text
stringlengths 0
190k
|
|---|
0704.1849.txt |@word neighbors:4 represent:1 sci:2 consider:1 remarkable:1 results:3 switches:1 edu:1 consists:1 gi:8 relationships:1 whose:3 calculate:2 description:1 monotonically:1 stable:7 nodes:60 worth:1 belonging:1 supported:1 rise:1 connects:4 induce:1 mixing:6 difference:2 condition:4 leads:2 squares:1 stimulus:5 large:9 epstein:2 small:4 reshuffling:6 dis:1 upper:1 smaller:2 tem:1 oscillation:2 prediction:1 sign:4 zero:1 imprinting:1 dynamics:18 substitute:1 established:1 power:2 sum:1 selected:1 contributed:1 near:3 networks:80 above:4 designing:1 new:2 net:1 method:4 contrast:1 coefficient:14 evolving:1 degree:49 respectively:1 realizations:2 modify:1 b2r:1 understanding:1 china:1 departamento:1 groups:1 address:1 represented:1 strong:1 equations:1 change:5 obtained:2 institute:1 study:1 studied:4 preferentially:2 vespignani:3 social:1 makes:1 attractor:31 named:1 via:1 br:5 apr:1 inducing:1 capocci:1 bogu:2 plot:1 use:3 usa:2 tightly:1 next:1 comparing:1 noting:1 therefore:3 taken:1 type:2 theoretical:1 more:9 kahng:1 rios:1 initial:3 under:5 normalized:1 cases:1 hold:1 producing:1 evolves:5 frequently:1 sneppen:1 middle:2 science:2 work:3 cai:1 values:1 following:2 example:1 scalefree:3 compare:1 weaker:2 gallos:1 wang:1 figure:2 give:4 process:11 sokolov:1 states:23 indicates:2 numbers:1 occur:1 weaken:1 azquez:3 end:1 shuffled:1 get:1 how:1 varies:1 adjacent:2 instead:1 mat:1 derived:2 wrong:2 fc:4 coming:4 law:2 berg:1 response:16 types:2 dynamical:6 four:1 sj:7 si:12 maintain:1 so:3 sn:1 fundamental:1 correlation:32 amit:1 acknowledges:1 rewiring:1 help:1 pointed:1 insight:1 satisfied:1 stability:1 held:2 paper:1 signs:1 mentioned:2 existence:1 its:2 before:2 group:1 chosen:3 interesting:1 sα:9 jij:4 decreases:2 forms:1 attraction:10 degrees:5 systems:27 clusters:2 might:1 into:7 versus:4 non:2 affected:1 lzu:1 fig:19 flipping:1 newman:3 effects:5 they:2 half:5 structural:1 february:1 university:2 realistic:3 each:6 found:1 side:1 characterized:2 square:5 financial:1 reduce:1 used:3 connect:3 changed:1 eq:7 special:2 out:1 leave:1 shown:7 networked:3 matrix:2 restricted:1 since:2 rev:18 disassortative:17 research:1 increase:2 attracted:2 seriously:1 investigation:1 rc:2 denoted:1 xu:2 occurs:1 shows:9 interactions:1 ısica:1 free:38 effect:4 asi:2 barab:2 generate:1 interaction:1 derivation:1 levels:2 retain:1 first:4 already:1 probability:1 number:12 approximately:2 another:2 robust:3 reached:2 ying:1 electronic:1 size:27 given:3 perturbation:1 checked:1 their:8 system:37 xin:1 traction:1 attach:2 assumption:2 too:4 undergoes:1 redner:1 rewired:2 fraction:11 realization:3 albert:2 imprinted:7 than:15 kind:3 determines:1 assortative:21 namely:1 modelled:1 computer:1 were:1 gives:2 lowest:1 randomly:4 brunet:1 need:2 hopfield:1 cascade:2 isolated:1 mechanism:2 note:2 high:5 take:1 online:3 xi:1 switching:1 fct:1 park:1 satisfy:1 react:1 connected:1 pair:1 class:2 average:9 disease:1 face:2 bracket:1 physics:2 cannot:3 slope:1 incorporate:1 show:2 retains:1 random:26 bring:1 relation:3 threshold:1 find:1 based:2 enough:1 only:2 caldarelli:1 circle:5 do:1 means:3 de:3 quantified:1 da:1 ones:5 nearly:1 reveal:2 evolution:12 pearson:13 bar:2 arxiv:1 summary:1 investigate:1 predicted:3 characteristic:1 gutfreund:1 respond:1 reveals:1 set:5 attached:3 sensitivity:10 correlations:2 see:2 individual:1 result:6 enhanced:2 uncorrelated:34 fails:1 exponent:1 review:1 artificial:1 symmetric:2 state:28 smallest:1 between:11 sompolinsky:1 ability:3 bianconi:1 complementary:1 attention:1 wu:2 come:1 problem:2 topology:1 both:7 many:2 region:4 equal:6 barrat:1 flipped:18 sensitive:5 dated:1 dorogovtsev:1 exceeds:1 attributes:2 whole:5 otherwise:2 among:1 fronczak:2 cn:1 color:3 sβi:1 respect:1 krapivsky:1 destroyed:1 described:2 second:5 disintegrate:1 been:3 yam:2 much:2 interest:2 expected:1 basin:22 choose:4 lanzhou:3 sfrh:1 modelling:1 fund:1 understand:1 external:1 irrelevant:1 case:9 attractors:2 pacs:1 value:5 easier:2 while:5 behavior:2 investigating:1 property:8 identical:2 larger:6 induced:1 portugal:2 elemy:1 thus:6 them:2 discrepancy:1 according:1 cluster:6 neurons:1 cond:1 neutral:1 sequentially:1 binary:1 different:5 grant:2 make:1 s2i:2 same:5 stimulated:13 complex:7 largest:1 units:2 higher:2 investigated:1 percolation:1 numerical:5 monotonic:3 possible:1 sys:1 persons:1 phy:1 edges:16 kim:1 variance:1 changing:2 lower:4 neural:1 stimuli:68 well:1 analysis:2 edge:2 greatest:2 entry:1 model:3 maslov:1 proposed:2 less:6 when:11 shape:2 underlying:2 barth:1 previous:1 hai:1 density:2 source:1 extends:2 lett:5 natl:2 real:2 assig:1 increased:1 satorras:4 term:3 increases:2 preference:1 using:6 progresses:2 bpd:1 necessary:1 like:1 discarded:1 goh:1 steps:1 either:1 arbitrary:1 right:4 often:1 exposed:1 some:3 back:2 s1j:1 s1i:7 acad:2 specified:1 hebbian:2 extended:1 classes:2 gradually:1 scale:38 does:3 moreno:2 proc:2 destroys:2 noise:3 ba:3 sheng:1 bm:7 notable:1 step:6 although:3 properties:2 about:3 extension:1 oh:1 simulation:1 neighbor:1 wang1:1 slightly:1 jian:1 spreading:1 within:1 numerically:1 functional:17 appropriate:1 because:2 responds:2 existed:1 few:1 sβj:1 support:1 there:3 los:1 low:3 way:2 analyze:1 was:4 function:3 jun:1 pastor:4 but:3 repeated:1 hierarchical:1 hc:1 directed:32 responding:4 intuitive:1 cij:4 robustness:5 flip:1 us:1 below:1 limit:1 critical:9 zhi:1 distribution:3 calculated:2 ordered:1 certain:2 contribute:1 influence:3 covers:1 general:1 exist:1 simulations:6 marsili:1 distributions:1 universidade:1 triangles:2 nn:1 no:2 na:2 whereas:1 generally:1 nf:5 application:1 other:8 becomes:1 mathematics:1 node:11 kinds:2 models:1 variation:1 stay:1 deriving:1 generated:1 important:2 additionally:2 structure:4 network:31 building:1 correlated:15 algorithm:1 assume:1 aveiro:2 curve:8 rule:2 responded:1 inset:7 starting:1 original:3 |
0704.1850.txt |@word neighbors:1 limited:1 sci:2 consider:1 ron:1 caused:3 rob:1 ceramic:1 dynamic:5 results:3 four:1 roy:1 scalar:8 tensile:6 entropy:1 go:1 contributions:4 localized:2 gr:6 certainties:1 depend:3 calculate:1 alamos:9 subjected:3 technique:1 tr:4 micrometers:1 quasi:1 behave:1 those:1 marks:1 dominated:2 include:2 cm3:2 porosity:2 indicating:2 ta:1 division:2 amplitudes:1 g0:3 continues:1 mg:1 induce:1 wave:10 crosses:1 figs:1 suggests:1 laser:2 fǫ:3 continued:2 deformations:1 common:3 induced:9 reciprocal:1 vibrational:1 level:2 diverging:1 isotherm:1 shock:75 gun:6 t0:2 integrated:2 large:6 launcher:2 millimeters:1 small:3 div:1 shows:1 glued:1 mo:47 mm:4 possibility:1 upper:2 employing:1 plastics:1 machined:1 consistent:3 prediction:2 µs:2 past:4 zero:9 doppler:3 design:2 traveling:2 rigorous:1 further:1 grooves:1 estimated:2 auspices:1 sesame:2 interatomic:1 appear:1 rate:5 opaque:4 giving:1 voids:2 assistance:1 selected:1 contributed:1 expressed:3 symmetric:1 consistently:2 axial:2 experiment:8 above:7 new:4 net:1 neu:1 acknowledgments:1 shocks:3 body:1 condensed:2 morgan:2 degree:1 proper:1 component:3 here:6 atoms:3 ranges:2 reported:3 compressed:1 ackland:1 address:1 represented:4 path:1 along:5 strong:2 equations:5 change:4 extreme:4 obtained:5 daughter:1 reconciling:1 ahead:1 broken:1 precursor:4 commonly:1 ignoring:1 trial:1 extremes:1 resulting:4 constitutive:2 published:3 usually:2 resonance:2 history:8 changes:2 involves:2 york:2 composed:1 formulated:2 useful:2 although:1 clark:3 apr:1 requiring:1 transit:1 prefer:1 treatment:1 marked:4 histories:4 visible:2 resolutions:1 total:4 unit:1 readily:1 use:2 refers:1 takes:1 usa:2 dubrovnik:1 term:2 predictions:7 few:7 camera:1 m3:1 usp:1 taken:3 means:1 type:4 until:2 more:7 flat:1 treated:1 loci:2 definition:1 becomes:1 under:2 mismatch:2 emission:10 surface:32 particular:1 known:1 cases:2 producing:1 must:3 sample:21 account:6 rotational:1 ma:1 strain:15 deformed:1 equation:6 work:30 accumulated:3 mj:1 eng:2 itself:3 temperatures:15 ms:3 about:2 metal:1 example:3 numbers:1 compare:1 radiance:1 figure:1 pauses:2 calculation:2 allowed:1 neglected:3 spall:4 involve:1 minimum:2 performed:10 hardens:1 exclude:1 sharp:2 times:1 occur:3 axis:1 information:1 respective:1 varied:1 pure:1 rather:4 s1:2 s0:2 damage:4 roughness:1 chemical:1 varies:2 instrum:1 thermodynamics:1 fourth:1 verlag:1 parameter:4 fp:2 product:1 de:1 magnitudes:1 mat:3 v02:1 may:17 thermodynamic:1 advice:2 after:4 diagram:1 barriers:5 produce:1 lay:2 records:1 waves:4 spectrometer:1 law:1 data:7 parallel:1 types:2 stress:46 dynamical:1 effective:3 light:1 spectra:1 explicit:2 element:1 accelerated:5 maintain:2 so:10 sn:1 allow:3 microseconds:2 alloy:1 representation:1 subsequently:1 first:1 order:3 terms:6 wavelengths:1 six:1 evident:1 jetting:1 developed:2 over:4 spallation:1 held:1 thermal:12 experiments:26 through:8 same:1 affect:3 mentioned:1 y0:3 cold:1 brittle:1 excitations:3 its:6 defects:3 τn:4 regions:2 difference:2 group:2 la:3 chosen:2 interesting:1 temporal:1 epoch:2 decreases:1 better:2 hugoniot:3 window:25 systems:1 constitutes:1 hidden:1 alter:1 shear:8 forest:8 non:3 good:4 greater:3 material:27 fig:10 chuck:1 elasticity:2 scaling:1 process:1 effects:4 they:1 accumulate:1 transparent:4 matched:4 represents:1 inversion:1 several:1 damian:1 stabilize:1 brightness:1 corners:2 university:1 presented:1 appropriate:1 benson:1 devore:1 sufficiently:1 morris:1 vibrations:1 transmitted:2 reasonable:2 each:6 found:1 repeating:1 higher:5 decreasing:1 mean:7 reactions:1 rodriguez:1 glues:2 ei:1 significantly:5 generation:1 ed:1 energy:12 sov:1 ea:1 solution:5 investigated:1 measure:3 laboratory:9 beyond:2 extract:1 er:2 ultimately:1 evidence:1 fundamentally:1 factors:1 gradient:4 open:1 since:1 lagrangian:1 increase:2 re:2 mediated:1 sustain:1 hill:1 u2s:1 suggesting:2 rn:1 gov:1 occurs:6 red:2 predicted:14 working:2 theory:1 lawrence:2 perfectly:3 free:11 standard:6 difficulty:1 reason:1 flyer:6 complicated:2 τn0:3 dynamics:7 adiabats:4 estimate:3 achim:1 e0:1 additional:4 uneisen:6 digitization:1 bowman:1 could:3 similarly:1 david:3 motion:2 machining:1 isotropic:2 projectile:20 corrections:1 repeats:1 crystallographic:1 origin:1 conversions:1 there:4 features:2 symmetry:1 omitted:2 reflected:1 system:2 channels:1 clear:1 hardening:3 done:1 specifically:1 directly:1 improvements:1 reached:2 thick:4 clarity:1 electronic:2 causing:1 size:1 passes:1 given:1 yuan:2 matt:1 temperature:67 likely:3 los:9 introduction:2 leading:1 smoother:1 gpa:22 least:2 plastic:58 their:2 nian:1 appl:4 listed:1 calculations:4 justified:1 hundred:1 unpublished:1 prone:1 exploring:1 way:2 releases:1 behind:1 wavelength:4 duration:1 accurately:2 plane:1 direct:1 released:6 part:4 too:2 deceleration:3 translation:1 foams:1 than:16 population:2 diffusion:1 jump:2 scheme:1 impractical:1 target:5 showed:4 ac52:1 programs:1 grey:1 submitted:3 selfconsistently:1 matter:7 states:12 future:1 stp:1 amplitude:4 were:35 hollenbach:1 powers:1 distinguished:1 peierls:1 collecting:1 polycrystalline:2 inadequacy:1 exert:1 lines:5 dynamically:1 spectrum:4 vogan:1 iii:1 any:7 relatively:3 acceleration:6 lie:1 lif:39 strength:39 min:1 source:1 self:1 aside:1 shocked:19 onset:1 high:12 internal:6 absorbed:1 take:1 detector:1 modulus:3 explanation:1 channel:4 tensor:3 multiple:4 trace:1 though:4 consistency:2 viscosity:2 lyon:1 impurities:1 did:3 most:2 boltzmann:1 impacting:1 drummond:1 occurred:1 definitions:1 phase:5 ahrens:3 measured:13 why:1 probes:1 idealized:1 ka:1 kg:1 considered:3 calculated:21 sometimes:1 flow:44 repeated:2 km:11 inflexion:2 electrons:1 mechanical:2 velocity:17 cracks:1 physics:7 hypervelocity:1 applied:2 precise:2 particularly:1 tron:1 show:3 isentropic:2 probe:1 infrared:2 purely:2 relation:4 solutions:1 sustained:1 keywords:1 correct:2 rough:1 thickness:1 ymax:4 principal:2 impact:22 boundaries:2 based:2 just:1 parameters:4 conduction:3 situations:2 explain:1 enough:3 calibrated:2 analytic:1 only:4 smallest:1 implemented:1 ellipsometry:1 acknowledge:1 constant:5 ceramics:1 local:3 achieve:1 gains:1 bonds:1 contracts:1 simplest:2 quantified:1 uniaxial:5 preferred:1 yielded:1 crude:1 cannot:2 probably:1 report:3 during:3 table:5 corrected:1 fe:1 processes:2 exhibiting:1 continuum:7 molybdenum:4 arxiv:3 yield:2 hyperelastic:1 imposed:1 croatia:1 hydrodynamic:4 fitted:2 wish:1 release:67 including:1 grad:2 06na25396:1 disperse:1 respond:1 ignored:2 set:2 reference:3 our:1 ual:1 national:9 testing:1 respect:1 maximum:3 observed:6 opposite:1 see:1 computer:2 gaps:1 powder:1 close:2 best:1 statistically:1 preparation:2 practice:2 capacity:1 parent:1 plasticity:2 crystal:1 ways:1 subsequent:2 review:1 artificial:1 materials:10 nucleation:1 pressures:7 state:32 un:1 various:1 between:8 tens:7 limit:2 subscript:1 before:1 conditions:7 across:2 speed:10 luo:4 hence:1 explosive:5 reproduced:3 notoriously:1 however:6 mechanics:1 rapid:1 windows:1 key:1 jets:1 separately:2 understanding:2 swift:5 tensors:2 concentrated:1 both:3 σn:1 limits:1 adiabat:5 many:4 taking:3 uncertainty:8 ramp:2 heating:15 against:2 stacey:1 strains:5 grain:1 dated:1 context:1 contribution:6 expression:1 lateral:1 comes:2 pits:1 arbitrarily:1 strongly:1 presumably:1 relevant:1 appeared:1 clarendon:1 excess:1 dislocations:2 dimensional:1 twin:1 simply:2 loaded:7 crystalline:1 cv:1 tabular:1 conference:1 pp:3 described:2 second:1 lattice:1 addition:1 mises:1 locally:1 curve:4 been:12 paulsen:1 int:1 reduction:1 much:3 interpret:1 interest:5 collected:1 dur:1 deduced:2 differently:2 stresses:2 direction:4 relations:2 corresponding:2 designed:1 formed:1 gas:7 gap:1 bulk:1 fritz:1 representative:1 systematic:1 astron:1 nrs:3 obscuring:1 c0:2 resid:1 present:1 case:5 uncertain:1 grains:2 pacs:1 solid:5 empirical:1 value:3 deformation:5 will:2 responding:1 near:2 ǫp:5 steinberg:17 compressions:2 behavior:2 applies:1 situation:1 region:2 identical:1 planar:3 orientation:1 mexico:2 von:1 formulation:2 thus:10 discrepancy:3 iv:1 ii:4 need:1 pressing:1 cond:4 deviatoric:5 barker:1 ragan:2 increased:2 result:5 different:10 propagation:1 optimization:1 make:3 radiation:5 lett:1 elevated:5 clearly:1 shorter:1 guinan:16 funk:2 schematic:1 largest:1 units:2 physica:1 regime:1 geophys:2 neutron:1 difficult:1 independent:1 used:11 eds:1 reflecting:1 kelvin:3 numerical:9 effect:6 stacy:1 v0:3 running:1 aggregate:1 projectiles:2 ucrl:1 recent:1 lower:6 largely:1 studies:1 fiske:1 modeled:1 well:4 roughly:1 analysis:3 without:8 thought:1 solids:1 contact:2 reflect:1 experimental:4 components:3 simulated:3 comparisons:3 model:17 otherwise:1 true:1 usual:2 load:1 velocities:1 softening:1 less:3 being:1 generally:3 accurate:3 rest:1 sources:1 shape:4 stored:1 atomic:1 aspect:1 cp:2 spatially:2 glue:1 scattering:1 captured:1 previous:1 tables:1 volumetric:1 loading:14 density:7 sheng:1 had:3 ideal:2 signals:2 discontinuous:1 potential:1 decompression:2 location:1 samples:1 inducing:1 accumulating:1 cochran:1 disrupt:1 gave:1 resolved:2 march:1 around:10 holian:1 dissipative:1 specimen:1 measurement:5 possible:1 possibly:1 increases:1 makes:1 background:1 vacuum:9 press:2 using:25 intersection:2 rear:1 counterintuitive:1 necessary:1 like:1 particle:4 should:3 reduces:1 adiabatic:1 porous:1 maintained:1 accelerating:2 deviate:1 specific:7 communications:1 private:1 deducing:1 indication:1 either:2 always:1 quintana:2 response:1 accuracy:2 stationary:1 signal:1 accessible:1 because:3 often:4 flatter:1 some:4 springer:1 complexity:1 pdiv:2 growth:1 complete:1 escape:1 oscillations:1 elastically:1 neglecting:1 nonzero:1 provided:1 scale:1 calculating:1 lead:2 function:2 res:1 measurements:24 recorded:1 integration:1 comments:1 instantaneous:1 when:12 fσ:3 assuming:1 three:2 proc:1 refer:1 measuring:1 varying:1 measures:1 assembly:1 power:3 slight:1 june:1 equivalent:1 stefan:1 uniform:1 agreement:5 expansion:1 infra:2 overall:1 pressure:23 ratios:1 standpoint:1 analyses:1 includes:4 properties:4 stage:1 comparison:1 conclusions:1 would:6 exaggerated:1 traces:3 discussed:5 dependence:1 o:1 practical:1 range:2 marr:1 ensure:1 greatly:1 slightly:3 emissivity:4 peak:3 converging:1 mathematical:1 soc:1 rev:2 significant:2 followed:1 follows:1 into:36 within:6 steady:1 locus:1 pair:1 velocimetry:4 cost:1 heated:1 proportional:1 reducing:1 methods:3 uncertainties:6 compression:15 elastic:24 artifacts:1 assumed:3 initial:8 long:2 overestimate:1 start:1 conservation:2 low:2 fraction:5 was:82 launching:1 manufacture:1 elsewhere:1 form:3 governs:1 reduce:1 adjusting:1 deviations:4 but:10 volume:2 heat:8 library:1 impedance:3 line:1 irreversible:1 oxford:2 made:5 accumulation:1 mtrl:1 inside:1 variations:3 up:4 us:2 ur:2 placed:1 below:3 converted:5 complications:1 emissions:2 spectroscopy:2 heterogeneous:1 spectrometry:2 similar:3 called:1 detailed:3 required:1 associated:3 defined:3 detectors:2 exceeded:3 metals:5 general:8 ap:1 engineering:2 together:2 simulations:14 arrival:1 sheath:1 uniaxially:1 ing:2 physical:2 again:1 compared:5 discriminate:3 no:9 amounts:2 dashed:4 percent:6 detail:1 reality:1 other:1 details:1 normal:13 spatial:2 department:1 pi:1 sufficient:1 deviation:1 releasing:4 livermore:2 excitation:4 separate:1 models:9 photon:2 problems:1 shown:1 variation:4 prepared:1 lens:1 meaning:1 important:2 allowing:3 included:4 structure:2 matrix:1 correlated:1 longer:1 garcia:1 assume:1 typically:1 carl:1 lanl:1 kinetics:1 governed:1 eos:17 portion:2 mass:2 presenting:1 time:7 conductivities:1 validation:1 others:1 |
0704.1851.txt |@word now:8 sci:1 consider:9 pointing:1 equalities:3 results:1 ds:1 scalar:10 computation:5 edu:2 denotes:5 rigidity:3 compact:15 whose:1 isometric:2 dηα:2 depend:1 paris:1 nonpositive:1 containing:1 kγ:2 finally:1 ie2:5 manifolds:28 under:3 tf:1 analogous:1 eβ:14 norm:1 r14:4 r12:4 r13:4 straightforward:1 g0:1 springer:1 choice:2 corollary:7 witten:2 every:1 invent:2 fab:2 matrices:2 condition:10 harmonicity:1 dim:1 level:10 list:1 t0:2 large:1 discrete:2 convenience:1 horosphere:1 rj:3 lw3:5 quick:1 eigenvalues:1 work:1 neighborhood:2 estimates:1 translating:1 second:9 further:2 cft:2 substitute:1 canonical:1 bilinear:1 εl:1 what:1 coframe:3 section:5 4r:50 3t:4 3n:9 above:14 sup:3 3c:1 coefficient:1 respectively:2 never:1 here:1 understanding:1 hkj:1 hki:1 tangent:9 departamento:1 groups:2 making:1 directions:1 kθ1:1 along:7 strong:1 equations:7 differential:7 obtained:2 niter:1 remark:4 study:1 vectors:2 spheres:1 adv:2 hospitality:1 suitable:1 quotient:4 diameter:2 divide:1 family:1 f1:1 apr:1 f2:3 limt:1 iz:3 des:1 corlette:8 rkk:6 kei:4 use:1 would:2 prove:9 sake:2 positive:3 give:2 uniqueness:2 chn:1 fei:1 comparing:1 fundamental:3 therefore:8 bochner:2 compactly:3 type:2 kostant:1 more:4 flat:1 initial:2 operators:3 curvature:52 berlin:1 pα:1 everywhere:2 particular:14 known:3 projective:2 eα:69 eγ:7 must:17 instructional:1 balls:2 contradicts:1 lw2:3 recall:3 equation:8 lw1:6 ril:2 geometry:1 cai:2 ishihara:2 following:17 jdt:1 trans:1 obtain:9 example:5 proof:14 claim:6 compare:1 wang:11 stated:1 calculation:1 sense:1 ready:2 ijkl:4 want:1 tam:2 sharp:4 r24:2 r23:2 verlag:1 e2t:9 iej:3 end:22 siu:3 provide:1 discussion:1 means:2 write:2 maps:2 holonomy:2 pure:1 ϕt:2 answer:1 instead:1 ordinary:1 iθ1:1 gordon:1 map:2 product:6 nonconstant:2 fx:2 bkm:3 after:1 curvatures:2 applications:3 levi:3 plane:2 ω2n:1 multiplication:1 fj:1 data:1 parallel:14 iθj:5 realized:1 iθi:7 iθn:1 outline:1 third:1 computations:1 centro:1 sp:4 explicit:2 ds2t:1 their:1 wishes:1 so:5 sm:7 exotic:1 holds:1 indeed:4 pointed:2 kong:2 dv:4 paper:2 satisfies:9 still:1 vari:1 its:7 before:3 derive:1 group:7 thank:2 fit:1 decay:3 interesting:4 fix:3 li:14 forms:5 lt:2 parts:1 2i3:1 choose:7 fij:8 covered:4 main:1 setting:2 yi:3 yk:3 yj:3 than:1 jα:5 they:4 identically:1 dηa:1 locus:1 qhn:10 e2n:8 structural:4 2t:104 eigenvalue:5 term:2 several:1 equality:2 2r:11 galloway:2 hαα:9 university:3 ve1:11 orthonormal:15 sufficiently:1 inequality:7 l2:1 each:2 2n:31 side:2 characterized:1 el:1 en:17 ei:26 ek:1 ej:21 energy:2 ηp:6 quaternionic:36 fr:5 ec:1 eb:2 isospectral:1 ball:1 hlj:1 hli:1 sectional:7 our:4 ep:6 special:1 out:4 jθ1:1 shown:1 matrix:2 space:13 gradient:1 restricted:1 since:21 research:2 similarly:4 contained:1 vector:14 geom:6 convergent:1 ω2q:3 formula:5 induced:2 suffices:1 ri:2 math:13 8n:1 theory:1 exterior:1 diagonal:4 free:1 standard:1 admits:1 base:1 california:3 ask:1 e4:12 estimate:9 e1:153 e3:13 e2:28 definition:4 dirichlet:8 ds2m:4 r1:16 r2:11 ds2n:2 argument:8 conformally:2 nonnegative:2 ahler:43 exponentially:1 δij:1 hence:18 βi:1 first:12 xj:3 xk:3 v1:5 xi:3 geodesic:7 rank:1 restrict:1 2u2:3 warped:2 done:1 least:7 berndt:1 open:1 given:12 rewritten:1 hyperbolic:8 introduction:1 f1a:2 system:1 construct:2 needed:1 assumption:5 convention:1 jej:1 dt2:2 jei:4 jen:5 busemann:1 pli:1 holomorphic:2 grant:1 centered:3 exactly:3 immediate:1 part:6 authors:3 natural:1 believe:1 institution:1 je2:5 distance:5 je1:7 showed:1 was:8 imply:2 subsequence:1 determined:6 contrary:1 were:1 radius:2 f11:2 iωi:1 qpn:4 ann:3 spectrum:4 generalization:1 endomorphism:1 say:1 need:1 any:18 hessian:1 ray:1 dη2:1 lie:1 generalizes:1 dη1:1 zero:4 depending:3 asserts:5 oriented:2 instance:1 εi:1 generalized:5 εk:7 εj:1 interior:1 heisenberg:5 formulas:2 patterson:1 trace:1 shall:3 sets:3 riemanian:1 metrics:1 most:1 r34:2 δki:1 class:2 tensor:7 fji:1 don:1 φ2r:6 considered:1 kj:1 ki:1 adopt:1 coincides:1 kn:19 hi:3 h2i:2 principle:1 exp:13 kz:3 ky:5 kx:5 positivity:1 fact:8 joining:1 show:2 supported:5 ηpr:1 dϕt:6 implying:3 minimizing:1 civita:3 substituting:1 d2:11 d1:6 capes:1 should:2 iei:8 lemma:23 only:11 ricm:8 geodesics:3 ien:5 constant:9 partially:2 local:6 preliminaries:1 sur:1 over:2 his:1 cheng:4 get:3 df:29 dg:2 de:2 db:1 dc:1 da:4 cannot:1 aforementioned:1 coframes:1 compute:6 dt:5 ahlerian:1 him:1 coth:8 qp:1 impa:1 ie1:13 conditions:4 arxiv:2 yield:1 fixed:2 qn:1 riemannian:16 satisfy:5 set:11 exists:7 ricci:8 frame:4 ends:7 see:5 geometrically:2 result:3 jx:5 theoretic:1 ke2:5 ke1:7 kej:1 brazil:2 ωpr:1 satisfying:14 fea:2 inequalities:3 visiting:1 federal:1 subsequent:1 regularity:2 consequence:1 symmetric:2 written:2 ωpq:4 between:2 geometria:1 invariant:2 boundary:2 approach:2 email:3 ken:5 notice:1 terms:2 jy:5 jz:3 nonparabolic:8 attention:1 however:2 fαβ:1 cut:5 comm:1 ji:1 key:1 jk:1 correspondence:2 tensors:3 wy:2 both:2 remarques:1 last:1 cot:6 cayley:1 taking:2 equal:1 connection:7 whole:1 holonomie:1 hτ:2 otherwise:9 among:1 16n:9 ch:2 co:1 fields:3 conclude:11 sullivan:1 cg:2 harmonic:17 ce:1 dimensional:8 2kl:1 cy:2 simply:1 moreover:9 actually:2 diff:1 uci:2 torsion:1 pq:4 e4t:1 basis:14 yau:4 locally:3 three:1 laplacian:6 interest:1 basic:3 e4n:1 riemanniennes:1 define:6 θj:8 field:1 θi:17 corresponding:5 maximal:2 irvine:5 jacobi:3 curves:4 systematic:1 derivative:1 c2:5 c1:5 denote:7 those:4 case:5 fii:3 structures:1 le:1 value:1 will:9 euclidean:2 near:1 suppose:3 applies:1 eii:1 situation:1 ein:2 iy:5 ix:5 unitary:1 geometric:2 almost:3 metric:9 ir:1 thus:1 surface:1 according:1 ii:2 ik:2 ij:12 iozzi:2 rik:5 dual:5 dη:2 vx:2 id:2 spaces:2 φr:3 φu:4 author:2 perhaps:1 realizing:1 same:2 poincar:2 fkx:1 complex:6 connectedness:2 modification:1 finite:13 isometries:1 independent:2 used:7 infinity:2 groupe:1 i4:1 hand:9 hγγ:4 v2:4 infinite:10 analyticity:1 cr:1 identity:1 lower:1 f1α:1 off:1 center:1 acknowledgement:1 well:3 components:3 lim:3 coordinate:1 archimedean:1 model:1 ωj:11 dimension:7 left:1 manifold:43 cosh2:1 cj:1 being:3 ci:4 rest:1 questions:1 facts:1 speed:1 previous:1 letting:2 note:5 rijkl:10 ads:2 readers:1 point:9 interested:1 theorem:41 ηa1:1 gave:1 real:1 iγ:2 emanating:1 spanned:2 dφr:1 know:2 bisectional:2 using:16 ams:1 necessary:1 like:2 follows:8 diffeomorphic:4 continue:1 yields:2 either:5 δg:1 works:1 hαβ:11 right:3 namely:1 some:3 growth:4 acad:1 choosing:1 respect:1 peter:9 transport:1 nonzero:1 endomorphisms:1 total:1 dimensions:1 2e:2 res:1 normal:2 hodge:1 flow:2 does:1 unit:1 tends:1 ωin:2 ωij:5 equivalent:4 bo:4 continuing:1 perpendicular:1 uff:1 bk:1 bp:15 br:1 superrigidity:1 properties:3 cε:1 quotients:1 pβ:1 comparison:8 about:4 asserting:1 usa:2 oi:1 ωi2:1 theorems:4 o:7 covariant:1 surfaces:1 automatically:1 berger:2 statements:1 ηb:7 ηa:7 subbundle:1 into:3 boundaries:1 integral:12 bound:1 nsf:1 jγ:2 weighted:2 references:1 been:1 ηq:12 einstein:5 operator:1 lastly:1 span:1 log:8 area:2 there:11 question:3 specifically:1 u2:1 ωp2:2 appl:1 inner:2 δlj:1 δli:1 sections:2 naturally:1 function:22 complete:32 form:18 ea:7 sequel:1 δkj:2 gaussian:1 volume:20 construction:3 matematica:1 cnpq:1 he:2 applying:3 versions:1 ωq:6 ωp:3 smooth:4 maximum:1 us:5 ωi:12 ieα:5 below:8 dms:1 limit:3 fluminense:1 besse:1 ωa:1 distribution:1 ωb:2 similar:5 professor:1 ab:12 proved:10 defined:9 certain:1 abstract:1 combining:4 general:2 globally:1 exist:2 θn:1 inf:4 erie:1 identities:3 universidade:1 constructed:2 again:1 functions:6 2dv:3 completeness:1 no:6 index:1 when:32 application:1 other:8 es:1 becomes:1 department:2 mathematics:2 theor:2 nt:4 arithmetic:1 star:1 zhou:3 remains:1 bundle:1 hausdorff:2 generated:1 bounded:17 hαγ:7 sides:2 structure:4 sinh:2 scient:1 implies:18 dω:3 assume:5 4t:12 curve:1 4s:298 together:2 4n:88 4i:12 n0:22 e3n:8 n2:2 4e:2 |
0704.1853.txt |@word represent:3 abundances:4 code:1 partial:1 consider:3 similarity:4 rev:2 magnetic:56 both:1 activated:2 results:10 illustrated:1 facilities:1 ionize:1 consists:1 follow:2 gm:2 disk:23 contributions:1 causes:1 gh:4 devoted:1 increase:2 inverse:2 depend:1 calculate:1 illustrates:2 young:1 protostars:4 environment:1 those:5 blackman:3 cm6:1 include:2 cm3:1 worth:3 activities:1 adiabatic:2 very:8 activation:3 rise:1 account:1 electron:3 l5:1 fall:5 condition:6 four:1 clouds:7 level:1 t4:1 shock:1 solution:6 t0:25 large:1 solid:4 settle:1 bodenheimer:2 small:1 sano:6 shows:4 concluded:3 upper:1 strongly:1 smaller:7 force:8 specially:1 10m:3 consistent:2 direct:1 pasj:1 approximation:3 surrounding:3 second:2 arizona:2 evaluated:2 go:1 equal:1 growing:1 further:1 dynamics:4 widrow:2 even:3 index:2 hide:1 combined:1 clock:1 dr0:13 ambipolar:3 nonaxisymmetric:1 expressed:2 uniform:1 switch:2 bipolar:1 jour:1 above:7 fractional:4 new:2 hajime:1 method:3 nakamura:4 3d:2 body:3 stefan:1 degree:3 respectively:6 never:2 component:1 equals:2 here:3 penston:3 following:7 free:12 aid:1 latent:1 dissipated:3 equations:12 great:1 sobolev:1 larger:2 provider:2 commonly:2 suggests:3 amount:1 klmn:2 drb:1 studies:3 plotted:3 prints:1 via:1 followed:2 figure:9 a21:1 apr:1 win:1 a22:1 highly:1 brought:3 inequality:1 total:2 planck:1 cloud:25 use:4 cosmological:10 would:2 4πr02:1 de0:3 positive:1 faint:1 next:1 few:1 noting:3 therefore:5 taken:1 inner:3 panel:7 type:2 theoretical:1 more:2 4au:1 almost:1 generate:3 becomes:1 marks:1 envelope:2 nn:2 validity:1 attained:1 appendix:3 basically:5 known:1 central:12 iv:2 iii:8 abundance:4 keeping:1 rotational:2 mc:14 tokyo:1 miyama:3 klm:2 equation:28 averaged:1 centrifugal:1 mk:1 labeled:2 anywhere:2 obvious:1 thin:2 hawley:3 under:2 could:5 stimulating:1 ions:2 weaker:1 rdisk:4 impacts:1 ionizing:2 process:3 loci:1 high:5 indicates:1 performed:3 palla:4 tan:7 νn:2 hydrogen:4 species:8 guarantee:2 needs:1 collisional:3 describes:1 dalgarno:4 holds:3 christlieb:2 chemical:13 far:3 galli:4 axis:6 parameter:1 sin:4 profile:3 map:1 astroph:1 spitzer:2 our:7 reaction:5 derived:1 different:1 replace:1 stars:15 value:2 date:3 horizontal:3 colella:2 efficiently:2 supersonic:1 stress:1 physical:4 dynamical:1 johnson:2 recombination:2 l57:1 lines:5 correspond:2 anytime:1 element:5 chief:2 cannot:1 so:5 fundamental:1 media:1 halos:1 order:5 typical:1 evolutionary:2 remnants:1 subsections:2 frebel:2 astronomical:1 soc:1 feature:1 matsumoto:3 course:1 thermal:6 paper:4 including:1 left:6 japan:2 satisfies:4 still:3 its:3 du:1 rapidly:2 probability:1 ln:2 interesting:1 2e0:9 solving:4 epoch:3 decreases:3 li:12 primordial:24 fig:9 main:3 might:1 ideal:1 maximal:2 non:2 affected:1 yl:2 yn:1 ye:12 processes:5 interstellar:1 effects:4 they:10 rotation:1 yr:1 day:1 wiley:1 4πr:2 bryan:6 term:2 several:3 2πr0:1 always:8 university:3 traced:3 ohmic:2 possibilities:3 magnitude:1 stopped:1 radial:2 instability:3 side:1 inutsuka:5 mean:5 umebayashi:4 reactions:5 activate:3 4πr2:2 4πr0:1 generation:1 magneto:2 enables:1 snapshots:8 gammie:1 society:1 owing:1 yoshida:4 expect:1 proportional:2 assumption:1 approximated:3 ev:4 neighbourhood:1 100m:1 flower:2 100k:1 ohsuga:1 gradient:1 since:16 lagrangian:1 denotes:10 particles:1 rare:1 formula:4 induced:1 issue:2 integrated:1 nν:2 after:1 offsets:1 interscience:1 mechanisms:3 little:1 possibility:3 quite:2 clarify:1 formation:19 york:1 besides:1 region:6 publ:1 beginning:4 e0:15 nishi:7 publication:1 r5:1 interaction:1 r0:41 r2:3 combining:3 starts:1 collapsing:17 transition:1 used:1 local:1 motion:5 plane:2 massive:5 assumed:2 consequence:1 onto:2 first:4 initial:13 suffix:1 symmetry:1 ignored:1 variables:1 powerful:1 number:4 reaches:1 will:1 directly:1 kobe:1 thick:1 angular:2 size:1 given:13 cartesian:1 temperature:8 jet:3 become:1 introduction:1 unknown:1 system:1 relations:1 their:3 cooling:7 accretion:65 rates:2 1d:1 calculations:6 dt2:1 1000k:1 structures:1 final:5 speaking:1 low:3 collapse:25 discussion:2 ratio:4 ncr:4 continuous:1 10g:1 remark:2 optical:1 apjs:2 authors:1 mext:1 rsw:1 than:20 coefficients:4 population:8 diffusion:6 distance:1 scheme:2 iwamoto:2 1m:1 heh:1 approximations:1 enabled:1 rate:16 limiting:1 kργ:1 matter:5 light:1 hollenbach:1 gives:2 treated:1 mini:1 fashion:2 explicit:2 torque:1 argument:2 curves:3 discussions:1 seed:8 compression:1 need:3 quasars:1 clearly:1 inefficient:1 strength:20 angle:1 form:2 able:1 efficient:1 lih:2 ideas:1 mechanism:6 converges:1 mckee:6 fitting:1 internal:2 take:1 negligible:2 switching:2 du0:1 regard:1 norman:12 opposite:1 russel:2 keeps:1 viscosity:1 most:4 boltzmann:1 apjl:1 net:4 phase:60 assessed:3 colliding:1 culture:1 especially:1 clear:2 later:4 metal:1 neutral:3 coppi:6 part:2 electrons:5 mri:10 exp:2 pattern:1 omukai:10 velocity:31 charged:4 physics:2 section:3 respect:1 quantity:1 science:3 hyper:1 apj:25 show:4 compositions:1 supported:3 ldiss:2 dissociate:1 relation:1 threshold:1 find:11 ground:1 larson:9 based:5 parameters:1 state:3 should:3 protostellar:1 only:5 molecules:3 developed:1 parabolic:1 employed:1 burkert:1 he:3 aghanim:7 umemura:6 equilibrium:2 continuity:2 do:1 predict:1 dm:1 3m:1 klein:1 means:1 velocities:2 scientists:1 fluid:4 satisfied:5 law:1 ionized:4 dyi:1 words:3 during:2 dt:12 silk:4 dr:2 falling:3 reveal:1 evolution:12 switched:1 continuum:3 fields:4 arxiv:3 summary:3 rotationally:2 investigate:4 hydrodynamic:1 through:2 fixed:3 inside:1 coefficient:1 set:5 turbulent:1 rm0:1 relative:1 differentiation:1 depends:2 radius:12 result:13 enhanced:2 li3:1 cyclotron:1 satisfy:1 contour:1 nonequilibrium:1 nakano:4 phases:2 exponent:1 subsequent:3 away:28 rikkyo:2 symmetric:2 enough:2 2πr:1 various:1 between:3 conditions:1 quantities:2 hence:1 ken:1 comparable:3 hernquist:2 recently:2 vertical:3 nature:1 importance:1 jp:2 weak:3 however:5 boss:3 derive:1 hypothesis:1 key:2 jets:6 outer:2 thank:1 received:1 cos:3 panels:3 taking:1 heating:4 figures:4 chernoff:2 behaviour:1 estimation:1 expression:2 σv:2 comes:1 among:1 cm:26 conclude:1 reasons:1 effective:1 16g:2 corresponds:1 hideki:1 stancil:4 dimensional:3 grants:1 regulated:1 coordinates:1 sequences:3 constant:2 throughout:7 along:1 runaway:1 considering:2 described:6 piecewise:1 addition:1 create:1 radiative:1 due:6 been:4 much:1 damping:1 progenitor:1 expected:6 ph:1 direction:3 emphasize:1 corresponding:1 25m:1 suppress:1 sufficient:2 formed:6 gas:42 lepp:4 coherent:1 scrutinized:1 astron:1 prestellar:3 present:2 case:5 multi:1 supernovae:1 frozen:12 empirical:1 profiles:1 ministry:1 employ:3 kepler:1 behavior:1 promising:1 promoted:1 irrespective:1 salpeter:2 susa:14 yi:4 vb:1 planets:2 coupled:3 vol:6 formulation:2 thus:11 encouragement:1 according:2 characterize:1 shibazaki:1 formulae:1 ym:2 technology:1 confirmed:2 formalism:1 maki:11 proto:1 suggest:1 formulations:1 radiation:6 same:6 any:1 unity:2 arguments:2 proved:1 relatively:1 higher:4 development:1 calculation:2 investigated:2 eds:2 l179:1 see:2 numerical:2 upon:4 hand:3 driven:3 bromm:8 hydrodynamics:2 1000m:1 interested:1 cr:1 recent:3 lower:5 center:6 whole:1 no:5 well:7 roughly:1 analysis:1 densities:1 materials:1 solve:5 works:1 dashed:2 position:4 binaries:1 latest:1 spherical:2 r03:1 r02:2 proposed:6 less:6 woodward:2 epochs:1 obtain:3 aside:1 sources:1 spherically:2 facts:1 r3:1 scattering:1 a11:1 previous:3 note:1 accreting:3 dissociation:2 density:28 absorption:3 point:1 seems:1 except:5 discuss:1 simple:1 valid:2 treatment:1 momentum:4 sonic:1 education:1 around:1 represents:5 evaluate:3 couple:1 amb:5 early:1 test:1 increases:7 five:1 know:1 press:2 turbulence:1 accepted:1 mod:1 loss:2 particle:7 follows:3 mhd:3 disks:3 flux:14 starting:1 simply:1 log10:4 suto:4 photodissociation:1 reduced:1 cooled:2 therein:1 optically:3 because:6 saigo:2 shea:6 some:4 back:1 okamoto:1 certain:1 understood:1 growth:1 b0:6 escape:1 home:1 infall:3 ourselves:1 transport:2 scales:1 sugiyama:1 5l:1 dense:3 demonstrates:1 stages:1 per:2 contrast:1 critical:5 unit:2 assuming:2 fragments:3 minimal:1 illustrate:1 core:9 run:28 slight:1 molecule:1 notations:1 each:3 γad:2 pressure:3 confrontation:1 although:2 found:7 rovibrational:2 proceed:1 stone:2 gm0:12 actual:4 universe:2 discussed:3 dependence:2 o:6 langer:7 kamaya:2 a2:2 characterized:1 rayleigh:1 comp:1 contours:3 dα0:2 machida:3 computational:1 opacity:1 presence:3 h2:12 h3:2 into:4 within:3 bound:1 ppm:1 three:2 assess:5 a9:1 square:2 references:2 heated:2 accumulated:1 abel:10 sports:1 polytrope:1 a3:1 log:1 comparing:1 transfer:5 acknowledged:1 there:3 u0:3 long:2 u2:1 dm0:4 conservation:3 whalen:2 fraction:12 astrophysics:1 mannings:2 viscous:1 was:3 energy:9 m0:12 function:2 medium:1 drive:1 triggered:1 forming:9 basic:1 but:1 astro:1 heat:1 related:1 mnras:5 line:2 true:1 hd:4 coupling:5 made:1 pomraning:1 gravitational:3 spatial:1 ionization:6 up:2 us:1 work:1 below:1 frequency:1 levermore:1 sum:1 fluctuations:1 distribution:10 balbus:3 called:1 detailed:4 ac:1 associated:1 puget:7 defined:4 flow:10 abstract:1 describe:2 denote:2 right:7 research:1 simulations:9 dε:1 distributions:2 proceeds:8 regime:3 nh:32 ni:1 functions:1 compared:3 dotted:1 polytropic:5 allow:1 whereas:7 when:10 ne:1 reality:1 field:51 other:8 statement:1 papers:1 department:2 snapshot:1 poor:1 briefly:1 elements:1 star:20 a10:1 excitation:1 a12:1 lline:1 drift:11 shown:5 includes:2 a1:3 generated:3 important:4 a5:1 a4:1 a7:1 a6:1 dissipation:12 a8:1 gets:4 structure:1 accreted:4 implies:1 faster:2 using:3 assume:2 values:1 required:1 curve:3 depth:1 mass:30 fact:2 reception:1 time:9 cores:3 nuclei:1 protostar:2 requires:1 bcr:15 once:1 |
0704.1854.txt |@word gdp:3 code:1 help:2 proposed:2 show:1 formula:1 find:3 valuable:1 gravity:1 laura:1 concept:12 distant:1 edu:1 speed:3 reasoning:2 gh:1 boundaries:2 copyright:1 title:1 chosen:1 explain:1 technique:2 should:1 source:1 theme:1 abs:1 whole:1 under:3 teaching:2 worth:2 first:2 overlaps:1 do:1 them:2 penumbra:3 around:1 than:3 far:1 showing:1 practice:1 connects:1 wave:1 remedy:1 worst:1 difficult:1 they:3 mathematics:1 world:1 discuss:2 like:1 articles:1 redistribute:1 name:4 learners:1 uncertain:1 arxiv:2 leave:1 courses:1 audience:1 either:1 second:4 small:1 forster:1 fault:1 side:1 domain:1 square:1 illustrating:1 people:1 ed:1 htm:1 hard:1 principles:2 him:1 licensed:2 b4:2 many:1 computer:1 design:1 examples:10 b2:1 our:1 out:1 economically:1 what:1 stands:1 progress:1 merge:1 away:1 learner:2 integration:1 overlap:1 yet:1 increase:1 participants:2 version:2 ra:1 provides:1 designing:1 illustrations:1 new:1 net:2 public:1 available:1 foundation:1 terms:1 ability:2 power:1 bh:1 even:1 modify:1 free:2 water:3 how:1 base:2 here:2 groups:1 ask:2 org:2 teach:2 strong:1 care:1 about:2 rare:1 her:2 license:2 most:1 coy:1 transferable:3 taking:1 called:1 gentler:1 april:2 plus:2 published:1 hence:1 sept:1 other:2 comes:1 software:2 comment:1 cambridge:1 extent:1 h3:2 waves:5 www:1 height:1 dimensional:3 smaller:1 learning:1 tidal:2 apply:1 your:1 illustrate:2 gpl:2 use:2 flaws:1 asks:1 howard:1 transfer:6 three:1 fast:1 next:1 live:1 workshop:1 ph:1 was:1 more:2 field:1 flaw:1 only:3 option:1 relationship:1 offer:1 offered:3 shallow:2 idea:1 volume:2 link:1 line:1 promote:2 nigeria:1 must:1 fragments:1 kind:1 ma:1 room:1 wherefore:1 gnu:3 contexts:1 science:1 gravitational:1 depends:1 dept:1 suppose:1 formats:1 following:2 bare:1 country:2 similar:1 example:14 connect:1 force:1 pyramid:2 shrinks:1 give:1 abstract:1 mind:1 argument:3 general:1 talking:1 engineering:1 diverse:6 laboratory:1 leaving:1 any:1 relatively:1 acceleration:1 end:1 delimit:1 no:1 discussion:2 when:3 ideas:1 clearly:1 kindler:1 globalization:1 subjects:1 electrical:1 solve:1 you:4 document:1 grasp:1 mit:2 higher:1 formulas:1 curriculum:1 volumes:1 separate:1 students:1 why:2 after:1 problems:2 drives:1 includes:1 discover:1 domains:1 v2:2 uses:1 mahajan:2 faculty:1 pages:1 billion:2 don:1 longer:1 third:1 read:1 bind:1 later:3 well:1 analysis:2 ocean:1 depth:2 without:1 so:3 fundamental:1 understand:1 operate:1 physics:2 section:1 travel:1 |
0704.1855.txt |@word sci:1 consider:2 chinese:1 cynthia:1 splitting:4 four:10 chair:1 contributions:2 extra:1 whose:1 tx:2 tu:1 charge:3 preserved:1 th:11 under:11 nsns:1 td:2 te:2 division:1 lust:2 global:2 string:28 kumar:1 n3a:4 keeping:3 results:1 electron:1 witten:2 papadimitriou:2 matrices:1 tri:1 t6:11 t2:3 marchesano:2 large:1 solved:2 vector:8 gut:5 relation:1 configurations:11 jhep:11 revolution:1 zi:1 orientifold:15 consistent:3 second:3 chen:9 further:1 salam:1 tev:4 linear:7 giving:2 diag:1 section:4 d3:1 above:3 new:5 acknowledgments:1 sli:6 satisfy:1 b666:1 ibid:2 respectively:10 neveu:1 ors:1 ching:1 china:1 groups:1 q12:2 pati:1 berkooz:1 along:1 quark:1 respect:1 z1:5 z2:29 z3:5 obtained:1 yij:1 broken:2 institute:2 richter:1 study:2 studied:1 weigand:2 products:1 uranga:5 action:2 decouple:3 implement:1 suitable:3 cancellation:5 via:15 projection:3 tau:1 apr:1 bs:1 replace:5 anomalies:1 neutrino:1 total:1 blumenhagen:7 usa:2 positive:1 coupled:1 athens:2 next:1 ramondramond:1 few:1 nucl:13 ust:1 therefore:2 usp:64 taken:1 type:16 theoretical:3 minor:1 duality:1 composite:5 operators:5 instantons:1 tested:1 iia:13 particular:1 known:2 hold:1 iii:4 must:2 me:1 md:1 account:1 stabilized:1 erratum:2 challenge:1 subsectors:1 theories:1 values:1 splittings:2 ms:1 following:3 example:3 decoupled:1 beijing:1 wang:1 xcd:7 do:5 anomalous:1 preserving:1 organized:1 generically:1 high:7 numbers:19 woodlands:1 arise:3 la1:5 la2:5 la3:5 goal:1 polchinski:1 provide:1 discussion:2 six:1 lepton:1 neveuschwarz:1 mµ:1 ordinary:1 parameter:1 fourdimensional:1 product:1 description:1 may:9 after:2 xc3:2 wrong:1 plane:6 phenomenological:4 representations:2 fl:1 parallel:1 short:2 natural:1 sectors:1 higgs:2 sr:1 sp:34 lines:1 su:29 element:1 kraniotis:1 so:5 sm:6 sl:6 representation:7 order:2 se:2 sd:2 houston:1 acts:1 subsections:3 leigh:1 hierarchy:1 top:6 mainly:2 satisfied:2 years:1 paper:2 bifundamental:1 still:1 avenue:1 its:6 before:1 orbifold:2 group:2 la:1 masses:15 tori:3 coordinates:3 li:9 parts:3 lr:1 tors:1 hidden:28 main:1 image:2 texas:1 non:10 combination:2 grand:1 break:12 xd:3 rotation:1 discuss:3 february:1 stabilize:1 university:1 classified:1 advent:1 possibilities:1 realistic:10 l2:6 l3:6 each:4 found:1 2n:1 constraints:3 tilted:5 cmc:1 energy:4 fr:1 cascales:1 seesaw:1 obtains:2 astroparticle:1 into:1 lai:7 shown:1 rr:13 space:1 furthermore:2 since:3 rev:8 douglas:1 research:2 particles:20 stud:1 ref:3 correct:1 theory:13 contain:1 diagonal:3 standard:4 completely:3 put:5 sheet:1 e1:1 e2:3 pairs:2 chiral:15 could:1 days:1 keep:1 xc1:2 place:1 βi:4 first:3 exotic:6 ibanez:3 vacua:4 symmetry:51 xb:3 xc:3 variables:1 xa:3 number:2 rank:1 fluxes:1 george:1 given:10 πa:2 tadpoles:7 rewritten:1 srednicki:1 introduction:1 adjoint:4 iaa:3 construct:1 iab:2 their:5 station:1 fermions:3 wrapped:2 structures:1 big:1 academy:2 hui:1 mech:1 lhc:1 center:1 third:3 preparation:1 matter:2 classes:1 were:4 symmetries:7 ann:1 spectrum:14 ming:1 close:1 flatness:3 seem:2 constrained:2 intersecting:17 lie:1 constructions:1 angle:2 mia:3 able:1 mechanism:4 note:5 sciences:2 internal:1 take:1 green:3 mayes:6 fundamental:1 collaboration:1 tations:1 breaking:5 singlet:3 beta:1 represen:1 honecker:2 give:15 consequences:3 viii:2 kk:1 orlich:1 torus:12 doe:1 part:3 left:1 physics:4 χi:1 sector:32 think:1 muon:1 supported:1 xd4:2 gauge:64 d6:52 subtle:1 d4:1 font:1 find:2 homology:3 q4:4 parameters:2 explain:1 should:1 only:6 generators:1 subsection:1 ied:1 abelian:1 closed:1 de:9 expectation:1 da:3 sagnotti:1 words:1 q34:2 combinations:2 during:1 ds:1 liu:4 qr:1 introduced:1 fields:1 arxiv:7 multiplicity:2 cycles:3 ql:1 available:1 moduli:2 phenomenologically:1 langacker:4 observed:1 cvetic:4 college:1 projections:1 greece:1 discussions:4 recently:2 review:3 supergravity:1 label:1 symmetric:10 correctly:1 between:1 conditions:12 preserve:1 notice:1 terms:4 wrapping:6 jv:1 however:2 n1a:4 invisible:1 lb:2 heterotic:1 concentrated:1 observable:11 last:1 many:1 conclusions:2 equal:1 mixings:3 flipped:1 present:6 dated:1 tli:1 ll:1 comment:1 tively:1 simple:1 effective:1 ca:4 ce:2 cd:2 dimensional:13 taylor:1 anti:7 cancel:1 table:24 branes:27 strong:5 collider:1 addition:4 three:16 been:4 defined:1 magnetized:1 xd3:2 define:2 θi:1 corresponding:6 both:1 bachas:1 zwirner:1 lift:1 angles:2 cosmology:1 c3:1 c1:1 general:2 ott:2 those:7 case:1 pacs:1 xa1:2 xa2:2 rectangular:5 will:8 while:4 replaced:5 supersymmetry:6 cancelled:2 mitchell:4 couplings:5 hdi:1 ix:2 orientation:1 played:1 almost:1 n2b:2 n2a:6 thus:6 them:1 iv:7 ii:7 dual:1 ia:1 vanish:1 fermion:3 begining:1 different:2 d12:1 grant:1 generic:3 same:8 any:4 complex:6 phenomenology:3 φi:2 nanopoulos:9 shiu:7 instanton:2 nib:2 nia:6 ri2:1 ri1:1 antoniadis:1 stack:10 cycle:1 dark:2 weakly:1 uncancelled:1 charges:3 well:4 roughly:1 xbd:11 solve:1 gaillard:1 model:22 charged:4 unified:2 just:1 obtain:3 actions:1 multiplet:3 intersection:9 ads:2 generator:1 density:2 rigid:1 guts:2 seems:1 valid:1 lett:8 vii:2 yukawa:3 around:4 multiplets:1 possible:2 early:1 unification:3 xe1:2 xe2:2 vacuum:1 world:1 unique:2 advanced:1 mod:2 tl:1 like:11 semi:1 follows:2 interestingly:4 flux:3 schwarz:4 become:6 soft:2 therein:1 parity:1 because:5 old:3 dimitri:1 discrete:1 some:3 b4:1 cs:1 b2:1 moreover:10 orientifolds:8 scale:30 ellis:1 footing:1 superfields:9 tadpole:5 does:1 o6:9 intersections:3 either:1 bd:2 ba:6 bc:1 equivalent:8 l1:6 q2l:4 bi:5 how:4 q2r:4 wells:1 although:3 2m:1 properties:1 hadron:1 about:2 sri:3 discussed:4 dudas:1 a2:1 cvetiˇc:10 act:2 angelantonj:1 2k:2 vi:2 cambridge:1 nonequivalent:1 presence:1 mj:1 due:2 down:6 right:1 references:1 wrap:1 existed:1 anism:1 hep:7 additional:8 removing:3 there:14 question:1 noticed:1 low:3 way:1 was:2 complete:2 form:2 effects:2 respec:1 relaxed:1 brane:34 villadoro:1 fg03:1 vevs:12 factorized:1 minkowski:1 ωr:4 variations:11 particle:6 us:4 planes:4 problem:2 similar:3 calculated:1 camara:1 aa:8 ac:2 ab:6 ai:4 abstract:1 contribute:2 denote:2 globally:1 quantum:5 conserved:1 exist:1 supersymmetric:11 campus:1 constructed:4 functions:1 no:2 na:13 handed:2 xb2:3 field:9 other:12 role:1 er:1 briefly:4 kinds:2 models:13 problems:4 variation:5 a1:1 generated:3 important:1 n1:7 structure:2 kors:1 building:7 dvn:1 coupling:3 stacks:15 mass:4 schellekens:1 walker:1 serious:1 n2:7 n3:7 original:3 |
0704.1856.txt |@word consider:2 forbidden:1 four:2 scalar:5 consists:2 ver:1 calculate:1 th:1 dsj:1 magnetic:3 string:2 wave:6 mixing:1 nishikawa:3 hamiltonian:2 kondo:1 adjust:1 phase:2 small:1 noted:1 configurations:3 consistent:3 direct:1 tex:1 second:1 dynamics:2 even:1 established:2 appear:4 while:2 g28:1 axial:2 above:1 method:4 body:5 respectively:2 component:2 here:3 mev:3 groups:1 strong:1 obtained:1 lipkin:6 search:3 multiquark:1 institute:3 shift:3 study:1 reports:1 ignoring:1 b612:1 stressed:1 narrow:5 studies:1 via:1 spatially:2 apr:1 explained:1 apply:1 total:1 use:1 d71:3 would:4 predictions:1 next:1 calculation:1 nucl:2 m0:2 carlson:1 taken:1 theoretical:7 fourquark:5 naive:1 known:1 must:1 high:1 account:1 tokyo:2 science:2 work:3 uudd:1 reproduce:1 example:1 f0:5 f1:32 reasonably:1 give:1 predict:3 accept:1 states:14 indicates:1 allowed:3 discussion:1 parameter:2 nonet:3 description:1 replacing:1 different:1 data:1 natural:1 ss:16 light:4 spectra:2 ones:1 barnes:1 polyakov:1 kkπ:1 order:3 interpretation:4 pandharipande:1 pointed:1 interpreted:1 stability:1 resonant:2 paper:1 mentioned:2 japan:6 its:3 revived:1 group:1 thank:1 decay:9 chosen:1 masses:2 d32:1 attraction:1 systems:3 main:1 might:3 cls:1 non:1 good:2 yo:5 propose:3 yazaki:1 oka:1 framework:2 tails:1 now:1 discuss:2 association:1 yitp:1 stabilize:1 university:1 d43:1 found:1 d41:1 difficult:1 en:6 aubert:1 accelerator:1 energy:6 society:1 decays:4 expect:1 our:1 out:1 napolitano:1 space:3 unnatural:2 rev:20 research:2 content:3 may:3 vector:2 dominated:2 ref:5 possibility:6 quark:10 hand:2 godfrey:2 pairs:1 interaction:2 ministry:1 tetraquark:14 diquark:3 turn:1 b592:1 hence:1 promotion:1 hadrons:2 exotic:4 major:1 ono:1 striking:1 researches:1 channels:2 tetsuo:1 wilczek:2 kanada:6 system:1 adopted:1 antisymmetrized:1 calculations:2 molecular:1 baryon:2 authors:1 oge:1 constituent:2 than:5 variational:2 culture:1 zero:1 annihilation:2 letters:3 were:4 lowest:3 motivation:1 close:5 need:1 any:1 c71:2 c76:1 fitting:1 potential:3 analogy:1 mit:1 channel:5 play:1 though:2 collaboration:3 molecule:1 petrov:1 pair:3 branching:1 observation:1 considered:1 calculated:1 adopt:1 typeset:1 takeuchi:1 proceedings:1 physics:3 particularly:1 supported:2 threshold:2 rough:1 find:1 partners:3 based:2 b196:1 parameters:1 horiuchi:2 enough:1 should:4 only:3 candidates:2 dominant:2 gev:14 get:1 syst:1 dd:1 expectation:1 cannot:1 nearly:1 closely:1 meguro:1 qq:10 arxiv:1 summary:1 bag:1 investigate:1 predicted:4 pentaquark:3 okayama:1 observed:3 argued:1 namely:1 computer:1 result:1 existence:1 discussions:1 terms:1 alternative:1 nakano:2 nuclear:1 symmetric:2 state:19 closed:1 between:2 babar:1 triplet:2 recently:2 however:1 key:1 outer:1 configuration:4 suppressed:2 suggested:6 0s:1 interpretations:1 many:2 region:9 estimation:1 experimental:3 among:1 ibaraki:1 a625:1 color:8 hybrids:1 grants:1 anti:2 dudek:1 considering:1 three:3 been:4 a359:1 much:1 interest:1 expected:4 ph:2 corresponding:1 leps:2 understand:2 evidence:1 spin:7 present:3 weinstein:2 applied:1 karliner:2 near:1 aid:1 eidelman:1 a20:1 almost:1 characteristics:1 refs:3 claimed:1 partner:2 technology:2 d15:2 confirmed:1 suggest:1 formulations:1 d19:1 same:5 higher:2 assignment:2 amd:2 recent:1 lower:4 suitable:1 modes:1 well:2 solve:1 components:4 firstly:1 organization:1 model:8 proposed:1 being:1 valuable:1 assigned:1 flavor:3 yet:2 previous:1 b575:1 candidate:3 regarded:1 seems:1 isgur:3 lett:8 input:2 yukawa:1 around:1 evaluate:1 tetraquarks:1 possible:3 using:1 burns:3 mod:2 theor:2 like:2 particle:1 ignore:1 flux:4 indication:1 morimatsu:3 sakai:1 works:1 essential:1 therein:1 parity:4 because:3 understood:1 suppl:2 meson:25 isoscalar:7 tube:4 quarks:3 mesons:10 assuming:2 prog:2 minimal:1 scientific:1 kyoto:2 conventional:3 properties:1 hadron:3 stancu:1 oh:1 discussed:5 diakonov:1 o:3 d68:1 efforts:1 slightly:1 osamu:1 into:3 within:3 due:1 lies:1 references:1 determine:2 sports:1 theoretically:1 hep:2 few:1 there:1 long:1 width:11 hidaka:1 conservation:1 low:1 way:1 was:5 function:1 but:1 gain:2 coupling:2 jaffe:6 us:2 kk:9 below:2 ud:19 called:1 int:1 certain:1 general:2 exist:1 education:1 kirk:1 ornqvist:1 other:5 role:1 details:1 normal:1 department:1 ns:4 shimizu:2 picture:3 denote:1 a0:2 important:1 lead:1 coulomb:1 pseudo:1 d27:1 4q:8 mass:22 time:1 |
