:3 scardicchio:1 au:1 physical:1 incorrect:1 functions:10 no:1 amounts:1 whereas:1 generally:1 other:2 role:3 papers:1 department:1 mathematics:1 arithmetic:1 principle:2 stat:3 superposition:1 berman:1 dissipation:1 fermi:2 lichtenberg:1 longer:1 requires:1 packets:3 together:1 inset:2 time:17 n0:9 4e:2 izrailev:4 original:2 |
0705.1648.txt |@word consider:1 depends:1 magnetic:26 luminosities:1 results:4 ginzburg:3 per:2 grateful:1 consists:1 gm:2 layers:1 whose:5 const:2 quasi:1 under:2 tc:4 ta:1 zhang:1 2rg:2 continues:3 2rb:1 anonymous:1 fall:2 bounding:1 exact:2 condition:2 rotating:4 accompanying:1 did:1 shock:3 prolonged:1 large:5 team:1 small:4 upper:1 smaller:3 force:1 computation:1 penetrates:1 direct:1 modified:1 approximation:4 surrounding:1 rate:7 estimated:1 even:3 what:1 clock:1 assistance:1 while:1 axial:1 cusumano:2 above:1 3b:2 3a:1 3e:1 body:1 synthetic:1 afterward:1 full:1 explosion:3 respectively:3 never:1 here:2 understanding:1 ranges:1 bisnovatyi:2 depend:1 along:1 strong:2 equations:2 appears:3 change:1 contraction:1 panaitescu:2 institute:1 study:1 allows:2 bow:3 stella:2 narrow:1 via:2 useful:1 classification:1 extra:1 explained:1 excellently:1 analyzing:1 kogan:2 total:1 discuss:1 use:1 takes:1 would:1 remains:4 next:1 a50:1 therefore:3 until:1 more:1 successful:1 becomes:7 envelope:1 br2:1 curvature:1 berlin:1 terminates:1 particular:1 hole:6 must:2 kumar:2 account:1 rotational:3 hour:1 centrifugal:5 erg:1 values:1 flare:8 following:1 example:1 weaker:1 wang:4 figure:4 process:5 relativistic:5 ambient:1 naturally:3 high:2 collision:1 lorentz:2 arise:1 evidently:1 axis:1 information:1 end:1 instant:1 decelerated:1 gcn:1 delay:1 located:2 answer:1 verlag:1 parameter:7 isotropic:1 simplicity:1 l51:1 may:2 reconciled:1 earlier:1 mcore:3 stars:3 mankind:1 grow:1 types:1 curve:8 effective:4 computations:2 light:6 thorne:4 cannot:1 so:1 allow:1 wind:1 produces:2 essence:1 astronomical:1 insight:1 displayed:2 satisfied:1 interpreted:2 stability:2 ended:1 paper:1 kinetic:1 its:12 before:1 group:1 lc:1 decay:1 energies:1 temporal:1 relativity:2 exhibits:2 late:1 fig:6 them:1 entire:1 bat:1 penetration:1 effects:7 half:1 rotation:4 now:2 yu:1 day:1 strive:1 easily:2 explains:1 university:2 level:1 kerr:9 sufficiently:1 l4:1 bursts:9 l1:1 mean:1 significantly:2 energy:23 eb:2 grbs:2 fraction:1 grav:2 year:1 quantum:2 our:3 operation:3 eq:2 event:3 out:2 space:1 since:1 increase:2 rg:5 ra:4 rb:3 formula:2 100s:1 shows:4 after:7 barrier:2 yale:1 mechanisms:1 free:1 solution:1 extraordinary:2 approaches:1 formation:2 york:1 telescopes:1 interaction:1 r3:1 starts:1 collapsing:1 times:1 turn:1 massive:2 xiang:1 onto:1 exhibited:1 first:4 origin:1 initial:8 features:2 symmetry:1 powerful:1 reaches:1 2a2:1 adopted:1 impossible:1 angular:11 size:1 iω0:1 jet:7 introduction:1 top:1 sep:1 protracted:1 mukhopadhyay:2 approximately:3 their:2 cooling:1 1b:1 master:1 hundred:1 frame:5 gives:1 shell:3 collapse:14 schwarzschild:1 moscow:2 released:3 part:1 lazzati:2 x2:3 x3:1 x0:2 x1:1 than:8 population:1 begins:3 tutukov:3 plateaux:3 accordance:1 hoyle:2 zero:1 limiting:1 ss:1 determined:6 aas:1 were:1 toward:1 steep:1 sees:1 7m:1 torque:1 spectrum:1 curves:1 headings:1 close:3 seen:1 any:1 sternberg:1 vietri:2 wilson:2 angle:1 newtonian:2 latter:2 ozernoy:7 apj:5 note:1 flares:2 take:1 forces:2 xrt:1 acquires:1 explanation:1 formulas:1 begin:1 ray:31 price:1 object:2 reach:1 most:2 jept:1 thank:1 extremely:1 class:2 latex:1 especially:1 behaves:1 average:1 stronger:1 magnetorotational:2 fowler:2 velocity:3 effect:1 sibgatullin:2 atmosphere:1 intensity:2 show:6 ergosphere:3 discovered:2 earth:1 agrees:3 slow:1 ratio:3 parameters:5 ies:1 state:1 universal:1 should:1 only:1 usov:2 black:9 factor:5 lipunov:11 achieve:1 equilibrium:2 do:1 move:1 correctly:1 contracts:1 restframe:1 beam:1 observatory:1 new:1 during:6 dt:5 years:1 dr:2 areas:1 gray:1 evolution:5 l45:1 luminosity:10 arxiv:1 yield:1 oppenheimer:1 prokhorov:1 clocks:1 predicted:1 activity:2 release:3 interiors:1 view:1 set:3 computed:4 reference:3 burst:20 violated:1 maximum:2 observed:9 see:4 radius:13 result:5 discussions:1 terms:6 precursors:2 best:1 subject:1 invoked:1 ways:1 subsequent:1 away:1 opening:1 xray:4 macros:1 written:1 future:1 radiated:2 membrane:1 αm:6 recently:2 nature:5 importance:1 supernova:1 weak:6 however:2 otherwise:1 manko:2 rapidly:2 swift:3 inertia:1 observer:2 abruptly:2 both:4 dates:1 ωb:1 last:1 rightward:1 many:1 equal:3 ln:1 merging:1 figures:2 exceeds:2 comes:2 allowance:2 cm:1 point:1 simple:1 seems:1 cg:1 period:2 coincidence:1 l29:1 chincarini:2 moreover:1 throughout:1 forms:3 described:2 second:8 union:1 come:1 three:2 been:2 2a20:1 magnetized:2 describes:1 combined:1 certain:1 ph:4 hardly:1 cherepashchuk:2 systems:1 engine:3 referee:1 corresponding:2 thousand:1 observers:1 angles:1 astron:1 c3:1 c2:4 c1:1 c5:1 case:8 supernovae:1 ejection:1 value:1 precursor:1 near:2 abrupt:2 behavior:4 situation:2 balance:2 a20:2 l87:1 seven:1 equator:1 metric:3 thus:1 surface:3 itself:1 quasars:1 vanish:1 helium:1 comments:1 orbital:1 binary:2 different:1 radiation:4 same:1 clearly:1 unity:3 complex:1 virtually:5 schematic:1 dimensionless:1 several:5 events:6 neutron:4 satellite:1 optic:1 conversion:1 moment:1 arep:2 v5:1 macdonald:1 opportunity:1 lower:1 shaded:1 scenario:2 variety:2 well:2 without:1 volkoff:1 model:9 paradigm:10 soviet:1 researchers:1 left:2 distances:1 just:1 less:1 kramer:2 rest:4 intervals:2 distant:2 predicts:1 followed:1 speed:1 postnov:1 preprint:1 infinitely:1 had:1 transparent:1 iω:2 source:1 transformed:1 plateau:15 theorem:1 input:1 plasma:1 momentum:10 real:1 fate:1 disappearance:1 breaks:1 providing:1 possible:1 corresponds:1 early:1 increases:7 indicative:1 know:1 press:1 emergence:1 collapsar:2 loss:2 like:3 follows:2 maintained:1 meszaros:4 loses:1 flux:2 yields:1 lose:1 decrease:2 soft:2 reduced:2 exceed:1 because:5 2x:1 some:1 back:1 hair:1 understood:1 b2:1 redshifts:2 duration:5 provided:1 scale:2 dropping:1 bottom:2 demonstrates:2 recorded:1 inside:3 stops:1 instantaneous:1 does:1 tends:1 pattern:1 core:12 location:1 seconds:5 viscosity:1 agreement:1 stellar:4 how:1 become:1 fainter:1 post:1 prepared:1 properties:2 stage:1 about:4 central:3 carried:1 decelerates:1 drag:1 sake:1 a2:4 horizon:4 2x2:1 gamma:19 letters:1 redshift:1 into:6 radiate:3 due:4 gehrels:4 references:1 sov:1 elementary:1 leblanc:2 compression:1 shells:1 measured:1 springer:1 troja:5 u0:1 long:4 collimated:1 conservation:1 way:2 astrophysics:1 was:3 opens:1 synthesis:1 function:1 form:2 hr:1 progenitor:2 delayed:1 but:3 astro:4 repeatedly:1 mnras:2 true:1 collapses:1 longer:2 evident:1 3bc:1 gravitational:14 up:5 us:1 um:10 limit:1 faded:1 stages:2 similar:2 calculated:1 detailed:1 constant:7 beamed:1 abstract:1 influence:1 general:3 ap:1 conserved:1 right:1 lifetime:1 approximated:1 physical:3 again:1 compared:1 no:3 whereas:1 when:3 vanishes:1 field:18 other:1 grb:9 star:10 separate:1 durations:1 emission:1 a0:1 meaning:1 important:3 afterglow:6 allowing:1 dissipation:2 astronomy:2 structure:2 faster:1 holes:2 mass:3 time:10 |
0705.1649.txt |@word logarithm:1 represent:3 eriksson:3 consider:6 induces:1 magnetic:6 results:1 leads:6 scalar:2 drastically:1 entropy:6 comments:1 go:2 partial:2 increase:3 inverse:2 depend:3 tr:6 charge:2 efficiencies:1 those:1 weakening:1 directions:1 stochastic:24 analogous:1 include:3 bilocal:1 xth:2 overlaps:1 applied:1 belonging:2 amplitudes:4 advantage:1 orthogonal:1 very:7 frequencies:1 continues:1 microworld:2 atoms:1 wave:9 electron:3 putting:1 stays:1 little:1 matrices:2 condition:1 look:1 generalised:1 entire:2 ip:3 presented:1 tra:6 solution:1 large:6 discrete:1 vector:4 phase:4 succession:1 small:10 eigenvalues:1 equation:2 favoured:1 percival:1 zn:1 squared:1 occurrence:2 zj:1 renormalized:2 ml0:9 d3:2 measurable:1 sign:1 rate:2 enhancement:1 zz:2 follow:1 further:1 dynamics:7 functioning:1 linear:10 even:2 nothing:2 what:2 plays:1 stands:1 apparatus:15 v2:1 section:10 agrees:1 current:3 version:2 goes:1 new:3 increasing:6 method:1 contrast:1 paradoxical:1 outgoing:12 full:2 sinks:6 splits:1 qm0:3 bifurcation:2 component:4 here:16 understanding:3 bremsstrahlung:1 sink:1 separate:1 others:1 represented:2 path:1 along:4 principle:1 equations:4 appears:1 change:9 z3:2 incoming:6 inhomogenous:1 technical:1 involved:2 studied:3 sx:7 atom:2 products:3 professor:1 ekx:2 identity:1 narrow:1 makes:2 involves:3 orthonormality:1 followed:3 figure:7 distributed:1 explained:3 marked:1 outcomes:2 brought:1 summation:3 apply:1 propagators:1 unit:1 conventional:2 takes:5 would:4 physics:1 probabilities:11 positive:4 negative:4 sµ:1 next:3 ψj:30 ψk:16 depicted:1 noting:1 call:1 m0:2 ψl:10 m2:6 taken:1 stage:1 type:3 until:1 diagrams:10 more:8 separated:1 hermitean:1 started:2 becomes:2 under:2 emission:9 long:2 appendix:4 labelled:2 particular:2 known:2 cases:3 hold:1 must:1 ρa:5 involve:1 account:1 quantized:1 indicates:4 ml:2 originally:2 work:1 modified:1 mk:3 mj:3 macroscopically:2 bias:4 values:12 lindgren:1 freedom:6 following:5 making:1 averages:1 example:1 control:1 f1:1 f2:1 renormalization:2 indicated:1 stated:1 process:30 numerator:3 sense:5 neglected:1 states:33 unbiased:2 assumptions:1 degenerate:2 allowed:1 distinguishable:1 occur:1 narrowly:1 goal:2 mutually:1 rather:4 technology:1 discussion:2 means:2 feature:1 orthogonality:1 how:4 mj0:8 pure:3 xln:1 enx:3 instead:5 zdirection:1 ensemble:19 product:2 rise:1 description:5 inherent:1 may:4 thermodynamic:3 earlier:2 space:3 mapping:3 diagram:4 per:1 plane:2 involvement:1 faculty:1 drastic:1 fj:7 geometrical:1 bkx:5 parallel:2 constants:1 recursive:3 sz:3 changes:1 short:1 outline:1 imply:1 beam:1 register:1 lines:1 packets:1 element:3 used:5 correlation:1 sf:8 se:1 typical:1 restriction:5 six:1 interpretation:2 produces:1 developed:2 over:17 dy:1 microsystem:12 satisfied:1 interpreted:2 paper:4 through:13 stayed:1 statistical:2 lattices:1 argued:1 japan:1 rohrlich:1 still:1 pointer:4 its:5 before:3 derive:1 xl:2 adjoint:1 decay:8 energies:1 decreases:1 absence:1 production:2 microscopic:1 systems:2 grahn:1 jacobi:1 hidden:1 jens:1 split:4 non:20 influences:1 polarizations:1 evolution:1 introduce:4 answer:1 they:5 half:1 now:4 transparent:1 easily:4 february:1 2p:3 corners:2 university:1 level:1 2x:35 leading:1 orthonormal:1 did:1 each:10 linked:1 done:3 2n:2 side:2 characterized:1 mean:4 spinor:2 en:2 bx:2 directly:1 weight:6 ej:3 generation:1 series:2 energy:7 revised:1 staying:1 related:2 frequency:2 connect:1 entering:3 measurement:27 quantum:28 our:5 approximated:1 transitions:1 eq:1 yet:2 out:6 shown:2 matrix:19 combine:1 factors:11 restricted:1 since:4 crucial:2 cancels:1 particles:8 ejx:13 mk0:7 m2j:1 wick:1 evaluation:1 rj:5 after:4 theory:12 written:1 diagonal:7 quite:1 curved:1 nth:1 reason:1 complicated:1 e1:2 e2:3 interaction:33 could:2 transition:13 m20:1 running:1 motion:2 ordering:1 place:12 trimodal:1 assumed:10 hence:3 moving:2 ej1:2 first:7 xj:11 xk:3 initial:18 xn:2 features:1 probability:11 variables:31 ipµ:1 number:8 transform:1 channels:2 entanglement:3 smaller:1 simplified:3 fast:1 another:1 dt:1 reached:2 precisely:2 open:1 size:1 given:9 perturbation:1 similarly:5 introduction:1 unknown:6 eqs:1 system:18 relations:2 their:3 returns:1 assumption:2 rates:1 fn:1 linearities:1 πx:1 frame:1 gives:4 progr:1 collapse:1 enhancing:1 nilsson:1 centered:3 continuous:2 debate:2 larger:1 part:2 simulate:2 manifestation:1 x1:2 representing:1 than:3 specify:1 diffusion:2 detection:3 kind:3 third:1 holds:1 was:6 see:11 modelled:1 final:35 recording:1 sweden:1 determined:1 kth:2 amplitude:6 were:2 treated:1 irreversibly:1 fig:6 enhanced:1 rewrite:1 strengthen:2 calculation:1 unchanged:2 pass:1 argument:1 generalization:1 already:3 say:2 close:2 need:1 inhibiting:1 seem:1 any:4 viewed:5 relatively:1 angle:1 relationship:1 zero:6 convenient:1 fourier:1 deexcitation:3 mechanism:2 note:3 k2:10 carina:1 absorbed:3 take:6 analogy:1 rzazewski:1 so:6 detector:2 modulus:1 channel:3 circles:1 multiple:1 centre:3 trρ:2 analyse:1 denominator:6 reach:2 δee:2 justify:1 z2:2 most:2 involving:4 thank:2 position:3 device:1 colliding:1 analytically:1 measured:1 subsection:1 manifested:2 divergences:1 unequal:1 reduces:1 consequences:2 considered:2 calculated:1 later:2 coincides:1 order:5 feynman:5 metastability:2 exp:1 mechanical:1 velocity:1 anticoincidence:1 typically:1 notion:1 fact:1 precise:2 emerging:1 think:4 show:3 pkx:2 random:9 infrared:1 soluble:1 helv:1 relation:1 corner:1 trivial:1 find:5 stepwise:1 ground:2 impact:1 based:1 simulating:2 parameters:1 original:1 inserted:1 negligible:2 should:5 only:8 going:2 positively:1 factor:4 emitting:2 circle:1 hamiltonians:1 local:1 dn:2 above:1 notation:3 get:6 overall:1 generalise:1 famous:1 cannot:1 dz:1 rest:1 reversal:1 δxx:1 during:1 respectively:3 manuscripts:1 pk:4 fk:6 e1x:3 processes:5 contributes:1 places:1 qx:4 arxiv:2 fixes:1 factorization:3 fixed:1 emx:1 approaching:1 intervening:1 available:3 set:14 observer:1 δjk:8 correlations:2 j0:17 packet:3 relative:4 depends:5 result:11 successive:3 w0:4 discussions:2 jx:1 particle:5 subject:1 probable:1 macroscopic:2 review:1 exchange:3 label:1 symmetric:1 case:3 state:74 αb:6 jth:3 between:18 reading:2 conditions:1 arrival:1 wf:1 ends:1 terms:7 creating:1 nature:5 initially:1 jauch:1 emitted:2 however:1 acknowledgements:1 fl:8 jk:1 interface:1 article:1 2pj:2 come:1 problem:1 wx:3 suggested:1 observable:4 cos:1 last:1 anders:1 many:4 taking:9 uncertainty:2 according:4 against:1 chosen:2 connection:2 became:2 context:1 ηmin:1 whole:9 experimental:1 aa:13 relevant:2 fields:1 cm:2 point:8 appeared:1 relaxation:1 corresponds:1 ingoing:3 walk:7 pm:1 2nx:10 moreover:5 considering:1 strong:1 described:12 second:6 basis:9 suppressed:1 ai1:3 due:5 been:7 xη:7 detected:1 confident:1 reduction:3 describes:2 pf:8 combined:1 interest:1 electrodynamics:2 pj:26 degrees:6 ph:2 pn:1 pl:6 choose:1 describe:3 corresponding:11 both:1 influence:5 concerning:1 formed:1 photon:6 coherent:2 external:1 c1:2 spin:3 present:1 p2:2 attractors:1 p0:11 p1:1 abandoned:1 5a:1 experiment:1 value:8 excited:2 will:5 near:1 replaced:2 safely:1 shall:12 situation:4 5b:1 procedure:2 weakens:2 unitary:2 a25:1 almost:1 averaging:1 thus:17 them:3 equal:5 characterize:3 itself:5 im:1 seen:1 ready:2 interacts:1 decisively:1 increased:1 different:15 propagation:19 make:1 radiation:2 cross:2 same:11 clearly:1 unity:1 verifies:1 quant:2 emphasize:1 copying:8 modification:1 resulting:2 composition:1 generated:1 higher:1 development:2 independent:2 clear:1 extended:1 peaks:1 i1:1 absorb:1 i2:1 unimodal:4 moment:2 levels:1 experimenter:1 infinite:2 changing:2 totally:2 tradition:1 normalization:2 mappings:2 simulates:1 lower:1 shaded:1 off:1 pµ:1 k22:1 expression:4 well:6 analysis:1 bohr:4 without:9 components:7 sets:3 coordinate:1 quantitative:1 model:10 charged:4 generalisation:2 being:3 rosen:2 rotated:2 xei:1 competitive:1 imprint:4 sources:4 identify:2 atomic:1 immediately:1 momenta:3 scattering:29 eigenstates:3 previous:1 letting:1 enters:1 density:18 absorption:7 photons:7 had:3 except:1 discuss:1 passive:1 source:6 homogenous:1 priori:2 transformed:1 instrument:1 easy:1 theorem:1 spin1:1 eigenstate:4 momentum:7 build:2 identical:1 acta:1 spinless:1 around:4 maria:1 represents:3 z1:2 2δjk:3 term:5 inhibition:1 entangled:2 using:5 bit:1 highly:2 weights:2 meaning:2 nakanishi:3 appearing:2 like:3 semi:2 alternatively:1 signal:9 performing:1 extremely:1 niels:1 manifest:1 specific:4 collect:1 kazimierz:1 steps:4 either:2 follows:1 become:1 revision:1 soft:8 qualitative:2 spins:3 sketch:2 because:3 old:1 often:1 classical:12 identified:1 understood:3 b2:2 respect:1 factorizable:1 describing:2 dimensions:1 sufficiently:1 electromagnetic:1 measurements:1 recorded:1 integration:2 overlap:2 k1:13 does:1 lattice:2 assuming:2 unstable:1 straightforward:1 refer:1 measuring:5 kristian:1 biased:3 bl:5 martin:1 use:6 bj:15 bk:13 step:7 simplex:2 qˆ:5 refers:1 normalisation:1 science:1 about:1 carried:4 extension:1 simplify:3 kinoshita:2 am:1 discussed:3 dependence:3 realistic:1 reduced:1 remains:1 range:1 a2:1 plus:1 modal:1 connected:1 introduced:5 slightly:4 functions:1 aim:1 considerations:1 equally:2 rev:4 letters:1 presence:1 into:21 within:22 splitting:1 three:3 down:1 variable:3 references:2 einstein:3 operator:2 proportional:4 ai2:2 bjx:11 relativistic:1 k12:1 detectors:3 statistics:1 shells:1 transfer:4 support:1 there:10 approximate:1 specifically:1 ordered:2 start:2 low:1 way:6 forward:1 m1:3 analyze:1 sections:2 therefore:3 function:4 form:2 enough:1 metastable:4 happen:1 restrictions:1 denoting:1 but:11 bj0:1 insertions:2 ρjk:1 active:1 copied:2 ωx:4 made:4 consist:1 up:6 us:4 theoretical:1 below:4 limit:9 sum:3 distribution:15 define:2 similar:2 average:4 strengthens:2 gisin:2 mechanics:6 strengthening:1 constant:2 ln:4 defined:7 certain:4 abstract:1 sketched:1 linearity:2 general:7 multimodal:4 single:2 4p:1 walks:1 formalism:2 distributions:3 compete:2 again:1 mutual:1 compared:2 paradox:1 no:6 whereas:3 when:4 detail:4 nx:1 field:12 dominating:1 other:3 role:2 details:1 normal:1 mathematics:2 really:1 conclusion:2 picture:1 elements:7 semiclassically:1 includes:1 a1:1 develops:1 important:3 peak:1 included:4 transfers:1 needed:2 structure:1 blx:8 ago:1 gedankenexperiment:3 correlated:1 implies:2 happening:2 practically:1 assume:9 resolution:1 interval:1 changed:3 theor:1 together:4 ckx:3 factorizes:2 mass:4 time:13 far:2 starting:3 having:1 normalized:1 |
