text
stringlengths
0
190k
0705.0328.txt |@word roberts:1 sco:1 eda:2 fukui:1 caused:5 magnetic:1 global:3 results:4 switches:1 systemic:2 garching:1 broader:1 edu:2 extinctions:1 3a2:1 gm:3 bergin:12 cases:1 causes:2 layers:21 looking:1 certainly:1 snell:1 ergs:2 ungerechts:2 vs:1 tmb:1 protostars:1 supported:3 quasi:5 critical:1 reipurth:1 caha:1 indications:1 stable:11 l133:1 td:3 presentation:1 indicating:4 2mass:1 tafalla:7 applied:2 esther:1 amplitudes:1 garden:1 acoustic:2 far:1 frequencies:2 modes:6 wave:3 every:1 contours:1 dispersions:1 difference:4 continued:1 uwe:2 trigger:1 leads:1 clouds:4 broderick:1 presented:1 did:1 positions:7 integrating:1 trd:2 lombardi:5 occurs:1 large:3 globule:47 differential:1 l17:1 aas:1 small:3 radio:1 drop:2 shows:6 dip:3 round:1 selfabsorption:2 concluded:2 upper:2 force:1 evaluating:1 oscillation:12 trend:2 semadeni:1 consistent:5 estimates:5 direct:1 pulse:1 cfa:1 approximation:2 likely:8 street:1 value:5 follow:1 further:2 l1512:1 estimated:5 situated:3 linear:8 blue:7 established:1 what:5 errors:2 appear:6 rate:1 sun:1 section:3 while:3 l1689b:1 pulsating:4 values:2 reversals:1 increasing:1 method:3 contrast:2 thin:4 body:1 full:1 simultaneously:3 lee:4 degree:1 iram:4 respectively:3 even:2 component:5 residual:1 here:3 understanding:1 ranges:1 reported:2 asymmetry:6 intercept:4 separate:1 others:1 iras:2 strong:1 equations:1 appears:4 benson:3 obtained:7 search:1 arc:1 shift:1 study:4 larger:2 hydrostatic:3 suggests:3 pico:1 survey:2 whereupon:1 myers:9 guidance:1 diameter:1 useful:2 explained:1 vb:2 dennison:1 ebert:1 apj:20 visible:2 remnant:1 turning:1 evans:3 michel:1 resolutions:2 extinction:36 reactions:1 cloud:26 narayan:1 use:2 doublepeaked:1 usa:2 msx:2 until:1 finally:2 charles:1 comparing:2 kinematics:1 therefore:9 thermally:4 taken:1 type:1 vlsr:5 marginally:1 more:9 separated:1 flat:3 symposia:1 formally:1 thus:5 umich:1 emission:29 interacted:1 visual:10 transient:2 everywhere:1 apjs:2 emitting:1 1tl:1 2gm:1 producing:1 potential:1 vpk:4 carried:1 abundance:7 high:8 account:2 rotational:2 ma:1 hour:1 isotopologues:1 beamwidths:1 equation:1 averaged:2 mi:1 mj:1 nonradial:1 suggestive:1 paragraph:1 nine:1 temperatures:1 widths:6 following:1 under:2 southwest:1 example:3 f1:1 weaker:1 figures:1 figure:15 give:1 calculation:1 expanding:6 sense:7 suggestions:2 dependence:2 states:1 sphere:4 breathing:1 hilton:1 mixer:1 magnitudes:5 ascension:2 exclude:1 isothermal:4 hydrogen:1 species:5 presently:1 azquez:1 respective:1 arbor:1 dsc:1 decaying:1 provide:2 clarke:2 berlin:1 idl:1 saito:1 garay:1 regions:4 maps:5 chopper:1 qgm:1 schloerb:1 widespread:1 sin:3 hundreds:1 profile:9 map:16 description:1 spitzer:2 may:15 quantified:1 starless:8 derived:7 flattens:1 complicated:1 modest:1 plane:2 distortions:1 mag:7 waves:1 date:1 spectrometer:1 april:1 geometrical:1 data:17 heidelberg:1 introduced:1 dynamical:7 third:1 keil:1 curry:1 spectra:28 lines:34 correspond:1 ghz:3 st:2 rather:1 so:8 speeds:3 fundamental:1 correlation:4 acknowledges:1 order:6 outflowing:1 displays:2 integrated:9 saturated:1 closely:1 indebted:1 indeed:3 over:7 displayed:3 years:6 matsumoto:2 dv:9 thermal:13 paper:5 deposits:1 motions:27 kinetic:5 yamaguchi:1 avenue:2 its:18 roots:1 chemical:1 derive:1 outer:17 thank:2 fit:6 ln:2 vth:2 klessen:1 expectations:1 exhibits:1 ds:6 forms:2 h2:2 detected:4 vexp:2 systems:1 zhou:1 might:1 deformation:1 underestimate:1 correspondence:1 stability:3 them:1 mardones:2 greater:1 entire:1 ωr0:1 propose:2 material:7 ottawa:1 very:1 effects:2 they:5 half:1 feature:1 rotation:6 goldsmith:1 association:3 densities:1 mystery:1 bachiller:1 stabilize:1 brightness:1 evaporation:1 university:5 traced:1 νa:1 alem:1 magnitude:4 mode:19 reasonable:1 each:2 crossing:2 found:4 bona:1 difficult:1 traces:1 side:2 carlos:1 mean:3 oscillatory:6 shock:4 frerking:2 significantly:5 hundred:1 energy:6 gaussian:6 related:1 frequency:8 static:2 measure:1 globules:8 summary:2 event:1 es:1 out:8 canada:1 shown:4 unbound:2 redman:2 space:1 gradient:10 since:3 projected:1 research:1 increase:2 contained:1 mccaughrean:1 dominated:2 rem:1 suggesting:1 squares:2 cause:3 hco:38 red:3 hydrodynamic:2 foreground:1 after:1 xω:5 theory:1 offsets:1 million:1 mechanisms:1 possibility:3 standard:1 hankel:1 reason:1 formation:5 fuller:1 estimate:10 compression:1 r0:1 waterloo:1 language:1 r3:1 geometry:1 determining:2 could:13 transition:2 mac:1 noted:1 motion:12 produce:1 ism:4 signature:1 rybicki:1 south:1 first:1 origin:1 bonnor:1 initial:1 sinθ:1 strengthened:1 studentship:1 number:2 reaches:1 fits:4 done:2 least:3 directly:2 thick:7 clarity:1 open:1 angular:5 size:1 jes:1 given:7 perturbation:1 suppl:1 temperature:5 indicate:4 introduction:1 system:1 approximately:4 their:11 confirming:1 perturbations:2 listed:3 calculations:3 gaseous:1 white:2 molecular:18 williams:2 observations:17 shifted:5 collapse:3 discussion:1 17h:3 asymmetric:9 postgraduate:1 reversed:9 interesting:1 resulted:2 part:5 pasj:1 somewhat:3 manifestation:1 july:1 freeze:3 than:14 hispano:1 peaked:6 distance:8 parts:1 observatory:1 showed:4 ara:1 double:6 zero:2 hanawa:2 comito:1 irvine:1 determined:10 intensities:1 amplitude:2 were:24 radius:5 toward:2 pulsation:7 interactive:1 exhibit:2 function:3 fashion:1 bs8:1 ann:1 damped:1 spectrum:1 headings:1 seen:4 seem:1 clearly:2 relatively:1 wilson:2 angle:1 depending:1 self:21 responsible:1 able:2 isolated:2 mechanism:1 note:4 centered:3 fitting:2 internal:6 absorbed:2 pparc:1 vobs:2 transitory:1 better:1 switching:1 channel:1 hyperfine:4 spectral:2 play:1 towards:1 components:3 though:2 probed:2 centro:1 depths:1 most:4 involving:1 germany:1 significant:9 position:5 phase:1 grateful:1 measured:5 class:1 insightful:1 abe:1 latex:1 arizona:1 constructed:3 observation:2 surprising:1 neighboring:2 clear:5 adopt:1 stronger:2 km:32 face:2 pipe:7 ballesteros:2 proceedings:3 optical:1 undepleted:2 velocity:44 effect:1 typically:1 assistance:2 respect:1 slope:2 spherical:3 particularly:1 show:8 emphasize:1 probe:2 12m:4 herbst:1 infrared:2 area:1 beamwidth:2 relation:4 astrophys:1 convolved:1 rough:2 find:6 staff:1 wilner:2 highest:2 ratio:2 quoted:1 parameters:2 macros:1 explain:2 catalogue:1 only:6 corresponds:2 arcseconds:1 molecules:5 postulated:2 hipparcos:1 experiencing:1 oscillate:2 thousands:1 equilibrium:8 ser:1 do:1 his:1 dominant:5 above:2 means:1 michigan:1 overall:3 outflow:2 beam:3 cannot:3 reversal:1 report:1 dr:3 tbd:2 becomes:1 prime:1 reveal:1 cold:1 centaurus:1 bar:1 embedded:1 held:1 bisect:1 fields:1 arxiv:3 tuned:1 investigate:1 predicted:2 doubles:1 discussing:1 inside:2 calar:1 kernel:1 bars:1 set:2 constructing:1 reference:4 problem:1 configured:1 turbulent:8 grey:3 observed:23 differentiation:1 intensity:6 individual:2 sec:1 result:2 sea:1 close:1 tyndall:1 contour:2 best:1 subject:1 surfaces:1 project:1 error:1 pattern:5 away:2 nebula:5 tucson:1 kind:1 case:1 state:9 smallest:1 various:1 wavelet:1 huard:3 between:8 marks:1 numerous:1 across:9 comparable:7 august:2 relative:4 nature:1 initially:1 spacing:2 supernova:1 ktk:1 however:10 jl:3 overlaid:1 harvard:2 hypothesis:1 key:1 group:1 l1157:1 inertia:1 l1521f:1 suggested:1 both:7 essentially:3 keto:8 limits:1 many:1 autocorrelator:1 uncertainty:1 explore:1 against:4 energies:1 roman:1 densely:1 present:1 bristol:3 receiver:1 exceeds:2 contribution:3 whole:2 nearby:1 comment:1 pre:1 adjusted:1 unclear:1 co:6 extent:1 cm:7 point:4 simple:1 narrower:1 period:6 height:2 dimensional:8 simply:2 cosθ:1 virial:1 cs:24 table:6 ogawa:1 throughout:2 appeared:1 considering:1 broadening:1 west:3 alves:13 tatematsu:1 due:2 been:8 pc:13 reduction:1 describes:1 deposited:1 onishi:4 expected:3 ph:3 important:1 fig:7 alto:1 direction:4 adopted:1 corresponding:5 deeper:1 nrc:1 thousand:1 gas:16 θd:1 argument:1 pringle:2 fest:36 observe:1 external:1 systematic:2 astron:2 former:1 spain:2 sound:10 uncertain:1 grains:1 solid:4 reliable:1 profiles:20 l1544:2 near:7 behavior:1 applies:1 situation:1 balance:1 region:2 depleted:1 layer:3 n2h:1 almost:1 av:15 explanation:3 non:1 surface:3 ii:3 characterize:1 vr:2 itself:1 attributed:1 dual:2 aspects:1 jewitt:1 diagnostic:1 portray:1 cjl:1 grant:1 perhaps:2 suggest:4 35m:3 cross:2 same:10 any:1 another:2 complex:5 split:2 evaluate:1 units:1 resulting:4 several:2 fide:1 higher:1 wheel:1 independent:1 outside:2 used:4 peaks:3 see:5 drives:1 v0:3 average:9 moment:1 levels:2 purpose:1 dust:8 kandori:2 passing:1 paredes:2 lower:4 center:8 scenario:1 nevertheless:1 adapted:1 calibration:1 well:2 springerverlag:1 analysis:4 without:1 thought:1 patterns:2 triggering:1 edge:3 does:1 redshifted:5 gravitationally:5 l101:1 grid:3 model:3 chemistry:2 latter:1 pulsationally:2 left:3 aikawa:3 cout:5 proposed:2 less:6 being:1 designating:1 obtain:1 rest:1 gravity:1 sources:3 shape:2 topped:1 turbulence:2 facts:2 spatially:1 fich:1 october:1 speed:12 yet:1 previous:2 wind:1 sampled:2 preprint:1 arcsec:1 hawai:1 density:7 scorpio:1 absorption:7 conclude:1 sky:1 goodman:4 exceed:1 signals:1 source:10 c18:61 inner:2 constant:1 role:1 east:4 excited:2 match:1 nasa:1 real:1 northeast:1 saturation:2 b59:2 lada:14 around:4 slowest:1 jeans:3 absence:1 possible:4 smithsonian:1 harmonic:1 dark:2 possibly:1 denotes:1 indicative:7 marked:1 background:3 denser:1 press:3 using:13 highly:1 correcting:1 occurring:1 like:1 sizes:1 δv:3 workshop:1 caselli:2 velocities:3 ignore:1 indication:2 unperturbed:3 reduced:1 jean:1 omico:1 right:6 plausible:2 village:1 some:4 calculated:5 trends:1 b0:1 nonetheless:1 sight:1 escape:5 images:1 kawamura:1 extended:2 infall:2 opacities:1 provided:1 total:3 dense:5 calculating:1 lead:1 confirm:3 deposition:1 measurements:5 nonthermal:7 depletion:7 defined:2 efficiencies:1 decomposition:1 provides:1 assuming:3 eso:2 unstable:1 three:1 bessel:1 tk:1 demonstrated:1 inclination:1 core:17 process:2 power:1 slight:1 radially:1 radial:1 oscillating:2 agreement:1 expansion:26 linewidths:2 stellar:2 pressure:9 taurus:1 shapes:1 offset:1 plots:3 imaginary:2 comparison:7 about:3 central:2 would:4 origins:2 package:1 column:2 choi:1 ob:4 o:61 langer:4 range:6 a2:2 simplification:1 scatter:1 slightly:7 µmh:1 considerations:2 perturbed:2 cambridge:1 opacity:2 presence:3 previously:3 into:3 within:4 splitting:3 bound:7 negative:4 assess:1 lies:2 appropriate:1 because:3 references:1 determine:1 speculated:1 factor:1 mizuno:1 tracy:1 telescope:4 additional:1 few:2 assumed:4 support:9 there:8 walmsley:1 smoothing:1 dispersion:8 width:11 much:1 low:6 stars:3 ed:3 astrophysics:3 examination:2 yrs:1 was:34 strict:1 hz:2 north:4 form:1 forming:1 believe:1 differences:2 denoting:1 but:12 astro:3 plume:1 5s:2 hl:3 mnras:2 line:50 removed:2 absent:1 made:5 gravitating:1 evident:3 whether:1 characteristic:1 gravitational:4 variations:1 maximum:2 us:2 theoretical:1 below:3 decays:1 those:7 uk:2 gregersen:3 distribution:7 similar:13 display:3 30m:1 detailed:3 viable:1 ac:1 broadened:2 associated:2 cin:4 blueshifted:6 minutes:1 abstract:1 b68:14 mike:1 deep:1 evidence:4 globally:1 oscillations:2 single:4 referee:1 au:1 periods:3 planets:1 our:3 rawlings:1 modeling:1 distributions:3 inc:1 functions:2 dotted:2 no:6 amounts:1 when:1 subsonic:5 field:4 other:6 compares:1 spatial:6 department:1 particular:1 optically:10 apparent:2 star:7 excitation:1 mr2:1 models:1 extincted:1 setting:1 uniformly:1 variation:3 prepared:1 scale:5 bounded:1 peak:15 iω:1 rp:3 astronomy:1 needed:2 structure:4 building:1 bulk:1 assume:2 ta:2 v5:1 required:2 coherent:2 together:1 depth:1 declination:2 mass:10 time:2 moreover:2 cores:15 n2:30 protostar:2 resolution:11 veleta:1
0705.0329.txt |@word partial:1 consider:1 remarkable:1 lagrangian:1 global:1 results:17 four:2 eds:2 consists:1 remarkably:1 contributions:3 hold:1 concerned:1 show:1 charge:1 investigation:1 bakker:1 stable:2 γa:6 case:2 string:1 advantage:1 md:1 very:4 rise:1 keeping:1 splitting:1 αrs:1 every:1 experimentally:1 difference:1 exact:1 condition:1 hamiltonian:1 turns:1 erratum:1 solution:1 m2a:2 large:2 λnf:7 shows:2 dip:1 correct:1 smaller:1 trend:1 consistent:2 estimates:1 approximation:4 second:6 evaluated:2 correlator:1 dynamics:1 estimated:1 errors:3 plays:2 sum:3 selected:1 find:2 current:1 consistently:1 above:2 method:3 satisfy:1 pictorially:1 ibid:1 exchange:2 respectively:1 error:8 here:5 understanding:2 mev:18 ansatz:4 causality:1 along:1 strong:1 change:2 obtained:4 noticeable:1 institute:1 involved:3 study:1 allows:1 resulting:2 implement:1 makes:1 via:1 useful:1 faustov:2 scales:2 apt:24 ebert:1 gluon:2 meson:7 causal:1 use:1 graphs:1 takes:2 would:2 stated:1 finally:3 properties:1 few:3 nucl:6 m1:2 m0:1 qcd:10 taken:2 means:2 type:1 theoretical:8 diagrams:1 more:5 preparation:1 knows:1 skullerud:1 spoils:1 normalized:2 particular:1 cases:1 given:3 iii:1 must:1 high:5 account:5 crosses:2 ma:9 mc:1 mb:1 equation:8 averaged:1 modified:1 ρn:3 mu:1 values:2 splittings:1 ms:1 confining:1 numbers:1 claim:1 renormalization:2 give:1 calculation:2 relativistic:1 choice:1 neglected:1 states:12 contradicts:1 performed:2 unphysical:1 celoria:1 recursive:1 rather:3 s1:1 s0:1 zachariasen:2 far:1 parameter:1 priori:1 tension:1 mat:3 singular:1 replacing:4 overall:2 derived:2 applications:1 inst:2 fits:1 twofold:1 summarize:1 wave:1 data:8 stress:1 effective:6 computations:1 light:6 sp:1 acknowledged:1 sh:1 green:1 representation:2 order:7 least:1 laboratory:1 indeed:1 over:1 displayed:1 through:1 signs:1 differs:1 existence:2 still:2 excitations:1 its:1 tendency:1 meff:1 group:2 thank:1 ln:4 masses:12 solving:1 resort:1 absence:1 according:1 fig:4 total:2 main:2 dyson:1 eur:1 non:5 good:2 safe:1 kuzmenko:1 evolution:1 landau:1 framework:6 ferro:1 effects:3 they:1 half:1 nov:1 yu:2 developments:1 chromodynamics:1 eigenvalue:3 term:2 dirac:1 simonov:2 billo:1 reasonably:1 prosperi:9 each:1 crossing:1 αexp:16 difficult:2 last:1 heavy:2 domain:1 weighted:1 series:1 energy:8 principles:1 ball:2 static:1 combining:1 loops:1 our:8 avoided:1 extract:2 out:3 shown:1 rs:1 restricted:1 since:1 squared:1 testify:1 research:1 increase:1 rg:3 m2j:1 get:1 squares:1 issue:1 integrated:1 math:4 hcm:1 theory:2 associate:1 singularities:4 fisica:1 quark:11 small:1 region:2 estimate:2 dubna:2 interaction:2 retained:1 could:3 m21:1 m22:1 counterpart:1 turn:1 massive:6 alkofer:1 corrections:1 teor:3 hadrons:1 neglect:1 first:4 extracting:1 χ2m:1 jhep:2 smekal:1 number:2 channels:1 antiquark:4 hurdle:1 tot:5 precisely:1 differ:1 perturbation:1 checked:1 similarly:1 introduction:1 leading:1 eqs:1 system:2 relations:1 their:4 confirming:1 scheme:4 williams:1 gives:1 reversed:2 continuous:1 part:3 somewhat:1 authors:1 oge:2 constituent:3 than:4 albeit:1 hepph:1 hundred:2 correlate:2 zero:2 φaµ:2 roberts:1 determined:1 were:1 russia:1 w2:4 exhibit:2 enhanced:1 quasipotential:1 correction:1 mind:1 spectrum:7 curves:1 substantial:2 clearly:2 dosch:3 wilson:1 self:1 efremov:1 note:4 k2:3 fitting:1 potential:4 so:1 caselle:1 eff:4 hyperfine:2 circles:1 play:1 added:1 though:1 singlet:1 involving:1 charm:1 preliminary:1 inserted:1 deviations:1 fiz:4 average:3 milano:3 vertices:2 feynman:1 points:5 exp:2 aµ:1 shirkov:6 typically:1 technical:1 dot:1 quantity:3 particularly:1 rayleigh:1 supported:1 infrared:1 attempts:1 relation:2 threshold:3 d3:1 nlo:3 ground:1 q2:31 based:1 state:5 should:1 analytic:2 only:6 explicitly:2 local:1 handle:1 gev:14 di:3 spurious:2 rept:1 freezing:2 joint:1 ones:2 gφ:1 drawn:1 safer:2 dr:1 processes:1 fields:1 solovtsov:3 arxiv:5 acknowledgments:1 qa:11 baker:2 including:1 fixed:2 view:1 kernel:2 bars:1 set:6 computed:1 achieved:2 imposing:1 sensitivity:1 asterisks:1 relative:3 mentioned:1 see:8 sec:1 result:1 w1:4 discussions:1 terms:2 instance:1 αs:18 exploited:1 ritz:1 luscher:1 nuclear:1 justifies:1 written:1 αe:18 between:2 crude:1 invariant:1 approach:7 nambu:1 triplet:1 recently:1 reproduced:1 tensorial:1 attention:1 focus:1 wj:2 however:2 vanishing:3 rapid:1 comm:1 originates:1 suggested:1 both:4 essentially:2 improved:2 qft:1 taking:2 conclusions:1 reproduces:1 against:1 called:1 chosen:2 context:1 σs:1 σr:1 contribution:2 perturbative:6 whole:2 experimental:9 q10:7 among:2 adjusted:1 relevant:1 point:2 color:1 asymptotically:1 dimensional:2 pole:2 grants:1 simply:1 spans:1 dependent:2 moreover:1 throughout:2 technicalities:1 three:5 been:9 reduction:2 much:3 combined:3 expected:1 yad:1 ph:4 box:1 corresponding:1 observable:1 arcsin:2 sectors:2 bulk:1 confinement:3 determination:2 external:1 prescription:1 denote:1 spin:3 eiq:1 extracted:2 schmidt:1 uncertain:1 solid:1 reliable:1 aip:2 value:7 barbashov:1 euclidean:2 while:2 replaced:2 match:1 behavior:1 shift:1 drs:1 salpeter:2 loop:13 galkin:2 uncertainty:1 mz2:1 refs:3 ir:4 iv:1 ii:1 suganuma:1 reads:1 im:1 conf:2 qj0:1 rid:1 orbital:1 different:1 italy:1 sensitive:1 hecht:1 same:4 φa:23 strange:1 modification:3 finite:3 higher:2 independent:2 used:1 weisz:1 numerical:1 effect:1 hand:3 running:1 sazdjian:1 von:1 recent:2 lower:2 supports:1 mention:1 nevertheless:1 expression:1 well:1 analysis:1 obviously:1 severe:1 dashed:2 model:4 distances:1 being:1 generally:1 reviewed:1 sources:3 adjustable:1 world:2 bogoliubov:1 previous:1 4m2:3 cut:1 hint:1 lattice:4 belongs:1 lett:6 relevance:1 extensive:1 excited:1 momentum:4 read:1 devised:1 iε:1 nesterenko:3 using:2 ruled:1 theor:4 like:3 particle:1 exploiting:1 efimov:1 exploit:2 mexp:5 specific:1 remind:1 imposes:1 yields:2 sezione:1 analyzing:1 papavassiliou:1 therein:2 satisfactory:2 some:4 q20:7 suppl:2 respect:1 matching:1 provided:1 scale:7 quarks:2 does:2 provides:1 unavoidably:1 prog:2 badalian:2 proc:4 refer:3 montaldi:1 q2a:4 scientific:1 power:2 slight:1 problems:1 agreement:6 expansion:1 step:1 bs:15 refers:1 universit:1 hadron:1 comparison:2 about:4 pasechnik:1 discussed:2 dependence:1 o:11 rfbr:1 practical:1 plus:1 introduced:2 rev:8 inclusion:1 into:5 within:6 numerically:1 bound:5 due:1 down:4 references:1 nsp:2 proportional:1 theoretically:2 hep:4 additional:1 area:1 transfer:2 support:1 yao:1 dispersion:2 width:1 low:5 stars:1 jinr:2 was:3 synthesis:1 function:4 complete:2 form:2 phenomena:4 m2:4 triangular:1 but:1 sophisticated:1 boucaud:1 properly:1 m02:3 atom:1 encoded:1 line:4 infn:1 characteristic:1 up:2 quantitatively:2 bethe:2 below:8 limit:4 iterated:1 problem:4 agree:1 detailed:1 constant:2 bethke:1 defined:3 universal:2 orbit:1 general:2 globally:1 quantum:3 exist:1 simulations:3 formalism:4 fizika:1 physical:2 functions:2 us:1 no:1 amounts:2 eq:6 whereas:2 when:2 schwinger:2 field:1 other:3 role:3 details:2 ns:1 deviate:1 picture:1 vertex:1 variation:1 stay:1 a1:1 gev2:1 complications:1 diamonds:1 brambilla:2 ghost:2 correlated:2 coupling:22 algorithm:2 physics:1 tricks:1 curve:1 dσ:2 having:1 implied:1 mass:5 time:1 observables:1 resolution:2 original:1
0705.0330.txt |@word roberts:1 sco:1 eda:2 fukui:1 caused:5 magnetic:1 global:3 results:4 switches:1 systemic:2 garching:1 broader:1 edu:2 extinctions:1 3a2:1 gm:3 bergin:12 cases:1 causes:2 layers:21 looking:1 certainly:1 snell:1 ergs:2 ungerechts:2 vs:1 tmb:1 protostars:1 supported:3 quasi:5 critical:1 reipurth:1 caha:1 indications:1 stable:11 l133:1 td:3 presentation:1 indicating:4 2mass:1 tafalla:7 applied:2 esther:1 amplitudes:1 garden:1 acoustic:2 far:1 frequencies:2 modes:6 wave:3 every:1 contours:1 dispersions:1 difference:4 continued:1 uwe:2 trigger:1 leads:1 clouds:4 broderick:1 presented:1 did:1 positions:7 integrating:1 trd:2 lombardi:5 occurs:1 large:3 globule:47 differential:1 l17:1 aas:1 small:3 radio:1 drop:2 shows:6 dip:3 round:1 selfabsorption:2 concluded:2 upper:2 force:1 evaluating:1 oscillation:12 trend:2 semadeni:1 consistent:5 estimates:5 direct:1 pulse:1 cfa:1 approximation:2 likely:8 street:1 value:5 follow:1 further:2 l1512:1 estimated:5 situated:3 linear:8 blue:7 established:1 what:5 errors:2 appear:6 rate:1 sun:1 section:3 while:3 l1689b:1 pulsating:4 values:2 reversals:1 increasing:1 method:3 contrast:2 thin:4 body:1 full:1 simultaneously:3 lee:4 degree:1 iram:4 respectively:3 even:2 component:5 residual:1 here:3 understanding:1 ranges:1 reported:2 asymmetry:6 intercept:4 separate:1 others:1 iras:2 strong:1 equations:1 appears:4 benson:3 obtained:7 search:1 arc:1 shift:1 study:4 larger:2 hydrostatic:3 suggests:3 pico:1 survey:2 whereupon:1 myers:9 guidance:1 diameter:1 useful:2 explained:1 vb:2 dennison:1 ebert:1 apj:20 visible:2 remnant:1 turning:1 evans:3 michel:1 resolutions:2 extinction:36 reactions:1 cloud:26 narayan:1 use:2 doublepeaked:1 usa:2 msx:2 until:1 finally:2 charles:1 comparing:2 kinematics:1 therefore:9 thermally:4 taken:1 type:1 vlsr:5 marginally:1 more:9 separated:1 flat:3 symposia:1 formally:1 thus:5 umich:1 emission:29 interacted:1 visual:10 transient:2 everywhere:1 apjs:2 emitting:1 1tl:1 2gm:1 producing:1 potential:1 vpk:4 carried:1 abundance:7 high:8 account:2 rotational:2 ma:1 hour:1 isotopologues:1 beamwidths:1 equation:1 averaged:2 mi:1 mj:1 nonradial:1 suggestive:1 paragraph:1 nine:1 temperatures:1 widths:6 following:1 under:2 southwest:1 example:3 f1:1 weaker:1 figures:1 figure:15 give:1 calculation:1 expanding:6 sense:7 suggestions:2 dependence:2 states:1 sphere:4 breathing:1 hilton:1 mixer:1 magnitudes:5 ascension:2 exclude:1 isothermal:4 hydrogen:1 species:5 presently:1 azquez:1 respective:1 arbor:1 dsc:1 decaying:1 provide:2 clarke:2 berlin:1 idl:1 saito:1 garay:1 regions:4 maps:5 chopper:1 qgm:1 schloerb:1 widespread:1 sin:3 hundreds:1 profile:9 map:16 description:1 spitzer:2 may:15 quantified:1 starless:8 derived:7 flattens:1 complicated:1 modest:1 plane:2 distortions:1 mag:7 waves:1 date:1 spectrometer:1 april:1 geometrical:1 data:17 heidelberg:1 introduced:1 dynamical:7 third:1 keil:1 curry:1 spectra:28 lines:34 correspond:1 ghz:3 st:2 rather:1 so:8 speeds:3 fundamental:1 correlation:4 acknowledges:1 order:6 outflowing:1 displays:2 integrated:9 saturated:1 closely:1 indebted:1 indeed:3 over:7 displayed:3 years:6 matsumoto:2 dv:9 thermal:13 paper:5 deposits:1 motions:27 kinetic:5 yamaguchi:1 avenue:2 its:18 roots:1 chemical:1 derive:1 outer:17 thank:2 fit:6 ln:2 vth:2 klessen:1 expectations:1 exhibits:1 ds:6 forms:2 h2:2 detected:4 vexp:2 systems:1 zhou:1 might:1 deformation:1 underestimate:1 correspondence:1 stability:3 them:1 mardones:2 greater:1 entire:1 ωr0:1 propose:2 material:7 ottawa:1 very:1 effects:2 they:5 half:1 feature:1 rotation:6 goldsmith:1 association:3 densities:1 mystery:1 bachiller:1 stabilize:1 brightness:1 evaporation:1 university:5 traced:1 νa:1 alem:1 magnitude:4 mode:19 reasonable:1 each:2 crossing:2 found:4 bona:1 difficult:1 traces:1 side:2 carlos:1 mean:3 oscillatory:6 shock:4 frerking:2 significantly:5 hundred:1 energy:6 gaussian:6 related:1 frequency:8 static:2 measure:1 globules:8 summary:2 event:1 es:1 out:8 canada:1 shown:4 unbound:2 redman:2 space:1 gradient:10 since:3 projected:1 research:1 increase:2 contained:1 mccaughrean:1 dominated:2 rem:1 suggesting:1 squares:2 cause:3 hco:38 red:3 hydrodynamic:2 foreground:1 after:1 xω:5 theory:1 offsets:1 million:1 mechanisms:1 possibility:3 standard:1 hankel:1 reason:1 formation:5 fuller:1 estimate:10 compression:1 r0:1 waterloo:1 language:1 r3:1 geometry:1 determining:2 could:13 transition:2 mac:1 noted:1 motion:12 produce:1 ism:4 signature:1 rybicki:1 south:1 first:1 origin:1 bonnor:1 initial:1 sinθ:1 strengthened:1 studentship:1 number:2 reaches:1 fits:4 done:2 least:3 directly:2 thick:7 clarity:1 open:1 angular:5 size:1 jes:1 given:7 perturbation:1 suppl:1 temperature:5 indicate:4 introduction:1 system:1 approximately:4 their:11 confirming:1 perturbations:2 listed:3 calculations:3 gaseous:1 white:2 molecular:18 williams:2 observations:17 shifted:5 collapse:3 discussion:1 17h:3 asymmetric:9 postgraduate:1 reversed:9 interesting:1 resulted:2 part:5 pasj:1 somewhat:3 manifestation:1 july:1 freeze:3 than:14 hispano:1 peaked:6 distance:8 parts:1 observatory:1 showed:4 ara:1 double:6 zero:2 hanawa:2 comito:1 irvine:1 determined:10 intensities:1 amplitude:2 were:24 radius:5 toward:2 pulsation:7 interactive:1 exhibit:2 function:3 fashion:1 bs8:1 ann:1 damped:1 spectrum:1 headings:1 seen:4 seem:1 clearly:2 relatively:1 wilson:2 angle:1 depending:1 self:21 responsible:1 able:2 isolated:2 mechanism:1 note:4 centered:3 fitting:2 internal:6 absorbed:2 pparc:1 vobs:2 transitory:1 better:1 switching:1 channel:1 hyperfine:4 spectral:2 play:1 towards:1 components:3 though:2 probed:2 centro:1 depths:1 most:4 involving:1 germany:1 significant:9 position:5 phase:1 grateful:1 measured:5 class:1 insightful:1 abe:1 latex:1 arizona:1 constructed:3 observation:2 surprising:1 neighboring:2 clear:5 adopt:1 stronger:2 km:32 face:2 pipe:7 ballesteros:2 proceedings:3 optical:1 undepleted:2 velocity:44 effect:1 typically:1 assistance:2 respect:1 slope:2 spherical:3 particularly:1 show:8 emphasize:1 probe:2 12m:4 herbst:1 infrared:2 area:1 beamwidth:2 relation:4 astrophys:1 convolved:1 rough:2 find:6 staff:1 wilner:2 highest:2 ratio:2 quoted:1 parameters:2 macros:1 explain:2 catalogue:1 only:6 corresponds:2 arcseconds:1 molecules:5 postulated:2 hipparcos:1 experiencing:1 oscillate:2 thousands:1 equilibrium:8 ser:1 do:1 his:1 dominant:5 above:2 means:1 michigan:1 overall:3 outflow:2 beam:3 cannot:3 reversal:1 report:1 dr:3 tbd:2 becomes:1 prime:1 reveal:1 cold:1 centaurus:1 bar:1 embedded:1 held:1 bisect:1 fields:1 arxiv:3 tuned:1 investigate:1 predicted:2 doubles:1 discussing:1 inside:2 calar:1 kernel:1 bars:1 set:2 constructing:1 reference:4 problem:1 configured:1 turbulent:8 grey:3 observed:23 differentiation:1 intensity:6 individual:2 sec:1 result:2 sea:1 close:1 tyndall:1 contour:2 best:1 subject:1 surfaces:1 project:1 error:1 pattern:5 away:2 nebula:5 tucson:1 kind:1 case:1 state:9 smallest:1 various:1 wavelet:1 huard:3 between:8 marks:1 numerous:1 across:9 comparable:7 august:2 relative:4 nature:1 initially:1 spacing:2 supernova:1 ktk:1 however:10 jl:3 overlaid:1 harvard:2 hypothesis:1 key:1 group:1 l1157:1 inertia:1 l1521f:1 suggested:1 both:7 essentially:3 keto:8 limits:1 many:1 autocorrelator:1 uncertainty:1 explore:1 against:4 energies:1 roman:1 densely:1 present:1 bristol:3 receiver:1 exceeds:2 contribution:3 whole:2 nearby:1 comment:1 pre:1 adjusted:1 unclear:1 co:6 extent:1 cm:7 point:4 simple:1 narrower:1 period:6 height:2 dimensional:8 simply:2 cosθ:1 virial:1 cs:24 table:6 ogawa:1 throughout:2 appeared:1 considering:1 broadening:1 west:3 alves:13 tatematsu:1 due:2 been:8 pc:13 reduction:1 describes:1 deposited:1 onishi:4 expected:3 ph:3 important:1 fig:7 alto:1 direction:4 adopted:1 corresponding:5 deeper:1 nrc:1 thousand:1 gas:16 θd:1 argument:1 pringle:2 fest:36 observe:1 external:1 systematic:2 astron:2 former:1 spain:2 sound:10 uncertain:1 grains:1 solid:4 reliable:1 profiles:20 l1544:2 near:7 behavior:1 applies:1 situation:1 balance:1 region:2 depleted:1 layer:3 n2h:1 almost:1 av:15 explanation:3 non:1 surface:3 ii:3 characterize:1 vr:2 itself:1 attributed:1 dual:2 aspects:1 jewitt:1 diagnostic:1 portray:1 cjl:1 grant:1 perhaps:2 suggest:4 35m:3 cross:2 same:10 any:1 another:2 complex:5 split:2 evaluate:1 units:1 resulting:4 several:2 fide:1 higher:1 wheel:1 independent:1 outside:2 used:4 peaks:3 see:5 drives:1 v0:3 average:9 moment:1 levels:2 purpose:1 dust:8 kandori:2 passing:1 paredes:2 lower:4 center:8 scenario:1 nevertheless:1 adapted:1 calibration:1 well:2 springerverlag:1 analysis:4 without:1 thought:1 patterns:2 triggering:1 edge:3 does:1 redshifted:5 gravitationally:5 l101:1 grid:3 model:3 chemistry:2 latter:1 pulsationally:2 left:3 aikawa:3 cout:5 proposed:2 less:6 being:1 designating:1 obtain:1 rest:1 gravity:1 sources:3 shape:2 topped:1 turbulence:2 facts:2 spatially:1 fich:1 october:1 speed:12 yet:1 previous:2 wind:1 sampled:2 preprint:1 arcsec:1 hawai:1 density:7 scorpio:1 absorption:7 conclude:1 sky:1 goodman:4 exceed:1 signals:1 source:10 c18:61 inner:2 constant:1 role:1 east:4 excited:2 match:1 nasa:1 real:1 northeast:1 saturation:2 b59:2 lada:14 around:4 slowest:1 jeans:3 absence:1 possible:4 smithsonian:1 harmonic:1 dark:2 possibly:1 denotes:1 indicative:7 marked:1 background:3 denser:1 press:3 using:13 highly:1 correcting:1 occurring:1 like:1 sizes:1 δv:3 workshop:1 caselli:2 velocities:3 ignore:1 indication:2 unperturbed:3 reduced:1 jean:1 omico:1 right:6 plausible:2 village:1 some:4 calculated:5 trends:1 b0:1 nonetheless:1 sight:1 escape:5 images:1 kawamura:1 extended:2 infall:2 opacities:1 provided:1 total:3 dense:5 calculating:1 lead:1 confirm:3 deposition:1 measurements:5 nonthermal:7 depletion:7 defined:2 efficiencies:1 decomposition:1 provides:1 assuming:3 eso:2 unstable:1 three:1 bessel:1 tk:1 demonstrated:1 inclination:1 core:17 process:2 power:1 slight:1 radially:1 radial:1 oscillating:2 agreement:1 expansion:26 linewidths:2 stellar:2 pressure:9 taurus:1 shapes:1 offset:1 plots:3 imaginary:2 comparison:7 about:3 central:2 would:4 origins:2 package:1 column:2 choi:1 ob:4 o:61 langer:4 range:6 a2:2 simplification:1 scatter:1 slightly:7 µmh:1 considerations:2 perturbed:2 cambridge:1 opacity:2 presence:3 previously:3 into:3 within:4 splitting:3 bound:7 negative:4 assess:1 lies:2 appropriate:1 because:3 references:1 determine:1 speculated:1 factor:1 mizuno:1 tracy:1 telescope:4 additional:1 few:2 assumed:4 support:9 there:8 walmsley:1 smoothing:1 dispersion:8 width:11 much:1 low:6 stars:3 ed:3 astrophysics:3 examination:2 yrs:1 was:34 strict:1 hz:2 north:4 form:1 forming:1 believe:1 differences:2 denoting:1 but:12 astro:3 plume:1 5s:2 hl:3 mnras:2 line:50 removed:2 absent:1 made:5 gravitating:1 evident:3 whether:1 characteristic:1 gravitational:4 variations:1 maximum:2 us:2 theoretical:1 below:3 decays:1 those:7 uk:2 gregersen:3 distribution:7 similar:13 display:3 30m:1 detailed:3 viable:1 ac:1 broadened:2 associated:2 cin:4 blueshifted:6 minutes:1 abstract:1 b68:14 mike:1 deep:1 evidence:4 globally:1 oscillations:2 single:4 referee:1 au:1 periods:3 planets:1 our:3 rawlings:1 modeling:1 distributions:3 inc:1 functions:2 dotted:2 no:6 amounts:1 when:1 subsonic:5 field:4 other:6 compares:1 spatial:6 department:1 particular:1 optically:10 apparent:2 star:7 excitation:1 mr2:1 models:1 extincted:1 setting:1 uniformly:1 variation:3 prepared:1 scale:5 bounded:1 peak:15 iω:1 rp:3 astronomy:1 needed:2 structure:4 building:1 bulk:1 assume:2 ta:2 v5:1 required:2 coherent:2 together:1 depth:1 declination:2 mass:10 time:2 moreover:2 cores:15 n2:30 protostar:2 resolution:11 veleta:1
0705.0331.txt |@word limited:1 measurements:2 partial:1 consider:4 nω:5 rev:2 desirable:1 results:11 four:3 scalar:1 generalize:1 overlap:4 consists:1 follow:1 umer:1 contributions:3 gr:1 compact:1 whose:1 calculate:1 finally:3 those:3 th:4 under:2 include:1 norm:4 applied:3 supported:1 straightforward:2 very:2 frequencies:1 rise:1 translations:1 springer:1 wave:4 putting:1 summarized:1 gambhir:1 condition:1 treating:1 leads:1 clouds:1 disregarding:2 hamiltonian:8 turns:1 gui:1 selfconsistently:1 rˆ:1 ri:2 large:4 solved:1 vector:6 marinelli:1 formally:1 small:1 exhibits:1 enforce:1 cfm:1 ze:1 consistent:1 dimensional:1 approximation:19 zero:4 yoccoz:8 estimated:1 canonical:3 spectral:1 nlj:2 stands:2 cast:1 section:7 find:1 current:2 consistently:1 annals:1 bαβ:1 above:9 new:3 increasing:1 method:8 body:7 full:1 lee:1 eexp:1 exchange:1 respectively:2 component:2 here:5 mev:10 avancini:3 slater:1 coupling:2 equations:5 εn:2 change:1 ıguez:1 obtained:9 generalizing:1 numerator:1 noticeable:1 involved:2 study:1 changed:1 allows:2 completely:1 brazilian:1 usually:1 implement:2 makes:3 ipa:2 santa:1 ground:3 e14:1 refitting:1 translational:1 rkl:4 total:13 cloud:1 m2σ:5 use:3 would:2 positive:1 contains:2 charge:13 next:2 discrepancies:1 few:1 nucl:5 noting:1 therefore:1 relativistic:7 taken:7 more:6 rk0:1 alberto:3 brings:1 operators:4 corrected:3 thouless:1 known:5 cases:1 iii:5 fermionic:6 account:6 ρb:2 quantized:1 equation:7 fµν:2 det:1 reads:4 reproduce:2 fock:1 values:5 ms:2 following:3 root:4 lσ:1 calculation:7 introduces:2 neglected:2 lω:1 states:11 numbers:2 want:2 unphysical:1 rodr:1 respective:1 provide:1 discussion:1 justifiable:1 feature:1 write:2 far:1 m2ω:11 parameter:1 classify:1 gordon:3 suffer:1 product:2 description:1 may:6 after:6 treatments:1 applications:2 modest:2 explored:1 waves:1 fits:1 summarize:1 derives:1 data:1 fm:4 constants:2 stress:3 short:1 physical:1 remember:1 third:2 read:1 light:1 birse:1 explicit:1 ones:1 so:8 sc:1 definitions:1 eisenberg:1 order:6 breaking:1 gω2:2 nucleon:14 developed:2 over:1 move:1 displayed:1 paper:3 including:5 still:2 its:2 before:1 rh:1 longitudinal:1 energies:2 interesting:1 masses:2 d35:1 schuck:1 boson:1 degrees:7 choose:2 main:3 might:2 non:2 good:1 outlined:1 greiner:1 break:1 subtraction:2 coimbra:2 cep:1 now:6 represents:2 term:6 dirac:4 oxygen:2 fiolhais:3 university:1 presented:3 theory:4 magnitude:1 reasonable:2 each:1 found:1 michaels:1 mean:17 spinor:1 square:5 ei:4 due:1 energy:37 solution:2 isospin:1 expect:1 quantum:5 our:7 eq:1 ep:3 out:4 shown:6 gv:2 matrix:1 space:2 restricted:2 furthermore:1 since:4 lagrangian:5 projected:2 denotes:1 particles:1 denoted:1 receiving:1 ref:7 correct:1 rj:1 linear:6 mσ:1 interactions:2 mω:5 free:9 quark:1 approaches:1 york:1 dω0:2 interaction:2 chiral:1 feasible:1 motion:10 turn:1 massive:1 corrections:3 oscillator:4 onto:1 first:3 major:1 already:3 symmetry:3 rms:5 number:3 restrict:1 clear:1 smaller:1 done:2 least:2 another:1 ring:3 invariance:1 given:4 rewritten:1 similarly:2 introduction:2 opportunity:1 system:7 relations:1 their:2 intermediate:1 too:4 calculations:2 dealing:1 variational:1 final:1 recovered:1 gives:2 shifted:1 shell:5 2am:4 zeroth:1 pa2:2 transverse:1 part:6 believe:1 representing:2 coefficients:2 ofmass:1 kind:1 holland:1 sections:1 approximations:4 second:3 annihilation:3 determined:1 were:4 bare:1 opolis:1 treated:2 peierls:9 function:6 rewrite:2 correction:24 modern:1 say:1 grices:1 conjugate:3 close:1 recover:1 occupied:1 relatively:2 built:1 florian:1 pa:2 self:2 able:1 note:2 instance:3 fitting:1 without:9 gσ:3 take:3 mit:1 gω:8 unperturbed:1 ripka:1 even:2 begin:1 exactly:1 serot:2 though:1 quote:1 most:3 alpha:1 commutation:1 soliton:1 ka:5 ckb:2 considered:3 calculated:3 traditional:1 kr:4 exp:9 uδ:1 physics:7 fact:1 quantity:1 saying:1 show:3 nσ:8 rti:3 bring:1 radii:1 fermions:1 uβ:1 d3:10 schmid:2 help:2 symmetric:1 partially:1 based:1 proposed:1 parameters:7 written:2 should:2 only:7 explicitly:2 factor:1 hamiltonians:1 do:2 dk:6 klein:3 means:2 spurious:3 de:2 da:5 cannot:1 progress:1 compute:1 dr:8 pωi:2 extract:1 gs:2 fields:7 arxiv:2 expansions:3 common:1 double:3 wilets:1 view:1 kernel:5 set:5 computed:2 reference:4 achieved:1 correlations:1 j0:9 j1:1 ωt:2 relative:1 see:4 radius:20 result:4 sea:1 recently:1 acts:1 techniques:1 brazil:2 evaluation:2 interacting:2 federal:1 nuclear:13 review:1 uα:5 uγ:1 label:1 αa:2 state:20 difficulties:1 cambridge:1 closed:5 invariant:3 approach:2 publishers:1 terms:7 extend:1 attention:1 eˆt:1 however:3 spectroscopic:1 jie:1 ket:1 both:4 last:1 many:3 region:1 conclusions:3 equal:1 quantization:3 chosen:2 hω:5 figures:1 hσ:6 contribution:8 0i:1 finds:2 experimental:5 ck:2 unshifted:1 blaizot:1 cm:21 point:2 ca:6 harmonic:6 proton:3 bδ:1 anti:1 bα:2 bβ:1 bγ:1 respect:1 cp:1 considering:2 pp:6 described:7 perspectives:1 observing:1 guzm:1 three:4 been:2 defined:4 pollock:1 much:3 treat:1 interest:1 basic:1 expected:2 harwood:1 systems:2 field:24 determinant:1 arises:1 divergence:2 commutes:2 coherent:7 systematic:1 demand:1 prescription:1 worked:2 careful:1 present:1 case:7 extracted:1 pacs:1 expanded:3 single:6 value:3 heidelberg:1 calcium:2 situation:1 eik:3 property:1 procedure:6 portugal:2 vol:1 vi:2 binding:7 iv:2 ii:6 ik:1 henley:1 fermion:2 different:1 formalism:3 perform:3 same:5 pσ2:1 parts:1 emphasize:1 modification:2 finite:3 shan:1 neutron:1 difficult:1 used:3 numerical:3 ri2:1 effect:1 hand:1 hartree:15 totally:1 circumvented:1 normalization:2 lower:1 off:1 center:10 well:7 c63:1 analysis:1 academic:1 contact:1 solve:2 components:3 sets:1 coordinate:3 position:1 model:21 centerof:1 latter:1 usual:5 spherical:6 just:4 being:1 percent:1 identically:1 drdr:1 obtain:7 rest:2 sources:1 projection:18 polarization:1 density:3 parametrization:1 potential:4 treatment:1 horowitz:2 heavier:1 lagrangians:1 momentum:7 aspects:2 eigenfunction:1 eigenvalue:1 iα:2 advances:1 iγ:1 vα:3 vacuum:3 press:1 using:16 unique:1 translationally:2 necessary:1 like:1 particle:11 follows:1 specific:1 steps:1 exploiting:1 become:1 nucleons:9 hαβ:2 catarina:1 because:1 parametrizations:1 classical:1 creation:3 some:3 pσ:2 table:8 pω:7 ourselves:1 meson:21 describing:2 lfree:4 per:1 mesons:19 everything:1 proj:5 assuming:1 prog:1 readily:1 bessel:1 mesonic:5 refer:1 ısica:1 obey:2 slight:1 equivalent:1 radial:2 expansion:2 broken:1 although:2 properties:3 publishing:1 comparison:2 valence:3 carried:1 freedom:7 discussed:3 o:6 convenient:1 must:3 bounded:3 introduced:2 computational:1 inclusion:3 into:4 within:6 functional:1 negative:1 nucleonic:5 appropriate:1 determine:1 operator:10 approximately:1 technically:1 spinors:2 assumed:1 approximate:1 long:1 rcm:2 quadratic:1 way:4 irrespective:1 was:4 lowest:1 north:1 complete:1 form:9 effects:1 lint:2 but:11 applicable:1 neutral:1 hn:5 cnpq:1 true:1 he:8 made:2 applying:1 represent:1 up:2 us:9 international:1 below:1 projecting:1 ωl:2 meng:1 fluctuations:1 problem:3 similar:3 called:3 walecka:1 worthwhile:1 int:2 abstract:1 describe:1 bβα:1 denote:1 multiparticle:1 conserved:2 journal:2 corresponding:2 work:7 distributions:1 universidade:1 dα:2 again:1 functions:2 compared:4 no:5 na:6 nb:1 hpp:1 when:2 application:1 other:5 spatial:3 department:1 company:1 draw:1 intend:1 zhou:1 models:7 variation:5 important:4 nucleus:8 allowing:1 included:4 omega:4 needed:1 suffers:1 longer:1 souder:1 ieα:1 sigma:4 factors:3 together:2 mass:16 depto:1 observables:4 nuclei:13 2mω:1 original:3 once:1
0705.0332.txt |@word holman:4 monte:1 consider:2 chain:1 d74:1 spie:1 dynamic:2 results:6 laura:1 trodden:1 gr:1 increase:3 albrecht:1 nonlocal:1 program:1 present:2 th:4 under:2 tegmark:2 cahn:1 dramatically:2 case:13 supported:4 string:2 very:2 every:3 interpreting:1 summarized:1 condition:1 chapel:2 themes:1 hamiltonian:2 proc:1 anisotropy:2 list:1 cmb:9 large:3 race:1 team:1 markov:1 noted:1 degeneracy:1 force:1 oscillation:6 riess:3 edu:2 zero:2 further:1 dynamics:2 estimated:5 carlo:1 wmap:6 aim:1 what:1 plays:1 appear:1 fact:1 dr2:1 current:9 goes:1 rssd:1 crotts:1 backreaction:9 respectively:9 here:6 agreement:1 reported:1 explore:1 others:1 path:2 along:1 appears:1 change:1 obtained:1 search:1 shift:3 inspired:1 larger:5 pinning:1 prior:4 survey:3 ervin:1 action:1 changes:1 emerge:1 hst:3 mather:1 4a3:1 highly:2 scaled:1 visible:1 total:1 univ:3 planck:3 landscape:8 d73:1 conventional:1 usa:1 remains:1 contains:1 predictions:1 comparing:1 therefore:2 m2:1 survive:1 type:1 contours:9 fractions:1 flat:2 liddle:2 becomes:1 conducting:1 curvature:47 aware:1 correspondingly:1 labelled:1 known:1 central:1 lcdm:2 iii:1 utexas:1 integrating:2 equation:10 values:3 evolved:1 universe:33 following:2 example:4 history:1 wang:5 cosmological:5 give:2 ds2:1 bennett:1 ratios:1 assumptions:3 performed:2 allowed:3 mpc:1 rather:1 discussion:1 maps:1 nontrivial:6 kamionkowski:1 answer:1 parameter:2 sin:1 sne:2 may:2 derived:4 plane:1 sn1a:1 data:28 constants:1 branches:1 sectors:1 spectra:1 correspond:8 st:1 so:1 sn:2 allow:2 putting:1 subsequently:1 order:2 figs:3 interpretation:2 kiefer:1 perlmutter:1 2rx:1 constrained:1 satisfied:1 course:1 experiments:5 including:2 lss:2 satisfies:1 its:7 galaxy:2 observational:4 outer:7 la:2 interesting:2 solving:2 decreases:1 late:1 degrees:2 fig:16 melchiorri:1 h0:4 arguments:1 versus:1 non:1 good:1 motivated:6 greater:1 thereby:1 effects:1 they:1 now:5 hall:1 yw:1 term:15 finite:1 mcmc:2 fixed:1 university:1 presented:2 hepth:1 each:2 zcmb:3 found:4 traces:1 exquisite:1 constraints:7 differential:1 significantly:4 superhorizon:2 energy:22 idea:1 used:1 astrophysical:2 expect:1 measurement:3 quantum:6 our:19 eq:6 special:2 out:3 leave:1 shown:1 space:4 oklahoma:1 since:3 rev:5 qc:1 denotes:2 content:4 investigation:1 dominated:1 hill:2 induced:1 issue:1 shows:5 turning:4 theory:2 ast:1 confidence:18 lmt:1 surveys:3 brooks:1 monotonic:1 org:1 likelihood:2 degeneracies:1 hubble:8 interaction:3 geometry:12 determining:1 could:2 cosmic:10 times:1 motion:1 massive:1 yun:1 hence:1 staggs:1 first:3 there:2 features:1 nhn:1 geodesic:1 reaches:1 2a4:1 done:1 drastic:1 illustrate:1 πr:1 given:6 introduction:1 pinned:1 indicate:1 perturbations:2 master:2 types:2 calculations:1 eqn:5 hetdex:1 dt2:1 cycle:3 recovered:1 gives:2 shifted:3 ratio:1 mersini:7 baryon:2 imprinted:1 part:2 suntzeff:1 than:3 2ax:1 oscillate:1 distance:5 kind:1 wilkinson:1 houghton:6 unfortunately:1 princeton:1 rate:1 submitted:1 collaboration:2 project:2 matter:7 future:3 amplitude:1 were:1 contrasted:1 bet:1 prd:1 correction:1 say:1 need:1 seen:4 cosmology:4 any:1 acceleration:1 baas:1 strength:1 gravity:4 note:2 phillips:1 absorbed:1 take:1 spergel:1 norman:1 index:1 friedman:1 reach:1 most:1 bridle:1 plan:1 significant:1 preliminary:1 phase:3 acknowledgements:1 extremely:1 class:3 especially:1 implications:1 km:1 doe:1 points:1 constrain:4 oscillates:3 physics:6 wavenumber:1 parkinson:2 selection:3 show:1 lewis:1 probe:3 stringent:1 astrophys:3 rough:1 trivial:1 find:3 ground:2 fg02:1 based:4 knowledge:1 parameters:9 state:6 should:3 only:3 factor:3 integrate:1 bernstein:1 local:1 above:4 get:2 vary:2 de:1 overall:1 assumed:1 da:1 joint:9 nearly:1 closely:1 report:1 differentiating:1 takahashi:2 regarding:2 approach:1 arxiv:13 grav:1 patch:2 investigate:3 paper:1 contain:1 through:5 cycles:2 set:1 observer:1 phenomenologically:1 maximum:1 detection:1 depends:3 legacy:1 result:2 close:2 halliwell:1 contour:7 ways:1 currently:1 ωk:45 outside:1 various:1 closed:5 between:2 conditions:2 discovery:1 notice:1 ability:2 nature:1 supernova:3 however:1 implementing:1 huth:1 probing:1 improve:2 both:2 desired:1 career:1 density:3 enabling:1 unc:1 nearby:1 among:1 relevant:1 point:3 simple:2 cb:1 ca:1 period:6 adding:1 leads:1 respect:2 second:1 considering:3 better:1 hawkins:1 described:4 geometries:2 basis:1 trajectory:10 locally:1 due:3 been:2 implicit:1 hawking:1 basic:1 expected:2 ph:13 wx:1 pm:1 corresponding:4 sufficient:1 cheng:1 precision:1 observers:2 representative:1 astron:2 those:1 applied:1 extracted:1 look:1 supernovae:1 value:2 will:2 dept:1 while:4 replaced:1 study:2 hewitt:1 studied:2 vol:1 metric:1 wkb:1 thus:2 falmer:1 iv:1 ii:1 ia:5 different:2 null:1 9qh:1 grant:3 perform:1 make:1 cumulative:1 radiation:1 same:3 clearly:1 shifts:2 quant:1 wavepacket:4 mukherjee:3 modification:1 dimensionless:1 gets:1 independent:2 investigated:1 http:5 see:3 effect:4 phy:1 levels:7 entanglement:2 php:1 recent:1 lower:1 task:1 scenario:2 well:2 analysis:4 more:2 observations:2 components:3 coordinate:5 model:21 otherwise:1 usual:1 nc:1 appropriately:1 being:1 captures:1 obtain:1 inflaton:1 differentiation:1 momenta:1 yet:1 captured:1 previous:1 heuristic:1 conclusions:1 scales:1 except:1 day:2 2df:2 samples:1 pparc:1 motivating:1 increased:1 sussex:1 possible:2 dark:10 test:1 increases:1 background:3 vacuum:1 press:3 using:1 emergence:1 apj:6 intertwined:1 like:2 particle:3 bn1:1 become:2 reduced:1 imprints:4 www:4 knox:1 classical:8 some:1 kolb:1 suppl:1 universes:2 scale:6 lead:2 affects:1 measurements:1 integration:1 microwave:3 does:2 esa:1 assuming:1 sdss:5 chains:1 robertson:1 bf:1 run:1 freedman:2 radial:1 oscillating:18 use:3 expansion:2 notably:1 shifting:5 br:1 acoustic:2 plots:7 hilbert:1 brighton:1 about:2 goods:1 ok:1 would:6 constraint:1 freedom:2 year:5 dependence:4 o:1 clas:1 range:2 important:2 d68:1 horizon:2 ou:1 allowing:2 considerations:1 redshift:2 h2:3 into:1 within:3 numerically:2 bound:1 nsf:2 three:4 down:2 thinned:1 einstein:2 uncertainties:4 hep:5 additional:1 h02:2 initial:7 question:1 inner:7 crucially:1 was:2 function:6 tight:1 jury:1 complete:1 form:2 but:3 hu:1 astro:13 verde:1 hn:7 hm:3 mnras:3 line:2 level:2 dissipative:2 proposal:2 made:1 compute:1 gravitational:2 ωr:3 robustness:1 bounds:8 us:4 below:1 frequency:2 ωm:18 uk:2 percival:1 ωb:3 similar:2 eisenstein:1 strongly:1 constant:18 v36:1 int:1 pia:1 contribute:1 denote:1 globally:1 formalism:1 functions:2 compared:3 no:2 priors:2 wavefunction:2 when:8 field:2 lsst:1 other:3 role:3 details:1 spatial:2 department:3 conclusion:3 deviation:1 models:11 setting:1 deriving:1 a3:1 a2:3 a4:2 ubc:1 included:3 astronomy:3 n2:1 structure:1 relativity:1 assume:2 age:3 rs:1 together:3 n5:1 presenting:1 time:14 walker:1 observables:2 decoherence:1 astier:1 once:1
0705.0333.txt |@word homomorphism:23 consists:8 sch:2 whose:10 γr:15 γw:1 patched:1 under:23 injectives:5 γf:7 γe:47 discriminants:1 subbasis:1 p2:2 rise:1 exception:3 p1:2 every:38 manin:1 bρ:11 disturb:1 induction:4 glues:1 solution:1 vector:54 indices:1 hcm:1 glued:1 submodules:39 direct:8 second:21 tangential:2 subordinate:1 even:11 filtration:7 complexities:1 xvii:1 above:25 new:8 increasing:1 consisting:6 coefficient:3 guillemin:1 notions:1 never:2 residual:14 here:24 refinement:3 path:3 obtained:7 gla:5 study:2 codegeneracy:1 glr:2 suitable:3 changes:1 remembering:1 projection:21 classification:1 elaborated:1 replace:8 rπ:7 rρ:1 bre:8 total:6 unit:6 cheating:1 reflected:1 would:12 cohomological:2 e1:7 bundles:10 chooses:2 γrs:1 call:10 therefore:75 m3:6 m2:21 type:17 tell:1 kε:3 composite:1 berlin:4 hold:1 tx1:2 must:6 md:147 springer:5 ma:2 pursue:2 ndimensional:1 setup:2 mn:6 mi:2 theories:6 endow:1 mx:9 give:27 preserving:2 caused:1 want:3 xij:4 unordered:5 end:8 ocker:1 renumbering:1 provide:1 verify:4 hom:15 how:10 nontrivial:1 w23:4 answer:4 symposium:1 ordinary:2 classify:1 lan:2 description:17 replacing:3 after:9 diagram:45 summarize:1 arch:1 heidelberg:2 types:2 gluing:1 third:2 hypotheses:1 ultimate:1 order:7 operations:4 restriction:24 interpretation:1 over:78 satisfied:4 london:1 thesis:9 satisfies:4 before:3 sheaf:39 imm:12 writing:2 easier:1 connectedness:1 maximal:14 them:12 xa:1 combination:1 coproducts:1 they:27 singularity:2 prilozhen:1 represents:1 simplices:2 classified:2 properness:2 reasonable:2 each:49 higher:3 side:2 associative:1 mean:2 meets:1 ιa:2 ιb:2 principles:3 ιf:1 combining:1 xp:3 rv:2 rp:16 rq:7 rr:6 wsp:2 gradient:1 restricted:6 unlabeled:1 crucial:3 rd:69 re:41 rf:14 unrelated:1 weighted:9 ra:4 rb:1 rl:1 rm:145 rn:18 ri:64 sma:2 rk:2 gromov:2 linear:48 little:1 free:14 standard:4 admits:1 wanted:1 r0:1 r1:8 r2:14 r3:1 starts:1 e2pq:8 maximality:2 δij:1 already:1 features:1 primary:2 rank:8 restrict:5 another:9 illustrate:1 similarly:7 xii:1 top:13 xik:1 transitively:1 tot:7 needed:2 too:2 1e:1 ordered:2 submersion:2 ranging:3 collapse:1 alonso:1 rmodules:1 tool:2 realization:1 1this:2 reparametrized:2 finitely:54 expx:4 target:9 likely:1 xi1:1 classes:3 stratified:13 glueing:1 enables:1 powers:1 sees:2 rewrite:3 mind:1 spectrum:26 seen:13 acyclicity:1 epq:18 contents:2 ray:1 jxr:22 realm:2 homological:3 latter:2 oriented:5 forces:1 indexed:2 jxk:1 circles:1 mˆ:1 object:2 simplify:2 regular:11 exercises:2 observation:2 neighborhoods:2 partition:3 flow:3 vertices:6 points:47 principle:6 notion:2 implying:2 d1:1 x1:77 explain:7 topological:78 geodesics:1 continuity:13 do:24 sense:10 subspaces:19 coefficients:12 df:7 dg:1 dd:37 1if:1 preferred:2 reconstruct:1 dt:5 covering:9 fields:2 eves:1 twice:1 bad:1 riemannian:2 observes:3 observed:1 depends:3 homalg:3 result:14 w1:10 dµ:1 alternative:1 best:1 techniques:1 said:2 fn2:1 away:3 symmetric:5 µn:11 simplest:1 approach:2 preserve:3 embeddings:1 extend:3 adding:1 modify:1 restricting:3 weak:15 however:4 equals:1 vassiliev:7 news:1 topology:88 xˆi:1 ranges:1 essentially:1 cov:1 0y:1 faces:5 argue:1 abbreviate:2 nˆ:9 polynomial:9 diff:40 j02:7 commutative:10 puts:1 basis:9 union:11 ai1:2 three:2 been:1 much:1 interest:1 basic:3 algebras:8 exactness:1 res1:15 families:2 lift:4 j0r:51 manifolds:31 applied:1 topologize:1 transformation:1 aim:1 euclidean:9 near:9 neat:4 applies:3 property:21 procedure:3 iy:1 ix:23 ip:1 ir:2 verges:1 iv:10 ii:26 need:19 ik:6 ij:2 im:9 il:2 id:39 containing:1 pry:4 make:4 prx:15 complex:7 split:6 independent:5 numerical:1 hand:16 funktsional:1 bredon:1 weakly:1 xjj:1 academic:1 prescribes:3 claims:2 quotient:34 possesses:1 left:23 just:26 subsheaf:1 identify:21 transforms:1 facts:3 yet:1 previous:12 gki:1 rkr:1 nilpotent:1 bp1:1 tuples:4 collections:1 easy:18 2this:1 possible:8 spanned:2 unique:10 poset:1 advanced:1 appearing:1 texts:3 bpi:2 permuting:1 unnecessary:1 bpn:1 informative:1 arbitrary:1 immersions:14 fibrewise:11 right:9 deal:3 truncated:3 sends:6 gγ:2 dense:10 bottom:4 exhausts:1 normal:2 everything:3 exposition:1 linearly:4 ˆi1:1 properties:12 takes:3 chapter:42 dˆ:1 o:28 ψr:1 ensure:1 surjections:1 slightly:3 automatically:1 considerations:1 soc:1 statements:2 2for:1 down:1 lies:16 balanced:2 reducing:1 methods:1 topologies:8 support:3 approximate:2 pages:1 way:30 m1:10 was:9 m0:5 form:25 concatenated:1 converse:2 denoting:5 forgetful:5 illuminating:1 grassmannian:3 removed:2 true:11 versions:1 supp:12 compactification:3 inside:7 preimage:6 complications:1 coverings:5 coends:1 b1:6 strengthening:1 proved:9 codimensions:4 computing:2 homogenous:2 stronger:2 abstract:3 convergent:7 proves:6 exist:3 promised:2 face:4 distributions:1 check:4 triangles:2 dα:1 ni:4 nm:1 nx2:1 na:30 whereas:3 when:27 vanishes:3 ny:7 unambiguously:1 tid:2 erentiables:1 functorial:1 preceding:1 sheafification:4 variable:1 ξb:2 ξe:7 assume:39 interval:1 modules:30 together:13 factorizes:1 time:2 n1:1 n2:1 xk1:3 chain:2 global:4 focus:1 leads:3 computation:4 lll:3 hdim:1 row:5 devoted:3 certainly:8 inverse:10 depend:12 graph:1 noncompact:5 finally:7 analogous:1 leary:1 advantage:1 orthogonal:1 choice:13 orientations:1 entries:1 exact:19 dim:43 presented:1 did:2 turns:3 jv0:2 leave:1 involution:7 golubitsky:1 dir:2 upper:1 work:6 says:4 sign:22 colim:24 preimages:8 spectral:56 appear:1 goes:1 satisfy:2 understanding:1 tangent:10 groups:19 along:14 appears:3 change:2 sending:27 my:54 vectors:5 example:50 spheres:2 useful:5 subcategory:4 diffeomorphisms:4 extra:1 inducing:1 merely:3 prefer:1 working:1 prove:34 sake:1 positive:6 eσ:2 going:4 criteria:1 compactly:3 diagrams:1 introducing:1 duality:12 ua:16 ooo:4 equipped:2 appendix:22 everywhere:1 eλ:5 cases:1 cardinality:1 yjj:1 cap:4 labeled:1 values:5 following:56 making:3 trans:1 claim:16 dedicated:1 subcategories:1 degenerate:1 december:1 permutations:1 spv:1 verlag:4 s2:1 discussion:1 s0:1 write:10 nyi:1 criterion:8 fourth:2 obius:1 map:308 product:31 mat:1 may:2 needs:2 applications:2 mac:3 produce:7 designed:1 representations:2 data:1 lifting:1 rmodule:3 natural:13 remember:3 homotopies:1 whenever:5 sr:1 sp:35 yielding:1 st:12 si:5 sh:3 so:73 sn:1 sc:1 representation:25 sa:5 talk:2 sd:50 serving:1 neighbourhoods:11 indeed:10 mainly:1 immer:1 course:5 omitting:1 differs:1 still:4 derive:4 group:12 sν:4 interesting:3 coordinates:5 forms:1 constitutes:1 τy:5 main:27 correspondence:2 non:4 introduce:4 identically:2 now:55 discuss:2 possess:1 term:1 equality:6 name:2 corners:5 orthonormal:1 em:12 el:1 domain:2 en:3 ei:13 ej:2 ed:19 ex:7 happen:1 ev:1 ep:5 neighbourhood:19 er:3 shown:4 hcq:1 space:116 looking:2 contained:2 formula:19 squares:3 hcn:7 shows:7 earlier:2 theory:6 hull:5 quite:1 homeomorphism:10 complicated:1 remainder:1 e0:10 care:1 equivariantly:2 impose:1 thing:2 fc:4 place:1 qqq:3 think:13 first:60 xj:5 xk:8 intuition:1 xi:30 xn:7 xm:12 xb:3 u1:6 variables:1 coming:1 xd:14 stalk:1 xy:10 xr:27 ring:7 open:54 ont:1 given:29 necessarily:9 checked:1 structured:1 yii:1 indicate:2 brevity:2 1d:7 1f:2 structures:2 speaking:1 gives:14 cup:3 continuous:99 proving:6 transverse:22 parametrized:1 x2:70 x3:42 x0:21 copy:1 than:4 specify:1 require:2 computes:1 were:1 decompose:2 interpolations:2 ann:3 turned:1 generalization:10 say:13 recover:1 saw:3 any:87 functors:8 mapping:3 ideas:3 converges:15 note:28 ideal:37 take:13 interior:3 destroy:1 coincide:1 switching:1 formulas:1 sure:1 straightening:1 opposite:2 e1pq:4 algebraic:8 pair:3 sa1:1 sa0:1 brno:1 considered:1 later:7 monoid:1 typically:1 4this:1 cosimplicial:4 precise:3 show:27 spaces:61 corner:1 ground:1 homology:27 fibre:28 slov:1 fibrations:1 state:1 only:42 explicitly:3 germs:3 excision:1 get:58 lighten:1 mx3:1 space1:1 cannot:2 invariant:7 enjoys:1 closure:4 skeleta:1 mapped:4 nondecreasing:1 finishing:1 kernel:21 surjectivity:3 j4:1 j0:37 relative:2 namely:6 differentiable:1 rmd:3 fails:1 satisfying:7 ways:1 subsequent:1 αa:21 outside:5 between:24 αi:3 justified:1 reading:1 x21:4 across:3 x22:2 rm2:6 rm0:10 rm1:9 jx:1 jy:4 vertical:1 ju:1 xvi:1 jq:1 jr:1 inclusions:7 jh:2 ji:1 jj:1 jets:19 article:4 come:2 σk:3 σh:4 σn:5 many:2 according:15 σd:12 enabling:1 σz:4 σy:4 embedding:14 σr:1 σp:6 expression:3 fix:9 comes:3 among:2 characterization:1 overview:1 γ0s:1 lagrange:1 constant:14 naturality:3 considers:1 considering:3 amer:1 submanifold:27 aˆ:8 locally:54 springerverlag:1 reflective:1 x2m:1 direction:13 formed:1 toronto:1 observe:9 ınek:1 evidence:1 those:14 case:65 situation:5 orientation:6 metric:3 concatenation:5 couples:1 middle:2 good:2 fibration:2 hϕ:13 uxk:1 different:6 dε:2 verified:1 doctor:1 hψ:2 same:42 verifies:1 constructed:7 extended:4 trivially:2 running:4 µk1:2 changing:1 supports:34 no:14 roughly:3 without:5 extensible:1 fixing:1 coordinate:13 model:1 reward:1 dimension:8 monoids:1 isometry:2 manifold:46 being:20 generally:5 resp:2 actions:3 speed:1 blow:3 lebesgue:1 thinking:3 except:1 setting:7 contractible:3 complements:1 real:6 around:2 res0:15 decomposed:1 using:22 decomposes:2 mod:6 scalars:1 identifying:2 serves:2 either:12 xviii:1 reduced:3 satisfactory:1 tvs:3 moreover:25 images:3 thinks:1 nonzero:4 provided:6 dimensions:2 theorem1:1 critical:1 kms:3 provides:4 projectives:1 arrow:9 power:1 equivalent:18 bilin:1 osculation:1 injectivity:1 comparison:1 trivialization:1 ok:1 oe:6 theorems:1 discussed:1 ob:4 dually:1 acyclic:9 morphism:2 ηe:5 cambridge:2 jι:1 inclusion:45 unbounded:1 image:30 references:1 determine:1 strip:1 bijective:7 metrizable:1 area:1 there:97 start:7 low:1 lot:1 plusieurs:1 complete:1 enough:19 lane:1 applying:4 embedded:1 minkowski:1 submanifolds:12 embed:1 agree:9 obtains:1 taylor:1 af:1 ai:8 certain:9 ak:2 describe:8 am:5 general:28 ap:1 liverpool:1 associating:2 formulation:2 ax:2 adjunction:2 again:28 igu:2 deserve:1 graduate:3 field:5 implied:1 mathematics:3 briefly:1 vertex:1 a1:10 important:7 bounded:3 included:2 subdivision:1 mass:1 resolution:3 original:3 alo:3 outlining:1 consider:22 alg:4 splitting:6 commute:2 generalize:3 presheaves:4 follow:3 disk:4 content:2 preserves:10 careful:1 tx:13 ty:3 tv:3 tt:2 equivalence:6 tr:5 tn:2 th:8 ti:2 tf:1 tg:6 td:3 presentation:1 norm:2 ta:3 returning:1 very:6 translations:2 induce:2 corollary:29 condition:21 µkn:1 unlike:1 schatzman:1 t2:1 joined:1 t0:14 t1:4 smale:3 proposition:36 rj:2 small:3 anal:2 tej:1 neighborhood:17 zero:14 further:6 canonical:34 bilinear:2 what:15 section:54 brief:1 aˇr:1 version:13 issues:1 intersect:3 sup:1 seemed:1 glaeser:5 method:1 full:3 component:3 behaviour:1 investigating:1 directions:3 strong:11 generalizing:2 allows:2 action:25 specialize:4 diffm:2 uniquely:1 via:18 2we:1 family:29 vii:1 ask:1 equivariant:2 readily:1 proceed:2 distinct:13 contains:5 ψi:1 ψl:1 hirsch:4 taken:5 more:25 presheaf:12 immersion:6 constructs:2 parallelepiped:2 particular:25 known:7 projective:4 imbedding:1 seminorm:8 recall:3 equation:1 des:1 det:1 paragraph:1 taut:7 canonically:1 nonsingular:1 history:1 f0:9 f1:7 compare:1 stated:2 share:1 states:1 sphere:4 numbers:3 hyperplane:1 endowing:1 information:2 respective:4 goal:3 rather:5 acts:2 american:1 maps:105 simplicity:6 algebra:23 fx:4 suppose:22 singularities:5 orbits:2 plane:4 fd:9 fg:1 fi:8 horizontal:1 fn:8 short:9 λv0:1 spectra:6 foliations:1 map1:1 specifying:3 fundamental:6 september:1 essence:1 1we:1 through:7 y1:35 existence:3 y3:5 y2:5 its:55 affine:92 actually:3 systems:3 relate:1 sheaves:23 deformation:1 yi:27 yk:10 yj:7 yn:17 yd:2 number:4 yy:4 sssr:1 compound:1 oxford:1 yp:2 bigger:4 easily:34 finite:82 homomorphisms:7 mathematician:1 always:6 level:3 labeling:1 2d:8 iff:2 fψ:7 found:2 weight:7 generation:6 reduce:5 idea:11 functor:26 finish:1 expect:1 try:3 ftt:1 discrete:2 ux1:1 induces:11 denotes:13 hill:1 izv:1 denoted:10 induced:21 evaluation:4 biproduct:4 base:1 put:2 definition:17 pairs:1 nonnegative:2 aberdeen:1 semialgebraic:1 consequence:2 assign:1 singleton:1 perturb:1 nc1:1 geodesic:1 construct:21 tf1:1 passes:1 kol:1 jet:31 introduction:7 least:18 assumption:6 statement:10 bijections:1 recovered:1 observations:2 behind:1 akad:1 immediate:1 nci:1 part:27 ncn:1 translation:2 γhol:5 determined:4 pairwise:1 fˆ:5 group1:1 idempotents:1 tσ:2 lie:9 generalizes:2 constructions:2 depending:1 lim:14 k1:14 generalized:1 ex1:2 towards:1 colimit:15 kan:2 most:19 nothing:2 stands:1 kg:1 prolongation:9 kj:1 clear:13 sometimes:2 cover:4 kn:16 exi:1 countable:5 kr:1 exp:2 barrel:4 posses:1 lying:3 particularly:2 converge:2 relation:7 find:12 inductive:2 factor:1 integrable:4 circle:5 abelian:18 hir:4 triangle:4 ϕx:15 notation:6 dependent:1 express:3 ϕp:1 ϕr:4 ϕi:12 preparing:1 ϕk:5 ϕj:1 combinations:6 ϕd:8 alexander:12 resolve:1 transversal:3 arxiv:1 factorization:1 investigate:2 common:5 set:59 ser:1 splittings:1 see:28 individual:2 close:3 theoretic:1 matter:2 unions:1 various:4 permutes:1 contrary:1 conditions:14 concatenate:1 monomorphism:1 complementary:6 complement:5 attention:1 eˆi:1 vanishing:2 distinguish:2 both:26 last:18 generator:1 vietoris:1 thom:13 context:1 whole:7 orientable:1 point:27 simple:2 corresponds:4 parametrization:1 dimensional:57 simply:10 fibres:20 pr:2 kernels:2 ensures:3 pq:2 described:8 publishing:1 pb:2 reduction:1 describes:1 pe:1 pk:2 pi:5 pn:3 empty:1 surjective:38 addison:1 generating:1 homologically:1 great:1 understand:2 whitney:1 bτ:2 p0:7 replaces:1 look:1 bσ:7 straight:3 while:6 replaced:3 compactness:9 shift:1 engl:1 vol:6 origin:7 itself:7 vanish:1 whitehead:1 lengths:1 belong:2 intrinsic:2 emphasize:1 modification:2 products:7 composition:23 interpolation:30 used:7 paths:1 nbhd:2 uses:2 purpose:6 analysis:1 obviously:11 concrete:1 parametric:2 λs:1 gelfand:1 λv:2 λg:2 λf:2 λi:11 λn:6 λl:1 homeomorphisms:3 submodule:23 conclusions:1 guaranteed:1 source:7 theorem:69 guarantees:2 remaining:4 reparametrization:5 isomorphisms:2 big:1 showing:4 additivity:1 integer:2 bit:5 imposed:1 follows:20 disks:2 yields:4 translated:1 mcgraw:1 pointwise:1 topologically:37 terminology:1 mathematical:3 sketch:1 often:2 some:47 back:2 understood:2 strongest:1 examples:22 transversely:1 ourselves:2 describing:2 pev:3 providence:1 behave:2 homeomorphic:3 forgets:1 varying:1 bn:6 bi:5 bj:5 chart:11 step:4 weil:6 bp:11 br:1 bz:1 integers:1 asserting:1 anything:1 extending:7 idv:1 range:2 idm:2 eτ:1 cech:10 consequently:8 into:21 isomorphic:6 pullbacks:2 germ:1 span:2 classically:1 sequence:77 question:7 u0:9 long:2 ixp:3 sections:38 arise:4 sdr:1 line:4 collapses:1 directed:1 ux:1 up:15 us:55 ul:3 ui:18 uk:1 sum:2 continuously:3 ud:31 ix0:3 similar:6 called:23 associated:11 defined:35 exk:2 single:8 associates:1 defines:4 dashed:7 nai:9 nan:1 backs:1 application:4 gro:2 grm:17 nice:1 draw:1 elements:21 problems:1 polynomials:10 generated:60 allowing:3 sides:1 structure:43 lang:1 independently:1 implies:7 unneth:1 required:1 orbit:4 equivalently:5 depth:1 na1:1 weights:4 far:2 having:3 partial:7 gr:3 funct:1 results:8 gx:7 gg:3 gf:8 gd:20 go:1 gm:2 gl:1 aˇs:1 gj:4 gi:14 gh:8 compact:75 compose:1 concerned:5 stably:1 send:1 uniqueness:1 stable:3 decomposition:9 include:1 sent:2 economical:1 g0:3 balls:1 categories:3 arrange:1 notes:1 evx:2 inspection:1 noted:1 zj:3 fold:3 imply:1 eλl:2 concludes:1 rrr:5 index:1 ct0:1 invertible:4 morse:1 giving:3 analogously:1 expressed:1 hereditary:2 expresses:3 exercise:1 codimension:56 degree:11 respectively:1 gathered:1 prescribe:1 eλ1:2 desired:2 identifications:2 objects:1 coequalizer:1 consideration:1 deduced:1 remark:10 stalks:6 technical:1 involved:1 composing:1 contradiction:5 suggests:1 resulting:6 makes:4 heart:1 wij:7 apply:8 tools:1 use:22 homotopic:4 usa:1 remains:6 next:13 few:5 doubt:1 coend:1 multiplying:1 started:1 becomes:4 lim1:2 tttt:2 iii:11 coface:1 isomorphism:51 ρp:1 infinitesimal:2 obvious:13 stabilizer:3 fulfill:1 proof:107 cokernels:1 weaker:2 assumptions:11 something:2 dk:10 aff:10 holds:12 varies:1 instead:4 de:1 singular:15 immersed:2 philosophy:1 collection:6 unnaturally:1 multiplication:10 cokernel:1 purely:1 pullback:17 correspond:5 element:11 diffeomorphism:7 baire:4 lε:4 realizes:1 allow:4 op:18 lλ:1 rt0:1 differentiability:1 closely:2 produces:3 interpreted:3 comma:1 looks:2 circumscribed:1 1it:1 mentioned:5 colimits:2 lf:1 outer:1 chosen:2 choose:14 lp:2 nakayama:1 nyn:4 defining:4 serre:2 subtraction:1 rotation:1 iϕi:1 tensoring:2 university:3 identified:15 l6:1 l2:3 l0:2 l1:3 identifies:1 subset:68 leray:3 w12:5 constitute:2 elementary:1 books:1 measure:1 our:35 hlc:1 special:9 out:7 category:32 res:11 jjjj:2 reformulate:1 rei:5 rel:2 lecture:1 postpone:2 suffices:3 math:7 diagonal:1 completely:4 york:5 monographs:1 monoidal:6 geometry:1 could:12 re1:2 times:4 pasting:1 hence:55 phrased:2 isbn:5 plainly:1 bijection:11 intuitively:1 precisely:9 quality:1 πa:5 πd:1 ordering:1 πk:2 adjoint:15 system:9 relations:4 their:12 appl:1 fonctions:1 behaved:1 posets:1 commutativity:7 tuple:1 explanation:1 exactly:6 reflecting:1 retraction:1 cochain:7 subsequence:2 f12:1 radius:2 providing:1 ny1:4 disjoint:17 turn:2 clearly:48 mappings:3 studying:1 able:3 switch:1 fxk:1 meeting:1 cdim:1 unless:4 asserts:2 who:2 connected:6 sb:1 segment:1 class:15 tensor:14 consequences:2 gather:2 fx1:1 fx2:1 proceedings:1 construction:23 se:4 fact:20 absorbing:2 text:2 supported:4 anyway:1 chapters:4 ki:9 trivial:5 agrees:1 principal:6 q0:6 q2:2 based:4 eigenspace:2 controls:1 should:7 lemma:84 bases:1 inherited:1 local:27 interested:4 achieve:1 xdd:1 means:4 ones:3 words:18 ttt:2 shx:22 shy:5 differential:14 nauk:1 michor:1 contain:2 qi:1 fixed:16 qm:2 transversality:33 requirement:1 temporarily:1 modulo:7 constructing:3 exists:14 precomposition:1 module:56 finiteness:1 terms:14 wa:5 ϕx1:1 nondegenerate:2 written:3 identification:5 closed:64 progress:1 boundary:8 luk:1 grothendieck:2 labelings:1 injectively:1 interpolate:1 job:1 x1k:1 hypothesis:3 key:1 configuration:11 ker:26 restrictions:2 limits:4 freely:1 taking:21 equal:4 presentations:1 homotopy:33 admit:1 passing:2 holonomic:1 hφ:1 otherwise:2 ck:1 ci:2 ch:5 co:6 cn:3 cm:2 conclude:6 cohomology:58 cf:2 ab:6 sε:2 sequences:4 respect:7 cq:1 cp:15 cw:5 addition:2 associativity:1 charts:4 treat:1 1the:1 define:60 determinant:1 arises:2 corresponding:19 finishes:2 commutes:7 eˆj:1 sufficient:2 subspace:59 spanier:2 derivative:6 improved:1 present:3 reverse:1 multi:6 subsets:31 wellknown:1 value:1 will:47 va:50 ress:1 geometric:1 almost:4 vi:14 vj:4 thus:15 vn:4 vo:1 vp:3 vr:3 dual:1 complexes:1 xsε:3 generic:2 unity:3 parts:1 adjointness:1 set1:1 gets:7 incl:4 difficult:2 ball:1 infinity:1 upon:1 effect:2 v0:9 v1:12 infinite:4 identity:1 nevertheless:3 well:17 thought:7 sets:9 firstly:2 position:7 arising:1 usual:5 cˇ:8 half:1 obtain:9 sources:1 underlying:5 rest:4 glue:3 bibliography:2 reasons:4 book:1 extends:1 stratum:2 seminorms:9 know:6 press:3 intersection:6 necessary:2 like:4 alternatively:5 lose:1 become:4 works:2 page:4 because:9 classical:2 smoothly:1 ideals:37 j01:7 choosing:3 convex:44 proper:29 proofs:6 happens:2 denseness:1 nonempty:1 avoid:1 overlap:1 does:21 summand:5 assuming:9 intersections:4 slight:2 pp:11 expansion:1 wesley:1 prohibited:1 simplex:16 although:2 derived:5 injective:13 quotients:5 about:14 actual:3 extension:10 getting:2 triviality:1 introduces:1 compatible:1 a2:3 transitive:1 cofinal:4 converging:4 equally:1 subbundle:4 h2:1 h0:1 stratification:2 functional:1 square:7 forget:2 mere:2 additional:5 transfer:11 justifying:1 quadratic:1 inner:3 sociated:1 biggest:1 vas:5 naturally:1 function:34 hp:11 but:31 hu:1 volume:2 hh:4 hi:1 hn:2 hm:4 convergence:4 hc:7 he:1 made:1 compute:2 society:1 whether:3 shrunk:1 smooth:83 w31:4 below:1 limit:9 demonstrate:2 problem:3 piece:1 intersects:2 int:3 universal:4 sion:1 denote:49 igusa:2 relates:1 inf:1 proceeds:1 inc:1 functions:17 variety:1 claiming:1 detail:1 other:51 hpm:1 kinds:1 my1:2 hcp:2 bundle:82 hausdorff:17 lution:1 function1:1 hnc:2 auxiliary:3 starting:2 factors:1 paracompact:13