0704.1857.txt |@word precise:3 monte:5 concept:1 partial:8 consider:2 chain:85 rev:5 forbidden:1 lack:1 results:28 leads:1 extrapolated:3 latter:1 overlap:2 grateful:1 consists:5 gyration:3 expressions:1 contributions:5 dimensionality:3 const:1 calculate:1 copolymers:1 paris:1 segments:1 technique:2 tr:20 rf:5 pedagogical:1 mackintosh:1 tail:1 does:4 squeezing:1 petersburg:1 excluded:10 under:4 lh:2 worth:1 indicating:2 p2:12 digit:1 supported:1 string:1 advantage:1 evolves:1 very:12 peaks:6 2rb:2 choice:2 indication:1 every:1 figs:1 dispersions:1 summarized:1 vastly:1 associated:2 polymeric:1 exact:2 condition:5 four:2 presented:8 positions:1 notes:1 correct:1 large:6 globule:1 macromol:1 small:6 3b:1 reliable:1 configurations:19 sevick:5 averaged:1 force:9 dealing:1 consistent:3 estimates:2 direct:2 understanding:1 cosh:2 jump:22 zero:5 resultant:1 follow:1 rigorous:1 qualitatively:2 accompanying:1 carlo:5 linear:3 even:1 employ:1 what:1 errors:1 blobs:6 giving:1 d2:5 sum:8 near:3 expressed:3 nonequivalence:1 axial:1 above:1 view:2 obvious:1 3a:5 method:4 contrast:6 3d:3 coefficient:1 subdivided:1 condensed:1 full:9 escaping:2 degree:4 staudinger:1 respectively:6 concepts:1 spacing:1 vol:1 here:7 conformation:9 behaviour:1 following:3 explore:1 inverse:4 them:1 free:66 separation:1 excess:9 m22:4 monomer:15 along:1 quite:7 table:12 change:9 ensembles:1 obtained:9 great:1 ntr:1 shift:1 study:2 stretching:10 allows:2 completely:1 through:2 approaches:1 suggests:4 reduction:4 usually:1 narrow:1 changes:3 elongated:2 plotted:19 useful:1 macromolecule:3 scales:5 france:1 encounters:1 vii:2 prefer:1 marked:1 contradictions:1 rus:1 summation:1 support:2 rarely:1 unit:2 horizontal:2 plot:9 use:3 lecture:1 asymptotic:2 sharper:1 remains:2 escapes:1 negative:1 perm:11 next:2 scenarios:1 comparing:1 sample:1 disregarding:1 examination:1 therefore:4 vi:2 taken:5 means:2 theoretical:15 reflects:1 more:8 smeared:1 attractive:1 almost:1 th:1 ejected:1 clearly:1 becomes:7 naive:1 apparent:1 corrected:1 curvature:1 surprisingly:1 spinodal:1 appendix:5 normalized:2 sharply:1 known:1 iii:4 must:2 escaped:65 account:1 ttr:21 mc:4 integrating:1 avoiding:6 setup:2 work:2 modified:1 mk:6 values:27 three:2 widths:1 growing:1 meet:1 flory:3 root:2 example:1 gorbunov:1 performed:1 control:3 compare:2 links:1 give:5 sense:1 neglected:1 belonging:1 states:14 νd:1 minimum:9 estimating:1 allowed:2 sharp:2 counting:1 ratio:4 respective:1 end:53 varied:3 sit:3 rather:1 discussion:3 holds:1 ping:1 american:1 chemical:1 far:2 nontrivial:1 criterion:1 get:2 instead:2 those:6 looses:1 parameter:41 rfbr:1 product:1 description:4 undergoing:1 may:3 thermodynamic:9 earlier:3 different:7 diagram:1 corrections:2 wrong:1 explored:1 physik:1 fh:4 summarize:1 deutsche:1 fl:5 parallel:1 constants:2 forschungsgemeinschaft:1 complimentary:1 branches:5 effective:1 approximation:2 lines:9 plateau:3 st:1 height:9 provide:3 eisenriegler:1 sh:2 so:5 allow:1 decreasing:1 kurt:1 order:64 singlemolecule:1 binodal:2 coexisting:1 indeed:5 confining:2 stays:1 satisfied:1 finitesize:1 paper:3 including:4 statistical:1 jimenez:1 existence:1 kinetic:1 still:2 fwhm:4 its:3 ima:1 write:1 some:6 difference:8 probability:3 fit:9 how:1 ln:6 interesting:1 lateral:9 conway:1 vicinity:2 decreases:6 forms:3 imp:5 accord:1 according:2 somewhat:1 systems:3 nimp:70 derivative:1 defining:1 deformation:1 eur:1 versus:5 eventually:1 pruned:2 good:5 affected:2 chapman:1 focus:1 their:2 numerically:1 press:2 rewritten:1 landau:30 underneath:1 framework:1 walls:3 effects:8 they:6 half:5 oxford:1 singularity:1 now:1 discuss:2 nor:1 develops:1 represents:2 february:1 several:2 imprisoned:83 khokhlov:1 always:3 university:3 level:2 concave:1 identified:1 2d:19 2e:1 2f:3 magnitude:1 2a:4 2b:3 unconfined:2 2l:6 accompanied:1 universit:1 2h:2 side:2 characterized:1 bond:2 subset:2 hsiao:1 square:4 financial:1 directly:6 weight:5 energy:61 hard:1 fitting:13 gaussian:29 related:3 each:11 straightforward:1 strips:2 expect:3 combining:2 closedform:1 our:8 happen:1 beyond:1 eq:53 mat:1 deals:1 shown:30 flower:2 fundamentally:1 space:5 restricted:1 furthermore:1 since:13 crucial:1 popova:1 denotes:2 increase:2 attracted:1 acting:2 rg:4 rb:1 formula:4 rn:6 ref:3 occurs:2 shows:4 cigar:3 solvent:3 theory:17 barrier:2 interactions:7 b36:1 discontinuity:2 differ:1 possibility:2 standard:3 reason:1 complicated:1 term:8 ask:1 estimate:5 generate:1 log:2 definition:2 grosberg:1 geometry:2 determining:1 recipes:1 transition:90 m21:3 used:1 keep:1 length:22 plane:1 hence:5 undergo:1 distinguish:1 top:1 first:22 already:1 features:1 step:2 number:21 reaches:3 approximate:1 will:4 employing:1 least:1 another:3 thick:1 precisely:2 skvortsov:5 size:21 given:22 πa:7 smaller:2 reference:2 decrease:1 similarly:1 introduction:1 data:13 eqs:16 behaves:1 precludes:1 system:4 πl:2 heights:2 indicate:2 attack:1 1b:1 chem:5 listed:6 calculations:1 lifetimes:1 dfg:1 molecular:2 williams:5 gives:9 way:1 asymmetric:5 academy:1 explanation:1 continuous:1 prediction:7 part:3 too:1 simulate:1 representing:1 than:9 coefficients:7 population:1 distance:28 perfectly:3 third:2 accordance:1 require:3 victor:1 see:13 matter:1 differently:1 determined:7 contrary:1 supposed:1 were:3 sec:7 guttmann:1 russia:1 m2:10 ansatz:1 bs4:2 pistons:3 correction:2 conventional:1 curves:15 crossover:4 electrochemical:1 z0:5 conjugate:1 close:2 seen:2 seem:1 saw:3 any:4 relatively:1 estimated:2 angle:1 built:1 depending:1 general:1 thoroughly:1 self:6 able:2 converges:1 note:2 ideal:3 edge:2 absorbed:1 take:1 forces:5 finding:1 negligible:2 coincide:1 beirut:2 accuracy:2 sets:1 fails:1 falls:1 most:2 germany:1 position:3 phase:13 coil:7 analytically:1 measured:1 why:1 appear:1 kb:2 γimp:1 found:4 especially:2 considered:2 neighboring:2 clear:8 partition:8 cover:1 dimension:1 graphs:1 points:14 metastability:1 exp:4 analogy:1 physics:7 section:1 fact:2 laws:1 slope:3 mainz:2 phenomenon:3 show:5 random:2 converge:1 purely:1 attempts:1 relation:2 drawings:2 trivial:1 find:2 d1:1 symmetric:3 grafted:7 finally:5 based:10 simulating:2 outside:2 should:6 only:8 going:2 enriched:2 factor:3 parabolic:2 invisible:1 des:2 interested:1 hall:1 equilibrium:11 do:3 over:2 dm:3 dominant:1 dh:1 di:1 dependent:1 de:1 overall:1 expects:1 aα:2 theta:1 trust:1 multiplied:1 ds:2 differentiating:1 alexander:1 stability:1 extract:1 bar:1 densities:1 progressive:1 conditions:2 arxiv:1 grassberger:3 comprising:1 microscopy:1 summary:2 europhys:3 langmuir:2 predicted:12 contain:1 analytical:9 compressibility:2 vincent:1 fixed:11 fugacity:2 locating:3 set:2 captures:1 predicts:3 seq:6 sep:1 undergoes:1 2c:2 ends:1 around:1 up:1 relative:10 depends:1 computer:2 radius:6 result:2 discussions:2 terms:4 rajagopalan:1 best:9 phases:2 exponent:3 pictures:2 sites:3 incorporating:1 boundaries:1 state:78 difficulties:2 various:12 µh:1 closed:1 between:18 piston:7 approach:5 wide:1 perfect:2 comparable:1 recently:1 extend:1 nature:2 wn:6 interfaces:1 weak:3 however:6 acknowledgements:1 continuously:1 york:3 regime:8 would:3 fluctuations:4 analyzed:1 modeling:2 configuration:5 meaningful:1 distribution:13 abruptly:2 both:9 attached:1 taking:4 density:1 equal:7 against:22 agree:1 chosen:2 figures:1 dated:1 variance:13 contribution:1 estimation:3 disappears:1 finds:1 experimental:2 compressed:2 detailed:6 relevant:1 point:37 simple:6 address:1 corresponds:1 walk:2 interface:1 haynes:1 written:1 simply:3 stretched:4 underrepresented:1 respect:3 steels:1 throughout:2 better:1 strong:3 described:5 tuning:1 second:5 piecewise:1 analogies:1 equations:1 overlook:1 due:12 johannes:1 acα:1 much:4 slowly:1 logarithmic:1 interest:2 basic:1 expected:3 flexible:3 meeting:2 cohen:1 fig:67 direction:1 describe:1 corresponding:7 fesc:8 mushroom:3 received:1 clarity:1 quantities:3 further:3 new:3 bulk:1 implied:1 confinement:3 understand:2 systematic:1 c2:16 c1:12 bs3:1 present:5 ill:1 case:4 exception:1 p1:12 macromolecules:7 subsets:3 solid:4 variances:7 straight:3 supports:1 value:19 gnb:1 while:11 abrupt:3 behavior:15 error:1 situation:4 region:4 rosenbluth:2 london:1 polymer:23 larger:8 linked:1 characteristics:6 walks:5 thus:5 site:1 surface:1 iv:7 ii:5 middle:4 vs:1 cond:1 c0:2 concentration:2 gimp:4 φp:5 containing:4 classified:1 develop:1 parabola:1 grant:1 lengths:1 suggest:2 make:1 belong:1 intrinsic:2 cross:1 same:12 adsorption:2 unity:2 schematic:3 steps:2 units:2 finite:15 pan:1 difficult:2 fimp:7 independent:4 investigated:3 unconventional:1 leonid:1 numerical:11 upon:1 effect:2 hand:5 driven:1 average:35 moment:2 compared:5 scale:1 internal:1 infinite:2 changing:2 correspond:1 scaling:11 lower:3 mech:2 off:1 milchev:1 analyzing:2 failing:1 well:5 analysis:6 non:3 without:2 studying:1 comparisons:2 model:29 essential:1 drawing:1 left:1 simp:18 cosh2:2 just:1 minima:8 being:2 generally:1 accurate:2 obtain:6 rest:2 detail:1 confined:21 shape:2 identify:2 atomic:1 questions:1 immediately:1 resc:1 paul:1 ithaca:1 down:1 previous:1 adding:1 overlapped:1 cut:1 weg:1 conclusions:1 cornell:1 consequence:1 conclude:1 except:1 mathematically:1 lattice:6 potential:1 histograms:2 blob:38 evidenced:1 stable:1 prominent:1 divided:6 identical:2 aspects:3 increased:1 easily:1 evaluate:1 possible:2 increases:7 macromolecular:1 using:7 sampling:2 weights:1 apart:1 anticipation:1 theor:1 necessary:1 like:6 sizes:2 polymers:2 qualitative:1 strictly:1 δs:1 separately:3 grants:1 yields:1 either:2 follows:1 become:2 reduced:5 making:1 because:3 sequence:1 lebanon:1 springer:1 calculated:2 growth:2 b1:6 b2:4 escape:28 proper:1 uncertainties:1 exists:1 happens:1 pronounced:3 subramanian:1 total:6 dimensions:1 lead:2 affects:1 tube:1 sfb:1 per:12 instantaneous:2 critical:6 esc:6 linearly:1 prof:1 anne:1 chains:23 grafting:5 locate:2 biased:1 retains:1 jumps:9 ration:1 agreement:5 stem:13 binder:3 symp:1 although:2 hsu:2 generic:2 analyses:1 includes:1 properties:2 comparison:6 bimodal:1 high:2 sepa:1 tuned:1 discussed:1 meaning:2 o:1 simulation:5 distinct:1 range:1 a2:13 coiled:1 obeys:1 stuart:1 experiences:1 introduced:2 slightly:4 conformations:1 block:1 homogeneous:1 equally:1 markovian:1 presence:1 h2:2 noting:1 into:7 within:3 obtaining:1 predictions:13 mushrooms:1 nothing:1 appropriate:1 right:1 accounts:1 raises:1 determine:1 strip:25 proportional:1 prefactors:1 gennes:1 significantly:1 a3:1 pharmaceutical:1 statistics:1 institut:1 compression:12 segment:1 construct:1 there:8 question:1 transform:1 long:3 dispersion:4 width:15 describes:4 low:3 fraction:13 irrespective:2 m1:9 analyze:4 was:19 knowledge:1 function:18 delicate:1 cosgrove:1 form:8 enough:1 metastable:7 crown:7 criteria:1 but:14 histogram:1 volume:12 monomers:48 properly:2 delta:1 line:7 partially:6 pull:1 wise:2 pincus:3 inhomogeneous:1 whether:3 characteristic:2 inside:3 smooth:4 maximum:4 us:3 ur:1 limit:8 cake:1 demonstrate:1 problem:6 define:2 similar:2 called:1 additional:1 regimes:1 strongly:6 ab:1 constant:5 ag:1 defined:5 certain:1 universal:2 contribute:3 influence:1 deep:1 evidence:1 dashed:9 single:5 exist:1 together:2 simulations:12 controlled:1 distributions:1 check:1 constructed:1 nh:2 again:1 functions:7 transitions:7 dotted:3 no:3 asymmetry:1 na:13 nb:9 when:5 vanishes:1 other:10 branch:5 spatial:2 department:1 saws:2 out:2 deviate:1 m2α:1 conclusion:1 poor:1 picture:15 stat:2 star:1 separate:1 models:9 uniformly:1 thanks:1 helpful:1 a1:16 gutenberg:1 important:3 peak:6 suited:3 studied:2 variable:1 cloizeaux:2 implies:1 algorithm:3 assume:1 starting:1 proposed:2 required:1 curve:22 rule:2 rh:1 depth:4 dramatic:1 mass:1 4h:2 demonstrates:1 determination:2 n2:1 requires:1 lett:4 |
0704.1858.txt |@word limited:1 measurements:2 luminosities:1 illustrated:1 higher:5 edu:1 supposedly:1 under:1 starbursts:1 case:2 rescue:1 very:5 ical:1 fan:5 difference:1 entire:1 alma:26 turns:1 large:1 quick:1 relation:1 youngest:1 programme:1 pasj:1 rhoads:1 likely:3 maloney:1 targets:1 even:5 what:3 appear:2 brief:1 current:2 axel:1 sixth:1 obvious:1 emitters:1 dwarf:1 degree:1 iram:1 hours:1 objects:11 l27:1 concluding:1 ratio:5 strong:1 extreme:1 obtained:1 great:1 remarks:1 technical:1 study:1 funded:2 host:1 herrmann:1 published:1 narrow:1 studies:4 plotted:4 spatially:1 scales:1 apr:1 highly:3 apj:8 apm:1 total:1 planck:1 plot:2 earliest:1 indicated:2 would:3 predictions:1 few:3 taken:2 more:4 israel:2 equip:1 bertoldi:5 ouchi:1 reionizing:1 emission:9 normalized:1 sharply:1 particular:4 antennas:2 sample:1 rotational:1 mm:1 science:1 values:1 temperatures:1 following:2 point:1 figure:1 calculation:1 high:18 imaging:1 magnitudes:1 ascension:1 feasible:1 axis:2 end:3 monoxide:1 turn:1 rather:1 discussion:1 get:1 regions:1 how:1 pure:1 significance:1 overdense:1 undergoing:1 seds:3 may:5 max:1 diagram:1 cimatti:1 date:2 horizontal:1 revealed:1 goal:1 kurk:2 lines:5 correspond:1 ghz:10 fp6:1 allow:1 decreasing:1 pleasure:1 order:3 typical:3 evolutionary:1 help:2 reservoir:1 indeed:1 over:2 years:1 richards:1 argued:1 mbh:1 kinetic:1 still:1 its:2 galaxy:8 perfect:1 machine:1 derive:1 rapidly:1 thank:1 masses:2 redshift:14 l75:1 better:2 detected:2 systems:7 mail:2 bout:1 main:2 them:2 good:1 evolution:1 band:17 they:3 hennawi:1 yr:2 discuss:1 easily:1 brightness:1 fully:1 drop:1 astronomie:1 cowie:1 fabian:1 found:7 spectroscopically:1 quarter:2 tracer:2 referred:1 generation:1 frequency:5 townes:2 measure:1 our:2 transitions:5 out:2 shown:1 mcmahon:1 space:4 lae:8 riechers:1 linear:2 frank:1 galaxies:8 given:5 reason:1 bursts:1 formation:5 brightest:1 matsuda:1 put:2 detecting:3 lmc:1 telescopes:1 millimeter:1 transition:3 cosmic:4 keep:1 iye:2 receivers:1 place:1 ism:3 first:1 major:1 already:1 manuscript:1 number:1 reaches:1 long:1 supressed:1 carry:1 reached:1 qsos:1 size:1 taniguchi:4 surveys:1 temperature:1 their:4 introduction:1 top:1 system:1 airborne:1 indicate:1 cooling:2 rates:1 observations:5 luhman:2 vla:2 molecular:6 murayama:2 low:6 shifted:1 noname:1 sternberg:1 estimate:3 observable:3 part:1 holder:1 than:5 population:1 observed:3 observatory:1 malhotra:3 roberto:1 second:1 project:1 solomon:1 sed:1 contrary:1 stacey:4 poglitsch:3 lowest:1 reionization:5 mind:1 quasars:3 clearly:4 strength:2 laes:5 able:2 note:2 phillips:2 ideal:1 strengths:4 play:3 towards:1 fundamental:1 normal:2 object:1 molecule:1 most:3 phase:1 alpha:2 inserted:1 why:1 sub:1 observation:1 average:1 sometimes:1 stronger:2 mjy:2 wiklind:1 principle:1 constrain:5 hashimoto:1 typically:2 envelope:1 show:1 cdm:1 typ:1 infrared:1 radio:1 fine:1 find:1 wilner:1 based:2 ngc:1 dynamical:4 distributed:1 should:2 brighter:1 only:6 factor:1 fuel:1 local:2 kashikawa:1 exceptional:1 de:1 ionized:2 words:1 report:1 ajiki:1 regarding:1 resolve:6 densities:1 luminosity:3 arxiv:1 european:1 nrao:1 shimasaku:1 mergers:1 scoville:1 achieved:1 national:1 yost:1 detection:3 ara:1 see:7 individual:2 result:1 insitut:1 close:1 luminous:1 concern:1 detect:1 ways:1 review:2 currently:3 µm:1 various:1 between:2 numerous:1 discovery:3 available:2 alighieri:1 recently:1 era:1 importance:1 key:4 carbon:3 both:2 collaborators:1 missions:1 limits:1 cox:3 vanden:1 etc:1 merging:1 context:1 morokuma:1 σv:1 nearby:1 presumably:1 co:30 characterization:1 reasons:1 corresponds:2 environments:2 simply:1 consideration:1 ic10:1 decline:1 hattori:1 helfand:1 gerin:2 addition:1 due:1 been:6 much:1 interest:1 expected:4 ph:4 geis:3 fig:10 corresponding:2 received:1 ota:1 gas:8 observe:1 covered:1 djorgovski:1 present:2 fuv:1 p3:1 p1:1 ladders:1 value:1 excited:4 will:18 dominik:1 many:2 investigating:1 di:1 henkel:1 ir:1 thus:3 apjs:1 apjl:2 vs:1 confirmed:1 l55:1 perhaps:1 same:1 any:1 epoch:2 potentially:1 arguments:1 difficult:1 satellite:1 used:4 constraining:1 compared:2 recent:1 lower:1 framework:1 maiolino:4 well:2 studying:3 routinely:1 starforming:6 quasar:1 sources:3 underlying:1 distant:1 harrison:1 immediately:2 alternative:1 wagg:1 density:1 carilli:7 sky:1 weiss:4 eckart:1 source:1 heidelberg:1 around:2 possible:5 early:4 kpc:6 press:1 using:2 accepted:1 weiß:1 like:1 sizes:1 flux:1 hosts:1 either:1 right:1 stern:2 some:1 pierre:1 j2000:2 nagao:1 redshifts:10 extended:1 lfir:6 bottom:1 though:1 l11:1 l13:1 critical:3 eliminate:1 provides:1 demonstrated:1 measuring:1 sfr:3 agreement:1 notably:1 step:1 properties:3 comparison:2 central:1 lyman:2 universe:3 discussed:1 l17:1 union:1 range:3 furusawa:1 act:1 mpia:1 metallicities:1 presence:1 image:1 within:1 interstellar:2 lies:1 subaru:1 references:1 determine:1 desireable:1 mere:1 diameters:1 measured:1 madden:4 stark:2 serego:1 detectable:1 editor:1 fraction:1 keating:2 was:1 downes:1 function:2 medium:2 but:5 hu:2 astro:4 magnitude:2 line:22 highest:5 j1148:4 genzel:1 arrays:1 cii:23 up:1 ur:1 record:1 distribution:1 walter:9 similar:1 nature:2 successfully:1 metal:1 abstract:1 aj:1 deep:2 evidence:2 neri:1 single:1 simulations:1 partly:1 physical:2 beyond:2 no:2 field:2 other:1 role:3 ulirgs:3 poor:1 star:3 excitation:2 qso:4 problems:1 metallicity:2 important:2 graphically:1 coverage:1 chris:1 astronomy:1 needed:2 structure:2 agn:2 implies:2 resolving:1 declination:1 mass:2 back:1 resolution:6 |
0704.1859.txt |@word consider:2 gp:1 skip:1 equalities:1 tadeusz:6 consists:1 gk:2 whose:1 tp:2 alberto:1 multilinear:2 norm:1 conjecture:1 random:1 g2:2 g1:2 results:2 every:1 δgi:1 condition:4 irreducible:1 discrete:6 science:1 upper:2 grundlehren:1 estimates:4 second:4 reine:1 odd:1 theory:2 even:1 nonlinear:1 sum:2 sup:15 new:1 method:1 satisfy:1 full:2 ryszard:6 groups:9 address:1 strong:5 obtained:3 institute:2 studied:1 makes:1 convolution:14 classification:1 apr:1 følner:4 inverses:1 use:5 prove:2 positive:1 contains:1 next:6 m1:1 therefore:4 type:31 duality:3 operators:15 ital:1 berlin:1 particular:2 known:1 springer:1 flp:1 der:1 work:1 remain:1 values:2 following:2 trans:1 proof:13 give:1 calculation:1 scand:2 lorentz:2 reprove:1 verlag:1 holds:3 maps:1 instead:1 map:1 fr:2 mat:1 may:1 max:1 mapping:2 fa:1 fk:6 fm:12 fn:33 introduced:1 imply:2 author:1 so:1 representation:4 order:1 indeed:1 satisfied:1 interpreted:1 banach:3 satisfies:2 group:17 chosen:1 fix:1 actually:1 estimating:1 lr:5 choose:1 lp:19 mail:1 amenable:7 number:2 yx:1 focus:1 now:1 2q:3 university:2 iff:1 inequality:8 radial:14 entirely:1 european:1 side:1 characterized:1 mean:3 homogeneous:1 product:1 ofstr:1 measure:6 our:2 special:1 shown:2 matrix:1 space:5 restricted:7 since:2 fellowship:1 stud:1 denoted:1 math:9 normed:1 linear:6 cowling:1 free:13 standard:1 york:1 estimate:6 χ2k:2 phrases:1 nonnegative:6 turn:1 length:3 hence:8 first:6 xn:2 probability:5 qαn:6 primary:1 another:1 open:1 given:5 similarly:2 introduction:2 their:1 gives:6 completed:1 part:1 norms:1 coefficients:1 showed:3 namely:1 determined:2 cohen:1 argument:1 say:1 angew:1 any:7 generalizes:1 min:9 able:1 δnm:1 coincide:1 gmail:1 most:2 regular:1 letter:1 marie:1 later:1 countable:1 χf:8 χe:31 χn:50 χm:9 χl:3 χk:9 section:1 came:1 show:1 supported:1 spaces:7 indicator:1 knowledge:1 colloq:1 lemma:4 only:8 going:1 generators:3 constant:2 triangle:1 get:4 trees:1 words:5 consecutive:1 secondary:1 arxiv:1 qn:1 kernel:1 set:2 ser:1 exists:2 observed:1 see:2 computer:1 w2:6 w1:6 subject:1 unione:1 definite:1 tend:1 symmetric:4 between:1 invariant:4 subscript:1 conditions:2 fx:2 terms:2 attention:1 weak:27 predual:1 key:1 amer:1 wx:4 fnp:1 f2k:2 many:2 taking:3 f2n:2 f2m:2 com:1 amenability:1 simple:1 harmonic:1 simply:1 moreover:2 cq:3 ct:1 considering:1 been:5 commission:1 pk:9 pl:1 define:1 subspace:1 observe:1 general:1 those:2 case:1 value:1 choices:4 will:9 while:2 situation:1 property:1 wroclaw:2 almost:1 vi:1 thus:3 itself:1 supremum:1 wissenschaften:1 different:2 grant:1 suggest:1 same:5 clearly:1 complex:4 modification:1 finite:7 interpolation:9 used:1 infinity:1 hand:5 infinite:1 poland:2 well:2 analysis:2 machinery:1 components:1 mnisw:1 left:3 obtain:4 facts:1 previous:1 letting:1 valid:4 theorem:15 heidelberg:1 erated:1 using:2 unique:1 advanced:1 mod:13 necessary:1 δx:21 δy:10 follows:2 kesten:3 yields:1 arbitrary:1 δg:1 reduced:2 right:1 some:1 algebraically:1 examples:1 choosing:1 respect:2 meda:1 setti:1 does:1 decomposition:1 mtkd:1 proc:2 power:1 equivalent:3 boll:1 host:1 2n:1 simpler:1 om:1 cn1:2 theorems:2 2k:25 soc:3 letters:3 into:7 functional:2 because:1 references:1 determine:2 operator:10 rely:1 log:3 transfer:1 support:1 there:7 inner:1 way:2 was:1 function:3 form:3 true:1 raising:1 he:2 applying:2 supp:1 up:1 ul:1 below:1 problem:1 called:6 proved:1 defined:1 abstract:1 am:2 deep:1 denote:3 exist:2 walks:1 inf:1 bergh:1 defines:1 again:1 functions:10 curie:1 other:6 nonamenable:2 np:2 mathematics:3 n201:1 conclusion:1 elements:1 generates:1 bounded:4 mathematischen:1 tricky:1 implies:5 dω:1 assume:1 rule:2 notion:1 n1:1 4a:1 |
0704.1860.txt |@word similarity:1 onken:2 asymp:1 assembled:1 relationships:1 whose:1 gamut:1 under:4 worth:2 stipulate:1 figs:2 affect:6 suffices:1 solid:3 vector:5 falco:1 direct:1 surrounding:1 likely:7 even:14 errors:1 selected:1 above:3 new:7 net:4 increasing:9 evolving:1 never:1 mei:1 residual:1 here:5 richstone:8 met:1 active:1 path:1 logarithmic:2 obtained:2 rests:1 study:22 changed:1 approaches:1 changes:1 attractor:4 prints:5 secure:1 explained:1 replace:1 remnant:1 hindsight:1 total:2 would:17 tail:1 m1:4 therefore:12 m2:4 robertson:11 type:1 holz:1 populations:1 brings:1 hole:3 pogge:1 must:1 md:1 ma:2 work:2 springel:10 example:4 milosavljevi:1 relativistic:1 involve:1 indicates:1 degenerate:1 isothermal:1 david:1 zotti:1 end:8 how:13 bressan:1 actuality:1 merritt:6 undergoing:1 after:16 kennicutt:1 diagram:2 modest:1 law:1 effective:1 summing:1 maintain:1 green:7 correlation:40 order:1 interpretation:1 feedback:9 over:14 vastly:1 before:1 fit:3 matured:1 fig:13 versus:2 eventually:2 them:1 affected:3 combination:2 l151:2 break:2 effects:6 they:6 represents:2 l37:1 barton:1 luca:1 lauer:8 each:11 side:1 mean:8 telescope:1 evolve:5 extract:1 array:1 quantify:1 crucial:1 re:1 newly:1 forth:1 linear:33 gasrich:1 formation:7 forcibly:1 estimate:1 r0:1 created:2 starts:1 cosmic:2 giallongo:2 tempting:2 onto:1 already:2 thereof:3 another:7 radiate:1 clarity:1 illustrate:5 toy:1 xie:1 similarly:1 eqs:1 intermediate:1 rates:3 observations:6 hypothetical:1 insightful:1 collapse:1 centered:1 dissipationless:3 requisite:1 matteo:10 scenes:1 matter:3 tonry:1 tion:1 enables:1 treu:5 kolchin:2 quench:1 mind:1 spectrum:1 seen:5 regulate:1 ray:1 latter:2 responsible:3 causing:3 2006a:10 2006b:6 isolates:1 circles:5 blue:4 shallow:2 though:1 replenished:1 object:3 involving:1 tozzi:1 mstellar:3 points:18 principle:1 sum:2 incorporate:1 random:3 colors:2 subtle:1 tremaine:6 situations:1 explain:3 burkert:2 oct:1 do:7 di:10 de:3 preferred:1 despite:3 runs:1 greene:6 implication:1 mergers:72 reference:1 zamorani:1 observed:3 depends:4 radius:1 result:3 discussions:3 subject:2 drawn:9 shields:5 preserve:1 parallels:1 nature:1 however:19 equals:2 extent:1 received:2 oiii:1 cox:6 uncertainty:1 heating:1 merging:30 expense:1 con:1 behaviors:2 blaizot:1 represented:1 wider:2 aller:1 three:3 been:6 quickly:4 much:10 interest:1 progenitor:1 expected:2 dry:1 locations:1 aip:1 spontaneously:1 applies:1 balance:1 conf:1 suggest:2 make:1 cumulative:7 amount:2 several:5 grows:1 fairly:2 numerical:1 differing:1 coevolution:1 hand:1 hans:1 normalization:9 cycle:6 mentioning:1 scenario:8 monaco:1 just:7 quasar:5 ideas:1 assigned:2 transforms:1 facts:1 somerville:2 yet:2 previous:2 passive:1 easy:1 possible:4 l89:1 background:1 hunt:3 specific:2 arbitrary:2 right:1 flatter:1 somehow:1 pinkney:2 critique:1 mcleod:1 bottom:1 normal:9 comments:2 spawned:1 exposition:1 core:1 predicting:1 powerlaw:12 properties:2 months:1 haehnelt:6 o:2 slightly:1 considerations:2 mbh:146 presence:1 bound:3 chooses:1 lies:1 reducing:1 support:1 initial:44 editor:1 way:3 brotherton:1 astrophysics:3 was:1 gabasch:2 martel:1 form:3 forming:2 differences:1 giacconi:2 removed:1 true:1 builds:1 inside:1 mgal:92 mgas:3 kaspi:4 stages:1 abstract:1 graff:2 evidence:2 conserved:1 exist:1 simulations:13 accounting:1 distributions:3 triangles:4 constructed:1 mclure:2 no:11 whereas:2 generally:3 actor:1 role:1 jenkins:2 escala:2 models:3 dissipation:2 marconi:3 abscissa:3 time:18 overplotted:1 switched:1 focus:2 morphology:2 depend:6 choice:1 exact:2 fontanot:4 level:1 did:1 dif:1 quick:2 upper:2 l97:1 slower:3 findings:1 saglia:1 appear:2 axes:1 current:4 shared:1 christiansen:1 supporting:1 dwarf:1 understanding:2 address:1 alone:2 along:3 appears:3 change:3 jord:1 noticeable:1 institute:2 studies:7 emerge:7 regardless:4 merely:1 undergone:9 hierarchically:1 sake:1 tightly:1 scenarios:8 opposed:1 bender:3 criteria:2 theoretical:1 today:1 introducing:1 apparent:1 appendix:4 insights:1 impey:2 labeled:1 growing:2 equilibrium:1 gravitationally:3 figure:29 predict:1 arise:2 sample:4 ngal:1 rescaling:1 conversely:1 occur:4 discussion:7 pure:4 parameter:1 product:1 may:18 produce:8 deviates:1 data:12 grow:4 natural:3 correlate:5 zentner:1 so:11 definitions:1 aforementioned:1 indeed:1 pointed:1 mainly:1 years:3 course:1 episodes:4 statistical:7 peterson:6 still:5 tendency:9 observational:4 thank:1 acknowledge:1 interesting:3 jim:1 decreases:8 forms:1 decreased:1 main:7 texas:1 non:2 thereby:2 scaling:12 warranted:1 half:3 halo:2 possibilities:2 realistic:6 entirely:1 realism:1 individually:1 significantly:2 ed:2 gaussian:3 challenges:1 eq:1 emerges:2 ultimately:2 space:2 furthermore:3 increase:2 blakeslee:1 appenzeller:1 squares:4 correct:1 shows:8 theory:1 dietrich:1 mechanisms:2 possibility:5 quite:1 escud:2 complicated:1 besides:2 fixed:1 widths:1 place:2 massive:7 first:4 origin:1 intuition:2 benefited:1 symmetry:1 rachel:1 stsci:3 long:2 directly:2 message:1 open:1 size:1 given:3 necessarily:2 kochanek:1 1a:5 ciotti:11 1b:4 draft:2 white:1 fraction:2 mostly:1 tommaso:1 than:22 wide:2 future:3 were:6 quataert:1 outcome:2 pre:3 san:1 argument:2 any:4 efficient:1 aside:1 converges:4 note:1 emphasis:1 potential:1 take:1 observationally:2 begin:1 multiple:1 opposite:1 track:1 incidence:1 latex:1 especially:4 surprising:1 considered:8 average:6 phil:1 implications:2 drive:2 typeset:1 typically:1 slope:21 spaced:1 show:7 londrillo:1 ratio:13 histories:2 jannuzi:2 only:15 black:7 get:2 unimportant:1 cannot:1 soltan:2 magorrian:4 bonning:2 summary:1 relative:5 namely:1 corre:1 uncorrelated:2 parent:9 ways:2 subsequent:1 review:3 outside:1 between:21 vertical:1 gratefully:1 virial:2 come:2 many:5 region:1 propagation:1 comes:2 sampling:1 considering:1 sensible:1 west:1 locally:1 markedly:1 production:1 combined:1 followup:3 direction:3 formed:2 external:1 grillmair:2 those:4 case:4 hughes:1 promising:1 situation:2 coupled:1 bias:3 different:8 same:12 epoch:1 arguments:2 physical:2 events:6 driver:2 roughly:3 without:2 model:3 blandford:3 being:4 when:9 multiples:1 heuristic:2 segan:1 rose:1 except:4 samples:1 real:1 aspects:1 around:2 dark:2 using:4 adams:3 faber:4 either:3 always:1 reduced:1 redshifts:1 trujillo:1 slice:1 confirm:1 maoz:2 depletion:6 critical:1 greyscale:1 bentz:2 refer:1 measuring:1 biased:1 reasonable:1 late:3 tree:2 notable:1 biases:2 ratios:1 standpoint:2 refers:2 emulateapj:1 central:19 origins:2 hopkins:11 discussed:1 factors:2 practical:1 greatly:2 ot:1 inclusion:1 communication:1 references:4 lively:1 determine:2 speculated:1 lastly:5 log:25 there:8 dispersion:7 detectable:1 low:8 stars:3 slopes:4 complete:4 enough:2 regard:1 sophisticated:1 mnras:15 assl:1 isolating:2 regimes:1 strongly:4 ohm:1 taylor:1 certain:1 aj:1 fellow:1 ar:1 lifetime:1 again:1 tight:8 deviation:1 a3:1 important:1 a5:1 a4:1 a6:1 tendencies:2 pool:2 mass:101 original:1 represent:5 aring:7 consider:8 caused:1 lack:4 generalize:1 follow:2 disk:9 reasoning:6 causes:1 fellowship:1 init:4 program:1 far:1 discrepant:1 puzzles:1 corollary:1 condition:2 randomness:1 large:4 small:3 20th:1 past:4 rate:9 pass:1 further:3 what:7 hernquist:10 clock:2 section:3 version:2 fractional:1 contrast:4 revealing:1 full:3 component:3 christy:1 strong:4 colored:4 prior:1 bulges:8 skepticism:1 followed:2 lanzoni:1 menci:1 eddington:1 silva:1 takes:1 faint:2 comparing:2 minor:23 more:27 flat:1 salviander:4 emission:1 particular:2 dex:2 evolves:1 keeping:1 science:2 equation:3 remain:3 history:3 compare:1 cosmological:3 suggestions:1 states:1 sphere:1 sense:1 sharp:1 axis:1 goal:1 rather:4 acts:1 bimodality:1 gebhardt:9 explains:1 ensemble:2 simplicity:1 monte:9 galactic:1 incorporated:1 capture:1 emulate:1 weaknesses:1 plane:4 caon:1 parameterized:1 fundamental:9 salimbeni:1 remnants:1 reservoir:2 reversing:1 through:8 boylan:2 avenue:1 its:2 islam:6 style:1 peng:12 absence:1 systems:2 might:14 motivated:1 seeking:3 cen:2 morphologically:1 anticipated:1 framework:1 yu:2 easily:1 miralda:2 fully:1 presented:3 2a:3 2b:3 difficult:1 heavy:1 µinit:8 energy:1 reduce:2 idea:5 yoshida:2 measurement:1 event:1 robert:1 since:1 dominated:4 issue:4 occurs:1 circumstance:3 dressler:3 reason:5 beginning:1 definition:7 pairs:1 bring:2 thread:1 consequence:6 undergo:3 major:41 probability:1 thereafter:2 number:23 illustrating:1 mbulge:31 differ:2 koo:1 introduction:1 least:2 sargent:1 assumption:4 feulner:1 shifted:1 relationship:6 behind:2 immediate:1 part:4 bower:2 unrealistic:1 albeit:1 determines:2 contrary:1 toward:12 cleaner:1 7b:1 7a:1 strengthen:2 ager:1 randomly:5 headings:1 quasars:3 bhs:9 lie:1 depending:3 lin:1 generalized:1 finding:1 experienced:4 dunlop:2 most:7 significant:3 position:2 measured:3 postman:1 deviations:1 clear:2 totic:1 exp:1 velocity:3 physics:16 ivison:1 converge:2 relation:76 find:1 merger:33 distributed:1 wayne:1 factor:5 merged:2 dominant:1 invoke:2 dependent:1 secular:1 trees:6 closely:2 combinations:1 during:3 silk:6 vergence:1 arxiv:8 common:1 activity:1 doubles:1 set:1 ferrarese:5 achieved:1 locale:1 undergoes:1 cattaneo:2 see:12 close:1 contour:2 analog:1 fontana:1 pictures:1 currently:2 woo:5 danese:1 conditions:4 seeded:1 dalla:1 creating:1 initially:3 attention:1 premise:1 both:9 connection:1 became:1 context:1 corrupt:1 drory:1 whole:1 baltimore:1 arbitrarily:3 bell:1 reasons:3 corresponds:2 simply:1 luis:1 decline:3 described:2 due:4 ph:1 walter:1 referee:1 wheeler:1 gas:9 gao:2 gal:5 understand:1 systematic:1 attractors:1 aaron:1 look:2 frozen:2 budget:1 while:7 match:2 behavior:8 error:2 rix:10 arching:1 vol:1 averaging:1 apjs:1 itself:8 santos:1 virtually:1 netzer:2 higher:1 development:1 used:3 levels:2 uses:1 blain:1 robust:1 yuan:1 recent:2 noll:1 lower:13 shape:3 useful:4 cut:3 conclusions:1 source:1 haardt:1 location:6 theorem:6 march:1 showing:3 apj:41 follows:3 disks:1 continue:2 yields:1 popular:1 often:2 some:7 back:2 understood:1 trends:1 towards:2 examples:1 mirror:1 curious:3 giveon:1 scale:1 l11:1 l13:4 smail:1 pei:1 tends:1 dating:1 proc:1 run:1 bh:41 agreement:1 constraint:1 exaggerated:1 simulation:8 range:1 into:4 within:1 locus:3 revisits:1 controversies:1 primarily:1 proportional:1 ellipse:4 uncertainties:1 arrow:1 statistics:8 question:1 specifically:1 rees:3 repeatedly:1 line:5 croton:6 up:3 continuously:1 schechter:17 similar:7 steepen:2 constant:3 worthwhile:2 defined:4 likewise:1 influence:1 single:1 graham:5 steeper:3 puzzling:1 priors:1 shallower:2 explaining:2 lucia:1 develops:1 perna:2 agn:8 correlated:1 implies:3 practically:2 σbh:5 required:1 holes:3 implied:2 correlates:2 presenting:1 requires:1 having:5 once:2 illustrates:1 results:4 existing:5 illustrated:2 edu:1 go:1 issues:2 compact:1 contours:2 dickinson:1 include:1 implicitly:1 entire:4 experiencing:1 michael:1 borys:2 smaller:4 progenitors:4 substituting:1 carlo:9 enjoyed:1 experiment:4 3b:5 3a:3 exercise:1 body:1 degree:2 leh:1 respectively:2 l21:3 following:4 objects:10 others:1 consideration:1 extreme:4 involved:1 larger:6 shades:1 resulting:3 shaded:1 examining:1 scales:2 private:1 scaled:1 addressed:3 decrease:6 apply:3 causal:1 use:4 asymptotic:2 remains:2 piatek:1 malkan:3 started:1 becomes:1 occurred:1 normalized:2 crosses:3 erwin:1 scatter:38 weaker:2 purposes:1 high:6 effectively:1 assumptions:1 pulling:1 something:1 weaken:2 holds:1 located:1 elliptical:3 instead:4 constraints:1 profile:1 filippenko:4 kormendy:8 efficiently:1 rutledge:1 ambiguous:1 light:1 counter:1 chapman:1 chien:1 martini:2 devriendt:1 evolutionary:3 interpreted:1 produced:4 including:2 galaxy:82 complicate:1 masses:22 redshift:4 li:4 primordial:3 degrees:1 clusters:2 alexander:1 defining:2 greater:1 february:2 profound:1 identified:2 merge:18 l1:1 identifies:1 traces:2 l9:2 subset:1 wandel:1 chung:1 related:1 special:3 out:4 fundamentally:2 favata:1 cause:5 red:5 8b:2 8a:1 galaxies:69 completely:2 early:5 franx:1 could:4 frenk:1 times:3 explored:2 hence:1 retain:2 diminishes:1 facilitate:1 randomizes:1 ziegler:1 randomized:1 l35:1 l31:1 histograms:2 sijacki:3 relations:8 their:9 accretion:7 declines:1 final:8 explanation:2 exactly:1 epochs:1 colleagues:1 ara:1 visited:1 steep:14 steer:1 exhibit:1 fail:1 granato:3 clearly:4 mechanism:2 instance:4 intrinsic:4 why:6 consequences:1 stronger:4 hierarchical:1 normally:1 fact:8 selection:4 terminate:1 rotating:1 pozzetti:1 trivial:1 based:3 hopp:1 should:6 ambiguity:1 partially:1 local:2 colberg:1 means:4 bear:1 ones:2 words:1 steepness:2 symbols:1 evolution:18 luminosity:5 navarro:1 cycles:9 view:1 correlations:3 turbulent:1 seitz:1 madau:1 statistically:1 closer:1 nuclear:2 tend:3 state:2 correctly:1 progress:4 comparable:6 cristiani:2 hypothesis:2 interpretations:1 equal:1 figures:9 marta:1 otherwise:3 detailed:3 relevant:5 co:1 conclude:1 chakrabarti:1 sequences:2 respect:1 addition:3 wills:1 darren:1 immense:1 agreements:1 define:2 corresponding:5 sufficient:3 replenishment:6 keeton:1 covered:1 general:4 present:4 dissipational:2 ejection:1 value:5 choices:1 will:21 revisited:1 discoveries:1 examines:1 chaotic:1 thus:6 surface:2 vs:5 impervious:1 kollmeier:2 perhaps:2 radiation:2 member:1 unity:1 parts:1 mehlert:1 finite:2 infer:1 residing:1 effect:9 tremonti:1 frequently:1 judgment:1 tighter:3 nevertheless:1 calibration:1 well:2 thought:5 accreting:1 drawing:1 kauffmann:7 lest:1 less:2 nipoti:2 generous:1 preprint:1 density:10 smith:1 simple:5 ought:3 identical:1 increases:1 five:3 immediately:1 necessary:1 like:2 bulge:17 qualitative:1 martin:1 lation:1 therein:3 because:27 nucleus:1 growth:8 spheroid:1 lead:1 does:9 assuming:1 stellar:10 host:6 offset:2 supermassive:2 gained:1 about:13 universe:4 seeds:1 tailed:1 insufficient:1 upward:1 thermore:1 astronomy:3 van:3 albada:3 inner:2 volonteri:8 naturally:5 function:30 basic:4 but:10 astro:1 construction:1 ho:16 convergence:24 ha:1 truncation:1 evident:1 instructive:1 whether:4 gravitational:3 below:9 limit:17 distribution:31 jenny:1 linearity:9 dearth:1 identities:1 eric:1 functions:9 compared:6 vestergaard:6 nonetheless:1 cˆ:1 barth:5 other:29 details:3 branch:4 conclusion:3 symposium:1 star:7 shown:13 krause:1 friends:1 acknowledgment:1 heidt:1 guiderdoni:1 4b:2 4a:1 |
0704.1861.txt |@word replacing:11 vila:1 japan:1 consider:4 datum:1 results:8 month:2 scalar:1 proposition:7 kato:7 covered:1 localized:1 inverse:1 depend:1 interactions:1 ıa:1 tl:1 tm:10 c5:3 under:2 ıo:2 applied:4 straightforward:1 ll2:1 vera:17 corollary:5 treating:1 solves:1 hamiltonian:1 induction:7 t2:1 solution:12 t0:58 t1:4 large:1 vector:2 fourier:3 small:6 eigenvalues:1 anal:4 abbreviated:1 employing:1 2k1:44 φu0:10 2k3:4 estimates:2 direct:1 riesz:1 approximation:1 go:1 second:3 evaluated:1 l2x:16 estimated:3 even:1 nonlinear:12 plays:1 tipo:1 ak3:3 ak2:4 ak1:8 ak0:19 near:2 ak4:1 wxxx:1 version:1 kumano:1 above:10 sup:8 expresses:1 increasing:1 equivalent:1 satisfy:2 full:1 respectively:5 navier:1 behaviour:1 strong:4 equations:46 appears:1 change:2 contraction:4 obtained:5 remark:9 sobolev:2 technical:1 study:3 larger:6 masuda:1 domains:1 suitable:1 studies:1 york:1 via:2 useful:1 classification:1 apr:1 merely:1 replace:1 unitary:1 summation:1 apply:1 univ:2 linearly:1 wang:1 recurrence:1 use:6 asymptotic:1 intensively:1 distinct:1 positive:8 ψp:1 negative:1 ψt:6 noting:1 therefore:8 taken:3 indiana:1 associated:3 type:10 vl:2 operators:3 odinger:5 b2ǫ:2 particular:1 known:1 cases:1 iii:1 brasil:1 valued:2 regularizing:2 henri:3 equation:10 work:1 vega:5 del:1 norm:1 lipschitz:2 following:17 im:1 example:2 proof:6 f0:2 f1:8 f2:7 f3:11 f4:2 f5:2 indicated:1 process:1 sense:5 organized:1 ann:4 involve:1 assumptions:1 bk1:8 bk2:8 bk3:8 v0k:12 boussinesq:1 lemma:15 provide:1 verify:1 holds:1 utilize:1 kenig:5 write:1 maps:2 pure:3 oscillatory:1 map:3 wakabayashi:1 v01:1 mat:1 fx:7 max:9 after:2 derived:2 mapping:1 applications:3 inst:3 waves:5 improving:1 fi:1 law:1 revealed:1 constants:8 natural:1 outline:1 third:3 whenever:1 maintain:1 so:2 expression:1 subsequently:1 octavio:1 order:3 typical:1 operations:1 restriction:1 schwartz:1 cutoff:1 a02:4 indeed:5 over:2 insight:1 fξ:5 paper:4 through:1 thesis:1 mentioned:1 existence:2 satisfies:3 solitary:3 group:1 directional:1 temporal:1 kluwer:1 translation:1 lu:2 lr:1 choose:3 mail:2 main:3 setting:1 a92:3 non:3 duhamel:1 combination:1 janeiro:1 integral:1 introduce:2 scaling:1 mention:1 effects:1 they:2 singularity:5 now:5 it0:4 term:11 φk:4 dirac:3 2s:2 off:8 iwanami:1 sufficiently:1 inequality:2 l2:49 mode:1 2b:1 each:5 2m:2 bona:3 side:7 kappeler:1 differential:2 l30:1 linares:2 series:1 energy:1 revised:1 reduce:1 idea:3 xr:7 measure:3 concepci:4 our:4 v00:1 shown:3 matrix:1 space:12 furthermore:1 since:8 crucial:1 denotes:2 may:1 geom:1 stud:1 rn:6 size:1 u2x:1 math:12 benjamin:1 linear:7 localization:1 departamento:3 standard:1 atica:3 reason:1 necessarily:1 a210:3 ask:1 e4:3 estimate:9 ash:2 e1:2 e3:2 e2:17 definition:1 interaction:4 r1:8 r2:87 phrases:1 times:2 introduction:2 int:1 c23:1 universidad:2 hence:8 fractional:1 first:3 origin:2 xk:2 initial:15 xl:27 xb:23 u1:1 variables:5 sistema:1 number:1 transform:1 multiplying:1 u3:1 another:1 a3k:1 smoothing:8 illustrate:1 dispersive:4 taniguchi:1 given:3 long:2 smaller:1 similarly:2 resonable:1 data:14 system:49 assumption:9 aa0:47 calculations:2 tom:1 gear:2 para:2 2aa:8 tool:1 continuous:2 part:3 authors:1 norms:1 x3:46 x0:43 x1:1 than:6 vxxx:5 last:2 uk3:10 see:1 uk0:16 project:2 publ:1 were:1 toward:1 treated:1 vx2:1 tangential:1 comput:1 generality:1 craig:2 cohen:1 argument:6 already:1 analysis:1 seen:1 any:8 latter:1 j3:9 k3:131 k2:146 k1:178 internal:3 ck1:4 take:9 ck3:4 ck2:4 new:1 mit:1 bilinear:2 trace:1 eaire:2 fondap:1 involving:1 preliminary:1 pair:2 analytically:1 class:2 ufrj:2 soliton:1 nonlinearity:1 dordrecht:1 principle:2 occasion:1 vries:21 section:7 fact:1 laws:1 show:6 leibniz:1 supported:1 ix0:44 x2:11 spaces:1 solutions:9 tµ:2 keywords:1 cnpq:1 dilation:8 principal:1 completion:1 finally:2 copyright:1 l2t:3 directly:1 true:2 enough:1 should:1 analytic:5 only:4 going:2 coefficients:3 a03:3 constant:11 local:3 interested:1 do:2 a01:4 handle:1 notation:3 get:1 de:33 freezing:1 da:1 ak11:2 dx:32 3b:8 report:1 during:1 dt:8 a82:2 a83:2 evolution:4 saut:1 arxiv:1 hr1:8 2b2:1 method:1 supp:3 wish:1 fixed:3 a4k:1 set:3 exists:7 sep:15 j1:30 j2:19 uk2:20 depends:2 mauricio:2 result:7 w0:1 subject:1 brazil:2 satisfying:3 interacting:1 functionals:1 boundaries:1 state:2 cambridge:1 between:2 justified:1 conditions:2 notice:1 terms:5 initially:1 weak:1 wt:1 hypothesis:2 article:1 amer:1 distribution:1 improve:1 received:1 essentially:1 enables:1 improved:1 a103:7 c25:1 vk2:9 vk3:20 equal:1 comm:4 whole:1 fix:2 ck:5 necessary:1 cl:2 simple:1 simply:1 moreover:4 ogawa:1 throughout:1 c31:3 duke:1 decoupling:1 observing:1 locally:3 three:2 been:3 gevrey:8 defined:4 reduction:2 belongs:1 treat:1 u10:1 ph:1 ak:19 fk:5 define:4 aj:3 corresponding:1 both:3 quantities:1 matem:3 hayashi:1 c21:1 chile:3 derivative:4 c3:12 c2:14 c1:60 c0:16 c7:2 c6:2 those:6 c4:14 case:7 dξ:2 p0:8 look:1 subsets:1 continua:1 single:5 value:3 will:4 while:1 suppose:9 aid:1 property:1 procedure:2 ix:2 a23:5 coupled:31 almost:1 a29:3 metric:1 vk:29 thus:2 ii:1 rio:1 regularity:8 vt:3 vx:7 uxxx:5 anymore:1 generic:1 acknowledgments:1 make:1 belong:2 same:4 poincar:3 hxs:10 hxr:3 several:3 independent:4 used:4 infinity:1 effect:10 hand:9 v0:21 v1:1 v3:1 moving:1 purpose:1 invariance:2 lower:1 weakly:2 schr:5 a0k:3 disappears:1 simplicity:1 well:12 posedness:6 physics:2 academic:1 hx1:45 without:2 solve:1 english:1 firstly:1 model:3 lin:2 arbitrarily:1 obtain:31 rest:3 equa:2 immediately:1 mahony:1 scattering:1 yet:1 previous:1 adv:1 adding:3 unique:5 generator:5 b17:9 point:10 except:1 lattice:1 priori:1 easy:1 theorem:8 diagonalization:1 guarantees:1 euler:1 generalized:4 real:6 around:2 showing:2 posed:6 possible:1 know:1 press:3 integer:1 accepted:1 loss:1 appearing:1 like:1 follows:6 performing:2 separately:2 korteweg:21 integrals:1 arbitrary:2 become:1 pointwise:1 reduced:1 terminology:1 mathematical:3 right:7 classical:1 some:7 a17:4 deduce:1 repeat:1 acad:1 b1:19 b2:28 respect:1 proper:1 a11:3 kdv:18 udec:1 provided:2 scale:1 cut:8 newark:1 critical:1 steps:1 l3:3 l0:2 power:1 oes:2 journal:2 l1:12 bk:15 step:2 casilla:2 accompanied:1 bx:1 properties:2 stokes:1 about:1 commutator:1 prove:5 o:16 important:1 ll:23 bounded:1 slightly:1 therein:1 soc:2 ingenier:1 into:2 obtaining:1 functional:3 suppl:1 linearization:1 because:1 references:2 strauss:1 operator:11 additional:1 conicyt:1 support:2 there:12 question:1 u0:29 ponce:7 u2:10 start:1 conservation:3 way:10 was:4 osaka:1 function:9 hx:3 complete:1 form:2 phenomena:1 but:1 bǫ:1 volume:1 gain:3 delta:3 line:2 a5:2 commun:1 applying:5 ux:7 whether:2 ut:3 uv:1 smooth:5 up:5 us:4 um:1 ulveda:15 uk:98 sum:1 continuously:1 problem:7 similar:11 u00:1 strongly:1 bourgain:2 taylor:1 proved:2 choosing:4 35q53:1 certain:3 abstract:1 describe:2 am:4 ao:1 general:1 globally:3 ap:1 conserved:1 exist:4 rule:1 ing:1 distributions:2 a1k:2 again:1 functions:4 analyticity:11 no:1 commutes:1 b16:10 field:2 other:3 role:1 spatial:1 mathematics:3 nica:1 b18:8 conclusion:1 a15:6 a14:7 briefly:1 a16:10 denote:1 a10:3 models:1 why:1 problems:1 a18:6 a1:10 a0:12 a3:16 a2:8 a9:5 massachusetts:1 a7:9 studied:1 variable:6 a8:7 grimshaw:2 structure:2 implies:1 coupling:1 using:22 assume:3 cauchy:3 dτ:2 pseudo:2 xbs:110 mass:1 time:10 appl:4 original:2 |
0704.1862.txt |@word secondly:1 sci:1 consider:7 remarkable:1 funct:2 eaires:1 global:7 results:5 extensively:1 leads:4 mild:1 limites:1 kato:4 consists:1 follow:1 displaying:1 localized:1 compact:1 u3:36 depend:2 indices:1 ginibre:2 paris:1 tt:1 technique:3 young:1 γu:14 ıa:1 uniqueness:6 tm:1 c5:1 th:1 under:1 aux:1 through:1 ıo:2 ingredient:1 straightforward:5 very:1 wave:1 vera:8 corollary:2 microlocal:1 condition:4 presented:1 suffices:2 henri:1 solution:43 t0:37 large:2 solved:4 differential:2 small:2 anal:2 solutions:22 velo:2 l2b:2 slower:1 estimates:15 pulse:2 approximation:5 second:5 constantin:1 concludes:2 estimated:1 even:1 established:1 nonlinear:26 mt:15 alr:1 section:12 contributed:1 analogously:1 uniform:1 below:2 sur:1 above:6 sup:6 new:1 d1:6 method:2 u2α:4 coefficient:5 completion:1 mauricio:2 implying:1 respectively:2 calculates:1 here:4 desired:2 possibility:1 others:2 xα:1 equations:29 appears:3 change:1 obtained:3 remark:9 sobolev:11 difficulty:1 c2n:2 study:4 studied:2 sbornik:1 experience:1 guide:1 amount:4 makes:1 involves:2 via:1 l1loc:2 classification:1 bounds:2 apr:1 γv:1 apply:2 des:1 establish:1 linearly:1 derivatives:8 use:6 asymptotic:1 would:1 prove:14 remains:1 positive:8 contains:1 negative:2 strauss:3 next:2 few:2 therefore:5 indiana:1 type:13 more:2 israel:1 formally:2 becomes:1 inclined:1 odinger:16 basically:1 particular:5 known:2 cases:1 must:2 evolves:1 valued:3 rα:22 integrating:18 equation:70 work:1 modified:1 pour:1 temam:3 cai:2 vega:2 del:1 norm:11 following:6 vt:12 example:1 proof:17 claim:6 eqns:2 indicated:1 give:1 organized:1 states:1 numbers:2 rescaling:1 guarantee:1 boussinesq:1 provide:1 holds:1 kenig:2 write:1 far:1 turk:1 parameter:1 oscillatory:1 map:1 product:3 replacing:3 max:2 long:2 ball:2 consequence:1 tmax:2 inst:1 nirenberg:2 waves:1 improving:1 choice:1 data:16 grow:1 constants:2 2l2:3 induction:6 third:2 linares:1 so:4 fundamental:1 decreasing:1 sb:1 subsequently:1 octavio:1 order:12 ec:2 least:1 help:2 indeed:5 over:13 ordre:1 choose:2 years:1 course:1 paper:4 including:1 existence:16 satisfies:2 still:1 ieee:1 its:5 hloc:7 sciences:1 derive:2 group:1 decay:5 chosen:4 lj:1 d33:1 complex:5 systems:1 lp:2 lq:1 derivative:3 main:15 variables:2 maximal:1 them:1 motivated:1 integral:2 mention:1 cutting:1 uν1:15 they:3 half:1 now:8 outlines:1 dielectric:1 mystery:1 term:20 fully:2 times:4 sufficiently:3 inequality:13 l2:40 each:18 2l:7 found:1 2n:6 polynomially:2 2h:2 2i:1 kappeler:3 weighted:6 ei:2 weight:17 vdx:8 series:2 energy:2 idea:3 related:2 decays:3 obtains:1 ec1:1 concepci:3 our:5 nonlinearities:1 special:2 standard:7 try:1 shown:1 space:10 furthermore:1 since:8 crucial:1 may:1 adv:1 u2x:1 math:11 shows:4 benjamin:1 fiber:3 linear:8 state:1 departamento:2 mapping:2 atica:2 reason:1 necessarily:1 intermediate:1 estimate:28 e1:2 e3:1 e2:1 definition:3 ponce:3 r1:1 r2:1 phrases:1 could:1 similarly:3 nonnegative:1 int:1 place:2 universidad:2 hence:22 quadratically:1 adjoint:1 first:9 there:23 ono:1 omitted:2 possessing:3 number:1 approximate:3 set:1 specifically:3 impossible:1 u2:67 xt:1 dispersive:15 given:12 kodama:3 their:3 introduction:1 top:1 construct:2 indicate:1 assumption:5 calculations:4 airy:2 scheme:1 ıficas:1 inner:2 relationship:2 tool:1 continuous:5 studies:2 part:4 riesz:1 x2:1 believe:1 holder:1 than:3 coefficients:6 showed:3 require:1 iteration:4 see:5 subsequence:4 contrary:2 were:1 treated:5 motivation:1 outstanding:1 craig:8 cohen:1 quelques:1 matem:2 already:3 conjugate:7 need:2 any:8 solitons:1 gagliardo:2 depending:8 lin:2 ideas:1 instance:3 goodman:3 take:5 techniques:1 udx:5 persistence:4 calculus:1 bilinear:1 begin:1 shall:4 object:1 most:3 significant:1 representation:1 multiply:2 iterate:1 class:2 linearized:2 considered:1 calculated:6 possesses:1 optical:2 occasion:1 vries:11 sum:3 fact:2 laws:1 nls:1 show:3 leibniz:1 converge:1 norms:7 gauge:3 hasegawa:2 keywords:1 substituting:1 uβ:1 d2:16 d3:7 fifth:1 subtracting:7 q1:3 q3:2 q2:3 based:2 enough:3 zα:15 aubin:1 lemma:17 only:14 vxxx:1 factor:2 integrate:2 local:15 preliminaries:1 hope:1 nj:3 do:2 his:1 notation:3 get:1 de:18 aim:1 cannot:1 dx:525 dy:2 lineaire:1 wσ:31 dt:19 du:2 ds:18 differentiating:5 eme:1 evolution:3 increasing:1 bona:2 saut:5 approach:2 arxiv:1 expansions:1 contain:1 nondecreasing:1 fixed:1 approximations:1 satisfy:1 multiplying:5 exists:16 sep:1 physically:1 maximum:1 observed:1 namely:1 result:8 w0:30 ebx:1 subject:1 elect:1 satisfying:2 degree:1 ways:1 subsequent:1 nature:1 uα:281 supj:2 deducing:1 written:1 un:5 various:2 between:1 mathematical:1 conditions:5 blow:1 terms:21 kawahara:1 extend:1 complementary:1 ju:1 weak:2 however:2 jl:1 vanishing:1 concentrate:1 hypothesis:3 rapidly:1 valid:2 both:2 c20:1 last:4 limits:1 always:1 powers:2 region:2 infinitely:1 according:4 propagation:3 poincar:2 embedding:2 passing:1 expression:2 arbitrarily:1 cj:1 carvajal:2 abbreviate:1 cl:2 d32:2 simply:1 constant:10 throughout:1 cw:1 considers:1 considering:4 strong:4 arbitrary:4 due:2 been:3 35q53:1 cient:1 belongs:3 damping:1 basic:3 ann:1 define:4 arises:1 corresponding:2 eθ:28 commutes:1 quantities:1 sufficient:4 bicontinuous:1 argument:2 hayashi:6 generalizing:1 chile:2 c3:6 c2:6 c1:3 denote:4 those:1 c4:2 case:5 p1:1 look:2 exponential:4 estimations:2 le:1 value:7 choices:1 will:11 while:3 suppose:1 compactness:1 behavior:2 error:1 property:8 taking:1 procedure:3 coupled:1 vol:8 characteristics:1 vj:17 thus:10 non:5 uxx:10 encountered:1 regularity:28 itself:1 im:87 contradiction:2 vx:2 c0:26 uxxx:13 different:2 develop:2 generic:1 same:7 tells:1 parts:10 quant:1 largest:1 proved:9 finite:3 higher:9 independent:4 used:4 infinity:5 imply:1 optic:1 effect:4 hand:6 v1:10 v2:18 v3:11 v4:4 v5:9 infinite:3 frequently:1 pures:1 lower:1 weakly:8 schr:16 whole:1 well:5 posedness:4 analysis:3 burgers:2 without:1 solve:1 firstly:1 model:2 dimension:4 usual:1 proposed:1 obtain:25 completed:1 ozawa:1 integer:6 stabilization:1 cn:18 letting:2 adding:1 tn:21 point:2 seems:1 except:1 setting:2 theorem:28 guarantees:1 transformation:3 generalized:6 real:5 2t:1 depends:11 replaced:1 showing:1 iβ:11 possible:2 vα:109 know:1 vη:14 using:21 unique:10 moreover:2 vξ:5 formal:1 imposed:1 like:3 semi:1 follows:12 signal:1 performing:3 separately:5 korteweg:11 integrals:1 lose:1 works:1 continuation:1 reduced:1 terminology:1 therein:1 because:4 often:1 sequence:3 some:8 stat:1 growth:1 acad:1 choosing:2 respect:2 kdv:13 udec:1 provided:2 diff:6 dimensions:1 lead:3 univ:1 though:1 integration:1 does:3 assuming:3 steps:1 minimal:3 power:2 uniformly:4 equivalent:3 2c:2 step:3 casilla:2 2m:1 approximating:4 properties:5 guaranteed:1 uxxxx:3 integers:2 une:1 eaire:1 theorems:1 discussed:2 o:8 side:4 monomode:2 extensions:1 2j:3 consequently:2 other:13 duke:2 ingenier:1 letter:1 into:1 obtaining:1 bound:2 suppl:1 variable:3 appropriate:1 right:4 references:2 eσ:1 operator:3 probleme:1 additional:1 u5:10 assumed:1 initial:28 u1:55 u0:67 fast:1 smoothing:10 dispersion:1 start:1 conservation:2 lions:2 appeal:1 way:13 was:7 function:13 gronwall:4 complete:1 form:9 2iβ:4 but:5 staffilani:2 gain:19 line:4 removed:2 true:3 applying:8 ux:33 ut:23 smooth:8 up:3 us:3 um:18 mth:1 ulveda:1 limit:1 uk:16 uj:3 problem:14 similar:13 called:1 strongly:5 interval:9 associated:2 defined:8 certain:4 abstract:1 u4:9 general:4 ap:1 proves:1 exist:1 rule:1 vn:3 journal:4 tα:3 check:1 esolution:1 high:1 functions:12 differentiable:1 eq:1 when:1 vanishes:1 multipliers:1 priori:12 spatial:5 mathematics:1 bc0:6 conclusion:1 conclude:2 cauchy:3 briefly:1 repeat:1 completes:1 extra:2 time:13 ξt:2 probl:1 important:1 bounded:24 included:2 ξb:4 faster:2 tsutsumi:2 assume:5 quantifying:1 d22:6 together:3 original:1 4n:1 remarked:1 appl:2 starting:2 having:1 semilinear:1 |
0704.1863.txt |@word limited:2 monte:1 quarks:3 sch:1 represent:3 squared:1 magnetic:2 dynamic:1 results:20 kernphysik:2 existing:1 founded:1 mp2:1 garching:1 broader:1 consists:2 bars:5 whose:1 fitted:5 depend:1 corrections:4 quasi:7 filled:1 those:3 under:2 analogous:1 include:1 indicating:2 case:3 supported:8 amplitudes:4 presently:1 downstream:1 very:3 activated:1 continues:1 keeping:1 unchen:2 bjorken:1 electron:3 every:1 orientations:2 upstream:2 resonant:3 exact:1 fakult:1 condition:1 generalised:2 four:2 school:1 kinematic:1 incoherent:13 presented:6 smc:5 list:1 applicable:1 leptoproduction:4 selections:2 leave:1 differs:1 vector:12 small:26 outer:1 settings:1 noted:1 upper:1 smaller:2 tel:2 consistent:9 estimates:3 measurable:1 approximation:2 zero:11 value:3 further:3 estimated:5 carlo:1 targets:3 subscripts:1 errors:18 plays:1 stands:1 apparatus:1 diffractive:4 section:9 selected:3 mw:3 cell:4 experiment:9 sur:1 selecting:1 c29:2 originate:1 consisting:1 contrast:2 full:1 ibid:2 exchange:10 respectively:2 unobserved:1 component:1 here:4 behaviour:1 reported:3 asymmetry:41 slow:1 aρ1:53 aρ2:5 directions:4 ratio:7 along:1 mnii:1 table:2 logarithmic:1 obtained:11 incoming:2 noticeable:1 clarify:1 cern:8 inspired:2 studied:3 allows:4 b513:1 c18:1 amount:3 resulting:1 suggestion:1 resonance:2 shaded:1 studies:2 cancellation:1 missing:2 plotted:1 composed:1 diameter:1 yamada:1 absorbers:2 gluons:3 straw:1 explained:1 collaborating:1 modifying:1 first:6 visible:1 gluon:1 protvino:1 quarkantiquark:1 meson:11 during:1 select:4 arneodo:1 plot:1 use:2 fluctuation:1 indicated:1 would:2 d75:1 remains:1 positive:1 relates:2 contains:2 nagoya:2 france:1 alessandria:1 calculation:4 nucl:7 kinematics:3 dnp:2 qcd:2 aperture:1 turin:3 more:3 separated:1 israel:2 initiated:1 h1:2 becomes:1 b463:1 validity:1 discussed:2 particular:1 calorimetric:1 given:6 behalf:1 sample:25 account:2 comes:1 mc:4 erratum:2 shielded:1 science:2 equation:1 spill:1 protons:2 d56:1 remain:1 assumptions:1 values:18 mp:1 following:3 mx:1 vary:2 proof:2 define:1 references:1 figure:6 process:7 accepts:1 arise:2 india:1 effort:1 high:7 indicates:3 identified:2 grasso:1 performed:3 magnitudes:1 sharp:1 spb:1 times:2 calculated:4 federation:1 information:5 unmeasurable:1 end:1 varied:1 rather:1 antiparallel:2 divided:1 pythia:5 technicians:1 fraas:2 trieste:4 varies:2 instrum:1 fit:4 opposite:2 instead:1 field:2 axis:1 parameter:4 dominance:2 dwm:1 product:1 kroll:3 description:4 may:6 overall:1 photoproduction:7 after:5 reflect:1 depolarisation:3 consequence:2 tdep:1 designed:1 physik:3 faculty:1 spectrometer:4 effects:8 acceptances:5 data:22 grow:1 aα:1 flux:2 organization:1 natural:3 liquid:1 beam:18 light:1 gratefully:1 author:1 june:1 lost:1 their:3 fraction:4 so:3 enters:1 taking:1 kaons:1 adams:3 order:10 bins:5 typical:1 exclusive:32 interpretation:2 aforementioned:1 nucleon:22 numbers:2 indeed:1 over:1 exchanges:4 mx2:1 undetected:1 installed:1 produced:4 paper:3 including:4 wolf:1 emiss:15 reconstruct:1 japan:2 still:1 its:5 before:2 effect:3 lepton:4 accepted:1 le:1 longitudinal:8 decay:1 energies:3 interesting:1 presence:1 li:1 aviv:2 absence:1 production:24 fig:10 gpds:4 bin:5 covered:1 weeks:1 main:1 work:1 no:6 eur:6 magnet:3 non:11 within:6 cea:1 material:2 cover:6 number:11 significant:4 they:7 front:1 fluxes:4 configurations:3 inelastic:11 yu:10 overlap:1 represents:1 term:2 several:3 university:17 covering:1 arrows:2 2y:1 oppositely:1 bielefeld:3 bonn:4 each:14 found:6 universit:11 higher:2 referred:2 different:5 domain:4 determine:1 weight:2 bump:1 energy:11 revised:1 related:6 f0:1 strips:1 ex:1 fist:1 bands:2 laboratory:2 meth:1 eq:4 ep:1 special:1 out:3 large:12 shown:7 dominates:1 funding:1 matrix:2 factors:1 unnatural:6 dst:1 miyazaki:2 interference:5 semi:2 research:4 particles:3 similarly:1 investigation:1 asymmetries:11 hint:1 rc:3 formula:3 ref:9 foundation:3 linear:1 interactions:2 b429:1 million:1 diagonal:1 free:2 quark:1 cut:5 hep:5 estimate:5 dubna:2 hermes:17 generate:1 pairs:2 language:1 ministry:1 could:1 finland:2 βx:1 sm2:2 sm1:2 ist:1 silicon:1 gpd:2 technische:1 produce:1 virtuality:1 freiburg:2 neglected:2 hadrons:7 neglect:1 first:1 origin:1 relate:2 variables:2 primary:1 clear:1 antiquark:1 nonperturbative:1 another:2 2a1:1 angular:4 spread:1 little:2 management:1 temperature:1 forschung:1 aichi:1 introduction:3 leading:2 top:6 system:3 approximately:3 parallel:2 indicate:3 station:1 listed:3 difference:2 unpublished:1 relations:1 gives:1 ictp:1 originating:2 shell:2 way:1 geneva:1 academy:1 moscow:2 zeus:1 contribute:1 transverse:6 hut:1 multiwire:1 parameterisation:4 electroproduction:1 than:4 blind:1 wide:6 target:46 pt:4 double:7 helsinki:4 rate:1 submitted:1 recording:1 systematical:1 future:1 reggeons:3 amplitude:3 were:14 bauer:1 collins:1 treated:1 russia:3 perturbative:3 mini:1 parameterised:2 false:4 takes:2 hodoscopes:1 unchanged:1 locations:1 correspond:2 width:1 chambers:4 final:3 orders:4 warsaw:5 lid:4 issue:1 angle:4 para:1 check:1 latter:1 c74:1 predominantly:1 note:1 sciences:1 internal:2 lip:1 negligible:1 detector:1 reversed:1 channel:4 accuracy:2 circles:1 even:2 identification:1 fct:1 scintillator:2 test:2 centre:1 track:3 collaboration:3 object:1 molecule:1 most:7 breitweg:1 involving:1 but:3 mππ:6 preliminary:2 pair:1 acknowledgements:1 measured:13 brno:1 appear:1 diffractive:2 deviations:3 fiz:1 observation:1 considered:1 average:5 diffraction:1 detectors:3 points:2 sources:2 exp:1 factorisation:2 quadratic:2 left:8 physics:8 technical:2 2m2:2 mainz:2 selection:1 lebedev:1 e665:6 show:2 german:1 text:3 detection:1 charles:1 scattered:8 infrared:1 rotating:1 σstat:2 threshold:1 kbn:2 exclusivity:1 agrees:1 help:1 partonic:2 q2:76 based:1 parameters:1 microwave:1 bildung:1 b113:1 outside:1 should:1 only:3 generators:1 rich:2 factor:13 five:1 helmholtz:1 searched:1 e143:1 exchanged:1 2mp:1 mixture:1 dominant:6 gev:49 ivanov:2 dependent:8 syst:1 de:2 spub:2 pions:2 joint:1 cannot:1 dz:1 negative:1 reversal:3 compass:27 soltan:1 represented:1 yad:1 runs:1 increasing:1 traverses:1 b647:2 strahlen:1 arxiv:1 factorization:1 summary:1 sum:4 experiments:4 ecnica:1 recoiling:1 switzerland:1 through:1 inside:1 thanks:1 deuteron:11 requirement:2 set:2 statistical:13 reference:1 σa:2 prague:3 cuts:10 gvmd:1 observed:3 culture:1 intensity:2 result:3 lisbon:2 lisboa:1 recently:1 institutes:1 frequency:1 skill:1 standard:4 flavour:1 detect:1 setting:1 parent:2 position:1 purpose:1 nuclear:6 positivity:2 complementary:1 dipole:2 tend:1 d58:2 state:2 smallest:1 various:7 finger:1 staff:1 regge:2 invariant:2 approach:3 d55:1 mainly:2 available:2 sections:8 comparable:3 dalla:1 terms:5 iron:1 relative:1 biswas:1 figure:3 weak:1 however:4 wi:1 agencies:1 prediction:6 p2t:17 maximilians:1 hypothesis:1 jr:1 bundesministerium:1 multiplier:1 rapidly:1 jetp:1 come:4 remaining:1 improve:1 both:12 fnu:2 panels:1 installation:1 σl:6 region:7 uncertainty:9 hours:2 equal:5 agree:1 regions:1 april:1 mev:1 und:2 contribution:11 σp:3 whole:7 photons:7 experimental:7 σt:4 strongly:2 necessary:1 cm:3 ca:1 contamination:1 cf:3 proton:8 sampling:1 na:2 grants:3 applicability:2 cancel:3 cr:1 trust:1 pqcd:2 broadening:1 xα:1 described:3 second:6 basis:1 addition:6 acceptance:4 radiative:2 due:14 been:5 detected:2 extraction:1 increase:1 describes:1 deposited:2 skewing:1 minimise:1 expected:5 muons:5 ph:7 originates:1 lett:7 direction:3 arises:1 corresponding:5 reaction:20 quantities:1 longitudinally:6 photon:10 precision:1 anthony:1 coherent:4 observe:1 determination:1 external:1 systematic:16 stems:1 c2:4 c1:3 denote:2 spin:28 present:11 applied:5 extracted:1 heavier:1 processes:2 ryskin:3 triggers:2 evaluated:2 excited:1 will:3 institute:8 while:4 bochum:2 theoretical:1 error:15 couplings:1 procedure:1 resolved:2 larger:5 orientation:2 portugal:1 almost:2 von:2 simulations:1 thus:3 frankfurt:1 off:4 ii:1 limit:2 mod:1 σd:2 technology:3 desy:1 orbital:1 italy:4 grant:2 thesis:2 radiation:1 cross:17 same:8 aφ1:1 pomeron:4 reconstructed:2 parts:1 largest:1 φi:2 dapnia:1 ludwig:1 events:29 european:1 independent:1 used:15 see:4 assignment:1 collab:18 hand:1 running:1 uses:1 scale:2 changing:1 exponential:1 passing:1 finite:1 cycle:1 centred:1 lower:1 tracking:3 schr:1 center:1 airapetian:3 largely:1 acknowledge:1 polarisation:8 well:5 analysis:11 without:1 intervals:1 edge:1 schc:3 components:3 sets:2 calcutta:1 model:6 fulfilling:1 arising:1 fermilab:1 charged:5 goloskokov:3 muon:15 adeva:2 proposed:2 nd:5 removed:1 obtain:2 valuable:1 assigned:1 eµ:2 via:1 atomic:2 world:1 momenta:1 scattering:12 strikman:1 tables:3 emerging:1 now:1 preprint:2 dissociation:2 density:2 trigger:4 regarded:1 except:4 signals:1 source:2 other:4 extends:2 inner:1 samples:5 c13:1 role:4 east:1 heidelberg:2 momentum:10 collected:1 real:3 photo:1 around:1 depends:1 checking:1 evaluate:1 possible:8 munich:1 early:1 experimentalphysik:1 increases:2 helicity:6 background:17 govt:1 using:7 abe:1 coincidence:1 occurring:1 c12:1 imposed:1 like:3 particle:2 signal:1 separately:1 indication:1 either:2 modified:1 martin:2 become:2 dilution:5 nucleons:4 e155:1 reasonably:2 spins:1 grouping:1 portuguese:1 shed:1 because:6 qed:1 czech:6 mostly:1 q20:2 understood:1 towards:4 scatters:1 affects:2 respect:2 multiple:1 extended:4 neglecting:1 uncertainties:3 exists:2 nonzero:2 provided:2 total:10 excitation:2 lead:2 bottom:5 electromagnetic:1 highest:6 measurements:8 recorded:1 exceeding:1 per:2 mesons:7 e78:1 decomposition:1 eliminate:1 assuming:1 allowing:1 proc:2 displayed:1 lowest:1 calorimeters:3 vertex:2 standalone:1 tubes:2 nmc:4 although:5 accompanied:1 yamagata:2 therefore:4 between:5 hadron:4 panel:5 constrains:1 about:16 kinematical:17 carried:1 extension:2 stations:1 ranges:1 dependence:9 o:8 simulation:2 compatible:4 range:25 a2:1 fibres:2 obeys:1 c42:1 mean:1 d60:1 match:1 tecnologia:1 rev:9 differences:1 parity:8 instruments:1 into:8 formulae:1 bound:1 three:4 down:1 included:4 appropriate:1 sphn:1 rising:1 parton:1 balanced:1 proportional:2 mrad:1 sports:1 d62:1 pb:5 statistics:1 institut:7 additional:3 area:2 normalised:2 support:3 there:3 approximate:1 long:1 dispersion:2 gif:1 conservation:1 low:5 scintillating:2 jinr:1 forward:1 anosov:1 was:29 naturally:1 function:9 hard:1 gaseous:1 complete:1 urnberg:1 funds:1 m2:2 jul:1 erlangen:2 taken:7 magnitude:4 recoil:2 schilling:1 atom:1 russian:1 line:2 funda:1 hg:3 he:2 extend:2 infn:3 made:3 applying:1 pion:2 cells:7 up:2 devices:1 ur:6 covers:1 placed:2 below:1 decays:2 physikalisches:4 planes:1 distribution:6 stages:1 similar:3 called:1 polarised:22 yvette:1 detailed:1 fractions:1 b61:1 interval:1 associated:1 magnets:1 inclusive:11 ai:2 certain:1 abstract:1 escape:1 reggeon:2 deep:6 general:2 twist:3 right:8 our:4 education:3 distributions:9 universidade:1 triangles:1 physical:1 vertical:3 ni:4 compared:6 us:1 humanities:1 amounts:1 transversely:1 when:2 defined:2 virtual:12 event:11 teubner:1 valid:1 republic:1 details:2 financial:1 suppress:1 department:4 mathematics:1 nr:3 nu:1 polarisations:2 picture:1 stat:1 elements:2 suppl:2 tracks:2 models:1 gas:1 kt:3 drift:3 lepto:3 a1:14 a0:3 generated:5 important:1 nucleus:3 peak:9 additionally:1 mediated:1 variable:3 astronomy:1 b79:1 structure:4 nikolaev:1 deuterons:6 correlated:1 ciˆencia:1 isoscalar:1 pocti:2 typically:1 required:1 curve:5 saclay:1 together:2 utilised:1 scientific:1 mass:12 time:8 nuclei:4 resolution:2 avoid:2 resonances:1 |