0705.1650.txt |@word crampton:1 extrapolated:1 luminosities:3 four:2 consists:4 oldest:3 whose:1 presents:1 under:1 rise:1 dlas:88 figs:2 terlevich:1 encounter:1 herbert:3 degeneracy:10 miller:1 consistent:4 direct:4 approximation:1 surrounding:1 likely:6 gawiser:3 chen:3 estimated:4 blue:2 established:1 errors:1 selected:19 above:3 new:9 contributes:1 1997b:2 1997a:4 intercepts:1 here:3 ionization:21 reported:1 active:3 interpret:1 obtained:21 study:11 vogt:1 adopting:1 explained:3 circumvent:1 unit:23 would:6 therefore:6 type:6 until:1 fractions:2 populations:2 successful:1 starburst:2 mosconi:1 hold:1 must:1 abundance:78 mg:33 onig:1 mb:1 mn:4 deharveng:1 ms:6 give:2 involve:1 indicates:6 degenerate:1 times:6 absolute:6 provide:6 far:1 hou:3 adjacent:1 answer:2 ercole:3 undergoing:1 kennicutt:4 demanding:1 ladbeck:2 summarize:2 types:3 third:2 correlation:14 order:6 wind:1 hashimoto:1 interpretation:2 feedback:2 office:1 over:11 savaglio:5 fit:3 imf:8 better:5 production:1 fig:41 inaf:1 versus:9 them:5 affected:1 break:3 effects:13 they:27 den:3 brightness:1 each:6 lasting:2 telescope:4 series:1 used:9 combining:1 substantially:1 mccarthy:1 content:3 comprehensive:6 linear:1 surveys:3 free:3 formation:216 gasphase:1 estimate:1 telescopes:1 cosmic:2 ism:1 signature:1 corrections:12 onto:2 already:4 features:1 rank:2 hook:1 thick:12 service:1 similarly:4 top:2 needed:3 accretion:2 rates:19 observations:3 ranging:3 recchi:4 gyr:73 distance:2 scenario:2 showed:3 second:6 matter:3 iron:5 pasp:1 galactocentric:4 solely:1 rao:2 mind:1 lbg:4 seem:5 unaffected:1 relatively:11 strength:1 latter:2 degenerated:2 observatoire:1 circles:5 object:4 assesses:1 germany:1 phase:1 assessed:1 acknowledgements:1 episode:2 observation:3 calculated:1 metal:5 inferred:1 inoue:1 accounted:1 parenthesis:1 calura:11 incomplete:1 pks:7 probe:1 implying:1 radii:4 layout:1 spite:2 rich:1 do:9 di:6 de:4 despite:3 report:1 barlow:1 iwamoto:1 covering:2 nicely:2 fields:1 release:1 implication:1 aloisi:1 reference:1 observed:42 depends:2 radius:7 result:5 discussions:1 best:18 techniques:1 drawn:1 shaver:1 approach:3 terms:2 nature:3 handful:1 weak:8 however:17 contamination:1 boiss:1 improve:1 suggested:2 received:1 cor:19 irregular:76 uncertainty:2 heating:1 against:3 l141:1 mildly:1 contribution:1 argue:1 timescale:1 comprehension:1 basis:2 three:23 been:3 much:7 interest:2 expected:4 quantities:1 chile:2 aretxaga:1 sfrs:17 aim:2 seven:2 iwata:3 ii:12 kellogg:1 conf:1 ia:3 id:1 confirmed:2 suggest:1 make:1 clearly:3 accumulating:1 several:7 european:2 independent:3 published:1 counterparts:5 hand:4 kim:1 episodic:9 academic:1 left:4 quasar:7 identify:1 thanks:1 sightlines:2 yet:2 previous:1 drozdovsky:1 spread:6 marginal:1 zavadsky:26 possible:9 possibly:1 background:3 unique:1 hunt:2 specific:4 detections:1 arbitrary:1 right:5 old:4 pettini:17 successfully:1 indirect:2 maeder:4 bottom:2 cerro:1 cora:2 illustration:1 properties:21 o:35 constituting:1 tiepolo:2 plus:1 efforts:3 slightly:2 obs:30 metallicities:7 presence:2 obtaining:2 son:1 contrasts:1 methods:1 zqso:2 initial:2 c58:2 width:7 way:12 astrophysics:2 was:10 underestimated:1 medium:1 gaseous:1 form:5 forming:15 becoming:1 kueyen:1 magnitude:3 incorporation:1 solar:12 magellanic:1 removed:1 fort:3 inside:2 strongest:1 dordrecht:1 panels:3 emit:1 fulfills:1 computing:2 abstract:1 covers:2 evidence:3 gemini:2 exist:2 accounting:1 distributions:6 check:1 triangles:3 physical:4 ni:22 dotted:25 no:14 whereas:2 when:9 burgarella:1 unambiguously:2 papers:5 test:3 jenkins:2 picture:4 models:69 alleviated:1 marconi:1 diamonds:3 explosions:1 younger:2 longer:1 assume:5 interval:2 together:2 time:11 l17:1 global:6 focus:1 leads:4 manages:1 garching:2 grateful:1 extremities:1 arcsec:1 certainly:1 inverse:1 depend:2 technique:4 finally:5 analogous:1 advises:1 keck:4 petitjean:3 advantage:1 unchen:1 clouds:1 presented:2 did:1 hawaii:1 solved:2 upper:7 work:10 slower:1 trend:13 charbonnel:1 spectrograph:2 revista:1 wolfe:26 filled:7 satisfy:1 dwarf:82 prescriptions:6 groups:1 monier:1 appears:1 blackburne:1 dusty:1 studied:16 irregulars:6 usually:2 studies:6 churchill:1 absorbers:3 hunstead:1 undergone:1 russell:2 working:1 visit:1 predictions:1 prep:1 diagrams:1 absorptions:1 beers:1 cases:1 modified:1 gathers:1 values:15 following:8 want:1 predict:3 topic:1 performed:2 allowed:3 spanning:1 hydrogen:1 cayrel:1 discussion:2 exceptional:1 chemical:28 criterion:1 parameter:1 sne:4 may:14 southern:2 produce:1 revealed:1 cosmology:3 si:38 cannot:1 so:5 halos:1 typical:17 indeed:19 mainly:5 osservatorio:1 years:1 episodes:3 statistical:3 differs:1 still:3 observational:3 derive:7 thank:1 acknowledge:1 interesting:1 williger:1 forms:1 zdla:36 dwarfs:3 ours:1 main:5 non:1 disparate:1 evolution:22 half:1 now:2 halo:2 bursts:6 spectroscopically:1 metalrich:1 individually:1 weighted:3 bursting:53 ed:1 owing:1 naming:1 adequately:1 shown:2 space:1 increase:1 investigation:1 suggesting:1 squares:2 shows:8 theory:1 romano:2 fisica:1 diagnostic:1 california:1 widths:1 impose:1 place:1 massive:4 first:12 symmetry:1 fast:1 directly:1 open:1 angular:1 size:1 given:10 indicate:2 cooling:2 iau:1 structures:4 gives:3 inefficient:4 mostly:2 continuous:50 accurately:2 transverse:1 viegas:2 than:25 population:11 wide:3 unige:1 unfortunately:1 accordance:1 require:2 kishimoto:1 future:1 were:13 inferring:1 lick:1 correction:2 turned:1 argument:1 any:3 note:4 take:1 resembling:1 highredshift:1 trace:1 remarks:1 especially:1 surprising:1 considered:10 average:10 adopt:2 quiescent:3 abraham:1 typically:2 quantity:1 molaro:1 show:15 bright:3 threshold:6 data:18 line:13 slow:1 ratio:19 proportion:1 histories:53 gratton:1 only:22 going:1 cb58:4 get:3 morphological:1 ionized:1 nearly:1 conjunction:1 gen:2 median:1 summary:5 dopita:2 predicted:6 reveals:1 burst:39 physically:1 relative:14 namely:3 fails:3 extragalactic:1 subsequent:1 label:1 enough:1 between:35 2002a:5 2002b:1 arrival:1 spectroscopy:1 jr:1 analyzed:1 lopez:2 σi:1 erb:3 outflows:1 many:2 region:2 according:2 izw18:1 comes:3 nearby:1 among:3 period:2 maintained:1 moreover:2 considering:5 lyman:2 hardly:1 formed:2 qso:6 observe:2 mauna:1 careful:1 former:2 those:5 case:8 regimes:5 supernovae:1 profiles:1 refractory:5 proves:1 promising:1 characteristics:1 ellison:4 discrepancy:1 bias:5 different:38 proto:2 media:1 same:14 epoch:3 underestimate:2 regime:5 investigated:11 jorgensen:1 kubo:1 ois:9 relies:2 largely:2 components:1 model:99 laboratories:1 dimension:2 being:4 generally:3 underline:1 sampled:1 cl:3 seems:2 except:8 samples:3 nakasato:2 real:1 rules:1 astronomico:1 early:2 grid:1 voigt:1 using:5 accepted:1 ruled:4 either:2 always:1 output:2 meara:1 cr:5 duration:17 cristina:1 confirm:1 depletion:21 critical:3 provides:1 moderate:2 measuring:1 biased:2 equivalent:1 broken:1 biases:1 ratios:44 comparison:11 hopkins:1 favorite:1 mean:2 redshift:62 references:1 determine:6 accumulated:1 theoretically:1 log:30 area:27 assumed:3 there:2 dispersion:3 low:30 stars:15 complete:2 lane:1 mnras:12 faster:1 applying:1 prantzos:1 ωm:1 2003b:2 2003a:5 agree:2 connect:1 detailed:5 certain:2 describe:3 tytler:1 deep:9 general:2 ar:7 lifetime:1 again:4 elemental:10 field:1 poor:1 durations:2 important:4 peak:7 included:1 møller:7 building:1 l63:1 curve:38 having:6 mass:21 resolution:1 external:4 represent:7 abundances:37 consider:9 lack:2 follow:1 disk:40 ti:4 mpc:1 straightforward:3 very:28 izotov:2 fall:2 difference:1 damped:3 large:14 small:3 programme:1 neighborhood:6 rate:22 timescales:4 enhancement:3 further:5 what:1 sub:1 section:5 sfhs:6 method:3 contrast:1 full:5 compilation:1 component:1 concluding:1 strong:5 publisher:1 allows:1 milky:5 imaging:4 via:3 2000b:3 2000a:2 requiring:1 select:4 readily:1 proceed:1 contains:1 nucl:2 taken:4 more:13 flat:1 corrected:6 emission:22 tested:1 particular:3 known:5 producing:1 dex:2 none:3 science:2 der:1 des:1 debated:1 nine:13 evolved:3 tosi:3 history:39 turnshek:3 ions:2 compare:5 cosmological:1 steidel:12 minimum:4 exclude:2 sauverny:1 information:1 goal:2 rather:1 ryd:1 maps:1 explains:1 ensemble:1 galactic:10 derived:20 reflect:1 fe:98 choice:1 schulte:2 short:7 spectra:8 ledoux:3 negligible:2 sect:14 help:1 swamped:1 developed:2 w7:1 boissier:1 paper:34 through:1 existence:3 its:4 rapidly:1 energies:1 detected:9 systems:9 good:1 propose:1 matteucci:23 yr:17 hereafter:2 fully:1 level:1 bonifacio:1 found:7 universit:2 characterized:28 referred:3 heavy:1 bruzual:3 everyone:1 energy:1 expect:3 measurement:6 operation:1 beyond:1 really:2 since:17 dominated:2 sbs:1 asp:1 ast:1 favored:8 difficulty:1 reason:2 brightest:1 definition:6 consequence:1 dipartimento:1 major:2 probability:3 number:5 equating:1 koo:2 introduction:1 leading:4 least:1 sargent:1 hundred:1 too:2 nomoto:7 bowen:3 optical:1 authors:3 focusing:1 believe:1 king:1 molecular:1 determines:1 determined:3 contrary:4 toward:42 motivation:2 ages:13 quasars:3 confirms:1 orders:2 karl:1 lie:1 zero:2 astronomia:1 majority:2 internal:2 finding:4 kobulnicky:2 play:1 hires:4 populate:2 most:9 significant:3 measured:5 gorosabel:1 clear:2 sometimes:1 cover:2 km:2 traditional:1 kr:3 part:2 velocity:9 particularly:3 glazebrook:1 relation:1 find:6 thielemann:1 impact:1 indicator:3 parameters:5 e11:12 conselice:2 factor:2 dominant:2 lyα:5 dependent:1 observatory:3 closely:1 during:6 arxiv:1 highresolution:1 investigate:1 common:6 switzerland:1 obscure:1 doublet:1 set:8 art:1 ser:1 achieved:2 lifetimes:2 ara:2 see:41 individual:1 close:1 various:3 nestor:1 available:4 recently:2 statistically:1 complementary:1 spectroscopic:1 shortlived:1 distinguish:1 both:11 last:1 sensitive:2 connection:3 context:1 whole:3 dustier:1 point:4 smith:2 recycling:1 corresponds:19 simply:1 morphologies:1 throughout:1 decline:1 described:1 enhancements:1 due:12 pc:2 collected:1 ph:4 photoionization:4 kunth:2 gas:23 covariance:1 briggs:1 understand:1 representative:7 fuv:1 uncertain:1 look:1 grains:1 solid:13 reliable:4 while:9 error:12 computed:4 reddy:4 rix:1 vol:2 apjs:4 encountered:1 lambas:1 itself:1 centuri:1 null:1 italy:2 odorico:4 grant:2 resulting:3 ray:1 composition:1 higher:12 literature:1 jakobsson:3 levels:5 purpose:1 recent:3 lower:17 older:1 tsujimoto:1 analysis:7 tissera:1 calibrated:1 howk:7 distances:3 alternative:1 tables:1 kluwer:1 conclusions:1 evaluate:1 dessauges:27 helpful:1 follows:2 interestingly:3 disks:3 e00:12 yields:22 weiner:1 qualitative:1 often:1 some:4 separated:2 trends:1 examples:2 sight:3 infall:3 savage:2 scalo:5 measurements:5 per:23 efficiencies:14 minimal:7 aj:1 agreement:8 step:3 santa:2 relating:1 franco:1 constrains:1 consumption:1 tracing:2 deserves:1 range:11 consequently:1 accessible:1 into:4 within:13 nsf:1 edmunds:1 shapley:6 proportional:2 statistics:1 few:9 question:1 long:5 brun:2 zwaan:2 analyze:1 sections:2 overestimation:2 properly:1 link:3 injection:1 papovich:1 consist:1 characteristic:2 up:5 us:1 theoretical:1 today:3 boldface:1 continuously:3 similar:6 called:3 associated:9 defined:6 redshifts:17 thomsen:3 single:19 diverse:2 reservoirs:1 stiavelli:1 steeper:2 tentative:2 dashed:16 points:13 grb:11 draw:1 elements:21 afterglow:1 structure:1 independently:1 implies:3 quantifying:1 eroux:4 required:1 heats:1 fitted:1 enrichment:1 once:1 results:12 existing:2 illustrated:3 ge:3 contributions:1 centers:1 adelberger:9 nucleosynthetic:1 disposal:5 young:8 send:1 excluded:1 dickinson:4 include:1 ionizing:1 fynbo:8 vlt:3 experiencing:3 notes:1 eve:2 try:1 chiappini:11 concluded:1 zn:38 smaller:1 hulst:1 zf:1 croom:1 annibali:2 access:2 volatile:1 pristine:1 meynet:5 bergeron:2 respectively:14 youngest:1 objects:12 l25:2 separation:1 l26:1 deduced:2 great:1 larger:9 suggests:5 preferentially:1 survey:2 prochaska:25 shaded:3 apj:36 decrease:5 use:6 usa:1 remains:2 next:1 eleven:5 panel:8 started:1 becomes:1 transient:1 iii:4 sample:46 account:5 crosses:2 reproduce:11 thin:20 drops:1 control:2 weaker:5 verheijen:1 lbgs:1 discussed:4 pieces:1 high:62 assumptions:2 andersen:2 six:9 uves:5 regions:9 trieste:4 hjorth:3 forest:1 profile:2 blocks:1 fits:7 qsos:1 bradamante:2 light:1 separations:1 correspond:3 element:6 allow:2 evolutionary:2 struggles:1 produced:4 including:1 jimenez:2 mentioned:1 galaxy:64 warren:1 le:2 outer:24 located:1 masses:7 age:54 lu:3 degrees:1 covered:1 defining:1 rotation:2 day:3 srianand:2 february:1 university:1 identified:7 kpc:28 mode:1 tracer:1 reproducing:7 related:4 fraction:4 measure:4 l15:1 our:45 transitions:1 out:13 maximizes:1 matrix:1 mcmahon:1 supports:1 integrated:2 red:1 franc:9 interactions:1 galaxies:146 approaches:2 greggio:1 hubble:3 determining:2 could:3 keep:1 counterpart:1 explored:1 levshakov:2 hence:14 ionic:3 south:1 kendall:2 manuscript:1 succeeds:1 reaches:1 reached:1 quality:2 unknown:1 histograms:1 system:7 adopted:12 their:29 nebular:1 intermediate:5 explanation:1 crosssection:2 detection:4 bei:1 limiting:1 exhibit:1 lines:6 cohen:1 curves:1 need:3 constrained:5 intersecting:1 nucleosynthesis:2 instance:1 concerns:3 sfr:29 giavalisco:4 sfh:21 preliminary:1 intrinsic:11 why:4 atypical:3 stronger:4 deuterium:1 hierarchical:1 diagnostics:3 maillettes:1 obscuration:2 fact:7 selection:6 supported:6 bring:2 debate:1 principal:1 based:8 knowledge:1 sembach:4 hopp:1 should:7 panagia:1 fuel:1 local:5 achieve:1 means:7 ones:5 words:1 symbols:6 processes:1 densities:12 luminosity:4 differential:1 contain:1 hewett:1 view:1 requirement:2 constrain:4 nitrogen:2 hν:1 correlations:4 enhanced:2 luminous:2 mexicana:1 dla:166 tend:3 state:1 identification:1 routine:1 tens:2 progress:1 comparable:1 reproduced:2 supernova:1 kea:1 efficiency:25 reproduces:15 hypothesis:1 key:2 distribution:20 limits:2 career:1 salpeter:4 equal:2 vladilo:14 figures:1 estimation:2 otherwise:1 strongly:3 ch:2 co:3 cm:2 conclude:1 wall:1 ca:1 uco:1 table:13 cu:3 addition:3 yan:1 treat:1 paranal:3 determinant:1 myr:9 corresponding:3 present:5 prochter:1 value:2 will:12 wild:3 almost:2 thus:17 surface:5 examined:3 demanded:1 radiation:1 cross:5 mulchaey:1 parts:1 largest:2 difficult:2 effect:3 dust:40 requests:1 center:1 nevertheless:1 modeled:1 well:11 patterns:45 sets:6 position:1 spherical:1 less:6 accurate:1 sofia:2 obtain:1 sources:1 clocks:1 density:18 absorption:11 sky:2 spirals:2 saturation:1 cruz:3 five:1 press:2 immediately:1 necessary:1 like:1 bulge:2 sissa:1 therein:1 shed:1 because:9 grids:1 sequence:1 library:1 proper:1 happens:1 lead:2 broad:3 avoid:1 overlap:2 instantaneous:1 does:1 assuming:2 eso:5 demonstrated:1 disentangle:1 stellar:8 host:4 although:6 stage:1 about:5 rare:7 column:19 universe:11 dependence:1 compatible:1 constraints:2 previously:1 h0:1 interstellar:2 square:4 van:4 additional:2 leitherer:1 spiral:61 overestimate:1 inner:17 function:24 offprint:1 north:1 hs:2 but:17 astro:4 neutral:3 hi:2 highest:1 made:2 compute:2 whether:3 wish:1 below:2 limit:11 demonstrate:1 problem:4 contribute:1 periods:2 proceeds:4 compared:2 variety:1 other:26 details:1 predominant:1 star:212 class:3 metallicity:29 astronomy:2 baker:1 determination:4 indirectly:1 |
0705.1652.txt |@word secondly:2 xσi:1 sci:6 pointing:1 represent:1 iecn:1 results:5 leads:5 roy:1 proposition:16 generalize:1 computation:3 eme:1 follow:2 primes:16 minuscule:1 causes:1 devoted:1 oslo:1 certainly:2 analytic:1 tu:18 removal:1 finally:3 th:2 under:3 discretion:1 worth:1 norm:1 g7:2 case:3 conjecture:28 g4:3 g3:3 g2:3 advantage:2 g0:2 very:8 conjectured:1 g9:3 choice:7 corollary:7 every:6 additional:1 difference:6 exact:1 condition:4 υi:8 level:21 did:1 issue:1 t4:16 t2:40 solution:2 t1:36 large:15 interchanging:1 science:1 small:5 sieves:1 upper:14 smaller:2 publ:1 α2j:2 estimates:1 direct:1 second:6 concludes:1 chen:57 further:4 reine:1 friedlander:3 d4:5 theory:4 even:9 aim:2 what:2 appear:1 3s:1 d2:20 section:8 xρ:1 analogously:1 d3:3 version:2 en:1 gi:1 above:3 sup:1 new:11 principal:1 method:7 satisfy:3 g5:3 κi:2 respectively:10 4s:4 here:7 desired:6 xθ:4 les:2 china:1 others:1 2kl:1 sieve:51 observing:1 z1:4 z2:3 obtained:6 remark:4 dp1:8 technical:1 involved:1 elaborate:2 larger:1 allows:7 p2:399 domains:1 proof:43 involves:1 uniquely:2 control:1 via:1 useful:1 divide:3 classification:1 extra:2 merely:1 replace:3 hardy:3 f3:2 summation:3 apply:9 des:1 e7:6 unit:1 f5:2 use:14 additive:1 asymptotic:1 would:4 prove:26 remains:4 positive:9 give:13 negative:1 next:8 process:1 ψi:1 therefore:4 m2:1 fouvry:7 8u:4 type:3 vj:14 more:12 vl:4 ap1:37 vi2:1 particular:3 known:2 multiset:1 cases:2 verified:1 iii:1 eγ:6 must:4 couples:1 quartic:1 henri:1 recall:1 equation:1 work:1 modified:1 dev:1 cai:13 mp:7 den:1 following:15 making:3 example:1 history:3 f0:2 f1:3 f2:2 weaker:1 f4:2 triple:1 indicated:1 stated:3 calculation:4 f9:2 table:2 belonging:1 weighting:2 assumptions:2 numbers:4 sense:1 standard:1 mn:4 occur:1 absolute:1 s9:2 end:1 g1:3 s3:14 2eγ:3 s1:26 holds:2 s4:18 machine:1 acta:10 obius:1 simplicity:1 product:4 description:2 cartan:1 may:2 max:18 hence:5 b6:4 improving:1 representations:2 g8:2 cuboids:2 short:5 third:5 s2:14 lemmas:11 2g7:1 eliminated:1 summing:1 linnik:2 sj:6 si:17 so:2 increasing:3 nancy:3 decreasing:10 definitions:2 g14:2 g13:2 order:28 ec:1 g10:3 elie:1 s0:1 help:2 indeed:1 over:2 mathematicians:1 paper:4 london:3 dw:3 satisfies:2 still:1 its:1 before:10 write:13 mod2:1 derive:1 lb:6 thank:1 la:1 chosen:1 interesting:2 writing:2 better:7 estimating:1 lu:8 systems:1 mail:1 main:3 might:1 maximal:2 qq:1 non:2 affected:1 rosser:3 propose:2 noticing:11 introduce:5 functional:5 fr:1 2p:4 resolve:2 they:5 half:1 oxford:1 trondheim:1 now:8 yu:1 4f0:1 2t:14 verify:2 term:5 equality:2 2s:14 always:1 delicate:1 υj:1 2d:1 sufficiently:12 l4:1 inequality:28 l2:6 l3:7 each:2 2l:1 found:1 2n:2 side:4 mean:10 domain:1 weighted:13 ek:1 nombres:1 idea:4 numeric:2 t3:34 combining:6 suite:1 our:7 special:2 out:2 try:2 matrix:1 factors:5 open:1 since:18 e5:3 denotes:1 replacing:3 contained:1 reader:1 formula:5 suffices:2 math:11 shows:4 i2:10 linear:8 free:1 quite:5 quart:1 difficulty:2 complicated:6 e8:10 put:8 e4:4 estimate:10 e6:2 e1:5 e3:10 e2:5 r4:4 definition:12 r0:11 r1:25 r2:15 r3:8 sinica:6 could:4 similarly:16 iterative:1 times:1 xσ1:6 place:6 hopeless:1 consequence:1 βn:9 view:6 first:14 ding:4 there:6 manuscript:1 majorize:1 variables:2 powerful:3 number:24 improvements:1 approximately:1 another:1 fi:4 carry:1 precisely:1 xv:4 maple:1 coprime:1 given:9 moduli:1 needed:1 introduction:2 goldbach:28 system:4 relations:2 their:3 πp:2 assumption:7 convention:2 dt3:8 dt2:8 dt1:8 premiers:1 speaking:1 gives:6 arith:6 becomes:1 proving:2 immediate:1 technique:1 because:1 somewhat:1 x2:5 x3:1 x0:5 x1:18 than:14 coefficients:3 x5:1 f7:2 divisible:1 double:28 dans:2 richer:2 richert:3 determined:3 historical:2 vinogradov:6 f13:4 f10:2 dt4:8 treated:2 decompose:2 factorable:16 f8:1 ann:1 argument:8 say:1 angew:1 2t1:4 vn2:1 need:7 element:1 any:19 contents:1 estimated:2 zero:1 depending:2 general:1 lim:4 ideas:1 mr2:2 εr:1 note:1 decomposing:1 εi:2 take:5 subintervals:2 destroy:1 switching:8 formulas:4 cnrs:1 established:3 umr:1 most:6 αr:8 letter:1 preliminary:3 device:1 extremely:1 exponent:1 γi:4 dordrecht:1 clear:3 later:1 cover:1 sf:2 principle:8 exp:1 quadratic:1 sum:12 fact:7 quantity:4 precise:1 show:8 cdn:6 supported:1 norms:1 relation:1 solutions:1 d6:10 analogue:1 d5:3 trivial:4 find:7 d1:220 q1:25 q2:19 based:2 parameters:8 representation:3 state:1 completes:9 lemma:75 only:7 x4:8 rich:1 factor:4 attained:1 employed:1 chinese:2 sur:2 dn:100 dl:2 his:7 handle:1 dk:1 notation:3 get:5 de:2 famous:1 iwaniec:11 dx:2 dy:1 dv:8 reconstruct:1 dt:132 du:51 dp:9 dq:5 prime:50 αj:24 dpp:1 conditions:8 arxiv:1 remove:1 nθ:1 arithmetica:1 dpn:4 fixed:1 τk:4 approaching:1 2p1:1 injections:1 4g0:1 set:10 ser:1 exists:3 x11:1 tu2:3 2c:1 up:1 see:18 p21:2 result:17 p22:1 recently:3 best:1 subject:1 satisfying:8 inequalities:17 ways:2 compensation:1 written:3 smallest:1 x29:2 between:5 αi:1 subscript:1 reading:1 αm:6 αn:4 sections:1 terms:12 nature:1 wk:12 however:1 tuv:1 wu:32 uω:1 key:1 article:1 problem:34 improve:2 essentially:2 improved:6 kluwer:1 many:1 taking:5 according:2 f14:4 2e3:4 contribution:2 adapted:1 comes:3 otherwise:8 arbitrarily:1 among:1 autour:1 cn:7 point:1 simple:4 2i2:1 2i1:1 twin:28 cx:1 sequences:2 bν:1 li:20 ct:2 pr:2 combines:1 xα:2 described:2 equations:2 three:8 ai:4 much:4 change:2 certain:1 pj:11 oε:1 pi:3 define:11 direction:1 referee:1 corresponding:5 easy:2 sufficient:1 propositions:8 σi:1 observe:1 last:3 careful:3 present:3 applied:2 p3:248 p1:328 p6:3 look:1 p4:56 p5:18 plain:1 estimations:2 value:12 will:3 near:1 suppose:4 error:7 au:1 gave:1 davenport:3 inspired:1 procedure:2 studied:1 attains:1 intervalles:2 almost:2 vi:25 von:1 vk:1 thus:28 equal:2 ii:11 mangoldt:1 bombieri:12 supremum:1 different:1 ap:7 author:1 limitations:1 make:4 problems:1 ep3:2 same:4 clearly:5 parts:2 φd:3 emes:1 modification:1 proved:6 finite:1 infer:1 pan:11 difficult:5 independent:2 used:8 imply:3 i1:9 comprehensive:1 numerical:5 hand:4 4cn:1 v1:25 v2:3 purpose:1 4d1:2 ab:4 identity:10 recent:1 lower:14 suitable:3 acknowledgement:1 expression:1 min:2 well:21 roughly:1 analysis:1 obviously:4 academic:1 without:3 solve:1 sets:1 firstly:2 johan:1 stating:2 usual:2 uhp:1 proposed:1 less:2 being:1 obtain:20 mr1:1 intervals:6 immediately:4 2f7:1 previous:1 adding:2 generous:1 adp:22 adq:1 thinking:1 5t:10 seems:4 5s:1 improvement:4 appeared:1 add:2 belongs:1 treatment:1 5k:1 theorem:48 5a:1 remaining:1 euler:3 ross:2 real:3 depends:2 easily:6 replaced:2 sums:4 possible:1 know:2 press:2 integer:18 mod:15 modifications:2 necessary:4 like:2 follows:9 xεi:2 yields:7 integrals:3 multiplicative:2 works:1 page:4 t22:7 lager:1 exceed:1 right:4 methods:4 sequence:4 some:12 petits:2 b4:2 b5:2 deduce:21 acad:1 b1:4 b2:2 moreover:1 proofs:6 provided:1 lead:1 2e:1 avoid:1 shall:13 integration:2 does:1 decomposition:1 innovation:1 2f:1 proc:1 refer:1 inserting:14 bc:7 kyoto:1 equivalent:1 l1:2 inria:1 bt:1 pq:3 plb:2 although:1 arithmetical:5 universit:1 simpler:3 integers:4 central:1 sharper:1 dd1:1 theorems:10 ob:1 o:60 vitolo:2 beijing:2 distinct:2 progressions:2 ti:3 introduced:3 slightly:3 other:2 duke:1 soc:3 into:16 splitting:2 bound:15 due:5 a9:2 square:1 references:2 elementary:1 france:1 institut:1 log:191 strictly:1 placing:1 approximate:1 long:2 start:1 dropping:1 way:4 salerno:2 2m:1 was:6 treat:1 function:31 complete:2 form:6 differences:1 but:9 hk:66 related:1 agreeable:1 2d1:4 true:1 he:5 oδ:33 applying:6 4x:2 whether:1 characteristic:7 mat:1 bounds:11 us:13 ωi:2 below:9 limit:1 uk:15 distribution:5 uf:2 similar:12 detailed:2 instead:2 ac:5 interval:6 constant:22 ad:24 defined:9 selberg:4 abstract:1 b3:2 denote:6 littlewood:3 exist:2 halberstam:3 poincar:1 again:1 functions:5 nl:2 mathematik:1 when:5 application:5 valid:2 es:2 ap3:4 mathematics:1 er:1 nt:1 arithmetic:2 pν:2 elements:2 grupp:3 preceding:1 uniformly:4 a1:2 ξi:1 important:3 variable:1 subsums:2 merten:1 scient:1 dϕ:1 implies:20 using:13 vandœuvre:1 eralis:1 required:4 factorisable:3 together:1 eor:2 weights:5 4h:1 n0:80 4a:2 starting:1 having:2 once:1 |