0705.0334.txt |@word partial:1 consider:14 gp:4 alg:3 erations:1 results:2 ga:1 follow:2 extra:1 whose:1 matsumura:1 paris:2 graph:3 tq:9 γk:8 sml:3 those:1 under:2 hermann:1 localizations:1 spec:8 belonging:1 g1:4 transitively:1 corollary:8 every:7 exact:5 condition:1 arrange:1 groups:3 dim:6 annihilated:1 irreducible:6 t1:9 large:1 solved:1 vector:1 gabriel:2 originally:1 homomorphism:5 says:2 zero:25 reine:1 canonical:6 even:1 what:1 invertible:1 incompatible:1 d2:4 section:5 sur:1 above:1 new:1 d1:4 contrast:1 satisfy:1 degree:2 respectively:2 answers:1 xλ:5 fibrations:1 ements:1 address:1 path:1 enveloppante:1 obtained:3 remark:7 divisor:2 canadian:1 study:2 studied:2 6n5:1 masuda:1 domains:2 proof:16 makes:2 classification:1 f1:13 vii:1 replace:1 texts:2 trdegk:4 apply:1 linearly:1 use:4 additive:1 russell:1 would:1 prove:6 distinct:2 contains:3 epimorphism:1 m0:6 associated:1 ψa:2 type:1 fractions:1 flat:5 israel:1 ti:1 particular:12 known:5 projective:1 hold:1 ml:33 springer:3 isomorphism:7 recall:1 equation:1 des:1 paragraph:1 den:1 following:14 root:1 example:2 deg:1 claim:4 conjecture:1 assumptions:1 sense:1 spanning:1 absolute:1 rather:1 s1:5 holds:2 write:6 maps:5 pure:1 answer:1 verlag:3 fp:3 map:2 samuel:1 frac:12 algebra:22 may:8 after:1 containing:1 diagram:1 consequence:1 inst:1 fi:5 summarize:1 fm:3 constants:1 natural:1 lemmas:1 element:8 si:3 so:40 asserts:1 lifted:1 sc:1 restriction:1 acts:1 indeed:4 over:47 paper:4 existence:1 satisfies:7 its:1 sλ:5 accepted:1 derive:1 group:3 chosen:1 fix:2 affine:28 choose:5 mail:1 main:2 sheaves:1 into:2 non:1 factorial:1 autk:1 autr:1 now:5 s0:9 term:1 finite:4 equality:1 always:1 university:1 theory:2 each:4 classifies:1 side:1 associative:1 bertin:1 subset:5 el:1 domain:25 weighted:1 completions:1 fq:7 series:1 osaka:2 functor:2 conventions:1 ex:1 our:1 xp:9 special:1 canada:2 essen:1 rp:5 matrix:2 unital:1 since:1 research:1 contained:2 daniel:7 rational:3 reader:1 lecture:1 suffices:3 uv:2 math:12 shows:3 benjamin:1 linear:4 localization:4 aω0:1 free:4 pleasant:1 completely:1 base:3 york:1 generate:1 log:1 definition:10 r0:28 derivation:2 geometry:1 phrases:1 moment:1 keep:1 turn:1 derivations:8 hence:7 onto:1 xj:1 already:1 xn:4 bijection:1 variables:4 primary:1 rank:2 transcendence:5 xy:5 done:2 ring:9 fj:1 subring:3 given:5 embeddings:1 reference:2 introduction:1 least:1 1a:1 assumption:1 statement:1 scheme:2 gives:7 proving:1 part:2 authors:1 x2:35 x1:46 coefficients:2 finitely:5 determines:1 imply:1 preparation:1 rewrite:1 ann:1 mind:1 say:1 angew:1 additif:1 chapitres:1 any:7 eaux:1 generalizes:1 constructions:3 subgraph:1 depending:1 convenient:1 fourier:1 k3:1 instance:3 ideal:3 k0:32 generalized:1 jacobian:1 xi:3 regard:2 sm:2 shall:2 gλ:4 birkh:1 algebraic:6 said:1 connected:2 cummings:1 pair:1 class:13 indeterminates:3 don:1 consequences:2 characterizes:2 clear:3 later:2 implications:1 vertices:2 graphs:1 points:2 fact:4 joining:1 uottawa:1 particularly:1 show:2 supported:1 notations:1 purely:1 spaces:1 trivial:14 d0:3 principal:1 homology:2 bourbaki:1 miyanishi:2 assertion:4 should:1 lemma:13 only:5 going:1 transcendental:1 local:6 notation:2 means:3 michigan:3 de:4 hartshorne:1 words:1 progress:1 du:1 ds:1 secondary:1 closure:1 determinants:1 αm:1 arxiv:1 borrow:1 fixed:1 automorphismes:1 kernel:5 set:6 exists:13 achieved:1 differentials:2 module:13 edition:1 see:7 geometrically:2 result:3 lnd:17 ebre:3 subject:1 surfaces:20 satisfying:10 rings:3 ωk:2 closed:10 between:1 αi:2 invariant:10 conditions:3 perfect:1 triples:1 nilpotente:1 however:1 le:1 key:1 ker:10 cor:1 last:1 reverse:1 desired:1 many:3 equal:2 nserc:1 etc:1 une:1 sheaf:6 comment:1 among:1 cn:1 point:1 simple:1 ca:1 cf:5 2nd:1 dimensional:8 adjoining:1 polynomial:8 moreover:2 throughout:1 commutative:3 basis:9 locally:12 due:1 ai:4 reduction:2 belongs:2 algebras:6 abstract:1 empty:1 define:5 surjective:2 corresponding:3 gal:3 nonconstant:5 present:1 case:11 will:1 limanov:14 suppose:7 situation:2 di:6 iy:2 daigle:11 larger:1 almost:1 thus:4 surface:3 according:1 rin:1 noetherian:1 id:1 different:1 grant:1 things:1 belong:2 clearly:1 ωr0:2 units:1 proved:6 several:2 subalgebra:1 infer:1 difficult:1 lie:1 i0:4 i2:1 groupe:1 hand:2 viewing:1 auser:1 normalization:1 premiers:1 suitable:1 well:4 helv:1 edge:1 dimension:2 being:1 obtain:6 actions:3 transforms:2 facts:1 illinois:1 note:15 intersection:9 infinitely:1 nilpotent:10 cl:1 wright:2 interested:3 extends:2 theorem:18 usage:1 transformation:2 noether:1 subfield:2 possible:1 possibly:1 know:1 background:1 using:4 unique:1 grenoble:1 showing:1 follows:14 reduces:1 automorphisms:3 yields:1 arbitrary:4 multiplicative:2 nice:1 essential:2 factorially:4 sketch:1 because:7 sequence:6 some:29 algebraically:6 ideals:2 acad:1 b1:2 zariski:1 nonzero:3 vol:2 slice:5 avoid:1 normal:9 subclass:1 prop:1 affines:1 does:3 unit:1 refer:3 bm:2 equivalent:6 δi:2 ufd:8 bi:3 injective:6 extension:15 ϕij:4 o:6 regular:2 ox:2 introduced:1 consequently:4 other:2 op:1 consulting:1 inclusion:1 makar:14 image:1 integral:11 isomorphic:4 three:1 right:1 references:1 raises:1 reducing:2 statistics:1 van:1 additional:1 there:19 question:3 faithfully:1 appl:1 was:6 therefore:1 complete:9 form:1 converse:1 but:4 construction:2 true:1 ωx:5 applying:4 characteristic:23 ωr:16 smooth:24 us:2 below:2 planes:3 problem:1 ωb:4 k1n:1 adopt:1 ordered:1 ag:1 droites:1 defined:4 ak:2 pic:1 denote:1 chap:1 proves:2 exist:2 plan:1 defines:3 again:1 ematique:1 no:3 when:3 graduate:2 field:45 valid:3 department:1 mathematics:6 conclusion:1 conclude:1 elements:4 vertex:1 polynomials:2 a1:13 generated:4 a2:15 variable:2 structure:1 implies:14 assume:4 space:1 modules:3 ottawa:2 requires:1 4a:1
0705.0335.txt |@word valve:1 sci:1 consider:2 bellaterra:1 rev:18 magnetic:8 excellent:1 desirable:2 focus:2 octahedral:5 go:1 partial:3 localized:4 layers:3 parcollet:1 lsda:5 xiong:1 vacancies:2 ıa:3 charge:2 monotonically:2 present:3 weakening:1 unrelaxed:5 include:1 cm2:1 norm:1 ın:1 division:1 probe:1 very:4 rise:2 stroud:1 choice:1 oxides:1 electron:7 experimentally:1 soler:3 parameter:2 treating:1 believed:1 dominate:1 level:4 altering:1 positions:2 cavendish:1 large:2 lsmo:11 further:1 eigenvalues:1 barbara:1 marezio:1 degeneracy:1 perovskites:2 mn:21 force:1 colossal:1 miller:1 literature:1 approximation:3 fold:1 zero:4 street:1 enhancement:1 substituting:1 qualitatively:1 spectral:1 errors:1 centering:6 giving:1 localization:1 t2g:3 casoli:1 cell:4 experiment:1 sur:1 above:2 spintronics:1 3c:1 falling:1 commensurate:2 willmott:1 method:2 relaxation:4 3d:4 full:1 exchange:3 perdew:1 orr:1 even:2 here:2 understanding:2 reported:1 magnetism:1 mev:1 gga:7 possibility:1 berkeley:2 represented:1 consideration:1 along:2 strong:3 respect:1 change:2 obtained:4 antisymmetric:1 institute:1 shift:3 study:1 studied:1 funded:1 controversy:1 exploitation:1 resulting:2 published:1 narrow:1 studies:2 composed:1 elect:1 although:3 tarantino:1 ground:1 madingley:1 nma:1 integrations:1 acknowledge:1 highly:2 decrease:1 venkatesan:1 unit:1 dxz:2 plot:1 use:1 dxy:4 would:6 remains:2 quasi:1 next:1 discrepancies:1 eleven:1 tm:2 fontcuberta:1 therefore:2 distortions:6 theoretical:1 today:1 more:4 jmp:1 ti:1 corrected:1 salje:3 downing:1 particular:2 known:2 hole:2 potential:1 had:1 dex:2 high:2 keeping:1 ma:1 science:1 der:1 work:6 mu:1 radaelli:1 remain:1 zhan:1 values:4 indicating:1 those:1 im:1 ernzerhof:1 example:1 address:1 numbers:1 nearest:1 compare:1 challenging:1 eg:6 give:1 dependence:1 states:10 performed:3 arise:1 uab:1 la0:2 la1:2 weaken:1 ramesh:1 ferromagnetically:1 goal:1 decaying:2 carriers:2 rather:1 tilt:5 breaking:1 occur:1 sic:2 methodology:1 hueso:2 buenos:1 acta:2 4s2:1 displacements:1 encia:1 oscillatory:2 multiferroic:1 description:2 manganites:5 may:3 after:2 dx2:3 epsrc:1 constraint:1 applications:1 plane:6 matt:1 date:1 3s2:1 revealed:1 constants:1 included:1 ordej:2 effective:2 martins:1 sr:5 manganese:1 stimulate:1 pickett:2 allow:2 correlation:5 representation:1 order:7 considerations:1 indeed:2 mainly:2 satpathy:1 distortion:2 experiments:5 through:3 daniel:1 banach:1 argued:1 y2:3 its:6 tendency:1 before:2 wadati:1 regions:1 hayward:1 batio3:1 la:5 energies:1 decreases:1 better:1 subsurface:1 degrees:1 systems:1 argentina:2 main:1 might:1 lx:1 oudovenko:1 versus:1 non:1 good:2 motivated:1 rotations:1 number:1 underneath:1 band:2 effects:1 they:2 half:8 discuss:2 structural:10 accommodate:1 february:1 2p:1 oxygen:5 fully:3 university:5 presented:1 identified:1 possibilities:1 magnitude:3 dz2:4 instabilities:1 instability:5 traces:1 side:1 characterized:1 bond:1 comisi:1 cost:1 significantly:1 energy:7 reduce:1 principles:2 related:4 decays:4 laboratory:1 pseudopotentials:1 minority:1 gale:1 pbe:1 shown:4 driving:1 space:1 gradient:3 furthermore:1 since:8 induces:1 ry:1 research:1 fellowship:1 nominal:1 wu:1 newly:1 induced:2 correct:1 burke:1 shows:2 stat:1 foundation:1 theory:3 interactions:3 cheong:1 ascertain:1 ısica:1 departamento:1 monotonic:1 difficulty:1 approaches:1 california:4 hand:2 interaction:1 anchez:1 geometry:2 could:3 transition:1 moment:2 4p6:1 length:3 explored:1 due:1 tempting:1 configurations:2 onto:1 interact:1 first:3 origin:2 reversing:1 kohnsham:1 ono:1 symmetry:4 primary:1 smaller:2 done:1 defects:2 knight:1 thick:1 electronic:10 given:1 temperature:3 indicate:1 dft:1 top:1 system:5 occupancy:1 their:2 modes:1 observations:2 calculations:9 free:1 majority:1 molecular:3 structures:3 national:1 gives:1 shifted:2 inter:1 c4v:1 park:1 accurately:1 kept:1 than:3 whereby:1 kind:2 polarized:3 double:1 marianetti:1 likely:1 matter:2 future:1 were:7 conicet:1 result:2 behaviors:1 ev:4 san:1 pseudocubic:3 harris:1 unchanged:2 mind:1 defect:1 already:1 substantial:2 pdos:1 close:1 seen:1 slab:11 any:1 lie:1 angle:4 built:1 self:1 scott:1 mechanism:1 relaxations:2 polarization:5 sciences:1 ideal:2 materials:4 generalized:2 forces:3 siesta:1 mazin:1 singh:3 εf:2 surfaces:4 play:1 towards:7 sol:1 anglada:1 phases:1 most:3 optimized:2 importantly:3 aires:1 position:2 retaining:1 marie:1 measured:1 pages:1 surprising:1 magnon:1 calculated:4 metal:3 face:1 curie:2 yang:1 electrons:3 brey:1 constrain:1 oscillates:1 physics:1 fact:2 thomas:1 axes:1 particularly:2 show:1 causes:1 doped:3 kwon:1 gehring:1 2g:1 earth:1 find:3 occupation:1 based:5 parameters:4 itinerant:1 conduction:1 observe:1 enough:2 should:4 only:2 explicitly:1 screening:1 molecules:1 uppermost:1 local:3 hope:1 briefly:1 do:1 dominant:1 dyz:2 bonds:2 junquera:2 de:8 tilting:3 argyriou:1 ones:1 dz:1 preparing:1 reversal:1 competing:1 fujimori:1 during:1 densities:1 aluminum:1 arxiv:1 optimally:1 gral:1 3e:1 mtrl:1 shi:2 fixed:1 cells:1 thanks:1 signatures:1 bars:1 fair:1 sensitivity:1 correlations:1 0he:1 observed:5 mentioned:1 see:1 electrostatic:1 online:1 descriptions:1 discussions:1 unaltered:1 vardeny:1 techniques:2 octahedra:3 sists:1 fails:1 error:1 away:1 dipole:2 propagates:1 favor:1 state:8 determined:1 between:3 affecting:1 temmerman:1 across:2 ferroelastic:6 cancelling:1 comparable:1 nol:1 recently:2 nature:3 interfaces:1 however:8 csic:1 orbitals:3 interface:1 atoms:8 originates:1 suggested:1 both:4 essentially:1 resistant:1 many:1 taking:1 decay:3 patthey:1 hamada:2 dated:1 oshima:1 hwang:1 experimental:5 kotliar:1 among:1 ci:1 relevant:2 characterization:1 color:1 seems:1 ca:1 mno3:4 mno6:1 supercell:2 constant:3 cu:1 considering:2 described:2 mathur:1 geometries:1 source:1 addition:3 solovyev:1 markedly:1 been:6 screened:1 mart:2 reduction:1 much:1 slowly:1 interest:1 osofsky:1 expected:2 pi:1 fig:6 crystallogr:2 direction:3 deeper:1 ınez:1 concerning:1 haule:1 gap:1 bulk:22 lift:1 repetition:1 spin:12 dmr:1 spain:1 case:1 troullier:1 pacs:1 orthorhombic:1 terakura:1 value:6 will:3 while:2 replaced:1 behavior:2 promising:1 situation:1 tunneling:1 couplings:1 real:1 layer:10 orientation:2 vf:1 coupled:1 almost:1 characteristics:1 thus:5 surface:63 ii:1 strain:1 cond:2 savrasov:1 affected:1 different:2 grant:1 lengths:1 suggest:1 paz:1 millis:1 lett:5 same:1 shifts:1 complex:1 5s2:1 units:1 finite:2 higher:1 koinuma:1 used:3 jorgensen:1 cubic:6 kelvin:1 numerical:1 upon:1 effect:2 possible:3 driven:1 insulating:1 levels:3 portal:1 kim:1 artacho:4 frequently:1 validate:1 glazer:1 recent:2 lower:3 shaded:1 off:6 center:7 hopping:4 changes:4 random:1 well:4 without:1 termination:4 model:1 chemistry:2 photoemission:4 bending:1 distances:2 magnetization:1 ferroelectrics:1 noz:1 λt:2 woodward:2 accurate:2 obtain:3 3p6:1 indicative:1 atomic:10 metallic:9 λo:2 compared:2 captured:1 previous:1 interestingly:1 density:5 character:3 nacional:1 lattice:8 ggas:1 other:1 treatment:1 jong:2 mno2:3 resolved:1 popovic:1 rhombohedral:1 around:1 breaks:1 repetitions:1 results:7 bic:1 early:1 dipolar:1 grid:1 vacuum:1 using:3 picozzi:1 mod:1 energ:1 manganite:2 spaldin:1 like:3 splitting:1 reduces:2 redfern:1 valence:2 kawasaki:1 reduced:2 spins:2 murgia:1 because:1 omica:1 begin:1 oh:1 doping:1 closer:1 ferroelectric:2 pronounced:1 scale:1 bottom:1 broad:1 per:1 competitions:1 sr0:2 does:2 demonstrated:1 limitations:1 core:1 buckling:6 remembered:2 agreement:5 santa:1 found:3 relating:1 properties:10 neighbours:1 central:1 ferromagnetic:3 a0:2 discussed:5 metallicity:2 o:9 essential:1 pz:1 range:1 must:1 ensure:1 emilio:1 srx:1 introduced:1 road:1 cutoff:1 conserving:1 cambridge:5 garc:2 presence:2 previously:1 into:3 within:5 obtaining:1 functional:5 three:1 down:2 phase:7 determine:1 theoretically:2 terminated:1 institut:1 additional:1 few:1 support:2 there:2 appl:2 deposited:1 was:4 magneto:1 ohnishi:2 morrison:1 function:2 elsewhere:1 triggered:5 piezoelectric:1 some:1 relaxed:10 differences:1 but:2 back:1 multiferroics:1 oxygens:1 line:3 relaxes:1 alq3:2 hybridized:1 whether:1 characteristic:1 mat:2 smooth:1 up:3 devices:2 until:1 crystal:2 below:2 fermi:3 uk:3 ue:1 distribution:1 similar:4 display:1 uc:1 strongly:1 ab:4 ordered:1 defined:2 describe:2 influence:1 littlewood:1 single:2 rule:1 our:14 ax:1 campus:1 sasaki:1 physical:1 perovskite:2 semicore:1 us:1 locality:1 dashed:2 whereas:1 when:3 nas:2 interested:1 role:1 filippetti:1 department:3 ferrari:2 out:2 deviate:1 conclusion:1 poor:2 polar:2 perpendicular:1 energetic:1 condens:3 initio:2 carpenter:1 cb2:1 cb3:1 bonding:2 important:3 variable:2 magnetoresistive:1 sides:1 structure:12 yoshimoto:1 correlated:1 coupling:5 odds:1 required:1 barcelona:1 having:1 phonon:2 neighbouring:1 original:1
0705.0336.txt |@word represent:1 measurements:3 sci:1 chain:1 maximum:1 mahadevan:1 rev:9 magnetic:26 both:2 results:5 gg:1 facilities:1 ge:1 snic:1 oso:1 kato:1 ward:1 localized:1 increase:4 simon:1 tu:1 ıa:1 charge:2 preserved:1 under:2 tc:9 indicating:1 placed:1 applied:1 doped:1 kumar:1 very:2 could:1 balcells:1 splitting:2 electron:5 difficult:1 experimentally:2 difference:2 leads:1 level:1 anisotropy:1 unusual:1 guo:1 large:1 ml:2 drop:1 dis:1 perovskites:8 upper:3 alff:8 tomioka:1 ritter:3 cros:1 femoo6:1 terakura:3 approximation:3 likely:1 zx:1 earth:1 qualitatively:1 estimated:2 even:1 xos:1 ycr:1 ohkubo:1 t2g:5 cell:1 experiment:1 above:1 spintronics:1 new:2 net:3 increasing:2 method:1 filled:2 3d:5 revealing:1 magnetometry:1 justification:1 erb:3 degree:2 exchange:2 alkaline:1 cro2:1 here:1 desired:1 magnetism:1 gga:4 address:1 ratio:2 along:2 strong:3 change:2 box:1 search:1 institute:2 shift:1 study:1 studied:1 m3m:3 krockenberger:2 resonance:1 changes:2 sawada:1 diamagnetic:1 winkler:1 scales:2 monochromator:1 sample:3 highly:1 esrf:2 total:3 planck:1 unit:1 plot:1 indicated:1 heisenbergstr:1 jpn:1 tubes:1 france:1 mediate:1 fontcuberta:3 therefore:2 taken:1 theoretical:1 more:3 hahn:2 becomes:1 about:3 validity:1 malgrange:1 berlin:2 normalized:1 known:2 cases:2 carried:1 high:7 springer:2 endpoint:3 room:3 science:2 mo:3 dfg:1 vr:1 mu:1 oxide:1 vs:2 obvious:1 fe3:2 ms:2 following:1 ta:2 example:1 purity:1 ions:2 conf:1 figure:5 calculation:2 december:1 tay:1 generically:1 days:1 states:6 numbers:1 la3:1 afm:1 end:1 invoke:1 carriers:3 discussion:1 european:2 pure:1 axis:2 circular:1 product:1 minority:4 manganites:1 may:1 max:1 after:1 different:3 fc:1 erroneously:1 data:5 fm:2 fo:2 realized:1 short:1 natural:2 sr:3 acknowledged:1 overnight:1 element:1 so:4 correlation:1 order:3 horng:1 indeed:1 over:1 distortion:5 experiments:1 including:3 existence:1 kinetic:5 still:4 tendency:1 sikora:1 ld:1 derive:1 group:3 la:1 ll:1 fig:9 insulator:5 non:4 good:1 motivated:1 w5:1 material:1 blasco:1 band:14 noz:1 half:7 survives:1 now:1 finite:1 oxygen:2 fully:5 university:2 presented:1 filling:4 magnitude:1 l2:2 stockholm:1 each:1 ferrimagnetic:9 out:1 side:3 mater:1 24e:2 el:1 boger:1 series:2 energy:8 4b:2 kobayashi:1 quantum:2 our:2 ev:3 special:1 mat:2 navarro:2 shown:4 fundamentally:1 uppsala:2 gradient:3 interference:2 research:1 semiconductor:1 re:6 rm:3 rn:2 induced:7 ref:1 shows:7 8c:2 concluded:1 standard:1 completely:1 e9:1 put:1 temperature:21 saha:1 r3:5 roomtemperature:1 transition:8 moment:11 edges:2 consequence:1 crm:3 rybicki:1 halfmetallic:1 already:1 xo:1 number:2 twisted:1 clear:1 synthesize:1 zo:1 electronic:1 opel:2 ysr:1 sates:1 system:1 tot:1 chem:1 listed:1 calculations:5 ordered:1 crucible:2 structures:1 ranging:1 evacuated:2 shifted:1 sealed:1 explanation:1 sizable:1 signaling:1 authors:1 kanamori:2 attempt:1 than:2 wide:1 polarized:8 18f:4 zsr:1 double:12 arb:4 tunable:1 project:1 matter:1 sweden:2 determined:2 intensities:1 str:1 were:2 ber:1 providing:1 result:2 5d2:1 5d3:1 argument:1 delin:4 say:1 substantial:1 longo:1 further:3 hexagonal:3 confirms:1 occupied:3 orders:1 ray:3 oates:1 thoroughly:1 ideas:1 mechanism:5 metallic:7 note:2 majority:4 ideal:1 horowitz:1 generalized:3 online:4 darmstadt:3 negligible:1 channel:3 opposite:1 most:1 regular:1 germany:3 condens:1 phase:3 measured:4 why:1 trigonal:1 observation:1 calculated:4 metal:7 curie:5 electrons:2 nuclear:1 dos:1 µtot:1 physics:1 reactor:1 ωcm:1 show:1 supported:2 teresa:3 substituting:1 borowiec:1 find:1 cr3:2 based:2 just:1 parameters:2 itinerant:1 conduction:2 only:6 factor:1 curr:1 local:2 mixture:1 notation:3 de:4 beam:1 marquina:1 words:1 3b:4 respectively:1 ssf:1 klein:1 3a:4 evolution:2 crw:1 arxiv:1 remove:1 summary:1 emu:1 investigate:1 london:1 graf:1 view:1 ser:1 lnp:1 spintronic:1 observed:4 intensity:3 computer:1 bare:1 powder:4 enhanced:1 close:2 conductivity:4 octahedra:1 inorg:1 fang:1 compounds:2 pattern:1 review:1 diluted:1 sites:4 state:2 operative:1 between:3 kth:1 tolerance:1 µb:5 nature:1 okuda:1 however:3 ferrimagnetism:3 orbitals:4 key:1 suggested:2 received:1 ferrimagnets:1 reehuis:2 acknowledge:1 equal:2 neutrons:2 stuttgart:1 tovar:2 dated:1 experimental:2 magn:2 ch:1 polycrystalline:2 simple:1 excess:1 corresponds:1 antisite:1 doping:5 pp:1 described:1 instrument:1 addition:1 due:3 been:8 mart:1 combined:3 collected:2 marx:1 sarma:2 lett:6 obtained:2 direction:1 6c:4 corresponding:2 µcr:2 bandstructure:2 ınez:1 photon:1 stoichiometric:1 understand:1 hmi:1 spin:23 case:2 intriguing:1 kimura:1 pacs:1 solid:2 single:1 value:2 will:2 while:2 pressed:1 behavior:8 irrespective:1 property:1 walther:1 mader:1 changed:1 coupled:1 vol:1 squid:3 thus:2 site:15 ii:6 wojcik:1 superconducting:2 itself:1 cond:1 against:1 vv:1 ic:1 technology:2 orbital:1 confirmed:1 constrained:1 verified:1 yo:1 majewski:4 radiation:3 same:2 clearly:3 wilhelm:3 split:1 units:4 several:2 neutron:9 higher:3 magnetometer:1 oriented:1 eds:2 peaks:1 see:10 cubic:6 dasgupta:1 effect:1 hysteresis:2 driven:3 insulating:3 levels:1 opinion:1 cr:12 recent:2 well:2 analysis:1 0x10:4 ibarra:3 materials:6 residuals:1 tokura:2 quantitative:1 model:1 possesses:1 left:4 magnetization:5 proposed:1 moments:7 resp:1 compound:4 spinorbit:1 alternative:1 scattering:3 polarization:3 candidate:1 density:1 thinking:1 point:1 royal:1 evidences:1 jules:1 color:4 unambiguously:1 nato:1 cub:1 samples:4 5d:10 extensive:1 hybridization:1 resolved:2 rhombohedral:4 okimoto:1 showing:1 possible:2 early:1 increases:1 vacuum:1 using:4 unique:1 grenoble:1 xsr:1 melting:1 cz:1 alternatively:1 signal:2 holes:1 disorder:1 reduced:1 spins:1 sketch:2 right:5 sleight:1 refinement:3 aldrich:1 zcr:1 table:6 gross:5 io:2 lead:2 confirm:1 gapped:1 tube:2 meitner:2 extensively:1 per:3 sr2:28 lattice:3 assuming:1 osmium:1 o6:1 demonstrated:1 l3:1 berthet:1 nmr:1 performed:1 selecting:1 agreement:5 rue:1 bp:1 although:1 xanes:3 nanosystems:1 comparison:2 conducting:1 fillings:1 ferromagnetic:4 kawasaki:1 oe:1 dependence:1 o:5 range:3 cooled:1 os:25 soc:1 facility:2 into:4 within:2 garc:1 markedly:1 down:2 device:2 because:1 heated:2 refined:2 jeng:1 institut:2 kapusta:1 synthesized:2 refinements:4 support:1 there:2 hex:1 class:2 width:2 appl:6 low:3 way:2 brandt:1 was:7 naturally:1 synchrotron:3 considerably:1 5d1:1 underlines:1 but:1 cedex:1 gain:2 line:2 highest:2 rietveld:1 antiferromagnetic:1 up:2 quantitatively:1 crystal:6 below:2 fermi:1 unusually:1 zajac:1 define:1 called:1 detailed:2 associated:2 6a:1 defined:1 flow:1 contribute:1 metals:1 engineering:1 wavelength:1 frontera:3 perovskite:5 compared:2 ideally:1 amounts:1 dichroism:1 field:3 xcr:1 other:2 department:2 ns:1 deviation:1 quartz:3 temperatures:3 rubi:2 convincing:1 prepared:1 a3:1 a2:1 peak:3 conductivities:1 pellets:1 structure:18 impurity:2 philipp:2 xmcd:8 coupling:4 sigma:1 space:3 diffraction:5 orbit:2 inset:7 corundum:1 time:1 jansen:2 4d:1 4a:2 ags:3 having:1 ul:1
0705.0337.txt |@word secondly:2 miyazaki:1 schlegel:6 limited:1 saves:1 desirable:2 cci:2 extends:1 four:14 obstruction:1 prefix:1 consists:8 sci:5 localized:4 forget:1 whose:8 pedro:1 calculate:17 aug:1 paris:1 similarity:1 29b:4 insertion:1 quadruple:2 29a:1 presents:5 γj:3 γi:2 under:9 curr:3 worth:2 lack:1 every:16 affect:1 ala:1 φnk:1 vast:2 prize:1 ref:7 selfconsistently:1 solution:42 hsu:1 hco:1 convenience:2 vector:7 indices:12 subindex:1 shows:1 c04:1 commented:1 force:6 specially:4 consistent:7 direct:6 nair:1 approximation:41 elegant:1 second:24 ecd:1 rigorous:2 pande:1 chem:90 even:18 established:3 disk:3 forgetting:1 selected:2 dynamical:2 above:37 designing:1 new:21 increasing:3 ˆl:2 consisting:1 pioneering:1 simultaneously:1 mec:2 never:1 equals:1 here:20 atoms:27 ionization:2 met:1 departamento:1 interpret:1 contraction:13 digits:3 suitably:2 study:3 changed:1 approaches:6 reports:1 permit:1 advantages:1 suitable:5 changes:3 orthonormality:5 9a:6 9c:3 9b:1 9d:2 raphson:1 highly:1 brought:1 anions:1 total:15 unit:6 derivatives:15 quasi:1 hartreefock:1 would:26 older:1 steering:1 occupying:1 definiteness:1 call:1 therefore:20 recommend:1 survive:1 type:23 until:3 separated:1 drawbacks:2 mineola:1 holy:1 successful:1 conclusions:1 naive:2 γl:3 interpenetrate:1 odinger:19 hermann:1 aufbau:4 eternally:1 organic:3 physically:5 hold:4 must:52 me:8 md:3 springer:3 word:4 rα:8 rβ:2 mo:3 work:16 cancellations:1 theories:3 bordner:1 suggestive:1 mp:2 concepts:8 im:1 root:1 example:43 wang:2 indicated:3 relativistic:5 distributions:3 implementations:1 involve:1 indicates:4 caution:1 want:12 displacement:1 uab:6 absolute:1 unmeasurable:2 end:11 thousands:2 recovers:1 very:24 hot:1 λab:3 types:4 ordinary:1 ψin:2 gordon:17 description:3 ladder:1 after:16 containing:3 demanding:2 edificio:1 lax:6 lay:6 laz:6 arch:1 parallel:2 constants:3 ψi0:1 ψi1:1 interscience:1 ordej:2 effective:6 ıa:1 austin:1 hypotheses:1 greek:3 complexity:6 algorithms:18 enter:4 operate:2 order:52 operations:1 origin:2 interpretation:1 devote:1 diagonalizes:1 over:8 vary:1 satisfied:3 cohen:1 pascal:1 london:4 innovative:1 satisfies:2 before:7 difference:3 somewhere:1 lefthand:1 fix:4 writing:2 better:6 complex:21 differently:5 hidden:1 easier:1 overcome:3 emphasize:1 theo:1 them:51 remedy:1 interdisciplinary:1 prevented:1 furman:1 farkas:3 they:47 eigenvalue:19 netherlands:1 reasonably:2 dbd:1 shao:4 loss:4 improvements:4 each:48 bona:1 chapt:2 side:18 bond:4 schemes:1 submatrices:1 oneparticle:1 saika:2 principles:1 contracting:1 bra:3 literature:13 24s:1 substantially:1 laboratory:4 herbert:1 extract:1 δγk:3 δγi:3 is3:1 quantify:1 forty:1 particles:4 re:2 mα:1 ra:7 reader:11 gov:3 ri:2 independence:3 customarily:2 linear:29 barrier:1 abramowitz:1 bottlenecks:1 given:12 free:1 standard:2 frey:1 1r:1 formation:2 corrects:1 estimate:1 wanted:2 universally:1 enormous:1 r0:4 r1:1 cysteine:1 days:2 silicon:1 goedecker:1 grishin:1 δij:3 corrections:1 uses:1 stewart:3 separable:1 already:9 features:2 render:3 timeindependent:1 another:11 semiempirical:1 electronic:41 illustrate:1 he:1 cartesian:11 similarly:1 tor:1 lega:1 eqs:14 needed:12 zeros:2 too:10 hypothetical:1 ordered:2 variational:24 ranging:1 alonso:35 twoelectron:1 serve:1 took:1 morozov:2 somewhat:2 nh2:1 sulphur:1 positively:4 begins:2 distance:3 target:1 showed:4 approximations:8 database:1 tree:3 rate:2 matter:6 spoiled:1 tackled:3 powers:2 minus:2 seminal:1 φnα:3 rewrite:1 boston:1 modern:11 spectrum:3 seed:1 manner:1 seen:3 seem:1 contents:1 relatively:2 affairs:2 ponder:1 implemented:2 λl1:1 convenient:10 latter:7 responsible:1 fourier:1 communicative:1 thorough:1 metallic:2 fitting:2 chipman:1 forces:1 swaminathan:1 davidson:2 circles:4 εαi:1 continuous:3 shall:27 object:4 aabcd:2 birkh:1 simplify:2 involving:6 ensure:1 letter:3 phase:2 iterate:1 unorthodox:2 torsional:1 heyden:1 dummy:3 doi:1 environmental:1 calculated:13 points:23 principle:16 enterprise:1 camb:1 sum:22 dover:3 saying:2 superindex:1 76b:1 labels:4 soluble:1 attempts:2 solutions:23 keywords:1 endeavour:1 analogue:1 availability:1 proposed:6 spite:1 implementation:2 situations:2 cpu:1 woodgate:1 judged:1 integrate:4 constant:4 jauregui:1 do:22 cheng:1 coefficients:13 dd:2 de:10 db:3 dc:1 preferred:2 stos:9 dz:3 dx:18 despite:11 report:1 dr:27 normalizable:1 hall:10 runs:3 kollman:2 textbooks:2 acknowledgments:1 twice:1 bad:1 shull:1 protocols:1 analytical:6 nα:22 implication:1 precluding:1 cerny:1 mandatory:1 reference:4 depends:16 electrostatic:1 result:15 best:2 techniques:1 said:8 exponent:6 schwegler:3 consistency:2 away:1 propagates:1 clamped:4 symmetric:3 score:2 hopefully:5 conceptual:5 drawn:1 approach:10 terms:36 nature:4 restricting:1 however:48 huang:1 contamination:3 carbon:6 packages:3 improve:5 suggested:1 ranges:1 essentially:2 renders:4 ill:1 readers:1 strange:1 distinction:3 contribution:1 expense:1 com:1 asked:1 explanatory:3 height:1 karen:1 comprehension:1 polynomial:7 trust:1 asks:1 basis:60 simplification:1 three:19 been:41 much:15 interest:2 basic:10 expected:13 basin:2 correction:3 obtained:15 deeper:1 attacked:1 quantities:3 excite:1 argument:2 generalization:3 doubts:2 spin:76 applied:3 formalization:2 solvable:1 transformation:13 aim:2 euclidean:2 near:2 viii:1 applies:2 property:6 leaves:2 procedure:21 tzp:1 dobson:1 szabo:1 canc:1 kohn:2 conditioned:2 ii:2 disjoint:1 ij:3 experts:1 n2s:2 casting:1 confirmed:2 descent:1 integrodifferential:1 perform:10 suggest:3 make:16 clearly:3 drawback:4 quant:11 split:6 avoids:1 several:4 woolley:1 hermiticity:4 independent:29 numerical:11 differing:1 counterparts:1 hand:26 kij:7 kii:1 auser:1 jkj:1 potentials:1 hartree:156 normalization:7 centred:8 suffices:2 kept:6 immaterial:4 academic:3 savings:2 contact:1 elstner:1 left:11 unified:1 world:2 assembling:1 protocol:2 just:14 newton:2 overcoming:1 proposes:1 thanks:1 facts:1 shorthand:2 yet:2 functionally:2 previous:22 adding:3 subfamily:1 vid:1 5z:1 regarded:6 character:4 hay:1 belongs:3 transformed:4 requiring:2 iσ:1 save:1 plasma:1 cramer:1 contrarily:3 bornoppenheimer:1 advances:2 breaks:1 posed:2 possible:21 spanned:3 possibly:1 boxes:1 rotate:2 arag:2 unique:1 advanced:5 apart:9 appearing:7 tˆ:2 performing:2 specific:3 remind:2 steps:8 schwarz:1 sparse:4 arbitrary:6 valence:17 www:4 right:8 old:2 deal:7 truncated:2 successfully:1 born:21 linearly:8 paragraphs:5 rα2:2 indistinguishability:3 woodcock:1 proceeding:3 electromagnetic:1 opposite:5 everything:1 asking:4 exposition:1 landscape:1 newfoundland:2 yields:1 2df:1 core:9 algorithmic:1 minimization:2 bifi:2 riera:1 translated:1 substituted:2 olsen:3 substitution:1 joule:1 properties:18 takes:5 hund:1 bowler:1 numerator:1 o:44 opin:3 misleading:1 plus:4 spins:1 shared:1 efforts:1 slightly:4 conformations:1 automatically:3 lieb:8 considerations:4 primitive:24 statements:2 facility:1 obtaining:1 bound:3 down:2 lies:3 hermitian:8 acad:3 formidable:1 refined:1 reducing:3 often:5 comparing:3 support:1 suffice:1 approximate:6 class:3 accordingly:2 physicists:1 fraction:1 was:14 lowest:15 head:17 form:35 forming:1 δkl:1 differences:2 remarking:1 powerfully:1 marinari:1 true:12 φnlm:2 flavour:3 versions:6 prevents:2 inside:9 friesecke:1 maximum:3 achieving:1 discretized:2 simplifying:1 ψe:17 b1:8 hurley:1 proved:4 semicolon:1 ln:1 exist:8 moln:3 simulations:1 door:1 dβ:5 check:5 constructed:11 nn:16 no:20 na:4 whereas:10 wavefunction:53 generally:1 vanishes:2 ng:5 chakraborty:1 interested:7 digital:1 test:1 ns:2 superfluous:1 realize:2 picture:5 simons:1 prot:2 initio:3 spoils:2 preceding:1 miscellaneous:1 variable:3 dense:1 singapore:1 faster:1 coulomb:20 assume:6 pseudo:2 memorial:2 together:13 remarked:2 observables:1 nuclei:25 laws:1 annu:2 profits:1 basically:3 concept:6 customary:4 chain:1 subindices:1 oss:1 global:14 focus:2 leads:5 roy:3 computation:3 vega:1 row:3 certainly:2 dimensionality:1 depend:12 essentials:2 caldwell:1 technique:1 environment:3 charge:14 analogous:3 division:1 rαβ:1 advantage:2 orthogonal:9 emphasizes:1 choice:18 cook:1 ma:22 1s:15 exact:17 χd:2 car:1 mc:5 level:4 did:4 turns:6 reactivity:1 standards:3 leave:4 discrete:5 recall:5 quick:1 postdoctoral:1 upper:1 mn:3 slower:1 scheraga:1 dealing:5 sign:8 threshold:1 cost:8 yang:1 adds:1 appear:10 celebrated:2 current:2 goes:1 international:4 unrestricted:2 appeal:1 filled:8 satisfy:9 supporting:1 multipole:5 ostlund:1 groups:2 alone:5 112b:1 xα:1 change:4 criterium:2 box:2 instituto:1 institute:5 petersen:1 studied:5 funded:1 commonly:9 ud:3 trial:1 cervantes:1 simultaneous:2 battelle:1 usually:2 conveniently:1 studies:2 kcal:7 adjustable:1 useful:5 macromolecule:1 bounds:1 sistemas:1 f2:2 logical:2 fba:3 1st:2 rarely:2 planck:1 handled:3 baer:1 sake:1 positive:2 optimize:1 explicitly:5 memory:1 scope:4 theoretical:7 introducing:4 molecules:22 visual:1 appendix:13 virtue:2 cases:19 effort:4 easiest:1 dunning:2 lowercase:1 valued:4 schaffer:1 avoiding:3 oscillator:1 ıaz:1 reviews:4 cai:10 fock:143 values:13 achieve:4 9th:1 following:16 making:3 arrive:7 meant:3 figure:4 permutations:5 2la:2 peters:1 topic:3 dxk:2 performed:21 allowed:8 beran:1 hydrogen:11 occur:2 verlag:2 azquez:1 greengard:2 requirements:2 richland:1 fortunately:1 discussion:14 means:5 berlin:2 orthogonality:7 chemical:12 friesner:2 fourth:2 familiar:1 optimal:4 parameter:2 map:1 product:17 mat:1 hydrogens:5 influenced:1 may:64 uli:3 spot:1 respective:2 residues:1 applications:11 aos:1 improving:1 journals:1 grow:1 sz:1 stress:3 natural:2 outline:3 johnson:3 conscious:1 explicit:1 yielding:6 corona:1 st:1 si:7 so:36 sn:3 definitions:3 talk:1 typical:4 imagining:1 aforementioned:6 correlation:2 indeed:6 thresholds:1 mainly:1 soc:9 years:3 course:15 experiments:1 statistical:3 differs:1 cold:1 still:11 emits:1 derive:7 group:5 chandrasekhar:2 how:7 interesting:1 jij:7 vicinity:2 coordinates:32 jii:1 forms:3 attraction:2 pervade:1 constitutes:3 main:8 decades:1 non:31 jørgensen:3 lalo:1 introduce:14 scaling:17 qualified:1 flint:1 half:2 mathar:1 now:51 discuss:8 developments:4 accommodate:2 term:18 equality:2 name:2 rendering:1 drop:3 proteins:4 establishing:1 orthonormal:3 quarter:1 multiply:5 ann:2 domain:2 en:12 ζa:19 ee:4 ed:4 gaussian:28 bradley:1 year:1 happen:3 ev:3 eq:117 es:2 tried:1 canada:1 shown:8 ciarlet:1 space:47 51a:1 51b:1 interference:2 looking:4 contained:2 europhys:1 kedziora:1 rational:1 dominate:1 correct:3 managed:1 unifying:1 theory:26 plotkin:1 state:25 plm:3 million:1 hirao:1 possibility:7 minimized:1 quart:1 complicated:8 org:1 manninen:1 e0:4 e2:4 derivation:9 language:2 mos:4 impose:4 iterative:18 fb:3 motion:4 turn:8 place:2 79b:1 79a:1 think:5 frequent:1 first:55 xj:11 intuition:5 xi:27 xn:19 symmetry:6 striking:1 afer:2 variables:17 pa:1 transform:2 xz:2 clumsy:1 xy:2 simplified:2 specifically:1 directly:4 carry:1 impossible:5 open:6 angular:26 size:12 1p:3 little:2 necessarily:4 anyone:1 indicate:5 fmm:2 ukj:4 convention:1 handbook:3 white:12 biopolymers:1 speaking:1 way:56 mostly:2 pople:27 kirkpatrick:1 observable:1 upperbound:1 hut:2 pnl:1 x2:9 x1:21 representing:1 than:33 intrinsically:1 wide:1 rugged:1 third:2 keil:1 were:8 ang:1 generality:2 sab:2 topics:5 turned:1 locations:1 dynamically:1 dash:4 say:13 gab:3 won:1 molnar:1 saw:1 any:45 conversion:3 computationally:5 γk:5 efficient:8 ideas:7 note:32 sciences:1 emphasis:2 potential:12 take:9 online:1 objective:1 ˆi:1 becoming:1 formulas:1 begin:2 sure:4 multiple:2 norman:1 normal:1 price:3 knew:1 molecule:10 paid:1 algebraic:1 beta:12 satisfying:2 successive:2 pair:13 analytically:6 precludes:3 pages:1 sali:1 119b:1 room:2 considered:12 average:3 later:4 drive:1 peptides:1 typically:30 quantity:4 precise:4 drastically:1 show:5 atom:10 spaces:5 decompositions:1 spurious:1 imagined:1 line:2 ground:20 pearlman:1 ratio:1 enough:8 analytic:1 only:94 going:2 closed:5 get:6 straightforwardly:1 simplistic:1 cannot:5 2me:1 differentiating:1 prime:1 regarding:9 θαa:9 yield:4 though:1 diu:1 gilbert:1 discussing:1 worrying:1 crystal:1 imposing:3 reductio:1 relative:4 namely:5 differentiable:1 λba:1 uncorrelated:1 steric:1 invoked:3 eigenfunctions:4 tackling:1 ways:1 subsequent:4 review:41 definite:1 functionals:5 label:5 αa:6 importance:2 outside:2 john:8 between:19 αi:2 prentice:1 diagonalized:3 multiplied:4 notice:4 comp:16 εij:1 jr:4 sutcliffe:3 ji:4 multiplies:1 multiplier:2 spark:1 come:2 σi:2 universit:1 tractable:1 many:26 region:2 according:4 contract:2 energies:5 marked:1 expression:27 comes:3 among:17 characterization:1 socci:1 bader:1 lagrange:26 cancel:1 moreover:6 fruitful:1 squaring:1 locally:1 concede:1 cosine:1 combined:7 marx:1 fig:9 engine:3 direction:3 bryngelson:2 indirect:1 oψ:1 formed:7 ansatzs:1 6s:4 external:1 stems:1 rephrased:1 6z:1 careful:1 irrelevant:2 former:3 those:26 sound:1 macromolecules:4 isolated:3 vecchi:1 trick:1 cast:2 editorial:1 promising:1 situation:8 polymer:1 coupled:8 characteristics:3 canceled:1 dangerously:1 affected:1 protein:1 technology:3 yl:2 different:54 develop:1 combination:9 etc:10 pay:1 same:70 mole:5 antisymmetry:2 html:1 arguments:6 eri:7 physical:11 status:1 extended:3 jorgensen:1 closest:1 absurdum:1 kelvin:1 drives:1 finitedimensional:1 constraining:1 changing:4 ahlrichs:3 hariharan:1 implements:1 snow:1 largely:2 minimize:3 traded:1 locality:2 ujl:3 incorporated:1 severe:1 without:8 solve:12 extensible:1 alleviate:2 ujk:4 coordinate:2 model:2 otherwise:1 dimension:3 researchers:2 charged:5 vˆn:7 minima:1 being:26 when:25 vˆe:1 rest:8 topol:1 summed:2 speed:1 heuristic:4 alphabetical:1 struct:9 hint:1 thinking:6 tirado:1 seems:3 except:3 improvement:5 gss:7 setting:1 treatment:3 versa:2 heavier:2 eigenstate:11 momentum:21 ross:1 real:24 aspects:1 around:2 represents:1 read:4 sums:6 180o:1 ên:5 grid:3 acronyms:2 vacuum:1 using:51 accepted:1 ruled:1 vertically:1 adams:1 particle:13 either:10 integrals:21 voluntarily:2 stationary:20 reduced:4 104a:1 conditional:1 pacific:2 nucleic:1 table:11 images:2 treatments:1 provided:4 dimensions:1 footing:1 filling:1 computing:4 models:1 84b:1 provides:1 y20:1 y21:1 o2:2 refer:2 schaefer:2 scientific:3 power:1 equivalent:1 wavefunctions:16 notably:1 broken:2 symp:2 2m:1 francis:1 2n:5 rearranging:1 acc:1 comparison:2 out2:1 central:3 origins:1 feig:1 discussed:23 91b:1 practical:13 mutually:3 estimator:2 greatly:2 act:1 xnn:1 amber:1 heavy:6 inclusion:2 image:5 numerically:1 garc:1 75c:1 75b:1 75a:1 accounts:6 operator:45 nowadays:3 theoretically:1 fast:4 shells:34 assumed:6 strictly:1 there:47 papp:1 start:3 lions:1 low:2 liang:2 series:2 strict:2 complete:4 newtonian:1 regard:2 sophisticated:1 unreliable:1 trying:2 applying:1 improved:2 naming:1 multiplicity:1 schreiner:1 miguel:1 embedded:1 monopole:1 connect:1 strongly:1 ac:16 taylor:3 ad:1 cbj:3 certain:7 describe:3 am:4 ao:1 general:30 imagination:2 examine:1 arises:1 vn:3 lcao:2 gradients:1 jargon:1 misura:1 again:13 stationarity:2 storage:2 field:17 prism:4 valid:1 remarks:3 spatial:28 forcing:1 seeger:2 deviation:1 briefly:2 60s:1 separate:1 time:22 fis2006:1 deriving:1 a0:1 important:9 nucleus:10 included:5 tricky:1 acids:1 kilogram:1 gradient:9 mimic:1 mass:6 restricted:10 evenly:1 starting:8 original:6 represent:4 monte:1 semantic:1 consider:4 scf:51 splitting:4 month:1 mp4:1 commute:1 assessment:1 follow:6 expressions:11 denotes:5 reasoning:3 reluctant:1 tz:3 equivalence:1 spirit:5 program:2 spain:5 th:19 nodes:1 te:1 presentation:1 norm:4 subtleties:3 case:65 belonging:4 amplitudes:1 jensen:3 straightforward:1 far:3 print:1 sons:5 worst:2 fall:1 fab:7 manageable:2 condition:6 hamiltonian:20 applicable:3 large:18 adjust:2 unproblematic:1 scalings:1 small:16 biological:2 anal:1 ericsson:1 zero:27 design:4 further:15 reine:1 canonical:3 residue:1 gorelik:1 what:8 nonlinear:1 assured:1 brackets:4 section:30 version:15 scientists:1 method:24 zaragoza:3 condensed:2 obara:2 indistinctly:1 component:3 orbitals:126 behaviour:11 operating:1 ansatz:8 irrespective:1 directions:4 strong:3 equations:88 marder:1 search:17 antisymmetric:3 introductory:2 allows:12 experience:1 hao:1 amount:2 permutation:3 action:2 sticking:2 via:6 followed:3 family:6 marginal:2 vii:1 byrd:1 put:2 aimed:6 sch:2 select:1 readily:2 recurrence:2 conventional:1 proceed:2 levine:1 distinct:3 ψp:18 contains:7 finally:23 ψj:47 ψk:43 bottleneck:1 ψi:59 ψn:23 ψl:23 ψm:3 taken:16 ψa:11 rhee:2 entails:1 more:36 conformational:1 operators:19 corrected:1 dykstra:1 stick:1 particular:38 known:9 foundations:2 producing:1 ık:1 sigal:1 keeping:4 strain:3 science:5 equation:26 det:4 peeters:1 remain:6 paragraph:3 indicating:1 strategies:3 dec:1 specialized:1 f1:2 compare:5 omit:1 brown:1 share:1 accept:1 states:8 minimum:20 numbers:15 sense:9 sharp:1 lacks:1 species:4 axis:1 information:6 needs:4 rather:7 csizmadia:5 breaking:2 foreseen:1 larsen:1 311g:2 acta:4 simplicity:2 ζb:13 ζc:7 ζd:7 intended:4 angew:1 rearrangement:1 wiley:7 derived:6 mapping:1 fa:7 state1:1 momany:1 coming:1 charmm:1 geometrical:1 harsh:1 e24:1 short:6 resemble:2 author:1 secs:5 negligible:7 specifying:1 fundamental:8 alphabet:2 playing:1 helv:1 funct:1 hierarchy:1 developed:5 paper:2 through:8 existence:3 kinetic:1 intelligently:1 its:12 roots:1 tˆn:5 rapidly:1 termed:6 tˆe:5 drabold:1 solving:4 φb:16 conjugation:1 actually:9 clashes:1 absence:2 φc:1 systems:12 uhf:45 good:10 schematic:3 propose:1 hunter:3 noticing:3 zener:2 obeyed:2 framework:2 hierarchical:1 yz:2 130a:1 oxford:3 yu:1 easily:8 finite:10 2p:11 designation:2 2s:14 always:3 calvo:1 presented:4 2z:4 payed:2 parisi:1 inequality:1 fide:1 radial:7 2l:6 found:17 repeating:2 energetically:1 2h:1 2i:2 referred:4 constructing:1 reactions:1 as1:2 generation:1 energy:59 reduce:5 idea:2 investigated:1 expect:4 rokhlin:2 quantum:67 beyond:5 really:2 mcallister:1 solved:13 since:46 induces:1 projected:1 research:6 ftc:2 denoted:9 issue:3 occurs:3 ruskai:1 koopmans:4 guess:9 onuchic:3 difficulty:2 reason:4 sba:3 imagine:1 ask:9 untransformed:1 beginning:2 guest:1 definition:7 pairs:1 benefits:1 geminal:1 computers:4 tate:1 exponentially:1 universidad:2 consequence:6 major:3 probability:12 laguerre:3 relate:1 number:52 done:6 construct:7 pablo:33 says:1 miss:1 differ:5 errors:1 introduction:13 leading:3 5th:1 least:2 2fb:1 assumption:3 tighter:1 statement:2 86a:1 scheme:17 exponents:12 recovered:1 calculations:22 behind:1 l2l:1 part:41 contracted:26 authors:1 focusing:2 off:3 believe:1 separability:2 oscillate:1 albeit:2 kind:4 molecular:86 determines:1 double:1 sto:23 annihilation:1 charges:3 determined:1 contrary:1 supposed:1 fˆ:16 treated:1 lambrecht:2 comput:1 picked:1 footnote:11 krylov:1 77a:1 gillan:1 sentences:1 elsevier:2 orders:1 brooks:4 depending:8 lim:3 self:14 hgp:4 majority:3 recognizing:1 build:2 analogy:1 finding:8 2d:3 unconstrained:6 eff:1 gill:9 kab:3 towards:3 electric:1 ccj:2 most:31 significant:4 accepting:1 probabilistic:1 stands:2 kg:2 kj:4 clear:6 sometimes:1 complejos:1 physica:1 traditional:1 electrons:47 li2:1 physics:72 lying:4 parr:1 ambiguities:1 hyper:2 scattered:1 cdi:1 cdj:3 converge:3 norms:1 minimizing:1 relation:8 fine:4 find:15 occupation:1 sorin:1 cell:1 depended:2 dividing:1 distributed:1 experiment:1 factor:6 integrable:1 circle:4 stegun:1 bipm:1 toronto:1 notation:38 dependent:6 landscapes:1 express:3 cheaper:1 wolynes:3 subfamilies:1 feels:2 polarized:1 ϕi:1 fastest:1 closely:1 ϕj:1 combinations:6 lattices:1 twobody:2 continuum:1 arxiv:1 remove:1 oppenheimer:19 investigate:1 common:19 inefficient:1 knapp:1 rives:1 river:1 wrote:1 approaching:1 set:71 ser:2 achieved:8 principal:2 see:88 individual:2 sec:15 descriptions:1 cleverly:1 close:12 uα:4 uβ:3 smallest:2 pairwise:3 conditions:4 pictured:1 doubly:11 available:3 matricial:1 recently:1 statistically:3 missing:1 attention:2 spectroscopic:2 vanishing:1 selectively:1 δab:2 distinguish:2 31g:10 both:28 folding:1 reverse:4 components:6 skr:1 improves:2 context:3 whole:16 experimental:2 point:38 simple:12 acted:1 asymptotically:2 steele:1 corresponds:6 proton:3 dimensional:7 carlo:1 simply:12 consideration:1 faraday:1 zeta:7 throughout:1 along:1 skolnick:1 described:12 raise:2 create:1 due:28 laplacian:1 strategy:2 reduction:4 describes:1 evenness:1 kronecker:2 anisotropic:1 combine:1 ph:3 empty:1 lett:10 ram:1 partly:2 trudy:1 remark:5 gap:1 neumann:1 systematic:1 assigning:1 ligands:1 c2:1 look:4 exponential:3 frozen:1 reliable:1 estimations:1 empirical:1 receive:1 while:18 optimization:6 behavior:2 error:1 guide:1 unitary:15 bris:2 arching:1 vol:6 gaµ:12 conjugate:7 reads:6 itself:2 rij:10 triple:1 ready:1 rid:1 vanish:3 eigenfunction:3 grant:1 barnes:2 belong:4 rules:1 virtually:1 resulting:3 composition:1 day:1 higher:9 development:3 used:54 attempted:1 moment:4 levels:4 moving:4 necessity:3 vargas:1 circumvented:2 recent:2 eigenvectors:1 lower:10 task:4 21g:2 underlies:1 spent:1 analysis:1 obviously:2 concrete:1 converged:1 thoroughly:1 exponentials:1 chemistry:43 parametric:1 spend:1 parametrically:5 know:7 things:1 exploits:1 λu:3 mol:17 reviewed:4 tasks:1 δψk:7 atomic:22 λd:2 λk:1 λi:4 saunders:1 discipline:2 tables:1 cuu:2 clark:3 kluwer:1 extracted:4 excites:1 guaranteed:1 ee0:7 theoret:2 dixon:1 theorem:15 mod:4 spin1:1 remaining:5 gs:1 generalized:6 operaˆ:1 big:1 couple:1 φ0k:2 matters:1 philos:1 entangled:1 appendices:1 macromolecular:1 integer:2 bit:2 76a:1 projects:1 formal:2 scuseria:9 modifications:1 counterintuitive:1 imposed:6 differentiations:1 semi:1 systematically:1 follows:10 interestingly:1 separately:3 behaviours:1 continue:2 unstable:1 endre:1 popular:2 essential:3 permittivity:1 mathematical:15 grouped:1 methods:35 some:27 back:1 b4:1 understood:1 trends:1 added:3 hunziker:1 examples:3 b2:1 b3:1 ourselves:1 scale:3 describing:1 decision:2 measurements:1 integration:1 per:3 pes:2 104b:1 connecting:3 eliminate:1 slash:1 prog:1 proc:7 minimal:7 bd:13 varying:1 run:3 ba:2 bb:1 bo:1 bh:1 perpendicular:3 restrictive:1 step:21 cgs:4 subtract:3 hilbert:8 von:1 constrains:1 integers:3 anything:4 constraint:4 simulation:1 deserves:1 range:6 repulsion:2 yla:3 ylm:2 consequently:5 block:4 computational:30 intl:10 into:31 within:1 integral:5 appropriate:4 alpha:12 proportional:6 nobel:1 rows:1 few:1 placing:3 question:1 long:5 bosons:1 δlk:1 δlj:1 rhf:47 sections:6 considerably:1 himself:1 arise:1 zhang:1 murphy:1 boys:3 properly:1 77b:1 c02:1 delta:2 russian:1 dy:1 pain:1 considerable:1 intuitive:4 up:24 us:26 paired:1 accustomed:1 uk:1 naµ:2 highlight:1 similar:8 called:35 dill:1 associated:15 defined:33 likewise:1 singly:1 globally:1 quantification:1 single:20 unwise:1 formalism:11 defines:1 countable:1 codes:1 sˆz:6 amounts:1 multipliers:23 rewriting:1 application:3 priori:6 coded:1 biol:4 department:3 200x:2 bonneau:1 draw:1 elements:13 energetic:1 calculating:12 aser:2 problems:7 polynomials:1 prepared:1 meaning:1 allowing:1 vectors:5 sides:6 structure:10 furthest:1 independently:4 correlated:3 algorithm:7 vice:2 neill:1 required:3 sˆ2:6 contemp:1 equivalently:1 depth:2 failures:1 having:6 once:7 φ1k:1 code:1 partial:1 illustrates:2 edn:4 results:10 illustrated:2 eds:7 kato:2 go:4 contributions:3 issues:12 compact:3 λij:16 simon:9 monomer:1 concerned:1 young:1 suits:1 uniqueness:3 jab:2 helps:1 late:1 106a:1 include:4 dramatically:1 resources:1 ingredient:1 confirmation:1 pulay:5 84a:1 parameterize:1 implicitly:1 continues:1 harmonics:4 wave:1 unstructured:1 electron:79 rotational:1 nichols:1 pσ:4 nieto:1 binkley:4 matrices:8 positions:6 notes:3 challacombe:4 fewer:1 try:1 integro:3 dealt:1 eigenvalues:18 inspection:2 enforce:2 smaller:3 za:5 86b:1 hirata:1 imply:1 compensates:1 enclosed:2 uncomfortable:1 substituting:1 dynamics:3 odd:1 zr:1 index:11 124b:1 3s:4 3p:5 analogously:2 expressed:6 henceforth:2 consistently:1 infinitesimal:1 3n:3 rα1:2 capital:4 3c:1 3b:1 3a:1 frisch:6 3g:8 3f:1 3e:1 3d:1 body:4 justification:2 lee:3 degree:2 exchange:19 respectively:16 gathered:1 desired:1 objects:6 separation:2 cab:1 slater:16 sine:1 ıguez:1 great:3 trans:1 parameters:3 technical:5 involved:5 larger:7 leaving:1 suggests:1 products:7 opinion:1 implement:2 proof:3 makes:3 composed:1 jˆj:9 named:3 transformations:1 φkn:1 scales:2 apr:1 jˆb:4 app:1 eiφ:2 decrease:3 names:1 lanczos:2 tools:1 standing:2 use:29 exciting:1 kutzelnigg:1 usa:5 commun:4 remains:1 asz:2 next:16 calculation:9 depicted:6 krishnan:1 screening:1 sort:1 clever:4 formally:1 diagonalize:2 kim:1 becomes:3 om:1 normalized:12 diffuse:4 iii:7 had:6 depiction:1 account:4 augment:1 effectively:1 ρi:2 bally:1 getting:1 angstr:1 obvious:3 publications:3 meet:1 drops:1 coffin:1 dropped:5 control:1 weaker:1 reserved:1 biophys:4 process:8 91a:1 chim:3 high:1 sought:7 assumptions:3 pawlowski:1 something:1 intuitions:1 rodr:1 gcd:2 dzp:1 six:4 regions:1 located:1 galli:1 instead:6 sin:1 stand:1 exemplify:1 blocks:5 dzv:1 abuse:2 distances:2 multiplication:3 winter:1 ambiguous:1 dα:5 coupling:2 computations:3 light:3 issn:2 lines:4 correspond:9 redundant:1 element:5 extremal:1 encyclopedia:1 asserts:1 hid:1 subsequently:1 divided:2 δmn:2 expressing:1 poor:1 produces:3 move:3 meter:1 interpreted:3 produced:1 comma:1 circumscribed:1 mentioned:6 2sp:2 operative:4 write:19 le:3 exclusion:1 la:15 chosen:18 masses:1 lk:2 li:3 lect:1 previously:1 degrees:8 choose:6 derivative:17 defining:2 eme:1 pure:3 dab:1 dac:1 factorial:1 dan:1 material:1 attains:1 mention:5 subtraction:2 sij:3 rotation:2 handy:2 biomol:2 assess:1 february:64 dirac:3 university:5 identified:1 magnitude:1 l2:4 l1:2 references:5 constraints:44 subset:3 profile:1 tuples:1 doing:2 related:20 constitute:8 elementary:2 computable:1 separating:3 our:4 eigenstates:8 special:12 out:17 minimizations:1 matrix:54 occupied:19 rev:14 trickier:1 posteriori:1 socalled:1 lecture:1 supports:1 math:7 vdz:1 approached:2 interactions:1 habana:1 discontinuity:1 ısica:2 diagonal:10 completely:6 york:8 ρij:1 monographs:1 nβ:17 interaction:4 waving:2 geometry:1 could:23 times:6 length:2 derivations:1 removing:1 hence:17 facilitate:2 unmodified:1 equates:1 swapped:2 powerful:1 alanine:1 pgs:2 proposing:4 reached:3 sherrill:1 precisely:4 quality:2 biasing:2 echenique:38 publication:1 los:1 ordering:2 data:2 adjoint:2 system:10 relations:6 their:29 appl:2 ulich:1 fermions:2 rated:1 perfectly:1 final:14 shell:36 vigorous:1 tuple:2 explanation:2 exactly:3 disguised:1 inflexion:1 zα:10 zβ:3 remember:1 flavours:1 limiting:3 appealing:3 exp:8 providing:1 enforced:1 unchanged:1 dunietz:1 lin:1 extremals:1 enforces:1 need:5 constrained:31 linked:2 roux:1 pursued:1 able:4 ghf:46 polarization:6 εl:2 εi:19 εk:6 εd:1 subject:2 εa:1 accuracy:6 calculus:1 adamson:2 allow:5 axiomatic:3 centre:9 oneelectron:3 co2:1 representation:1 mcyt:1 2mα:2 why:3 80c:1 hk:1 repeated:2 graphs:1 hi:6 χc:2 χb:9 χa:23 mechanical:5 ampere:1 prefactor:3 normally:2 fact:48 80b:1 selection:2 text:4 agreed:1 supported:3 anyway:1 12p:1 12s:1 99a:1 baldoni:2 99b:1 trivial:4 80a:1 unanimously:1 based:8 knowledge:3 barden:1 solovej:1 should:13 entities:1 nilsson:1 bases:1 candidates:2 quintuple:1 ambiguity:2 truncation:2 local:5 hope:3 exchanged:3 insight:4 bonds:2 ralston:1 syst:1 simplest:4 joint:2 ones:61 legitimate:2 words:3 probably:2 kong:2 procedures:4 areas:2 gray:4 processes:1 determinants:1 densities:1 differential:6 expansions:1 qz:2 she:1 contain:5 including:2 fixed:7 nist:5 view:2 ebd:1 knowing:1 requirement:6 multiplying:1 computed:6 exists:9 notational:2 transpositions:4 national:3 operates:5 computer:8 maday:1 operated:1 peterson:1 gmail:1 closer:3 exploited:1 imposition:3 λkj:3 nuclear:18 nightmare:1 diverge:1 written:16 difficulties:1 correctly:1 routine:2 tens:1 invariant:4 neither:3 frustrated:1 email:1 ends:1 horizontally:1 labelings:1 physicist:1 efficiency:1 ket:3 problem:77 restrictions:8 limits:1 taking:10 decay:2 equal:3 assure:1 hψ:2 grail:1 safely:1 grounds:1 aa:1 ci:3 relevant:12 co:2 cn:7 cm:6 cc:1 removal:1 ca:4 leipzig:1 harmonic:5 cd:4 ab:12 maximize:1 cs:2 respect:14 gto:11 sextuple:1 addition:7 int:1 slowly:1 hottest:2 define:10 determinant:8 uij:6 corresponding:17 subspace:2 cos:3 covered:1 last:8 c1:2 c0:1 present:9 multi:3 vtz:1 nd:15 appearance:1 value:26 choices:1 will:39 ar:5 orica:1 wilf:1 cusp:1 almost:3 refs:5 thus:15 surface:5 tu:1 vs:1 greater:1 orbital:20 moves:1 φa:22 unity:1 parts:10 northwest:2 pauli:2 largest:3 units:24 φi:75 φj:22 φk:28 φl:8 privileged:1 φn:3 difficult:9 practice:7 http:5 upon:4 effect:2 ferguson:1 infinite:8 frequently:3 expand:3 keep:2 mech:1 schr:19 center:2 nevertheless:7 adapted:2 well:13 bohr:1 sets:32 position:5 arising:2 stressed:2 spherical:15 routinely:2 less:11 moments:1 accurate:7 kkj:1 drdr:4 obtain:10 underlying:3 ritchie:1 chien:1 adv:6 web:2 conjugates:1 density:25 bell:2 mathematically:4 reasons:1 add:4 other:25 conjugated:1 nor:5 natl:3 diagonalization:15 vˆee:8 ski:1 identical:4 optimizations:1 increased:1 government:1 devised:1 fys:1 increases:1 five:3 community:1 press:5 immediately:2 variants:1 2nd:6 insert:1 c1i:1 necessary:5 like:46 success:3 sizes:2 alternatively:1 admitted:1 martin:1 δf:9 become:2 works:1 page:17 therein:2 parity:1 because:7 classical:14 arrows:1 phenomena:1 searching:1 wider:1 choosing:4 recommendation:1 proper:2 y00:1 neglecting:2 happens:2 montero:1 chichester:3 lead:3 parallelization:1 avoid:3 condens:1 overlap:5 instantaneous:1 does:19 assuming:3 reaching:1 dcd:8 pp:8 expansion:1 jung:1 although:25 imaginary:1 simpler:4 gained:4 a1:6 about:22 actual:7 carried:1 extension:1 saddle:3 column:2 freedom:13 particularity:1 dependence:5 a2:2 introduced:12 loops:1 discretization:3 letters:4 h2:2 preexisting:1 washington:1 functional:38 chemists:1 tackle:2 square:3 dipeptide:1 estimators:3 karplus:3 van:3 additional:11 noticed:1 tails:1 tannoudji:1 dropping:3 inner:1 function:38 eac:1 eab:4 but:41 volume:3 reminds:1 neutral:5 construction:6 gain:1 convergence:5 highest:1 hf:2 partially:4 made:17 compute:6 evident:2 whether:2 cells:1 official:1 placed:2 below:14 limit:5 ruling:1 iterated:2 steepest:1 distribution:2 λji:2 mechanics:9 devise:5 contribute:1 linearity:1 eris:29 denote:9 goodness:1 relates:1 mauri:1 levchenko:1 approximated:4 selsk:1 functions:45 compared:2 opls:1 ingredients:3 detail:4 virtual:2 envisaged:1 hutter:1 book:1 details:8 theor:1 expositions:1 repeat:2 ubingen:1 variation:4 helgaker:5 additionally:6 function1:1 auxiliary:3 prevalent:1 baker:5 factors:4 others:1 rule:3 intentionally:1 ortega:1 profit:4 portion:1 gelatt:1 compete:1 validation:1 rep:1 augmented:1