0704.1864.txt |@word limited:3 unavoidable:1 induces:1 desirable:1 schoenfeld:1 knbo3:1 quadrature:17 overlap:2 computation:1 consists:2 involved:1 contributions:3 centers:1 localized:1 admixed:3 content:1 simon:1 terms:1 calculate:1 knill:1 concerned:1 deterministic:4 aichele:1 containing:1 finally:2 foster:2 squeezing:1 present:3 stable:1 specht:1 dramatically:1 schori:1 zhang:2 very:8 frequencies:3 results:4 eq:1 resonant:3 laser:3 difference:1 condition:1 illustrated:2 slip:1 level:6 transmission:4 cause:1 avalanche:2 large:3 boozer:1 detected:2 variances:4 small:2 enhance:1 unconditioned:1 michler:1 optics:4 noted:1 related:1 compensated:1 oscillation:3 insignificant:1 miller:1 consistent:2 estimates:1 boca:1 feasibility:1 superimposed:1 nbi:1 enhancement:1 pass:3 chen:2 further:1 copenhagen:1 implemented:1 odd:1 click:2 quite:1 linear:2 spectral:9 will:6 what:2 nonlinear:4 essence:1 completely:3 giving:2 beattie:1 exactly:1 mw:3 find:1 current:2 homodyning:2 experiment:2 reconstruction:5 new:1 tualle:1 addi:1 revealing:1 processing:3 simultaneously:1 whose:1 respectively:2 error:2 lange:2 teleportation:1 julsgaard:2 atoms:2 them:2 separation:1 address:2 path:1 olsson:1 sherson:2 observing:1 implicit:1 supplying:1 benson:1 obtained:2 buck:1 arrive:1 institute:2 shift:1 leaves:1 losses:4 funded:1 typically:1 bow:1 amount:3 simply:1 procedure:1 admixture:4 usually:3 resonance:2 narrow:5 studies:1 fulfill:1 appropriately:1 via:3 spatially:1 although:1 figure:4 ions:1 lounis:1 qˆ:2 marked:1 highly:2 modulated:1 decrease:1 zavatta:1 counts:1 total:8 kobayashi:1 use:1 reflected:1 russell:1 waveguides:1 commun:1 distinct:1 beginning:1 poizat:1 negative:3 periodically:1 stored:1 few:2 depicted:2 estimated:2 memory:5 taken:2 heralded:5 doubling:1 hammerer:1 type:3 until:1 reflects:1 more:5 separated:3 diamond:2 bellini:1 initiated:1 schematic:1 becomes:1 silberhorn:1 ti:1 corrected:1 emission:1 curvature:1 lies:1 plant:1 attained:1 uncertain:1 discrepancy:2 particular:1 effort:1 must:6 franson:1 account:3 include:1 locked:1 room:1 quantized:1 tokyo:3 mm:4 science:5 setup:8 work:2 oscillator:8 tc:18 zhao:1 fock:4 values:4 emitters:2 ms:1 those:2 webster:1 pthr:2 hansen:1 spontaneous:2 example:2 performed:3 claim:1 ready:1 wang:1 links:1 do:3 process:3 implementations:1 states:7 effectively:1 lorentz:1 purity:12 degenerate:7 counting:5 simple:2 schmiedmayer:1 information:5 browaeys:1 rather:2 oslo:2 oscilloscope:1 enl:1 hamamatsu:1 arrangement:1 far:7 pure:3 instead:2 ordinary:1 parameter:5 lam:1 lan:1 fs:3 huge:1 db:2 aom:2 signature:1 derived:1 different:3 collection:5 diagram:1 applications:2 produce:2 wave:2 data:6 compatibility:1 efficiently:1 gaussian:1 purely:2 effective:2 concern:1 light:8 approximation:1 counter:2 ghz:1 bunkyo:1 lengths:1 precise:2 maintain:1 so:7 allow:1 correlation:12 turnstile:1 subsequently:1 operate:2 order:2 turns:1 pulsed:4 wigner:6 numbers:2 indeed:1 over:1 displayed:1 balanced:1 cross:3 produced:2 mixing:2 thermal:15 experiments:1 pulses:2 filters:4 mentioned:2 japan:2 fidelity:2 suffer:1 fwhm:2 its:1 blocked:1 jacobs:1 monitor:1 fit:2 how:2 sergienko:1 lo:7 temporal:6 tie:1 narrowest:2 permanent:2 systems:3 orange:1 main:3 norway:1 into:5 bunching:1 outside:3 pittman:1 non:6 within:5 biphotons:1 combination:3 splitter:3 mølmer:3 evolution:1 diodes:2 matsukevich:1 band:2 wise:1 they:4 half:2 ritchie:1 now:2 above:3 easily:2 finite:1 modulator:1 ribordy:1 brightness:8 off:2 university:3 presented:4 sideband:2 imamoglu:1 kurtsiefer:1 wong:1 trap:1 fields:4 done:4 repeating:1 polzik:5 traces:8 characterized:2 mean:2 individually:1 domain:1 storage:1 detect:1 nanometers:1 generation:16 series:3 fitting:1 vuletic:1 fidelities:1 society:1 frequency:25 see:3 measurement:14 quantum:31 wavelength:1 extract:1 event:3 special:1 out:2 shown:1 schiller:1 space:1 furthermore:2 since:4 rev:21 research:2 increase:2 ren:1 mattle:1 get:2 100s:1 correct:1 red:3 shows:2 foundation:1 blindern:1 fiber:2 theory:1 interactions:1 pumping:1 free:2 standard:1 approaches:2 included:1 brightest:1 besides:1 aˆt:12 estimate:1 likelihood:3 milburn:1 aˆs:6 pairs:4 interaction:2 entirely:1 hwhm:1 geometry:1 dip:2 could:1 iterative:1 times:3 filter:13 length:1 period:1 including:1 unknown:1 hence:4 discussions:1 epr:1 top:1 first:3 major:1 there:5 probability:2 becher:1 number:11 instances:1 kuzmich:2 inhibits:1 fast:1 another:2 electronic:4 size:1 given:2 grangier:3 rempe:1 temperature:1 likely:1 efforts:1 introduction:1 leading:1 antibunching:2 system:1 relations:1 needed:1 compromise:1 too:3 realization:1 normalization:1 scheme:4 low:13 shifted:1 danish:1 testing:1 instance:1 moerner:1 centered:1 difficult:1 explanation:1 continuous:7 optical:9 somewhat:1 schr:1 than:6 ocis:1 modes:14 wide:1 kind:2 double:1 require:1 rate:10 tunable:2 rarity:1 preparation:1 matter:1 solomon:1 determined:1 modulators:1 were:1 identical:2 matched:1 gives:1 lowest:1 fig:12 false:2 well:4 spectrum:2 curves:3 already:3 seed:1 keller:1 need:1 seen:1 weinfurter:2 demonstration:1 clearly:3 contents:1 conversion:11 strength:1 built:1 zero:2 efficient:3 latter:2 trapped:2 polarization:3 extracted:1 high:18 internal:1 build:1 online:4 finding:1 detector:6 mayer:1 gains:2 even:3 play:1 towards:4 electric:1 mlynek:1 shaped:2 molecule:1 most:2 poled:1 but:14 significant:1 device:1 america:1 measured:6 had:1 subtracted:1 nonlinearity:1 up:2 average:2 detectors:1 inferred:2 hayasaka:1 part:5 principle:1 ku:1 physics:2 assistance:1 dot:3 neergaard:2 kita:1 selection:1 shot:1 show:2 assert:1 diode:5 random:1 bring:1 bright:1 pump:14 threshold:4 rounded:1 networks:2 downconverted:1 based:6 ensembles:1 much:1 lvovsky:2 petroff:1 should:7 only:2 explicitly:1 corresponds:1 about:2 molecules:1 photo:4 thompson:1 employed:1 population:2 local:4 according:1 santori:1 lobo:1 dk:2 cryptography:2 means:3 dependent:1 beams:1 express:1 overall:2 truly:1 ourjoumtsev:1 beam:8 photoelectric:1 rest:1 invariant:1 during:1 symmetrically:1 shaping:1 takahashi:1 mckeever:1 processes:1 course:1 denmark:1 arxiv:1 shape:4 yield:1 method:2 reid:1 whether:1 investigate:1 paper:2 cf:1 shg:2 through:2 interference:1 generations:1 black:2 shapiro:1 kiraz:1 set:1 art:1 statistical:2 achieved:1 national:2 correlations:4 grosse:1 detection:14 intensity:2 individual:2 tomographic:4 enhanced:3 existence:2 versus:2 close:3 uncorrelated:4 arm:1 best:3 symul:1 recording:1 phases:3 still:1 enlightening:1 placed:2 nondegenerate:2 subsequent:1 away:3 ralph:1 increased:1 case:1 state:53 various:3 between:8 pairwise:1 before:1 shields:1 available:1 seeded:1 recently:2 nature:5 optimal:4 clean:1 weak:2 however:9 efficiency:28 vanishing:1 cut:1 here:2 demonstrate:2 come:1 problem:3 both:1 vuc:1 many:4 taking:1 uncertainty:2 parts:1 chosen:1 connection:1 improves:1 microcavity:1 contribution:6 estimation:1 expression:2 experimental:3 filtering:8 widen:1 afterwards:1 cm:2 point:1 color:6 overview:1 each:7 narrower:1 homodyne:15 coincidence:1 pelton:1 twin:1 cirac:2 anti:1 wider:2 points:2 second:3 quadratures:1 strong:3 transformations:1 cavities:8 aˆ:17 eiθ:1 due:6 been:15 pb:2 lu:1 detrimental:1 combined:1 goes:2 expected:7 ph:2 ppktp:2 empty:1 attractive:1 dots:2 histogram:1 tittel:1 sending:1 suppress:2 thousand:1 photon:74 depend:2 zeilinger:1 gts:6 observe:2 demand:1 former:1 protocols:1 applied:2 inhibit:1 klaus:1 acousto:2 nska:1 exponential:1 solid:1 might:2 brouri:2 value:7 aim:1 replaced:1 overcome:1 wilk:1 squeezed:2 property:2 noncritical:1 walther:1 opt:5 laflamme:1 almost:3 thus:5 downconversion:3 walmsley:1 conditioned:5 ii:1 coupler:1 good:1 cond:2 crystals:1 claimed:1 technology:1 currents:1 around:6 hong:1 qap:1 perform:1 dithering:1 make:1 indistinguishable:1 same:7 any:3 reconstructed:2 complex:1 quant:2 efficiencies:1 widely:1 filtered:2 several:6 pan:1 higher:4 independent:2 clear:1 used:6 optic:3 akira:1 blue:5 effect:6 driven:1 ion:1 compared:2 variance:13 entanglement:1 ideally:1 yuan:2 single:58 keep:2 lower:1 suitable:1 kept:1 center:2 acknowledge:1 floor:1 arrival:3 roughly:1 analysis:1 bohr:1 components:2 centres:1 tional:1 parametric:13 just:5 partly:1 when:1 observed:1 obtain:3 photonic:1 sources:5 bandwidth:20 relevant:1 atomic:5 hongo:1 yamamoto:1 alignment:1 ηs:2 opo:17 mirrors:1 generator:2 density:2 photons:24 smith:1 ideal:2 confirmed:1 signals:1 source:17 other:4 lett:13 samples:1 reason:1 input:1 disadvantage:1 remaining:1 bin:1 iθ:1 saturation:1 nielsen:6 loss:4 big:1 showing:1 digital:2 possible:1 harmonic:2 dark:1 possibly:1 entangled:3 background:1 vacuum:19 using:8 bit:1 poses:1 mod:1 semiclassical:1 scan:1 like:1 employs:1 kennedy:1 follows:1 stevenson:1 performing:1 niels:1 specific:1 communications:1 detections:1 grants:1 mhz:18 setups:1 output:8 works:1 orozco:1 signal:11 making:2 exceed:1 because:1 methods:1 classical:3 conditional:4 some:4 calculated:6 added:1 serves:2 escape:3 practical:1 herald:1 scale:1 cooper:1 lead:1 cavity:25 memories:2 avoid:1 measurements:5 recorded:4 integration:1 per:4 instantaneous:1 waveform:1 does:3 apd:10 anne:1 photocurrents:1 demonstrated:2 mode:32 measuring:2 pepper:1 noise:12 integrate:1 power:3 reach:3 equivalent:1 electrically:1 illustration:1 linewidths:1 reduces:1 beveratos:1 banaszek:1 plots:1 post:2 includes:1 properties:1 after:1 limitation:1 would:6 bars:1 basis:1 o:2 compatible:1 kwiat:1 range:2 nothing:1 mixed:2 insufficient:2 ou:2 peak:1 previously:2 image:1 photodetection:1 arms:1 down:13 phase:7 references:1 tiny:2 operator:3 fiur:1 theoretically:2 qed:1 wadsworth:1 statistics:2 additional:1 vac:1 loh:1 placing:1 long:2 plotted:1 trigger:22 mandel:1 way:1 was:7 function:27 medium:1 complete:1 three:1 jun:1 delayed:1 drummond:1 hu:1 suffers:1 gain:6 atom:3 attainable:1 role:1 production:4 made:3 applying:2 evident:1 bandwidths:1 inside:3 maximum:4 us:2 theoretical:2 crystal:6 below:6 converted:2 limit:2 kuhn:1 pumped:1 continuously:1 fluctuations:2 distribution:9 similar:4 emit:1 gisin:1 detailed:1 smeared:1 shih:1 heralding:2 ae:1 computing:1 defined:3 likewise:1 abstract:1 specified:2 meaningless:1 eu:1 kimble:2 our:4 tomography:4 controlled:3 four:1 physical:1 functions:5 codes:1 nm:4 sørensen:1 no:4 dashed:1 whereas:1 percent:2 matching:5 field:12 narrowband:1 highfrequency:1 dt:1 spatial:3 department:2 jenkins:1 ns:1 clicks:2 conclusion:2 superposition:1 separate:1 sided:1 become:1 odinger:1 commutator:1 generated:3 pumps:1 visibility:1 suppression:1 variable:1 matrix:2 jones:1 zbinden:1 correlated:3 regime:3 longer:1 fluorescence:1 corresponding:6 reiner:1 curve:1 together:1 furusawa:1 fsr:6 neighbouring:2 fitted:2 time:14 serious:1 original:1 basically:1 |
0704.1865.txt |@word partial:3 particular:1 results:4 four:1 sci:2 chair:1 whose:1 calculate:1 finally:2 th:1 under:5 norm:3 song:1 trigonometric:6 corollary:7 every:1 condition:26 presented:1 large:3 approximation:7 zero:1 nbn:1 even:4 plays:1 appear:2 rate:1 sum:4 uniform:1 above:1 sup:4 satisfy:1 degree:1 vall:1 here:1 china:2 zygmund:1 eikx:4 b2g:2 studia:1 implicit:2 generalizing:2 institute:1 fourier:14 classification:1 apr:1 replace:2 limn:2 establish:1 use:2 prove:4 positive:4 ψn:11 therefore:3 more:1 scotia:2 weakening:1 berlin:1 correspondingly:1 varying:1 known:2 hold:2 springer:1 valued:17 science:2 mv:25 values:1 following:4 example:2 proof:10 continuity:1 give:3 process:1 indicates:1 numbers:2 sense:2 weaken:2 holds:5 ping:3 write:2 acta:1 absolute:1 sin:8 may:2 max:12 derived:1 applications:1 constants:1 third:1 lemmas:1 grant:2 st:4 sk:1 so:1 ultimate:2 decreasing:4 zhejiang:2 order:3 approx:1 paper:4 satisfies:1 its:7 tending:1 derive:1 monotonicity:3 main:3 easier:1 propose:1 dan:1 they:2 now:3 yu:5 discuss:1 james:1 university:6 orthonormal:1 sufficiently:3 inequality:2 l1:16 found:3 2n:8 side:1 mean:4 en:9 ek:12 ee:1 series:16 ergebnisse:1 combining:2 our:2 special:2 canada:4 jackson:1 space:4 since:4 research:2 ref:1 math:5 theory:2 monotone:5 ψ2n:2 monographs:1 definition:5 nonnegative:4 hence:2 generalizations:1 first:1 number:3 done:1 occurrences:1 directly:1 l2π:16 given:3 xie:2 introduction:2 system:1 relations:1 indicate:1 1n:1 part:3 completes:2 coefficients:5 see:12 fˆ:74 gives:1 argument:2 generalization:6 say:1 conjugate:1 any:2 generalizes:1 depending:1 lim:29 able:1 converges:1 note:1 take:1 sufficiency:1 modulus:1 sn:28 most:1 pair:1 class:2 professor:1 later:1 tech:1 xavier:4 kx:3 section:5 fact:2 supported:3 spaces:3 keywords:1 lemma:13 only:12 equipped:1 integrable:1 regularly:1 his:1 dk:5 get:2 dx:5 arxiv:2 hangzhou:2 view:1 coefficient:1 depends:2 computer:2 result:17 arg:1 best:1 subject:1 satisfying:1 dn:1 µn:35 between:1 conditions:4 email:2 terms:1 ikx:2 jr:1 le:1 amer:1 come:1 both:3 cos:6 last:1 many:2 nserc:2 com:2 ck:8 cn:5 ca:3 hungar:2 period:1 2nd:1 sequences:1 boas:1 throughout:1 november:1 been:2 abstract:1 corresponding:2 c2:2 c1:2 present:1 case:2 value:4 will:1 replaced:1 poussin:1 a20:1 vol:1 thus:3 different:2 author:1 complex:17 proved:1 difficult:1 development:1 i1:3 i2:2 upon:1 monotonic:1 hand:2 v1:1 necessity:2 recent:1 weakened:1 edinburg:1 well:2 weakest:2 transforms:1 immediately:1 λk:1 λj:1 λn:12 λm:2 preprint:1 royal:1 add:1 theorem:18 transformation:1 generalized:3 real:8 possible:2 cf:1 press:2 integer:1 like:1 follows:4 yields:2 always:1 right:1 classical:4 sequence:11 some:3 economic:1 univ:1 proc:2 sheng:1 bn:3 bv:28 variation:4 although:1 2m:3 francis:4 theorems:1 o:32 idk:1 2k:6 consequently:1 soc:2 cambridge:2 nsf:1 references:1 abel:1 log:39 area:1 there:4 nova:2 way:1 ed:1 rcd:1 function:19 form:2 repeated:1 convergence:10 applying:4 below:1 similar:3 called:1 constant:4 ak:4 denote:1 proves:1 exist:1 inf:1 functions:4 integrability:1 when:1 nx:2 other:1 role:1 papers:1 department:2 mathematics:4 2dk:1 zhou:11 uniformly:1 polynomials:1 a0:2 important:1 bounded:4 implies:1 together:1 |
0704.1866.txt |@word limited:1 partial:5 consider:11 secondly:2 caused:2 global:41 desirable:2 results:1 leads:3 roy:3 lr3:2 proposition:27 computation:2 go:3 follow:3 gk:20 2r2:2 causes:1 whose:1 u3:2 referring:1 ginibre:4 tt:1 technique:3 young:1 nonlocal:3 quasi:6 prol:1 tj:13 helps:3 under:3 staffilani:1 multilinear:4 3l:1 norm:3 applied:2 lack:1 worse:2 straightforward:1 zhang:3 far:2 frequencies:2 pages:1 regional:1 springer:1 wave:25 dxdt:23 balls:1 every:1 prof:1 lrx:3 zeitschrift:1 difference:1 condition:2 notations:3 school:1 y1:3 presented:1 t2:18 solution:29 large:7 admissible:15 convenience:2 lr2:1 science:1 small:10 anal:3 gruyter:1 velo:4 prevent:1 grateful:1 lecture:1 estimates:16 direct:3 imply:3 cost:2 l2t:16 l2x:10 estimated:1 tempted:2 goes:1 index:2 what:1 nonlinear:22 contemp:1 giving:3 3r:2 section:22 while:5 shares:2 2r1:15 strichartz:45 fractional:2 new:4 nnk:1 increasing:1 method:6 respectively:2 l1:17 q3:4 here:2 ranges:1 china:4 ht2:2 making:5 xβ:5 along:1 xα:8 equations:22 logarithmic:1 deduced:1 box:2 sending:1 remark:3 sobolev:8 institute:1 study:2 studied:4 erateurs:1 prior:3 conveniently:2 fourier:16 makes:1 cancellation:4 quotient:1 via:1 ii1:4 convolution:6 classification:1 beijing:3 dxdτ:8 belongs:1 loosen:1 replace:1 hardy:4 flexibility:1 establish:7 use:11 asymptotic:2 prove:9 recalling:2 positive:1 contains:1 negative:9 strauss:2 few:1 linear:2 noting:1 therefore:5 conservation:1 means:1 type:2 subcritical:1 more:8 introducing:1 brings:3 operators:3 devotes:1 odinger:4 berlin:1 particular:1 known:4 l1x:19 cases:2 iii:5 derivation:1 yves:2 keeping:3 valued:1 integrating:1 recall:4 equation:50 modified:1 zhao:2 vega:3 following:16 meet:1 merely:3 example:1 def:22 proof:22 control:3 claim:1 5c5:1 5c4:1 5c3:1 5c2:1 5c1:1 give:4 process:2 allowed:1 organized:1 pieces:2 high:15 assumptions:1 recollect:1 want:2 sense:3 sharp:1 tao:6 endpoint:1 4j:1 νk:10 νj:29 ii2:3 information:1 needs:1 end:2 goal:1 fortunately:1 holds:2 dydx:6 orthogonality:7 kenig:3 write:5 how:3 sickel:1 paley:5 instead:2 verlag:1 parameter:5 sin:1 massive:1 iberoamericana:1 simplicity:1 product:6 de:4 description:1 23k:1 may:4 max:7 after:2 mapping:1 ball:2 consequence:1 cbms:1 inst:1 studies:1 ff:1 coming:3 choice:1 data:29 efficiently:1 eaires:1 natural:1 bootstrap:2 summing:1 sk:4 rather:1 so:4 decreasing:1 definitions:2 op:1 order:9 restriction:2 acts:7 dx:1 over:3 eqs:1 vary:1 soon:1 utilize:1 course:1 paper:6 including:3 banach:1 sogge:3 existence:9 satisfies:1 recovers:1 its:6 before:8 rapidly:1 lr1:2 decay:1 picard:2 fix:1 solving:2 troubles:1 better:7 resort:2 verifies:1 lr:14 choose:10 lp:5 lq:4 mail:2 main:2 easier:1 overcome:1 non:2 good:1 combination:1 views:1 integral:3 practice:1 introduce:3 4s:3 scaling:12 effects:1 they:1 optimal:2 arriving:1 thus:5 now:9 2s0:5 s0:40 bahouri:2 bony:8 2r:38 university:1 hamiltonian:2 identified:1 l6:3 sufficiently:2 inequality:32 l2:74 l3:6 reasonable:2 radial:4 found:2 soc:3 2i:6 2j:86 2k:26 oscillatory:1 int:1 defocusing:6 postponed:1 eh:33 doing:1 there:9 energy:13 used:3 inhomogeneous:1 frequency:23 obtains:2 combining:4 funct:2 our:18 nonlinearities:1 es:4 out:2 deals:1 shown:4 precisely:1 space:15 although:2 restricted:1 since:15 bad:1 denotes:2 f1:8 dominated:1 reader:1 denoted:1 formula:3 rn:8 supports:1 ri:3 math:11 shows:3 theory:9 free:4 standard:3 difficulty:1 applications:3 formation:1 york:2 ask:1 estimate:77 klainerman:3 r4:1 definition:14 pairs:7 interaction:1 r1:27 r2:11 r3:76 could:2 nonnegative:1 turn:2 american:3 keel:3 u20:6 gordon:15 tempting:3 navier:1 hence:5 think:1 first:8 already:1 champs:1 upper:2 number:2 u0:16 long:2 directly:1 ring:1 smoothing:1 appl:2 xu:3 dispersive:3 1p:2 given:3 1r:4 similarly:8 introduction:5 leading:2 c0:2 rewrite:1 construct:2 needed:1 assumption:4 cµ:1 final:1 speaking:1 gives:4 pures:1 para:2 academy:1 continuous:1 proving:2 lower:1 λk:8 task:1 l3t:2 part:18 authors:4 believe:3 egrales:1 than:10 center:1 kind:1 unfortunately:1 edition:1 require:1 depends:1 lim:1 subsequence:1 yang:1 fˆ:3 were:2 letters:1 decompose:1 colliander:1 collecting:1 lowest:1 generality:3 contradict:1 ann:1 mind:3 argument:8 generalization:1 lq1:4 say:1 variable:1 lq2:3 close:2 need:2 concentration:1 recover:1 any:5 forced:1 relationship:2 min:2 studying:1 miao:7 internat:2 mills:1 vecteurs:1 lp1:1 revista:1 note:1 instance:1 f2:3 take:3 2d:1 lectures:1 begin:1 established:5 arguing:5 firstly:3 regular:1 gallagher:2 ht:11 letter:1 possible:1 acknowledgements:1 class:3 xµ:3 lerner:1 nonlinearity:12 bernstein:5 adopt:1 flot:1 singuli:1 3s:2 planchon:2 lpk:1 principle:2 h2j:1 physics:2 sum:4 fact:8 laws:1 precise:22 nls:1 show:5 eres:1 supported:4 discovered:1 bring:1 spaces:6 solutions:3 rough:5 trivial:1 find:4 q1:9 sj:67 q2:6 based:1 much:2 enough:9 should:4 lemma:11 only:5 smallest:1 constant:7 truncation:1 local:13 preliminaries:1 achieve:1 do:2 his:1 triangle:1 above:11 klein:15 get:17 dependent:1 sup:6 decomposing:1 ones:1 words:2 dy:3 during:1 dt:4 conjunction:2 consist:1 arxiv:3 yield:2 twice:1 investigate:1 she:2 prevents:1 through:4 fixed:2 view:3 kernel:1 requirement:1 multiplying:1 res:3 exists:7 achieved:1 hβ:1 still:1 mentioned:3 see:13 radius:1 result:28 λj:23 discussions:1 terms:4 iu:2 best:1 et2:21 closes:1 fails:1 satisfying:4 exponent:1 fang:1 tend:1 state:1 difficulties:6 chemin:5 between:5 c2j:1 invariant:2 northholland:1 ends:1 recently:2 extend:4 uut:12 restricting:2 focus:1 however:4 js:2 jn:1 comm:2 key:5 multiplier:5 article:2 jf:2 amer:2 improve:4 both:1 essentially:1 last:2 usj:11 many:1 taking:1 c5:1 wu:1 embedding:2 hσ:2 com:1 comes:2 arbitrarily:1 cj:11 cn:1 point:3 cc:1 had:2 each:4 cg:1 harmonic:2 proved:6 cp:1 diff:2 ct:5 resorting:1 finally:4 described:1 second:6 estimating:1 addition:1 locally:1 due:1 been:7 homogenous:1 dropping:1 literatures:1 expected:1 flexible:5 utilizing:4 contraction:3 universal:1 fk:5 define:4 obtained:3 direction:1 controlled:4 sufficient:1 made:1 observe:2 triebel:1 derivative:8 c3:1 c2:4 c1:1 denote:4 former:1 present:1 c4:1 case:11 globally:3 p1:25 littlewood:9 eix:1 value:1 will:8 supp:4 zhang2:1 p2:1 suppose:2 behavior:2 property:5 conformal:2 inspired:1 weakens:1 ix:1 vf:109 almost:1 vi:1 engaged:1 them:2 iv:5 ii:10 wellposedness:2 regularity:11 supremum:1 vanish:1 superconformal:2 id:1 different:5 suggests:1 journal:5 make:10 belong:1 same:2 princeton:2 plancherel:2 another:1 complex:1 split:5 φi:3 several:1 infer:2 interpolation:5 calculation:1 extended:2 infinity:2 lxr:1 lpt:3 cubic:10 i1:13 i2:5 effect:2 hand:11 v0:16 v1:18 purpose:3 takaoka:1 hartree:9 identity:1 relies:1 coifman:6 suitable:3 schr:4 proceed:2 older:16 try:2 well:36 posedness:21 analysis:12 obviously:2 mathematische:1 without:2 solve:1 jersey:1 easily:7 very:1 position:1 jean:3 dimension:1 ck:5 lq3:2 proposed:3 less:3 obtain:15 rest:3 vanishes:1 thanks:2 facts:1 2jn:2 k2:1 scattering:8 previous:1 heuristic:1 family:1 infinitely:1 conclude:3 seems:1 international:1 priori:2 easy:2 theorem:17 transformation:2 gave:1 real:2 2j4:1 march:1 around:1 stein:1 represents:1 read:1 couple:1 posed:8 term:19 increases:1 know:2 fˆ1:2 press:3 using:11 ams:1 unique:6 grenoble:1 formal:1 loss:4 phenomena:1 semi:1 exploiting:3 sized:1 benefit:1 continue:1 steps:2 schwarz:3 follows:11 become:1 essential:3 mathematical:3 sketch:1 right:5 functional:1 methods:1 classical:4 sequence:1 mostly:1 some:24 back:1 deduce:1 2kσ:1 nothing:2 choosing:10 moreover:5 proofs:1 provided:3 throughout:1 lead:3 tools:1 shall:11 extensively:2 providence:4 critical:4 decomposition:7 provides:1 tends:2 yields:10 symbol:3 minimal:2 refer:3 differential:5 core:1 problems:1 equivalent:1 arbitrary:1 pp:1 broken:2 step:4 bp:6 br:3 notation:2 properties:6 meyer:6 stokes:1 about:3 es3:2 es2:27 l1t:40 discussed:1 drag:1 o:2 page:1 sake:2 range:2 ξk:8 2ch:2 mean:1 slightly:2 jsq:2 perturbed:4 computational:1 dξ1:2 22j:9 dξ2:3 previously:1 into:6 h1:9 obtaining:2 bound:6 nsf:1 latter:1 down:2 pair:3 because:2 references:1 evoking:1 operator:11 amsterdam:1 rnk:3 schrodinger:1 deal:1 refinements:1 support:8 initial:16 u1:20 transform:12 ponce:3 u2:51 restricts:1 cauchy:17 fˆk:2 low:18 way:3 series:1 notices:2 was:1 coarse:1 function:4 complete:6 hs:3 differences:2 jun:1 but:10 sophisticated:1 volume:1 pj:1 construction:1 paraproduct:1 pk:1 lindblad:2 dξk:2 he:2 pi:1 intuitive:1 society:2 whether:1 ut:58 uv:14 smooth:1 maximum:1 us:21 um:3 below:2 ui:2 continuously:1 problem:24 walter:1 similar:3 ub:1 detailed:1 bourgain:4 ac:1 sometimes:1 associated:1 b2:1 defined:9 certain:1 abstract:1 influence:1 35q55:1 general:4 meanwhile:1 ap:3 engineering:1 exist:1 partly:1 check:4 again:4 functions:3 compared:4 differentiable:1 no:2 when:14 detail:1 graduate:1 besov:5 application:1 other:6 details:5 becomes:2 mathematics:3 conclusion:1 completes:1 lt2:1 remains:2 morawetz:1 endeavors:1 polynomials:1 commutator:8 ξj:2 important:1 included:4 structure:1 implies:7 assume:5 dτ:4 tataru:4 together:2 bergh:1 mass:1 eℓ:2 time:5 n0:70 n1:21 once:1 resolution:3 original:1 semilinear:7 |
0704.1867.txt |@word precise:2 lack:2 desirable:2 results:2 generalize:1 follow:4 causes:1 certainly:1 inverse:1 aug:1 tt:1 tail:14 monotonically:1 γn:2 under:3 case:4 advantage:1 very:5 edn:2 every:1 trouble:1 difference:1 logarithmically:3 presented:1 gnu:3 solution:1 sliding:2 large:4 discrete:2 small:5 inspection:1 reliable:5 programme:1 upper:6 smaller:2 says:1 disciplines:1 consistent:1 estimates:17 direct:1 rate:1 haan:1 further:1 quite:1 scientific:2 even:1 established:1 what:1 errors:2 minimization:1 brackets:2 sum:2 experiment:3 bain:1 above:3 new:1 increasing:1 method:10 filled:2 justification:1 respectively:2 residual:2 here:1 met:1 ramsey:1 ansatz:1 groups:1 xν:1 strong:1 equations:1 implicit:1 logarithmic:8 obtained:2 identifiable:1 items:1 larger:3 allows:1 approaches:1 usually:2 involves:1 quotient:1 useful:1 unsatisfactory:1 technologies:1 raphson:1 scaled:1 viz:1 apply:2 establish:3 plot:3 asymptotic:4 would:1 probabilities:2 kmin:26 mation:1 m1:1 therefore:6 m2:1 taken:3 type:1 theoretical:4 brent:1 more:4 introducing:2 validity:1 visual:1 particular:1 known:1 cases:1 sample:3 account:3 indicates:1 science:1 equation:2 mn:1 mi:12 values:1 publications:1 starts:1 following:5 making:2 numbers:3 nearest:1 figure:17 give:4 calculation:1 share:1 states:1 unbiased:2 assumptions:3 performed:1 united:2 rather:2 discussion:2 get:2 algorithms:1 far:1 pure:1 instead:3 parameter:8 profile:6 ubiquitous:3 mat:1 may:6 max:15 applications:1 wrong:1 deviates:1 fits:1 minimizes:1 law:64 data:40 introduced:4 physical:1 generalizations:1 explicit:1 fp6:1 so:2 decreasing:1 representation:1 order:2 bins:2 cutoff:1 symbols:2 course:1 experiments:2 statistical:8 y1:1 y2:1 its:7 accepted:1 fit:15 ln:13 solving:1 exhibits:1 better:1 estimating:3 window:11 offers:1 degrees:1 systems:1 bin:2 mail:1 main:1 might:1 overcome:1 yi:15 non:1 good:1 ym:1 weakness:2 outlined:2 practice:3 newman:1 mention:1 they:1 identically:1 oxford:6 heiko:3 hall:1 finite:2 goldstein:1 university:3 morris:1 magnitude:1 each:4 found:2 repeating:1 higher:1 side:1 characterized:1 referred:1 duxbury:3 series:1 idea:1 related:1 society:1 approximated:1 beyond:3 aˆ0:2 aˆ1:2 special:2 out:2 shown:1 solved:2 restricted:11 furthermore:1 denotes:4 mate:1 hill:3 reader:1 squares:7 plotting:2 shows:3 linear:5 given:18 possibility:1 standard:11 difficulty:1 reason:1 org:1 estimate:24 likelihood:31 additional:1 derivation:1 determining:3 times:1 unknown:2 consequence:1 rudolf:2 first:4 size:3 xi:17 features:1 probability:20 xm:1 variables:1 number:1 resnick:1 least:8 another:1 pareto:1 quality:3 divided:1 illustrate:2 differ:4 introduction:2 leading:1 histograms:1 approximately:2 assumption:2 too:5 statement:1 normalization:1 exponents:3 gives:4 fraction:1 continuous:1 rejected:3 binned:2 authors:3 x2:1 x1:1 than:4 intrinsically:4 wide:1 kind:1 unfortunately:1 double:2 see:12 normalizing:1 determined:7 solely:1 peierls:2 turned:1 esti:1 generalization:1 crossover:8 say:1 keller:1 any:1 lie:1 genuine:2 zero:2 min:65 efficient:2 lim:1 able:1 sound:3 k1:1 generalized:1 performance:1 centre:2 measures:1 wells:1 falls:3 insets:1 most:4 detect:1 sponsored:1 significant:1 remarks:1 class:1 kc:65 considered:4 calculated:2 gsl:1 points:8 physics:5 section:5 quantity:3 slope:1 phenomenon:2 show:2 text:1 random:6 contemporary:1 pkc:5 find:1 pacific:1 q1:1 indicator:1 q2:1 based:9 parameters:1 implementation:2 situations:1 yen:1 distributed:1 ox1:2 only:4 annals:2 do:1 notation:1 means:6 de:1 expectation:1 cannot:1 drawn:7 reconstruct:1 procedures:1 prime:1 regarding:1 approach:5 arxiv:1 european:2 acknowledgments:1 qb:1 common:2 contain:1 fixed:2 reveals:1 set:11 computed:1 exists:1 argmax:3 violated:1 up:1 depends:2 computer:1 truncating:1 collects:1 violates:1 best:1 still:2 exponent:40 ways:1 boundaries:1 outside:4 smallest:1 various:4 chosen:3 probably:1 prentice:1 conditions:2 available:2 august:1 notoriously:1 missing:1 restricting:1 equals:3 concentrate:1 hypothesis:7 problem:1 concentrated:1 both:1 numerically:3 reported:1 many:2 according:1 against:1 fulfilled:1 sensitive:1 merging:1 sparseness:1 dated:1 variance:5 estimation:3 whole:1 schafer:1 experimental:2 among:2 point:9 simple:1 ca:1 asymptotically:7 corresponds:1 community:1 2nd:2 table:5 finally:2 second:1 quantile:1 been:9 mark:2 much:2 change:1 graphical:19 corresponding:1 hurwitz:4 quantities:1 binning:9 else:1 systematic:3 derivative:2 c2:3 general:3 present:2 applied:3 p1:10 exponential:1 pacs:1 solid:1 straight:2 empirical:20 value:1 will:8 behavior:1 error:9 di:1 procedure:6 versus:1 bisection:1 characteristics:1 regularity:1 bias:6 cond:1 contract:1 3np:2 different:3 open:1 make:1 cumulative:8 admit:1 same:4 clearly:1 several:1 grows:1 difficult:1 independent:3 used:4 http:1 numerical:4 effect:1 hand:2 tune:1 lower:5 off:7 well:5 analysis:2 obviously:1 γˆn:28 without:4 jersey:1 sets:4 nb:1 systematical:1 less:3 accurate:1 newton:1 obtain:1 rest:1 identify:1 using:1 inference:1 alternative:5 cut:7 preprint:1 had:3 mathematically:2 source:1 setting:1 plateau:1 samples:7 varying:1 kingdom:2 around:1 lacking:1 press:3 integer:1 unique:1 apart:1 englewood:1 necessary:2 like:1 identifying:1 systematically:4 follows:8 reduces:1 loses:1 keble:2 either:1 arbitrary:3 popular:1 reduced:1 therein:1 deviation:12 www:1 because:5 methods:27 namely:1 sequence:8 some:11 proportionally:1 summation:1 examples:1 respect:1 library:2 scale:3 broad:3 normal:2 conservative:1 engelhardt:1 does:1 assuming:3 minimal:1 biased:2 noise:2 inaccurate:2 power:67 derivatives:4 journal:1 bioessays:1 bi:13 paper:1 restrictive:1 powerlaw:5 plots:1 properties:2 noisy:1 drees:1 comparison:1 about:4 cliffs:1 carried:1 package:1 freedom:1 favorite:1 range:4 estimator:19 ox:1 mean:10 road:2 software:2 mathematical:2 computational:1 statements:1 into:7 within:6 obtaining:1 bound:3 lies:3 appropriate:2 references:1 tiny:1 determine:1 estimators:12 rounds:1 often:4 uncertainties:1 rely:1 statistics:3 deal:2 θˆn:9 assumed:2 there:4 long:1 width:2 way:4 forward:1 completely:3 was:6 function:15 offer:1 but:15 histogram:3 idealized:1 failure:1 kmax:19 underestimates:1 unreliable:4 line:1 infor:1 true:2 inside:1 maximum:28 us:1 work:1 grove:1 limit:3 uk:1 distribution:69 similar:2 called:1 pχ:1 detailed:1 ac:1 constant:1 classic:1 defined:2 certain:3 statistic:2 a1x:1 covers:1 denote:1 single:2 dθ:1 partly:1 ing:1 distributions:21 regime:17 functions:1 compared:1 no:6 index:1 whereas:1 ne:1 sleuth:1 application:1 other:5 details:2 test:9 conclusion:1 poor:1 calculating:1 separate:1 variation:1 a1:1 a0:3 generated:1 important:1 bounded:1 modelling:1 suited:1 variable:3 25e:1 independently:1 faster:1 partitioned:1 factors:1 equivalently:1 n1:1 n2:1 laws:3 having:3 |
0704.1868.txt |@word gd:7 homomorphism:7 sch:3 gp:1 sαs:1 results:5 invent:1 gg:1 eds:1 scalar:16 proposition:26 generalize:1 ga:3 projective:6 primes:2 gl:7 gi:2 consider:13 whose:3 inverse:3 depend:1 γp:1 tp:1 finally:3 th:1 under:5 decomposition:9 analogous:3 norm:1 case:22 g3:3 g2:13 g1:13 orthogonal:7 very:1 nµ2:1 continues:1 choice:5 isomorphism:2 every:5 rationality:1 entries:2 em:1 matrices:3 condition:3 immediately:3 level:6 irreducible:7 notes:2 t2:6 t1:4 large:3 vector:15 mλ:3 science:1 quick:1 semidirect:1 upper:1 mn:4 computation:2 mi:3 consistent:1 izvestia:1 elegant:1 second:6 progress:1 irreducibility:1 concludes:2 invariant:1 reine:1 odd:14 linear:4 even:17 index:3 bλ2:2 bo1:5 section:14 agrees:1 annals:1 en:4 above:13 new:4 gl2:17 rd:3 method:1 ordp:1 body:1 ξi:5 full:2 gruppen:1 ebeling:1 d1:1 respectively:3 component:3 here:16 understanding:1 modular:39 groups:5 address:2 along:1 table:1 z2:1 obtained:1 remark:9 divisor:2 involved:1 study:5 tµ:1 contradiction:1 izv:1 simultaneous:1 resulting:1 action:34 fourier:10 quotient:1 uniquely:1 petersson:7 useful:1 projection:4 classification:2 apr:1 sloane:1 unit:2 use:4 darstellungen:1 lecture:2 would:3 lemma:27 positive:15 contains:1 γi:2 comparing:3 m1:1 therefore:5 m2:46 doubling:1 type:12 more:8 zur:1 γm:2 vieweg:1 operators:41 ti:1 eν:11 berlin:1 appendix:1 eλ:81 particular:6 known:2 foundations:1 cases:1 verified:3 must:1 ρa:100 springer:8 valued:25 mm:1 recall:4 der:3 work:1 det:17 mh:2 mk:41 rλ:6 remain:1 obvious:2 princeton:2 following:9 root:1 example:3 fulton:1 proof:24 claim:2 compare:1 want:1 calculation:1 sphere:1 degenerate:4 sense:1 conversely:1 absolute:1 information:1 end:5 straightforward:1 provide:1 s1:3 acts:4 write:16 how:1 enr:1 vital:1 sig:22 plus:1 verlag:5 divides:3 fp:6 map:7 product:15 rise:3 packings:1 description:1 algebra:10 may:8 earlier:3 variant:1 applications:4 tries:1 plane:1 date:1 representations:7 summarize:1 law:2 heidelberg:1 nps:1 diagonal:1 natural:6 third:2 βh:10 sp:1 explicit:1 correspond:2 element:5 sk:5 so:6 fundamental:1 lξ:16 putting:3 order:3 restriction:1 milnor:1 duke:1 developed:1 over:5 fλ:12 mx2:2 choose:2 funtions:1 wissenschaften:1 paper:4 through:4 left:11 differs:2 still:2 its:4 mµ:5 group:31 thank:2 chosen:2 interesting:2 fix:1 gtm:1 actually:2 forms:53 ls:3 jacobi:6 shimura:5 e2πiz:1 defining:1 into:2 cusp:12 them:1 combination:1 elementary:2 sssr:1 course:1 wise:1 they:4 half:6 eµ:3 now:14 nor:1 n02:1 easily:9 february:1 finite:8 products:3 skoruppa:1 university:2 drop:1 identified:3 infer:1 sufficiently:3 2f:2 ussr:1 bonn:1 die:2 cusps:1 side:4 2k:3 subset:1 lectures:2 square:10 eh:2 weight:13 tuples:1 bump:1 series:2 revised:1 eb:2 p2ν:2 eisenstein:2 fist:1 ez:4 our:3 ep:3 er:1 try:4 matrix:2 rr:1 factors:4 since:8 induces:4 denotes:5 content:1 transforming:1 dλ2:1 rational:1 denoted:1 formula:14 get:3 suffices:5 ri:1 math:12 gram:1 mτ:4 theory:8 associate:2 singularities:1 given:11 free:1 standard:11 8z:1 reason:1 complicated:2 york:2 put:8 institut:1 pullbacks:1 generate:2 definition:12 pairs:1 r0:1 r1:9 r2:13 rallis:1 could:3 omit:1 funke:1 honest:1 adic:1 signature:17 hence:10 onto:1 first:7 already:2 metaplectic:5 shapiro:1 bijection:1 variables:1 number:1 exact:3 multiplication:5 multiplying:1 done:3 carry:1 ring:2 precisely:1 ser:1 coprime:24 taniguchi:1 differ:1 necessarily:2 checked:1 similarly:1 introduction:3 adjoint:4 system:1 relations:1 piatetski:1 1a:1 their:4 zagier:1 1d:1 easier:1 gives:6 holomorphic:15 m0:2 academy:1 tool:1 akad:1 part:3 jordan:1 values:3 x2:4 translation:1 than:3 coefficients:2 reflection:1 determines:1 automorphic:7 fold:1 divisible:2 double:10 imply:1 determined:2 treated:1 minus:1 borcherds:6 generality:2 ann:1 argument:6 generalization:1 endomorphism:2 angew:1 further:1 need:5 seen:3 st:4 any:5 viewed:5 zp:1 self:5 husemoller:1 converges:2 note:1 instance:5 causing:1 take:3 zu:1 coprimality:1 modulus:1 kac:1 bilinear:3 play:2 unless:4 cosets:4 koeln:2 birkh:1 simplify:1 involving:1 germany:1 gauss:2 accordance:2 representation:69 pair:4 prove:6 tλ:1 considered:1 kh:1 cover:4 proceedings:1 χa:9 milgram:2 hn:1 usual:6 bo2:8 fact:5 show:5 nτ:12 katata:1 relation:2 nagoya:1 decompositions:1 analogue:1 trivial:4 find:4 d0:1 principal:2 q1:8 sh1:4 sh2:8 q2:14 based:1 dividing:2 assertion:9 should:1 jan:12 analytic:1 only:11 difficulties:1 generators:2 subsection:2 gh:4 identification:1 constant:1 local:2 interested:1 abelian:2 subspaces:1 notation:5 means:3 ocherer:1 lighten:1 de:2 db:4 nobs:1 cannot:1 actions:10 dx:1 dy:1 lattices:5 subscript:1 prime:10 covering:1 arxiv:1 expansions:2 consisting:1 nauk:1 common:1 grassmannians:1 ramanujan:1 view:6 kernel:1 set:4 modulo:9 computed:1 bruinier:15 observed:2 edition:2 see:32 discussions:1 freitag:3 subject:1 y2:1 tensor:3 representatives:3 symmetric:2 smallest:1 various:1 γb:9 between:1 theta:2 neither:1 checks:2 commute:2 sections:1 notice:8 hecke:60 extend:6 nature:1 complement:1 p2n:1 however:8 p2k:3 multiplier:1 distinguish:1 ker:1 0r:1 both:3 essentially:1 eichler:1 fh:3 insbesondere:1 many:4 taking:2 equal:6 conference:1 ln:2 und:1 embedding:1 uni:2 contribution:1 genus:1 otherwise:2 comment:1 abbreviate:1 point:2 simple:1 had:1 jk:3 cf:2 dimensional:5 cs:2 moreover:17 throughout:5 mpi:1 considering:1 hendrik:1 oliver:12 commutative:6 discriminant:18 union:3 associativity:1 skew:3 sl2:8 reduction:6 belongs:4 pk:14 algebras:1 pn:1 inv:1 define:25 surjective:1 determinant:5 congruence:1 corresponding:11 restrictions:1 mcg:6 residue:1 subspace:2 observe:1 understand:3 mail:2 last:2 denote:10 present:1 p2:32 splits:2 ǫd:1 value:1 choices:1 will:5 ǫp:7 suppose:1 property:2 miyake:1 unitary:7 geometric:1 non:7 according:3 disjoint:7 cocycle:7 dual:3 claimed:1 chern:1 grundlehren:1 different:3 develop:2 mµ2:3 powers:1 corresponds:1 belong:2 same:5 clearly:1 liftings:1 complex:2 adjointness:1 φi:1 several:2 subalgebra:4 composition:3 consequence:2 independent:3 used:5 trivially:1 assignment:3 funktionen:1 siegel:1 hand:6 harris:1 uses:1 purpose:1 braunschweig:1 identity:2 recent:2 suitable:2 center:2 well:7 without:2 components:3 english:1 exponentials:1 entry:2 ihrer:1 dimension:1 subgroup:9 gdr:1 heegner:1 composing:1 identically:2 obtain:12 valuable:1 detail:2 press:2 integer:13 facts:1 λm:2 previous:4 preprint:1 generator:1 decomposes:1 auser:2 character:6 lattice:11 lifts:1 extends:3 developments:1 theorem:25 moody:1 transformation:2 euler:1 generalized:1 real:1 stein:12 rµ:1 eigenform:1 possible:1 bijective:1 summand:3 possibly:1 psr:2 using:11 gr:2 advanced:1 mod:18 loss:2 follows:17 δp:2 yields:2 arbitrary:1 mcgraw:2 works:2 essential:1 right:10 classical:3 sequence:4 some:2 begin:1 teil:1 respect:6 classes:1 hirzebruch:1 garrett:1 universita:1 comments:1 cτ:7 does:4 exposition:1 slash:2 pr:1 bb:2 equivalent:1 δi:4 expansion:7 bu:2 step:1 weil:43 cξ:7 br:4 2m:1 helvetici:1 imaginary:1 properties:5 injective:2 chapter:1 integers:7 central:4 extension:12 extending:1 pλ:3 basis:4 o:13 compatible:4 addition:1 important:2 extensions:3 nebentypus:1 consequently:3 considerations:1 cambridge:1 mλ2:2 conway:1 kuznetsov:1 image:2 integral:11 isomorphic:5 latter:1 appropriate:1 because:1 references:1 operator:20 span:2 suffice:1 there:1 quadratic:12 way:5 nikulin:1 was:3 grenzgebiete:1 eigenforms:1 function:13 considerably:2 ergebnisse:1 form:33 hs:2 but:4 construction:1 m02:4 russian:1 line:1 true:1 divisors:1 partially:1 again:1 coset:14 compute:6 whether:1 mat:1 below:1 sum:6 problem:1 similar:2 called:3 uber:1 ac:4 associated:13 ad:1 oddity:1 defined:14 ko:2 abstract:3 describe:2 am:13 general:7 continued:1 arises:1 exist:2 check:1 defines:9 nh:9 ni:2 functions:9 codes:1 nm:2 mathematik:1 when:4 vanishes:3 field:2 nz:9 other:3 role:2 details:1 branch:1 bundschuh:1 mathematics:5 shin:1 ns:8 nt:5 shows:6 arithmetic:2 nw:2 mathematisches:1 symposium:1 briefly:2 elements:5 shintani:1 symbol:1 a0:1 generated:7 a2:1 ξl:2 serious:1 mathematischen:1 implies:8 assume:10 requires:1 space:7 together:4 n0:2 antilinear:1 n2:5 starting:2 |
0704.1871.txt |@word limited:1 concept:2 gr:1 gv:1 rev:9 global:14 results:2 eccentricity:1 scalar:1 ωch:5 garching:2 edu:2 consists:1 gn:1 expressions:3 rot:2 pvac:1 consider:2 whose:1 depend:1 albrecht:1 caldwell:1 quasi:3 those:1 th:1 eccentricities:7 ingredient:1 sound:1 returning:1 very:5 rise:1 ostriker:1 geometrical:3 rotational:1 axes:1 cardoso:1 affect:1 difference:1 condition:4 timely:1 galaxies:1 roy:2 tear:1 turns:1 solution:2 ri:1 large:11 solved:1 small:4 configurations:7 force:1 specially:1 dealing:1 zc:3 past:1 go:1 imply:1 enhancement:1 follow:1 dynamics:16 bona:1 ohmer:1 λcdm:3 even:3 will:11 what:1 stands:1 invoking:1 section:4 antol:5 tremaine:1 current:3 3h:1 goes:1 fractional:1 ρu:1 hooke:5 contrast:1 publications:1 high:1 szydlowski:1 respectively:4 never:1 component:7 8g:1 grav:14 explore:4 objects:4 focused:1 astron:5 represented:4 consideration:1 along:1 strong:1 equations:10 appears:2 change:5 extreme:2 obtained:1 generalizing:1 ellipsoid:1 shift:4 larger:2 allows:2 reason:1 contradiction:1 resulting:1 poisson:2 pick:1 examining:1 via:3 followed:1 although:1 scales:10 apr:1 requiring:1 wik:3 petrosian:1 wii:1 apj:3 apply:1 glance:1 total:5 establish:1 planck:1 derivatives:1 conventional:1 d71:2 figure:5 would:5 positive:2 examined:1 finally:1 next:1 few:1 linear:1 approach:4 examination:1 ρrad:2 ikj:1 robertson:1 associated:6 diii:2 today:1 more:1 flat:3 definition:1 d70:1 fixed:1 d36:1 ωvac:8 known:3 iii:6 iik:15 evolves:3 account:1 ρb:7 mb:1 equation:47 work:1 det:1 modified:1 rλ:2 reproduce:2 ρr:1 values:7 era:2 following:1 ρx:8 geometrized:1 numbers:1 f1:1 compare:1 wang:3 cosmological:24 process:1 relativistic:1 neglected:1 topic:1 performed:1 want:2 sense:1 axis:1 copeland:1 ones:1 turn:3 rather:3 get:1 range:1 write:8 low:6 pure:2 parameter:2 dominance:2 isotropic:1 ρch:11 galactic:2 description:3 ζg:2 inflationary:1 max:1 after:2 derived:3 mota:3 explored:2 physik:1 δiα:1 response:1 constants:3 shaw:3 bogot:1 ad3:1 dynamical:7 effective:2 approximation:2 element:2 accelerated:7 maintain:1 so:7 order:10 typical:2 chakraborty:1 qh0:1 neglect:1 indeed:2 over:7 insight:1 soc:3 years:1 overdensity:1 paper:4 through:6 looks:1 mentioned:1 cold:5 still:2 its:1 ρeff:3 before:3 derive:2 fit:1 ln:3 inclusion:1 epoch:2 decreases:1 late:1 harko:1 pch:3 systems:4 van:1 mail:2 main:2 might:1 h0:3 oblate:8 non:5 within:1 combination:1 practice:1 dai:9 effects:36 they:1 insisting:1 rotation:2 now:2 bigger:1 barrow:3 2t:2 easily:1 term:4 finite:2 fully:1 university:2 traced:1 advent:1 2e:3 good:1 magnitude:1 2a:2 each:5 simplified:1 entirely:1 characterized:1 2k:2 homogeneous:2 int:1 differential:6 eh:1 due:1 generation:1 energy:43 hypergeometric:1 astrophysical:24 static:2 interplay:1 measure:1 quantum:3 our:2 ew:1 eq:7 out:1 emerges:1 shown:1 dominates:1 rs:2 restricted:1 furthermore:2 since:2 virialization:2 douglas:3 content:1 re:1 investigation:2 dominated:4 rel:1 sanabria:1 formula:1 izz:1 ηx:1 occurs:1 red:7 theory:2 singularities:1 ısica:1 vac:3 departamento:1 standard:2 approaches:1 formation:1 e5:1 enlarge:1 detecting:1 dω2:1 e2:11 kik:1 interaction:2 r2:6 nesseris:1 determining:2 could:2 ds2:1 v2:4 times:4 motion:1 quintessence:2 length:1 hopeless:1 universidad:1 hence:6 ρri:1 think:1 first:4 exotic:1 major:1 symmetry:4 relate:1 done:5 colombia:1 2a1:5 reached:5 angular:10 size:1 given:11 perturbation:1 introduction:2 eqs:1 behaves:1 system:9 approximately:1 semiaxis:1 1e:2 observations:1 passed:1 maclaurin:1 dt2:2 john:3 structures:15 ranging:1 speaking:1 gives:1 testing:1 way:1 mostly:1 schwarzschild:1 tool:1 exactly:1 serve:1 binney:1 part:1 debnath:1 skordis:1 than:3 distance:1 accordance:1 require:2 depends:1 matter:10 states:1 future:4 represents:2 pd3:1 distinguished:1 displays:2 ages:1 say:1 need:1 cosmology:12 any:1 acceleration:8 generalizes:1 polarski:1 newtonian:5 zero:2 studying:1 latter:2 aside:1 mechanism:1 note:2 instance:1 ideal:2 potential:9 generalized:1 analogy:1 negligible:1 unless:1 trace:3 established:1 friedman:2 measures:1 most:2 germany:1 significant:1 successive:1 phase:4 class:3 astro:7 especially:1 clear:1 stronger:1 perlmutter:2 sf:1 principle:2 arxive:2 velocity:16 usual:1 fact:2 dr2:6 show:3 definite:1 probe:1 zlatev:1 representatives:1 obtains:2 astrophys:3 d2:6 d3:5 chaplygin:28 impact:1 q3:1 ratio:3 proposed:1 parameters:8 situations:1 explain:2 written:8 only:6 explicitly:1 b73:2 factor:9 local:16 pointed:3 equilibrium:19 do:2 dm:1 above:2 invoke:1 nowakowski:7 dependent:12 de:3 fluid:1 redshift:2 q32:16 cannot:1 new:1 during:1 dt:8 dr:10 gen:1 evolution:3 densities:6 fields:1 arxiv:6 yield:1 baker:1 qc:1 3e:1 qi:1 enclose:1 nβ:2 αn:6 valid:1 view:1 set:3 mandatory:1 observes:1 extraterrestrische:1 observed:3 see:2 full:1 radius:2 eliminating:1 straus:2 close:1 violates:1 best:1 acquires:1 cents:1 invoked:1 tensor:15 subsequent:1 diluted:2 cosmologies:2 symmetric:1 d59:1 state:16 various:1 closed:1 between:2 boundary:1 conditions:3 discovery:2 notice:1 terms:5 reproduced:1 nature:1 importance:1 complement:1 however:6 reproduces:2 concentrate:4 jk:1 article:2 configuration:7 come:1 inertia:6 last:4 boehmer:2 taking:1 assumed:1 etc:1 connection:1 figures:1 contribution:10 expression:2 comes:1 among:1 relevant:3 co:3 space:4 point:2 corresponds:2 coincidence:1 xβ:3 simply:1 coordinates:2 virial:10 constant:16 nojiri:1 considering:1 forms:2 xα:4 described:2 second:2 addition:1 px:2 barreiro:1 three:2 been:6 ai:19 dropping:1 frw:1 interest:2 expected:1 ph:7 fig:2 direction:1 ınez:5 quantities:2 gas:22 ik:6 5e:3 representative:1 realms:1 clusters:1 present:11 wzz:1 case:13 external:1 pacs:1 ρcrit:1 value:4 employ:1 cast:1 while:5 b639:1 behavior:6 kinetic:5 situation:2 a21:2 coupled:1 almost:1 prolate:9 ii:4 reads:1 itself:1 mod:2 different:20 constrained:1 d10:1 ρcdm:4 make:2 radiation:5 lett:4 same:2 clearly:2 princeton:2 shifts:3 another:1 units:1 several:1 higher:1 used:4 infinity:1 friedmann:2 effect:2 hand:2 parametrized:1 moment:6 πik:3 moving:1 hep:1 a2i:3 interested:1 early:5 concordance:1 ellipsoidal:2 scenario:2 nevertheless:2 well:4 thought:1 without:1 solve:1 components:2 sets:1 model:20 bodies:4 left:1 spherical:6 λr:1 just:1 moments:1 wxx:1 newton:4 obtain:2 homogeneity:1 press:2 ch:5 unifies:2 spherically:1 facts:1 paul:1 speed:1 enters:2 density:18 seems:2 mathematically:1 internal:5 maintaining:1 theorem:5 relevance:2 extensive:1 ruled:1 euler:3 details:1 articles:1 iα:1 possible:1 dark:26 smallness:1 mon:3 background:19 vacuum:6 clustered:1 using:4 apart:1 necessary:2 like:3 semi:1 follows:2 reduces:4 velocities:4 isotropy:1 specific:1 δm:3 yields:1 either:1 become:1 reduced:1 mathematical:1 right:1 often:1 deal:1 d3r:1 some:5 back:2 examples:1 respect:2 proper:3 neglecting:1 ourselves:1 scale:15 bruck:1 lead:3 realistic:2 affects:1 though:1 aiα:3 integration:6 per:1 does:1 assuming:1 power:1 aαβ:1 use:5 expansion:17 step:1 br:4 2nβ:3 properties:12 stage:1 rare:1 constraint:1 universe:17 discussed:1 dependence:1 compatible:1 stretch:1 andes:1 perivolaropoulos:1 d66:1 astronomical:2 steinhardt:3 presence:1 h2:6 into:4 h1:4 bound:4 δik:6 lies:1 references:1 determine:3 einstein:3 proportional:1 godlowski:1 ρvac:19 theoretically:1 methods:1 nunes:2 institut:1 h02:2 strictly:1 there:1 redshifts:2 transform:1 long:2 dispersion:9 los:1 ixx:2 conservation:4 inner:1 fraction:1 was:2 knowledge:1 function:5 form:3 energies:1 collapsed:1 ωcdm:3 but:4 hu:1 volume:1 taken:1 gain:1 line:2 collapses:1 observation:1 ωx:9 qualitative:1 gravitational:9 variations:1 up:2 us:4 ur:1 2e2:1 converted:1 limit:7 minor:1 demonstrate:2 problem:2 stages:1 similar:1 called:4 expect:2 rightly:1 defined:1 certain:4 abstract:1 describe:1 influence:1 general:5 spite:2 regime:1 phantom:2 again:1 functions:4 no:1 when:5 vanishes:1 field:2 supplementing:1 other:3 tii:1 tik:3 test:1 conclusion:1 peebles:1 may:6 generates:1 models:16 includes:1 a1:18 a3:25 a2:11 allowing:3 variable:1 formal:1 structure:3 arcsin:3 implies:5 garcia:1 assume:2 starting:1 age:5 factors:2 together:2 nath:1 mass:5 time:29 walker:1 requires:1 once:1 |