0705.1653.txt |@word exponentiation:1 four:1 obstruction:12 asian:1 calculate:2 γv:2 aut:2 γm:9 γl:3 conjecture:22 every:5 solution:1 convenience:1 vector:18 red:7 direct:9 second:12 rigorous:1 even:5 established:1 ak2:1 above:6 new:6 contributes:1 consisting:1 coefficient:3 never:1 here:10 refinement:2 represented:5 contraction:1 obtained:24 rigorously:2 study:8 approaches:1 fourier:7 divide:1 tensored:1 explained:2 replace:1 counts:11 total:4 linearly:1 bundles:1 negative:2 tabulated:1 m4:1 therefore:9 m2:2 type:21 zeroes:1 snowden:1 under:2 hold:2 springer:1 quartic:10 ml:30 work:6 theories:5 mv:12 root:2 example:4 give:2 involve:1 indicates:1 cartan:1 degenerate:1 absolute:4 provide:1 hom:2 feature:1 recovers:1 after:8 memorial:1 diagram:2 summarize:1 law:1 parallel:1 types:1 kreuzer:2 ramanathan:1 third:1 chern:2 descends:3 green:2 order:2 interpretation:2 over:25 vary:1 satisfies:1 πdr:1 before:2 fit:1 sheaf:2 better:1 easier:1 maximal:2 they:1 kohnen:1 represents:1 invariants:48 each:12 trivializations:1 side:7 mean:1 lifted:1 schemes:1 series:17 contracting:1 literature:1 conjectures:7 restricted:1 crucial:1 re:2 rg:41 mα:7 reader:1 forth:1 independence:2 foundation:1 gromov:67 linear:4 associate:2 sextics:2 gromovwitten:2 free:1 standard:6 admits:2 r0:11 r1:4 mvv:2 iso:1 signature:3 corrections:1 onto:1 already:1 rank:15 spinning:1 grady:2 relations:3 another:1 degenerations:1 top:2 finitely:5 princeton:6 divisible:2 1l:1 classes:24 powers:1 borcherds:20 ran:4 modern:1 chen:1 seen:5 contents:1 relatively:4 homological:1 conjecturally:1 latter:3 isolated:9 quadric:4 residue:1 calculated:4 bracket:3 principle:1 section:44 soluble:1 solutions:2 d4:9 d2:15 d1:11 bourbaki:1 divisibility:13 explain:3 topological:4 x4:16 b463:1 dl:1 dm:5 dh:29 de:2 despite:1 dv:1 unfortunately:1 eme:1 acknowledgments:1 twice:5 depends:1 result:17 discussions:1 techniques:1 birational:1 tensor:1 away:1 symmetric:4 approach:9 d57:1 terms:9 however:7 zaslow:10 topology:2 essentially:1 cup:1 4h1:1 contribution:11 fnl:2 2ng:2 eminaire:1 polynomial:3 diff:1 basis:8 union:6 three:3 enumerative:2 much:5 basic:3 expected:1 algebras:1 correction:3 families:13 deeper:1 cotangent:2 lift:1 2n2:1 manifolds:1 applied:1 jams:1 euclidean:2 suppose:2 property:3 a20:1 a22:2 played:1 ii:9 intertwining:2 cone:3 containing:5 specialization:2 make:2 complex:12 descend:1 several:5 independent:2 i1:5 i3:2 i2:3 hand:1 characters:2 unconditionally:1 pursued:2 left:6 just:2 op3:1 facts:1 ottsche:1 yet:1 projection:4 infinitely:2 character:2 ruan:2 easy:1 5a:1 noether:77 possible:1 unique:2 specific:1 scheidegger:4 bps:23 right:12 zariski:1 bottom:2 hodge:30 t13:2 shifting:1 properties:2 o:8 nonvanishing:3 restate:1 duke:4 soc:1 statements:1 bound:4 down:1 lies:1 hermitian:1 acad:1 refined:3 often:2 c53:4 definiteness:1 vafa:8 nodal:18 support:2 initial:3 way:2 was:10 form:37 removes:1 encoded:1 true:1 integrality:1 cylinders:1 attached:2 preimage:1 heterotic:6 strengthening:1 moore:8 abstract:1 covers:2 proves:2 dλ:2 dβ:1 check:2 nj:2 nl:1 no:7 agreeing:1 galois:2 when:3 vanishes:5 ng:20 nx:17 interested:3 role:3 test:1 asterisk:1 assume:4 dτ:1 together:3 push:3 n2:5 precise:2 remarkable:2 2dk:2 invent:7 grateful:1 row:3 certainly:4 inverse:1 depend:1 eigenbasis:1 quasi:32 infinitesimally:1 elliptic:1 analogous:2 deforming:2 string:4 zhang:1 mg:1 choice:2 rationality:2 exact:3 dim:5 riemann:4 level:9 irreducible:2 upper:3 lefschetz:94 h14:1 contracted:2 manetti:2 satisfy:1 xξ:34 groups:2 address:1 along:4 appears:1 change:4 studied:1 usually:1 deg:1 griffiths:1 working:1 prove:3 positive:7 associated:22 vectorvalued:1 gopakumar:6 duality:9 validity:1 rigid:1 cases:4 cardinality:1 valued:23 avoiding:1 castelnuovo:4 values:5 following:28 trans:1 candelas:2 claim:1 2lh:1 expanding:1 sl2:10 counting:5 conversely:2 verlag:1 redundancy:2 discussion:2 write:6 pure:1 parameter:13 divides:1 map:21 product:5 may:15 applications:3 date:1 representations:1 data:2 grow:1 lifting:2 natural:2 outline:1 explicit:2 branched:3 so:6 definitions:5 acts:1 indeed:3 mainly:1 primitive:16 group:9 thank:1 summands:1 interesting:1 forms:48 main:2 correspondence:1 non:4 matches:1 conversations:1 half:7 now:7 term:9 equality:5 e2πi:2 january:1 roch:4 domain:4 weighted:1 ee:1 eg:2 hypergeometric:7 millson:3 space:40 contained:1 rational:6 formula:17 squares:1 correct:1 shows:9 earlier:1 theory:84 singularities:4 mapping:1 e8:6 fixed:2 derivation:2 transition:1 place:1 b457:1 qn:4 fractional:1 b453:1 first:14 origin:1 symmetry:8 xm:11 omitted:1 variables:6 long:1 directly:3 open:9 xt:4 1q:1 given:29 exists:3 vanishings:2 zagier:3 structures:5 hyperelliptic:1 gives:3 than:1 coefficients:12 effective:2 hypersurfaces:6 were:1 generality:3 ann:4 turned:1 argument:3 recover:2 any:6 ideas:1 potential:5 take:4 upside:1 formulas:3 multiple:1 normal:1 rankin:6 algebraic:7 skinner:1 pair:1 pencils:1 surprising:1 considered:1 dualizing:2 show:3 spaces:13 threshold:2 nlh:4 homology:1 fibrations:1 aτ:2 state:4 analytic:2 only:20 explicitly:3 black:1 equipped:2 ossa:2 nl0:1 contracts:1 coset:4 theta:4 closure:3 regarding:2 settings:1 yield:5 kernel:2 surjectivity:1 relative:13 y0:2 surgery:1 surfaces:66 fails:1 satisfying:17 harvey:5 review:4 between:4 geometric:3 reading:1 vertical:6 comm:1 many:11 expression:2 fix:4 comes:1 among:1 overview:3 period:4 moreover:1 considering:1 configuration:1 locally:2 mari:3 observe:1 proven:9 careful:1 former:1 case:19 characteristics:2 threefolds:1 middle:1 fibration:5 superconformal:1 different:2 same:5 dγ:1 cubics:1 arguments:4 trivially:1 siegel:1 harris:1 4d1:2 8n2:1 without:1 solve:2 components:7 model:4 dimension:7 heegner:7 manifold:5 topol:1 conclude:5 priori:1 versa:1 real:1 bryan:4 read:2 cg:2 using:10 ams:3 mod:29 reduces:1 faber:1 enriques:2 isotrivial:1 degenerating:1 either:2 integrals:4 fully:1 reduced:20 sym4:5 nonzero:8 gross:1 dimensions:4 maulik:28 2t12:2 decomposition:2 provides:3 refer:2 power:3 equivalent:4 looijenga:1 trivialize:1 artin:1 comparison:4 central:2 cornalba:1 discussed:4 morphism:8 inclusion:2 image:1 references:2 determine:8 operator:2 hep:4 refinements:1 strictly:1 there:17 low:3 complete:13 sophisticated:2 divisors:24 pull:2 multiplicity:13 ωs:3 2d2:3 ωk:6 submanifolds:1 ωc:1 agree:3 detailed:1 taylor:1 ag:5 holes:1 describe:1 general:2 invertibility:1 again:3 graduate:1 field:1 mathematics:2 briefly:1 a1:2 n0:5 a2:4 included:2 curve:20 starting:1 strings:4 represent:1 sci:3 consider:18 alg:3 scalar:7 mp2:27 lian:1 follow:3 expressions:1 disk:1 ihes:1 tx:2 fellowship:2 equivalence:3 ts:6 th:6 ti:2 nodes:1 tc:9 norm:7 degeneration:6 amplitudes:1 straightforward:1 very:5 conjectured:1 corollary:18 witten:67 difference:2 deformations:2 condition:4 induced:3 evaluation:1 t2:24 t1:22 large:3 kondo:1 small:6 anal:1 perspective:1 semiregularity:3 further:1 canonical:11 bilinear:3 brackets:4 sum:6 toric:2 intersect:1 sup:1 method:3 full:2 component:6 answers:1 modular:64 excess:5 directions:1 equations:4 tian:2 divisor:10 4we:1 allows:2 action:6 quotient:6 uniquely:3 via:16 mc:10 family:37 vir:4 equivariant:2 establish:2 takes:1 distinct:3 contains:1 finally:3 h1i:1 nucl:3 taken:3 more:7 compositio:1 operators:1 particular:4 known:3 projective:8 mvu:1 r2:3 equation:10 specializes:1 det:1 remain:1 nonsingular:10 vu:1 f0:5 f1:5 f2:4 f3:2 e2πiτ:1 stated:2 states:7 numbers:35 hyperplane:4 sense:1 information:2 goal:1 rather:3 orthogonal:5 enlarge:1 maps:16 e2k:1 simplicity:1 fr:1 algebra:2 fx:2 derived:2 treatments:1 plane:5 fi:1 evaluations:1 twisting:1 specifying:2 parameterizes:1 fα:3 fγ:2 paper:6 through:4 htop:3 existence:1 picard:20 systems:1 sheaves:1 deformation:6 motivated:1 yn:8 finitedimensional:1 yq:1 easily:6 behrend:2 always:1 presented:3 2z:1 inequality:1 2l:13 found:5 2n:3 2h:23 2k:2 weight:22 idea:1 quantum:4 dominates:1 since:21 induces:1 denotes:5 ramified:2 hilb:2 issue:2 occurs:1 fiber:12 localization:1 2h2:1 pub:1 base:4 dolgachev:2 definition:5 pairs:4 modularity:4 sextic:1 consequence:5 3a21:1 integrand:2 relate:1 number:19 preservation:1 least:3 differ:1 perturbation:3 introduction:2 construct:5 identity:7 calculations:13 scheme:3 exponents:1 holomorphic:12 statement:5 part:4 polarized:21 determines:7 fuchs:1 double:9 stu:4 determined:20 lie:4 constructions:1 depending:1 hyperplanes:3 h22:1 k3:110 k2:6 k1:4 jacobian:1 play:2 coincides:1 countable:1 exp:2 h2j:1 usual:4 physics:2 lying:2 thomas:3 2g:5 relation:9 find:2 dividing:2 e10:2 assertion:2 generators:1 factor:2 circle:1 his:1 triangle:1 notation:9 express:1 lattices:7 arxiv:3 doubled:1 set:18 bruinier:6 calabi:9 see:9 close:1 theoretic:3 108q:1 pisa:1 smallest:2 subscript:1 conditions:3 complement:2 vanishing:3 both:14 prescription:1 kirwan:1 connection:1 symplectic:3 context:1 tangent:2 arbitrarily:1 point:10 corresponds:2 2i1:1 dimensional:12 simply:3 bξ:4 described:1 transformations:2 discriminant:7 varieties:2 due:1 empty:3 generating:6 gal:2 recalled:1 p2:4 p3:7 p1:18 look:1 p4:2 p5:1 while:9 behavior:1 ǫt:1 unitary:1 triple:2 vanish:7 grant:1 modification:2 products:2 shah:2 composition:3 higher:4 used:6 subvariety:1 uses:1 stack:1 recent:2 older:1 underlies:1 analysis:1 λg:4 alternative:1 cut:1 liu:1 informal:1 shortcut:1 beauville:1 theorem:39 solvable:4 transformation:10 euler:4 fibers:22 stein:1 showing:1 integer:9 formal:5 follows:3 translates:1 separately:1 yields:12 mcgraw:1 mathematical:3 methods:1 spring:1 some:1 back:4 understood:3 examples:2 mirror:20 integration:2 proc:1 agreement:2 step:2 weil:1 relating:3 hilbert:2 27a2:1 biso:4 into:2 integral:7 nsf:2 locus:4 primarily:1 proportional:1 nst:1 span:2 riegler:2 question:1 specifically:1 forward:3 sections:2 gauss:1 line:11 considerable:1 2πi:2 characteristic:1 up:2 us:2 constant:1 defined:26 cover:6 congruence:1 single:2 defines:1 ks:7 fixing:2 application:3 points:4 department:2 arithmetic:2 givental:3 elements:8 calculating:5 polynomials:1 generated:2 allowing:1 sides:4 structure:5 huybrechts:1 implies:4 vice:1 graber:1 required:5 resolving:1 weights:1 everywhere:1 once:1 katz:3 informally:1 results:12 proposition:9 kc1:2 ga:1 edu:2 intricate:1 contributions:6 issues:1 compact:1 leung:5 stable:9 g4:4 g1:2 g0:2 ed2:2 ed1:2 configurations:1 folds:3 fold:4 imply:2 zw:1 index:3 invertible:2 giving:1 indian:1 poles:1 3l:1 lee:4 degree:55 respectively:10 fiberwise:5 morphisms:1 great:1 mations:1 larger:2 resulting:1 bd2:1 summation:1 apply:11 resolutions:1 use:5 usa:2 quadrics:1 few:4 trivializing:1 themselves:1 simpler:1 pencil:18 formally:2 recount:1 iii:7 fantechi:2 isomorphism:7 averaged:1 ρm:6 ρl:1 infinitesimal:1 obvious:1 codimension:1 proof:26 calculation:13 zinger:1 loci:1 high:3 effectively:1 dominant:2 kudla:3 holds:2 instead:5 sin:2 grushevsky:1 1if:1 singular:4 specifications:1 collection:1 multiplication:1 realized:1 chasing:1 lines:1 correspond:4 element:7 lβ:7 lξ:8 divided:1 produced:1 hypersurface:7 perfect:3 orbifold:1 la:2 ln:3 lk:5 lh:3 li:4 lu:1 degrees:16 ls:1 dq:1 lz:4 serre:1 cusp:8 straten:1 greater:1 practice:1 mention:1 university:2 sufficiently:5 l2:2 constraints:3 subset:2 related:2 elementary:3 eisenstein:1 relates:1 special:3 category:1 matrix:2 res:1 rev:1 obstructions:3 geom:6 suffices:3 math:25 completely:4 york:1 geometry:8 ahler:7 isotropic:1 hence:12 metaplectic:2 bijection:1 precisely:5 braces:1 unknown:1 system:9 unspecified:1 πr:1 their:1 final:1 klemm:7 exactly:4 l2ξ:2 automorphic:5 distinguished:2 nonprojective:1 symmetries:1 cohen:6 curves:20 λ2g:2 need:3 viewed:8 prohibits:1 studying:4 polarization:14 lectures:1 unless:1 connected:9 representation:9 intrinsic:1 class:36 constrain:1 fact:3 parkes:2 supported:1 12u:1 trivial:9 scuola:1 specified:2 jan:1 lemma:14 bases:2 local:15 pandharipande:33 differential:5 grassmannians:1 contain:3 cycles:2 view:4 moduli:32 computed:2 fibered:1 halving:1 differentials:1 finiteness:4 et2:18 et1:17 nuclear:1 dmα:1 written:3 identification:2 closed:2 invariant:9 boundary:1 hirr:4 meromorphic:1 mod0:2 hypothesis:2 key:2 amer:1 ker:2 taking:1 equal:2 admit:1 otherwise:2 ck:3 cl:1 cohomology:10 respect:11 ct:2 geometries:1 yau:20 copies:3 certain:1 define:9 pic:28 corresponding:4 commutes:1 sufficient:1 subspace:6 last:1 c1:11 c0:1 subsets:1 will:13 monodromy:3 revisited:1 vi:2 thus:1 surface:18 vr:1 against:3 dual:2 compactified:1 generic:11 finite:11 φm:4 ball:1 infinity:2 cubic:1 upon:4 v0:4 v1:2 v2:2 v3:1 expand:1 genus:28 off:3 well:5 sets:1 arising:2 subgroup:5 less:1 obtain:15 quartics:14 adv:1 mathematically:1 lattice:21 extends:1 match:3 ample:11 vγ:8 vδ:1 immediately:1 intersection:28 arbarello:1 vξ:11 loss:1 genericity:1 ad1:1 alternatively:1 δh:2 conrad:1 because:3 classical:20 sequence:4 choosing:1 nonempty:2 overlap:1 cτ:2 does:4 assuming:1 intersections:7 expansion:2 tautological:1 injective:1 quotients:2 about:4 b359:1 compatibly:1 dependence:2 carries:1 important:3 homogeneous:3 h2:16 h0:2 h1:2 functional:2 parameterizing:1 square:6 been:3 van:1 additional:1 pairing:3 sarnak:1 restricts:1 quadratic:1 notices:1 naturally:1 function:11 revised:1 triangular:2 but:1 construction:4 partially:2 count:2 made:1 elliptically:1 packard:1 gravitational:1 smooth:2 below:5 dms:1 interplay:1 intersects:1 int:1 universal:1 contribute:1 denote:23 our:6 identities:1 functions:11 conifold:1 variety:4 virtual:7 disjoint:1 other:4 theor:1 bundle:24 auxiliary:1 ranks:5 resolution:3 factors:3 rule:1 original:3 |
0705.1655.txt |@word sci:4 consider:2 skip:1 people:1 results:4 infinitesimally:1 computation:1 edu:1 markovi:3 disk:3 contributions:1 gi:2 compact:3 equivalence:6 kα:2 infinitesimally:3 norm:1 corollary:5 every:4 condition:5 riemann:4 solves:1 suffices:1 convenience:1 reich:14 anal:3 direct:1 zero:2 chen:3 further:1 dissertation:1 what:1 appear:1 giving:2 section:4 expressed:1 version:3 above:6 kyoto:1 new:1 consisting:1 coefficient:22 respectively:3 component:1 here:2 china:5 mes:6 z1:2 z2:2 z3:2 obtained:1 remark:2 shift:1 contradiction:1 domains:3 york:1 uniquely:14 useful:1 classification:1 beijing:1 univ:2 unit:4 use:1 takes:1 would:2 prove:3 sake:1 positive:5 contains:18 negative:2 ψn:7 therefore:3 indiana:1 more:8 normalized:1 excellent:1 known:1 cases:1 valued:1 word:2 science:1 equation:2 work:1 infinitesimal:6 values:2 following:7 proof:17 claim:2 dedicated:1 suggestions:1 νe:1 extremality:3 evidently:1 yang:1 denotations:1 end:1 discussion:1 get:3 maps:1 criterion:1 answer:4 teichm:20 simplicity:2 mat:1 may:1 fz:4 after:1 mapping:9 ball:1 applications:2 plane:1 constants:1 short:1 natural:3 imply:2 grant:1 element:1 extremal:92 dilatation:2 so:2 fan:2 order:1 restriction:5 holds:1 expects:1 paper:6 banach:2 existence:6 satisfies:4 still:1 its:5 before:1 chosen:1 interesting:2 fix:1 actually:2 forms:1 choose:1 bers:1 mail:1 main:3 might:1 correspondence:1 non:2 lipman:1 yn:7 introduce:2 bound:1 hamilton:2 tsinghua:2 now:2 easily:2 equality:1 always:3 university:1 inequality:8 l1:1 side:1 subset:2 domain:2 related:1 extended:1 measure:5 our:3 special:2 shown:1 space:10 furthermore:3 since:3 induces:1 research:1 re:9 dxdy:13 denoted:2 ref:1 math:9 shows:2 foundation:2 admits:3 collection:1 definition:2 phrases:1 similarly:2 gratitude:1 hence:4 onto:2 βi:17 first:1 xn:7 quasiconformal:11 primary:1 restrict:1 done:1 construct:1 precisely:1 open:4 given:11 hyperbolic:2 introduction:1 least:3 their:2 gives:3 holomorphic:1 completed:2 proving:1 jordan:4 believe:1 than:6 coefficients:24 target:1 roles:1 namely:3 determined:1 contrary:1 generality:1 ann:2 affirmative:1 say:3 need:3 any:13 mappings:7 depending:1 lim:13 latter:1 sciences:1 generalized:1 modulus:24 play:1 unless:1 simplify:1 satisfying:1 connected:8 but:1 pair:1 class:3 differentials:2 considered:1 professor:1 definitely:1 fact:1 particularly:1 show:4 supported:1 spaces:2 relation:1 carefully:1 find:3 fenn:2 completes:1 jan:1 lemma:24 only:5 explicitly:1 achieve:1 continuity:1 do:1 his:3 meanwhile:1 express:1 joint:1 ϕn:34 valuable:1 words:2 boundary:4 secondary:1 strebel:2 arxiv:1 method:2 qc:1 qi:1 meromorphic:1 requirement:1 set:14 ser:2 exists:15 national:2 j1:39 j2:2 depends:1 result:2 subject:1 surfaces:3 said:1 inequalities:2 fatou:2 µi:8 closed:1 between:2 µg:3 reading:1 conditions:4 counterexample:3 variability:1 notice:4 recently:3 points:2 however:2 jn:7 ji:47 key:1 restrictions:1 essentially:1 many:8 taking:1 edgar:1 tangent:1 otherwise:1 arbitrarily:1 among:1 cn:1 point:5 simple:1 each:1 infinitely:1 polynomial:1 moreover:2 throughout:1 cv:1 pr:1 pp:1 addition:2 three:2 defined:2 yao:9 abstract:1 referee:1 sufficient:1 nonconstant:10 denote:10 present:2 case:5 while:1 suppose:16 conformal:1 almost:12 triply:1 thus:9 disjoint:2 itself:1 id:3 author:3 perhaps:1 same:3 complex:4 runge:1 proved:2 subdomain:1 φn:3 independent:1 used:2 see:3 earle:1 hand:2 purpose:1 lower:1 acknowledgement:2 krushkal:1 well:2 analysis:1 obviously:1 academic:1 without:1 components:3 sets:7 left:1 proposed:1 being:1 obtain:3 rest:2 thanks:1 uller:20 doctoral:1 lebesgue:2 infinitely:7 conclude:2 setting:2 theorem:30 gave:1 posed:2 admitting:5 know:1 press:1 unique:5 loss:1 necessary:1 like:1 follows:4 continue:1 essential:1 beltrami:63 mathematical:1 because:2 sequence:11 some:5 acad:2 specified:1 proofs:1 uniqueness:1 dense:2 comments:1 does:3 exposition:1 tends:1 considering:1 problems:1 equivalent:11 pose:2 properties:1 about:2 mutually:2 extensions:1 introduced:2 considerations:1 functional:1 due:2 coefficients:6 right:1 references:1 there:24 accordingly:1 quadratic:1 call:1 was:6 naturally:1 function:2 form:1 converse:2 forgetful:1 preparations:2 construction:9 delta:10 applying:3 evident:1 whether:3 up:1 us:1 limit:1 problem:9 similar:1 called:8 constant:26 int:3 certain:1 universal:5 combining:3 general:2 exist:1 inf:3 constructed:5 again:3 functions:1 no:10 mathematica:1 when:2 defined:2 coefficient:11 other:8 republic:1 details:1 papers:1 department:1 mathematics:3 concerning:1 elements:9 zhou:1 uniformly:1 important:1 implies:3 assume:2 basepoint:2 implied:1 virtue:3 |