0705.0338.txt |@word chebyshev:1 partial:1 consider:15 chain:1 maximum:2 rev:3 global:4 results:16 leads:1 proposition:3 computation:1 c2:7 consists:1 follow:4 expressions:1 displaying:1 localized:1 3m:13 compact:2 whose:2 preserves:1 simon:4 depend:3 integral:1 combinatorial:1 knill:2 funct:1 acting:1 containing:1 recurrence:2 does:4 tk:3 under:6 analogous:5 bifurcations:1 applied:2 random:1 attractors:1 very:1 frequencies:1 equivalent:1 springer:2 choice:1 wεs:5 corollary:3 valued:1 every:43 manifolds:1 summarized:1 scoppola:1 difference:1 fractal:23 condition:4 dim:22 obvious:1 hamiltonian:27 issue:1 xyz:2 list:1 solution:2 t0:1 t1:1 large:15 discrete:7 vector:2 dealt:1 small:8 eigenvalues:1 anal:3 originally:1 solutions:1 intermittency:1 upper:18 smaller:3 says:1 transversally:1 estimates:2 approximation:1 rate:1 universit:1 recursions:2 dynamics:10 odd:1 canonical:3 spectral:16 established:5 what:1 3x:8 plays:1 appear:2 iterating:1 completely:1 anton:1 section:11 near:1 shares:1 find:4 3k:1 version:1 issues:1 above:11 sup:11 new:2 increasing:2 method:1 coefficient:1 leb:1 full:3 led:1 respectively:2 palis:2 2kx:2 here:5 inverse:3 tangent:2 situation:1 alone:1 along:2 strong:1 damanik:24 change:1 obtained:4 remark:4 tx:5 forum:1 remarks:1 polynomials:2 study:10 studied:1 allows:1 approaches:2 accomplished:1 periodic:11 survey:1 foliations:3 pick:1 usually:1 specialize:1 studies:1 honor:1 bk:13 bq:1 golden:1 via:2 useful:1 family:2 france:1 namely:2 put:1 apply:1 establish:1 renormalization:1 use:6 asymptotic:3 would:1 prove:10 probabilities:4 positive:2 contains:3 ej:4 negative:1 sµ:4 optimize:1 comparing:1 tm:4 call:4 therefore:9 typo:1 associated:4 type:18 until:1 more:6 separated:1 ir:5 operators:11 stable:7 odinger:19 unstable:6 berlin:2 appendix:3 rigid:1 particular:5 known:6 hold:5 iii:2 evolves:1 γn:1 mf:4 ma:1 erratum:1 recall:10 equation:4 averaged:4 thickest:2 mk:16 geometry:1 values:11 following:28 sturmian:1 specialized:1 example:4 address:4 proof:17 control:1 f1:1 compare:4 weaker:1 challenging:1 give:2 preserving:1 1980s:2 fibonacci:35 cubic:2 sense:2 counting:16 occur:1 absolute:1 hof:2 information:3 needs:1 lacks:1 goal:1 decaying:1 discussion:1 holds:10 american:1 viana:1 write:8 how:1 nontrivial:1 homoclinic:1 pure:1 optimal:4 parameter:4 serguei:2 exu:3 map:15 fr:1 description:4 singular:6 may:2 suppose:6 earlier:1 orbits:1 diagram:1 hence:5 birthday:1 inst:1 curiosity:1 date:1 fk:13 constants:6 times:3 lyapunov:1 induction:1 natural:5 dynamical:12 imply:2 slightly:1 spectra:9 explicit:6 su:15 diffeomorphism:4 si:1 cannot:1 so:7 realizes:1 allow:2 sl:16 taking:2 order:3 restriction:1 s0:1 words:1 ith:7 rand:1 numbers:7 indeed:2 over:1 insight:1 pesin:1 60th:1 approximants:1 statist:1 paper:4 mentioned:1 existence:1 its:9 dynam:2 before:2 derive:3 treat:1 energies:4 interesting:1 exhibits:1 actually:1 better:1 absence:5 choose:7 jacobi:1 mail:4 main:3 defining:2 easier:2 maximal:6 eventually:1 them:1 motivated:1 greater:1 combination:1 ya:1 numerically:1 inductively:2 runs:1 introduce:1 scaling:5 band:32 tails:1 hyperbolicity:3 they:4 instead:2 front:1 now:5 discuss:3 establishes:3 2t:6 easily:1 february:1 finite:3 stated:2 2r:9 2s:7 always:2 university:5 level:2 2x:7 wε:1 sufficiently:5 each:11 found:2 2n:1 polynomially:5 side:2 mean:1 subset:2 splitting:1 simplicity:1 edu:3 energy:2 hard:2 positioned:1 principles:1 related:2 society:1 f0:1 extended:2 expect:2 measure:12 quantum:7 our:18 extract:1 formulated:1 shown:6 matrix:2 space:1 since:20 crucial:2 denotes:1 replacing:1 contained:2 max:3 print:1 lecture:2 homeomorphism:1 forth:1 math:18 shows:4 theory:5 localization:1 monotone:1 abramowitz:1 houston:2 material:1 quasicrystals:5 governing:1 mapping:1 quick:1 reason:2 california:1 york:1 sλ2:12 ask:1 estimate:3 inductive:1 definition:7 dirichlet:1 brasil:1 r3:3 argument:1 hyperbolic:11 3kx:5 ck:2 david:1 turn:5 length:6 place:2 exponentially:2 cycles:1 consequence:4 facilitate:1 strictly:3 first:4 exotic:1 xk:21 formulas:1 initial:10 features:1 probability:1 xm:6 symbolic:2 number:8 nested:1 xy:1 simplified:1 least:2 directly:1 a3k:10 neighborhood:4 size:3 given:17 law:4 publication:1 similarly:3 introduction:6 adjoint:1 behaves:1 amsterdam:1 system:2 relations:1 1a:1 their:2 assumption:2 rates:1 statement:2 ballistic:1 exponents:1 gives:6 tool:1 continuous:9 proving:1 2ak:1 immediate:3 part:6 somewhat:1 x2:3 x3:1 translation:1 x1:4 than:4 finitely:1 kind:1 holland:1 cyclic:1 was:8 chicago:2 zero:7 killip:3 preparation:2 determined:1 were:4 perturbative:1 germinet:4 motivation:1 enumerated:1 lines:1 ann:1 spectrum:50 dynamically:1 kotani:2 zu:1 need:1 seen:1 saw:2 any:16 lie:2 dµ:5 lim:26 latter:1 fourier:1 ideas:1 converges:2 εm:5 liu:2 cantor:3 generalized:2 εk:8 coincide:1 caltech:1 even:1 cnrs:1 exactly:3 sm:3 trace:12 shall:1 measures:5 satisfy:1 systems:7 most:3 foliation:4 significant:1 pair:1 capacity:2 extremely:1 class:1 exponent:4 subspaces:2 constructed:1 especially:1 consequences:6 characterizes:1 considered:1 clear:1 later:2 cover:1 lλ:5 countable:1 graphs:1 proceedings:1 points:2 exs:4 exp:9 kx:2 physics:1 width:1 fact:6 quantity:4 precise:3 phenomenon:1 festschrift:1 show:4 schrdinger:1 supported:3 nφ:1 purely:3 spaces:1 relation:3 iochum:3 uniform:6 x0:3 kadanoff:2 orleans:1 based:2 parameters:1 outside:4 lemma:17 only:5 explicitly:2 2bk:2 notes:2 factor:2 employed:1 rice:4 local:4 interested:3 continuity:7 do:2 fλ:7 goes:3 notation:1 get:4 dependent:1 de:2 ones:1 fastest:3 dx:2 competing:1 dt:6 boundary:1 dq:1 stability:1 processes:1 ja:5 conditions:1 arxiv:1 stirling:1 kohmoto:1 hasselblatt:1 common:2 contain:1 nondecreasing:1 fixed:1 ql:2 hλ:1 takens:2 set:25 exists:9 unions:1 unpublished:1 hα:7 up:2 relative:1 manning:1 see:28 result:30 close:2 forthcoming:1 quasiperiodic:4 best:6 surfaces:2 fails:1 αu:8 inequalities:2 ways:2 review:1 state:5 various:1 closed:2 between:1 invariant:13 justified:1 approach:3 discovery:1 terms:4 initially:2 coverings:2 combining:1 conjugates:1 institute:1 key:1 amer:2 problem:2 improve:3 σk:50 both:6 essentially:2 last:3 reverse:1 x2k:6 cayley:1 career:1 many:3 region:2 infinitely:1 escape:1 equal:3 propagation:2 connection:1 improves:1 iv:1 context:5 whole:1 otherwise:1 comment:1 relevant:2 cn:9 point:7 appeared:1 ca:1 asymptotically:1 cf:2 ce:3 dimensional:10 non:1 coordinates:1 orl:2 moreover:4 mathematically:1 diff:2 considers:1 ct:8 pr:6 pp:1 described:1 belongs:1 basis:1 union:3 barry:1 locally:8 three:1 been:5 quickly:6 describes:1 asymptotics:1 interest:2 basic:1 combine:1 ph:1 topology:2 ak:29 pl:2 define:8 box:16 generating:1 enable:1 corresponding:2 finishes:1 σj:2 quantities:1 sufficient:1 resistance:1 coincides:1 ik:23 gap:2 fractals:1 recalled:1 stems:1 c3:1 consecutive:1 c1:3 general:13 present:1 c4:2 case:16 k2:4 limits:1 tang:1 schellnhuber:1 siggia:1 value:6 will:24 euclidean:1 while:3 replaced:7 behavior:3 aid:1 2k:21 inspired:1 procedure:1 n2k:1 vectors:2 almost:2 vi:2 metric:1 vk:2 thus:19 site:1 surface:3 according:1 ii:3 reads:2 ij:9 im:2 df:2 affected:1 c0:2 derives:1 technology:1 pδ1:3 capture:1 different:2 umr:1 grant:2 lengths:2 recursion:3 make:3 belong:1 lett:3 same:2 clearly:1 complex:1 wavepacket:11 matrices:10 bol:1 proved:6 several:3 rectifiability:1 dimb:19 independent:2 pandit:1 used:1 raymond:9 trivially:1 laboratoire:1 dimh:23 horseshoes:3 hand:9 action:1 intersects:1 levels:4 unimodular:1 potentials:2 infinite:1 invariance:2 cr:9 identity:1 recent:1 pures:1 2cr:3 lower:23 suffices:1 schr:19 mention:1 well:1 roughly:1 analysis:2 sensitive:1 sets:7 model:4 dimension:60 persistently:1 left:1 interpret:1 manifold:1 just:2 heavily:1 being:1 stegun:1 half:6 obtain:8 dover:1 intervals:8 λg:6 λf:5 using:11 facts:1 previous:5 letting:1 tables:1 intersection:1 preprint:1 diffeomorphisms:4 lebesgue:2 extracted:1 regarded:1 conclude:1 had:1 wen:2 improvement:2 reasons:1 ostlund:1 potential:9 extends:1 location:1 easy:1 theorem:26 extensive:1 take:1 real:5 bellissard:1 aspects:1 around:1 depends:3 plancherel:1 bands:17 implications:1 possible:4 jitomirskaya:1 early:1 department:1 boxes:1 know:3 press:3 immediately:3 unique:3 grenoble:1 mod:1 like:4 limk:1 equivalences:1 follows:19 disks:1 specific:1 yields:1 either:1 alternatively:1 popular:2 leaves:1 arbitrarily:1 mathematical:5 right:3 methods:2 deal:1 sequence:10 absolutely:2 some:9 stat:1 self:1 growth:2 b0:2 b1:3 respect:1 proofs:1 transport:4 δn:6 vol:1 dense:1 dimensions:10 confirm:1 stronger:1 univ:1 palindromic:1 everything:2 behave:2 statements:1 x3k:3 eans:2 kiselev:4 obey:1 power:7 slight:1 writing:1 stem:1 mattila:1 nowhere:1 although:1 2m:11 contracts:1 approximating:3 properties:14 takes:2 transitive:1 constructive:1 about:4 actual:1 usa:3 a0:3 commun:9 discussed:1 dependence:2 o:9 subshifts:1 empty:1 chaotic:1 obeys:1 done:1 mixed:1 introduced:4 consequently:6 duke:1 soc:2 cambridge:4 22k:6 previously:2 jε:5 spreading:9 obtaining:1 bound:37 nsf:2 due:3 phase:1 appropriate:1 because:2 references:3 operator:16 fruitful:1 mark:1 physical:1 often:1 log:102 combinatorics:2 transfer:10 support:3 there:20 3the:1 long:1 strict:1 much:1 handbook:2 way:11 labelling:1 sections:1 pasadena:1 naturally:3 function:8 north:1 form:3 enough:3 hs:4 but:5 hu:7 volume:1 cedex:1 hierarchical:1 convergence:1 line:14 true:1 providence:1 faster:2 iterates:1 embedded:1 bandwidths:3 ut:7 mat:1 bounds:15 us:18 below:7 dms:2 limit:7 critical:2 gorodetski:12 continuously:3 distribution:5 similar:3 called:3 leaf:1 detailed:6 c2m:4 gather:1 constant:13 defined:9 certain:3 abstract:1 describe:4 am:3 ergodic:3 covers:2 denote:11 aq:1 symposia:1 exist:3 together:2 inf:11 work:2 distributions:1 check:2 computational:1 regime:2 again:3 functions:3 nk:4 no:1 image:1 commutes:1 when:5 other:11 role:1 details:1 papers:1 np:1 mathematics:6 ns:4 draw:1 separate:1 models:1 symbol:2 setting:1 variation:1 a1:2 hausdorff:23 generated:2 important:4 bounded:18 tkα:1 lenz:5 gets:2 structure:4 implies:3 coupling:8 assume:5 expands:1 interval:2 orbit:2 governed:1 lying:4 time:7 appl:1 quasicrystal:1 e3k:4 having:1 once:2
0705.0339.txt |@word qia:22 consider:1 just:1 show:1 moments:1 over:1 find:8 results:18 friction:42 paper:1 xd3:11 thanks:1 part:1 consists:1 statements:2 rest:7 scattering:21 agrees:2 causes:3 bunch:21 write:1 overlapped:1 2σx2:2 longitudinal:1 system:1 1e:2 density:1 ln:5 cache:1 written:4 3mb:1 only:4 does:2 location:1 int:1 bnl:3 betatron:1 momentum:4 alexei:1 them:2 his:1 around:1 pjk:2 di:7 scattered:1 pja:16 comparing:3 introduce:1 accelerators:1 beam:6 electron:35 ionized:1 putting:1 negative:1 they:1 invariant:1 report:3 using:43 dt:21 now:6 rhic:2 parzen:3 particle:2 proc:1 arxiv:3 correct:3 qa:8 vector:2 n0:2 each:6 found:33 cms:12 depend:3 function:1 cosθ:9 smaller:3 force:43 computed:2 accelerator:1 our:2 doing:1 energy:1 d3:31 za:2 zb:2 relative:1 zero:1 growth:3 result:25 oscillations:2 terms:2 happen:1 eq:13 event:1 subject:1 subscripts:1 shown:8 dimensions:1 space:8 dropping:3 section:13 fedotov:1 while:1 uniform:5 collisions:19 acting:4 pb:3 above:4 between:5 compute:1 ref:1 occurs:2 funtion:1 βab:9 theory:19 vertical:2 cern:1 respectively:1 p2i:10 differ:1 here:7 interval:1 completely:1 derive:1 term:2 σab:25 november:1 tensors:2 change:4 e2:2 acc:1 definition:3 cos:4 derivation:2 angle:1 fa:12 via:8 emittance:5 scatter:2 vjk:2 addition:1 σy:2 σx:2 repulsion:1 procedure:4 treatment:1 σs:2 pdf:2 vja:2 expression:1 finds:5 first:3 vib:3 xi:17 fx:2 µc2:2 va:51 previously:2 vik:5 into:2 integral:1 number:2 due:20 references:1 alpha:1 cs:8 apply:1 ring:1 total:1 george:1 vj:1 methods:1 fj:4 ps:6 given:8 described:2 rewritten:1 indicate:1 introduction:1 px:4 xik:4 three:2 dispersion:8 defined:3 cooling:61 pa:16 rates:19 way:1 pj:1 slowly:1 ph:1 pi:4 pib:1 gives:3 synchrotron:1 obtained:2 direction:3 form:1 relevant:1 quantities:1 factor:3 transverse:1 volume:2 magnitude:4 angles:1 justify:1 x2:2 hold:2 than:3 those:5 emittances:7 case:4 high:1 kind:3 made:2 ma:11 mb:6 solid:1 rate:16 us:3 will:21 assume:1 below:3 kth:1 9th:1 following:1 distribution:5 ibs:15 similar:2 called:1 3ma:1 ions:25 vb:57 pik:5 rab:14 abs:1 give:7 process:1 pia:32 abstract:1 thus:4 sample:2 ap:3 single:1 conf:1 track:7 ia:2 any:2 present:6 no:1 s2:2 nb:18 get:1 when:11 cross:4 same:21 note:2 other:3 δna:4 generalized:1 see:1 becomes:2 finding:1 mass:1 gets:3 sin:6 evaluated:2 polar:1 used:7 http:2 components:3 fv:3 may:4 qja:6 org:2 time:1 factored:2 accel:1 ion:18 fb:13 produce:1 moving:1 fi:22 horizontal:2 measured:1 grow:2 tracked:1 gaussian:1 bjorken:1 off:2 center:1 coulomb:6 dω:13 considered:1 average:1 required:2 martini:1 2ma:4 electrons:11 exp:2 na:8 coordinate:2 velocity:2 quantity:1 physics:3 assistance:1 usual:4
0705.0340.txt |@word sci:1 consider:2 results:3 scalar:1 proposition:8 generalize:1 go:1 follow:1 tx:23 γq:2 equivalence:2 contained:1 quasi:2 those:1 semenov:1 analogous:1 norm:8 ingredient:1 prace:1 springer:1 embark:1 every:2 2γp:8 2γq:1 vast:1 complexvalued:1 t1:1 admissible:4 anal:1 smaller:1 illustrating:1 estimates:4 measurable:3 zero:2 sublinear:2 substitute:1 linear:14 amemiya:1 will:2 nonlinear:1 plays:1 euclidean:1 sum:1 goes:2 sup:1 replaced:1 increasing:3 method:3 here:2 desired:2 departamento:2 46e35:1 address:2 represented:2 studia:4 obtained:1 remark:1 trans:1 study:3 allows:1 γp:20 convolution:1 classification:1 uncentered:1 private:1 first:2 hardy:3 prove:3 positive:1 contains:1 definition:1 hilbert:1 few:1 m1:3 m0:3 more:3 duality:2 operators:30 px0:2 om:1 berlin:2 sharpley:1 particular:4 known:4 cases:1 alexei:1 account:3 valued:1 work:1 mi:1 lorentz:2 lipschitz:1 following:6 arrive:2 example:7 proof:24 define:1 give:4 attribute:1 bennett:1 organized:1 lϕ:25 sense:1 sharp:1 verlag:1 information:2 majorization:2 szeged:1 s3:2 s2:2 s1:3 holds:1 maps:1 nontrivial:1 get:1 acta:1 mat:3 singular:1 may:1 max:9 satisfies:2 mapping:1 fa:1 constants:4 natural:2 whenever:1 consequently:1 sp:1 explicit:1 bastero:1 sm:1 hardylittlewood:1 se:2 typical:1 developed:1 over:1 paper:6 london:2 banach:17 y1:5 y0:5 still:1 its:3 superior:1 ln:6 lech:2 better:3 condition:2 lp:54 lq:37 mail:2 main:3 maximal:3 non:1 good:1 ya:1 significant:1 identically:1 now:2 yu:7 groningen:1 equality:2 name:1 university:1 raynaud:1 concave:9 inequality:2 each:1 found:2 side:1 subset:1 weighted:1 formulate:1 ee:2 idea:1 ofstr:1 books:1 measure:7 our:10 special:1 out:1 space:27 since:6 differing:1 re:15 acting:1 u2q:1 formula:2 rn:1 math:13 theory:2 possibility:1 standard:2 atica:2 calder:2 put:3 estimate:7 publ:1 monographs:1 care:1 pairs:1 applications:1 phrases:1 ist:1 ltd:1 hence:7 tzafriri:1 generalizations:2 karlovich:9 xi:13 u1:17 number:2 erroneous:1 xp:2 open:1 illustrate:1 given:2 necessarily:2 similarly:1 introduction:2 their:1 intermediate:1 statement:3 infimum:1 gives:1 calculations:1 continuous:3 grafakos:2 took:1 employ:1 part:3 authors:1 norms:3 x0:105 x1:106 than:1 second:2 limiting:1 nakano:2 sweden:1 classes:2 historical:1 motivation:1 argument:1 generalization:1 conjugate:1 need:2 final:1 any:8 tρ:1 generalizes:1 min:11 lim:3 note:2 instance:1 analogy:2 new:1 coincide:1 rovisco:1 play:1 fct:1 finish:1 satisfying:1 remarks:2 pais:1 class:1 observation:1 tθ:2 considered:3 calculated:1 sometimes:1 coincides:1 kr:3 kp:27 kx:2 section:4 fact:3 precise:1 show:1 supported:1 spaces:30 based:1 steffensen:1 lemma:13 only:3 equipped:1 pointed:1 do:1 dm:10 above:6 means:1 de:4 cannot:1 words:1 despite:1 lattices:10 ds:9 arxiv:1 fulfilled:1 nondecreasing:2 ecnico:1 krein:1 view:1 set:4 exists:1 observed:2 see:14 result:5 lisbon:1 embeddings:2 dµ:11 best:3 subject:1 brazil:1 seminars:1 said:3 inequalities:1 fatou:1 functionals:1 symmetric:1 between:13 invariant:1 approach:2 notice:1 recently:1 august:1 ju:1 attention:1 key:1 distinguish:1 amer:2 infinity:1 restrictions:1 improved:1 modular:4 many:1 taking:4 equal:3 estimation:1 expression:1 matema:1 comment:1 cm:1 conclude:2 simple:3 smith:2 cf:2 grants:1 peetre:13 constant:24 forms:1 pq:1 pt:1 iψ:2 addition:1 due:3 springerverlag:1 belongs:3 ah:9 sfrh:1 arises:1 corresponding:1 both:4 matem:2 bull:1 general:5 present:1 case:9 aim:1 fubini:1 suppose:6 situation:1 property:1 yi:2 subadditive:16 portugal:2 thus:5 them:1 according:2 ii:1 itself:2 ready:1 technology:1 author:1 generic:1 same:2 clearly:1 complex:4 arguments:1 finite:2 luxemburg:3 interpolation:52 used:1 estadual:1 upon:1 campinas:2 hand:2 luth:1 shortly:1 well:5 obviously:1 concrete:1 lindenstrauss:1 sets:3 less:1 being:1 λx:2 obtain:6 lebesgue:5 olya:2 iϕ:19 lattice:2 qx1:1 theorem:26 guarantees:1 real:6 iθ:2 couple:5 possible:3 tica:1 increases:1 press:1 using:1 ams:1 intersection:1 like:2 bpd:1 follows:9 either:1 modified:2 arbitrary:1 rearrangement:2 works:1 because:1 classical:3 some:10 back:2 examples:1 convex:12 finite:2 dense:1 feder:1 eiθ:3 majorant:1 providence:1 decomposition:1 proc:1 refer:2 l1:1 bh:9 properties:3 chapter:1 about:2 theorems:1 generated:1 important:1 slightly:1 soc:3 communication:1 into:6 integral:2 functional:9 right:1 references:1 operator:13 utl:1 there:2 question:2 transform:1 much:1 lions:1 was:7 indeed:1 function:22 academic:1 complete:3 form:3 but:2 applying:2 gustavsson:2 uq:16 up:13 us:2 continuously:1 problem:2 called:3 proved:7 certain:1 abstract:1 combining:3 denote:4 transl:1 littlewood:2 chap:3 av:1 inf:11 universidade:1 functions:9 completeness:1 when:1 defined:8 other:2 role:2 details:2 department:1 mathematics:3 semin:1 a1:7 a3:5 a2:5 bounded:4 structure:1 dimensions:1 orlicz:36 implies:1 pocti:1 together:1 bergh:3 appl:1 having:1
0705.0341.txt |@word inverse:2 represent:1 homomorphism:9 consider:7 priori:1 invent:1 leads:2 proposition:1 entropy:1 edu:3 consists:1 gn:4 subobject:76 denotes:10 weakly:3 issues:1 restrictions:1 compact:108 preserves:19 anticipation:1 number:8 referring:2 advantage:2 subsemigroup:1 equivalence:42 acting:4 passage:1 finally:10 monotonically:1 tj:5 tk:1 whatsoever:1 stable:32 analogous:1 include:1 tb:4 norm:20 ta:9 brown:2 belonging:1 jensen:1 preserved:2 very:8 implicitly:1 rise:5 translations:1 springer:1 polarization:1 choice:5 corollary:3 valued:12 every:28 additional:4 entries:1 ui:14 emphasized:1 condition:4 wa:7 xmn:1 beginning:4 level:3 turns:1 t2:12 t3:1 t1:14 large:10 rj:2 kit:1 dealt:1 small:1 anal:2 referred:1 inspection:4 noted:1 zn:8 smaller:6 force:2 submodules:2 zd:2 lecture:1 direct:19 literature:1 approximation:2 yk2:1 second:26 value:1 pass:2 incidentally:1 reine:1 codomain:1 canonical:6 even:12 established:4 what:11 appear:4 invertible:5 kris:1 giving:1 ak2:3 sum:23 liberty:1 hereditary:17 comparision:1 sequential:5 en:6 above:73 sup:60 replaced:3 increasing:112 consisting:7 full:2 notions:2 degree:1 respectively:8 isometric:6 here:4 refinement:1 objects:9 xξ:2 address:1 represented:4 consideration:1 strong:2 equations:1 change:1 contraction:5 obtained:3 preorder:1 antisymmetric:4 thirty:1 suitably:1 technical:2 tni:6 larger:4 bv:1 ri:12 amount:1 resulting:4 akm:2 ak1:3 yi1:5 conveniently:1 suitable:3 makes:3 cancellation:1 sci:2 quotient:3 composed:3 stably:5 stabilization:3 projection:12 classification:12 tensored:1 requiring:2 replace:3 topological:1 establish:5 unit:18 readily:1 use:12 proceed:1 would:6 prove:5 remains:5 positive:23 contains:10 tends:1 properties:8 πsi:1 call:1 therefore:14 m3:1 m2:3 taken:2 compactly:59 until:1 more:4 british:2 becomes:3 operators:2 ti:36 s3:3 appendix:3 virtue:1 studied:1 particular:27 known:2 projective:11 hold:1 potential:1 must:29 majorized:7 account:1 isomorphism:50 concretely:1 fulfils:1 kaplansky:1 recall:16 equation:1 mn:10 modified:1 obvious:3 publications:1 containment:11 following:4 making:2 root:1 example:1 proof:47 kirchberg:3 continuity:1 weaker:3 degenerate:1 do:5 calculation:2 introduces:1 preserving:10 purposes:3 ann:2 pushed:2 t1j:1 council:1 sense:36 standard:1 conversely:4 absolute:1 information:2 cofinal:1 requirements:2 dh:8 thing:1 rather:4 verify:1 s1:63 holds:11 pedersen:1 whence:2 write:3 maps:28 edge:1 answer:1 instead:2 sii:2 voiculescu:1 sin:2 map:48 product:13 proc:1 blocks:3 description:4 algebra:102 may:41 max:3 after:8 derived:2 containing:3 collection:3 sni:6 diagram:12 consequence:4 cambridge:4 horizontal:1 compatibility:9 types:1 amenable:1 transitive:3 natural:18 outline:1 third:2 whenever:4 xnm:4 spectra:1 columbia:2 correspond:3 element:57 their:3 sj:9 si:154 cannot:1 so:57 sn:2 allow:1 s2:56 putting:1 elementary:2 cristian:2 order:54 se:1 restriction:1 bidual:1 closely:4 ith:12 duke:1 indeed:9 over:37 di:5 soc:3 murray:4 years:1 approximants:1 course:12 xi:87 including:1 looks:1 thesis:1 banach:1 y1:33 existence:3 still:8 its:8 before:3 aj:4 recalling:1 x21:2 rapidly:40 forwards:3 x1n:5 how:2 chosen:12 fix:1 inclusion:20 coordinates:1 actually:4 meantime:1 choose:26 constitutes:1 ours:1 main:2 might:5 image:23 correspondence:3 eventually:14 yk:4 yj:19 return:2 greater:7 combination:1 yn:22 ya:10 outlined:1 yb:6 impossible:1 introduce:1 isomorphic:67 scaling:2 yields:1 remarkably:1 cutting:1 preservation:3 they:10 now:28 association:1 easily:4 term:27 equality:2 homomorphisms:5 s11:2 always:3 university:4 classified:1 arrows:2 yk1:2 establishing:2 sufficiently:6 inequality:2 l2:1 each:85 x11:3 x12:3 x13:1 side:2 associative:1 upward:12 subset:14 square:2 ei:2 eh:2 short:1 series:1 stronger:3 functor:8 tracial:1 constitute:2 bijective:1 ξj:2 used:7 obtains:2 majorizes:3 funct:2 our:7 operation:9 special:7 out:3 category:23 leave:1 shown:26 monographs:1 matrix:4 space:2 furthermore:14 since:43 research:3 replacing:3 contained:63 reader:1 denoted:1 semiprojective:3 suffices:1 correct:1 math:16 shows:10 benjamin:1 earlier:9 theory:6 assured:1 associate:1 diagonal:12 quite:5 nth:2 completely:2 necessarily:5 subsequences:3 york:1 put:1 enlarge:1 subalgebras:3 hand:4 inductive:33 inevitable:1 union:6 definition:26 unital:5 backwards:1 r1:4 r2:4 applications:1 could:6 iterative:1 moment:1 quotients:2 keep:1 cuntz:86 american:1 place:3 tempting:1 hence:24 onto:6 strictly:6 first:45 separable:8 already:9 xn:40 reflexive:3 symmetry:1 majorize:1 xb:4 u1:2 bii:7 xa:6 primary:1 rank:40 adduce:1 xx:8 river:1 done:3 relations:6 another:11 theorems:5 stated:1 precisely:1 open:1 george:2 passes:2 given:51 cartesian:1 reference:1 similarly:2 introduction:1 adjoint:15 restricts:1 construct:3 needed:3 observations:1 statement:10 ordered:31 2e4:1 final:2 gives:5 v2n:1 commutativity:1 relationship:1 stinespring:1 tool:2 exactly:3 proving:3 immediate:7 za:6 forward:12 part:11 closures:1 somewhat:1 authors:2 x2:112 x3:14 x0:6 x1:84 representing:17 than:15 x4:2 finitely:18 distance:2 kind:1 determines:3 functoriality:4 edition:1 belong:1 coward:1 see:23 matter:3 subsequence:6 determined:4 kth:1 represents:4 were:1 result:2 pre:15 sees:6 give:1 summable:1 concludes:1 argument:2 lin:3 endomorphism:41 say:20 angew:1 close:20 need:10 seen:9 seem:1 st:7 apparently:1 any:28 viewed:3 functors:3 sk:2 mappings:1 zero:31 depending:1 lim:19 self:16 downwards:2 aside:2 converges:4 note:36 sciences:3 ideal:22 k0:1 take:1 analogy:1 encyclopedia:1 calculus:1 t2i:13 begin:1 continuous:6 fundamental:1 trace:1 shall:14 track:1 object:14 birkh:1 most:9 s1i:8 corresponds:1 homogeneous:1 extremely:1 class:20 sub:20 values:2 refine:1 don:2 takes:3 considered:10 clear:4 later:2 coincides:1 km:2 dimension:2 countable:16 notion:3 fact:39 minimal:4 saying:1 show:70 absorbing:2 supported:1 anyway:1 basic:1 purely:13 relation:89 expressed:1 subtle:1 analogue:1 d2:5 d1:5 completion:1 o:1 46l05:1 based:1 proposed:1 northern:1 vb2:4 hf:2 explain:1 basel:1 assertion:26 scientific:1 should:12 xm:1 lemma:15 only:18 smallest:1 generators:6 inherited:1 pointed:2 nj:1 dn:9 abelian:9 establishes:2 notation:5 means:3 uncountable:1 express:2 simpler:1 act:3 aim:1 ones:2 words:16 new:7 applying:2 combined:1 secondary:1 closure:17 m5s:1 endomorphisms:34 arxiv:1 yield:1 pertinent:1 homeomorphic:1 paper:1 li:1 mapped:1 ban:3 london:1 implication:2 fixed:13 embryonic:1 view:3 set:30 modulo:1 opposed:2 exists:19 j1:1 module:81 observed:1 mentioned:4 finiteness:1 individual:1 projections:8 recently:1 theoretic:14 acts:7 subject:2 fails:1 y2:33 tensor:1 down:1 nuclear:3 rings:1 representatives:1 prince:1 written:3 classes:37 various:1 jth:4 closed:35 between:19 o2:3 invariant:13 mathematical:5 approach:2 x22:2 preserve:3 perfect:1 comparable:1 terms:13 supn:1 vertical:2 nature:2 importance:1 weak:2 combining:2 however:1 inclusions:2 hypothesis:11 multiplier:5 article:2 amer:3 topology:1 both:8 essentially:1 x2n:5 last:5 cardinality:1 limits:10 desired:19 many:6 taking:5 equal:25 approximative:4 connection:1 context:2 section:4 passing:13 mean:3 whole:2 adjoin:1 otherwise:1 comment:2 detailed:1 presumably:1 lm:2 co:1 cn:10 point:5 simple:18 corollaries:1 cf:5 dimensional:1 adjoined:6 grants:1 simply:1 assertions:1 sequences:32 wider:1 respect:9 writing:1 considers:1 cu:86 quence:1 considering:4 better:2 described:11 commutative:7 addition:27 morphisms:2 copies:9 been:3 semiprojectivity:2 ai:47 much:2 ensured:1 interest:4 certain:4 transformed:1 ph:1 algebras:48 ak:3 partial:1 surjective:2 generating:4 arises:7 corresponding:9 commutes:1 suppress:1 concerning:7 toronto:6 spectrum:4 assert:1 language:1 tending:1 determination:1 proven:1 turn:1 c1:1 denote:10 cantor:1 present:11 case:49 k2:1 look:1 subsets:5 defining:1 single:2 ǫm:3 transformation:3 will:4 institute:1 while:2 associates:1 suppose:18 compactness:2 appeals:1 adjointable:5 property:7 k1:4 yi:21 vb:4 unitary:7 necessary:2 almost:4 von:4 thus:6 them:2 ii:7 intertwining:1 itself:5 anticipating:1 ym:9 supremum:58 alone:1 qualifier:1 different:3 inc:2 perhaps:3 things:1 make:1 s2i:13 s2n:1 same:25 clearly:6 antisymmetry:1 complex:1 xj1:1 emphasize:1 modification:1 products:2 elliott:10 finite:33 manifestly:1 composition:1 exhaust:2 algebraists:1 extended:1 infinity:3 imply:2 trivially:4 i1:1 cbd:1 reporting:1 require:1 asymptotic:1 average:1 viewing:1 uses:1 purpose:1 internal:1 infinite:14 changing:3 gong:1 identity:24 prescribed:1 pushforward:1 least:1 immaterial:1 nevertheless:1 ǫlm:7 idempotent:2 well:2 analysis:2 non:6 norms:2 concrete:13 directly:1 without:3 reflect:1 sets:2 coordinate:1 arising:13 latter:1 left:1 isometry:5 arbitrarily:6 world:1 looked:1 just:50 less:7 composing:2 vη:1 obtain:12 detail:1 questions:1 using:8 useful:1 alternative:1 yet:1 succeeding:1 adv:1 hai:1 polar:1 submodule:12 preprint:4 generator:1 instance:5 auser:1 conclude:1 seems:2 except:2 operator:4 belongs:9 extends:3 cua:14 theorem:57 semigroup:62 dhd:3 skk:1 specializing:1 real:14 seminorms:1 bij:2 isomorphisms:3 showing:2 sums:1 possible:3 additivity:2 possibly:3 pages:1 approximated:8 press:2 immediately:11 ams:1 unique:5 correcting:1 rørdam:8 like:1 follows:45 interestingly:1 comparability:1 automorphisms:5 indication:2 either:4 alternatively:2 eee:1 adjoining:2 pointwise:1 reduces:1 towards:1 fulfil:1 hn2:3 right:32 neumann:4 namely:10 sequence:154 some:61 under:1 choosing:7 algebraically:12 ah:5 deduce:4 functorial:2 acad:2 b1:4 b2:11 specified:2 images:16 kawamura:1 indirect:2 happens:1 provided:1 xn2:2 proceeding:2 opposite:1 ykm:5 selfadjoint:1 providence:1 does:8 decomposition:3 blackadar:2 summand:1 assuming:1 steps:1 straightforward:2 sided:2 convenient:1 refer:2 semigroups:9 ba:4 power:1 bc:2 equivalent:23 arbitrary:9 continuing:3 bi:8 bj:1 interval:1 translated:1 step:10 although:6 majorizing:1 approximating:2 refers:1 hilbert:121 stage:8 comparison:2 extension:5 algebraic:2 completing:1 toms:2 discussed:1 t1i:8 oa:1 reduced:1 compatible:20 intertwined:2 range:2 a2:18 ensure:4 continous:1 ynm:1 introduced:3 slightly:3 other:26 morphism:10 subobjects:22 raised:1 contractions:1 statements:1 automorphism:3 presence:1 into:9 within:4 ηk:1 functional:2 usefulness:1 appropriate:1 because:5 references:1 s22:2 approximately:13 next:10 theoretically:2 often:1 ontario:1 deal:1 assumed:7 suffice:1 there:26 question:4 approximate:10 u2:2 strict:1 accordingly:2 noting:2 preordered:1 inner:18 way:28 antisymmetrizing:1 m1:4 conceivable:1 was:13 naturally:4 function:6 building:3 hy:1 arise:2 complete:2 form:4 enough:10 troitsky:1 converse:1 triangular:1 but:28 uhf:1 repeated:1 construction:14 hn:23 ho:1 expressible:1 hm:5 russian:1 kasparov:1 true:3 partially:3 directed:11 b4:1 partitioning:1 made:2 compute:2 consist:1 society:2 whether:1 stabilizes:1 characterization:2 up:5 us:68 publishing:1 international:1 kk:1 below:9 un:4 limit:29 supm:1 uk:1 problem:3 stages:3 similar:3 called:2 s1n:1 aa:6 cbc:1 sometimes:1 proved:10 reconcile:1 suprema:15 af:5 defined:17 countably:58 abstract:6 describe:3 am:4 direction:2 singly:12 general:10 thomsen:1 engineering:1 proves:2 exist:11 promised:1 formulation:2 ideals:5 xn1:2 commuting:1 check:8 constructed:5 again:16 functions:1 unperforated:1 identified:2 nm:2 no:4 amounts:1 index:1 whereas:3 when:12 hnm:6 hn1:6 setting:5 neighbourhood:1 holding:1 department:2 mathematics:4 subalgebra:3 sufficient:6 conclusion:1 lance:1 canada:3 briefly:2 elements:27 generates:4 completes:2 respects:1 preceding:4 bundle:1 a1:20 ξi:18 generated:96 important:2 bounded:2 n1:2 dense:4 moreover:1 structure:8 upwards:2 ago:1 bcn:4 implies:10 longer:2 assume:2 starting:1 required:3 modules:70 berlin:1 together:4 original:4 equivalently:6 lift:1 time:5 push:12 recalled:1 n2:1 requires:1 having:3 representative:3
0705.0342.txt |@word besson:1 monte:1 rev:16 luminosities:2 results:3 per:1 contributions:2 content:1 depend:1 γs:6 technique:2 tween:1 efficiencies:2 those:1 under:1 include:3 connects:1 icant:1 splitting:1 mixing:4 affect:1 difference:6 syracuse:2 drutskoy:2 level:1 large:5 vector:2 small:2 concluded:1 upper:2 smaller:1 ten:1 insignificant:1 consistent:5 rate:3 further:1 estimated:2 carlo:1 machines:4 even:2 what:3 abe:1 section:10 selected:1 find:2 access:1 reconstruction:1 new:3 learned:3 boost:1 filled:1 million:2 respectively:3 here:3 reported:1 mev:14 operating:3 excess:1 bonvicini:1 along:1 standard:2 deduced:1 obtained:5 great:1 suitably:1 cern:1 study:3 larger:4 allows:2 leaving:1 amount:1 resulting:1 resonance:8 shaded:1 studies:4 eichten:1 via:3 followed:3 kinematically:3 offset:1 scaled:5 resolutions:1 total:3 establish:1 environment:1 use:2 would:3 distinct:1 suppl:1 nucl:1 noting:1 m1:1 therefore:2 criteria:1 taken:3 until:1 diagrams:1 more:3 separated:2 introducing:1 popped:1 normalized:1 particular:2 disfavor:1 behalf:1 must:1 high:1 mc:3 science:1 work:1 reproduce:1 assumptions:2 ms:1 byers:1 example:1 lυ:2 figure:4 sample:6 lorentz:1 performed:1 counting:1 evidently:1 axis:1 information:2 provide:3 s0:12 regions:3 pure:1 ordinary:1 firmly:1 dominance:1 fs:14 tornqvist:3 may:1 different:1 fb:6 plane:1 dominantly:1 data:14 yaouanc:1 attempt:1 third:1 spectra:2 yielding:1 element:1 cascade:1 si:1 so:1 order:1 exclusive:4 saturated:1 produces:1 over:2 expects:2 years:1 produced:1 through:1 its:5 machine:3 le:1 fit:3 decay:7 energies:1 masses:1 li:1 better:1 production:7 fig:4 versus:2 good:1 band:1 cusb:2 effects:1 they:1 dataset:1 discuss:1 sυ:2 ks0:1 university:1 sufficiently:2 mode:2 2b:1 each:3 found:4 difficult:1 side:1 heavy:1 sanda:1 hadronic:8 energy:5 reduce:1 eb:2 decays:13 ex:2 year:1 substantially:2 out:1 shown:4 matrix:3 since:1 squared:1 projected:1 particles:1 collisions:1 dominated:1 gaussians:1 induced:1 integrated:1 shows:1 foundation:1 ecm:1 confidence:1 diagonal:1 quark:4 signif:1 estimate:2 pairs:1 could:4 times:2 produce:2 onto:1 first:4 already:1 ono:4 symmetry:1 variables:1 timeindependent:1 number:1 channels:2 neglects:1 another:1 lovelock:1 2fs:1 given:1 width:4 introduction:1 unknown:1 system:1 their:2 intermediate:1 rates:3 too:1 eqn:2 final:11 gives:1 shell:1 predictable:1 crosssection:1 than:7 center:1 ofmass:1 determines:1 collaborations:1 sections:1 require:1 tree:1 second:1 states:15 determined:2 tion:1 result:1 pre:1 subprocesses:2 modeldependent:1 qpc:1 bs0:67 spectrum:2 dunietz:1 constrained:2 zero:1 odd:1 able:1 thorough:1 potential:1 channel:1 accuracy:1 circles:1 begin:1 collaboration:10 measures:1 most:1 involving:1 significant:2 position:2 pair:2 measured:7 branching:4 subtracted:1 average:2 later:1 detectors:1 drive:1 points:2 physics:4 sum:2 fitted:1 precise:2 cdf:2 selection:1 particularly:2 show:1 violation:3 text:3 probe:3 nυ:2 discovered:1 inconsistent:2 superimposed:1 indicate:1 d0:9 current:1 ratio:1 γcp:9 only:3 candidates:7 employed:2 dominant:4 gev:3 dependent:3 simplest:1 beam:3 report:2 reconstruct:2 ds:32 processes:2 continuum:6 luminosity:1 arxiv:1 yield:2 summary:1 including:1 set:1 above:1 computed:1 national:1 relative:1 cleo:25 arg:1 observed:2 techniques:1 away:1 p2b:1 future:2 various:4 between:5 invariant:4 enjoys:1 approach:1 recently:1 complementary:3 weak:1 gratefully:1 reproduces:1 huang:2 come:1 both:4 cos:1 limits:3 many:2 region:3 acknowledge:1 chosen:1 pdg:2 contribution:1 expression:1 finds:2 experimental:1 among:1 reconstructs:1 corresponds:1 lhcb:2 cp:9 pp:1 described:2 kinematic:1 computing:1 three:1 been:3 pb:1 combined:1 interest:1 collected:6 ph:1 describe:2 search:1 understand:1 nierste:1 c2:2 present:1 bπ:4 unlike:1 ǫi:1 abulencia:1 value:4 dept:1 while:1 σb:1 untagged:1 taking:1 loop:1 eidelman:1 bin:2 uncertainty:1 coupled:1 thus:2 itself:1 owing:1 containing:1 uqm:5 etc:1 φx:4 belle:18 make:3 cross:11 same:1 reconstructed:2 potentially:1 arguments:1 several:1 events:12 higher:2 used:4 peaks:1 hand:2 fleischer:1 uses:1 recent:1 lower:1 off:1 modes:3 makes:1 well:4 roughly:1 analysis:1 de:1 undertaken:1 model:9 left:3 stringent:1 exploits:1 less:1 being:1 generally:1 proximity:1 obtain:1 predicts:2 world:1 eigenstates:3 previous:2 candidate:2 conclusions:1 photons:4 measure:2 5s:40 improvement:1 source:1 lett:9 samples:2 overview:1 momentum:6 real:1 insensitive:1 observations:1 couple:1 measurement:4 possible:1 boxes:2 five:1 background:3 vacuum:1 using:16 σhad:1 particle:4 signal:6 serves:1 shapes:1 bππ:6 m12:2 yields:9 martin:1 soft:3 accessible:2 because:6 creation:1 neglecting:1 ebeam:4 provided:1 meson:5 lead:1 broad:1 measurements:6 recorded:1 overlap:1 mesons:12 contributing:2 does:3 provides:1 proc:1 measuring:2 bg:1 bi:1 bs:12 analyses:3 bx:1 hadron:3 about:12 rare:5 usa:1 months:1 discussed:1 o:1 simulation:2 insufficient:1 kaons:1 therein:1 presence:1 obtaining:1 mbc:17 assess:1 phase:3 right:2 references:2 determine:2 existed:1 statistics:1 hep:3 additional:1 area:1 inserted:1 support:1 there:2 occupy:1 low:3 fraction:4 was:3 function:1 pd:1 form:2 offer:1 relaxed:1 but:3 histogram:3 expected:7 line:1 partially:1 responding:1 multiplicity:1 up:1 below:2 frequency:1 limit:1 distribution:2 similar:2 obtains:1 strongly:1 fractions:5 inclusive:7 defined:1 certain:1 unitarized:1 artuso:1 distributions:2 triangles:1 physical:1 expect:1 variety:1 nb:5 hybrid:1 ng:1 ny:1 other:4 briefly:1 elements:1 models:1 searched:2 includes:1 charmonium:1 peak:5 ago:1 4s:13 inset:1 mass:14 time:2 starting:1
0705.0343.txt |@word silverstein:1 represent:2 allowed:1 consider:6 riotto:2 rev:19 particular:2 creminelli:7 results:16 orski:1 existing:1 weinberg:1 comments:2 φk1:1 consists:1 shot:4 systematic:1 14th:1 contributions:2 cases:1 rom:1 extra:1 certainly:1 depend:6 calculate:4 tx:1 cobe:1 acknowledges:1 lucchin:1 vs:3 supported:1 2004b:2 finally:7 those:12 determinations:2 under:2 tegmark:1 include:7 nongaussian:3 nishimichi:3 applied:3 luminosities:1 string:1 straightforward:2 dey:1 very:13 tends:1 pected:1 polarization:1 focus:1 integration:1 decide:2 e2:2 affect:4 emphasized:1 difference:4 grant:1 perspective:1 entire:1 sdss:12 level:8 did:1 turns:1 proposals:1 cmb:18 fewer:1 skewed:1 large:24 unrelated:1 progress:1 team:1 small:13 shows:6 lrg:3 equation:13 12th:1 configurations:19 uzan:3 smaller:12 2k1:2 thin:1 renormalized:1 dealing:1 zf:6 bromm:1 measurable:1 b21:3 approximation:6 go:1 second:12 noise:13 design:6 kaiser:2 spectrograph:1 correlator:1 chen:4 further:5 ter:1 d4:2 quite:3 linear:34 even:7 index:1 what:1 nonlinear:1 plays:1 appear:1 completely:2 d2:1 section:10 near:1 expressed:1 find:16 current:6 reheating:1 version:2 porciani:1 δq1:1 above:4 fractional:5 deal:1 obvious:1 increasing:2 ever:1 method:5 era:1 body:3 q1:6 full:6 led:1 9th:1 conf:1 respectively:11 realizations:1 component:4 equals:2 here:3 b31:1 behaviour:1 explore:1 them:1 address:2 represented:1 consideration:1 along:1 strong:2 equations:1 appears:1 yadav:2 obtained:3 remark:1 hansen:1 gpc3:22 shift:1 study:11 larger:9 allows:2 reason:1 example:3 prior:2 amount:3 tinker:2 survey:45 loop:7 poisson:1 hospitality:1 had:2 fourier:4 makes:4 helps:1 2f2:1 uniquely:1 prints:9 via:1 useful:6 ours:2 φkn:1 scales:32 11th:1 understanding:2 namely:1 taruya:3 th:1 compare:1 marked:1 highly:3 expect:5 apo:4 achievable:1 observation:3 apply:2 mmin:10 tools:2 planck:4 sophisticated:1 wang:1 pietroni:2 derivatives:1 use:13 done:1 figure:14 would:17 d75:1 sake:1 positive:2 continuous:1 contains:2 determined:3 predictions:4 next:1 comparing:1 mollerach:1 approach:6 m1:10 therefore:17 sensitivity:4 hikage:4 taken:2 exhaustive:1 simpler:1 type:2 theoretical:2 more:28 introducing:4 accuracy:1 upcoming:1 definition:2 clearly:2 becomes:2 getting:1 curvature:5 surprisingly:1 bartolo:3 domination:1 normalized:1 excellent:3 known:2 kulkarni:2 φk2:1 crocce:3 iii:1 largescale:1 abundance:2 high:18 equilateral:16 mcut:4 bouchet:2 ed:1 recall:1 challenge:1 averaged:1 wands:1 kunz:1 marginalized:11 values:12 emitters:4 evolved:2 s123:5 following:4 making:2 scherrer:2 ın:2 mo:3 optimistic:1 control:1 relative:1 f2:3 weaker:6 challenging:1 cosmological:8 give:1 process:1 zaldarriaga:6 choice:3 inaccessible:1 organized:1 ps:5 generically:2 sample:7 3yr:1 minimum:1 degenerate:3 arise:1 specific:1 spanning:2 times:2 mpc:30 information:13 hod:18 end:1 advantage:1 eiichiro:1 turn:1 provide:8 hexahedron:1 ssz:2 widefield:1 write:2 how:20 kamionkowski:1 optimal:2 gebhardt:2 parameter:13 play:2 suffer:1 simplicity:2 product:2 mar:2 ubiquitous:1 description:2 includes:1 inflationary:3 max:2 earlier:2 derived:8 respective:1 factored:1 constraint:1 less:1 corrections:7 4th:2 floor:1 tivity:1 date:1 horizontal:1 wave:1 data:12 lifting:3 repeated:1 theirs:2 diagonal:1 short:3 attempt:1 remember:1 third:2 sets:1 facilitate:1 spectra:4 explicit:1 departure:3 cosmology:9 rather:2 ho2:1 calculations:1 fundamental:3 correlation:7 halos:4 wfmos:4 sg:1 order:31 bins:9 six:3 interpretation:2 equil:1 pointed:1 spectral:1 mainly:1 mission:2 distortion:2 cip:4 overdensity:2 experiments:2 including:5 lss:4 statistical:3 vastly:1 differs:1 satisfies:1 still:4 kpc:1 its:1 galaxy:98 before:1 observational:3 style:1 thank:1 ln:2 interesting:2 inclusion:1 conduct:1 exhibits:1 actually:2 better:11 detected:1 primordial:51 fig:10 relate:1 total:1 hobby:1 main:5 might:1 easier:2 texas:2 eventually:1 non:88 good:2 motivated:3 thereby:2 largest:2 qs:5 introduce:2 break:1 units:3 effects:5 they:5 instead:1 yr:3 halo:17 josh:1 represents:2 february:2 φk:2 2p:2 2q:1 2r:1 zehavi:1 always:2 university:2 λcdm:1 realistic:3 νe:1 magnitude:6 pan:3 fields:3 acoustic:3 feldman:1 tracer:1 characterized:2 constraints:28 lifted:1 significantly:6 accelerator:1 populated:1 doing:1 there:3 energy:7 reduce:1 gaussian:26 nongaussianity:4 solution:2 inhomogeneous:1 owing:4 alfred:1 eisenstein:6 measurement:1 our:35 based:4 beyond:2 eq:27 tabulate:3 out:6 shown:7 dominates:2 matrix:14 space:15 restricted:1 furthermore:1 since:3 crucial:1 projected:1 cancels:2 melott:1 may:12 hill:2 lae:1 sloan:2 formula:1 accessible:1 gov:1 wandelt:2 viable:1 red:3 predicted:13 rlm:1 foundation:1 after:1 theory:11 found:3 senatore:1 million:3 galaxies:31 given:44 free:4 weakly:1 analytical:1 approaches:2 worse:1 formation:4 term:4 detect:3 intermediate:4 estimate:6 forecasts:1 e1:4 δq2:1 degeneracies:2 hubble:1 perform:1 geometry:5 determining:1 could:2 cosmic:2 jeong:2 keep:1 motion:1 thing:1 american:1 easther:1 due:7 assumed:3 hence:1 needs:2 discussions:1 degeneracy:8 austin:2 first:5 spergel:9 peculiar:4 upper:4 omitted:1 meet:1 powerful:1 number:33 ungarelli:1 simplified:2 specifically:1 takada:4 robust:1 thick:1 precisely:1 electronic:1 biasing:3 size:2 surveys:46 perturbation:9 discussed:1 likely:1 introduction:1 leading:6 top:4 least:2 kadota:1 their:5 perturbations:14 draft:3 fn:66 linearities:9 hetdex:6 brevity:1 white:1 babich:4 2fn:2 observations:3 couchman:1 deg2:3 correlations:1 kf3:2 discussion:1 baryon:4 tool:2 exactly:1 unaffected:1 hui:1 artifact:1 required:3 cyc:9 assumption:1 part:1 too:3 review:2 probably:1 believe:1 representing:1 than:29 positively:1 center:1 wide:3 kind:1 determines:1 log10:7 tree:7 zero:3 twodimensional:1 matter:31 future:4 quest:1 assumes:1 amplitude:5 were:1 tion:1 providing:2 bet:1 result:5 bhi:2 motivation:2 modeled:1 curvaton:1 takes:1 close:2 lines:12 correction:1 radial:2 measure:2 spectrum:20 curves:2 yielding:1 13th:2 already:2 say:3 substantial:1 headings:1 distorted:1 need:1 allen:1 predic:1 any:5 relatively:4 6th:1 rmin:1 angle:2 newtonian:2 liguori:2 studying:1 latter:2 able:1 gravity:2 apj:19 k3:46 k2:66 k1:64 potential:1 2006a:1 take:1 satisfactory:1 2006b:2 so:5 coincide:1 wmap:9 eprints:1 evaluated:1 belief:1 2001a:2 2001b:2 q123:2 multiple:4 allow:1 shall:16 probed:4 gaztanaga:2 denominator:3 reach:5 fails:1 falls:1 most:6 errors:19 importantly:1 matsubara:1 significant:2 bh1:2 bh2:2 intrinsic:1 why:1 probes:2 latex:1 parametrize:1 reduces:1 nonlinearity:1 considered:1 calculated:4 adopt:1 coincides:1 kn:1 typeset:1 astro:61 hierarchical:1 principle:1 exp:1 quadratic:1 constrain:6 usual:1 physics:5 sum:2 wavenumber:6 macqueen:1 dbi:2 selection:5 particularly:6 pope:1 show:24 glazebrook:2 probe:4 feasibility:1 ki:2 colombi:2 relation:4 naga:4 aggressive:1 heavens:4 affected:2 d3:9 decade:2 occupation:5 completion:1 cell:1 q3:2 q2:6 ratio:2 parameters:39 hope:1 negligible:1 should:18 only:13 explicitly:1 black:1 factor:8 local:15 over:8 achieve:4 lim:1 do:8 predict:2 dm:2 triangle:2 tracers:2 degrade:2 means:4 dependent:2 vary:1 zheng:1 subhalo:1 overall:2 account:4 joint:3 ones:2 futamase:1 nearly:1 words:3 altogether:1 during:2 table:8 quantifies:1 bardeen:1 combined:8 gray:1 evolution:14 densities:1 outperform:1 arxiv:11 median:2 multi:1 yield:6 twice:1 paper:6 common:1 qg:8 qi:10 bao:1 fixed:2 valid:2 techniques:2 tolls:1 enhances:1 set:2 computed:2 throwing:1 declines:2 national:1 hα:1 lot:1 up:6 observed:2 mentioned:3 depends:5 justification:1 sec:11 quantitatively:1 gazta:4 seo:3 terms:4 luminous:3 kf:4 best:6 subject:1 instance:2 reasonably:1 cole:2 vertical:1 dispensable:1 subsequent:1 away:1 complementary:1 justifies:1 forecast:1 outside:1 smallest:1 cooray:2 yahata:1 between:17 crude:1 invariant:2 kmax:58 conditions:7 15th:1 side:1 available:6 comparable:4 recently:3 extend:3 nature:5 conroy:4 wechsler:2 overestimates:1 suppresses:1 however:11 prediction:2 efficiency:1 vale:1 probing:1 news:1 configuration:3 come:2 distribution:14 improve:8 gaussianity:36 observable:1 essentially:1 planned:7 prescription:1 limits:7 adept:6 many:2 taking:2 conclusions:2 against:1 juszkiewicz:1 sensitive:7 admit:1 komatsu:15 norberg:1 mildly:3 forgotten:1 expand:1 variance:6 contribution:9 fnl:22 expression:2 finds:2 comes:1 otherwise:1 among:1 portant:1 cm:1 point:8 simple:7 sky:4 hkm:1 batavia:1 pueblas:1 dimensional:3 ab:5 simply:2 cancel:1 moreover:1 rep:1 throughout:1 factors:1 society:1 conference:1 forms:1 comb:5 described:2 lyth:2 lyman:4 three:5 been:11 sheth:8 much:16 melnick:2 pg:2 certain:1 expected:7 ph:58 universal:1 pl:6 choose:1 suggested:2 direction:1 arises:2 general:1 both:10 going:2 sufficient:1 woodruff:1 covariance:11 modelling:1 observe:1 determination:3 angles:1 els:1 improved:1 extract:4 former:1 present:6 case:5 extracted:1 bφ:5 uncertain:1 solid:5 reliable:1 harder:1 aip:1 value:6 will:3 while:17 pφ2:1 ongoing:1 fiducial:10 error:10 squeezed:2 property:1 temperature:1 guide:1 characterizing:1 unlikely:1 understand:1 bin:5 vb:6 vectors:1 vf:2 averaging:1 metric:1 simulations:7 thus:11 designs:2 apjs:1 ii:5 cluster:2 expressions:1 bias:67 il:1 triple:1 measured:3 limit:6 vanish:1 trusted:1 different:9 bernardeau:4 ignored:1 combination:1 suggests:1 generic:2 make:3 cumulative:1 radiation:1 cross:1 same:14 orders:2 d70:1 improves:3 φg:4 lite:1 resulting:1 nanopoulos:1 several:4 grows:6 durrer:2 higher:24 independent:9 satellite:2 used:12 see:7 numerical:4 upon:1 effect:7 hand:10 constraining:2 compared:2 uses:1 purpose:1 kˆ2:1 invariance:1 normalization:1 nag:1 experiment:2 lower:12 task:1 modes:7 scenario:1 largely:1 nevertheless:3 charlie:1 no:5 well:10 analysis:34 obviously:1 telescope:1 directly:2 without:2 greatest:1 fixing:1 position:2 model:16 fermilab:1 left:15 rms:1 excessive:1 proposed:4 object:1 being:5 qν:6 obtain:3 competitive:1 astroph:6 sources:1 scoccimarro:34 underlying:3 alishahiha:3 predicts:1 spherically:1 ωm:4 alternative:1 bi2:1 yet:2 previous:3 far:3 note:6 consequence:1 now:4 preprint:1 tong:1 density:42 mcdonald:5 practice:1 2004a:1 percent:2 smith:3 ideal:1 suto:1 improvement:2 add:2 chodorowski:2 treatment:2 easy:1 requiring:1 role:3 divided:1 real:2 insensitive:1 references:1 ruler:1 breaks:2 digital:1 tormen:4 possible:1 corresponds:3 dark:15 test:1 increases:6 inflation:2 background:3 using:5 replace:1 new:3 sefusatti:12 advanced:1 naturally:1 promising:1 necessary:3 like:1 particle:5 isosceles:1 follows:3 signal:9 extremely:1 columns:2 δq:1 ignore:1 yields:2 δk:6 fnal:1 δf:6 δg:2 δd:3 works:1 reduced:22 mathematical:1 exceed:1 because:6 pl3:2 parametrizations:2 hinted:1 reveals:1 successfully:1 some:1 back:1 10th:1 understood:4 growth:5 pφ:6 b1:79 b2:69 redshifts:10 oscillations:3 neglecting:2 recognition:1 anisotropies:1 provided:4 scale:15 instability:1 wmap3:3 detecting:2 measurements:4 cφ:3 microwave:2 conservative:9 2dfgrs:2 does:8 provides:2 assuming:3 ptot:4 utsi:2 proc:1 minimal:2 measuring:3 biased:3 bg:7 gruzinov:1 inaccurate:1 power:24 plot:3 equivalent:1 each:9 bh:1 bi:6 expansion:1 q2s:5 although:3 bs:1 targeting:2 post:2 refers:2 emulateapj:1 properties:1 bz:1 panel:13 pβ:1 comparison:3 about:5 pα:2 central:1 banday:1 extension:2 szapudi:2 column:3 universe:1 ωb:1 numerator:1 dependence:18 recognized:1 δc:3 range:8 estimator:3 plus:1 horizon:1 signalto:2 connected:2 mean:4 bulletin:1 other:20 considerations:1 astronomical:1 letters:2 redshift:64 h3:19 into:4 within:2 functional:1 negative:1 down:6 right:13 δk2:1 determine:2 δk1:1 proportional:3 per:1 clustering:3 loc:37 jing:2 hep:2 additional:2 few:2 transfer:1 support:1 initial:13 question:1 approximate:3 long:3 overestimate:2 kravtsov:1 describes:1 g2:1 low:12 way:3 series:1 astrophysics:9 was:4 contiguous:1 q12:1 opposed:1 function:24 form:8 δkn:1 distortions:2 agrees:1 triangular:3 but:6 eberly:1 volume:20 tabulates:1 bispectra:2 verde:8 related:3 mnras:11 line:2 sense:3 true:2 fry:8 fifth:1 partially:1 made:1 jaffe:1 croton:1 gravitational:13 access:1 detectability:1 maximum:7 us:6 lead:1 below:3 frequency:1 fermi:1 fαβ:1 fluctuations:19 percival:2 panels:16 similar:1 clear:3 jain:1 obtains:2 strongly:4 spike:1 taylor:1 constant:3 sight:1 flat:1 defined:3 stronger:2 abstract:1 describe:2 linearity:7 covers:1 dvali:2 ap:2 single:4 enable:1 baugh:1 laboratory:1 journal:4 work:3 check:1 triangles:1 physical:2 nh:5 qtree:2 functions:9 pillepich:2 nl:6 frieman:6 dotted:1 variety:1 dashed:9 whereas:3 populations:2 when:11 detail:1 ng:28 field:4 fairly:1 interested:1 statement:1 ambitious:2 spatial:8 department:3 ns:20 bispectrum:78 complications:1 picture:1 hivon:1 separate:1 models:13 fazio:1 nichol:3 precision:1 deriving:1 a0:3 generated:1 important:7 accounts:1 included:6 fisher:11 astronomy:2 must:3 structure:4 nasa:1 detailed:1 independently:1 correlated:2 factorized:1 standard:1 assume:14 sat:1 bottom:5 mask:1 strings:1 kayo:1 lift:1 mass:9 fact:5 push:1 matarrese:9 8th:1 requires:1 gangui:2 once:1
0705.0344.txt |@word homomorphism:1 comparatively:1 obstruction:7 rˆ:1 consists:1 consider:12 whose:6 paris:1 γn:5 under:11 injectives:1 spec:3 rise:3 every:39 induction:3 vector:28 shows:8 zdc:1 direct:6 horn:2 approximation:5 second:7 established:2 errors:1 filtration:4 above:12 new:3 net:1 counital:1 consisting:2 simultaneously:1 notions:1 mem:1 here:2 represented:9 path:3 obtained:1 study:1 completely:1 york:1 projection:2 explained:1 replace:5 total:8 univ:1 unit:9 would:1 negative:3 noting:5 call:2 therefore:21 type:3 duals:1 berlin:3 hold:1 must:20 springer:3 oles:1 mc:40 ml:6 mn:7 mi:7 mk:8 theories:2 norm:1 mr:7 example:3 give:7 preserving:1 cartan:1 end:1 verify:4 hom:29 recovers:1 hov:4 how:4 quillen:39 answer:1 classifying:3 description:5 diagram:4 adic:1 descends:4 hypotheses:1 decreasing:1 order:4 operations:15 restriction:1 over:40 satisfied:1 london:1 thesis:1 satisfies:13 fit:1 fix:1 differently:1 fin:1 maximal:5 they:1 alex:1 invariants:1 arrow:1 each:7 side:5 mean:2 schemes:5 series:2 sdcs:1 dga:2 combining:2 substantially:1 goe:3 restricted:2 crucial:1 mazur:1 daniel:2 mα:4 smi:4 rc:1 rn:4 ri:6 rk:5 eilenberg:6 linear:1 surveys:2 free:10 standard:6 cofibrantly:4 r0:1 isp:8 cofree:4 isa:2 onto:1 already:1 another:2 electronic:1 similarly:9 tot:86 john:1 positively:2 finitely:2 seminars:1 classes:6 kth:1 tion:1 powers:4 bridge:1 respecting:1 representability:7 spectrum:1 seen:2 seem:1 contents:1 gabriele:1 latter:2 forces:1 indexed:1 effectiveness:1 bilinear:1 object:44 birkh:1 extending:3 fibrant:19 observation:4 dol:2 calculated:2 coderivation:2 bracket:3 milgram:1 notion:6 saying:12 goerss:2 iǫ:4 gauge:1 analogue:1 d1:3 bourbaki:1 topological:3 adequate:1 axiom:1 continuity:1 do:2 dm:4 di:2 df:4 dg:18 dd:6 de:1 db:1 dc:8 da:6 dv:1 dw:1 dt:17 dr:9 ds:34 dq:1 eme:1 runs:1 increasing:1 covering:1 coproduct:2 observed:1 result:6 subject:2 said:7 tensor:4 rings:13 µr:4 µm:2 approach:1 torsors:1 preserve:2 terms:1 extend:3 weak:107 however:3 topology:2 adapting:1 essentially:2 cot:36 cof:2 cofibrations:15 eminaire:1 polynomial:2 strong:1 commutative:6 asks:1 basis:2 union:5 three:1 been:2 much:2 basic:1 algebras:35 topics:1 θm:2 cotangent:7 lift:3 applied:4 transformation:5 koszul:1 property:10 homset:1 cylinder:2 epimorphism:1 ir:4 iv:2 ii:4 disjoint:5 im:1 cone:3 id:4 suggest:1 make:3 unnormalised:1 complex:46 filtered:5 several:1 fairly:1 i1:3 hand:5 auser:1 schlessinger:3 covariants:1 weakly:7 scenario:1 left:40 graded:57 just:17 nilpotent:1 regarded:3 easy:2 coalgebras:12 opp:14 posed:1 descending:1 background:1 unique:6 lci:1 homotopical:1 arbitrary:5 fibrewise:1 www:1 right:29 sends:4 maxim:1 asking:2 dualising:1 properties:8 proceed:1 o:33 misleading:1 plus:1 surjections:10 slightly:2 automatically:2 nerve:4 soc:6 statements:2 factorising:1 lies:1 wβ:3 wα:2 suffice:4 initial:1 accordingly:1 way:1 was:2 lurie:7 form:15 converse:2 forgetful:3 true:1 flavour:1 skeleta:1 abstract:1 convergent:2 proves:3 exist:2 dλ:2 dε:1 physical:1 ni:9 nl:1 faithful:3 nn:2 no:3 nc:25 when:7 tin:1 setting:4 sponding:1 papers:1 ns:3 functorial:2 models:4 dω:1 assume:8 modules:7 governed:1 n0:5 characterising:2 stacks:28 chain:36 endofunctor:1 global:9 heller:3 inverse:6 technique:1 quasi:113 analogous:2 localizations:1 brown:3 charles:1 deforming:1 broadly:1 choice:1 anonymous:1 exact:43 level:5 yˆn:1 discrete:1 λnk:3 work:2 says:1 sign:1 functoriality:1 spectral:16 cˆk:10 manetti:7 tangent:14 groups:24 along:2 xα:6 bou:3 bidegree:1 domains:1 subcategory:4 compare:1 durham:2 inverses:1 additive:1 working:3 prove:6 positive:3 france:1 criteria:1 associated:16 diagrams:2 andr:6 coassociative:1 germs:1 surjection:25 appendix:1 cases:1 valued:3 values:1 following:11 making:4 trans:3 zametki:1 december:1 arise:1 confused:1 council:1 conversely:8 spf:89 verlag:2 dglas:9 lemma:91 s3:1 s2:2 s1:4 write:22 criterion:2 fourth:1 ensure:1 map:76 product:11 mat:1 may:24 applications:2 δvn:5 representations:1 data:1 lifting:3 natural:15 outline:1 homotopies:1 whenever:7 sp:61 quadrant:1 sj:1 si:1 so:77 sn:3 definitions:2 sa:1 unipotent:1 sf:1 neighbourhoods:1 pointed:1 differs:2 still:1 group:11 thank:1 quasismooth:2 forms:3 main:2 correspondence:6 non:12 half:2 now:41 term:2 james:1 domain:2 square:2 ea:1 conventions:1 ep:1 neighbourhood:2 shown:3 space:38 contained:2 groupoids:3 rational:1 formula:3 unifying:1 theory:14 orbits:2 complicated:1 inductive:2 rlp:1 care:2 transition:2 turn:6 first:14 xi:1 xn:10 symmetry:1 ring:3 open:2 given:112 necessarily:3 hinich:10 cofibration:25 convention:1 structures:4 gives:29 moscow:1 continuous:4 short:3 representing:3 than:8 wide:1 require:1 cˆλ:30 ann:2 argument:5 say:20 any:34 emes:1 functors:54 jardine:1 converges:2 note:26 sciences:1 ideal:9 take:21 mayer:1 begin:2 opposite:10 algebraic:5 ordinates:1 satisfying:7 formulae:1 remarks:6 pages:4 considered:5 coskn:7 cosimplicial:27 show:30 groupoid:2 spaces:25 transfinite:2 counit:1 homology:11 fibre:12 fibrations:31 reconciling:1 state:1 only:33 explicitly:4 equipped:5 get:2 ssp:1 aα:9 aβ:1 progress:1 bicomplexes:1 closure:4 vezzosi:3 seldom:1 yield:1 summary:1 kernel:18 j1:4 j2:1 relative:21 namely:1 college:1 corre:1 concern:1 detect:1 between:19 geometric:65 αm:3 αn:3 cit:1 jr:4 js:2 come:1 concentrated:5 σj:1 many:4 σa:1 conilpotent:11 enabling:1 embedding:2 sheaf:2 comes:1 generalisation:1 overview:1 maurer:1 constant:5 considering:2 mark:1 observe:36 former:1 those:6 case:4 limits:6 engineering:1 hdn:1 hdl:1 characteristics:2 fibration:64 quasiisomorphism:2 develop:1 formulations:2 same:8 constructed:2 extended:3 trivially:4 subcoalgebras:4 totally:1 weibel:1 roughly:1 without:3 model:52 ck:10 among:2 being:11 captures:1 resp:21 rest:1 topoi:1 topol:1 omissions:1 eorie:1 cofiltered:1 seems:1 contractible:3 hovey:1 cf:1 using:3 moreover:10 mod:2 bigraded:2 adams:4 identifying:1 reduces:1 automorphisms:1 either:2 multiplicative:1 tower:1 sympos:1 dold:6 factorisations:1 deduce:3 cr:5 images:1 matching:3 decomposition:3 expressing:1 projectives:2 dgla:11 power:3 equivalent:52 ltot:1 symm:30 artin:2 comparison:6 oe:5 theorems:4 acyclic:48 morphism:31 cambridge:3 inclusion:2 image:4 references:1 inverting:1 operator:1 loc:1 normalised:3 strictly:2 there:59 strict:10 hel:4 complete:1 regard:6 mλn:1 ωx:1 applying:2 monic:1 grothendieck:1 ωn:4 homotopy:52 simplicial:90 strongly:3 unrelated:1 ag:5 certain:1 ak:2 describe:3 am:4 general:4 together:4 formulation:2 again:1 field:16 valid:2 mathematics:3 0th:1 representable:9 zilber:4 includes:1 a1:7 cofibrant:19 a2:9 bounded:3 resolution:6 represent:2 sch:4 pth:1 alg:1 beware:3 splitting:1 presheaves:2 follow:4 research:1 reasoning:1 preserves:5 albrecht:1 tv:9 equivalence:114 tn:8 tj:3 preserved:1 th:3 tf:9 tg:1 qtot:2 llp:1 straightforward:2 very:4 induce:2 corollary:47 deformations:8 condition:14 small:74 anal:1 ga:10 zero:8 further:2 canonical:19 residue:8 what:1 sub:2 diag:2 section:21 version:1 sur:1 subspaces:1 sup:1 contrast:1 full:3 levelwise:4 respect:6 antisymmetric:1 allows:2 brutal:1 kontsevich:3 permutation:1 action:6 narrow:1 quotient:5 via:2 shuffle:4 pulls:1 establish:1 takes:3 contains:2 finally:7 taken:1 more:4 immersion:2 operators:1 particular:5 projective:13 cogenerated:1 vladimir:1 recall:10 des:1 canonically:5 dec:1 def:10 f0:2 f1:1 f2:1 pro:70 sense:25 yα:2 coalgebra:20 respective:1 rather:4 acts:1 maps:43 e2a:1 csp:37 algebra:27 fx:12 cohomologies:1 derived:34 mapping:8 coming:4 fi:1 horizontal:1 fm:2 fn:13 scsp:77 fundamental:2 fα:2 help:1 paper:1 existence:3 its:17 affine:3 systems:3 jacobi:3 sheaves:2 deformation:34 yi:1 motivated:1 yn:9 finitedimensional:3 framework:1 vect:2 smoothness:20 easily:1 fully:1 comultiplication:5 referred:1 functor:93 since:64 induces:2 denotes:7 denoted:6 induced:2 occurs:1 benjamin:1 ast:1 put:1 definition:148 american:2 transitively:1 number:1 least:2 formelle:1 minimality:1 kon:9 introduction:2 construct:1 statement:5 scheme:2 immediate:7 part:1 ncn:13 authors:1 double:3 contravariant:1 determined:1 bicomplex:1 lie:10 constructions:2 lim:29 lifts:1 play:1 codifferential:2 kan:7 most:2 jsp:6 moss:1 ebrique:1 ki:2 kn:1 bousfield:1 generalising:2 exp:28 completion:3 generators:3 columns:1 abelian:8 hir:2 notation:4 express:2 hin:14 alexander:1 endomorphisms:1 arxiv:6 common:1 e1n:2 set:51 retracts:2 plausible:1 see:11 degree:9 factorisation:2 pisa:2 unions:3 various:1 conditions:16 available:1 analogues:3 bisimplicial:1 both:10 operad:2 vietoris:1 context:4 pdf:1 point:7 corresponds:5 dimensional:16 adaptation:1 bβ:2 fibres:4 kernels:1 ensures:2 transformations:5 bertrand:2 swe:2 pb:4 pa:11 combine:1 dus:2 pn:5 surjective:52 generating:6 partly:1 modelling:1 gap:1 fund:1 understand:1 representative:2 p1:1 conception:1 look:1 while:2 loop:3 vol:1 drawbacks:1 rin:1 itself:1 vanish:2 grant:1 products:6 composition:13 higher:5 used:3 uses:1 necessity:1 dgz:122 artinian:34 ab:1 stack:16 homological:1 concrete:1 coboundary:1 alternative:1 λn:3 letting:1 theorem:45 cuk:10 remaining:1 marco:2 isomorphisms:17 showing:2 sk0:1 systematically:1 follows:16 yields:2 essential:1 terminology:3 mathematical:4 sketch:1 some:9 back:2 examples:1 pω:3 describing:1 integration:1 providence:2 behave:1 connecting:1 proc:1 minimal:7 bg:1 ba:1 bn:6 restrictive:1 become:1 integers:2 pη:2 complexes:29 range:1 extensions:41 replacement:2 consequently:1 into:6 isomorphic:20 pullbacks:1 rows:1 question:1 u0:1 long:12 epimorphisms:2 sections:1 consist:6 characteristic:18 up:6 us:7 un:16 accustomed:1 sum:1 similar:4 called:3 ordered:1 defined:18 likewise:1 single:1 defines:2 amounts:2 dashed:1 application:1 gra:1 retract:2 gro:7 dv1:1 arithmetic:1 gri:4 pridham:5 elements:4 calculating:1 problems:7 generated:8 formal:12 sweedler:1 structure:42 implies:34 gr0:2 gr1:1 required:18 equivalently:6 presenting:1 having:1 once:1 partial:1 gr:4 gp:1 results:6 existing:2 proposition:53 gc:5 gb:6 broader:1 edu:2 gn:3 gm:2 gj:9 equivalences:31 compact:5 concerned:1 send:1 uniqueness:1 ev0:9 ev1:8 ingredient:1 provides:1 isaksen:1 categories:21 evi:3 notes:4 michael:1 pullback:2 zn:2 zi:1 imply:2 giving:10 analogously:1 cell:9 referees:1 exercise:1 ibid:2 respectively:3 objects:20 z0:1 morphisms:25 remark:25 larger:1 vectk:2 contradiction:1 resulting:1 makes:3 boundedness:1 lims:1 limi:2 limm:1 apply:9 resolutions:1 use:8 remains:2 quotients:2 reflects:2 formally:1 smirnov:1 isomorphism:46 infinitesimal:1 proof:90 cokernels:1 calculation:1 reedy:17 purposes:2 pieces:2 pulling:1 sought:1 tan:42 pair:2 instead:1 sin:2 factored:1 abuse:1 multiplication:2 lines:1 correspond:2 element:3 pushouts:1 asserts:1 divided:1 saturated:8 geometricity:1 hirschhorn:1 colimits:3 le:1 outer:1 la:13 ln:29 ll:1 lj:1 li:5 degrees:3 choose:5 lq:19 lx:9 dag:1 pure:1 inductively:5 university:1 l0:5 homogeneous:1 erisque:1 related:1 society:2 our:15 out:1 category:107 res:2 integrates:1 obstructions:2 geom:2 lecture:5 suffices:11 math:19 diagonal:2 approaches:5 collection:1 qui:9 philip:1 monographs:2 geometry:4 length:2 hence:12 phrased:1 manuscript:1 reached:1 precisely:14 adjoint:14 πi:17 πn:14 system:4 πm:4 their:2 quadratic:1 final:3 retraction:2 cochain:28 maclane:2 submitted:1 negatively:5 hz:1 unchanged:1 need:7 clearly:9 sk:1 mil:4 studying:2 instance:1 sufficiency:1 mit:1 unless:1 class:20 pushout:2 hj:12 stronger:2 construction:3 hn:61 fact:4 characterisation:1 supported:1 trivial:47 agrees:1 principal:1 symmetric:9 q2:2 based:1 scuola:1 basel:1 should:3 cohesiveness:1 ambiguity:1 inherited:1 local:11 hopf:1 handle:1 means:6 words:1 differential:17 fixed:1 view:1 moduli:4 modulo:2 computed:1 exists:9 differentials:2 module:1 finiteness:1 lur:10 written:1 jective:1 identification:1 closed:10 invariant:1 boundary:2 hypothesis:2 key:3 amer:4 ker:12 diligent:1 taking:5 admit:1 otherwise:1 comment:1 co:6 cn:1 cocommutative:3 descente:1 cohomology:36 hm1:2 cx:5 sequences:5 cs:2 normalisation:10 cq:8 addition:4 nonnegatively:1 trinity:1 define:82 corresponding:10 adjunction:4 sufficient:2 hmr:2 subsets:2 harder:2 will:25 va:3 vi:3 thus:30 vn:13 dual:25 noetherian:1 finite:21 difficult:1 http:2 logic:1 phd:1 v0:2 v1:4 v2:3 identity:5 well:3 thought:1 sets:13 factorised:3 position:1 arising:2 usual:3 obtain:1 underlying:3 paul:2 bibliography:1 wei:2 skx:3 extends:2 skn:6 vα:14 know:5 press:1 immediately:1 intersection:1 necessary:2 like:1 δv:1 δw:1 admitted:1 nerves:1 works:1 italian:1 exhaustively:1 because:2 classical:7 sequence:31 homs:4 ideals:5 homc:3 does:1 summand:1 ps:1 cλ:35 simplex:1 although:2 injective:4 stage:2 extension:28 a0:7 compatible:4 carries:5 localised:1 h2:1 h0:16 h1:6 en:6 additional:3 vab:1 justifying:1 rcq:1 appl:2 naturally:1 function:2 hx:3 hs:2 eab:1 but:14 hu:2 volume:5 hi:32 etale:4 ho:37 hm:2 hb:2 ha:6 hf:4 truncation:2 etrie:1 compute:1 whether:1 wish:3 cells:2 smooth:111 exactness:2 below:1 limit:6 iterated:1 demonstrate:1 problem:2 strengthens:1 int:1 universal:3 denote:11 inj:4 relates:1 ind:11 identities:1 proceeds:1 inc:1 coequaliser:4 variety:1 other:6 compares:1 bundle:1 hausdorff:1 augmentation:1 rspec:1 homho:8 eom:1 eor:2 schechtman:1