0704.1872.txt |@word neighbors:1 concept:1 caused:2 magnetic:15 excellent:1 desirable:1 results:4 facilities:1 ginzburg:1 ga:1 consists:1 causes:1 evot:1 technique:4 cm2:1 nonlocal:22 does:1 present:1 th:2 under:1 largescale:1 tc:2 appleton:1 division:1 confirmation:1 ofthe:1 zhang:1 very:2 springer:1 fabricated:2 nikitenko:1 refractive:1 experimentally:1 stromberg:1 difference:4 clement:1 inset:1 kuleuven:1 induction:2 p5:1 damped:1 large:1 vector:2 affect:2 small:1 optics:1 programme:1 smaller:3 force:1 consistent:2 measurable:2 literature:3 sign:5 approximation:1 zero:2 design:1 value:1 0qx:1 further:2 rrr:3 index:3 what:2 rate:1 uniform:1 current:2 new:2 increasing:1 thin:1 edited:2 full:1 simultaneously:1 respectively:5 gathered:1 residual:1 reported:2 chilton:1 cylindrical:1 represented:1 based:3 along:2 implanted:2 superconductor:6 extreme:3 obtained:7 dec:1 covers:1 institute:2 study:1 larger:4 suggests:1 periodic:1 historical:1 action:1 changes:1 diamagnetic:1 adjustable:1 instr:1 marginal:2 layer:5 neutrons:4 monolayers:1 achievable:1 total:4 detecting:2 would:1 remains:1 positive:1 negative:1 tabulated:1 few:1 nucl:1 therefore:2 taken:1 parkin:1 type:10 theoretical:2 reflects:1 more:1 flat:3 1nm:1 apparent:1 instrumental:2 berlin:1 correspondingly:1 particular:1 applying:1 ward:1 must:2 schrieffer:1 account:1 room:1 mm:1 science:1 rutherford:3 theories:1 oxide:9 values:1 µsr:4 cal:1 following:3 meet:1 drops:1 root:1 example:1 purity:1 antwerpen:2 scan:1 magnitudes:1 stressing:1 sample:23 protective:1 numbers:1 council:1 allowed:2 sharp:1 fysica:1 information:2 united:1 requirements:2 verify:1 discussion:1 roughness:7 located:1 pure:6 answer:1 parameter:2 sin:1 profile:2 mat:1 afm:2 may:1 iuap:1 expectation:1 diagram:1 applications:1 deviates:1 mag:1 fits:2 yielded:2 data:18 parallel:4 beam:4 negligibly:1 light:1 d13:1 plateau:1 leiderer:1 st:1 used:4 progressively:1 fundamental:1 order:1 typical:1 pulsed:1 reversal:3 over:3 vary:2 interpreted:1 thermal:1 paper:1 london:3 statistical:2 during:1 still:1 ieee:1 its:3 before:1 le:4 outer:1 monitor:1 fit:5 decay:5 2λl:1 interesting:2 forms:1 detected:2 meissner:4 fig:12 tors:1 inconsistencies:1 hidden:1 main:1 instantly:1 versus:1 non:1 combination:1 matches:1 practice:1 introduce:1 landau:1 framework:1 resolve:2 penetration:5 effects:4 oxford:1 rotation:1 now:1 yu:3 possess:1 february:1 reflectivities:1 university:1 luetkens:2 gomes:1 kern:1 reasonable:1 found:3 side:1 characterized:2 mean:3 en:2 mansour:1 significantly:2 kang:1 energy:2 4b:1 related:1 kirk:1 frequency:1 measure:1 laboratory:2 meth:1 nonmonotonic:5 ru:1 shown:7 factors:1 kozhevnikov:1 since:1 goa:1 microscope:1 publish:1 research:6 nominal:2 asymmetries:1 hill:4 rl:1 instituut:1 ref:4 shows:2 theory:8 frank:1 sio2:1 free:2 ascending:2 difficulty:1 approaches:5 base:1 york:2 sensors:1 dubna:2 additional:2 suter:2 worth:1 voor:2 times:2 silicon:2 turn:1 length:2 specular:1 transfer:5 bulgaria:1 substrates:1 laboratorium:1 physik:1 matthias:1 reflected:2 clear:1 least:1 directly:1 trans:1 thick:3 clarity:1 quality:2 angular:1 size:2 temperature:2 introduction:1 unknown:1 top:1 achieved:1 theoretische:1 reflectivity:15 their:1 calculations:1 htm:1 shifted:1 option:1 mostly:1 wavelength:1 moscow:1 exactly:1 serve:1 direct:1 part:4 somewhat:1 authors:1 focusing:1 than:3 distance:2 polarized:8 second:1 modelled:1 project:2 determined:5 amplitude:3 were:8 enables:2 russia:1 exhibit:1 resistivity:2 electrodynamics:4 curves:5 seen:1 backscattering:2 any:2 ray:1 absorber:1 documents:1 angle:3 latter:1 laterally:1 high:3 potential:4 square:1 negligible:1 detector:1 conductivity:1 reversed:2 sn:2 pnr:12 allow:1 established:2 probed:1 incidence:2 reach:1 clearer:1 most:6 optimized:1 significant:1 phase:4 infrastructures:1 intrinsic:1 observation:2 nonlinearity:1 calculated:2 fritzsche:1 physica:2 universiteit:3 satija:1 definitely:1 exp:1 physics:3 fact:1 khasanov:2 distances:1 supported:1 evaporation:2 attempts:2 relation:1 thickness:12 agrees:1 decade:1 ratio:1 simulating:1 parameters:3 explain:1 boothroyd:1 enough:1 should:4 only:2 wood:1 factor:1 local:10 pointed:1 achieve:1 ox11:1 aksenov:2 de:1 overall:1 dc:1 degradation:1 joint:2 dz:1 words:1 penetrate:1 years:1 bardeen:1 gray:2 precession:2 substrate:7 fields:3 arxiv:1 yield:1 crc:1 qc:5 experiments:4 predicted:4 contain:1 through:1 inside:2 view:2 rms:1 bars:1 set:1 art:2 questions:1 attenuated:1 operates:1 observed:1 see:2 result:1 close:1 nonlocality:5 best:1 techniques:1 buzdin:1 consistency:1 nuclear:3 segment:3 assumed:1 µm:12 state:8 smallest:1 correctly:1 between:5 approach:4 reflectometry:3 recently:1 responses:1 nature:1 however:4 incident:1 extent:1 probing:1 mbar:1 problem:1 thank:1 both:3 last:1 limits:1 many:1 region:4 asymmetry:7 contract:2 sensitive:1 dated:1 refraction:2 distinction:1 magnetics:1 experimental:5 con:1 comment:1 detailed:1 key:2 characterization:1 simple:1 deposit:1 ac:2 hollow:1 interface:1 anti:1 path:2 moreover:1 grazing:1 ct:1 better:3 strong:1 zimmermann:1 instrument:1 discrimination:1 girard:1 due:6 tiny:1 pb:4 polychromatic:1 magnetized:1 much:1 deposited:2 change:2 expected:4 muons:2 swenson:1 pippard:5 controlled:1 quantities:1 sufficient:1 coherence:2 modelling:1 bulk:1 external:1 spin:12 former:1 those:1 applied:6 exponential:3 pacs:1 solid:4 profiles:2 air:2 will:1 near:2 intas:1 error:3 stopping:2 identical:1 cylinder:1 studied:2 refs:2 simulations:8 surface:12 ii:2 cond:1 technology:1 situ:1 rfbr:1 different:4 grant:1 perhaps:1 suggest:1 indistinguishable:1 same:2 clearly:1 another:1 several:1 neutron:20 european:2 fairly:1 safe:1 tinkham:1 effect:3 hand:1 appreciable:1 pdf:1 infinite:1 lower:1 reflection:4 well:2 commission:1 analysis:1 edge:1 incapable:1 sets:2 quantitative:1 model:1 whereas:1 preprints:1 morenzoni:3 muon:5 magnetization:2 cuprates:1 proposed:1 less:1 being:1 sofia:2 superconductors:8 shape:2 atomic:1 predicts:2 paul:1 lauter:4 scattering:3 λn:2 λl:6 adding:1 density:2 irradiated:1 fitting:2 source:1 wu:1 unambiguously:1 katholieke:2 samples:2 momentum:5 kingdom:1 saturation:1 kornilov:1 advances:1 progressed:1 possible:2 corresponds:1 belgium:3 using:2 crisp:4 like:1 semi:2 visible:1 signal:1 manual:2 specific:1 flux:1 dependencies:1 accuracy:1 indium:8 spins:2 www:2 leuven:4 exposed:1 some:4 back:2 table:1 provided:1 scale:3 cooper:1 confirm:1 broad:1 measurements:5 recorded:1 critical:2 provides:1 proc:1 minimal:1 measuring:2 performed:4 pose:1 agreement:1 pressure:1 although:1 mcgraw:1 plots:1 properties:4 bael:1 about:5 oe:20 horisberger:1 discussed:1 location:1 o:2 simulation:4 range:2 larmor:1 insufficient:1 consequently:2 soc:1 rev:11 polished:1 material:2 reassess:1 within:1 splitting:2 bound:1 down:3 appropriate:2 because:2 been:6 determine:1 next:1 nowadays:1 theoretically:1 uncertainties:2 rely:1 van:5 log:1 elastic:2 area:2 measured:5 support:2 there:1 noticed:1 collimated:1 appl:1 handbook:1 low:6 jinr:1 was:22 combined:1 questionable:1 medium:1 governs:1 but:3 principles:1 degrees:1 chaudhari:1 properly:1 grigoriev:1 russian:1 hc:3 line:3 ha:1 lynn:1 made:1 isis:4 supr:1 up:4 work:1 below:1 limit:4 verification:1 uk:1 didcot:1 demonstrate:1 distribution:1 average:1 strongly:2 penetrating:2 strengthening:1 associated:2 worthwhile:1 petrenko:2 geometrical:1 combining:1 metals:1 evidence:3 our:8 mck:1 formalism:1 distributions:1 film:13 physical:1 6th:1 nm:4 no:6 dashed:2 nb:7 when:2 depth:5 nx:1 field:21 other:4 electrical:2 details:1 normal:1 department:1 out:1 conclusion:2 deviation:2 briefly:1 quartz:1 absorption:1 superconductivity:4 models:1 time:1 variation:1 important:1 sides:1 structure:1 exposure:1 wafer:2 ta:1 curve:3 governed:1 perpendicularly:1 electromagnetic:2 resolution:4 lett:5 4a:1 |
0704.1873.txt |@word code:1 consider:3 skip:2 results:4 existing:2 leads:2 gf:1 proposition:6 cooperative:4 edu:2 consists:1 ψ1b:5 whose:1 cardinality:2 depend:2 calculate:4 aug:1 send:2 γt:3 those:8 under:3 sent:8 ucsd:1 case:8 r12:2 g2:6 g1:43 r11:4 very:3 summarized:1 matrices:2 syracuse:2 treating:2 achievability:1 transmission:5 large:1 discrete:2 vector:5 indices:7 markov:7 still:1 upper:1 l2b:11 computation:1 direct:3 past:2 rate:17 picked:1 equal:1 chen:3 further:1 theory:6 even:1 index:14 y1n:1 y1i:1 section:4 axes:1 brief:1 decoding:11 access:1 above:4 new:7 coefficient:4 j2b:6 qm1:2 respectively:7 intercepts:1 equals:1 here:5 reported:1 china:1 mes:1 strong:2 z1:9 z2:6 referring:2 obtained:4 asilomar:1 delimited:1 sender:3 assures:1 simultaneous:3 pick:1 fourier:1 cancellation:1 via:4 elaborated:1 apr:1 private:3 achievable:24 apply:3 total:1 establish:1 causal:1 kobayashi:4 standing:1 jan:2 use:4 feb:1 codewords:14 probabilities:1 positive:1 h1t:1 vol:6 m1:40 therefore:1 reciprocity:1 m2:11 swap:1 introducing:2 sharing:1 knows:2 relay:23 comparison:1 becomes:2 eferences:1 erkip:1 aware:1 known:3 cases:4 biao:1 iii:2 work:1 modified:1 oct:1 caratheodory:1 values:1 following:2 trans:7 example:1 proof:2 control:1 compare:2 computers:1 give:1 process:3 sense:1 organized:1 involve:1 allowed:2 tan:1 r23:3 x2i:2 r21:9 r13:2 information:12 respective:2 end:4 r10:3 s2:51 s1:7 zhang:1 r22:9 regions:1 e2c:1 instead:2 r20:5 inputs:2 blocks:2 description:4 max:1 after:2 derived:2 hong:1 factored:1 date:1 summarize:1 jiang:1 outline:1 lines:1 yielding:1 st:2 codebook:3 inform:5 negligible:1 l1b:11 definitions:1 order:2 bins:4 typical:6 help:1 over:1 kong:1 symbols:2 paper:6 looks:4 y1:51 ntroduction:1 satisfies:1 y2:21 ieee:9 its:2 perfect:1 x1i:2 outer:3 x1n:1 suboptimal:1 actually:3 better:2 h2:9 θt:3 fig:3 partitions:1 yi:1 them:5 good:1 propose:2 wcnc:1 identically:1 1b:3 nov:3 now:5 easily:2 transmitter:6 gets:1 always:1 university:1 qg1:1 l2:3 reasonable:1 each:10 found:2 2n:1 side:3 constraints:2 subset:1 el:1 generation:3 reduce:3 gaussian:13 related:1 investigated:1 combining:1 our:9 event:3 intended:2 shown:1 matrix:2 since:5 interference:22 denotes:2 denoted:3 correct:1 i2:1 cooperatively:2 motzkin:1 hull:2 story:1 standard:1 small:2 ecs:1 e1:5 generate:4 mimo:1 e2:3 βt:3 pairs:3 cording:1 r1:13 r2:12 v1:4 transition:1 messages:9 length:1 place:5 hence:2 relays:1 first:4 already:2 transmitters:5 probability:11 encoding:11 variables:4 coding:6 number:2 echo:1 channels:18 will:6 xx:1 simplified:2 xin:1 directly:2 theorems:1 message:15 tributed:1 quality:1 gamal:2 given:4 similarly:3 eqs:1 system:1 construct:1 their:1 assumption:3 rates:1 1i:2 perfectly:4 1n:1 maric:1 serve:1 broadcast:4 part:4 somewhat:1 x2:21 x1:21 chong:4 than:3 e21:2 scheme:2 determines:1 zero:2 tackles:1 limiting:1 were:2 identical:1 declare:6 result:2 ifc:1 generalization:1 randomly:6 close:4 need:2 recover:1 any:1 ω1b:13 min:1 improves:1 note:2 k2:11 k1:45 take:1 transmit:6 so:4 channel:36 multiple:3 established:1 who:1 systems:1 codeword:7 pair:3 encoder:2 i2b:2 αt:3 grove:1 h2t:1 average:1 partition:2 cover:1 constrain:1 review:2 slope:1 optimal:1 particularly:1 show:2 random:9 relation:1 degraded:10 y1b:1 find:2 feedback:1 q1:4 cell:10 indicator:1 q2:4 based:2 parameters:1 distributed:2 enough:1 penalty:1 only:6 ambiguity:2 factor:1 kramer:1 achieve:1 his:1 correctly:2 get:3 dc:1 joint:1 during:2 ita:1 closure:1 regarding:1 approach:2 arxiv:1 yield:1 investigate:1 dpc:4 common:11 ut:2 e1c:2 fixed:1 transmits:2 qn:1 eecs:1 set:11 computed:1 sep:1 throwing:1 j1:1 j2:8 achieves:1 individual:1 w2:29 w1:21 terms:1 weingarten:1 statistically:1 satisfying:3 capacity:27 inequalities:2 µt:2 user:30 definite:1 propagates:1 state:1 smallest:1 xamples:1 cooperation:9 between:5 hold:1 conditions:2 email:1 conferencing:14 available:1 recently:3 wb:1 receivers:2 weak:1 however:3 wt:1 comm:1 jointly:7 distinguish:1 distribution:1 shamai:1 both:10 essentially:1 x2n:1 last:1 cao:3 region:61 uncertainty:2 according:7 became:1 receiver:8 variance:2 whole:1 otherwise:4 arbitrarily:4 conclude:1 within:1 steinberg:1 ca:1 except:1 qs2:3 sequences:5 cs:1 conference:1 pp:4 pt:4 basis:1 union:1 three:1 been:1 strategy:3 workshop:1 combined:1 pe:8 extreme:3 define:1 wants:4 corresponding:2 received:1 covariance:2 binning:4 improved:2 denote:9 present:1 p2:10 p0:3 p1:20 washington:1 straight:1 employ:2 ain:1 suppose:4 error:9 taking:1 a21:3 memoryless:3 thus:6 iv:2 ii:2 unit:2 vt:3 ic:10 different:1 alphabet:3 make:1 same:6 parts:2 split:2 largest:1 k2b:4 finite:3 independent:3 used:3 i1:1 numerical:2 hand:1 syr:2 v2:19 uses:1 purpose:1 infinite:1 yates:1 expression:1 kˆ1:1 well:1 analysis:2 without:1 sets:5 model:1 spend:1 proposed:4 less:2 transmitting:3 aǫ:5 obtain:2 sources:3 previous:1 letting:1 han:4 application:1 guaranteed:1 ideal:1 signals:2 belongs:1 theorem:4 input:4 guarantees:2 remaining:2 gave:1 bin:11 march:1 capacities:1 possible:1 increases:1 know:1 using:2 unique:2 necessary:1 semi:1 follows:2 reduces:7 serves:4 output:4 because:1 sequence:2 sends:4 successfully:1 some:4 searching:1 pacific:1 examples:2 convex:2 s1b:4 superposition:11 icc:6 l10:5 l11:11 l12:9 l13:6 does:1 allocate:1 provides:1 assuming:1 proc:1 esults:2 2b:1 power:5 bc:2 equivalent:1 l1:1 simpler:2 y2i:1 about:2 y2n:1 constraint:1 prove:1 reliminaries:1 2i:2 mean:2 slightly:1 block:19 own:3 statements:1 previously:2 garg:5 into:12 h1:58 j1b:6 bound:10 remarks:2 formidable:1 log:6 strictly:1 there:5 u1:5 long:1 u2:39 decode:6 appears:1 aazhang:1 inner:2 forward:1 was:4 function:2 decoded:2 form:6 but:1 idea:1 hk:11 construction:1 decoder:1 elimination:2 longer:1 partitioning:1 made:1 applying:2 submitted:3 umerical:1 cells:3 bounds:8 k1b:15 below:4 limit:1 dirty:3 problem:4 more:1 similar:3 globecom:1 ac:1 later:2 intersects:1 defined:1 certain:2 abstract:1 general:3 diversity:1 allocating:1 ing:1 distributions:1 check:1 functions:1 encoders:4 no:7 whereas:1 when:11 ny:1 other:5 guarantee:1 details:2 department:1 nt:2 i1b:7 poor:2 users:7 a12:3 generated:3 generalized:2 needed:1 correlated:3 auxiliary:2 assume:3 resolving:2 exhausting:1 mimic:1 mass:1 time:2 n1:47 n2:3 backward:1 original:1 |
0704.1875.txt |@word limited:1 code:2 consider:1 remarkable:1 represent:1 fabricated:1 tensile:3 consists:1 gm:3 negf:3 whose:1 inverse:1 etching:2 lower:1 finally:1 behave:1 those:1 stable:1 gnr:40 fax:1 advantage:1 zhang:2 very:5 dell:1 induce:1 electron:3 worst:1 prof:1 iannaccone:6 molar:1 hamiltonian:5 louie:1 guo:2 solution:3 large:1 reich:1 demonstrated:1 small:2 degeneracy:1 nanoribbons:6 smaller:1 tel:1 vides:1 consistent:3 liang:1 morozov:1 zero:1 chen:3 leakage:4 ribbon:1 even:1 sub:2 nano:1 thickness:2 current:7 maultzsch:1 abs:2 fiori:7 above:1 new:1 net:1 increasing:1 public:1 3d:4 respectively:3 spacing:2 vol:10 atoms:4 mes:1 excess:1 along:1 strong:1 equations:1 logarithmic:1 obtained:1 trans:2 study:2 larger:2 amount:1 periodic:4 poisson:4 suitable:2 makes:1 lowers:1 via:1 useful:2 inducing:1 brought:1 wang:1 would:2 electrostatics:1 zig:1 fet:12 therefore:1 averaging:2 taken:1 theoretical:1 more:3 lowering:1 acceptable:1 factor:3 odinger:3 known:1 hole:1 iii:1 insights:1 high:1 account:1 strained:1 room:2 middle:2 science:2 equation:2 work:2 dev:4 oxide:2 mv:4 thin:1 under:1 dec:3 example:2 decoupled:1 control:2 nikonov:1 degenerate:1 nanoelectronics:1 suggestions:1 states:6 performed:1 novoselov:2 onclusions:1 occur:1 fets:23 provide:2 means:2 roughness:6 atomically:1 gate:9 mat:3 modulation:1 stripes:1 applications:2 parallel:1 realized:1 short:1 jiang:1 outline:1 effective:2 acknowledged:1 avouris:1 element:1 2d:1 cannot:1 so:2 allow:1 order:4 typical:1 fodor:1 developed:1 over:1 course:1 experiments:2 through:1 statistical:1 existence:1 still:1 ieee:3 its:1 thank:1 interesting:1 lateral:7 fruitful:1 whether:1 µa:3 fig:12 main:1 correspondence:2 donors:1 non:2 good:1 affected:1 unrolled:1 material:2 dai:1 band:16 mitigated:1 effects:1 they:1 instead:1 inelastic:1 semiconducting:1 hall:2 february:10 finite:1 fully:4 capability:1 sufficiently:1 intraband:1 2a:1 found:1 universit:1 european:1 el:1 house:1 energy:13 ec:1 conductance:1 firsov:1 our:3 lithography:1 beyond:2 description:1 shown:8 funding:1 acknowledgment:1 space:2 since:4 rev:2 research:1 increase:1 attracted:1 dominated:1 electronics:3 induced:3 evaluation:1 occurs:1 dubonos:1 foundation:1 linear:1 barrier:2 state:1 mechanisms:1 differ:1 possibility:1 extraordinary:1 org:2 estimate:1 subbands:1 definition:1 inter:1 informazione:1 geometry:2 could:2 silicon:1 length:1 edges:1 swing:1 consequence:1 programme:2 dipartimento:1 first:1 ntroduction:1 zag:1 clear:1 multiplying:1 defects:1 thick:1 open:3 several:1 engineer:1 tox:4 temperature:2 needed:2 leading:1 top:1 behaves:1 their:2 intermediate:1 draft:10 1d:1 ballistic:5 ordejon:1 way:1 transistor:3 stress:1 interband:1 drain:7 authors:1 off:1 than:4 diffusion:1 double:5 drift:1 project:1 electrostatic:1 ingegneria:1 projections:1 exhibit:2 rooks:1 lines:1 cohen:1 randomly:2 need:1 inhibiting:1 occupied:1 option:1 built:1 self:3 able:2 metallic:3 potential:5 take:1 performance:9 channel:19 play:2 electric:1 prohibitive:1 impurities:1 sheets:1 device:10 extremely:2 considered:8 average:1 ko:1 kurz:1 electrons:1 principle:2 son:1 show:3 doped:3 nanowire:1 threshold:2 rough:3 line:5 decade:1 caruso:1 impact:1 µm:6 based:5 conduction:2 iet:1 jan:1 only:6 tolerance:1 lemme:1 volts:1 adequate:2 hamiltonians:1 equilibrium:2 di:2 dependent:1 nanowires:1 elettronica:1 degradation:1 ionized:2 international:1 approach:1 itrs:1 arxiv:3 twice:1 investigate:1 nanoribbon:11 analytical:1 including:1 transistors:10 embryonic:1 view:1 set:1 art:1 computed:2 multiplied:1 sensitivity:1 comparable:2 roadmap:1 computer:1 quantitatively:1 discussions:1 close:1 best:1 pattern:1 rings:1 pisa:3 µs:3 atomistic:3 enough:1 smallest:1 between:1 probably:1 boundary:3 semiconductor:2 conditions:3 email:1 available:4 variability:3 ends:2 recently:1 reproduced:1 nature:1 however:1 yoon:1 gratefully:1 carbon:12 hundreds:2 last:1 2n:1 limits:2 density:1 equal:6 contract:1 relevant:1 point:1 appeared:1 armchair:1 semiclassical:1 framework:1 respect:3 suppressing:1 pp:9 decoupling:1 basis:1 pz:1 chirality:4 three:7 been:5 interest:1 electr:3 suppress:1 sufficient:2 precision:2 gap:21 confinement:2 baus:1 nanoscale:1 present:1 applied:2 align:1 voltage:4 engineering:1 value:1 will:1 while:2 behavior:3 tunneling:7 grigorieva:1 layer:1 lundstrom:2 almost:1 characteristics:5 graphene:20 fabricating:1 binding:4 ii:1 strain:11 cond:3 eras:1 seen:2 technology:3 orbital:1 different:3 italy:1 journal:1 suggest:2 same:3 highlighted:1 regime:1 showing:1 higher:3 literature:1 http:3 effect:10 hand:1 moment:1 compared:1 purpose:1 kim:1 robust:1 fabrication:2 recent:2 assumed:1 narrow:2 schr:3 largely:1 well:1 roughly:1 patterns:2 edge:11 model:3 recombine:1 lin:1 gates:1 proposed:1 accurate:1 obtain:3 gianluca:4 atomic:2 using:1 alternative:2 scattering:3 modulate:1 mosfet:1 han:1 tight:4 seems:2 eferences:1 capabilities:1 source:6 lett:4 electrical:3 useless:1 real:1 read:1 evaluate:2 couple:1 transconductance:2 inversion:1 cnts:3 confined:1 compressive:4 egap:4 dimensional:7 vds:12 steps:1 ouyang:1 experimentalists:1 giuseppe:4 works:2 reduced:2 sketch:2 because:1 simulator:1 klimeck:1 transport:2 pronounced:2 cnt:13 scale:1 cnr:1 realistic:2 affects:1 overlap:1 does:1 imputed:1 unipi:1 yields:1 esults:1 refer:1 sixth:1 informatica:1 oscillating:1 geim:1 boundaries:1 chiralities:2 properties:2 stage:1 comparison:1 about:1 valence:1 simulation:9 extensions:1 greatly:1 massimo:1 computational:1 letters:3 significant:2 into:1 within:2 integral:1 due:5 assess:1 proportional:1 additional:1 elastic:3 few:2 transfer:6 support:1 depicted:1 long:3 awarded:1 dispersion:2 width:9 phonon:1 fraction:1 etch:1 function:4 fundamentals:1 but:2 hu:1 films:1 nanotubes:3 atom:1 attainable:1 injection:1 consist:1 fabricate:1 characteristic:2 nanotube:5 devices:4 gaps:1 demonstrate:1 problem:4 similar:2 called:1 strongly:1 abstract:1 chan:1 thomsen:1 single:1 reservoirs:2 simulations:3 formalism:3 operation:1 cmos:1 physical:2 ev:4 nm:21 no:3 dashed:2 whereas:1 when:4 green:2 field:8 other:1 role:1 gnrs:6 elements:1 excitation:1 problems:1 ozyilmaz:1 important:1 peak:2 suppression:1 included:1 structure:1 required:1 holes:3 inset:3 observe:2 appl:1 requires:1 |
0704.1877.txt |@word homomorphism:1 consider:5 ede:1 equalities:1 results:2 leads:4 grateful:1 edu:1 partial:1 gl:5 row:15 certainly:1 compose:1 providence:1 graph:2 eigenvalues:1 equivalence:1 aus:1 present:2 under:8 connecting:6 analogous:1 undirected:1 presentation:4 lieb:1 discriminants:1 brown:1 updated:1 summand:3 orthogonal:6 very:2 crossings:1 choice:1 crosses:1 difference:1 erdmann:2 positions:2 notes:2 having:1 solution:2 vector:2 interchanging:1 indices:1 relation:1 setup:1 enjoy:1 carter:2 mail:1 direct:1 past:1 fold:1 zero:2 universit:1 linear:10 even:5 index:1 what:2 sub:1 chicago:2 trivial:1 section:1 slight:1 mw:2 d3:4 donkin:5 version:2 above:7 new:15 consisting:2 satisfy:4 full:2 lee:1 equals:2 here:4 ranges:1 modular:3 replacements:1 operating:1 groups:14 others:1 along:1 appears:2 change:2 contraction:1 obtained:5 generalizing:1 gln:41 my:1 larger:3 isotopy:1 amount:1 halverson:4 resulting:2 permutation:8 action:15 suitable:3 makes:2 brauer:29 sci:2 quotient:2 schur:50 via:4 although:1 family:3 apr:1 replace:7 bro:2 univ:1 hanlon:2 linearen:1 quasi:1 links:3 would:2 remains:1 positive:2 contains:2 only:1 vol:2 reductive:3 type:9 kostant:1 diagrams:31 more:2 duality:20 composite:5 submatrix:1 gruppe:1 surjection:3 berlin:2 particular:4 known:3 hold:1 iii:1 walled:5 springer:2 isomorphism:5 quantized:3 wassermann:1 originally:1 work:3 london:2 mu:2 remain:1 following:3 trans:4 root:1 example:4 reviewing:1 nearest:1 figure:11 stated:1 permutations:10 sln:12 depiction:1 numbers:5 spn:3 sense:2 handle:1 conversely:1 verlag:3 information:1 needs:4 csn:1 end:7 provide:4 acts:3 whence:1 braids:1 write:1 maps:3 varies:1 pure:2 cgln:6 parameter:2 specializations:2 csr:3 map:2 product:1 algebra:77 replacing:1 after:6 containing:3 cation:1 diagram:26 applications:1 inst:1 studies:1 demonstrating:1 coming:1 multiplication:7 representations:19 horizontal:6 types:1 sz:4 natural:4 outline:1 ss:1 sr:8 sq:5 dissertation:2 explicit:1 correspond:4 st:2 sk:3 rather:2 filtrations:2 green:2 sn:1 fundamental:1 keeps:1 sc:6 representation:14 sa:2 birman:3 order:1 restriction:1 duke:1 developed:1 over:10 michigan:1 vary:1 expects:1 years:1 through:1 left:7 japan:1 still:2 its:12 le:2 group:19 exclusion:1 adjoint:3 forms:1 stanley:1 constitutes:1 stephen:8 derivative:1 main:1 defining:1 into:1 semisimple:3 serre:2 good:2 return:1 intimately:1 murakami:3 similar:5 answer:1 they:1 oxford:1 now:1 easily:1 equality:1 name:2 2r:7 james:4 university:2 identified:4 labeling:1 composition:4 baxter:1 semisimplicity:1 each:8 found:1 entirely:1 side:3 associative:1 homogeneous:1 domain:1 weyl:21 formulate:1 osaka:2 idea:1 related:2 conventions:1 contracting:1 extended:1 ex:1 year:1 quantum:10 our:1 morton:1 special:1 out:1 rt:1 shown:3 tangle:1 jimbo:3 matrix:3 space:8 res:1 since:3 induces:3 denotes:2 blm:2 may:2 acting:3 adapt:1 rational:7 denoted:3 lecture:2 calif:1 ri:1 math:29 shows:4 wisconsin:1 theory:6 loyola:1 free:1 enveloping:7 admits:1 aachen:1 completely:1 base:1 york:1 imagine:2 ask:1 publ:1 combin:1 definition:1 tangles:1 dgs:2 determining:1 could:1 so:6 times:1 sequences:1 onto:2 think:2 first:7 already:1 features:1 number:5 multiplying:1 least:2 another:3 ring:2 precisely:3 open:1 given:7 allgemeinen:1 similarly:1 top:14 relations:4 their:2 statement:1 wenzl:4 speaking:2 gives:4 sl:12 continuous:1 part:3 differentiate:1 authors:2 iwahori:1 than:1 specify:1 connections:2 showed:2 double:1 second:2 preparation:2 arcata:2 yang:1 were:1 powers:1 formulated:1 sees:1 ann:1 ram:1 locations:1 endomorphism:1 enumerative:1 ringel:2 any:8 lie:5 leduc:3 der:2 internat:1 ideas:1 note:4 instance:2 ideal:1 take:2 interior:2 do3:2 do1:3 computation:2 formulas:1 unless:1 opposite:1 track:1 who:1 most:1 regular:1 connected:5 retaining:1 utilize:1 giaquinto:3 class:1 ka:2 macpherson:1 considered:3 coincides:1 vertices:26 km:2 points:1 principle:1 subgroup:1 fact:2 madison:1 show:1 queen:1 brief:1 manchester:1 centralizer:14 analogue:7 hereditary:1 d2:22 find:1 d1:22 ha:2 based:1 knowledge:1 ksr:2 homomorphic:1 jan:1 theme:1 annals:1 generators:4 pointed:1 columns:2 dn:1 do:1 dj:2 notation:1 dg:2 dd:2 simplest:1 tilting:1 joint:1 words:2 applying:4 dr:6 prime:1 die:1 fields:2 arxiv:1 twice:1 multiplicity:2 including:1 fixed:2 view:1 kernel:2 set:8 ser:1 signs:1 drinfeld:1 flip:10 observed:2 see:12 result:5 ebr:4 recently:2 centralizing:1 best:1 subject:1 lancaster:1 exploited:1 tensor:15 monoid:3 label:2 symmetric:6 enough:1 luc:1 various:2 between:4 invariant:1 geometric:2 approach:2 checks:1 knowing:1 ends:1 derangements:4 terms:3 hecke:2 vertical:6 comp:1 restricting:2 incident:2 ji:2 endg:2 amer:5 ja:2 last:3 2n:1 desired:1 many:3 quantization:1 stuttgart:3 admit:1 objects:3 figures:1 lusztig:4 context:1 otherwise:1 ci:9 cn:1 cl:2 simple:3 connection:1 address:1 cg:3 chakrabarti:1 dimensional:2 simply:4 quantizations:1 polynomial:7 moreover:1 bizarre:1 conference:1 pp:2 commutative:2 basis:7 tremendous:1 been:4 tensors:1 xδ:2 basic:2 ph:1 algebras:36 mary:1 define:2 surjective:1 generating:1 corresponding:6 commutes:1 doty:15 versions:9 bmw:3 chevalley:1 wales:2 obtainable:1 those:2 case:5 replaces:1 look:1 invariants:1 contexts:1 might:2 ǫn:8 deformation:1 will:4 while:1 replaced:1 situation:1 loop:1 wonder:1 correspondence:1 studied:3 almost:2 thus:8 dual:1 foreword:1 different:3 specialization:1 perhaps:2 cross:2 same:4 unity:1 html:1 split:1 modification:1 benkart:2 finite:4 subalgebra:3 events:1 symplectic:5 literature:1 http:1 hand:1 usually:1 edges:11 characters:3 infinite:3 opportunity:1 recent:1 kauffman:4 reprinted:1 idempotent:1 well:1 roughly:2 obviously:1 edge:5 endomorphisms:1 coordinate:1 position:1 con:1 dimension:4 monoids:2 usual:4 just:3 when:2 resp:3 obtain:3 actions:3 underlying:1 birmingham:1 integer:1 alternative:1 sullivan:1 previous:1 adv:1 preprint:1 algebren:1 had:1 liv:1 wall:9 dipper:3 other:9 lett:1 easy:1 semigroup:1 remaining:2 match:1 generalized:1 opp:1 quasihereditary:1 spanned:5 do2:2 knot:1 press:1 using:1 gr:2 advanced:1 occurring:1 abhandlungen:1 appearing:1 temperley:1 identifying:1 follows:3 permuting:1 statistics:1 yields:1 arbitrary:3 works:1 acad:1 berichte:1 www:1 right:5 often:3 classical:5 imaginary:1 sympos:1 some:4 back:1 pacific:1 b0:1 mixed:7 proper:1 category:1 thinks:1 happens:1 projection:1 bottom:14 darstellungen:1 though:1 multipli:1 does:1 decomposition:8 provides:1 proc:3 bd:3 shaker:1 power:1 intimate:1 equivalent:1 illustration:1 bw:2 br:34 inherent:1 relating:1 identifies:1 about:1 algebraic:7 column:2 oe:2 compatible:2 carries:1 identify:2 introduced:1 slightly:1 bimodule:1 organizers:1 subset:2 soc:6 cambridge:4 statements:3 inclusion:2 previously:1 ılinson:1 image:6 integral:9 isomorphic:2 son:3 appropriate:3 because:1 references:2 inverting:1 determine:2 rows:8 deal:1 module:13 combinatorics:2 removing:2 there:5 question:2 equation:1 appl:1 way:2 derangement:2 notices:1 was:2 naturally:2 jones:1 form:8 hr:2 regard:1 hw:2 tended:1 construction:2 link:1 removed:2 true:1 homfly:1 extend:1 arranged:1 uz:2 whether:1 characteristic:6 uq:3 up:1 us:1 bijectively:1 below:1 uk:2 problem:4 ua:1 called:1 obtains:1 uber:1 ac:1 proved:1 computing:3 defined:9 certain:5 abstract:1 describe:1 graphical:1 gesammelte:1 general:8 loops:4 single:1 together:2 research:1 commuting:2 check:2 defines:1 again:1 faithful:3 no:4 mathematik:1 separating:1 composing:1 illinois:1 field:5 valid:1 normal:1 mathematics:1 picture:1 elements:4 generates:1 expressible:1 sided:1 setting:1 vertex:3 polynomials:1 william:1 generated:2 tsukuba:1 ωfn:1 sides:1 structure:1 building:1 assume:1 factors:1 modules:8 rule:2 dρ:2 dramatic:1 presenting:2 original:2 |
0704.1878.txt |@word represent:4 partial:1 consider:2 springer:2 similarity:1 young:1 caused:1 particular:8 focus:3 existing:3 illustrated:2 computation:1 edu:1 follow:1 expressions:1 localized:1 row:1 compact:1 whose:2 certainly:2 inverse:8 calculate:3 integral:2 producing:1 tt:11 transferable:1 ts:33 nonlocal:15 vef:6 finally:2 investigation:1 those:6 under:1 tf:14 maryland:3 include:1 dramatically:1 divergent:1 division:1 straightforward:1 outside:6 very:31 vt:11 unaltered:1 none:1 results:39 electron:35 figs:1 prof:1 vlq:1 b864:1 bottleneck:1 exact:49 condition:4 four:1 differentiated:1 usa:1 unlike:3 presented:1 did:1 ref:7 notes:1 ri:2 large:14 ǫk:1 differential:2 robles:1 small:25 noted:1 foley:1 smaller:3 force:2 grateful:1 periodicity:1 transferability:5 direct:3 sign:1 approximation:2 second:11 cost:3 value:11 chen:2 further:6 bose:1 implemented:2 requiring:2 covalent:1 quite:2 inaccurate:3 even:4 dissertation:1 what:2 errors:10 adds:1 theories:1 section:5 reaching:1 near:5 expressed:1 uniform:14 current:1 version:2 lindhard:4 issues:1 above:1 new:6 subtracting:3 method:17 contrast:2 viii:1 body:10 edited:3 condensed:1 full:19 exchange:4 respectively:4 error:3 component:3 equals:3 orbitals:7 atoms:22 ionization:6 desired:1 explore:1 berkeley:3 path:1 along:3 lowmomentum:1 equations:6 appears:2 interpret:1 obtained:8 acharya:3 almost:1 noticeable:1 institute:1 larger:2 approaches:4 later:1 significantly:3 suggests:1 resulting:3 fˆ:7 tw:10 usually:1 complicated:1 fourier:11 changes:3 involves:2 king:2 useful:6 convolution:1 family:1 onebody:1 apr:1 problematic:3 natural:2 highly:1 scaled:5 rρ:1 kurth:1 support:1 total:16 tools:1 linearly:1 derivatives:2 use:20 indicated:1 would:5 prove:1 remains:4 positive:2 jpn:1 ψv:2 tail:2 next:2 predict:3 linear:14 therefore:3 vi:2 taken:2 means:1 theoretical:2 more:22 introducing:1 formally:5 vps:22 integers:1 thus:6 acceptable:1 factor:1 corrected:1 odinger:1 validity:1 surprisingly:2 tested:1 long:2 appendix:4 everywhere:1 normalized:2 varying:27 known:14 cases:5 hold:1 effort:1 analogous:1 supplemental:1 must:2 md:1 account:1 indicates:5 science:1 equation:8 work:6 actly:1 modified:4 cat:16 reproduce:10 remain:2 deficiencies:1 values:4 columns:3 ρv:26 following:6 making:1 arrive:1 root:1 example:2 perdew:3 ions:3 compare:5 weaker:1 wang:9 figure:11 give:10 process:2 choice:1 organized:1 high:9 sphere:1 satisfactory:1 performed:1 want:1 arise:4 dk:1 azquez:1 nonvanishing:1 respective:3 end:1 advantage:2 mape:4 fortunately:1 holds:2 feature:1 chemical:6 far:9 instead:4 absolute:4 parameter:9 pathway:17 weizs:2 oscillatory:3 levy:1 ft:2 mat:2 fw:2 may:7 thermodynamic:2 earlier:5 derived:1 mapping:2 alder:1 applications:4 produce:4 mae:2 designed:4 physik:1 bylander:1 cambridge:2 minimizes:1 wave:3 fl:5 response:18 efficiently:1 discusses:1 attempt:1 effective:6 ıa:2 description:1 lines:1 arrow:4 parameterized:2 their:4 provide:1 si:14 maintain:1 so:5 exchangecorrelation:1 allow:1 correlation:5 acknowledges:1 order:16 superscript:1 least:1 schwartz:1 considerations:1 henderson:1 developed:1 over:2 fft:1 vary:1 satisfied:1 cohen:1 stability:1 course:1 paper:4 including:2 argued:2 joubert:1 kinetic:34 still:3 its:8 regions:1 continuity:1 difference:4 rapidly:10 evans:1 decay:1 energies:11 solving:3 coordinates:1 li:1 forms:11 vts:21 noninteracting:9 lr:34 systems:32 lq:41 derivative:2 weeks:4 main:2 decades:1 easier:2 deviates:1 them:5 good:10 motivated:1 pauli:2 combination:2 lindgren:1 press:1 propose:3 dan:1 amenable:1 school:1 slight:1 garc:2 scaling:4 repulsive:1 subtraction:1 they:8 advantages:1 arriving:1 singularity:3 now:3 discuss:3 2s2:1 vidensk:1 easily:2 february:1 kps:15 dirac:1 alez:2 dreizler:1 always:1 university:5 level:1 leading:5 divides:1 magnitude:2 reasonable:3 radial:8 found:6 sham:6 cornerstones:1 typical:1 reproducing:1 homogeneous:4 el:1 square:1 eh:4 weight:5 fairly:1 scheme:1 energy:50 hard:1 reduce:3 idea:1 related:6 group:3 each:5 inhomogeneous:2 extended:6 connect:1 combining:2 quantum:3 laboratory:1 pseudopotentials:12 eq:48 out:4 try:1 shown:12 rp:2 αr:2 space:8 gradient:4 restricted:1 since:17 rev:30 cancels:1 research:1 fellowship:3 acting:2 vector:2 dominated:1 amplitude:1 rc:21 lecture:1 size:1 evaluation:1 correct:8 3s2:1 shows:6 virtues:1 after:1 a1133:1 theory:22 lawrence:1 hoffman:3 little:3 free:8 standard:3 ex:1 capture:1 completely:1 california:2 term:9 members:1 intermediate:2 acker:2 remainder:1 generate:2 additional:2 advance:1 r1:9 r2:15 ion:1 determining:4 could:11 selsk:1 harris:2 undesirable:2 friedel:1 unknown:2 dekker:1 discussions:1 ionic:1 incipient:1 first:7 major:1 initial:2 features:1 conditions:1 shapiro:1 omitted:1 variables:1 powerful:1 number:5 transform:2 ranges:1 improvements:2 done:2 construct:5 directly:8 electronic:1 several:3 illustrate:1 take:5 given:26 perturbation:8 checked:1 oscillation:2 table:12 similarly:2 introduction:2 dft:29 eqs:9 condens:2 system:26 vxc:4 needed:3 attack:1 perturbations:10 compromise:1 fermions:1 calculations:19 realization:1 percentage:2 variational:1 final:4 relations:1 gives:9 excellent:1 shell:12 grant:3 centered:2 detail:1 exactly:6 park:1 accurately:5 assumption:1 too:2 focusing:1 branches:1 tfw:11 believe:2 than:16 wide:3 john:1 determines:1 target:14 showed:3 approximations:11 likely:2 limiting:10 inversely:1 matter:2 determined:15 coulombic:1 supposed:1 str:1 were:4 radius:2 kf:14 treated:1 ev:8 boston:1 correction:3 conventional:1 turned:1 needs:1 alonso:2 outperforms:1 close:5 iii:5 seen:3 seem:1 clearly:2 relatively:12 chem:12 computationally:2 perrot:1 zero:1 depending:2 efficient:3 responsible:1 ideas:4 note:4 sciences:1 empirically:3 potential:44 best:2 analogy:4 online:4 performance:2 singh:1 yang:2 accuracy:6 δeh:1 kleinman:1 added:2 unless:1 components:4 though:4 any:2 logarithmic:1 satisfy:8 most:13 optimized:1 involving:2 significant:2 position:1 phase:1 analytically:1 class:4 inconsistency:1 deviations:1 cause:1 constructed:3 exc:6 surprising:1 considered:1 calculated:7 sometimes:1 ks:53 kr:3 kp:33 electrons:19 principle:4 exp:2 constrain:1 χl:3 physics:3 3q:3 fact:1 gain:1 thomas:5 structureless:1 show:4 text:1 supported:1 discovered:1 purely:1 minimizing:1 hohenberg:2 especially:2 data:2 find:6 ground:8 satisfies:2 q2:1 based:15 parameters:5 extending:1 implementation:1 λt:5 written:3 should:2 only:20 explicitly:1 inability:1 molecules:12 indeed:2 employed:2 constant:2 he:2 local:33 guided:1 achieve:2 meant:1 do:3 sharper:1 correctly:1 get:2 df:3 overall:1 da:1 unimportant:1 cannot:5 nearly:3 words:1 devising:1 combinations:2 conjunction:1 dr:12 justified:1 unfortunately:1 points:2 processes:1 pearson:1 densities:10 fields:1 arxiv:1 expansions:1 yield:1 summary:1 predicted:10 painter:1 through:1 fixed:1 require:2 transforms:2 properly:1 coefficient:1 requirement:1 set:5 computed:4 reference:4 achieved:1 physically:2 variations:1 national:1 maximum:1 relative:4 depends:3 justification:1 college:1 result:2 fail:1 recently:2 heavy:1 observed:1 nonlocality:8 incorporating:2 ability:1 closer:2 fails:1 satisfying:2 interacting:2 ways:1 nuclear:2 away:1 nature:1 functionals:6 grids:1 case:1 state:13 difficulties:1 various:12 markedly:1 closed:1 between:5 progress:2 boundary:2 approach:4 zunger:1 terms:5 reproduced:2 missing:1 2px:1 overestimates:2 weak:10 however:22 interpolate:1 carter:6 reproduces:2 derive:2 here:21 multiplier:1 virial:1 configuration:2 distribution:1 improve:2 both:14 prospects:1 last:2 limits:8 reported:2 many:7 region:3 conclusions:1 2kf:4 called:1 chosen:6 involve:1 dated:1 expand:1 beyond:2 mg:3 argue:2 expression:2 5w:13 sci:1 among:1 relevant:3 point:2 simple:16 address:1 cf:5 environments:8 parametrization:1 semiclassical:1 simply:2 boson:3 lagrange:1 proved:5 largest:2 throughout:1 expensive:3 xe:1 better:6 ensures:1 described:8 arbitrary:1 three:1 been:16 screened:2 devise:1 reduction:1 much:8 slowly:18 change:4 interest:1 basic:3 λtt:1 ph:1 unchanged:1 fig:15 generating:2 chai:4 corresponding:12 δts:1 quantities:1 natl:1 gas:7 essentially:4 δtt:1 determination:1 external:8 systematic:1 mail:1 constructing:1 improved:2 spin:1 dmr:1 present:4 applied:3 regimes:1 look:1 exponential:1 developing:1 solid:5 reliable:1 appearance:2 empirical:1 profiles:4 choices:4 will:20 technical:2 while:6 encountered:1 momentum:2 behavior:2 promising:2 report:1 investigating:1 eik:1 tλ:3 taking:2 procedure:4 stott:3 pratt:3 studied:1 costly:1 handy:3 coupled:3 vh:4 molecular:4 von:2 abrahams:1 kohn:7 non:1 iv:7 ii:4 need:2 ik:1 itself:2 cond:1 vw:14 limit:7 vanish:1 technology:1 fermion:1 teter:1 orbital:13 ne:3 different:8 develop:3 pseudopotential:9 perform:4 acknowledgments:1 fundamentals:1 lett:2 same:9 orders:1 selfconsistent:1 another:1 complex:1 arguments:2 widely:2 vext:14 units:1 dimensionless:3 regime:11 difficult:2 development:1 independent:1 used:37 suggestion:1 see:12 again:2 mtf:5 numerical:8 effect:1 hand:1 parametrized:2 average:1 codes:1 uses:1 potentials:11 infinite:2 hartree:4 normalization:2 recent:1 prescribed:1 linearize:1 suitable:1 schr:1 fys:1 no:10 well:3 phil:2 thought:1 incorporated:1 solids:7 materials:1 solve:4 diatomic:1 consistency:1 coordinate:2 quantitative:2 model:30 chemistry:5 arising:5 latest:1 lda:1 λw:4 proposed:10 less:3 being:1 generally:3 accurate:20 drdr:1 obtain:4 isolated:3 oxford:1 noble:2 atomic:31 predicts:1 immediately:2 differentiation:1 yet:1 previous:1 profitable:1 york:1 kluwer:1 density:128 emily:1 practice:1 workers:1 cl:1 seems:3 fitting:1 improvement:1 wavevector:8 color:4 analogue:1 valid:2 combine:2 treatment:4 easy:3 theorem:2 reason:2 input:4 mod:1 remaining:2 euler:6 gave:1 real:1 kaxiras:1 asymptotically:1 insensitive:1 mrsec:1 coulomb:2 ρks:6 advances:1 ceperley:2 possible:4 usefully:2 test:3 increases:1 predetermined:1 transfered:1 burden:1 mol:2 wavevectors:8 using:40 unique:3 moreover:1 δexc:1 helpful:1 tarazona:2 alexander:1 like:6 δv:2 reduces:1 yields:2 either:1 view:2 become:2 valence:42 reasonably:2 therein:2 indications:2 right:1 often:2 deal:2 smoothly:1 successfully:1 some:11 sensitive:2 acad:1 evaluated:2 parr:3 respect:2 oscillations:3 march:3 viral:1 gradually:1 scale:1 lead:1 bottom:3 herring:6 opposite:1 fluids:3 comments:1 models:51 does:4 connecting:1 bridges:1 provides:1 tends:1 indication:2 proc:3 refer:1 limitations:1 core:19 replaced:1 nonuniform:3 location:3 wavefunctions:1 notable:1 agreement:3 expansion:1 although:2 approximating:1 properties:2 gained:1 comparison:1 about:5 a1:4 carried:3 tf1:12 getting:1 commun:1 discussed:4 dependence:4 o:8 practical:1 range:4 a2:4 ensure:1 obeys:1 nucleus:8 efforts:1 introduced:3 zv:3 automatically:1 peak:1 lieb:1 integration:10 soc:3 computational:5 into:4 within:1 numerically:4 functional:22 nsf:2 due:3 assess:1 appropriate:1 because:8 references:2 determine:6 vp:1 conceptually:1 jeng:1 methods:15 rely:1 regarded:1 classical:3 her:1 assumed:1 suffice:2 there:11 approximate:4 fast:2 medd:1 tails:1 strict:1 quadratic:1 low:7 way:8 was:5 naturally:1 function:22 considerably:1 elsewhere:1 form:13 offer:1 vanishing:1 hq:42 but:18 hoped:1 expected:3 construction:2 profile:2 underestimates:1 solved:2 atom:9 removed:1 considerable:1 partially:2 partitioning:1 made:4 compute:1 qualitative:3 evident:1 sears:1 inside:2 smooth:6 up:2 verlag:2 below:5 salomonson:1 fermi:9 problem:4 similar:5 clear:2 expect:2 detailed:2 chac:4 ac:1 ab:6 associated:4 worthwhile:1 ln:2 defined:6 certain:1 universal:1 describe:7 chan:1 metals:1 general:9 single:4 ar:8 exist:2 dλ:2 our:15 crystals:1 distributions:2 check:1 gonz:2 physical:4 incorrect:1 traditional:1 functions:3 compared:5 completeness:1 variety:4 biochemistry:1 na:1 nc:5 when:11 vanishes:1 graduate:1 field:4 other:25 details:1 branch:3 becomes:2 department:2 deviate:1 nv:6 conclusion:2 poor:1 briefly:1 elements:1 generates:4 zhou:2 separate:1 initio:6 finite:1 setting:1 problems:2 madden:3 replace:2 a0:4 generated:3 important:3 invested:1 pathways:11 averaged:1 cores:1 generalized:2 structure:12 rq:2 jones:1 coupling:5 partitioned:1 required:1 rather:1 berlin:2 together:1 4q:2 gross:1 inset:3 arisen:1 understand:1 nuclei:2 mean:4 requires:3 original:2 once:4 |
0704.1879.txt |@word holds:1 hugh:1 over:2 both:1 results:5 known:1 paper:2 solutions:1 λk:2 expressions:1 find:1 subtracting:1 interscience:1 specifically:1 considered:1 analytic:1 series:1 eigenvalues:1 seems:1 indagationes:1 actually:1 lemma:7 complex:1 certain:2 systems:1 under:2 attained:1 circle:1 remaining:1 norm:2 first:2 real:3 do:1 non:4 than:1 get:2 very:1 fulfills:1 between:2 sums:5 term:5 obtain:9 newman:1 answer:1 corollary:7 sons:1 putting:1 max2:1 identically:1 using:3 now:4 matrices:1 bigger:1 2mm:2 prime:1 february:1 dc:1 follows:12 university:1 arxiv:3 2b2:7 large:3 sufficiently:1 theory:2 inequality:1 yields:1 math:8 reasonable:1 2m:3 2n:5 αn:1 equation:8 mathematical:1 kernel:5 zn:1 right:3 methods:1 ten:1 zk:12 mathematicae:1 some:5 b22:1 maximum:1 b4:3 see:9 result:3 b2:13 combining:1 discussions:1 further:2 estimated:2 eq:1 paul:2 best:1 er:6 erd:1 appear:1 sum:8 since:5 while:1 yet:1 henceforth:1 halves:1 written:1 harmonic:1 tends:1 values:2 construction:1 increasing:1 method:4 minimal:1 stockholm:1 choose:2 bi:1 wiley:2 bound:11 2b:1 power:13 bl:1 problems:4 tur:9 limα:1 diagonal:1 bj:1 bk:9 regional:1 b2k:3 york:2 references:1 limitation:1 interface:1 hal:1 estimate:2 equations:1 z1:1 interval:1 publication:1 chapter:1 definition:2 remark:2 last:3 sharper:1 vera:1 am:5 theorems:1 allows:2 o:8 side:3 published:1 ab2:4 improves:4 together:1 hence:1 bounded:1 contribution:3 slightly:1 explicit:2 otherwise:3 ck:2 there:2 cn:2 2nm:1 upper:5 apr:1 anda:2 hungar:1 washington:1 number:3 cbms:1 lies:1 2a2:1 approximately:1 another:1 bν:1 improvement:1 unit:1 conference:2 kernels:1 use:6 asymptotic:1 second:2 prove:5 introduction:1 positive:4 asz:1 cassels:1 fej:6 negative:4 been:2 defined:1 board:1 assumption:1 fraction:2 likewise:1 πx:1 john:1 revisited:1 possible:1 gives:3 function:5 θk:3 θi:1 corresponding:1 αn2:4 furthermore:2 estimates:1 theorem:15 independently:1 new:3 gap:1 volume:1 part:1 aequationes:1 particular:3 mb4:2 2n2:2 acta:1 general:2 true:2 former:1 negativity:2 must:2 case:12 valued:2 improved:1 mm:9 andersson:10 bounds:6 us:7 will:14 minimize:1 sweden:1 suppose:4 whether:1 following:4 problem:2 more:1 similar:1 example:1 assistance:1 proof:8 θj:1 mink:1 proved:5 give:3 szalay:1 numerator:1 abstract:1 thus:2 νx:1 pintz:1 denote:1 ii:2 need:1 minimum:2 exist:2 numbers:3 our:7 close:1 analysis:2 inf:9 absolute:1 foreword:1 asked:1 functions:1 constructions:1 θl:1 min:1 unbounded:1 convenient:1 means:1 when:7 same:1 montgomery:4 write:1 sciences:1 interested:1 b12:1 take:1 pure:6 contrasts:1 department:1 mathematics:3 inc:1 nt:3 sin:2 difficult:1 lectures:1 investigated:1 infinity:1 max:23 sided:2 denominator:2 upon:2 hand:3 applications:1 a2:25 αmm:1 value:1 unimodular:2 previous:1 fm:5 constants:1 constant:1 lower:13 n3:1 implies:7 third:1 assume:5 os:2 clear:4 page:2 stronger:2 su:1 obviously:1 4m:2 fact:4 decreasing:1 representation:1 n2:13 johan:4 its:1 section:2 se:2 applied:1 |
0704.1880.txt |@word secondly:1 exponentiation:1 magnetic:3 desirable:2 four:1 entropy:11 consists:1 whose:9 olshanii:2 const:2 calculate:1 daley:1 under:6 slowest:1 worth:1 conjecture:2 dynamic:1 rise:2 iτ2:1 dell:1 iτ1:1 every:2 cause:1 z12:5 solution:2 vector:1 force:1 consistent:3 direct:2 approximation:4 second:4 correlator:2 even:4 interatomic:1 above:4 new:4 coefficient:1 equals:4 here:7 atoms:3 reported:3 osterloh:2 j2r:3 represented:1 path:5 logarithmic:4 obtained:15 study:12 approaches:2 reports:1 ignoring:1 stressed:1 fourier:5 changes:1 projection:2 explained:1 highly:3 rτ:1 total:1 unit:1 kollath:5 plot:2 would:8 cirac:3 negative:1 m0:40 m2:17 until:3 separated:2 relax:3 successful:1 aware:2 interaction:1 excellent:1 hold:2 must:4 work:4 theories:4 macroscopically:2 modify:2 mr:1 exceptions:1 im:9 root:3 example:14 mz:2 renormalization:7 give:9 relativistic:1 organized:1 generically:2 times:27 aging:1 end:4 provide:2 travel:1 feature:3 how:6 ordinary:3 gordon:1 description:1 replacing:1 thermodynamic:3 oscillators:5 after:11 dietrich:2 diagram:1 italy:1 law:6 parallel:1 constants:1 third:1 complexity:1 correlation:45 order:19 interpretation:5 over:7 xi:2 london:2 resummed:1 satisfies:1 before:5 πr2:1 fix:3 expectations:1 quasiparticle:3 fig:10 imw:1 imz:1 emphasize:1 maximal:1 eventually:3 them:2 affected:1 greiner:1 effects:12 they:9 represents:1 netherlands:1 each:2 side:1 mean:8 independent:3 series:1 rieger:1 literature:2 content:1 re:1 rg:12 reader:1 ri:5 sinh2:4 turning:1 free:10 standard:2 formation:1 r2:3 chiara:1 correctness:1 arccos:1 corrections:3 uses:1 onto:1 speeds:1 already:7 features:8 lewellen:1 primary:18 thereof:1 restrict:1 adopted:1 another:8 revival:2 top:2 needed:1 confirming:2 ballistic:1 too:1 postulate:1 john:1 πw:1 collapse:2 tool:1 subleading:2 predictable:1 maximizing:1 distance:12 scenario:4 showed:2 zero:14 matter:4 classes:4 iωk:1 displays:2 quench:16 mind:2 manner:2 seen:2 relatively:2 realm:1 maxk:1 forces:3 residue:1 shall:2 denominator:1 phase:14 luttinger:4 cazalilla:1 observation:2 calculated:6 points:14 principle:3 sum:2 borgonovi:1 labels:1 solutions:1 calculable:1 substituting:1 tempted:2 d3:1 finally:6 explain:2 zwerger:2 topological:1 dn:2 do:5 dk:30 di:2 dd:5 de:1 despite:7 report:2 dp:9 unfortunately:2 normalizable:1 girardeau:3 nicely:1 fields:1 acknowledgments:1 analytical:8 thanks:1 reference:1 dziarmaga:2 observed:1 depends:11 w3:1 w2:2 w1:5 best:1 subject:3 tensor:2 propagates:1 simplest:3 c2k:2 approach:10 terms:10 extend:2 nature:5 eipk:1 however:16 wi:2 eipr:5 extent:3 bose:8 essentially:4 irregular:1 against:1 calabrese:4 receives:1 casimir:2 enolskii:1 0k:9 contribution:2 com:1 diffusive:1 appeared:1 excess:1 applicability:1 j02:1 basis:4 three:3 been:27 ansch:1 much:4 interest:3 basic:1 expected:6 eπt:18 θi:1 quantities:4 concerning:2 coherent:4 worked:3 spin:13 applied:2 exception:3 originate:1 excited:2 aim:1 euclidean:3 near:3 suppose:2 applies:7 property:3 procedure:1 cylinder:4 played:1 ip:1 ir:2 iv:5 ii:4 ik:1 cond:45 cone:6 conn:2 perform:2 things:2 make:2 complex:5 quant:6 ripoll:1 mixtures:1 several:6 grows:1 evolve:5 numerical:4 hand:2 insulating:1 normalization:3 whereby:1 hopping:1 campo:2 academic:2 feshbach:3 monthus:1 dominating:1 studying:3 quantitative:1 left:8 burrell:1 just:11 newton:1 σ0z:4 transforms:3 scattering:3 previous:15 elk:1 unique:1 infinitely:1 weiss:2 transformed:1 easy:3 iπ:1 iτ:1 cramer:1 contrarily:1 possible:9 firmer:1 collisional:1 replace:2 apart:1 appearing:1 performing:2 harmonically:1 specific:7 steps:1 arbitrary:4 right:5 cooper:1 bottom:1 investigations:2 everything:2 linearly:1 gapless:2 core:2 interferences:1 oscillating:5 dorner:1 properties:4 anomalous:2 o:26 essential:1 horizon:6 connected:16 lieb:2 presence:1 kuznetsov:1 obtaining:2 bath:1 down:3 amsterdam:4 often:1 rely:1 initial:23 transform:4 why:3 width:2 accordingly:1 way:8 was:9 therefore:3 only:30 form:12 denoting:1 heat:1 illuminating:1 true:5 absent:1 inside:1 maximum:4 simplifying:1 originating:1 conserves:1 convergent:1 conserved:3 exist:3 dθ:2 commuting:2 check:3 vengalattore:1 physical:5 nk:11 eventual:2 no:4 na:1 generally:2 vanishes:7 perturbative:2 interested:1 role:5 papers:1 shrink:1 picture:9 models:20 preceding:1 palma:1 variable:1 longer:1 assume:5 dτ:3 governed:3 exponentiate:1 time:114 observables:7 logarithms:1 chain:16 varying:1 souls:1 leads:1 inverse:4 depend:2 clarification:1 zone:4 recurrence:1 charge:4 elliptic:3 broadly:1 choice:4 exact:9 annihilated:1 europhys:2 riemann:1 level:3 turns:1 anisotropy:1 discrete:1 naber:1 science:2 governing:1 upper:7 findings:6 prediction:2 cosh:32 appear:1 g21:2 xπ:2 xφ:1 goes:1 falling:1 abrupt:1 realizations:1 understanding:6 along:1 change:2 sending:1 institute:2 smerzi:1 studied:5 eisler:1 unitarily:2 pasquale:1 pictorial:1 usually:1 resonance:1 plotted:1 useful:1 ipk:1 f2:1 ipr:4 translational:2 quenching:3 sake:1 eπ:2 explicitly:7 films:2 theoretical:7 introducing:1 molecules:2 apparent:1 validity:1 yurovsky:1 cases:6 insights:3 oscillator:1 modified:1 values:16 following:11 making:2 arrive:1 nearest:1 figure:1 predict:1 4t2:1 topic:1 performed:3 allowed:2 feiguin:1 fortunately:1 discussion:4 exceptional:1 write:5 pure:7 parameter:18 map:3 product:6 mat:45 may:11 residues:1 applications:1 ω2k:10 date:2 revealed:1 βeff:16 kurn:1 stress:4 natural:4 outline:1 liquid:2 maybe:1 explicit:2 so:18 sn:2 representation:2 typical:8 breaking:1 subsections:2 indeed:3 ttt:3 stability:1 course:4 experiments:1 statistical:4 differs:1 cold:2 still:9 group:12 interesting:10 decreases:1 forms:1 window:1 main:1 kasevich:2 non:31 introduce:2 scaling:13 a0k:9 half:10 arriving:3 now:6 discuss:6 developments:4 term:10 corners:2 wolfram:1 spinor:3 domain:1 weighted:1 ei:5 fixes:1 revised:1 gaussian:14 eb:1 iπk:1 approximated:1 eq:35 ep:1 shown:5 impurity:2 space:15 furthermore:5 transforming:2 investigation:2 emerged:1 suggesting:1 correct:2 shows:5 earlier:1 theory:26 fisica:1 possibility:1 quite:5 complicated:2 care:1 language:2 transition:9 motion:6 massive:3 think:1 first:20 origin:1 simplifies:6 xo:1 symmetry:3 striking:1 xb:3 variables:2 waves:2 xe:1 xy:8 simplified:1 fast:3 directly:4 impossible:1 open:5 size:1 given:21 necessarily:1 checked:2 anderson:2 2ωp:1 1d:7 white:1 speaking:1 gives:11 continuous:2 transverse:9 released:1 than:12 connections:1 effective:15 superfluid:1 cardy:8 future:5 were:2 generality:1 correction:3 bcft:1 argument:13 generalization:1 crossover:1 slab:12 any:14 numerics:2 subsystems:1 efficient:1 note:20 take:5 destroy:1 modulus:1 dzero:1 opposite:2 decreasing:1 successive:1 analytically:16 inserted:2 considered:22 average:2 later:2 typically:1 laws:3 precise:1 2m0:2 show:7 spaces:1 rounded:1 ground:12 slow:1 ratio:4 aφ:12 written:6 analytic:6 quasiparticles:1 going:1 normalizations:1 correctly:1 2mt:1 get:13 expectation:14 cannot:1 progress:3 attitude:1 predicted:1 mapped:2 physically:3 j0:4 j1:3 j2:2 bounds:2 relative:2 college:1 concern:2 ωj2:1 y2:1 subsequent:1 review:2 sites:1 boundaries:1 enough:3 between:2 fermi:1 diagonalized:1 across:2 multiplied:1 tsun:1 domb:1 concentrate:2 suppressed:2 σj:4 circumference:1 tractable:2 many:4 region:9 according:5 σz:5 dated:1 expression:3 comes:3 among:6 gangardt:1 characterization:1 continuation:8 period:2 translationally:1 grants:1 lagrange:1 moreover:1 considering:4 locally:1 cosine:3 damping:1 sachdev:1 borders:1 direction:4 oρ:1 external:3 evidence:1 those:7 case:58 developing:3 profiles:2 squeezed:1 eik:1 conformal:27 coupled:8 characteristics:1 couples:2 sudden:2 binary:1 different:18 propagation:1 same:20 arguments:2 regime:2 extended:3 trivially:1 driven:1 entanglement:13 changing:2 invariance:6 relies:1 modes:2 largely:3 random:3 roughly:2 without:1 solve:1 model:38 wessel:1 dimension:11 justify:2 comment:3 uhp:20 being:8 when:12 rest:1 speed:6 nonadiabatic:1 zoller:1 upton:1 ω0k:16 except:1 unambiguously:1 treatment:1 ruschhaupt:1 eigenstate:1 momentum:9 kingdom:2 thermalized:1 harmonic:5 vidal:2 confined:3 using:10 saleur:1 mod:1 particle:2 collective:1 either:1 integrals:4 always:5 stationary:5 reduced:1 reaches:1 moving:1 images:1 dimensions:15 eiθ:1 extensively:1 initio:3 critical:31 bessel:2 refer:1 power:8 equivalent:3 hansch:1 notable:1 broken:2 2m:2 refers:1 tonks:3 2n:3 vishwanath:1 central:4 ferromagnetic:1 krech:2 discussed:5 generated:1 greatly:1 neighbor:2 mixed:1 inclusion:1 yuzbashyan:3 numerically:1 dissipation:1 references:1 pathintegral:1 determine:1 strip:17 operator:15 nowadays:1 hep:1 log:10 prepare:1 assumed:2 there:12 dispersion:12 start:4 low:1 lot:1 complete:5 2vm:3 2vt:7 trying:1 dissipative:2 lukin:1 ωp:3 dφ:1 ωk:40 ωj:1 regimes:1 detailed:2 ac:1 diverges:1 certain:1 ak:16 describe:4 am:3 deep:2 general:34 formulation:1 again:3 completeness:1 field:48 d2k:4 valid:6 spatial:3 massless:2 peschel:1 briefly:2 fazio:2 berman:1 ote:1 a0:9 important:6 ising:19 igloi:2 included:1 barouch:4 curve:1 mass:5 izrailev:1 coherently:1 gericke:1 consider:21 trigonometric:1 scalar:3 commute:1 generalize:5 barankov:2 reasoning:1 particles:12 tt:2 equivalence:1 tr:7 tj:1 th:3 sound:2 global:1 amplitudes:2 straightforward:1 very:18 conjectured:2 induce:1 ultracold:2 difference:3 condition:12 hamiltonian:16 t2:3 t0:1 t1:4 large:41 2k4:4 2k0:1 p06002:1 rate:1 enhancement:1 further:1 bilinear:1 what:8 section:13 method:4 contrast:3 quenched:3 condensed:2 full:6 component:2 ansatz:1 quenches:6 relaxation:12 directions:1 strong:3 equations:1 allows:3 widera:2 periodic:2 manmana:2 action:2 specialize:1 via:4 suddenly:1 put:2 shlyapnikov:1 environment:1 distinct:1 quasi:12 comparing:1 nucl:1 taken:3 more:13 muramatsu:3 operators:16 surprisingly:1 particular:3 known:8 evolves:1 recovering:1 recall:2 remain:2 del:2 spontaneous:1 compare:2 rodriguez:1 states:5 numbers:1 sharp:2 robinson:1 axis:1 information:1 needs:1 advantage:1 rather:7 acts:2 βωk:2 liniger:1 explains:3 ensemble:11 simplicity:6 algebra:2 derived:1 mapping:12 φ2r:1 plane:16 coming:2 fm:5 short:5 resemble:1 perhaps:1 extrapolation:2 fundamental:2 playing:1 itj:1 help:3 quasiperiodic:1 soon:1 thermal:6 paper:5 through:4 existence:2 kibble:1 excitations:4 its:9 rapidly:1 continued:11 boson:5 actually:1 late:2 absence:2 systems:24 jacobi:3 good:1 motivated:1 gibbs:11 universality:8 reflected:1 framework:1 cosh2:3 oxford:3 2t:12 easily:5 2v:10 finite:21 2p:2 characterizes:1 presented:2 2x:6 2e:1 2b:1 found:7 universit:1 characterized:2 subsystem:1 generation:1 energy:16 hard:3 idea:3 expect:4 sketched:1 quantum:46 beyond:4 really:1 meijer:1 solved:1 since:13 denotes:1 dominated:3 induced:1 occurs:2 belief:1 localization:1 extraordinary:4 reason:2 auerbach:1 imagine:1 ask:1 guest:1 conformally:2 exponentially:11 consequence:5 dipartimento:1 integrand:1 major:1 thereafter:1 number:10 done:3 defects:1 zi:3 temperature:25 introduction:1 leading:9 least:3 assumption:4 calculations:4 scheme:1 exponents:1 observations:1 wenger:2 optical:6 sign:3 higbie:1 lebowitz:1 diffusion:1 kind:4 supposed:2 toward:1 treated:1 peierls:1 2t1:1 levitov:3 2t2:1 elsevier:1 cumbersome:2 cft:26 self:1 h21:1 extracted:1 k0:2 build:1 k4:6 unconstrained:1 play:2 towards:2 quote:1 measures:1 reach:2 most:11 eisert:2 measured:1 stands:1 clear:2 saturate:1 universiteit:1 kr:3 part:6 exp:2 velocity:7 physics:7 lying:1 particularly:1 phenomenon:5 relation:12 find:4 bravyi:1 causality:2 parameters:2 subsection:3 factor:6 integrable:10 dominant:2 gains:1 notation:1 dependent:11 zurek:3 ϕr:9 ϕm:2 ϕn:6 amico:2 ϕh:10 closely:2 combinations:1 during:3 coth:2 continuum:8 arxiv:1 garcia:1 common:1 activity:1 set:5 achieved:1 undergoes:1 see:16 sec:8 close:11 contour:2 currently:2 pisa:2 smallest:1 probably:1 conditions:28 available:5 ikr:1 recently:1 plastina:1 complementary:1 complement:1 attention:1 vanishing:6 ferromagnet:1 both:6 last:3 sensitive:1 context:1 extracting:1 whole:2 finds:1 experimental:4 sinh:4 point:66 simple:18 asymptotically:2 corresponds:12 dimensional:21 simply:6 pr:1 ensures:2 described:7 transformations:2 lattice:24 due:2 strategy:1 pc:1 describes:2 anisotropic:2 pk:7 ph:6 pn:1 lett:24 gas:5 gap:4 2im:1 understand:9 systematic:1 2ǫh:1 equilibration:1 p2:13 intriguing:1 look:2 exponential:10 ǫi:1 ǫh:3 while:6 behavior:31 loop:1 real:34 unitary:2 approximate:2 vol:1 von:1 reads:2 rij:1 vanish:3 fermion:3 twofold:1 grant:1 orders:1 virtually:1 modification:2 resulting:10 higher:4 development:1 used:4 olling:1 flows:2 liquids:2 purpose:1 robust:1 recent:4 lower:1 analysis:6 exponentials:1 oscillation:1 hastings:1 distances:1 reviewed:1 questions:4 alternative:1 conclusions:1 source:1 theorem:2 solvable:10 transformation:5 generalized:12 evaluate:1 showing:1 matters:1 entangled:4 synchronization:1 imposed:2 semi:2 follows:3 adiabatic:1 separately:1 continue:2 unstable:1 popular:1 disorder:3 reduces:3 spins:1 mathematical:1 methods:7 absolutely:1 some:20 back:1 understood:2 examples:4 oscillations:8 pronounced:2 scale:5 hypercubic:1 though:1 behave:1 bl:1 jumps:1 continuing:6 agreement:1 step:2 subtract:1 hilbert:1 bz:2 kinoshita:2 simulation:2 range:5 consequently:4 bloch:3 therein:1 computational:1 into:4 within:3 integral:21 predictions:2 appropriate:2 proportional:3 extremely:1 question:5 long:12 bosons:4 forward:1 analyze:2 sections:3 elsewhere:1 governs:1 repeatedly:1 line:1 relaxes:1 infn:1 2πg:1 characteristic:3 2πk:1 up:3 us:15 autocorrelation:2 fluctuations:6 similar:3 called:5 constant:3 defined:3 microscopical:1 globally:1 engineering:1 2ωk:10 formalism:1 multipliers:1 application:1 explaining:1 draw:1 elements:1 problems:2 prepared:2 meaning:1 allowing:1 structure:5 independently:3 correlated:3 gapped:3 far:11 requires:1 normalized:1 partial:1 gr:1 results:32 existing:1 illustrated:1 gn:4 contributions:2 lamacraft:1 gases:2 concerned:1 cradle:1 stable:1 include:1 probe:1 wave:4 matrices:1 incoherent:2 noted:1 disordered:8 zj:1 zk:2 seventies:2 sin2:14 dynamics:37 plays:1 superlattices:1 giving:2 analogously:1 consistently:2 slabs:1 3d:1 body:3 exchange:1 respectively:1 spacing:2 cubitt:1 separation:5 consideration:1 sine:1 z1:33 z2:26 technical:3 involved:1 larger:3 suggests:1 products:2 opinion:1 makes:1 involves:1 scales:1 apr:1 worthy:1 addressed:1 condensates:4 apply:1 tools:4 use:7 asymptotic:29 few:6 depicted:1 expanding:1 simpler:2 zij:1 bethe:1 eiωk:1 becomes:1 labelled:2 iii:3 hints:1 account:3 integrating:4 diehl:2 reproduce:1 thin:1 drops:1 averages:1 proof:3 weaker:1 calculation:10 high:1 effectively:4 lorentz:1 united:2 decaying:2 holds:1 πk:1 regions:1 instead:5 mccoy:3 sin:22 oz:1 profile:4 epsrc:1 verstraete:2 realized:1 computations:1 light:6 separations:2 correspond:3 integrability:1 encyclopedia:1 allow:3 nonequilibrium:2 ϕk:4 interpreted:1 symbols:1 saturates:1 lattices:4 mentioned:1 minguzzi:1 decay:5 chosen:1 lm:4 lk:10 eisenriegler:1 degrees:4 derivative:1 outlined:3 das:1 february:1 university:2 l2:1 mode:6 crossing:1 constraints:1 sadler:1 einstein:5 related:5 decays:4 static:1 tsou:1 our:10 transitions:2 eiht:2 out:7 matrix:9 rev:40 posteriori:1 rel:1 adaptive:2 tuchman:2 ref:19 interactions:3 diagonal:2 altshuler:2 clarify:2 completely:5 surely:1 demler:1 dirichlet:6 geometry:10 could:2 m20:6 keep:2 length:5 osborne:3 isotropic:1 hence:1 rudolf:1 dunjko:1 powerful:4 iht:3 p04005:1 blows:1 πc:2 unknown:1 condensate:9 πn:3 system:22 relations:3 πm:1 πr:33 their:8 attack:2 intermediate:1 fermions:2 πt:18 πx:9 perfectly:1 final:3 exactly:9 dynamical:2 fermionic:3 amplitude:3 leslie:1 providing:1 result:31 exhibit:1 gerbier:1 sen:1 need:10 clearly:5 gritsev:1 pursued:1 able:2 mechanism:1 concerns:3 reproducing:1 heisenberg:4 lectures:1 centre:1 σrz:2 rigol:4 polkovnikov:3 altman:3 propagate:2 class:5 exponent:1 subtracted:1 fact:23 superfluidity:1 emerging:1 supported:2 purely:1 rough:1 trivial:5 knowledge:1 should:9 candidates:1 muga:2 tune:1 employed:1 sengupta:2 local:12 equilibrium:16 means:6 ones:3 brillouin:1 years:1 procedures:1 produced:1 evolution:37 densities:1 expansions:1 calling:1 stamper:1 contain:1 nightingale:1 fixed:21 view:2 2p2:2 motions:3 exists:1 correlations:18 exploited:1 interacting:4 diverge:2 state:51 closed:2 crude:2 invariant:8 boundary:66 ends:1 2pt:2 emitted:1 reproduces:1 configuration:1 problem:8 observable:2 limits:2 freely:1 taking:6 equal:3 rams:1 dmrg:3 ln:6 safely:2 grounds:1 ck:18 strongly:6 relevant:4 cn:1 conclude:1 wall:1 cf:1 chakrabarti:1 ab:3 respect:4 geometries:2 addition:1 cauchy:1 slowly:1 orzel:2 arises:1 corresponding:4 tµν:3 sufficient:1 coherence:1 cos:49 bulk:10 finished:1 present:1 multi:1 value:23 will:19 ultra:1 almost:3 vi:4 refs:3 vk:5 thus:34 vm:6 surface:5 equilibrate:1 vt:2 dual:1 φr:2 hubbard:1 generic:5 pauli:1 largest:4 φi:5 gets:1 powell:1 difficult:3 http:1 effect:12 delft:1 infinite:5 identity:1 paredes:1 mech:5 off:2 well:7 firstly:2 position:2 arising:1 usual:1 magnetization:4 less:4 accurate:1 obtain:10 sources:1 predicts:1 vπ:1 density:16 thermodynamics:1 add:1 noack:2 diagonalization:2 details:3 identical:1 criticality:4 increases:2 know:6 immediately:2 insert:1 necessary:1 like:7 exploiting:2 qualitative:1 δk:4 become:1 works:3 soft:1 replacement:1 accessible:2 because:11 classical:2 kdk:1 phenomena:5 murg:1 proper:1 neglecting:1 happens:2 lead:1 leaded:1 esf:1 does:11 francoise:1 assuming:1 chains:6 trap:1 noise:1 expansion:12 although:1 offset:1 imaginary:12 σix:1 panel:2 actual:3 carried:1 saddle:2 freedom:4 dependence:13 compatible:1 introduced:4 own:1 previously:2 h0:16 h1:10 functional:2 square:3 van:1 additional:1 yasuda:1 pairing:3 smoothing:1 mandel:3 ed:2 naturally:1 function:70 but:27 volume:1 hi:1 hn:1 made:1 evident:2 whether:4 below:2 limit:24 distribution:2 piece:1 display:1 mechanics:4 montangero:1 int:1 universal:6 dawson:1 proceeds:3 functions:42 compared:3 hn1:1 other:13 special:4 stat:5 inescapable:1 variation:1 stay:1 else:1 coupling:5 4t:14 factors:1 persistent:1 rule:1 inset:2 bcs:1 |