0705.1657.txt |@word slope:1 partial:1 consider:3 sousa:2 magnetic:1 global:2 p20:1 four:2 scalar:26 commute:1 mp2:5 involved:1 gi:1 vev:1 preserves:3 inverse:1 kγ:1 charge:1 does:1 manifolds:3 th:15 under:4 kλ:4 include:7 4nh:2 kσ:1 case:8 g2:8 straightforward:2 ǫb:2 rise:11 differently:1 choice:6 nλσ:4 associated:1 parameter:1 matrices:1 arrange:1 treating:1 steeply:2 list:1 mp4:5 correct:2 leave:2 solved:1 convenience:1 vector:38 demonstrated:1 relics:1 indices:1 relation:3 hospitality:1 brax:1 jhep:5 extremizes:1 fµν:3 f21:5 consistent:7 sin2:4 b22:4 b21:4 ωab:2 imply:1 rz2:1 further:1 theories:2 even:1 index:6 giving:1 section:17 b628:1 d3:6 consistently:1 axial:2 version:4 celi:1 above:1 obvious:1 order:2 method:1 satisfy:5 full:2 den:1 bergh:1 trivedi:1 promising:1 component:3 here:4 behaviour:3 xλ:1 graviphoton:2 directions:6 σab:1 along:7 auxiliary:1 equations:2 appears:1 z2:2 institute:2 triholomorphic:1 study:2 studied:4 allows:2 suggests:1 superpotential:21 resulting:2 loop:1 real:1 formation:1 suitable:1 makes:1 composed:1 showing:1 useful:2 andrianopoli:3 extra:1 addressed:1 esole:3 total:1 research:1 linearly:2 use:4 proceed:2 gravitino:7 commun:1 remains:1 bx:1 contains:8 next:1 few:1 nucl:3 approach:2 call:1 therefore:1 taken:2 inλ:1 type:1 until:1 more:6 flat:8 pparc:1 permutations:1 rk1:2 rk2:2 rk3:1 px3:3 becomes:6 px1:1 px0:2 k0:3 curvature:1 ip2:1 derivation:1 appendix:2 rigid:10 observations:2 particular:3 known:11 cases:4 hold:1 must:10 rotational:1 ǫab:1 ρi:2 science:1 work:3 tuning:1 rλ:4 reviews:2 obstacle:1 values:2 mp:10 cam:2 freedom:4 following:4 making:2 spontaneous:1 example:2 impose:1 lσ:5 cosmological:1 give:11 calculation:2 ds2:1 sense:1 states:1 minimum:16 allowed:4 d65:1 fλσ:3 occur:5 gaugings:1 united:2 end:7 iz1:1 dilaton:2 discussion:1 means:6 orthogonality:1 write:2 how:12 nyi:2 instead:1 those:1 e2h:5 sin:25 d68:1 map:13 product:1 de:2 may:5 after:10 2g2:1 corrections:2 produce:1 fi:37 constants:6 changes:1 natural:1 effective:6 sp:3 explicit:1 su:8 cosmology:6 extremal:1 so:30 allow:5 ry2:1 lλ:9 ry1:1 six:1 indeed:1 over:2 fλ:3 satisfied:5 produced:2 gauged:4 paper:2 including:1 y1:1 kinetic:4 kibble:3 its:1 before:1 style:1 group:10 thank:2 kofman:1 maps:8 ln:3 interesting:1 coordinates:4 imn:2 hirano:1 complex:3 degrees:3 choose:6 mail:2 xyz:1 supersymmetry:17 generalised:1 them:1 gaugino:4 return:1 combination:1 binetruy:1 gauging:20 break:1 framework:1 walls:1 they:1 ξb2:1 rotation:7 now:3 discuss:1 zei:1 term:114 lies:3 always:3 2z:2 2e:2 magnitude:2 l2:2 isometries:6 each:5 found:3 2n:1 2h:1 2i:7 constraints:3 constructing:1 domain:1 disregarding:1 ei:1 eh:4 2nh:1 saclay:1 quaternionic:9 conventions:1 expect:1 supersymmetries:4 our:2 mapping:1 special:6 shown:4 matrix:5 space:3 rev:3 denotes:1 content:1 inflationary:8 settle:1 occurs:3 mλ:1 shows:1 foundation:1 8i:3 theory:60 differ:1 standard:1 complicated:3 van:5 axions:1 generate:7 e2:1 xuv:1 retained:4 chiral:3 angle:1 geometry:7 zagermann:1 could:3 transition:1 cosmic:8 ahler:19 iz2:1 δij:1 davis:2 bogomol:2 first:1 origin:1 major:1 there:4 vacua:1 symmetry:10 sloped:3 smaller:2 done:2 defects:1 reached:2 clarity:1 braces:1 size:2 compensator:3 given:5 needed:3 introduction:3 achieved:1 system:1 construct:9 herdeiro:1 their:4 perturbations:1 types:2 inflate:1 gives:13 holomorphic:2 stelle:2 relationship:1 b23:6 4b3:2 huv:1 part:4 suitability:1 believe:1 domains:1 than:3 iliopoulos:3 clarifying:1 sectors:3 was:19 require:1 second:4 limiting:1 matter:6 classes:1 were:5 f12:2 treated:1 ungauged:2 usefulness:1 symmetries:6 generality:1 sab:2 gently:1 generalization:1 unlikely:1 need:2 curved:3 turn:1 orders:1 contents:1 lie:2 dµ:2 fxy:1 zero:1 depending:1 gravity:1 mechanism:2 note:4 sciences:2 k1:5 potential:81 take:7 finding:1 unconstrained:1 linde:5 begin:2 towards:1 altered:1 submanifold:1 centre:2 breaking:1 most:3 position:1 phase:1 acknowledgements:1 class:3 hypermultiplet:6 consequences:1 considered:5 behaves:1 clear:1 barbieri:1 typeset:1 kq:1 kv:2 constrain:1 charged:3 physics:4 away:1 sector:11 hyper:4 show:6 grav:2 infn:1 supported:1 tures:1 appearing:2 rotating:1 ki:1 gauge:28 solutions:2 carefully:1 d7:6 analogue:1 find:3 completion:1 q0:1 slow:1 just:2 parameters:2 b113:1 state:1 topological:1 should:2 iei:1 ieh:2 only:13 circle:1 truncation:33 local:7 extremum:2 axion:1 abelian:6 move:3 get:5 alleviate:1 simplest:5 db:1 cannot:1 progress:1 combinations:1 during:2 aλ:2 freedman:1 runs:2 fields:13 arxiv:1 2b2:2 2b1:4 pλ1:4 imposed:1 semilocal:1 contain:1 qi:4 fixed:2 view:1 set:3 computed:4 exists:1 notational:1 sitter:2 notice:4 up:3 connections:2 depends:2 truncating:2 discussions:1 terms:39 burrage:2 subject:1 still:1 limit1:1 subsequent:1 review:4 supergravity:72 written:3 f20:3 between:3 invariant:3 previous:2 conditions:15 hence:1 ends:1 triplet:4 recently:2 parallels:1 do:1 extremized:1 analogues:1 however:7 killing:20 δj3:1 distinguish:1 rapidly:2 come:1 alters:1 topology:2 undetermined:1 both:8 σi:3 last:2 efolds:3 taking:1 density:1 relabel:1 vanishing:3 agree:1 chosen:2 connection:3 present:1 symplectic:3 embedding:2 contribution:1 expression:2 otherwise:1 minimises:1 generalisation:2 unclear:1 groups:1 conclude:1 simple:6 seems:1 corresponds:2 proeyen:4 dimensional:2 galileo:1 non:1 math:1 inflaton:5 respect:1 branes:1 considering:6 extrema:1 described:3 transformations:4 geometries:1 trajectory:3 px:1 locally:1 three:9 been:4 z1:2 reduction:9 describes:7 change:1 expected:1 pi:2 lx:1 define:1 direction:10 arises:1 supersymmetric:26 tµν:2 scalars:3 sufficient:3 formed:3 cos:13 ensuring:1 angles:5 derivative:1 lifting:2 general:2 spin:1 fayet:3 applied:2 p3:1 ǫa:4 p1:1 look:4 unlike:1 frozen:1 iξ1:2 will:7 momentum:4 shift:1 leaves:2 procedure:1 ix:4 vectors:10 vd:1 vf:1 coupled:4 iq:1 metric:2 damtp:2 thus:1 violating:1 vn:2 equal:1 ij:1 rij:4 il:1 dual:1 susy:2 orthogonal:1 vanish:3 superconformal:6 id:1 different:1 result:1 d15:1 containing:8 constrained:1 cea:1 generic:2 3z:4 make:1 iξ:1 admit:1 pλ2:3 pλ0:1 parts:2 quant:2 split:2 pauli:1 units:1 φi:4 nanopoulos:1 solution:1 pσ0:4 uncharged:2 european:1 status:1 independent:2 extended:2 see:1 i1:1 dasgupta:2 i3:1 trajectories:1 ri2:3 ri3:1 ri1:2 constraining:1 moment:18 waterfall:1 potentials:16 n22:1 invariance:5 tune:1 whereby:1 scenario:2 charges:5 spacetime:1 gφ0:1 parameterised:2 well:1 kallosh:8 analysis:2 without:1 thought:2 s21:1 components:4 entry:1 model:20 dh2:1 usual:1 isometry:6 kachru:2 world:1 manifold:19 kklmmt:1 being:1 hybrid:4 half:1 obtain:1 pλx:6 0wa:2 multiplet:12 k2:5 ψb1:2 ψb2:2 jcap:2 heuristic:1 vacuua:1 preprint:1 mix:2 point:3 had:1 except:2 iψ:1 add:1 setting:3 combine:1 lett:2 match:1 transformation:4 euler:6 gave:1 kingdom:2 loss:1 multiplets:5 couple:1 possible:9 galilei:1 rx1:1 inflation:40 vacuum:6 confined:1 using:2 unique:1 parameterisations:1 string:5 supergravities:1 minimised:1 necessary:2 like:2 follows:1 reduces:1 performing:2 separately:1 flux:1 bps:3 imposes:1 indication:1 either:5 arbitrary:2 kahler:1 nice:1 stationary:1 reduced:20 mathematical:2 because:3 truncated:5 some:4 truncates:1 b1:9 choosing:2 b3:10 unless:1 dvali:1 dimensions:1 lead:1 b476:1 shall:1 hodge:6 comments:1 esf:1 critical:1 decomposition:1 minimal:3 bogomolnyi:1 regain:1 ba:2 bb:1 selecting:1 equivalent:1 bi:7 bj:2 bk:1 broken:2 although:1 hsu:1 eiψ:2 super:1 properties:1 stage:1 would:4 extension:1 pλ:4 discussed:3 o:2 ensure:1 historically:1 west:1 2iφ:1 introduced:1 cambridge:2 presence:1 previously:1 into:7 within:1 rotations:1 down:2 rolling:1 holonomy:1 references:1 reducing:2 bosonic:1 rolls:2 prepotentials:1 hep:15 additional:2 comparing:1 support:1 initial:1 transform:1 long:1 start:4 restricts:1 ψi:1 way:8 f01:3 valley:5 sections:2 naturally:1 arise:1 complete:1 form:10 enough:2 leiden:1 brane:5 but:9 auria:2 construction:5 juv:1 true:1 coupling:2 ωx:1 made:3 compute:4 whether:4 wish:1 gravitational:1 maximum:2 us:5 theoretical:3 limit:11 uk:2 problem:2 display:1 aa:1 ac:2 ab:5 constant:15 b2:16 prepotential:4 defined:4 abstract:1 describe:1 resultant:1 urrestilla:1 b145:1 organised:1 corresponding:2 formalism:2 constructed:8 nh:6 achucarro:3 no:7 dressed:1 nc:4 when:6 vanishes:4 field:8 other:2 details:1 department:2 mathematics:2 rx3:2 rx2:1 nt:1 roll:1 nv:7 conclusion:2 mp5:1 picture:1 repeat:1 truncate:1 models:14 resembles:1 problems:2 cb2:2 ξi:6 a2:4 a9:1 embed:1 galicki:1 included:1 eventually:1 ξb:2 ξe:2 structure:7 building:2 kx:4 longer:4 ferrara:3 required:2 4s:4 original:2 lift:1 time:2 requires:11 strings:9 once:1 |
0705.1658.txt |@word represent:1 partial:1 maximum:1 results:1 leads:3 eds:1 gd:19 houches:1 c2:1 gn:5 centers:1 graph:3 tn:5 excluded:1 osterwalder:1 g2:8 straightforward:1 every:2 scoppola:2 condition:4 large:1 zn:2 estimates:2 sign:1 enclosed:1 rouen:1 rigorous:1 even:1 appear:1 section:2 intersect:1 values:1 acknowledgments:1 body:1 degree:3 les:1 separation:1 path:1 obtained:2 leaves:1 larger:1 spheres:3 sokol:1 rdk:1 quotient:1 diameter:1 useful:1 divide:1 use:1 would:1 positive:2 contains:1 france:1 therefore:1 known:1 foundations:1 cardinality:1 must:1 logarithm:1 mg:1 sphere:6 obvious:1 already:1 factorials:1 root:2 dn:6 dxn:4 dxk:1 sense:1 horizonte:1 end:1 discussion:1 di:12 write:2 ufmg:1 optimal:1 parameter:1 may:1 max:1 dx1:5 applications:1 value:1 short:2 sv:7 so:1 order:1 helv:1 over:2 course:1 paper:1 through:3 statistical:2 avenue:1 its:1 sλ:4 regions:1 le:1 thank:1 chosen:1 writing:1 better:1 degrees:1 systems:2 clusters:1 etienne:1 yi:4 non:1 yj:2 descendants:4 numerically:2 acta:1 multidimensional:1 february:1 inequality:2 universite:2 each:1 universit:1 constraints:2 subset:1 financial:1 series:3 hard:4 idea:1 precedes:1 our:3 shown:1 denotes:3 rd:1 formula:1 evaluation:1 math:3 benjamin:2 limλ:1 departamento:1 standard:1 atica:1 york:1 estimate:4 definition:2 keep:1 fugacity:1 hence:2 xj:4 xi:5 xn:10 rooted:1 number:3 precisely:1 xv:2 given:4 tor:1 dipartimento:1 saint:1 stora:1 ruelle:1 centered:1 x1:10 than:1 distance:1 determines:1 holland:1 showed:1 penrose:3 roberto:1 determined:1 insertion:1 generality:1 matem:1 say:1 substantial:1 manner:1 intersecting:1 convenient:1 converges:1 instance:1 edge:4 new:4 cnrs:1 shall:1 connected:2 letter:1 multiply:1 branching:1 partition:1 vertices:6 graphs:2 points:1 exp:1 sum:5 fact:1 show:1 dy1:2 find:1 d1:13 based:1 should:1 aldo:1 analytic:2 only:3 explicitly:1 factor:2 predecessor:4 get:4 de:4 trees:3 dyk:2 dv:2 du:1 arxiv:2 expansions:1 statist:1 fixed:1 bak:1 generations:1 set:6 computed:1 tree:5 bounds:2 see:3 radius:6 result:1 close:1 brazil:1 satisfying:1 xvi:1 xvj:1 between:1 approach:3 terms:2 however:1 comm:1 improve:2 improved:2 cayley:1 region:2 according:1 vergata:1 estimation:1 otherwise:1 ch:1 belo:1 point:1 simple:1 cd:4 dimensional:2 due:1 strategy:1 montecarlo:1 ph:2 families:2 concerning:1 formed:1 gas:5 observe:1 last:5 case:1 evaluated:2 trick:1 euclidean:1 fernandez:2 della:1 polymer:2 vd:15 equal:1 cluster:4 containing:1 italy:1 same:1 grand:1 finite:1 independent:1 used:1 laboratoire:1 numerical:1 upon:1 v2:2 edges:1 identity:3 recent:1 lower:1 well:1 without:1 roma:2 quantitative:1 model:1 usual:1 obtain:1 thanks:1 using:2 λn:4 preprint:1 conclude:1 except:1 improvement:2 lattice:1 setting:1 adi:1 scientifica:1 ricerca:1 possible:1 press:1 integer:2 unique:3 descendant:1 loss:1 ad1:1 follows:1 either:1 integrals:1 old:1 classical:5 choosing:1 dimensions:1 umr:1 power:2 expansion:4 pressure:6 bp:1 2n:3 about:1 dependence:1 o:1 simulation:1 mutually:1 obtaining:1 bound:4 phase:1 references:1 van:1 log:2 support:1 way:2 ed:1 function:1 north:1 regard:1 volume:5 matematica:1 convergence:4 cnpq:1 wτ:3 up:1 us:5 limit:1 called:3 mechanics:2 mathematiques:1 certain:1 abstract:2 contribute:1 denote:3 single:1 salem:1 corresponding:1 pfister:1 inc:1 compared:1 analyticity:4 no:1 amounts:1 other:1 hove:1 deviation:1 models:1 preceding:1 vertex:11 ising:1 implies:1 assume:1 benedetto:1 raphael:1 brydges:1 |
0705.1659.txt |@word limited:3 schlegel:2 similarity:3 ciao:1 magnetic:3 four:2 facilities:1 entropy:3 sfrs:1 fronts:1 under:3 updated:1 rise:1 every:1 terlevich:1 voit:15 logarithmically:1 chapel:1 grains:2 supports:1 solution:1 burke:1 bˆırzan:2 aeronautics:3 heckman:1 consistent:5 direct:1 approximation:1 surrounding:5 likely:3 birkinshaw:1 estimated:12 blue:4 disk:5 dept:2 ned:1 contributed:1 above:2 new:3 net:6 pandel:1 shocks:1 agreement:1 worrall:1 mem:8 wrapping:1 here:10 ionization:1 reported:4 interpret:2 obtained:13 study:2 enßlin:1 changes:1 diameter:2 prints:1 projection:1 highly:3 visible:7 wyse:1 deadtime:1 counts:2 total:14 unit:1 would:14 roychowdhury:2 therefore:9 type:1 tell:1 successful:1 conclusions:1 starburst:5 award:1 excellent:2 hole:2 aligned:2 supplemental:1 must:1 md:1 palomar:5 mm:2 setup:1 work:1 mi:2 suggestive:1 erg:17 temperatures:6 transparency:1 petersen:1 indicated:4 give:2 relativistic:1 indicates:3 david:4 absolute:2 end:4 provide:2 feature:10 how:3 hot:8 merritt:2 arcs:4 iue:8 after:4 kennicutt:3 lump:1 caldb:2 outbursts:1 spectrometer:1 summarize:1 law:3 lumb:1 third:1 complexity:2 maintain:1 green:2 theuns:1 order:5 triggering:2 interpretation:1 feedback:8 over:6 fit:6 imf:2 exhibits:1 better:4 hm:1 production:2 compelling:1 fig:7 fil:2 affected:1 band:28 they:3 structural:1 oxygen:1 brightness:19 reasonably:1 classified:1 lauer:3 each:19 feeds:1 calibrations:1 side:3 mean:11 telescope:14 mchardy:1 substantially:1 laboratory:1 postman:1 gradient:4 mason:3 re:2 ra:1 donahue:16 newly:2 outburst:1 enclosing:1 midpoint:1 little:1 free:3 formation:23 estimate:9 created:1 cosmic:3 filter:7 disturbed:1 ism:1 uses:2 onto:2 go3:1 stewart:1 already:1 features:11 sept:1 another:2 illustrate:1 service:1 similarly:1 approximately:4 needed:3 rates:8 observations:23 ranging:1 exposures:4 centered:6 binney:5 binned:5 somewhat:9 distance:1 zero:3 preparation:1 iron:1 pasp:2 bridge:2 ram:1 spectrum:20 ming:1 raw:1 seen:13 seem:1 ray:98 implemented:1 oriented:1 fitting:4 hatch:2 completed:1 circles:6 even:6 isophotes:1 though:2 replenished:2 object:2 extending:1 optimized:1 regular:1 gallagher:1 episode:1 observation:15 detectors:1 inferred:6 points:2 hintzen:7 rayleigh:1 radii:1 radio:49 bleeker:2 tremaine:2 northeast:1 quoted:1 explain:1 hri:1 rich:1 do:3 de:6 watson:1 christopher:1 supplies:1 dr:1 bar:32 wfpc2:5 bad:1 explanations:1 mergers:3 reference:2 nuv:1 generally:1 sensitivity:1 38m:4 unexpectedly:1 radius:5 result:3 best:6 subject:1 brazil:1 propulsion:1 away:1 µm:2 catalogue:1 µg:1 extend:3 rims:2 component:2 however:7 harvard:1 extent:1 clues:2 suggested:6 richstone:2 ohringer:1 uncertainty:3 heating:6 merging:1 f606w:3 contribution:4 com:1 timescale:2 perley:1 polynomial:1 broadening:2 basis:1 radiative:2 three:3 been:10 much:5 basic:1 expected:1 cardelli:4 deeper:3 suppress:1 chile:1 worked:1 applied:3 calcium:2 near:9 applies:1 stretching:1 donnelly:1 ii:15 conf:1 id:3 confirmed:4 suggest:6 make:3 complex:5 filtered:1 several:2 showing:1 independent:3 peaks:7 conversion:1 counterparts:2 hand:3 kim:1 reprojected:1 normalization:1 scenario:2 kawakami:1 left:11 stringent:1 facto:1 just:1 gravity:1 identify:1 farther:1 cˆot:1 scattering:1 yet:1 previous:1 visualization:1 had:2 5s:1 passive:1 mcnamara:9 board:1 east:12 plasma:8 usable:1 l81:1 possible:10 possibly:6 indicative:1 mushotzky:3 background:5 advanced:1 occurring:2 churazov:4 mayer:1 cooler:1 specific:1 detections:2 pesquisas:1 schwarz:1 sparse:1 night:1 soar:23 cooled:2 www:1 right:6 old:1 maxim:2 j2000:7 pinkney:2 separately:1 fov:1 speybroeck:1 proceeding:1 icm:12 cerro:1 core:11 rosat:1 pizzolato:2 hst:5 filaments:27 post:1 properties:1 haehnelt:2 o:6 slightly:1 presence:4 soi:4 obtaining:1 bound:1 lies:6 contrib:1 wan:1 carrasco:2 support:3 initial:1 approximate:6 inspected:1 pye:1 width:7 l135:1 fraction:1 resulted:1 ettori:1 was:50 lowest:1 medium:1 form:1 forming:1 soker:2 aperture:5 solar:3 cnpq:1 removed:3 true:1 inside:1 detectability:1 simplifying:1 trim:1 later:1 hotter:1 blueshifted:1 abstract:1 evidence:4 mediocre:1 distributions:1 archive:1 constructed:1 nh:2 vreux:1 nm:5 no:8 when:1 ne:3 composite:2 pasadena:2 test:1 jenkins:1 nw:10 optically:2 15s:1 models:7 variable:1 explosions:1 jones:6 regime:1 longer:1 assume:4 together:1 stripping:6 time:15 push:1 nuclei:5 l17:2 remarkable:1 focus:1 morphology:3 tenable:1 row:1 arcsec:5 certainly:1 depend:1 technique:2 passage:1 breeveld:1 finally:1 stabilizing:1 kaastra:5 southwest:1 encircle:1 advantage:1 minute:3 cool:18 clouds:1 presented:5 did:1 turns:1 standards:1 cooke:2 recall:1 overlaid:2 accumulation:1 prevent:1 heinz:1 l93:1 equipartition:2 spectrograph:2 oneto:1 spectral:5 appear:4 uniform:1 current:1 filled:1 subcluster:1 understanding:1 groups:1 alone:1 along:22 appears:3 box:1 jord:1 noticeable:1 canadian:2 institute:4 shift:2 simultaneous:1 suggestion:1 myers:2 studies:3 plotted:2 useful:1 griffiths:1 marked:1 tidal:1 emissionline:2 ariel:1 msu:4 scenarios:1 bender:1 theoretical:1 marginally:1 alastair:1 wvt:2 visual:1 emitting:2 1µm:2 clumps:1 labeled:2 following:1 making:1 figure:28 usno:1 council:1 allowed:1 spanning:2 rays:1 s3:1 discussion:2 range:3 positional:1 pure:3 map:18 may:26 fed:1 southern:3 fueled:1 produce:3 mag:5 revealed:5 natural:1 dynamical:4 beam:1 6th:1 sw:5 ghz:3 so:12 se:8 typical:5 wavelengths:2 schwartz:2 cutoff:1 years:7 pitch:1 peterson:6 supplemented:1 derive:1 monitor:5 acknowledge:1 interesting:3 vicinity:1 window:8 main:3 correspondence:3 non:1 matches:1 introduce:1 tucker:1 tails:1 now:4 twilight:2 discuss:8 nor:1 matched:2 