0705.0345.txt |@word limited:1 squared:2 global:1 results:1 existing:2 garching:1 expressions:2 contributions:2 hayato:1 phenomenon:1 depend:2 program:1 ev2:2 fukuda:1 cm2:1 p2:1 accelerator:1 unchen:1 resonant:8 ilias:1 difference:9 condition:1 obvious:1 hamiltonian:1 michael:1 solution:1 large:2 vector:1 small:5 m212:5 upper:3 smaller:4 oscillation:14 sin2:11 approximation:2 7th:1 estimated:3 t2k:2 section:3 nufact:1 current:2 experiment:27 above:1 new:4 scr:1 ek2:2 bilenky:7 here:7 understanding:2 ranges:1 mev:1 obtained:3 lipkin:1 search:1 institute:1 study:1 changed:1 approaches:3 gno:1 hospitality:1 via:1 apr:1 ipk:1 explained:1 neutrino:78 total:1 unit:1 d71:1 takes:1 usa:1 probabilities:3 positive:2 iek:2 next:2 scenarios:2 nucl:8 m2:3 type:2 more:1 raghavan:1 company:1 odinger:4 correspondingly:2 giunti:3 known:3 cases:2 factories:1 must:1 νe:2 account:4 quantized:1 feilitzsch:2 equation:6 mi:1 mk:5 ulk:10 values:1 following:4 example:3 performed:1 lτ:1 pontecorvo:2 give:1 states:17 kamiokande:4 assumptions:9 numbers:1 exclude:1 νl:32 feasible:1 νk:7 information:1 provide:1 six:1 regions:1 apollonio:2 parameter:7 sin:1 massive:1 may:1 sno:2 fundamental:1 physik:1 data:6 higgs:1 rather:1 sm:1 enter:1 daya:1 order:3 νll:2 holds:1 ossbauer:3 nucleon:1 september:1 produced:7 mixing:5 experiments:10 existence:1 still:1 lepton:2 le:1 group:1 thank:1 decay:1 energies:5 masses:8 fruitful:1 detected:4 production:2 main:1 might:1 eur:1 sakata:1 ahn:1 evolution:6 framework:2 superbeams:1 b579:1 now:1 discuss:3 term:1 university:1 miniboone:2 possibilities:1 2e:10 found:1 universit:1 pmns:1 2i:1 reactions:3 significantly:1 ek:11 generation:2 energy:11 applicable:1 ex:6 measurement:1 quantum:3 our:3 transitions:2 eq:5 shown:1 matrix:2 space:5 rep:1 crucial:1 research:1 m2i:1 m2k:3 correct:2 theory:3 interactions:2 possibility:3 standard:11 reason:1 york:2 estimate:1 dubna:1 e1:8 e3:1 e2:1 could:9 transition:9 times:2 introduction:2 technische:1 lµ:1 derivations:1 consequence:1 neglect:3 first:2 origin:4 major:1 initial:1 probability:9 altmann:1 number:1 gallex:1 hampel:1 2ek:1 impossible:1 given:8 unitarity:1 system:4 too:1 perfectly:1 part:2 frascati:1 than:5 oscillate:1 distance:2 kind:1 exptl:2 double:2 require:1 aims:1 determined:1 amplitude:2 were:3 providing:1 russia:1 rewrite:1 modern:1 spectrum:1 lbl:1 angle:2 mechanism:2 note:2 bogolubov:1 sakurai:1 arevalo:1 νkl:1 schwetz:1 allow:3 collaboration:15 neutrinos:18 most:1 connected:2 phase:4 measured:3 why:1 acknowledges:1 observation:2 considered:4 detectors:2 drive:1 proceedings:1 points:2 mechanical:1 shirkov:1 charged:1 physics:2 fact:1 sector:1 reactor:2 show:1 violation:1 accuracies:1 sage:1 relation:5 astrophys:1 find:5 impact:2 based:10 parameters:4 much:3 e12:2 e15:1 only:5 araki:1 do:2 means:2 simplest:1 joint:1 ones:1 negative:2 words:1 international:1 report:1 during:1 processes:2 fields:2 arxiv:3 bay:1 view:3 frame:1 cao:1 detection:2 see:10 result:3 discussions:1 recently:3 observed:4 flavor:15 phases:2 record:1 nuclear:1 review:1 definite:3 d58:1 favor:2 state:10 future:3 between:4 drawn:1 approach:5 notice:3 terms:3 emitted:1 weak:1 however:2 distinguish:4 kev:1 jetp:2 come:1 suggested:3 cos:1 improved:1 kamland:4 taking:4 uncertainty:6 equal:2 recoilless:7 propagation:8 planned:1 σr:1 expression:9 ll:3 experimental:1 point:6 cc:6 m12:1 cp:1 described:3 publishing:1 acts:1 addition:1 due:2 been:5 workshop:2 expected:2 pk:20 ph:7 pi:1 tan2:2 addison:1 direction:1 arises:1 leptonic:1 grimus:1 coherent:1 determination:1 evidence:1 present:3 case:8 p1:13 atmospheric:3 value:2 will:9 nonstationary:1 discoveries:1 unitary:1 von:2 thus:10 according:2 ii:3 optimistic:1 seattle:1 capture:2 different:23 italy:1 baseline:6 maki:1 nakagawa:1 make:1 cross:1 same:8 any:1 k2k:1 arguments:1 largest:1 several:2 events:1 literature:2 numerical:1 interscience:1 effect:3 hand:1 driven:3 v1:1 recent:2 schr:4 scenario:2 smallness:1 well:1 analysis:3 without:1 chooz:4 usual:2 distances:1 proposed:9 being:2 captures:1 ultrarelativistic:1 obtain:2 rest:1 momenta:4 conclusions:1 absorption:5 character:1 theoret:2 day:2 m223:6 source:2 other:3 lett:10 momentum:5 triumf:1 survival:1 possible:1 department:1 vacuum:1 using:1 mod:1 necessary:1 like:1 particle:1 follows:2 δl:2 indication:1 stationary:2 lsnd:2 because:3 some:1 suppl:6 cleveland:1 oscillations:22 confirm:1 kayser:1 prog:2 proc:6 ayres:1 wesley:1 although:1 analyses:1 super:4 superpositions:2 about:4 would:3 aguilar:2 mixed:7 germany:1 rev:9 tritium:5 into:5 washington:1 bound:3 three:5 remarks:1 ashie:1 references:1 determine:2 sov:2 proportional:1 hep:13 additional:2 assumed:1 support:1 there:1 question:1 nova:2 dispersion:1 describes:1 was:6 form:4 fundamentals:1 regard:1 jun:2 ht:2 neutral:1 recoil:1 solar:3 larger:1 proposal:1 he:3 evident:1 us:5 ul:6 demonstrate:1 minos:1 similar:1 mechanics:1 pik:2 int:1 abstract:1 general:1 conserved:1 exist:1 physical:1 ev:3 no:1 nc:4 field:2 interested:1 papers:1 test:1 theor:1 m1k:2 conclusion:2 a16:1 superposition:2 abdurashitov:1 emission:4 important:3 stodolsky:1 assume:3 interval:1 together:1 ip1:1 mass:7 came:1 time:17 antineutrinos:3
0705.0346.txt |@word four:2 consists:3 localized:1 whose:1 const:3 aus:1 under:11 rise:1 every:3 solution:45 vector:9 indices:1 deutsch:1 miller:1 estimates:2 approximation:4 crete:1 second:17 tangential:3 rigorous:3 even:5 errors:1 steplike:1 sheeted:1 ˆb:2 above:14 new:10 ˆj:9 consisting:2 coefficient:5 wrapping:1 here:22 path:3 obtained:2 study:4 completely:1 fourier:4 changes:1 tu:2 projection:3 classification:1 replace:4 modulated:3 univ:3 derivatives:3 would:3 negative:1 m5:23 m4:21 m6:7 m1:8 m0:21 m3:13 recommend:1 type:3 until:2 gohberg:1 solitons:11 naive:1 odinger:4 curvature:1 berlin:3 dirichlet:3 separates:1 must:5 springer:5 work:3 rθ:3 mt:1 flaschka:1 lipschitz:1 nlin:1 root:3 example:3 give:1 indicates:1 want:3 end:4 provide:2 verify:1 enl:1 recovers:2 how:3 ordinary:1 oscillatory:1 replacing:1 earlier:1 wrong:1 lax:1 constants:8 third:4 decreasing:3 acknowledges:2 order:21 deform:2 over:2 london:1 satisfies:10 before:2 noordhoff:1 fiz:1 fix:1 writing:1 uoc:2 eventually:3 them:1 combination:1 band:21 they:6 singularity:4 backgrounds:1 each:9 side:6 schemes:1 independent:2 series:2 semiclassical:1 used:3 combining:2 rr:14 restricted:2 crucial:2 particles:2 re:9 rg:1 multiply:1 ra:10 rl:5 foundation:1 linear:3 little:1 free:3 standard:1 admits:1 estimate:1 publ:1 r0:4 iλ1:1 iλ0:1 onto:1 monvel:1 already:2 primary:1 restrict:1 another:1 moduli:1 similarly:8 manakov:4 top:4 needed:2 perturbations:2 zeros:5 teschl:36 weakly:1 finitely:1 princeton:4 older:4 painlev:1 preparation:1 classes:1 enables:1 rewrite:3 spectrum:4 minp:2 seen:2 seem:1 tells:1 forced:3 latter:1 oriented:8 residue:1 though:1 denominator:1 birkh:2 extending:1 involving:1 vicinities:1 phase:50 observation:1 partition:1 definitely:1 principle:2 vries:6 dot:1 probl:1 o:35 random:1 implying:3 solutions:22 d1:6 situations:1 constant:11 do:1 dl:5 dj:8 subspaces:1 dd:5 de:7 dz:5 dt:3 dr:8 ds:2 runs:1 traverses:2 acknowledgments:1 twice:1 reference:1 δjk:1 observed:1 checks:2 projections:2 w0:2 discussions:1 subject:1 µw:12 symmetric:5 µj:11 approach:2 µb:1 preserve:1 terms:8 extend:2 nature:1 however:6 dµˆ:27 wt:2 contribution:4 genus:4 abbreviate:1 appeared:1 2nd:2 applicability:1 polynomial:3 basis:2 union:1 three:4 been:1 much:2 easy:2 concerning:2 lift:1 θq:1 applied:3 plasma:1 transformation:1 aim:1 near:25 suppose:4 applies:1 endpoints:1 inspired:1 ir:2 iv:1 ii:13 ij:11 im:9 id:1 containing:6 descent:3 make:6 complex:9 split:8 hierarchies:1 several:1 european:1 fairly:1 hand:3 auser:2 normalization:12 cycle:3 suitable:1 thm:6 left:13 just:3 solvability:1 identify:1 facts:1 scattering:13 previous:8 adding:1 zakharov:2 jost:2 belongs:2 innocent:1 hat:1 iν:11 bands:8 iε:2 possible:1 background:15 unique:6 apart:3 verein:1 appearing:1 performing:1 korteweg:6 schwarz:3 arbitrary:1 www:2 right:16 proceeding:1 bottom:5 jahresber:1 everything:1 core:1 kruskal:2 properties:4 counterclockwise:2 surround:2 plus:5 slightly:2 soc:4 ψq:17 publishing:1 presence:1 bound:1 lies:1 ppq:2 ussr:1 raises:1 sov:4 amsterdam:1 abel:2 methods:4 support:1 initial:4 approximate:2 noting:1 way:10 was:6 form:8 m2:17 true:5 inside:1 maximum:1 dordrecht:1 proved:1 cℓk:1 computing:1 abstract:1 proven:1 proves:2 exist:2 dλ:1 check:2 constructed:1 nh:1 nl:3 dotted:2 no:16 whereas:1 when:3 vanishes:4 interested:5 νˆj:3 nt:9 picture:3 models:1 felt:1 uniformly:11 variable:2 factorized:2 dω:12 dφ:1 together:1 time:16 inverse:12 depend:1 technique:1 recurrence:1 quasi:9 compensate:2 analogous:2 asymptot:1 keeping:1 dokl:3 choice:2 entries:1 exact:1 plemelj:2 riemann:84 dij:1 presented:1 leave:2 solved:4 science:3 upper:4 farkas:1 takhtajan:1 sign:1 spectral:13 appear:1 celebrated:1 uniform:2 annals:1 goes:1 international:1 satisfy:5 address:5 along:8 appears:1 change:2 institute:2 studied:1 resonance:1 studies:1 plotted:1 useful:1 prefer:1 isomonodromic:2 additive:1 handled:1 prove:4 positive:7 eφ:2 coalesce:1 explicitly:5 apparent:1 appendix:3 virtue:1 cases:2 logarithm:1 valued:15 deformed:2 modified:1 values:5 following:13 claim:6 figure:9 topic:1 dropped:1 conversely:2 algebrogeometric:1 normalize:3 darboux:1 discussion:2 write:3 pure:2 axis:1 map:5 product:1 mat:2 information:3 may:2 needs:1 applications:2 produce:1 data:4 branches:2 lemmas:1 explicit:2 si:1 so:8 definitions:1 indeed:6 pointed:1 stability:24 course:1 statistical:1 cuts:1 still:4 dynam:1 group:1 τk:1 interesting:2 gtm:1 coordinates:2 mail:2 main:3 happened:1 non:5 thereby:2 views:3 matches:2 introduce:6 half:1 now:17 developments:1 dj1:4 deift:8 term:2 dj2:4 roch:2 quarter:1 weighted:2 ek:11 ej:7 ed:1 gaps:4 es:7 living:3 shown:6 space:4 furthermore:4 looking:2 rational:2 formula:11 dominate:1 correct:3 shows:6 after:5 theory:12 derived:1 nonspecial:6 e1:2 e0:10 βt:4 fixed:3 transition:3 turn:1 place:1 gordon:1 think:2 first:28 oper:1 symmetry:5 variables:2 faculty:1 flipping:4 transform:8 long:12 directly:1 open:2 given:31 sheet:15 1z:1 convention:1 hyperelliptic:7 gives:2 holden:2 continuous:12 representing:2 than:3 coefficients:2 wide:1 accordance:1 require:1 future:2 were:3 generality:3 ann:1 say:6 collects:1 recover:2 any:10 ideas:1 converges:2 note:29 sciences:1 take:4 interior:1 coincide:3 formulas:2 begin:3 trace:2 arguing:1 price:1 surv:1 sheets:1 pair:1 considered:1 later:1 precise:1 show:13 discovered:1 ratio:2 ensembles:1 enough:2 analytic:18 only:11 going:1 get:4 cannot:3 theta:11 neither:1 secondary:1 summary:2 mapped:1 kernel:7 j4:1 j5:5 j1:5 j2:7 namely:2 sukhanov:2 unaltered:2 points:38 surfaces:4 satisfying:1 inequalities:1 review:1 definite:1 outside:1 between:7 geometric:6 across:1 gratefully:2 comm:5 article:1 jetp:2 come:1 σj:6 many:1 region:10 according:7 called:3 propagation:1 expression:4 period:3 innovations:1 pole:7 cancel:3 moreover:10 aˆ:1 wien:2 moerbeke:1 locally:3 odes:1 observe:8 spirit:1 case:26 single:13 invoking:1 situation:2 orientation:2 middle:1 different:14 pay:1 preparatory:1 same:11 extended:2 edges:5 changing:2 ablowitz:3 relies:1 coifman:1 without:5 solve:2 coordinate:5 being:3 generally:1 resp:3 rest:6 differentiation:1 nevanlinna:1 products:1 spyros:2 setting:5 lett:2 real:14 around:5 read:3 mon:1 using:18 velocities:1 integrals:4 characterizes:1 multiplicative:1 stationary:38 reduced:1 reidel:1 leningrad:2 pacific:1 nonzero:1 provided:2 venakides:1 refer:3 faddeev:1 equivalent:1 ration:1 polynomials:2 island:1 aℓ:7 2j:7 perturbed:12 cambridge:3 image:3 ηk:4 references:1 ηq:1 operator:9 log:20 assumed:2 there:22 start:2 assumes:2 complete:2 regard:1 pdes:1 divisors:2 ωq:5 ωp:43 assume:14 obtains:2 detailed:3 ac:2 ai:2 ak:1 aj:5 moved:1 general:5 aq:14 invertibility:2 dπ:12 controlled:1 bishop:1 again:7 spatial:1 mathematics:5 you:1 important:4 bounded:6 included:1 curve:7 original:1 sci:1 consider:10 pointing:1 splitting:3 scalar:7 disc:2 generalize:1 follow:2 research:2 combinatorial:1 tw:6 equivalence:1 tl:1 program:1 th:6 norm:2 belonging:1 straightforward:1 very:4 corollary:2 difference:4 deformations:3 condition:12 hamiltonian:1 evaluation:1 applicable:1 t1:5 large:2 herglotz:1 small:13 anal:1 programme:1 employing:1 neighborhood:6 tem:2 periodicity:2 rate:2 further:3 canonical:4 bilinear:1 what:3 nonlinear:17 section:25 version:1 intersect:1 method:10 component:2 behaviour:1 gesztesy:2 equations:11 search:1 divisor:14 extraordinary:1 fwf:2 periodic:40 pick:1 via:6 requiring:2 muskhelishvili:1 wanted:1 proceed:3 contains:4 finally:7 comparing:4 suffice:1 taken:1 more:6 initiated:1 operators:12 constructs:1 particular:11 known:3 none:2 recall:4 equation:20 det:1 nonsingular:1 history:1 compare:2 memoirs:1 stated:1 beals:1 states:2 sphere:1 minimum:1 numbers:4 sense:1 transcendent:1 νj:8 huge:1 respective:1 rather:4 orthogonal:1 e2g:3 implicitly:1 e2j:38 e2k:14 simplicity:1 algebro:6 ζj:3 ζk:9 singularities:3 plane:8 waves:1 fn:8 short:6 interpolates:1 sect:5 fundamental:2 hierarchy:3 quasiperiodic:2 paper:8 through:1 pane:1 existence:2 its:23 rapidly:1 gerald:3 conjugation:2 systems:5 jacobi:6 travelling:3 might:1 deformation:1 formulating:1 yu:2 smoothness:1 easily:2 finite:6 solves:4 always:7 evade:1 2e:2 2g:8 characterized:1 2k:4 mental:1 formulate:2 reduce:1 toda:40 expect:5 loops:1 http:2 discrete:1 since:31 denotes:6 dominated:1 longtime:1 izv:1 denoted:2 issue:1 monotone:2 guess:1 difficulty:1 perturbation:4 beginning:2 bulla:1 definition:7 exponentially:3 nω0:2 probability:1 perturb:1 nach:1 number:6 dinger:1 done:6 construct:2 differ:3 kodama:2 guaranteeing:1 introduction:1 leading:1 least:5 zabusky:2 assumption:7 passed:1 shifted:1 holomorphic:9 part:13 focusing:3 schr:4 believe:1 kind:11 determined:3 pairwise:1 doubly:3 motivation:1 summable:1 multivalued:2 conjugate:2 tφ:15 lie:9 generalizes:1 jour:1 zero:9 depending:3 lim:7 generalized:2 analogy:1 jacobian:2 unperturbed:2 kac:1 added:1 measures:1 chart:6 most:7 plan:1 soliton:11 arising:1 clear:1 kr:5 segur:3 exp:16 velocity:1 physics:2 lying:4 sector:1 phenomenon:3 m32:1 expressed:1 find:2 m51:1 dividing:1 m52:1 generators:1 factor:1 integrable:4 columns:1 abelian:18 notation:7 dependent:2 express:2 mclaughlin:1 remedy:1 during:1 transversal:1 sects:1 transitional:1 arxiv:1 factorization:11 investigate:2 set:6 art:1 ser:1 undergoes:2 see:28 sec:4 arg:4 close:9 αp0:4 contour:19 project:1 subscript:1 conditions:3 recently:2 vanishing:5 differentiability:1 both:6 last:4 connection:1 context:1 point:16 simple:5 asymptotically:8 dimensional:2 simply:2 pr:1 pp:1 pq:2 described:2 transformations:1 due:6 strategy:1 asymptotics:15 gap:17 neumann:1 fund:2 understand:1 p0:10 exponential:4 frozen:1 evaluated:2 while:9 replaced:2 behavior:10 error:1 loop:1 reads:1 obstacle:1 ready:1 rid:2 vanish:2 grant:1 virtually:1 survey:1 higher:3 univie:2 literature:1 paths:6 moving:1 purpose:4 hospitality:1 lower:3 rodin:2 analysis:3 edge:2 exponentials:2 shape:1 λg:1 λk:3 λj:10 alternative:1 cut:2 theorem:44 lj1:1 lj2:1 solvable:1 remaining:3 stein:1 showing:2 integer:1 m42:1 follows:20 m41:1 essential:6 mathematical:6 2iν:4 often:1 some:16 back:3 towards:1 resonances:1 novelty:1 integration:4 eliminate:1 proc:1 ba:4 bl:4 jumps:12 bi:1 bj:5 bk:3 step:3 bq:13 br:7 hilbert:47 range:6 extensions:1 fredholm:4 consequently:1 gamma:1 into:5 integral:18 appropriate:5 question:3 fast:1 vienna:2 russian:1 consist:1 2πi:20 us:7 similar:5 torus:3 associated:10 defined:38 chap:1 analyticity:2 polygon:2 priori:1 bℓ:3 department:1 problems:14 visits:1 lens:6 sides:1 structure:1 implies:5 required:4 diffraction:1 having:1 once:2 gr:2 results:1 eds:1 contributions:1 gj:4 compact:4 uniqueness:7 contours:2 include:1 2re:2 wave:3 matrices:4 transmission:2 shock:3 eve:1 eigenvalues:4 zj:167 zk:3 zg:6 jump:26 odd:1 index:2 invertible:1 analogously:1 m31:1 poles:23 justification:1 degree:4 exchange:3 respectively:13 lem:2 others:1 sine:1 z0:1 z1:1 z2:2 remark:15 leaving:1 resulting:1 makes:1 involves:1 app:1 uger:5 austria:1 apply:3 imaginary:4 use:15 asymptotic:34 commun:1 remains:7 next:9 stage:1 schro:1 formally:1 ap0:2 normalized:5 iii:11 account:1 crosses:3 erwin:1 anywhere:1 obvious:1 splittings:1 fulfill:1 proof:22 escapes:1 calculation:1 assumptions:2 dk:9 decaying:5 holds:4 regions:7 instead:1 valuedness:2 singular:11 inst:2 kra:1 lines:3 correspond:1 doklady:1 jussieu:1 37k10:1 move:3 including:2 looks:1 lattices:2 austrian:2 decay:2 chosen:5 choose:7 lp:2 ically:1 numerically:1 cutting:1 university:4 sufficiently:2 l2:15 isomonodromy:1 constraints:1 related:1 constitute:1 remove:1 ckℓ:9 measure:1 our:44 special:4 out:3 matrix:12 res:2 rev:2 cwt:1 ret:1 r2g:30 stud:1 suffices:2 integrated:1 math:29 diagonal:2 limε:2 clarify:1 approaches:3 york:1 additional:4 interaction:2 phrases:1 could:2 m21:1 m22:1 times:2 ltd:1 hence:22 precisely:5 dispersive:1 zψ:1 publication:1 adjoint:1 πi:1 relations:2 their:3 siam:1 explanation:1 reverses:1 holland:1 w6:5 limiting:5 result:6 symmetries:4 unchanged:1 curves:3 factorizations:1 enforces:1 need:7 apparently:1 clearly:5 viewed:1 concerns:1 unless:1 petrov:1 connected:1 tanaka:2 class:4 url:2 stronger:1 away:9 fact:12 akhiezer:5 supported:1 purely:3 trivial:3 principal:1 q0:1 based:1 basel:2 should:2 lemma:21 quasimomentum:1 local:5 hope:1 meant:3 cube:1 means:1 leitner:1 words:2 areas:3 evolution:1 differential:21 expansions:1 michor:6 contain:2 cycles:3 view:1 requirement:2 computed:3 exists:4 w0t:2 differentials:7 edition:1 computes:1 greece:1 boutet:1 buslaev:2 state:1 invariant:2 boundary:7 meromorphic:12 transpose:1 interpolate:1 hypothesis:5 key:1 τj:3 amer:3 ker:1 thank:2 hits:1 limits:12 taking:2 equal:4 admit:2 otherwise:3 ck:24 cj:3 co:1 conclude:1 cg:4 cf:24 ce:2 vicinity:1 respect:9 cw:17 addition:2 copies:1 rhode:1 cauchy:15 compensating:1 define:6 arises:2 corresponding:11 bull:1 c2:3 νei:2 present:3 multi:2 splits:1 value:5 will:42 revisited:2 inherits:1 almost:1 thus:13 surface:23 claimed:1 sits:1 cjk:2 generic:1 radiation:2 cross:2 unity:1 parts:5 gets:1 infer:2 infinity:2 cubic:1 effect:2 infinite:3 identity:2 numbered:1 off:3 reflection:10 well:5 ξp0:2 sets:1 cj2:12 cj1:14 soviet:4 usual:2 nonanalytic:1 obtain:6 underlying:7 adv:2 lattice:49 add:1 extends:2 nor:1 match:2 groningen:1 know:1 press:3 intersection:1 loss:3 necessary:2 like:2 alternatively:1 δj:1 δi:1 become:1 works:2 because:1 classical:4 regularized:1 growth:2 choosing:2 proper:1 kdv:1 proofs:2 avoid:1 esf:1 does:2 intersections:1 expansion:1 although:1 approximating:1 simpler:3 about:1 actual:2 extension:2 dependence:1 compatible:1 introduced:1 egorova:5 tackle:1 square:1 isospectral:5 van:1 collisionless:4 appl:2 function:27 north:1 hr:3 hq:21 but:8 volume:1 construction:4 etφ:3 convergence:1 ha:6 made:2 compute:1 whether:1 smooth:1 below:6 limit:2 steepest:3 problem:54 mechanics:1 int:1 denote:3 periods:4 ink:2 ind:5 functions:19 courant:1 variety:2 other:14 details:2 branch:5 conclusion:2 zhou:8 stay:5 else:3 baker:5
0705.0347.txt |@word consider:7 global:5 focus:2 afosr:1 leads:1 ginzburg:1 gm:6 zinn:1 contributions:1 hole:3 row:1 dimensionality:1 simplify:1 tr:3 including:1 critical:3 under:2 regal:1 discontinuously:1 amplitudes:4 expressing:1 frequencies:1 wave:5 every:1 figs:1 redefinition:3 zwierlein:2 matrices:2 condition:1 illustrated:1 wegner:1 anisotropy:5 proposals:1 large:1 discrete:1 vector:1 science:3 indices:1 eigenvalues:2 inconsistent:1 dilute:1 zh:1 direct:1 approximation:2 second:8 perspective:1 chem:1 odd:4 linear:4 even:4 plays:1 trapping:2 representative:1 giving:2 near:2 access:1 above:2 ˆi:1 increasing:2 contrast:2 satisfy:4 led:1 eksp:1 sint:2 component:5 here:5 atoms:3 magnetism:4 inverse:1 separation:2 others:1 along:1 equations:5 legend:1 obtained:1 wesley:1 institute:1 shift:1 study:1 studied:1 allows:1 suggests:1 resulting:1 uβα:1 permutation:1 action:3 imaging:1 useful:2 classification:1 hermite:1 addressed:1 analyzing:3 translational:1 total:1 y2:2 usa:2 distinct:1 positive:1 next:1 call:1 theoretical:3 diagrams:15 more:2 separated:3 introducing:1 populations:1 stable:2 ward:3 fermionic:5 parameterize:1 decouples:1 equation:2 constraint:3 mi:3 remain:1 infinitesimal:2 values:2 decoupled:1 give:5 anomalous:1 rapp:1 generically:2 states:40 minimum:1 chin:1 numbers:1 degenerate:4 allowed:2 mn:1 breaking:2 information:1 s0:2 ultracold:6 occur:1 chemical:9 necessary:1 sin:3 classify:1 simplicity:1 mat:2 may:2 derived:1 fulde:1 diagram:3 applications:2 negele:1 constants:1 stress:1 liquid:1 ss:1 lines:6 redundant:1 element:1 generic:4 si:4 so:2 fundamental:1 amit:1 order:20 acts:3 interpretation:1 satisfied:1 mixing:1 mαβ:7 through:5 y1:2 y0:2 y3:2 still:3 excitations:4 refs:1 regions:7 derive:3 group:3 maps:1 fiz:1 li:1 absence:1 degrees:1 systems:3 derivative:1 scribes:1 imbalance:1 eventually:1 non:8 combination:1 landau:1 break:2 effects:1 they:2 identically:1 oxford:2 now:5 discuss:2 february:1 2p:2 x0:3 always:5 university:2 classified:2 orthonormal:1 each:4 2m:2 2n:1 difficult:1 mean:11 individually:2 detect:1 energy:6 ef:5 frequency:1 interplay:2 quantum:2 transitions:10 eq:7 out:1 respects:1 shown:2 fundamentally:1 factors:2 rev:13 denotes:3 m2i:2 dominate:1 ref:1 occurs:3 shows:2 theory:2 interactions:6 diagonal:6 free:2 small:3 california:2 term:3 compressibility:1 goldschmidt:1 log:2 definition:1 competes:1 interaction:3 organic:1 determining:2 transition:3 δij:1 teor:1 eters:1 βi:2 first:13 exotic:1 pairing:30 features:1 symmetry:8 quasiparticle:3 variables:1 number:3 walter:1 xs:1 wilczek:1 given:6 temperature:3 similarly:1 top:6 system:2 construct:2 identity:7 white:1 leggett:1 gives:4 enhancing:1 exactly:1 accurately:1 x2:3 sublevels:1 x1:3 population:3 jump:1 favors:4 summary:1 zero:9 tunable:1 superfluid:2 amplitude:2 were:1 iωn:3 distinguished:1 exhibit:2 function:2 ann:1 locations:1 viewed:1 prohibits:2 partridge:1 depending:1 orland:1 selective:1 k2:1 potential:8 take:1 online:3 green:1 mit:1 channel:1 unless:1 trace:2 normal:11 honerkamp:2 grassman:1 reach:1 most:2 involving:1 overlapping:1 letter:1 pair:3 measured:1 kb:1 observation:1 partition:1 points:5 metastability:5 exp:1 overdetermined:1 constrain:1 physics:2 superfluidity:10 larkin:1 signatures:2 ferrell:1 show:1 text:1 supported:1 terminate:3 multicomponent:7 implying:3 colors:1 radio:1 fermions:10 find:1 boundaries:2 parameters:3 outside:1 only:11 explicitly:2 rich:1 local:1 do:2 mixture:2 ˆf:5 notation:1 dd:1 expectation:2 nearly:1 invariant:1 combinations:3 bardeen:1 takahashi:3 liu:1 dps:28 densities:4 fields:1 arxiv:1 yield:1 tuned:1 experiments:2 nα:9 nβ:1 fixed:13 set:1 physically:1 detection:1 see:1 enhanced:1 discussions:1 terms:3 analog:1 satisfying:2 tensor:1 ways:2 complementary:1 symmetric:8 state:16 various:1 between:8 αi:2 limit:2 lowered:1 approach:1 notice:1 recently:1 tuning:1 nature:1 uj:1 weak:1 however:3 vanishing:1 harvard:2 suppressed:2 both:7 essentially:2 providing:1 many:1 region:1 acknowledge:1 equal:1 against:2 enabling:1 wt:7 hofstetter:3 dated:1 expand:1 expense:1 experimental:1 grounds:2 comment:2 among:2 point:6 color:3 polynomial:1 respect:1 v2i:6 described:1 transformations:1 decoupling:2 skew:1 locally:1 three:6 appears:1 describes:1 expected:1 microscopic:3 meeting:1 fig:10 addison:1 direction:1 arises:2 corresponding:1 quantities:1 gas:2 cos:2 new:2 spectrum:1 external:2 denote:1 those:3 case:2 pacs:1 solid:1 single:1 value:1 spontaneously:2 while:6 multicritical:4 behavior:1 situation:1 unpaired:4 unitary:5 coupled:1 vol:1 vi:2 vj:1 thus:1 them:2 couples:1 middle:2 cond:2 partner:1 technology:1 fermion:1 different:7 hubbard:1 grant:1 lengths:1 distributions:1 lett:8 same:2 complex:1 arguments:1 mixtures:1 regime:2 higher:1 development:1 independent:3 used:3 trivially:1 drives:5 sarma:1 hγδ:1 potentials:1 robust:1 invariance:1 six:1 tune:1 eigenvectors:2 off:3 fully:1 minimize:1 no:1 well:5 analysis:2 without:2 academic:1 solids:1 contact:1 feshbach:2 components:14 con:1 left:2 unified:1 magnetization:13 generally:1 superconductors:1 obtain:1 using:1 momenta:1 scattering:1 stratonovich:1 previous:1 york:2 density:11 except:1 wu:1 internal:1 attractive:1 cua:1 uαγ:1 uαβ:2 hat:1 transformation:3 momentum:1 real:1 rescaled:1 breaks:3 results:1 possible:8 press:1 δz:2 bicritical:3 mod:1 phenomena:2 imposed:2 particle:7 follows:1 specific:1 δm:2 yields:1 arbitrary:1 δg:1 works:1 hαβ:4 because:1 methods:1 some:2 competition:2 diagonalizing:1 anisotropies:11 describing:7 bottom:4 resonances:2 contributing:1 does:2 provides:1 gapless:5 tributions:1 broken:1 relating:1 properties:1 cδ:1 constrains:2 about:1 justin:1 saddle:4 column:1 discussed:2 essential:1 constraints:3 cambridge:1 presence:1 ndseg:1 maxwell:1 into:3 within:3 nsf:1 phase:25 hermitian:1 right:3 operator:1 proportional:2 bosonic:1 ovchinnikov:1 additional:2 there:2 transform:1 kinast:1 quadratic:2 bartenstein:2 way:1 was:1 naturally:1 lowest:1 form:4 offer:1 metastable:3 superfluids:2 but:4 a550:1 construction:1 hn:2 gain:1 refael:1 he:1 supr:1 us:1 paired:13 below:1 meta:1 ui:3 spectroscopy:1 ωn:3 fαβ:2 demonstrate:1 matsubara:1 similar:2 later:1 associated:1 describe:3 general:3 conserved:5 exist:1 work:1 identities:5 physical:4 ni:1 functions:2 dotted:1 floor:1 dashed:1 wavefunction:3 when:9 vanishes:1 field:17 pasadena:1 role:1 ellipses:1 branch:1 department:2 principle:1 elements:3 generates:1 separate:4 preceding:1 time:1 includes:1 develops:1 massachusetts:1 fermi:2 gap:1 structure:5 matrix:7 condensation:3 domany:1 coupling:4 expands:1 dτ:1 having:1 equivalently:1 mass:1 nelson:1 gapped:3 n1:1 n2:1 requires:2 gαβ:2 bcs:3
0705.0348.txt |@word partial:1 results:1 leads:1 eds:1 edu:1 consists:1 expressions:1 supposedly:1 b382:1 vacuous:1 finally:1 those:1 analogous:1 applied:2 misinterpretation:1 wave:4 fall:1 resonant:4 condition:2 riemann:2 hamiltonian:2 notes:1 solution:2 deals:1 originally:1 zn:2 says:1 dealing:1 consistent:1 second:1 dynamics:1 baumgartel:1 even:2 what:8 incompatible:1 fine:1 section:1 poles:2 above:1 reply:4 method:12 justification:4 led:1 never:1 answers:1 fulfill:1 alone:1 eikr:1 obtained:3 eigensolution:1 shift:1 benatti:1 suggests:1 action:1 rafael:1 criticism:1 followed:1 assertion:1 hardy:21 apply:1 establish:1 standing:3 use:5 would:2 prove:1 sake:1 next:1 usw:13 therefore:3 type:2 more:4 unwarranted:2 introducing:1 operators:1 apparent:1 everywhere:1 normalized:1 particular:1 objections:1 must:1 gadella:1 springer:3 recall:1 equation:3 remain:1 obvious:2 following:2 making:1 root:1 numbers:1 compare:1 stated:1 states:19 assumptions:1 something:1 lacks:1 verlag:1 goal:2 rather:1 acts:2 write:1 how:1 parameter:2 sin:1 may:3 collection:1 wrong:3 plane:4 waves:1 representations:1 choice:10 nussenzveig:1 sw:2 quadrant:1 provide:1 so:2 ultimate:2 asserts:2 representation:6 acknowledges:1 order:1 schwartz:1 london:1 la:12 energies:1 actually:2 choose:1 mail:1 main:3 wellknown:1 overcome:1 eur:1 theo:2 them:1 thereby:1 ya:1 regarding:1 introduce:5 mention:1 they:1 half:2 now:1 represents:1 gamow:19 always:1 university:1 presented:1 sufficiently:1 l2:4 arrow:8 radial:1 2m:7 characterized:1 subset:1 square:1 energy:4 quantum:19 our:1 beyond:2 eq:5 out:3 shown:4 space:4 restricted:1 since:3 particles:1 hill:1 jolla:1 denoted:1 lecture:1 correct:1 math:9 shows:3 theory:17 standard:19 reason:1 california:1 york:5 afterward:1 impose:1 turn:2 exponentially:2 hence:1 onto:1 think:1 first:2 restrict:1 done:1 construct:1 another:4 clarity:1 angular:1 given:1 introduction:1 leading:1 least:2 their:2 assumption:1 shell:1 than:2 albeit:1 kind:1 accordance:1 see:6 were:1 san:1 mind:1 argument:2 civitarese:1 vilenkin:1 need:1 tells:1 lie:1 zero:4 refute:1 potential:2 take:1 spectral:1 hq:1 antoniou:2 though:1 who:1 falls:1 regular:2 position:3 why:3 inconsistency:1 constructed:2 consequences:2 traditional:1 kr:1 points:1 mechanical:1 physics:3 fact:3 show:5 bring:1 spaces:10 inconsistent:4 d2:1 find:2 causality:1 explain:1 iet:1 should:1 analytic:12 only:4 going:1 factor:1 axiom:4 meant:1 do:1 newton:1 goes:1 means:1 de:15 cannot:2 rocca:1 new:5 paoli:1 dr:8 gen:5 evolution:1 arxiv:5 yield:1 proponents:2 requirement:1 physically:5 variations:1 j1:1 j2:1 edition:1 namely:1 arc:2 inequivalent:1 closer:1 eigenfunctions:7 ways:2 identification:2 correctly:1 between:1 progress:1 boundary:3 conditions:3 ikr:1 importance:1 however:1 limits:3 against:1 finds:1 comment:4 point:1 continuation:5 ca:1 height:1 simply:4 considering:1 three:1 basic:1 ph:10 lett:2 relations:1 general:2 fortschr:1 convergent:1 present:1 case:1 look:1 exponential:1 pacs:1 choices:3 will:9 φbg:3 property:1 unitary:2 vol:2 thus:7 surface:2 vs:1 different:7 author:11 perform:1 make:1 same:1 any:7 complex:3 quant:10 arguments:2 φh:3 finite:1 used:2 infinity:3 parravicini:1 inadvertently:2 hand:1 v0:3 uses:1 purpose:1 potentials:1 infinite:2 off:2 framework:1 well:1 bohm:3 academic:3 without:1 claims:1 spherical:1 gelfand:2 proposed:1 shilov:1 obtain:2 identify:1 regardless:1 scattering:4 blow:1 ultradistributions:1 conclusions:5 mathematically:3 jost:1 belongs:2 treatment:1 easy:1 theorem:2 momentum:1 generalized:2 eigenfunction:1 showing:1 possible:3 department:1 press:3 using:5 2nd:1 formal:1 follows:1 imposes:1 arbitrary:3 become:1 works:2 because:3 madrid:11 some:1 back:1 growth:1 choosing:2 ourselves:1 recognition:1 eiqr:1 provided:1 lead:2 lippmann:4 shall:5 everything:1 does:1 ucsd:1 provides:3 tends:2 refer:1 bg:10 agreement:1 although:2 mcgraw:1 properties:4 about:1 working:3 o:1 act:5 introduced:2 other:1 flawed:1 into:2 within:1 integral:3 functional:1 appropriate:1 references:1 operator:2 conceptually:1 criticisms:1 additional:1 assumed:1 there:3 transform:2 dispersion:1 way:8 was:9 function:4 differences:1 but:6 repeatedly:1 delta:1 irreversible:1 proposal:2 applying:2 whether:2 inside:1 smooth:1 up:1 us:3 iqr:1 below:1 planes:1 distribution:4 called:2 mechanics:11 fulfills:1 associated:4 int:1 abstract:1 doesn:4 denote:2 distributions:2 check:1 physical:6 diego:1 functions:37 no:1 objection:1 whereas:1 when:4 schwinger:4 valid:1 test:17 conclusion:1 elements:1 bollini:1 problems:1 floreanini:1 meaning:1 suffers:1 implies:1 faster:1 calls:3 assume:1 time:9 serious:1 once:1
0705.0349.txt |@word represent:2 extrapolated:1 consider:1 chain:3 magnetic:4 excellent:1 γn:3 results:3 leads:1 facilities:1 avalanche:1 edu:1 go:1 follow:2 questionable:1 rigidity:5 γz:3 inverse:1 number:11 technique:1 baf2:1 charge:4 tm:4 those:3 determinations:1 stable:1 downshift:1 fukuda:1 cm2:4 ta:5 federation:1 sherrill:6 very:4 degrader:2 continues:1 none:2 should:1 fall:1 experimentally:1 difference:3 anne:1 entire:1 presented:1 transmission:1 large:1 evy:1 34s:1 small:3 lise:3 upper:1 mn:1 44s:1 protons:1 consistent:1 parameterization:3 estimates:1 prediction:1 second:1 further:1 estimated:1 targets:5 even:2 3z:3 rate:1 section:5 uniform:2 current:1 steiner:4 experiment:2 symbols:2 new:7 net:3 increasing:2 43s:1 43p:1 counters:1 body:6 27f:1 ranged:1 respectively:1 unobserved:4 understanding:1 hours:2 reported:1 mev:6 ansatz:1 groups:1 excess:1 path:3 along:2 logarithmic:1 obtained:1 search:4 sobolev:1 daughter:2 photomultiplier:1 institute:1 shift:1 study:8 larger:2 allows:1 tantalum:1 simultaneous:1 products:10 pick:4 usually:1 makes:1 plotted:1 tasks:1 followed:1 highly:1 neutrons:7 decrease:1 deadtime:1 total:1 plot:1 figure:1 usa:3 intense:1 msu:1 msr:1 france:2 predict:1 nucl:6 come:1 stetson:1 themselves:1 until:1 more:5 om:2 binding:3 under:3 mismatch:1 emission:4 33s:1 particular:1 known:2 mounted:1 iii:2 charity:2 me:3 high:3 mg:13 mb:5 science:2 setup:2 work:17 mi:3 reproduce:1 labeled:1 values:5 temperatures:1 ishihara:1 example:1 factor:2 stolz:4 indicated:1 process:7 weissman:1 saito:1 states:2 indicates:1 numbers:3 counting:1 nuclides:1 creates:1 respective:1 varied:1 provide:3 discussion:1 located:3 pure:1 map:1 product:1 ibrahim:1 after:1 different:1 residues:2 iwasaki:1 plane:7 inst:2 studies:1 fits:1 develop:2 data:19 parallel:2 attempt:1 effective:1 joint:1 light:3 ablation:1 sp:2 lines:3 redundant:1 cascade:1 si:15 extrapolation:3 so:1 sn:2 acknowledges:1 order:1 operations:1 nucleon:2 developed:1 over:4 years:1 stability:1 thermal:2 experiments:1 scott:1 statistical:3 japan:2 its:3 winger:2 reactant:1 rapidly:2 decay:2 energies:7 preferentially:1 masses:3 forms:1 production:15 fig:11 feasible:1 qgg:10 clusters:1 37s:1 versus:1 acknowledgments:1 good:1 combination:1 fragment:10 runs:2 diodes:1 projectiles:1 framework:3 tails:1 yu:3 realize:1 february:1 university:4 drop:1 identified:1 powell:1 sufficiently:1 charged:1 40s:1 reasonable:1 each:9 found:5 entirely:1 higher:4 heavy:2 reactions:7 significantly:2 mueller:5 series:2 energy:9 idea:2 mm2:1 astrophysical:1 ex:1 measure:1 laboratory:3 meth:2 summary:1 extract:1 out:4 shown:3 unbound:1 souliotis:1 factors:3 res:1 rep:2 since:1 rev:10 particles:3 rf:1 investigation:1 dominated:1 transfer:3 ref:3 occurs:1 shows:2 foundation:2 linear:1 frank:2 hirai:1 contain:2 orr:1 given:1 isotope:4 standard:1 39s:1 term:1 dubna:1 supercon:1 created:1 widths:2 could:1 phy:2 pfaff:2 times:1 silicon:8 instrum:1 separator:9 projectile:11 undergo:1 first:2 exotic:4 o16:1 miura:1 primary:2 yariv:1 dripline:3 rasmussen:1 blank:1 reached:1 thick:4 open:1 angular:2 dispersive:1 properties:2 temperature:1 introduction:1 behaves:1 system:2 approximately:3 plastic:4 their:1 rates:2 normalization:1 calculations:3 peripheral:1 grant:2 ratio:5 asymmetric:1 moscow:1 45s:1 somewhat:1 authors:2 pna:1 than:7 relative:3 level:1 target:25 sections:18 enabled:1 see:3 limiting:2 determined:2 magnesium:2 were:10 aoi:2 toward:1 acquisition:1 normal:2 ang:1 correction:1 heaviest:2 seen:1 kelley:2 orders:1 hua:1 lie:1 angle:1 imai:2 smooth:2 note:1 oliveira:1 recommended:1 online:3 davies:1 detector:2 residue:2 begin:1 regard:1 multiple:2 populate:1 though:1 sets:1 chart:1 most:13 optimized:1 significant:1 phase:1 measured:4 isotopic:1 especially:1 considered:1 neighboring:1 average:3 inferred:1 32s:1 32p:1 tech:1 exp:2 pattern:1 usual:1 physics:2 fitted:1 slope:1 show:2 morrissey:10 text:1 supported:1 scattered:1 evaporation:3 ummerer:1 stepwise:1 ground:1 yanagisawa:1 slow:1 based:4 pickup:2 lansing:3 only:5 sequential:1 41p:1 thoennessen:1 rich:15 41s:1 acknowledge:1 various:1 achromatic:1 pointed:1 plate:1 dominant:1 michigan:4 lukyanov:2 overall:1 l41:1 beam:6 lighter:4 tungsten:8 during:2 averaged:1 procedures:1 falling:1 produced:2 processes:2 settings:1 relied:1 arxiv:1 neutronrich:1 yield:1 tarasov:7 qg:5 rigidities:1 excesses:1 available:2 set:2 sep:1 lifetimes:1 national:4 maximum:1 observed:11 intensity:1 38s:1 seitz:1 existence:1 cyclotron:4 optimum:2 closer:1 placed:1 ways:1 nuclear:6 tend:1 µm:3 f22:1 state:5 identification:2 between:5 geometric:1 arrival:1 borcea:1 emitted:1 recently:1 statistically:1 31p:1 weak:1 efficiency:2 analyzed:2 amer:1 suppressed:2 isotopes:18 reaction:7 reverse:1 region:5 uncertainty:1 against:2 ln:1 dated:1 σr:3 gr:1 expression:2 36s:1 experimental:3 among:1 separation:2 cm:1 point:4 simple:2 ca:7 cf:1 46s:1 wapstra:1 applicability:1 cancel:1 respect:1 decline:2 described:5 basis:1 addition:2 discrimination:2 acceptance:3 three:2 been:5 pb:1 trigger:1 combined:2 expected:2 totaling:1 differently:1 enable:1 flight:4 both:1 25f:1 precision:1 bulk:2 systematic:3 general:1 present:6 case:3 heavier:2 uncertain:1 exponential:4 pacs:1 solid:1 reliable:1 value:2 remaining:1 will:2 dept:2 near:1 bombarding:3 beryllium:6 behavior:1 ducting:1 would:1 coupled:1 refs:2 thus:3 surface:1 iv:1 ii:1 superconducting:1 sudden:1 precipitous:1 conf:1 partner:1 audi:1 confirmed:1 kwan:2 irradiate:1 sensitive:1 distributions:5 make:1 35k:1 cross:23 same:1 shifts:1 35s:1 largest:1 several:2 events:2 neutron:26 difficult:1 independent:1 used:5 schiller:2 upon:1 hand:1 running:1 purpose:1 focal:7 recent:1 lower:3 abrasion:1 changes:1 underlies:1 well:3 nuclide:2 analysis:2 portillo:1 without:1 scintillator:5 simulated:1 position:4 model:5 chemistry:1 left:2 less:1 lowest:1 atomic:5 yet:1 previous:1 cut:1 monitored:1 candidate:1 had:1 signals:1 color:3 setting:5 lett:5 east:3 excited:7 momentum:5 depends:1 melting:1 sakurai:2 possible:1 proton:3 using:4 intranuclear:1 moreover:1 riken:1 richard:1 loss:3 necessary:1 like:2 particle:5 sizes:1 gade:1 signal:2 performing:1 ganil:1 either:4 follows:1 become:1 delaunay:1 function:5 right:2 staff:1 plausible:1 some:1 table:2 provided:3 demonstrates:1 tube:1 measurements:9 seaborg:1 magnitude:1 provides:1 yields:3 fragments:6 proc:1 measuring:1 gomi:1 reaching:1 equivalent:1 agreement:2 step:1 although:1 baumann:3 panel:3 comparison:3 about:3 kinematical:1 central:1 carried:3 dependence:3 o:8 range:3 plus:3 mahoney:1 42s:1 intermediates:1 final:1 facility:1 image:6 bound:3 due:3 down:1 proportional:1 unambiguous:1 inserted:1 support:1 long:1 peters:1 describes:1 low:5 jinr:1 astrophysics:1 kinematics:1 slopes:1 was:20 hz:2 bazin:4 differences:1 jun:1 but:8 hausmann:1 straight:2 russian:1 line:3 highest:2 observation:2 fragmentation:9 builds:1 thibault:1 systematics:9 up:9 us:1 nscl:3 crystal:1 below:3 continuously:1 distribution:2 panels:6 similar:1 expect:1 pin:1 abstract:1 describe:1 evidence:2 luther:1 ar:18 predictions:2 our:1 pileup:1 48s:1 amthor:1 compared:1 dashed:1 whereas:1 when:2 47s:1 other:2 compares:2 details:2 nat:1 becomes:1 gelbke:1 briefly:1 excitation:1 models:2 fraenkel:1 symbol:1 variation:2 includes:1 a1:4 important:5 nucleus:3 astronomy:1 structure:1 phosphorus:1 individual:1 starting:1 rather:1 tsang:1 mass:15 time:3 nuclei:21 once:1 requires:2 augmented:1
0705.0350.txt |@word origin:1 axes:1 index:1 being:3 indeed:2 move:1 obtain:1 course:2 scalar:4 paper:1 through:2 url:1 grateful:1 using:1 substituting:2 satisfies:1 preferable:1 d2:9 find:2 diagonalized:1 note:2 unique:1 group:7 treat:1 parameters:4 much:1 masses:2 tr:5 laid:1 should:3 diagonalizes:1 only:5 html:1 fig:1 easy:1 theorem:7 mail:2 circle:10 formal:1 defining:3 take:1 directed:1 them:2 cubic:1 get:4 sharipov:8 operator:7 landau:1 yields:1 they:1 optimal:11 immediately:1 ams:1 now:1 moreover:1 me:1 special:1 2q:1 brought:1 induced:1 equality:1 like:2 russia:1 even:1 follows:2 university:1 arxiv:1 laying:3 orthonormal:1 derive:1 optimally:1 vector:11 steps:1 lifshits:1 each:1 small:1 eigenvalues:3 2n:2 fixed:2 equation:5 characterized:1 mean:6 lie:4 www:2 square:6 transform:1 formulas:1 publishers:1 some:12 back:2 him:1 deflection:1 tex:1 polynomial:3 see:6 street:1 radius:8 result:2 choosing:1 combining:1 our:3 λmin:5 best:2 subject:1 projections:1 provided:1 intersection:1 multidimensional:1 tensor:4 space:3 section:1 shall:1 definite:1 associated:4 its:11 symmetric:1 written:1 does:1 com:1 above:2 ufa:2 formula:15 problems:1 order:1 acknowledgments:1 minimal:6 basis:2 terms:3 linear:2 state:1 d1:2 upon:1 arbitrary:1 use:1 here:1 standard:1 am:1 reason:1 threedimensional:1 found:1 circular:1 decision:1 approximating:3 inertia:5 previous:1 suggested:1 definition:3 algebra:1 versions:1 geometry:1 similar:1 taking:3 vectors:5 o:1 side:2 fulfilled:1 analogies:1 place:1 due:1 ageev:1 hence:1 ru:3 expression:4 uniquely:1 projection:1 classification:1 point:5 simple:1 into:5 address:1 cg:1 primary:2 system:1 dimensional:7 right:2 references:1 invariant:2 cs:1 respect:2 sufficiently:1 mass:3 unit:2 math:1 passes:1 given:8 described:1 takes:4 comparing:1 introduction:1 positive:1 rebuild:1 three:3 next:2 distinct:1 rcm:9 however:1 quadratic:10 call:1 therefore:1 calculations:1 expanding:1 boom:1 huge:1 was:1 theoretical:1 more:3 function:3 flat:1 corresponding:2 form:19 both:1 quantities:2 relative:1 exactly:1 but:1 idea:1 phone:1 part:1 ho:1 straight:5 known:1 line:5 general:1 than:3 remember:1 case:7 distance:1 account:2 made:1 third:1 invariants:1 approximations:1 value:4 euclidean:4 while:1 determined:1 assume:3 planes:2 following:8 design:1 problem:1 define:1 root:6 called:1 procedure:1 proof:1 mechanics:1 constant:1 cell:1 do:1 defined:2 averaging:1 abstract:1 thus:1 non:9 denote:3 flatness:8 say:2 smaller:1 exist:1 degenerate:5 sense:1 trace:2 ic:1 any:1 axis:1 again:2 goal:2 perform:1 technological:1 means:2 eigenvalue:3 same:2 write:2 very:1 need:1 other:1 details:2 fourth:1 nauka:1 resembling:1 mathematics:1 parameter:1 moscow:1 higher:1 visually:1 product:2 http:2 intended:1 calculating:1 normal:2 may:1 derived:1 substitute:1 hand:2 replace:1 plane:23 along:1 cases:1 constants:1 eigenvectors:1 prove:1 vol:1 center:4 algorithm:1 considered:2 onto:2 approximation:3 well:1 physics:1 typeset:1 their:4 rather:1 points:22 algorithms:4 mechanical:1 n1:2 n2:2 once:1 canceled:1 having:2 lying:1 quantity:5
0705.0351.txt |@word represent:1 routhian:1 partial:1 gr:4 remarkable:1 similarity:1 vectorial:1 results:1 hσν:2 four:4 scalar:3 generalize:2 sci:1 whose:3 preserves:1 depend:8 hµσ:1 equivalence:7 finally:3 under:2 analogous:2 applied:1 wave:1 electron:1 hµν:6 bringing:1 condition:1 preuss:3 leads:2 2κc:3 riemann:1 hamiltonian:4 turns:1 henri:1 solution:1 vector:9 indices:4 gauge:1 shows:1 effective:1 force:1 protons:1 consistent:1 elegant:1 second:10 street:1 dynamics:1 canonical:1 even:1 guarantees:1 nonlinear:1 plays:1 giving:2 contracted:2 expressed:3 current:2 experiment:1 goes:2 lifshitz:2 new:2 exercise:1 full:2 degree:1 respectively:2 qµν:18 grav:1 qαβ:3 represented:6 equations:32 nachr:1 interpret:1 obtained:1 generalizing:1 antisymmetric:4 oxford:2 larger:1 allows:1 suggests:1 resulting:1 action:11 suitable:1 changes:2 uniquely:1 emerge:2 via:3 extra:2 δvµ:1 replace:2 first:4 fµρ:2 apply:1 total:3 univ:3 eddington:4 derivatives:3 usa:1 covariant:4 positive:2 contains:2 charge:6 sµ:7 therefore:4 taken:1 indiana:2 astr:1 possible:1 defining:1 lowering:1 becomes:2 odinger:3 curvature:9 berlin:3 magli:1 varying:3 projective:6 cases:1 must:2 springer:2 ρe:4 integrating:1 g00:2 equation:15 fµν:4 det:1 theories:2 ρu:1 freedom:2 sandberg:1 arrive:1 averages:2 geometrized:1 define:3 cosmological:1 give:3 relativistic:2 choice:1 sitzungsber:3 lorentz:8 numbers:1 arise:2 unphysical:4 verlag:1 chru:1 goal:1 write:1 how:3 nonsymmetric:1 ρ2e:1 instead:1 field:41 rept:1 mat:1 replacing:1 fy:1 after:1 derived:3 levi:1 inst:1 cambridge:3 fρσ:2 kijowski:12 meaningful:1 natural:1 dynamical:2 third:1 correspond:3 thorne:1 gµα:2 so:2 ultimate:1 fundamental:1 enter:1 catto:1 order:1 gµν:48 over:1 fν:2 symbols:1 paper:3 through:1 its:5 find:4 lg:3 sν:4 masses:2 relativity:7 curls:1 coordinates:1 gen:3 lect:1 degrees:1 pergamon:2 derivative:4 overcome:1 correspondence:1 freeman:1 non:1 crucial:1 material:1 landau:2 framework:2 hamilton:7 they:1 identically:1 sσ:1 sρ:1 wetensch:1 represents:2 term:5 2s:1 always:1 university:1 presented:1 theory:9 found:1 side:3 lorentzian:1 homogeneous:1 energy:4 related:4 contracting:1 obtains:1 combining:1 quantum:2 eq:31 out:1 shown:1 martellini:1 space:3 restricted:2 since:5 lagrangian:43 denotes:2 particles:2 may:2 formula:3 math:5 unifying:1 linear:5 free:2 standard:1 york:2 lma:1 e2:2 interaction:1 transition:1 motion:2 appearing:1 massive:1 signature:1 consequence:1 origin:4 variables:4 geodesic:1 restrict:2 another:1 precisely:1 given:5 derives:1 similarly:2 eqs:6 amsterdam:1 least:1 indicate:1 1c:2 quadratic:1 statement:1 francaviglia:1 variational:1 gives:5 continuous:1 part:12 representing:1 than:1 covariantly:1 showed:2 accordance:1 zero:2 contravariant:2 matter:18 sciel:1 decompose:1 rend:1 generality:1 reproduces:1 electrodynamics:1 dynamically:6 affine:53 conjugate:1 need:2 onigl:1 any:1 symmetrized:1 gρν:2 latter:1 gravity:9 note:3 potential:2 generalized:4 forces:2 unconstrained:1 calculus:1 akad:4 electric:4 algebraic:4 gµσ:8 intrinsic:1 class:1 considered:1 stronger:1 kl:1 principle:5 velocity:3 physics:2 satisfies:1 quantity:2 show:4 jµ:5 purely:34 attempts:1 relation:6 civita:1 substituting:4 d4:11 boundaries:1 knowledge:1 enough:1 only:3 explicitly:4 constant:1 local:1 do:2 legendre:4 means:2 dg:1 between:5 inclusion:1 cannot:2 negative:1 dt:4 aν:4 geometric:1 continuum:2 fields:1 arxiv:1 yield:3 qc:4 contain:1 traceless:2 riemannian:1 ricci:25 imposing:1 violated:1 depends:14 result:6 tulczyjew:2 subject:2 uν:5 gravitation:10 tensor:66 symmetric:14 written:6 simplest:4 invariant:2 pgµν:1 preserve:1 terms:4 extend:1 nature:1 fields:4 weak:1 however:1 vanishing:1 multiplier:2 configuration:1 tensors:7 uσ:3 both:4 last:1 according:2 neutrons:1 connection:42 dated:1 expression:3 experimental:1 configuration:2 affine:3 simple:1 lagrangians:7 corresponds:5 colon:1 lagrange:3 bν:1 torsion:12 due:1 bianchi:2 symmetrizing:1 pj:4 combine:1 pi:9 ann:1 corresponding:5 tµν:3 quantities:1 wheeler:1 ρuµ:2 vµ:4 bull:1 denote:2 former:1 c4:1 case:4 replaces:2 reciprocal:1 pacs:1 will:3 while:5 schouten:1 metric:34 ir:1 thus:4 equal:1 attributed:1 containing:1 righthand:1 make:2 formulations:1 same:4 poincar:1 emphasize:1 symplectic:2 status:1 independent:2 used:1 generalizes:1 hand:1 constraining:2 invariance:4 identity:3 electromagnetism:3 schr:3 well:1 without:5 arising:1 dimension:2 torsionless:3 unified:1 obtain:1 vanishes:1 sources:11 identify:2 momenta:1 poplawski:3 christoffel:2 enters:1 density:49 regarded:1 scales:1 δpi:1 source:4 add:1 valid:2 transformed:2 lett:1 east:1 transformation:9 momentum:5 polon:1 tests:1 unification:1 rev:2 palermo:1 decomposed:1 february:1 relativ:3 know:1 rµν:13 using:3 unified:4 8πg:1 vν:2 formal:1 loss:1 imposed:2 like:1 particle:3 follows:4 reduces:1 velocities:1 δs:6 detg:1 δq:2 yields:7 either:2 arbitrary:3 δg:2 mathematical:2 right:1 δrµν:3 classical:7 acad:2 respect:19 gνσ:3 electromagnetic:26 cρ:2 circ:1 does:10 proc:1 uµν:3 equivalent:9 agreement:1 pressure:1 hilbert:2 cδ:1 constrains:1 ferraris:5 affect:3 constraint:8 gνβ:2 dependence:4 act:1 introduced:1 consequently:8 automatically:1 jν:3 differentiation:2 presence:1 maxwell:14 into:2 obtaining:1 three:2 because:1 definition:2 einstein:15 proportional:1 gσν:4 there:4 accordingly:6 conservation:2 way:2 gravit:3 antisymmetrizing:1 bloomington:1 was:1 misner:1 palatini:5 δgµν:4 function:4 form:7 2gµν:1 removes:1 jul:1 pµν:23 construction:4 aµ:2 level:1 raising:1 sourceless:2 applying:2 gravitational:13 variations:4 us:2 wiss:4 fluid:1 fαβ:4 distribution:1 more:2 mechanics:4 associated:3 dgµν:1 semicolon:1 introducing:1 describe:1 general:13 modify:1 conserved:3 exist:1 formulation:15 ottingen:1 curl:3 formalism:2 identities:1 functions:1 no:1 uµ:7 defined:3 field:1 setting:1 role:3 spatial:1 department:1 defines:2 conclusion:1 picture:1 differential:2 generates:1 separate:1 variation:13 generated:1 tρσ:1 variable:2 structure:2 lm:1 implies:1 assume:3 dπ:1 mass:6 time:2 4e:1 gαβ:1
0705.0352.txt |@word slope:1 consider:1 remarkable:1 represent:2 helical:1 rev:2 magnetic:38 global:3 edn:1 results:5 leads:3 eds:1 computation:1 edu:1 consists:2 follow:2 expressions:1 disk:17 cases:4 issues:1 depend:4 aug:1 finally:2 outwards:1 stable:2 suite:1 case:1 amplitudes:1 very:2 continues:1 choice:1 every:1 conserved:1 solves:1 level:3 solution:1 large:7 small:5 sano:10 midplane:1 configurations:1 concluded:1 upper:1 strongly:1 smaller:2 miller:2 uncomfortably:1 kato:5 approximation:1 zero:14 alfv:4 initialized:1 dynamics:2 remarkably:1 linear:3 even:3 nonlinear:1 const:1 rate:1 while:1 uniform:3 reminiscent:1 version:2 kyoto:2 net:10 increasing:1 evolving:2 led:1 respectively:4 error:2 component:1 equals:2 here:4 understanding:2 reported:2 mep:1 address:1 ratio:10 equations:2 change:1 box:18 search:2 parameters:1 institute:2 involved:1 study:3 allows:2 suggests:2 dependencies:2 usually:1 shaded:2 studies:2 copes:1 followed:1 scales:4 apj:13 rφ:16 visualization:1 total:3 linearly:6 use:2 would:3 few:1 approach:2 therefore:3 taken:1 raft:1 balbus:5 meridional:1 blackman:7 keplerian:4 normalized:2 particular:4 known:1 hole:3 iii:1 must:6 account:4 ma:1 miyama:2 equation:2 averaged:1 values:17 evolved:1 hawley:12 making:1 closing:1 scatter:2 lφ:1 figure:10 give:1 arise:1 purposes:1 implementations:1 states:1 indicates:1 minimum:2 performed:3 allowed:1 sought:1 isothermal:3 reynolds:1 spanning:1 goal:2 provide:2 discussion:2 six:2 write:1 how:1 hot:1 vital:1 disappear:1 parameter:2 sin:1 goodman:1 profile:1 simplicity:1 rise:1 description:3 our:1 after:1 3rd:1 davis:1 lω0:7 waves:1 fits:2 law:1 data:1 grow:1 types:4 predictors:1 stress:11 natural:2 effective:4 ss:1 maybe:1 spectra:1 lines:4 correspond:2 perform:1 negligible:1 fundamental:1 suggest:1 order:8 kallman:1 wavelengths:1 unsolved:1 saturated:9 indeed:4 over:1 displayed:1 stability:2 thermal:4 paper:2 through:6 its:1 earlier:1 style:1 thank:1 fit:5 jim:1 kolmogorov:1 better:2 ohmic:1 lr:2 fig:2 lz:1 h0:5 shear:2 eventually:1 non:5 good:2 motivated:1 processes:1 scaling:5 framework:1 effects:4 they:7 half:1 employed:2 dimensionless:5 easily:1 february:1 hereafter:1 characterizes:1 university:5 presented:1 realistic:1 magnitude:4 mode:2 each:7 instability:3 entirely:1 δvφ:1 inutsuka:3 mean:5 domain:4 en:4 generation:1 series:2 energy:17 used:4 applicable:1 ornsson:1 astrophysical:5 increases:1 expect:1 measure:1 into:2 relates:1 beyond:1 shearing:14 out:4 shown:3 driving:1 factors:2 quantify:2 furthermore:1 since:2 yoshizawa:2 may:3 mediated:1 sustain:1 ra:1 emerged:1 ref:1 shows:1 arizona:2 theory:4 frank:3 mechanisms:1 governing:1 standard:4 threedimensional:2 intermediate:1 r0:4 geometry:1 count:1 keep:1 length:3 gordon:1 hence:1 retain:1 first:3 origin:2 there:3 variables:1 papaloizou:4 armitage:2 another:1 reached:1 electronic:1 angular:13 size:12 given:1 necessarily:1 likely:1 introduction:1 leading:1 system:1 adopted:2 their:5 accretion:12 draft:1 listed:1 consistent:2 final:3 ias:1 too:1 correlations:1 fraction:1 mostly:1 psaltis:7 wavelength:4 abramowicz:1 obtained:4 artifact:1 appreciation:1 assumption:1 threaded:1 because:1 tan:4 than:2 modes:2 king:6 princeton:1 approximations:1 see:9 submitted:1 determined:1 stratified:6 were:5 addressing:1 l189:1 spectrum:2 extents:1 departure:1 headings:1 need:1 turner:1 seek:1 orders:4 lie:1 strength:3 relationship:1 encompassing:1 responsible:2 able:5 mechanism:5 note:6 ideal:1 internal:2 2006a:4 build:1 observationally:1 extrapolating:1 play:2 unless:1 allow:1 though:1 arguing:1 correlation:2 viscosity:5 accurately:2 most:9 ebruary:1 letter:1 alpha:5 class:5 latex:1 considered:1 clear:2 saturate:1 flow:5 inferred:3 typeset:1 magnetorotational:1 velocity:4 effect:1 physics:4 fact:2 laws:2 precise:1 emerging:1 parker:1 bj:1 show:1 past:1 fukue:3 rotating:1 pump:1 substituting:1 decade:1 o:1 based:1 spite:1 outside:1 jap:1 only:3 explicitly:1 black:3 various:5 adequate:1 roughly:2 local:6 do:1 wide:1 overall:4 fluid:1 ones:1 unstratified:1 despite:1 nordlund:4 boundary:4 symbols:3 runs:4 resolve:1 krolik:1 fields:4 arxiv:3 remove:1 mineshige:3 investigate:1 discs:1 including:2 implication:1 discussing:1 bars:2 set:7 questions:1 achieved:2 testing:1 turbulent:13 zones:1 depends:2 radius:1 result:4 discussions:1 close:1 best:7 subject:1 dln:2 label:2 boundaries:1 pressures:1 state:9 unable:2 identification:1 between:3 orbiting:1 subscript:1 conditions:5 multiplied:1 comparable:3 terms:1 vertical:18 nature:1 importance:1 however:3 efficiency:1 harvard:1 no:1 key:2 distinguish:1 both:5 prescription:2 limits:1 many:1 region:2 escape:1 equal:2 enabling:1 etc:1 tout:2 expression:4 among:1 relevant:2 co:1 extent:1 characterization:1 simple:1 aspect:1 height:8 simply:1 spans:1 cs:2 associated:4 buoyancy:1 considering:3 described:1 second:2 radiative:1 due:2 been:3 magnetized:2 describes:2 combined:1 ph:3 b0z:3 systems:1 stresses:10 direction:1 enable:1 corresponding:5 quantities:1 concerning:1 gas:3 remark:1 pringle:5 understand:2 external:1 systematic:1 astron:1 last:2 present:1 sound:6 p0:6 solid:2 might:2 estimations:1 budget:2 value:12 will:5 near:1 fiducial:1 behavior:1 promising:1 balance:1 taking:1 characterizing:4 resolved:1 almost:1 characteristics:1 thus:1 them:2 according:3 ii:1 characterize:2 itself:1 ig:2 different:2 kwan:1 l57:1 perhaps:2 things:1 same:6 any:1 unity:2 periodic:3 shakura:2 steeper:1 grows:1 difficult:1 development:2 independent:1 investigated:1 numerical:25 corotating:1 pessah:9 flows:3 publ:1 driven:10 domains:1 compared:1 necessity:1 sunyaev:2 lower:2 weakly:1 center:1 nevertheless:1 floor:1 well:4 torkelsson:4 more:4 observations:2 residuals:1 fixing:1 coordinate:1 model:1 magnetohydrodynamic:1 velocities:1 proposed:1 being:1 valuable:1 predicts:2 using:2 regardless:1 speed:6 yet:1 tables:1 preprint:2 candidate:1 density:2 conclude:1 parametrization:1 discuss:1 appeared:1 lett:1 relevance:1 extensive:1 mod:1 plasma:3 momentum:12 identical:1 saturation:13 livio:2 around:1 stein:4 2006b:4 possible:3 smithsonian:1 boxes:4 grid:6 background:1 press:3 turbulence:13 characterized:1 advanced:1 prominent:1 necessary:2 like:1 lost:1 mhd:9 disks:9 server:1 specific:3 flux:14 unstable:5 arbitrary:1 become:1 differentially:1 therein:2 adiabatic:3 often:1 agreement:1 δbr:1 some:2 growth:1 respect:1 transport:11 scale:17 hundredths:1 dimensions:1 fromang:2 footing:1 comments:1 instantaneous:1 track:1 does:1 unit:1 provides:1 indication:1 blaes:2 refer:1 equipartition:2 power:1 disentangle:2 aws:1 equivalent:2 pose:1 perpendicular:2 expansion:1 pressure:15 step:1 ratios:1 found:2 emulateapj:1 bz:1 artin:1 stone:5 carried:4 δb:1 dependence:12 recognized:1 simulation:3 stand:1 efforts:1 predictor:6 functions:1 soc:1 cambridge:5 significant:3 hirose:1 ogilvie:3 maxwell:1 puzzle:1 within:2 stratification:1 three:2 dissipation:6 schemes:1 references:2 determine:1 proportional:4 comparing:1 assumed:2 initial:7 long:2 vaz:1 way:1 astrophysics:2 slopes:1 viscous:1 opposed:1 function:4 tight:3 annulus:1 but:2 astro:3 hi:1 related:3 scope:1 mnras:5 implies:2 line:6 highest:1 posted:1 volume:1 circulation:1 whether:1 characteristic:1 maximum:1 us:1 work:1 tucson:2 those:1 fluctuations:2 problem:3 piece:1 average:3 detailed:2 constant:4 implications:3 abstract:1 describe:2 chan:7 ap:1 examine:1 penna:2 simulations:43 az:19 eric:1 physical:9 qα:1 nj:1 codes:1 courant:1 dotted:4 variety:1 dashed:4 brandenburg:6 generally:2 aipc:1 field:12 other:1 role:4 department:2 raine:3 mri:23 holt:1 calculating:1 models:4 problems:1 transported:1 important:5 variable:1 jeremy:1 astronomy:1 structure:1 regime:1 coupling:1 algorithm:2 4l:1 heats:1 time:5 gammie:3 resolution:11 having:1
