text
stringlengths 0
190k
|
---|
0704.3657.txt |@word limited:4 similarity:1 magnetic:1 entropy:1 parameterization:1 whose:8 calculate:1 aug:1 electricity:1 under:1 rise:1 figs:3 govern:1 school:1 cmb:43 vector:23 math:5 indices:1 consistent:3 likely:2 straylight:1 even:1 christ:1 reheating:1 above:4 new:2 increasing:1 coefficient:1 evolving:1 residual:2 here:6 hundreds:1 reported:2 represented:5 contraction:1 study:3 changed:1 approaches:2 fourier:4 spacetime:1 mutual:1 projection:2 replace:1 total:3 denotes:1 unit:4 plot:3 would:4 negative:1 m1:4 therefore:12 m2:5 robertson:1 curvature:1 foregrounds:2 aligned:3 must:3 gruppuso:3 work:5 theories:3 mv:26 hansen:8 root:4 example:4 defer:1 give:1 relativistic:1 cited:1 preserving:1 provide:5 feature:1 revisit:1 how:1 nontrivial:3 significance:2 renyi:1 description:1 replacing:1 meaningful:1 lar:1 third:12 summing:1 algorithms:3 correlation:15 first:3 order:9 restriction:1 interpretation:3 over:13 satisfies:2 before:2 directional:1 fix:1 exhibits:1 complex:8 fig:11 weeks:7 easier:1 maximal:3 band:1 effects:2 they:12 multidimensional:1 eigenvalue:1 each:10 side:1 mean:2 solution:1 used:9 combining:1 combinatorial:1 multiply:1 nontrivially:1 gov:1 i2:1 standard:8 ecliptic:1 formation:1 mvs:44 cosmic:8 filter:1 ordering:3 arccos:2 onto:1 polyhedron:2 already:1 vittorio:1 features:2 rank:1 ℓj:3 ℓi:1 ℓm:4 cartesian:2 similarly:1 toh:5 perturbations:1 observations:7 john:1 tool:5 somewhat:1 peculiar:1 positively:1 enabled:1 second:2 normalizing:1 represents:3 enables:1 spectrum:5 seen:3 rakic:4 relatively:1 implemented:1 harper:1 thoroughly:1 latter:1 thorough:1 oriented:1 fitting:1 wmap:13 blue:1 denominator:4 regular:3 germany:1 phase:1 acknowledgements:1 calculated:8 vertices:5 points:2 principle:1 quantifying:1 sum:3 dot:1 probe:7 implying:1 substituting:2 d5:1 hobson:2 θjk:2 coefficients:20 do:3 dm:2 dd:1 de:7 dc:1 preferred:2 da:2 despite:1 dv:2 marinucci:1 textbooks:1 fields:3 analytical:1 tation:1 reference:6 observed:5 depends:6 radius:1 discussions:2 alternative:8 best:1 techniques:1 a2ℓ:2 tensor:1 verkhodanov:2 symmetric:5 simplest:1 c2j:1 c2i:1 approach:4 wd:1 terms:5 extend:1 nature:2 however:7 equals:1 contamination:3 topology:1 c22:2 received:2 cos:14 c21:4 ilc:7 ill:1 against:1 hinshaw:2 variance:1 genus:1 inflaton:1 very:5 royal:1 2nd:1 gorski:7 polynomial:18 conference:1 basis:2 three:7 been:10 expected:3 θj:2 graphical:1 θi:2 quantities:4 xxx:3 coherent:3 maximally:2 spin:5 applied:1 originate:1 remaining:1 near:2 applies:1 property:5 leaves:1 characterizing:1 a20:1 hone:1 make:2 atiyah:3 iφi:1 drawback:1 avoids:1 several:1 independent:25 i1:1 numerical:14 evil:1 normalization:3 ellipsoidal:1 copernican:1 claims:1 eimφ:1 just:3 rotated:1 homogeneity:2 identify:1 spherically:1 campbell:3 rotates:2 previous:2 candidate:1 instance:2 ease:1 had:1 coplanar:1 easy:2 rescaled:1 iα:1 bands:1 breaks:1 disagreement:1 possible:5 indicative:1 background:6 unique:5 apart:1 appearing:1 isotropy:6 schwarz:9 arbitrary:4 differencing:1 statistic:2 opposite:1 microwave:8 linearly:1 gsfc:1 elucidate:1 substituted:2 substitution:1 properties:7 planarity:22 banday:7 increasingly:1 numerator:1 wavelets:1 o:2 soc:13 maxwell:5 xyz:1 rotations:1 shellard:1 down:3 lies:1 tetrahedral:1 support:1 transform:2 way:1 astrophysics:1 was:8 lowest:4 form:4 forming:1 hemisphere:3 maximum:5 classic:1 abstract:2 evidence:1 exist:4 simulations:1 distributions:5 check:1 constructed:1 no:6 agreeing:1 when:7 reality:1 acton:2 tesileanu:1 papers:1 test:2 roll:1 models:5 uniformly:1 cℓ1:1 factorized:1 dφ:4 dτ:4 together:3 factorizes:1 n1:2 n2:2 global:3 leads:1 roy:11 computation:2 remarkably:2 row:1 certainly:1 depend:4 technique:1 2004c:2 2004b:4 2004a:4 vec:1 analogous:1 orthogonal:5 3s1:2 choice:4 orientations:1 advised:1 hannay:8 exact:1 riemann:3 presented:1 anisotropy:5 mn:1 findings:1 sℓ:3 prediction:5 sign:2 appear:4 axes:3 uniform:3 current:1 goes:1 shared:1 aℓm:39 satisfy:1 multipole:70 perpendicular:2 magnetism:1 cos2:3 alone:2 appears:1 change:1 aℓ2:1 aℓ1:2 vectors:58 funded:1 spheres:1 studies:4 plotted:7 useful:2 merely:1 wealth:1 