0704.1881.txt |@word gs:2 consider:6 chain:1 illustrates:2 induces:1 forbidden:1 results:12 leads:2 softer:1 generalize:1 computation:1 edu:1 incorporation:1 follow:1 gm:4 contributions:1 gj:3 gi:2 increase:1 heller:5 inverse:1 caveats:1 equivalence:5 tr:3 corrections:1 finally:1 program:1 pathria:1 heavyside:1 th:2 under:2 analogous:2 include:4 applied:3 conjecture:2 r12:1 returning:1 very:6 differently:1 unfamiliar:1 wave:6 p1:1 every:1 telling:1 ρe:1 little:2 matrices:4 rn:3 encounter:1 treating:1 randomness:1 moderate:1 obvious:1 hamiltonian:2 positions:3 large:31 adjust:1 rj:1 guiding:2 science:1 manifestly:1 study:1 degeneracy:1 upper:1 averaged:1 direct:5 sign:5 approximation:6 zero:4 perspective:4 problematical:1 gn:1 incidentally:1 further:3 chem:1 requiring:2 canonical:15 even:4 what:3 appear:2 section:2 associate:1 near:3 uniform:2 version:3 3n:1 above:3 kleinert:1 new:7 avenues:1 increasing:1 method:5 body:2 full:3 exchange:1 respectively:1 never:1 spacing:1 here:5 diagonal:12 behaviour:1 desired:1 z8:1 ansatz:1 separation:1 address:1 κt:5 path:12 along:3 quite:1 respect:1 z1:1 change:1 extreme:1 obtained:4 derivable:1 almost:1 generalizing:1 antisymmetric:1 nth:1 oxford:2 inspired:1 changed:2 allows:1 completely:1 suggests:1 periodic:3 permutation:3 identity:1 conveniently:1 fourier:7 changes:4 ekr:1 emerge:2 via:1 useful:3 convolution:1 polymer:3 apr:1 problematic:1 merely:1 vii:1 iet:1 brought:1 apply:1 total:6 establish:2 standing:1 use:7 superpositions:1 would:2 distinct:1 adam:1 give:1 next:3 few:2 explicitly:1 therefore:1 vi:2 taken:3 emerges:1 rearranging:1 more:5 attractive:1 permutations:2 formally:1 definition:1 becomes:10 factor:6 pairs:1 permit:1 carrying:2 rigid:1 normalized:1 particular:2 known:10 foundations:1 hole:2 reflections:1 iii:2 must:9 involve:2 ma:2 integrating:1 recall:2 equation:3 work:1 det:1 γr2:1 remain:1 values:1 rewritten:1 freedom:2 following:3 making:3 arrive:1 averages:2 example:4 something:1 control:1 compare:1 wang:1 figure:2 stated:1 allowed:2 purposes:1 states:6 dxn:4 assumptions:1 reviewing:1 want:1 sense:2 orbits:2 axis:1 information:3 needs:1 end:2 recovery:1 isj:1 rather:5 interacts:2 discussion:2 holds:3 feature:2 chemical:1 brian:1 varies:1 kri:1 consist:1 opposite:2 krn:2 ensemble:14 simplicity:1 product:2 de:2 coming:2 inherent:1 may:4 thermodynamic:2 after:2 derived:4 dx2:2 dx1:1 constraint:1 reflect:1 applications:1 plane:6 fd:5 induce:2 waves:7 choice:1 types:2 namely:1 proceeds:1 short:25 advocated:1 dynamical:1 light:1 odd:1 lines:1 summing:1 element:2 inquire:1 si:1 so:8 correlation:5 arrived:1 looking:1 order:5 typical:2 restriction:1 interpretation:3 closely:1 ith:7 considerations:1 numbers:1 developed:1 over:28 insight:1 2πkr:2 course:4 thermal:4 paper:5 through:5 xpn:4 statistical:15 vastly:1 mentioned:2 existence:2 kinetic:6 still:2 unchecked:1 roots:1 write:2 kp2:2 kp3:1 surviving:1 fit:1 how:2 energies:2 interesting:5 inclusion:1 x1d:1 complex:2 coordinates:10 actually:2 initial:1 absence:1 according:1 degrees:2 systems:5 pergamon:1 inquiry:1 might:2 image:2 yi:12 symmetrization:2 them:3 motivated:1 combination:2 reservoir:1 practice:1 fig:7 reflected:5 records:1 walls:8 billiard:2 try:3 they:1 st:1 arriving:2 killed:1 association:1 densities:2 develops:1 eigenvalue:1 february:1 finite:1 2r:4 characterizes:1 university:2 level:1 loosely:1 establishing:1 2d:8 sufficiently:2 each:6 2m:15 2n:2 difficult:2 traces:1 side:1 kpn:2 constraints:16 subsystem:3 domain:3 weyl:1 ei:1 directly:1 ek:1 series:3 energy:29 hard:3 idea:4 related:4 extended:4 begun:1 quantum:16 wavelength:2 beyond:2 eq:28 enclosure:1 really:1 stands:2 shown:5 container:1 matrix:13 space:11 open:3 since:13 squared:1 chaos:1 particles:40 collisions:5 4πd:1 dominated:1 gaussians:1 emerged:1 reader:1 formula:3 get:2 dxdp:3 ri:7 hcl:3 shows:2 foundation:2 provide:1 theory:3 interactions:1 easily:1 dx3:4 given:10 free:5 standard:6 hankel:3 approaches:4 necessarily:3 complicated:1 york:1 imagine:1 put:2 upon:1 generate:2 shortest:2 additional:1 degeneracies:3 βv:2 interaction:1 bring:1 r2:6 route:1 similarly:1 used:5 times:3 repulsive:2 βe:2 length:1 place:2 consequence:1 moving:1 configurations:1 βh:3 first:3 origin:1 already:1 xn:14 features:1 probability:1 xm:1 supposing:1 number:5 iht:4 traveled:1 exact:2 symmetry:4 urbina:2 least:2 another:3 xr:8 reached:1 electronic:1 stage:1 size:1 differ:1 long:3 temperature:10 srednicki:3 introduction:1 interact:1 behaves:1 system:8 relations:1 πr:3 their:4 assumption:1 ballistic:2 expand:1 statement:2 served:1 final:2 gives:5 back:1 grant:1 relationship:3 bouncing:2 relative:1 helpful:1 required:2 part:4 too:1 somewhat:1 x2:7 natural:1 x1:21 than:3 xj:3 gst:1 past:1 holland:1 showed:1 accordance:2 require:2 second:3 gij:1 matter:2 future:1 amplitude:1 providing:1 treated:1 pre:1 symmetries:4 generality:2 localized:1 radial:1 argument:4 yielding:1 say:2 unlikely:1 events:1 constrained:1 apparently:1 any:13 viewed:2 paths:3 depending:2 convenient:2 able:1 histories:1 contact:1 note:5 k2:21 ideal:3 potential:20 take:5 analogy:1 xi:6 green:35 coincide:2 subject:4 reversed:1 adopted:1 2mr2:2 formulas:1 begin:1 added:1 multiple:1 trace:8 shall:1 denominator:2 extending:1 boltzmann:9 involving:3 propagate:1 encodes:1 significant:1 phase:9 colliding:3 cases:2 why:1 eigenfunctions:3 distributed:1 ka:2 bounced:1 takes:1 surprising:1 considered:2 average:19 sometimes:1 implications:2 kn:5 z3:1 kr:27 points:2 wasserman:1 artificially:1 exp:3 mechanical:1 north:1 link:3 physics:3 sum:1 fact:3 quantity:2 thomas:1 hyper:1 particularly:1 show:1 random:16 xp1:4 purely:1 relation:1 fermions:7 focussing:1 find:4 principal:1 symmetric:1 sj:1 ensembles:13 proportion:1 written:3 negligible:2 should:1 rij:1 analytic:1 only:9 going:1 formulation:1 indeed:6 local:5 preliminaries:1 hope:2 dn:7 do:2 his:1 establishes:2 notation:4 means:2 familiar:5 express:1 ρcl:10 wolynes:1 unimportant:1 cannot:4 eiet:2 dx:8 expresses:1 bead:1 dt:3 procedures:2 gen:5 nearly:1 contributes:1 continuum:2 conditions:1 arxiv:1 stirling:1 gutzwiller:3 yield:1 acknowledgments:1 2πi:5 underlying:1 source:1 though:1 including:2 fixed:12 discussing:1 2kt:1 ik1:1 set:1 computed:1 exists:1 multiplied:1 unpublished:1 correlations:5 j0:6 connections:1 edition:2 see:3 individual:1 sec:3 result:17 discussions:1 nonstandard:2 incorporating:2 techniques:2 ergodicity:3 interacting:8 underpinning:1 ways:2 away:3 ranged:2 yet:2 boundaries:3 arbitrary:1 outside:1 identification:2 closed:3 between:12 fermi:1 boundary:3 approach:4 across:3 knowing:1 p2d:5 terms:6 iπδ:1 kp1:3 component:1 clean:1 restricting:1 however:7 deterministic:1 harvard:3 hypothesis:12 key:1 jd:13 separately:1 configuration:1 come:2 problem:1 thank:1 suggested:1 both:3 interpretations:1 many:10 taking:2 infinitely:1 iooss:1 equal:2 qcl:2 connection:5 probable:3 berry:18 context:3 retarded:3 dkn:2 contribution:4 mean:1 confronted:1 nearby:1 strongly:2 hold:1 dk1:2 rpw:8 cl:4 simple:4 tracing:2 corresponds:3 2nd:2 dimensional:2 z4:1 taylor:1 z5:1 constant:7 throughout:1 z6:1 exponent:2 math:5 considering:2 save:1 unusual:2 z7:1 che:1 basis:3 trajectory:4 create:1 locally:1 due:2 been:4 ikn:1 difference:1 stora:1 z2:1 pe:1 ph:1 territory:2 pn:1 chandler:1 dk:4 choose:1 interparticle:5 direction:1 arises:3 corresponding:2 etc:4 quantities:1 sufficient:1 gas:5 essentially:2 derive:1 lives:1 wavevectors:2 present:2 case:12 extracted:1 intriguing:1 chains:1 solid:1 appearance:1 ǫn:11 value:1 remaining:2 will:10 cast:1 while:1 suppose:3 momentum:1 evaluating:1 dirichlet:1 richter:3 spacial:1 procedure:1 manner:1 ix:1 unitary:1 chaotic:3 averaging:3 av:2 thus:6 non:2 vn:1 iv:6 ii:1 reads:2 im:10 seen:1 return:1 vanish:2 acquires:1 examine:1 binary:1 different:6 recover:2 handled:1 prior:2 perform:1 seek:1 make:6 indistinguishable:1 same:8 wherein:1 antisymmetry:2 noninteracting:14 quant:1 pauli:1 several:2 grows:1 dated:1 development:1 independent:1 literature:1 singapore:1 somewhere:1 trajectories:4 ri2:1 effect:5 counterparts:1 possible:4 action:2 uses:1 purpose:1 potentials:4 normalization:6 deflects:1 lower:1 off:4 reflection:2 expression:2 nonetheless:1 well:7 circumstance:1 thought:1 approached:1 without:3 spectator:1 lim:4 coordinate:7 position:2 chemistry:1 dimension:3 usual:4 distances:4 less:1 being:1 nd:2 obtain:1 sources:1 morette:2 identify:2 aspect:1 using:10 γri:1 rir:1 scattering:2 eigenstates:4 isi:1 emerging:1 density:28 point:4 had:1 except:2 wavevector:2 wall:19 valid:2 treatment:1 theorem:1 possess:1 transformation:1 ought:1 gave:1 real:5 iκ:1 rev:2 demands:1 iβ:3 term:17 possibly:1 increases:4 mol:1 confined:4 immediately:1 emergence:1 apart:2 semiclassical:15 2dn:1 necessary:1 like:2 particle:40 follows:1 qualitative:1 microcanonical:12 specific:2 imposes:1 yields:3 either:2 integrals:1 always:2 become:1 conclusion:1 soft:2 essential:3 scatterers:1 parity:2 because:2 methods:1 classical:18 phenomena:1 play:2 bounce:2 understood:1 evaluated:1 nondiagonal:1 images:5 small:2 neglecting:1 happens:1 provided:2 dimensions:8 lead:3 tools:1 investigations:1 contributing:3 rewarding:1 does:6 provides:1 assuming:3 propagating:2 bessel:12 biology:1 felt:1 scientific:1 power:2 dropped:1 equivalent:8 wavefunctions:1 communicate:1 expansion:2 step:1 although:3 found:1 imaginary:5 properties:5 asymptotic:11 comparison:1 about:6 central:1 world:1 most:4 disorder:1 discussed:1 dependence:1 recognized:2 reduced:4 mutually:1 regular:1 plus:1 introduced:1 slightly:1 automatically:2 stationary:5 cambridge:2 followed:1 presence:4 unbounded:1 into:5 within:3 integral:10 bound:1 nsf:1 getting:1 accommodate:1 nothing:1 appropriate:9 square:1 references:2 δk3:1 national:1 k1:5 operator:4 proportional:1 statistics:6 van:4 log:3 classically:3 delos:2 strictly:1 there:7 question:1 transform:6 specifically:1 accordingly:1 bosons:7 way:9 ed:1 singled:1 was:3 propagator:17 naturally:1 function:45 arise:1 complete:1 form:13 δkn:1 some:7 identities:1 but:12 gaussian:12 volume:4 hn:2 atom:2 convergence:1 remote:3 line:1 removed:2 true:2 hd:3 butterworth:1 compute:1 2πd:3 embedded:1 whether:3 wish:1 2πm:1 up:5 us:2 2πn:1 gratifying:1 below:1 limit:28 leaves:2 boldface:1 planes:1 autocorrelation:1 distribution:4 define:2 similar:1 called:1 distance:5 mechanics:13 partition:2 vleck:4 contributors:1 defined:2 certain:1 universal:1 mirror:1 condition:3 ergodic:2 general:2 proper:1 single:3 exist:1 our:6 ind:1 formalism:2 distributions:1 eric:1 defines:1 again:7 functions:14 compared:2 nn:1 no:6 wavefunction:9 when:3 vanishes:1 2dd:1 other:5 role:1 spatial:2 department:2 out:5 principle:2 explaining:1 elements:1 generates:1 semiclassically:4 overwhelmingly:1 kt:1 problems:1 ultimately:1 includes:1 meaning:1 graphically:1 included:2 generalized:1 2i:3 ago:1 correlated:1 implies:1 longer:4 assume:1 factors:2 orbit:1 together:2 having:2 delta:1 wavenumber:1 time:34 far:4 starting:2 original:2 others:1 |
0704.1882.txt |@word neighbors:4 limited:1 partial:2 consider:8 secondly:1 alg:2 graham:1 particular:1 desirable:2 results:10 existing:5 leads:5 generalize:1 broader:1 c2:2 dist:1 expressions:1 denotes:1 reasoning:1 causes:1 whose:6 terms:2 graph:4 deterministic:1 easiest:1 recurrence:12 finally:4 monotonically:1 indicate:1 present:1 nodes:32 dramatically:2 recasts:2 maximize:1 supported:1 very:8 alternatives:2 vt:4 connects:3 choice:17 morally:1 balancing:3 affect:1 difference:3 exact:6 condition:1 entire:3 unlike:1 presented:3 solution:14 occurs:4 large:5 discrete:2 math:3 recall:3 small:14 upper:3 averaged:1 illustrating:1 eλx:1 estimates:1 past:1 fold:1 rate:2 traveling:8 rigorous:1 qualitatively:2 janson:1 even:5 established:2 what:2 nonlinear:1 sub:1 giving:1 sum:4 selected:4 expressed:1 uniform:2 d0:3 above:1 new:22 3a:1 increasing:1 method:2 contrast:3 degree:70 respectively:2 error:1 here:5 following:1 explore:3 pause:1 ansatz:1 making:2 equations:8 appears:2 change:1 great:1 arrive:3 daughter:1 rigorously:2 institute:1 root:23 leaves:2 studied:1 allows:1 los:1 suggests:3 amount:3 resulting:3 poisson:7 ak1:2 real:2 hospitality:1 deg:3 changes:4 involves:2 genuinely:1 via:1 useful:1 although:1 apr:1 merely:1 marked:1 replace:3 analyzing:1 1st:1 summation:1 support:1 total:3 establish:2 asi:1 select:1 readily:1 derivatives:1 use:5 asymptotic:8 remains:2 positive:7 stated:1 single:1 only:7 laboratory:1 few:3 doubt:1 overhead:1 opposed:1 vi:1 lambiotte:1 simpler:2 w911nf:1 start:3 minor:2 more:7 introducing:1 formally:1 brings:1 validity:3 eλ:1 excellent:3 known:2 cases:2 hold:1 iii:1 analogous:1 must:2 crosses:1 ma:1 evolution:2 science:3 equation:15 work:1 mj:2 remain:1 values:2 growing:1 im:1 drops:1 averages:5 example:1 initial:4 figure:2 give:3 process:6 attribute:1 allowed:2 purposes:1 high:1 collision:1 minimum:5 numbers:4 want:1 sense:1 sharp:1 information:2 end:1 processors:1 rather:6 discussion:1 breaking:1 utilize:1 recovers:1 write:3 criterion:2 attachment:1 renaud:1 instead:5 wave:8 product:2 description:1 may:1 suppose:1 after:2 variant:1 ewi:4 davis:1 explored:1 fe:2 cambridge:1 ties:3 law:10 data:4 types:1 recursive:12 plies:1 realized:2 natural:2 preferential:1 third:1 whenever:1 approximation:2 grant:1 correspond:1 extremal:1 so:7 sect:2 allow:1 decreasing:1 order:5 typical:2 holds:2 dx:2 hierarchy:1 indeed:5 over:5 vary:1 confirm:1 course:2 simplifies:2 differs:1 satisfies:3 still:2 ieee:1 its:9 roots:1 before:2 regions:1 derive:2 rapidly:1 decay:4 chosen:2 interesting:1 solving:5 exhibits:3 writing:6 better:3 degrees:4 choose:5 alter:1 versus:1 them:4 someone:1 greater:5 seeking:1 lambert:4 fig:6 introduce:1 effects:3 they:2 arriving:1 souza:1 now:7 discuss:1 2t:1 minimalist:1 several:1 always:2 university:4 sufficiently:2 good:1 jmax:9 reasonable:1 each:15 2n:12 alea:1 mean:1 differential:5 transforming:1 directly:1 approximates:1 related:2 decays:6 ey:1 connect:3 measure:2 our:6 ew:2 beyond:3 eq:4 event:2 mat:6 shown:3 network:15 solved:2 furthermore:2 since:11 rev:6 research:2 replacing:1 emerged:1 correct:2 announced:1 shows:1 foundation:1 theory:2 log1:1 derived:1 albuquerque:1 governing:1 quite:1 admits:2 analytical:1 approaches:3 california:1 york:1 estimate:7 barab:1 definition:6 derivation:2 recast:2 could:1 similarly:1 plot:2 ck:1 times:1 creates:1 mitzenmacher:3 erfc:3 exponentially:4 target:1 hence:3 probab:3 justifying:1 first:5 rand:1 already:1 probability:7 variables:1 number:16 reaches:1 randomized:3 gases:1 another:2 reached:1 precisely:2 quality:4 appl:1 size:4 given:7 their:4 introduction:1 leading:4 system:1 least:2 attach:3 assumption:5 master:4 1e:9 siam:1 final:1 speaking:1 gives:4 fraction:4 albert:1 than:13 wide:2 beijeren:1 redner:3 ben:1 unfortunately:1 naim:1 double:1 tree:13 namely:3 normalizing:2 determined:3 doubly:3 amplitude:1 outcome:2 minus:1 behaviors:2 function:7 motivation:1 mahmoud:1 boston:2 correction:1 generalization:2 summing:1 randomly:6 substantial:1 further:3 need:3 seen:1 seem:1 any:3 relatively:1 mappings:1 zero:1 depending:1 convenient:1 latter:2 zon:1 note:10 instance:6 potential:1 build:1 analogy:1 algorithms:3 aro:1 circles:1 criteria:2 begin:2 added:1 altered:3 shall:1 simulated:1 plugging:4 depths:1 most:3 saarloos:1 involving:1 2e:4 accepting:1 analytically:3 measured:1 concrete:1 µx:1 especially:1 ke:6 average:12 steady:2 physica:1 points:4 principle:6 exp:2 mechanical:1 velocity:6 typically:1 section:1 quantity:2 precise:2 selection:6 particularly:1 show:2 smythe:1 random:29 12n:1 implying:1 relation:4 substituting:1 cnls:1 find:12 decade:1 d1:11 q1:15 q2:9 knowledge:2 situations:2 written:3 should:1 moments:1 theme:1 going:1 transcendental:2 factor:1 parabolic:1 employed:1 local:2 interested:1 achieve:1 nj:2 dn:4 do:4 intractable:2 correspondence:1 dj:20 dk:2 distance:6 mascheroni:1 between:1 increases:2 trees:7 cannot:1 words:1 3b:1 during:1 dt:2 geometric:1 dq:2 acm:1 processes:2 reading:1 lat:1 continuum:2 conditions:4 arxiv:1 acknowledgments:1 statist:1 qi:4 qk:2 qj:35 valid:1 requirement:1 set:5 exists:2 iteration:2 national:1 up:4 achieves:1 see:9 computer:3 sec:3 result:2 w1:2 close:3 alternative:1 best:3 subject:2 closer:2 satisfying:1 exponent:2 position:2 complementary:2 diverge:1 state:3 smallest:9 various:1 closed:3 simplest:1 understood:1 simplifying:1 boundary:5 c2i:4 approach:2 jobs:1 nature:3 azar:2 comp:1 focus:1 however:9 wi:4 dellago:1 unusually:1 distinguish:1 problem:2 cristopher:1 concentrated:2 both:8 improved:1 reverse:1 limits:2 many:3 region:2 equal:1 contract:1 ln:46 improves:1 iv:2 context:3 exceeds:1 variance:2 argue:1 hwang:1 finds:2 comes:1 otherwise:1 load:4 exhibit:1 ci:34 ch:1 point:3 simple:4 poissonian:2 ca:1 asymptotically:3 harmonic:2 simply:2 decreases:2 applicability:1 zeta:1 actually:1 krapivsky:7 squaring:1 equivalent:1 been:4 ai:20 much:3 slowly:1 asymptotics:1 interest:1 expected:2 define:2 wants:1 addison:1 direction:3 aj:2 corresponding:3 quantities:2 sufficient:1 assert:1 observe:6 understand:1 imax:2 incoming:1 c1:1 crossover:1 those:1 case:12 broder:2 look:2 exponential:9 pacs:1 contexts:3 batch:1 value:5 choices:15 will:3 while:7 optimization:1 neat:2 dqj:5 behavior:12 applies:1 di:14 procedure:1 maximal:2 layer:1 larger:6 mexico:1 almost:1 averaging:3 thus:15 herein:1 according:3 ii:4 characterize:1 reads:1 itself:1 cond:6 n2s:1 vanish:1 grown:2 different:5 d12:9 etc:1 perhaps:1 recursion:1 cumulative:10 lett:3 same:1 tells:1 arguments:1 copying:1 largest:5 knuth:1 finite:4 grows:7 higher:1 used:1 infinity:1 closest:2 ni:4 lowing:1 numerical:9 effect:4 hand:1 allocation:1 v1:6 n21:1 normalization:1 relies:1 mech:1 proceed:1 minimize:1 studies:1 majumdar:3 well:2 roughly:2 analysis:3 without:1 amounts:1 contact:17 solve:4 dashed:1 organization:1 model:22 ccf:1 possesses:1 distances:5 unsolvable:1 just:1 less:5 being:1 generally:2 observed:3 networks:1 obtain:12 rest:1 reviewed:1 front:6 shape:2 drmota:2 paul:1 yet:4 adv:1 heuristic:1 struct:2 similarities:1 seems:1 appeared:2 add:1 setting:2 location:1 easy:2 solvable:1 transformation:1 euler:1 identical:1 depends:1 showing:1 sums:2 possible:3 whichever:3 press:1 using:4 helpful:1 desire:1 wesley:1 tail:7 necessary:2 like:1 alternatively:1 reduces:3 yields:2 follows:1 become:1 works:1 therein:1 exceed:1 often:1 some:4 back:1 self:2 viz:3 growth:7 alamos:1 choosing:2 multiple:1 2qj:1 matching:1 2eµ:1 proceeding:1 contacts:5 broad:1 decision:5 though:2 integration:1 overlap:1 everything:1 does:4 provides:1 assuming:2 fol:1 sys:1 proc:1 prob:4 minimal:1 bf:1 power:16 2q1:1 problems:1 q2j:1 agreement:2 broken:2 step:3 symp:1 rep:1 santa:2 properties:1 stage:2 integers:1 about:1 simplify:1 am:1 discussed:2 o:18 simulation:8 addition:1 range:5 ensure:1 obeys:3 neighbor:1 processor:1 cutoff:1 referenced:1 into:8 within:2 numerically:4 bound:4 nsf:1 down:1 thankful:1 square:1 references:1 determine:3 proportional:1 statistics:1 van:3 log:20 comparing:1 probabilistic:1 strictly:1 there:9 long:2 dispersion:2 width:3 quadratic:2 low:1 way:1 notices:1 m1:2 exceptional:1 was:2 assumes:1 therefore:10 lowest:5 rasmussen:1 complete:3 form:2 upfal:3 differences:1 agrees:1 but:8 26th:1 hierarchical:3 hn:10 hc:1 line:1 highest:6 true:1 karlin:2 fragmentation:1 compute:2 adler:1 q21:1 patashnik:1 trans:1 maximum:16 us:6 below:3 limit:9 fluctuations:4 distribution:47 attaches:5 similar:4 called:2 obtains:1 firm:1 constant:9 sight:1 computing:2 defined:2 cki:7 ak:8 2hn:2 influence:1 proven:1 evidence:1 engineering:1 together:1 formulation:1 dη:1 distributions:1 check:1 regime:6 again:5 radically:3 compared:1 nm:2 no:4 aeronautical:1 trials:1 when:21 detail:2 logk:1 other:4 branch:1 becomes:2 department:3 mathematics:1 ns:1 illusion:1 2dj:4 node:39 stat:2 generates:1 models:2 uniformly:2 a1:4 generated:1 variable:5 furthest:1 algebraic:1 implies:1 assume:6 physics:1 required:1 rule:2 equivalently:2 depth:46 dramatic:2 mass:1 time:9 n1:1 n2:14 joining:1 requires:2 having:1 others:1 once:1 |
0704.1883.txt |@word sci:1 gr:1 sandia:3 magnetic:9 lack:3 results:5 kersting:1 uner:1 edu:1 whose:1 calculate:3 technique:2 plasmons:1 environment:1 finally:2 under:1 unit:1 cm2:5 ingredient:1 applied:1 supported:1 frequencies:1 atoms:1 wave:2 electron:8 sons:1 figs:1 affect:1 difference:2 level:6 transmission:12 damped:1 magnet:1 σxx:13 optics:1 employing:1 haas:1 consistent:1 direct:3 pulse:5 approximation:1 zero:1 10t:1 even:1 index:1 current:1 experiment:6 new:4 increasing:1 method:1 filled:3 thin:1 coefficient:6 edited:6 condensed:2 full:2 simultaneously:1 lei:1 2degs:4 here:1 diagonal:2 reported:2 palik:1 operating:1 mes:1 address:1 along:1 z0:2 change:1 box:1 study:1 studied:2 allows:6 through:5 yˆ:1 simultaneous:2 permit:1 resonance:8 fourier:2 studies:3 fitting:1 magnetoconductivity:5 mobility:13 apr:1 understanding:1 semiconductors:2 eiφ:1 decrease:1 txx:1 planck:1 linearly:1 reflector:1 gaas:5 use:2 usa:2 coupled:2 charge:1 properties:2 vol:2 m0:2 furdyna:1 theoretical:1 more:1 ambiguity:1 company:1 apparent:1 berlin:3 particular:1 hole:1 given:2 states:3 springer:3 rotational:2 quantized:2 science:2 setup:1 averaged:1 values:1 temperatures:1 making:1 example:1 history:1 wang:1 figure:4 sample:8 effectively:1 hilton:1 numbers:1 νc:9 times:1 occur:1 verlag:1 information:1 verify:1 pp:5 delay:1 submillimeter:1 instrum:1 2deg:15 mat:1 modulation:1 earlier:1 ultrahigh:1 millimeter:1 produce:1 fits:1 data:3 ambiguous:1 effective:3 studenikin:1 element:4 marton:1 sm:1 increase:1 order:3 houston:1 kono:3 administration:1 over:2 vary:1 thermal:1 including:2 linewidth:10 fit:2 decay:3 highlights:1 resort:1 detected:1 offers:1 systems:2 texas:1 affected:1 landau:12 shubnikov:1 effects:1 oxford:1 hall:1 wiley:1 nos:1 february:1 university:1 2y:2 sufficiently:1 magnitude:3 transmitted:6 each:1 inherent:2 traces:1 referred:1 domain:6 significantly:1 doing:1 ed:1 energy:2 eb:1 frequency:8 expect:1 measurement:5 quantum:7 our:6 transitions:2 extract:2 shown:3 space:1 σyy:1 rev:5 research:1 semiconductor:1 daniel:1 ren:1 electronics:1 induced:4 induction:1 shows:5 foundation:1 after:2 theory:1 interactions:1 mechanisms:1 albuquerque:1 free:3 standard:1 completely:2 advantages:2 york:3 kaufmann:1 created:1 determining:2 could:1 david:1 creates:1 turn:2 plane:1 potemski:1 first:1 exotic:1 symmetry:1 unfilled:2 number:1 enlarged:1 directly:1 thick:1 clarity:1 electronic:1 appl:2 little:1 sheet:1 temperature:3 system:4 assumption:2 observations:1 scheme:3 fieldinduced:1 ranging:1 scans:1 optical:3 manipulation:1 than:2 wide:1 john:2 holland:1 second:2 matter:2 determined:4 amplitude:6 were:1 identical:1 lowest:2 rad:1 modeled:1 modern:1 measure:1 spectrum:2 reno:1 operated:1 seen:1 concentration:6 recover:1 any:1 viewed:1 relatively:1 studying:1 isolated:1 admittance:1 polarization:2 extracted:4 high:9 materials:1 online:2 subject:1 spectral:3 multiple:1 electric:6 trace:4 measures:1 wells:1 twolevel:1 petrou:1 phase:9 measured:3 ure:1 kg:1 observation:1 sensing:1 broadened:1 metal:1 traditional:2 electrons:1 clean:1 north:1 dos:2 physics:2 dover:1 emerging:1 phenomenon:1 intensity:1 show:2 doped:1 infrared:1 waveforms:3 impedance:1 subtracting:1 ratio:4 explain:1 only:1 molecules:1 employed:1 rice:2 do:1 dependent:2 de:2 dc:1 methods:2 polarized:1 report:1 du:1 processes:1 nicholas:1 substrate:2 fields:5 arxiv:1 summary:1 2πi:1 common:1 pulses:1 set:1 pfeiffer:1 exists:1 ftir:5 national:3 conductivity:13 detection:5 see:1 computer:1 result:6 enhanced:1 cyclotron:11 techniques:8 detect:1 tensor:6 nuclear:1 state:3 between:5 µe:3 crooker:1 terms:1 tsui:1 component:1 suppresses:1 weak:1 however:1 spectroscopic:1 dip:1 incident:3 configuration:1 both:5 0t:2 many:2 region:1 parts:6 contract:1 sensitive:3 dated:1 refraction:1 experimental:1 otherwise:1 detailed:1 separation:2 cm:3 color:2 mittleman:2 ultrashort:1 dimensional:3 cr:3 ps:3 combines:1 addition:3 west:1 due:2 been:3 much:1 combined:1 empty:1 fig:8 obtained:1 lived:1 corresponding:1 kronig:4 coherence:1 gas:3 kramers:4 coherent:8 observe:1 determination:6 representative:1 systematic:1 landwehr:1 nuss:1 present:1 case:2 novel:1 splits:1 pacs:1 solid:2 originate:1 single:1 value:3 will:3 while:1 overcome:2 applies:1 situation:1 xx:2 resolved:1 larger:1 mexico:1 almost:1 molecular:1 thus:1 surface:1 equal:1 superconducting:1 cond:1 commonly:1 elsevier:2 eberly:1 different:2 grant:1 make:1 radiation:2 same:1 clearly:1 kuzmany:1 complex:9 finite:3 difficult:1 used:2 effect:4 levels:6 lower:1 thz:33 makes:2 no:3 well:2 analysis:1 academic:1 solids:2 without:5 allow:1 corporation:1 model:1 laboratories:1 arising:1 proposed:1 being:1 observed:4 wagner:1 obtain:1 ne:5 atomic:3 gated:2 scattering:3 density:2 absorption:1 alternate:1 ideal:1 signals:1 priori:1 transformed:1 lett:4 samples:4 input:1 real:6 saturation:4 9b:1 increased:1 advances:1 absence:1 increases:1 allen:1 background:1 press:1 using:8 orenstein:1 vertically:2 necessary:1 like:2 success:1 systematically:1 signal:1 performing:1 temporally:1 either:3 martin:1 security:1 disorder:1 28t:1 because:1 often:1 discrete:1 creation:1 phenomena:3 oscillations:8 transport:1 provided:1 highlighting:1 broadband:1 broad:2 measurements:5 sachrajda:1 waveform:3 rashba:1 retro:1 prog:1 propagating:1 measuring:1 noise:3 elucidate:1 oscillating:1 conventional:1 terahertz:5 although:1 offset:2 tds:7 plots:1 imaginary:6 lockheed:1 permitted:1 conducting:1 would:2 origins:1 dependence:2 o:2 range:3 carrier:2 chou:1 signalto:1 into:1 determine:5 amsterdam:3 utility:1 additional:1 there:2 transform:2 long:3 width:1 detectable:1 handbook:1 low:1 was:5 formation:1 assumes:1 function:4 successfully:2 drude:1 elsewhere:1 form:1 some:1 removes:1 photoconductive:1 technologies:1 highest:2 true:3 especially:1 arrays:1 prevents:1 us:3 dmr:2 spectroscopy:9 demonstrate:1 similar:1 hz:1 intersubband:1 constant:1 abeles:1 sion:1 engineering:1 exist:1 laboratory:1 work:1 film:1 physical:1 compared:1 variety:1 eq:1 when:1 detail:2 field:18 other:1 electrical:1 department:1 perpendicular:4 elements:2 lineshape:2 superposition:4 photon:1 generated:1 important:1 additionally:1 algaas:4 confinement:1 mass:4 time:13 ultrafast:2 n2:1 rep:1 coherently:2 |
0704.1884.txt |@word replacing:1 eda:1 partial:8 consider:5 chain:2 pigeon:2 results:8 gy:1 gx:2 four:1 proposition:3 follow:3 princ:2 dα:15 seemed:1 devoted:1 whose:1 cardinality:8 depend:2 send:1 finally:5 present:2 th:4 ti:15 applied:4 conjecture:2 random:2 ginn:1 g1:4 g0:4 very:1 dq:4 rise:1 quadruples:1 definability:1 gz:2 cofinality:4 corollary:21 every:17 rm:11 bounding:5 difference:1 aichi:1 condition:24 school:1 dominate:1 turns:1 quintuple:2 list:1 large:3 involution:7 recall:4 small:3 dαi:2 maharam:1 force:3 miller:1 consistent:6 soukup:15 13a:1 past:1 second:6 further:5 canonical:1 even:4 established:1 incompatible:3 section:28 analogously:1 hereditary:1 witnesses:2 sequential:1 above:19 sup:11 new:1 journal:1 satisfy:10 realizing:1 8a:1 notions:1 respectively:11 component:1 here:4 desired:6 separation:3 address:1 xβ:1 isomorphically:3 along:1 strong:4 appears:1 obtained:6 sending:7 remark:2 generalizing:1 algebra:2 technical:1 study:2 studied:2 contradiction:12 pinning:1 suggests:1 subclaim:6 products:4 sjm:1 adopting:1 formulated:3 tightness:2 brendle:7 classification:1 f1:2 apr:1 replace:1 ask:1 boolean:2 names:14 apply:1 glance:1 establish:1 denotes:3 readily:1 use:1 freese:6 identifies:2 would:2 prove:12 sake:1 positive:1 sends:4 ψq:1 saka:2 countability:1 properties:3 distinct:7 vol:1 noting:1 call:4 therefore:2 knaster:1 type:6 more:8 sort:1 introducing:1 slim:4 rk0:1 weakening:2 club:7 initial:3 under:5 pβi:1 berlin:1 pα:70 s0m:3 s0n:7 particular:18 known:6 projective:5 hole:2 hold:16 iii:2 capturing:1 must:3 γn:6 isomorphism:7 submodels:3 involutions:7 science:3 work:1 ordinals:5 erd:2 remain:2 values:5 thin:1 following:47 isc:1 root:14 example:5 proof:38 f0:2 claim:25 indicated:1 give:1 pξ:5 inaccessible:13 organized:1 annals:4 fundamenta:4 assumptions:2 reviewing:1 sense:1 interpreted:1 axiomatization:1 g1n:3 end:3 recursive:2 rather:1 gch:7 s1:9 holds:51 negation:5 write:2 maps:2 cardinal:25 pure:4 optimal:1 parameter:2 sim:1 simplicity:1 product:28 fs:13 intended:1 binary:2 may:17 max:1 after:4 variant:2 mapping:11 diagram:3 applications:2 cambridge:1 summarize:1 choice:3 βn:16 types:1 plies:1 transitive:1 natural:4 imply:4 lemmas:4 grant:2 8e:5 correspond:1 element:11 sk:4 si:6 sh:18 so:7 sn:4 s2:5 definitions:1 antichain:4 sg:1 order:18 sd:24 fα:13 fβ:2 s0:32 jα:6 dx:3 numbers:2 over:9 move:1 mainly:1 fξ:2 meager:10 course:1 aη:1 paper:3 same:5 mentioned:2 japan:4 satisfies:17 still:2 its:10 suffix:1 τn:5 sκ:1 singular:1 chosen:3 lo:1 fix:3 inclusion:1 translation:2 actually:5 dβi:1 parts:1 fig:15 dβn:1 main:1 might:1 into:2 yi:1 13b:2 them:2 good:1 than:3 yn:8 nada:1 inductively:1 dai:1 introduce:3 nation:6 mention:1 they:7 half:1 now:10 discuss:1 counter:3 easily:9 finite:10 name:32 invariants:4 university:4 arrows:1 identified:2 sufficiently:1 inequality:1 each:13 dominating:3 2n:1 side:8 characterized:1 subset:18 domain:1 formulate:1 principles:24 related:1 society:2 used:6 measure:4 separating:1 our:7 naming:1 xp:1 out:4 shown:9 dominates:1 matrix:6 furthermore:4 since:40 induces:1 research:1 looking:1 combinatorial:21 ζi:14 denoted:1 formula:5 rn:1 induced:1 reg:5 math:1 shows:6 sω2:29 sω1:1 working:5 theory:4 reformulated:1 8b:1 asz:15 argument:5 8d:2 shelah:6 completely:1 besides:1 put:3 org:2 returning:1 axioms:7 definition:28 pairs:1 language:1 recast:1 filter:10 ordering:13 length:6 maximality:1 place:1 hence:31 promotion:1 βi:5 first:11 xk:2 xi:4 xn:27 features:2 bijection:7 clause:4 number:11 instances:2 done:4 construct:8 4b:1 thick:1 precisely:3 open:3 given:3 necessarily:2 similarly:8 introduction:1 smoother:1 system:24 least:8 their:4 ℵn:1 fn:5 ordered:1 posets:4 gives:3 isomorphic:4 centered:1 recursively:5 exactly:3 immediate:1 assumption:3 part:3 authors:1 x0:33 x1:2 bijections:2 aβn:1 distance:2 holland:1 showed:2 accordance:1 see:19 preparation:1 pairwise:4 recovered:1 were:1 toward:1 spectra:1 generality:4 lines:1 cohen:24 spectrum:3 generalization:1 already:1 say:9 pγn:3 disjoint:2 seen:6 seem:1 null:10 any:61 relatively:2 forced:5 constructions:1 mappings:1 min:24 latter:1 note:36 ideal:12 build:1 analogy:2 kobe:3 reals:20 hp:42 realizes:2 begin:2 added:4 unless:1 gβ:4 gα:13 shall:18 arguing:1 who:2 archive:1 most:3 regular:20 automorphism:1 segment:3 class:1 observation:1 consequences:2 dom:36 considered:2 clear:4 later:1 countably:1 countable:15 kunen:6 points:2 principle:21 refining:1 zfc:7 fact:1 precise:1 show:31 supported:2 spaces:1 relation:4 definable:12 keywords:1 trivial:1 find:6 ground:4 q0:2 coloring:4 just:3 parameters:1 explain:1 assertion:4 should:2 lemma:89 only:11 going:2 attained:7 partially:2 axiom:4 do:43 notation:3 df:11 uncountable:8 between:2 jαi:5 cardinals:5 aα:24 aβ:4 closely:1 aζ:6 conjunction:1 qiα:1 dp:1 aξ:3 g0n:3 addresses:1 covering:3 qx:6 arxiv:1 summary:2 supp:55 underlying:1 common:2 ciesielski:2 qi:1 implication:1 fixed:6 set:25 constructing:1 exists:3 sep:2 graduate:1 unpublished:1 namely:1 decided:1 college:1 result:3 y0:15 theoretic:2 subject:1 kurt:1 fails:2 said:2 consistency:13 rado:2 review:1 consequence:1 lusin:2 idx:2 enough:11 closed:4 simplest:1 αi:2 invariant:2 neither:2 conditions:6 αn:9 terms:8 extend:1 jp:2 weak:6 extent:1 distinguish:1 come:1 improve:2 both:4 extendable:16 last:2 universit:1 cov:15 many:7 infinitely:2 according:1 etc:7 connection:4 colloquium:1 0g:1 context:1 sβ:3 gr:1 com:1 otherwise:18 among:1 ch:27 afterwards:1 cq:9 cf:7 bζ:6 bη:1 adjoining:1 assertions:2 sequences:2 cs:51 proved:12 bξ:3 aαn:8 sticks:1 pr:3 aiming:1 xα:14 bα:4 commutative:1 basis:4 px:1 copies:7 been:4 much:1 interest:1 basic:1 colorings:1 choose:4 antichains:1 relations:2 corresponding:5 versa:5 concerning:1 else:4 assert:1 yk:2 otp:4 c1:5 c0:6 standard:5 case:5 explicitly:1 p0:71 wfn:19 look:2 subsets:13 will:4 dept:1 while:2 suppose:36 applies:1 aid:1 property:13 inherits:1 maximal:9 satisfying:1 almost:2 ip:61 thus:26 surprisingly:1 ii:4 exchanging:1 ij:1 dual:1 ready:1 technology:1 around:1 capture:2 different:2 combination:1 author:2 generic:28 make:3 pγ0:3 enumeration:4 clearly:4 checking:1 freie:1 thinning:2 arguments:2 largest:1 modification:1 filtered:1 several:1 investigated:1 embedding:2 i1:8 i0:8 logic:6 effect:1 hand:8 moment:1 dxα:2 infinite:2 pβn:5 chang:2 identity:1 prikry:7 nevertheless:1 depending:1 well:16 non:17 without:5 sets:7 model:30 submodel:1 usual:2 weakenings:1 proposed:1 less:2 being:1 obtain:1 rest:3 homogeneity:9 yuasa:2 tcl:1 relevant:1 situation:1 facts:1 rn1:7 rn0:8 yet:1 previous:1 letting:1 adding:10 elementarity:2 density:2 seems:2 except:1 silver:7 add:2 treatment:1 easy:9 theorem:51 role:1 successor:2 take:1 real:7 march:1 forces:11 isomorphisms:7 iα:11 devised:1 showing:2 rng:1 possible:15 topology:1 possibly:1 press:1 immediately:1 variants:2 unique:1 poset:12 loss:4 necessary:3 like:2 semi:10 follows:44 dβ0:1 yields:1 either:5 arbitrary:4 simply:1 downward:1 stationary:47 terminology:1 pβ0:5 mathematical:4 because:5 often:2 deal:1 sequence:12 xq:1 pαi:1 some:37 pαn:4 clubs:1 pη:4 examples:1 choosing:1 respect:4 proper:10 orderings:2 dense:3 cγα:7 nonempty:1 dissertation:1 though:4 does:13 inaccessibility:1 steps:2 notational:1 minimal:1 refer:1 vacuously:1 replaced:2 scientific:1 power:1 slight:1 equivalent:6 bh:16 pα0:4 cκ:7 step:3 cξ:1 found:1 drawn:1 cα:19 injectivity:4 injective:6 jα1:1 pβ:18 pγ:5 about:2 asserting:1 pζ:16 uniformity:1 extension:26 cω2:1 dˇ:1 discussed:2 quartet:1 compatible:7 remains:1 dγ:1 extensions:3 g1α:15 introduced:8 os:2 cofinal:6 homogeneous:6 own:1 statements:5 plethora:1 previously:1 unbounded:10 h0:6 h1:6 implications:1 ηi:12 down:1 extending:1 references:1 always:1 elementary:4 next:4 shrinking:1 additional:1 combinatorics:1 assumed:1 support:21 there:84 question:2 approximate:1 dγα:4 start:4 borel:7 mathematicae:3 was:4 naturally:1 function:4 north:1 complete:2 form:16 something:1 juh:15 but:4 repeated:1 construction:7 ec:1 true:2 he:1 algebras:2 arranged:1 whether:2 characteristic:1 8c:2 variations:2 us:4 sacks:5 below:7 those:1 iterated:1 problem:7 define:2 similar:6 called:5 s1n:7 ac:2 constant:2 s1m:3 fans:2 defined:24 likewise:1 abstract:1 influence:1 denote:10 engineering:1 proves:1 exist:5 formulation:2 ax:8 dβ:3 check:4 constructed:3 again:2 functions:4 codes:1 no:6 index:1 proceedings:1 ng:1 productively:2 application:1 other:14 coded:3 details:1 mathematics:1 forcing:25 g0α:15 nice:5 elements:10 intend:1 models:10 problems:3 closedness:1 important:1 bounded:3 ξn:5 gap:2 omega:1 needed:1 structure:6 implies:23 vice:5 assume:30 cpa:2 together:9 once:1 starting:3 orders:1 4a:1 |
0704.1885.txt |@word dynamic:1 four:11 prefix:1 entropy:2 increase:7 calculate:10 tween:1 under:4 cytochrome:4 wji:2 dispense:2 p1:1 every:4 affect:1 vast:1 school:1 pooled:4 supports:3 lenski:2 solution:3 humidity:2 vector:6 diversity:1 enhance:1 markov:5 consistent:3 estimates:2 direct:1 approximation:19 likely:4 chen:1 chem:1 even:5 errors:1 mutational:55 organisms:3 selected:9 contributed:3 en:1 above:12 new:12 net:1 increasing:3 evolving:17 here:11 met:7 active:2 chen1:1 elaborate:1 approaches:2 reports:1 tolerance:3 changes:6 york:1 appropriately:1 offs:1 divide:1 highly:26 counts:1 total:12 univ:1 unit:1 dna:15 would:5 negative:2 noting:1 m1:1 therefore:29 survive:1 type:1 until:1 fractions:1 populations:42 adjacency:2 excellent:2 kgi:1 origin:1 must:5 me:1 mg:1 ma:2 room:2 mm:10 ml:18 work:15 theories:1 temperatures:4 mr:1 exceptions:1 example:2 impose:1 wang:2 indicated:5 give:4 involve:1 indicates:1 caution:1 candelas:1 indifferent:1 absolute:3 end:5 turn:2 provide:4 machine:7 how:8 classify:1 description:1 thermodynamic:6 earlier:3 confirmed:1 polymerase:5 summarize:2 parallel:4 types:4 attempt:2 third:2 mutagenesis:6 recombination:10 summing:2 complexity:1 maintain:2 correlation:1 order:6 blind:4 interpretation:3 over:12 vary:2 simplifies:1 evolvability:10 oven:2 experimentally:4 before:5 heretofore:1 better:3 differently:1 hidden:1 maximal:1 eventually:2 them:3 combination:1 fixation:3 effects:6 they:10 structural:1 represents:3 several:5 reasonably:1 reasonable:1 each:48 side:3 independent:5 combining:1 substantially:2 laboratory:3 rt:1 network:30 gradient:4 quantify:1 crucial:1 re:4 ra:3 reader:2 free:3 standard:6 biological:3 estimate:7 r1:11 r2:3 created:1 tolerant:1 serrano:1 purpose:1 synonymous:2 primary:1 rank:1 another:4 illustrate:1 xia:1 similarly:4 approximately:3 plentiful:1 needed:1 perturbations:1 rates:7 listed:2 john:1 insightful:1 repeatable:1 showed:1 princeton:2 approximations:15 zero:6 project:1 plasmid:21 biochemical:2 tion:1 solely:1 minus:4 acquisition:1 extracting:1 seminal:1 mini:4 rewrite:2 spectrum:9 rigorous:1 manner:1 seen:1 contents:1 relatively:3 thoroughly:1 latter:1 isolated:2 fitting:2 causing:2 mutants:51 acquire:1 wells:10 accurately:4 anatomy:1 simplify:8 regular:1 organization:1 phase:1 manifested:1 constancy:1 calculated:5 inferred:1 notion:1 biosystems:2 moriyama:1 random:20 subtle:1 hobson:1 implementation:2 situations:2 explain:1 folded:13 electrophoresis:1 screening:3 do:7 dl:2 dm:3 dj:1 wide:1 dc:2 preferred:1 yielded:4 ds:1 acknowledgments:1 peroxide:4 mathematically:1 clarified:7 generally:3 observed:2 depends:4 radius:1 cloning:1 w1:1 best:1 capacity:3 µt:3 µm:21 µl:15 unable:1 mum:1 drawn:1 µg:8 approach:4 terms:13 assays:2 wa:1 nature:7 gmin:2 wm:46 however:16 otherwise:1 extent:4 contamination:3 carbon:7 wx:1 faced:1 essentially:2 waterman:1 reported:1 against:1 planned:1 exceeds:1 variance:1 com:1 sigmoidal:2 codon:5 mutations:99 represented:1 viruses:5 wider:1 three:3 been:7 extraction:1 much:8 replicate:5 interest:1 basic:3 expected:2 obtained:2 life:1 families:1 quantities:4 νmin:11 applied:3 exception:1 publicly:1 remaining:5 suppose:1 aid:1 property:2 study:1 procedure:7 tions:1 ii:1 ib:1 grown:5 containing:8 perform:1 suggest:2 make:9 plated:1 angew:1 complex:2 unrecognized:1 plates:18 colonies:2 electro:1 rna:2 templates:1 fairly:1 pipette:1 counterparts:4 hand:4 normalization:1 kept:2 academic:1 simulated:1 possesses:2 left:3 protocol:7 just:3 identify:1 yet:1 functionally:6 previous:8 kanagawa:1 had:12 spread:1 transformed:4 tolerable:1 breaks:1 sussex:1 possible:7 background:4 clustered:1 unique:1 occurring:1 cooler:1 performing:1 specific:3 steps:1 arbitrary:3 cooled:1 www:1 right:4 somehow:1 shapes:1 ice:2 probed:1 landscape:1 genotypes:1 shaker:2 predicting:1 binomial:1 substitution:1 mgcl2:2 properties:8 chapter:1 plos:2 ruiz:2 o:27 slightly:1 soc:1 beneficial:2 bath:1 down:1 acad:7 support:1 initial:9 approximate:1 width:1 fraction:24 was:62 synthesis:1 lowest:1 form:8 simplifications:1 differences:1 drummond:3 berg:1 pagerank:1 removed:3 true:1 m9:1 bounds:2 epps:6 phosphate:1 simplifying:1 abstract:1 evidence:3 misfolded:1 conserved:1 exist:1 accounting:1 distributions:4 check:1 physical:1 nm:7 no:7 na:113 when:12 vanishes:2 ng:2 ny:1 setting:4 role:3 holding:1 papers:1 test:6 nu:1 scored:3 preceding:1 variable:1 longer:2 assume:6 time:9 pellets:2 cheme:1 neighbors:1 concept:1 chain:4 equalities:2 osv:1 leads:2 mild:1 comments:1 primer:2 row:4 depend:2 graph:1 flash:1 environment:1 finally:1 stabilizing:3 division:1 keck:1 zhang:1 lynch:1 entries:3 exact:4 minute:2 level:5 did:4 irreducible:2 guo:1 quasispecies:1 leave:1 discrete:1 science:1 round:1 tenths:1 upper:5 measurable:1 bacterial:1 mj:2 bacteria:4 spectral:1 current:6 suspect:1 goes:2 principal:11 mp:1 genes:10 genet:1 water:1 change:12 wait:1 institute:3 simultaneous:1 throughput:2 franklin:1 poisson:4 usually:3 reagents:1 studies:10 extra:6 prefer:1 marker:2 rarely:1 additive:3 centrality:2 encode:1 theoretical:6 marginally:1 introducing:2 claus:1 appendix:8 cases:2 originally:2 reviews:1 values:37 following:3 bioengineering:1 arrive:1 nearest:1 figure:12 predict:2 arise:2 sample:3 performed:12 allowed:1 hydrogen:3 occur:5 discussion:2 spreads:2 chemical:2 criterion:16 parameter:3 product:6 may:9 max:2 clone:1 maa:6 produce:3 designed:2 data:11 natural:9 outline:1 liquid:2 crutchfield:1 eng:1 explicit:1 yielding:1 st:1 sk:1 cse:1 so:23 sa:1 typical:1 webpage:1 indeed:1 pointed:1 entity:1 stability:69 course:2 experiments:38 nitrogen:1 coli:9 argued:1 still:11 tendency:1 supplemented:4 derive:3 thank:1 decreases:1 offers:1 non:2 evol:4 views:1 processes:1 introduce:2 bound:6 half:4 recap:1 now:14 hall:1 maintaining:1 term:6 equality:2 name:3 neutrality:14 proteins:62 realistic:2 cliffs:1 unselected:19 domain:3 square:1 significantly:2 ed:1 ec:1 yield:3 adequately:1 gonzalez:1 living:1 shown:14 factors:3 furthermore:1 plasmids:1 looking:1 contained:3 internet:1 shows:3 agarose:1 theory:8 plotkin:1 derived:1 contain:1 divergence:2 possibility:1 quite:6 california:3 care:2 cycles:4 derivation:2 language:1 selections:1 transition:2 initiate:1 place:1 think:1 first:14 xj:2 sanchez:1 xi:1 surviving:1 dimethyl:1 u1:1 specifically:6 directly:3 carry:2 xp:21 open:2 size:15 given:14 genotype:1 νmax:17 1a:1 indicate:7 cooling:1 1b:1 structures:3 1o:2 gives:1 way:1 mostly:7 continuous:1 eliminates:1 released:1 than:28 population:102 relative:9 effective:2 favors:5 require:1 future:3 magnesium:1 were:52 bauer:1 remained:1 occupies:2 argument:1 generalization:1 ant:3 turner:1 occupied:1 any:7 20o:1 efficient:1 note:15 sciences:2 attempted:1 subtilis:1 begin:3 multiple:8 buffer:5 molecule:2 falls:2 detect:1 rationale:1 successive:1 escherichia:4 inequalities:4 especially:1 discarding:1 average:38 drive:1 numbering:2 ferrari:1 typically:2 show:9 discovered:1 threshold:7 fifth:1 enough:1 only:11 going:1 enriched:1 get:1 genera:1 cannot:2 nearly:1 recombinant:1 gel:3 median:4 denaturation:3 predicted:7 london:1 fellowships:1 maximum:1 connections:2 namely:2 unaltered:1 satisfying:1 αt:3 subsequent:2 behind:2 between:7 prentice:1 reading:4 across:3 multiplied:2 parent:14 parental:7 jp:2 js:1 jl:1 jm:3 jn:1 densely:1 ji:1 jj:2 jk:1 analyzed:2 je:1 come:2 ja:1 jb:1 reaction:8 parentheses:1 survival:1 mono:1 according:1 enabling:1 propagation:1 expression:9 comes:3 among:5 destabilized:1 colony:3 period:1 sampling:2 bm3:4 grants:1 loeb:1 amino:10 markedly:1 incubation:2 combined:2 engine:1 bme:1 chan:1 resistance:4 observe:1 those:8 case:14 levitt:1 kimura:2 single:38 arnold:9 many:7 situation:2 versus:2 characteristics:2 stabilities:8 lipman:1 perez:1 protein:91 technology:2 sauer:1 different:20 revolutions:1 author:2 same:13 coworkers:9 figures:1 events:2 drives:1 driven:1 edges:2 cr:2 roughly:7 without:7 components:1 model:2 ccf:1 justify:1 summer:1 being:2 captures:1 carboxylic:1 relevant:4 minimized:1 segal:1 generator:1 seems:1 except:1 pasadena:1 treatment:1 samples:2 extensive:1 disrupt:1 aspects:1 eigenvalue:8 read:3 digital:2 mol:10 using:18 englewood:1 m10:1 nutrients:1 reduces:1 discarded:3 benefit:2 either:9 fully:1 stationary:7 adami:2 twelve:1 exposed:1 nucleic:3 specified:1 viral:2 genetics:7 dimensions:1 undergraduate:1 provides:2 refer:1 measuring:1 biased:1 georgiou:2 seconds:3 equivalent:5 fitness:3 evolve:10 absorbance:4 frances:3 complementation:1 comparison:1 stone:1 enzymatic:3 origins:1 og:1 discussed:3 greatly:1 neighbor:1 concentrations:1 acyclic:1 cambridge:2 references:1 determine:3 heated:3 accumulated:7 conceptually:1 75o:1 sparser:1 assumed:1 there:9 start:4 low:3 cultures:7 irreversibly:3 complete:2 cloned:1 irreversible:4 improved:1 embedded:2 stanford:1 lysozyme:2 robustness:55 quantitatively:2 eigenvector:12 detailed:4 gone:1 ac:1 ag:1 certain:1 describe:7 am:1 deep:7 general:4 ar:3 diverged:2 file:19 controlled:1 gradients:1 moves:3 again:6 biochemistry:1 graduate:2 caltech:3 forcing:1 briefly:3 separate:1 drift:1 deriving:1 important:4 bounded:1 sonication:1 pool:1 acids:3 starting:4 original:7 represent:1 sci:7 consider:3 mnt:6 debris:3 cooperative:1 cameron:1 expressions:1 reasoning:1 fellowship:1 program:1 nodes:7 te:6 tb:6 urea:23 very:1 mpj:1 heme:4 balancing:1 difference:8 t4:1 list:1 large:14 small:9 thermocouple:2 abbreviated:1 antibiotic:3 monomorphic:55 stochastically:1 rate:21 design:1 enhancement:1 further:5 subscripts:1 what:3 froissart:1 clock:2 sun:1 sum:3 microbiology:1 version:1 fractional:4 method:5 contrast:1 edited:1 full:2 hours:5 selective:1 threads:1 excess:6 equations:23 search:1 tµ:3 allows:1 experience:4 amount:12 vii:1 ask:1 analyzing:1 detecting:1 select:2 proceed:1 probabilities:2 contains:2 comparing:2 taken:1 more:36 site:2 known:2 evolves:5 hour:1 recall:1 equation:44 bias:3 evolved:14 f0:10 f1:1 compare:2 bioscience:1 numbers:8 sense:1 g3:1 νi:14 offspring:2 νk:1 information:5 rather:6 breaking:1 stayed:2 freshly:2 tawfik:1 advice:1 variant:3 connectivity:3 fh:6 bloom:8 fm:23 resemble:1 enzymes:1 spectra:2 overnight:1 developed:1 fraser:1 fersht:1 trade:1 thermal:6 paper:3 through:1 brin:1 y1:2 y0:4 its:11 rapidly:4 sodium:1 pcr:41 solving:3 actually:1 absence:1 systems:3 differed:2 might:3 good:2 ym:3 framework:1 motivates:1 accumulate:6 smoothness:1 goldstein:2 always:2 presented:2 2x:1 infer:1 inequality:3 found:2 referred:1 constructing:1 reactions:6 generation:58 energy:1 hard:2 reduce:3 idea:4 deterministically:1 measurement:4 lysis:1 beyond:2 event:2 ibarra:1 solved:1 since:21 research:3 denoted:2 evaluation:1 occurs:2 drifting:1 favored:2 neutrally:12 siegel:1 difficulty:1 reason:1 members:4 imagine:1 put:1 matthews:2 beginning:3 generate:3 definition:2 desai:1 nonnegative:1 wpo:1 exponentially:1 consequence:1 undergo:1 major:2 probability:20 encoding:3 relate:2 number:27 utilized:1 done:1 blank:1 equating:1 differ:3 perturbation:3 temperature:8 least:5 assumption:3 mosaic:1 calculations:12 molecular:5 recovered:2 too:1 eyre:1 option:1 prediction:4 part:1 believe:2 albeit:1 grew:3 determines:2 determined:6 treated:3 comput:1 randomly:11 concentration:5 null:3 lid:6 wilson:1 destabilizing:2 self:3 majority:1 k1:9 costs:1 finding:1 play:2 added:5 node:6 measures:3 most:6 virus:1 experiences:6 significant:1 position:1 extremely:1 branching:1 ka:1 unequal:2 νk1:1 clear:3 sometimes:1 km:14 optical:1 ruggedness:1 clean:1 predoctoral:1 phenomenon:3 converge:4 relation:1 denatured:3 find:1 occupation:1 multichannel:1 parameters:1 distributed:1 destabilize:1 failed:1 enzyme:4 factor:1 tations:1 columns:1 template:11 landscapes:1 express:2 obtain:8 closely:2 during:14 pellet:2 arxiv:1 underlying:6 common:2 activity:15 wrote:1 bars:1 set:9 ser:1 godoy:1 undergoes:1 tended:1 culture:3 see:4 individual:4 polymorphic:72 untested:1 fontana:1 libraries:2 smallest:1 probably:4 subscript:2 spectrophotometer:1 missing:1 competent:1 both:13 folding:4 sensitive:1 connection:1 became:1 context:1 experimental:12 arbitrarily:2 point:3 simple:1 corresponds:5 flattest:1 unfolded:1 simply:7 adaptation:2 throughout:1 raval:4 complication:1 described:15 thermodynamics:1 create:2 due:9 screened:1 pc:1 describes:4 pf:1 pd:1 pe:2 pj:1 ph:4 pi:6 po:41 pm:18 assigning:1 equilibration:15 p2:1 k2:8 eration:1 exponential:5 p5:1 frozen:1 tolerate:3 empirical:1 while:6 error:30 computed:5 weinreich:1 binding:1 saturation:1 baseline:1 ewm:6 barnes:1 elevated:1 emphasize:1 widely:1 survey:1 higher:12 used:40 domains:1 levels:4 arrived:1 appreciable:1 robust:5 eigenvectors:2 lower:3 database:1 analysis:7 accumulation:1 consistency:4 equilibrated:7 chemistry:1 press:4 tables:1 conclusions:2 internal:1 parents:1 transformation:1 bin:17 bio:1 format:1 kast:1 showing:2 additivity:1 smallness:1 helpful:1 overriding:1 imposed:3 lost:4 systematically:1 follows:1 signal:2 ignore:1 deleterious:1 continue:1 yields:5 byproduct:1 mathematical:13 google:1 methods:6 metabolic:1 some:10 back:1 understood:2 towards:5 30o:3 scale:2 describing:1 annu:2 measurements:22 per:19 tends:2 proc:8 minimal:3 run:1 bl:1 continuing:1 biophysical:6 bk:2 step:1 bw:2 plots:1 constraint:4 range:2 block:2 into:16 within:4 nsf:1 retaining:1 appropriate:1 proportional:4 fibr:1 measured:10 question:3 long:2 occupy:3 analyze:1 sections:3 etc:4 files:1 ligation:2 potassium:1 murphy:1 properly:2 link:1 repeatedly:1 line:1 directed:1 supplementary:1 intuitive:2 us:4 prep:4 uk:1 similar:7 called:3 saturate:1 constant:7 defined:9 influence:1 engineering:2 modeling:2 formalism:3 kp:1 genome:1 nat:1 jd:5 explaining:1 elements:7 exp:1 provided:2 prepared:3 meaning:6 allowing:4 structure:3 independently:1 correlated:3 algorithm:1 required:1 sawyer:1 equivalently:1 came:1 walker:1 requires:4 having:1 once:3 illustrates:1 results:9 existing:1 gf:7 broader:1 edu:5 contributions:1 biol:11 stably:5 uniqueness:1 stable:11 undirected:1 dramatically:1 indicating:6 assay:3 expressing:1 p0i:22 conditions:2 engineered:3 matrices:1 fewer:1 noted:4 zl:2 smaller:2 folds:3 replicates:11 fold:10 picked:10 dynamics:6 acid:16 giving:3 assisted:1 expressed:4 networks:7 cell:7 consistently:1 experiment:6 3l:1 body:1 justification:4 chose:1 degree:2 respectively:6 growing:1 others:3 extreme:2 great:1 dividing:1 epidemiology:1 larger:5 resulting:1 implement:1 gene:23 makes:5 holmes:1 named:2 apr:1 wij:6 decrease:1 names:5 summation:1 use:12 asymptotic:1 usa:9 remains:5 chi:2 next:15 few:6 chloride:2 started:1 becomes:2 carrying:2 normalized:5 starter:2 choe:1 account:1 stabilized:2 reproduce:1 obvious:2 thin:1 averages:1 dropped:1 control:8 taq:2 links:1 plate:12 process:8 high:8 assumptions:1 monoxide:5 epistasis:1 animal:1 instead:3 stock:2 gardner:1 mixed:3 multiplication:1 da:3 primers:1 correspond:2 manganese:1 element:2 allow:3 subsequently:1 divided:1 bins:10 evolutionary:13 move:2 interpreted:2 produced:3 jimenez:1 contaminated:2 raw:2 strikingly:1 lb:11 la:1 chosen:5 estimating:1 lu:1 dmso:3 greater:2 python:1 material:1 mention:1 p12:1 day:2 university:2 identified:1 sufficiently:8 magnitude:2 shaking:1 experienced:1 constraints:1 related:3 measure:6 our:17 transitions:2 out:4 matrix:17 res:2 rev:5 performs:1 maximized:1 adaptive:3 cause:4 math:1 interactions:1 diagonal:1 completely:2 convolutions:1 log:1 determining:1 could:6 times:1 counterpart:1 length:1 retain:2 suffix:1 reached:2 histograms:2 system:2 occupancy:1 their:18 biochem:1 final:15 prone:23 shell:1 explanation:2 exactly:3 lists:1 45o:1 limiting:1 reproduction:2 wilke:9 result:1 enforced:1 unchanged:1 curves:2 robot:6 need:2 constrained:3 demonstration:2 clearly:1 viewed:2 min:2 able:2 mix:4 accuracy:1 claremont:2 connected:6 nucleotide:21 why:3 hj:1 consequences:1 hh:1 fact:11 selection:31 supported:5 multicellular:1 hb:1 subtracting:1 based:5 pressures:1 should:10 terminal:1 score:1 molecules:1 thresholds:1 achieve:1 equilibrium:8 means:3 quantified:5 µe:1 ones:1 wise:1 evolution:87 substrate:1 numerous:1 doublings:3 ascertain:1 fixed:1 generations:15 view:3 enhances:1 statistical:1 shake:1 humans:1 intensity:2 computer:2 gmail:1 maynard:1 centrifugation:2 tend:5 favor:2 written:2 closed:2 stadler:1 progress:1 connectivities:1 email:1 ability:3 importance:1 wj:1 efficiency:2 key:1 david:2 lu1:1 wilbur:1 freely:1 taking:5 equal:17 ln:1 catalyze:1 jersey:1 mutating:1 sequenced:3 aa:1 unclear:1 co:6 unfold:1 wall:1 ca:1 ce:1 walk:3 distinguish:2 maximize:1 sequences:21 table:8 rpm:3 second:9 addition:5 genetic:3 slowly:1 treat:1 topology:2 define:1 contribute:3 corresponding:6 t50:16 sufficient:2 bulk:1 ensuring:1 bull:1 last:2 iverson:1 present:1 moya:1 value:12 promotes:2 will:18 mutant:33 wkm:9 thus:7 vm:15 equilibrate:1 capture:2 perhaps:2 began:3 member:1 units:2 inc:1 twelfth:2 difficult:2 http:1 wk1:8 php:1 identity:4 numbered:2 polymorphism:5 off:1 nonetheless:1 well:26 hartl:2 sets:2 comparisons:3 usual:1 less:5 moments:1 accurate:10 identically:2 wagner:1 mfm:6 eµ:3 manifestation:1 stored:3 predicts:2 purified:2 macroscopic:1 coordination:4 web:1 rapid:1 density:1 smith:3 bench:1 lattice:3 add:2 valid:1 natl:7 usage:1 identical:5 tests:2 fluctuating:1 increased:4 morphic:1 increases:1 five:1 scheme:2 sequencing:4 immediately:5 variants:2 insert:1 like:3 success:1 sizes:4 become:3 works:1 page:1 because:9 pauling:1 sequence:31 concentrator:1 quantitites:1 growth:3 lead:2 broad:1 avoid:1 bacillus:1 does:1 mutation:45 demonstrated:2 limitations:1 biology:4 decline:6 journal:1 overall:1 pressure:1 host:1 although:1 approximating:4 after:28 about:6 rare:2 carried:1 column:6 insufficient:1 introduced:6 equally:1 own:1 previously:4 functional:35 assess:1 weighted:2 van:10 additional:23 artifacts:1 justifying:1 overestimate:1 function:5 funnel:1 ewpo:1 hs:1 but:13 volume:2 collected:3 neutral:60 gain:2 convergence:3 ha:1 he:1 made:5 compute:1 whether:12 cells:7 harvested:3 below:6 limit:17 demonstrate:1 distribution:30 minutes:14 mitochondria:1 int:1 recognize:1 exceeded:1 ergodic:1 denote:1 jesse:3 functions:6 compared:3 variety:1 percent:5 detail:1 other:12 chance:1 space:5 4o:7 4m:2 volumes:2 indirectly:1 |