0705.0353.txt |@word neighbors:7 represent:3 concept:1 managed:1 consider:1 limited:1 perl:1 rev:6 global:2 concern:1 focus:4 existing:2 four:5 eds:1 higher:4 computation:1 consists:1 follow:2 mill:1 ejk:4 issues:1 reluctant:2 devoted:3 whose:6 glimpse:1 ario:1 conferences:1 graph:6 similarity:1 γu:5 ıa:2 finally:2 those:5 excluded:2 under:2 γc:4 moderated:1 nodes:10 include:3 worth:1 resources:2 activities:1 collaborate:5 advantage:2 very:2 dynamic:1 void:4 rise:1 differently:1 fat:1 results:10 every:1 chooses:1 fall:1 mixing:11 specific:2 difference:1 arrange:1 entire:1 francois:1 presented:2 transmission:1 ref:1 companies:112 large:14 eur:1 vector:1 small:11 enhance:1 inspection:3 programme:11 bd:1 strongly:1 smaller:1 slower:1 findings:2 trend:3 prediction:1 literature:1 budget:2 synergy:3 go:1 second:4 displays:1 scarcity:1 7th:1 further:1 dynamics:1 implemented:2 observatories:1 investment:1 linear:2 universities:105 established:1 what:3 rate:1 giving:1 section:2 axes:1 analogously:1 networks:34 access:1 univer:1 new:10 falling:1 contributes:1 acknowledgments:1 contrast:2 coefficient:15 compact:1 chose:1 degree:65 respectively:1 gathered:1 even:4 component:9 equals:1 here:6 understanding:3 modular:2 selective:4 focused:3 free:8 groups:6 address:1 directions:1 path:4 along:1 appears:2 logarithmic:1 suggest:1 obtained:6 almost:1 noticeable:1 environment:1 technical:1 involved:4 study:7 larger:4 suggests:8 base:1 products:1 social:2 usually:2 studies:2 plotted:2 emerge:1 offs:1 regardless:3 classification:1 exhibit:1 search:1 prefer:2 highly:1 bfm2003:1 analyzing:1 names:2 apply:1 total:6 establish:3 asi:5 select:2 plot:7 use:2 hierarchically:2 takes:2 working:2 positive:2 objectives:1 contains:1 tail:2 centrality:4 few:2 betweenness:10 therefore:8 availability:1 criteria:1 taken:2 scope:1 type:5 today:1 more:14 separated:3 editorial:1 started:1 neglected:2 company:12 factor:1 training:1 cooperate:2 industrial:1 visual:1 appendix:4 basically:2 particular:1 cases:1 given:6 iii:1 had:4 organizations:1 account:1 crosses:2 cluster:1 pursue:1 science:6 points:7 work:1 functional:1 fast:1 london:1 friendly:1 itself:2 values:1 indicating:2 growing:1 field:4 example:3 something:2 nearest:5 prompt:1 bogu:1 links:12 florida:1 arise:1 organized:3 pieces:1 high:7 numbers:1 sense:1 sharp:1 ist:1 calculated:1 axis:3 information:16 needs:1 united:1 end:1 verify:2 purpose:1 spreads:1 berlin:1 feature:1 surpassed:1 how:9 pair:3 instead:1 eight:2 classify:2 belongs:1 fp:9 guimer:1 description:1 mendes:4 may:6 max:1 βc:2 internet:2 applications:4 informs:1 plane:2 designed:1 records:10 improving:2 participant:8 horizontal:1 law:10 data:9 grow:1 efficiently:1 natural:1 effective:2 following:5 6th:1 ltd:2 assortativity:3 robot:3 fp5:23 accelerated:2 ones:1 so:4 increasing:1 allow:1 correlation:4 taking:1 acknowledges:1 order:3 origin:1 six:1 hierarchy:1 indeed:3 over:3 entries:2 mainly:5 years:3 held:1 already:1 through:6 statistical:1 mentioned:2 existence:2 still:1 depicts:1 its:13 tendency:3 before:2 technologies:1 bridges:1 group:5 verifies:1 fit:1 decay:2 chosen:1 interesting:2 coarser:1 review:1 actually:2 better:1 absence:1 offers:1 degrees:7 systems:2 policy:3 clusters:3 main:3 defining:1 finer:1 versus:1 freeman:1 them:15 good:2 return:3 impossible:2 fig:19 finish:1 encouraging:1 scaling:2 framework:9 metabolic:3 effects:1 they:18 communities:3 now:1 wiley:1 competitiveness:1 represents:2 february:1 several:5 lies:1 always:2 university:12 classified:9 leading:1 infer:2 possibilities:1 reasonable:3 each:11 found:9 universit:1 european:8 eases:1 carlos:2 mean:7 homogeneous:1 cartography:1 financial:2 significantly:2 evolve:1 energy:2 reduce:3 onica:1 related:5 society:4 decays:3 interplay:7 firms:1 eu:2 our:13 approximated:1 programmes:7 special:2 out:5 ru:1 shown:5 rey:2 network:45 timeconsuming:1 vch:1 quantify:2 furthermore:3 since:23 crucial:2 disassortative:2 fp6:1 research:36 increase:6 si:1 participants:38 rc:1 suggesting:1 sme:7 squares:11 issue:4 integrated:1 red:7 shows:2 after:2 turning:2 theory:2 risen:1 interactions:2 million:2 ısica:2 little:1 departamento:3 standard:1 atica:1 completely:3 necessarily:3 biological:1 estimate:1 barab:5 generate:1 shortest:7 βu:2 pairs:1 interaction:2 service:5 ministry:1 could:5 modularity:6 satorras:1 priorities:5 keep:1 filter:6 turn:2 levels:6 place:2 due:5 universidad:2 hence:4 baltic:1 promotion:3 onto:1 first:7 starting:1 organize:1 major:1 initial:1 features:2 probability:6 computer:1 opez:2 question:1 parser:1 number:23 linking:2 clear:1 improvements:1 done:1 neglects:1 another:2 spanish:1 comprises:1 corporations:2 precisely:1 quality:4 size:13 differ:2 dated:1 likely:1 similarly:1 introduction:2 totally:1 5th:2 riga:1 europe:1 system:1 approximately:2 their:26 confirming:1 patterns:1 observations:5 fmf:1 handbook:1 siam:1 ranging:1 oltvai:2 gives:3 exploring:2 relationship:6 using:2 relative:1 albert:3 euros:2 immediate:1 direct:2 binned:1 reflecting:1 corroborating:1 focusing:1 off:2 eliminated:2 than:16 distance:17 level:7 third:2 roles:1 recruitment:1 collaborations:18 assortative:10 namely:1 αc:1 project:12 matter:1 states:1 future:1 contrary:2 were:13 providing:2 result:12 pre:1 lowest:1 addressing:1 fran:1 false:1 modern:2 measure:4 curves:1 randomly:3 medium:3 socio:1 manner:6 need:1 seen:5 seem:3 seek:1 any:4 relatively:1 paths:6 gal:1 europa:1 able:1 min:1 efficient:1 self:5 transference:1 isolated:1 mechanism:1 note:5 oliveira:3 potential:3 take:4 finding:1 subject:1 mit:1 circles:11 blue:7 santiago:1 differences:1 fct:1 advances:1 opposite:3 collaboration:1 who:2 techniques:1 clearer:1 paid:1 most:3 connected:13 accordance:1 quantitative:2 nothing:2 αu:1 extremely:1 pages:1 check:3 remark:1 laboratories:1 consequences:1 considered:2 neighboring:1 average:29 sometimes:1 flow:4 vertices:26 physica:1 bipartite:1 traditional:1 graphs:3 competitors:1 regards:1 nuclear:1 physics:1 institutions:9 fact:10 goals:1 slope:2 selected:1 show:4 text:1 random:6 scattered:1 ravasz:2 connect:2 implying:1 seems:2 participate:2 keywords:1 range:2 believed:1 find:14 fifth:1 partners:5 proximity:1 promote:2 based:6 knowledge:10 situations:1 explain:1 distributed:1 enough:1 supported:1 should:3 entities:4 only:19 ambiguity:1 developed:1 integrate:2 employed:1 mechanics:1 local:1 interested:1 merged:1 do:6 viewpoint:2 means:12 dependent:2 de:5 ki:3 joint:7 cannot:2 negative:1 words:1 despite:4 during:4 shaping:1 areas:1 typos:1 reveal:1 evolution:5 pearson:1 resource:1 covering:2 fields:2 subprograms:2 arxiv:1 twice:2 investigate:1 common:2 sustainable:2 identify:2 qk:3 qj:2 satisfy:1 set:5 art:1 computed:1 exists:1 supporting:1 encourages:1 comparable:1 up:1 connections:2 see:7 decided:1 us:4 japan:1 close:1 institutes:1 best:2 encouraged:2 closer:1 instance:2 said:1 capacity:1 exponent:3 nets:2 user:1 currently:1 consequence:1 tend:7 state:1 smallest:1 cambridge:1 cooperation:1 between:44 probably:1 approach:6 across:1 schuster:1 knowing:1 adv:1 notice:2 terms:2 ability:1 institution:3 nature:4 comp:3 attention:6 weak:1 however:11 killing:1 lj:1 implementing:1 cut:3 extent:1 jk:2 analyzed:1 cities:1 problem:1 improve:4 both:12 collaborators:3 σm:3 reported:1 σc:2 many:13 region:2 acknowledge:1 according:3 display:3 connection:1 krahmer:1 planned:1 cover:1 dorogovtsev:3 uni:1 passing:1 argue:1 whole:3 σu:3 albeit:1 among:4 ci:2 separation:2 conclude:3 color:1 guaranteed:1 others:2 period:3 community:3 dedication:9 initiative:2 spans:1 table:5 throughout:4 cu:1 considering:2 sensible:1 three:1 described:2 union:7 create:2 charts:1 been:3 mark:1 whom:3 much:2 coarse:1 interest:1 basic:2 expected:1 applying:1 ph:1 topology:3 choose:5 website:1 6a:1 life:4 emphasize:1 corresponding:6 tecnolog:1 clarity:1 subprogram:2 formed:1 protect:1 enterprises:3 finished:2 observe:2 determination:1 external:2 competitive:1 evidence:3 coordination:1 former:2 spain:2 case:5 disconnected:1 pacs:1 straight:1 empirical:1 value:5 will:1 while:14 policies:1 error:1 endpoints:2 discoveries:1 havlin:1 studied:1 portugal:1 played:4 linked:3 thus:9 non:10 encouragement:3 ii:1 characterize:1 bias:1 turns:1 technology:4 different:10 verified:2 perform:1 pay:1 juan:3 lett:1 same:6 campus:1 complex:11 split:5 geographical:1 largest:9 avoids:1 vespignani:1 demonstration:1 finite:4 grows:5 difficult:2 development:9 independent:4 used:6 http:2 peaks:4 ni:1 sociometry:1 hospitals:1 published:1 effect:3 times:3 hand:3 moment:1 edges:7 uses:1 paving:1 internal:1 frequently:2 nation:3 opportunity:1 normalization:1 newman:5 task:1 net:1 center:1 database:1 nevertheless:1 makes:1 depending:1 well:4 analysis:3 thought:1 academic:2 edge:4 components:2 sets:3 organization:6 model:1 otherwise:3 investments:2 researchers:1 usual:1 distances:1 just:1 less:10 being:6 downwards:1 observed:4 obtain:6 rest:2 assigned:1 oxford:2 distant:1 parks:1 human:1 positions:1 foresee:1 forrest:1 yet:1 previous:1 profitable:2 web:2 aiming:2 interestingly:1 mix:1 regarded:1 point:3 character:2 evidences:1 appeared:2 setting:1 plateau:1 technological:7 reach:1 5a:1 remaining:2 5b:1 real:2 fluctuating:1 depends:1 demands:1 rules:2 collaborating:2 composition:1 possible:2 bollob:1 increases:1 five:2 press:3 world:2 emergence:1 execution:1 moreover:3 projects:20 mod:1 necessary:1 sizes:5 follows:4 reduces:2 sized:2 either:2 become:1 essential:3 farthest:2 www:1 because:2 old:1 methods:2 deal:1 sequence:1 understand:1 madrid:2 commercial:2 creation:4 some:10 remarking:1 competition:1 identified:1 certain:1 understood:1 growth:3 context:1 respect:1 strogatz:1 mat:1 pronounced:1 scale:11 describing:1 cois:1 lead:1 confirm:4 detecting:1 univ:3 avoid:2 though:4 recorded:2 per:1 linkages:1 does:2 connecting:4 provides:2 innovation:6 moderate:1 participation:4 illustrate:2 conference:1 biased:1 measures:4 scientific:3 power:9 reaching:1 elucidate:2 splitting:1 shareholders:1 graduates:1 step:2 pajek:2 although:2 inherent:1 proceeded:1 relating:1 refers:1 meyer:1 about:4 central:2 would:5 package:1 industry:23 citizens:1 dependence:1 o:2 addition:4 whence:1 economic:1 characterized:2 neighbor:2 mixed:1 insufficient:1 efforts:1 constraints:1 consequently:3 bollobas:1 mathematical:1 soc:1 ingenier:1 presence:9 previously:1 communication:2 into:7 year:6 implications:1 dataset:3 assess:1 services:1 accounts:2 effort:1 proportional:1 reducing:1 mere:1 clustering:10 statistics:1 span:1 log:10 commission:4 transfer:7 support:2 there:10 available:8 depicted:2 long:1 intermediaries:2 spread:3 2ni:1 low:1 way:5 biggest:1 analyze:6 was:23 naturally:1 function:5 fragmented:1 successfully:2 complete:2 form:8 makse:1 electr:1 jun:1 pastor:1 but:11 collected:1 repeated:1 hierarchical:9 link:5 segregation:1 jeong:1 encoded:1 line:2 highest:1 amaral:1 considerable:1 partially:1 absent:1 riordan:1 made:5 compute:4 pocti:1 happen:1 whether:1 characteristic:1 inside:1 smooth:1 maximum:1 quantitatively:1 international:1 record:3 below:1 miguel:1 sum:1 heterogeneous:1 fluctuations:1 distribution:18 define:3 similar:7 called:4 expect:2 detailed:1 diverges:1 constant:2 play:5 viruses:1 sfrh:1 defined:7 likewise:2 abstract:1 contribute:3 influence:3 6b:1 doesn:1 general:3 single:1 departments:1 journal:1 education:3 distributions:3 universidade:1 pub:1 again:2 beyond:2 nn:4 no:4 whereas:5 when:14 duplications:2 application:1 other:33 role:7 genome:1 income:3 kqk:1 kodama:1 conclusion:1 node:4 picture:1 kinds:2 living:1 models:1 searched:2 vertex:7 fis2006:1 meaning:1 important:8 vectors:2 williamson:1 structure:9 thematic:1 independently:3 implies:3 faster:5 algorithm:3 assume:1 aveiro:2 space:1 modules:4 lasted:1 together:1 transient:1 time:3 far:1 management:1 once:1 requires:3 having:2 bornholdt:1 virtue:1
0705.0354.txt |@word neighbors:1 peacock:2 monte:3 code:1 evidence:1 consider:2 chain:4 lagrangian:1 astron:5 narayanan:2 results:24 roy:4 mild:2 amendola:4 employing:1 parameterization:2 consists:1 follow:2 mon:4 involved:1 weakly:5 schlegel:1 bassett:4 const:2 calculate:7 albrecht:3 linder:4 technique:3 send:1 keeping:2 finally:5 compensate:4 indicate:2 those:4 ti:5 tegmark:2 cahn:1 include:5 detect:1 applied:4 updated:1 amplitudes:2 mpc:18 advantage:1 dey:1 far:3 desirable:1 yepes:1 percival:5 sirko:3 implicit:1 every:1 additional:3 anonymous:1 summarized:1 specific:1 nishioka:1 difference:8 enter:1 croft:5 entire:2 utsi:8 moderate:1 immediately:1 presented:2 did:2 positions:2 proposals:1 cmb:11 t0:4 damped:1 large:11 convenience:1 vector:1 interpolating:1 affect:1 team:1 small:5 enhance:1 markov:3 der:1 tresse:1 degeneracy:1 still:3 upper:4 averaged:4 force:2 coordinate:1 riess:4 trend:1 consistent:3 edu:1 sound:6 direct:1 filled:2 past:1 astrophys:3 second:3 perspective:1 surface:1 gawiser:3 further:3 recalculate:2 estimated:1 carlo:3 λcdm:1 even:3 compile:1 nonlinear:11 plays:1 appear:2 rate:1 selected:1 expressed:1 thickness:1 current:2 wiggles:3 largescale:1 version:2 sigma:3 transformed:2 above:5 fractional:7 sine:1 rssd:1 contributes:1 method:21 contrast:7 body:8 christian:1 chose:3 averaging:2 respectively:14 presence:1 realizations:1 component:2 here:2 ranges:1 evident:1 l25:1 ober:3 alone:2 consideration:3 along:2 strong:6 observing:2 appears:2 dref:2 box:12 convert:1 over:8 dividing:2 noticeable:2 root:2 study:3 larger:5 completely:1 commonly:1 example:2 significantly:3 trial:1 survey:12 rosenbluth:2 poisson:1 sternwarte:1 usually:1 fourier:2 studies:1 sci:1 plotted:4 diameter:6 via:13 spatially:2 although:2 tran:1 scales:7 requiring:1 prefer:1 calcu:1 highly:2 scaled:5 visible:1 addressed:1 decrease:1 o:1 achievable:1 org:1 eastwood:2 pdfs:3 total:1 redo:1 planck:9 cloud:1 derivatives:3 use:19 ellipse:6 takes:2 would:8 errors:4 found:2 developed:1 pref:4 predictions:2 tightly:2 properties:1 error:19 few:1 linear:7 wood:2 therefore:6 zaldarriaga:2 taken:1 themselves:1 noisy:1 type:2 theoretical:1 tracers:2 more:17 chem:1 flat:3 αvi:1 upcoming:1 started:1 conclusions:2 apparent:4 lightcone:1 visibility:1 glass:1 needed:1 geophysics:1 normalized:1 bristol:1 particular:7 known:3 cases:2 aligned:1 iii:2 must:3 sample:19 account:2 crosses:2 verde:1 indicates:1 equation:7 work:1 modified:1 reviews:1 itself:1 values:12 evolved:4 following:10 under:2 springel:4 scatter:3 history:1 compare:6 weaker:4 cosmological:36 stated:3 predict:1 expanding:1 referee:1 carroll:2 purposes:3 originates:1 dependence:5 high:4 unbiased:5 minimum:1 caused:2 numbers:5 com:1 particles:11 cmbfast:2 simulation:21 axis:2 information:2 counting:1 goal:1 eiichiro:1 giallongo:1 provide:3 softening:1 means:1 differences:6 feature:1 jochen:1 regions:1 how:5 hot:1 iso:1 constraints:13 parameter:40 sin:1 massive:1 oscillatory:11 wave:3 filippenko:1 ft:2 lai:1 lae:2 advice:1 after:3 derived:15 davis:2 catalog:4 produce:3 phenomenological:1 designed:1 fits:1 horizontal:1 νth:5 data:21 parallel:6 repeat:1 baseline:1 convolution:1 introduced:1 attempt:2 dynamical:2 effective:1 interpolated:2 ss:1 candles:1 spectra:27 lines:23 evrard:2 cosmology:22 cannot:4 so:2 sect:6 decreasing:3 halos:1 sa:1 wfmos:3 order:1 bins:1 typical:2 undo:1 receives:1 schuecker:1 sapone:2 help:1 produces:2 indeed:1 perlmutter:2 fft:2 vary:1 choose:2 distortion:7 produced:4 already:4 through:1 statistical:2 reconstruct:2 mentioned:1 existence:1 gaztanaga:3 cole:4 gioi:1 its:10 galaxy:40 before:3 observational:3 blake:11 derive:11 efstathiou:2 probability:5 fit:9 acknowledge:1 chosen:2 interesting:2 πki:2 degrades:1 varies:3 coordinates:1 prediction:1 hockney:2 detected:1 parts:3 fig:43 van:1 recombined:1 mail:1 main:1 defining:1 into:3 happened:1 versus:2 eventually:1 them:4 good:3 motivated:1 combination:5 output:1 matches:1 numerically:1 gadget:1 processes:1 introduce:3 scaling:34 effects:13 they:3 instead:4 balances:1 yu:2 day:3 halo:3 reconstruction:6 easily:3 term:3 gebhardt:3 pgal:1 xli:1 zehavi:1 always:1 level:3 zp:2 sugiyama:2 sufficiently:3 theory:2 kpc:1 each:10 acoustic:7 identifies:1 possibility:1 bond:2 square:3 tilted:1 primarily:1 fairly:4 miknaitis:1 ed:1 energy:21 frequency:1 reduce:2 snapshots:7 applicable:1 living:1 literature:1 yoshida:2 eisenstein:24 astroparticle:2 measurement:8 substantially:4 our:28 margins:2 differ:3 eq:4 optimistic:1 shown:12 15h:1 divide:1 matrix:1 space:51 god:1 astier:2 since:18 crucial:1 semi:1 denotes:1 astrophysikalisches:1 traversed:1 dominated:1 hill:3 denoted:1 formula:1 squares:2 ref:6 correct:4 shows:3 log:3 doppler:1 suffer:1 volker:1 uncertainties:6 million:17 galaxies:20 given:9 free:2 standard:10 mcmc:2 reason:2 complicated:1 usual:1 enlarge:1 estimate:4 generate:4 care:1 degeneracies:5 hubble:16 benefits:1 geometry:1 determining:2 could:3 unity:1 cosmic:3 frenk:3 times:3 window:1 length:2 place:2 isotropic:18 hatton:1 hence:5 esa:2 neglected:1 diminishes:1 quercellini:1 assign:2 first:10 origin:2 spergel:5 unless:1 weller:1 peculiar:2 matthias:1 obtained:11 sn:7 number:7 parkinson:1 improving:1 utilized:1 smaller:1 ciardullo:1 construct:3 frequently:1 zh:2 ring:2 precisely:3 open:1 angular:6 surveys:15 perturbation:1 nichol:2 observer:6 table:2 their:5 introduction:1 unknown:3 top:5 structured:1 system:4 least:3 gpc:7 koehler:4 draft:1 observations:12 calculations:1 realization:1 hetdex:4 white:5 scheme:7 structures:1 smoothed:3 too:3 shifted:4 converting:1 fraction:2 discussion:2 wavelength:2 baryon:5 completed:2 exactly:3 imprinted:2 transverse:3 released:1 part:9 macqueen:1 apjs:3 advocated:1 sollerman:1 than:10 modes:1 distance:11 translate:1 target:4 l45:1 gottl:3 require:2 typically:1 imply:1 aims:1 final:1 project:3 matter:24 future:4 amplitude:2 recombination:1 identical:1 tion:1 enables:2 madore:1 extracting:1 complex:1 modeled:1 sees:2 shrinks:1 correction:1 sevilla:1 spectrum:87 curves:2 correspond:1 raw:5 substantial:3 manner:1 qualitatively:1 need:2 seen:1 element:1 any:1 karl:1 dozen:1 lie:1 depict:1 angle:5 aj:1 zero:3 kny:1 efficient:1 studying:1 able:3 apj:28 note:1 centered:5 fitting:44 2006a:3 build:1 2006c:1 2006b:2 xi:5 estimates:2 wmap:1 aliasing:2 adopted:1 unperturbed:1 circles:1 formulas:1 play:1 towards:2 a3:3 track:1 twodimensional:1 collaboration:3 sets:2 neutrinos:1 troughs:1 accurately:7 most:2 regular:2 germany:1 significant:2 remarks:1 baryons:2 including:2 sophisticated:1 measured:9 probes:1 astro:4 deviations:2 constructed:2 especially:4 calculated:1 later:1 stronger:2 holtzman:2 piso:1 points:5 electrons:1 principle:1 exp:3 schulz:1 dataset:1 velocity:4 constrain:8 left:9 physics:3 away:2 fitted:2 quantity:1 precise:1 selection:1 shot:12 l57:1 show:14 glazebrook:11 accuracies:1 feasibility:1 dependences:1 bin:1 purely:1 attempts:1 relation:3 inconsistent:1 participate:1 threshold:1 find:7 subsections:2 cell:1 lacey:1 datasets:1 ratio:3 knowledge:1 parameters:36 baryonic:1 explain:1 casertano:1 should:3 analytic:1 only:13 gpc3:2 surveyed:2 factor:13 nyquist:1 emitting:1 bernstein:1 thousands:1 oct:1 achieve:5 do:8 dl:1 his:1 sdss3:1 zeldovich:2 wide:1 dependent:10 constructive:1 de:15 amplifies:1 da:10 among:2 joint:2 unimportant:1 october:1 words:1 probably:1 report:2 during:1 dt:1 interpreted:1 freedman:3 huff:2 evolution:6 densities:1 biometrika:1 haiman:2 approach:1 thanh:1 arxiv:6 scoccimarro:1 remove:1 acknowledgments:1 angulo:5 twice:1 investigate:3 paper:6 predicted:2 jenkins:1 bao:70 fixed:9 gibson:1 approximations:3 aldering:1 www:3 shell:2 compressed:1 computed:1 reference:22 achieved:1 principal:2 robustness:1 correlations:2 deconvolution:1 identify:1 maximum:1 observed:11 marginalize:1 depends:2 computer:1 metropolis:2 piza:2 w0:19 seo:9 terms:1 luminous:1 contour:4 best:8 techniques:4 gravitation:1 aforementioned:2 degree:1 consistency:1 ways:1 intrinsic:1 review:2 panels:2 rings:2 cosmologies:7 tend:1 favor:1 state:4 determined:4 finger:1 simplest:1 seljak:2 propagated:1 kmax:1 previous:2 conditions:1 multiplied:2 emitted:1 catalogs:13 docs:1 wa:12 missing:1 deliver:1 were:8 weak:3 however:5 interpolate:2 boss:1 σk2:1 deter:1 vrad:2 kmin:1 key:3 wp:2 distinguish:1 article:2 iterative:2 distribution:7 improve:2 received:1 essentially:1 ωb:9 last:2 weinberg:1 hickey:1 many:1 uncertainty:12 according:3 attributed:1 display:3 ln:1 pdm:1 komatsu:2 tightens:2 context:1 variance:3 requests:1 argue:1 periodogram:1 steinmetz:1 otherwise:2 originating:1 unclear:1 fields:2 point:3 simple:8 smith:2 evaluate:1 corresponds:5 sampling:1 dimensional:18 analyzed:1 publishers:1 taylor:1 non:3 decreases:1 polynomial:1 respect:4 throughout:2 mission:1 couchman:1 mare:1 light:46 goldhaber:1 feldman:2 addition:4 equations:2 three:8 been:2 metropolishastings:1 int:1 increase:1 cosine:1 damping:2 challis:1 anisotropic:7 combine:2 ph:4 z3:2 define:2 field:8 25h:1 relations:6 corresponding:21 impairs:1 both:11 quantities:1 sufficient:1 complementary:1 precision:3 depend:1 mine:1 observe:4 determination:1 systematic:4 derivative:2 consecutive:1 kaos:4 extract:1 present:7 case:17 extracted:5 propose:1 supernovae:3 ap:6 solid:19 might:1 reliable:1 originate:1 aip:3 value:15 alter:3 will:6 stubbs:1 behavior:1 promising:1 property:1 procedure:7 due:14 vectors:1 orientation:6 coupled:1 almost:7 vi:1 designs:1 discrepancy:1 equal:4 comoving:6 comparing:1 bias:38 noao:1 cone:42 conf:1 ia:4 limit:1 unsatisfactory:1 lymanα:1 comments:1 explicitly:1 different:18 constrained:2 develop:2 thereby:2 sensitive:1 suggest:1 reconstructed:8 radiation:3 same:7 clearly:3 shifts:2 epoch:1 drawback:2 potentially:1 schematic:1 largest:3 products:1 dimensionless:1 several:2 start:1 higher:9 development:1 independent:7 tighten:1 used:17 http:3 peaks:3 see:11 cubic:1 assignment:3 numerical:2 effect:7 hand:1 constraining:13 v2:1 levels:2 uses:3 pdf:9 robust:3 sunyaev:2 php:1 contribution:1 off:1 lower:7 task:2 musyc:1 center:3 scenario:1 nevertheless:2 changes:2 no:1 well:5 analysis:4 calibrated:2 solve:2 does:4 redshifted:1 simulated:3 very:5 position:3 model:14 whereas:3 hastings:2 spherical:1 distances:7 proposed:4 less:7 being:1 percent:1 accurate:6 wagner:14 obtain:1 rest:1 sources:1 shape:5 distant:1 integer:1 uller:1 k2:3 yamamoto:2 scattering:1 width:1 based:1 adding:1 intersection:1 density:21 photons:4 conclude:2 appropriately:1 suto:1 source:2 book:2 extends:1 teller:2 samples:5 input:2 prominent:1 plasma:2 transformation:2 details:1 real:27 insensitive:2 around:6 thank:1 ruler:5 enable:1 possible:2 harmonic:1 dark:38 increases:4 grid:7 know:1 background:1 vacuum:1 using:18 accepted:1 apart:3 vertically:1 displaced:1 like:1 particle:8 identifying:1 follows:1 signal:1 velocities:1 accelerating:2 sized:1 2007b:5 arithmetic:1 2007a:4 analyzing:1 accuracy:8 essential:1 cooled:1 stretched:1 marginalized:2 twelve:5 indications:1 performing:1 methods:7 namely:3 summation:1 linearly:2 growth:9 evaluated:1 sight:7 redshifts:24 oscillations:8 candle:1 little:1 ourselves:1 anisotropies:2 pronounced:1 scale:27 lead:1 realistic:3 purple:2 measurements:19 vasey:2 microwave:1 useful:2 critical:1 connecting:1 select:4 provides:4 assuming:10 eso:1 compute:3 sdss:2 proc:2 bined:1 measuring:5 biased:15 noise:15 obey:1 power:117 plot:2 performed:2 radially:1 radial:1 oscillating:2 perpendicular:1 expansion:8 interval:2 overall:5 pressure:2 step:4 plc:4 hst:2 σp:1 plots:3 analyses:1 subtract:3 between:9 panel:3 comparison:2 about:8 works:1 universe:12 completing:1 discussed:1 factors:22 strolger:1 lation:1 range:10 plus:2 kaiser:3 horizon:6 bean:1 efforts:1 referred:2 slightly:2 contours:6 confidence:9 soc:4 rev:3 suppression:9 followed:1 redshift:95 h2:3 h0:16 within:3 integral:2 functional:1 negative:2 assess:3 included:2 appropriate:3 right:10 references:1 tiny:1 determine:6 einstein:1 approximately:3 pivot:5 next:2 maurogordato:1 spline:1 cones:3 clustering:3 aniso:1 jing:3 statistics:1 institut:1 x2i:1 shells:2 assumed:4 there:5 question:1 transform:1 lowering:1 smoothing:5 occupy:1 quadratic:1 low:2 way:7 astrophysics:1 analyze:2 was:5 moriond:1 cancel:1 combined:1 function:19 recompute:1 gronwall:3 complete:3 form:4 signs:1 attempted:1 collapsed:1 distortions:2 tailored:1 but:8 hu:10 volume:7 expected:5 construction:1 related:1 estimation:1 mnras:7 line:26 true:7 he:1 cic:3 hogg:1 made:1 applying:2 wρ:1 understood:1 whether:3 gravitational:1 smooth:2 up:2 us:1 warren:1 below:1 converted:1 ωm:19 reflects:1 observation:1 problem:2 matsubara:2 similar:6 agree:3 nature:1 expect:2 strongly:9 celestial:1 constant:20 b2:1 computing:1 defined:2 certain:3 abstract:1 measure:10 direction:3 general:3 dashed:16 single:4 arises:1 initial:7 dλ:2 dw:3 simulations:13 grateful:1 ortsell:1 distributions:1 check:1 physical:6 incorrect:4 functions:4 compared:1 dotted:12 variety:1 priors:10 discerned:1 when:3 detail:1 virtual:2 tight:1 other:9 role:2 potsdam:2 holding:2 becomes:2 test:2 snapshot:11 ns:5 concerning:1 mock:14 deviation:2 peebles:2 reestablished:1 calculating:1 provided:2 models:11 describe:4 bottom:6 helpful:3 deriving:2 dor:1 generated:2 important:6 allowing:1 additionally:2 variable:2 fisher:1 astronomy:2 friends:4 ellipses:3 structure:6 offprint:1 relativity:1 independently:2 implies:1 geometrical:1 algorithm:2 tested:1 assume:3 resolution:2 lowered:1 required:3 eos:18 sheth:1 mass:7 fact:1 volumes:2 time:3 baugh:2 understand:1 nuclei:1 mean:17 starting:3 peiris:1 hilger:1
0705.0355.txt |@word remarkable:1 tts:1 constituents:1 astronomical:1 results:1 eds:1 showed:1 keywords:1 mopra:2 research:1 ural:1 previous:1 compact:1 x000000000000000x:1 title:1 source:2 only:3 fig:1 baan:1 text:1 l133:1 accurate:3 details:1 australia:4 papers:1 corresponds:1 ostrovskii:3 birth:1 atca:3 press:1 g351:1 association:3 densities:2 sources:3 positions:4 university:3 arxiv:1 flux:1 investigate:1 val:1 small:1 study:1 referred:1 csiro:2 caswell:1 lenin:1 www:1 telescope:3 national:1 maxim:1 observed:2 see:2 ellingsen:2 http:1 transitions:1 targets:3 out:4 blue:1 bottom:1 spectrum:1 detections:5 its:1 state:1 various:1 between:1 international:1 row:2 conditions:2 email:1 contrast:1 shows:1 available:1 web:1 respectively:1 component:1 given:3 brooks:1 quite:1 following:1 rows:1 although:1 found:1 hobart:1 iras:1 box:2 search:2 sobolev:4 rare:2 carried:1 outflows:2 region:1 o:1 survey:1 massive:2 pdf:1 malyshev:1 proc:1 cambridge:2 campaign:1 facility:2 previously:1 offset:1 number:2 apj:1 interface:1 crossroads:1 references:1 spots:1 table:1 array:1 appeared:1 nsw:1 surveys:2 gpo:1 jet:1 union:1 top:1 there:1 cesaroni:1 been:3 indicate:1 confirming:1 outflow:2 observations:2 iau:3 ph:1 molecular:2 was:1 voronkov:8 more:2 maser:2 form:1 forming:1 line:1 but:1 prediction:1 astro:1 astrophysics:1 atnf:1 mnras:1 tasmania:2 active:1 than:1 g343:1 churchwell:1 unlike:1 require:1 second:1 po:1 theoretical:1 were:3 believed:1 russia:1 detailed:1 henkel:1 figure:1 abstract:1 menten:2 epping:1 walmsley:2 ap:1 au:2 slysh:2 ave:1 simple:1 absolute:1 wilson:1 dotted:1 no:4 regions:1 majority:1 methanol:4 other:1 masers:10 poster:2 new:1 widespread:1 higher:1 symposium:3 used:1 star:2 energetic:2 trace:1 temperatures:1 may:1 downloaded:1 southern:2 driven:1 ekaterinburg:1 significant:1 measured:3 class:4 searches:1 doi:1 ss:1 clear:1 spectra:6 chapman:1 ghz:11 thought:1 proceedings:2 components:1 correlation:1 typical:1
0705.0356.txt |@word holman:11 jason:1 consider:1 caused:1 asteroids:1 focus:1 existing:3 known:2 menou:1 edu:1 go:1 follow:4 expressions:1 disk:1 transits:8 gj:1 maciejewski:2 transiting:16 inverse:1 calculate:1 zone:2 technique:2 seager:3 those:1 stable:3 te:2 σtt:5 brown:4 conjecture:1 confirmation:1 amplitudes:5 garden:1 very:5 trojan:46 induce:2 results:3 difficult:1 underscore:1 resonant:1 emphasized:1 dvorak:1 σti:2 t0:2 large:5 guiding:2 small:8 refer:1 challenge:2 degeneracy:2 upper:5 l96:1 andor:1 periodicity:8 consistent:3 measurable:1 sinusoid:2 cfa:1 likely:4 street:1 pasp:1 further:4 dynamics:2 linear:3 even:6 what:1 errors:1 sub:4 rate:1 sum:1 offsets:1 near:7 current:1 above:1 method:9 body:4 pose:1 led:1 lee:2 extrasolar:14 rossiter:1 4s:1 here:3 explore:1 separation:2 alone:1 laughlin:4 strong:2 interpret:1 extreme:1 search:4 sasselov:1 institute:1 study:2 larger:1 steffen:7 schwarz:2 periodic:3 published:3 harrington:3 resonance:6 sinusoidal:4 studies:2 uniquely:1 appropriately:1 prints:1 via:4 useful:1 hst:1 transit:47 photometric:6 integrations:1 highly:1 apj:20 egress:1 analyzing:1 support:2 should:1 analyses:1 readily:5 plot:1 eye:1 excursions:1 would:15 prove:1 dermott:3 faint:2 cho:1 occupying:1 predict:4 asteroid:1 therefore:4 taken:1 survive:2 theoretical:1 more:8 separated:1 initial:2 ti:7 keplerian:2 trail:1 trojans:26 actual:1 cases:1 aligned:1 must:2 peale:2 ma:1 middle:2 science:5 originally:1 work:2 theories:2 perturb:1 mt:11 obvious:1 mp:6 under:1 merely:1 hansen:1 root:2 example:3 history:1 compare:1 challenging:1 scan:1 process:1 share:1 high:1 caution:2 o:1 distant:2 ratio:4 terrestrial:4 information:1 monitoring:2 goal:1 rather:2 verify:1 discussion:1 clarkson:1 algorithms:1 astronomers:1 hot:1 adapted:1 axis:1 parameter:1 sin:1 circular:3 upto:1 npl:1 may:6 max:1 lag:1 orbits:8 modest:1 produce:1 designed:1 requirements:1 perturbing:1 data:4 types:1 efficiently:2 short:2 physical:4 outline:1 light:1 lines:2 gilliland:2 149026b:1 winn:7 allow:1 acknowledges:1 order:1 typical:2 ingress:1 noyes:2 interpretation:1 help:1 ith:2 indeed:1 vary:1 ttv:21 murray:11 outer:1 stability:1 cambridge:3 including:2 motions:1 during:1 astrobiology:1 mayor:1 fischer:1 observational:2 style:1 rapidly:1 thank:1 interesting:1 masses:5 solving:1 detected:2 offers:1 systems:7 mail:1 might:1 versus:1 eventually:1 non:3 good:1 affected:1 greater:2 eccentricities:2 powerful:1 outlined:1 13m:1 number:2 pilat:1 effects:1 they:1 association:1 josh:1 easily:2 term:5 miralda:2 university:1 identified:5 composition:1 sufficiently:2 l4:10 l5:10 sato:1 each:6 found:1 photometry:1 mean:8 square:2 significantly:3 series:2 universities:1 tsiganis:1 gaussian:2 extended:1 measurement:3 our:7 approximated:3 shapiro:1 shown:2 space:4 periodicities:2 since:2 research:2 fellowship:1 encourage:1 dominated:1 squares:1 correct:1 shows:1 after:1 theory:1 interactions:3 mechanisms:3 ntt:8 quite:4 prepared:1 escud:1 formation:7 imaging:1 intermediate:1 detecting:7 log:1 hubble:2 perform:1 lithwick:3 could:20 times:4 motion:7 sahu:2 place:2 massive:6 signature:7 hence:2 undergo:1 travel:1 strictly:3 frequent:1 first:1 major:1 already:3 features:1 probability:1 reveals:1 causing:1 primary:3 references:1 simplified:1 least:1 another:1 precisely:2 angular:3 given:2 perturbation:2 similarly:2 introduction:1 unknown:1 top:3 system:12 offset:2 their:3 confirming:1 perturbations:9 observations:34 hypothetical:1 realization:1 iau:1 1m:3 williams:1 low:2 disks:1 fabrycky:1 contains:1 exactly:1 accurately:2 discover:1 gaudi:12 librating:3 than:11 center:5 detection:5 mclaughlin:1 malhotra:3 01a:1 ktt:7 require:1 imply:1 submitted:1 gladman:3 future:4 amplitude:17 were:3 michtchenko:3 result:2 function:2 false:1 reanalysis:1 neptune:2 measure:1 direct:2 headings:1 10s:3 need:1 turner:1 null:2 any:4 studying:1 able:1 mid:2 note:1 fitting:1 potential:1 generalized:1 interior:1 so:3 subject:1 accuracy:1 displacement:3 continuous:1 multiple:4 investigations:1 gaidos:2 most:2 significant:5 pair:1 measured:7 latex:1 deviations:4 incomplete:1 alarm:1 nicholson:1 inferred:1 points:4 chiang:4 velocity:7 left:1 typically:2 fact:1 planetary:7 signatures:5 particularly:5 show:2 converge:1 discovered:2 joshi:1 solutions:1 threshold:1 earth:9 ground:4 giant:8 based:7 tobs:3 parameters:2 hf:1 explain:2 dynamical:3 distributed:1 negligible:1 either:1 colloq:1 analytic:2 only:4 candidates:3 oscillate:2 tations:1 dominant:4 secular:2 stop:1 nearly:2 timing:28 impractical:1 saturn:1 secondary:1 reveal:2 evolution:1 resolve:1 l45:1 conditions:1 arxiv:3 public:1 common:2 through:2 fixed:7 inside:1 approaching:1 rms:3 ebf:1 set:2 statistical:2 sensitivity:2 deming:3 observed:5 depends:1 radius:4 migration:4 operated:1 chambers:4 uncorrelated:2 techniques:4 phases:1 detect:3 erdi:1 subsequent:1 away:1 currently:2 its:3 macros:1 outside:1 determined:2 between:3 orbiting:7 limit:6 before:2 approach:1 µc:3 available:1 comparable:1 recently:1 aas:1 parent:2 nature:5 targeted:1 attention:1 however:7 spectroscopic:2 wu:2 harvard:2 hypothesis:1 clues:1 analyzed:1 modeling:1 both:5 prospects:1 roig:2 limits:1 many:5 uncertainty:3 equal:2 contract:1 sensitive:6 periodogram:2 teukolsky:1 28m:1 timescale:8 point:5 simple:1 guaranteed:1 period:14 sampling:2 dimensional:1 lagrange:4 observatories:3 escude:1 considering:1 ps:7 sari:1 second:3 dan:1 rasio:7 due:18 been:5 immense:1 much:6 complicated:1 interest:1 mars:1 expected:1 ph:6 reflex:1 fig:8 enable:2 diversity:1 25m:1 formed:1 precision:2 morbidelli:4 δti:7 thommes:2 denote:1 present:3 missions:1 applied:1 heyl:3 atmospheric:2 resides:1 single:4 horseshoe:1 will:14 while:4 ongoing:1 error:1 discoveries:1 habitable:2 thus:4 surface:2 apjl:1 itself:1 exterior:1 levison:1 beaug:1 orbital:11 different:6 constrained:1 inc:1 grant:2 perhaps:1 suggest:2 indistinguishable:1 shorter:1 matthew:1 unity:1 complex:1 potentially:2 circularization:1 several:2 cumming:3 higher:1 used:2 centuries:1 see:3 eccentric:1 effect:2 companion:8 constraining:1 v5:1 changing:1 ttvs:3 lower:2 scargle:1 sidereal:1 makes:1 modeled:3 well:3 analysis:2 telescope:2 without:1 residuals:1 sets:2 model:5 charbonneau:5 bodies:3 marcy:1 agol:11 jupiters:1 bottom:3 proposed:2 less:2 being:1 connell:1 valuable:2 shape:1 identify:3 librations:2 zdziewski:1 regardless:1 alternative:1 previous:2 preprint:3 density:1 had:1 k1:3 signals:2 priori:1 remaining:1 resolved:1 around:2 putative:1 possible:4 smithsonian:1 possibly:1 increases:2 provide:3 guide:1 press:3 using:6 unique:1 advanced:1 rocky:1 atmospheres:1 necessary:1 like:2 semi:1 sizes:1 signal:6 shaped:1 sized:1 flux:1 detections:1 limi:1 byproduct:1 decrease:1 reduced:1 interpreting:2 δa:1 right:2 theorists:1 methods:7 some:1 searching:2 jupiter:3 duration:3 unless:1 konacki:4 mccarthy:1 provided:3 lead:1 confirm:1 resonances:1 companions:6 2f:1 comments:1 moon:1 critical:1 cnc:1 fortney:1 demonstrated:2 inclination:2 scientific:1 radial:8 aj:2 stellar:4 ratios:2 209458b:1 tidal:1 lomb:1 exciting:1 properties:2 about:7 central:2 origins:1 swarms:1 anomalous:1 scott:1 practical:1 range:1 ensure:1 constraints:3 queloz:1 integration:1 own:3 presence:2 previously:1 three:3 contrasts:1 gomes:1 weather:1 determing:1 computational:1 proportional:1 reducing:1 initially:1 often:2 eccentricity:1 uncertainties:3 additional:5 extremely:2 astrometric:2 there:5 libration:13 long:3 awarded:1 strict:1 detectable:2 rowe:3 stars:5 l137:1 astrophysics:2 valencia:2 was:3 σph:2 form:1 forming:1 but:5 ford:15 astro:6 butler:3 magnitude:2 solar:5 mnras:4 dissipative:1 hd:7 exoplanets:1 gravitational:3 burrows:1 variations:8 up:4 planet:55 placed:1 frequency:1 epicyclic:1 uk:1 planes:1 demonstrate:1 problem:1 velocities:1 similar:5 mechanics:1 celestial:1 abstract:1 combining:4 fellow:1 ap:2 examine:1 au:1 periods:1 planets:28 simulations:1 cresswell:2 eric:2 regime:1 mutual:2 dotted:3 no:1 generally:1 nas:1 other:6 test:3 deviate:1 star:12 superposition:3 60s:1 models:5 become:1 rv:2 variation:1 helpful:1 chance:1 richardson:2 fisher:1 astronomy:1 structure:1 searches:2 longer:3 tested:1 assume:1 odds:1 required:1 curve:1 orbit:7 nasa:3 mass:26 nelson:2 time:12 serious:1 4d:2 evenly:1 once:4
0705.0357.txt |@word limited:4 corbelli:1 madsen:1 four:3 entropy:1 heliocentric:1 parameterization:1 paris:1 kawata:1 under:2 inwards:2 worth:1 updated:1 affect:1 vast:1 vector:1 succession:1 force:1 construed:1 consistent:30 estimates:1 direct:1 surrounding:1 second:1 street:1 qualitatively:3 maloney:1 even:3 selected:3 above:6 increasing:2 disney:2 kicked:1 here:4 hundreds:2 ionization:4 asymmetry:1 ascribing:1 obtained:1 study:6 changes:1 karachentsev:1 rosenberg:1 highly:1 visible:1 remnant:1 total:9 unit:1 plot:5 would:11 noting:1 kinematics:1 therefore:11 type:2 until:1 fractions:2 populations:3 successful:1 ascribe:1 disruption:1 warm:15 must:1 abundance:1 mg:1 pursue:1 work:1 mi:4 boyce:1 transparency:1 akin:1 springel:3 example:1 transition:1 indicated:1 give:2 cited:1 pinto:2 end:2 provide:1 feature:1 how:2 hot:8 significance:3 description:1 after:3 meaningful:1 types:1 third:1 schneider:1 hypotheses:1 davies:1 correlation:1 over:8 vary:1 satisfied:1 japan:1 fidelity:1 before:1 fit:3 fig:7 overcome:1 versus:4 eventually:1 them:5 hawthorn:1 affected:2 combination:1 prevented:1 l153:1 collide:2 band:1 bang:1 effects:2 they:14 brightness:1 reasonably:1 reasonable:2 each:21 minutiae:1 side:2 mean:2 afforded:1 telescope:1 minchin:2 extract:1 ring:1 excepting:1 particles:13 tufte:5 chvc:2 linear:2 associate:1 free:1 differing:1 subtended:1 formation:28 muller:5 ata:1 τcool:2 ism:2 moving:5 onto:6 speeds:1 stewart:1 another:1 thick:1 annotated:1 top:2 needed:1 accretion:27 observations:34 ranging:3 inflow:1 collapse:1 centered:1 deschˆenes:1 gyr:6 peculiar:1 distance:25 showed:5 rate:15 matter:2 boulanger:1 historical:2 tion:1 enables:1 ran:1 seed:2 manner:2 relatively:4 vietri:2 apj:16 infalling:2 circles:2 though:8 prohibitive:1 braun:5 complexes:60 putman:15 phase:1 inconsistency:1 observation:6 metal:1 points:3 mock:1 nπ:1 random:1 radii:4 radio:1 subtle:1 extraplanar:1 d0:8 proposed:1 explain:1 woodgate:1 do:12 dm:1 dk:1 de:8 drinkwater:1 report:2 rˆi:3 dr:5 maciel:1 t04:11 mergers:2 plagued:1 traverse:1 sensitivity:6 observed:45 centric:4 radius:21 result:4 limiting:1 subject:1 capacity:1 symmetric:1 disprove:1 conductive:1 terms:2 extend:1 confusion:1 however:2 suggested:3 received:1 essentially:1 uns:2 merging:2 raimond:1 contribution:1 timescale:3 haynes:1 basis:3 radiative:6 three:12 been:22 quilis:1 much:8 interest:1 expected:1 deeper:2 quantities:4 coherent:5 spin:1 applied:3 tang:1 say:3 near:3 leaves:1 vogel:1 iv:1 ii:2 characterize:1 conf:1 ia:1 containing:1 cools:1 make:4 kilborn:2 complex:16 split:2 avoids:1 independent:3 satellite:7 numerical:4 monotonic:1 rain:1 hand:1 osawa:1 opportunity:1 scenario:2 meade:1 greatest:1 simulated:63 quantitative:1 left:6 just:2 photo:1 rotated:2 identify:1 spherically:1 sightlines:1 yet:1 previous:2 mckee:1 regarded:1 character:2 wright:1 observationally:2 possible:10 collisionally:1 vobs:1 contradict:1 niels:1 specific:3 detections:1 schwarz:3 sparse:1 right:5 excerpt:1 contaminating:1 bottom:2 fox:2 comments:1 totals:1 contributing:1 linearly:2 unstable:1 peek:5 teuben:1 properties:2 chaff:1 o:4 efforts:1 slightly:1 raised:1 metallicities:2 facility:1 orders:1 down:4 acad:1 kravtsov:2 joseph:1 way:13 was:12 medium:1 gaseous:4 form:4 offer:1 forming:1 removes:2 solar:9 magellanic:14 removed:2 true:3 inside:2 maximum:3 mgas:1 moore:2 trig:2 arnal:1 covers:1 evidence:3 exist:3 simulations:37 morras:1 distributions:4 physical:5 nh:7 no:7 tip:1 ekers:1 interested:1 test:2 jenkins:2 optically:2 picture:2 superposition:1 models:6 pandian:1 treesph:3 catalogs:2 longer:1 assume:3 ferrara:1 ryder:1 stripping:1 time:5 observables:4 neighbors:2 global:1 maller:3 certainly:1 inverse:1 depend:1 analogous:9 vej:1 advantage:1 seemingly:1 nor:1 clouds:164 did:1 auld:2 prevent:1 l97:1 slower:2 trend:1 prediction:1 driel:1 current:1 sequential:1 goes:1 filled:2 satisfy:1 understanding:4 groups:2 along:3 appears:1 wait:1 institute:2 root:2 dominantly:1 funded:1 noticeably:1 plotted:2 useful:4 extra:3 bullock:3 tidal:1 prove:1 predictions:2 scenarios:1 criteria:9 scope:1 today:1 acceptable:1 everywhere:1 effort:1 spekkens:1 parameterize:1 tokyo:2 values:5 following:1 webster:1 nearest:2 figure:12 confused:1 sph:7 refine:1 hydrogen:4 arbor:1 linsky:1 discussion:3 chemical:1 parameter:4 map:1 may:19 membership:1 deviates:1 date:1 data:21 grow:1 natural:1 ss:1 irwin:1 cosmology:3 inform:2 si:1 condensations:5 so:3 halos:6 typical:2 indeed:6 thresholds:1 years:2 course:2 experiments:1 lsr:3 cuts:3 cold:1 still:1 tendency:1 observational:5 group:5 thank:2 interesting:1 vicinity:2 coordinates:1 forms:1 main:2 brinks:1 coincidental:1 correspondence:1 non:3 within:13 conversations:1 processes:4 scaling:2 half:3 now:5 discuss:5 halo:71 arrows:1 kerp:1 realistic:1 instability:5 individually:1 domain:5 square:3 significantly:5 populated:1 ed:3 ef:1 snapshots:22 astrophysical:2 dence:1 year:5 shown:7 space:5 increase:1 investigation:1 dominate:1 correct:1 shows:6 earlier:3 possibility:1 california:1 carl:1 kaufmann:2 gibson:4 impose:1 catalog:3 motion:2 place:3 massive:11 first:6 origin:10 spergel:1 striking:1 potter:1 simplified:1 long:1 directly:1 impossible:1 array:3 angular:9 size:8 given:6 indicate:3 cooling:22 white:4 structures:5 williams:1 gives:1 fraction:9 continuous:3 accurately:1 undertaken:1 representing:2 than:21 population:15 iceberg:1 unfortunately:3 future:3 were:9 outcome:1 addressing:1 ann:1 dash:2 quadrants:1 allen:1 any:2 stadel:2 conversion:1 computationally:1 note:11 potential:3 online:1 converged:1 green:1 mayer:2 switching:1 hyperfine:1 track:1 price:1 decreasing:3 invoked:2 latex:1 surprising:1 considered:3 average:5 adopt:1 implications:1 typeset:1 gyrs:1 typically:7 quantity:2 heap:1 show:12 supposition:1 discovered:1 inconsistent:2 slow:1 ratio:2 galfa:1 conduction:3 teyssier:1 enough:4 only:12 ser:1 morphological:1 2002a:2 ionized:4 nearly:2 hinges:1 boselli:1 physically:1 namely:1 uvb:1 detect:3 extragalactic:13 ways:1 review:1 outside:3 kilometer:1 between:13 reproducible:1 2002b:2 across:1 jy:5 originated:1 come:1 resides:1 outflows:1 many:6 region:7 nomenclature:1 comes:2 nearby:9 hvc:41 walder:1 moreover:1 lyman:1 suppressed:1 abstract:1 andrey:1 formed:3 photon:1 observe:2 diffuse:2 standard:7 sound:2 walterbos:1 profiles:2 ongoing:4 fiducial:1 cannot:3 wadsley:2 planar:3 orientation:1 characteristics:8 metric:1 discrepancy:3 carraro:1 different:6 l53:1 harsh:1 l57:1 theorized:1 same:5 wilhelm:1 underestimate:1 events:1 closest:1 kelvin:1 drives:1 driven:1 running:1 changing:1 vantage:2 largely:1 minimize:1 roughly:2 without:1 sonneborn:1 model:4 being:2 when:5 rest:8 speed:9 captured:3 photons:1 except:1 treatment:2 avillez:2 veilleux:1 blok:2 around:17 read:1 early:1 using:3 accepted:2 particle:2 reduces:1 velocities:16 either:2 always:1 twelve:2 sommer:14 gross:1 kaiser:1 conservative:1 moos:1 provides:1 refer:3 measuring:1 equivalent:1 found:9 exciting:1 emulateapj:1 comparison:6 stone:1 central:1 origins:2 discussed:5 generated:6 underway:1 redshift:1 instruments:1 references:1 determine:4 heated:2 burton:5 area:3 there:12 dispersion:2 detectable:1 henning:2 low:9 stars:4 chvcs:10 complete:1 sophisticated:1 mnras:7 faster:1 assl:3 applying:2 quantitatively:1 2003b:2 2003a:3 tripp:2 connect:1 strongly:1 describe:2 general:1 ap:1 examine:1 formulation:2 lifetime:1 bajaja:1 again:1 momjian:1 field:2 spatial:2 deviation:6 symbol:4 includes:3 important:3 peak:1 accounts:1 included:2 condensation:1 curve:1 parsons:1 mimic:1 dramatic:1 mass:44 accreted:1 starting:2 original:2 represent:5 sci:1 consider:1 crucial:1 lack:3 debris:1 disk:24 former:1 tail:1 program:2 those:6 fountain:3 mpc:2 bowers:1 very:16 fall:3 difference:4 arecibo:1 condition:1 large:16 small:6 past:1 zero:3 further:5 what:1 hernquist:2 sun:5 section:7 version:3 method:4 contrast:1 condensed:13 full:2 bailin:1 cylindrical:1 condenses:2 berkeley:1 strong:1 observing:3 colored:1 identifiable:1 myrs:5 amount:1 miville:2 milky:11 heiles:5 via:2 requiring:2 viz:1 establish:1 takes:1 levine:1 distinct:1 haffner:1 taken:2 vlsr:4 more:21 flat:1 jerjen:1 depen:1 hoffman:1 corrected:1 particular:3 known:6 kulkarni:2 linder:1 none:1 equation:2 scramble:1 history:4 ions:1 compare:14 cosmological:3 cortese:1 minimum:4 sense:3 exclude:3 strongest:1 broadly:3 rather:3 christlieb:1 maps:3 larsen:13 mould:1 galactic:42 incorporated:1 rudd:1 wakker:19 mapping:1 kalberla:3 plane:2 fe:1 coming:1 lifecycle:1 parameterized:1 banks:1 parameterizes:1 ivcs:2 help:2 thermal:7 paper:5 through:2 kinetic:1 suffer:1 its:2 style:1 solving:1 systems:3 might:1 vgsr:4 good:2 generously:1 yr:2 easily:4 hereafter:5 fully:2 radial:8 2m:2 heavy:1 neil:1 energy:1 hard:1 idea:1 expect:3 measurement:1 beyond:4 event:2 catalogued:1 since:2 projected:9 research:1 dominated:1 occurs:1 asp:1 difficulty:1 reason:3 base:1 members:1 beginning:1 generate:2 definition:1 retained:1 positioning:1 terribly:1 consequence:1 fallen:1 feed:1 major:1 upper:1 number:22 enlarged:1 bland:1 fluxes:7 temperature:2 koo:1 introduction:1 leading:2 least:1 assumption:7 scheme:1 relationship:1 oort:1 part:5 authors:2 albeit:1 determined:2 contrary:1 toward:5 ages:2 headings:1 copenhagen:1 lie:1 wilson:1 lia:3 flared:1 depending:2 self:1 onset:1 majority:5 analogy:1 analogs:3 catinella:1 towards:1 reach:2 most:7 significant:8 position:7 measured:2 deviations:1 clear:2 sometimes:1 cover:1 km:30 velocity:52 physics:1 particularly:2 phenomenon:1 evaporation:2 carefully:1 find:9 parameters:2 assertion:2 factor:2 circle:9 columns:1 dominant:1 accreting:1 dependent:1 resolve:3 l06:17 arxiv:1 obscure:1 set:6 bart:1 achieved:1 plausibly:1 see:9 individual:4 ari:1 arm:2 currently:1 various:2 oppel:1 champagne:1 seeded:1 recently:2 creating:1 missing:2 sole:1 distinguish:2 both:8 galactocentric:10 improved:1 thom:3 sensitive:1 load:1 point:7 simple:2 smith:2 recycling:1 simply:1 church:1 throughout:1 described:4 due:3 pc:1 describes:1 ph:4 pi:1 empty:1 generating:3 referee:1 partly:1 gas:37 modelling:2 understand:1 solid:1 budget:1 while:1 error:1 richter:1 alike:1 vectors:2 vol:3 apjs:3 grant:1 barnes:1 belong:1 wherein:5 agertz:3 sabatini:1 higher:6 used:5 knezek:1 comprehensive:2 monolithic:1 viewing:1 uses:1 purpose:2 recent:4 dark:5 lower:16 gsr:6 analysis:6 consistency:2 distances:9 boer:3 shape:1 miniati:2 atomic:2 filipovic:1 cut:2 danks:1 source:2 haardt:2 location:1 remaining:1 finder:1 big:1 showing:1 like:3 sgi:1 lost:1 follows:2 disks:1 flux:26 yields:1 byproduct:1 weiner:3 often:1 some:14 back:1 hartmann:2 trends:1 accelerate:1 infall:2 savage:2 scale:7 describing:1 scalo:1 eliminate:1 run:4 aj:2 agreement:1 viewpoints:1 br:2 plots:8 tracing:1 stanimirovi:3 baes:1 simulation:52 range:6 computational:1 into:11 razoumov:2 nsf:1 clustering:5 rows:1 extremely:1 specifically:2 occupy:1 rees:2 murphy:1 line:2 collapses:2 characteristic:3 uv:2 up:4 us:6 malin:1 marginally:1 planes:1 similar:17 kh:4 associated:2 defined:4 stripped:2 kathryn:1 single:2 tentative:1 rains:1 dashed:1 tumlinson:1 grouped:1 department:2 dashes:1 elements:1 generates:1 provided:1 problems:1 drag:1 evan:1 allowing:1 brosch:1 structure:2 implies:2 algorithm:2 age:1 required:1 far:1 beers:1 having:3 once:2 code:3 results:4 pearce:1 p07:1 centers:1 compact:1 excludes:1 does:3 excluded:2 include:1 indicating:5 overlaps:1 ionizing:1 lockman:1 juliane:1 continued:1 entire:1 positions:4 shock:2 smaller:3 zi:1 blitz:2 imply:1 dynamics:1 λcdm:1 m31:1 access:1 consistently:2 experiment:3 body:1 lee:2 respectively:3 objects:3 extreme:1 great:1 involved:1 larger:1 survey:1 makes:1 dnrf:1 scales:6 scaled:1 addressed:1 apply:1 cloud:28 use:3 stream:9 remains:2 breakup:2 next:1 few:8 depicted:1 historically:2 becomes:1 heij:1 sample:6 account:1 averaged:1 reproduce:2 fulfill:2 performed:3 process:5 high:14 reynolds:1 conversely:1 six:1 regions:3 spurious:1 varies:1 sig:1 instead:3 goldsmith:1 sim:1 circular:1 profile:1 frac:1 connors:2 monaghan:1 demonstrating:1 nificantly:1 light:1 lines:1 allow:2 subsequently:1 bins:1 enes:1 koribalski:2 move:2 symbols:3 including:3 galaxy:44 chosen:1 nordlund:1 masses:12 primordial:1 choose:2 freeman:2 greater:5 outlined:1 material:3 asymmetrical:1 satellites:3 rotation:4 transparent:1 university:3 identified:8 magnitude:1 l1:1 crossing:1 accompanied:1 identifies:1 constraints:5 sadler:1 related:1 meta:1 measure:5 our:20 transitions:1 out:8 shull:1 galaxies:15 conflicts:1 interaction:1 determining:2 could:6 frenk:2 times:1 condense:2 length:6 hence:1 diminishes:1 plainly:1 powerful:1 woerden:10 improvements:1 westmeier:5 l39:1 unknown:2 sep:1 hvcs:104 system:3 adopted:3 their:12 intermediate:1 rocha:2 final:1 shell:1 explanation:1 constituent:1 discriminating:1 providing:2 false:1 linked:1 angle:4 min:2 studying:1 nucleosynthesis:1 able:3 gravity:4 mechanism:2 highvelocity:1 accuracy:1 unless:1 centre:2 eight:2 preliminary:1 scrambled:3 snapshot:15 fact:1 selection:5 ulations:1 supported:1 rough:1 based:1 baryonic:5 sembach:2 should:6 ambiguity:1 fuel:2 local:11 equilibrium:1 cube:1 michigan:1 overall:10 supernovæ:1 ones:1 fects:1 gray:2 evolution:4 densities:2 denmark:1 mebold:1 contain:1 fixed:1 pertains:1 exists:3 overcooling:1 frame:5 hα:1 operates:1 usefulness:1 madau:2 conductivity:1 closer:2 seigar:2 tend:1 identification:2 progress:1 neither:2 comparable:4 attention:1 andromeda:23 efficiency:1 hypothesis:3 key:1 probing:1 galacto:4 problem:1 david:1 observable:1 limits:3 taking:2 etc:1 detailed:4 co:1 cm:5 conclude:3 ca:2 decreases:2 maximize:1 cs:2 respect:2 kinematic:2 addition:3 define:3 myr:12 corresponding:1 bulk:4 otz:1 last:1 present:6 oosterloo:1 multi:1 harder:1 value:4 will:17 vc:1 satisfying:3 almost:1 vi:3 thus:5 examined:1 sequentially:1 capture:1 radiation:1 indistinguishable:1 difficult:2 maddalena:1 reporting:1 upon:4 effect:8 dust:2 destruction:2 off:1 center:7 modeled:1 well:8 bohr:1 thought:4 sets:7 comparisons:1 spherical:1 reside:2 softening:3 less:6 accurate:1 staveley:2 underlying:2 distant:13 preprint:1 density:9 absorption:1 sky:9 day:1 maintaining:1 unprecedented:1 match:1 resolved:2 jesper:1 increased:2 masquerade:1 mitaka:1 elapsed:1 increases:2 loss:1 necessary:3 helpful:1 excluding:3 sizes:1 δv:2 qualitative:2 sized:1 become:1 therein:1 classical:2 growth:2 lead:1 demonstrates:1 avoid:1 thilker:5 kpc:42 assuming:1 limitations:1 disentangle:2 selecting:2 journal:2 stellar:2 although:2 worthy:1 simpler:1 about:3 column:1 own:5 previously:1 interstellar:1 dataset:5 weighted:2 terminated:1 van:11 bothun:1 transfer:3 spiral:1 smoothing:1 inner:1 flynn:2 naturally:1 function:4 tasker:1 but:8 astro:4 neutral:13 hi:18 highest:2 he:1 made:1 evident:2 whether:4 wish:5 portinari:2 maries:1 below:2 limit:5 demonstrate:1 distribution:26 contribute:2 dearth:1 trailing:1 compared:11 percent:1 barth:1 other:9 details:3 conclusion:1 star:3 variation:3 metallicity:2 astronomy:4 upwards:1 resolution:23 4m:1 8th:1
0705.0358.txt |@word limited:2 lognormal:1 luminosities:1 four:1 facilities:1 woods:3 entropy:1 ciar:1 consists:2 ergs:2 waerbeke:6 γt:5 presents:1 under:4 inwards:1 updated:1 rise:2 every:1 valdes:2 voit:4 cause:1 solution:2 falco:2 degeneracy:3 10h:1 faintest:1 consistent:4 estimates:25 direct:5 second:4 tangential:10 multiwavelength:1 detrended:1 even:4 established:1 errors:9 excised:1 selected:7 above:3 new:3 net:1 sodre:1 agreement:15 mea:1 27m:1 here:19 met:1 pratt:1 interpret:1 obtained:6 study:10 approaches:1 ignoring:1 changes:2 diameter:3 projection:2 discontinuous:1 highly:1 9s:2 total:6 plot:6 would:2 campusano:1 noting:1 kinematics:1 therefore:15 distortions:5 gladders:2 berlin:1 former:2 excellent:11 aligned:1 mathez:1 work:3 erg:1 temperatures:10 ms:33 henry:6 exceptions:1 springel:1 indicated:2 give:1 broadhurst:2 indicates:4 want:2 magnitudes:4 isothermal:4 provide:5 how:3 hot:1 significance:1 description:2 earlier:2 millimeter:1 modest:1 law:9 lumb:2 attempt:3 substructures:1 effective:2 schneider:5 order:4 interpretation:4 feedback:2 over:4 expects:1 zel:1 thesis:1 newar:1 before:1 37m:1 fit:27 fix:1 better:5 schmidt:2 shear:20 versus:2 them:3 affected:3 safe:1 band:12 effects:8 they:7 benabed:1 wenk:2 calibrating:1 reasonably:1 luppino:4 reasonable:1 each:11 calibrations:1 side:1 mean:17 telescope:5 1996a:3 1996b:3 used:31 combining:2 network:1 rs:3 gradient:1 cameras:1 crucial:2 rvir:3 mccarthy:2 re:10 ra:1 reader:2 rh:1 foundation:1 surveys:5 free:1 standard:1 formation:2 sheet:4 estimate:19 telescopes:4 r1:7 r2:5 cosmic:6 filter:1 xmmnewton:1 corrections:1 mellier:3 stewart:2 polarisability:1 relations:7 another:5 surement:1 top:1 approximately:2 needed:1 master:3 observations:19 eqn:4 exposures:6 17m:1 cccp:6 bacon:1 somewhat:3 bardeau:6 distance:5 ktx:1 enabled:1 likely:2 project:4 matter:10 flatfielded:1 enables:2 heymans:3 modern:2 spectrum:2 raw:1 manner:4 seen:2 seem:1 ray:41 strength:1 latter:5 predominantly:2 circles:1 blue:1 object:2 victoria:2 tozzi:1 observation:1 flow:2 inferred:3 points:9 principle:2 quantifying:2 sum:1 fitted:4 probe:2 cl0024:7 colors:5 subtle:1 proposed:2 explain:1 gioia:3 rich:3 do:11 dl:4 r2500:10 yee:7 de:2 yielded:1 a1689:5 reconstruct:1 ds:3 covering:1 fields:1 wfpc2:2 4πg:1 4πf:1 explanations:1 v8p:1 reference:2 sensitivity:1 detection:2 depends:7 radius:38 result:12 discussions:1 best:16 techniques:2 ensures:2 cosmologies:1 unable:2 hopefully:1 approach:6 terms:2 weak:56 however:19 residual:3 clues:1 improve:2 0s:2 essentially:2 ohringer:3 lensed:1 uncertainty:9 heating:1 merging:1 contribution:8 16h:3 scientifique:1 quinn:1 polynomial:1 equations:1 three:2 been:25 confident:1 much:5 interest:4 expected:11 huchra:1 mcl:1 applied:1 xbacs:1 remaining:2 employ:1 fainter:2 procedure:3 ii:3 characterize:3 voges:1 suggest:3 make:4 complex:2 split:1 dimensionless:2 several:2 independent:8 numerical:6 tyson:3 sextractor:1 suffices:1 scenario:1 mezzetti:4 centres:1 paradigm:1 carlberg:8 quoted:1 ρbg:2 rotated:1 identify:4 thanks:5 yet:1 previous:4 adding:1 mix:1 53m:1 5s:5 dubinski:2 wright:2 transformed:2 5h:6 rescaled:1 tormen:1 possible:2 grego:1 mushotzky:1 background:3 advanced:2 apart:1 detections:1 steps:1 www:1 right:1 deal:1 deflection:1 j2000:1 statistic:2 counts:4 separately:1 speybroeck:2 proceeding:1 icm:4 soto:2 microwave:1 core:2 rescale:1 hst:1 filaments:1 normalisation:5 properties:19 nevalainen:4 o:3 lacked:1 slightly:2 considerations:1 soc:1 contains:2 statements:1 presence:2 bound:1 fern:1 lies:1 raises:1 reducing:1 neumann:1 poss:3 support:1 interlopers:1 accordingly:1 fraction:4 was:8 underestimated:1 medium:1 form:2 becoming:1 differences:3 removes:1 taken:6 magnitude:9 removed:1 true:1 fort:1 complications:1 σtot:1 panels:1 hotter:1 moore:2 lowering:1 abstract:1 covers:1 evidence:6 peres:2 simulations:8 accounting:1 distributions:3 check:2 physical:2 polarisation:1 whereas:2 when:6 vanishes:1 interested:1 papers:1 test:3 models:10 polarisabilities:1 15h:1 3h02:1 jones:1 scharf:1 assume:7 interval:1 gorenstein:2 pointecouteau:1 time:1 slope:20 concept:1 focus:3 parker:1 comments:1 grateful:1 devoted:1 arcsec:2 inverse:1 depend:1 technique:3 mahdavi:1 finally:4 determinations:1 orientations:1 5kev:2 cool:9 presented:19 did:3 anisotropy:7 hawaii:5 skewed:1 ms1512:1 mn:1 findings:2 trend:1 appear:1 bc:1 kuijken:2 understanding:1 groups:3 alone:4 along:7 appears:2 thirty:1 canadian:9 institute:1 52m:1 eke:2 studied:29 commonly:2 hydrostatic:1 suggestion:1 usually:1 studies:16 lowers:3 pritchet:1 useful:5 subarcsecond:1 bullock:2 predictions:1 france:2 theoretical:2 marginally:1 introducing:1 apparent:6 cases:4 given:14 clumps:1 collision:1 values:14 following:2 gravitationally:1 figure:24 predict:2 chip:3 rc:1 sample:35 usno:3 council:3 14m:1 r22:1 14h:1 a370:6 rays:1 requirements:1 borch:1 fortunately:2 discussion:3 parameter:3 23m:1 may:8 rmax:5 applications:1 mag:1 improving:1 data:52 sz:3 stress:1 corless:2 dynamical:6 cosmology:8 so:4 coadded:2 halos:2 definitions:1 typical:1 tornatore:1 constituents:1 mainly:1 years:3 course:1 lss:1 motions:1 argued:1 cold:3 still:2 observational:3 accepted:1 derive:8 thank:1 interesting:2 decreases:2 decades:1 non:4 matches:1 evolution:3 introduce:1 09h:1 09m:1 half:3 now:3 discuss:4 halo:4 matched:4 equality:2 name:8 advent:3 fabian:6 weighted:1 retrieve:1 significantly:7 collisionless:1 inhomogeneous:1 approximated:1 es:1 canada:5 shown:4 100h:1 furthermore:1 increase:1 contained:1 m200:6 correct:9 shows:13 complicates:3 theory:1 quite:3 escud:1 complicated:4 care:1 diagram:1 lanzetta:1 arnaud:8 motion:1 turn:1 massive:3 first:9 origin:1 symmetry:2 enhances:1 omitted:1 inspected:1 directly:3 array:1 open:4 angular:5 size:8 1s:2 necessarily:1 checked:1 kravtsov:1 indicate:9 cooling:4 1h:6 white:11 structures:2 gives:3 way:6 dolag:1 accurately:3 holder:1 than:22 intrinsically:1 population:1 wide:8 unfortunately:2 require:3 hoekstra:38 were:10 bauer:2 johnstone:2 pre:2 correction:9 occupies:1 bartelmann:2 distorted:1 allen:14 hsieh:2 recover:1 any:1 stadel:1 conversion:1 efficient:1 converges:1 note:15 potential:1 interior:1 norman:5 probed:1 printed:1 fcg:4 baryons:1 unlensed:1 probes:1 latex:1 surprising:3 considered:5 average:9 adopt:3 implications:1 a383:4 abraham:1 typically:13 precise:2 show:6 bright:3 xmm:4 astron:1 ratio:4 state:2 analytic:1 only:12 virmos:1 expectation:1 aim:1 cannot:3 murray:1 progress:3 dye:1 conjunction:1 reveal:1 regarding:1 median:1 yield:1 summary:2 helsdon:2 predicted:1 limousin:3 ignored:5 relative:3 uncorrelated:3 a963:5 ways:2 review:1 definite:1 yahil:1 enough:1 between:20 2002a:2 geometric:1 2002b:3 checks:1 multiplied:1 vertical:2 jr:1 virial:12 pixels:1 many:7 region:2 interloper:1 semboloni:1 fahlman:6 nearby:1 azimuthally:1 color:11 sampling:1 constant:2 considering:1 intracluster:1 computing:1 mark:1 springerverlag:1 combined:2 wants:1 enable:2 6s:3 coherently:1 stems:1 careful:1 diffuse:1 those:4 case:6 stacked:3 engineering:1 profiles:2 hdf:2 ongoing:1 situation:1 misalignment:1 henk:1 discrepancy:1 cluster:105 bias:2 different:9 verified:1 same:5 archive:1 html:1 underestimate:2 sunyaev:1 boehringer:1 modes:1 minimize:2 no:6 roughly:1 without:1 components:1 model:30 l107:1 resp:2 speed:1 samples:6 around:2 spectacular:1 digital:2 psf:13 early:1 department:1 mon:1 using:26 aiming:1 correcting:1 21h:1 miralda:2 reduces:2 fully:1 40m:1 a68:5 table:21 images:23 reiprich:2 matching:1 girardi:5 kaiser:13 confirm:1 critical:5 provides:6 refer:2 markevitch:7 arrow:1 power:11 biases:2 2m:1 comparison:20 central:5 discussed:6 tremendous:1 wolf:3 concentrations:2 redshift:42 instruments:1 image:9 references:2 determine:9 einstein:11 area:3 assumed:3 astrometric:3 there:3 dispersion:18 low:4 stars:12 slopes:3 assumes:1 sophisticated:1 mnras:21 applying:1 improved:1 systematics:3 ωm:3 agree:4 detailed:3 metzler:6 taylor:2 certain:1 describe:1 deep:8 examine:4 reliability:2 file:1 gradients:1 incorrect:2 completeness:1 tight:3 valid:2 spatial:2 poor:1 briefly:1 separate:1 stocke:1 deriving:1 a2:3 peak:2 coverage:1 included:6 l61:1 l63:1 mass:143 cores:5 original:3 arcminutes:4 consider:1 caused:9 lack:3 quadrature:1 follow:5 expressions:2 murante:1 arnouts:2 causes:2 tx:2 removal:2 mpc:14 very:7 discrepant:1 czoske:4 dispersions:6 difference:2 condition:1 list:13 large:46 adjust:1 small:26 σdyn:1 zero:2 further:2 briel:1 section:7 cfh12k:7 method:5 contrast:1 full:2 behaviour:1 39m:1 excess:1 strong:6 observing:2 search:1 allows:2 amount:1 published:5 brightest:3 cosmetic:1 vir:3 select:3 readily:2 eye:1 levine:2 distinct:2 faint:6 comparing:1 squires:9 ridge:1 aperture:23 more:13 flat:1 corrected:4 emission:1 tested:2 particular:5 known:3 gravel:1 science:1 equation:2 nine:2 caveat:1 dec:1 history:1 compare:6 cosmological:3 neglected:1 sphere:5 cnoc1:5 exclude:1 information:4 needs:5 goal:1 rather:1 reject:2 l9:1 ensemble:3 schultz:1 ζc:4 galactic:1 fu:1 m500:7 derived:10 orbits:1 catalog:12 virialised:1 coming:3 pat:1 imagers:1 parameterized:2 negligible:1 fundamental:1 rband:1 reservoir:1 developed:2 distortion:10 paper:14 through:6 suffer:1 its:4 style:1 rapidly:1 l71:1 actually:1 systems:4 might:5 alter:1 focussed:1 good:11 a2390:6 bryan:5 moscardini:1 hereafter:1 2r:1 always:1 level:6 chandra:4 2a:1 radial:1 found:10 referred:2 weight:1 generation:1 energy:1 expect:3 measurement:17 bluer:1 since:1 projected:8 research:6 sloan:1 induced:1 foreground:1 offsets:2 reason:2 imaging:8 members:9 generate:1 definition:2 benefits:1 similarly:3 wolter:1 mazzotta:1 fischer:4 probability:1 relate:1 number:12 cadc:2 done:2 defects:1 differ:1 temperature:25 introduction:1 moderately:2 gpc:1 assumption:2 wisotzki:1 scheme:2 too:4 pipelines:1 optical:1 bower:1 asca:7 king:2 18m:1 determined:3 timate:1 7d:1 7c:1 7b:1 7a:1 7s:1 cleaned:1 concentration:4 lie:2 self:7 finding:1 extrapolating:1 added:1 most:9 significant:4 comparisons:1 measured:9 clear:6 focussing:1 km:7 part:13 clean:2 kt:2 velocity:23 physics:5 cdm:3 relation:28 find:26 parameters:7 merger:1 kleinheinrich:1 factor:5 circle:1 columns:1 redsequence:1 dominant:1 albeit:1 dependent:1 listed:14 hii:1 spikes:1 arxiv:1 remove:3 dovich:1 bars:2 tereno:1 iteration:1 astrometry:6 see:9 individual:3 close:1 soucail:1 various:10 conditions:2 cfht:6 available:3 catalogs:3 sparsely:1 complement:1 spectroscopic:4 31m:1 distinguish:1 observer:1 both:7 recherche:1 dahle:5 last:1 emss:1 barely:1 nserc:1 sensitive:5 meylan:1 point:1 reasons:2 smith:3 kovacs:1 corresponds:4 community:1 dimensional:2 homogeneously:1 throughout:1 consuming:1 described:3 due:3 ph:4 pi:1 sanders:1 radii:22 gas:4 convert:1 determination:4 representative:1 systematic:6 solid:5 while:2 error:15 fernandez:1 computed:2 00h:3 apjs:3 vikhlinin:7 modification:1 resulting:7 relatively:6 higher:10 literature:6 lilje:1 comprehensive:1 uses:4 purpose:1 robust:1 stack:1 recent:8 dark:7 lower:9 older:1 analysis:33 magnified:1 edge:4 mobs:1 distances:1 reviewed:2 shape:6 intervals:1 cut:2 conclusions:1 source:18 location:1 ruled:1 transformation:1 finder:1 bin:1 matters:1 8πg:1 forman:3 like:1 semi:1 follows:2 signal:44 ignore:2 flux:1 yields:5 33rd:1 often:4 some:5 towards:1 sight:10 scale:19 diaferio:1 measurements:35 saas:1 integration:1 smail:2 innovation:1 minimal:1 ponman:2 run:1 swarp:1 cnoc:1 jumps:1 processing:3 aj:1 confidence:3 step:4 elixir:2 overdensities:1 intense:1 analysing:1 pipeline:2 pκ:2 reduced:5 range:14 complimentary:1 consequently:3 seeing:14 into:7 within:12 integral:1 locus:2 lensing:110 proportional:1 uncertainties:1 sequence:6 balogh:2 sections:1 considerably:1 relaxed:1 line:17 considerable:2 raising:1 rejection:2 consist:1 up:4 us:5 a209:5 spectroscopy:1 horner:12 similar:12 associated:1 defined:3 cover:1 redshifts:10 single:1 steeper:5 dashed:3 accounted:5 shallower:1 polarisations:1 provided:3 lens:3 meaning:1 structure:17 correlated:1 implies:1 algorithm:1 complicating:2 required:3 diffraction:1 equivalently:2 declination:1 far:2 requires:6 having:1 results:31 eds:1 amplified:1 contributions:1 ebeling:5 arif:1 contours:5 excluded:1 stable:1 maryland:1 include:2 random:1 01h:2 positions:2 notes:1 attempts:1 deals:1 smaller:3 cfi:1 bleeding:1 biased:2 imply:1 enclosed:5 dynamics:1 λcdm:3 abell:5 respectively:2 jointly:1 analysed:2 objects:11 others:1 59m:1 zeropoints:1 extreme:1 great:4 larger:16 suggests:1 preferentially:1 survey:11 shaded:2 makes:2 involves:1 scales:6 photometric:12 private:2 apj:39 addressed:1 decrease:1 use:20 fee:1 remains:1 hudson:1 next:2 few:3 camera:5 themselves:1 noisy:2 reflects:1 33m:1 detrending:1 account:4 a2219:5 a2218:5 obvious:2 freedom:1 scatter:12 refine:1 5c2:1 calculation:1 high:4 effectively:2 assumptions:6 ascension:1 sis:8 marginalising:1 regions:6 spurious:2 varies:1 numerous:1 elliptical:1 instead:4 profile:12 singular:4 space:1 kneib:12 fits:3 bertin:2 andez:1 light:5 lines:1 correspond:8 allow:3 astronomical:1 02h:2 overdensity:2 including:1 during:1 mentioned:4 shapes:7 galaxy:17 le:1 la:1 ln:3 masses:34 degrees:2 communication:2 clusters:94 pixel:1 archival:3 richness:1 outlined:1 13h:3 february:1 university:3 radians:1 poole:1 nfw:20 sufficiently:1 morris:2 kpc:2 l1:2 accounts:1 traces:1 experienced:1 constraints:2 subset:1 fare:1 doing:1 related:10 measure:12 our:53 out:10 lecture:1 ref:1 red:9 8b:1 retrieved:1 8a:1 galaxies:59 completely:1 8s:3 franx:2 likelihood:4 hubble:1 interaction:1 geometry:4 could:6 frenk:6 times:6 isotropic:1 hence:5 manuscript:1 powerful:1 l37:1 mvir:8 quality:5 fair:6 simulated:1 adopted:6 their:14 intermediate:3 final:2 explanation:2 lists:3 observed:27 submitted:1 amplitude:5 mackey:1 providing:1 need:5 clearly:1 studying:1 agency:1 able:2 instance:4 borgani:6 accuracy:3 centre:5 who:2 bolometric:4 but:27 σre:1 intrinsic:1 annulus:8 fact:10 selection:5 12h:2 text:1 supported:3 texp:2 purely:1 ccds:1 rough:1 agrees:4 based:22 knowledge:2 should:5 ellingson:3 arcseconds:2 combo:1 employed:2 local:1 achieve:1 equilibrium:2 overall:2 ones:1 words:1 averaged:2 chips:5 areas:1 gray:1 processes:2 haiman:2 luminosity:18 differential:1 navarro:7 processed:1 contain:1 jetzer:1 view:4 shapiro:2 statistical:9 exists:1 national:4 xray:2 usefulness:1 σcrit:3 operated:2 recently:5 luminous:5 m2500:20 cole:1 maddox:1 tend:1 dls:3 written:1 identification:2 routine:1 crude:1 invariant:1 comparable:1 ability:1 importance:1 complicate:2 key:2 kev:9 distribution:26 succesful:1 limits:2 taking:1 equal:3 etc:1 relevant:5 conclude:2 ca:1 contamination:20 48m:1 respect:1 escude:1 uncorrected:1 addition:4 indicators:3 outliers:2 define:1 field:11 arises:1 corresponding:4 received:1 sufficient:2 57m:1 covered:1 c2:1 present:5 multi:1 maccacaro:1 subsets:1 value:23 will:7 lx:7 almost:2 thus:6 surface:21 examined:1 orbital:1 pis:1 35m:2 cross:1 schild:1 largest:2 units:4 difficult:3 http:1 effect:13 phd:1 v2:1 mosaic:2 scaling:4 center:4 nevertheless:2 well:18 residuals:1 sets:1 position:3 spherical:2 less:4 increasingly:1 accurate:8 obtain:3 26m:1 sources:13 distant:7 web:1 density:36 absorption:1 sky:3 lake:1 capabilities:1 meisenheimer:1 simple:7 combine:2 warrant:1 unprecedented:1 match:1 resolved:2 increased:2 increases:5 know:2 denser:1 clowe:5 evrard:7 alternatively:1 become:1 r500:3 because:17 mohr:1 brainerd:2 discontinuities:1 proper:1 lead:5 demonstrates:1 avoid:2 overlap:2 does:5 assuming:4 eso:1 demonstrated:1 noise:2 11m:1 complication:2 uvic:1 although:11 after:1 panel:11 governato:1 pointings:2 about:10 actual:1 column:30 universe:4 introduces:1 dependence:1 important:4 introduced:1 own:1 cypriano:2 h0:2 square:1 tiny:1 estimators:1 2kev:1 van:8 additional:12 overestimate:1 inner:1 naturally:1 function:20 north:1 overlapping:1 astro:5 hierarchical:2 hm:1 convergence:3 made:2 compute:1 places:1 whether:2 gravitational:7 variations:2 below:3 limit:3 problem:2 contribute:1 circularizes:1 babul:4 ing:1 megacam:2 compared:12 variety:1 percent:2 detail:9 other:13 details:2 variation:3 astronomy:2 exposure:3 factors:1 4s:2 searched:1 understand:2 loken:2 augmented:1