positive:1 predictions:3 opposed:1 associated:1 marginally:1 apparent:4 visual:1 appendix:4 wands:2 values:6 following:3 making:1 l101:1 figure:10 predict:4 anomalous:9 permutations:4 sample:1 performed:1 dennis:21 evidently:1 s2:9 discussion:2 s0:1 orthogonality:1 pind:1 write:2 pure:3 parameter:2 aℓℓ:1 map:18 product:3 may:6 max:1 southern:1 applications:1 explored:1 representations:2 revealed:1 cˆℓ:4 natural:7 vielva:2 su:2 cosmology:3 quadrant:1 sj:1 si:12 so:6 sn:2 jain:2 representation:11 prefactor:1 indeed:2 pointed:1 course:2 statistical:11 differs:1 derive:2 group:1 interesting:1 coordinates:4 window:1 tors:1 mail:2 main:1 non:12 introduce:1 hamilton:2 half:1 now:4 discuss:4 term:2 equality:1 james:1 spinor:1 domain:1 square:1 significantly:3 gaussian:68 nongaussianity:3 challenges:1 inhomogeneous:1 astrophysical:1 year:5 gonzalez:1 shown:5 reducing:1 space:7 3rh:1 increase:1 contained:3 gaussians:1 ble:1 dominate:1 theory:2 possibility:2 quite:1 complicated:3 tegernsee:1 org:1 remainder:1 gott:2 derivation:4 iterative:2 place:3 2005d:4 2005a:4 2005b:2 2005c:4 exotic:1 spergel:3 symmetry:2 variables:1 lond:1 trispectrum:3 xy:2 simplified:1 directly:6 impossible:1 angular:8 size:1 given:11 necessarily:1 checked:2 fortuitous:1 convention:1 1m:1 gives:3 exploring:1 copi:13 x2:2 representing:1 than:8 specify:1 require:1 future:2 were:7 correction:1 occupies:1 argument:2 generalization:1 say:1 flatness:1 any:19 computationally:2 ideas:1 note:2 emphasis:1 potential:1 zou:3 green:2 modulus:2 multiple:1 investigations:1 falls:1 printed:1 contrasts:1 analytically:8 latex:2 especially:1 considered:3 adopt:2 implications:1 typeset:1 mrd:1 quantity:8 precise:1 spaced:4 show:2 balbi:1 slow:1 ensembles:10 written:5 analytic:4 only:16 explicitly:2 black:1 legendre:1 dyn:1 nearly:1 median:1 rotationally:4 predicted:1 mapped:2 rms:1 eriksen:8 starkman:4 relative:1 namely:4 college:1 uncorrelated:2 y3:1 satisfying:4 review:2 functionals:1 label:2 colours:1 enough:1 between:12 geometric:1 multiplied:1 vertical:2 comp:1 sutcliffe:3 comm:1 fluctuations:4 analyzed:2 originates:1 gaussianity:7 tractable:1 many:1 according:3 laplace:2 multipoles:13 expression:1 nearby:1 among:1 donoghue:4 exploit:2 constant:8 computing:1 barreiro:1 mark:8 harmonics:3 direction:11 restrictions:1 arcsin:1 observers:2 observe:1 external:1 diffuse:1 those:3 case:10 supernovae:2 investigating:1 planar:12 orientation:2 metric:1 bias:1 different:11 develop:1 d13:1 same:10 physical:1 breakdown:1 extended:1 director:1 octahedron:1 edges:1 lachieze:3 totally:1 huterer:3 costa:7 modes:2 minimize:1 without:3 solve:1 components:4 coordinate:5 model:25 being:3 skyrmion:1 aspect:1 lett:2 complements:1 schupp:3 naselsky:2 momentum:2 real:8 aspects:1 nielsen:2 spectacular:1 2u:2 early:2 inflation:5 mon:11 vacuum:1 using:15 accepted:1 mod:1 multiplicative:1 inter:4 decimal:2 conditional:1 images:2 joao:1 provided:1 yℓm:10 wmap3:14 footing:1 decomposition:1 y20:1 majorana:5 scientific:1 power:9 bacry:2 equivalent:8 inherent:1 rearranging:1 comparison:4 central:2 discussed:2 mixes:1 practical:1 convenient:1 aℓ:8 ox:1 road:1 backus:2 cambridge:2 numerically:4 references:2 determine:2 operator:1 spinors:2 hep:1 removing:1 there:11 dispersion:1 low:7 labelling:2 bogomolny:8 lambda:1 complete:2 jun:1 amongst:1 correlated:1 applying:1 minkowski:1 assume:1 emissions:1 agree:1 expect:1 strongly:1 ac:1 certain:3 describe:2 general:5 examine:3 file:2 av:1 again:2 completeness:1 field:1 spatial:1 mathematics:1 1bj:1 forcing:1 bispectrum:4 deviation:1 polar:1 separate:4 a1:1 a0:2 a3:2 important:3 a4:1 coverage:1 studied:4 included:1 l67:1 mask:1 directors:2 original:1 represent:1 monte:1 consider:1 scalar:4 expressions:1 iu2:1 astrophysicists:1 re:2 th:1 straightforward:2 burigana:1 far:2 interpreting:1 difference:1 condition:4 randomness:1 evaluation:2 sanz:1 large:6 small:2 grateful:1 ten:1 so17:1 tex:1 zero:2 further:7 canonical:1 fℓ:5 advantageous:1 section:10 method:6 full:22 component:1 behaviour:1 directions:5 increments:1 nth:1 geophys:1 permutation:1 action:1 highfield:1 uniquely:4 via:2 family:1 requiring:1 pdfs:3 