fabian:10 instabilities:4 instability:1 entirely:1 photometry:1 weighted:1 significantly:2 ed:1 revised:1 gaussian:2 snapshots:1 astrophysical:4 year:4 wavelength:8 canada:1 space:6 coincidentally:1 increase:1 nominal:1 gaussians:1 ikebe:1 suggesting:4 shows:8 earlier:1 million:3 possibility:1 quite:3 rgs:3 california:4 language:1 arnaud:2 widths:1 transition:1 motion:7 uggen:6 massive:1 neglect:1 first:1 origin:2 symmetry:1 reveals:1 feige:1 maccagni:1 impossible:2 array:4 open:1 angular:4 size:4 given:1 paramo:1 structured:1 indicate:2 cooling:30 white:1 structures:17 national:5 continuous:1 astrophysics:1 than:24 population:1 wide:4 l48:1 were:23 johnstone:2 pre:1 sao:1 aller:1 correction:4 locations:5 say:1 allen:1 turner:1 any:3 wcs:2 lumps:1 connell:2 note:8 phillips:1 potential:1 take:1 interior:1 coincide:1 strengths:1 multiple:2 trace:1 opposite:1 correlation:1 arcsecond:1 spangler:2 importantly:1 latex:1 surprising:1 considered:1 average:2 adopt:1 implications:1 priedhorsky:1 quantity:1 show:6 discovered:1 bright:6 data:28 xmm:16 ratio:8 behind:1 lansing:2 analytic:1 only:6 going:1 black:6 helmholtz:1 carolina:1 viewpoint:1 routine:1 broadest:2 rafferty:2 cannot:3 nearly:2 distinctly:1 symmetrically:1 magorrian:2 median:1 yield:1 summary:3 fainter:2 boselli:1 kernel:1 bautz:2 relative:10 detect:3 extragalactic:1 label:1 outside:1 between:22 affecting:2 mekal:1 across:8 august:1 vertical:1 flow:5 jr:1 dome:1 clayton:1 condensing:1 jets:1 pixels:12 concentrated:1 many:1 region:10 contract:2 voronoi:1 xspec:1 comes:2 nearby:4 stream:2 color:5 pos:1 analyzed:3 werner:3 spans:1 constant:1 intracluster:1 lyman:5 capable:1 mark:2 nng:1 combined:3 crawford:6 direction:10 lanes:1 elvis:1 photon:1 observe:1 grillmair:1 diffuse:1 those:1 case:1 profiles:2 refractory:1 promising:1 salpeter:2 coolest:2 orientation:3 discrepancy:1 cluster:23 bias:1 ambient:1 technology:4 different:1 propagation:1 dithering:1 same:11 physical:2 events:4 visually:1 extended:5 closest:1 kelvin:1 companion:44 edges:1 sunyaev:1 roughly:1 severe:1 without:3 relief:1 coordinate:2 ccd:5 model:2 noao:2 being:1 telemetry:1 fueling:1 neon:1 rest:2 baldwin:2 guides:1 captured:1 reprocessed:1 hint:2 photons:2 seems:5 except:2 improvement:1 instrument:1 bigger:1 versa:1 grating:3 struck:1 skies:1 around:7 spectacular:1 psf:1 dark:1 inflation:1 grid:1 confined:1 world:1 correcting:1 identifying:1 velocities:7 kennea:1 either:5 always:1 reduced:2 respect:4 images:9 imager:3 provided:4 kaiser:4 confirm:3 cavity:1 finkbeiner:1 moon:1 depletion:1 provides:1 greyscale:1 markevitch:5 power:2 seconds:3 notable:1 mckernan:1 ratios:1 exciting:1 comparison:2 om:5 central:12 cavities:1 hicks:2 fringe:2 discussed:2 kawano:3 decelerated:1 iwasawa:1 redshift:6 image:60 ltsa:1 rising:1 determine:1 operator:1 accumulated:2 log:1 assumed:3 astrometric:3 there:10 shirey:1 dispersion:1 low:6 stars:5 assumes:1 complete:1 draine:2 mnras:18 proposal:1 datasets:1 arranged:1 embedded:1 flats:1 agree:1 nature:2 detailed:4 taylor:2 describe:1 deep:4 general:6 ar:1 file:1 av:2 gradients:1 beyond:4 personnel:1 field:15 nasa:3 spatial:7 stocke:2 carnegie:1 includes:3 pointings:2 a0:2 a2:1 flattened:2 peak:20 included:3 n2:1 l67:1 curve:2 mass:6 cores:2 resolution:12 original:3 arcminutes:1 outlining:1 since:12 pointing:4 lack:5 angstroms:1 higher:7 mccarthy:2 former:1 program:1 2masx:1 tf:1 mpc:2 very:8 swallows:1 induce:1 ultraviolet:3 fall:1 bubbles:5 difference:1 triangulate:1 large:14 small:7 fringing:2 appearance:2 pasj:1 past:3 rate:18 timescales:2 enhancement:1 further:6 gunn:2 what:2 sub:1 sun:4 version:1 contrast:1 revealing:1 full:4 iraf:2 hours:2 excess:5 strong:3 losses:1 amount:5 eilek:1 narrow:10 elongated:1 imaging:12 suddenly:1 marginal:1 uvw1:8 uvw2:8 decrement:1 extinction:21 iglesias:1 distinct:4 faint:1 comparing:1 taken:7 more:7 flat:3 m87:1 corrected:4 emission:91 instrumental:1 hardcastle:1 particular:1 known:3 mounted:2 middle:2 science:2 nine:1 evolved:1 dea:3 dec:3 history:1 compare:1 minimum:4 numbers:2 species:1 axis:4 information:5 goal:1 utilize:1 maps:5 gebhardt:3 galactic:9 derived:6 catalog:1 plane:7 short:3 interpolated:4 fallen:1 spectra:7 l59:1 september:1 developed:1 mazzotta:7 thermal:1 paper:1 through:10 filters:2 existence:1 itt:1 its:10 jacoby:1 detected:3 systems:6 van:1 might:4 alter:1 good:1 return:1 oke:2 yr:7 vecchia:2 bryan:1 hereafter:2 fully:1 level:1 2d:1 chandra:18 2a:1 radial:4 aligns:1 energy:1 yoshida:1 expect:1 inflated:1 event:1 surrounded:1 projected:6 research:5 dominated:1 hill:1 induced:2 occurs:1 foreground:1 asp:1 dressler:2 brightest:14 earliest:1 beginning:1 generate:1 definition:1 diffused:1 unresolved:1 omit:1 harris:3 prejudice:1 clump:5 exhibited:1 knots:8 major:1 lucia:1 upper:6 dithered:1 number:5 utilized:1 jernigan:1 fluxes:1 differ:1 temperature:18 jet:1 introduction:1 leading:1 smoother:1 least:7 passed:2 molecular:2 shifted:1 relationship:4 optical:32 bower:2 authors:1 hoeft:2 double:2 grey:3 levels:2 aas:1 toward:1 interactive:1 nulsen:9 7m:2 paerels:2 headings:1 lie:3 rochester:2 extracted:3 internal:10 cropper:1 added:1 populate:1 index:3 most:6 significant:2 comparisons:1 plaa:1 measured:4 mach:3 clear:1 broadened:3 km:25 part:2 electrons:3 clean:1 velocity:34 ruszkowski:3 physics:3 accuracies:1 detection:1 scattered:3 croston:2 relation:2 parameters:1 merger:1 fukazawa:1 conselice:1 3h:4 factor:7 circle:2 spurious:2 observatory:8 valuable:1 during:1 alexander:2 continuum:8 arxiv:2 blanton:1 wellman:2 common:3 activity:2 obscure:1 vink:1 set:2 art:1 ser:1 ferrarese:3 unpublished:1 astrometry:1 ara:1 see:5 arc:2 sec:4 close:5 contour:5 project:1 speed:2 currently:1 tamura:3 orbiting:1 conditions:1 pictured:1 available:3 dalla:2 creating:1 complementary:1 spectroscopic:6 distinguish:1 observer:1 both:15 last:3 barely:1 l23:1 sensitive:3 ferrigno:1 context:1 fordham:1 point:5 simple:1 smith:1 corresponds:5 coincidence:2 dimensional:1 header:1 observatories:3 throughout:1 adaptively:2 described:2 create:3 due:3 pc:1 reduction:1 pa:3 collected:1 slits:1 ph:1 pi:2 blob:2 photoionization:1 gas:54 gao:1 systematic:4 ılchez:1 uncertain:3 exponential:2 straight:1 empirical:1 dusty:3 while:5 behavior:1 depleted:1 resolved:5 rit:1 owen:1 itself:3 starlight:1 barnes:1 elevated:1 shorter:1 vikhlinin:3 interpolation:1 used:8 slyz:1 flows:2 zwicky:2 moving:8 purpose:1 recent:2 early:2 lower:10 task:2 database:1 seward:1 analysis:6 edge:7 consistency:1 distances:1 shape:2 using:10 patel:1 cut:1 majority:1 source:25 location:4 input:1 bin:3 march:1 couple:1 emanating:1 forman:6 like:1 apj:35 semi:1 shaped:2 follows:2 signal:2 pounds:1 shapes:1 flux:11 indication:1 popular:2 clipping:1 faber:2 often:1 begelman:3 some:6 back:2 trends:1 towards:4 sight:1 mirror:1 pronounced:1 scale:17 measurements:4 sasseen:1 per:12 l13:2 centroid:1 ponman:1 bg:1 run:1 tabor:4 obscures:1 use:3 br:6 plots:3 obscured:1 subtract:1 constraint:2 idl:2 seeing:5 computational:1 into:4 within:12 integral:1 appropriate:3 frames:1 uncertainties:1 interacted:3 extremely:1 long:11 balogh:2 files:1 filamentary:4 inches:2 don:1 line:77 gravitating:1 croton:3 ut:2 uv:19 up:9 us:5 cis:1 3c84:1 spectroscopy:3 houck:1 horner:1 similar:12 called:1 sometimes:1 associated:7 defined:5 stripped:2 redshifts:1 single:3 amounts:1 nas8:1 conselho:1 coded:1 department:1 explaining:1 draw:1 prepared:2 daly:1 sides:3 structure:13 agn:21 lane:4 correlated:1 implies:3 vice:1 age:7 required:3 holes:3 implied:1 correlates:1 presenting:1 once:2 code:1 partial:1 issued:1 results:5 existing:2 broader:3 edu:6 winds:1 contributions:1 centers:5 compact:1 young:2 contours:8 ingredient:1 vla:5 sarazin:13 electron:1 mathis:1 positions:7 noted:2 concluded:1 encloses:2 smaller:2 carter:1 acis:1 jump:1 imply:2 dynamics:2 reproduce:2 gavazzi:2 blobs:1 zhao:1 abell:4 cordova:1 3d:1 chose:1 respectively:2 jointly:1 identifications:2 objects:1 sink:1 separation:5 consideration:1 extreme:2 northern:1 larger:10 leaving:1 suggests:6 resulting:1 scales:2 scaled:4 apply:2 tools:1 confidence:1 kenneth:1 consumption:1 kowal:1 romanishin:5 next:2 few:1 camera:4 examination:1 started:1 stone:1 trail:1 normalized:1 account:1 diehl:3 recession:3 drops:1 performed:1 wedge:2 weaker:1 process:6 purposes:1 high:12 effectively:1 slit:30 assumptions:2 pulling:1 sought:1 springel:1 reynolds:2 varied:1 six:2 regions:7 located:3 elliptical:3 filament:14 circular:8 profile:1 filippenko:2 kormendy:2 1998b:2 1998a:2 light:9 counter:2 lines:15 correspond:3 element:1 mjy:2 bins:3 astronomical:1 insight:2 meter:2 interpreted:1 produced:1 including:7 mentioned:1 fwhm:5 galaxy:37 outer:1 chosen:2 masses:4 lj:1 estimating:1 lu:1 degrees:4 clusters:11 defining:1 pixel:16 archival:9 fourth:1 outlined:2 material:3 innermost:1 front:6 souza:1 rotation:2 university:3 identified:6 poole:1 kpc:15 frayer:2 crossing:1 references:1 constraints:4 verbunt:1 related:2 frequency:1 obsid:1 our:15 out:6 termination:1 adaptive:1 cause:2 integrated:1 red:5 shut:1 interactions:3 discontinuity:1 galaxies:17 completely:1 8s:1 shortest:1 hubble:4 interaction:16 could:5 frenk:2 times:3 counterpart:1 length:5 davis:2 receding:1 south:10 l36:1 l35:1 l33:1 l31:1 koekemoer:1 quality:1 mittaz:3 nebulae:1 statler:3 unknown:2 system:23 their:5 nebular:2 accretion:3 final:2 explanation:1 exactly:1 megan:1 argon:1 reflecting:1 manifestation:1 institution:1 observed:5 ipac:1 individual:4 providing:2 distinguished:1 exhibit:1 function:4 elongation:1 kennedy:1 gentle:1 kepler:1 unlikely:1 steepened:1 need:1 curved:4 constrained:2 apparently:1 clearly:2 illuminated:2 angle:9 triggered:1 agency:1 able:1 mid:1 mechanism:2 oliveira:1 gρ:1 provoked:1 detector:1 accuracy:1 omma:2 unless:1 centre:1 sfr:7 eight:1 parallactic:1 intrinsic:2 class:1 volume:1 subtracted:5 radiating:1 neighboring:1 oscillated:1 fact:1 ho:3 blueward:1 supported:1 rotating:6 12s:1 superimposed:1 subtracting:2 highest:1 based:6 nachrichten:1 sparks:2 virgo:1 arcseconds:6 fuel:1 employed:1 ngc1275:2 local:1 michigan:3 overall:1 joint:1 ones:1 wise:6 procedures:1 processes:2 luminosity:13 differential:1 tuned:1 navarro:1 hydrodynamic:2 fixed:1 view:3 catastrophic:1 frame:4 hα:76 turbulent:1 intensity:3 ar3:1 geometrically:1 enhanced:1 operated:3 luminous:3 cold:4 closer:2 interacting:1 nebula:17 xray:1 macros:1 state:4 masking:1 progress:1 neither:1 ends:1 opening:3 efficiency:2 hypothesis:1 key:1 kev:10 problem:1 interpretations:1 limits:1 taking:1 deficits:2 figures:3 passing:1 estimation:1 otherwise:1 relevant:1 co:3 cm:15 conclude:2 cd:5 cxc:1 table:4 uncorrected:1 second:3 addition:1 kahn:1 indicators:2 enlarging:1 define:3 arises:1 corresponding:6 sufficient:1 binning:1 behalf:1 present:10 multi:7 maccacaro:1 align:1 harder:1 value:6 will:4 fielding:1 discoveries:1 supply:3 transited:1 almost:1 thus:2 surface:19 greater:2 perhaps:1 juan:1 administration:3 northwest:1 infer:1 residing:1 http:2 fielded:1 v3:2 v5:1 dust:15 numbered:1 off:3 center:17 tessellation:1 l149:1 modeled:1 well:3 perseus:1 thought:1 redshifted:3 position:11 arising:1 kauffmann:4 ny:1 less:8 increasingly:2 obtain:2 sources:6 distant:1 predicts:1 sputtering:1 adu:1 preprint:1 tight:1 absorption:1 carilli:4 sky:16 nacional:1 nath:1 extends:2 divided:1 identical:1 sonic:1 putative:1 smithsonian:2 kellogg:1 five:2 knot:13 turbulence:1 loss:1 necessary:1 incompletely:1 sizes:1 bulge:1 hosts:2 become:1 works:1 page:1 because:5 growth:1 trudolyubov:1 broad:2 does:7 assuming:3 noise:1 slight:1 stellar:6 pressure:3 host:2 astronomische:1 although:1 offset:3 supermassive:1 about:25 actual:3 extension:2 column:2 universe:1 compatible:1 important:2 belsole:1 nucleus:18 l9:2 software:2 rectify:1 previously:1 washington:1 tiny:2 ridge:1 additional:4 vrtilek:1 smoothing:1 trigger:2 inner:3 synchrotron:2 north:13 insures:1 but:23 astro:1 gain:1 swp:1 hc:1 kraft:1 partially:1 made:4 longslit:1 whether:5 gravitational:1 smooth:2 placed:1 below:3 limit:10 ruling:1 distribution:3 bandpass:3 sanders:2 myr:2 lobes:8 babul:1 trailing:1 a1795:2 mutual:1 compared:1 calibration:7 portion:1 other:6 details:6 baum:2 conclusion:1 star:27 tides:1 metallicity:1 astronomy:4 exposure:7 starting:1 bcg:56 cavagnolo:2 perpendicularly:1 |
0705.1660.txt |@word secondly:1 writings:1 homomorphism:11 comparatively:1 dynamic:11 four:1 weizsacker:1 whose:2 under:3 ontological:4 summarizes:1 accardi:1 rise:2 every:8 experimentally:1 school:1 vector:3 commented:1 specially:2 consistent:6 direct:1 second:4 rigorous:2 expressive:2 eigenspaces:1 even:11 incompatible:3 specification:1 als:2 birkhoff:3 irrevocable:1 above:2 new:17 simultaneously:5 here:4 atoms:3 represented:7 path:3 interpret:4 obtained:1 substance:1 rigorously:2 study:8 approaches:2 karin:1 studi:1 changes:4 criticism:1 projection:9 explained:1 plenum:1 visible:1 achievable:2 circumvent:3 unit:1 would:21 chooses:1 leaks:1 call:1 therefore:3 type:8 tell:1 ascribe:3 odinger:28 berlin:3 must:18 me:4 springer:3 join:1 work:4 theories:7 concepts:2 my:3 eri:1 fraassen:40 give:8 organized:1 stressing:1 indicates:1 want:2 magnitudes:7 end:4 hoc:3 thing:1 provide:6 feature:8 how:8 significance:2 answer:5 symposium:2 ordinary:1 actuality:13 description:18 thermodynamic:1 after:4 predicated:1 diagram:1 summarize:1 law:5 attempt:1 acknowledged:2 hypotheses:1 complexity:1 maintain:1 decreasing:2 order:15 operations:5 restriction:1 interpretation:107 over:17 vary:1 satisfied:2 london:1 thesis:2 satisfies:1 before:1 fit:1 sheaf:11 better:1 hidden:12 schmidt:7 shear:2 maximal:3 eventually:1 them:2 effects:2 they:22 represents:5 each:21 mean:2 fairly:2 series:1 principles:2 restricted:2 crucial:1 content:4 hooker:1 rj:1 scopes:1 barrier:1 associate:1 free:1 standard:1 admits:3 assures:2 attributions:6 wanted:2 r1:1 starts:1 chiara:1 days:2 disturbed:1 onto:7 appreciable:1 already:5 features:7 primary:1 philosophical:3 another:2 orthocomplementation:2 dipartimento:1 needed:3 master:1 witnessing:1 postulate:8 john:1 collapse:7 tool:1 ıficas:1 western:1 begins:1 distance:2 showed:2 princeton:2 likely:1 preparation:2 matter:3 historical:1 enables:1 fashion:5 modern:6 spectrum:2 talking:1 emphasizing:1 seen:4 seem:2 seek:1 relatively:2 affairs:5 latter:3 responsible:1 isolated:2 2006a:7 forces:1 2006b:4 broglie:1 shall:1 object:1 letter:1 acknowledgements:1 observation:6 dom:1 inferred:1 definitely:1 principle:5 sum:4 came:1 dover:1 random:2 implying:1 attempts:1 partially:2 quoted:4 spite:4 situations:1 explain:4 topological:11 summarizing:1 adequate:1 continuity:1 do:16 mixture:2 di:2 de:15 preferred:12 criticized:1 despite:1 kochen:17 reference:1 depends:2 decided:3 projections:2 w1:3 w0:4 discussions:1 subject:4 said:2 tensor:1 pasted:1 away:2 yet:1 symmetric:1 conceptual:2 approach:5 terms:38 wb:2 wa:10 nature:3 confusion:1 restricting:1 however:16 wi:12 extent:1 faced:2 received:2 uncertainty:3 against:1 und:1 rigourously:1 logic:21 distinction:11 contribution:2 argue:1 asked:2 zalta:2 appeared:2 character:15 directions:1 written:1 speak:1 conference:1 commutative:1 basis:8 union:2 three:2 been:12 spread:1 interest:2 basic:1 algebras:4 formalized:2 location:1 families:1 quantities:5 locations:1 bohmian:8 applied:2 formalization:1 transformation:1 aim:2 applies:1 property:20 leaves:1 characterizing:1 ii:2 disjoint:3 interacts:1 itamar:1 containing:1 perform:1 things:4 linked:1 complex:1 quant:9 mixtures:3 avoids:1 evolve:1 numerical:2 differing:1 hand:8 possessed:5 academic:2 quantitative:1 possesses:4 left:2 unified:1 departed:2 just:4 subsheaf:1 newton:2 assigned:5 proposes:3 identify:1 human:1 yes:1 eigenstates:1 previous:4 visualization:1 poses:1 regarded:4 had:7 emphasis:5 belongs:1 easy:1 possible:41 possibly:3 unique:3 contradict:1 2007b:2 2007a:2 calculus:1 www:1 right:2 old:3 people:1 butterfield:2 somehow:1 born:27 election:3 escape:2 electromagnetic:2 quarks:1 imposes:1 properties:75 chapter:1 indeterministic:1 constituting:1 statements:1 presence:1 remarks:1 neumann:4 existed:1 support:3 class:2 accordingly:2 conservation:1 editor:1 way:14 music:1 was:29 form:5 piron:2 converse:2 ford:1 31st:1 illuminating:1 true:9 versions:2 maximum:1 dordrecht:3 jauch:2 fulfills:1 proved:6 item:1 abstract:1 proves:1 exist:2 distributions:2 constructed:1 nj:1 no:32 when:18 reality:7 unambiguously:1 role:1 papers:1 superfluous:1 unitarily:1 picture:4 intend:4 superposition:4 anpcyt:1 variable:1 ballentine:2 assume:2 proposed:8 together:6 time:16 moreover:1 observables:14 laws:3 concept:8 doctor:1 global:14 themes:1 manages:1 grateful:1 chair:1 certainly:2 clarification:1 show:3 passage:1 ıa:1 answered:2 finally:3 analogous:2 predicate:3 orthogonal:1 seemingly:2 choice:4 entries:3 exact:4 dim:3 solves:1 presented:4 did:3 irreducible:3 ecnicas:1 discrete:1 science:6 equation:4 says:4 occurrence:3 dealing:3 specker:9 spectral:16 appear:1 current:1 annals:1 reply:1 appeal:1 paradoxical:1 annalen:6 understanding:1 abandon:1 alone:2 appears:2 change:5 box:1 instituto:1 orthomodular:23 accomplishes:1 institute:1 studied:1 commonly:1 example:7 accomplished:1 simultaneous:1 usually:1 resonance:1 studies:2 genuinely:1 regardless:2 merely:2 prefer:1 compare:1 logical:5 contradictions:4 translational:1 projector:2 prove:3 sake:1 handles:3 encode:1 scope:5 associated:9 selects:1 theoretical:10 constrains:5 validity:1 cautious:1 valued:4 cat:3 reviews:1 values:35 following:24 making:2 arrive:1 claim:1 degenerate:1 attribute:1 arise:1 heard:1 performed:1 allowed:3 conversely:1 occur:2 verlag:2 rays:2 requirements:2 winter:2 discussion:4 spreads:1 fourth:1 speaks:1 map:6 product:5 quantenmechanik:3 may:40 max:1 spot:1 applications:1 pasting:1 revealed:1 compatibility:4 stress:2 natural:6 outline:1 whenever:1 maybe:2 explicit:1 introducing:2 so:22 representation:5 acausal:1 talk:2 exclusive:1 indeed:5 pointed:1 years:1 course:3 experiments:2 statistical:10 still:2 pointer:1 tendency:1 ronde:11 thank:1 acknowledge:1 interesting:1 modalities:14 forms:1 τw:1 main:9 happened:1 correspondence:1 non:14 thereby:1 processes:4 introduce:1 half:2 now:11 discuss:4 maintaining:1 term:4 name:1 january:1 establishing:1 possibilities:10 realistic:3 entirely:3 cliffs:1 realism:1 el:5 arbitrariness:1 ed:4 manifests:1 avoided:2 eq:1 shown:5 space:32 furthermore:1 interference:1 collisions:1 investigation:1 correct:5 shows:2 earlier:1 theory:42 variant:10 possibility:39 quite:5 homeomorphism:1 1999b:2 forbids:1 unwin:1 derivation:1 language:3 qm:1 transition:6 british:1 motion:3 turn:5 flanders:1 place:4 think:2 first:14 origin:2 striking:2 variables:11 specifically:1 directly:1 impossible:3 open:5 george:1 given:30 necessarily:2 1u:1 structured:1 response:1 draft:1 structures:1 speaking:1 gives:10 correlations:2 continuous:3 representing:1 than:7 unfortunately:1 require:1 were:5 outcome:7 pre:1 topics:1 argument:1 generalization:1 ant:1 say:15 allen:1 recover:2 any:9 subsystems:2 ideas:8 note:1 sciences:2 ideal:1 take:6 objective:8 coincide:3 sure:1 investigations:1 correlation:5 algebraic:5 pair:2 precludes:2 pages:1 forever:2 especially:1 considered:7 later:8 sigma:2 quantity:6 precise:3 determinate:6 contemporary:6 