0704.1886.txt |@word footing:1 homomorphism:17 consider:3 illustrates:1 dynamic:4 results:7 leads:2 proposition:6 consists:5 semantic:1 clarified:1 denotes:1 reasoning:1 equivalences:1 whose:18 preserves:9 pedro:1 calculate:1 advantage:1 tt:7 stably:8 ts:2 languages:1 finally:4 program:8 those:11 under:9 analogous:2 presentation:2 worth:2 ingredient:1 applied:2 groupoid:9 already:4 straightforward:6 very:3 reader:1 hughes:2 choice:2 implicit:1 corollary:6 every:8 interpreting:1 ramified:4 word:2 difference:1 categories:7 rightmost:1 tilings:1 presented:7 bn:4 ςx:7 notes:1 idl:20 large:1 involution:9 vector:1 interchanging:1 section:3 small:1 lise:1 concluded:1 mn:2 says:1 hyp:2 pmr:1 dealing:2 variables:1 direct:2 past:2 second:3 pass:1 further:1 theories:1 analogue:1 canonical:3 even:2 what:3 adds:1 sub:5 giving:2 abi:1 sum:2 selected:3 analogously:2 uniform:1 current:1 tarski:1 version:1 goes:1 sup:42 relational:4 preserved:2 satisfy:7 full:7 led:1 notions:1 degree:5 mem:1 respectively:9 never:1 component:3 certainly:1 here:3 canonically:2 inverse:10 lindenbaum:18 groups:2 address:3 consideration:2 enveloping:1 appears:1 interpret:3 morphisms:3 obtained:10 preorder:3 remark:3 generalizing:2 technical:2 study:2 larger:1 allows:1 suggests:3 base:2 products:1 moerdijk:1 ctl:5 que:3 conveniently:2 suitable:3 makes:2 quotient:9 uniquely:3 equivalence:4 useful:2 subcategory:6 family:5 extra:2 apr:1 contrarily:1 congruence:7 logical:2 replace:3 nondeterministic:1 flexibility:1 boolean:2 generality:1 apply:1 quantales:41 univ:1 relating:3 unit:12 use:4 subsumes:2 bilinear:1 handled:2 would:3 prove:16 formulated:1 beginning:1 abbreviations:2 motivate:1 tl:2 reflexivity:2 next:2 classically:3 noting:1 call:2 therefore:3 paterson:1 knaster:1 taken:1 zorn:2 themselves:1 simpler:1 tell:1 more:6 preserving:2 ecnica:2 becomes:2 operators:9 germs:1 constructs:1 stone:1 editors:1 particular:14 known:5 hold:16 iii:2 must:2 characterizes:1 ii:2 account:1 isomorphism:14 join:7 concretely:2 recall:2 equation:3 when:3 mi:2 universidade:2 london:2 preliminaries:1 emerson:1 paragraph:1 obvious:10 following:33 meet:2 caa:2 example:7 def:3 proof:22 subcategories:2 abelian:2 process:1 sense:3 confused:1 sake:1 bk4:10 want:1 arise:3 ist:1 conversely:1 occur:1 axiomatization:5 information:1 respective:2 end:2 lemma:8 deserves:1 rather:4 verify:1 hom:4 negation:3 s5:36 s4:25 write:6 maps:2 opposite:1 instead:1 map:13 product:7 de:5 mat:1 algebra:7 may:7 after:2 derived:1 diagram:1 applications:2 produce:2 adjunctions:3 multiplication:14 representations:5 recursive:2 stress:2 transitive:1 natural:8 dynamical:1 third:1 concern:1 lemmas:1 explicit:1 correspond:3 element:19 provide:2 so:6 sl:4 definitions:1 transitivity:2 order:14 operations:3 least:13 interpretation:9 joins:14 indeed:1 pointed:21 summarized:1 satisfied:4 interpreted:5 symbols:4 course:4 paper:7 through:1 mentioned:3 existence:4 satisfies:22 still:1 its:6 hazewinkel:1 before:1 superior:2 monotonicity:1 lo:2 temporal:5 modalities:6 lj:2 conjugation:1 writing:1 better:1 lw:2 according:2 systems:13 mail:2 freely:2 defining:7 image:2 correspondence:1 eventually:2 ym:6 pure:12 coproducts:2 bisections:1 jα:3 za:1 mention:2 they:8 yq:2 yp:4 now:19 nor:1 easily:7 localic:2 finite:5 induction:6 homomorphisms:4 methuen:2 always:6 w2:3 arrows:5 identified:4 inequality:4 each:28 found:1 entirely:1 side:1 characterized:3 referred:2 subset:4 lie:1 domain:5 differential:1 directly:1 meets:5 series:1 eg:9 ef:4 rosenthal:1 idea:1 functor:8 axiomatizations:3 frames:9 used:2 ex:4 quantum:1 our:3 operation:5 eq:4 ring:1 special:1 description:2 category:19 respects:4 clarity:1 rr:4 unital:39 furthermore:3 since:10 rx:1 bad:1 research:3 looking:1 similarly:9 contained:1 groupoids:9 stud:1 poci:2 denoted:1 formula:3 induced:2 supports:1 math:5 shows:1 earlier:1 theory:4 monotone:4 diagonal:1 possibility:2 standard:3 pleasant:1 mulvey:2 cartesian:1 formation:2 besides:1 approach:1 companion:1 remainder:1 axioms:6 additional:6 definition:33 pairs:3 fixed:7 monoidal:2 language:2 v1:3 geometry:1 could:1 impose:4 times:2 counterpart:2 turn:2 length:1 schemata:1 ltd:2 hence:27 onto:1 think:1 phrased:1 first:5 singleton:1 xi:8 xn:27 reflexive:1 bijection:1 conjugacy:7 supplement:1 preservation:1 restrict:1 lat:22 xy:3 done:5 relations:28 another:2 infinitary:1 distributive:3 precisely:3 illustrate:1 1q:3 given:7 necessarily:2 embeddings:1 interesting:1 their:6 introduction:3 cambridge:3 adjoint:13 behaves:1 system:10 construct:1 imposing:3 encyclopaedia:1 too:1 bijections:1 scheme:5 structures:6 1l:17 gives:1 free:5 assign:1 para:1 explanation:1 exactly:2 proving:2 foliation:1 required:2 part:2 logicians:1 x2:2 x3:1 x0:27 x1:15 gmail:1 than:4 semantics:23 kind:1 equals:4 heyting:1 penrose:1 sections:1 tree:1 namely:3 tecnico:1 project:1 classes:1 contrary:1 implication:2 monomorphism:2 departamento:1 treated:1 distinguished:1 projections:1 pre:6 bridge:1 failing:1 symmetries:1 ana:1 objects:12 bs4:9 foliations:1 argument:2 generalization:2 endomorphism:7 say:5 joyal:1 conjugate:5 need:2 seen:7 regards:1 any:15 tierney:1 functors:3 paths:1 constructions:1 mappings:1 zero:1 convenient:1 latter:4 internat:1 able:1 ideas:1 zq:2 note:1 instance:8 ideal:1 take:2 k4:23 indexed:4 coincide:3 techniques:1 recursively:1 rovisco:2 formulas:8 play:1 added:1 shall:30 lα:2 colimit:1 centro:2 birkh:1 most:2 ecnico:1 immediate:3 plenty:1 preliminary:1 pair:11 pais:2 residuation:1 future:5 class:2 give:2 dom:2 clear:6 adopt:1 coincides:4 traditional:1 categorical:1 points:3 locales:3 omit:1 left:11 notion:4 fact:16 science:1 saying:1 show:2 supported:16 implying:1 johnstone:1 spaces:2 relation:21 codomain:1 determined:2 trivial:1 find:1 make:2 completion:1 execution:2 aς:5 based:7 knowledge:1 true:1 representation:1 specified:3 written:2 topological:4 should:5 analytic:1 only:10 αb:3 generators:20 summarizing:1 equipped:13 various:3 employed:1 distributes:2 axiom:8 meant:1 do:3 over:16 above:7 notation:2 means:11 familiar:1 ϕw:4 scientists:1 ssq:28 aα:1 words:6 new:2 lattices:36 conjunction:5 neither:1 areas:1 closure:9 stability:4 qs:2 qu:10 qt:7 qy:3 endomorphisms:7 arxiv:1 yield:1 consisting:1 twice:1 coproduct:4 qz:4 involutive:54 including:4 qk:9 qj:11 remains:2 available:1 set:37 modulo:1 constructing:1 exists:1 locale:17 iteration:1 frame:18 ends:1 monomorphisms:1 y1:8 see:14 computer:2 usefulness:1 w1:23 y0:4 lisboa:4 close:1 subject:1 satisfying:13 tensor:15 αv:6 monoid:10 αx:5 rings:1 consequence:3 connective:1 αa:1 unions:1 smallest:1 identification:2 closed:8 between:7 geometria:1 geometric:1 equiv:1 conditions:24 αn:1 preserve:6 publishers:2 notice:3 terms:6 extend:1 missing:1 wn:14 complement:1 however:3 jr:30 js:2 ww:5 hypothesis:1 wi:6 extent:1 amer:1 holds:5 topology:2 both:5 interpretations:3 commenting:1 instant:2 kluwer:2 many:1 taking:3 equal:3 presentations:3 etc:9 pdl:3 iv:2 context:2 logic:41 mean:1 com:1 0l:1 otherwise:2 kripke:12 co:3 key:1 point:10 simple:4 overview:2 ca:1 leeuwen:1 corresponds:4 simply:6 adaptation:2 path:2 moreover:3 li:4 semigroups:6 longman:1 pp:3 pq:4 described:6 commutative:1 pt:1 addition:4 resende:4 due:4 been:3 tensors:7 ai:4 much:1 foliated:2 interest:1 basic:1 expected:2 reflective:2 algebras:8 universal:10 partial:1 define:14 surjective:2 direction:1 arises:2 corresponding:2 adjunction:5 ϑw:2 aα2:1 am:32 propositions:1 auser:1 instituto:2 wilce:1 ensuring:1 last:1 general:5 assigning:1 manifolds:2 case:6 pitman:1 multi:1 main:1 subsets:1 operational:1 value:3 will:12 while:1 replaced:1 theoretical:1 applies:2 situation:1 property:10 quantale:78 portugal:2 vol:4 assigns:3 thus:25 concatenation:2 intuitionistic:12 vp:1 itself:3 triple:3 greater:2 sequentially:1 binary:12 containing:2 cresswell:2 verified:3 executed:1 intended:1 isomorphisms:3 same:10 clearly:1 ya:1 largest:2 proved:3 several:1 subalgebra:1 independent:4 extended:2 embedding:1 complemented:1 assignment:1 hand:3 usually:3 purpose:2 necessity:6 infinite:1 distributivity:4 qjr:3 identity:2 yy:5 suffices:3 programs:5 idempotent:3 well:4 analysis:1 obviously:1 thought:1 academic:2 without:1 greatest:1 sets:4 model:5 matema:2 arising:1 self:3 monoids:1 usual:10 graded:21 just:9 less:1 being:12 hybrid:1 topos:1 obtain:16 rest:2 detail:1 unary:4 via:2 atomic:1 aspect:1 world:4 facts:2 qjα:1 alternative:1 powerset:1 succeeding:1 previous:7 adv:2 ts4:5 unique:3 generator:4 infinitely:1 regarded:5 conclude:7 rosick:1 theoret:1 mathematically:1 lattice:57 corollaries:1 easy:7 theorem:8 stable:5 semigroup:3 guarantees:1 remaining:2 generalized:4 real:1 tests:1 explained:1 aspects:1 reuse:1 worlds:2 rules:4 outermost:1 showing:6 repetitions:1 possible:10 bijective:1 cf:2 possibly:1 know:1 background:2 press:4 immediately:2 intersection:1 necessary:1 like:2 δx:2 university:1 follows:12 mit:2 separately:2 lawson:1 either:2 tica:2 arbitrary:9 ljs:1 pointwise:3 quantal:2 terminology:1 making:3 mathematical:1 preorders:2 because:10 classical:10 sends:1 sequences:1 some:9 connectives:5 examples:7 b2:2 respect:4 images:1 conveys:1 soc:1 ourselves:2 jlj:1 provided:3 describing:1 feder:1 ςb:11 grading:9 normal:7 comments:1 conservative:1 ςt:3 does:4 ςq:28 provides:2 leftmost:1 adjoints:4 tk:9 refer:5 selfadjoint:1 scientific:2 bm:7 equivalent:4 bi:4 bk:22 bt:10 step:2 bq:4 although:1 bs:5 propositional:23 obscured:1 properties:20 quotients:10 about:2 actual:2 bimodal:41 extension:3 algebraic:8 theorems:8 meaning:3 o:5 essential:1 mutually:1 whence:1 plus:1 associative:2 modal:61 nucleus:15 introduced:1 automatically:2 morphism:3 tecnologia:1 equally:3 contains:3 jθ:2 followed:1 inclusion:2 into:3 obtaining:2 isomorphic:4 assess:1 remarks:1 appropriate:1 right:4 references:2 frm:2 operator:19 mere:1 logics:5 van:1 deal:1 utl:1 support:20 there:24 composing:2 appl:1 handbook:1 editor:2 way:18 coecke:1 was:5 att:1 opposed:2 harel:1 complete:10 form:4 believe:1 converse:1 denoting:2 forgetful:2 but:6 neutral:1 construction:5 etale:8 sistemas:1 implies:5 injection:9 funda:1 valuation:1 made:2 intuitive:2 society:1 whether:3 inside:1 up:4 us:11 bijectively:1 grothendieck:1 similar:11 called:6 aa:13 θj:3 ab:16 associated:3 moore:1 ag:2 af:2 defined:22 abstract:2 describe:7 condition:10 accessibility:11 covers:1 denote:13 ap:4 single:1 proves:2 av:2 ay:5 ax:2 az:5 check:1 computational:1 defines:4 again:4 completeness:6 no:3 galois:1 whereas:1 generally:1 rs:1 sublattice:1 other:15 role:1 details:2 mathematics:3 out:2 rt:3 briefly:1 elements:6 kinds:1 models:6 symbol:1 remarked:1 inherited:1 a1:1 generated:8 important:1 bounded:3 variable:3 dense:2 kozen:1 disjunction:1 union:1 structure:10 ςa:24 occurrence:1 ciˆencia:1 using:6 fund:1 assume:6 4b:4 american:1 space:2 together:2 4c:2 equivalently:4 noncommutative:2 time:5 far:1 nuclei:7 4a:1 starting:1 strings:1 once:2 |
0704.1888.txt |@word homomorphism:5 sergei:1 phung:23 ginzburg:1 consists:3 kassel:1 analiz:2 whose:6 marcos:1 paris:2 investigation:2 under:5 hermann:1 rise:3 every:2 manin:8 basics:1 induction:3 solution:1 convenience:2 vector:25 math:29 guiding:1 enjoy:1 xiσ:3 submodules:1 bialgebra:5 direct:7 second:5 even:27 scv:1 above:12 new:7 increasing:2 consisting:12 coefficient:4 notions:1 never:2 here:11 represented:2 contraction:1 obtained:2 leaves:1 gld:1 ignoring:1 tσi:2 suitable:6 schur:1 projection:2 classification:1 explained:1 gurevich:4 highly:2 total:2 univ:2 unit:5 would:1 remainder:1 supergroups:1 negative:1 iq:1 therefore:35 centre:1 m2:2 type:7 duals:2 supergroup:2 ematiques:1 muse:1 berlin:2 warm:1 hold:2 must:5 md:2 springer:3 mm:1 ml:3 mn:2 mi:5 mt:23 cibils:1 mr:2 example:43 contragredient:1 give:4 extia:4 preserving:2 dualization:2 reviewing:1 mail:3 end:75 provide:1 hom:59 bstract:1 how:1 ordinary:17 description:3 replacing:1 after:3 diagram:5 summarize:3 polishchuk:1 like:2 green:2 decreasing:3 order:10 operations:2 restriction:3 recurrent:1 over:24 satisfied:4 london:3 satisfies:3 before:3 superdeterminant:1 symmetry:2 fiz:1 fix:16 writing:8 connes:4 fij:6 fii:2 interdisciplinary:1 subcomodule:2 xiℓ:2 tableaux:1 they:9 kirillov:2 represents:1 comodules:5 reasonably:1 lorenz:24 arrow:1 each:12 qkℓ:2 side:5 associative:1 series:23 principles:1 combining:1 jimbo:2 restricted:1 fellowship:1 ra:7 rb:8 reader:2 rn:16 forth:1 ri:8 interchanging:1 rk:5 turning:1 linear:25 associate:1 free:7 standard:14 nth:3 r1:4 r2:4 δij:1 signature:1 generalizations:1 already:2 primary:1 rank:1 zelevinsky:1 ℓm:1 gradu:1 antisymmetrizer:4 similarly:14 xij:21 xik:1 xin:5 master:16 ordered:5 athematics:2 requisite:1 princeton:2 xi1:7 xi2:7 classes:1 1n:1 powers:3 sees:2 manner:1 seen:3 chapitres:1 convenient:1 latter:3 fourier:2 indexed:1 nen:1 2εi:3 rℓ:1 object:8 complexes:4 regular:2 partition:1 flow:1 yang:14 principle:1 notion:1 gauge:1 koszulity:6 d2:4 d1:3 bourbaki:1 claude:1 drinfel:2 axiom:1 dn:14 do:2 dj:5 establishes:1 di:18 de:6 ρcv:1 reversal:2 dt:5 du:2 runs:1 bab:2 bak:1 reference:3 δji:3 result:3 discussions:1 ebre:1 techniques:1 said:6 tensor:18 rings:2 symmetric:28 conceptual:1 µa:3 µb:1 preserve:2 terms:10 wb:1 restricting:5 however:4 adapting:1 iℓ:7 ung:2 uni:1 eferences:1 polynomial:7 commutative:4 basis:59 been:10 tuynman:1 interest:2 basic:2 algebras:58 exactness:2 supersymmetric:3 concerning:3 berezin:3 applied:1 nonquadratic:1 transformation:1 aii:1 applies:2 koszul:53 property:6 epimorphism:3 ip:1 tions:1 ii:3 ij:18 im:32 exterior:4 march:2 percy:1 id:8 make:1 format:5 complex:12 roland:5 split:3 tannakian:1 several:1 grows:1 independent:2 i1:13 i2:8 hand:9 characters:2 niu:1 weakly:3 xji:1 academic:1 thm:1 claims:1 av1:1 left:10 unified:1 graded:42 just:2 newton:2 ℓth:1 facts:2 nicolas:2 hai:25 enters:1 han:2 character:4 ideal:10 macdonald:1 belongs:2 easy:1 iσ:6 spanned:1 possibly:1 background:3 unique:3 grenoble:2 specific:1 arbitrary:7 right:13 dimitri:1 deal:1 sends:5 grading:19 normal:1 hodge:1 comments:1 asking:1 bra:1 niversity:2 confluent:4 super:18 properties:8 proceed:1 chapter:1 beilinson:1 algs:25 05a19:1 o:16 alge:1 primitive:1 macmahon:13 bound:1 down:1 remarks:1 soergel:1 acad:2 combinatorics:2 physicists:1 fraction:1 rela:1 was:5 gij:5 supercommutator:7 δkb:1 δkc:1 form:30 δka:1 denoting:2 δki:1 true:1 again:4 versions:3 inside:2 dordrecht:2 submitting:1 cℓm:2 proved:3 qij:6 abstract:1 determinantal:3 proves:6 dλ:3 check:3 constructed:1 xkj:1 ni:1 nj:1 no:26 generally:1 vanishes:1 setting:5 tid:1 picture:1 functorial:4 gijs:1 nonreduced:2 assume:15 interval:1 modules:5 together:3 vietnam:1 n0:2 phisms:1 global:4 leads:5 unmixed:3 certainly:2 inverse:2 depend:1 finally:7 ebres:1 analogous:3 ciences:1 zhang:4 choice:1 entries:4 exact:9 partitions:4 dim:44 presented:1 zeilberger:4 guo:1 involution:4 science:1 der:1 work:4 says:1 villa:1 sℓ:2 sign:2 nstitute:1 spectral:1 stands:1 xσ:1 celebrated:1 current:1 satisfy:5 aint:2 realizations:1 extna:1 groups:5 address:3 along:3 sending:1 shift:1 studied:2 usually:2 hospitality:1 montreal:1 subcategory:1 extra:5 wang:1 additive:2 working:1 prove:7 positive:4 visit:2 live:2 anticommutes:1 introducing:1 duality:7 coassociative:1 appendix:4 cases:4 originally:1 following:42 positselski:1 arrive:1 claim:4 permutations:1 occur:1 verlag:3 s2:2 s1:1 write:5 etingof:6 nyn:1 pure:11 parameter:3 map:48 product:15 mat:1 may:4 max:1 fueled:1 representations:4 compatibility:2 natural:7 outline:3 whenever:1 sr:4 explicit:6 st:1 sk:9 so:35 sn:92 sm:3 representation:11 michel:2 ogievetsky:1 aforementioned:1 indeed:11 pointed:2 soc:7 derive:1 tora:12 thank:2 summands:1 thang:1 offers:1 ours:1 main:1 formulæ:1 non:3 thereby:4 chelsea:1 introduce:1 hamilton:1 khudaverdian:2 now:11 discuss:1 inversion:1 equality:4 e2πi:1 james:4 teoret:1 xℓ:10 em:2 en:6 ei:39 ed:2 ev:1 eq:1 shown:3 monographs:1 space:18 furthermore:5 epartment:1 contained:3 pyatov:2 formula:9 shows:7 theory:7 quite:1 yuri:1 besides:3 e1:1 e0:1 cycles:1 language:1 place:1 gordon:1 view:6 think:1 first:6 xj:31 xk:7 xi:98 xn:27 xl:1 xm:3 variables:2 xd:30 specifically:1 ring:14 interchange:1 given:54 necessarily:3 checked:1 categorical:1 brevity:1 1d:2 white:1 supermanifolds:1 gives:6 way:4 proving:2 x2:7 x1:29 than:3 coefficients:3 foata:3 yi1:1 were:2 published:1 pre:1 rend:10 ann:2 generalization:3 say:2 any:21 functors:1 multiparametric:1 facult:1 note:14 sciences:1 emphasis:1 potential:1 take:2 symmetrizer:2 formulas:5 multiple:2 trace:1 investigations:1 algebraic:3 automorphism:2 pair:2 considered:1 later:2 precise:1 show:9 notations:1 spaces:6 counit:6 yoneda:3 aτ:1 state:2 only:10 explicitly:7 black:1 equipped:2 embeds:1 cannot:1 aν:2 settings:1 yield:2 summary:1 characteristic:7 x22:3 communicated:1 kernel:3 j1:3 namely:1 y0:1 parshall:1 fails:1 satisfying:8 inequalities:1 ways:1 review:1 bialgebras:1 between:4 checks:1 αn:4 notice:1 foreword:1 jq:1 jm:2 jn:2 berezinian:3 comm:1 ji:1 jj:5 article:7 combinatory:1 concentrated:5 σj:4 σi:7 σn:1 many:1 according:2 voronov:2 concentrate:1 embedding:5 expression:2 comes:3 pole:1 grants:1 assertions:1 moreover:17 specializing:1 marc:2 ker:24 mart:1 motives:1 nred:4 ınez:1 offered:1 violette:5 noncommutative:9 careful:1 those:1 case:21 etienne:1 xiii:3 darin:1 situation:1 coassociativity:1 motivated:2 different:1 verified:1 combination:2 formulations:1 same:3 jℓ:2 pak:10 pan:1 superspaces:10 extended:1 leonid:1 yd:3 invariance:1 totally:1 rance:1 components:9 coordinate:1 dimension:12 being:6 when:14 actions:1 oxford:3 dominique:1 except:1 dipper:1 treatment:1 real:3 aspects:2 rules:1 using:11 mod:14 lˆe:2 identifying:3 either:2 multiplicative:1 reduced:7 reidel:1 comodule:11 deduce:1 images:1 nonzero:7 provided:1 dimensions:3 decomposition:3 provides:2 porter:1 refer:2 semigroups:1 power:11 equivalent:7 universit:2 artin:4 william:1 central:4 oc:1 aℓ:19 act:1 mixed:4 oq:3 op:1 berger:14 cambridge:1 jian:1 inclusion:9 image:6 references:3 determine:1 elementary:3 essen:1 log:1 assumed:1 there:12 mathematischen:1 start:2 cisely:1 idb:7 jun:1 applying:5 grothendieck:5 aa:1 ab:2 ai:1 certain:6 aj:23 am:2 general:15 ar:3 au:1 gorenstein:1 av:5 grassmann:3 yoga:1 benoit:23 graduate:1 field:7 valid:1 mathematics:4 a1:5 commutator:1 a3:1 a2:3 recherches:1 resolution:5 original:3 represent:1 sci:2 consider:7 alg:6 lack:1 scalar:2 montr:1 follow:2 research:3 preserves:1 tx:6 combinatorial:1 tv:6 tu:4 tr:7 ts:4 tq:1 tn:20 tm:2 tj:7 th:4 ti:24 presentation:2 straightforward:1 returning:1 corollary:8 deformations:1 condition:7 pbw:2 t4:2 t5:1 t2:3 t1:1 mλ:6 inversions:1 superalgebras:50 segre:2 zero:2 further:3 canonical:9 opted:1 richard:1 section:5 brief:1 version:6 subspaces:15 learned:1 edited:2 full:1 christian:1 component:3 ranges:1 equations:2 mult:1 generalizing:1 antisymmetric:2 amount:2 permutation:2 action:4 uniquely:2 via:8 followed:1 family:2 texts:1 takes:3 quasi:1 ψi:3 taken:1 more:7 initiated:2 operators:9 tℓ:7 particular:20 known:4 recall:18 equation:14 des:2 det:6 edex:1 remain:1 canonically:1 def:2 f1:4 stated:3 yx2:2 states:2 numbers:1 sense:2 νn:26 needs:1 φii:1 goal:1 rather:2 maps:19 lexicographical:2 acta:1 specializations:1 simplicity:1 fr:1 ubiquitous:1 algebra:95 mapping:1 ζn:6 fg:1 fi:15 fj:1 gℓm:2 fm:1 short:2 onto:2 departure:1 fundamental:2 help:1 ith:1 developed:1 paper:1 through:1 signs:2 y1:4 existence:1 y2:1 its:10 affine:3 actually:2 deformation:1 supersymmetry:7 yi:22 yk:6 yj:1 ym:14 yn:12 finitedimensional:1 framework:1 vect:4 φi:3 h98230:2 yu:1 easily:3 homomorphisms:3 always:4 iff:1 inequality:3 turns:1 comultiplication:4 found:1 2n:5 hard:1 functor:8 kℓ:1 obtains:6 quantum:31 since:19 induces:1 denotes:6 denoted:7 induced:1 evaluation:3 occurs:1 enveloping:1 mmm:2 base:1 put:9 definition:2 pairs:1 zjk:1 zji:8 sylvester:2 evu:1 american:1 exponentially:1 consequence:5 exhibited:1 number:4 done:3 hochschild:1 distributive:4 subring:1 passes:1 differ:1 multiplicativity:1 introduction:6 least:1 assumption:1 dt3:3 dfg:1 immediate:1 part:4 authors:3 translation:1 yℓ:12 king:1 kind:2 cyclic:1 qλi:1 aims:1 contravariant:1 str:13 idempotent:2 igor:2 idempotents:2 tσ:13 lie:4 generalizes:1 self:1 k0:1 generalized:2 analogs:1 chart:1 confluence:5 most:1 88k:1 appear:5 clear:2 athematik:1 ext:2 exp:2 physics:2 phenomenon:1 deligne:1 grundlehren:1 relation:6 finn:1 superalgebra:61 completion:1 ymp:9 merkulov:1 generators:16 ymd:2 factor:3 his:3 notation:7 closely:1 during:1 reprint:1 alexander:2 ym1:4 ym0:3 ym2:1 transversal:2 arxiv:11 doubles:2 set:10 topics:1 see:46 analog:2 permuted:1 zki:1 various:3 conditions:1 hecke:22 δab:2 both:8 useable:1 last:5 reverse:2 poincar:4 context:2 finds:1 point:2 simple:4 corresponds:4 parametrization:1 dimensional:10 simply:1 asserted:1 throughout:5 pp:1 described:3 publishing:2 pu:1 due:4 reduction:11 pa:6 kronecker:1 ph:3 pi:23 pn:7 96k:1 generating:6 lives:14 representative:1 systematic:1 p2:1 p0:2 p1:1 forgetting:3 while:12 replaced:2 evaluating:1 vbj:1 δsr:1 vectors:1 vol:6 rij:5 owes:1 ready:1 vanish:1 confirms:1 grant:1 belong:3 ermany:1 products:3 subalgebra:2 composition:1 arrives:1 dimk:1 felix:1 viewing:3 recent:2 analysis:1 landmark:1 entry:1 λr:7 gelfand:1 reviewed:2 λi:6 λn:16 letting:5 submodule:1 kluwer:1 internal:2 theorem:41 remaining:1 bij:12 bii:1 evaluate:2 bib:1 integer:2 formal:1 follows:17 ees:1 doron:1 yields:14 alternatively:1 translated:2 composites:1 mathematical:6 often:2 some:18 pierre:1 examples:7 δbc:2 shall:3 prop:4 providence:1 proc:4 temple:1 minimal:7 bd:3 bg:5 ba:4 bb:14 bm:7 bn:1 martin:23 continuing:1 bi:12 bj:10 rue:1 step:2 hilbert:7 idv:8 completing:1 idu:1 idr:1 range:1 extensions:2 consequently:1 ida:3 supercharacter:10 nsa:1 into:11 isomorphic:6 primarily:1 span:1 question:1 long:1 milne:1 translate:1 sections:3 rees:1 delta:1 russian:2 injection:1 considerable:1 consist:1 cij:4 up:1 us:4 cir:1 garoufalidis:4 sum:8 similar:2 called:20 ub:1 associated:10 defined:24 char:5 chap:5 defines:4 superanalysis:1 amounts:5 fixing:1 application:3 priori:1 bℓ:1 elements:33 generates:1 sided:1 polynomials:1 replace:3 generated:25 sweedler:1 structure:7 implies:13 required:1 orbit:1 equivalently:2 requires:1 having:4 gs:1 ppendix:1 results:1 existing:1 gf:1 proposition:32 gc:3 gb:3 ga:2 edu:1 gm:3 gl:6 contributions:1 gi:8 superspace:16 supercommutative:9 stable:1 include:1 g2:2 algebr:1 putting:4 antipode:1 matrices:10 categories:2 notes:2 michael:1 noted:1 evv:2 zi:1 jump:1 imply:1 odd:12 victor:1 invertible:7 expressed:2 expresses:1 degree:24 respectively:13 desired:3 objects:6 others:1 consideration:1 morphisms:5 remark:2 trans:1 involved:1 vbi:2 resulting:3 aνn:1 hexagon:1 makes:5 montpellier:2 wis:1 sgn:4 use:8 usa:1 recalling:1 next:1 process:1 zij:3 χsu:1 becomes:10 arranging:1 iii:1 δca:2 isomorphism:21 gℓ:1 ρn:12 ρr:6 obvious:2 publications:2 proof:15 calculation:2 purposes:1 holds:23 brian:1 shimura:1 instead:1 afq:1 blocks:2 collection:3 inst:2 multiplication:7 correspond:1 element:13 sdim:7 morphism:25 discussion:2 facilitated:1 including:1 lattices:2 operative:1 le:3 chosen:2 labor:1 supermatrix:9 degrees:24 choose:3 nakayama:1 defining:12 semisimple:3 wolfgang:1 material:2 superdimension:5 articles:1 tensoring:1 niversit:1 coaction:10 university:3 quantiques:1 identifies:1 baxter:2 weyl:1 related:4 operator:20 variety:1 ckℓ:1 our:11 special:4 out:5 category:15 matrix:16 develop:1 matd:2 lecture:3 suffices:4 red:8 diagonal:2 approaches:1 york:4 niederle:1 applications:2 geometry:4 keep:1 length:6 hence:18 ntroduction:1 bijection:1 precisely:3 hyperbolic:1 ordering:2 πn:4 relations:28 their:3 appl:1 pavel:1 behaved:1 tuple:1 explanation:1 exactly:4 supercharacters:1 tacitly:1 cyn:21 cym:2 varieties:1 subsequence:1 ber:8 endomorphism:3 clearly:2 complete:2 mills:12 leverhulme:1 concerns:2 εi:2 subject:9 heisenberg:2 lectures:1 unless:3 deploy:1 alain:1 sfq:8 connected:6 but:6 definitions:1 class:1 fji:14 χs:30 fact:11 isomorphisms:11 supported:4 isomor:1 duisburg:1 trivial:2 principal:1 q2:3 based:2 commutators:2 lemma:7 bases:9 inherited:1 employed:1 hopf:2 means:2 familiar:3 stavros:1 fℓm:1 words:3 qr:4 approach:3 transposition:1 differential:3 qa:3 qc:1 involutive:1 contain:1 aei:1 fixed:5 qn:4 modulo:2 exists:1 transpositions:4 module:7 computes:1 qti:2 written:7 identification:3 invariant:2 publishers:1 endr:1 importance:1 transpose:1 interpolate:1 jie:1 hypothesis:1 koteck:1 group:13 amer:4 tensors:4 ontents:1 restrictions:1 cayley:1 taking:2 equal:4 etc:5 otherwise:3 comment:1 ci:2 co:9 cm:2 conclude:1 cb:2 ca:5 cf:3 sequences:7 respect:5 cw:1 cv:8 cu:6 bbi:3 associativity:5 universal:1 define:11 describe:5 corresponding:4 commutes:5 scalars:1 subspace:8 bull:1 repetition:1 expounded:1 present:4 ibp:1 multi:1 splits:2 will:25 lx:4 rbi:1 cvi:1 inherits:1 vd:5 vi:16 vj:1 thus:32 vm:3 vn:12 dual:20 φij:7 noetherian:3 generic:6 s2n:1 lett:2 parts:1 largest:2 cjs:1 finite:11 schelter:4 phh:1 cubic:4 effect:2 v1:17 v2:1 infinite:2 distributivity:5 identity:8 numbered:1 acknowledgement:1 modeled:1 well:4 patterns:1 sets:1 supertrace:8 usual:15 yiℓ:1 less:4 monomial:2 obtain:13 underlying:1 paul:1 adv:2 vσ:4 preprint:2 imparts:1 hall:1 lattice:7 extends:4 natl:1 incarnations:1 identical:9 know:3 press:4 helpful:1 δv:12 δw:1 δu:7 δl:1 δi:5 δa:16 therein:1 parity:27 because:6 classical:2 sequence:4 algebraically:1 ideals:1 growth:1 homh:4 choosing:3 transport:1 happens:1 lead:2 cσ:5 injects:1 cτ:1 does:3 summand:1 selecting:1 expansion:1 clarendon:1 x11:3 monomials:12 injective:6 simpler:1 deriving:1 about:1 actual:1 carried:1 extension:7 a0:5 stephenson:2 compatible:1 carries:1 important:1 introduced:4 homogeneous:92 dubois:5 square:1 additional:4 pairing:4 restricts:3 quadratic:11 naturally:2 function:7 eal:1 preparations:1 volume:1 construction:1 hn:46 ho:22 ha:13 he:1 compute:1 society:1 wish:2 below:5 piece:2 obstacles:1 interchanges:2 inv:5 linearity:1 denote:24 identities:4 functions:4 nonetheless:1 detail:2 other:13 details:4 phism:2 completes:1 june:1 koblitz:1 starting:2 factors:4 rule:4 volumes:2 augmented:1 |
0704.1889.txt |@word superfluidity:1 chain:1 represent:1 results:4 existing:1 leads:2 entropy:5 overlap:1 follow:1 remarkably:1 row:5 hemmer:1 griffin:3 inverse:1 referring:1 re:1 similarity:1 presents:1 finally:1 indicate:2 those:1 tf:7 nodes:1 tc:17 sound:37 breathing:28 amplitudes:1 g2:2 g1:3 very:6 frequencies:12 emphasizes:1 focus:2 figs:1 fall:1 experimentally:1 zwierlein:2 matrices:1 treating:1 presented:1 t2:3 solution:3 t0:2 large:8 shenoy:1 schirotzek:2 small:2 equation:3 vs0:1 findings:2 consistent:4 direct:2 sign:4 approximation:4 second:33 profiles:8 chen:6 dynamics:1 correspond:1 even:1 what:1 appear:1 chicago:2 near:4 uniform:1 experiment:2 above:2 boundary:2 principal:3 contrast:6 temperatures:2 body:1 condensed:1 full:1 led:1 respectively:4 here:11 following:1 focused:1 andrews:1 address:3 along:1 standard:1 equations:22 appears:1 change:1 obtained:4 great:2 institute:1 study:1 larger:1 published:1 principally:1 resonance:1 changes:1 helps:3 via:4 useful:1 explained:1 addressed:1 decrease:1 condensates:1 total:2 establish:2 readily:2 franck:1 use:5 eye:2 indicated:1 distinct:1 predictions:2 few:1 noting:1 therefore:1 associated:3 theoretical:3 more:10 becomes:1 about:2 known:1 cases:2 fermionic:1 pδ:1 science:4 originally:1 work:3 theories:1 vs:7 values:2 ωho:4 den:1 exceptions:1 arrive:1 broad:1 decoupled:6 compare:1 figure:8 calculation:1 high:1 chih:1 chin:3 numbers:1 tan:1 information:1 straightforward:1 january:1 provide:3 purpose:1 s0:4 chemical:4 how:1 opposite:1 grimm:2 schunck:1 profile:3 mat:2 undergoing:3 may:3 thermodynamic:2 earlier:2 derived:1 treatments:1 convincingly:1 produce:2 combescot:1 horizontal:1 choice:1 kurn:1 stress:1 branches:1 dynamical:1 ss:1 lines:8 derivatives:1 rather:4 so:2 chien:1 order:10 typical:4 help:3 riedl:2 indeed:4 over:1 eqs:1 top:1 stamper:1 paper:3 through:1 argued:3 minguzzi:1 excitations:1 its:1 rapidly:2 thank:1 ln:2 interesting:2 plot:1 solving:2 decreases:1 edge:7 absence:1 distinguishing:1 microscopic:3 systems:1 jacobi:1 ours:1 setting:2 shaeer:1 non:2 good:1 greater:1 conversations:1 fig:7 introduce:2 landau:1 scaling:1 framework:1 effects:1 they:4 fingerprint:1 now:1 nor:1 nos:1 2t:1 eigenvalue:1 february:1 james:1 university:1 drop:1 arrows:2 mode:29 radial:4 found:3 side:1 el:1 differential:2 ek:2 series:1 literature:2 entering:1 measure:1 our:13 approximated:1 special:1 ketterle:3 zaremba:1 ultimately:1 dominates:1 matrix:2 restricted:1 rep:1 since:2 rev:18 denotes:1 increase:2 collisions:2 contained:1 suggesting:1 ref:7 red:5 shows:4 theory:3 associate:3 rmax:2 little:2 possibility:1 quite:2 approaches:1 dependencies:1 generate:1 rewritten:1 pairs:5 r2:1 could:1 transition:3 v2:1 linearized:1 turn:1 exponentially:1 assign:2 frequent:1 first:14 features:2 upper:3 variables:7 number:3 directly:1 kfa:8 calculational:1 precisely:1 open:1 given:4 necessarily:1 temperature:17 similarly:2 unitarity:12 leading:1 interact:1 system:1 turlapov:6 their:6 assumption:3 fermions:2 calculations:1 bartenstein:2 leggett:1 observations:1 free:1 jank:1 trapped:5 serve:3 linearize:1 part:2 too:1 somewhat:1 than:4 coefficients:1 population:1 iωt:1 scheme:2 bec:6 require:1 zero:4 superfluid:4 future:2 str:1 were:1 accessed:1 tion:1 kf:4 result:4 function:2 stajic:4 fluctuation:1 spectrum:1 curves:2 crossover:7 vn0:1 seen:1 constrained:1 any:1 relatively:3 numerics:2 self:2 mechanism:1 note:2 mix:2 potential:6 online:4 green:4 subject:1 stringari:2 circles:1 residue:1 begin:1 normal:5 condensate:4 viscosity:1 vnj:1 vni:1 most:2 importantly:1 jul:1 pair:2 analytically:1 why:1 denschlag:2 deviations:1 doi:1 observation:2 surprising:1 calculated:4 playing:1 velocity:3 justify:1 physics:1 dot:1 precise:1 emerging:1 show:4 isentropic:2 text:1 supported:1 implying:1 relation:1 abo:1 find:8 ground:2 based:4 explain:1 blue:2 outside:1 should:3 only:3 black:2 developed:1 local:5 equilibrium:6 continuity:1 do:1 cheng:1 gehm:1 between:3 fluid:17 liu:1 nearly:1 applying:1 dt:1 conjunction:1 neither:1 dp:1 reveal:1 increasing:2 densities:1 approach:1 arxiv:2 summary:1 experiments:4 hydrodynamic:1 analytical:3 luo:2 satisfy:1 set:1 exists:1 achieved:1 arrives:1 bounds:1 observed:3 differs:1 depends:1 radius:1 descriptions:1 eliminating:1 terms:4 dµ:1 techniques:3 phases:1 eigenfunctions:1 currently:1 dmr:1 state:4 identification:1 john:1 simplest:2 probably:1 subscript:2 conditions:2 discovery:1 recently:1 amplitude:2 nature:1 importance:2 attention:1 weak:3 however:1 vanishing:1 fluctuations:3 bose:8 come:1 kosztin:1 both:4 panels:3 region:3 wu:1 against:1 figures:1 dated:1 contribution:2 ωf:5 whole:1 finds:1 experimental:6 among:1 point:1 simple:2 others:1 harmonic:2 simply:1 wider:1 moreover:2 strong:1 described:2 decoupling:3 basis:1 three:1 been:9 yan:1 treat:1 interest:3 choose:2 describe:1 corresponding:1 chun:1 quantities:3 sufficient:1 gas:4 convert:1 gap:3 understand:2 denote:2 spirit:2 present:5 case:7 p0:2 novel:1 pacs:1 solid:3 value:4 astrakharchik:1 will:6 cast:1 while:5 euler:1 behavior:6 situation:1 procedure:2 unitary:5 coupled:7 almost:2 refs:1 thus:2 vn:6 sity:1 ij:1 cond:2 limit:1 vanish:1 heiselberg:2 disappear:1 mrsec:1 containing:1 grant:1 lengths:1 cross:1 same:2 clearly:2 complex:1 arguments:1 coworkers:1 vext:8 units:1 finite:9 higher:9 independent:6 used:1 see:1 numerical:3 upon:2 counterparts:1 πij:1 hydrodynamics:1 validate:1 expand:1 recent:2 lower:7 off:1 modes:25 fully:3 nevertheless:1 studies:1 well:6 analysis:2 s20:1 calibrated:1 solve:1 claims:1 model:1 dimension:2 oscillation:3 left:1 spherical:6 lda:1 leyronas:1 just:1 inouye:1 feshbach:1 obtain:2 identify:1 atomic:1 aspect:1 spherically:1 alternative:2 yielding:1 scattering:1 guides:2 previous:2 density:6 thermodynamics:1 valid:2 hecker:1 lett:14 easy:1 input:1 momentum:1 hybridization:1 eigenfunction:2 altmeyer:2 possible:1 corresponds:2 increases:1 wright:1 confined:2 using:1 color:3 fingerprints:2 like:2 particle:2 identifying:1 systematically:2 follows:1 collective:3 velocities:2 δs:5 δp:15 ignore:1 vortex:1 either:1 arbitrary:1 δt:22 because:6 noncondensed:2 sequence:1 successfully:1 some:4 back:1 understood:1 complete:3 respect:1 oscillations:3 vsi:1 vsj:1 δn:2 bottom:1 gapped:1 measurements:3 extensively:1 per:2 everything:1 eliminate:3 expressing:1 propagating:2 demonstrated:1 trap:22 measuring:1 core:2 reaching:1 jochim:1 equivalent:1 each:1 agreement:1 expansion:1 pressure:2 clancy:2 although:4 properties:2 simpler:1 thomas:10 extension:1 constraint:1 column:1 discussed:1 dependence:7 o:1 essential:1 ξk:1 mixed:1 consequently:1 miesner:1 considerations:1 presence:1 into:1 within:3 numerically:1 nsf:2 negative:1 variable:2 right:2 determine:3 einstein:2 reducing:1 assumed:1 there:8 gases:10 kinast:7 dispersion:1 accordingly:1 joseph:2 bosons:1 low:1 way:1 was:4 naturally:1 lowest:13 insensitivity:1 elsewhere:1 form:1 superfluids:1 but:3 hu:1 hh:1 ho:1 ns0:1 line:1 considerable:2 he:1 made:2 compute:1 evident:1 ωq:2 levin:6 smooth:1 up:3 us:1 different:4 below:2 frequency:8 fermi:12 imbalanced:1 demonstrate:1 problem:2 ωb:3 similar:5 called:2 regimes:1 strongly:2 taylor:1 constant:2 reconcile:1 pseudogap:4 combining:1 general:2 tosi:1 rule:1 gradients:1 nns:1 check:1 regime:5 functions:1 thermodynamical:9 nn:7 no:1 dashed:5 when:4 illinois:1 field:1 other:2 role:1 branch:2 spatial:2 department:1 ns:9 hydrodynamical:2 nv:1 excitation:1 center:2 shown:7 polynomials:1 important:2 peak:2 included:1 nated:1 needed:1 structure:1 nn0:1 condensation:2 coupling:3 assume:1 curve:1 approxima:1 investigated:1 time:2 n0:8 original:1 bcs:6 |
0704.1890.txt |@word monte:1 extrapolated:2 consider:1 similarity:1 rev:14 varying:1 results:11 ds:1 leads:1 scalar:1 microwave:1 computation:1 parameterization:1 expressions:1 nwo:1 contributions:5 gj:1 reynaud:1 emig:4 aug:1 technique:2 tm:14 under:4 dominated:1 analogous:2 include:1 dramatically:1 resources:2 case:2 advantage:1 far:1 frequencies:1 aarseth:1 conditions:2 every:1 figs:1 affect:1 difference:3 exact:2 illustrated:1 differentiated:1 solves:1 solver:2 evaluation:3 solution:1 integrated:2 large:2 discrete:1 vector:2 small:3 optics:3 equation:1 chew:1 force:39 periodicity:1 renormalized:1 past:1 zero:8 design:1 qualitatively:2 estimated:2 carlo:1 linear:2 even:2 employ:1 what:1 christ:1 giving:1 sum:1 expressed:1 uniform:2 cell:2 above:1 lifshitz:3 new:3 avenues:1 method:17 contrast:1 3d:6 body:6 full:1 chose:1 multipole:1 respectively:1 iannuzzi:1 here:6 desired:1 explore:2 objects:3 separation:3 path:2 along:4 balian:1 change:4 obtained:2 institute:1 study:1 studied:1 spheres:1 periodic:1 resulting:1 pick:1 action:1 fourier:1 changes:2 involves:2 plotted:3 composed:1 via:4 useful:1 discontinuous:1 problematic:1 cylinder:5 brought:1 electromagnetics:1 txy:4 txx:5 summation:1 resolutions:1 total:8 unit:5 schaden:1 plot:3 use:2 additive:3 would:2 remains:1 positive:1 rodriguez:1 nucl:1 program:1 therefore:3 scope:1 theoretical:1 corners:2 more:6 pfa:8 formally:1 becomes:1 award:1 visual:1 dirichlet:1 iw:9 particular:2 known:5 cases:2 1µm:1 high:2 te:9 ma:3 norwood:1 science:4 originally:1 work:3 unknowns:1 vs:3 crossed:1 three:2 making:1 trans:1 specialized:1 example:2 spruch:1 rodrigues:1 weaker:1 kenneth:1 give:2 predict:1 magnitudes:1 involve:1 indicates:1 numbers:1 arise:2 sought:1 axis:1 regularization:1 decaying:1 rather:1 feature:2 hampered:1 very:1 adjacent:1 instead:1 map:2 de:1 may:1 numerically:2 derived:2 plane:1 faculty:1 drastic:1 data:1 parallel:6 stress:19 attempt:1 effective:1 computations:1 approximation:3 lines:3 element:3 green:11 correlation:1 representation:1 subsequently:1 integrand:2 order:5 typical:3 neto:1 over:4 spectral:2 course:1 experiments:1 statistical:2 dw:2 still:1 ieee:1 its:1 before:1 perfect:12 regions:1 derive:1 rapidly:1 decay:1 lateral:6 hanke:1 suboptimal:1 positivedefinite:1 forms:1 degrees:2 fig:14 intl:1 might:1 easier:1 non:10 greater:1 reveal:3 propose:1 polarizations:2 material:1 operator:2 federico:1 scaling:2 walls:3 polder:1 effects:2 they:1 closer:1 oxford:1 employed:1 now:1 dielectric:6 uscher:2 netherlands:2 publication:1 edge:1 university:1 2d:9 l4:1 component:1 l3:1 reasonable:1 each:1 found:2 side:2 mean:3 domain:1 ei:3 another:3 ek:2 ej:3 there:2 energy:4 solvers:1 used:3 applicable:1 alejandro:1 frequency:5 quantum:2 our:9 beyond:2 eq:4 w2:1 shown:6 nonoscillatory:1 space:1 gradient:1 restricted:2 furthermore:3 since:3 induces:1 research:2 fellowship:1 dsj:1 formula:3 adaptive:1 squares:17 ref:12 sliding:1 red:4 shows:2 theory:2 interactions:3 divergence:2 standard:4 approaches:1 complicated:2 log:1 interaction:9 geometry:9 could:1 iterative:1 caption:1 length:3 exponentially:1 δij:2 conductors:1 generalizations:1 first:6 corrugated:1 staggered:1 symmetry:2 slabs:1 xx:1 xy:1 long:1 directly:3 joannopoulos:1 illustrate:2 dispersive:1 given:3 necessarily:1 temperature:2 indicate:1 leading:1 interact:1 least:2 their:1 calculations:2 white:1 scheme:1 structures:1 gives:1 asymmetric:1 reflecting:1 than:2 milton:1 relative:2 behaved:1 require:1 second:3 preparation:1 revzen:1 differently:1 determined:1 were:1 minus:1 perturbative:1 behaviors:1 prd:1 lambrecht:1 dielectrics:1 fluctuation:2 correction:1 ming:1 conjugate:1 need:1 cumbersome:1 apparently:1 any:4 ray:3 quadrature:1 gies:3 efficient:4 pursued:1 latter:1 able:2 isolated:2 metallic:7 polarization:1 sciences:1 ideal:1 without:2 generalized:1 forces:10 so:1 techniques:3 accuracy:3 circles:2 formulas:1 multiple:3 electric:1 decreasing:2 most:2 involving:1 letter:2 ˆj:2 analytically:2 extremely:1 deˆ:1 causality:1 hj:2 acknowledges:1 especially:1 surprising:2 hk:2 metal:15 universiteit:1 points:1 tech:1 bodies:2 pattern:2 effect:2 left:1 physics:4 fact:1 gold:3 supported:1 degrades:1 converge:1 purely:3 solutions:1 algorithms:1 find:1 subtracting:1 impact:1 boundaries:1 fg02:1 based:5 implementation:2 blue:4 enough:1 negligible:1 should:1 only:3 bases:1 black:2 capasso:1 adequate:1 plate:6 handle:1 goes:1 distance:4 finitedifference:1 familiar:1 simplest:4 2a:1 cannot:2 nearly:2 piston:4 cylinders:1 net:3 gray:2 resolve:1 fields:5 arxiv:1 expansions:1 consisting:2 predicted:3 isolation:1 analytical:1 grad:1 approximations:7 pitaevskii:1 bars:2 computed:6 signs:1 observed:1 radius:1 result:5 contour:1 subject:1 surfaces:1 visualize:1 αu:1 tensor:10 ways:1 scattering:1 currently:1 dmr:1 artificial:1 symmetric:2 iri:1 outside:1 difficulties:1 various:3 closed:1 between:12 mihai:1 boundary:3 approach:2 terms:1 reproduced:1 comp:2 interfaces:1 however:3 nsec:1 efficiency:2 harvard:1 demonstrate:1 monotonicity:1 problem:3 both:3 limits:1 reported:1 many:2 gratefully:1 against:1 connection:1 cylindrical:1 casimir:14 contribution:1 expression:1 organisation:1 experimental:4 strongly:1 fi:1 point:3 simple:5 exploit:4 invariant:5 applicability:1 straighforward:1 respect:1 actually:1 unusual:1 described:3 geometries:15 basis:2 hertzberg:1 due:8 been:8 tensors:2 much:2 expected:1 ph:1 ann:1 attractive:3 dots:2 stresses:1 direction:1 arises:1 corresponding:2 sufficient:1 theorem:2 further:1 neumann:1 maps:2 c2:2 present:3 applied:1 handling:1 exponential:1 pacs:1 solid:2 engineering:3 will:3 replaced:1 error:3 langfeld:1 planar:1 coupled:1 thus:1 surface:8 fluctuating:1 contract:1 technology:1 currents:1 different:1 grant:1 perform:1 make:1 lett:9 clearly:1 kardar:3 complex:1 modification:1 plates:11 finite:7 difficult:1 calculation:1 extended:1 solved:2 numerical:3 monotonic:7 phy:1 uses:2 infinite:3 changing:1 electromagnetism:4 center:3 nevertheless:1 variety:1 well:2 analysis:1 approached:1 materials:5 comes:1 components:1 repulsive:2 arising:2 researchers:1 usual:2 distances:1 routinely:1 proposed:1 less:2 being:1 storage:2 proximity:4 yee:1 obtain:2 golestanian:1 reviewed:1 bordag:1 using:9 macroscopic:1 captured:1 visualization:1 vidi:1 note:1 density:2 cavalcanti:1 wavevector:2 wall:3 developments:1 requiring:1 mann:1 5a:1 match:2 nanoscale:1 real:2 vrije:1 around:2 spectacular:1 evaluate:1 showing:1 possible:5 department:2 grid:4 vacuum:3 world:2 part:2 depicts:1 mod:1 like:3 semi:1 sizes:2 follows:1 qualitative:1 validations:1 specific:1 starting:1 arbitrary:9 become:1 because:4 often:1 classical:5 some:2 competition:1 sight:1 nonzero:1 dimensions:3 electromagnetic:3 size:1 future:1 integration:1 per:4 duplantier:1 does:1 demonstrated:2 either:1 process:1 scientific:1 oscillating:1 agreement:1 although:5 plots:3 imaginary:9 comparison:1 limitation:1 onofrio:1 freedom:2 jm:1 capable:1 dependence:2 o:6 range:1 obeys:1 artech:1 discretization:3 cambridge:2 jian:1 presence:2 pergamon:1 into:2 within:3 integral:9 nsf:2 uncontrolled:2 right:1 inverting:1 steven:1 computational:9 amsterdam:1 methods:8 additional:1 multilayer:1 refinements:1 support:1 initial:1 fast:3 dzyaloshinski:1 way:1 was:7 gij:4 function:12 drude:1 agrees:1 but:4 volume:1 failure:1 repeated:1 hi:2 gain:1 klich:1 convergence:1 line:3 removed:2 davide:1 subtracted:2 2πc:3 made:1 compute:4 jaffe:4 whether:1 us:1 historically:1 discretized:1 below:4 limit:2 fluctuations:1 distribution:1 similar:1 agree:1 mechanics:1 separated:2 associated:1 computing:1 defined:1 contribute:1 metals:1 general:2 examine:1 scardicchio:3 doe:1 check:1 four:2 physical:1 incorrect:1 marachevsky:1 functions:2 compared:1 no:3 dashed:1 whereas:2 when:1 field:2 other:3 tij:7 spatial:2 test:1 nonmonotonicity:1 conventionally:1 brevik:1 problems:1 important:1 massachusetts:1 dissipation:2 astronomy:1 structure:3 source:1 resolution:2 required:2 equivalently:1 inset:6 time:2 requires:2 normalized:5 |
0704.1891.txt |@word gt:15 homomorphism:1 chain:1 global:2 results:3 four:2 proposition:10 restated:1 gn:1 compact:6 whose:3 preserves:1 equivalence:2 tr:2 uniqueness:17 manifolds:11 under:1 analogous:1 brown:5 g1:1 g0:1 pages:1 springer:1 choice:4 endpoint:2 orientations:1 cellular:2 entries:2 coincidences:1 neighborhood:6 lefschetz:12 further:1 zr:4 zs:2 even:1 index:21 what:2 appear:2 giving:1 section:5 version:4 above:11 new:1 method:1 coefficient:8 relationships:1 respectively:2 xfe:11 here:1 desired:3 brooks:3 path:3 strong:2 appears:5 obtained:3 generalizing:1 technical:1 allows:1 rocky:1 uniquely:1 appropriately:1 homotopic:17 equivariant:1 pera:2 would:4 prove:4 remains:1 contains:2 call:2 assistance:1 taken:1 more:2 sort:1 starting:1 jiang:1 particular:2 known:3 iii:1 must:5 none:1 valued:1 originally:1 work:5 hopf:1 following:6 proof:13 f0:1 f1:1 stated:2 preserving:1 pieces:1 states:1 indicates:1 numbers:2 straightforward:1 provide:1 write:1 maps:12 lift:14 ordinary:1 map:8 ft:17 may:2 after:1 analagous:1 different:2 applications:5 fe:1 computation:2 data:2 lifting:1 calves:3 homotopies:4 lemmas:2 explicit:2 element:7 si:2 so:6 fundamental:2 order:1 over:2 furnishes:1 paper:5 existence:5 satisfies:5 its:3 roots:1 group:3 thank:2 chosen:1 fix:3 choose:2 main:1 weber:2 correspondence:1 combination:1 they:2 now:1 discuss:1 term:1 name:1 homomorphisms:1 always:1 university:1 wong:1 each:2 found:1 entirely:1 traces:1 subset:5 lifted:1 disregarding:1 fq:2 eg:11 related:6 elementary:1 literature:2 our:11 orientability:3 hart:4 special:2 rt:51 gon:3 matrix:2 space:3 robert:1 since:8 denotes:3 eprint:1 denoted:3 formula:1 induced:2 suffices:1 math:2 shows:2 theory:30 polyhedra:1 diagonal:1 free:2 california:1 advisor:1 axioms:26 definition:3 language:1 could:1 american:3 βg:7 consequence:2 first:3 already:1 conjugacy:1 number:13 restrict:1 says:1 open:9 given:9 necessarily:2 leverage:1 needed:3 introduction:1 meaningful:1 zπ:2 twisted:1 least:2 their:3 identity:2 statement:1 final:1 gives:4 tuple:6 continuous:1 natural:1 than:1 coefficients:3 require:3 ranging:1 project:2 classes:15 doubly:1 mountain:1 modern:1 argument:1 say:2 substantial:1 need:3 reidemeister:44 any:17 viewed:2 paths:2 mappings:1 self:1 isolated:9 note:3 instance:1 lifts:13 generalized:4 lectures:1 unless:1 trace:36 dissertation:5 who:1 most:1 said:1 connected:3 locality:1 pair:1 coin:26 eı:1 class:6 give:4 clear:1 partition:1 stronger:2 points:14 sum:4 fact:1 show:3 contemporary:1 ki:3 spaces:1 relation:2 trivial:1 find:1 realizing:1 based:2 parameters:1 admissable:12 unions:1 topological:2 lemma:12 only:11 explicitly:1 constant:1 local:25 axiom:21 abelian:2 his:1 notation:1 means:3 between:3 cannot:1 christopher:1 him:1 closure:1 produced:1 covering:6 arxiv:2 common:2 fixed:32 view:1 annalen:2 set:12 computed:1 connections:1 see:5 result:11 triples:2 subject:1 satisfying:4 enough:1 αf:17 invariant:1 approach:2 terms:1 weak:4 hypothesis:2 distinguish:1 topology:2 both:3 taking:1 equal:3 homotopy:17 σx:2 comes:1 otherwise:2 orientable:6 necessary:1 point:47 appeared:2 coincidence:64 dimensional:1 respect:3 cq:4 throughout:2 cw:1 transformations:1 basis:1 union:1 px:13 py:3 three:4 relatedness:3 tuples:7 ensured:1 expected:1 abstract:1 define:4 concerning:1 selfmap:2 observe:1 general:1 spirit:1 present:1 case:2 subsets:3 will:14 transactions:2 property:4 orientation:2 von:1 thus:11 iv:1 ii:2 characterize:2 triple:4 vx:4 endpoints:1 id:4 containing:2 author:3 journal:2 demonstration:1 make:3 same:10 complex:2 proved:3 finite:3 difficult:1 independent:2 used:3 trivially:1 uses:1 invariance:8 interested:1 normalization:13 recent:2 lower:1 modeled:1 well:5 mathematische:2 without:1 sets:2 dimension:3 manifold:3 mimicked:1 guided:1 obtain:3 integer:3 alternative:1 projection:3 letting:3 oriented:1 doctoral:2 other:2 treatment:1 theorem:28 fares:4 transformation:1 take:1 nielsen:8 sums:1 additivity:9 early:1 possibly:3 five:3 know:2 using:7 unique:7 mod:2 modifications:2 appearing:2 like:3 follows:3 either:1 arbitrary:1 essential:2 specifies:1 methods:1 some:17 somehow:1 extended:1 peter:1 ourselves:1 nonzero:8 provided:1 nonempty:1 though:1 does:3 connecting:1 provides:1 refer:1 slight:1 equivalent:1 use:4 simplex:1 properties:1 extension:1 angeles:1 slightly:3 mathematical:3 locally:2 previously:1 into:2 bound:1 appropriate:1 references:1 bijective:1 additional:2 assumed:1 there:15 u1:8 approximate:1 u2:8 los:1 handbook:1 editor:1 way:1 was:5 additionaly:1 function:8 form:3 but:5 made:2 ux:20 society:3 differentiable:8 those:1 demonstrate:2 isolating:6 similar:1 called:4 strengthening:1 associated:2 defined:9 universal:2 denote:2 associates:2 ind:34 accounting:1 jezierski:1 again:1 weakened:2 no:5 detail:1 disjoint:4 setting:2 mathematics:2 sufficient:1 conclusion:1 briefly:1 elements:5 generated:1 nonorientable:4 implies:1 established:1 notion:3 implied:1 requires:1 having:1 |