readily:1 probabilities:1 finally:2 comparing:1 more:15 highorder:1 parallelepiped:1 particular:5 producing:1 equation:3 den:1 compare:5 cosmological:11 ds2:1 states:3 sphere:16 minimum:1 axis:6 information:7 rather:5 maps:17 ensemble:15 galactic:5 algebra:1 ζi:20 ζj:10 ζk:1 derived:3 treatments:1 plane:9 horizontal:1 author:1 parameterized:1 perhaps:2 fundamental:3 ith:1 mission:1 paper:5 through:3 existence:1 kinetic:1 its:13 roots:17 style:2 actually:1 good:1 number:6 framework:4 φi:6 oxford:3 octahedral:1 easily:2 fully:1 assemblies:1 level:2 2a:1 2b:1 found:3 2i:1 characterized:1 as2:2 quadrupole:6 accelerator:1 hard:2 connect:1 quantum:3 beyond:2 since:14 induces:1 research:2 dominated:1 denoted:1 issue:3 occurs:2 foreground:2 interscience:1 confidence:1 reason:1 conditioning:1 pairs:1 launch:1 consequence:1 castle:1 integrand:2 probability:57 geodesic:1 defects:1 battye:2 perturbation:2 temperature:2 introduction:1 construct:1 assumption:4 statement:1 smoothed:1 park:11 undefined:1 albeit:1 determines:1 double:2 determined:1 pairwise:1 cabella:1 randomly:1 lie:3 constructions:1 depending:1 internal:4 jacobian:4 finding:3 added:1 measures:5 most:7 significant:2 nothing:2 extremely:1 southampton:2 deviations:1 pℓm:1 clear:3 antipodal:3 exp:10 velocity:1 physics:5 particularly:6 relation:1 carefully:1 find:6 parameters:5 discord:1 distributed:5 ox1:1 freedoms:1 subsection:5 factor:8 pℓ:9 dependent:2 international:1 during:2 continuum:1 arxiv:2 investigate:1 common:1 mezei:3 set:6 see:4 arg:1 close:1 contour:2 probable:1 currently:1 dipole:3 various:6 probably:2 available:1 statistically:14 2m:1 attention:1 distinguish:1 both:1 last:1 sensitive:1 context:1 pdf:35 whole:1 finds:1 point:21 simple:6 corresponds:3 dimensional:5 simply:1 church:1 described:6 transformations:1 discriminant:2 due:4 laplacian:1 strategy:1 azimuthal:1 pe:6 anisotropic:3 ph:41 determination:2 systematic:3 p2:4 p3:12 look:1 p5:1 solid:1 reliable:1 finelli:1 while:1 replaced:2 error:4 unitary:1 vol:1 averaging:3 herein:4 triple:3 eigenfunction:1 products:1 higher:4 literature:2 lilje:5 levels:1 uses:1 recent:3 lower:3 analysis:11 obviously:2 consistency:1 chemistry:1 distances:1 rindler:2 reviewed:1 simi:1 cut:1 conclusions:1 signals:1 source:1 theorem:3 transformation:2 showing:1 ringberg:1 integer:1 helling:4 rotate:1 systematically:2 confront:1 signal:3 translates:1 indication:1 essential:3 spins:1 mathematical:4 methods:9 absolutely:1 some:8 understood:1 b2:1 scale:6 l16:1 integration:4 connecting:1 tends:1 proc:2 prob:4 run:1 bc:1 agreement:2 bv:1 plots:3 hilbert:2 handled:1 changing:1 anything:1 constraint:1 novikov:1 reduced:2 range:2 repulsion:4 into:5 integral:5 suppl:3 martinez:1 appropriate:5 primarily:1 frames:1 proportional:1 clustering:1 statistics:12 shading:1 u1:5 u0:7 u2:17 analyze:4 gauss:2 properly:1 line:4 considerable:1 leboeuf:1 uv:1 up:1 us:3 uk:3 highlight:1 similar:4 called:2 ordered:2 defined:2 chao:1 globally:1 yℓ2:1 yℓ1:1 formalism:3 defines:1 friedmann:1 polygon:1 application:3 clean:1 calculating:1 problems:3 polynomials:9 prepared:2 meaning:2 desert:1 structure:2 dimensions:1 independently:3 land:17 implies:3 algorithm:1 required:2 equivalently:5 nasa:2 weights:5 walker:1 requires:2 having:1 normalized:4 mollweide:1 katz:3 results:9 kate:7 issues:1 concerned:1 intensive:2 contours:1 tegmark:6 include:2 random:28 antipode:2 matrices:1 noted:2 configurations:4 smaller:2 sin2:4 sin3:1 astrophys:10 imply:1 enclosed:1 manipulating:1 carlo:1 λcdm:1 3x:2 giving:2 henceforth:1 poles:1 3a:2 d2ℓ:2 degree:1 respectively:3 spacing:2 separation:1 others:2 invented:1 northern:2 involved:1 suggests:1 resulting:2 makes:1 involves:4 examining:1 scales:11 eiφ:1 improbable:1 addressed:1 topological:1 anomalies:1 summation:1 tools:2 use:4 next:2 few:1 zaldarriaga:1 themselves:1 becomes:1 labelled:2 reconstructed:1 account:2 integrating:1 obvious:2 universe:8 averages:1 stereographic:7 weaker:1 calculation:1 high:2 assumptions:2 tan:4 δm1:2 counting:1 mutually:4 six:1 arrangement:1 dwb:1 varies:1 pair:2 sin:5 demonstrating:1 realized:1 introduced:4 light:1 separations:1 redundant:1 