supposition:1 spaces:4 imagined:1 dice:2 behind:1 only:33 explicitly:3 enriched:3 1995b:1 get:1 designated:2 cannot:14 prentice:1 regarding:7 resource:1 physicists:2 though:5 mapped:2 uncover:1 discussing:2 reveals:1 physically:2 bounds:1 relative:2 namely:4 points:1 satisfying:2 eigenfunctions:1 ways:4 review:4 definite:17 justifies:1 outside:3 between:40 geometric:1 reading:5 notice:3 concentrate:2 article:3 come:2 σi:2 vub:1 many:5 pertain:5 according:2 dated:1 expression:2 comes:2 among:4 jammer:5 characterization:6 continuation:2 maintained:4 grants:1 assertions:1 liberal:1 considers:1 considering:2 wien:1 formed:1 photon:1 observe:1 careful:1 spirit:1 those:9 case:23 myself:2 conception:2 photographic:1 chap:1 situation:5 region:1 kolmogorovian:4 endowed:2 agnostic:2 middle:3 sheaves:1 different:21 verified:1 april:1 commuting:2 same:15 data:2 attributing:3 arguments:1 physical:46 events:7 status:1 extended:2 assigns:4 singapore:1 maeda:4 modes:1 roughly:1 without:5 solve:1 very:6 model:3 dimension:1 summer:1 dickson:10 being:3 generally:1 topos:1 contextuality:6 flavor:1 thinking:1 seems:2 interested:1 treatment:1 empiricist:2 espagnat:2 momentum:1 real:9 aspects:4 eigenvalue:3 rules:2 early:5 world:10 accepted:2 decomposes:1 pitowsky:1 acquainted:1 particle:4 facing:1 always:9 recalls:1 inter:1 reidel:1 deduce:1 specified:2 complementarity:2 thinks:1 nonzero:1 provided:3 conservative:1 critical:1 decomposition:9 provides:6 refer:9 measuring:2 scientific:3 power:2 modality:11 equivalent:2 found:3 standpoint:1 refers:3 central:5 theorems:9 discussed:3 meaning:6 mutually:2 cambridge:7 inclusion:3 communication:1 image:4 references:1 determine:1 einstein:4 operator:11 her:1 assumed:2 there:43 italia:1 decisive:1 intends:1 complete:10 newtonian:2 regard:1 philosophers:1 extend:1 applying:2 embedded:3 stanford:5 organize:1 detailed:2 ac:1 ab:1 ad:3 ai:9 certain:8 ak:2 aj:5 am:1 general:9 formulation:2 again:2 sublattice:9 reduct:1 field:4 subdirect:1 mathematics:3 briefly:3 separate:1 contextually:1 includes:1 important:10 nucleus:2 massachusetts:1 delineate:1 enrichment:1 impossibility:1 bacciagaluppi:20 resembles:1 original:4 represent:5 semantic:1 consider:12 pointing:1 forbidden:1 lack:3 correo:1 scalar:1 commute:1 talks:1 denotes:2 reasoning:2 particles:3 referring:3 equivalence:4 th:2 stochastic:1 belonging:3 attribution:10 straightforward:1 far:2 puzzles:1 sons:1 fan:1 interpreting:5 fall:2 verh:1 difference:2 condition:5 leads:3 unlike:1 large:1 small:1 titled:1 healey:3 perspective:3 further:2 remarkably:1 canonical:1 what:23 sub:1 deeply:1 section:32 brief:3 version:7 attitudes:1 subspaces:6 scientists:1 full:2 christian:1 behaviour:1 concluding:1 ontario:1 november:1 equations:3 pict:1 allows:8 experience:1 published:1 via:10 family:11 suddenly:1 ask:1 establish:1 environment:1 takes:4 probabilities:20 charge:1 chaotic:1 archives:3 characteristics:1 taken:7 more:12 thrown:1 knows:1 thus:25 operators:7 constructs:2 emission:1 particular:12 known:9 foundations:14 evolves:1 recall:4 der:8 remain:2 del:1 learn:1 canonically:1 history:3 f1:2 f2:2 stated:3 states:41 collision:8 minimum:1 numbers:3 sense:9 information:4 needs:2 court:1 rather:5 ghirardi:2 enlarge:1 maps:1 buenos:2 reject:1 simplicity:2 intended:2 algebra:18 wiley:1 derived:1 develop:4 plank:1 short:2 spectra:1 specifying:1 fundamental:1 help:1 developed:3 soon:3 distortion:1 held:3 paper:10 through:5 existence:7 its:29 rapidly:1 actually:7 wrw:1 detected:2 strange:2 microscopic:1 systems:16 argentina:1 might:4 good:1 return:2 propose:1 framework:3 permissible:1 oxford:3 bounded:1 easily:2 gets:1 homomorphisms:4 characterizes:1 level:5 iff:2 inherent:1 referred:3 formulate:1 desirability:1 energy:2 hard:1 idea:9 deterministically:1 investigated:2 obtains:1 measurement:18 quantum:131 beyond:1 event:3 really:6 wondered:1 solved:2 since:5 research:3 acting:1 hill:1 occurs:4 benjamin:2 causally:1 pleasant:1 reason:1 members:2 put:4 beginning:2 generate:1 revolutionary:1 definition:1 pairs:1 terribly:1 consequence:5 assign:3 enlarges:1 probability:38 feel:1 relate:1 thereafter:1 number:2 construct:1 distributive:1 story:1 introduction:1 least:1 assumption:3 expand:1 statement:7 scheme:2 recovered:1 part:3 jordan:6 believe:2 convinced:2 separability:1 albeit:1 kind:8 determines:6 double:1 determined:4 contrary:3 supposed:1 interactive:1 motivation:3 beziehungen:1 conjugate:1 copenhagen:9 bohm:14 generalizes:1 zero:1 self:2 majority:1 recognizing:2 internal:1 build:1 added:6 singles:1 measures:1 most:6 aires:2 significant:3 nothing:4 probabilistic:9 deviations:1 clear:7 ks:20 electrons:1 physics:30 phenomenon:1 relation:18 fine:1 find:2 causality:1 assertion:2 unhappy:1 factor:1 his:18 founding:1 zurek:4 express:1 famous:3 closely:2 shared:1 during:2 preconditions:1 him:2 contextual:17 homeomorphically:1 arxiv:9 factorization:7 investigate:2 croatia:1 common:2 zur:2 apparatuses:1 satisfy:2 set:38 aspect:2 throwing:2 see:14 individual:4 sec:8 descriptions:3 conicet:2 close:1 forthcoming:1 probable:1 smallest:1 various:4 conditions:4 supersedes:1 pictured:1 interpretational:7 dalla:1 recently:1 complementary:7 initially:1 complement:2 attention:1 untouched:1 distinguish:2 both:9 last:2 annual:1 connection:2 became:3 context:10 whole:4 experimental:2 point:8 simple:1 acted:1 community:1 improper:2 simply:2 nacional:1 pp:1 described:4 perspectives:1 create:1 due:3 whom:1 reduction:1 describes:1 ph:9 pi:3 empty:1 addison:1 wheeler:4 gas:1 remark:4 kramers:2 fund:2 understand:2 func:4 demand:5 assigning:4 uncertain:2 look:1 expanded:1 empirical:2 eigenstate:5 while:1 replaced:2 behavior:2 guide:1 espacio:1 enriching:2 von:8 reads:3 itself:5 investigaciones:1 result:9 belong:1 read:4 discourse:12 emphasize:1 subalgebra:3 conflict:1 development:3 used:1 trivially:1 lie:1 assignment:3 moment:1 levels:6 purpose:3 necessity:3 brussels:2 recent:2 task:1 analysis:7 obviously:1 stating:2 comprise:1 presume:2 press:5 atomic:17 using:1 λj:7 alternative:3 letting:1 cut:1 kluwer:2 correcting:1 guaranteed:1 empirically:1 eager:1 rˆole:2 parents:1 describable:1 theorem:47 guarantees:1 remaining:3 march:1 lacking:1 isomorphisms:1 emergence:3 projects:1 formal:4 imposed:2 follows:4 separately:2 continue:1 mcgraw:1 essential:3 mathematical:15 pertaining:6 33rd:1 methods:1 fathers:1 some:13 back:3 pσ:1 examples:1 sight:2 delivered:1 gradually:1 measurements:6 dieks:38 jumps:2 agreement:1 bj:4 bk:2 propositional:3 hilbert:14 pβ:2 uffink:2 pα:2 entailed:1 tracing:2 weizs:2 modal:112 dubrovnik:2 into:13 within:6 primarily:1 presupposes:2 1999a:2 statistics:5 degli:1 question:14 long:1 borel:3 mks:9 forward:1 analyze:5 sections:8 rimini:2 himself:3 elsewhere:2 governs:2 great:3 link:1 repeatedly:1 atom:5 line:2 treats:1 rejection:1 characteristic:3 up:4 us:13 ur:4 similar:1 called:9 uber:2 ordered:2 interventions:1 defined:21 single:4 formalism:12 denying:1 defines:1 grw:1 paradox:1 uranium:1 priori:1 electrical:1 elements:8 problems:1 generated:4 allowing:1 structure:15 independently:1 correlated:1 implies:2 equivalently:1 presenting:1 international:3 requires:1 having:3 once:3 partial:4 results:3 existing:1 eds:8 proposition:13 ga:3 edu:3 go:9 issues:1 xxii:1 concerned:1 deterministic:3 uniqueness:2 excluded:1 include:4 sent:1 wave:25 electron:1 wishes:2 putting:1 matrices:2 positions:1 try:2 assignments:1 eigenvalues:4 noted:8 configurations:1 smaller:1 jump:1 biorthogonal:2 zu:1 dynamics:3 apparatus:7 giving:1 analogously:1 expressed:5 consistently:3 expresses:2 led:1 degree:3 respectively:3 leo:1 believed:1 objects:1 focused:1 slater:2 deduced:1 scienze:1 clarendon:1 technical:2 contradiction:1 spines:2 resulting:2 makes:3 casilla:1 consejo:1 falsity:1 apt:1 outcomes:5 boolean:44 apply:1 tools:3 causal:13 standing:1 use:5 ontology:1 superpositions:2 remains:8 cagliari:2 next:1 classically:1 doubt:1 themselves:1 formally:1 started:1 becomes:4 inclined:1 popper:1 sharply:1 iii:1 discontinuously:4 account:14 isomorphism:2 obvious:1 universe:3 meet:1 certainty:1 proof:2 plate:1 process:9 assumptions:1 bene:2 something:8 intelligible:1 six:1 instead:1 plato:3 blocks:1 philosophy:17 physik:9 realized:2 introduced:5 light:2 correspond:2 element:6 encyclopedia:2 allow:4 presuppose:1 holds:1 saturated:4 move:2 interpreted:12 lattices:3 mentioned:4 chosen:5 csco:1 willing:1 degrees:2 choose:1 inconsistencies:2 defining:1 weber:2 pure:6 orthodox:3 commitment:1 hands:1 worlds:3 dirac:7 university:11 identified:1 accompanies:1 astronom:1 universita:1 magnitude:4 conservatism:1 mode:2 truth:6 doing:1 staying:1 related:9 frequency:1 measure:4 our:22 special:3 out:9 matrix:5 lecture:1 umbrella:1 maintains:1 ısica:1 clarify:2 completely:3 surely:2 york:4 holism:1 subalgebras:2 acker:2 enz:1 interaction:3 determining:1 could:10 constituents:1 ltd:1 retain:1 uple:1 possessing:2 powerful:1 iafe:1 precisely:6 ordering:1 unknown:1 adjoint:2 system:59 relations:2 their:6 posets:1 completed:1 exactly:12 reflecting:1 july:1 microphysics:1 delimits:2 dynamical:16 distinguishes:3 submitted:3 visited:1 negatively:1 providing:1 w2:2 false:1 factorizations:2 need:4 1988b:2 1988a:3 constrained:1 apparently:1 clearly:5 able:7 heisenberg:29 unless:1 centre:1 collaboration:1 who:2 connected:1 device:1 intrinsic:1 why:6 deny:1 consequences:10 url:3 gather:1 face:1 mechanical:1 occasion:1 constrain:1 fact:15 supported:1 purely:1 definable:1 debate:1 principal:3 postulates:1 knowledge:6 should:4 hector:1 bases:1 postulated:2 isham:2 local:16 hall:1 meant:2 handle:2 means:9 beltrametti:1 joint:2 ones:2 words:3 quantifier:1 quantifies:1 areas:1 evolution:7 qt:1 ubacyt:1 differential:1 fixes:1 determinante:1 contain:1 fixed:2 pertains:1 ql:1 view:7 conform:1 requirement:2 constructing:1 exists:12 hβ:5 frame:5 hα:5 packet:2 edition:3 acquires:1 closer:3 interacting:1 vol:1 state:75 difficulties:3 closed:1 understood:1 stories:1 neither:1 publishers:3 wl:1 wj:2 configuration:1 distribution:4 observable:31 interpretations:45 instant:1 limits:2 taking:4 equal:3 fulfilled:1 etc:1 admit:3 ck:1 cj:4 adding:1 respect:9 kinematic:1 addition:4 trajectory:1 cient:1 reservations:1 proposal:6 define:10 describe:4 corresponding:9 valuations:6 moved:1 subspace:6 assert:1 fellow:1 present:12 subsets:4 contexts:4 semantical:1 appearance:2 value:52 will:14 determinism:2 aristotelian:2 almost:1 vi:4 vj:1 zeitschrift:4 respected:1 propensities:1 greater:2 perhaps:2 radiation:2 parts:1 pauli:4 φj:1 φk:2 difficult:2 http:4 complemented:1 conceived:1 upon:1 effect:2 identity:1 correspondent:1 schr:28 center:2 nevertheless:1 well:8 bohr:12 thought:4 utrecht:1 sets:5 position:6 usual:13 restore:1 less:1 accurate:1 das:1 obtain:1 underlying:1 predicts:1 macroscopic:2 density:7 absorption:1 supply:1 mathematically:1 lattice:24 ignorance:15 other:14 developments:1 propositions:34 five:2 know:6 burden:1 nor:2 belgium:1 immediately:1 intersection:2 necessary:1 like:4 lost:1 smets:2 become:2 preclude:1 because:7 classical:35 phenomena:3 algebraically:1 recommendation:1 proper:1 orthonormal:1 lead:1 sufficiently:1 demonstrates:1 avoid:3 overlap:1 does:9 assuming:1 demonstrated:1 limitations:1 obey:1 reaching:1 demonstration:1 journal:8 wesley:1 prohibited:2 although:2 paste:1 about:54 actual:36 extension:17 freedom:2 consciousness:1 recognized:2 compatible:19 recognizes:1 transitive:1 projectors:7 own:5 letters:2 h2:1 h1:1 clifton:3 functional:1 actualized:1 van:42 noticed:1 inner:1 function:20 building:1 but:39 hk:2 construction:2 contradictory:1 potentiality:5 bub:21 valuation:15 he:10 count:1 made:2 wise:1 evident:1 whether:9 wish:1 placed:1 limit:1 pl:6 demonstrate:1 problem:12 mechanics:91 recognize:2 meaningless:1 denote:1 sublattices:4 aristotle:1 pip:1 inc:1 variety:1 detail:1 virtual:1 book:2 details:1 conclusion:1 kinds:1 expressible:1 sustains:1 stay:2 chance:1 auxiliary:1 factors:1 rule:12 portion:1 |
0705.1661.txt |@word magnetic:1 comparatively:1 dynamic:17 four:2 consists:1 regularize:1 const:5 γv:1 γk:30 under:7 cm2:1 unrenormalized:2 govern:1 experimentally:1 logarithmically:5 encounter:5 ǫf:2 wegner:1 solution:9 indices:5 enhance:1 coordinate:2 consistent:5 direct:2 approximation:9 likely:1 qualitatively:8 implemented:2 even:22 established:1 new:16 increasing:2 coefficient:4 never:1 equals:1 here:25 atoms:3 represented:1 canet:1 logarithmic:13 obtained:3 study:3 settles:1 guide:1 fourier:2 changes:7 akf:2 appropriately:1 explained:2 replace:7 visible:3 total:4 9u:1 propagators:1 unit:2 derivatives:34 would:14 chooses:1 m4:1 call:3 therefore:42 m2:24 type:5 until:1 brings:2 naive:3 correspondingly:2 ward:4 hold:2 must:4 quartic:11 permits:3 work:3 mi:1 concepts:1 exceptions:1 cond:5 example:12 renormalization:22 give:1 relativistic:65 preserving:1 organized:2 involve:6 indicates:1 end:3 provide:1 travel:1 ultracold:2 how:9 nontrivial:6 answer:1 description:12 replacing:1 thermodynamic:6 after:5 diagram:1 summarize:1 law:1 meaningful:3 constants:6 attempt:1 effective:49 green:7 correlation:38 order:83 g11:5 interpretation:2 over:8 expects:10 affect:3 integrands:1 before:6 bervillier:1 fix:1 exhibits:4 destroyed:1 fig:3 persist:2 walet:1 maximal:3 them:2 affected:3 combination:12 break:1 repulsive:4 effects:20 they:12 structural:1 vidal:1 invariants:2 reasonably:1 reasonable:1 mean:15 macrophysics:1 combining:3 substantially:1 extract:3 driving:1 gradient:5 restricted:1 crucial:3 particles:8 re:2 gersdorff:1 reader:1 mλ:3 rk:22 numerical:4 linear:43 normalized:1 associate:3 free:6 standard:3 admits:1 particularities:1 tial:1 proportionality:3 estimate:2 r2:4 starts:1 incorporated:1 signature:1 corrections:11 generalizations:1 condensate:14 already:10 features:19 synonymous:1 restrict:2 nonperturbative:2 another:1 q02:25 dupuis:1 vojta:1 similarly:2 tor:1 dπ:1 eqs:7 approximately:3 needed:1 confirming:1 zeros:1 too:3 legs:1 kf2:1 lower:2 somewhat:2 distance:20 last:1 approximations:1 second:21 matter:2 classes:2 tion:2 enables:1 powers:5 minus:1 perturbative:3 sees:1 modern:1 spectrum:3 b486:1 seen:3 arbi:1 relatively:2 strength:11 gies:2 mermin:4 convenient:1 latter:1 though:4 vortices:1 extending:1 involving:14 phase:148 luttinger:6 constancy:1 observation:4 characterizes:3 partition:1 flow:125 vertices:6 accounted:2 principle:2 notion:3 probe:6 infrared:42 implying:5 attempts:1 gauge:2 solutions:6 subtle:3 d2:3 situations:1 summarizing:1 rich:1 constant:30 dn:1 do:10 di:3 dd:2 stop:2 dc:5 reversal:1 despite:3 dt:1 dr:5 ds:12 runs:3 contributes:4 4πs:1 greens:3 fields:21 δφa:1 δφb:2 reference:1 observes:7 depends:21 w4:1 w3:3 w2:8 w1:5 subject:1 c2s:9 exponent:12 away:5 symmetric:14 weichman:1 simplest:19 µd:1 approach:8 wf:8 terms:41 extend:6 modify:1 restricting:2 wk:1 however:27 extent:1 bose:4 topology:1 suggested:1 essentially:6 cou:1 distinction:1 contribution:8 argue:4 disappears:4 con:1 behaviors:1 presumably:3 polynomial:1 16u:1 basis:1 three:10 been:8 basic:2 expected:5 ann:1 quantities:11 rescalings:1 spin:2 castro:2 spontaneously:1 aim:1 euclidean:8 near:9 viii:9 applies:10 property:4 procedure:1 ix:5 spacelike:1 ir:11 iv:4 ii:7 im:1 ia:1 containing:1 perform:3 suggest:2 make:1 complex:14 split:1 dimensionless:26 several:6 grows:2 independent:11 bornholdt:1 trajectories:3 hand:10 normalization:3 suitable:7 spacetime:1 preceeding:1 quantitative:10 possesses:1 unified:7 just:1 attractor:1 disfavoring:1 identify:1 transforms:2 scattering:3 yet:1 previous:1 adding:3 enters:1 freire:1 infinitely:1 interprete:1 had:1 iσ:1 noether:1 rescaled:4 possible:12 background:6 judge:1 performing:1 steps:1 arbitrary:24 deal:1 successfully:1 φmn:2 eiqx:2 dense:25 everything:1 gapless:4 unstable:5 core:1 particular:18 φm1:1 properties:27 anomalous:24 o:40 nonvanishing:12 d67:1 automatically:2 bath:1 presence:20 rotations:4 bound:3 negative:6 down:1 pair:2 raises:1 sov:2 wλ:1 methods:1 c57:1 k12:2 rely:1 initial:12 iq0:1 accordingly:1 fraction:3 irrespective:1 was:1 lowest:4 form:17 heat:1 incorporation:1 encoded:2 true:1 absent:2 coset:1 supr:1 devices:1 fermi:2 b64:1 b69:1 sq0:13 covers:2 conserved:2 exist:4 physical:20 radically:1 no:32 whereas:11 nc:13 generally:1 vanishes:30 setting:5 role:18 philosophenweg:1 ns:2 nt:2 picture:10 a16:1 a10:1 truncate:2 models:43 ξr:11 variable:2 gets:2 faster:2 assume:3 dχ:1 dτ:1 governed:6 time:40 n1:6 quantity:4 restored:1 logarithms:1 concept:1 remarkable:1 global:4 leads:2 computation:12 3a3:1 primes:1 devoted:1 inverse:15 depend:17 λn1:1 quasi:4 monotonically:1 analogous:2 advantage:1 antiferromagnetism:1 frequencies:2 keeping:1 exact:7 solves:1 presented:1 turns:2 mb:2 discrete:4 settle:3 annihilates:1 upper:6 mn:1 findings:3 measurable:1 sign:2 tetradis:4 y3:2 g22:2 appear:6 shares:2 suspect:1 goes:1 shared:1 addi:1 understanding:2 address:4 laughlin:1 appears:4 change:9 shift:2 studied:4 domains:5 conveniently:1 problematic:1 additive:2 working:1 intensively:1 positive:8 quasiparticles:2 memory:1 introducing:3 apparent:1 validity:3 appendix:25 virtue:1 thouless:10 cases:2 fermionic:3 logarithm:1 parameterize:3 k02:2 c48:1 modified:6 values:35 believed:1 modifies:1 dxx:1 predict:1 expanding:5 arise:3 performed:4 allowed:4 rescaling:6 occur:3 s3:1 s2:9 discussion:10 s0:3 chemical:10 criterion:5 fourth:1 extensions:3 parameter:37 mat:5 information:1 may:62 max:1 applications:1 produce:1 drastic:1 grow:1 natural:1 dynamical:9 liquid:7 higgs:1 whenever:3 explicit:1 yielding:1 so:35 sm:3 definitions:1 typical:4 acts:4 indeed:18 mainly:3 feature:1 stability:1 course:4 statistical:1 omitting:1 differs:2 still:6 sλ:17 tending:1 derive:2 group:6 thank:1 interesting:6 vicinity:3 coordinates:3 constitutes:1 main:3 non:22 scaling:33 bogoliubov:1 now:20 discuss:10 nor:2 term:74 name:2 establishing:2 ters:1 goldstone:91 domain:2 square:1 ei:2 ef:2 conventions:2 wavelength:1 approximated:2 avoided:1 eq:85 shown:4 space:27 furthermore:4 cancels:2 increase:1 attracted:7 investigation:5 suggesting:1 formula:1 dominate:6 correct:3 shows:16 theory:14 possibility:3 quite:4 complicated:3 besides:4 care:1 transition:63 iterative:1 turn:4 massive:2 ture:1 neglect:3 first:14 origin:1 xk:2 xi:2 symmetry:71 omitted:2 variables:2 approximate:5 simplified:1 long:33 directly:5 carry:1 open:1 xt:20 size:16 1p:1 given:31 necessarily:3 theoretische:1 indicate:1 realization:1 gives:5 way:5 moscow:1 continuous:4 transverse:1 x2:7 absorbs:1 eliminated:1 x1:2 than:13 specify:2 wide:1 third:2 accordance:1 superfluid:2 protected:1 decompose:2 questionable:1 addressing:1 generality:3 correction:4 argument:2 generalization:2 crossover:15 recover:4 any:8 mapping:2 note:17 potential:27 take:12 destroy:1 coincide:2 wonder:2 specifying:1 begin:1 trace:3 opposite:2 price:1 formulae:1 contrasts:1 hugenholtz:1 surprising:1 considered:5 average:12 feynman:1 typically:8 laws:2 precise:7 show:5 notations:2 threshold:2 ground:1 slow:3 ratio:7 analytic:2 only:64 indepen:1 legendre:1 get:2 rept:1 a73:1 expectation:6 2mb:11 unimportant:2 cannot:4 boundary:4 differentiating:1 ssb:13 yield:5 summary:2 mapped:1 reveals:4 violated:1 relative:5 namely:4 ur:1 violates:5 points:30 αv:10 ways:1 enough:5 between:22 