0705.0359.txt |@word magnetically:1 limited:1 monte:1 consider:1 remarkable:1 magnetic:10 excellent:1 concern:2 lognormal:5 leads:1 c3:2 consists:1 follow:3 disk:3 cases:1 seemed:1 const:1 calculate:3 technique:1 finally:1 program:1 infinitesimally:2 contours:7 excluded:3 under:2 include:1 indicating:3 ta:1 tafalla:1 division:1 supported:2 straightforward:1 very:7 tends:1 ostriker:1 choice:1 rotational:2 orientations:2 affect:2 indicate:1 clouds:3 immediately:1 level:7 resolution:3 skewed:1 large:2 small:6 upper:5 work:4 force:1 findings:3 consistent:2 sin2:3 direct:1 approximation:1 likely:4 noise:1 qualitatively:1 carlo:1 even:2 employ:1 combined:1 chicago:4 mouschovias:5 ambipolar:1 axes:3 favour:1 uniform:11 consistently:1 axial:14 new:1 falling:1 originate:1 method:3 contrast:2 respectively:3 here:4 agreement:1 mnras:3 desired:1 objects:5 cos2:3 groups:1 ratio:2 along:6 strong:1 appears:2 z2:1 extreme:1 obtained:4 great:1 parameters:12 institute:2 larger:1 typically:1 prior:1 preferentially:3 survey:3 domains:2 complicated:1 myers:4 studies:1 elongated:4 diameter:1 fix:1 ratios:12 family:3 extra:2 triaxial:5 apj:11 aimed:3 cloud:15 ringing:1 plot:3 use:5 indicated:1 usa:2 distinct:2 chi:1 examined:1 negative:1 scenarios:1 calculation:2 live:2 therefore:1 distortions:1 encode:1 conservation:1 associated:1 theoretical:1 minor:3 more:1 becomes:1 stone:1 discrepancy:2 varying:4 ward:4 aligned:1 iii:1 high:3 account:2 crosses:1 pursue:1 mn:1 modified:4 theories:4 reproduce:1 infinitesimal:1 values:14 thin:2 following:2 trans:1 obtain:1 example:1 numbers:1 control:2 cosmological:2 process:2 datapoints:1 smirnov:1 whitworth:1 sample:5 indicates:1 orion:12 assumptions:2 performed:1 sense:1 occur:2 axis:5 normalize:1 2σx:2 rather:1 verify:1 discussion:2 revisit:1 regions:3 submillimeter:3 oblate:21 dotted:2 instead:1 those:2 absolute:1 parameter:2 sin:1 circular:1 simplicity:1 spitzer:1 may:4 starless:6 derived:5 mac:2 plane:6 ζy:1 truly:1 data:15 prolateness:1 natural:1 preferential:1 light:1 grant:2 lines:3 correspond:4 annealing:1 ones:1 so:4 allow:1 decreasing:1 order:1 terms:1 ameliorate:1 vary:1 distortion:1 paper:1 through:2 statistical:7 left:2 y0:1 y2:1 its:5 observational:6 style:1 derive:2 outer:1 probability:7 fit:2 maps:2 chosen:1 interesting:1 klessen:3 coordinates:1 li:6 better:2 absence:1 offers:2 degrees:4 fig:4 main:1 defining:1 alter:1 eventually:1 non:1 affected:1 seeking:1 introduce:1 they:3 half:1 looney:1 rotation:1 discuss:1 easily:1 february:2 always:1 university:2 identified:2 benson:3 sufficiently:1 each:1 found:3 quarter:1 tracer:1 mean:1 domain:5 square:1 significantly:3 series:1 energy:1 gaussian:4 involves:1 our:16 beyond:1 eq:5 100m:1 mediates:1 factors:2 gradient:2 quantify:1 since:5 projected:7 increase:1 acting:1 flattening:4 induced:2 occurs:1 math:1 shows:4 basu:10 theory:2 ast:1 confidence:1 diagonal:1 standard:1 formation:14 fuller:2 likelihood:43 log:1 parametrized:1 fixed:5 kunz:2 determining:2 could:1 area:1 v2:1 times:1 edges:1 tangled:1 ism:1 hence:1 appropriateness:1 south:2 first:2 major:3 features:2 symmetry:1 variables:3 xa:1 powerful:2 number:2 smaller:4 least:1 directly:1 robust:2 array:1 dividing:2 angular:2 opportune:1 given:2 necessarily:1 checked:1 publication:1 simulated:1 introduction:1 system:2 construct:2 their:9 assumption:3 observations:6 molecular:13 low:3 originating:1 disks:2 fraction:2 centered:1 elongations:2 isophotes:1 serve:1 rejected:1 binney:2 released:1 binned:1 part:2 pavlidou:1 authors:1 x2:1 x0:3 than:7 intrinsically:1 diffusion:1 unfortunately:1 triaxiality:4 double:2 zero:1 project:1 future:1 were:4 phy:1 gives:1 scuba:2 elongation:2 dynamically:3 modern:1 spectrum:1 randomly:1 manuscript:1 constrained:1 onigl:1 any:3 viewed:3 angle:2 latter:1 axisymmetric:5 predominantly:1 polarization:1 goodman:3 potential:3 take:1 acquires:1 towards:1 norman:1 investigations:1 incidence:1 falls:1 most:8 beta:10 printed:1 significant:3 pair:3 intrinsic:23 latex:1 deviations:2 especially:2 calculated:2 later:1 implications:2 face:2 ballesteros:1 heating:1 principle:1 exp:2 maxima:1 physics:3 fact:2 space:3 selection:1 particularly:2 show:1 tassis:4 random:5 submillimetre:1 purely:1 corner:1 thickness:6 find:2 principal:1 q1:2 giant:1 q2:2 based:2 knowledge:1 ellipsoid:4 much:1 protostellar:3 only:5 explicitly:2 thompson:4 circle:1 local:1 peaked:8 simplest:1 overall:2 preferred:1 yielded:1 joint:4 unimportant:1 cannot:2 bolometer:1 nearly:1 words:1 timing:1 reconstruct:2 dt:1 dq:1 infrequent:1 processes:1 maclow:1 fields:2 arxiv:1 yield:2 acknowledgments:1 rotationally:2 investigate:1 discs:1 common:1 qj:1 favoring:1 qn:2 l39:1 requirement:1 set:6 erroneous:1 observer:1 imposing:1 sensitivity:2 kolmogorov:1 turbulent:2 observed:7 see:3 result:9 discussions:1 close:5 techniques:1 probable:2 enlightening:1 subsequent:1 review:1 brunt:1 symmetric:1 favor:1 implicit:1 smallest:4 various:1 between:10 progress:1 approach:2 available:1 comparable:2 recently:1 however:7 key:1 clues:1 come:1 distribution:65 thank:1 concentrated:1 both:2 cos:3 toward:1 improved:1 region:1 konstantinos:1 equal:3 ln:4 admit:1 σx:4 mildly:1 pdf:3 masses:1 detailed:1 ci:11 ch:2 timescale:1 point:1 corresponds:2 grants:1 decreases:1 maximize:1 respect:3 forms:4 complication:1 second:1 addition:1 discrimination:1 due:4 quickly:1 confident:1 reduction:1 distinguishing:1 change:1 expected:8 figure:5 ph:1 contraction:2 define:1 direction:1 referee:1 families:1 concerning:2 determination:2 angles:5 astron:1 prestellar:5 c2:3 c1:4 present:1 case:8 tetra:1 solid:2 might:1 straight:1 expanded:1 value:5 transformation:3 will:6 reviews:1 while:3 weaken:1 deproject:1 uncertainty:2 orientation:3 almost:1 isothermality:3 prolate:11 simulations:1 nutter:3 surface:2 encountered:1 ii:2 ay:17 bias:5 il:2 ax:12 different:8 martini:1 spheres:1 perform:1 appreciable:1 σy:5 same:4 largest:1 finite:10 events:1 independent:2 used:7 goodwin:3 peaks:3 numerical:1 effect:3 flows:1 hand:3 driven:3 viewing:3 levels:1 user:1 frequently:2 opportunity:2 normalization:1 recent:2 paredes:1 lower:6 maximizing:1 scenario:2 makes:1 roughly:3 analysis:11 edge:2 temperature:1 consistency:1 model:2 parametric:1 lin:1 preference:4 routinely:1 quoted:1 appropriately:1 being:1 percent:1 axisymmetry:3 shape:30 intervals:3 transforms:1 turbulence:5 projection:3 oriented:1 corroborated:1 density:3 gmc:5 scales:1 sky:4 dubinski:1 pileup:1 source:2 priori:1 transformed:1 treatment:4 unprecedented:1 momentum:2 details:3 bin:1 lacking:1 represents:1 results:5 possible:2 early:1 department:1 increases:1 mon:1 coaxial:1 using:5 unique:1 semi:4 sizes:1 follows:2 caselli:2 performing:1 shapes:24 steps:1 either:1 obvious:1 resolved:1 become:1 soft:1 signal:1 indications:1 because:3 methods:1 briefly:1 hartmann:2 sight:2 spans:1 was:2 provided:1 gradually:1 scale:1 dimensions:1 lead:3 avoid:1 measurements:1 comments:1 does:2 select:1 assuming:5 three:2 minimal:1 limitations:1 core:43 biased:1 object:3 slight:3 perpendicular:2 expansion:1 who:1 biases:2 although:4 plots:1 analyses:1 bx:10 properties:2 after:1 panel:8 comparison:2 about:4 actual:1 would:8 anything:1 discussed:1 acm:1 range:2 obeys:1 emissivity:1 ciolek:4 converging:1 soc:1 image:1 within:3 functional:10 nsf:2 dataset:6 appropriate:2 right:1 references:1 primarily:2 sized:1 ellipse:4 uncertainties:3 additional:3 few:3 assumed:5 support:1 there:6 question:1 start:1 dropping:1 maximumlikelihood:2 stars:1 astrophysics:2 conceivable:2 sections:1 naturally:1 function:10 north:2 form:7 kerton:1 forming:2 relaxed:1 differences:1 marchesi:1 but:1 approximates:1 astro:1 convergence:1 line:12 fragmentation:3 datasets:1 gravitational:2 maximum:26 us:1 below:1 limit:2 problem:1 stages:1 similar:1 strongly:3 constant:1 defined:4 abstract:1 singly:4 dξ:1 single:4 au:1 predictions:1 file:1 wavelength:1 dζ:1 controlled:1 formalism:2 distributions:15 regime:2 completeness:1 kavli:2 no:3 amounts:1 dashed:2 when:2 field:8 other:4 ellipses:7 spatial:1 test:7 sufficient:1 deviation:1 draw:1 repeat:1 star:2 important:6 flattened:1 peak:6 additionally:1 heitsch:1 astronomy:1 jones:7 independently:3 algorithm:1 assume:1 requires:1 interval:2 ryden:2 nasa:1 mass:3 time:2 far:1 cores:42 gammie:6 debate:1 original:1 once:1
0705.0360.txt |@word represent:1 consider:2 caused:1 magnetic:14 thouless:1 r1f:13 edp:1 bohm:1 computation:1 lll:7 go:1 follow:1 reasoning:2 localized:2 r1i:11 whose:3 baym:2 derivations:1 charge:6 mediated:1 indicate:1 z1i:6 z1f:6 include:1 dramatically:1 brown:2 abelian:1 schrieffer:1 very:1 implicitly:1 springer:3 probability:2 mixing:1 ui:1 difference:3 condition:2 treating:2 hamiltonian:3 cause:2 michael:1 applicable:1 occurs:1 large:2 discrete:1 vector:1 interpolating:1 enclosing:1 mπn:1 optics:1 configurations:3 smaller:2 zi:4 zf:4 coefficient:1 approximation:1 zero:2 evaluated:1 picked:2 correlator:4 odd:2 even:1 what:1 sum:1 8m:1 centers:1 indian:1 above:1 fractional:7 new:1 increasing:1 method:1 filled:1 body:1 edited:2 condensed:1 girvin:1 exchange:2 respectively:2 shankar:1 here:2 understanding:2 ranges:1 2kf:1 objects:1 mes:1 eikx:1 directions:1 path:1 along:12 obtained:1 wen:3 property:3 incoming:2 institute:1 involved:1 study:4 larger:1 experience:2 example:1 p2:2 products:2 studies:3 involves:1 york:1 halperin:1 via:2 requiring:1 polonica:1 elucidated:1 translational:1 traversing:1 clockwise:4 establish:1 imaginary:2 use:1 takes:2 usa:1 ψp:3 contains:1 quasiparticles:8 ψk:1 kane:1 ψn:5 shortest:1 means:1 type:2 historically:1 more:3 zeroes:1 preparation:1 becomes:2 equipped:1 stone:1 carrying:1 particular:2 known:2 cases:1 hold:1 fermionic:1 topic:1 account:1 tunnel:2 science:1 work:2 reproduce:1 values:1 confining:7 scatter:2 decoupled:1 f0:1 heart:1 stated:1 india:2 states:9 assumptions:1 degenerate:2 magnitudes:1 verlag:2 stemmed:1 information:3 end:2 provide:2 s2:1 breaking:1 xˆ:1 hanbury:2 strikingly:1 anyon:9 gate:1 parameter:2 exponentially:1 oscillatory:1 ubiquitous:2 description:2 r2i:10 may:2 r2f:12 derived:1 mapping:1 reflect:1 spectacularly:1 mag:1 coming:2 law:7 sp:1 effective:2 grant:1 lines:1 correspond:2 st:1 z2f:6 green:1 jain:1 order:2 z2i:6 interpretation:1 produces:1 indeed:1 over:1 dy:1 gauged:1 experiments:5 through:2 statistical:2 existence:2 still:1 excitations:2 its:2 bunch:1 sciences:1 derive:1 exclusion:3 decay:2 energies:1 interesting:1 zˆ:2 37b:1 complex:1 exhibits:3 absence:4 parts:1 systems:5 alter:1 lx:3 ly:7 yi:2 them:1 motivated:1 yn:1 camino:1 introduce:1 landau:3 effects:4 they:2 twoparticle:4 now:3 hall:12 nor:1 represents:1 february:1 several:3 2p:4 rendering:1 university:1 level:2 realistic:3 2f:2 2a:1 each:6 2m:2 feldman:1 2i:2 en:3 directly:1 formulate:1 proposals:2 energy:3 ef:2 gaussian:1 related:2 eb:6 decays:1 expect:1 measure:1 quantum:12 our:9 beyond:1 eq:3 ep:1 out:1 prange:1 shown:7 matrix:5 restricted:1 furthermore:1 urbana:2 interference:2 projected:1 particles:7 replacing:1 rf:6 investigation:1 denoted:1 ref:3 ri:6 shows:5 interactions:2 treatments:1 small:4 auerbach:2 intermediate:1 retrieves:1 definition:1 uiuc:1 r1:2 r2:5 geometry:4 could:1 linearized:2 turn:1 length:7 place:1 gordon:1 incorporated:1 hence:1 degeneracy:1 top:1 first:2 separable:2 xi:3 xn:2 features:5 symmetry:1 quasiparticle:2 variables:2 xf:2 traverse:1 least:1 another:6 angular:1 aharonov:1 size:2 wilczek:2 dispersion:1 given:9 salient:1 anyons:19 start:1 eqs:1 system:4 aharonovbohm:2 1a:1 their:4 1b:1 zeros:2 fermions:13 consistent:2 1f:2 1i:2 final:1 relationship:1 trapped:1 wavelength:1 relative:5 took:1 x2:4 x1:4 than:2 intrinsically:1 reflection:4 wide:1 translate:1 cimento:1 second:1 limiting:3 project:1 future:1 amplitude:6 treated:1 function:2 l183:1 fashion:1 nuovo:1 explicit:2 sen:1 need:1 element:3 clearly:1 paths:6 strength:1 angle:5 efficient:2 pursued:1 note:1 k2:11 high:1 potential:10 take:2 so:1 explanation:1 altered:1 electric:1 centre:1 goldman:1 impurities:4 involving:1 propagate:1 letter:1 phase:11 exponent:1 deviations:1 kf:3 consequences:1 phil:1 physica:1 points:9 electrons:3 principle:2 exp:8 velocity:1 physics:7 lying:1 quantity:1 sector:1 signatures:3 show:5 comtet:1 supported:2 dependences:2 attempts:1 gauge:2 range:2 find:3 gefen:1 symmetric:1 laughlin:7 situations:1 noteworthy:1 enough:2 topological:3 entities:1 only:2 explicitly:2 4πl2:1 factor:3 employed:1 circle:1 exchanged:1 do:1 move:1 gains:1 distance:2 champaign:1 words:1 distinctly:1 dv:1 neither:1 processes:1 bar:1 settings:1 arxiv:1 qb:4 common:1 contain:1 qh:7 4πm:1 kernel:29 requirement:1 set:2 ser:1 fascinating:1 phenomenologically:1 physically:2 assa:1 correlations:8 chamon:1 lett:13 hosting:1 detection:2 see:4 individual:1 bare:1 result:2 enhanced:1 discussions:1 close:1 correlators:4 instance:2 satisfying:1 eigenfunctions:1 nuclear:1 away:1 sites:1 tend:2 boundaries:2 case:10 state:8 closed:1 between:7 progress:1 geometric:2 conditions:1 across:1 comparable:1 restricting:1 terms:2 nature:3 attention:3 however:2 iπν:1 reproduces:1 distinguish:1 configuration:2 suppressed:1 received:1 many:1 acknowledge:1 equal:2 propagation:1 dated:1 experimental:2 nearby:1 mechanics:1 relevant:2 co:5 separation:2 point:5 simple:5 except:2 dimensional:3 analyzed:2 anti:2 cancel:1 respect:1 kernels:6 described:1 geometries:5 addition:1 px:2 py:2 due:1 screened:1 quasihole:1 int:1 much:3 treat:1 interest:2 expected:2 fk:2 fig:12 direction:5 corresponding:3 observable:1 quantities:1 bulk:13 representative:1 acta:1 presented:3 those:2 applied:1 multi:1 p1:2 couple:1 quasiholes:2 value:2 rectangular:1 will:2 while:4 momentum:5 behavior:5 situation:4 tunneling:13 loop:3 iy:2 identical:1 vf:2 played:1 fill:1 thus:6 surprisingly:1 ii:7 cond:1 il:1 limit:5 vanish:1 fermion:2 arovas:1 different:3 perhaps:1 excludes:1 suggests:1 perform:1 make:1 safi:1 indistinguishable:1 same:2 any:3 noninteracting:1 arguments:4 advances:1 finite:4 events:1 extended:1 lie:3 upon:2 effect:2 counterparts:1 hand:1 edges:4 moving:1 kim:1 lengthscales:1 yf:3 off:1 center:4 immaterial:1 no:2 well:2 analysis:2 picks:1 bunching:1 academic:1 edge:20 components:2 studying:1 coordinate:3 model:2 paradigm:1 charged:1 less:1 reiθ:1 observed:1 valuable:2 using:1 reality:1 scattering:3 eigenstates:6 previous:1 leinaas:1 rapid:1 application:1 haldane:1 alternate:1 k1:10 setting:2 treatment:2 relevance:1 mod:2 ought:2 real:1 rescaled:2 aspects:1 depends:1 evaluate:1 breaks:1 possible:3 background:1 vacuum:2 confined:1 integer:5 apart:1 fradkin:1 like:1 particle:38 follows:1 manifest:2 specific:2 flux:1 either:1 martin:1 become:2 inter:1 scatterers:4 right:1 vortices:1 phenomena:1 sensitive:1 born:1 oscillations:1 multiple:1 translates:1 pronounced:2 devillard:1 dimensions:1 bottom:1 opposite:3 filling:1 does:1 provides:2 assuming:1 dst:1 obey:1 power:5 perpendicular:3 anticlockwise:2 paper:1 plots:1 bangalore:1 properties:5 gained:1 about:2 would:2 constraint:1 dependence:3 convenient:1 carries:1 must:1 obeys:1 act:1 rev:17 significant:1 presence:7 into:4 within:2 nsf:1 predictions:2 lies:2 determine:1 strip:5 proportional:2 bosonic:1 statistics:10 radii:2 area:1 assumed:3 justifying:1 initial:1 u1:1 u2:1 ordinate:3 width:7 bosons:12 low:1 under:2 astrophysics:1 analyze:1 was:5 lowest:2 hard:1 complete:1 form:11 some:1 becoming:1 ets:1 but:2 principles:1 illuminating:1 hc:1 illustrative:1 wherein:1 made:1 vishveshwara:2 b5:1 whether:1 mat:1 2πm:1 up:4 theoretical:1 2πp:1 dmr:1 un:2 fermi:3 demonstrate:1 problem:1 similar:1 called:1 purcell:1 detailed:1 separated:1 associated:3 defined:2 certain:1 describe:2 myrheim:1 single:17 proves:1 exist:1 twiss:2 formalism:1 physical:1 faithful:1 variety:1 wavefunction:5 when:5 vanishes:5 illinois:1 field:11 other:4 role:1 details:1 eduardo:1 department:2 conclusion:1 picture:2 elements:2 zhou:1 models:1 centered:1 remarked:1 drift:1 deriving:1 reiφ:1 kivelson:2 impurity:3 implies:1 coulomb:1 perturbatively:1 required:1 having:2 4m:3 mass:5 smooth:1 time:2 starting:3 4c:2 external:1
0705.0361.txt |@word magnetic:1 bandgap:3 results:2 existing:1 leads:1 eds:2 proposition:1 edu:2 expressions:1 alu:2 γj:1 finally:1 elliptic:2 umich:1 γc:1 tg:1 analogous:1 p2:11 amplitudes:1 federation:2 very:1 wave:3 electron:1 p1:31 refractive:1 experimentally:1 difference:2 condition:2 level:1 transmission:12 supports:1 2κl:6 solution:1 vector:4 optics:3 equation:2 concluded:1 periodicity:1 sign:1 street:1 design:1 chen:1 iσ2:1 iσ1:1 index:6 nonlinear:27 uniform:4 establishes:1 new:7 consisting:1 filled:2 coefficient:5 edited:1 respectively:1 here:1 address:3 directions:1 strong:1 equations:3 z1:2 dp1:2 dotdashed:1 institute:2 vectors:2 commonly:1 pico:1 launched:3 usually:2 resonance:3 composed:1 spatially:1 although:1 a21:4 substitution:1 plenum:1 fbg:1 conventional:4 indicated:2 usa:2 positive:2 negative:6 assuring:1 therefore:1 resonator:1 theoretical:1 more:3 separated:1 introducing:2 solitons:3 γl:8 mismatch:1 award:4 varying:2 known:1 middle:2 science:1 originally:1 work:1 printing:1 values:4 thin:1 9th:1 following:3 making:1 f2:1 figure:4 neglected:1 states:1 indicates:1 numbers:2 jensen:2 motion:3 arbor:1 s2:1 s1:1 acts:1 feature:2 parameter:1 sin:2 de:2 modulation:1 wiley:1 southern:1 applications:2 designed:1 waves:2 fl:1 parallel:2 constants:2 realized:1 effective:6 resemble:1 light:5 metamaterials:2 sh:1 sn:2 arizona:3 media:1 poynting:3 order:1 typical:1 feedback:8 facilitated:1 entity:1 stability:1 including:2 existence:1 facilitates:1 avenue:1 its:1 directional:1 exhibits:1 forms:2 degrees:1 fig:14 jacobi:2 couplers:2 nims:3 versus:1 gibbs:1 was:1 material:4 landau:1 p12:2 effects:2 discuss:1 dielectric:1 susceptibility:2 february:1 university:3 kerr:1 oppositely:1 2f:1 inherent:1 entirely:1 aceves:2 homogeneous:3 ed:1 energy:4 related:1 frequency:2 static:1 quantum:1 our:1 beyond:1 eq:4 ru:1 shown:4 since:1 rev:4 attracted:1 bragg:1 suggesting:1 ref:1 occurs:1 math:1 shows:4 fiber:2 linear:10 abramowitz:1 approaches:1 formation:3 york:3 veselago:1 bistability:10 counterpart:1 length:4 u21:1 u22:1 christodoulides:1 utilizes:1 sipe:2 number:1 channels:12 another:1 electronic:3 illustrate:2 given:2 boulevard:1 introduction:1 eqs:1 system:3 relations:2 their:1 joseph:1 california:1 structures:6 dfb:4 discussion:1 academy:1 moscow:3 continuous:1 wabnitz:2 optical:12 focusing:1 coefficients:8 reflection:1 distance:1 kind:1 holland:1 fundamental:2 enabled:2 limiting:1 individual:1 were:2 eggleton:1 san:1 ann:1 curves:2 self:1 mills:2 mechanism:9 sciences:1 potential:1 εj:3 switching:1 channel:20 formulas:1 electric:1 iφ2:1 opposite:4 who:1 importantly:1 letter:1 phase:5 intrinsic:1 soliton:5 nonlinearity:4 considered:1 soviet:1 bowden:1 steady:1 kl:3 graphs:1 points:1 exp:6 velocity:1 physics:5 χj:2 dot:3 dover:1 phenomenon:2 show:1 supported:1 nlc:9 relation:2 solutions:2 threshold:1 κa2:1 find:1 κa1:1 parameters:1 distributed:1 written:4 should:1 transcendental:1 constant:2 dn:7 xxxiii:1 dependent:1 michigan:2 µj:4 dz:3 closely:1 dy:1 evolution:1 settings:1 dissertation:1 arxiv:1 summary:1 qb:1 qe:1 predicted:1 peak:1 fixed:2 κl:9 γp2:1 intensity:1 computer:1 aro:2 mur:1 ieee:1 propagates:1 state:2 dms:1 various:1 between:4 progress:1 boundary:2 conditions:1 rita:1 eecs:1 nature:1 initially:2 attention:1 however:2 incident:1 σj:1 cos:2 enabling:1 propagation:3 layered:1 figures:1 dated:1 context:1 refraction:1 periodic:5 perot:1 corresponds:2 anti:1 decreases:1 moreover:1 pp:1 described:2 analogies:1 three:2 been:2 garmire:1 pc:1 basic:2 expected:1 ph:3 important:1 define:1 direction:4 corresponding:2 both:4 gap:7 coherent:1 andrei:1 external:1 those:2 case:14 multi:1 novel:2 pacs:1 solid:7 directionality:3 will:1 while:4 nonstationary:1 property:4 loop:1 a20:1 real:1 a22:2 studied:2 coupled:1 vol:1 characteristics:1 couples:1 coupler:22 ik:1 rfbr:1 shalaev:1 different:2 az:1 grant:1 suggest:1 cross:1 same:4 shifts:1 complex:1 schematic:1 units:1 regime:1 higher:1 peaks:1 nim:28 effect:1 flows:1 lower:1 modes:2 krug:1 well:1 academic:2 materials:1 arising:1 when:2 stegun:1 engheta:2 photonic:1 using:2 speed:1 4a1:1 tables:1 k2:1 point:3 lett:5 input:6 identical:2 αc:1 spatial:2 increases:1 vacuum:1 press:2 δz:1 part:1 unique:1 bistable:3 necessary:1 like:1 follows:1 reduces:1 velocities:2 orlando:1 output:3 permittivity:1 mathematical:2 muri:1 susceptibilities:1 uspekhi:1 multistable:1 matching:1 iφ1:1 provided:1 cavity:1 resonances:2 critical:1 assuming:3 propagating:2 power:14 processing:1 notable:1 bi:1 santa:1 found:4 properties:4 comparison:1 waveguides:1 freedom:1 gratings:1 discussed:1 carrier:1 wolf:1 functions:3 significant:1 presence:1 previously:1 into:4 nsf:1 amsterdam:1 there:1 u1:2 u2:1 dispersion:1 appl:1 handbook:1 forward:2 metamaterial:1 function:5 north:2 elsewhere:1 form:5 properly:1 russian:3 line:16 directed:1 made:2 sterke:2 iqz:1 devices:1 photonics:1 tucson:1 owing:3 continuously:1 distribution:1 similar:2 originating:1 associated:2 pim:29 defined:3 flow:2 abstract:1 describe:1 general:2 engineering:2 permeability:1 distributions:1 film:1 physical:1 diego:1 nj:1 compared:1 no:3 dashed:9 generally:1 slusher:1 electrical:1 branch:1 becomes:1 department:3 mathematics:1 2dn:3 may:2 βj2:1 a1:15 a0:3 a2:18 fabry:1 variable:1 structure:8 coupling:7 natalia:1 assume:1 curve:1 agrawal:1 notion:1 backward:5 stacks:1
0705.0362.txt |@word four:7 consists:4 paris:2 under:5 divergent:5 affect:1 bringing:1 solution:1 vector:18 regularizations:2 jhep:2 consistent:1 approximation:1 elegant:2 second:12 implemented:1 4x2:3 even:13 ˆb:3 above:24 new:2 increasing:1 ever:1 coefficient:5 simultaneously:1 applies:2 equals:1 here:14 refinement:1 supermultiplets:1 logarithmic:1 obtained:7 study:2 approaches:3 fourier:2 settled:1 cancellation:14 appropriately:2 explained:4 brs:1 replace:1 brought:1 propagators:21 unit:1 derivatives:10 would:10 m4:7 m1:3 m0:4 m2:124 type:1 schroeder:1 naive:2 warr:3 berlin:1 separates:1 ward:10 hold:1 must:13 ii:1 springer:1 ma:8 quartic:12 tb:3 fµν:3 mi:2 theories:65 ere:1 erg:7 my:1 example:13 transition:2 renormalization:32 give:9 weinberg:1 involve:5 want:8 keep:3 guarantee:2 end:5 provide:4 feature:2 how:18 answer:1 ordinary:4 preferable:1 bphz:1 replacing:3 after:13 diagram:22 lat:1 constants:3 effective:112 summing:4 fictitious:1 correlation:18 order:19 restriction:1 interpretation:1 over:20 satisfied:1 satisfies:2 integrands:1 before:5 somewhere:1 expectations:1 exhibits:2 writing:1 kaplunovsky:1 fig:12 renormalizable:1 versus:1 generalised:1 them:7 affected:1 combination:1 break:3 effects:2 they:18 singularity:2 rµ:1 uscher:1 hepth:2 bonn:1 each:18 series:3 used:11 combining:1 vilkovisky:1 ghosts:2 extract:2 restricted:1 crucial:1 content:2 rg:1 adapt:2 ri:3 independence:1 numerical:1 turning:1 linear:12 mω:3 mψ:3 free:3 standard:18 indices:1 r0:6 chiral:21 r2:3 starts:1 tempting:1 signature:1 corrections:3 already:12 features:1 render:1 restrict:1 another:5 illustrate:3 igarashi:1 rewritten:1 similarly:8 needed:1 master:2 too:6 burgess:1 unbroken:2 a39:1 somewhat:11 finitely:1 last:4 showed:2 tree:15 rate:1 correlators:3 matter:10 powers:9 minus:1 perturbative:3 sees:1 rewrite:2 respecting:1 modern:3 mind:1 seen:4 regulate:2 contents:1 relatively:3 strength:1 convenient:7 latter:9 localities:1 amusing:1 though:2 bruce:1 denominator:2 simplify:3 involving:18 marie:1 inconsistency:1 don:1 flow:18 vertices:13 curie:1 yang:5 principle:4 sum:14 channels:1 infrared:19 gauge:198 subtle:1 d4:32 d2:13 make:6 implementation:1 cousins:1 topological:1 coefficients:5 integrate:5 do:21 dd:27 de:3 preferred:1 da:5 dz:2 dx:17 dy:4 dv:13 dt:5 du:13 ds:5 contributes:1 fields:47 gaum:1 disaster:1 reference:2 naturalness:1 depends:6 result:10 dµ:1 brst:8 techniques:3 said:1 tensor:8 µp:6 approach:1 preserve:4 terms:104 parallels:1 extend:1 restricting:1 however:25 topology:1 cos:3 extracts:1 receives:1 contribution:29 argue:3 disappears:1 collecting:1 had:5 polynomial:2 basis:1 three:2 been:8 quickly:1 much:4 basic:5 expected:3 supersymmetric:35 quantities:1 concerning:3 generalization:1 spin:1 applied:1 spontaneously:1 euclidean:3 suppose:1 aij:2 property:1 procedure:7 ip:1 ir:63 obeying:1 im:4 ia:1 ig:7 containing:4 perform:5 realizing:1 complex:5 potentially:3 split:2 dimensionless:2 several:6 independent:8 i1:12 laboratoire:1 i3:4 i2:26 i4:10 hand:2 vainshtein:1 normalization:1 changes:2 left:8 just:18 able:3 transforms:2 campbell:1 previous:1 adding:9 infinitely:4 character:2 easy:5 opt:1 insensitive:1 breaks:8 possible:9 eorique:1 seff:1 background:32 lcl:1 apart:1 appearing:2 performing:1 specific:3 arbitrary:17 right:2 deal:2 somehow:1 born:1 contributing:1 shifting:1 kuzenko:1 super:2 properties:3 takes:3 anomalous:3 o:33 plus:2 adel:1 automatically:1 statements:1 presence:9 xyz:1 formulae:1 obtaining:3 down:2 rewritings:1 methods:2 unambiguous:1 transform:2 class:1 supergraphs:2 accordingly:2 way:17 call:1 was:7 form:20 back:2 cedex:1 encoded:1 removed:1 true:5 absent:7 iqx:1 complications:1 computing:13 abstract:1 textbook:1 convergent:9 exist:1 dλ:1 check:5 physical:2 ni:4 no:18 when:37 vanishes:5 setting:2 role:5 variable:1 longer:2 dψ:5 assume:1 necessitates:1 together:4 factorizes:1 time:5 dϕ:1 precise:6 logarithms:2 roo:1 skip:1 global:10 leads:4 computation:13 inverse:1 depend:6 finally:6 mixte:1 4g12:1 choice:3 noninvariant:1 emphasized:1 exact:8 level:5 did:2 irreducible:3 work:4 dealing:2 sign:2 tetradis:1 appear:1 celebrated:1 current:1 annals:2 international:1 satisfy:3 prescriptions:1 xλ:1 change:1 institute:1 shift:4 studied:3 ourself:1 buchbinder:3 usually:4 cˆ0:3 adjustable:1 useful:2 extra:5 f2:4 parma:1 modifying:1 flexibility:1 working:2 prove:2 covariant:4 positive:1 france:1 explicitly:23 renormalisation:3 theoretical:1 diagrams:28 introducing:3 sharing:3 appendix:6 everywhere:1 cases:2 fermionic:5 logarithm:2 avoiding:1 modified:5 values:2 following:5 modifies:1 degenerate:1 figure:3 expanding:2 permutations:1 allowed:2 fλρ:15 fλσ:8 occur:1 dxa:4 verlag:1 regularization:30 howe:1 divided:2 means:3 write:2 criterion:2 parameter:5 product:2 may:7 produce:3 designed:2 representations:4 nonrenormalization:1 maybe:2 explicit:33 yielding:1 su:1 st:4 so:15 representation:13 acts:1 indeed:16 mainly:1 years:1 course:14 statistical:2 cuts:1 still:7 group:13 interesting:6 jij:1 constitutes:1 main:1 puzzle:1 happened:1 non:82 thereby:2 matches:2 introduce:9 now:24 discuss:10 term:25 name:1 drop:1 spinor:1 arbitrariness:2 ee:1 hypergeometric:1 conventions:1 eq:7 shown:8 space:2 furthermore:2 lagrangian:2 cancels:4 looking:1 transforming:3 formula:2 squares:1 shows:2 theory:47 derived:1 possibility:1 quite:4 complicated:8 remainder:2 care:2 impose:8 turn:5 massive:7 βn:2 rewrites:2 first:33 origin:1 symmetry:20 variables:1 xa:19 xz:1 xy:1 specifically:1 directly:8 xp:2 xq:2 given:39 necessarily:1 checked:1 unitarity:1 indicate:1 seiberg:2 realization:2 speaking:1 gives:11 mostly:1 than:6 specify:2 were:4 pre:1 troublesome:1 correction:1 argument:3 invalidated:1 say:1 recover:2 any:33 note:26 take:5 cnrs:2 sure:2 trace:3 decreasing:1 beta:1 importantly:1 βfunction:1 rosten:2 considered:1 later:2 berg:1 feynman:17 typically:6 2m2:6 ovrut:2 2m4:3 show:5 jµ:10 inconsistent:1 aρ:31 aσ:3 ratio:1 analytic:1 only:35 going:4 holomorphy:1 get:19 rept:1 expectation:1 cannot:2 aλ:60 aν:10 closure:1 yield:2 imposing:1 namely:1 unaltered:1 wonder:1 ways:2 review:1 label:1 enough:3 between:3 diagonalized:1 checks:1 multiplied:1 bonini:2 multiplies:1 suppressed:2 originates:1 many:17 region:3 according:3 called:2 expression:9 σu:4 continuation:2 superfield:1 insist:1 pole:8 cancel:19 constant:19 considering:1 slavnov:6 come:1 locally:1 differently:1 observe:1 external:14 evidence:4 former:1 those:3 case:18 eis:1 chap:2 cancelled:3 promised:1 coupled:3 susy:19 peskin:1 worry:4 different:15 etc:1 same:28 shifts:2 arguments:1 constructed:1 extended:3 siegel:2 arose:1 changing:1 invariance:31 modes:14 locality:2 without:6 comes:1 fixing:4 dimension:1 summer:1 being:6 generally:2 resp:8 actions:10 infeld:1 diagrammatic:2 multiplet:17 villars:1 seems:1 parametrization:1 lets:1 interested:2 treatment:2 momentum:41 real:1 around:1 represents:1 read:1 multiplets:9 sums:2 harmonic:2 vacuum:4 using:32 decomposes:1 counterterm:10 particle:5 reduces:2 serves:1 either:3 integrals:41 fully:1 loosely:1 deduce:1 respect:1 reasons:2 provided:3 dimensions:12 extensively:1 critical:3 decomposition:1 provides:3 refer:1 dimensionally:8 scientific:1 2c:2 broken:2 2m:1 2n:2 theorems:4 discussed:13 generated:2 nonanomalous:1 practical:2 obeys:1 west:2 berges:1 cambridge:1 numerically:1 references:2 speculated:1 technically:1 hep:14 log:89 assumed:1 there:27 start:1 low:9 labelling:1 assumes:1 complete:7 aµ:5 arranged:2 improved:1 ellwanger:1 shifman:1 detailed:3 ab:26 ai:4 certain:5 describe:2 am:1 general:23 loops:12 formulation:1 again:19 c20:1 field:49 wetterich:1 valid:1 majorana:10 d2n:3 massless:17 oneself:1 separate:4 vertex:11 includes:1 deriving:1 a2:21 a4:17 tricky:1 perturbatively:1 mass:15 starting:5 coherently:1 represent:2 consider:10 ceases:1 splitting:1 scalar:11 follow:1 expressions:3 zinn:4 particles:4 preserves:3 tr:19 spirit:2 program:1 alvarez:1 th:12 presentation:1 ta:5 subtleties:1 1pi:31 amplitudes:1 straightforward:2 very:7 translations:1 witten:1 ultraviolet:2 difference:4 condition:3 treating:1 louis:1 large:5 small:5 employing:1 grateful:1 renormalized:4 zero:11 further:4 bilinear:2 what:5 opted:1 section:11 supermultiplet:5 lhomond:1 version:3 issues:1 sup:2 aaν:1 erieure:2 method:9 full:10 strong:4 equations:13 allows:3 wilsonian:90 stelle:1 pick:1 action:136 ization:1 options:1 via:3 establish:1 proceed:1 contains:8 comparing:1 nucl:10 qcd:1 taken:3 more:26 operators:1 spoils:1 stick:1 particular:15 known:8 recall:1 equation:5 compare:5 f3:4 marchesini:2 share:1 numbers:2 sense:3 sharp:1 νn:2 needs:3 advantage:1 polchinski:1 rather:1 breaking:2 priori:4 algebra:14 singularities:10 reflect:1 coming:4 fi:3 associ:1 arnone:1 sect:2 fundamental:1 remnants:1 ith:2 hierarchy:1 through:2 its:4 boson:2 actually:9 resort:1 absence:2 microscopic:2 might:6 supersymmetry:12 return:1 pauli:1 framework:1 yz:1 speculate:1 easily:4 finite:29 2p:6 always:4 2x:3 2d:1 2e:2 2g:7 turns:1 found:2 universit:1 2k:1 heavy:7 energy:8 reduce:2 idea:1 obtains:3 quantum:10 operation:1 beyond:2 really:6 since:23 issue:8 occurs:2 difficulty:2 reason:3 put:1 definition:2 renomalization:4 4p2:4 integrand:7 number:3 done:1 differ:1 perturbation:5 guaranteeing:1 introduction:12 leading:3 least:5 calculations:1 scheme:2 recovered:1 shifted:1 holomorphic:1 part:14 authors:1 2f3:1 2f2:1 double:2 contrary:2 motivation:1 footnote:1 cumbersome:2 orders:1 lie:2 wilson:2 depending:2 lin:26 k2:1 internal:3 generalized:1 play:2 added:2 most:5 ke:24 kj:2 clear:8 physics:4 ambiguities:1 hyper:6 converge:2 relation:1 fine:1 find:3 reminiscent:1 parameters:8 writes:1 generators:2 factor:17 abelian:6 triangle:2 dependent:10 him:1 exhibiting:3 arxiv:17 iγµ:19 common:5 cri:2 set:7 undergoes:1 see:27 individual:2 bare:2 cutoffs:6 various:8 costant:1 probably:1 conditions:6 recently:1 attention:1 vanishing:10 ike:1 distinguish:2 remaining:3 both:9 prescription:32 iγ1:3 quantization:1 context:2 whole:3 finds:3 arbitrarily:3 point:19 simple:4 lagrangians:3 2i2:5 corresponds:4 dimensional:31 simply:4 throughout:2 ps:19 pp:1 described:1 transformations:1 due:7 reduction:5 asymptotics:1 pe:5 pj:1 ph:2 pi:12 pn:1 lett:7 addison:1 generating:3 itoh:1 assigning:1 p2:56 p3:2 p0:1 p1:5 look:4 p4:1 solid:1 expanded:6 evaluated:9 sonoda:2 while:12 replaced:4 behavior:2 couplings:17 loop:181 unitary:2 vol:1 supergraph:1 encountered:1 rin:1 itself:1 vanish:2 fermion:9 lengthy:1 rules:3 modification:1 higher:13 literature:2 sym:1 uses:2 purpose:3 recent:1 normale:2 subleading:1 obviously:13 regulating:1 consistency:3 parametric:3 questions:3 world:1 alternative:3 letting:1 cut:1 conclusions:1 theorem:3 guarantees:2 transformation:4 evaluate:3 catalan:2 modifications:2 imposed:1 follows:1 manifest:2 separately:1 imposes:2 yields:5 byproduct:1 exploiting:1 often:1 some:17 pierre:1 understood:1 trends:1 pρ:3 examples:4 sight:1 ourselves:1 scale:16 yl2:1 integration:4 minimal:1 inserting:1 continuing:1 agreement:2 rue:1 bt:1 step:1 become:2 subtract:1 constrains:1 pλ:2 pe2:1 pν:1 remains:2 range:1 gamma:1 cutoff:100 into:8 within:6 integral:34 appropriate:7 zuber:1 regularizes:1 question:4 long:9 u2:2 propagator:5 arise:2 repeatedly:1 line:7 intuitive:2 uv:49 up:10 us:16 similar:9 ki:13 associated:1 defined:7 single:3 defines:1 dashed:1 rewriting:1 bracket:1 coded:1 nice:1 generates:2 meaning:1 structure:2 independently:1 implies:2 required:2 notion:3 equivalently:1 incomplete:1 far:1 requires:2 having:3 results:5 existing:1 eds:1 gn:9 gm:1 contributions:31 lptens:1 excludes:1 superspace:5 concerned:4 include:3 ingredient:1 g2:6 g0:1 implicitly:1 continues:1 wave:2 matrices:2 severely:1 diverging:1 deals:3 dealt:1 manifestly:10 eigenvalues:1 trr:31 noted:3 smaller:1 zk:1 le2:3 substituting:1 odd:2 obey:1 plays:2 giving:7 3r:1 slight:1 batalin:2 expressed:2 poles:1 flowing:1 3c:2 3g:3 3d:1 nonlinearly:1 kopper:1 believed:1 objects:1 separation:3 rocek:1 z2:1 remark:1 receive:3 larger:2 leaving:1 resulting:2 situations:2 grisaru:1 implement:12 makes:1 involves:5 formulated:1 scales:1 integrations:5 scaled:1 addressed:1 anomalies:12 sgn:2 apply:4 orderings:1 use:16 commun:2 recalling:1 next:6 few:5 simpler:3 ecole:2 becomes:3 account:1 integrating:8 infinitesimal:1 obvious:9 drops:1 proof:8 calculation:1 energymomentum:1 pieces:1 high:12 effectively:2 lorentz:21 fρλ:2 varied:1 six:1 regions:3 instead:10 94b:1 sin:2 counterterms:10 singular:7 renormalizability:2 computations:2 light:5 lines:4 allow:1 discussion:7 produces:1 produced:1 including:4 mentioned:4 converting:1 perfect:3 chosen:1 masses:9 derivative:12 defining:5 eur:1 gaugino:1 practice:3 operator:2 mention:3 p12:1 subtraction:1 front:2 rotation:1 realize:1 dirac:4 university:2 traced:1 morris:2 l2:4 traces:2 reproducing:2 doing:4 related:1 elementary:7 remove:2 measure:1 separating:1 our:22 special:1 out:18 respects:2 matrix:8 integrates:1 m2i:8 wick:3 ref:6 integrated:4 math:2 interactions:4 diagonal:3 completely:4 interaction:1 re2:1 could:9 times:1 length:1 hence:13 quadratically:1 powerful:2 precisely:2 adjoint:8 behaves:1 adopted:1 their:10 intermediate:2 fermions:17 perfectly:2 final:1 denominators:1 shell:1 udu:1 exactly:11 attanasio:1 manifestation:1 exhibit:1 borninfeld:1 symmetries:18 keller:1 need:3 clearly:11 studying:1 mills:5 polarization:2 mix:2 concerns:1 sevrin:1 who:1 but:21 why:4 linearized:1 constrain:1 fact:2 physique:1 supergravity:1 rotating:2 bring:2 trivial:2 q2:2 based:4 knowledge:1 should:19 ambiguity:3 local:29 meant:1 inλ:1 displayed:1 overall:1 ones:4 applying:1 determinants:3 places:1 expansions:1 tuned:1 contain:3 fixed:2 view:1 requirement:2 modulo:1 computed:11 exists:1 computes:2 p22:1 ke2:7 dνn:2 flin:3 correctly:1 invariant:84 p2e:5 dν1:2 reproduced:1 bilal:3 implementing:2 reproduces:3 onofri:1 limits:1 taking:1 equal:5 april:1 safely:1 relevant:8 conclude:1 cf:4 cd:9 taylor:5 normalisation:1 treat:1 anomaly:7 define:11 lgh:1 corresponding:19 commutes:1 scalars:2 lgf:1 essentially:1 c2:4 c0:8 present:10 multi:4 value:8 will:50 revisited:1 refs:2 thus:23 orthogonal:2 generic:3 divergences:15 cross:1 parts:2 diagonalize:1 gets:12 difficult:2 cubic:1 effect:1 infinite:6 expand:6 off:2 reflection:1 nevertheless:5 well:19 sets:2 usual:13 less:4 increasingly:1 obtain:10 detail:4 sources:1 momenta:31 4m2:2 density:2 lattice:3 add:10 adj:3 identical:1 press:1 immediately:3 necessary:2 like:12 alternatively:6 regulated:1 works:1 replacement:2 because:1 qed:6 classical:10 regularized:10 proper:4 iˆn:8 happens:2 lead:6 avoid:1 does:14 iˆ4:5 iˆ1:3 iˆ2:10 iˆ3:4 complication:1 expansion:16 wesley:1 qe2:1 although:7 stage:1 about:7 actual:1 justin:4 freedom:1 introduces:1 dependence:10 important:11 2cd:1 introduced:1 projectors:1 bergshoeff:1 functional:5 bosonic:4 additional:1 quadratic:19 function:12 overlapping:3 construction:2 convergence:1 made:2 compute:23 evident:1 instructive:1 whether:7 meeting:1 gravitational:1 below:10 convince:2 limit:6 problem:3 piece:2 mechanics:1 universal:2 contribute:4 denote:1 identities:15 proceeds:1 functions:23 qλ:8 qν:8 cˆ:7 other:7 details:1 branch:1 conclusion:3 ghost:9 function2:1 coupling:6 factors:1 rule:1 4g:1
0705.0363.txt |@word limited:1 abundances:7 consider:5 represent:1 magnetic:21 results:3 know:1 disc:1 bvd:1 consists:1 follow:1 mill:1 causes:1 poorly:1 certainly:2 careful:1 const:1 calculate:1 re:2 respectively:3 dickman:2 disturbances:1 mannings:1 protostars:1 simplify:1 quasi:5 under:1 include:1 case:2 g0:1 very:5 ostriker:2 summarized:2 method:1 squares:1 clouds:18 issue:1 t2:1 applicable:1 t0:6 integrated:1 large:8 discrete:1 small:2 concluded:2 10k:2 mn:1 force:5 occurrence:4 blitz:1 cosh:1 approximation:4 elegant:1 likely:2 alfv:1 evaluated:1 equal:3 further:1 dynamics:3 estimated:2 hennebelle:7 selfgravitating:1 index:1 what:1 nonlinear:6 appear:2 rate:18 ambipolar:16 near:1 expressed:1 folini:2 birk:2 above:3 fractional:2 net:11 increasing:1 consisting:1 ρt:1 coefficient:2 iran:2 galaxies:1 component:3 here:6 ionization:3 following:3 objects:1 clumpiness:1 ratio:1 along:3 quite:1 equations:9 contraction:1 obtained:3 solid:3 institute:2 study:1 larger:3 allows:1 hydrostatic:1 suggests:2 chemical:1 poisson:1 complicated:1 narrow:1 studies:3 frictional:1 kg1:1 via:2 spatially:1 family:1 scales:4 specified:1 visible:1 total:2 cloud:10 plot:2 use:6 would:2 arms:1 next:1 few:1 approach:1 therefore:3 m3:1 criteria:3 scope:1 minor:1 more:2 separated:1 fragmentary:1 becomes:2 company:1 occurred:1 everywhere:1 apjs:1 separates:1 known:3 cases:1 iv:1 burkert:1 clumps:5 must:2 abundance:2 high:1 account:2 collision:3 ρi:2 science:1 equation:22 work:3 semadeni:2 modified:1 lorentz:1 values:11 temperatures:2 evolved:1 believed:1 example:1 impeded:1 ions:2 compare:2 figure:4 give:2 process:1 introduces:1 cited:1 states:1 indicates:1 assumptions:1 performed:1 slip:1 sense:1 reidel:1 isothermal:2 hydrogen:2 occur:4 needs:1 rays:4 goal:2 acts:2 species:7 regions:11 maps:1 constructed:1 oblate:1 goldsmith:6 ryu:1 parameter:2 ensemble:2 profile:5 tension:1 substructure:1 may:9 treatments:1 tied:1 reflect:1 modest:1 produce:2 fd:2 trapping:1 waves:3 horizontal:1 law:1 data:2 parallel:2 monoxide:1 short:1 attempt:1 substructures:1 ss:2 clump:1 description:2 lines:4 parameterized:2 fraction:1 condensations:6 so:7 shade:2 operate:1 order:3 typical:4 wavelengths:1 devriendt:1 least:1 asghar:6 hierarchy:1 indeed:2 displayed:1 murray:2 interpreted:1 stability:1 held:1 thermal:50 paper:5 through:1 motions:3 left:1 argued:1 existence:1 still:1 its:7 tendency:1 observational:3 passot:3 derive:1 outer:2 imf:1 chosen:3 interesting:1 masses:1 c18:1 intermixed:1 fig:17 clusters:1 main:1 might:1 variables:1 ideal:1 non:2 combination:1 press:1 propose:1 outlined:2 evolution:5 b2:5 coolants:2 effects:1 they:9 half:1 now:1 heyvaerts:1 densities:3 easily:2 vturb:4 hereafter:1 alez:1 always:1 university:3 2z:1 applied:1 tielens:1 coagulation:1 mode:3 reasonable:1 instabilities:2 instability:44 difficult:1 side:1 inutsuka:3 mean:1 en:1 λc1:1 significantly:2 formulate:2 λc2:1 there:7 energy:5 idea:1 used:8 constitute:1 literature:1 expect:1 ez:2 wavelength:4 approximated:1 transitions:3 eq:2 out:2 category:1 deals:1 shown:2 solved:1 2πgσ:5 since:5 research:2 particles:2 collisions:2 investigation:3 induced:1 hcn:1 hco:2 shows:3 plotting:1 arizona:1 linear:5 mechanisms:2 differ:1 standard:8 necessarily:1 formation:9 term:1 put:1 estimate:1 generate:1 log:11 diagram:2 hily:1 derivation:1 created:2 geometry:1 widths:1 could:1 transition:1 cosmic:5 times:2 motion:1 length:2 plane:6 ism:2 transfer:1 3km:6 onto:1 purpose:1 origin:1 major:1 already:1 blant:1 maragha:3 number:2 ortho:3 clear:1 improvements:2 adopted:3 directly:2 compensated:1 thick:1 size:1 given:9 perturbation:2 temperature:11 introduction:1 relations:1 their:2 cooling:32 assumption:2 rates:2 calculations:1 iau:1 molecular:46 structures:2 ranging:1 williams:3 gives:2 collapse:1 para:2 relative:5 exactly:2 contribute:2 accurately:2 transverse:1 technique:1 optical:1 nh3:1 authors:1 natural:1 sign:1 than:4 horvath:1 modes:3 diffusion:4 distance:1 valley:1 andersson:1 intensity:1 1l:1 inversely:4 determined:3 were:1 hollenbach:1 solely:3 questionable:1 motivation:1 fashion:1 lightly:1 rewrite:1 mohsen:1 dynamically:1 curves:2 dash:3 headings:1 des:1 perault:2 seen:2 slab:40 clearly:1 gathering:1 relatively:2 acceleration:1 strength:2 triggered:1 zero:2 depending:1 self:15 gravity:2 mechanism:3 coolant:3 sciences:1 fitting:1 maintain:1 take:1 interior:1 negligible:2 coincide:1 play:1 towards:1 beyond:1 trace:1 probed:1 molecule:3 phases:3 depths:1 complexes:1 significant:3 phase:4 falle:2 analytically:1 4πgρ:1 sub:2 volume:1 vapor:1 kg:8 koyama:3 calculated:1 ensues:1 flow:1 drive:1 km:5 inoue:2 construction:1 electrons:1 kt:1 velocity:17 usual:1 physics:2 section:2 respect:2 magnetohydrostatic:4 selection:1 apj:18 show:2 isentropic:8 supported:2 friction:2 purely:1 relation:1 solutions:3 carefully:1 substituting:2 rough:1 uniform:2 fine:1 find:7 giant:1 finally:1 based:5 parameters:3 conduction:3 situations:1 explain:1 dynamical:2 distributed:1 state:9 should:3 only:9 going:1 black:2 molecules:1 factor:1 integrate:1 falgarone:3 γcr:6 local:1 g01:12 merged:1 equilibrium:18 continuity:1 do:3 loss:1 wide:1 dependent:1 db:1 fluid:6 first:1 petit:1 ionized:6 dz:1 dv:1 dt:9 silk:2 µg:1 dp:2 takahashi:2 processes:3 shu:6 fields:3 arxiv:1 doubled:1 summary:2 twice:1 investigate:2 federman:2 contain:1 including:2 gravitational:2 forˆets:1 set:1 statistical:3 our:3 turbulent:5 observed:3 mentioned:2 see:4 individual:1 lesch:1 pineau:1 precursors:1 contour:1 subject:1 surfaces:1 instance:1 bifurcate:1 gravitation:2 review:2 importance:1 enough:1 various:3 between:6 loewenstein:2 reading:1 conditions:2 available:1 variability:1 comparable:1 terms:1 vertical:1 initially:2 interfaces:2 points:2 boss:1 le:1 analyzed:2 boiss:4 suggested:2 ranges:1 triggers:1 many:4 taking:1 uncertainty:1 heating:25 against:1 fluctuation:1 energies:1 merging:1 grain:1 context:1 contribution:2 argue:1 expression:1 finds:1 detailed:1 ch:4 co:4 cn:3 simple:1 ca:1 dimension:1 steele:2 isobaric:27 walder:1 dimensional:3 dot:1 carbon:3 cs:2 moreover:2 runaway:1 considering:6 accurate:1 most:1 described:3 publishing:1 thermodynamics:1 simplification:1 radiative:2 due:4 been:6 pc:6 magnetized:6 much:1 slowly:1 treat:1 interest:1 basic:2 ph:1 universal:1 choose:1 sanders:2 graphical:1 arises:1 corresponding:1 300m:2 quantities:1 formed:2 gas:19 ray:1 gazol:1 pringle:2 representative:1 systematic:1 general:1 present:2 sound:1 p0:2 appreciate:1 margulis:1 grains:2 frozen:1 bania:1 straighten:1 value:6 alter:1 will:2 while:3 slh:6 irrespective:1 balance:2 depleted:1 studied:2 vd:5 approximate:1 vol:1 prolate:1 ir:1 thus:4 surprisingly:1 surface:3 according:1 ii:1 characterize:1 allen:1 ib:2 acknowledgments:1 fulfilled:2 different:7 kwan:4 sensitive:1 apparently:1 make:1 welty:1 same:2 varies:1 shorter:1 another:1 complex:1 contents:1 schematic:1 leep:1 dimensionless:3 several:2 pan:3 higher:2 development:1 calculation:3 investigated:6 numerical:1 slyz:1 effect:6 flows:1 hand:2 ion:5 levels:1 introduce:3 dust:3 interested:2 recent:1 audit:2 weakly:3 lucas:2 scenario:2 largely:1 onedimensional:1 polytropic:1 well:3 roughly:1 analysis:4 without:3 solve:2 components:1 position:1 model:2 vazquez:2 parametric:2 lin:2 polynomial:1 charged:3 spherical:1 proposed:2 being:1 nd:1 multiplied:1 obtain:3 competitive:1 mid:1 sources:1 identify:1 atomic:1 turbulence:1 reviewer:1 gry:1 speed:1 previous:1 mckee:1 vd2:1 kluwer:1 density:29 absorption:2 except:1 evidences:1 nt:1 valid:3 easy:1 input:1 intersection:1 plasma:3 transformation:1 momentum:1 generalized:2 stiele:2 aspects:1 depends:1 represents:3 thermalized:1 jeans:3 possible:2 allocates:1 makes:1 average:1 using:1 variants:1 accepted:1 8πg:1 generated:1 insert:1 necessary:3 particle:1 sizes:1 follows:6 mhd:1 flux:1 unstable:5 patrick:1 whittet:2 deviation:1 because:10 dordrecht:1 often:1 smoothly:1 blending:1 some:6 choosing:1 understood:1 growth:1 revisit:1 sight:2 table:6 duration:1 neufeld:2 scale:9 dense:1 lubow:1 integration:1 per:6 depletion:3 critical:4 unit:3 assuming:2 fragments:1 cnm:1 liszt:2 assembly:1 2b:5 reaching:1 reach:1 equivalent:1 perpendicular:2 expansion:1 γad:17 pressure:9 symp:1 although:3 found:2 comparison:3 about:1 central:2 carried:1 oh:1 column:3 discussed:3 dependence:6 o:4 langer:2 roueff:1 range:4 a2:5 obeys:1 neighbor:1 rollinde:3 equally:1 own:1 presence:1 h2:12 into:5 within:2 numerically:3 interstellar:3 down:1 appropriate:1 references:1 approximately:4 proportional:4 marscher:4 uncertainties:1 van:1 compression:2 comparing:1 assumed:1 hartquist:2 initial:12 u1:3 spiral:1 stark:1 u2:3 width:1 conservation:1 low:5 way:7 ed:3 astrophysics:4 melnick:1 analyze:2 was:6 naturally:1 function:21 fragmented:3 medium:2 complete:1 form:10 forming:2 differences:1 but:6 wnm:1 astro:1 neutral:9 magnitude:3 related:1 atom:1 mnras:5 isotopic:1 line:4 he:1 fragmentation:2 compute:1 gravitating:11 2πg:4 hartmann:1 characteristic:1 inside:1 up:2 us:1 considered:5 tucson:1 books:1 how:1 continuously:1 fluctuations:3 distribution:3 similar:1 display:2 regimes:3 strongly:1 ac:1 constant:6 moore:3 puget:1 defined:1 steady:3 abstract:1 describe:2 condition:5 direction:1 water:1 ap:2 au:11 planets:1 simulations:1 gradients:1 formalism:2 russel:1 gonz:1 physical:2 functions:2 compared:3 eventual:1 variety:2 when:4 detail:1 reality:1 field:15 other:4 role:2 spatial:2 department:1 hydrodynamical:1 dishoeck:1 conclusion:2 optically:1 picture:1 briefly:1 elements:1 star:4 models:1 drift:24 variation:1 emission:1 drag:3 important:4 heitsch:3 dissipation:2 astronomy:2 probes:1 structure:7 nn0:1 condensation:3 regime:1 dω:3 assume:1 typically:1 required:1 curve:4 dρ:2 gradient:7 mass:5 lying:1 time:11 n0:23 cores:3 gammie:2 requires:2 compromised:1
0705.0364.txt |@word represent:1 interspecies:1 consider:8 illustrates:1 rev:35 asymm:2 separates:1 bandgap:7 splitting:3 leads:2 ghrist:1 mild:1 computation:1 perturbations:2 expressions:2 centers:1 localized:1 aligned:7 referring:1 collisions:1 shrinkage:1 subjected:1 ıa:1 quasi:10 filled:1 present:7 th:1 stable:68 tg:1 include:1 norm:10 trippenbach:1 case:28 belonging:2 supported:1 amplitudes:2 g2:13 g1:14 very:7 rise:7 results:13 porto:1 figs:8 herrero:1 refractive:4 resonant:1 experimentally:2 difference:3 matrices:1 condition:4 look:1 four:1 school:1 squares:1 presented:8 did:2 ref:6 solution:10 sipe:1 large:2 discrete:2 defocusing:1 elsewhere:1 progress:1 angelis:1 dealt:1 small:2 eigenvalues:4 refer:2 optics:4 linearizing:1 relative:1 concluded:1 upper:1 strongly:1 smaller:1 tel:2 zi:1 direct:5 sign:2 approximation:2 across:1 zero:2 profiles:7 concludes:1 growing:2 further:4 bandgaps:6 odd:7 rrr:7 yang:2 spectral:2 index:4 what:1 nonlinear:18 plays:1 trapping:1 rate:2 section:10 labeled:1 reminiscent:1 carr:1 axial:2 version:2 currently:1 above:13 destroyed:1 waveguide:1 filled:3 3d:1 coefficient:8 troyer:1 full:6 frohlich:1 ibid:17 becs:2 presence:2 never:2 component:16 khaykovich:1 here:7 atoms:6 reported:5 explore:2 andrews:1 pancake:1 strecker:1 represented:1 consideration:1 κv:1 strong:11 equations:14 stenger:1 change:2 obtained:1 great:1 arrive:2 antisymmetric:63 weinstein:2 shift:2 study:3 studied:9 allows:1 approaches:1 reports:2 leaving:1 recently:2 periodic:7 kolokolov:2 action:3 resonance:1 shaded:3 makes:1 numerical:6 composed:1 emerge:3 followed:1 stenholm:1 elaborated:1 castin:1 vii:2 kevrekidis:3 marked:1 scaled:1 weaker:1 decrease:1 issue:1 condensates:3 apply:1 glance:1 total:5 linearly:10 wang:1 use:2 done:1 takes:3 waveguides:5 commun:1 remains:1 contains:1 negative:1 next:1 proukakis:1 approach:2 therefore:4 taken:2 themselves:3 rearranging:1 type:7 theoretical:1 subcritical:1 more:4 separated:2 flat:1 israel:2 formally:2 oberthaler:3 comparison:2 towers:1 becomes:5 ballagh:1 under:3 mismatch:16 odinger:1 everywhere:1 normalized:4 particular:11 known:1 central:1 cases:8 iv:2 iii:2 me:4 states:15 works:1 tunnel:1 science:2 equation:6 work:7 modified:1 remain:2 values:8 burnett:1 following:1 making:2 nlin:1 spontaneous:8 example:6 decoupled:3 dn:1 bistability:5 dual:9 figure:6 give:4 hydrodynamic:1 organized:1 treutlein:1 topic:2 effectively:3 coullet:1 numbers:1 degenerate:1 sense:1 dominant:2 species:8 simple:1 ratio:7 respective:4 frantzeskakis:2 end:3 turn:1 rather:4 breaking:19 feature:4 occur:1 chemical:4 how:1 criterion:5 adjacent:1 opt:15 instead:1 ordinary:2 absolute:1 parameter:1 divides:1 de:2 minguzzi:2 description:1 modulation:4 demonstrates:6 garc:1 spot:1 dx2:1 diagram:1 brazhnyi:1 plane:2 demonstrating:1 faculty:1 mak:2 wave:6 parallel:8 types:4 curve:2 kurn:1 realized:1 introduced:2 branches:9 dynamical:1 imply:1 whenever:4 light:1 kraenkel:1 partly:1 lines:1 correspond:1 carusotto:1 alias:3 switch:2 so:1 abdullaev:2 fundamental:14 decreasing:1 uˆ0:3 g12:17 typical:8 displays:1 ding:1 albiez:1 words:1 indeed:2 over:1 summarized:2 displayed:9 soc:4 interpreted:2 stability:27 stamper:1 experiments:2 including:4 signs:4 mentioned:4 existence:4 its:12 before:5 regions:3 located:1 temporal:1 lm:1 feldmeier:1 li:2 aviv:2 attraction:34 absence:1 systems:25 arrange:1 definitely:1 deformation:2 split:1 versus:6 closure:1 them:10 interdisciplinary:1 entire:2 outlined:1 mixtures:1 qs:24 investigated:2 flipping:3 band:9 walls:2 repulsive:14 effects:2 they:21 focus:1 breathers:2 hall:2 yv:1 represents:2 term:1 several:2 capuzzi:1 stabilize:1 always:7 university:1 cell:1 2x:9 identified:1 sufficiently:1 quintic:1 trap:12 2b:9 each:6 crossing:1 found:20 beneath:2 decouple:1 mean:2 different:1 morsch:1 bifurcation:51 transform:3 evolve:2 energy:1 try:1 reduce:1 related:3 gaps:6 separating:5 our:3 beyond:3 nonlinearities:3 out:5 ketterle:1 emerges:1 shown:19 jackson:1 schmelcher:1 rr:35 solved:3 quantify:1 savage:1 since:1 interference:1 increase:4 replacing:1 bragg:8 europhys:1 dominated:3 ra:10 rb:2 cooper:1 excellence:1 newly:1 induced:7 supports:2 occurs:4 math:2 shows:3 foundation:1 fiber:1 turning:1 linear:28 interactions:2 easily:1 lisak:1 kaup:2 possibility:1 quite:6 completely:7 supercritical:2 formation:2 besides:1 md2:2 marzlin:1 hand:3 e0:2 milburn:1 klitzing:1 pairs:1 interaction:10 entirely:1 created:1 raghavan:1 transition:2 kivshar:5 linearized:2 counterpart:5 manakov:3 length:1 along:2 place:1 wright:1 approaching:1 condensate:2 first:15 origin:1 initial:1 symmetry:19 tiecke:1 variables:1 waves:1 powerful:1 number:4 system:93 obeying:1 ensher:1 simplified:1 long:1 another:1 carry:1 ψxx:2 given:4 perturbation:2 checked:2 similarly:2 introduction:3 gpe:14 eqs:28 twisted:18 1a:19 their:11 1b:13 rates:1 1d:3 realization:1 eur:3 speaking:1 too:16 shifted:1 kamchatnov:1 sengstock:1 grant:1 undergoes:1 trapped:2 asymmetric:94 reversed:1 continuous:2 park:1 17b:1 transverse:6 generate:1 larger:3 optical:11 somewhat:1 norms:4 natural:1 representing:1 than:6 coefficients:1 modes:1 distance:1 aaa:5 holland:1 bec:14 kuklov:1 second:1 ohberg:1 roberts:1 contrary:1 williams:2 amplitude:13 were:19 inouye:1 gives:3 treated:2 result:3 iφt:2 symmetries:1 shrinks:1 sukhorukov:2 kennedy:1 spectrum:15 curves:1 chen:1 alike:1 qualitatively:4 bigelow:1 seen:1 seem:3 border:8 any:3 rocca:1 relatively:4 walser:1 misaligned:2 strength:9 partridge:1 interconversion:2 destabilizing:1 tends:4 self:9 scott:1 note:9 instance:1 potential:11 ostrovskaya:3 online:21 objective:2 coincide:1 tool:1 stringari:1 shenoy:2 even:3 exactly:2 unless:1 2gf:1 opposite:3 satisfy:1 chart:1 falls:1 rearrange:2 complexes:1 walraven:1 connected:1 skinner:1 phase:8 theocharis:1 segment:1 r31:1 counterpropagating:2 stands:1 soliton:49 constructed:2 nonlinearity:8 considered:13 clear:1 sometimes:1 stronger:3 inferred:1 physica:2 breather:2 looked:1 erez:1 proceedings:1 accounted:3 anker:1 exp:2 ankiewicz:1 ky:1 usual:1 fact:4 son:1 nls:4 drastically:1 ruostekoski:1 show:5 past:1 labels:3 dependences:3 discovered:1 focusing:1 solving:1 solutions:24 svistunov:1 fermion:2 substituting:2 asymmetry:6 d2:2 r50:1 impact:1 µm:1 finally:2 based:7 knowledge:1 erec:2 merges:1 state:5 worthy:2 only:8 cubizolles:1 equipped:7 irrelevant:2 integrable:1 pelinovsky:1 boris:1 do:2 mixture:5 normalizations:1 goes:2 notation:1 means:2 beams:1 diamonds:1 dominate:1 stripes:2 bear:1 ones:28 fastest:1 dx:2 despite:1 lattices:13 respectively:24 gen:1 nearly:1 areas:1 prime:1 evolution:3 settings:2 fields:3 arxiv:1 chu:6 summary:1 investigate:1 paper:2 cf:5 predicted:4 double:1 through:3 fixed:3 pertains:2 graf:1 pitaevskii:3 salomon:1 reveals:2 corney:1 set:4 detail:1 exists:1 problem:9 lett:15 maximum:3 observed:5 see:7 changes:3 buryak:1 akhmediev:2 close:5 dµ:1 best:1 points:1 closes:2 bifurcate:7 said:2 vertical:4 µu:1 pattern:1 µv:1 equal:5 µs:2 tend:2 symmetric:77 tantamount:2 enough:4 various:4 inset:1 between:28 marks:1 conditions:1 deforms:1 wide:1 blow:1 notice:1 terms:6 extend:1 nature:2 weak:11 however:7 characteristic:1 selectively:1 demonstrate:3 distinguish:1 bose:3 louis:1 alters:1 suggested:1 both:20 cos:9 panels:3 locatelli:1 region:3 ballpark:1 according:1 display:1 sov:2 propagation:1 figures:2 mildly:1 disappears:1 experimental:1 otherwise:2 aa:46 relevant:1 destabilized:4 afterwards:2 point:10 appeared:1 continuation:1 asymptotically:2 complies:1 period:2 dimensional:6 destabilizes:1 anti:9 giovanazzi:1 κu:1 cr:1 nicola:1 actually:1 lithium:1 ps:1 mathieu:2 jetp:1 cornish:1 eberly:1 continuations:1 addition:3 claussen:1 three:2 iψt:2 smerzi:3 int:1 belongs:1 growth:3 donley:1 interest:1 basic:2 expected:1 featuring:1 empty:2 fig:68 direction:3 lived:1 corresponding:11 am:4 sufficient:1 gas:2 gap:74 coherent:1 confinement:1 spie:1 lewenstein:1 spin:7 former:3 those:2 bifurcations:12 applied:2 multi:1 laser:2 splits:4 unlike:3 pacs:1 solid:1 originate:1 engineering:2 value:8 transformation:3 will:7 while:18 replaced:1 behavior:4 cattani:1 situation:8 tunneling:4 pertain:1 identical:1 planar:6 compliance:1 attains:1 coupled:24 vol:1 vi:2 refs:4 vk:5 thus:5 site:2 off:1 ii:2 coupler:1 itself:1 im:3 la:1 triple:2 electr:1 property:1 conserve:1 examine:1 binary:7 different:8 verified:1 qas:10 fibers:1 lengths:1 suggest:1 make:1 coexisting:1 eigenvalue:9 indistinguishable:1 same:12 clearly:1 shifts:1 complex:3 quant:1 arguments:1 pauli:1 largest:3 units:4 finite:9 grows:1 higher:1 independent:1 used:1 insets:3 peaks:4 singlecomponent:1 cubic:1 baizakov:2 cigar:1 effect:2 counterparts:8 displace:1 depict:1 impede:1 aceves:1 potentials:2 infinite:23 champneys:1 yuan:1 tomio:1 prescribed:1 lower:3 residing:1 schr:1 traps:6 acknowledgement:1 studies:1 depending:1 well:10 center:1 analysis:7 patterns:1 observations:1 without:8 feshbach:1 does:3 components:9 dashed:3 coordinate:3 model:40 salasnich:4 latter:10 mismatched:16 less:1 being:4 generally:3 accurate:2 photonic:1 reviewed:1 infeld:1 aschbacher:1 shape:1 underlying:3 identify:3 atomic:2 using:1 localize:1 giorgini:1 scattering:2 move:1 emerging:1 conjugates:1 tight:1 cornell:4 regarded:1 scales:1 character:5 cavalcanti:1 confirmed:1 signals:1 lattice:23 setting:1 extends:3 attractive:15 eiermann:1 role:1 ferrari:1 bifurcating:8 designate:1 real:4 igf:1 explained:1 around:1 disappearance:1 bif:6 bands:4 showing:1 spatial:5 implications:1 possible:3 admitting:1 corresponds:1 finding:1 increases:1 vandenberghe:1 pu:1 mol:7 confined:1 immediately:1 part:4 stephanov:1 color:21 mod:4 meaning:1 necessary:3 adams:1 semi:23 shaped:2 systematically:1 follows:3 reduces:2 strictly:1 extremely:1 zoom:1 translates:1 shapes:3 roth:1 arthur:1 continue:1 unstable:36 either:14 vakhitov:2 become:1 mode:1 inter:2 stationary:4 reduced:3 gammal:1 parity:1 rubidium:1 methods:1 some:3 competition:1 ertmer:1 understood:1 ols:19 examples:3 loaded:1 computers:1 michinel:1 adhikari:2 myatt:1 matthews:1 nonzero:1 gross:2 gradually:1 describing:1 illustrated:2 merge:2 electromagnetic:3 filling:1 per:5 whole:2 when:8 critical:3 κcr:3 assuming:4 bifurcates:4 fantoni:2 viz:1 closely:1 demonstrated:1 2a:10 core:23 truscott:1 indicated:1 equivalent:1 radial:1 bi:2 symm:2 burt:1 although:2 instability:6 generic:1 imaginary:1 stay:1 properties:2 von:1 panel:2 sub:2 thomas:1 ol:20 actual:1 would:2 extension:1 extending:1 coexist:1 gratings:9 discussed:1 dependence:3 o:1 simulation:1 bourdel:1 range:1 repulsion:26 shlyapnikov:1 coexists:1 mixed:3 referred:1 slightly:2 bloch:10 miesner:1 peak:1 perturbed:1 trombettoni:1 φxx:2 undergo:1 into:26 numerically:2 bound:14 due:2 pair:1 appropriate:1 because:1 been:8 determine:1 einstein:3 operator:2 iµt:4 theoretically:2 kruse:1 additional:1 vˆ:4 area:1 assumed:1 support:2 there:2 u0:5 u3:1 u2:1 wieman:3 anderson:1 quadratic:1 way:1 salerno:4 forward:1 malomed:19 analyze:1 was:26 naturally:3 function:2 konotop:5 medium:1 complete:1 form:7 peng:3 reatto:3 becoming:1 regard:2 triangular:1 but:14 juxtaposed:1 collected:1 recoil:1 atom:4 r53:1 line:3 true:1 prokof:1 phillips:1 made:2 surprising:1 embedded:7 nu:20 inside:3 up:6 hulet:1 crystal:1 below:12 frequency:1 limit:2 diagrams:1 continuously:1 2πx:1 distribution:1 define:2 similar:21 called:2 originating:2 khz:1 kh:1 constant:2 directly:1 pin:1 defined:5 gpes:3 influence:1 generating:1 deep:1 general:1 schnee:1 quantum:1 single:20 tosi:2 exist:6 predictions:1 simulations:5 article:1 families:33 intra:2 physical:4 dalfovo:1 functions:6 ev:1 nm:1 no:5 amounts:1 eq:7 subgap:9 rhombuses:1 field:3 fedele:1 other:11 electrical:1 branch:32 solitons:167 department:1 mathematics:1 really:1 shrink:1 nv:19 conclusion:2 conclude:1 picture:2 stat:1 may:18 separate:1 models:6 resembles:1 problems:2 variation:1 includes:2 generated:4 allowing:1 additionally:3 iω:1 tackle:1 fermi:1 developed:1 structure:1 anderlini:1 schreck:1 implies:1 coupling:25 pseudo:9 persistent:3 jenkins:1 depth:2 observe:1 mass:1 time:3 cores:19 meystre:1 backward:1 having:1 provided:2 parola:3