element:4 subsequently:1 s1:6 wigner:1 interpreted:1 produced:3 whilst:1 mathematicians:1 including:5 regions:2 efstathiou:2 chosen:2 degrees:7 latitude:1 derivative:1 outlined:1 practice:1 asymmetrical:2 das:1 rotation:4 transparent:1 february:1 verifying:1 university:4 magnitude:1 mode:3 µ2m:1 constraints:1 homogeneous:1 exacerbated:1 society:1 frequency:3 measure:11 our:11 special:2 out:1 rey:3 matrix:1 rev:12 chaos:1 maximized:1 supports:1 integrated:2 red:2 unwieldy:1 release:2 completely:19 york:1 geometry:1 determining:1 times:1 counterpart:1 counterintuitively:1 isotropic:14 assumed:2 south:1 vickers:1 powerful:1 precisely:3 lemaˆıtre:1 bears:1 data:33 system:7 realistically:1 their:15 wilkinson:2 final:4 exactly:3 treatise:1 penrose:2 distinguished:1 enforced:2 unchanged:1 curves:2 ghz:1 disjoint:2 constrained:1 apparently:1 clearly:3 angle:9 rigopoulos:2 studying:1 oliveira:7 accuracy:4 calculus:1 sm:1 collaboration:2 who:2 connected:1 class:2 volume:4 consequences:2 fact:4 octopole:29 µm:5 based:5 should:4 employed:3 local:1 cube:1 means:2 ralston:2 overall:3 joint:12 words:1 quantifies:1 bondi:1 densities:1 luminosity:1 contain:2 cℓ:3 fixed:8 traceless:1 computed:1 exists:2 acquired:1 frame:15 correlations:5 geometrically:1 tend:2 state:2 difficulties:1 correctly:1 invariant:8 tent:1 publishers:1 tolman:1 s2ℓ:7 hypothesis:1 key:1 configuration:23 distribution:39 antipodes:1 observable:1 equal:1 etc:3 otherwise:1 comment:1 magueijo:12 qℓ:5 unclear:1 conclude:1 harmonic:6 respect:6 cv:1 piecewise:1 addition:2 bianchi:1 anomaly:1 define:3 arises:1 corresponding:5 3c22:2 cayon:1 angles:3 astron:11 c2:36 c1:35 repetition:1 present:5 novel:1 unlike:1 align:1 harder:1 value:2 will:18 frameworks:1 almost:1 thus:11 surprisingly:1 surface:1 sity:1 examined:1 generic:1 indistinguishable:3 another:3 largest:3 party:7 difficult:2 http:1 upon:1 effect:1 v1:1 v2:2 fellowship:2 concordance:1 nevertheless:1 colour:1 well:2 s22:2 s21:4 sets:3 position:2 usual:3 spherical:11 less:2 moments:1 identically:2 sources:1 underlying:4 distant:1 adv:1 density:32 sky:4 mathematically:2 other:14 combine:1 divided:2 identical:2 tests:2 ζik:1 inversion:1 increases:1 stereographically:1 five:2 press:3 necessary:3 like:1 keble:1 because:3 sequence:1 wider:2 choosing:2 dc2:5 dc1:7 avoid:1 cosines:1 does:9 assuming:2 locate:1 noise:1 reaching:1 expansion:2 stellar:1 clarendon:1 although:9 about:9 extension:1 freedom:7 dependence:1 a2:8 krl:2 bohigas:1 prosen:2 equally:3 own:1 unattractive:1 glenn:1 previously:3 van:1 additional:1 quadratic:1 naturally:1 function:41 north:1 iy3:1 buv:1 but:9 astro:39 compute:3 evident:1 signed:1 below:2 limit:3 demonstrate:1 problem:4 mechanics:1 dots:3 int:1 ergodic:1 ind:2 functions:13 compared:2 courant:2 q2ℓ:5 compares:1 details:1 stat:1 zheng:3 variation:1 portion:1 furthermore:4 |
0704.3658.txt |@word aln:1 homomorphism:2 consider:3 gp:8 alg:1 results:2 scalar:1 proposition:1 computation:3 kato:1 bvj:2 expressions:1 analytic:1 equivalence:4 tr:2 tn:6 uniqueness:4 tm:2 ti:5 belonging:4 string:1 orthogonal:1 very:2 springer:1 choice:7 every:2 partitions:1 am0:1 presented:1 irreducible:12 t2:3 t1:8 convenience:2 vector:32 irreducibly:1 science:1 gauge:1 shiga:1 direct:2 zero:1 irreducibility:1 canonical:14 even:1 t2k:2 xω:4 plays:1 abe:5 sum:3 sj1:1 fock:18 subspaces:2 s12:3 new:3 consisting:1 msk:1 satisfy:3 respectively:3 never:2 here:1 kurims:1 represented:1 strong:1 equations:3 appears:2 differential:1 remark:3 commutant:1 study:2 vectors:10 sjk:3 products:1 akn:4 sjl:2 permutation:2 action:3 makes:1 uniquely:3 useful:2 family:12 f1:2 apr:1 univ:1 unit:3 use:3 tn1:1 would:1 prove:2 contains:1 uniformly:1 reflexivity:1 hilbert:3 comparing:1 linear:2 m1:8 therefore:9 sentation:1 theoretical:2 more:1 solitons:1 operators:7 appendix:3 osp:1 particular:2 known:3 hold:1 iii:8 keeping:1 car:4 equation:2 mn:2 zhao:1 permutative:23 mq:8 following:8 repre:1 example:7 proof:11 wedge:5 mackay:1 memoirs:1 give:1 πj:5 states:1 contradicts:5 assumptions:1 o:60 sense:4 robinson:1 recursive:11 provide:1 s2:7 s1:9 holds:16 write:11 maps:1 nontrivial:1 significance:1 