notice:2 suppresses:1 concentrate:4 jetp:3 suppressed:2 concentrated:2 circumference:2 kogut:1 many:10 region:7 according:10 σd:2 comes:3 continuation:3 lagrange:1 cancel:1 associated:19 fruitful:1 considering:1 tuning:1 oder:1 sachdev:1 b422:1 x2m:1 direction:11 b68:1 observe:10 external:11 6w:3 irrelevant:6 those:2 case:24 microphysical:1 promising:1 investigating:2 cq0:1 coupled:1 characteristics:1 good:2 pistolesi:2 different:17 etc:1 pay:1 same:14 shifts:1 arguments:5 propose:1 regime:99 extended:9 drives:2 driven:2 running:36 invariance:6 cr:2 modes:10 roughly:2 without:9 solve:3 components:13 very:17 model:44 dimension:43 manifold:1 being:3 when:1 differentiation:3 seems:4 except:7 improvement:1 interested:2 lett:12 overview:1 momentum:45 real:18 aspects:5 around:3 2u:1 read:2 sums:1 plings:1 vacuum:5 using:4 mod:2 detk:6 adams:1 particle:18 reduces:2 either:2 integrals:3 fully:1 multiplicative:1 inter:1 satisfactory:1 shortcoming:1 specified:2 nonzero:25 capability:1 dimensions:32 gapped:2 juttner:1 stops:15 critical:71 decomposition:1 moderate:2 restoring:1 refer:1 eiϑ:2 process:1 eiϕ:1 power:6 equivalent:2 broken:2 explicitely:2 refers:1 2n:5 comparison:3 central:1 ferromagnetic:1 acd:1 discussed:9 practical:2 obeys:12 act:2 sensitively:2 berges:3 outlook:2 cambridge:2 inclusion:2 numerically:3 dissipation:2 ηs:91 determine:1 einstein:2 conceptually:1 technically:2 hep:1 prepare:1 removing:1 strictly:1 there:11 strict:6 low:11 decisive:1 complete:2 powerlike:6 aµ:3 longer:5 minkowski:3 ωt:1 quantitatively:1 ωc:6 disordering:1 ωd:10 regimes:5 detailed:2 ab:5 certain:1 ak:4 describe:3 general:13 reliability:1 together:4 av:3 gradients:3 moves:1 λw1:1 again:9 field:42 wetterich:16 valid:8 spatial:1 massless:5 poor:1 requested:1 briefly:5 separate:1 vertex:5 includes:1 a1:7 a0:1 a3:13 important:16 bounded:1 a4:2 observables:2 included:2 a8:1 condensation:1 mass:5 starting:3 original:1 consider:10 concern:1 scalar:3 generalize:1 follow:2 zinn:1 preserves:1 tr:4 preserved:1 th:1 kξ:1 sound:10 1pi:2 amplitudes:1 straightforward:4 far:5 translations:1 induce:2 ultraviolet:6 difference:4 condition:4 hamiltonian:2 t2:1 applicable:1 large:48 small:53 employing:1 renormalized:27 zero:21 perspective:2 pass:1 further:4 canonical:2 what:2 nonlinear:9 diag:1 section:6 brief:1 4w2:1 version:1 contrast:14 full:3 loose:1 component:7 ranges:1 situation:13 directions:2 strong:9 equations:25 transformation:2 search:1 allows:3 experience:1 periodic:1 stiffness:1 published:1 action:54 specialize:1 via:1 extrapolations:1 marginal:1 vii:2 takes:4 contains:3 finally:4 comparing:2 nucl:4 taken:2 iteratively:1 minor:1 more:19 kˆ:3 operators:2 domination:2 varying:1 known:12 none:1 shielded:1 recall:5 equation:26 det:19 remain:3 scherrer:1 spontaneous:10 deg:1 compare:3 neglected:10 cation:1 minimum:12 numbers:1 sense:8 influenced:5 needs:2 polchinski:1 rather:13 breaking:14 enlarge:1 influences:2 3w2:2 simplicity:2 fs:2 derived:1 treatments:1 reflect:1 plane:1 response:2 short:3 birse:1 author:1 parameterized:1 interpolates:1 generic:1 sect:24 parameterizes:2 baier:1 soon:1 thermal:1 paper:17 y1:2 existence:4 kinetic:17 y2:2 excitations:8 its:11 rapidly:1 energies:2 boson:13 actually:6 absence:2 pend:1 microscopic:22 systems:25 skipped:1 universality:5 strinati:2 framework:2 oxford:1 speculate:1 easily:4 2v:5 2w:5 2p:4 trary:1 2s:7 always:21 level:3 2z:1 φm:5 2d:10 stopped:2 2a:3 radial:23 2m:33 universit:1 2i:1 characterized:12 2k:1 transforming:1 transform:2 weight:2 energy:5 hard:1 idea:1 bosonization:1 investigated:1 obtains:7 quantum:55 beyond:4 dominates:6 solved:1 since:36 induces:4 denotes:4 acting:1 dominated:11 induced:4 issue:9 occurs:9 b38:1 found:8 reason:1 definition:9 pairs:1 bring:1 persists:4 inbetween:1 exponentially:5 consequence:7 undergo:1 integrand:1 relate:3 number:18 fancy:1 smaller:4 done:3 neglects:1 guess:1 perturbation:2 temperature:14 introduction:2 leading:13 least:1 scheme:1 exponents:16 recovered:1 shifted:2 para:1 immediate:3 employ:3 part:7 b231:1 translation:2 traps:1 determines:2 dtn:1 determined:3 ǫm1:1 substantial:1 concentration:2 orders:1 lie:2 wilson:7 kˆ2:1 built:1 depending:7 lim:4 self:1 extracted:3 k1:5 k0:22 analogy:2 k4:1 mouhanna:1 play:8 towards:14 singles:1 measures:1 reach:2 most:4 extremely:3 deviations:2 kg:7 kf:25 clear:2 sometimes:1 cover:1 kl:4 electrons:2 reflections:1 exp:3 velocity:11 physics:27 sector:1 particularly:1 phenomenon:1 relation:6 3u:9 find:35 stepwise:1 occupation:2 impact:1 parameters:8 heavily:1 factor:1 circle:1 abelian:6 dominant:3 dependent:6 express:2 closely:1 combinations:3 during:1 sects:2 arxiv:2 investigate:6 common:2 approaching:1 set:8 δa1:3 plausible:2 see:10 bare:9 close:5 τc:7 uλ:1 smallest:1 various:1 conditions:2 missing:2 initially:3 attention:1 vanishing:11 δac:1 distinguish:1 remaining:1 both:22 prospects:1 improved:1 sensitive:1 context:3 whole:1 finds:28 experimental:9 arbitrarily:1 nonrelativistic:6 simple:37 asymptotically:8 corresponds:16 dimensional:25 simply:9 described:14 transformations:7 tomonaga:6 px:1 due:22 reduction:1 describes:13 galilei:14 anisotropic:1 z3:2 interparticle:2 gas:6 precision:1 understand:1 systematic:1 houghton:1 gab:2 p2:1 k2:11 replaces:2 look:3 exponential:1 evaluated:6 while:34 replaced:6 behavior:71 litim:2 couplings:35 loop:3 sizeable:2 reads:9 vanish:14 lengthy:1 anymore:3 emphasize:6 modification:1 higher:7 used:3 sym:1 uses:1 purpose:2 robust:4 subleading:3 task:1 nozi:1 obviously:1 consistency:1 stating:1 λs:3 distances:6 λq:1 λw:15 λc:4 shape:2 questions:1 λd:1 λk:7 λn:1 tables:1 conclusions:3 source:2 internal:3 location:5 theorem:5 relevance:1 heidelberg:2 loss:3 evaluate:4 matters:5 appendices:1 dq0:9 diehl:3 formal:1 scaled:1 modifications:2 follows:6 collect:1 continue:2 yields:23 sketch:1 often:3 some:11 b4:1 understood:2 added:2 δbd:1 scale:42 integration:16 prop:1 b605:2 eliminate:1 tends:2 prog:1 minimal:3 bf:1 agreement:1 br:2 range:20 repulsion:3 block:2 cutoff:36 into:8 within:19 integral:6 retaining:1 appropriate:6 proportional:3 δlr:1 institut:1 dimensionful:1 measured:1 twodimensional:1 question:7 u0:4 fast:4 bosons:23 sections:2 propagator:29 underlines:1 lint:2 link:1 line:7 infers:1 characteristic:23 up:7 us:8 par:1 exploration:1 uk:2 sum:2 continuously:1 fluctuations:23 matsubara:2 similar:15 torus:1 ordered:46 defined:7 influence:7 inferred:1 single:1 cure:2 formalism:1 defines:3 nan:1 priori:1 generates:1 excitation:1 provided:2 problems:1 generated:8 fisher:5 structure:1 independently:1 correlated:2 implies:16 implied:1 eiθ:1 accidental:1 requires:5 once:6 partial:7 results:14 gg:3 reinserting:1 go:1 gm:1 contributions:3 δd1:2 gases:1 concerned:3 stable:16 include:9 ingredient:2 g2:1 g1:1 continues:1 wave:4 mixing:1 matrices:1 diverging:2 integrating:1 trg:2 try:1 transmutation:1 inspection:1 dilute:18 disordered:23 jump:1 imply:2 concludes:2 dynamics:3 obey:5 bde:1 index:2 plays:5 3w:5 3v:2 expressed:2 kosterlitz:9 experiment:5 led:1 degree:1 sint:4 following:5 explore:5 z4:2 z1:2 z2:2 extreme:5 remark:1 technical:1 involved:3 larger:7 suggests:3 resulting:3 involves:6 formulated:1 scales:11 app:11 integrations:1 δc1:2 expect:7 addressed:1 decrease:3 anomalies:1 apply:2 use:20 feb:1 asymptotic:12 remains:15 next:8 few:2 depicted:1 2ρu:43 2πnt:1 dxt:2 formally:1 becomes:29 labelled:1 δcd:1 iii:2 justin:1 account:3 crosses:1 m2λ:17 decouples:1 averaged:1 reproduce:2 ρu:28 weaker:2 iχ2:1 lρ:1 calculation:2 purposes:1 high:3 effectively:14 lorentz:2 pawlowski:2 counting:1 varied:3 decaying:1 holds:4 located:1 varies:1 instead:6 counterterms:1 demonstrates:1 physik:1 realized:4 separations:2 correspond:4 subsequently:1 six:4 dx:2 produces:1 move:1 artefact:4 interpreted:1 including:11 hypersurface:5 mentioned:2 delamotte:1 write:2 ld:1 longitudinal:1 decay:7 chosen:3 zˆ:2 lr:7 choose:5 derivative:29 iϕ2:1 lz:1 violating:7 practice:3 bar:2 rotation:1 ηv:2 university:2 sufficiently:2 magnitude:1 mode:22 l0:3 kph:64 accounts:1 reproducing:1 homogeneous:5 ferromagnetism:1 kosterlitzthouless:1 related:8 constitute:1 decays:4 static:2 subdominant:3 measure:3 relates:2 transitions:12 special:5 out:5 matrix:5 rep:2 rev:13 m2r:1 ref:5 math:1 interactions:9 diagonal:3 approaches:12 anyhow:1 interaction:16 could:4 keep:2 length:28 retain:1 pines:1 reaches:5 reached:4 precisely:5 uzunov:2 beliaev:2 start:4 zφ:4 behaves:4 system:13 relations:3 their:4 intermediate:1 fermions:1 final:2 explanation:1 exactly:2 diminish:1 distinguishes:1 richer:1 limiting:3 distinguished:3 result:7 exhibit:2 symmetries:10 fluctuation:7 unchanged:1 qˆ0:5 dq1:2 need:7 demonstration:1 linked:2 2vd:13 concerns:3 accuracy:4 2πn:1 clash:1 eres:1 collaboration:1 connected:1 class:2 consequences:4 dent:1 graphs:1 χb:2 χa:4 constrain:1 fact:6 superfluidity:1 violation:3 purely:1 rough:1 trivial:3 agrees:1 q1:8 q0:82 q2:3 based:3 ksr:12 should:17 local:13 equilibrium:1 sengupta:1 familiar:1 overall:2 words:1 evolution:11 a87:1 paramagnetic:1 differential:3 qc:5 contain:2 fixed:134 view:3 requirement:1 computed:3 exists:7 frame:1 respect:17 b301:1 merits:1 enhanced:13 p22:1 closer:1 closes:1 phases:1 interacting:5 pattern:1 diverge:1 state:3 identification:1 closed:4 invariant:11 neither:2 ends:3 importance:7 weak:1 key:3 jχ:1 limits:1 taking:2 equal:2 ln:56 admit:1 grounds:1 comment:3 strongly:6 relevant:28 conclude:12 cf:9 cd:1 diverges:5 decreases:8 cs:13 table:7 slowly:1 degrees:1 define:9 pic:1 corresponding:18 truncations:7 sufficient:2 c2:2 c6:1 present:10 eif:2 appearance:1 value:59 will:83 vd:13 almost:1 vi:3 formulation:5 thus:6 surprisingly:1 sity:1 vw:1 perhaps:1 φb:3 parts:1 schematic:1 units:3 castellani:2 finite:11 infer:6 infinity:2 mcgovern:1 cubic:4 effect:2 phe:1 v0:1 v1:1 v2:2 v3:1 infinite:11 expand:3 destruction:1 reflection:1 nevertheless:7 well:23 sets:6 less:1 wagner:4 obtain:9 sources:3 floerchinger:2 predicts:1 momenta:21 macroscopic:10 adv:1 density:45 point:120 sφ:3 combina:1 thermodynamics:1 add:1 extends:1 attractive:6 match:1 tests:1 spinless:1 criticality:1 increases:10 know:2 press:2 vλ:1 insert:1 necessary:3 like:10 lost:2 alternatively:1 qualitative:17 susceptibilities:1 δr:1 become:4 works:1 replacement:1 parity:1 because:1 classical:38 smoothly:2 phenomena:4 choosing:1 neglecting:4 happens:4 lead:3 broad:1 does:15 assuming:1 demonstrated:1 explicite:2 inaccurate:1 expansion:8 pressure:2 imaginary:2 simpler:1 about:1 carried:1 extension:5 b352:1 freedom:1 triviality:1 introduces:1 dependence:15 compatible:3 a2:11 introduced:2 equally:2 functional:26 tiny:1 bosonic:10 additional:13 restricts:1 quadratic:6 crucially:3 asymptotics:2 function:23 but:14 volume:8 construction:1 truncation:73 compute:3 instructive:3 whether:1 antiferromagnetic:1 4v:1 below:2 frequency:2 limit:22 piece:2 int:1 universal:1 contribute:4 denote:2 our:56 ing:1 identities:5 functions:23 compared:2 detail:2 other:17 compares:1 details:8 theor:1 variation:1 acknowledgment:1 4z:1 coupling:50 pointlike:9 bcd:1 4w:2 4u:1 4n:1 4d:3 expands:1 |
0705.1662.txt |@word sco:1 maciejewski:1 pointing:1 edu:2 consists:2 sct:2 als:1 whose:1 applied:1 g0:1 quadruples:1 presented:1 large:2 small:2 warszawa:1 bd:1 smaller:1 periodicity:1 second:4 value:2 further:1 spectral:1 sub:1 k1iii:1 suspect:1 pulsating:1 new:5 increasing:1 method:1 degree:3 residual:6 behaviour:5 objects:5 separation:2 search:2 study:1 changed:1 step:2 periodic:5 survey:3 changes:1 classification:3 photometric:1 private:1 use:1 would:1 faint:1 scenarios:1 m1:5 m2:3 aperture:3 type:8 more:2 separated:1 ujazdowskie:1 vmax:1 cases:1 none:1 work:1 values:1 believed:1 detached:1 dec:2 deg:1 triple:1 figure:12 sample:1 performed:4 information:2 end:1 rather:1 scuti:1 fr:2 may:5 after:2 spot:3 catalog:1 mag:5 data:2 types:2 pulsations:4 light:22 issn:1 so:1 counted:1 help:1 over:1 years:1 course:1 paper:1 mentioned:1 thank:1 exhibits:1 better:1 mail:1 might:1 pixel:1 them:3 primary:4 they:1 half:1 sorted:1 brightness:2 classified:1 identified:1 magnitude:1 each:2 found:4 photometry:1 side:1 significantly:1 ed:5 ec:16 frequency:2 our:2 out:4 category:1 shown:1 mason:2 investigation:1 ra:2 detecting:1 iterative:1 days:2 used:1 times:1 first:2 origin:1 already:1 number:1 stsci:1 spots:4 another:2 given:1 system:2 construct:1 listed:3 iau:1 observations:2 fabrycky:3 explanation:1 part:1 x2:1 than:1 kind:1 observatory:1 showed:1 double:3 see:1 determined:1 amplitude:1 were:7 exhibit:2 turned:1 curves:6 raw:1 need:1 ray:1 strength:1 lib:1 majority:1 k1:1 quote:1 object:3 tyc:3 significant:1 phase:22 acknowledgements:1 subtracted:1 order:1 blend:2 bulletin:1 pigulski:4 show:1 supported:1 find:1 subtracting:1 only:1 pointed:1 columns:1 above:1 get:1 designated:1 ones:1 during:1 pojma:5 secondary:4 budapest:1 exhibiting:1 arxiv:1 vizier:1 doubles:2 automatic:2 variations:1 plausible:2 namely:2 radius:1 result:1 close:3 best:1 probable:1 catalogue:4 smallest:1 various:1 available:2 variability:11 recently:2 nature:1 however:1 spectroscopic:1 comm:1 pixels:1 both:3 estimation:1 among:1 period:8 cd:1 blending:3 moreover:1 three:1 been:1 combined:1 collected:1 ph:2 pl:2 present:1 p2:4 p1:4 nski:5 evaluated:1 will:1 eclipses:3 procedure:2 iv:1 ii:1 examined:1 vv:1 declinations:1 ia:2 ie:1 id:4 orbital:1 binary:3 different:2 grant:1 same:2 wds:1 largest:1 higher:2 ibvs:10 visually:1 investigated:2 database:1 poland:1 analysis:4 contact:2 components:1 model:4 binaries:9 mnisw:1 left:1 minima:1 shape:1 multiples:1 accepted:1 sky:4 fitting:1 astrouw:2 source:1 remaining:1 sgr:1 big:1 possible:1 using:4 2nd:1 like:2 semi:1 signal:1 2007b:1 2007a:2 some:2 b5:1 examples:1 table:4 images:2 star:3 14th:1 esd:17 simbad:1 semidetached:2 digitized:2 who:1 asas:8 poleski:1 analysed:2 bv:1 comparison:1 aca:2 identifier:1 cautions:1 into:1 due:4 down:1 references:1 determine:1 refined:1 additional:11 astrometric:1 there:1 inspected:1 stars:12 resulted:2 examination:1 was:13 form:1 but:1 hu:1 astro:2 subjectively:1 automated:1 mnras:1 line:1 removed:1 true:1 hd:1 made:2 whether:1 attached:1 us:1 puls:5 detailed:1 abstract:1 aj:1 periods:4 again:2 cephei:2 no:1 whereas:2 when:3 other:6 details:1 konkoly:1 n203:1 kinds:1 separate:2 models:1 variation:1 variable:3 independently:2 apertures:1 curve:17 together:1 simplified:1 depth:1 searched:1 eclipsing:8 resolution:2 original:3 once:1 |
0705.1663.txt |@word partial:2 consider:8 springer:1 copy:1 lack:1 four:9 entropy:2 garching:1 computation:3 go:1 xjk:1 expressions:1 excluded:1 gk:4 xxi:4 whose:1 weierstrass:1 const:1 bx1:2 graph:1 bx3:2 tu:1 quadruple:1 finally:5 does:6 indicate:1 th:2 under:8 necessary:4 discriminants:3 applied:1 g3:3 g2:3 very:2 joshi:1 bilinear:1 quadruples:1 conditions:1 induce:1 unchen:1 corollary:1 every:1 affect:1 difference:2 bringing:1 2rr:1 condition:6 arrange:1 groups:1 leads:4 hamiltonian:2 irreducible:3 list:12 solution:7 zentrum:1 discrete:15 adjust:1 scalings:1 recall:2 inversions:1 hyy:2 anal:1 permutability:1 equation:51 programme:1 zn:1 h13:1 says:1 h14:9 consistent:22 direct:4 sign:4 sergeev:3 integrability:12 arnold:2 further:5 accompanying:2 4x3:1 linear:22 subscripts:1 nonlinear:5 appear:1 section:10 analogously:6 expressed:1 find:1 consistently:1 version:1 conics:1 above:1 new:3 method:2 contrast:2 3d:23 satisfy:4 full:1 simultaneously:1 degree:6 respectively:3 even:1 here:4 papageorgiou:1 cac:1 εx2:3 inversion:7 hkl:1 others:1 directions:1 depend:2 maillet:1 strong:1 equations:66 appears:3 z2:2 z3:2 obtained:2 spite:3 algebra:1 institute:1 shift:1 studied:2 allows:6 reason:1 suggests:2 simultaneous:1 resulting:2 permutation:2 action:1 had:1 suitable:3 studies:1 pathological:1 york:1 uniquely:1 formulated:1 term:1 projection:1 family:1 brought:3 pxi:1 pxl:1 apply:1 glance:1 univ:1 unit:2 readily:1 derivatives:1 use:7 takes:1 prove:1 covariant:1 positive:1 whittaker:1 γi:1 cauchy:1 properties:4 few:1 κx2:1 therefore:10 taken:1 themselves:1 type:19 theoretical:1 more:10 zeroes:1 sharing:1 elliptic:2 νy:1 operators:1 curvature:2 surprisingly:1 berlin:3 virtue:2 particular:8 known:4 projective:2 cases:16 hold:5 potential:1 must:7 ramani:1 account:1 valued:2 ma:1 quartic:4 h10:2 h11:2 setup:1 des:1 det:4 remain:1 shabat:1 values:11 capel:1 novikov:2 following:18 nlin:1 root:3 example:13 proof:7 korepanov:2 figure:7 give:2 calculation:1 permutations:1 organized:1 ℓx:1 p41:10 δxl:2 sn2:2 numbers:1 degenerate:6 sense:4 nonlin:2 r23:1 r22:1 ratio:1 information:1 respective:1 end:1 notation:4 awkward:1 rather:2 conversely:1 six:4 feature:1 arrangement:1 maps:8 extended:3 criterion:2 adjacent:3 answer:1 acta:1 obius:21 classify:4 product:1 rise:1 blocks:1 description:1 singular:10 may:21 after:3 dx3:2 dx2:2 dx1:2 diagram:3 consequence:1 wrong:1 plane:1 lax:3 coming:1 multiplication:1 data:3 compatibility:2 types:2 goal:1 2x2:1 outline:1 imply:2 slightly:1 explicit:1 correspond:2 element:1 their:5 si:3 cannot:4 so:7 sn:19 fundamental:2 keeps:1 representation:3 operations:2 holds:2 help:1 developed:1 over:1 russian:1 course:2 paper:3 through:1 statistical:1 reconstruct:1 existence:3 satisfies:2 still:2 its:8 itp:1 before:1 xl:13 unessential:1 shifts:4 chosen:1 interesting:1 fix:1 affine:19 actually:4 destroyed:1 degrees:1 systems:24 van:1 mail:3 hidden:1 image:1 arguments:2 them:2 return:1 influences:1 quispel:1 acklund:2 landau:1 volkov:2 p14:2 they:3 identically:1 front:2 multidimensional:2 now:1 yu:7 hxy:1 nor:1 reconstruction:2 easily:1 february:1 several:1 indeed:6 name:1 2r:1 lies:1 always:4 classified:4 2x:1 possibilities:1 x21:4 each:12 2l:1 found:9 universit:2 x13:25 2h:1 2i:3 2j:1 2k:2 baxter:7 2hx:1 int:4 differential:3 successively:1 directly:1 there:5 idea:4 related:6 applicable:1 equivalence:1 investigated:1 quantum:4 relates:1 sokolov:1 numeration:1 out:5 ru:1 shown:6 solved:3 res:3 since:16 induces:1 research:2 geom:1 rational:2 formula:4 ri:9 math:17 shows:3 performing:1 theory:2 associate:1 derived:1 differ:2 possibility:1 indices:2 completely:1 yuri:1 usual:1 put:1 hep:1 associative:1 µxy:2 presently:1 r4:5 definition:10 pairs:6 r0:1 r1:9 r2:11 r3:4 geometry:4 starts:1 impose:1 turn:2 technische:2 3r1:1 βa:1 h02:2 hence:1 neglected:1 degeneracy:5 onto:1 βi:1 first:8 xj:31 xk:9 journal:1 already:3 xn:4 symmetry:12 degx:5 variables:20 xij:21 number:2 xy:9 another:1 carry:4 compensated:1 precisely:1 open:1 between:1 given:6 checked:1 table:1 similarly:1 introduction:1 unknown:1 top:2 xik:1 system:18 relations:1 1a:1 needed:1 assumption:6 master:2 statement:3 reducible:2 dfg:2 final:2 gives:1 free:1 commutativity:1 asymmetric:1 completed:1 continuous:1 lists:1 technique:1 task:1 pnm:2 favorable:1 x2:130 quad:14 x1:111 than:3 x4:66 dynamical:2 kind:1 third:1 cyclic:1 divisible:1 double:2 zero:4 classes:1 supposed:1 were:4 ber:1 treated:1 russia:1 symmetries:2 generality:3 rewrite:1 linearizable:1 zamolodchikov:1 argument:2 curves:2 say:2 factorizations:1 manner:1 need:1 seen:2 constrained:1 any:15 ax2:4 ax1:3 built:1 der:1 h24:1 latter:5 h21:3 h20:3 h23:10 h22:3 note:4 k2:1 k1:1 edge:6 generalized:1 neither:1 xi:37 coincide:11 canonical:5 analogs:1 surfaces:2 exactly:2 allow:4 normal:1 