0705.0365.txt |@word monte:5 extrapolated:1 caused:1 magnetic:27 lack:1 results:8 illustrated:1 per:1 correa:2 phonon:2 hold:1 depend:1 calculate:2 alamos:3 young:8 ıa:1 finally:1 monotonically:1 tanaka:2 antiferromagnetically:2 sound:1 supported:1 straightforward:2 antiferromagnetism:1 very:2 conditions:1 wave:4 kimura:1 resonant:4 experimentally:3 difference:2 condition:1 treating:1 hamiltonian:3 anisotropy:2 magnet:6 vector:3 c33:2 small:3 fl:1 dimer:1 smaller:5 force:1 haas:1 measurable:2 past:1 zero:4 value:6 chen:1 further:2 qmc:4 chem:1 carlo:5 theory:2 blue:2 interatomic:1 sum:1 axes:1 cell:2 experiment:2 above:1 new:3 net:1 increasing:1 method:2 supporting:1 condensed:1 exchange:7 respectively:1 component:3 orbitals:1 atoms:3 reported:2 tracks:1 path:1 along:16 strong:2 change:7 instituto:1 hansen:1 institute:1 shift:1 leaves:1 larger:1 typically:1 hydrostatic:1 amount:1 resulting:3 interac:1 poisson:2 published:1 proportionality:1 changes:1 lowers:1 varshni:1 via:4 nearest:2 inducing:1 visscher:1 total:4 unit:3 kawashima:2 tn:1 use:2 would:2 remains:1 suppl:1 next:1 cottam:1 therefore:2 distortions:2 taken:2 means:1 until:1 more:3 aronson:1 becomes:2 under:1 eν:2 interaction:6 normalized:1 excellent:1 known:1 aligned:1 c44:1 states:1 room:3 tokyo:1 equation:1 work:3 oscillator:1 mk:7 values:2 temperatures:1 equilibrium:1 stimulating:1 numbers:1 ions:3 lacerda:2 predict:1 neglected:3 desenvolvimento:1 sample:2 indicates:1 assumptions:1 performed:2 degenerate:1 sharp:1 sawai:1 dj:1 dennis:1 dxc:5 occur:1 axis:35 afm:10 magnetostriction:25 busse:1 bonds:3 feature:1 chemical:1 varies:2 contrasts:2 adjacent:3 flow:1 parameter:10 mat:1 may:1 wiley:1 lab:1 diagram:3 plane:3 law:1 data:8 parallel:1 sz:7 diagonal:1 effective:1 sr:20 lines:2 yielding:3 trevor:1 negligible:1 correlation:8 taking:1 hellman:1 first:2 order:11 couplings:1 six:1 tallahassee:2 zvyagin:1 over:1 vary:1 distortion:2 thermal:1 experiments:1 through:1 japan:1 its:2 before:1 massey:1 gµb:1 lc:2 fit:1 la:2 susceptible:1 exhibits:2 estimating:1 djc:5 fig:12 xc:21 argentina:1 freeman:1 acknowledgments:1 good:2 affected:1 greater:1 thereby:2 integral:1 effects:2 compound:3 oxford:1 tetragonal:9 inelastic:1 structural:1 february:1 always:1 university:3 2x:1 identified:1 magnitude:5 reasonable:1 each:1 found:1 higher:1 betts:1 el:1 comisi:1 another:1 fisk:2 energy:5 idea:1 ec:10 investigated:2 magnets:1 measure:3 quantum:10 laboratory:3 extract:3 nonmonotonic:3 large:1 shown:9 electronic:1 oklahoma:1 since:10 rev:8 increase:1 attracted:1 extrapolate:1 mediated:1 induced:2 ref:1 occurs:1 red:2 shows:2 linear:4 interactions:5 cheong:2 fisica:1 possibility:1 quite:2 dependencies:2 included:1 york:1 hc2:12 hc1:16 organic:3 created:3 determining:3 could:2 transition:1 florida:2 creates:2 turn:1 length:3 zapf:3 unknown:1 onto:1 crystallographic:1 major:1 xo:4 symmetry:3 omitted:1 number:2 gpa:2 directly:2 clarity:2 open:1 wosnitza:1 given:1 temperature:9 likely:2 become:1 leading:2 eqs:1 system:7 response:4 their:1 appl:1 1d:1 calculations:2 percentage:1 molecular:2 ambiguous:1 explanation:1 stress:5 required:1 reflecting:1 nh2:6 than:4 observed:1 determines:1 dtn:12 bec:3 depends:3 magnetocaloric:1 matter:1 determined:5 str:1 were:5 tion:1 steep:1 raman:1 sao:1 san:1 cryostat:1 attenuation:1 4sc:6 tozer:1 distorted:1 allen:1 confirms:1 any:1 sat:1 eq:3 presents:1 able:2 chiba:1 instance:1 high:6 take:1 forces:2 modulus:8 2c13:1 heisenberg:1 electric:1 probed:1 sherman:1 molecule:2 centro:1 significant:1 phase:4 measured:9 class:1 deviations:1 acknowledges:1 subtracted:1 neighboring:1 calculated:1 broadened:1 metal:1 physica:1 doe:1 takeuchi:1 feynman:1 mechanical:2 tlcucl3:1 physics:2 fact:1 laws:1 thomas:1 currently:1 show:1 text:1 probe:1 wins:1 minimizing:1 keywords:1 substituting:1 magnons:1 find:1 ground:2 merlin:1 ratio:1 knowledge:2 parameters:4 explain:1 written:1 conselho:1 being:2 only:4 convoluted:1 molecules:2 factor:1 constant:2 nhmfl:2 nj:1 cube:1 dominant:2 sengupta:1 dependent:1 de:5 uniaxial:3 leisure:1 nearly:1 closely:1 competing:1 report:1 lei:1 dr:1 bˆ:1 bar:1 fields:7 arxiv:1 summary:1 jaime:4 characteristic:1 valid:1 moduli:4 computed:1 our:6 national:4 up:1 relative:6 intensity:1 bare:1 result:1 discussions:1 subject:1 brazil:2 exponent:1 compounds:1 phonons:1 away:1 halides:1 sites:2 boundaries:1 state:10 various:1 between:21 approach:1 terms:3 creating:1 spacing:1 focus:1 however:5 jr:2 disallow:1 hypothesis:1 here:3 probing:1 bose:2 ja:4 jc:13 suggested:1 both:1 many:1 region:2 uncertainty:1 equal:1 zeeman:1 sensitive:1 became:1 dated:1 filho:4 exceeds:1 contribution:2 mean:1 experimental:4 stretches:1 relevant:1 co:2 cl:13 simple:1 magnetoelastic:1 decreases:1 respect:1 crystalline:1 cu:1 described:2 aˆ:1 addition:1 create:1 due:2 been:8 lopez:1 much:3 combined:1 interest:1 expected:2 tering:1 lett:3 shoulders:1 c23:1 quantities:1 mce:2 kashiwa:1 gap:1 kenzelmann:1 determination:1 external:1 c2:5 c1:4 spin:17 stillwater:1 present:2 applied:6 novel:1 ǫe:2 pacs:1 solid:3 straight:1 ǫm:4 remaining:1 will:1 cnpq:1 near:2 behavior:3 error:2 investigating:1 tsukamoto:2 procedure:1 vectors:1 orientation:1 coupled:1 thus:10 strain:2 cant:2 vs:3 cond:1 weakest:1 orbital:1 overlayed:1 combination:1 lengths:4 suggest:1 millis:1 paulo:1 niedermayer:1 universality:1 ray:3 neutron:4 difficult:1 independent:1 used:2 effect:4 ion:3 insulating:1 moving:1 resonance:1 lower:3 weakly:2 c66:1 studies:2 well:1 roughly:2 analysis:1 solids:1 modelled:2 comes:1 components:1 model:6 magnon:2 usual:1 distances:1 magnetization:5 cuprates:1 less:1 increasingly:1 obtain:3 lemmens:1 cˆ:1 atomic:1 harrison:3 scattering:3 previous:2 now:4 density:1 bell:1 fitting:2 nacional:2 lattice:19 belongs:1 extends:1 attractive:1 easy:1 c12:2 c11:2 excited:1 egan:1 migliori:3 increased:1 showing:1 papers:1 absence:2 term:3 early:1 vibrations:1 know:1 canted:2 confined:1 using:6 orenstein:1 energ:1 necessary:1 like:1 shaped:1 superexchange:6 specific:2 eel:2 integrals:1 softness:1 inter:1 soft:1 spins:6 therein:1 omico:1 because:6 omica:1 palm:1 table:2 gradually:1 cooper:1 esr:2 resonances:5 measurements:8 thank:1 overlap:4 critical:1 prog:1 chains:3 prob:1 demonstrated:1 lowest:1 power:2 radial:2 agreement:2 expansion:1 pressure:4 step:1 br:1 substitution:1 rus:1 properties:1 comparison:2 about:1 works:1 ok:1 ferromagnetic:3 based:1 dependence:14 o:2 bariloche:2 neighbor:2 srz:1 bond:7 jν:1 soc:1 sarrao:2 previously:2 instruments:1 into:1 within:3 splitting:1 nsf:1 down:2 ultrasound:4 right:1 references:1 castro:1 determine:3 einstein:3 proportional:3 reducing:2 theoretically:1 vanishingly:1 elastic:6 assumed:2 support:1 there:1 question:1 dispersion:1 los:3 conservation:1 bosons:1 was:1 treat:1 function:13 speculate:1 form:1 murphy:1 but:1 volume:1 heat:2 link:2 hm:4 line:2 longer:1 oosawa:1 consist:1 whether:1 antiferromagnetic:2 maximum:1 quantitatively:1 theoretical:2 crystal:6 below:1 spectroscopy:4 demonstrate:1 similar:1 batista:4 strongly:2 khz:1 saturate:1 ordered:1 diffraction:3 combining:1 single:3 kcucl3:1 simulations:4 crystals:1 ing:1 universidade:1 ni:21 functions:2 compared:2 e33:1 nm:2 nn:10 no:1 dashed:1 whereas:1 when:3 detail:1 field:22 other:3 spatial:8 test:1 ny:1 picture:2 francisco:1 kindo:1 calculating:2 a2:4 peak:1 variable:3 structure:2 condensation:2 coupling:9 assume:2 expands:1 lanl:2 curve:1 together:2 inset:3 quantity:2 resolution:1 once:1
0705.0366.txt |@word now:1 gr:1 proposed:1 rayleigh:4 crucial:2 over:6 global:1 scattered:1 results:3 notations:1 implying:1 uller:1 cold:2 still:1 contributions:1 δta:3 ground:2 diffusons:1 eaire:1 difference:1 number:1 just:1 paris:1 explain:1 δtab:3 actually:1 sharing:1 only:6 explicitly:1 those:1 indeed:1 kastler:1 grow:1 into:1 overcome:1 ta:2 yi:2 interference:1 yj:1 amplitudes:1 rev:3 outside:1 very:1 undergone:1 possible:2 backscattering:1 mention:1 they:2 during:2 assaf:2 hall:1 condition:2 like:2 leads:2 equality:1 incoherent:1 transmission:2 positions:1 arxiv:1 large:2 inequality:3 either:1 follows:2 become:1 universit:1 fixed:1 disorder:1 inside:1 degeneracy:4 scatterers:2 square:5 transforming:1 mesoscopic:2 cond:1 correlations:4 pulse:2 physikalisches:1 intensity:7 obtains:1 our:1 transitions:2 eq:9 situation:1 even:1 what:1 total:1 pinpoint:1 lead:1 visiting:1 function:1 diffusing:1 since:2 please:1 contributing:1 contradiction:1 state:2 performs:1 between:1 whereas:1 intensities:1 order:1 ref:1 occurs:1 coefficient:2 perfect:1 particular:1 full:1 complex:1 written:1 each:2 agreement:2 atoms:6 completely:1 mes:1 found:1 alone:1 path:2 along:5 configuration:3 implicit:1 obtained:1 both:1 reverse:1 always:1 transition:3 zeeman:1 fulfilled:1 atom:4 resulting:1 exponentially:1 contribution:1 undergo:2 photons:1 experimental:3 first:1 comment:1 among:1 xi:3 point:2 schwartz:2 explained:2 corresponds:2 system:1 expect:1 smaller:1 precisely:1 bayreuth:2 angular:1 cloud:1 size:2 given:1 institut:2 additional:1 would:1 prove:1 probabilities:1 leading:1 pairing:1 add:1 least:1 appears:1 their:2 cauchy:2 observations:1 second:1 scheme:1 final:1 more:1 raman:2 arises:2 enough:1 initial:1 factor:1 photon:5 but:1 labeyrie:1 coherent:1 coherently:1 authors:5 sublevels:1 than:1 present:1 must:3 case:4 states:5 applying:1 exponential:1 equation:2 averaged:2 see:1 will:1 contrary:1 behavior:1 error:1 following:1 fluctuations:2 eur:1 calculated:1 enhancement:1 claim:1 ab:3 diffuson:1 ai:6 ak:1 aj:4 share:1 non:1 lin:1 sample:1 reads:3 proves:1 akkermans:2 o:2 tab:2 conjugate:1 unphysical:1 dominant:1 any:1 physical:1 ijkl:1 paths:9 different:3 degenerate:1 latter:2 means:2 when:2 lett:3 same:6 note:1 internal:10 emphasize:1 becomes:1 modulus:2 nice:1 de:1 contribute:2 mat:1 calculating:1 may:1 laboratoire:1 preceding:3 effect:1 brossel:1 france:2 wrong:1 germany:1 letter:4 pair:1 law:1 why:2 recent:1 lower:2 implies:1 light:1 average:3 correspond:1 obviously:1 points:1 eichmann:1 correlation:6 left:1 sum:8 fact:1 usual:1
0705.0367.txt |@word monte:1 consider:2 caused:3 zmin:1 luminosities:1 results:16 four:3 follow:1 ror:1 schlegel:2 devoted:1 hold:1 depend:1 paris:2 show:2 environment:1 finally:2 critical:2 present:1 include:1 lack:1 broadly:1 very:1 void:3 tantalizing:1 should:2 affect:4 lpnhe:1 difference:1 exact:1 jha:3 3h4:1 impressive:1 presented:2 cause:1 bright:1 large:3 valle:2 small:1 guy:6 averaged:1 riess:4 estimates:1 empirical:1 evaluated:1 qualitatively:1 estimated:1 carlo:1 λcdm:1 blue:2 what:2 errors:3 current:2 version:6 goes:1 change:3 method:1 contrast:1 coefficient:1 relationships:1 ensure:1 simultaneously:1 respectively:1 error:1 component:1 here:3 selective:1 excess:16 ratio:1 along:2 quite:3 interpret:1 extreme:3 cardelli:2 convert:3 technical:1 study:1 studied:1 ple:1 suggests:2 amount:2 survey:4 within:3 milky:7 usually:2 weakens:1 studies:3 departures:1 via:2 useful:1 corr:2 requiring:1 vii:1 apj:12 refitting:1 trained:1 total:1 tools:1 use:4 figure:7 usa:3 prove:1 hudson:2 france:1 comparing:1 going:2 therefore:7 conley:4 panagia:2 themselves:1 type:3 marginally:1 more:11 separated:1 flat:1 hubble:28 lightcurve:2 tested:1 carrying:1 normalized:1 known:1 cases:2 given:2 effort:1 must:3 md:2 account:2 mb:5 science:1 challenge:1 package:1 mw:1 bias:5 values:7 following:2 making:1 scatter:2 wang:4 cosmological:1 bubble:26 process:3 pieces:1 sample:16 assumptions:1 something:1 magnitudes:3 exclude:1 simple:2 absolute:1 requirements:1 goal:1 rather:1 discussion:1 regions:2 how:6 significance:1 instead:2 parameter:6 inappropriate:1 sne:24 galactic:1 our:7 earlier:1 derived:2 constraint:1 reflect:1 produce:1 mag:3 fits:10 law:5 data:15 vasey:3 salt2:9 natural:1 effective:2 light:19 snls:6 departure:1 parameterized:3 cosmology:6 provide:2 so:4 sn:42 menlo:1 abscissas:1 parameterizes:1 order:4 talk:1 wavelengths:1 interpretation:1 help:1 p99:2 developed:2 thresholds:1 vary:2 interpreted:3 cuts:1 differs:2 existence:1 its:1 galaxy:1 style:1 derive:1 thank:1 fit:12 maps:1 qold:1 interesting:1 redshift:4 actually:1 late:8 estimating:1 fig:5 might:5 into:9 non:2 good:3 affected:1 greater:2 combination:1 elliptical:1 introduce:1 scaling:1 band:2 effects:11 they:3 february:2 hereafter:2 zehavi:2 university:3 level:1 possibilities:1 in2p3:1 stockholm:1 each:1 found:6 photometry:1 mean:3 telescope:1 fairly:2 idea:1 related:3 challenges:1 search:1 expect:3 year:1 relates:1 bluer:1 out:5 canada:1 shown:4 3rd:1 space:2 gradient:1 astier:3 since:4 research:1 rb:6 squares:1 issue:2 correct:2 red:1 after:5 turning:1 linear:3 galaxies:3 little:1 possibility:2 standard:2 approaches:2 complicated:4 besides:1 estimate:4 incorporates:1 training:2 determining:1 could:5 days:3 times:2 βe:1 βc:1 corrections:1 first:2 number:1 restrict:1 multiplying:1 least:4 another:1 robust:1 electronic:1 differ:2 long:1 checked:1 indicate:1 introduction:1 top:2 relations:1 their:2 assumption:1 draft:2 observations:1 giovanelli:2 frame:1 fitters:10 gives:3 relationship:7 explanation:2 exactly:1 park:1 accurately:1 task:1 technique:1 part:1 too:2 somewhat:1 manifestation:1 peculiar:1 malmquist:6 toronto:2 relative:2 observatory:1 favors:2 require:5 measured:6 grey:1 submitted:1 preparation:1 determined:2 assume:1 were:1 perrett:1 displays:1 objects:1 lines:2 correction:9 measure:5 curves:2 reassuring:1 mlcs2k2:26 headings:1 host:1 clearly:1 relatively:1 mostly:1 pain:1 latter:2 mechanism:1 note:2 phillips:3 fitting:3 potential:1 absorbed:1 take:3 circles:1 even:4 cnrs:1 beyond:2 allow:2 most:7 jul:1 letter:1 possible:3 intrinsic:9 latex:1 give:6 observation:2 surprising:1 fitter:1 calculated:3 atypical:1 implications:1 km:10 typeset:1 hints:1 artificially:1 narrow:1 velocity:2 salt:19 fact:1 slope:2 selection:3 particularly:1 log10:1 text:2 purely:4 colors:14 minimizing:2 relation:23 inconsistent:1 tempted:1 trivial:1 find:6 implying:1 parameters:8 implementation:1 than:10 brighter:1 only:6 wood:3 formulation:1 local:7 meant:1 do:4 dl:2 incorrect:1 handle:1 distance:5 dependent:3 simplest:1 overall:1 expectation:1 words:1 boils:1 during:1 candles:1 disentangling:1 cleanly:1 resolve:1 m5s:1 luminosity:15 arxiv:2 remove:2 whether:1 predicted:1 fainter:2 excesses:2 fixed:1 black:1 set:1 smooth:1 unpublished:1 testing:1 albeit:1 bounds:1 detection:1 ara:1 depends:1 legacy:1 sec:3 result:4 discussions:1 best:3 subject:1 detect:2 placed:1 incorporating:1 favor:1 outside:1 difficulties:1 various:3 between:11 probably:2 approach:2 across:3 available:1 handful:1 terms:1 sparsely:1 nature:2 supernova:4 restricting:1 however:4 mlcs:1 packages:5 problem:1 both:3 essentially:2 monopole:1 prescription:1 conclusions:1 against:1 sensitive:1 intercept:1 disappears:1 nearby:4 arbitrarily:1 relevant:1 necessary:1 sullivan:1 ca:3 address:1 environments:4 except:2 cz:9 m15:2 bβ:2 wider:1 respect:2 suppressing:1 better:1 unusual:1 strong:1 described:2 tuning:1 three:4 been:4 reduction:1 describes:1 combined:2 basic:1 expected:2 ph:2 obtained:1 arises:1 deeper:1 precision:2 external:1 systematic:1 enforces:1 evidence:10 former:1 those:1 applied:3 look:1 supernovae:3 raw:1 solid:1 harder:1 examine:1 value:27 easier:1 will:7 institute:2 behavior:2 applies:1 balance:2 procedure:1 della:2 would:8 almost:1 vi:1 av:11 cluster:1 vs:1 ia:21 worry:1 different:13 baseline:1 prior:5 perhaps:3 make:1 cross:1 same:7 any:7 epoch:1 uncertainty:1 independent:5 used:12 http:1 again:2 slac:1 disagree:1 effect:5 hand:3 driven:1 constraining:1 kim:2 dust:31 changing:1 opportunity:1 recent:4 weakly:1 sed:1 programs:1 makes:1 modeled:2 well:5 analysis:9 ccm:5 without:3 residuals:3 sets:1 model:8 arising:1 left:3 distances:3 less:1 generally:2 observed:2 obtain:1 rest:1 press:1 shape:14 underlying:2 distant:5 scattering:1 previous:1 sampled:1 preprint:1 density:2 seems:1 prieto:2 color:60 samples:1 refit:1 real:1 around:2 breaks:1 measurement:1 term:2 test:3 increases:1 dimmer:1 know:1 unlikely:1 using:14 correcting:1 imposed:1 like:10 particle:1 sifto:13 follows:1 interestingly:1 continue:1 steps:1 either:2 δh:10 alternatively:1 simply:1 reasonably:1 empirically:2 right:4 some:6 certain:1 sight:1 unless:2 provided:1 extinction:7 medd:1 bottom:2 avoid:1 measurements:3 whole:1 does:8 eliminate:1 assuming:1 demonstrated:3 refer:1 measuring:1 meanings:1 elucidate:1 equivalent:1 aj:2 agreement:4 step:1 reduces:1 although:1 offset:1 analyses:1 emulateapj:1 takes:1 comparison:1 about:1 actual:1 carried:1 hopkins:1 universe:1 based:1 anomalous:1 dependence:3 range:3 plus:1 grouping:1 slightly:2 faint:1 presence:2 h0:1 johns:1 disentangled:1 due:5 down:2 appropriate:2 because:1 references:1 raises:1 determine:1 altavilla:2 technically:1 uncertainties:1 additional:7 assumed:2 support:2 there:3 question:4 approximate:1 specifically:1 much:1 low:7 way:7 astrophysics:2 slopes:1 analyze:1 was:3 function:1 considerably:2 elsewhere:1 adjusting:1 differences:1 conclusively:1 but:11 sophisticated:1 astro:4 draine:2 magnitude:4 larger:2 mnras:2 line:4 removed:1 true:1 considerable:2 framework:1 made:1 applying:1 full:1 default:1 variations:1 maximum:1 considered:2 below:2 converted:1 ωm:2 reflects:1 demonstrate:1 distribution:2 piece:5 similar:11 agree:1 tripp:2 strongly:1 constant:5 flow:1 abstract:1 describe:1 general:1 globally:1 single:3 wavelength:5 work:2 check:1 redder:2 high:3 functions:1 compared:4 kavli:1 no:5 dashed:1 when:2 field:1 other:10 details:1 department:1 really:1 models:1 rv:9 includes:1 meaning:1 important:2 peak:12 astronomy:1 independently:1 longer:1 utoronto:2 required:2 curve:17 covariances:1 portion:6 mass:1 time:13 serious:1 requires:3
0705.0368.txt |@word schlegel:1 unhatted:1 four:1 assembled:1 poorly:1 whose:1 calculate:1 quadruple:22 pastorello:4 void:3 p0:7 handling:1 affect:3 wegner:1 cmb:7 straight:3 pooley:1 10o:1 miller:1 consistent:16 estimates:3 direct:2 empirical:2 approximation:1 likely:7 qualitatively:1 even:6 established:1 errors:47 selected:1 contributed:1 bipolar:4 above:21 new:4 contributes:1 ever:1 simultaneously:1 kowalski:1 never:1 residual:9 here:7 reported:3 cardelli:2 study:19 completely:1 changes:2 attractor:4 prints:4 projection:1 2δm:1 highly:3 total:3 linearly:1 would:3 negative:5 tabulated:2 kinematics:1 m2:2 robertson:1 type:3 brings:1 excellent:2 aligned:2 must:2 room:1 example:6 defer:1 wang:34 give:4 bennett:2 indicates:2 calibration:1 want:2 magnitudes:5 times:2 absolute:5 provide:2 revisit:1 far:3 significance:7 description:1 after:14 diagram:31 wrong:1 law:6 meaningful:1 parallel:1 constants:1 bootstrap:4 davies:1 correlation:10 order:3 decl:1 over:10 vary:2 before:2 fit:30 better:2 harmonics:2 weeks:1 supercluster:4 versus:2 them:2 combination:1 band:5 effects:6 they:4 schommer:2 represents:1 brightness:1 reasonably:1 lauer:2 each:11 side:1 mean:3 inserts:3 1996c:2 1996x:2 rv:5 superscripts:1 particles:3 ra:6 rb:13 linear:14 given:23 free:5 standard:7 ecliptic:1 formation:1 corrects:1 estimate:5 telescopes:5 cosmic:3 days:2 filter:1 sahu:1 unknown:5 corrections:5 primary:2 restrict:2 another:4 thick:1 clarity:1 illustrate:3 top:6 needed:4 listed:1 2003du:3 tool:1 peculiar:49 distance:25 zero:6 project:1 matter:2 enables:1 minus:2 raw:1 seen:4 fitting:7 circles:4 blue:1 shall:1 extending:1 involving:2 phase:2 calculated:2 flow:33 inoue:2 accounted:1 principle:1 parenthesis:1 came:1 reductions:1 probe:4 colors:1 courteau:1 proposed:1 explain:1 do:4 explorations:1 dm:4 krisciunas:5 de:1 dc:4 da:1 watson:1 dq:1 runs:1 heaviside:1 nicely:1 fields:3 reference:5 sensitivity:2 observed:18 result:2 discussions:1 best:9 subject:2 symmetric:3 unable:1 propagated:1 approach:8 terms:5 nature:3 however:10 improve:1 suggested:2 essentially:1 uncertainty:2 against:1 0o:1 haynes:2 perley:1 targeting:1 three:3 been:11 much:2 interest:2 expected:4 dots:2 25o:4 mci:2 quantities:2 coherent:11 spie:1 1991t:1 reddening:5 applied:5 near:1 applies:2 property:1 anchor:1 procedure:1 ir:1 ia:3 confirmed:1 suggest:3 make:4 sollerman:1 potentially:1 several:1 independent:2 hand:3 kim:2 opportunity:1 weakly:1 incapable:1 quantitative:1 anupama:2 left:13 just:1 diameter:1 epochs:1 rotated:3 criterions:1 yet:2 previous:7 jose:1 oliveira:1 hamuy:3 belongs:1 projects:1 clocchiatti:1 homogenizing:1 l87:1 l81:1 bands:2 possible:5 possibly:1 background:1 standardization:3 isotropy:1 2007b:2 schwarz:1 2007a:2 right:13 born:1 bottom:3 microwave:1 korteweg:1 particular:1 minimization:2 arbitrary:1 properties:4 o:8 plus:2 efforts:1 slightly:3 contours:14 functions:3 1990n:2 presence:4 bound:1 often:1 rely:1 support:1 width:1 way:2 astrophysics:3 m1:2 was:4 lowest:2 underestimated:1 form:4 offer:1 differences:5 failure:1 true:1 slope:3 understood:3 inside:3 anen:1 maximum:23 panels:5 b2:7 abstract:1 evidence:1 sometime:1 simulations:2 distributions:3 check:1 triangles:2 physical:6 dotted:9 no:13 whereas:3 generally:2 dekel:4 test:6 picture:1 salzer:1 models:7 preceding:1 variable:1 15o:1 assume:4 together:1 time:4 snia:36 remarkable:3 global:1 leads:1 remarkably:3 certainly:1 uneven:2 zone:3 environment:2 finally:1 compensate:1 marks:2 advantage:1 orthogonal:1 hatted:1 exact:4 jha:25 level:21 did:2 supergalactic:2 upper:8 l91:1 findings:1 riess:15 measurable:1 adds:1 postman:2 axes:4 shares:1 uniform:1 current:5 axial:1 satisfy:1 explosion:1 realizations:1 agreement:6 groups:5 address:1 appears:2 change:1 unidentified:1 noticeable:1 studied:5 usually:1 noticeably:1 studies:15 plotted:5 emerge:1 extra:1 positive:5 predictions:1 criteria:1 theoretical:1 diagrams:5 introducing:1 acceptable:2 apparent:1 visual:1 vmax:5 capturing:1 longitude:1 values:10 following:2 figure:45 significances:1 sample:72 performed:5 allowed:1 distinguishable:1 winter:1 discussion:1 pure:5 optimal:3 parameter:9 map:1 sne:37 information:2 may:22 use:3 explored:2 1993b:2 mag:25 revealed:1 stress:1 natural:1 candles:3 cosmology:7 so:5 sn:22 typical:3 wavelengths:1 indeed:5 perlmutter:7 mainly:1 argues:2 course:1 statistical:6 still:2 observational:2 group:1 curly:1 apex:6 interesting:3 coordinates:5 decreased:1 texas:1 non:3 evolution:1 introduce:5 hamilton:1 now:2 nor:1 term:6 drop:1 siegrist:1 zcmb:6 spectroscopically:1 weighted:6 significantly:13 gaussian:2 ec:6 gaps:1 authenticity:1 approximated:1 shown:33 space:4 furthermore:2 squared:1 suggesting:4 formula:2 squares:1 correct:2 shows:18 complicates:1 possibility:3 quite:2 bumps:2 complicated:1 impose:1 motion:23 plane:4 first:4 origin:1 symmetry:11 seasonality:2 moduli:9 simplified:1 impossible:1 array:1 open:1 angular:3 size:3 little:3 necessarily:1 2001el:2 2004eo:3 indicate:1 realization:2 white:1 structures:2 gives:7 mostly:2 artifact:1 suntzeff:3 than:22 coefficients:14 wide:1 resampled:1 future:5 were:8 correction:21 dash:1 1992a:2 any:4 note:5 phillips:8 potential:3 observationally:1 performance:1 modulus:4 normal:1 decreasing:1 formulae:1 probes:1 latex:1 especially:3 average:10 quantity:2 precise:1 show:31 ground:1 ratio:4 enough:2 only:20 parabolic:1 get:1 nearly:1 secondary:1 reveal:5 reveals:1 relative:2 violates:1 points:10 extragalactic:5 alarming:1 importance:2 behind:1 between:8 across:1 notice:1 vertical:3 analyzes:1 clayton:1 paramter:1 analyzed:3 motivations:1 σi:1 parentheses:1 acquiring:1 many:1 region:1 according:1 nearby:10 color:29 sampling:2 anti:1 constant:9 considering:4 stretch:2 oder:1 absence:2 mark:1 combined:1 hardly:1 fig:20 direction:19 observers:1 dramatic:3 suspected:2 careful:1 those:12 case:4 supernovae:22 aviles:1 cluster:2 bias:2 worry:1 different:26 formulations:1 same:22 dominants:1 decreases:1 week:1 investigated:1 costa:2 random:6 roughly:2 severe:1 without:2 components:7 coordinate:2 model:24 l105:1 justify:1 summer:1 being:5 when:5 rest:2 application:2 photons:1 seems:2 parametrization:1 improvement:3 instrument:1 samples:9 extensive:1 around:16 reddened:2 cf:1 dark:3 using:20 correcting:2 reduces:5 faber:1 either:1 downward:1 reduced:4 satisfactory:1 rms:1 deduce:5 redshifts:14 conventionally:1 stanishev:2 confirm:1 recorded:1 conservative:1 decomposition:1 provides:3 moderate:1 refer:2 reasonable:2 power:2 equivalent:1 broken:1 earlier:4 lucey:3 discussed:1 stand:2 redshift:57 landy:2 references:1 determine:3 area:1 assumed:12 there:10 dispersion:18 low:8 lou:1 bubble:4 assumes:1 complete:1 regard:1 sophisticated:1 mnras:6 woudt:1 applying:2 robustness:1 quantitatively:2 ωm:11 2003b:8 2003a:2 agree:3 tripp:5 strongly:1 patat:2 intercept:2 certain:1 aj:7 moved:1 deep:1 general:3 av:5 corresponding:3 operation:1 fill:1 incorrect:1 again:8 field:75 lsst:2 valid:1 poor:1 polar:5 separate:1 a1:4 important:6 peak:1 coverage:1 included:2 l63:1 curve:19 knowledges:1 observe:1 mass:1 original:6 monte:11 consider:2 pointing:4 caused:2 lack:2 month:1 follow:1 causes:1 content:1 c0:3 elias:3 mpc:7 very:14 dispersions:9 difference:1 subsets:1 applicable:1 large:21 small:7 past:5 rate:1 pasp:1 further:6 1998bu:2 canonical:1 subscripts:1 what:1 sub:8 section:3 brief:1 thickness:1 learned:1 500km:1 method:59 edited:1 full:10 compilation:1 component:19 inverse:1 excess:2 directions:3 strong:3 equations:9 search:1 allows:2 prior:1 amount:3 published:2 y10:1 2000e:2 1999ee:2 family:1 requiring:1 smac:2 put:1 extinction:32 select:1 readily:1 conventional:14 taken:4 more:10 flat:2 definition:1 corrected:8 leonard:2 varying:1 known:3 evolves:1 none:1 science:1 equation:22 dec:12 cosmological:8 share:2 marginalized:7 numbers:5 arise:2 axis:12 huge:1 needs:2 goal:2 rather:2 maps:2 simplicity:1 galactic:9 tried:1 derived:12 mapping:1 2002bo:2 horizontal:3 bloom:1 shortcomings:1 spectra:3 khokhlov:1 fundamental:2 help:2 thermal:17 paper:9 through:2 existence:1 its:6 l79:1 actually:4 late:1 detected:2 lira:2 alter:1 good:4 propose:1 encouraging:1 motivates:1 kawabata:1 bigger:1 fully:2 found:26 heavy:1 weighs:1 quadrupole:1 undetectable:1 energy:2 reduce:4 expect:1 measurement:3 inspections:1 beyond:4 since:2 projected:1 research:1 issue:1 favored:1 extraordinary:1 reason:2 ask:1 panstarrs:1 assign:1 major:2 probability:6 number:3 2005cf:3 done:2 construct:2 guess:1 temperature:1 introduction:3 moderately:1 least:4 assumption:4 observations:11 nomoto:1 favorably:1 norma:1 optical:13 willick:1 determined:5 pairwise:1 aas:1 toward:8 motivation:1 7o:2 randomly:2 headings:1 aldering:1 concentration:1 built:1 depending:1 kraan:1 majority:1 added:1 reach:1 most:7 significant:15 seasons:1 measured:8 deviations:2 clear:1 cover:1 km:39 branchini:1 part:1 velocity:83 physics:1 ambiguities:1 particularly:1 gold:1 accuracies:1 scattered:1 minimizing:2 relation:10 carefully:1 find:1 indicator:1 parameters:26 heavily:4 distributed:2 columns:2 dominant:4 dependent:4 during:1 silk:2 arxiv:5 remove:1 investigate:4 bars:2 set:12 signify:1 see:13 individual:3 sec:35 descriptions:1 close:3 axially:3 currently:1 dipole:42 smallest:1 various:2 radburn:2 avoidance:3 recently:3 statistically:2 baade:2 both:15 last:1 sensitive:3 improves:2 whole:3 airborne:1 point:2 simple:3 sky:14 rosa:3 throughout:1 decline:2 pp:1 described:6 due:13 reduction:7 describes:2 ph:1 nugent:1 wheeler:2 precision:3 determination:1 systematic:20 surveys:3 p2:17 intriguing:1 p1:16 solid:14 reliable:1 budget:1 mlm:53 behavior:1 error:21 apjs:1 itself:1 baseline:1 survey:4 higher:8 used:8 comprehensive:1 flows:1 levels:9 uses:1 appreciable:1 robust:1 recent:2 lower:8 analysis:4 obviously:1 calibrated:1 consistency:1 distances:7 hypothesized:2 shape:4 intervals:1 questions:1 alternative:2 tables:2 cut:6 conclusions:1 decomposes:1 source:5 location:4 input:1 transformation:1 showing:1 bip:1 apj:28 imposed:1 systematically:2 follows:1 signal:1 shapes:2 yields:6 popular:1 mathematical:3 velocities:13 methods:12 some:6 streaming:54 b0:28 b1:4 sight:1 30o:1 candle:1 kirshner:5 hannestad:1 scale:15 chornock:1 measurements:1 per:2 minimal:1 foley:2 bi:1 step:1 constraint:4 simulation:4 deserves:1 range:6 into:6 within:5 shapley:5 proportional:4 clustering:3 uncertainties:5 question:2 fast:1 analyze:1 sections:4 considerably:1 great:4 larry:1 line:5 up:3 prep:1 similar:3 associated:3 defined:2 dof:9 thomsen:1 diverse:2 friedmann:1 tentative:1 dashed:6 grouped:1 bracket:1 bmax:6 dale:1 generates:1 prepared:1 allowing:1 fisher:1 aitoff:2 independently:2 correlated:6 implies:2 algorithm:2 practically:2 required:2 depth:2 fitted:6 walker:1 requires:1 having:1 evenly:1 illustrates:1 results:21 illustrated:1 ga:4 contributions:1 excludes:1 helps:1 excluded:1 tegmark:2 include:3 dramatically:1 confirmation:2 fynbo:1 colormagnitude:1 continued:4 mathis:1 entire:6 understandings:2 smaller:10 zi:3 sin2:1 zc:2 imply:1 carlo:11 scientific:1 index:3 reaching:1 abell:1 precisions:1 exercise:2 degree:3 1999aa:2 respectively:22 objects:1 l27:1 z0:13 deduced:13 remark:2 burstein:1 technical:1 larger:14 contradiction:1 suggests:5 resulting:6 makes:2 scales:5 scaled:1 hardy:1 addressed:1 decrease:2 apply:3 clockwise:2 confidence:9 hudson:5 next:2 few:3 examination:1 conley:6 panel:15 becomes:1 normalized:3 iii:1 reproduce:1 obvious:4 bipm:4 universe:24 averages:1 scatter:3 dl:3 high:5 assumptions:2 employs:1 located:2 sin:7 filippenko:5 fits:32 light:31 lines:21 allow:3 divided:1 bins:4 saturated:1 symbols:3 galaxy:7 perfect:2 outer:1 chosen:2 circumstellar:1 degrees:5 choose:1 latitude:5 covered:1 interstellar:1 subtraction:1 day:6 zehavi:5 university:1 identified:8 magnitude:47 l0:25 l1:1 constraints:4 homogeneous:1 related:2 measure:1 our:5 tabulate:1 out:8 matrix:1 astier:3 rev:1 performs:1 cause:1 red:1 tully:1 galaxies:12 approaches:2 york:2 campusano:1 hubble:62 interaction:1 determining:1 could:2 keep:1 isotropic:1 removing:1 davis:2 powerful:1 reaches:1 l33:1 precisely:1 observer:1 data:52 system:2 adopted:2 their:3 intermediate:1 giovanelli:5 final:3 explanation:1 exactly:1 too:1 detection:2 inversely:2 amplitude:11 exhibit:1 false:1 fluctuation:1 curves:5 unlikely:3 need:3 apparently:1 marginalizing:1 able:4 hoeflich:1 polarization:1 decomposing:1 nuisance:1 intrinsic:24 class:1 astro:1 stronger:1 proceedings:1 constrain:1 fact:7 eldar:1 12o:1 bring:1 octopole:1 superimposed:1 rough:1 subtracting:1 based:12 should:5 ambiguity:1 employed:5 local:20 achieve:2 overall:4 joint:2 drawn:1 procedures:1 processes:1 luminosity:1 expansions:1 tightening:1 fixed:2 view:2 requirement:1 motions:5 exists:1 acquired:2 frame:8 correlations:3 sparsely:1 pattern:15 macros:1 difficulties:1 identification:1 correctly:1 neither:2 weighing:1 yahil:1 supernova:27 key:1 configuration:1 distribution:11 monopole:23 equal:4 attributed:1 figures:11 freudling:1 relevant:2 conclude:2 harmonic:2 m15:16 adding:1 table:19 li:6 hawkins:2 second:1 addition:1 montecarlo:1 outflow:1 indicators:1 bbv:7 controlled:1 sufficient:3 cos:13 bulk:3 clusters:5 improved:2 c1:3 repetition:2 present:1 multi:4 atmospheric:1 unlike:1 value:9 will:15 deviant:1 vi:1 thus:5 vp:6 perhaps:2 unity:4 parts:1 largest:1 units:1 difficult:3 upon:1 effect:5 v5:1 dust:17 frequently:2 tighter:1 off:4 center:4 bootstrapping:1 modeled:3 well:13 patterns:4 residuals:11 position:2 decliners:1 spherical:5 1994d:2 excessive:1 less:5 sources:2 underlying:1 wether:1 preprint:1 1989b:2 density:3 smith:7 reasons:1 extends:3 dqc:4 dqm:4 unprecedented:1 match:1 identical:1 putative:2 press:2 prominent:1 like:2 success:2 δv:1 δm:1 accessible:1 deviation:3 shed:2 because:6 phenomena:1 library:2 σi2:1 pinpoint:1 lead:2 broad:1 does:7 assuming:2 limitations:1 noise:3 disentangle:1 expansion:10 host:3 although:6 offset:2 analyses:6 vpec:9 noisy:1 about:15 actual:1 carried:1 extension:2 column:9 freedom:8 introduces:2 dependence:6 compatible:1 carries:1 a2:5 introduced:2 equally:4 previously:1 1991bg:1 functional:3 assess:2 square:1 kolatt:1 additional:2 inner:1 maza:2 function:6 but:31 histogram:3 volume:4 convergence:1 smooth:9 below:24 converted:1 limit:3 problem:2 universal:1 goodness:3 worse:1 goldhaber:4 mutual:1 compared:6 nonetheless:1 percent:1 detail:2 other:6 details:2 branch:2 star:1 zhou:1 variation:1 covariance:2 upwards:1 rule:1 searched:1
0705.0369.txt |@word consider:2 pointing:1 results:7 roy:1 computation:1 edu:1 talks:1 issues:1 excludes:1 inverse:1 deterministic:13 nonlocal:2 intensive:1 finally:2 present:1 under:7 include:1 tb:3 worth:1 ta:3 case:11 conjecture:3 very:2 rise:1 choice:2 corollary:5 every:11 fall:1 condition:17 beginning:1 immediately:1 forth:1 notes:1 solution:1 leave:1 vector:1 eigenvalues:2 cmu:1 noted:1 dis:1 work:1 says:1 consistent:2 horn:1 zero:2 even:4 index:1 what:2 invertible:2 d2:3 section:4 remain:1 expressed:1 version:1 subspaces:1 values:3 bn:2 exercise:1 satisfy:1 full:4 whose:2 respectively:2 never:1 feng:1 here:3 plenio:1 bj:10 address:1 appears:1 change:1 obtained:1 remarks:1 technical:1 study:2 studied:2 reason:2 simultaneous:1 products:1 symmetrical:1 bob:2 studies:1 appropriately:1 equivalence:1 useful:1 subcategory:1 unitarity:1 decrease:1 apply:4 use:4 takes:2 would:2 prove:1 remains:2 positive:11 next:3 ψj:28 ψk:9 noting:1 call:2 therefore:1 themselves:1 type:2 until:1 more:8 mellon:1 duality:6 initial:1 operators:22 ying:1 carrying:3 particular:2 known:4 cases:2 hold:4 iii:9 must:6 kraus:6 science:1 equation:1 mn:1 det:15 labeled:1 obvious:3 www:1 following:6 duan:1 arrive:1 example:4 proof:10 locc:24 compare:1 weaker:3 indicated:1 process:1 preserving:1 organized:1 states:25 numbers:2 sense:1 guarantee:1 information:3 end:1 majorization:8 discussion:4 holds:6 maps:10 pure:26 ensemble:2 map:21 product:12 replacing:1 mapping:3 collection:11 applications:1 demonstrating:1 maj:2 constants:2 johnson:1 phases:2 light:1 summing:1 so:12 decreasing:1 sb:3 sa:3 order:2 operations:15 help:1 september:1 indeed:1 satisfied:6 produced:1 course:2 paper:2 bistochastic:1 mentioned:1 satisfies:1 its:4 derive:3 thank:1 unitaries:10 chosen:3 lo:2 erators:1 actually:1 choose:1 fij:2 schmidt:40 might:4 acknowledgments:1 greater:2 combination:1 gets:1 conversations:1 they:2 now:1 yu:1 discuss:2 easily:2 term:1 several:2 equality:6 university:4 orthonormal:2 inequality:4 each:2 found:3 side:2 mean:2 majorized:2 square:1 vlad:1 ed:1 deterministically:17 arrives:1 majorizes:7 quantum:7 our:5 operation:38 differ:2 special:1 out:5 category:2 divincenzo:1 shown:2 accomplish:1 matrix:4 space:3 xv:2 robert:1 since:8 rev:7 research:1 increase:2 may:2 acting:1 multiply:2 print:3 lecture:1 supports:6 shows:2 foundation:1 theory:1 state:23 given:3 clarify:1 completely:1 carried:2 proportionality:2 members:1 org:1 remainder:1 generate:1 definition:1 qj:1 anselmi:1 geometry:1 could:1 involve:1 nonnegative:1 turn:2 incorporated:1 hence:1 onto:3 think:1 first:1 separable:52 xi:1 probability:1 majorize:1 u1:2 number:1 rank:17 raise:1 multiplying:1 another:3 carry:1 u2:1 electronic:1 little:1 checked:2 rewritten:2 likely:1 needed:1 introduction:1 adjoint:3 achieved:1 system:5 least:2 fmn:2 their:1 statement:1 convention:2 wootters:1 national:1 gives:2 relationship:1 pittsburgh:1 exactly:1 part:9 bennett:1 than:9 coefficients:25 roles:2 fuchs:1 depends:1 fm1:1 matter:1 outcome:4 sees:1 rewrite:2 cohen:1 argument:2 zyczkowski:2 smaller:1 need:2 any:8 relatively:1 multipartite:1 depending:3 convenient:1 note:5 other:3 combining:1 finding:1 coincide:1 caltech:1 channel:12 play:1 added:2 unless:2 trace:1 shall:1 who:1 systems:1 most:1 phase:2 kay:1 inserted:2 class:2 unequal:1 observation:1 consequences:1 considered:1 average:2 later:1 bipartite:7 typically:1 sum:3 fact:4 precise:3 shor:1 show:3 random:10 spaces:5 relation:1 trivial:2 find:1 kar:1 removed:1 based:1 just:2 situations:3 outside:1 only:13 bases:1 factor:4 local:9 dj:2 means:3 syst:1 between:2 dyn:1 cannot:8 new:1 closure:2 bengtsson:2 arxiv:3 yield:1 summary:1 common:1 mapped:10 qi:1 through:1 implication:1 fixed:2 qm:3 communicated:2 view:1 set:2 exists:1 sep:1 unpublished:1 connections:1 opposite:1 see:10 sec:7 result:7 incorporating:1 subject:1 instance:1 suspects:1 satisfying:1 tensor:2 sets:2 written:3 various:1 µj:6 neither:1 αj:3 conditions:9 multiplied:1 terms:2 qubits:1 transpose:3 however:2 wu:2 hypothesis:1 unnormalized:1 ket:2 both:10 reverse:3 many:1 conclusions:1 equal:7 connection:1 dated:1 interesting:2 pdf:1 share:1 whole:2 comes:1 otherwise:2 cj:2 relevant:2 point:1 simple:1 others:1 dimensional:7 simply:1 false:1 throughout:1 described:1 transformations:2 basis:7 addition:1 due:1 been:4 pb:5 pa:5 interest:1 corollaries:1 ph:4 define:2 corresponding:4 received:1 sufficient:3 subspace:1 andrew:1 hayashi:1 external:1 those:2 applied:4 semidefinite:1 main:2 pacs:1 expanded:1 harder:1 value:2 will:10 while:4 proves:3 replaced:2 applies:1 situation:3 unitary:18 5th:1 thus:9 vm:10 vn:2 iv:6 ii:8 characterize:1 itself:1 properties:1 dual:2 vanish:1 different:1 open:5 grant:1 same:16 tells:2 complex:3 quant:4 copying:2 largest:1 φj:11 finite:1 independent:2 used:2 http:1 imply:1 uses:3 entanglement:6 identity:2 pennsylvania:1 makes:1 nonetheless:1 well:3 analysis:1 obviously:3 thought:2 solve:1 studying:1 kets:1 dimension:7 left:3 popescu:2 less:3 obtain:2 transforms:1 questions:1 λd:1 λj:7 previous:2 density:3 characterization:1 seems:4 interested:2 transformed:3 lett:1 theorem:13 playing:1 transformation:7 chuang:1 take:1 identical:5 nielsen:9 mor:1 sums:1 possible:4 spanned:2 collections:1 possibly:1 entangled:5 press:3 using:7 modifications:2 necessary:6 helpful:2 follows:1 alice:3 specific:1 either:5 arbitrary:1 translated:1 works:1 reduced:2 mathematical:1 exceed:1 because:6 classical:2 some:5 back:2 pρ:1 b0:1 b1:7 specified:1 nonzero:2 dimensions:5 avoid:1 though:3 subclass:1 does:4 provides:3 inserting:1 bm:31 equivalent:7 expansion:2 how:1 br:1 hilbert:1 incomparable:1 deriving:1 about:1 griffiths:1 usa:1 extension:1 simplify:1 discussed:2 carries:1 mixed:2 consequently:1 projectors:1 automatically:1 op:1 cambridge:6 statements:1 previously:3 communication:2 into:4 chefles:1 isomorphic:1 nothing:1 appropriate:1 right:4 url:1 determine:1 operator:8 proportional:12 assumed:1 support:3 there:11 question:4 specifically:1 why:1 doubt:1 low:1 way:3 was:1 pasadena:1 form:9 smolin:1 converse:2 but:13 larger:2 hb:24 ha:26 true:4 he:1 evident:1 horodecki:4 whether:3 minkowski:2 us:5 um:18 assume:2 un:7 problem:2 pm:9 similar:1 called:3 detailed:1 proved:1 worthwhile:1 defined:3 aj:4 am:18 general:13 chap:1 ar:1 exist:2 inf:1 ericsson:1 no:4 rains:1 whereas:1 when:21 field:1 setting:1 role:2 becomes:1 department:1 kinds:1 carnegie:1 a1:5 a0:1 important:3 sides:3 implies:4 ranks:5 physics:1 factors:1 changed:1 having:2 impossibility:1 implied:1 dot:1 restricted:5 ghosh:1 original:1 once:1
0705.0370.txt |@word concept:1 consider:3 rev:11 magnetic:1 global:1 results:1 godoy:1 leads:2 commute:1 computation:1 edu:1 adjustment:3 displaying:1 whose:2 physica:2 depend:2 paris:1 subjected:7 ıa:1 tail:2 kendon:1 pdt:1 stochastic:1 include:1 tc:2 montevideo:1 applied:2 lack:1 jensen:1 far:1 frequencies:1 wave:7 suggests:1 resonant:4 experimentally:2 fractal:1 condition:4 four:2 hamiltonian:2 knight:1 t2:1 solution:1 t1:2 large:4 evy:17 vector:2 small:1 inspection:1 unexpected:1 force:1 consistent:2 mantica:1 jump:1 second:4 christensen:1 design:1 dynamics:5 chem:1 established:1 what:1 nonlinear:1 sub:10 uniform:1 waiting:6 aperiodic:2 above:1 new:1 kicked:4 degree:1 never:1 here:3 bi:1 cylindrical:1 address:1 appears:3 change:2 obtained:8 instituto:1 generalizing:1 study:5 studied:2 tial:1 p2:1 periodic:1 action:1 resonance:8 implement:1 makes:1 plotted:5 siri:4 technologies:1 flexibility:1 apply:1 linearly:1 readily:1 standing:1 tn:2 takes:1 prove:1 remains:1 coins:1 finally:1 call:2 therefore:1 candidates:1 associated:1 noisy:1 type:1 theoretical:1 lutz:2 more:2 sort:1 ublica:1 initial:1 operators:11 odinger:1 particular:2 cases:1 evolves:1 thousands:1 equation:2 work:1 mt:1 casati:2 values:4 shlesinger:2 following:1 numbers:1 figure:2 uruguay:1 calculation:2 choice:1 organized:1 implementations:1 states:1 fibonacci:5 hides:1 allowed:1 robinson:4 occur:1 information:2 discussion:1 six:2 range:2 very:1 parameter:9 ensemble:2 map:1 product:1 irrational:2 may:2 jahnke:1 fb:1 cambridge:2 destructive:1 types:1 short:2 physical:1 dynamical:3 light:1 correspond:3 element:1 representation:1 order:3 ammann:1 typical:1 produces:2 developed:1 over:1 move:1 mainly:1 satisfied:1 paper:2 pulses:1 existence:1 cold:1 milman:1 its:4 before:2 la:1 matrices:1 temporal:1 absence:1 microscopic:1 systems:11 zhou:1 mail:1 decades:1 into:1 them:3 greater:1 universality:1 fig:13 number:1 break:1 they:4 2t:1 february:1 kamenev:1 fully:1 university:2 evo:1 each:1 found:1 2i:2 proposals:1 energy:3 gaussian:4 challenges:1 frequency:1 changed:2 quantum:19 our:2 eq:1 shown:3 matrix:1 driving:1 space:3 rep:2 interference:1 diffusive:3 acting:1 rational:3 xu:1 ref:1 shows:3 klafter:2 numerical:1 localization:1 ısica:1 free:1 standard:11 davidovich:1 reason:2 perturbation:1 generate:2 computers:1 obstacle:1 running:1 times:2 counterpart:1 int:1 place:1 universidad:1 consequence:1 retain:1 substrates:1 first:1 already:1 bartlett:1 symmetry:2 striking:1 variables:1 primary:3 romanelli:4 smaller:1 periodical:1 qkr:24 open:1 angular:3 aharonov:1 size:1 given:2 law:9 zumofen:1 system:7 their:3 intermediate:1 ballistic:14 bharucha:4 calculations:2 white:1 ribeiro:1 exponents:1 recovered:1 trapped:1 environmental:1 part:1 theorie:1 than:1 diffusion:2 wilkinson:1 accordance:1 antiresonance:1 future:1 williams:1 behaviors:2 symmetries:1 electrodynamics:1 unchanged:1 argument:1 tregenna:1 say:1 manner:1 need:1 seem:1 any:1 rotor:5 strength:5 raussendorf:1 εt:2 self:1 mechanism:1 take:2 strengths:1 schomerus:2 multiple:1 sequence:7 simplify:1 kempe:1 coin:1 class:1 tensor:1 characterizes:1 calculated:1 donangelo:2 detuned:1 dent:1 optical:1 left:2 fact:1 madison:1 show:5 random:2 chuang:1 threshold:1 zaslavsky:2 trivial:2 find:1 ratio:1 proposed:3 parameters:5 situations:1 state:1 moments:3 only:1 black:1 essence:1 commensurable:1 alternation:2 dl:7 means:1 de:7 pendence:1 lattices:1 dt:1 du:1 secondary:6 gray:1 evolution:7 qw:21 arxiv:4 motion:1 investigate:2 common:1 shi:1 set:1 turbulent:1 observed:3 depends:3 full:2 exponent:6 nuclear:1 outside:1 between:8 invariant:1 recently:2 ability:1 nature:1 jm:1 wu:1 jj:1 article:1 atoms:2 inertia:1 both:5 cos:1 last:1 kicking:1 acknowledge:1 according:1 σz:2 σy:1 figures:2 dated:1 variance:1 expression:1 experimental:2 afterwards:1 point:1 simple:1 period:2 walk:5 dimensional:1 maintained:2 sequences:1 wider:1 table:1 code:1 transformations:1 addition:1 chirality:4 due:1 been:4 imperfections:1 defined:1 ph:10 define:1 dots:3 sanders:1 direction:1 corresponding:3 coherence:1 essentially:2 external:1 kicks:1 prescription:4 those:1 case:8 laser:1 pacs:2 solid:1 value:3 aim:1 contemp:1 while:2 steinberg:1 momentum:2 behavior:23 situation:1 property:1 unitary:3 chaotic:1 thus:4 site:1 ij:1 capture:1 different:5 verified:1 projector:1 author:1 suggest:1 fractals:1 same:8 clearly:1 quant:11 pauli:1 units:2 dimensionless:1 several:3 grows:4 higher:1 clear:1 investigated:2 lie:1 trajectories:2 bala:1 hand:2 moment:4 uses:1 infinite:1 frequently:1 identity:1 niu:1 concordance:1 schr:1 zagury:1 patterns:1 pineda:1 position:3 model:3 fujita:1 usual:3 just:1 being:1 generally:1 obtain:3 abal:2 spanner:1 shape:1 using:2 multiples:3 previous:1 han:1 similarities:1 alternate:1 except:2 spread:1 combine:2 lett:7 samples:1 eigenstate:2 kick:3 generalized:1 identical:1 criticality:1 showing:2 possible:1 corresponds:1 raizen:4 press:2 integer:4 like:1 follows:5 qualitative:2 always:2 completely:1 because:1 classical:2 exposed:1 phenomena:2 polynomial:1 scale:4 ballistically:1 cavity:1 resonances:8 sundaram:3 does:2 bessel:1 destroys:1 noise:14 power:9 processing:1 agreement:1 constructive:1 step:7 hilbert:3 asymptotic:4 most:2 freedom:1 dependence:2 briegel:1 aℓ:4 introduced:1 other:2 op:1 ingenier:1 modalities:1 previously:1 spreading:5 numerically:2 functional:1 right:2 operator:6 behind:1 additional:1 support:1 there:2 u1:11 u0:15 facultad:1 way:2 was:1 function:12 indepen:1 form:1 hs:4 differences:1 but:2 repeated:1 construction:1 larger:1 hc:4 line:5 uy:1 evident:1 whether:1 characteristic:4 us:1 ur:1 mth:1 gauthier:1 today:2 highlight:1 distribution:15 similar:2 average:4 proved:2 moore:4 ai:1 certain:1 aj:1 mosseri:1 ini:1 walks:1 inf:1 face:1 regime:4 again:1 no:1 dashed:1 when:11 field:1 build:1 interested:1 details:1 nt:2 conclusion:1 deviation:10 excitation:2 models:1 berman:1 shepelyansky:1 includes:1 a0:1 generated:1 important:3 additionally:1 variable:1 lution:1 implies:1 assume:1 4t:1 interval:5 interacting:1 parallelism:3 time:21 walker:2 decoherence:3 izrailev:1 once:1
0705.0371.txt |@word measurements:1 consider:3 rev:16 magnetic:23 splitting:12 existing:1 leads:2 commute:2 follow:1 remarkably:1 localized:2 rigidity:1 compact:1 whose:3 inverse:2 depend:2 producing:1 rayleigh:2 environment:1 does:1 antiferromagnetically:1 γc:6 up0:2 sound:16 ınguez:1 kπ:1 amplitudes:1 advantage:1 far:1 frequencies:1 vt:4 martinez:2 conditions:2 wave:14 electron:1 resonant:5 affect:2 difference:1 matrices:3 deformations:4 condition:7 illustrated:1 speed:3 europhys:4 exponential:1 immediately:1 level:3 anisotropy:5 tanh:1 t2:3 solution:6 large:8 solved:1 differential:1 fourier:1 small:12 upper:1 smaller:1 force:1 tem:1 oscillation:1 haas:1 sin2:2 prediction:1 pulse:3 maintain:1 approximation:1 rate:2 qualitatively:2 dynamics:5 linear:11 even:1 eia:1 nonlinear:1 appear:1 lehman:1 trivial:1 section:5 axes:1 cell:1 ˆa:2 experiment:2 above:8 lifshitz:1 new:5 contrast:1 temperatures:1 coefficient:1 full:1 chose:1 exchange:2 component:1 equals:3 here:1 understanding:1 magnetism:1 cos2:3 relaxation:1 xβ:2 luis:2 along:2 strong:2 equations:25 change:2 obtained:3 antisymmetric:1 involved:1 study:7 studied:7 allows:2 usually:1 resonance:14 mz:6 makes:1 uniquely:1 projection:1 substitution:1 apply:1 total:6 schilling:1 σiy:1 unit:2 challenging:1 ıa:1 conventional:3 would:2 positive:1 ul0:8 contains:1 physics:1 ψj:2 iq:3 ψi:2 therefore:3 vi:1 dny:3 jacobsen:2 possible:1 more:3 separated:1 formally:1 gyromagnetic:1 suggestions:1 operators:1 factor:1 emission:1 rigid:2 cases:1 iii:3 must:5 pseudospin:3 bedford:1 account:1 rotational:1 strain:1 tunnel:3 equation:9 mn:1 london:1 ferro:1 unknowns:1 bias:1 obvious:1 three:2 growing:1 making:1 spontaneous:1 numbers:2 want:1 preserving:1 organized:1 states:13 villain:1 confirmation:1 performed:2 degenerate:1 allowed:2 axis:3 hoc:1 rather:1 s2:1 discussion:3 means:1 feature:2 write:1 located:1 adjacent:1 ordinary:1 absolute:1 parameter:2 sin:4 product:1 express:2 mat:2 staircase:1 may:5 use:1 derived:2 confirmed:1 produce:1 fe:1 physik:1 waves:32 choice:1 grow:1 constants:1 sz:2 stress:3 andez:2 natural:1 dynamical:2 effective:1 sech:2 grant:1 ghz:6 provide:2 cannot:3 so:6 allow:3 decreasing:1 cherenkov:1 order:5 help:6 produces:1 developed:1 over:4 despite:1 insuring:1 ferromagnets:2 stability:1 paper:6 through:7 statistical:1 leuenberger:2 mentioned:1 existence:2 satisfies:1 still:2 excitations:5 its:6 paramagnets:4 solitary:5 derive:1 longitudinal:2 decay:7 interesting:1 vicinity:4 coordinates:2 li:2 meantime:1 absence:4 degrees:1 systems:1 rabi:1 postpone:1 deformation:3 maximal:1 non:9 good:1 integral:1 evolution:1 attains:1 yang:2 effects:3 they:7 landau:1 rotation:7 now:2 possess:1 represents:1 february:1 2q:1 2s:3 university:1 hamiltonian:19 sufficiently:1 magnitude:1 mode:2 l0:1 each:3 acoustic:12 side:2 characterized:1 homogeneous:2 tensor:4 int:1 qz:2 ei:2 significantly:4 independent:6 generation:1 magneto:23 ef:9 reduce:2 displacement:9 related:3 sn0:2 frequency:9 ey:1 ex:1 magnets:14 measurement:1 quantum:5 wavelength:5 transitions:1 eq:22 ep:1 twists:4 out:1 respects:1 shown:1 matrix:2 space:1 spectrum:2 res:1 rep:1 since:1 crucial:1 particles:1 replacing:1 vector:1 dominated:1 rb:1 rn:2 ref:2 ri:1 shows:1 commutation:1 theory:5 interactions:3 possibility:3 standard:1 reason:1 perturbation:3 york:3 put:1 morello:1 estimate:1 hand:2 generate:3 xie:1 driven:1 interaction:15 vˆ:3 created:1 geometry:2 starts:1 running:1 linearized:1 motion:7 length:4 plane:4 signature:1 consequence:5 onto:1 neglect:1 soli:1 first:2 origin:1 initial:1 stevens:1 ziolo:1 reaches:1 twisted:1 xz:1 xx:1 done:1 relations:1 another:3 quality:1 angular:4 size:4 city:1 given:9 boulevard:1 temperature:1 likely:1 introduction:3 unknown:1 eqs:9 behaves:1 system:17 approximately:1 sech2:1 their:1 assumption:1 ton:1 molecular:21 low:5 free:1 tejada:3 supersonic:1 alonso:2 park:1 transverse:7 mech:1 somewhat:1 x2:1 sign:2 than:5 coefficients:1 population:6 distance:2 polarized:1 determines:1 accordance:1 magnet:5 zero:9 determined:3 contrary:1 amplitude:6 sec:1 gives:1 jongh:2 result:3 lowest:1 torque:3 argument:3 novak:1 say:1 ultrasonic:2 increment:1 close:4 need:1 concentration:1 any:2 viewed:1 angle:5 convenient:1 latter:2 responsible:2 note:5 high:3 fictitious:3 acquires:1 formulas:1 santiago:1 unless:2 shall:4 friedman:1 molecule:2 algebraic:1 ˆs:2 phase:2 acknowledgements:1 why:1 maci:1 eigenfunctions:1 kb:1 values:2 observation:3 average:2 prepare:1 αy:1 part:3 principle:2 exp:1 narrow:1 velocity:2 typically:1 ˆz:2 fact:2 laws:2 show:4 supported:1 reference:1 relation:4 solutions:3 substituting:4 d2:1 d3:2 ground:6 q0:4 q2:4 ratio:2 parameters:1 much:1 eαβ:2 specified:1 written:4 should:14 n2z:2 entities:3 only:8 molecules:10 indeed:1 sessoli:1 local:10 interested:1 do:2 iωt:3 dependent:1 de:4 fulde:2 aβ:2 reversal:1 ˆi:2 compute:1 boundary:1 iqx:1 produced:2 processes:1 qx:2 arxiv:1 rinton:1 experiments:2 common:1 though:1 contain:1 nα:1 solitons:1 unison:1 magneton:1 exists:1 spinup:1 maximum:2 relative:1 collectively:1 see:10 individual:1 college:1 w2:1 terms:6 techniques:1 satisfying:3 interacting:6 c2t:16 ul:7 phonons:5 distinctive:1 away:2 inhomogeneous:1 uα:4 propagates:1 santos:2 state:21 between:6 ui:3 αk:2 fields:1 paramagnetic:3 c2l:7 µb:1 el:1 notice:2 recently:1 ability:1 gµb:8 initially:3 however:2 jr:1 characteristic:1 vanishing:1 bose:1 ferromagnet:2 come:1 suggested:2 both:1 cos:8 last:3 many:3 region:2 according:2 zeeman:1 quantization:1 sensitive:1 context:1 bronx:1 argue:1 whole:1 originating:1 very:4 point:4 harmonic:1 environments:1 magnetoelastic:2 wider:1 respect:1 ct:11 considering:2 broadening:2 described:4 basis:3 west:1 due:10 been:9 duy:2 magnetized:1 describes:3 dnx:1 interest:1 superradiance:2 expected:1 applying:1 ph:9 fig:9 direction:3 describe:4 corresponding:3 observable:1 γe:1 gap:6 bulk:5 external:2 imation:1 presented:1 spin:47 travelling:1 yuan:1 case:6 dξ:6 eis:2 laser:1 unlike:1 pacs:1 solid:2 value:3 easier:1 will:10 situation:1 fernandez:2 coupled:10 phenomenological:2 averaging:1 dohm:2 thus:2 surface:13 iv:2 ii:2 cluster:1 n2y:4 n2x:2 cond:2 crystals:7 chudnovsky:11 interacts:2 conserve:2 increased:1 containing:1 satisfy:1 radiation:1 lett:10 same:2 complex:1 split:1 pauli:4 higher:2 evolve:1 investigated:1 slightly:2 upon:1 effect:6 hysteresis:1 inhomogeneities:1 exceeds:2 moment:1 levels:10 necessity:1 invariance:1 n20:1 2mω0:1 expand:1 lower:2 weakly:1 ωnx:1 modes:8 nevertheless:1 no:3 epr:1 analysis:1 bohr:1 superparamagnetic:1 components:3 coordinate:1 model:5 parametric:1 distances:1 magnetization:23 being:5 generally:1 rotated:1 obtain:7 transforms:1 summed:1 macroscopic:5 alignment:1 density:1 absorption:1 δmax:2 cl:1 dicke:2 lattice:7 valid:1 extends:1 treatment:1 easy:4 relevance:1 excited:3 momentum:4 hybridization:1 real:1 saturation:1 around:4 easily:1 results:4 term:3 sarachik:1 corresponds:1 dipolar:3 know:1 press:1 using:1 moreover:1 mod:1 loss:2 rotate:2 alternatively:1 reduces:2 velocities:1 yields:1 arbitrary:2 become:1 disorder:1 reduced:1 spins:13 function:2 beneficial:1 right:2 classical:2 lectures:1 hartmann:1 growth:1 ux:1 oscillations:1 generates:1 nonzero:2 lima:1 describing:2 opposite:1 integration:4 per:1 behave:2 provides:1 assuming:1 prog:1 unstable:2 propagating:1 demonstrated:3 core:1 equivalent:1 oscillating:1 bi:1 gatteschi:1 although:2 accompanied:3 imaginary:1 about:1 ui0:2 freedom:1 certainty:1 discussed:4 dependence:1 practical:1 range:5 repulsion:2 introduced:1 consequently:1 accessible:1 garc:1 presence:2 pergamon:1 into:6 within:1 numerically:1 elasticity:2 nsf:1 twostate:1 down:2 ultrasound:9 ηq:1 einstein:1 operator:2 proportional:1 hidalgo:2 elastic:32 aharony:1 assumed:2 there:5 question:1 u0:3 long:4 dispersion:7 width:6 ut0:2 conservation:3 inner:1 way:1 2m:1 was:3 energy:5 opens:1 m0:1 raman:1 form:2 soliton:7 hern:2 but:2 volume:4 ignited:1 made:3 uy:16 garanin:6 uz:1 whether:1 ut:7 inside:5 up:10 us:2 until:1 crystal:19 below:2 limit:1 problem:1 dnz:1 similar:5 nature:2 obtains:10 strongly:1 constant:7 ad:1 defined:4 pseudo:2 ez:3 determinant:2 general:5 twist:2 single:2 our:4 follows:2 reflecting:1 work:1 law:1 ni:2 compared:7 sˆz:2 nm:1 2ds:1 variety:1 fascinating:1 populations:1 when:9 christou:2 nx:16 field:30 nz:12 hph:1 detected:1 es:1 becomes:3 department:1 ny:30 politi:1 stat:1 coherence:1 superposition:1 excitation:2 setting:1 prepared:3 a0:1 generated:6 important:2 bounded:1 mechanical:1 astronomy:1 decoherence:2 structure:2 source:1 independently:2 implies:1 coupling:6 assume:1 normally:1 required:1 curve:1 together:1 4q:1 sity:1 phonon:10 mass:2 time:3 n0:32 cores:1 n2:1 requires:1 gαβ:2