e2n:2 fp:1 map:1 product:3 proc:1 description:7 algebra:40 may:1 after:2 derived:1 mapping:1 hence:21 curiosity:1 date:1 fi:3 summarize:2 law:3 physical:2 computations:1 explicit:1 sk:1 sj:18 si:9 sn:15 sm:12 verify:4 representation:63 order:1 restriction:5 acts:2 interpretation:2 closely:1 correlation:1 interpreted:1 symbols:1 course:1 paper:2 london:1 statistical:1 japan:1 satisfies:8 okounkov:1 before:1 derive:1 group:3 interesting:1 fix:5 boson:16 actually:1 mπ:2 according:1 lr:1 systems:2 lq:6 mail:1 correspondence:5 hyperfinite:1 them:1 introduce:2 a0n:1 they:2 multiindices:1 speculate:1 nor:2 noji:1 finite:1 always:8 university:1 orthonormal:9 representa:1 l2:5 each:21 2l:2 found:1 2n:15 suffixes:2 em:1 en:6 idea:1 extended:2 obtains:1 impossible:2 quantum:1 our:1 operation:2 special:1 shown:4 jimbo:1 unital:3 restricted:2 furthermore:8 induces:1 smn:1 ajn:2 math:13 shows:4 theory:8 reformulated:1 state:2 hull:1 diagonal:1 free:4 standard:1 york:1 e1:2 universally:1 rewritten:1 definition:13 sm1:1 cuntz:19 δij:3 consequence:3 ritsumeikan:1 first:3 separable:1 xn:7 xa:1 construct:1 representations:41 xs:3 fj:21 πb:5 given:8 embeddings:1 reference:8 introduction:1 system:9 relations:6 their:9 assumption:2 fermions:10 statement:7 realization:2 normalization:1 speaking:1 recursively:1 part:1 corresponded:1 cyclic:23 double:1 depends:1 preparation:1 determined:1 f12:19 tion:1 result:2 motivation:1 symmetries:1 ann:1 anj:3 endomorphism:2 anp:1 any:39 lin:3 efi:1 ideal:1 generalized:1 analogy:1 δnm:2 tool:1 davidson:1 sl:1 most:1 nonlinear:1 an1:1 automorphism:1 2tr:1 pair:2 class:5 branching:9 especially:1 considered:1 ki:5 coincides:1 km:5 kl:3 kp:13 kt:1 physics:3 notion:1 fact:7 laws:5 2m1:2 show:10 tb1:2 random:1 converge:1 notations:1 miwa:1 relation:2 find:1 ock:2 spite:1 explain:1 f21:16 lemma:12 only:3 explicitly:1 generators:13 subsection:1 constant:1 exchanged:1 do:1 his:1 dj:8 above:1 viewpoint:2 means:1 bratteli:2 tbi:2 words:1 kusatsu:1 justified:2 rfs:5 conditions:1 arxiv:1 jorgensen:1 common:1 fixed:1 set:5 exists:10 δjk:1 j1:6 see:11 college:1 descriptions:1 existence:2 inequivalent:1 2mq:3 subject:1 satisfying:12 commutation:1 representatives:1 shiraishi:2 written:5 closed:1 between:1 invariant:1 neither:2 approach:1 commute:1 replacing:2 terms:2 rims:1 jp:1 however:6 awata:1 jl:1 endc:1 comm:3 key:1 jk:3 bose:2 amer:1 both:2 freely:1 jn:3 became:1 embedding:4 unitarily:4 among:2 ci:8 cn:3 point:1 simple:4 except:1 dimensional:1 simply:4 spans:1 polynomial:2 respect:4 naturality:1 pp:1 basis:10 addition:1 int:1 basic:1 ph:1 algebras:16 pn:8 define:15 restrictions:1 sufficient:1 subspace:15 noncommutative:1 understand:1 2n1:2 denote:1 case:3 k2:1 classifications:1 rbs:10 bω:17 many:1 situation:1 unitary:5 vj:12 vk:3 iv:2 ii:14 dual:1 fermion:8 higashi:1 author:1 make:1 s2i:1 same:2 complex:1 several:6 subalgebra:12 isometries:1 development:1 independent:1 used:1 unboundedness:1 hand:2 v1:10 v2:10 purpose:1 infinite:14 a2l:2 a2m:4 a2n:20 cycle:2 off:1 acknowledgement:1 nevertheless:1 studies:1 well:4 ccr:3 without:1 commutations:1 endomorphisms:1 claims:1 arising:2 hyper:1 spurred:1 obtain:10 actions:1 press:1 identify:5 thanks:1 immediately:1 λj:8 λi:2 multiples:1 previous:1 conjugates:1 preprint:1 generator:1 infinitely:1 excites:1 seems:3 k1:18 iω:1 belongs:1 lett:2 easy:1 theorem:9 semigroup:1 mod:1 transformation:1 gave:2 decomposed:2 sums:5 finding:1 vacuum:8 amq:2 using:3 unique:1 formal:14 meaning:3 like:3 particle:2 follows:7 δm:3 δj:5 mathematical:1 because:12 often:4 sequence:1 some:2 examples:1 kawamura:4 2np:3 dense:8 does:1 o3:1 o2:14 kyoto:1 equivalent:9 l1:6 bi:4 bv:3 bw:2 2m:7 notation:3 properties:3 injective:1 comparison:1 about:1 algebraic:1 generated:6 oa:2 important:2 extensions:1 introduced:1 subset:1 soc:2 cambridge:1 unbounded:3 into:9 h1:2 ηj:6 ηi:1 references:1 selecta:1 operator:6 anticommutation:1 strictly:1 there:14 bosons:15 way:3 call:5 was:1 toeplitz:1 function:1 complete:2 form:1 regard:2 but:2 pitts:1 construction:2 compute:2 embedded:1 uq:1 up:4 us:1 limit:1 jω:7 iterated:1 embed:1 similar:1 called:5 eigenvector:1 s1n:1 mechanics:1 ac:1 proved:1 defined:7 certain:3 abstract:1 describe:1 am:5 general:3 engineering:1 exist:3 defines:1 functions:1 nk:1 nl:2 nm:5 nn:5 no:8 commutes:2 when:7 other:5 role:1 np:14 mathematics:2 elements:5 sided:1 problems:2 a18:1 odake:1 a1:5 a3:2 a2:2 a4:1 structure:2 ghost:1 implies:11 assume:16 space:8 pseudo:1 n0:1 n1:18 n2:3 |