0704.1892.txt |@word words:1 show:1 over:4 λi:1 λn:2 nilpotent:1 either:1 h2:3 choose:1 sydney:1 theorem:3 jacobi:1 mail:1 θu:1 transformation:1 abelian:1 non:1 australia:1 string:1 eigenvalue:2 cannot:1 they:2 acta:1 aλ:1 now:2 dim:5 school:1 university:1 arxiv:2 math:3 each:1 eigenvalues:4 bai:2 series:1 some:2 direct:1 algebraically:4 donald:2 result:1 subject:1 αu:2 appear:1 αv:1 sum:2 since:5 denotes:1 rd:1 re:1 engel:3 ra:2 closed:4 contrary:1 minimal:1 common:1 linear:2 associate:1 component:1 answers:1 statistics:1 key:1 address:1 ask:1 subalgebras:2 definition:1 derivation:1 phrases:1 ordering:1 hence:1 com:1 first:1 classification:4 apr:1 communication:1 h1:5 primary:1 private:1 dimensional:9 represented:1 done:1 apply:1 nsw:1 little:1 necessarily:1 transformations:1 working:1 basis:1 distinct:2 question:1 been:1 their:1 inner:1 aλ1:2 algebras:4 was:2 therefore:1 corresponding:1 complete:1 subspace:1 but:1 hn:5 must:2 case:1 again:1 aλn:1 characteristic:2 work:1 zero:1 while:1 suppose:8 codimension:3 sinica:1 following:1 eigenvector:1 proof:1 references:1 wang:2 abstract:1 thus:3 xiao:2 denote:2 char:4 say:1 au:1 cartan:1 arise:1 commuting:1 any:1 lie:7 containing:1 author:2 barnes:4 holds:1 field:4 mathematics:2 subalgebra:11 map:1 product:1 algebra:5 may:3 derived:1 a1:6 a0:1 infinite:1 identity:2 eigenvectors:2 implies:1 assume:2 so:4 components:1 dimension:1 |
0704.1893.txt |@word monte:1 concept:1 homomorphism:2 consider:2 caused:1 magnetic:19 global:2 dynamic:1 four:3 fortiori:1 consists:1 remarkably:1 lle:1 polarity:1 whose:1 aligned:1 depend:2 δv:1 ts:2 charge:4 th:1 under:1 analogous:4 spec:1 case:6 belonging:1 string:4 very:1 rise:1 springer:1 print:1 witten:2 affect:1 exact:2 deformations:2 condition:3 leads:1 anisotropy:1 nucl:1 t2:3 solution:2 t0:2 large:3 vector:5 indices:1 equation:2 configurations:2 work:1 century:2 ten:1 disclination:1 sin2:1 sin3:2 cosh:11 dissipation:1 value:1 chernodub:2 further:1 dynamics:4 chem:2 carlo:1 established:1 what:1 errors:1 appear:3 tewari:1 ˆz:1 axes:1 expressed:2 uniform:1 erg:1 poles:4 lifshitz:1 amounting:1 revealing:1 condensed:1 simultaneously:1 respectively:2 equals:1 here:6 hundreds:1 water:3 ansatz:2 groups:1 november:1 quite:2 anchoring:2 z2:2 spite:1 institute:1 study:2 vectors:2 permit:1 action:2 plotted:1 composed:1 via:2 stabilization:1 homotopic:2 classification:2 scales:1 semiconductors:1 lizzi:1 bend:1 viz:1 inorganic:1 total:1 unit:4 readily:1 derivatives:1 use:1 cosmological:1 covariant:1 teor:2 fel:3 contains:1 predictions:1 next:3 coalesce:1 live:1 approach:1 therefore:1 taken:1 survive:1 type:1 theoretical:2 more:2 introducing:1 zh:2 elliptic:1 vacuums:2 acceptable:1 ti:1 curvature:1 shellard:1 bogdanov:2 particular:1 known:1 inhabited:1 iii:1 carried:1 involve:1 account:1 monopoles:4 ma:1 mc:1 der:5 stations:2 theories:1 labeled:3 regions:1 values:1 thin:1 evolved:1 following:1 drops:2 example:3 numbers:2 control:1 indicated:2 abelian:22 process:2 states:5 sphere:1 shtengel:1 minimum:1 performed:3 degenerate:1 tan:2 linearized:1 evidently:1 simple:1 axis:3 aging:7 goal:1 polikarpov:1 divided:1 shirkov:1 strikingly:1 criterion:2 oblate:1 adjacent:1 parameter:6 sin:14 nematic:11 tension:1 express:1 sommerfeld:1 mat:1 algebra:2 may:16 thermodynamic:2 singularities:1 diagram:1 applications:1 revealed:2 fm:3 constants:1 hedgehogs:1 realized:2 liquid:3 vanadium:3 su:9 st:1 coal:2 so:10 allow:1 correlation:1 lξ:2 definitions:1 volovik:3 order:8 gµν:3 hedgehog:2 jα:1 help:1 over:2 mainly:1 lavrentovich:4 years:1 stability:2 thermal:1 experiments:4 including:2 mentioned:1 existence:3 kibble:1 excitations:1 its:3 hampered:1 group:11 lc:1 decay:1 energies:1 lo:1 fix:1 coordinates:4 attraction:1 degrees:1 fig:9 deformation:1 eur:1 correspondence:1 non:15 junction:13 greater:1 universality:1 sol:6 tails:1 they:4 identically:1 oxford:1 sorted:1 nov:1 hall:1 it0:1 it1:2 susceptibility:1 term:4 preferable:1 reasonably:1 classified:1 ify:1 hepth:1 2d:1 morris:1 mode:1 each:3 found:2 2n:3 yung:1 characterized:2 mean:2 homogeneous:1 ieaµ:1 ei:1 formulate:1 energy:16 t3:2 owing:2 expect:1 amsterdam:1 quantum:3 our:6 special:1 out:2 living:1 shown:1 impurity:1 space:5 nuovo:1 since:2 lagrangian:2 denotes:1 particles:2 rameter:1 contained:1 denoted:1 ri:1 announced:1 chemically:1 sinh2:1 theory:3 interactions:1 frank:1 free:10 standard:1 threedimensional:1 formation:1 besides:2 χ2a:1 estimate:2 publ:1 beginning:1 lyotropic:2 definition:2 pairs:1 interaction:2 bates:2 chiral:1 r3:1 geometry:4 transition:2 keep:1 motion:1 length:2 lozano:1 isotropic:1 consequence:1 bogomol:1 onto:1 exhibited:1 first:2 note:2 symmetry:2 ignored:1 number:3 twisted:1 defects:11 another:1 carry:1 α2d:1 open:1 angular:1 cartesian:1 requirement:1 introduction:1 data:1 cheremushkinskaya:1 system:6 relations:1 parallel:1 their:11 too:1 final:1 observations:1 isomorphic:1 asymmetric:1 moscow:2 direct:1 optical:1 wide:2 kind:1 holland:1 accordance:2 distinguishes:1 cimento:1 inversely:1 superfluid:1 were:7 russia:1 descriptions:1 ann:1 defect:1 randomly:1 winding:3 mater:1 analysis:2 precipitating:1 4k1:1 need:1 concentration:1 fµν:1 relatively:1 lie:2 angle:1 depending:2 convenient:2 mechanism:1 oriented:2 k2:2 k1:2 potential:4 take:1 analogy:2 interior:3 strengths:1 formulas:1 play:1 opposite:3 vortices:2 systems:1 impurities:2 splay:2 connected:2 polyakov:1 phase:9 wastes:1 measured:2 class:2 bogolubov:1 considered:1 ki:1 part:1 χa:1 velocity:1 typical:1 physics:4 χh:1 bais:2 boojums:10 discovered:1 gauge:12 solutions:1 trivial:1 d3:1 rev:13 ratio:1 proposed:1 parameters:8 varied:1 explain:1 topological:16 should:2 only:4 experiment:1 generators:2 pairing:1 factor:1 windings:1 local:2 equilibrium:3 do:3 means:1 dependent:2 de:2 overall:1 supposes:1 aγ:1 closely:1 combinations:1 during:1 aν:1 boundary:1 volkov:3 continuum:1 fields:4 coalescence:5 arxiv:2 invariants:2 yield:1 graw:1 paper:1 nayak:1 contain:1 analytical:1 approximations:1 view:1 kernel:1 moduli:1 exists:1 hν:2 φel:1 gfµν:1 observed:2 see:7 radius:2 result:2 dµ:4 annihilation:8 phases:4 singularity:1 tensor:1 matter:3 review:1 nature:1 definite:1 dipole:1 favor:1 radu:3 αd:1 between:5 invariant:1 geometric:1 conditions:1 publishers:1 vorton:4 terms:3 solitary:2 however:3 ggµν:1 vanishing:1 analyzed:1 je:1 configuration:6 sols:10 topology:6 both:1 cos:18 last:2 generator:3 numerically:4 taking:1 conclusions:2 according:3 called:1 fiz:2 connection:1 dated:1 whole:1 rodgers:1 experimental:1 stretches:1 sinh:3 cm:1 point:3 reasons:1 lagrangians:1 corresponds:1 dimensional:1 oshikawa:1 boson:1 constant:1 cp:1 basing:1 along:1 jetp:4 described:1 triviality:1 addition:1 equations:4 locally:1 kσi:1 due:5 been:3 azimuthal:1 expected:1 harwood:1 ph:2 algebras:1 annihilating:1 define:4 direction:2 corresponding:3 droplets:8 concerning:3 locations:1 bulk:3 noncommutative:1 pis:1 c3:1 c1:1 hµ:2 applied:4 thermoelectric:1 pacs:1 leave:1 estimations:3 appearance:1 balachandran:2 nematics:1 will:3 loop:2 maximal:1 coupled:1 almost:2 characteristics:1 prolate:2 simulations:2 them:1 surface:14 iv:1 ii:1 characterize:1 cond:1 il:1 φs:1 make:1 radiation:1 same:1 coworkers:1 algorithm:1 φj:3 decreases:1 φm:1 difficult:1 week:1 investigated:1 numerical:2 effect:1 hand:1 director:6 usually:2 v2:15 arrived:2 kim:1 maa:1 changing:1 landau:1 barry:1 scenario:1 yates:1 charges:3 well:2 k24:3 ufn:1 academic:1 without:2 solve:1 components:1 coordinate:1 model:4 chemistry:1 usual:1 spherical:2 ny:1 magnetization:2 just:2 mol:1 ci:1 homogeneity:1 shape:6 tasks:1 superconductive:1 questions:1 summed:1 useful:1 macroscopic:1 yet:2 projection:3 k3:5 integer:1 density:4 haldane:2 extra:1 character:2 parametrization:1 boojum:4 discuss:2 lattice:1 lett:9 theorem:1 stable:1 solvable:1 trebin:1 around:2 lacking:1 phenomenology:1 sonin:2 possible:2 admitting:1 increases:3 know:1 background:1 vacuum:2 press:1 using:2 meaning:1 necessary:1 aqueous:1 qualitative:2 ignore:2 flux:2 vortex:2 schakel:1 unstable:2 either:1 arbitrary:1 become:1 soft:1 topologically:1 preskill:1 assertions:1 therein:1 ecology:2 methods:2 sequence:1 some:1 competition:2 specified:1 provided:1 prasad:1 confirm:1 electromagnetic:3 though:1 bps:1 conditionally:1 does:4 connecting:1 provides:1 o5:15 mineev:1 gubarev:1 power:2 unfixed:1 cryst:1 broken:1 standpoint:2 includes:1 bakker:1 properties:2 integers:1 about:4 komineas:1 actual:1 ferromagnetic:1 saddle:1 coexist:1 freedom:1 dependence:2 o:13 practical:1 mutually:1 obeys:1 simplification:1 introduced:1 ivanov:1 stretch:1 disclinations:1 h2:11 into:2 within:1 rotations:2 functional:1 hensel:1 down:1 pair:2 because:1 references:4 sov:2 frames:1 ǫijk:1 gennes:2 often:1 saupe:1 statistics:1 van:5 additional:1 elastic:7 support:1 there:6 question:1 approximate:1 long:4 inasmuch:1 vortons:8 bogomolny:3 was:3 function:1 north:1 annals:1 form:2 but:5 volume:4 films:1 neutral:1 aµ:1 russian:3 attainable:1 eksp:2 raising:1 he:3 absent:1 prototype:1 rotation:1 annihilate:3 metrics:1 whether:1 up:1 us:3 supplied:1 shifman:1 limit:3 problem:1 monopole:1 similar:1 agree:1 regimes:1 associated:2 ad:1 nauka:1 defined:2 describe:1 influence:2 micrometers:1 proven:2 denote:2 twist:2 ap:1 dν:4 exist:1 relates:1 crystals:2 floating:1 formalism:2 parsed:1 physical:1 write:1 compared:1 no:1 whereas:3 lately:1 field:29 other:4 role:2 percents:1 polar:1 connect:1 condens:2 models:1 aggregates:1 expressing:1 generated:1 important:2 included:2 revolve:1 principally:1 droplet:6 independently:2 coulomb:1 practically:1 assume:1 sigma:1 blaha:1 together:1 neighbouring:1 mass:1 time:7 chur:1 dϕ:1 strings:5 |
0704.1895.txt |@word partial:2 consider:2 similarity:1 global:1 menon:1 leads:2 consists:1 expressions:1 d01:1 diffusive:3 granular:24 γl:5 analogous:1 applied:2 very:2 nicodemi:2 wave:1 experimentally:1 difference:1 common:1 dinsmore:1 presented:1 turns:1 nagel:1 large:16 vector:1 small:12 eigenvalues:1 unifying:1 optics:1 configurations:3 prevent:1 dilute:2 slower:1 consistent:1 prediction:1 dynamics:16 linear:1 nonlinear:1 dufty:3 s111:1 new:1 contributes:1 consisting:2 coefficient:2 condensed:1 component:1 here:6 explore:1 relaxation:4 active:1 consideration:2 equations:4 extreme:1 precursor:1 study:3 larger:1 herrmann:1 suggests:1 kaneko:1 studies:3 composed:2 emerge:1 scales:7 apr:1 scaled:1 marchetti:2 total:5 use:1 would:1 predictions:2 few:6 m1:9 therefore:1 m2:9 taken:1 type:3 more:6 flat:1 sharing:1 successful:1 glass:4 particular:3 cases:2 slowest:1 majority:1 account:1 effectively:1 ρk:4 concepts:1 following:2 hansen:1 example:1 f1:5 f2:5 process:2 india:1 high:4 sphere:5 numbers:2 isothermal:1 species:7 yang:2 decaying:2 rather:1 chemical:1 nontrivial:2 stemming:1 influences:1 familiar:1 sij:1 ρ2k:3 description:4 wiley:1 designed:1 coming:1 summarize:1 effective:2 negligibly:1 switch:1 media:3 order:4 sd:1 developed:1 insight:1 years:1 experiments:4 statistical:1 its:1 longitudinal:1 decay:2 interesting:1 masses:4 microscopic:1 systems:3 weeks:1 main:3 eventually:1 framework:1 effects:4 das:1 inelastic:1 structural:4 february:1 mode:5 candela:2 glasses:2 domain:1 hard:7 sinha:4 static:9 expect:1 our:3 special:1 out:3 emerges:1 matrix:5 factors:2 vch:1 rep:1 since:3 rev:1 research:2 particles:6 collisions:1 dominated:5 emerged:1 dominate:2 predicted:1 theory:2 retained:1 transition:3 confocal:1 motion:1 turn:1 length:6 first:3 striking:1 number:4 glassy:5 gases:1 size:2 given:3 temperature:3 introduction:1 system:14 indicate:1 intermediate:1 observations:2 molecular:3 final:1 exploring:1 kirkpatrick:1 caging:4 x2:4 x1:3 representing:1 than:1 coefficients:1 diffusion:2 d02:3 roles:1 matter:6 future:3 enables:2 fluctuation:2 spectrum:1 seen:1 concentration:2 relatively:1 realm:1 roux:1 efficient:1 convenient:1 self:1 onset:1 k2:2 take:1 analogy:2 play:1 viscosity:2 significant:2 χt:4 average:1 focussing:1 physica:1 points:1 tech:1 brey:2 physics:3 segregation:1 phenomenon:1 kaper:1 bagchi:1 probe:1 bring:1 slow:5 ratio:1 factor:2 equilibrium:3 do:2 predict:1 mixture:13 get:1 dependent:1 liquid:6 de:2 fluid:3 ones:2 nearly:1 words:1 combinations:2 liu:1 processes:1 densities:3 arxiv:1 microscopy:1 walsworth:2 hydrodynamic:14 compressibility:3 valid:1 ρ1k:3 view:1 set:2 correlations:2 observed:1 see:6 result:2 techniques:2 instance:6 scattering:1 review:13 definite:1 colloids:2 state:3 between:4 approach:3 comparable:1 terms:4 nature:1 efficiency:1 configuration:1 come:1 both:2 limits:1 triggers:1 conclusions:1 packing:3 against:1 grain:1 dated:1 context:3 ck:4 relevant:1 point:2 simple:1 granularity:1 exploit:1 jammed:3 crystalline:1 testable:1 described:3 addition:1 due:1 been:3 slowly:1 interest:1 basic:1 expected:1 lett:1 determinant:1 controlled:1 gas:2 dramatic:1 understand:3 wavevectors:1 mct:1 diffuse:1 present:1 case:5 novel:1 grains:6 pacs:2 frozen:1 caged:1 institute:1 while:1 dense:10 behavior:4 couplings:1 studied:1 coupled:1 thus:4 equal:1 ii:3 cond:1 barrat:1 grown:1 binary:8 spheres:20 journal:2 suggest:1 make:1 cross:1 emphasize:1 mixtures:11 finite:1 neutron:1 fairly:1 extended:11 effect:1 liquids:4 hydrodynamics:2 vibrated:2 recent:2 modes:8 well:3 analysis:6 s22:6 materials:1 firstly:1 model:1 mair:2 softening:1 captures:1 atomic:5 thakur:1 k2ρ:1 macroscopic:1 coniglio:1 density:14 similarities:1 wavevector:2 arrest:1 other:1 transformed:1 location:2 input:1 momentum:2 generalized:8 aspects:1 around:1 weitz:1 background:3 using:2 sizes:3 exploiting:1 facets:1 susceptibilities:1 soft:1 reduces:1 mathematical:1 because:1 fierro:1 some:3 ourselves:1 transport:2 happens:1 scale:1 colloidal:2 lead:1 gotze:1 fluids:1 provides:1 prog:1 reaching:1 s12:4 s11:7 stem:1 bangalore:1 about:1 central:1 disorder:2 constituting:1 consequently:1 letters:3 letter:4 inclusion:1 edts:1 into:4 down:5 amsterdam:1 gennes:2 diameters:3 elastic:1 area:1 there:4 fast:1 low:1 fraction:1 huan:2 analyze:3 raman:1 survives:1 complete:1 governs:2 forming:3 differences:2 illuminating:1 gain:1 made:3 compositional:2 characteristic:1 mat:1 up:1 us:4 limit:2 fluctuations:14 similar:2 laplace:1 mechanics:1 proved:1 worthwhile:1 defined:1 abstract:1 describe:1 slowing:4 levitt:1 prasad:1 check:1 physical:13 mutual:1 compared:4 edwards:1 field:1 narrowing:2 interested:1 role:2 confine:2 jamming:9 picture:1 draw:1 peak:3 describing:1 structure:7 harbola:1 regime:1 coupling:2 tested:1 equivalently:1 mass:5 northholland:1 time:3 n1:10 n2:11 |
0704.1896.txt |@word limited:1 concept:1 consider:2 remarkable:1 interference:14 magnetic:5 particular:4 results:2 illustrated:2 eds:1 bergmann:1 expressions:1 research:1 phenomenon:2 compose:1 depend:4 calculate:1 irrelevant:1 tr:4 young:1 quadruple:1 quasi:1 does:2 under:2 tb:7 worth:2 ta:11 case:8 wb:9 amplitudes:4 orthogonal:1 very:3 could:1 rise:1 seemingly:1 wave:16 should:1 resonant:2 difference:2 exact:1 level:1 make:1 large:1 vector:9 jonckheere:1 nonn:1 small:2 eigenvalues:1 optics:1 noted:1 smaller:1 disordered:1 consistent:2 direct:1 sign:1 zero:2 displays:1 qualitatively:1 even:2 fine:1 sum:1 localization:1 jaeger:1 find:1 consistently:1 experiment:4 above:2 net:1 contrast:1 pioneering:1 outgoing:10 full:3 christian:1 notions:1 respectively:2 here:5 atoms:26 generic:1 objects:2 separation:1 address:1 directions:2 path:37 along:4 implicit:2 change:3 extreme:1 obtained:2 incoming:7 technical:1 involved:1 study:1 studied:1 amount:1 resulting:1 miniatura:1 hospitality:1 implement:1 suitable:1 examining:1 useful:1 family:1 heart:1 apr:1 explained:1 visible:1 traversing:1 total:3 establish:1 unit:5 projector:3 would:3 commun:1 recalling:2 positive:1 finally:1 france:1 noting:1 m1:1 therefore:4 m2:1 themselves:1 stage:2 more:1 duality:11 comparison:1 successful:1 operators:2 visibility:11 tested:1 varying:1 cases:2 hold:1 must:1 ρa:2 high:1 account:1 ρb:1 science:2 des:1 oscillator:1 dramatically:1 geometry:6 values:2 temperatures:2 arrive:1 example:2 ions:1 wang:2 give:2 process:2 preserving:1 sample:2 effectively:1 numbers:4 degenerate:1 allowed:1 analysis:1 conversely:1 occur:1 axis:2 information:8 kwiat:1 provide:2 discussion:1 acts:2 feature:1 entangled:1 georg:1 how:1 pure:3 opt:3 optimal:1 parameter:2 ensemble:1 circular:3 fare:1 map:2 mat:1 may:1 after:1 corrections:5 wrong:1 plane:8 faculty:2 data:1 parallel:2 natural:2 light:7 grant:2 explicit:1 orzer:1 st:1 rather:2 so:5 eichmann:4 inplane:1 order:1 exclusive:1 saturated:2 indeed:2 over:4 choose:2 experiments:2 london:2 cold:1 recovers:1 its:6 before:1 perfect:1 supplemented:1 thank:1 encompasses:1 exhibits:1 actually:1 lu:2 degrees:6 fig:5 alter:1 maximal:1 non:1 reemitted:1 polarizations:5 practice:2 obeyed:2 effects:2 they:2 focus:2 oxford:1 now:3 channels:2 2p:2 kǫ:1 university:1 events:1 sufficiently:2 fringes:2 each:1 qubit:5 universit:1 interfering:2 side:1 ei:1 weight:1 mesoscopic:1 principles:1 interferometer:2 owing:1 measurement:3 quantum:7 our:4 gordan:2 event:1 witness:1 out:3 leave:1 simplify:1 matrix:3 factors:2 quantify:1 rep:1 since:5 crucial:2 semi:1 michelson:1 europhys:2 get:1 dominate:1 ref:1 occurs:2 interchanging:1 linear:3 circumstance:1 guess:1 standard:1 completely:3 ρin:13 proportionality:3 conditioning:1 put:1 maret:1 care:1 interaction:2 recast:1 route:1 transition:9 imry:1 turn:1 consequence:4 undergo:1 onto:1 think:1 first:7 separable:1 initial:13 probability:5 omitted:1 reaches:1 restrict:1 thick:1 bayreuth:2 angular:8 size:1 interchange:1 given:6 rempe:1 temperature:1 bears:1 eqs:1 yin:1 amsterdam:1 system:3 their:3 outof:1 lucioles:1 too:1 scheme:1 final:9 store:2 denominators:1 trapped:1 ch:1 reversed:2 transverse:1 because:1 infer:1 sublevels:2 than:1 coefficients:3 center:2 diffusion:1 relative:1 kind:1 polarized:1 determines:1 holland:1 double:9 second:3 normalizing:1 matter:1 states:15 future:1 were:1 result:1 pre:1 lowest:1 berthold:1 mind:1 argument:1 say:2 manner:2 further:2 vaidman:1 clearly:1 elsewhere:1 paths:12 strength:8 lin:1 propagation:1 mechanism:1 polarization:15 extracted:1 internal:7 take:2 finding:1 detector:2 modulus:1 channel:4 hyperfine:1 play:1 broglie:1 multiple:5 trace:1 opposite:3 schwindt:1 impurities:1 most:4 germany:1 position:1 pair:1 intrinsic:1 observation:2 surprising:1 mobile:1 average:4 points:1 electrons:2 principle:3 urr:1 pattern:1 recoil:1 physics:6 shimony:1 fact:2 laws:1 sector:1 selected:1 particularly:1 structureless:1 show:1 detection:1 supported:1 scattered:2 bright:1 relation:6 scatterer:3 uniform:2 d2:1 spacings:1 ground:12 ratio:1 knowledge:9 situations:2 operational:1 only:2 factor:1 admixture:1 employed:1 do:1 sense:1 distance:1 dependent:1 familiar:2 de:2 quantified:2 cannot:1 report:1 during:1 du:1 processes:2 arxiv:2 summary:1 traversed:1 guessing:2 set:2 national:1 nus:2 clebsch:2 observed:5 intensity:1 geometrically:1 us:1 2pu:1 dyadic:3 analog:1 deflecting:1 probable:1 arguably:1 positivity:1 definite:1 dipole:2 label:1 symmetric:2 state:26 smallest:1 between:5 invariant:1 available:5 triplet:1 terms:1 ability:1 wa:11 nature:2 qubits:1 weak:1 however:1 vanishing:1 analyzed:2 understanding:1 both:8 equal:5 zeeman:1 sensitive:1 dated:1 context:3 attributes:1 contribution:2 finds:1 experimental:2 grounds:1 relevant:2 point:1 betting:1 excess:1 height:1 described:1 pu:2 addition:1 three:1 been:1 much:2 combined:1 interest:1 basic:1 expected:2 itano:1 ph:1 differently:1 compromises:1 arises:1 corresponding:5 suppress:1 photon:19 coherent:11 antisymmetric:1 spin:7 present:1 applied:1 labeyrie:3 photons:4 pacs:1 solid:1 means:1 examine:1 value:3 will:3 dephasing:2 preselected:1 bergou:1 applies:1 situation:8 endpoints:2 real:1 vectors:2 phenomenological:1 thus:3 them:1 conditioned:3 characterize:1 cond:1 triple:1 different:2 april:1 perhaps:1 media:1 granted:1 same:2 any:1 quant:1 pauli:1 largest:1 several:1 intermediary:1 difficult:1 used:1 peaks:1 see:1 singapore:3 numerical:1 effect:5 hand:1 doublets:1 experimenter:1 unpublished:2 wpd:2 circumvented:1 recent:1 interferometers:2 off:1 whereby:1 scenario:1 nevertheless:1 well:4 know:1 bohr:1 patterns:2 contact:1 components:1 coordinate:1 quantitative:5 drawing:1 left:2 less:1 storage:1 half:1 stored:5 atomic:6 uller:3 scattering:27 yet:1 mimicking:1 application:1 regarded:1 priori:2 slits:1 lett:9 spin1:1 excited:3 momentum:4 identical:2 aspects:3 around:1 depends:1 read:1 multiplets:1 pσ1:1 possible:2 helicity:1 background:2 press:1 englert:3 wbs:1 loss:1 like:7 particle:9 follows:1 either:1 scatterers:6 wiersma:1 right:4 classical:1 sequence:2 some:2 cnrs:1 understood:4 scatters:2 b2:2 complementarity:1 extended:1 transport:6 happens:2 pronounced:1 umr:1 magnitude:1 connecting:1 linearly:1 propagating:2 demonstrated:1 refer:1 cord:1 rank:1 reaching:1 perpendicular:9 although:1 found:4 post:1 singlet:2 takes:1 stokes:1 about:2 actual:3 carried:2 eaire:1 coexist:1 freedom:6 certainty:1 fringe:7 discussed:1 mutually:1 a2:2 wolf:1 mixed:2 financial:1 therein:1 equally:2 rev:12 pergamon:1 into:1 backscattering:6 nothing:2 rubidium:1 references:1 determine:1 einstein:1 operator:9 proportional:1 physical:1 institut:2 elastic:2 measured:1 support:1 there:3 low:2 irrespective:4 was:1 naturally:1 hz:1 survives:1 north:1 illuminated:1 form:4 denoting:1 but:7 pierre:1 contradictory:1 atom:12 line:1 hg:1 made:1 compute:1 born:1 uu:4 wish:2 inside:1 distinguishability:11 quantitatively:1 below:2 physikalisches:1 demonstrate:1 problem:1 semiclass:1 similar:1 display:2 detailed:1 bearing:2 associated:3 particlelike:1 measure:1 influence:1 direction:6 textbook:1 general:1 cbs:9 single:1 proves:1 akkermans:1 rule:1 work:1 simplest:2 regime:1 nk:1 ideally:1 nn:2 no:7 whereas:2 when:8 field:1 other:3 role:1 details:2 department:2 weights:2 nice:1 optically:1 nonzero:1 elements:4 star:1 superposition:1 time:1 meaning:1 important:1 bounded:1 peak:4 averaged:1 structure:4 coupling:1 assume:2 odds:3 required:1 together:1 mass:2 restricted:1 far:1 |
0704.1897.txt |@word secondly:1 gu:1 concept:9 partial:1 consider:3 sergei:1 caused:1 comparatively:1 results:10 arranging:2 scalar:3 computation:1 maxima:1 expressions:1 involved:2 minuscule:1 reasoning:3 localized:1 row:1 layers:24 whose:1 inverse:3 depend:2 calculate:1 notomi:1 tr:1 former:1 nπ:2 finally:3 according:2 restriction:2 those:5 th:1 under:1 analogous:4 juang:1 summarizes:1 applied:3 jπ:1 straightforward:1 outside:3 very:6 frequencies:1 peaks:3 rise:1 account:3 seemingly:1 wave:27 engelen:1 merlin:1 every:3 trough:1 refractive:5 resonant:2 affect:1 difference:1 fractal:3 newly:1 condition:7 groups:1 redistribute:2 prize:1 solves:1 level:2 transmission:20 ref:1 applicable:1 occurs:2 large:3 discrete:2 vector:2 quick:1 biological:1 drop:1 referred:1 optics:1 noted:1 upper:3 smaller:1 compensated:2 disordered:1 periodicity:3 foundation:4 altering:1 dealing:1 consistent:1 direct:2 pulse:3 approximation:2 elegant:1 rate:5 design:4 enhancement:5 equal:6 further:6 steadystate:1 mπ:2 even:4 index:5 what:4 appear:3 completely:1 giving:1 3b:1 sum:7 localization:1 transforms:1 zhang:1 expressed:3 thickness:4 anywhere:1 causes:3 above:2 lifshitz:1 new:4 net:1 commensurate:3 consisting:3 multitude:2 3d:1 coefficient:3 vanishes:1 evanescent:1 degree:3 respectively:7 loose:2 modify:1 equals:1 atoms:2 lack:1 desired:3 mev:1 dover:1 governing:1 mes:1 address:2 directions:1 causality:1 safer:1 strong:1 equations:4 appears:7 change:4 obtained:12 property:3 incoming:1 splitting:1 institute:1 shift:4 study:1 larger:1 funded:1 nussallee:1 through:3 guide:2 published:1 suggests:1 amount:2 minsk:1 differing:1 lightwave:1 eigenvalues:2 usually:1 resonance:2 shaded:1 studies:3 involves:2 transmittance:5 dowling:3 via:1 regardless:5 discontinuous:2 vii:2 fundam:2 assertion:1 affected:1 pythagorean:1 demir:1 support:2 raymond:1 total:7 univ:1 linearly:2 gaas:2 use:6 triples:1 takes:4 would:7 commun:2 distinct:3 nine:3 contains:2 examined:1 negative:1 nobel:6 dη:3 linear:2 going:1 call:3 opposed:1 characteristics:2 taken:4 scope:3 associated:2 butterworth:1 resonator:4 refs:2 more:12 coupled:1 substances:2 organized:1 ooi:1 emission:8 integrate:1 visual:2 backwards:1 everywhere:1 normalized:1 known:6 actual:2 cases:6 hold:1 iii:3 potential:35 must:4 fan:1 states:14 none:1 sutherland:2 pushed:1 ticle:1 equation:5 work:5 modified:3 remain:2 vs:1 values:8 mp:2 concepts:2 believed:2 making:5 arrive:3 spontaneous:5 example:3 stimulating:1 point:3 relative:1 compare:2 renormalization:1 figure:6 airy:1 choice:1 allowed:2 neglected:2 smirnov:1 sake:1 involve:2 indicates:1 minimum:1 numbers:2 ave:1 particles:2 standard:2 occur:6 multilayers:12 dk:2 soc:1 surrounded:1 decaying:1 provide:4 interacts:1 discussion:2 holds:3 differences:2 innumerable:1 arrangement:6 delay:3 located:2 impinging:1 occasionally:1 pair:1 get:1 opt:4 instead:1 flow:1 axis:1 parameter:4 simplicity:1 snd:1 mar:1 mat:1 inherent:4 may:1 overall:2 advice:1 earlier:2 derived:1 different:6 therefore:2 applications:3 plane:4 engineered:3 physik:1 waves:9 summarize:1 geometrical:3 meaningful:1 excited:1 types:3 varied:1 ambiguous:1 tion:1 induction:1 natural:2 effective:2 resemble:1 whenever:1 light:9 kuipers:1 spectra:3 lines:1 correspond:4 dragon:1 rather:8 secs:1 fp6:1 so:7 expression:4 allow:3 4i:1 increase:2 heuristically:1 d0:4 order:1 turns:1 typical:1 wavelengths:1 reproduced:1 words:1 produces:2 indeed:3 over:9 top:1 vary:2 satisfied:1 structuring:1 paper:7 including:1 mentioned:2 existence:1 still:5 ieee:1 its:11 chemical:1 derive:3 group:3 probability:1 chosen:5 interesting:1 lateral:1 presence:3 vicinity:2 needed:1 edge:1 forms:1 estimating:1 absence:1 complex:10 microscopic:1 systems:4 yeh:1 schrödinger:2 derivative:2 travelling:1 main:1 alter:1 conclude:1 finer:1 correspondence:3 non:9 belarus:3 motivated:2 greater:3 universität:1 integral:12 outlined:1 practice:1 impossible:2 introduce:3 reflected:1 band:3 walls:1 equidistant:5 effects:2 they:7 half:1 j02:1 1b:2 now:3 hall:1 dielectric:8 structural:1 represents:4 term:1 finite:21 name:2 thankful:1 inhomogeneity:6 university:2 presented:2 2d:3 micro:1 transmitted:2 bonn:3 each:6 heinemann:1 found:5 entirely:1 quarter:3 out:4 side:3 characterized:1 constraints:8 homogeneous:10 el:1 lectures:1 gratefully:1 directly:1 leavitt:1 mesoscopic:2 energy:20 barnett:7 inevitably:1 related:9 solution:6 breakthrough:1 inhomogeneous:10 used:7 obtains:1 accumulated:1 quantum:31 relates:1 beyond:2 eq:44 ep:12 special:2 description:1 deals:1 shown:6 eds:1 opened:1 space:14 vch:1 open:2 furthermore:1 since:4 squared:1 detailed:1 research:2 semiconductor:2 re:3 posteriori:1 europhys:1 d21:1 rational:2 reader:2 denoted:1 lecture:2 electronics:1 size:3 sensor:1 integrated:8 shows:1 exactly:2 condens:2 experienced:1 branches:2 telecommunication:1 barrier:9 passes:1 rouhani:1 contain:2 divergence:1 attempt:1 free:11 quite:2 reason:2 dependencies:1 proportionality:2 york:2 besides:1 element:2 van:1 limit:2 additional:2 definition:2 pairs:2 interaction:3 derivation:1 geometry:8 determining:2 transition:5 ist:1 counterpart:2 tor:1 length:2 place:2 leading:1 barriers:7 undergo:2 assign:1 first:4 origin:1 flynn:1 major:2 already:3 features:1 symmetry:2 u1:5 supposing:1 number:14 restrict:1 intuitively:1 obey:1 least:2 another:3 joannopoulos:1 2k0:1 thick:1 electronic:9 appl:3 engineer:1 dispersive:1 πc:1 given:11 limited:3 asymptotic:1 likely:1 width:2 introduction:3 2mω0:10 eqs:17 structured:3 system:6 relations:12 their:4 intermediate:1 brevity:1 too:5 calculations:3 dwell:2 molecular:3 structures:15 loudon:7 1d:9 accompany:1 grant:1 academy:1 explanation:1 continuous:4 wiley:2 transverse:1 forschungsgemeinschaft:1 part:1 pars:1 packet:1 authors:2 x2:1 constituent:26 x0:1 representing:1 than:12 coefficients:2 std:1 distance:1 nanostructures:4 resembles:1 princeton:2 horizons:1 was:7 require:1 themselves:1 zero:2 normalizing:1 matter:7 compensation:4 determined:3 nanostructured:1 regions:1 were:2 stricter:1 gives:1 integer:6 result:2 exhibit:1 raman:1 formulated:2 fashion:1 sees:1 electrodynamics:6 pass:1 mind:1 spectrum:10 curves:2 deutsche:1 randomly:1 posible:1 say:1 violating:1 alike:1 need:1 seen:16 regards:2 constrained:1 slab:3 any:19 dobrzynski:1 relatively:1 paths:2 counter:1 rearranged:2 laws:1 min:1 binarity:1 lim:2 latter:3 depicted:1 isolated:1 onset:1 instance:1 k1:3 without:6 generalized:2 analogy:4 online:2 finding:3 green:2 dα:1 projects:2 transparent:2 accuracy:1 spectral:15 towards:2 altered:1 fundamental:3 trace:1 normal:2 bertolotti:4 incidence:2 correct:1 wells:8 schematic:1 insets:1 most:1 petrov:1 involving:4 germany:1 but:15 gets:1 phase:16 analytically:4 why:1 avishai:1 chakraborty:1 chemistry:2 especially:2 considered:2 clear:2 bowden:2 coincides:1 km:2 optical:46 electrons:1 principle:1 exp:4 mechanical:5 nanostructure:1 dos:46 effect:1 left:2 physics:8 section:6 fact:3 quantity:1 slope:1 emerging:1 parker:1 deviation:3 show:5 absorbing:1 random:1 mechanics:1 relation:11 solutions:5 mater:1 economou:1 d2:1 eliminated:1 stepwise:16 d1:4 slow:1 based:1 parameters:8 j12:1 guidance:1 state:1 should:4 ed:2 only:16 aperiodic:2 rich:1 quasiperiodic:2 parabolic:1 employed:2 helmholtz:2 bogaerts:1 local:14 pointed:1 achieve:5 dn:1 do:3 2mp:3 dj:8 gains:1 notation:2 means:2 dependent:3 beams:1 de:6 stop:1 landau:1 foremost:1 aim:1 cannot:4 valuable:1 dx:1 despite:3 report:1 during:1 table:6 averaged:5 3a:2 evaluated:2 areas:2 following:1 processes:2 increasing:1 nazarov:1 bas:1 qw:9 course:1 conditions:2 seldom:1 arxiv:1 alteration:1 acknowledgments:1 kohmoto:2 experiments:1 contrast:1 t01:1 conforms:1 analytical:2 pulses:2 fixed:1 qm:3 d20:3 cρ0:1 view:2 monochromatic:1 traverse:1 set:6 our:1 physically:2 undergoes:1 national:1 correlations:1 j0:16 j1:13 potent:1 observed:1 see:26 individual:1 sec:6 us:6 arg:1 discussions:1 terms:1 limiting:1 hulst:1 subject:3 ωj0:3 ωj1:2 said:1 interacting:1 handed:1 scattering:1 review:1 eigenstates:1 enough:2 difficulties:1 closed:2 between:14 ramsauer:2 neither:2 previous:4 approach:2 across:3 reinhardt:1 available:1 admittedly:1 recently:2 ability:1 vertical:1 sections:1 singlelayer:1 interfaces:1 ikx:1 points:28 however:13 otherwise:1 incommensurate:1 combinations:2 incident:1 yeung:1 extent:4 soukoulis:2 interface:1 portion:3 understanding:1 ωc:1 suggested:1 restrictions:2 essentially:2 limits:4 always:1 many:5 region:6 conclusions:2 ec:1 hence:5 attributed:1 emit:1 mathematical:1 propagation:11 refraction:1 uni:1 mean:2 whole:7 messiah:1 monograph:1 con:1 arbitrarily:3 among:2 ch:1 necessary:3 periodic:12 simple:3 character:2 asymptotically:1 period:1 ultrashort:2 2nd:1 dimensional:4 represented:2 ev:8 sterke:1 simply:1 applicability:1 path:4 respect:2 mathematically:3 along:1 considering:2 ensures:1 described:2 second:1 basis:1 analogies:1 help:1 ledbetter:1 due:7 been:10 underlying:1 reduction:1 much:1 complicated:2 treat:1 goes:1 basic:2 anisotropic:1 fig:19 dots:1 digits:1 direction:2 contribute:2 diversity:1 both:18 quantities:2 sufficient:2 photon:2 defect:2 bulk:1 implied:1 dramatic:3 understand:1 enforces:1 nanoscale:1 general:7 cantor:1 present:6 case:25 explicitly:1 requirement:1 laser:1 potentials:1 solid:2 nd:1 engineering:2 value:7 eigenstate:1 will:9 complexity:1 optimization:1 replaced:1 behavior:1 promising:1 aid:1 tunneling:5 taking:4 manner:1 identical:1 layer:22 find:1 played:1 vol:1 vi:2 im:3 thus:5 them:4 iv:2 ii:6 good:2 cond:1 commonly:1 crystals:7 ultracompact:1 busch:2 controversy:1 technology:1 k0:3 around:2 binary:8 confirmed:1 unaffected:2 verified:2 assure:1 media:17 make:2 recurrent:1 quadratic:4 lett:8 same:17 shifts:1 parts:1 widely:1 modification:20 dimensionless:1 several:3 composition:1 higher:1 independent:4 investigated:2 infinity:2 centuries:1 singapore:3 djafari:1 numerical:4 mutual:1 haus:1 hand:4 inhomogeneities:2 purpose:1 nanocrystals:2 infinite:9 pioneers:1 heterostructure:1 totally:4 preset:1 recent:1 bhattacharya:1 suitable:1 off:1 reflection:7 largely:2 nevertheless:2 onedimensional:1 no:8 well:20 kept:1 obviously:2 solids:1 materials:5 redistribution:2 possesses:1 figs:3 subtraction:1 r01:1 discretely:1 mcphedran:1 just:2 less:2 being:1 when:8 lowest:1 photonic:8 homogeneity:1 assigned:1 press:3 shape:1 intervals:3 atomic:2 questions:1 using:3 spatially:1 ωj:3 macroscopic:1 yet:1 heterostructures:7 far:2 note:11 absorptive:1 rapid:1 candidate:1 density:7 ease:1 alternate:1 had:2 advancement:1 seem:1 discuss:1 appeared:2 valid:1 nor:2 clipped:1 possess:3 5a:1 remaining:1 scientific:3 build:1 real:2 manage:1 increased:1 rev:18 molding:1 rules:1 outermost:1 showing:1 spatial:1 possible:9 corresponds:2 schematically:1 inhibition:1 indicative:2 makes:2 background:2 vacuum:5 confined:1 world:4 color:2 guaranteed:1 imposed:2 like:5 particle:9 follows:2 reduces:1 adv:1 manifest:1 sized:4 fork:1 steps:2 either:2 integrals:3 arbitrary:5 rearrangement:6 become:1 stationary:3 efimov:1 unexplored:1 pertaining:2 because:5 often:1 namely:1 sequence:2 multilayered:1 resonances:4 fresnel:1 sequences:2 phenomena:4 springer:2 certain:3 broglie:1 examples:1 moreover:1 multiple:3 scalora:5 distribution:2 electric:1 provided:4 scale:4 represent:2 acknowledged:1 confirm:2 compressors:1 though:1 integration:9 per:1 does:5 unit:1 provides:2 prog:1 yariv:1 propagating:4 demonstrated:1 2a:2 limitations:1 itself:2 rep:1 2c:1 fabricated:1 pp:3 broken:2 step:4 retaining:1 kam:1 although:2 2m:2 plots:1 imaginary:1 falls:1 nefedov:1 properties:21 proceed:1 comparison:1 limitation:1 central:2 sharper:2 constraint:1 freedom:4 am:1 discussed:2 dependence:7 o:1 remains:2 range:1 regular:2 formulas:1 together:1 tighter:1 fulfilled:1 introduced:3 consequently:1 bloch:1 fabry:1 therein:2 outlook:1 cambridge:1 accompanied:3 maxwell:1 into:6 within:8 numerically:5 isomorphic:1 three:1 down:2 nothing:1 right:3 references:2 karle:1 determine:2 elementary:7 proportional:2 alas:2 iguchi:1 physical:11 institut:1 compression:2 area:2 multilayer:22 transfer:1 apparently:1 there:6 question:5 u0:10 awarded:1 dispersion:18 start:1 conservation:8 way:7 series:1 metamaterial:1 opens:1 naturally:1 function:9 medium:10 arise:1 interest:1 form:3 energies:2 some:10 regard:1 delayed:1 extended:2 volume:1 kroemer:1 properly:1 v0:6 heuristic:2 russian:1 helpful:1 line:3 sense:4 true:2 considerable:1 2d0:1 constitute:1 made:3 arranged:1 intuitive:1 deterministically:1 fabricate:1 characteristic:2 inside:1 ωr:2 up:3 devices:3 par:1 crystal:1 below:1 frequency:22 ωm:5 uj:1 continuously:1 demonstrate:2 problem:4 define:3 similar:8 called:1 clarke:1 strongly:2 bearing:1 required:1 constant:3 resemblance:1 defined:5 likewise:2 universal:4 mirror:1 influence:1 advancements:1 metals:1 denote:2 single:8 exist:2 governed:1 interchanged:1 aperiodically:1 corresponding:5 formalism:1 internal:2 krauss:1 regime:5 nj:7 compared:5 nn:1 variety:1 dashed:1 generally:1 detail:1 zhukovsky:9 reality:1 field:1 sakoda:1 other:9 role:2 details:3 investigations:1 becomes:6 mathematics:1 really:1 solely:1 realize:2 reflections:2 optically:1 elements:7 kinds:2 separate:1 models:1 fazio:2 time:5 problems:1 bottom:1 variation:2 spectrally:1 chirp:2 meaning:5 important:2 technol:1 allowing:1 suppression:2 velocity:5 variable:1 dense:1 au:1 gap:2 unless:1 sides:1 structure:57 subdivision:1 longer:7 algorithm:1 dω:8 assume:2 normally:1 interval:6 berlin:2 rule:7 impossibility:1 observe:1 mass:2 useful:1 electromagnetic:11 n0:9 n1:9 n2:1 dϕ:3 requires:2 having:2 fully:1 once:1 |
0704.1898.txt |@word consider:9 magnetic:10 global:2 results:3 leads:3 scalar:4 offdiagonal:1 per:1 expressions:5 contributions:6 causes:1 devoted:1 replacements:1 depend:6 emig:2 sahni:1 γr:22 concerned:1 technique:4 acting:11 finally:2 tm:4 those:2 th:7 under:8 arranged:1 analogous:1 include:1 kν:5 divergent:2 interacting:1 dowker:4 string:6 straightforward:1 frequencies:1 tends:1 gqm:6 kirsten:2 ultraviolet:1 summarized:1 bounding:1 difference:1 condition:5 identity:1 four:1 induced:46 minkowskian:2 presented:12 lombardo:2 evaluation:5 eigenmodes:1 t2:3 large:21 vector:4 small:1 eigenvalues:3 anal:1 configurations:1 application:2 force:4 2k2:3 deutsch:1 renormalized:2 consistent:1 coefficient:2 past:1 second:3 street:1 value:5 further:3 dynamics:1 barbashov:1 ηf:23 primes:1 bilinear:2 index:1 plays:2 nano:1 diag:1 section:10 analogously:1 uniform:3 axial:1 scoccola:1 goes:1 new:6 subtracting:1 method:4 satisfy:2 vev:18 bezerra:4 respectively:2 component:8 here:6 hqm:3 tensors:1 cylindrical:92 brevik:3 consideration:4 along:1 ascending:1 equations:2 stresses:4 great:1 involved:1 study:1 brazil:1 allows:1 expression:5 reports:1 p2:3 base:1 resulting:1 usually:1 πa:1 t22:7 spacetime:5 relation:3 plotted:3 being:4 azimuthal:8 useful:1 figure:13 scales:1 apr:1 planar:1 highly:1 rφ:1 gordon:2 summation:18 apply:2 total:2 unit:2 schaden:2 derivatives:1 use:1 y2:1 asymptotic:19 covariant:1 positive:3 dxx:4 negative:3 next:1 comparing:1 nucl:4 approach:1 therefore:1 expanding:1 taken:2 qci:1 type:2 theoretical:3 more:2 separated:1 introducing:5 stecher:1 conductor:3 operators:1 ti:1 validity:1 ra:1 everywhere:1 particular:7 known:2 candelas:1 cases:3 prudnikov:2 γa:22 account:1 te:4 integrating:1 science:1 equation:3 work:2 modified:8 theories:1 remain:1 paragraph:1 values:33 subnuclear:1 attain:1 wedge:60 f2:4 renormalization:3 cosmological:1 plate:8 calculation:1 energymomentum:2 organized:1 topic:1 sphere:2 yν:1 numbers:4 employs:1 unphysical:1 ic:1 axis:2 information:1 regularization:1 turn:3 discussion:3 acts:1 regions:8 located:2 nontrivial:1 behave:3 opposite:2 elliptical:1 parameter:10 sin:24 circular:2 product:1 proc:1 coming:4 may:3 after:5 derived:4 applications:2 plane:9 plana:8 april:1 parallel:5 types:2 stress:3 dynamical:1 effective:6 computations:1 explicit:1 summing:2 element:1 nas:1 green:1 specifying:1 fundamental:1 ned:1 taking:5 representation:1 integrand:1 order:13 interpretation:1 dx:14 jν:5 developed:1 over:21 fν:2 years:1 report:1 paper:4 including:3 signs:2 satisfies:2 still:1 its:3 before:1 perfect:2 write:1 ln:3 interesting:3 coordinates:4 edge:9 complex:1 systems:1 romeo:3 mail:1 main:18 decades:1 non:2 xa:18 gies:2 combination:2 janeiro:1 material:1 introduce:3 framework:1 walls:1 cutting:1 repulsive:2 effects:1 they:2 half:6 front:2 now:6 b572:1 t21:9 4πr:1 easily:1 february:1 finite:9 alex:1 2q:18 always:6 university:2 magierski:1 2y:2 micro:1 inequality:1 mode:21 qx:1 found:3 wolfram:1 side:5 square:26 golestanian:1 series:7 energy:46 frequency:1 related:3 elementary:1 investigated:10 expect:3 entering:1 quantum:17 our:2 operation:1 extract:4 buscher:1 special:3 out:2 shown:1 rep:1 since:3 rev:19 contained:1 investigation:3 ren:9 bulgac:1 izv:2 i0:3 formula:52 squares:2 ref:7 math:4 tracelessness:1 commutation:1 theory:6 written:2 khemani:3 variant:2 abramowitz:1 contain:1 dominated:1 diagonal:10 standard:3 hankel:2 approaches:1 dependencies:1 complicated:2 york:3 gasiorowicz:2 8q:1 e3:3 e2:2 netic:1 r3:1 geometry:33 determining:1 could:2 conformally:2 cosmic:5 traceless:1 appearing:1 int:1 exponentially:3 hence:5 mello:2 first:9 sanchez:1 πi:1 features:1 symmetry:1 xm:1 waves:3 xf:1 number:1 done:3 another:1 xr:13 angular:1 interchange:1 given:25 perturbation:1 checked:1 needed:1 introduction:2 leading:23 eqs:1 saharian:13 system:1 relations:5 πr:1 their:3 zeros:3 too:2 calculations:1 wirzba:1 πx:2 perfectly:8 ictp:1 shell:95 sin2:2 tool:1 exactly:2 transverse:3 quandt:3 part:29 manifestation:1 x2:13 x3:6 x0:5 than:1 coefficients:1 cyl:61 distance:3 kind:1 molecular:1 determines:1 third:1 accordance:3 double:1 approximations:1 marichev:2 zero:2 scarpetta:2 limiting:5 annihilation:1 determined:5 enables:4 bordag:7 lowest:4 remained:1 electrodynamics:1 ann:5 turned:1 spectrum:2 curves:2 correspond:2 graham:4 close:3 seen:6 regards:1 constrained:1 intersecting:1 angle:16 min:1 convenient:2 self:1 gravity:1 arm:3 note:7 instance:2 k1:1 potential:2 generalized:8 forces:15 interior:12 davies:1 circles:1 inequalities:1 continuous:1 multiple:1 electric:11 investigations:2 most:2 involving:2 formulae:25 cylindrically:1 class:4 tensor:27 tν:1 takes:1 considered:9 behaves:2 calculated:1 later:1 implications:1 neutral:1 traditional:1 kq:6 points:17 proceedings:1 exp:5 mechanical:1 jν2:2 kz:2 physics:2 sum:12 quantity:2 subtly:1 show:1 supported:1 notations:7 purely:1 gauge:1 solutions:3 substituting:5 tend:2 find:6 fifth:1 help:1 boundaries:15 q2:4 based:1 parameters:4 outside:5 should:2 analytic:2 only:1 princeton:1 specify:1 factor:6 mazzitelli:4 milton:4 local:3 equilibrium:2 continuity:2 do:2 dominant:2 dk:10 notation:2 means:1 dependent:3 de:4 dominate:2 expectation:15 ssr:3 aα:2 closely:1 international:1 dv:1 during:1 αk:2 schr:1 prime:1 densities:8 fqm:2 upper:1 fields:12 arxiv:1 expansions:9 wightman:1 grav:4 acknowledgments:1 rinton:1 t11:4 trunov:1 europhys:1 though:3 t00:5 fixed:4 qm:2 inside:14 view:2 kernel:2 set:3 above:2 lπ:2 edited:1 testing:1 j0:1 j1:1 up:4 namely:1 radius:4 result:6 corre:1 fail:1 terms:23 contour:1 conductivity:1 surfaces:2 satisfying:1 imposition:1 halved:1 intersected:1 scattering:1 away:2 opening:8 diverge:4 symmetric:7 state:3 difficulties:1 various:5 between:3 invariant:1 boundary:39 conditions:11 recently:1 28q:1 nature:2 attention:1 however:1 jr:1 jq:2 jm:17 p2w:2 concentrate:1 ellipticity:1 armenia:1 configuration:1 suppressed:5 valid:2 divergence:1 both:5 cos:14 last:2 0w:13 many:2 region:33 nabla:1 sov:2 etc:1 manifestations:1 figures:1 dalvit:2 casimir:18 expand:1 contribution:25 safely:1 finds:5 experimental:3 0m:4 among:1 ci:1 relevant:2 point:5 continuation:1 brychkov:2 corresponds:7 coincidence:1 dimensional:1 cancel:1 respect:6 zeta:4 mathematical:2 aαi:2 conference:1 geometries:4 eπi:1 addition:4 oder:1 due:10 been:5 2pl:1 rezaeian:1 ai:2 interest:4 applying:1 ph:1 ak:2 pl:1 lett:8 obtained:6 scardicchio:3 corresponding:63 received:1 quantities:4 coincides:1 modelling:1 argument:3 neumann:1 confinement:2 external:1 angles:1 derivative:1 c3:2 c2:2 c1:2 convergent:3 present:6 case:20 k2:13 unlike:1 pacs:1 akad:1 originate:1 evaluated:11 rectangular:1 will:8 contemp:2 near:13 behavior:6 shift:1 cancelled:3 langfeld:1 robin:1 cylinder:4 a4:17 coupled:2 iq:6 characteristics:1 refs:5 thus:2 surface:6 ii:2 rio:1 ik:1 gosdzinsky:1 exterior:10 c0:2 vanish:1 k0:1 different:5 education:1 grant:1 tqm:4 divergences:5 same:13 kardar:2 parts:27 modification:1 plates:5 several:2 used:4 infinity:1 see:16 singapore:2 i1:1 eccentric:1 effect:7 hand:7 constraining:1 edges:4 conductors:1 pettersen:1 potentials:1 infinite:2 i12:1 fabrication:1 normalization:4 recent:1 lower:1 off:5 modes:10 makes:1 well:3 analysis:2 without:22 comes:17 components:11 lim:3 coordinate:1 position:2 latter:11 subtraction:1 distances:7 manifold:1 less:2 increasingly:1 stegun:1 obtain:5 aside:1 oxford:2 spherically:1 differentiation:1 alternative:2 reality:1 macroscopic:1 ministry:1 polarization:1 marachevsky:2 integer:3 density:14 products:1 yu:2 conclude:1 except:1 discuss:1 iω:1 source:2 other:2 attractive:7 wet:1 mod:1 solvable:1 momentum:24 take:1 real:1 ambjørn:1 iν:5 depends:2 spruch:2 evaluate:2 spatial:2 sums:3 term:21 nesterenko:7 pos:1 know:1 coaxial:9 vacuum:50 press:2 using:16 replace:3 advanced:1 like:2 rotate:1 imposed:1 semi:2 particle:1 kennedy:1 follows:7 frolov:1 specific:1 flux:1 δm:3 unstable:2 kqm:15 integrals:7 arbitrary:2 popular:1 become:1 pirozhenko:1 works:1 yerevan:2 therein:2 right:11 methods:2 deal:2 discontinuities:1 creation:1 some:1 regularized:1 breach:2 matematika:1 b2:1 specified:2 2qm:3 nonzero:1 vol:2 scale:1 describing:1 electromagnetic:11 tube:1 normal:2 integration:5 classical:1 does:3 deficit:3 summand:1 assuming:5 bessel:12 tk:5 2a:1 eigenfunctions:9 scientific:2 radial:3 oscillating:1 expansion:1 pressure:6 weigel:4 subtract:1 properties:1 von:1 orthonormalization:1 conducting:12 onofrio:1 world:2 discussed:4 dependence:2 o:3 tii:16 a2:4 nj:1 act:1 2x0:1 introduced:5 consequently:1 renormalised:1 cutoff:7 own:1 firstly:1 presence:8 0s:6 into:11 within:1 integral:6 odd:1 references:3 polarizable:1 einstein:1 operator:2 proportional:2 abel:8 conceptually:1 22q:2 technically:1 relativistic:1 hep:7 additional:5 shells:2 jhep:1 assumed:1 there:3 apps:1 transform:1 mostepanenko:2 handbook:1 way:5 ed:1 was:3 function:29 complete:1 form:16 m2:4 volume:2 x2q:2 heat:2 delta:1 russian:1 encoded:1 removed:3 vevs:37 absent:3 cylinders:2 jaffe:7 characteristic:1 gravitational:1 ωt:2 us:8 iqm:16 below:2 2πr:1 limit:20 planes:1 fluctuations:4 problem:5 similar:2 strongly:2 diverges:4 defined:5 3q:1 abstract:1 describe:1 influence:1 general:4 single:5 formalism:1 aφ0:2 dγ:5 fizika:1 physical:4 again:1 functions:20 lambiase:3 no:11 eq:6 whereas:4 when:5 vanishes:5 schwinger:1 field:46 interested:1 role:2 details:1 sponding:1 tik:10 department:1 resf:1 conclusion:1 polar:1 denote:3 generates:1 models:1 dittrich:1 problems:2 includes:1 qπ:1 a3:3 important:4 curvature:1 qφ:2 variable:2 armenian:1 replacement:3 sides:19 structure:3 t12:1 coupling:2 coulomb:1 4q:3 perpendicularly:1 observables:1 dover:1 original:1 |
0704.1899.txt |@word represent:1 l17:2 rol:2 consider:4 illustrates:1 luminosities:1 results:9 dumas:1 leads:1 eccentricity:2 disc:8 grateful:1 consists:1 moon:1 cases:1 compact:12 terms:1 ergs:3 caldwell:1 young:2 finally:1 efficiencies:1 award:1 those:1 priddey:1 stable:2 road:1 jensen:1 evolves:4 very:2 fall:2 mixing:1 levay:1 presented:1 soderberg:1 large:1 heger:4 fruchter:10 science:1 small:1 gammarays:1 woosley:7 pooley:1 dis:1 favoured:1 natarajan:1 garnavich:2 riess:1 progenitors:8 le1:1 rate:2 tanvir:4 further:4 hucht:1 berlind:1 blue:3 established:1 what:2 appear:1 section:3 axes:1 kalogera:1 suggestive:1 expressed:1 lgrbs:10 petro:1 template:1 new:1 increasing:1 acknowledgments:1 explosion:1 den:3 degree:1 error:1 here:4 met:1 explore:2 objects:2 operating:1 possibility:1 separation:8 excess:2 based:2 strong:1 change:1 box:1 institute:3 larger:1 commonly:1 prior:1 amati:1 survey:1 pindor:1 plotted:2 via:5 apr:1 madingley:1 explained:3 antineutrino:2 highly:2 apj:8 neutrino:2 total:3 burud:1 plot:2 use:2 indicated:1 would:2 remains:2 likelihood:1 predictions:1 gibbons:1 scenarios:1 few:1 cappellaro:2 taken:3 candidates:1 themselves:2 type:2 l61:1 more:7 ejected:1 starburst:2 envelope:7 antennae:1 tested:1 petrovic:1 particular:1 known:3 kulkarni:1 hole:14 producing:2 must:1 md:1 account:1 mc:4 middle:1 decouples:1 der:1 work:2 centrifugally:2 reviews:1 levan:6 remain:2 ms:3 hainaut:1 following:7 example:1 dn:3 compare:3 wang:1 figure:5 give:3 grant:1 high:4 effectively:1 minimum:5 performed:1 tidally:2 firmly:1 swedish:2 piran:1 andersen:1 rather:2 helium:5 fynbo:4 pedersen:3 located:1 vital:1 answer:1 axis:2 pathway:2 product:1 sne:6 galactic:1 undergoing:1 sauer:1 may:11 max:2 after:2 r2c:1 orbits:1 flattens:1 produce:5 heuvel:3 data:2 types:1 short:1 attempt:1 belczynski:1 light:9 proto:1 separations:2 correspond:1 ledoux:1 extrapolation:1 davies:3 sn:6 inspiral:2 correlation:2 guenther:1 order:4 se:1 typical:1 evolutionary:2 produces:3 gorosabel:3 radiation:1 over:1 ens:1 years:1 nugent:1 including:3 its:3 galaxy:5 lf:1 derive:1 rapidly:6 chosen:1 masses:13 relativity:1 decreases:1 li:1 forms:1 production:1 systems:12 gehrels:1 clusters:10 main:3 might:1 pixel:3 non:1 good:1 motivated:1 greater:1 eccentricities:1 material:10 innermost:1 runs:2 number:2 effects:1 they:2 half:1 rotation:9 now:2 brightness:1 always:1 university:2 sufficiently:7 filling:1 bursts:11 each:1 found:1 realisations:1 constraints:1 subset:1 telescope:1 energy:10 frequency:1 idea:2 related:1 grbs:13 fraction:6 eisenstein:1 assumption:1 kasliwal:1 out:1 living:1 shown:4 ejecting:1 space:2 oechslin:2 rep:1 since:2 rz:1 research:1 berger:1 fellowship:1 equate:1 ajl:2 rc:4 newly:4 occurs:1 red:3 foundation:1 ofek:1 ultraluminous:1 wong:1 galaxies:7 free:1 standard:1 necessarily:1 formation:5 beginning:1 j0737:1 hubble:1 created:1 brown:1 could:1 echevarria:1 sahu:1 conducted:1 explored:2 massive:11 transfer:1 davis:1 retain:1 undergo:1 calkins:1 first:3 major:3 initial:3 probability:2 chevalier:1 rhoads:2 primary:4 channels:1 adopted:1 carry:1 arzoumanian:1 open:1 angular:6 size:1 given:4 1r:1 jet:1 introduction:1 top:1 moderately:1 system:2 least:3 roche:2 their:10 accretion:7 rates:3 observations:2 calculations:1 white:2 scheme:1 gives:1 pinpointing:1 nomoto:2 way:1 baryon:1 bhattacharya:2 persson:1 released:2 lazzati:1 somewhat:1 natural:1 sollerman:3 than:10 explodes:3 population:6 king:2 mclaughlin:1 observatory:1 holland:2 surrounding:1 require:2 measured:1 likely:6 annihilation:2 sweden:1 iron:2 were:5 providing:2 stanek:1 san:1 remained:1 lines:4 chandar:1 ages:1 rau:1 unlikely:1 20m:1 any:1 viewed:1 collapse:16 conversion:2 min:2 mechanism:1 note:1 pparc:1 academy:1 so:1 channel:2 infalling:5 circles:2 even:1 fuels:1 towards:1 ray:19 centre:1 price:1 object:5 neutrinos:1 hjorth:4 cordes:1 most:2 eight:1 significant:3 phase:3 extremely:1 class:1 sub:1 lee:1 7al:1 observation:1 fills:1 torus:9 metal:1 drive:1 km:3 martini:1 ks:2 cameron:1 points:1 patat:1 whitmore:1 physics:2 fitted:1 currently:2 leicester:2 kaper:1 supported:3 synchronous:1 rotating:6 radii:2 postdoctoral:1 schmidt:1 keywords:1 analogue:1 uniform:1 trivial:1 find:2 o:2 ratio:1 parameters:3 ngc:3 wallenberg:1 gull:1 conselice:1 only:2 black:23 indeed:1 local:2 ruiz:2 larsson:2 spun:1 do:1 distance:1 lobe:2 between:4 assumed:3 bersier:2 watson:2 words:2 during:2 dahlen:1 dr:1 secondary:10 well:2 evolution:3 luminosity:6 arxiv:1 summary:2 discs:7 common:3 through:2 strolger:1 bars:1 constructing:1 burst:7 undergoes:1 0ha:1 ebh:1 transferred:1 observed:19 see:3 radius:5 close:1 luminous:1 masetti:2 dwarf:1 phases:1 visiting:1 wijers:3 subsequent:2 review:1 melvyn:1 various:1 lgrb:3 across:1 klose:2 wd:2 recently:1 creating:1 vertical:1 hosting:1 baade:1 supernova:13 emitted:1 weak:2 however:3 yoon:1 efficiency:1 no:1 key:5 jd:1 shapes:1 come:1 concentrated:3 both:2 essentially:1 limits:2 vreeswijk:3 many:2 according:1 against:2 tout:1 contribution:1 kouveliotou:3 baltimore:1 nearby:1 strongly:1 point:2 simple:3 royal:1 period:1 environments:1 maintained:1 starling:1 table:1 ferrero:1 deng:1 late:1 sari:1 described:3 second:4 addition:1 cv4:1 due:2 been:4 much:1 progenitor:9 expected:2 ph:20 fig:5 suggested:2 mcl:4 diversity:2 champion:2 observable:1 sufficient:1 formed:14 andrew:3 hypernovae:1 weisberg:1 c2:3 spin:1 present:2 case:2 olszewski:1 50m:1 uncertain:2 look:1 supernovae:9 pacs:1 coventry:1 nakar:1 originate:5 mtot:3 castro:7 will:11 while:6 pian:3 match:1 rbh:1 penprase:1 sousa:1 almost:1 thus:3 ellison:1 surface:2 matheson:1 ii:1 cluster:6 deeg:1 ic:3 ib:1 ie:1 orbital:2 binary:15 containing:5 suggests:1 suggest:4 locking:4 cross:1 same:2 schild:1 resulting:1 several:3 events:1 neutron:20 higher:1 mazzali:2 used:1 maeda:1 jakobsson:2 upon:3 ferguson:1 moment:1 frequently:1 greiner:2 krisciunas:1 tighter:1 nicastro:1 corecollapse:2 lower:3 scenario:1 restricted:1 variety:1 mainsequence:1 thought:2 edge:1 components:1 model:10 binaries:13 left:2 kawabata:1 just:1 less:2 being:2 distribute:1 astroph:1 lorimer:3 identify:1 thanks:1 questions:1 merge:1 nousek:1 previous:1 rapid:1 density:3 tirado:4 had:1 source:3 location:1 momentum:6 identical:1 livio:1 around:12 spectacular:1 harding:1 frail:1 possibly:4 increases:1 marked:1 background:5 rns:1 using:3 accepted:1 necessary:4 semi:3 alternatively:1 alice:1 specific:1 janka:2 yields:1 either:2 martin:1 bulik:1 because:1 often:1 classical:2 sequence:3 plausible:3 creation:4 some:11 dwarfs:1 calculated:1 duration:5 neglecting:1 mccarthy:1 basic:2 lead:1 bottom:1 companions:1 fox:1 per:1 instantaneous:1 contributing:1 critical:3 cenko:1 provides:1 assuming:3 indication:1 thorsett:1 foley:1 core:25 power:1 reaching:1 bh:17 stellar:7 host:9 bw:1 although:5 tidal:4 post:1 properties:2 stage:5 brien:1 about:3 central:4 usa:1 constraint:1 discussed:1 factors:1 7rh:1 langer:3 probabilities:4 range:2 tribution:1 macc:4 mean:1 slightly:1 create:1 gamma:16 peak:1 kann:1 cambridge:1 mbh:1 redshift:2 mbd:1 windhorst:1 into:2 within:4 bound:1 pursimo:1 three:2 lies:1 hathi:1 references:1 lund:3 smette:1 spline:1 significantly:2 follows:2 van:4 podsiadlowski:2 metzger:1 removing:1 support:1 there:7 question:2 spiral:2 long:9 start:1 l133:1 low:2 stars:24 was:2 naturally:2 function:3 complete:1 form:9 forming:1 warwick:1 astro:20 macfadyen:1 link:1 solar:1 mnras:5 l20:2 line:1 collapses:1 he:4 versions:1 whether:3 gravitational:1 burrows:1 variations:1 maximum:2 different:2 below:1 owing:1 uk:2 demonstrate:2 distribution:10 stages:1 similar:1 clear:2 nature:4 originating:2 taylor:1 associated:1 up:2 challis:1 abstract:1 fellow:1 pix:1 single:2 exist:2 our:3 knut:1 lifetime:1 ramirez:2 distributions:10 frontera:1 functions:1 filippenko:1 izzard:1 nonetheless:1 when:7 tight:4 other:3 grb:12 department:2 ns:20 palazzi:2 poor:1 picture:1 transferring:2 star:22 models:4 6m:1 cb3:1 important:1 pathways:2 astronomy:2 møller:2 l65:1 implies:1 assume:2 typically:1 age:2 required:5 holes:6 orbit:5 together:3 mimic:1 mass:17 time:5 far:2 jansen:1 requires:2 |