0705.0372.txt |@word managed:1 consider:6 shoten:1 results:13 leads:1 c3:1 proposition:13 entropy:1 grateful:1 constants:1 follow:1 expressions:1 gk:2 reparameterization:1 whose:5 iin:1 depend:4 paris:1 concerned:1 equivalence:5 c6:2 eγ:2 excluded:1 under:2 stochastic:6 analogous:1 include:2 case:21 collaborate:1 risk:1 advantage:5 very:1 choice:1 corollary:7 mixing:1 affect:1 difference:1 jacod:3 randomness:16 obvious:1 unlike:1 transmission:1 induction:1 dawid:10 tokyo:1 applicable:4 large:4 evy:2 small:1 enforce:1 martingale:9 ville:3 says:3 measurable:22 second:9 exchangeable:1 infinity:3 gn:5 further:2 required:1 even:6 synthesis:1 what:2 plays:6 appear:1 rate:7 giving:1 decisions:1 section:7 analogously:1 current:2 version:8 goes:1 capital:28 values:4 net:1 increasing:5 ever:1 dubins:4 fujiwara:11 coefficient:2 chaotic:1 chose:1 degree:2 1987b:2 respectively:3 1987a:9 equals:1 understanding:1 akio:1 making:1 represented:2 ratio:5 standard:4 mises:2 appears:1 interpret:3 obtained:4 remark:7 ahead:1 economics:1 sbornik:1 denominator:1 significantly:1 p2:8 amount:1 california:1 usually:1 surely:6 makes:11 sup:7 york:6 lois:1 useful:3 takeuchi:1 vii:3 logical:1 worrying:1 flexibility:2 limn:2 achievable:1 apply:1 opponents:1 standing:1 derivatives:4 use:8 henri:1 additive:3 asymptotic:7 would:4 prove:10 remains:7 positive:7 give:4 semimartingale:5 predictions:18 finetti:4 next:3 vol:1 competition:1 therefore:9 criteria:3 popper:1 k0i:2 means:2 gauthier:1 type:1 until:3 reflects:1 more:10 formally:2 weakening:1 advance:6 successful:3 becomes:12 ien:1 hurt:1 tested:4 regrouping:1 appendix:1 cantelli:2 observations:3 particular:4 known:4 foundations:2 cases:5 hold:3 producing:1 weaknesses:1 eβ:2 logarithm:6 springer:2 valued:1 vladimir:1 integrating:1 science:1 getting:1 modified:3 minimum:1 renders:1 achieve:4 royal:3 following:20 strategies:23 example:4 proof:28 transition:2 stated:3 process:2 allowed:1 dependence:2 high:1 assumptions:1 numbers:3 want:1 sense:17 liptser:2 absolute:8 information:8 end:8 goal:2 awkward:1 rather:3 eni:7 s1:1 holds:11 differences:1 write:2 far:3 criterion:4 fourth:1 simplifies:1 instead:1 guarantee:1 greatly:1 simplicity:3 product:1 includes:1 singular:2 may:2 max:2 after:3 sceptic:101 applications:1 spirit:1 society:4 representations:2 law:8 types:1 gaussian:1 realized:1 natural:2 third:1 whenever:2 explicit:3 summing:3 element:2 sk:3 s3:1 switch:1 so:9 sect:3 allow:2 decreasing:5 sc:4 definitions:2 playing:8 restriction:1 interpretation:1 developed:1 over:7 move:4 mainly:1 intuition:3 parts:1 interpreted:2 stability:1 course:2 paper:5 statistical:6 differs:1 existence:5 satisfies:3 still:1 ieee:1 its:7 before:7 s2:2 derive:1 sequential:1 manuscript:1 la:2 chosen:6 fix:2 better:1 annales:1 continue:3 choose:5 qn:1 main:3 might:2 correspondence:1 non:7 good:1 qualifies:1 finance:1 combination:1 obtaining:1 practice:1 introduce:1 avoids:1 they:8 half:7 1b:11 singularity:6 now:12 discuss:1 wiley:3 establishes:1 represents:1 february:1 finite:5 indeed:1 name:1 fails:6 always:5 university:1 drop:1 concave:1 xγ:4 iwanami:1 applied:3 inequality:18 breach:1 each:13 feldman:2 side:2 referred:1 heavy:1 en:4 directly:1 ek:1 iterated:4 idea:1 related:3 deficiency:1 computable:1 expect:4 measure:24 our:12 happen:9 satisfied:1 event:21 special:6 space:5 customary:1 announces:23 since:9 inadequacy:1 transforming:1 denoted:1 formula:1 get:2 objectivity:1 suffices:5 ri:1 math:1 shows:2 earlier:3 theory:12 written:1 discrete:1 divergence:10 possibility:1 quite:1 krieger:1 complicated:1 bayes:1 equipped:1 detecting:1 hand:3 beginning:1 rewritten:1 definition:2 english:1 geometry:1 could:2 impose:2 nonnegative:14 counterpart:2 american:1 gordon:1 tempting:1 unknown:1 βn:5 shiryaev:13 βi:2 first:15 cǫ:5 major:1 there:15 probability:38 variables:1 restrict:1 intuitively:1 multiplying:1 done:2 another:8 infinitary:1 carry:1 force:6 precisely:1 schnorr:1 xu:3 stochastics:1 given:7 checked:1 exists:4 guaranteeing:7 introduction:1 leading:1 provenance:1 least:6 1a:26 their:9 assumption:8 master:1 too:2 statement:5 convention:3 show:1 especially:2 gives:14 kolmogorov:1 fraction:2 discussion:2 continuous:1 proving:2 prediction:3 pni:53 part:47 predictable:1 somewhat:2 x2:2 translation:1 believe:2 than:5 coefficients:1 greenwood:2 finitely:1 distance:4 kind:1 unfortunately:2 sections:1 namely:4 kakutani:2 normalizing:1 matter:3 subsequence:1 denominators:1 declares:1 false:1 generality:1 modern:1 argument:5 already:1 say:7 manner:1 need:4 seen:1 null:3 any:15 sasha:1 zero:7 elaborations:1 efficient:2 lim:11 latter:2 aside:4 mechanism:1 masse:1 mix:1 recommended:2 issuing:1 generalized:1 measurability:1 coincide:3 accuracy:3 play:17 regard:2 unless:2 normal:1 price:1 who:2 plugging:1 react:3 most:1 regular:3 ajek:2 representation:4 pair:3 filtration:1 measured:2 nagaoka:2 divergences:4 forever:1 constructed:4 observation:3 considered:2 clear:2 sometimes:2 coincides:3 kn:92 order:1 countable:1 investing:2 proceedings:1 principle:4 exp:10 left:1 typically:1 notion:7 forecasters:17 laws:1 precise:5 selection:1 phenomenon:1 nonpositive:1 random:1 chapters:1 russian:2 spaces:2 relation:2 carefully:1 substituting:3 find:1 d0:2 computability:3 indicator:1 based:7 behind:3 should:4 contiguity:1 lemma:26 only:25 annals:3 subsection:3 rich:29 factor:4 attained:2 integrable:2 truncation:1 local:8 sure:2 continuity:7 do:3 his:11 perpendicularity:1 above:2 notation:3 exceptional:5 calibration:1 de:7 stop:1 ξn2:4 soon:3 methods:2 joint:5 cannot:3 rest:2 words:1 new:6 systems:1 him:11 closure:1 processes:3 hellinger:9 arxiv:1 method:2 redefined:1 prevents:1 albeit:1 dpn:12 fixed:1 discussing:1 valid:3 view:2 blackwell:4 satisfy:1 requirement:2 set:14 ses:2 computed:1 fair:1 achieved:4 violated:1 testing:13 respect:1 identify:1 achieves:1 edition:6 see:19 result:10 discussions:1 close:11 theoretic:34 notions:2 closer:1 αs:2 satisfying:1 likelihood:2 inequalities:1 deducing:1 falsify:1 outside:2 various:1 between:12 geometric:1 approach:6 wide:1 notice:4 never:8 terms:4 supn:3 attention:1 weak:2 however:6 jr:1 ln2:15 complicate:1 diverges:2 distribution:2 suggested:1 both:10 essentially:1 parentheses:2 last:1 many:2 taking:3 infinitely:30 according:3 against:2 players:9 merging:8 became:1 jeffreys:1 context:2 logic:1 exceeds:5 mean:3 expression:6 fni:16 otherwise:6 arbitrarily:2 forecasting:4 point:2 forecaster:59 connection:2 ca:1 berkeley:2 vast:1 corresponds:1 cd:1 active:6 cx:1 framework:3 sequences:5 cs:1 proved:3 indefinite:1 5e1:1 considers:1 pr:2 pp:2 strong:1 arbitrary:2 due:1 been:6 strategy:46 hotelling:3 takemura:1 logarithmic:1 expected:1 pk:4 pi:25 pn:10 define:2 adapting:1 direction:1 senses:1 corresponding:1 rhul:1 restrictions:1 am:1 assert:1 ensuring:2 huntington:1 bayesian:1 c2:2 c1:3 careful:1 former:2 those:1 c4:1 paying:1 p3:1 p1:7 look:1 subsets:1 ǫd:3 ǫk:11 reliable:12 empirical:2 value:7 will:65 complexity:1 suppose:6 property:4 procedure:1 played:1 almost:6 von:2 them:5 encouragement:1 iv:1 ii:157 player:1 regularity:1 itself:1 properties:2 fn:18 rid:3 alone:1 k0:3 acknowledgments:1 binary:2 different:2 open:1 etc:1 generic:1 pay:1 make:4 cumulative:2 problems:1 accomplished:1 same:2 poincar:1 complex:1 bernoulli:1 modification:2 several:4 events:3 extended:2 http:1 ni:2 published:1 forecasts:1 uses:2 infinite:7 changing:1 invariance:1 randomized:1 identity:1 relies:1 lower:2 kni:8 studies:1 depending:4 well:5 phil:1 approached:1 without:4 c5:1 convenient:2 comparisons:1 soviet:1 kns:2 know:2 opinions:7 world:1 protocol:31 causality:1 just:2 less:1 being:1 resp:13 paragraph:1 2c:2 obtain:10 competitive:10 sources:2 cease:1 immediately:1 differentiation:2 regardless:1 alternative:1 previous:1 villars:1 dropped:1 martingales:4 density:2 informal:1 guaranteed:6 simple:5 interested:4 transformed:1 easy:5 theorem:68 dqn:5 guarantees:5 match:1 take:5 real:2 holding:3 rules:1 replaced:2 showing:1 possible:5 cf:1 game:28 amari:2 mathematics:4 press:1 using:8 apart:1 disadvantage:1 loss:1 imposed:2 replacing:2 success:3 follows:6 kullback:3 specific:1 imposes:1 either:6 martin:1 popular:2 become:9 ie:2 pointwise:3 prior:1 essential:1 terminology:1 mathematical:5 βni:43 right:1 often:1 deal:1 sequence:6 shen:1 2x:1 conditional:3 some:6 back:1 pacific:1 japanese:1 understood:1 deduce:2 enyi:2 asserted:2 duration:1 proofs:1 vovk:30 ourselves:1 happens:11 savage:2 recently:1 lead:1 2e:4 absolutely:1 transactions:1 providence:1 does:7 exposition:1 provides:1 assuming:1 borel:4 refer:2 measures:13 algorithmic:9 power:1 slight:1 remembered:1 selecting:1 equivalent:5 submartingale:3 agreement:1 solomonoff:3 constructive:1 multiplicative:1 step:8 although:1 output:2 concreteness:1 refers:2 critique:1 optimize:1 takes:1 chapter:3 about:9 works:1 central:2 anything:1 simplify:1 theorems:8 factors:1 o:5 mutually:2 carries:1 ensure:4 stand:5 horizon:1 act:6 mixed:1 introduced:2 slightly:2 other:4 automatically:4 subset:1 mixture:5 cruder:1 statements:2 computes:1 unbounded:1 into:2 within:5 integral:7 bound:6 combine:1 nothing:1 because:3 references:2 elementary:1 sufficiently:2 bankruptcy:1 statistics:7 institut:1 log:2 assumed:1 strictly:1 initial:4 question:1 long:1 start:3 much:5 way:3 ed:1 was:12 naturally:1 function:11 recommends:1 form:4 antecedent:1 becoming:3 kabanov:3 but:13 principles:1 subjective:3 etude:1 economic:1 state:3 gain:1 learned:1 convergence:3 unreliable:2 line:1 removed:1 true:4 he:7 made:4 compute:1 versions:3 whether:4 levin:1 bounds:3 us:12 foresight:1 below:3 growth:7 limit:4 uk:1 ωn:34 ussr:1 problem:2 similar:5 called:4 strengthens:1 ex:1 advantages:1 pii:19 ac:1 later:3 constant:15 czechoslovak:1 ln:106 defined:2 stronger:2 abstract:1 specified:1 condition:3 general:5 quantification:2 proves:2 exist:2 journal:6 inf:4 moves:5 distributions:2 check:1 doklady:1 dα:1 again:3 functions:5 compared:1 no:4 whereas:3 nc:1 when:17 detail:1 reality:22 application:2 setting:5 supermartingale:1 papers:1 gambling:1 forcing:2 deviate:1 arithmetic:1 ny:1 deviation:1 symposium:1 elements:2 completes:3 provided:1 leibler:3 reached:1 disclosed:1 stay:2 generated:1 important:6 bounded:3 ξn:21 variable:1 formal:1 sides:4 bulk:1 implies:4 dω:12 assume:5 invest:1 invests:1 shafer:10 berlin:1 equivalently:1 weights:3 fact:6 time:4 doob:1 n2:1 dover:1 starting:2 original:1 normalized:8
0705.0373.txt |@word syzygies:1 magnetic:4 four:11 entropy:24 whose:3 aug:1 under:3 rise:4 vibrational:3 solution:9 convenience:1 vector:1 degeneracy:16 jhep:20 construed:1 consistent:1 direct:1 ωab:2 approximation:1 second:5 rigorous:1 established:1 above:19 new:8 net:1 contributes:1 unintegrated:1 coefficient:5 agreement:1 wrapping:5 here:13 obtained:4 study:4 projection:6 total:6 unit:1 would:6 motivate:2 noting:1 call:1 type:8 duals:1 successful:1 hole:36 hold:1 must:5 kumar:1 fµν:1 theories:3 example:1 give:5 preserving:4 generically:3 want:6 berenstein:1 end:1 provide:3 feature:2 how:3 description:3 oscillators:3 after:10 demanding:2 microstate:1 dω23:1 attempt:2 effective:1 fictitious:1 jabbari:2 order:5 g10:2 restriction:1 interpretation:3 over:9 vary:1 satisfied:3 satisfies:3 before:2 asymptotes:1 writing:3 fij:6 potentially:1 eventually:2 them:4 combination:3 break:3 they:5 invariants:1 backgrounds:1 each:5 cfts:1 side:2 lifted:3 financial:1 sinha:3 poincare:2 combining:1 extract:1 gussich:1 crucial:1 reader:2 ds25:3 turning:7 linear:4 associate:1 standard:2 chiral:2 r2:2 created:1 ds2:1 δij:1 ds2s:1 onto:1 lahiri:1 subtlety:1 primary:1 another:3 rewritten:2 needed:1 somewhat:1 corresponded:1 warmup:1 kraus:1 preparation:1 tion:1 pioline:1 fashion:1 sees:1 mind:2 quantising:4 seen:1 tells:1 contents:1 strength:2 reall:5 latter:1 nilsson:1 shall:3 regular:1 phase:11 partition:2 yang:3 poynting:1 sum:1 pope:2 probe:4 ending:1 iǫ:8 gauge:37 solutions:28 keywords:1 d4:2 d3:14 d0:3 make:3 proposed:1 claude:1 explain:1 topological:1 integrate:1 hamiltonians:1 do:4 df:1 de:2 dz:2 dt:2 dr:2 runs:1 fields:13 µ2i:9 acknowledgments:1 twice:1 counted:2 thanks:1 emergent:1 observed:1 radius:3 result:9 discussions:2 subject:2 tensor:1 away:2 rings:1 supergravity:4 yet:3 symmetric:1 dias:1 il2:1 simplest:2 preserve:16 terms:14 however:5 huang:1 wz:2 cos:45 cot:6 contribution:1 argue:2 presumably:1 tong:1 2nd:1 trust:1 mathur:5 basis:1 simplification:2 guica:1 three:12 been:1 much:2 expected:4 tan2:5 supersymmetric:11 excite:2 2n2:2 applied:1 transformation:2 fubini:1 near:27 applies:1 leaves:2 procedure:4 iz:1 obeying:2 ik:3 ij:1 cone:1 suggest:1 realizing:1 complex:6 quant:3 split:1 isometries:1 independent:11 emphasise:2 counterparts:2 hand:2 3n2:1 kim:2 n22:2 scenario:1 βb2:1 βb1:2 quoted:1 identify:2 transforms:1 spherically:1 rotates:1 eigenstates:1 previous:1 adding:1 vibration:1 proeyen:1 transformed:1 easy:1 iτ:1 gustav:1 breaks:1 possible:2 caps:1 possibly:1 apart:1 dµi:1 appearing:1 specific:3 remind:1 bps:49 schwarz:1 arbitrary:1 right:6 deal:1 indirect:1 electromagnetic:15 comments:2 super:4 o:4 horizon:31 eight:1 ǫijkl:5 presence:1 puzzle:1 bound:7 wrap:1 fortsch:2 iδij:1 vafa:1 support:1 initial:1 transform:1 why:2 fraction:3 was:14 form:15 attempted:1 analyse:2 parametrise:1 rγ2:1 bounds:1 fermi:2 stages:1 b1:39 gaiotto:3 abstract:1 evidence:2 conserved:2 exist:5 dθ:1 accounting:1 dβ:1 check:2 constructed:3 ni:2 no:2 whereas:1 when:15 vanishes:1 role:2 picture:3 ξq:1 ξi:3 ξj:1 variable:2 assume:2 dτ:1 governed:1 time:13 n1:7 n2:21 n3:5 global:19 leads:11 computation:4 reichmann:1 depend:1 charge:7 promoting:1 analogous:5 string:5 orthogonal:3 forcella:2 keeping:2 choice:1 exact:1 annihilated:1 did:2 leave:3 solved:3 round:1 upper:6 work:4 sign:5 appear:1 suspect:1 goes:1 satisfy:14 gutowski:6 understanding:2 cos4:6 cos3:2 cos2:13 address:1 alone:1 along:4 appears:1 popescu:1 studied:2 spheres:1 accomplished:1 poisson:1 hospitality:1 myers:2 useful:2 extra:1 merely:1 aganagic:1 projector:2 explicitly:2 compactly:3 theoretical:1 duality:2 claus:1 appendix:2 cases:2 fermionic:1 4l:9 valued:1 deformed:3 oscillator:3 quivers:1 values:2 achieve:1 cam:1 following:6 making:1 arrive:2 8l2:1 expanding:1 arise:1 plethystic:1 allowed:2 counting:20 evidently:1 s2:1 discussion:3 s5:13 write:2 fourth:1 parameter:5 may:12 produce:1 ω2n:2 2l2:10 natural:3 explicit:1 yielding:1 su:2 so:8 maximisation:2 sonner:3 indeed:2 years:2 statistical:3 differs:1 still:2 derive:1 group:1 thank:4 interesting:4 coordinates:38 forms:1 correspondence:1 non:14 introduce:2 scaling:1 half:5 now:19 term:7 drop:1 realise:1 entirely:1 individually:3 el:3 ei:9 conventions:1 σ2l:3 rl2:1 shown:8 space:20 furthermore:4 investigation:1 emerged:1 suggesting:1 formula:2 correct:2 earlier:2 theory:4 divergence:1 possibility:2 e1:36 e3:35 e2:27 zaffaroni:2 derivation:2 impose:1 motion:16 turn:6 hanany:4 tafjord:2 promotion:1 first:3 origin:1 simplifies:3 symmetry:7 variables:3 xa:2 simplified:1 directly:2 carry:5 ring:1 open:11 angular:11 squashed:2 given:15 yin:2 physically:1 1l:1 gives:13 rabinovici:1 bekenstein:1 way:8 proving:1 transverse:2 j3:2 than:4 coefficients:2 braine:1 accordance:2 were:4 conjectural:1 ann:1 turned:4 argument:5 say:1 any:6 note:7 potential:4 take:5 smicro:1 sure:2 multiple:2 opposite:1 track:1 probes:10 surprising:1 later:3 typeset:1 quantity:2 show:4 discovered:1 raju:1 ground:1 fibre:3 feng:3 fibrations:1 aφ:1 written:4 only:4 going:1 black:61 get:4 partitioning:4 cannot:1 progress:1 hedge:1 gauged:4 predicted:1 imposing:4 j1:2 j2:2 maximum:2 college:1 surgery:1 surfaces:1 satisfying:4 commutation:1 ways:8 review:5 colours:1 between:4 justified:1 notice:2 killing:4 js:1 σi:1 quantised:1 many:1 embedding:6 expression:2 comes:2 period:1 dφ21:1 dφ22:1 anti:10 stretched:1 constant:4 branes:21 considering:1 submanifold:1 locally:1 dρ2:1 direction:4 dramatic:1 jǫ:1 spirit:1 those:2 case:21 minwalla:2 developing:1 hdg:2 conformal:1 strominger:5 coupled:1 metric:10 regularity:1 fibration:2 susy:2 superconformal:4 different:2 commuting:1 same:24 poincar:13 investigated:1 running:1 invariance:1 modes:5 charges:5 kallosh:1 without:9 solve:4 components:3 coordinate:9 model:2 ωlab:1 gates:1 being:1 actions:1 hint:1 seems:1 lett:3 momentum:21 real:3 around:2 vacuum:1 world:38 ruled:1 particle:1 identifying:2 either:1 satisfactory:1 provided:2 dimensions:2 propagating:1 equivalent:2 eiφ:1 central:1 discussed:2 obeys:1 referred:1 ds210:1 cambridge:3 inclusion:1 references:1 determine:3 einstein:3 operator:1 goliath:1 hep:51 h03:3 h02:6 h00:11 start:1 pull:1 applying:1 embedded:1 dφ:2 jω:7 ac:1 ab:4 conundrum:1 certain:4 ak:2 describe:2 general:10 associating:1 together:5 ax:2 adsm:1 again:7 field:29 valid:1 spatial:3 mathematics:1 balasubramanian:1 perpendicular:1 ads5:24 ads2:13 commutator:2 a2:2 included:1 gaugeinvariant:1 observe:1 mass:2 strings:7 iǫ0:6 sci:1 consider:6 follow:2 expressions:1 correa:1 preserves:2 former:1 program:1 preserved:5 th:51 very:3 conjectured:1 coloured:2 minded:1 difference:2 deformations:1 condition:17 treating:1 switches:1 hamiltonian:8 t3:36 large:3 small:4 ten:2 zero:11 further:10 canonical:2 bilinear:2 what:5 brackets:3 contributions:2 section:17 abl:1 version:1 warnick:1 avenues:1 method:1 full:5 component:1 directions:3 berkooz:1 equations:30 ahead:1 pick:2 action:4 via:1 ask:1 clifford:1 silva:2 proceed:1 finally:2 comparing:1 nucl:7 sitter:1 more:7 flat:1 operators:8 broke:1 particular:1 known:4 none:2 h11:5 equation:6 det:11 γkl:4 compare:3 states:16 sphere:7 numbers:4 sense:2 information:1 needs:1 rather:3 breaking:2 csc:5 dσ2:1 dσ3:1 dσ1:1 algebra:3 ζi:5 ζj:1 waves:29 invasion:1 kinney:1 jevicki:2 implausible:1 paper:9 existence:3 excitations:1 its:1 style:1 microstates:14 solving:4 absence:3 microscopic:9 systems:2 quantise:2 deformation:1 supersymmetry:33 motivated:4 martelli:1 perceived:1 anticipated:1 obeyed:1 suryanarayana:7 2v:2 2r:1 2b:1 2l:18 found:7 2n:4 2k:3 mikhailov:2 energy:8 reduce:2 expect:1 quantum:33 organised:1 missed:1 since:13 denotes:1 equate:1 induced:5 occurs:1 basu:1 b32:1 reason:2 base:2 put:1 sbh:8 recast:1 just:2 sheikh:2 consequence:1 feel:1 fluxed:4 number:26 instances:1 done:1 least:2 calculational:1 fluxes:26 equating:2 introduction:2 leading:4 construct:1 dt2:1 holomorphic:2 part:7 off:1 kind:1 horizons:1 double:1 anticipate:1 annihilation:2 determined:1 treated:1 bhg:28 2t3:1 conjugate:6 orders:1 speculative:1 h23:2 h22:13 extracted:1 pparc:2 analogy:1 finding:1 unconstrained:2 play:1 electric:6 rhs:1 most:2 mohaupt:1 significant:1 stands:1 clear:3 exp:7 velocity:7 physics:2 hyper:1 cot2:1 relation:12 find:7 occupation:1 giant:48 parameters:1 generators:1 factor:9 giants:38 meanwhile:1 dependent:2 correia:1 combinations:2 during:1 spikes:1 arxiv:52 investigate:4 set:4 achieved:2 plausible:1 see:9 focuses:1 various:2 conditions:7 biswas:1 vanishing:1 condi:1 both:9 collaborators:1 connection:1 context:3 whole:2 supply:1 simple:3 asymptotically:3 corresponds:2 coincidence:1 dimensional:10 simply:1 ensures:1 described:2 transformations:1 cederwall:1 px:3 due:2 pi:1 generating:1 2iv:1 lives:1 systematic:1 demand:1 attractors:4 look:1 exponential:1 while:8 von:1 reads:4 normalisable:1 2g3:1 2g5:1 higher:2 used:6 h33:6 moving:1 lower:2 analysis:10 prokushkin:1 using:7 alternative:1 γijkl:1 efi:1 source:1 mandal:3 remaining:3 periodicity:1 cargese:1 squashing:1 appendices:1 integer:6 projects:1 helpful:1 imposed:1 aξ1:1 follows:7 flux:8 yields:2 creation:2 some:7 back:1 pρ:2 pφ:20 examples:1 b2:38 b3:35 pψ:4 integration:1 minimal:1 inserting:1 varying:1 dictates:5 bi:3 dictated:2 hilbert:3 integers:3 anything:1 constraint:6 pe1:8 pe2:6 pe3:9 range:2 gamma:3 seeing:1 into:7 integral:2 proportional:4 next:4 question:2 sections:2 considerably:1 bǫ:1 maximised:2 travelling:1 up:3 us:18 un:2 uk:2 planes:1 fluctuations:3 similar:2 called:1 associated:6 defined:5 single:2 sasaki:3 rewriting:1 nick:1 bracket:1 department:1 nice:1 meaning:1 structure:1 ago:2 bases:1 implies:4 required:1 holes:24 far:1 having:1 partial:1 gr:1 results:4 gk:4 issues:1 compact:1 simon:1 dα2:2 g5:1 g3:1 g2:1 wave:5 putting:1 telling:1 matrices:3 eigenmodes:1 configurations:16 encloses:1 sin2:8 imply:1 enclosed:1 cft:3 odd:1 index:1 chicago:1 giving:2 expressed:1 3n:2 3l:3 justification:1 lee:2 objects:3 sinh:1 consideration:1 extreme:1 rdt:1 involved:1 larger:1 suggests:3 resulting:4 grisaru:1 makes:1 involves:1 4a2:1 scales:1 maldacena:2 wit:1 use:3 asymptotic:6 remains:1 θdψ:1 doubling:1 simpler:1 westerberg:1 becomes:1 carrying:3 labelled:1 iib:2 account:6 integrating:6 reproduce:1 obvious:1 drops:1 dropped:1 calculation:1 lω:10 bena:1 tan:7 mcgreevy:1 fρλ:1 sit:1 holds:1 parametrised:1 instead:1 constraints:14 sin:48 tension:2 collection:1 realized:4 computations:5 light:1 lines:1 correspond:4 extremal:1 gravitons:21 s1:1 unsolved:1 closely:1 ωl2:1 ln:2 lu:2 degrees:4 choose:4 defining:3 descendants:4 landau:1 graviton:1 das:3 front:1 rotation:2 dirac:2 university:2 l4:6 l5:1 l2:28 l3:1 l8:1 warner:1 doing:1 related:6 elementary:1 static:4 supersymmetries:22 our:6 popping:1 out:7 matrix:1 rev:6 integrated:1 diagonal:1 completely:1 dirichlet:1 geometry:25 could:7 david:1 ahler:1 length:1 hence:10 noncommutativity:1 cy3:1 there:22 manuscript:1 precisely:4 πa:2 4g5:1 system:4 relations:3 herdeiro:1 their:5 fermions:1 wrapped:1 πx:3 benvenuti:1 final:2 townsend:2 shell:1 tuple:1 exactly:4 chong:2 sadri:1 julian:1 need:6 constrained:2 viewed:1 studying:1 mills:3 instance:1 kunduri:1 lectures:3 centre:1 collaboration:2 plugging:1 propagate:1 class:11 4l2:11 romelsberger:1 4l4:2 lλ:25 snapshot:1 mechanical:8 fact:3 dbi:2 supported:1 rotating:1 purely:1 trivial:6 agrees:1 pξi:10 baryonic:2 sparks:1 should:9 jan:1 2bl:1 µi:5 hopf:2 hope:1 overall:1 densities:7 differential:2 grav:3 qc:1 fuzzball:2 contain:1 pξ1:9 including:1 fixed:3 superstars:1 view:1 moduli:2 computed:1 exists:2 argued:1 cvetic:2 enhanced:1 missing:8 state:8 identification:1 closed:1 invariant:5 ωl:1 reproduced:1 reproduces:1 butti:1 configuration:9 undetermined:1 limits:1 taking:5 equal:1 2e2:1 otherwise:1 conclude:1 harmonic:3 θe1:2 θe2:1 respect:1 addition:4 aligning:1 bianchi:9 hawking:1 proposal:1 define:3 arises:2 corresponding:6 subspace:1 angles:1 present:2 multi:1 lucietti:1 harder:1 value:1 choices:1 will:30 simons:1 damtp:2 thus:10 surface:4 dual:46 orbital:1 az:2 fkl:2 cross:1 unity:2 parts:3 gets:1 difficult:1 upon:2 v3:6 v5:2 expand:1 supercharges:3 well:1 thought:5 sets:2 firstly:1 arising:3 realised:1 spherical:1 less:2 obtain:2 sources:1 predicts:1 momenta:10 macroscopic:5 preprint:1 ads:12 density:4 point:2 thermodynamics:1 extends:1 match:1 details:7 identical:1 five:7 insert:1 necessary:1 like:8 qualitative:1 become:1 wonders:1 because:2 classical:4 gauntlett:1 briefly:1 algebraically:1 choosing:1 happens:1 encouraging:1 lead:4 does:2 dipoles:1 assuming:1 6a2:1 demonstrated:2 obey:2 analysed:1 expansion:1 σil:1 although:2 imaginary:3 stage:1 about:2 carried:3 6ab:1 freedom:4 dependence:2 quantisation:7 carries:2 important:3 introduced:1 dorey:1 em:1 own:1 bergshoeff:1 spinor:8 bosonic:1 βg1:1 van:1 additional:9 vac:1 2m:2 naturally:1 function:2 brane:30 but:8 volume:38 construction:1 dξi:3 hg:1 he:2 count:5 made:1 compute:4 evident:1 wish:2 below:1 limit:2 demonstrate:4 problem:7 piece:2 mechanics:5 contribute:3 denote:3 separating:1 interchanged:1 identities:9 proceeds:1 diego:1 functions:3 compared:1 susskind:1 ingredients:1 detail:2 other:4 special:1 figueras:1 conclusion:1 toumbas:1 bundle:1 auxiliary:1 original:1 portion:1 4m:1 volumes:1 understand:1 4d:1 4a:1
0705.0375.txt |@word consider:5 chain:1 rev:19 global:4 correo:1 p02:1 ge:1 go:1 gn:1 gk:2 gj:9 sch:2 compact:1 retzker:1 effort:1 technique:3 th:2 under:3 hume:1 g2:1 g1:1 evolves:1 frequencies:3 wave:4 electron:1 resonant:1 experimentally:1 condition:2 leads:1 kaszlikowski:1 level:5 proposals:1 assignments:2 excellence:1 red:3 optics:1 jaynes:1 possibility:1 direct:1 pulse:3 approximation:1 second:1 reznik:1 manipulating:2 dynamics:5 implemented:1 theory:1 blue:4 established:2 appear:1 selected:1 access:2 experiment:1 schmid:1 subspaces:3 new:2 ˆj:3 increasing:1 method:6 ˆn:4 d1:5 respectively:1 here:3 courtens:1 selective:12 inversion:1 jaynescummings:1 along:2 taylor:1 appears:1 great:1 shift:3 study:2 studied:1 allows:1 through:2 permutation:1 resonance:7 suitable:4 king:1 composed:1 matos:2 via:6 useful:2 projection:1 addressed:1 jˆx:1 lima:1 manipulate:2 standing:1 use:2 would:1 prove:2 distinct:1 nonsymmetric:4 hilbert:3 partite:1 peru:1 meyer:1 type:1 theoretical:1 more:5 chiaverini:1 becomes:1 operators:4 corrected:1 validity:1 particular:1 known:1 cases:3 iii:1 must:1 high:3 eiω1:1 eiω0:1 science:1 mn:1 oscillator:1 cat:1 remain:1 fock:1 del:1 ms:2 concepts:1 following:1 fulfill:1 roos:1 example:3 control:4 ions:15 choice:1 permutations:1 states:31 effectively:1 numbers:1 want:2 sense:1 maximilian:1 subsystem:1 lamb:1 information:2 requirements:1 winter:1 produces:1 six:1 write:2 how:1 stemming:2 instead:1 sin:1 agarwal:1 may:5 ancilla:1 after:2 santos:3 diagram:1 applications:7 ω2j:5 produce:4 shelving:1 fk:3 verstraete:1 realized:2 effective:5 lines:1 yielding:1 ghz:2 allow:4 lambda:1 sackett:1 order:4 se:1 typical:1 operations:1 noteworthy:1 tavis:3 move:1 displayed:1 experiments:1 including:1 twoqubit:1 lasers:4 still:1 excitations:14 its:2 riebe:2 derive:2 remark:1 probability:1 kiesel:1 interesting:1 zˆ:2 writing:1 wineland:3 degrees:4 fig:2 rabi:1 affner:2 travelling:2 schmidt:2 might:1 rwa:1 them:1 propose:2 cel:2 introduce:1 they:2 now:3 discuss:1 inhomogeneously:3 ℓk:2 february:1 several:1 university:1 hamiltonian:10 sideband:6 establishing:1 realistic:1 mode:2 each:1 found:1 universit:1 characterized:1 homogeneous:6 en:2 another:1 eschner:1 ej:7 generation:3 there:2 energy:1 related:1 deterministically:1 frequency:1 knill:1 measurement:2 quantum:5 our:1 happen:1 transitions:1 eq:9 special:1 out:1 divincenzo:1 shown:2 driving:1 space:3 furthermore:1 induces:1 europhys:1 hill:1 fran:3 ref:1 rj:2 numerical:1 linear:2 interactions:8 ısica:2 transfer:1 departamento:2 asc:1 qualify:1 term:1 interaction:7 angle:1 could:3 transition:5 ck:4 positiondependent:1 motion:3 doublet:1 universidad:2 ionic:18 atz:1 first:3 ieee:1 already:2 symmetry:1 opez:2 omitted:1 number:16 restrict:1 clear:1 done:1 long:1 directly:1 electronic:2 angular:2 illustrate:1 given:4 necessarily:1 fondecyt:1 rewritten:1 similarly:1 introduction:1 interact:1 system:8 their:2 assumption:1 realization:1 initialized:1 dfg:1 scheme:1 collapse:1 trapped:7 giedke:1 stress:1 optical:2 manipulation:3 believe:1 than:2 secci:1 population:2 ofmass:1 1j:1 zagury:1 require:1 icm:1 matter:1 determined:5 were:1 tion:1 published:1 hz:1 addressing:1 rewrite:1 turned:1 generalization:1 correspond:2 manner:4 ω1j:7 weinfurter:1 any:3 multipartite:8 strength:2 realm:1 depending:2 efficient:1 convenient:1 overcoming:1 note:2 k2:1 k1:1 potential:1 schliemann:1 generalized:2 ωeff:13 ancillary:3 eff:8 heisenberg:1 even:1 play:1 towards:1 fundamental:1 opposite:1 kar:1 involving:2 germany:1 cummings:4 letter:1 successive:2 britton:2 probabilistic:2 christ:1 considered:2 ki:1 astonishing:1 part:1 exp:2 mogeneous:1 physics:2 fact:1 quantity:1 gulde:1 thomas:1 shot:1 inspire:1 show:2 german:1 supported:1 rotating:1 fleischhauer:1 ck0:3 d2:2 availability:1 d0:3 ground:2 based:2 parameters:3 turchette:1 entangling:1 distributed:1 written:2 operational:1 jan:1 only:1 sequential:2 kaler:1 constant:1 achieve:1 boulder:1 σn:1 dk:11 means:1 dependent:4 mainly:1 de:7 dc:1 cannot:1 geg:1 adiabatically:1 evolution:3 fields:3 arxiv:2 tuned:2 financially:1 pulses:1 fixed:3 approximations:1 nist:1 view:1 becher:2 set:2 sep:1 frame:1 plausible:1 collectively:2 terms:2 ieiφ:1 analog:1 techniques:2 ωj0:3 interacting:1 dk0:14 resonantly:1 milman:1 blatt:2 motional:6 symmetric:19 initially:1 state:27 between:3 conditions:3 recently:2 nature:3 importance:1 wn:4 however:1 scalability:1 deterministic:1 maximilians:1 selectively:3 ozeri:1 barrett:1 both:1 cos:3 2n:1 similar:3 conclusions:1 itano:2 fulfilled:1 olica:1 dated:1 filho:2 qubit:5 expression:1 τd:1 experimental:2 unitarily:1 among:1 relevant:1 point:1 wootters:2 ca:3 harmonic:1 dimensional:1 homogeneously:2 anti:1 moreover:2 sen:2 considering:1 described:2 tuning:4 basis:2 cens:1 romero:1 three:1 been:8 t2:2 detuning:4 compensating:1 pk:2 ph:2 systems:1 oth:1 generating:2 general:3 subspace:20 precision:2 fortschr:1 milenio:1 coherent:1 external:1 chile:2 maximally:1 spin:2 spirit:1 present:1 aid:1 case:14 multi:1 laser:7 look:1 pacs:1 will:15 preselected:1 suppose:1 situation:1 procedure:1 unitary:1 coupled:2 von:2 vk:1 iv:1 ii:1 reads:1 bastin:1 k0:12 monroe:1 unanyan:1 sequentially:2 different:5 grant:1 acknowledgments:1 make:1 same:1 shorter:1 shifts:4 quant:2 physical:1 ludwig:2 difficult:1 used:2 benhelm:1 nim:1 permit:1 jˆk:1 hand:1 ion:6 levels:3 hospitality:1 entanglement:2 robust:1 ab:1 ωk:1 tune:3 reichle:1 off:2 center:2 scenario:1 raussendorf:1 well:3 δ0j:5 components:1 fk0:1 claims:1 model:4 arising:1 dimension:1 entangled:5 gates:2 proposed:3 cj:8 obtain:1 chwalla:1 select:1 tasks:1 atomic:2 paul:1 candidate:1 application:2 excites:2 dicke:24 exclusively:1 improvement:1 jost:2 internal:5 lett:12 blakestad:1 spin1:1 excited:1 momentum:2 iφ:1 tests:1 marcus:1 replaced:1 showing:1 possible:2 munich:3 corresponds:2 threelevel:1 ciencias:1 average:1 projects:1 helpful:1 loss:1 like:1 should:2 collective:18 adiabatic:1 extremely:1 yields:1 arbitrary:2 setups:1 initiative:2 jˆ:15 reduced:2 pontificia:1 qed:1 deal:1 thiel:1 some:1 santiago:2 selectivity:4 gilmore:1 respect:1 proper:1 myatt:1 seidelin:1 provided:1 total:1 lead:4 cavity:1 sfb:1 per:1 instantaneous:1 eliminate:1 assuming:2 propagating:1 proc:1 demonstrated:1 trap:1 disentangle:1 selecting:1 casilla:1 stay:1 properties:2 nanosystems:1 carried:1 freedom:4 discussed:1 dependence:1 o:2 langer:3 briegel:1 carrier:2 wolf:1 2j:2 discard:1 introduced:2 considerations:1 previously:1 usach:1 into:3 obtaining:2 ηi:2 due:3 accounts:1 arecchi:1 proportional:1 reducing:1 bosonic:2 additional:1 assumed:1 initial:6 vedral:1 stark:6 rowe:1 way:4 eg:1 naturally:1 raman:5 kielpinski:1 form:2 metastable:1 but:3 ho:1 atom:1 applying:1 inhomogeneous:4 lukin:1 inside:7 us:6 ur:1 below:2 limit:1 spectroscopy:1 ωc:1 ωe:1 called:1 ac:4 cirac:1 associated:3 computing:1 lancaster:1 universal:1 measure:1 2mν:1 eu:1 single:4 diverse:1 exist:1 ing:1 apartado:1 regime:1 ansel:1 discriminate:3 jcr:1 no:1 index:1 tailoring:1 thanks:1 field:5 other:3 role:1 es:1 department:1 conclusion:1 uhne:1 picture:3 solano:9 superposition:3 excitation:6 condens:1 initio:1 khaetskii:1 prepared:4 delft:1 generated:1 conicyt:1 needed:1 building:1 coupling:7 values:1 persistent:1 together:1 phonon:2 leibfried:2 mass:1 time:5 n0:19 decoherence:2 once:1
0705.0376.txt |@word four:1 localized:1 whose:6 const:1 paris:3 superficially:1 under:2 hermann:1 divergent:2 rise:1 every:3 experimentally:1 bringing:1 prize:1 solution:4 enclosing:2 specially:1 pulse:2 approximation:1 surrounding:1 second:2 rigorous:1 even:3 established:1 above:1 new:20 men:1 atoms:1 reported:3 represented:2 bogdan:1 interpret:2 obtained:7 study:3 fourier:4 hoffman:3 criticism:1 golden:2 discontinuous:1 explained:1 univ:1 derivatives:7 negative:2 call:1 oscar:1 ascribe:1 berlin:2 hold:1 must:3 ii:1 springer:1 join:1 mc:1 permits:1 work:9 theories:2 transparency:1 concepts:2 my:3 example:3 renormalization:1 give:3 organized:1 magnitudes:2 hoc:1 turn:2 verify:2 how:2 nontrivial:1 field:15 sato:2 transforming:1 after:5 law:1 third:1 acknowledged:1 green:1 enter:1 order:6 operations:1 restriction:1 interpretation:3 over:4 london:2 rewarded:1 integrands:2 before:6 better:1 weeks:1 them:2 combination:1 similar:4 repulsive:2 they:11 singularity:1 eigenvalue:1 each:1 side:2 mean:1 series:1 principles:2 literature:1 substantially:1 particles:3 fellowship:1 interchanging:1 linear:5 associate:2 free:1 enormous:1 created:1 starts:1 δip:5 moving:1 primary:1 adopted:1 categorize:1 illustrate:1 fiction:2 needed:1 too:2 difference:1 centered:2 definitions:1 took:1 rejected:1 toronto:1 distance:1 princeton:4 matter:8 kth:1 tackled:2 boston:1 modern:2 mind:1 spectrum:1 rau:1 seen:1 seem:1 contents:1 strength:1 harper:1 convenient:1 definite:2 recommended:1 completed:1 shall:2 birkh:1 metrics:1 simplify:1 involving:1 vicinities:1 phase:1 acknowledgements:1 exico:3 observation:1 flow:1 inferred:1 points:1 principle:3 notion:1 reprinted:1 dover:2 labels:1 prix:1 attempts:2 gauge:1 conclusion:3 proposed:1 do:1 establishes:2 de:6 dt:1 finally:3 fields:1 maciej:1 simplification:2 reference:1 observed:1 depends:1 decided:2 result:4 techniques:1 said:1 tensor:1 eigenstates:1 symmetric:1 simplest:1 conceptual:1 propagated:1 encounters:1 never:2 terms:2 nature:1 modify:1 weak:1 however:8 huang:1 topology:1 bras:1 received:1 essentially:2 refinement:1 ill:1 uncertainty:1 und:2 faces:1 monograph:3 had:7 infinitely:3 wider:1 conference:1 commutative:2 three:6 been:15 much:1 interest:3 basic:2 topics:2 supersymmetric:2 deeper:2 quantities:3 concerning:1 worked:5 applied:2 formalization:1 nski:41 property:1 procedure:12 mexico:2 iv:1 obeying:1 gosdzinsky:1 id:1 conn:1 memorial:1 things:1 make:2 complex:1 quant:1 influenced:1 differing:1 hand:2 auser:1 potentials:13 prescribed:1 recurse:1 contact:1 left:2 birth:1 quoted:1 assigned:1 thanks:1 tilde:1 followed:2 scattering:1 yet:1 previous:1 infinitely:1 royal:2 easy:3 iπ:1 gave:3 possible:3 background:2 advanced:2 apart:1 appearing:1 scheidegger:2 arbitrary:6 calculus:2 right:1 old:1 deal:1 people:1 successfully:1 born:16 paragraphs:1 electromagnetic:1 quarks:1 specific:2 core:1 meanings:1 rosas:5 substituted:1 leptons:1 hadamard:2 super:1 permitted:1 chapter:2 anomalous:1 o:7 nonvanishing:1 soc:3 presence:2 maxwell:1 puzzle:1 bound:1 lies:2 acad:5 reducing:1 methods:3 initial:1 transform:1 class:5 way:4 researchers:1 queens:1 was:30 underestimated:1 medium:2 form:4 forming:1 analyse:1 mercado:1 true:2 contradistinction:1 arrays:2 inside:1 hyperfunctions:1 crystal:1 more:11 proved:1 abstract:2 dθ:2 dζ:24 perez:1 distributions:8 grundlagen:1 no:6 whereas:1 when:6 vanishes:2 build:1 interested:2 role:1 papers:2 test:3 company:2 picture:1 models:1 preceding:2 mechanical:3 variable:5 longer:1 assume:1 daily:1 time:11 observables:2 laws:2 concept:6 remarkable:2 skip:1 leads:3 grateful:1 row:1 devoted:1 certainly:1 depend:1 editors:2 crater:1 ıa:3 finally:2 marks:1 analogous:1 rαβ:2 frequencies:1 choice:1 advised:1 ma:1 emphasized:1 exact:1 preuss:1 presented:2 did:1 die:1 leave:1 solved:5 yale:1 der:8 unexpected:2 occurrence:1 dealing:2 measurable:1 riesz:2 sign:1 cost:2 substitutes:1 substitute:1 appear:1 satisfy:1 understanding:1 appears:1 change:1 sobolev:3 brilliant:1 studied:3 poisson:3 usually:1 conveniently:1 studies:2 boykin:3 useful:1 hermite:2 merely:1 prefer:1 should:6 planck:1 additive:1 working:1 positive:3 sensu:1 properties:6 bialynicki:1 overviews:1 theoretical:5 smeared:1 introducing:1 club:1 ip2:1 ip3:1 appendix:1 ip4:2 cases:2 lapidus:2 tokyo:1 modified:1 ıaz:1 values:4 following:7 expanding:1 topic:2 dropped:1 regularization:5 darboux:2 discussion:2 write:1 till:1 fourth:1 parameter:2 divides:1 redundance:1 product:2 quantenmechanik:2 influenced:1 may:3 max:1 applications:4 representations:1 waerden:4 dynamical:5 whenever:3 cosmology:1 so:5 representation:3 talk:2 schwartz:3 indeed:6 years:10 experiments:1 statistical:2 derive:1 group:4 wallace:2 finished:1 interesting:2 coordinates:2 main:2 correspondence:1 non:6 thereby:1 conversations:1 hamilton:1 acta:4 now:5 ordinary:4 developments:1 term:1 equality:1 name:1 advent:1 realistic:3 atstheorie:1 different:2 domain:2 square:1 ed:2 approximates:1 year:1 eq:1 canada:2 shown:3 accomplish:1 opened:3 space:5 furthermore:2 mehra:4 attracted:2 formula:1 correct:1 shows:1 earlier:1 theory:29 divergence:1 departamento:1 quite:2 axioms:1 training:1 derivation:2 motion:23 thing:2 gordon:1 invitation:1 first:1 origin:3 intuition:1 variables:2 symbolic:1 directly:2 xs:4 open:1 engineer:1 necessarily:2 typing:1 structures:1 nordheim:1 continuous:5 x0:1 copy:1 than:8 were:12 troublesome:1 remained:1 ann:1 argument:1 say:2 himself:1 any:5 warsaw:2 facult:1 ideas:2 sciences:1 potential:4 take:6 begin:1 trautman:1 multiple:1 opposite:1 algebraic:1 sheets:1 formulae:1 remarks:2 eigenfunctions:1 considered:5 later:8 simplifications:1 typeset:1 quantity:2 precise:1 show:1 atom:1 contemporary:1 representatives:1 spaces:1 title:1 written:2 only:1 going:1 get:2 assistant:1 gen:4 closure:1 intuitive:1 ignored:1 publishers:1 espa:1 namely:1 surfaces:2 commutation:2 ways:1 review:1 functionals:1 cinvestav:3 behind:1 between:4 justified:1 reading:1 infinite:2 analyzed:1 comb:1 reaction:3 many:2 according:2 called:2 deduction:1 propagation:2 expression:2 among:2 jammer:5 kennefick:1 dutt:2 pol:5 associated:1 considering:2 unusual:1 tential:1 those:2 case:5 christiansen:3 eih:6 eik:1 taking:1 attributed:1 susy:1 different:1 verified:1 same:3 speech:1 physical:5 investigated:1 singapore:5 sudarshan:2 akademie:1 changing:1 without:3 model:2 dimension:3 bodies:1 consisted:1 being:2 rest:1 infeld:57 manipulation:1 relevant:1 polish:1 speed:2 eorie:3 refinements:1 seems:2 except:2 treatment:1 momentum:4 real:7 aspects:1 rules:3 early:1 formalize:1 using:3 mod:1 acquainted:1 particle:2 either:2 integrals:3 reduced:1 cabo:1 madrid:1 provided:2 dimensions:2 critical:1 provides:1 scientific:1 power:1 sitzungsberichte:1 equivalent:3 discussed:1 practical:2 organizers:1 cambridge:3 garc:3 references:1 determine:1 einstein:21 operator:2 nowadays:3 theoretically:1 log:2 seba:2 ortiz:5 there:4 lon:1 hertz:1 start:1 stars:2 labelling:1 decisive:1 complete:2 newtonian:2 enough:2 tarrach:1 mcyt:1 mat:1 ωk:4 kapitza:1 simplifies:1 strongly:1 celestial:1 ad:1 exhausted:2 certain:6 am:13 general:16 ap:1 examine:1 together:2 formulation:3 politics:1 again:1 graduate:1 field:3 narrowing:1 spatial:1 mathematics:3 differential:2 students:2 remarked:2 miriam:1 important:1 thorn:1 mass:1 resembles:1 gαβ:4 represent:3 sci:3 consider:1 bull:5 month:1 scalar:1 commute:1 expressions:1 present:3 th:3 enjoying:1 belonging:1 amplitudes:2 returned:1 very:6 interpreting:1 fac:1 goenner:1 applicable:1 large:1 small:4 ten:2 zero:4 further:1 canonical:1 what:4 nonlinear:2 section:4 brief:1 version:1 sur:1 method:7 movement:2 edited:1 fields:2 excess:1 concluding:1 equations:25 search:1 prior:1 amount:1 periodic:2 published:10 action:2 shorthand:1 family:2 requiring:1 first:8 conventional:1 charge:2 taken:1 defining:3 ugge:1 operators:4 emission:1 particular:3 known:1 foundations:5 taub:1 science:1 equation:6 des:4 eigenkets:2 history:2 stated:1 states:1 fundamenta:1 numbers:2 sense:6 sharp:1 information:1 needs:1 cours:1 rather:2 fix:2 acknowledging:1 algebra:3 singularities:7 orbits:1 inconceivable:1 fl:1 resemble:1 departure:1 coutinho:1 sect:1 fundamental:2 playing:1 developed:2 soon:1 paper:15 its:6 continued:1 actually:1 might:1 good:4 somebody:1 number:3 oxford:3 gets:2 goldstein:1 always:3 2d:1 turns:1 found:2 energy:3 idea:6 expect:1 measurement:1 quantum:36 beyond:1 really:1 discrete:2 robert:1 since:1 research:3 tαβ:3 denoted:1 occurs:1 relativit:1 put:2 beginning:2 definition:1 just:4 accumulation:2 american:1 consequence:1 integrand:4 botany:1 probability:1 geodesic:1 done:4 temperature:1 introduction:4 least:3 assumption:1 calculations:4 scheme:1 elaboration:1 warmly:1 statement:1 akad:1 immediate:1 part:1 jordan:2 believe:1 kind:1 double:2 determined:1 intensities:1 electrodynamics:5 cumbersome:1 lie:1 depending:2 lim:2 self:3 generalized:7 gill:1 added:1 jerzy:4 albert:1 most:1 measured:2 cover:1 rockefeller:1 kr:1 reflections:1 physics:16 converge:1 fine:1 find:1 assertion:1 emoire:1 factor:1 his:12 dominant:1 notation:2 adheres:1 during:1 him:2 progressive:1 arxiv:1 factorization:1 oppenheimer:1 difficulties:1 zur:1 wrote:2 annalen:1 set:3 ser:1 uses:1 plausible:1 see:24 sec:2 descriptions:1 close:1 conditions:1 recently:2 attention:3 succeed:1 both:2 last:4 connection:2 became:1 context:4 whole:3 experimental:1 fulfilling:1 reconsidered:1 point:9 simple:2 przanowski:2 corresponds:1 improper:13 simply:1 pp:7 publishing:1 acceptance:1 collaborator:1 extends:2 ph:1 po:1 lett:1 remark:2 neumann:5 lives:1 intriguing:1 solid:1 institute:3 replaced:1 engineers:1 unitary:1 vol:5 von:5 polon:5 vanish:2 read:1 stimulated:1 higher:2 development:4 used:7 domains:2 arrived:3 vreg:3 recent:1 poland:2 blanco:1 nola:1 analysis:1 concrete:1 atomic:1 world:10 alternative:2 theorem:6 relevance:2 guarantees:1 solvable:1 transformation:10 useless:1 showing:1 2iλ:1 quest:2 formal:1 skeptical:1 follows:2 ignore:1 collect:1 popular:1 mathematical:8 sketch:1 often:1 sgn:2 some:9 remarking:1 understood:1 delivered:1 scale:1 integration:10 behave:1 proc:3 performed:1 pleba:37 hilbert:4 sidered:1 range:7 regular:2 bloch:1 seeing:1 into:3 integral:6 montesinos:1 appropriate:1 controversies:1 proportional:1 lone:1 long:2 forward:1 analyze:4 boya:1 gauss:1 properly:1 delta:20 line:4 considerable:1 consist:2 characteristic:1 up:3 us:5 spectroscopy:1 chelsea:1 laplace:1 uber:2 constant:2 reconcile:1 influence:1 single:1 diverse:2 formalism:1 grt:1 application:3 electrical:1 lucio:1 draw:1 calculating:1 sided:1 problems:3 prepared:1 meaning:3 birula:1 sides:3 structure:1 independently:1 age:2 required:2 ip1:2 incomplete:1 walker:1 requires:2 having:1 once:1 partial:1 gr:4 results:11 eds:1 go:1 contributions:1 equivalences:1 concerned:1 young:1 breach:1 sent:1 expressing:1 wave:2 electron:4 wishes:1 trough:1 mixing:1 nieto:4 matrices:1 entire:3 notes:1 ryan:1 deals:1 epstein:1 dealt:1 eigenvalues:4 optics:1 concluded:2 smaller:1 sukhatme:1 sin2:1 insertion:1 manipulating:1 dynamics:3 plays:1 giving:1 henceforth:2 publications:2 body:1 led:1 degree:1 exchange:1 respectively:1 growing:1 objects:4 implicit:1 deduced:1 great:2 technical:1 involved:1 leaving:1 products:1 antecedents:1 honor:1 composed:1 formulated:1 scales:1 manage:1 names:1 vols:1 duck:2 use:6 usa:4 pedagogical:1 definition:8 depicted:1 formally:1 becomes:2 occurred:2 iii:5 account:1 challenge:2 thin:1 proof:1 process:2 high:1 something:1 dk:1 united:1 six:1 instead:1 singular:11 multiplication:2 light:1 lines:3 redundant:1 allow:1 holds:1 mielnik:2 produces:1 astronomical:1 insight:1 including:2 effect:1 fine:1 le:2 la:2 chosen:1 relativity:16 previously:2 lu:1 derivative:4 eur:1 pure:2 practice:1 transparent:1 dielectric:1 worlds:2 dirac:43 university:7 related:1 elementary:1 books:1 measure:1 our:4 special:1 out:2 matrix:4 haymaker:1 rep:1 rev:5 math:10 interactions:1 ısica:2 diagonal:1 limε:1 approaches:2 york:8 geometry:2 could:5 area:1 times:3 derivations:1 ltd:1 hence:5 scarf:1 manuscript:3 improvements:2 hyperbolic:1 festival:1 adjoint:1 system:2 relations:1 their:17 perfectly:1 final:1 commutativity:1 explanation:1 exactly:4 negro:5 modifications:1 july:1 haven:1 remember:1 holland:1 limiting:3 need:3 apparently:1 instance:2 concerns:1 subject:3 accuracy:1 heisenberg:18 lectures:2 axiomatic:3 collaboration:6 who:4 connected:1 sb:1 why:2 stronger:1 face:1 looked:1 fowler:2 holstein:1 fact:3 supported:1 purely:2 based:2 operational:3 means:5 familiar:1 bear:1 words:2 densities:1 approach:5 differential:1 edition:1 acquires:1 state:2 progress:1 neither:2 find:1 reproduced:1 importance:2 key:1 approval:1 ket:1 distribution:3 paraphrasing:1 observable:4 limits:1 invited:1 theoreticians:1 equal:2 zeeman:2 admit:1 ch:3 sequences:1 respect:1 kinematic:1 cauchy:6 treat:1 faced:3 corresponding:1 moved:1 covered:1 spain:2 quotation:1 unlike:1 appearance:1 value:5 will:6 almost:4 thus:11 surface:1 claimed:1 partner:1 greater:1 began:1 radiation:5 parts:1 pauli:1 finite:3 reinterpretation:1 v0:1 student:1 frequently:1 well:5 thought:1 mathematische:1 position:3 usual:1 deltas:1 sources:4 allgemeine:1 preprint:1 mathematically:2 lattice:1 add:2 book:5 conacyt:1 attractive:2 ski:1 ought:1 elapsed:1 know:1 nor:2 press:8 immediately:1 dimensional:3 necessary:2 like:2 modified:1 become:1 works:4 because:1 classical:3 sequence:2 briefly:1 finite:4 does:5 differentiable:3 although:2 transformations:2 about:4 extension:1 dependence:1 ondes:2 introduced:7 converging:1 own:3 owe:1 pergamon:3 functional:1 zoology:3 van:6 noticed:3 atkinson:1 function:54 north:1 but:9 gaussian:2 volume:2 collected:1 contradictory:1 he:7 made:2 whether:1 gravitational:6 formalized:1 wiss:1 limit:6 problem:29 mechanics:19 robinett:1 meaningless:1 inc:2 functions:34 ematique:1 nonetheless:1 defined:4 other:7 details:1 defines:1 undefined:1 regularizing:1 expressible:1 stay:1 factors:1 persistent:1 rule:1 scientific:4 stachel:1 expands:1
0705.0377.txt |@word represent:1 ihom:6 homomorphism:6 gr:33 results:2 scalar:5 proposition:16 edu:1 consists:13 follow:2 gl:1 gk:2 gi:17 consider:5 whose:9 preserves:1 c0:1 depend:1 graph:3 equivalence:1 contained:3 according:1 submatrix:1 swap:1 th:2 under:7 multilinear:7 presentation:2 alternating:3 applied:3 π2i:3 g1:7 orthogonal:7 very:1 matn:53 corollary:8 endpoint:10 putting:1 signed:1 entries:3 em:1 matrices:9 condition:7 generalised:1 dim:1 school:1 did:1 suffices:3 notes:1 t2:5 standardness:1 t0:3 t1:5 involution:1 commute:1 indices:2 nagata:1 says:1 zi:13 zj:8 mi:6 so17:1 bialgebra:1 direct:1 sign:4 zero:11 pass:1 faithful:1 psu:1 odd:4 canonical:1 even:10 index:6 what:1 filtration:6 appear:2 invertible:2 sum:5 expressed:2 donkin:1 version:5 above:3 3b:1 construction:3 row:27 method:4 satisfy:1 degree:13 deduces:1 respectively:1 aij:1 equals:1 here:7 specialise:1 following:6 groups:6 address:1 represented:2 path:8 standard:10 equations:14 z1:2 interpret:1 morphisms:1 obtained:6 remark:4 endpoints:1 gln:21 my:1 vectors:1 funded:1 suggests:1 products:4 action:13 highfield:1 proof:15 y4:1 brauer:12 schur:5 via:1 projection:1 extra:2 bs:4 texts:1 equivariant:1 composes:2 apply:3 research:1 unit:3 use:8 would:1 prove:4 distinct:1 kalgebra:1 contains:6 soton:1 next:2 vol:2 linear:5 ǫj1:2 call:1 therefore:5 reductive:3 type:1 diagrams:3 duality:1 definition:5 composite:1 initial:5 stable:1 berlin:2 particular:3 known:4 cases:1 hold:1 iii:15 must:6 springer:3 isomorphism:10 grant:1 recall:1 equation:1 work:1 det:1 occurs:3 infinitesimal:5 canonically:1 adjusted:1 trans:1 root:1 example:3 deg:14 give:3 calculation:1 permutations:1 pieces:1 indicates:1 procesi:3 spm:1 spn:39 sense:4 every:1 ist:1 4in:1 verlag:1 end:1 holds:8 write:2 maps:7 nontrivial:1 criterion:1 pure:2 instead:1 map:13 product:3 mat:2 algebra:64 may:4 after:1 derived:5 epsrc:1 diagram:17 multiplication:7 representations:11 horizontal:5 types:1 natural:18 whenever:1 sr:5 sp:3 sv:1 su:1 element:7 sk:1 sp2m:4 green:3 fundamental:7 representation:5 birman:1 acts:2 submatrices:2 over:20 symbols:10 paper:2 preliminary:2 signs:1 y1:4 y3:1 still:1 y5:1 its:20 before:1 derive:3 group:24 thank:1 singular:4 bringing:1 ll:5 jij:1 conjugation:5 parts:1 ls:1 lp:2 wales:1 defining:10 semisimple:6 arguments:5 maximal:2 prime:3 them:1 h1:2 introduce:1 pfaffians:1 they:1 identically:1 now:31 yu:2 matched:2 easily:4 gets:1 equality:1 xli:1 2s:7 invariants:6 university:2 drop:1 arrows:1 identified:2 formalisation:1 semisimplicity:1 l2:1 each:16 2m:1 monomials:8 associative:4 subset:4 domain:6 weyl:10 ei:6 ek:1 ej:1 ej1:1 idea:1 related:1 joined:1 elementary:1 used:1 our:6 morton:1 ep:1 special:1 out:1 shown:2 matrix:10 space:11 furthermore:10 since:20 induces:1 δi1:2 denotes:3 acting:6 vector:12 rational:3 denoted:3 lecture:1 induction:1 ri:2 math:9 shows:3 asr:1 earlier:1 theory:5 associate:2 free:1 enveloping:8 asb:1 base:1 york:2 put:5 subalgebras:1 remainder:1 generate:3 irreducible:7 v0:7 pairs:1 cycles:4 geometry:1 determining:3 omit:1 maths:1 modules:1 nonnegative:1 length:5 derivations:1 δij:6 consequence:1 lth:2 rudolf:8 top:9 first:15 already:2 xn:4 indeterminate:1 variables:1 number:6 tableaux:7 concini:7 another:2 xr:2 xs:2 ring:4 precisely:7 xv:2 size:1 given:13 e1:3 indicate:1 introduction:1 xij:1 xil:1 relations:1 consisting:2 assumption:2 statement:4 wenzl:2 cycle:4 gives:6 similitude:2 commutativity:1 way:2 exactly:2 j2:2 x2:3 x3:1 x1:13 representing:2 than:1 coefficients:5 king:3 determines:1 showed:2 accordance:2 double:17 require:2 see:13 contrary:1 were:1 toward:1 powers:1 projections:1 subcoalgebra:2 witt:1 motivation:1 prl:5 cohen:1 turned:1 argument:1 correspond:1 endomorphism:5 say:2 need:2 seen:2 citeseer:1 any:7 lie:5 nλ2:1 latter:1 note:14 ideal:40 take:3 finding:2 so:14 begin:2 continuous:1 shall:1 z2:2 algebraic:6 berele:2 connected:9 position:1 remarks:4 jantzen:1 southampton:1 observation:1 kk:3 clear:5 later:2 coincides:2 kn:3 nondegenerate:1 points:3 wasserman:1 left:4 section:5 fact:6 show:11 chapters:1 spaces:3 relation:2 centralizer:3 longer:1 trivial:1 find:1 dilation:1 principal:2 hanlon:1 bourbaki:1 assertion:5 should:1 terminal:5 lemma:6 only:11 bases:4 generators:16 stated:1 ǫi1:2 columns:2 do:1 his:3 closed:9 notation:11 means:5 dd:1 de:6 yielded:1 closely:1 new:2 du:11 closure:2 stability:1 endomorphisms:5 arxiv:1 summary:1 nλ:5 cr:7 mapped:1 fixed:1 view:2 coefficient:1 set:16 their:1 exists:1 nuv:2 j1:5 module:2 j3:4 mentioned:1 namely:2 result:8 vertices:13 iu:2 theoretic:1 y2:1 vertical:1 monoid:3 factorisation:4 uα:3 functionals:3 label:2 symmetric:1 state:1 identification:1 correctly:1 between:3 invariant:14 approach:1 checks:2 extend:1 confusion:1 jv:2 attention:1 transpose:1 jr:8 δj1:2 eli:2 french:1 endk:27 amer:1 come:1 ja:6 restrictions:1 essentially:2 cor:6 reverse:1 brown:1 taking:2 equal:7 agree:1 endb:2 symplectic:49 embedding:1 fix:1 comes:2 otherwise:1 ci:1 point:11 centraliser:23 dimensional:2 simply:6 xi:2 polynomial:26 proved:3 throughout:1 considering:2 most:1 commutative:5 second:2 basis:13 ai1:3 due:1 been:1 defined:25 covectors:1 pf:3 change:1 frt:2 algebras:14 ann:3 empty:1 define:16 surjective:2 6a:1 corresponding:8 both:4 scalars:2 sufficient:3 subspace:8 2in:1 observe:2 mail:1 c1:1 general:1 assigning:1 those:4 case:7 ǫi:13 ǫl:6 will:14 replaced:1 applies:2 situation:2 property:11 procedure:1 inherits:3 yi:2 orientation:2 epimorphism:2 vi:1 ir:8 thus:1 non:1 iv:9 ii:17 middle:7 ij:3 onto:1 dual:3 vanish:10 id:4 different:2 author:1 make:1 same:5 clearly:7 princeton:1 complex:1 split:2 advances:1 finite:2 subalgebra:6 independent:3 finish:1 http:1 paths:3 i1:3 assignment:1 i3:2 subvariety:1 domains:1 edges:5 uses:1 infinite:4 totally:4 identity:4 subgroups:1 relies:1 lower:1 acknowledgement:1 edition:2 xjl:1 variety:1 well:3 academic:1 thm:14 edge:3 components:1 sets:2 entry:7 dimension:3 monoids:3 subgroup:4 graded:11 just:2 distribute:1 obtain:3 actions:1 pfaffian:1 torus:1 shape:4 identify:2 immediately:3 multiples:4 adv:1 adding:1 yr:1 preprint:1 density:1 ease:1 boston:1 dipper:1 tuples:3 combine:1 easy:2 theorem:36 elp:7 coalgebras:5 5a:3 depends:2 isomorphisms:3 evaluate:1 sums:3 spanned:2 reprint:1 bisymmetric:5 know:1 press:2 integer:4 unique:6 mod:4 imposed:1 2r:5 identifying:1 follows:18 tγ:1 html:1 separately:2 either:2 arbitrary:6 el2:4 el3:2 el1:4 terminology:1 because:2 methods:1 classical:4 oriented:1 sgn:5 some:5 algebraically:4 ideals:1 sym2:1 deduce:1 choosing:1 respect:4 proper:1 proofs:2 zariski:1 matching:2 nonzero:11 automorphisms:1 dense:6 dimensions:1 bottom:8 nonempty:1 avoid:2 comments:1 prop:2 does:3 decomposition:2 linearly:2 leftmost:1 refer:1 plr:6 equivalent:4 l1:2 ufd:3 syms:3 symr:10 br:16 found:1 transpositions:1 injectivity:1 injective:6 chapter:1 integers:2 about:1 a0:2 column:5 dependence:1 regular:6 positive:4 introduced:2 other:4 automatically:1 morphism:2 homogeneous:12 soc:1 faithfulness:1 inclusion:1 eisenbud:1 image:5 within:4 integral:3 isomorphic:5 ut:1 lies:1 en:2 references:1 ai3:2 determine:2 bijective:1 substitutions:4 ωfn:1 rows:3 span:4 strictly:1 there:6 depicted:1 like:1 appl:1 abovementioned:1 biggest:3 was:6 gij:7 gii:2 naturally:1 function:9 complete:2 form:7 enough:1 sequel:1 but:4 hu:1 hk:1 hi:2 hl:1 he:1 responding:1 arranged:1 consist:2 versions:1 characteristic:15 up:1 us:2 commutating:1 below:6 ui:1 duv:13 uk:2 problem:1 piece:2 similar:3 called:9 ac:2 partition:1 associated:5 ai:16 certain:4 covector:2 denote:12 ar:5 right:4 submonoid:7 commuting:4 defines:1 ni:1 functions:27 traversed:2 entirely:1 no:11 when:2 vanishes:2 graduate:1 field:3 interested:2 mathematics:2 1bj:1 doty:3 elements:26 generates:2 translated:1 polynomials:4 a1:4 commutator:1 generated:8 a2:1 formal:1 structure:1 implies:3 auxiliary:1 using:2 assume:11 π2r:1 homk:5 together:1 itself:1 remarked:1 once:4
0705.0378.txt |@word neighbors:1 r1r:1 consider:5 chain:17 magnetic:5 splitting:1 garching:1 computation:1 edu:2 reson:5 follow:1 whose:1 leung:1 paris:1 syntheses:1 glaser:9 under:15 division:1 evolves:3 unchen:1 electron:3 resonant:1 presented:4 turns:1 pacs:1 large:1 guiding:1 small:2 sin2:1 pulse:22 rate:8 street:1 uk:4 dynamics:3 chem:4 substitute:1 belief:3 bilinear:2 sequential:1 new:1 net:1 method:4 palmer:1 simultaneously:1 proc:1 here:5 desired:5 magnetism:2 selective:4 cos2:1 relaxation:2 represented:2 path:2 along:12 equations:1 change:1 obtained:1 search:1 suitably:2 popescu:1 studied:4 steffen:1 article:1 twamley:1 resulting:1 action:3 resonance:6 suitable:3 concatenations:1 involves:1 via:1 useful:1 divide:1 pling:1 achievable:1 apply:1 total:3 conventional:7 takes:4 usa:1 de1:1 neighbours:1 next:1 linear:6 encode:1 type:2 achieving:3 separated:1 relax:1 becomes:1 operators:18 berlin:2 particular:1 known:1 iv:1 iii:1 high:1 springer:2 ma:2 bowman:1 science:3 equation:11 work:1 london:2 paragraph:1 values:1 concepts:1 following:8 strategies:1 sci:1 example:1 decoupled:2 performed:2 control:18 nearest:1 figure:3 give:1 bennett:1 states:3 sphere:4 minimum:7 numbers:1 want:1 tal:1 tan:2 r22:6 advancing:1 information:2 goal:1 pp:2 technische:1 delay:1 how:3 adjacent:1 optimal:14 ensemble:1 schultz:1 inputs:1 designer:1 singular:1 may:2 dr12:1 applications:3 produce:1 physik:1 waves:1 choice:1 efficiently:1 λ2k:4 short:1 natural:7 effective:1 explicit:1 trilinear:2 so:9 subsequently:3 2ikz:2 order:12 2ikx:2 preparing:1 operations:1 gershenfeld:1 pulsed:1 interpretation:1 developed:5 over:1 displayed:1 symbols:1 experiments:4 through:8 thesis:1 yamaguchi:1 its:1 before:3 d4k:5 derive:1 chosen:2 dahleh:1 solving:1 scribed:1 forms:1 fig:11 imy:2 imz:3 them:3 greater:1 numerically:1 practice:2 introduce:1 geodesic:4 effects:1 oxford:2 formulating:1 multidimensional:1 now:17 wiley:1 february:1 vidal:1 cory:1 2r:1 university:1 hamiltonian:11 proteins:1 sin:6 l2:2 d3k:5 each:3 universit:1 2i:5 2j:15 significantly:5 formulate:1 series:1 hard:4 reduce:1 principles:2 skelton:1 frequency:2 static:1 encodings:1 quantum:12 our:2 eq:5 special:2 out:2 shown:3 accomplish:1 rr:1 λ1k:4 furthermore:2 since:1 rev:6 rf:1 ri:1 shows:2 benjamin:1 earlier:1 theory:3 mechanisms:1 given:4 free:1 navin:2 approaches:2 thrust:1 steering:2 shortest:3 advance:2 r1:4 r2:8 r3:5 times:1 creates:2 πj:14 length:1 uggen:2 transfer:50 think:1 first:8 xk:4 major:1 initial:6 encoding:4 pines:1 u1:2 variables:2 number:1 synthesize:1 xy:1 another:2 electronic:1 synthesizing:1 size:1 little:1 necessarily:1 similarly:2 introduction:1 unknown:4 system:8 approximately:1 intermediate:2 realization:1 white:1 john:1 frame:1 gives:2 exactly:1 immediate:1 optical:2 x2:10 x3:12 x1:9 representing:1 than:6 x4:10 x5:1 target:2 showed:2 second:1 final:7 preparation:1 havel:1 future:1 contrary:2 amplitude:3 were:1 steer:1 san:2 ann:1 modern:1 correspond:1 1r2:1 manner:1 need:3 curve:2 reiss:2 paths:1 strength:2 angle:2 majumdar:1 efficient:12 ideas:3 polarization:1 take:2 finding:3 mit:2 play:1 continuous:1 multiple:6 fitzsimons:2 simplify:1 involving:1 propagate:7 significant:1 phase:1 soliton:1 clear:1 part:1 mechanical:2 physics:1 laws:1 brockett:2 show:8 rotating:1 minimizing:1 chuang:1 substituting:1 find:4 postulates:1 finally:2 based:2 ensembles:1 parameters:1 implementation:1 x6:1 written:1 should:2 only:2 geodesics:5 factor:1 i4:2 hamiltonians:4 achieve:2 coherences:6 notation:1 get:6 succeeded:1 expectation:1 fastest:1 dx:1 bodenhausen:1 during:1 dt:12 dr:2 differentiating:1 evolution:13 mattis:2 arxiv:1 optimally:4 paper:4 common:1 analytical:1 pulses:9 eecs:1 set:2 art:1 computed:1 achieved:3 sensitivity:1 transferred:5 see:1 result:2 enhanced:1 best:2 techniques:4 yamamoto:1 ways:3 nuclear:3 currently:1 λn:1 state:20 various:2 closed:1 between:7 propagated:2 geometric:1 warren:2 numerous:1 x23:1 x22:1 available:1 recently:3 ability:1 extend:2 nature:1 qubits:2 iky:1 spectroscopic:1 harvard:2 selectively:1 magn:5 key:3 analyzed:1 separately:1 cos:5 x2n:6 last:4 2n:5 met:1 many:2 taking:1 equal:1 propagation:5 dated:1 context:1 ernst:3 whole:1 con:1 arbitrarily:2 detailed:1 relevant:1 pastawski:1 point:2 simple:1 address:1 period:3 pole:1 simply:1 sequences:3 inx:3 lagrange:1 ensures:2 described:5 transformations:4 basis:1 trajectory:1 create:1 due:1 been:6 strategy:2 much:1 expected:1 ph:4 systems:4 direction:1 controlled:1 fahmy:1 suppress:1 coherence:6 coherent:3 observe:1 external:2 spin:68 present:2 applied:1 main:1 laser:1 developing:1 contexts:1 single:1 value:1 rectangular:2 will:7 adi:1 couplings:7 generate:2 unitary:10 coupled:5 vol:1 metric:6 thus:2 xiao:1 according:1 ii:1 wave:1 ric:1 sequentially:2 make:3 same:4 shorter:3 quant:4 units:17 finite:1 evolve:4 used:2 diego:2 i3:3 i2:2 effect:1 architectures:1 changing:1 yuan:3 recent:1 i2x:5 i2y:20 i2z:7 inital:1 schr:1 whereby:2 minimize:1 expression:1 i1z:3 well:2 analysis:1 academic:2 savings:1 trains:1 chemistry:2 d1k:5 routinely:1 proposed:3 kramer:1 rotated:1 front:1 shape:1 identify:1 world:1 λk:15 followed:4 rotates:1 speed:1 rotation:3 letting:1 note:1 application:1 irradiated:2 except:1 setting:1 lett:3 natl:1 euler:1 generalized:1 identical:1 caspers:1 schulte:2 advances:2 possible:10 leifer:1 press:3 using:7 depicts:5 advanced:1 loss:1 rotate:2 like:1 shaped:4 reduces:2 λ4k:4 specific:1 steps:12 either:1 arbitrary:3 soft:1 reduced:1 spins:7 acad:1 methods:12 sequence:2 protein:1 creation:5 understood:3 examples:1 table:2 duration:4 indirect:1 transport:2 shapes:1 esr:1 per:6 heitmann:1 connecting:2 8i:1 chains:10 demonstrated:1 cantly:1 usaj:1 nmr:5 scientific:1 equivalent:2 processing:2 use:1 clarendon:1 step:15 br:1 relating:1 optimize:1 stage:1 about:1 levstein:1 carried:1 constraint:1 o:3 essential:1 larmor:1 lieb:1 cambridge:2 h2:5 into:3 h1:5 rotations:1 three:1 pair:2 appropriate:1 references:1 lution:1 operator:12 reducing:1 rely:1 statistics:1 topologies:2 there:2 lon:1 depicted:1 fast:1 u2:2 appl:1 way:1 ed:2 subsequent:2 was:3 propagator:1 synthesis:4 hz:2 kane:1 north:1 form:1 concatenated:1 collapsed:1 taken:1 schweiger:1 hb:2 hc:13 ha:3 coupling:10 applying:5 rabitz:1 2πj:1 maximum:1 placed:1 spectroscopy:6 problem:13 stages:1 similar:1 called:1 mechanics:1 linden:1 cirac:1 constant:5 iny:1 inz:4 computing:4 defined:1 certain:2 engineering:2 corresponding:1 commuting:1 again:1 compared:3 i1y:10 i1x:12 sørensen:1 no:1 amounts:1 field:2 d2k:5 other:4 department:2 conclusion:1 picture:2 transferring:3 superposition:2 khaneja:9 4i:2 problems:1 prepared:1 herbr:2 important:1 ising:13 variable:1 transfers:4 dimensions:1 jones:1 implies:1 faster:4 assume:1 cally:1 governed:1 time:38 decoherence:2 resolution:1 indirectly:2