0704.3659.txt |@word aoki:1 limited:2 ψlj:2 gs:46 consider:10 gv:41 lagrangian:1 forbidden:1 results:6 four:44 scalar:38 12c:1 into:1 ga:2 go:1 follow:2 remarkably:1 gl:2 contributions:3 causes:1 devoted:1 whose:1 terms:4 calculate:1 concerned:1 φgr:1 finally:1 rg:67 γo:7 those:3 4nc:8 stable:2 must:2 worth:1 case:16 dαg:4 δgv:3 straightforward:1 very:13 choice:1 witten:1 stays:1 difference:2 exact:1 condition:1 twoloop:1 identity:1 leads:1 school:1 level:4 gatti:1 turns:4 eigenmodes:1 solution:3 mesonic:1 large:28 kondo:1 adjust:1 transmutation:1 science:1 small:11 eigenvalues:2 noted:5 attracting:1 upper:1 squared:1 specially:2 contrasting:1 renormalized:12 gv2:5 approximation:30 zero:7 value:9 equal:2 dynamics:12 quite:1 linear:1 even:5 tells:1 tsuchiya:1 appear:1 fine:13 section:16 while:4 lengthy:1 axial:1 infinitesimal:2 morozumi:1 goes:5 new:4 increasing:1 method:4 contrast:1 edited:1 evaluating:1 degree:3 respectively:1 here:8 free:2 address:2 represented:3 depend:1 along:1 strong:7 equations:42 appears:2 logarithmic:1 obtained:16 brauner:2 institute:1 shift:1 study:4 studied:5 allows:1 wilsonian:5 adopt:1 p2:2 procedure:1 ψli:10 stressed:1 usually:3 decouple:1 suitable:1 makes:2 via:1 useful:1 addresses:1 scales:2 marginal:1 belongs:1 vii:2 maldacena:1 highly:1 sizeable:1 analyzing:1 summation:2 apply:3 m2φ:8 meson:2 planck:1 csaki:1 flavors:11 derivatives:1 use:5 hierarchically:1 asymptotic:1 would:6 intensively:1 covariant:1 taking:3 continuous:2 negative:2 properties:3 scenarios:1 phenomenological:2 mation:1 4nf:1 call:1 therefore:20 qcd:7 taken:1 scope:2 type:3 theoretical:1 diagrams:17 more:3 introducing:2 duality:1 composite:3 becomes:5 operators:29 under:5 wijewardhana:3 appendix:3 observations:1 known:6 tanabashi:1 cases:5 iii:2 carried:3 quartic:6 reducing:1 decay:1 equation:16 fµν:1 modified:1 theories:35 nagoya:1 erg:5 values:5 following:3 spontaneous:2 example:4 performed:2 compare:1 renormalization:16 figure:2 give:4 calculation:3 discussed:6 ψrj:8 organized:1 indicates:1 ψri:2 numbers:8 allowed:1 sharp:1 times:1 simple:1 guarantee:1 influenced:1 polchinski:1 rather:8 describes:2 discussion:2 breaking:6 write:1 far:1 nontrivial:2 edge:1 illustrated:1 pure:2 instead:3 hierarchical:1 parameter:13 divides:1 zaffaroni:1 o1:1 simplicity:6 may:39 max:1 ladder:33 akiba:1 containing:1 substitute:1 diagram:5 corrections:6 iwasaki:2 studies:4 discard:1 wave:1 meaningful:1 constants:1 realized:5 miransky:3 dynamical:3 effective:10 higgs:7 light:1 explicit:7 correspond:2 su:7 arnone:2 maintain:1 so:13 realizes:1 sm:1 banks:3 representation:1 order:15 typical:1 hierarchy:5 indeed:3 over:1 presence:1 paper:5 through:4 ameliorated:1 mentioned:1 japan:2 expansion:3 lg:1 group:5 δgs:2 how:4 interesting:3 solving:11 lj:1 vicinity:2 decreases:3 li:14 better:1 window:13 offers:1 fig:31 renormalizable:1 pass:1 alter:2 supersymmetry:1 eur:2 correspondence:2 eventually:2 non:32 good:1 practice:4 introduce:1 functional:1 break:1 framework:5 they:1 rotation:1 now:2 realize:3 easily:7 term:5 dirac:1 2r:1 harada:1 always:4 university:1 drop:1 sufficiently:1 morris:3 finely:1 each:2 found:29 higher:7 cfts:4 side:1 mean:2 6nc:5 significantly:1 independent:3 series:2 energy:1 hard:1 reduce:1 meade:1 used:2 owing:3 terning:2 fierz:2 1nc:1 quantum:3 our:6 ew:2 beyond:4 eq:9 out:9 respects:1 shown:25 lastly:1 matrix:1 space:8 rep:1 since:12 induces:1 research:1 rd:1 vector:2 rattazzi:1 wick:1 induced:8 ref:3 viable:1 rj:9 shows:5 trajectories:3 theory:18 interactions:3 divergence:1 diagonal:1 possibility:1 standard:1 clarify:1 approaches:2 perturbation:2 besides:2 randall:1 shrock:1 interaction:17 hamed:1 chiral:10 dgs:7 caused:1 followings:1 irrespectively:1 keep:1 int:1 derivations:1 unknown:1 consequence:1 dgv:5 neglected:2 