0704.1900.txt |@word represent:1 logarithms:1 partial:1 consider:4 switched:1 crucial:1 global:4 desirable:1 leads:3 scalar:5 generalize:2 consists:1 follow:2 contributions:1 extra:1 certainly:1 truong:1 equivalence:1 tr:1 trivial:1 finally:1 program:1 those:1 excluded:1 under:8 include:2 u2:1 belonging:1 rtn:1 amplitudes:4 g2:1 very:3 rise:2 3s2:1 interpreting:1 decide:1 pukhov:1 resonant:1 difference:1 continued:1 condition:2 level:1 turns:2 nucl:1 t2:1 solution:1 large:4 vector:3 small:2 relation:6 jhep:2 strongly:1 work:2 oscillation:1 renormalized:2 miur:1 direct:1 approximation:1 threshold:1 second:6 perspective:1 rigorous:1 dynamics:1 tev:1 goes:1 even:3 transverse:1 froissart:1 sub:1 fine:2 section:2 expressed:1 version:2 poles:2 above:2 new:1 method:2 satisfy:1 full:3 evaluating:2 exchange:5 dubovsky:1 understanding:1 lu:1 consideration:1 strong:1 observing:1 appears:1 interpret:3 knowledge:1 obtained:4 leutwyler:1 involved:1 study:7 dominantly:1 reason:1 commonly:1 couplings:10 p2:1 nonforward:1 usually:1 studi:1 specialize:1 higgsless:1 lowers:1 via:1 distler:1 scales:2 forbid:1 requiring:1 imagine:1 propagations:2 apply:3 total:1 causal:9 linearly:1 asymptotic:2 working:2 prove:1 distinct:1 positive:7 negative:4 next:2 scenarios:1 linear:2 call:2 therefore:6 qcd:7 theoretical:2 more:5 composite:1 operators:5 apparent:1 particular:1 known:1 hold:1 must:2 high:2 account:2 quartic:8 inertial:1 constraint:4 modified:1 theories:1 assumptions:2 values:1 three:1 believed:1 spontaneous:1 example:4 compare:1 give:1 process:1 expanding:1 sense:1 neglected:3 states:3 lorentz:5 numbers:1 allowed:2 legendre:1 action:1 axis:1 dominant:1 respective:1 turn:1 provide:2 s2:5 discussion:1 holds:1 write:2 trieste:2 coleman:1 parameter:2 de:1 fu:1 singular:1 may:9 after:1 singularities:1 residues:1 consequence:5 produce:2 value:1 waves:1 drastic:1 choice:1 meaningful:1 realized:1 callan:1 natural:1 effective:14 higgs:12 light:5 explicit:1 su:8 element:1 s3:3 ones:2 negligible:2 fundamental:4 enter:3 taking:1 representation:2 order:10 breaking:7 dx:2 eqs:2 interpreted:1 produced:2 gauged:3 experiments:2 cuts:1 existence:1 satisfies:2 still:2 its:7 operative:1 before:1 style:1 derive:4 imf:5 energies:2 matrices:1 masses:3 relativity:4 boson:8 actually:2 estimating:1 absence:2 production:1 choose:1 renormalizable:2 overcome:1 correspondence:1 measurement:2 non:12 good:1 peskin:1 greater:2 combination:1 gasser:1 outlined:1 noticing:1 introduce:1 subtraction:1 they:5 nov:1 now:2 discuss:1 porto:1 term:4 finite:1 invariants:1 hamiltonian:2 ananthanarayan:1 sufficiently:2 l4:1 inequality:1 l2:2 internazionale:1 l1:3 crossing:7 2m:1 entirely:2 side:1 lorentzian:1 constraints:9 goldstone:4 domain:3 significantly:2 series:1 energy:8 reduce:2 extended:1 isospin:1 interplay:1 measure:1 quantum:3 our:5 ew:2 beyond:1 eq:4 special:4 out:3 gonzalez:2 respects:2 matrix:6 m2z:3 space:1 gradient:2 nuovo:1 since:6 lagrangian:13 denotes:1 particles:1 dominated:2 rattazzi:1 get:2 induced:2 evaluation:1 shows:1 bijnens:1 theory:15 interactions:1 derived:7 differ:1 possibility:2 standard:4 difficulty:1 completely:1 superiore:1 estimate:3 hamed:1 derivation:2 transition:3 ds2:2 v2:2 motion:2 introduction:2 corrections:3 view:1 think:1 first:1 informations:1 already:1 rothstein:1 symmetry:12 upper:1 variables:2 exact:3 smaller:1 another:1 precisely:1 given:2 necessarily:1 reference:1 unitarity:3 unknown:2 adjoint:1 realistically:1 their:4 assumption:7 too:2 bosons:7 scheme:1 final:1 observations:2 ratio:1 tool:2 exactly:1 serve:1 stress:1 electroweak:3 optical:2 authors:2 x3:2 than:7 coefficients:18 modes:1 wide:1 polarized:3 require:2 zero:2 fermionic:1 determined:1 amplitude:18 kuang:1 gives:1 perturbative:6 symmetries:3 operationally:1 subdominant:1 respecting:1 mind:1 argument:1 regime:3 unlikely:1 seen:2 constrained:2 any:11 contents:1 fabbrichesi:1 forced:1 studying:1 latter:7 internal:1 take:2 so:2 beirut:1 channel:3 altered:1 sm:9 avanzati:1 though:1 consistency:1 what:1 extending:1 propagate:4 significant:2 analytically:1 extremely:1 xµ:1 appelquist:1 subtracted:1 surprising:1 considered:1 request:2 typeset:1 takeuchi:1 graphs:1 chiral:8 principle:5 exp:1 velocity:2 constrain:1 justify:1 positivity:2 fact:4 applied:1 sector:3 hyper:1 super:3 show:2 supported:1 gauge:10 solutions:1 keywords:1 rough:1 d2:2 completion:1 eboli:2 causality:4 scuola:1 parameters:2 written:2 should:1 analytic:3 only:4 annals:1 constant:3 partially:1 importantly:1 do:4 insight:1 triangle:2 gev:1 notation:1 di:2 nicolis:1 custodial:1 lhc:1 pions:2 cannot:5 lighter:1 he:2 dp:1 processes:2 resolve:1 course:1 arxiv:10 tuned:1 twice:2 bad:1 analytical:12 valid:2 remains:1 exists:2 achieved:1 frame:1 notice:4 up:3 observed:2 see:3 result:6 close:1 analog:1 appear:2 interacting:1 pattern:2 review:1 complementary:1 definite:2 propagates:1 symmetric:3 state:3 future:1 between:2 invariant:1 approach:4 comparable:2 terms:3 extend:1 nature:4 importance:1 weak:4 however:1 vanishing:2 enters:1 hypothesis:2 come:1 improve:1 reaction:1 wanders:1 region:2 mrtn:1 wu:1 agree:1 chosen:1 context:5 cµ:3 zerwas:1 contribution:4 experimental:4 arbitrarily:2 detailed:1 relevant:3 cm:1 conclude:4 simple:2 seems:2 lagrangians:1 running:1 pole:3 cx:1 simply:1 belyaev:1 respect:2 cp:1 considering:1 complication:1 described:1 tuning:1 equations:2 due:2 been:4 much:2 interest:1 basic:1 expected:1 ph:10 define:1 field:2 direction:1 rather:2 corresponding:1 mizukoshi:2 sufficient:1 longitudinally:3 photon:2 precision:2 gap:1 arkani:1 determination:1 vµ:8 derivative:7 mandelstam:1 general:12 present:1 case:12 multi:1 reliable:2 vecchi:2 will:1 while:1 behavior:3 irrespective:1 property:1 guide:1 loop:4 coupled:1 them:4 macroscopic:1 clearly:1 vs:1 limit:3 different:3 italy:1 generic:1 acknowledgments:1 make:1 cross:1 same:1 poincar:1 complex:5 arguments:1 pauli:1 modification:1 electro:1 european:1 independent:1 zumino:1 used:5 infinity:1 imply:1 lie:1 boosted:1 effect:2 hand:3 parametrized:1 constraining:2 moment:1 v4:2 invariance:3 yuan:2 conveniently:1 normalization:1 relies:2 off:5 center:1 scenario:4 pµ:1 variety:1 well:6 roughly:1 analysis:5 pham:1 without:1 solve:1 comes:1 sets:1 model:2 left:1 stringent:4 less:3 being:1 when:2 accurate:1 paragraph:1 obtain:1 effects:1 underlying:2 transforms:1 multiplet:1 scattering:14 yet:1 previous:1 grinstein:1 4m2:6 cut:5 preprint:1 superluminal:1 conclusions:2 point:3 guaranteed:1 improvement:1 interested:1 lett:1 easy:1 theorem:3 iπ:1 violations:1 transformation:1 real:3 tests:1 around:2 read:1 evaluate:1 iε:7 possible:1 smallness:1 usual:1 background:4 vacuum:3 using:5 part:4 stable:1 vν:4 adams:1 necessary:1 like:7 particle:3 signal:1 admitted:1 manifest:1 separately:1 unstable:2 sezione:1 arbitrary:1 become:2 works:2 exceed:1 because:8 luminal:2 some:6 certain:1 strongest:1 evaluated:1 oscillations:3 neglecting:1 matching:1 provided:1 scale:10 axiomatic:1 lead:2 realistic:1 electromagnetic:1 avoid:1 conservative:1 everything:1 kilian:1 does:3 eliminate:1 assuming:2 prog:1 propagating:1 minimal:1 object:1 fermions:2 equivalent:1 martin:1 expansion:1 although:2 collider:2 imaginary:3 dictated:2 properties:2 proceed:1 kinematical:2 actual:1 would:4 most:2 anomalous:9 dependence:1 o:9 compatible:1 convenient:1 range:3 connected:1 introduced:1 cutoff:1 rev:11 presence:4 unbounded:1 into:3 bound:14 predictions:1 toublan:1 appropriate:2 references:1 wess:1 frames:1 proportional:1 conceptually:1 hep:10 log:6 elastic:4 assumed:2 strictly:3 there:5 approximate:2 noticed:2 dispersion:5 strict:1 quadratic:4 quanta:3 low:3 way:4 forward:4 translate:1 was:1 function:4 form:1 m2:5 but:4 idealized:1 magnitude:1 novaes:1 true:1 observation:1 infn:1 made:1 inside:1 uv:3 bounds:23 cim:1 tell:2 below:2 complications:1 sum:1 approaches:1 similar:1 called:1 expect:1 mechanics:1 taylor:1 associated:1 defined:6 coincides:1 abstract:1 contribute:2 denote:2 globally:1 single:2 approximated:1 physical:4 compared:3 analyticity:6 no:12 whereas:1 boos:1 generally:2 application:2 other:3 branch:1 massless:1 deviation:1 briefly:1 polynomials:1 important:2 included:1 structure:2 implies:2 coupling:2 pion:2 garcia:2 assume:4 requires:1 divergences:1 together:3 equivalently:1 implied:1 mass:9 time:1 far:3 starting:1 having:2 |
0704.1901.txt |@word code:2 illustrates:1 crucial:1 ppendix:1 truncated:2 results:1 leads:1 known:2 entropy:34 computation:1 edu:2 consists:2 follow:1 expressions:1 whose:2 cardinality:2 terms:1 hayden:1 tr:2 environment:2 finally:1 those:1 th:1 under:1 sent:1 conjecture:24 supported:1 performs:1 straightforward:1 conjectured:1 ρb:5 every:1 exact:2 condition:1 entire:2 transmission:1 trc:2 solution:1 noiseless:4 registers:2 indices:1 equation:1 upper:1 averaged:1 degrading:1 coefficient:2 past:1 priors:1 rate:9 further:1 blue:1 index:3 nel:1 ˆs:2 onclusion:1 sum:1 selected:1 expressed:1 uniform:1 access:7 ˆb:11 version:2 above:2 new:3 ˆj:3 cˆs:1 westmoreland:2 satisfy:1 led:1 evaluating:2 respectively:4 here:2 strong:8 equations:1 differential:1 obtained:4 sending:1 sender:1 institute:2 study:1 accomplished:1 resulting:1 poisson:1 schumacher:2 bob:17 proof:5 spatio:1 via:1 apr:1 yuen:3 convexity:2 addressed:1 aimed:1 achievable:8 viz:1 total:1 use:14 additive:4 would:2 prove:1 probabilities:1 positive:2 negative:1 live:1 therefore:1 λmk:3 theoretical:1 more:5 duality:4 operators:4 envelope:3 appendix:2 particular:1 hannel:2 hold:1 iii:2 negativity:1 must:4 ρa:3 ρc:2 valued:2 ma:2 devetak:1 setup:1 work:5 fock:2 values:2 budgets:1 following:1 trans:4 unconditional:1 deg:2 jindal:1 compare:2 theorems:1 figure:2 transmissivity:2 bennett:1 states:19 minimum:9 o:2 conversely:1 information:21 respective:2 advantage:1 provide:1 holds:1 regions:9 maps:1 pure:1 instead:5 goldsmith:1 map:3 product:2 giovannetti:4 may:1 after:1 derived:2 minimized:2 collection:1 diagram:1 povms:1 produce:1 minimizes:1 revealed:1 dα:3 third:1 joint:6 light:3 lines:1 summing:1 codebook:1 inform:4 annealing:1 green:1 ultimate:9 media:1 putting:1 first:1 bipartite:2 developed:1 over:12 thermal:3 paper:2 through:2 ntroduction:1 ieee:4 its:3 derive:1 monotonicity:1 thank:1 matrices:1 temporal:2 writing:1 better:2 complex:1 fig:8 ηn:1 maximal:1 non:4 than:1 splitter:5 propose:1 introduce:1 now:2 realize:1 maintaining:1 transmitter:6 finite:5 corners:1 university:2 sufficiently:1 inequality:3 transmitted:1 mode:10 truth:1 each:3 found:2 mean:6 en:1 inputs:5 ed:1 gaussian:18 measure:1 quantum:24 our:1 eq:3 es:1 out:4 large:1 shown:5 acknowledgment:1 space:5 uantum:1 holevo:10 research:6 modulation:3 investigation:1 rb:10 rc:9 electronics:2 suffices:1 correct:1 red:2 shows:2 theory:5 hull:1 diagonal:1 free:1 completely:1 jozsa:1 mimo:4 definition:1 pairs:1 yard:5 derivation:1 route:1 multiplicativity:1 messages:3 mac:6 wehrl:6 hence:3 interact:1 βk:3 initial:1 xn:2 probability:4 encoding:6 omitted:1 variables:1 coding:1 number:10 channels:14 done:2 message:5 size:1 given:4 similarly:1 πj:1 eqs:6 πn:2 their:3 rates:4 scheme:1 bits:2 store:1 gives:1 proving:2 broadcast:46 optical:2 authors:1 alphabets:2 guha:4 maximizing:3 wootters:1 sth:1 see:3 limiting:1 annihilation:2 future:1 bridge:1 modulating:1 argument:1 ρˆk:2 randomly:2 outperforms:1 say:1 need:3 seen:1 constrained:1 any:1 zero:3 min:1 weingarten:1 agency:1 maximum:1 note:1 ˆi:1 projects:1 mit:2 channel:74 heisenberg:1 multiple:12 trace:1 established:1 simulated:1 what:1 extending:1 eisert:1 drummond:1 successive:4 pair:3 class:1 considered:5 average:4 order:2 principle:1 exp:2 gain:2 spatiotemporal:1 show:7 random:1 converge:1 attempts:1 spaces:2 chuang:1 lloyd:4 substituting:1 degraded:14 decade:1 principal:1 yen:4 distributed:1 tracepreserving:1 completes:1 only:1 black:1 rich:1 factor:1 attained:1 employed:1 achieve:2 get:1 overall:1 beam:5 codeword:2 despite:1 dt:3 conjunction:1 lossless:2 closure:1 communicates:1 arxiv:1 rinton:1 allocations:1 fixed:2 shapiro:6 modulo:1 computed:3 exists:3 achieved:2 unpublished:1 bounds:2 detection:10 depends:1 defense:1 sec:3 result:6 discussions:1 recently:3 optimum:2 subject:4 satisfying:2 capacity:44 subsequent:1 review:1 nature:2 fano:2 state:38 heterodyne:4 between:4 caves:1 wc:13 wb:9 extend:1 receivers:4 eˆs:2 weak:1 iscussion:1 bose:1 shamai:1 σj:1 limits:1 many:1 region:27 equal:1 etc:1 receives:2 receiver:7 exceeds:1 jersey:1 purities:1 ci:1 cn:1 steinberg:1 asymptotically:1 cf:1 dimensional:4 maximize:1 lagrange:1 cs:3 proved:1 second:4 pp:1 pt:5 basis:1 equivalent:1 three:1 been:2 povm:3 describes:1 pj:11 ph:3 pi:9 systems:1 describe:2 corresponding:1 received:3 nrc:2 nrb:3 photon:7 gap:1 coherent:18 evidence:3 present:1 multi:3 unlike:1 solid:1 budget:1 will:5 while:1 suppose:2 reliably:1 maccone:4 von:16 thus:2 them:1 iv:2 ii:2 dual:1 technology:2 alphabet:5 began:1 lett:2 same:1 concavity:1 quant:3 split:1 schematic:1 evaluate:2 several:2 independent:4 jeffrey:1 used:2 imply:1 possible:3 uses:5 user:7 infinite:2 recent:3 lower:1 modes:7 scenario:1 nevertheless:1 charlie:16 starved:1 sets:3 model:1 nb:2 comprise:1 tamagawa:1 proposed:1 less:2 obtain:1 cˆ:3 bandwidth:1 lossy:3 ozawa:1 summed:1 λk:3 ng:15 previous:1 integer:1 density:4 photons:2 eferences:1 treatment:1 theorem:2 input:15 mod:1 identical:1 nielsen:1 rev:9 advances:2 capacities:4 term:2 spanned:2 homodyne:4 know:1 vacuum:5 press:2 using:11 moreover:1 advanced:1 helpful:1 ˆbs:2 necessary:1 photonnumber:1 sizes:2 envisioned:1 follows:5 collective:2 strictly:1 alice:11 communications:2 ai:2 either:1 evolutions:1 output:22 ˆbi:3 reduces:1 shor:1 circles:1 because:7 neumann:16 classical:25 sequence:2 sends:1 conditional:1 some:3 convey:1 convex:1 provided:1 per:3 does:1 connecting:1 assuming:2 minimal:1 noise:5 power:4 bc:7 bn:1 conventional:1 binomial:1 bs:2 hilbert:4 noisy:6 comparison:2 vishwanath:2 ρˆi:1 constraint:2 dˆ:1 tracing:2 codewords:1 ρˆa:3 ρˆb:17 ρˆc:11 practical:1 wolf:1 modal:3 mixed:1 cambridge:4 communication:9 into:2 within:1 bound:5 lies:1 ηs:6 einstein:1 operator:2 bosonic:39 statistics:1 log:3 her:1 assumed:1 support:3 there:6 long:1 decode:1 pa:5 inner:1 way:1 resulted:1 was:6 opposed:1 function:1 decoded:1 complete:1 form:2 converse:2 encodes:2 encoder:1 pwb:9 pwc:18 transmitters:2 serafini:1 line:5 true:5 considerable:1 coupling:2 made:1 applying:1 up:1 us:2 achieving:1 below:1 limit:4 dirty:1 distribution:4 similar:1 entropies:1 associated:1 defined:1 abstract:1 specified:1 chan:1 proven:1 general:2 dashed:1 single:12 exist:1 laboratory:2 distributions:2 physical:1 mutual:2 codes:1 na:15 whereas:1 when:18 vanishes:1 multipliers:1 nas:2 other:2 shannon:2 spatial:1 nkj:2 enyi:2 denote:2 users:1 symbol:2 uniformly:1 generated:1 important:2 bounded:1 massachusetts:2 prepares:2 implies:1 auxiliary:1 assume:1 starting:1 carrying:1 mass:1 reception:2 hirota:1 requires:1 |
0704.1902.txt |@word limited:1 remarkable:1 rev:25 magnetic:1 excellent:1 dynamic:2 fabricated:1 ginzburg:3 lll:6 intricate:1 remarkably:1 gl:5 gi:14 layers:1 whose:3 inverse:3 depend:1 description:1 misses:2 presents:1 quasi:1 critical:2 those:1 th:2 under:2 tg:4 td:8 tc:9 supported:1 g0:2 very:2 continues:1 amorphous:2 focus:1 novel:1 matsuda:1 randomness:1 100t:1 conjugating:1 quartic:2 level:1 sensor:1 anisotropy:20 t2:1 solution:1 excellence:1 small:1 stiffer:1 der:1 locus:1 zn:1 glassy:3 thin:3 renormalized:1 consistent:1 blatter:1 approximation:2 hirata:1 second:2 further:2 theory:5 even:2 colorbar:1 axes:1 agrees:1 access:1 experiment:2 above:5 renders:1 increasing:1 method:1 3d:3 coefficient:2 quenched:2 condensed:1 full:1 simultaneously:1 degree:2 respectively:4 khaykovich:2 understanding:1 reported:1 china:3 pancake:4 address:1 along:2 appears:1 superconductor:1 ref:2 dividing:1 institute:1 involved:1 study:2 studied:1 contradiction:1 pinning:2 suggests:2 simultaneous:1 resulting:3 stiffness:1 nelson:1 usually:1 bod:4 plotted:1 ceram:1 although:2 scales:3 apr:1 concurrently:1 marked:1 highly:1 decrease:5 tamegai:1 brg:3 estimate:1 readily:1 gaas:1 improves:1 remains:1 positive:1 continuous:1 weizmann:2 giamarchi:1 sports:1 few:1 monotonically:1 ψn:1 therefore:4 ψb:1 ψa:1 theoretical:2 more:1 flat:1 israel:3 relax:1 rehovot:1 becomes:5 naive:1 apparent:1 ooi:2 validity:1 glass:8 reversible:2 normalized:1 separates:3 hole:2 mounted:1 high:9 mg:1 mc:1 tokyo:2 science:5 originally:1 averaged:1 mi:1 sweeps:1 values:6 temperatures:8 believed:2 strategies:2 stimulating:1 beijing:1 figure:3 calculation:3 thermally:4 neglected:1 sample:3 effectively:1 numbers:1 unveiled:1 rescaling:3 weaken:1 hod:7 lacks:1 breaking:3 varies:1 atu:1 contrasts:1 ryu:1 parameter:2 dominance:6 simplicity:1 mat:1 singular:1 may:4 overall:1 earlier:2 diagram:7 plane:4 konczykowski:1 mag:1 fits:3 data:2 fo:39 liquid:2 onto:1 lines:38 departure:1 parameterized:1 bunkyo:1 cannot:1 so:27 enter:1 subsequently:1 acknowledges:1 order:6 typical:1 ith:1 produces:1 indeed:3 over:10 mainly:1 hanaguri:1 symbols:3 thermal:17 tth:11 japan:2 still:7 its:10 thank:1 fit:8 energies:3 succeeds:1 decreases:3 li:4 resort:1 teitel:1 fig:18 hidden:1 defining:1 non:1 good:1 affected:2 material:1 landau:1 scaling:11 lesser:1 penetration:1 subtraction:1 they:1 sweeping:1 now:1 hall:1 february:1 oxygen:3 fully:1 university:3 traced:1 2d:7 peking:1 magnitude:1 each:1 varlamov:1 found:4 shaking:5 homogeneous:1 rodriguez:1 england:1 ed:1 energy:7 gaussian:2 related:1 balanced:1 interplay:1 measurement:1 separating:1 our:1 transitions:2 nonmonotonic:1 shown:2 space:1 electronic:2 crucial:1 research:1 bragg:1 flattening:2 dominated:1 conjectured:1 induced:2 induction:6 shows:7 foundation:4 linear:3 free:4 completely:1 proportionality:1 detecting:1 hc2:1 incorporates:1 derivation:1 ministry:1 recast:1 transition:17 length:1 mab:1 isotropic:3 chiao:1 hence:1 βh:3 first:3 symmetry:5 enhances:1 number:1 utilized:1 defects:1 directly:1 thick:4 precisely:1 open:2 equating:1 given:1 temperature:19 indicate:1 leading:1 system:1 1a:1 their:3 1c:1 too:1 ordered:1 perfectly:1 gives:1 collapse:3 enhancing:1 klemm:1 dasheddotted:1 albert:1 rsb:2 depinned:3 part:2 than:2 coefficients:2 effective:6 fuchs:1 zero:2 matter:2 states:1 mochiku:1 amplitude:5 were:3 outcome:2 treated:1 behaviors:1 function:2 jpn:1 geshkenbein:1 unchanged:1 defect:1 crossover:1 ertas:1 replicated:1 close:1 concentration:2 unaffected:1 apparently:1 clearly:2 complete:2 koshelev:1 latter:2 mechanism:3 instance:1 fitting:5 potential:2 bisection:5 online:4 negligible:2 hightemperature:2 towards:7 signifying:1 arguing:1 decreasing:1 fails:1 insets:2 most:1 optimized:1 letter:1 phase:9 bsf:1 measured:5 model:11 manifested:2 probes:1 subtracted:1 calculated:3 partition:1 stronger:2 physica:8 artificially:1 ku:1 physics:5 naively:1 lying:1 slope:3 larkin:2 zeldov:3 show:3 german:1 doped:6 evaporation:1 purely:1 relation:1 threshold:1 d2:1 find:1 portier:1 ratio:1 parameters:5 explain:1 avraham:1 should:1 only:2 yeshurun:1 factor:1 local:4 equilibrium:4 dominant:3 gains:5 dh:1 get:2 dependent:2 db:4 account:1 yielded:2 simplistic:1 ones:4 closely:1 competing:1 dw:1 dt:5 stability:1 qt:1 israeli:1 bisect:1 fields:3 arxiv:1 yield:1 summary:1 optimally:1 europhys:1 predicted:1 though:2 mapped:1 fixed:2 reveals:1 set:3 ratios:1 national:2 relative:6 culture:1 bare:1 result:2 enhanced:1 clem:1 discussions:1 terms:1 alternative:1 clarifies:1 closer:1 phases:5 yamaguchi:1 tensor:1 tend:1 symmetric:1 state:1 various:2 between:3 αh:4 ends:1 recently:1 nature:4 however:2 bscco:5 configuration:1 both:3 last:1 resides:1 solely:1 region:3 layered:1 dated:1 context:1 cacu2:3 whole:1 con:1 reside:1 relevant:2 separation:1 point:1 color:7 sweep:2 polynomial:1 moreover:1 throughout:1 olsson:1 geometries:1 addition:1 three:2 kierfeld:1 glazman:1 pf:1 interpret:1 disordering:2 direction:1 corresponding:2 deeper:1 coherence:1 gas:1 c2:5 irrelevant:1 present:3 applied:1 bisecting:1 pacs:1 solid:7 chap:1 will:1 while:1 behavior:8 aid:1 balance:1 taking:1 procedure:1 weakens:2 program:1 layer:3 minerva:1 characteristics:1 thus:2 shibauchi:1 discrepancy:1 cond:1 il:1 motivated:1 technology:1 different:3 education:1 grant:1 parisi:1 suggest:1 lett:13 same:2 shifts:7 parts:2 finite:1 higher:7 independent:6 used:1 dewhurst:1 effect:1 counterparts:1 levels:1 kim:1 heterostructure:1 tung:1 recent:1 break:2 center:2 nevertheless:1 mikitik:2 modeled:1 well:2 analysis:2 approached:1 sets:2 quantitative:3 rosenstein:3 stating:1 maxima:1 magnetization:4 rescales:1 just:1 increasingly:1 captures:1 superconductors:2 effects:1 vanishes:1 oxford:1 disperse:1 hongo:1 taiwan:1 bi2:3 yet:4 captured:1 discontinuous:2 extends:1 location:1 samples:7 republic:1 transformation:3 scientific:1 take:1 resolved:1 rescaled:2 increased:2 secondorder:1 breaks:3 sugano:1 results:2 term:3 opd:10 increases:2 doyle:1 background:1 using:1 doniach:1 moe:1 melting:17 sizes:1 interestingly:1 identifying:1 specific:1 vortex:6 steps:2 either:1 inter:3 disorder:30 essential:1 accessible:1 functional:2 vortices:3 some:2 somehow:1 competition:1 haim:1 deduce:1 flatten:2 doping:25 nonzero:1 scale:1 describing:1 µm3:1 µm2:1 affects:1 measurements:3 integration:1 overlap:1 sr2:3 does:1 provides:1 o8:3 yields:1 demonstrated:1 manifesting:1 inaccurate:1 power:1 dictates:1 agreement:1 expansion:1 binational:1 step:2 depinning:2 br:2 tokunaga:1 constrains:1 asserting:1 freedom:2 oe:3 od:1 dependence:9 o:2 reduced:2 range:1 concentrations:2 insufficient:1 slightly:2 soc:1 sod:8 lowtemperature:2 presence:1 noting:1 into:1 obtaining:1 elasticity:5 due:4 down:3 rendering:1 rising:1 einstein:1 crystalline:1 reducing:1 kapitulnik:1 vinokur:4 elastic:1 definiteness:1 extremely:1 support:1 sequence:1 limit:1 long:1 overestimate:1 accordingly:1 quadratic:2 low:9 brandt:1 was:5 hz:2 irreversibility:1 form:1 hs:1 collapsed:5 but:3 hu:1 gain:1 line:32 true:1 collapses:3 faster:1 made:1 arrays:1 characteristic:2 supr:1 maximum:8 us:1 work:1 crystal:1 below:11 hsinchu:1 shtrikman:1 fluctuations:12 similar:2 supercond:1 detailed:2 ac:2 constant:4 int:1 certain:2 ez:1 influence:1 intimately:1 single:1 replica:4 crystals:1 ing:1 physical:1 again:1 beyond:1 analyticity:1 faithful:1 dotted:5 no:1 dashed:9 generally:1 depth:1 field:7 other:1 role:2 department:4 out:2 conclusion:1 exp:1 accidental:1 models:2 cubitt:1 a2:1 flattened:2 accounts:1 structure:1 upwards:1 algaas:1 implies:1 coupling:2 perturbatively:1 inset:5 mass:2 fitted:2 resembles:1 4a:1 4b:1 stacks:2 once:1 |
0704.1904.txt |@word gs:1 consider:5 maximum:2 rev:5 results:5 scalar:6 const:5 calculate:2 hump:4 similarity:1 nonlocal:36 compensate:3 kη:5 those:1 stable:4 applied:2 proved:1 downstream:2 far:1 icar:1 choice:2 figs:5 bottleneck:7 condition:1 entire:1 steeper:1 ref:2 solution:11 large:18 math:1 small:25 inertial:3 upper:3 compensated:1 direct:1 approximation:7 rate:2 even:2 nonlinear:1 plays:3 giving:1 axes:1 tripiccione:1 while:2 above:3 basset:1 obvious:1 acknowledgments:1 3e:1 exchange:3 respectively:2 equals:2 here:1 reported:3 possibility:1 separation:3 excess:1 represented:1 strong:3 equations:7 logarithmic:2 box:1 increments:1 succi:2 rigorously:1 involved:1 study:1 studied:1 allows:2 schumacher:1 usually:1 triad:1 fourier:1 makes:1 involves:1 via:1 stabilization:1 scales:25 problematic:1 substitution:1 plenum:1 private:1 visible:1 obukhov:1 readily:2 use:2 takes:3 would:1 physics:1 comparing:1 therefore:6 dns:6 reconnection:1 type:3 more:2 israel:1 sharing:1 formally:1 stokes:1 becomes:1 corrected:1 normalized:2 known:4 cases:2 iv:1 iii:1 must:1 reλ:1 account:3 groeling:1 tunnel:1 recall:1 equation:10 rλ:22 values:4 ishihara:1 following:3 nlin:2 numbers:19 figure:16 process:1 reynold:1 neglected:1 high:2 indicates:2 performed:4 r29:1 reynolds:19 provide:3 regions:1 very:1 pure:1 instead:1 preferable:1 woodward:1 may:1 after:1 fluid:5 corrections:4 wave:3 data:15 constants:4 short:1 dynamical:3 effective:4 spectra:11 correspond:2 rather:1 cannot:3 negligible:1 order:4 wind:1 prefactor:6 s3:1 closely:1 itakura:1 developed:2 mainly:1 stability:3 course:1 experiments:3 london:1 statistical:2 japan:1 still:1 its:3 tendency:1 before:1 asymptotes:1 thank:2 fit:6 located:1 ln:8 interesting:1 vicinity:3 actually:1 fig:9 decreased:1 schmidt:2 shear:2 versus:2 non:26 universality:2 scaling:26 effects:3 now:2 term:2 indeed:2 parameter:6 arrows:2 sufficiently:1 mode:1 instabilities:3 found:4 mean:1 homogeneous:2 directly:1 series:1 energy:21 idea:1 related:4 investigated:1 separating:1 laboratory:1 beyond:2 eq:14 shown:13 jerusalem:1 jackson:1 watanabe:1 space:4 dnss:1 since:2 crucial:1 denotes:1 europhys:1 rc:7 supports:2 independence:1 shows:5 asymptote:11 linear:2 interactions:31 given:1 governing:1 amati:1 york:2 intermediate:2 estimate:2 muller:1 interaction:3 determining:1 could:4 gotoh:4 noted:3 place:1 isotropic:10 navier:1 hence:1 comte:1 first:7 variables:2 number:9 clear:2 dominating:6 another:1 precisely:1 sheer:1 perturbation:8 checked:1 rewritten:1 their:2 introduction:1 eqs:2 anderson:1 construct:1 indicate:3 perturbations:1 calculations:1 realization:1 structures:1 speaking:1 gives:3 relationship:9 dubrulle:2 zeroth:2 newell:2 part:3 than:2 wide:1 determines:1 showed:1 kaneda:1 kink:3 nakano:2 determined:7 were:1 providing:2 comput:1 dynamically:1 argument:2 curves:8 crossover:1 substantial:1 seem:1 sirovich:1 orders:2 relatively:1 cascade:3 self:1 graner:1 mechanism:3 instance:7 intends:1 k5:1 online:1 so:4 mit:1 circles:3 viscosity:8 overlapping:2 significant:6 position:2 measured:2 kc:7 cause:1 kd:25 considered:2 average:2 steady:1 physica:2 ks:8 principle:1 exp:1 velocity:2 tubes:1 wavenumber:4 slope:2 drastically:1 phenomenon:2 show:6 supported:1 relation:1 solutions:2 substituting:3 fine:1 find:1 inspiring:1 based:1 foias:1 e11:2 situations:2 should:14 analytic:6 only:3 factor:1 adequate:2 local:36 continuity:1 dominant:1 dk:3 means:2 df:1 de:1 nonconservation:2 ones:3 nearly:2 dx:1 invariant:1 steepness:1 processes:1 kadomtsev:2 arxiv:2 paper:5 hydrodynamic:3 fixed:2 ignored:1 art:1 exists:1 kolmogorov:15 clebsch:2 observed:3 see:18 actively:1 result:1 discussions:1 close:1 nonlocality:1 best:6 capacity:1 exponent:1 ways:1 consequence:1 enough:1 identification:1 cooperation:1 between:8 drawn:2 approach:11 law:4 αn:2 available:1 ends:1 terms:1 statistically:2 nature:2 she:1 however:6 efficiency:1 hypothesis:1 suppressed:1 suggested:2 both:4 toward:2 last:1 many:1 taking:3 falkovich:1 according:3 against:1 variance:1 contribution:1 experimental:1 uno:1 ck:2 among:1 presumably:3 relevant:3 point:1 character:1 asymptotically:1 corresponds:3 cd:2 dimensional:13 applicability:2 moreover:2 described:1 second:1 addition:1 three:5 been:5 asymptotics:1 expected:1 correction:2 obtained:3 corresponding:9 yaglom:1 covariance:7 new:4 spectrum:12 understand:1 present:1 case:2 pacs:1 solid:8 straight:2 yakhot:3 value:6 will:4 near:3 replaced:1 behavior:2 situation:4 balance:2 correspondence:2 vol:1 formulation:1 equal:1 ii:2 strain:6 edgar:1 different:3 develop:1 same:11 unity:2 ciliberto:1 dimensionless:6 physical:2 νs2:1 higher:1 independent:2 used:3 numerical:7 effect:8 flows:1 hand:1 hydrodynamics:1 normalization:1 recent:2 lower:1 mech:4 modes:1 scenario:2 well:4 roughly:1 academic:1 edge:1 quantitative:2 dimension:1 bellot:1 benzi:2 just:5 less:1 when:4 obtain:4 formulated:1 turbulence:16 adv:1 hint:1 zakharov:2 seems:1 passive:5 add:1 valid:1 transformed:1 lett:4 versa:1 compares:1 plasma:1 real:1 analogy:2 baudet:1 breaks:1 possible:2 cf:6 grid:2 know:1 press:3 using:9 like:1 corrsin:2 alternatively:2 specific:1 flux:4 vortex:3 triadic:2 unstable:4 follows:3 become:1 therein:1 sketch:2 right:1 flatter:1 phenomena:2 stat:1 calculated:2 provided:1 scale:17 ess:1 fluids:7 overlap:1 does:1 provides:2 moderate:7 porter:1 power:6 journal:1 2c:1 agreement:5 expansion:3 references:1 instability:3 filaments:2 properties:1 comparison:4 pλ:4 discussed:1 dependence:2 o:2 simulation:1 range:6 introduced:1 considerations:3 soc:1 cambridge:1 communication:1 into:8 integral:3 sreenivasan:5 due:1 dissipation:8 ηs:18 determine:1 laval:3 reducing:1 additional:1 there:8 approximate:1 long:1 accordingly:1 conservation:1 low:2 way:1 lohse:1 viscous:6 was:4 naturally:1 function:6 complete:1 form:3 but:4 toschi:1 doi:1 line:2 removed:1 dissipative:1 characteristic:3 verma:1 up:2 us:10 below:4 problem:1 called:4 regimes:7 mechanics:1 constant:5 eclet:2 classic:1 certain:2 universal:2 denote:1 manley:1 exist:1 simulations:7 controlled:1 regime:19 compared:1 no:5 eα1:1 nazarenko:4 whereas:1 generally:2 field:1 other:1 role:5 briefly:1 intend:1 variable:1 vice:1 resolution:2 monin:1 interval:1 together:2 time:1 appl:1 starting:1 eθ:1 |
0704.1905.txt |@word limited:1 partial:1 consider:12 crucial:1 magnetic:2 desirable:1 results:11 four:1 roy:1 scalar:57 generalize:3 hyperboloid:3 follow:1 expressions:4 iosif:1 contributions:27 reasoning:1 ζa:2 whose:1 depend:4 calculate:10 cobe:1 irrelevant:1 tr:2 corrections:46 trivial:1 finally:4 present:7 th:6 x02:1 td:1 include:1 equalities:1 γe:4 divergent:2 applied:1 conjecture:2 probe:1 provides:1 straightforward:3 alambertian:1 very:3 2γe:1 mpl:10 conditions:3 induce:3 wave:5 kirsten:1 hdt:1 ultraviolet:2 traced:1 nonminimal:7 difference:2 condition:8 leads:1 mild:1 basics:1 solves:2 level:12 ds25:1 anisotropy:1 nucl:2 applicable:2 large:7 solved:2 qpr:4 progress:1 tagirov:4 small:11 enhance:1 refer:4 fakir:1 proof:2 jhep:1 abbreviated:1 approximately:2 compensated:1 coordinate:3 methodical:1 renormalized:7 consistent:2 sin2:1 cosh:1 approximation:7 dϕ0:1 second:4 enhancement:6 equal:2 further:1 dynamics:2 theories:3 12z:1 splitting:1 canonical:2 spectral:22 index:16 what:1 plays:1 appear:1 diag:2 section:9 3w:1 near:3 expressed:1 current:1 version:1 poles:4 above:9 8πgn:2 new:3 contributes:1 method:6 contrast:1 futamase:1 ibid:1 respectively:3 modify:1 here:7 ranges:1 sinh:1 represented:1 ratio:8 quite:3 equations:6 appears:1 logarithmic:6 obtained:4 remark:1 dividing:1 suitably:1 institute:2 spontaneous:1 study:4 studied:1 reason:1 leaving:1 resulting:3 procedure:1 stressed:1 action:11 suitable:1 spacetime:1 drg:1 uniquely:1 particle:1 useful:2 accumulate:1 figure:4 4mpl:1 m2ϕ:14 spinoza:1 ǫq:5 anomalies:1 gumjudpai:1 apply:1 total:1 establish:1 propagators:1 linearly:2 d72:1 plot:1 use:26 x42:2 working:2 distinct:1 super:2 resolves:1 contains:1 3mpl:1 quasi:3 next:7 scenarios:1 comparing:2 live:1 sitter:38 renormalisation:3 relativistic:1 means:3 type:1 theoretical:1 htm:1 more:9 flat:4 tsujikawa:1 formally:2 furthermore:1 becomes:3 problem:2 curvature:21 appendix:2 observing:1 observations:3 particular:6 known:3 candelas:1 hold:1 fermionic:1 account:5 works:1 defines:2 evolution:1 quartic:4 mb:1 recall:2 equation:23 work:11 det:2 modified:1 unimproved:2 reproduce:1 infinitesimal:1 values:6 era:1 following:13 making:9 arrive:6 root:1 example:3 history:2 f1:1 sub:1 renormalization:20 cosmological:9 chosen:1 calculation:6 expanding:3 organized:1 chung:2 sphere:1 lϕ:12 numbers:1 arise:2 ǫc:5 tions:1 νn:2 breaking:1 e2t:1 regularization:3 rescaling:1 end:4 dww:3 rather:1 discussion:3 get:2 xˆ:2 write:5 how:3 pure:1 coleman:4 constraints:3 parameter:15 dd:3 simplicity:3 ζb:2 d74:1 chernikov:3 cosmic:2 algebra:2 inflationary:32 illustrate:1 after:11 needs:1 straightforwardly:1 diagram:1 hence:6 4th:1 deviates:1 pg:4 cambridge:1 summarize:2 choice:5 data:5 gradshteyn:1 constants:5 stress:6 physical:2 dynamical:3 effective:38 whenever:1 light:4 spectra:3 summing:1 cosmology:2 sj:1 gravitons:2 allow:1 reduced:2 representation:1 subsequently:1 order:21 gµν:9 prefactor:2 baryogenesis:1 produces:1 indeed:7 over:1 eqs:9 constrained:1 satisfied:2 equality:2 course:1 paper:3 including:1 resummed:1 dw:5 differs:1 dilemma:1 satisfies:1 still:8 its:5 itp:2 before:2 exhibits:1 derive:2 group:15 render:1 singular:1 located:2 ln:39 solving:1 vicinity:1 coordinates:4 writing:4 late:1 production:3 degrees:2 fig:2 disagrees:1 main:3 fin:1 h0:1 good:1 affected:1 was:2 solve:2 peculiar:1 cover:1 sϕ:3 geodesic:2 break:1 framework:13 effects:10 they:5 identically:1 front:1 now:19 discuss:1 easily:2 term:9 netherlands:2 dirac:1 exits:1 odintsov:4 fully:1 university:1 drop:2 annals:4 by3:1 2z:1 infer:1 rh:1 kruislaan:1 magnitude:2 mode:7 radial:1 simplified:1 x12:2 2h:11 side:3 characterized:1 nonperturbative:1 differential:5 significantly:1 superhorizon:2 counterterms:5 generation:4 series:3 energy:5 reduce:1 24h:5 related:4 cmb:2 νd:9 dx12:1 used:3 obtains:2 proportional:4 quantum:89 our:39 eq:30 out:1 shown:2 precisely:1 rq:2 space:34 symanzik:4 since:9 squared:3 denotes:6 rd:7 may:3 rg:5 ren:2 hwang:1 rc:4 scaling:1 intimately:1 postpone:1 induced:3 ref:5 integrated:1 shows:1 exactly:1 provide:3 8n:11 theory:26 normalized:1 interactions:1 wilkinson:1 contain:1 possibility:1 standard:12 mϕ:3 indices:7 completely:3 york:1 intermediate:1 iop:1 finite:3 log:1 hc2:1 definition:6 hubble:11 interaction:2 magnetogenesis:1 derivation:3 r2:1 r3:1 recast:1 determining:1 could:3 conformally:1 ds2:1 times:2 motion:3 turn:1 conducted:1 massive:3 consequence:3 neglected:3 view:1 neglect:1 first:8 origin:4 sanchez:3 already:1 symmetry:4 shapiro:1 xb:10 xa:8 number:12 lond:1 contour:1 improving:1 ηq:5 smaller:1 done:2 relations:4 mixing:1 clarity:1 several:2 occurrence:1 given:15 perturbation:13 table:1 similarly:2 introduction:1 leading:12 condensate:3 construct:1 unruh:1 their:3 perturbations:3 master:1 fermions:8 statement:2 dt2:1 ordered:1 veff:3 final:3 speaking:1 too:2 back:2 form4:1 shell:1 calculations:1 ryzhik:1 duration:1 acquire:1 assumption:1 part:3 univ:1 differentiate:1 somewhat:1 authors:4 x2:2 natural:2 x0:3 than:2 x4:1 modes:1 contribu:1 distance:5 δw:12 last:4 edition:1 bubble:1 require:1 tree:6 imply:3 correlators:2 nakano:1 matter:6 future:2 amplitude:1 linear:2 bare:2 gives:3 solely:1 minus:1 decompose:1 w2:2 exhibit:1 buchbinder:1 electrodynamics:1 correction:5 correlator:1 mind:1 spectrum:18 generalization:1 latter:1 manner:3 close:1 need:4 curved:5 element:1 any:5 viewed:1 minimally:5 zero:1 academic:1 convenient:4 self:6 able:1 davies:1 converges:1 note:5 potential:18 square:1 generalized:3 reparametrization:1 gets:1 xi:4 so:1 acquires:1 even:5 begin:2 keldysh:1 trace:1 established:3 ıve:2 enter:1 falls:1 z2:1 most:2 importantly:1 ht:3 significant:2 definitions:6 why:1 divergences:1 deviations:2 observation:1 surprising:1 year:3 calculated:6 later:2 implications:2 zξ:2 necessary:1 feynman:2 reaction:1 principle:2 puchwein:2 analogy:1 quadratic:1 constrain:2 usual:2 physics:3 fact:7 quantity:3 sector:1 incorporate:2 euler:2 show:2 12h:4 futhermore:1 infrared:13 soluble:1 spaces:4 relation:7 solutions:2 hc:1 d4:1 d2:1 find:2 impact:2 slow:41 based:5 proposed:1 parameters:31 much:2 observe:1 negligible:1 should:3 only:12 3h:7 coefficients:1 factor:2 circle:1 do:2 insight:1 dominant:4 dh:10 di:2 dependent:1 secular:1 de:42 db:1 expectation:3 da:1 dz:6 nearly:1 dx:5 µd:2 during:19 dt:9 selfinteracting:1 differentiating:1 miao:3 extract:1 resolve:1 evident:1 fields:5 arxiv:28 yield:1 summary:1 qc:7 experiments:1 she:3 though:1 characteristic:1 through:2 fixed:2 remains:4 enhances:1 wmap:3 set:1 thesis:2 ricci:5 violated:1 correlations:2 hη:3 elizalde:3 opposite:1 namely:2 radius:1 result:17 enhanced:9 terms:11 maekawa:1 theoretic:2 kinetic:1 best:1 techniques:3 tensor:19 consistency:2 purpose:1 hybrid:1 garbrecht:1 justifies:1 tend:1 written:2 determined:4 various:2 teaching:1 between:3 invariant:11 boundary:1 bunch:1 approach:3 x22:2 observational:2 notice:2 recently:1 vertical:1 wn:2 focus:1 however:10 abbreviating:1 reproduces:1 vrg:3 spergel:1 rapidly:1 suppressed:8 holds:2 originates:1 observable:3 improved:15 2n:11 always:1 powers:4 taking:4 decay:2 nikhef:3 quantization:2 fulfilled:2 etc:1 komatsu:1 embedding:2 contribution:20 perturbative:1 whole:2 experimental:2 detailed:2 inflaton:13 cn:4 point:5 simple:2 corresponds:6 coincidence:1 dimensional:10 foldings:13 regulated:1 renormalize:2 consideration:1 ante:1 respect:3 cq:1 indefinite:1 presented:1 considering:1 forms:1 strong:1 lyth:1 dx22:1 locally:1 radiative:17 due:4 been:2 annales:1 primordial:2 change:7 interest:2 basic:1 mean:2 ph:15 improve:1 unchanged:1 choose:3 graphical:1 arises:4 corresponding:4 tµν:3 both:9 6h:2 quantities:1 subscripts:1 photon:5 precision:1 noh:1 ordering:1 dramatic:1 deeper:1 receive:1 prescription:2 c1:1 denote:1 spin:1 former:1 those:2 case:13 novel:1 pacs:1 resummation:5 value:7 will:5 euclidean:1 while:6 momentum:1 evaluating:1 poincare:1 conformal:9 couplings:2 loop:17 lently:1 vb:2 larger:4 equiva:1 coupled:12 chaotic:3 characteristics:1 refs:7 thus:6 surprisingly:1 according:2 ii:2 disfavored:2 reads:2 cone:1 seen:1 claimed:2 aspects:1 rid:1 vanish:1 fermion:2 ig:5 different:5 recover:1 develop:2 fraction:1 perhaps:1 make:2 cumulative:4 2νn:1 same:3 orders:1 amplified:1 epoch:1 parts:5 emphasize:1 big:1 products:1 nonminimally:5 solution:4 grows:1 higher:2 breakdown:1 independent:1 weinberg:7 http:1 bristol:1 see:6 trivially:1 iε:2 upon:3 unobservably:2 hand:8 running:4 priory:1 introduce:3 infinite:1 completeness:1 invariance:4 expand:2 keep:1 adη:1 subleading:1 suffices:1 off:1 proceed:2 scenario:1 smallness:1 nevertheless:1 expression:19 well:5 roughly:1 analysis:9 concrete:1 without:2 utrecht:2 machinery:1 studying:1 firstly:1 position:2 model:25 arising:1 possesses:1 comprise:1 left:1 lagrangian:2 manifold:1 just:2 sloth:2 generally:1 rµν:1 obtain:10 gravity:1 λb:31 relevant:4 actually:2 immediately:2 alternative:1 schwinger:1 λn:5 down:1 previous:1 jcap:1 polarization:3 enters:1 density:1 hℓ:1 photons:2 scales:1 had:1 prokopec:12 improvement:5 add:1 valid:8 lett:3 eigenstate:1 match:1 take:2 real:1 yukawa:3 around:2 represents:1 read:1 evaluate:2 couple:1 advocate:1 disagreement:1 iδ:2 cf:1 early:1 possibly:1 inflation:37 five:1 bando:1 background:17 vacuum:10 press:1 using:1 unique:3 gr:7 like:1 counterterm:2 massless:4 appearing:1 replacing:1 precise:1 follows:12 qualitative:1 performing:1 ηab:2 manifest:1 specific:1 yields:6 raine:1 λfp:1 arbitrary:6 become:3 callan:4 reduces:5 towards:1 sketch:1 because:8 classical:30 whe:1 some:6 classically:1 choosing:2 leuvenlaan:1 ah:3 cs:4 growth:1 evaluated:1 b2:1 specified:1 proper:1 curious:1 kugo:1 anisotropies:1 scale:15 dimensions:2 sufficiently:1 stronger:1 broad:1 shall:7 integration:1 microwave:4 contributing:1 models:17 does:8 exit:2 unit:1 expressing:1 assuming:1 prog:1 steps:1 three:3 proc:1 minimal:1 2a:1 inserting:2 pr:15 radiometer:1 denominator:2 integrals:1 power:1 performed:1 bn:4 each:2 expansion:2 lasts:1 although:2 found:5 hadamard:1 refers:1 notation:2 hilbert:1 asymptotic:2 x32:2 ξh:1 about:1 postbus:1 would:1 constraint:5 freedom:2 discussed:1 dependence:2 o:18 must:3 nonvanishing:1 sake:1 range:6 a2:2 horizon:3 introduced:6 gamma:2 allowing:1 soc:1 rev:18 ηc:3 presence:2 h2:8 into:16 within:15 integral:5 h4:3 negative:1 lagrangean:9 rendering:2 appropriate:1 right:2 16πgn:1 determine:4 einstein:3 operator:1 amsterdam:1 eht:3 hep:7 additional:1 few:1 strictly:2 there:3 approximate:2 specifically:2 pages:2 again:2 detectable:1 bosons:1 way:3 xµ:1 sections:1 propagator:15 cancel:1 combined:1 function:3 runs:1 complete:2 form:10 enough:1 but:8 idea:1 astro:14 properly:1 insertions:4 line:4 ha:1 extend:1 absent:2 made:4 applying:2 consequences:1 embedded:2 uu:4 minkowski:3 gravitational:6 uv:2 interacting:2 up:1 us:3 until:1 insert:2 below:2 limit:17 uk:2 organize:1 fluctuations:8 distribution:1 define:1 clear:1 expect:1 aa:1 changes:1 constant:7 ad:1 classic:1 defined:13 certain:1 pole:1 contribute:2 am:1 liddle:1 general:5 dξ:1 separating:2 single:1 tsamis:1 dλ:1 woodard:9 formalism:2 metric:4 constructed:1 friedmann:7 functions:10 compared:8 nl:4 no:2 na:2 erratum:1 when:25 vanishes:1 ng:9 field:29 grd:1 other:13 role:2 spatial:1 ns:26 roll:41 weak:1 conclusion:2 deviation:1 ξz:1 calculating:2 separate:1 students:1 vega:4 uniformly:1 includes:2 deriving:3 a0:1 generated:7 important:9 validity:1 ξn:2 characterising:1 boyanovsky:4 ξb:35 needed:1 structure:4 turns:1 dϕ:22 implies:7 coupling:30 assume:1 typically:2 required:2 theor:2 together:3 implied:1 mass:15 time:17 far:1 observables:4 once:1 requires:1 having:2 basically:1 |
0704.1906.txt |@word neighbors:12 represent:1 sci:2 gr:3 directions:1 magnetic:1 scf:5 results:18 projected:5 four:12 commute:1 mp2:2 higher:1 consists:3 follow:1 mccarthy:1 contributions:5 reasoning:1 localized:8 consider:2 compact:1 whose:1 inverse:1 const:1 calculate:1 zone:2 albrecht:4 effort:1 segments:1 technique:1 orthonormalized:2 interactions:2 removal:1 environment:4 charge:5 program:4 those:5 under:2 include:3 norm:1 ta:1 applied:6 pulay:3 o9:1 orthogonal:5 very:4 could:1 percent:1 3s1:3 account:5 induce:2 wave:2 oxides:3 ble:1 electron:34 putting:1 figs:2 prof:1 mixing:1 affect:1 1s:3 matrices:1 illustrated:2 ro:4 regarding:1 hamiltonian:11 ref:3 bonds:1 having:1 presently:1 o2:1 large:9 solved:1 vector:1 small:13 configurations:5 strongly:1 smaller:5 compensated:1 infancy:1 consistent:2 φrn:2 culations:1 approximation:6 surrounding:3 second:6 enhancement:1 go:1 rigorous:2 further:2 hybrids:2 implemented:4 situated:1 quite:2 wilson:2 index:1 interatomic:1 stands:2 3s:27 sun:1 section:1 3p:20 optoelectronics:1 supplied:1 uniform:1 cell:2 experiment:2 above:2 nine:1 net:2 increasing:1 method:1 3d:1 body:1 condensed:1 full:1 rubio:1 plesset:2 respectively:3 never:1 modify:1 grey:2 here:7 bi:1 ionization:2 reported:2 mev:1 mermin:1 brooks:1 groups:1 relaxation:28 active:30 tz:2 along:1 strong:1 equations:4 eikr:2 change:1 differential:5 obtained:9 apical:1 arrive:1 tx:3 shift:4 study:3 larger:6 allows:1 polarize:2 orthogonalization:3 prior:1 periodic:8 characterizing:1 usually:2 graaf:1 changes:8 cancellation:1 plotted:1 lowers:1 via:2 chim:1 projection:3 elaborated:2 apr:2 collected:1 semiconductors:1 plenum:1 modifying:1 visible:1 anions:2 venkatesan:1 total:2 tools:1 planck:1 unit:2 plot:1 use:5 additive:1 takes:2 would:2 prove:1 contains:1 negative:2 next:5 a50:1 going:1 ψn:4 therefore:5 films:1 themselves:1 simpler:1 type:3 theoretical:1 minor:1 more:10 relax:1 composite:1 binding:1 operators:1 factor:1 site:19 1s2:1 berlin:1 normalized:1 diffuse:1 employed:8 known:5 cases:1 iii:7 must:1 ultraviolet:1 high:2 mg:40 orner:2 defines:1 sphere:2 tunnel:2 science:1 work:2 modified:1 london:2 slater:1 ashcroft:1 oxide:6 fock:14 values:8 splittings:1 cal:1 following:3 making:1 merely:1 trans:2 example:4 stoll:10 heart:1 ıˇzek:1 figure:1 give:2 calculation:6 noci:10 crystallizes:1 share:1 states:26 effectively:1 incremental:1 performed:8 degenerate:1 arise:3 2px:8 occur:1 absolute:2 united:1 pino:1 roetti:3 rather:2 divided:1 six:1 feature:2 chemical:4 occuring:1 causing:1 adjacent:1 chichester:1 plus:2 othnitzer:1 verlag:1 proc:1 description:4 ayala:1 may:6 max:3 after:2 derived:2 minimized:2 sophistication:1 hence:1 shukla:6 produce:4 designed:2 physik:3 horizontal:1 choice:2 data:10 response:2 types:1 fo:4 short:7 outline:1 imply:2 facilitate:1 zno:1 element:3 provide:2 green:1 fundamental:6 correlation:46 representation:7 order:3 restricted:1 sd:1 holds:1 interpretation:1 numbers:7 developed:2 pointed:1 move:1 mainly:2 facilitated:1 years:1 produced:1 held:1 experiments:1 through:2 scuseria:2 mentioned:1 existence:3 facilitates:1 still:1 excitations:2 its:5 operative:1 before:2 write:1 systeme:3 group:3 ligand:5 how:1 energies:3 interesting:1 solving:1 vicinity:1 actually:3 multiconfiguration:1 offers:1 microscopic:2 systems:4 clusters:5 main:1 outside:1 them:1 good:6 thereby:3 mg10:1 groundstate:1 ladik:2 material:3 fig:15 investigated:2 sol:1 yang:2 band:51 tails:3 effects:37 they:7 instead:3 now:2 transparent:2 nor:1 represents:3 february:1 finite:4 2p:29 oxygen:23 2s:20 university:2 level:3 orthonormal:1 sufficiently:1 magnitude:1 each:5 found:6 universit:1 pao:2 cisd:3 bridging:5 domain:2 schemes:1 vanishingly:1 weight:3 disentanglement:1 oneparticle:1 energy:20 reduce:1 gaussian:6 used:4 deficiency:1 gaps:2 static:2 expect:2 entering:2 sketched:1 quantum:9 our:9 ev:34 extract:1 brings:1 out:5 shown:6 hughes:1 matrix:27 space:2 open:3 rep:2 since:10 induces:2 optimally:1 denotes:2 increase:2 attracted:2 posteriori:1 investigation:1 denoted:1 rn:1 induced:7 supports:1 occurs:2 physics:1 stat:1 regards:1 sp3:1 theory:3 barrier:1 localization:6 diagonal:9 free:1 standard:2 approaches:1 complicated:1 york:1 put:1 estimate:2 process:2 orb:2 e0:5 shortest:1 e2:1 longrange:2 incorporates:1 pairs:1 r1:3 r2:2 widths:8 route:1 transition:1 alloyed:1 so:5 keep:2 counterpart:1 int:2 plane:3 place:2 enough:1 corrections:21 ionic:4 onto:3 eqs:2 first:7 major:1 o14:2 toulouse:1 step:1 ignored:1 quasiparticle:5 third:3 thereafter:1 number:5 reaches:1 bartlett:3 enlarged:1 done:1 construct:1 directly:4 neighborhood:3 electronic:4 summarize:1 size:3 idea:1 given:6 checked:1 asymptotic:1 quality:4 indicate:1 introduction:1 top:1 2p6:1 system:16 least:3 their:3 appl:1 fortuitous:1 listed:7 calculations:42 scheme:3 final:1 recovered:1 discussion:1 shifted:1 shell:7 3p1:3 igarashi:1 centered:7 sony:1 contribute:1 immediate:3 employ:1 part:6 too:1 somewhat:5 kept:4 knowles:1 than:7 relative:1 molecular:4 determines:1 correlate:1 hirata:3 kudin:1 double:5 approximations:2 summary:1 measured:2 transferred:1 ranging:1 annihilation:1 determined:3 polarizes:2 magnesium:2 str:1 were:20 insightful:1 treated:1 distinguished:1 usefulness:1 lowest:5 addressing:1 jpn:1 corre:1 correction:4 modern:1 mind:1 few:3 already:1 manuscript:2 substantial:4 increment:1 wannier:25 need:1 affinities:1 occupied:7 ray:2 lif:1 estimated:1 angle:1 zero:1 depending:1 efficient:1 studying:1 self:3 responsible:2 able:2 gravity:2 rocksalt:2 polarization:27 extracted:1 potential:5 take:1 converged:1 algorithms:1 concern:1 accuracy:1 surf:1 added:10 relatively:1 optimizes:1 investigations:1 buffer:11 kowalczyk:1 enter:1 horsch:3 effective:8 difference:3 most:1 optimized:4 fcc:1 germany:3 ensure:1 busso:1 future:1 segment:1 jørgensen:1 constructed:2 wiley:1 surprising:2 considered:1 arising:1 clear:3 adopt:2 metal:2 dovesi:5 construction:2 electrons:7 exp:1 thank:1 normally:1 lying:6 precise:1 insulators:2 show:2 reductions:1 variational:1 notations:1 mg2:6 radii:2 expressed:4 shirley:1 analogue:1 find:1 ǫhf:2 ground:15 impact:1 rev:14 finally:1 based:10 parameters:1 iwata:1 conduction:38 occ:1 written:1 negligible:1 should:3 surroundings:4 only:4 explicitly:1 black:3 molecules:4 essence:1 admixture:1 various:2 rice:1 local:12 discuss:3 pj:1 ser:1 predict:1 dominant:1 epitaxial:1 means:1 dependent:1 displayed:1 secular:2 between:14 mgo:16 fulde:14 expects:1 inclusion:1 ones:1 nearly:2 mention:1 allowed:2 report:1 applying:3 thomson:1 procedures:1 becomes:1 qq:1 processes:2 contributes:1 substrate:1 continuum:2 emb:2 komplexer:3 conditions:1 arxiv:1 median:1 tuned:1 2s2:1 investigate:1 paper:2 antiferromagnetic:1 including:2 previous:1 differs:1 inside:1 farther:1 kernel:2 set:10 2p5:3 constructing:1 reference:3 achieved:1 variations:1 correlations:13 kernels:1 module:4 freeze:1 observed:1 opposite:2 see:14 radius:2 result:4 sea:1 japan:1 discussions:1 recently:1 hole:28 acts:1 techniques:2 preparation:2 phases:1 cole:1 compounds:2 subsequent:4 review:1 sites:18 eigenstates:1 tjeng:1 state:19 smallest:1 identification:1 chosen:1 closed:4 simplest:1 nagahama:1 wise:2 neither:1 blocked:2 approach:6 reinhardt:2 available:1 multiplied:1 2pz:2 terms:13 spectroscopy:2 extend:1 nature:2 2py:2 wn:5 attention:1 weak:1 however:6 utz:2 renewed:1 orbitals:53 extent:1 contamination:1 interface:2 carbon:1 atoms:1 remaining:1 originates:1 suggested:2 both:8 0p:1 0q:1 prescription:1 perturbational:1 many:1 region:24 conclusions:2 according:1 called:6 regions:2 stuttgart:2 sβα:2 dated:1 context:2 contribution:2 expression:1 experimental:8 nearby:2 among:3 ci:13 separation:3 point:5 cc:1 cb:9 ca:17 represented:1 lations:1 non:3 confirmed:1 mcscf:1 fukushima:1 constant:6 zeta:9 crystalline:1 broadening:4 pp:1 configuration:1 described:1 leads:3 basis:23 addition:6 shells:8 due:6 been:2 appears:1 pc:1 reduction:7 describes:1 treat:1 basic:1 expected:2 prototype:3 partial:1 choose:2 fink:2 determinant:1 occupancy:1 controlled:2 parkin:1 quantities:1 concerning:1 ando:1 essentially:1 new:1 gap:28 bulk:3 parentheses:2 determination:1 systematic:1 decreased:1 improved:1 spin:2 ligands:8 present:5 case:5 multi:1 schmidt:2 being:1 solid:5 reliable:1 ǫn:1 value:4 transformation:2 will:6 optimization:2 involved:2 situation:2 vos:1 tnn:6 taking:2 procedure:2 computed:2 kingdom:1 vectors:1 coupled:1 refs:3 thus:5 surprisingly:1 iv:1 ii:5 cluster:30 itself:1 cond:2 triple:6 turns:1 rnn:2 orbital:18 different:12 italy:1 spheres:5 make:2 eigenvalue:1 lett:6 same:11 yuasa:1 shifts:3 complex:5 largest:2 several:3 composition:2 φn:3 difficult:2 development:1 extended:1 embedding:6 koopmans:1 effect:15 nonorthogonal:1 paulus:1 ion:7 insulating:1 levels:1 energetically:1 purpose:3 potentials:2 infinite:3 hartree:11 dielectric:7 recent:1 frozen:9 lower:4 task:1 off:4 center:2 hopping:15 framework:1 nevertheless:3 studies:2 well:4 analysis:6 malrieu:2 ψrn:2 solids:4 materials:5 comes:1 components:1 sets:16 thf:1 chemistry:3 photoemission:1 latter:4 left:1 bending:4 composed:1 lda:2 routinely:1 cuprates:1 proposed:1 less:2 vαβ:2 lih:1 accurate:4 half:1 obtain:1 rest:1 press:4 atomic:6 harrison:3 alternative:1 coordination:5 taken:2 adv:1 note:2 cut:2 density:7 extra:12 character:3 exclusively:1 2s1:3 simple:1 add:1 other:4 treatment:3 cations:3 reason:1 ley:1 excited:4 sawatzky:1 build:1 resolved:1 acta:1 optimizations:2 march:1 around:8 depends:1 easily:1 bands:38 possible:1 pisani:1 increases:1 philos:1 makes:1 similarly:1 mol:1 average:1 using:6 advanced:2 loss:5 like:9 particle:11 follows:2 reduces:1 performing:2 background:1 separately:4 werner:2 yields:2 alternatively:1 completely:1 downwards:1 valence:25 introduce:1 essential:1 towards:2 twelve:3 sketch:3 because:8 methods:5 doll:2 shen:1 layered:1 creation:1 some:7 springer:1 library:1 trends:1 growth:1 acad:1 choosing:1 table:18 proper:1 little:1 soc:2 koster:1 diagonalizing:1 anion:1 scale:1 sharma:1 calculating:1 lead:1 stronger:1 normal:1 extensively:1 overlap:5 sch:2 contributing:1 counteracts:1 does:1 lattice:4 provides:1 o6:1 fragments:1 moderate:1 analyzed:1 ions:11 refer:1 core:7 particular:1 dresden:3 scientific:1 slight:4 nishimoto:1 equivalent:1 wavefunctions:6 agreement:5 overall:1 host:1 olsen:1 although:2 plots:1 post:1 properties:1 von:2 orthonormalization:2 acc:1 comparison:2 about:7 inter:5 central:5 carried:2 extension:3 package:2 column:6 compared:2 slightly:1 discussed:2 o:47 reduced:2 mutually:1 range:20 helgaker:1 repulsion:1 kaiser:1 neighbor:9 eight:1 referred:2 consequently:1 bloch:3 mechanics:1 computational:3 presence:5 into:7 within:9 functional:3 cardiff:1 three:1 down:1 appropriate:1 explain:1 polarizable:1 determine:5 operator:5 fruitful:1 reducing:1 nowadays:1 significantly:1 moeller:1 institut:1 additional:5 area:1 removing:1 there:7 approximate:1 long:9 takeuchi:1 dispersion:1 width:6 hoppings:12 much:2 low:6 way:3 xps:1 was:8 suzuki:1 theory1:1 function:1 tight:1 medium:1 form:3 offer:1 dolg:5 relaxed:3 izotov:2 but:3 crys:3 boys:2 neutral:2 pfaffenwaldring:1 oxygens:2 related:5 academic:1 line:1 removed:2 hf:32 broer:2 de:1 fujino:1 commun:2 pi:1 compute:1 embedded:1 mtrl:1 mat:2 molpro:6 attached:4 up:2 ur:3 nearest:17 crystal:10 below:2 projecting:2 hand:1 neighboring:2 fαβ:2 problem:2 define:2 similar:5 calculated:2 detailed:2 nnn:7 ab:5 associated:9 photoelectron:2 computing:3 defined:2 wards:1 o32:1 influence:3 direction:1 denote:1 substantially:1 single:4 torino:1 mrci:2 corresponding:5 nearestneighbor:1 formalism:2 intra:1 sasaki:2 physical:1 tedious:1 again:4 functions:21 beyond:2 nn:21 no:4 amounts:2 allow:1 whereas:5 wavefunction:8 when:13 virtual:4 field:1 narrowing:3 accounted:3 role:2 ǫx:1 spatial:3 theor:2 predominant:1 sufficient:1 poor:1 picture:3 draw:1 elements:22 snn:4 energetic:1 excitation:1 separate:5 initio:5 chem:25 owdin:2 includes:3 generated:3 important:1 included:10 møller:2 structure:11 upwards:4 correlated:3 saunders:3 longer:4 coulomb:1 typically:1 interval:1 holes:1 together:1 hnn:9 dr:1 text:3 fact:3 time:2 walker:1 starting:2 original:2 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.