sets:1 effective:1 surv:2 algebraic:4 ordering:1 germany:2 remarks:2 rhombic:1 class:2 g23:1 yamilov:1 soliton:2 h2y:1 h2x:2 considered:6 later:1 flow:2 vertices:10 physica:1 face:3 graphs:5 yang:7 diagonals:2 hietarinta:3 coincided:1 physics:3 notion:5 lying:1 precise:1 αb:1 show:1 supported:3 notations:1 bring:6 multiplicities:1 relation:4 solutions:5 x3:109 kx3:2 δx3:4 δx2:5 δx1:8 d1:2 q1:10 q3:6 q2:5 based:6 q4:6 parameters:13 much:1 should:2 lemma:5 only:8 explicitly:2 black:1 coefficients:4 factor:7 integrable:17 constant:9 resp:1 achieve:1 dn:2 do:6 cube:17 δxk:5 δxj:2 δxi:5 admissible:3 dg:1 de:2 straightforwardly:1 watson:1 ones:4 closely:2 suris:9 lattices:1 hij:11 boundary:1 differentiating:1 alexander:1 kα:4 qy:1 fields:5 arxiv:7 modern:1 yield:1 hyperbolic:3 proved:1 κxy:1 fixed:2 valid:6 view:2 searching:1 requirement:1 set:5 modulo:3 suppl:2 unpublished:1 signs:2 relative:7 see:7 justification:1 result:1 p22:9 bobenko:7 best:1 situation:1 polyhedral:2 kα2:2 said:2 µy:2 l149:1 αy:1 definite:1 liouville:1 determined:2 various:1 roots:3 simplest:1 αi:1 probably:1 subscript:1 approach:8 x23:27 x22:4 multiplied:1 notice:3 vorlesungen:1 recently:1 reproduced:1 useful:1 analogues:2 however:5 veselov:5 white:1 comm:2 tum:1 spoil:1 russ:1 solv:1 come:2 problem:5 both:3 realizable:1 x2i:1 reverse:1 biquadratic:30 taking:1 uncertainty:1 according:9 fulfilled:4 etc:1 admit:1 context:1 faces:17 h211:1 distinction:1 expression:2 h12:21 comes:1 otherwise:3 suggest:1 ci:1 solving:1 cn:2 space:1 point:3 simple:5 seems:2 ca:1 leipzig:1 corresponds:5 quadrilateral:4 coincidence:2 dimensional:11 concluding:1 cx:3 simply:1 invariant:2 polynomial:29 moreover:8 appeared:2 pr:1 forms:3 most:2 transformations:15 second:3 discriminant:1 equivalent:5 simplification:1 px:1 three:14 defined:4 bianchi:2 change:15 basic:1 combine:1 ph:1 meeting:1 abstract:1 exhaustion:1 choose:1 direction:1 cx3:2 corresponding:10 easy:1 restrictions:1 quantities:1 sufficient:1 formed:1 coincides:1 cambridge:1 6r:2 qx:1 xxj:3 c1:2 presented:1 present:1 case:24 invariants:10 leave:1 means:2 tetrahedron:14 examine:1 value:2 deformation:1 will:10 while:1 replaced:2 aij:1 irrespective:1 di:1 property:14 conformal:1 procedure:2 iy:1 shortened:1 commutative:4 played:1 thus:4 non:9 iv:3 ik:4 itself:1 triple:1 turns:7 finds:1 l145:1 different:9 descent:2 grant:1 generic:1 x123:19 make:2 same:10 clearly:1 h00:2 complex:1 quadrilaterals:1 descend:1 hierarchies:1 hxx:1 difficult:1 used:2 cubic:1 i3:14 i2:15 effect:1 flows:1 hand:3 edges:13 h34:16 invariance:1 identity:3 mappings:2 correspondent:1 theater:1 center:1 nevertheless:1 changes:6 mangazeev:1 well:3 analysis:4 obviously:3 hx3:5 hx2:1 hx1:1 without:5 solve:3 consistency:19 coordinate:3 model:1 possesses:4 left:2 just:3 λy:1 λx:1 grammaticos:1 obtain:1 aside:1 assigned:2 identify:1 transforms:1 using:2 differentiation:2 hjl:1 hji:1 singularity:1 hjk:6 previous:5 classification:10 guaranteed:1 deconstructing:1 theoret:1 qx2:2 lattice:11 priori:4 transformed:1 lett:4 versa:1 theorem:18 extensive:1 solvable:1 transformation:3 take:2 identical:1 pair:8 around:3 dealing:1 possible:9 chernogolovka:1 know:1 mathematics:1 press:1 equality:2 variants:2 mod:1 loss:2 imposed:3 like:2 δx:12 δy:1 follows:2 λx2:2 qxi:4 separately:1 x24:3 yields:2 either:4 arbitrary:5 multiplicative:1 bazhanov:2 mathematical:1 copies:2 right:3 methods:2 namely:2 formulas:1 kashaev:1 some:9 back:3 understood:3 examples:6 respect:15 kdv:3 provided:1 lead:2 bottom:2 opposite:6 nijhoff:3 classical:1 whole:2 esf:1 equal:3 eliminate:1 provides:1 core:1 faddeev:1 algorithmic:1 scientific:1 bc:1 vertex:5 bn:1 δi:1 bi:1 step:4 although:1 relating:1 bx:3 x12:36 stage:1 viallet:1 simplify:1 freedom:1 basis:1 a3:1 o:12 side:1 compatible:2 remains:3 carries:1 important:1 qx3:2 connected:1 introduced:1 consequently:1 2x4:1 automatically:1 mechanics:1 own:1 statements:3 mikhailov:1 h2:1 h3:1 into:16 h1:1 integral:1 functional:2 due:5 included:1 appropriate:3 square:4 references:1 determine:1 proportional:1 strasse:1 next:1 institut:1 additional:3 assumed:3 h01:2 initial:3 question:1 qx1:3 quadratic:1 structure:2 way:5 notices:3 decisive:1 was:13 function:4 hx:1 hy:1 complete:4 form:22 pencils:1 identities:1 l67:1 but:8 principles:1 elimination:1 delivers:1 adler:9 partially:3 made:1 applying:1 inhomogeneous:1 switch:1 characteristic:1 up:13 us:7 ur:1 krichever:2 below:3 empty:1 demonstrate:2 distribution:1 called:5 b1:1 detailed:1 linden:1 ac:3 ab:3 associated:9 ai:1 certain:1 ak:1 describe:1 linearity:1 cx2:2 proven:1 general:8 teubner:1 single:3 proves:2 sublattices:1 our:6 ay:1 ax:2 exist:2 commuting:3 check:4 defines:2 tedious:1 again:2 functions:3 no:5 mathematik:2 when:3 vanishes:1 field:1 other:10 role:1 details:1 brings:1 test:1 cp1:2 principle:1 juni:1 denote:4 separate:1 models:3 problems:1 polynomials:56 a1:1 a0:7 ba:1 a2:4 variable:10 goursat:1 trapezoidal:1 building:1 independently:2 implies:5 algorithm:2 vice:1 assume:5 requires:1 factors:4 curve:6 considering:1 noncommutative:1 fact:1 wholly:1 time:1 appl:1 4d:1 starting:1 |
0705.1664.txt |@word aa:2 fpi:4 ao:1 cosh:1 ga:1 go:1 m2π:2 uν:2 aπ:1 hep:1 uµ:3 quarks:10 tr:1 nf:2 symmetric:5 retr:1 γo:4 mº:3 mρ:11 mπ:5 may:1 dg:1 mpi:4 beta:60 vµ:2 sinh:1 lat:1 ma:10 λphys:1 nfc:2 mc:8 lº:1 mo:2 arxiv:1 su:3 fπ:18 fundamental:5 βc:1 sg:1 sf:1 |
0705.1665.txt |@word partial:3 consider:1 remarkable:1 switched:1 results:6 wiringa:1 aumer:1 although:2 scalar:4 consists:2 denotes:5 inverse:1 depend:1 referring:1 atzold:1 byrd:2 finally:1 foster:1 those:5 th:3 under:1 r12:1 nski:1 choice:3 ishikawa:11 vls:5 difference:7 coon:2 presented:1 turns:1 πnn:1 large:2 solved:1 kondo:1 vector:9 hanly:1 small:5 noted:1 upper:1 force:7 consistent:1 sign:1 likely:1 displays:1 chen:1 further:2 theory:1 blue:6 aim:1 what:2 gl:6 plays:3 appear:1 section:3 multimedia:1 3n:10 above:2 international:1 contributes:1 acknowledgments:1 nakamura:2 body:4 edited:1 kamada:1 exchange:6 kzz:9 respectively:3 component:12 here:1 reported:1 mev:56 inversion:10 av18:57 excess:1 equations:2 appears:1 obtained:2 remark:1 spite:1 study:2 studied:2 scatter:1 amount:1 published:1 t21:15 studies:2 cancellation:2 plotted:1 formulated:1 projection:1 twonucleon:1 private:1 matsuoka:1 durham:2 analyzing:12 total:4 m2π:1 imaginary:2 plot:2 use:1 mb:2 takes:1 usa:1 breakup:2 examined:3 predictions:1 nonnegligible:2 tabulated:1 discrepancies:1 comparing:5 nucl:7 call:1 therefore:1 taken:2 type:1 until:1 minor:2 more:3 introducing:1 successful:1 thus:4 appendix:1 particular:1 known:1 hold:1 iii:1 hints:1 tokyo:1 science:1 work:4 protons:1 modified:1 reproduce:7 deficiencies:1 values:4 following:2 klages:1 example:1 deg:7 figure:1 give:3 process:2 cited:1 viviani:2 states:3 kyy:8 minimum:5 numbers:1 arise:1 amplitudes:4 r23:1 occur:1 axis:2 information:1 argonne:2 provide:1 means:1 xˆ:2 θmax:4 plus:1 parameter:2 description:3 may:6 reaction:1 different:4 treiman:1 effects:1 wave:1 data:24 fm:2 kxx:10 third:1 ichihara:1 ueno:1 kxz:8 st:2 coelho:1 sj:1 si:1 green:5 order:2 worsens:1 typical:1 nucleon:17 pointed:1 displayed:4 course:1 paper:1 including:1 looks:1 thesis:1 unfavorable:1 japan:1 still:1 its:1 fischer:1 fit:2 energies:10 interesting:4 zˆ:1 boson:1 forms:1 attraction:3 systems:3 mail:1 good:1 nishimori:1 fig:21 introduce:1 bound:1 scaling:2 repulsive:2 effects:11 they:3 closer:1 now:1 easily:1 february:1 hatanaka:1 hereafter:1 university:3 oppositely:1 realistic:5 each:3 higher:5 reproducing:6 en:12 nogga:1 directly:1 ed:4 energy:25 related:1 deficiency:2 investigated:1 isospin:1 expect:1 proportional:2 laboratory:3 eq:3 ep:3 out:2 shown:4 space:2 restricted:1 since:2 rev:16 cancels:1 research:2 acting:1 rg:1 denoted:1 witala:4 ref:18 red:6 shows:4 uber:1 mπ:1 interactions:1 mechanisms:2 quite:2 term:1 seventeenth:1 shortest:1 chiral:1 readjusting:1 leading:1 first:1 features:2 markoff:1 kievsky:3 relations:1 another:3 open:1 angular:3 phenomenological:3 necessarily:1 introduction:2 unknown:1 goldberger:1 amsterdam:1 system:3 construct:1 their:2 epelbaum:1 calculations:27 variational:1 final:1 recovered:1 gives:3 difference:1 exactly:1 part:3 favorable:3 simulate:1 coefficients:1 kind:1 effective:1 niessen:1 see:5 project:1 determined:4 were:2 treated:1 result:1 modern:1 defect:1 curves:20 qualitatively:1 need:1 seen:1 kelley:1 clearly:3 lie:1 strength:4 angle:6 latter:3 hosono:1 lij:1 polarization:9 extracted:1 concerns:1 take:2 forces:3 online:6 converged:1 so:43 coincide:1 golak:1 circles:5 universities:1 added:1 sets:1 iupap:1 significant:1 pair:2 r31:1 considered:1 calculated:3 wick:1 points:1 principle:1 kz:1 ky:1 kx:1 physics:2 oguri:1 precise:1 mckellar:1 v18:2 particularly:1 show:5 text:1 supported:1 miwa:1 saito:1 threshold:2 slaus:1 q2:1 based:1 knowledge:1 parameters:2 explain:3 produces:1 state:3 only:2 black:6 factor:2 chiyoda:1 local:3 interested:1 carolina:2 exchanged:1 do:2 triangle:1 get:2 dependent:4 syst:3 de:1 overall:1 pions:2 beam:1 remedy:1 pendence:1 combinations:1 procedures:1 gen:1 reveal:1 processes:1 resolve:1 nicely:1 arxiv:1 summary:1 fixed:1 deuteron:7 constructing:1 sensitivity:1 maximum:5 observed:2 depends:1 truncating:1 tornow:5 close:1 incorporating:1 brazil:2 tensor:31 nuclear:3 blatt:1 dipole:1 artificial:1 enough:1 between:6 progress:1 available:1 triplet:1 terms:2 reproduced:2 originated:1 jp:1 however:3 incident:2 analyzed:1 distribution:1 improve:4 observable:2 essentially:1 σl:7 powers:1 region:1 reproduces:1 against:1 called:1 etc:2 dated:1 contribution:3 experimental:16 σt:5 among:1 point:2 color:6 overview:1 2nf:4 proton:4 sakai:1 table:4 conference:1 koike:1 addition:1 three:6 been:2 expected:1 ph:1 barrett:1 choose:2 remedies:1 direction:2 rather:2 corresponding:1 both:5 sufficient:1 understand:2 angles:2 spin:22 former:1 present:4 case:2 ockle:6 look:1 pacs:1 solid:11 empirical:2 value:4 will:2 while:1 behavior:2 procedure:1 scadron:2 3nf:44 dominantly:1 pickup:1 almost:4 characteristics:2 refs:1 binding:15 discrepancy:1 ij:5 vt:7 rik:1 elsevier:1 schiavilla:1 yˆ:2 confirmed:1 robilotta:1 sensitive:2 il:3 make:1 cross:3 same:1 emphasize:1 several:1 neutron:4 difficult:1 independent:5 calculation:5 used:1 maeda:2 numerical:1 effect:19 hand:4 v0:7 phy:1 changing:1 single:1 recent:2 lower:2 off:1 center:2 b257:1 well:6 without:2 solve:1 components:8 simulated:2 coordinate:2 position:1 model:14 fujita:1 arising:3 proposed:1 nd:1 das:1 obtain:1 a426:1 momenta:1 scattering:26 note:2 improvement:1 other:5 plateau:1 theorem:1 prominently:1 heavier:1 momentum:2 rosati:1 around:2 zeitnitz:1 decomposed:1 possible:1 corresponds:1 smallness:2 increases:3 76b:1 using:1 particle:1 follows:1 consensus:1 howell:3 nucleons:1 essential:2 because:5 namely:1 truncated:1 oriented:1 successfully:1 some:3 understood:1 examples:2 b3:2 kohn:1 gradually:1 lead:1 confirm:1 demonstrates:1 measurements:2 does:2 tends:1 proc:1 demonstrated:1 schwarz:1 destroys:1 faddeev:1 object:1 power:11 gmax:2 agreement:1 display:1 br:1 analyses:1 von:1 about:9 works:2 central:2 dependence:4 o:3 range:2 repulsion:1 act:1 s61:1 triton:9 cutoff:2 equally:1 differences:1 presence:1 communication:1 into:2 integral:1 functional:1 due:2 coefficients:1 operator:2 accumulated:1 uncertainties:1 deal:1 elastic:5 few:4 transfer:2 haase:1 long:1 low:3 way:1 forward:2 was:1 3nfs:13 function:1 north:2 form:4 differences:2 schwindt:1 but:5 lemaitre:1 optical:1 rjk:1 partially:1 2πe:14 pion:5 whether:3 up:3 quantitatively:1 below:3 gould:1 demonstrate:2 problem:1 walter:3 similar:2 agree:2 strongly:1 ac:1 developing:1 computing:1 defined:1 abstract:1 denote:1 mertens:1 examine:1 governed:1 our:4 ay:27 imai:1 formalism:1 kyushu:1 physical:1 compared:1 dotted:11 no:2 dashed:11 when:1 overshoots:2 field:1 valid:1 role:4 becomes:1 department:1 pedroni:2 really:1 shimizu:3 reflections:1 explaining:3 models:5 problems:1 variation:1 stoks:1 peak:1 failures:1 tendencies:1 conclusive:2 jones:1 coulomb:4 nakashima:2 required:1 curve:5 orbit:8 together:1 equivalently:1 mass:2 observables:18 lett:3 |
0705.1666.txt |@word externally:1 sci:1 consider:4 remarkable:2 caused:1 magnetic:5 global:3 results:3 consists:2 λik:2 λij:3 tz:9 calculate:1 tx:4 ty:4 segments:1 technique:1 tp:2 environment:1 finally:1 does:3 under:5 analogous:1 supported:1 obi:1 fan:1 underscore:1 locked:1 em:1 macromolecules:1 randomness:3 olaf:1 implying:2 positions:1 anisotropy:6 large:3 discrete:3 vector:1 small:6 tru:3 terminating:3 dis:1 work:1 zero:6 imprinting:1 nematics:1 rigorous:1 replicated:1 chem:2 linear:4 neo:1 what:1 nonlinear:4 near:2 infinitesimal:1 above:3 φzz:1 values:2 martensitic:1 nes:3 3d:1 full:4 whose:1 respectively:7 modify:1 directions:2 depend:1 along:15 strong:1 appears:1 change:2 stresses:1 convert:1 study:1 larger:2 conti:1 simultaneous:1 resulting:2 usually:1 changes:1 focussed:1 appropriately:1 followed:1 griffiths:2 clark:1 scales:1 replace:2 uzz:4 establish:1 unit:3 use:1 takes:1 usa:2 commun:1 positive:1 negative:3 france:3 doubt:1 distortions:3 until:1 diagrams:4 more:5 flat:2 formally:2 relax:1 uxz:8 validity:2 hotta:1 uxx:9 particular:2 ward:3 aligned:1 must:1 me:1 md:1 rotational:3 ma:1 integrating:1 equation:1 constraint:5 det:5 theories:2 reproduce:1 remain:1 anywhere:2 crossed:3 making:1 trans:1 transition:4 figure:2 process:2 discussed:1 allowed:1 sphere:1 φij:3 numbers:1 arise:1 σxz:3 simple:1 axis:5 information:1 respective:2 provide:2 biaxial:16 breaking:1 dependent:1 oblate:3 familiar:1 φyy:1 parameter:4 sin:2 nematic:20 express:1 description:2 may:1 different:2 dc:7 diagram:12 levi:1 plane:18 incompressibility:2 physik:1 response:18 σzz:2 sz:8 sy:9 sx:2 physical:1 effective:1 sr:4 lines:3 st:1 rather:6 ones:2 so:1 eni:1 representation:1 words:1 order:26 acts:1 interpretation:2 closely:1 produces:1 over:1 vary:1 choose:1 produced:3 experiments:3 including:2 affect:1 satisfies:1 gion:1 its:2 before:1 derive:1 energies:1 olmsted:1 vicinity:1 exhibits:5 forms:1 absence:1 fig:11 stephen:1 hidden:1 might:3 deformation:2 shear:3 happens:1 versus:1 them:1 return:1 schematic:1 combination:1 tained:1 ye:2 landau:1 break:2 modification:1 effects:1 they:1 half:2 oxford:5 rotation:5 now:4 discuss:1 dielectric:1 2u:1 february:1 university:5 magnitude:1 reasonable:1 each:2 aligns:1 universit:1 2h:2 characterized:3 mean:1 goldstone:2 orientational:2 domain:1 energy:9 ea:1 displacement:1 ey:2 ex:2 measure:1 separating:1 our:8 beyond:3 rheology:1 out:1 conjectures:1 shown:6 matrix:2 space:8 σyy:1 since:1 lagrangian:1 converts:1 increase:1 rei:1 rc:4 rn:3 induced:2 ri:1 shows:2 8h:1 turning:2 theory:4 frank:2 enforcing:1 free:4 clarify:1 supercritical:6 york:1 approach:1 rises:1 temperature:6 language:1 geometry:1 persists:2 linearized:2 creates:1 monodomain:1 isotropic:7 δij:3 consequence:2 generalizations:1 first:12 xj:1 initial:1 shears:2 lond:1 symmetry:6 ez:2 tricritical:5 xz:1 xx:4 xy:2 s0:6 priest:1 open:1 between:3 equating:1 given:1 reference:6 similarly:1 ordering:1 construct:1 their:3 mukhopadhyay:1 perturbations:1 ukk:1 too:1 calculations:1 gives:2 continuous:1 serve:1 stress:30 σkj:2 part:3 than:7 distance:1 kind:1 target:2 favors:5 second:9 matter:1 states:5 determined:2 w2:1 exhibit:4 symmetries:1 turned:1 argument:1 curves:8 further:2 macromol:1 hexagonal:1 clearly:1 angle:1 convenient:1 note:1 ideal:2 lifts:1 generalized:2 terentjev:5 new:1 modulus:5 brand:1 begin:1 induces:1 electric:4 uyy:1 uyz:1 germany:1 ht:2 phase:26 homogeneous:1 measured:5 deviations:1 kf:2 calculated:2 maier:1 lattice:1 points:9 metastability:1 χa:2 mechanical:6 physics:3 slope:2 emerging:1 particularly:1 show:2 random:1 terminate:1 bring:1 duisburg:2 relation:1 civita:1 find:1 boundaries:1 written:1 should:3 only:2 interested:1 equilibrium:8 do:1 contracts:1 liquid:6 de:4 uniaxial:12 preferred:2 cannot:1 dz:4 dx:5 dy:5 hij:1 exhibiting:1 continuum:1 fields:4 arxiv:1 yield:1 summary:1 paper:1 predicted:1 mapped:1 compressibility:1 describes:1 traceless:1 ignored:3 moduli:3 set:3 ser:1 exists:4 fext:6 undergoes:1 unpublished:1 maximum:1 relative:4 depends:1 w3:2 saupe:1 subject:1 surfaces:9 phases:2 tensor:8 λkj:1 clearing:1 away:2 dmr:2 materials:1 symmetric:2 state:6 correctly:1 simplest:2 invariant:2 boundary:3 conditions:3 terms:1 vertical:1 nature:2 however:3 vanishing:3 configuration:2 topology:1 both:3 cos:2 ranjan:1 elastomer:4 strains:4 dated:1 desimone:1 behaviors:1 stretches:1 point:14 cc:4 coexistence:5 high:3 dimensional:1 cz:3 cy:1 cx:1 simply:1 ordered:1 throughout:3 uchida:1 considering:1 described:1 basis:2 stretch:1 aligning:3 three:1 cauchy:2 slowly:1 treat:1 expected:1 pk:5 meeting:1 define:2 obtained:1 direction:7 controlled:1 quantities:1 formed:1 gas:1 worcester:1 bulk:1 external:6 c3:4 general:3 c5:16 case:1 blume:2 look:1 ǫe:1 pacs:2 σxx:62 align:1 value:6 spontaneously:3 will:9 while:1 replaced:1 behavior:3 applies:1 endpoints:1 λt0:1 couplings:1 procedure:1 polymer:1 detailed:1 stretching:2 prost:1 prolate:3 thus:12 surface:11 ii:3 strain:19 ij:3 cond:1 cone:1 triple:1 vx:1 mrsec:1 containing:1 any:5 grant:1 locking:1 lett:4 same:1 orders:1 parts:1 gibbs:1 units:1 finite:4 grows:2 independent:1 imply:1 see:1 again:1 upon:1 functions:1 director:1 domains:1 47a:1 purpose:1 robust:1 identity:4 bhattacharya:1 mech:2 modes:1 pennsylvania:1 well:3 analysis:1 phil:1 crosslinks:1 solids:3 without:1 components:3 easily:2 model:16 arising:2 usual:1 just:2 λt:1 generally:1 predicts:1 useful:1 alignment:1 λxx:7 rapid:1 density:2 rheological:1 other:5 combine:1 plateau:6 samples:4 eur:3 lubensky:4 liq:1 real:1 increased:1 susceptibility:1 showing:2 term:1 harmonic:1 trφ2:1 mol:1 press:3 using:2 unique:1 apart:1 modifications:3 imposed:3 like:1 semi:20 eez:1 δu:1 yields:1 either:1 δf:1 anti:1 soft:28 reduced:2 replacement:1 because:3 often:1 classical:1 picture:1 some:1 sure:1 ezj:1 nonzero:3 cp:4 describing:2 fachbereich:1 measurements:1 critical:11 linearly:1 provides:2 minimal:10 refer:3 measuring:1 minimization:1 σik:1 σij:6 equivalent:6 perpendicular:2 cryst:2 broken:2 softness:1 properties:4 effectively:1 about:3 would:1 impose:1 coexist:5 introduces:1 o:1 addition:1 extensions:1 warner:5 considerations:1 soc:1 rev:7 φxx:3 martensite:1 presence:1 into:7 rotations:3 elasticity:3 nsf:2 pair:1 acad:1 microstructure:1 primarily:1 ǫijk:1 essen:1 gennes:4 terminated:2 fill:1 additional:1 elastic:10 there:6 hex:1 philadelphia:1 long:2 spread:1 pa:1 low:2 way:1 was:1 function:3 complete:2 form:3 becoming:1 hv:1 but:6 fiso:8 volume:3 anisotropic:4 hn:1 hc:3 line:11 uu:5 characteristic:2 mat:1 up:2 crystal:2 below:1 growth:1 limit:1 reflects:1 planes:5 similar:4 average:1 meanfield:1 later:1 associated:4 qij:2 defined:1 uij:5 crosslinking:2 evidence:1 engineering:1 exist:1 interchanged:1 crystals:3 internal:1 regime:6 ni:1 nj:1 transitions:1 dotted:1 no:2 dashed:2 whereas:2 nc:11 when:8 rubber:2 field:8 unambiguously:2 department:2 rt:6 briefly:1 vertex:1 rv:1 prepared:3 elastomers:7 vectors:1 variable:1 astronomy:1 structure:3 breaks:1 assume:1 curve:8 emery:2 mass:1 4h:1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.