approaching:1 think:1 first:4 origin:1 initial:2 kurachi:2 symmetry:16 jhep:6 omitted:1 nc2:1 number:11 sports:1 restrict:3 enlarged:2 warped:1 simplified:1 adopted:1 another:3 robust:1 jaeckel:2 electronic:2 illustrate:1 blobs:2 given:43 necessarily:1 similarly:1 introduction:1 leading:15 eqs:2 αg2:11 approximately:1 their:4 borel:1 just:1 fermions:7 calculations:1 seiberg:3 scheme:7 structures:1 murayama:1 unbroken:3 gives:5 shell:1 lot:1 kubota:1 exactly:3 barbieri:1 part:6 attanasio:1 somewhat:2 eliminated:2 than:9 coefficients:1 infinitesimally:3 houghton:1 last:2 giudice:1 pµ:1 depends:1 nakano:1 determined:1 contrary:4 supposed:1 enables:1 perturbative:15 lowest:1 symmetries:1 remained:1 respecting:1 lines:3 violet:1 mind:1 peculiar:1 manner:1 seen:9 seem:1 cft:6 relatively:1 wilson:2 strength:1 gies:2 speculative:1 d61:1 kaya:1 note:4 extracted:1 potential:4 amusing:1 schematically:2 coincide:1 3c2:1 unperturbed:1 play:1 towards:6 unless:1 fundamental:2 though:1 singlet:7 most:1 beta:33 involving:1 significant:1 polyakov:1 phase:23 plays:1 analytically:2 class:1 stands:7 deviations:1 especially:3 considered:1 calculated:1 later:2 coincides:1 porrati:1 holdom:1 proceedings:1 points:42 mechanical:1 friedland:1 sd:1 physics:2 sum:5 quantity:1 sector:1 incorporate:4 walking:1 drastically:1 sakai:2 show:3 supported:1 infrared:1 gauge:90 solutions:2 αcr:1 d4:1 trivial:9 find:4 slow:1 linked:3 knowledge:1 parameters:3 written:1 should:10 only:12 explicitly:8 generators:1 12c2:3 local:3 oct:1 demonstrated:1 abelian:3 dm:1 sense:1 above:3 viewpoint:1 means:7 dependent:1 de:1 ones:2 nearly:1 combinations:1 kanazawa:5 ds:11 evolution:5 converge:2 arxiv:2 2b1:3 2b0:3 contain:1 analytical:1 fixed:140 discussing:1 transforms:1 ignored:1 set:6 clearly:3 exists:4 phenomenologically:2 culture:1 see:4 yoshi:2 descriptions:1 existence:3 discussions:3 close:2 dµ:10 λi:1 incorporating:3 acquires:2 instance:1 phases:1 mechanically:1 interacting:1 αy:20 review:3 procedures:1 enough:2 6c2:7 various:8 αg:45 between:1 crude:1 invariant:6 boundary:3 approach:11 attention:1 recently:3 reproduced:1 extend:4 superior:1 cannot:3 weak:4 suppresses:1 jp:2 however:18 2αy:6 vanishing:3 rapidly:1 suppressed:1 both:1 improved:3 kogut:1 many:5 region:6 infinitely:1 reproduces:1 dated:1 context:1 nprg:22 contribution:1 whole:1 otherwise:1 among:1 relevant:10 point:112 2nc:19 45bc:1 asymptotically:1 2nf:8 dimensional:11 grants:1 simply:2 boson:1 moreover:2 improvement:2 math:2 described:2 tuning:13 second:1 addition:2 trajectory:9 due:4 been:15 morikawa:1 gherghetta:1 faithfully:1 much:2 combined:1 bonini:1 erases:1 expected:1 ph:4 anomaly:1 lett:11 box:2 direction:5 enable:1 supersymmetric:4 sub:2 scalars:1 maximal:2 arkani:1 systematic:1 c2:20 4c2:1 general:1 irrelevant:2 present:4 aid:1 applied:3 pacs:1 leave:2 reliable:6 evaluated:11 spontaneously:1 will:7 euclidean:1 near:7 behavior:2 involved:3 irrespective:1 gubser:1 ultra:1 conformal:18 couplings:35 loop:32 yi:3 larger:3 3nc:4 coupled:3 almost:1 endowed:1 refs:2 ir:46 thus:12 them:5 surface:6 iv:2 ii:3 examined:2 φij:1 limit:1 vanish:1 fermion:6 result:4 different:4 gs2:6 develop:1 author:1 perform:2 make:2 cross:2 same:10 any:5 8nc:1 dµν:2 grand:1 according:1 dimensionless:4 electro:1 difficult:1 machacek:1 fairly:3 investigated:2 infinity:3 slightly:3 singapore:2 luty:2 numerical:1 effect:3 flows:25 hand:6 action:4 running:1 terao:8 purpose:1 infinite:2 frequently:1 invariance:4 landau:3 expand:1 recent:1 scaling:2 lower:6 2gs:5 off:1 modes:1 2gv:4 13r:1 higgsless:1 well:12 leff:1 analysis:19 thought:2 directly:1 without:3 solve:2 does:6 dashed:4 five:3 model:6 dimension:40 technicolor:1 world:2 proposed:1 less:6 rotated:1 obtain:1 rosten:2 vanishes:2 thanks:1 aspect:2 immediately:1 flavor:19 ministry:1 previous:4 adv:2 adding:1 vaughn:1 ads:3 conclusions:2 thinking:1 seems:1 discuss:4 lattice:1 add:1 aµ2:1 transformed:1 blob:1 easy:1 inducing:1 reason:1 mod:2 transformation:1 momentum:3 take:5 rescaled:1 explained:1 yukawa:61 around:6 represents:2 read:1 evaluate:5 february:1 superfield:1 smallness:1 increases:3 denotes:1 unification:1 bando:2 sumi:1 crossed:1 using:4 unique:1 color:1 essential:1 theor:8 necessary:2 like:5 particle:1 follows:1 reduces:1 performing:1 specific:1 unstable:4 fully:1 become:1 works:1 reduced:8 shed:1 because:1 classical:1 do:3 spring:1 some:12 self:1 certain:1 understood:2 deduce:1 a16:1 b0:5 examples:2 respect:6 classes:1 scale:21 represent:6 dimensions:17 lead:1 shall:4 future:2 integration:1 propagators:1 critical:13 connecting:4 kobayashi:2 prog:6 proc:3 o2:1 minimal:1 standing:1 scientific:3 power:2 dρσ:1 problems:1 equivalent:1 conventional:2 illustration:1 broken:9 step:1 substituted:1 although:7 δg:1 matumoto:1 analyses:2 intense:1 bz:26 constrains:1 comparison:3 about:2 zaks:3 extension:2 tuned:1 anomalous:51 dependence:3 o:5 simulation:1 practical:1 tremendous:1 a2:1 nothing:1 stand:4 done:1 positive:3 okui:2 ov:9 introduced:1 os:8 vi:3 cutoff:8 primitive:1 rev:20 accompanied:1 wegener:1 dyson:1 a6:1 numerically:2 bound:3 three:3 down:2 lies:3 appropriate:2 right:3 operator:17 next:3 theoretically:1 casimir:1 acknowledgements:1 hep:6 deal:1 there:9 nucl:11 long:3 start:2 quadratic:1 low:1 way:2 analyze:1 was:8 function:26 considerably:1 kanaya:2 phenomena:1 appelquist:3 but:7 hi:1 related:1 salpeter:1 line:9 hf:1 truncation:3 approxi:1 made:1 ψf:1 uv:12 up:1 us:12 bethe:1 marchesini:1 fermi:41 shibata:1 demonstrate:1 problem:9 similar:1 called:6 b1:6 strongly:3 ac:2 ab:3 constant:1 defined:1 flow:4 abstract:1 describe:2 resultant:1 meanwhile:1 karabali:1 examine:6 exist:2 dλ:15 formulation:1 yanagida:1 controlled:1 education:1 tedious:1 again:1 functions:7 compared:3 dotted:4 no:3 extract:1 nc:115 when:13 tc:1 nf:84 schwinger:1 field:17 wetterich:2 other:11 role:2 massless:9 deviate:1 pν:1 deviation:1 briefly:1 elements:1 suppl:4 generates:2 truncate:1 models:13 gouvea:1 vertex:1 yamawaki:7 includes:1 a1:1 a3:1 important:4 a5:1 a4:2 a7:1 2nc2:1 a9:1 a8:1 structure:4 building:1 implies:1 coupling:67 pion:1 perturbatively:1 required:3 mass:25 time:1 hubisz:1 once:2 |
0704.3660.txt |@word neighbors:1 consider:1 ceases:1 magnetic:25 results:1 leads:3 gd:1 inverse:1 iii:8 γu:2 tn:19 gatchina:1 does:6 petersburg:2 stable:6 tf:9 tb:2 indicating:1 federation:1 zhang:1 very:2 assuming:1 conditions:1 wave:6 oxides:1 kimura:2 every:1 condition:6 switches:1 presented:6 turns:2 solution:12 large:4 vector:7 guha:1 small:2 noted:1 configurations:2 smaller:1 sin2:5 direct:1 past:1 second:12 θc1:15 concludes:1 further:2 even:1 r123:1 stands:1 sum:1 uniform:1 current:1 katsura:2 broholm:2 above:9 increasing:2 acknowledgments:1 contrast:6 dagotto:1 satisfy:1 simultaneously:1 exchange:5 respectively:10 here:1 mev:3 them:2 cos2:2 others:1 consideration:5 along:8 strong:7 appears:4 obtained:2 great:1 institute:1 larger:7 spinel:1 kaneko:1 makes:1 lowers:1 dzyaloshinskii:1 apr:1 inducing:1 semiconductors:1 qc1:1 support:1 total:1 unit:2 takes:6 would:2 γj:3 remains:3 positive:2 contains:1 definiteness:1 depicted:1 pnpi:1 criteria:1 taken:1 type:3 diagrams:1 started:1 becomes:3 naive:3 interaction:5 particular:5 cases:1 hold:6 producing:1 me:11 sample:1 account:3 room:1 rogado:1 science:1 equation:2 mn:1 mk:1 lawes:4 values:2 temperatures:4 following:2 obtain:3 sinusoidal:1 nearest:1 indicated:1 high:1 indicates:2 numbers:1 spb:1 occur:1 axis:8 end:1 siz:1 discussion:3 holds:3 evidently:1 write:1 zn2:1 criterion:3 elliptical:1 those:1 sin:7 simplicity:1 mat:3 o22:1 diagram:11 consequence:1 produce:3 fe:1 president:1 parallel:6 constants:5 fo:8 ambiguous:1 realized:1 drop:1 effective:1 lines:2 st:1 sj:4 si:4 so:23 order:19 typical:1 2sj:1 produces:1 soon:2 years:1 stability:3 thermal:2 magnetoelectric:16 satisfies:1 its:1 blake:2 ligand:1 energies:1 meantime:4 according:2 microscopic:1 systems:1 might:1 huang:1 non:2 greater:2 parabola:1 practice:1 landau:1 mention:1 they:1 miyasaka:1 rotation:2 now:6 discuss:8 dielectric:1 2u:1 february:1 finite:2 equality:2 2s:1 hamiltonian:1 inequality:3 fields:1 accompanied:2 2j:2 mean:4 el:1 macrophysics:1 successively:2 ej:1 energy:11 reduce:1 idea:1 mnwo4:1 ex:3 magnets:1 quantum:1 our:1 transitions:12 eq:22 really:2 projections:1 magnet:1 shown:8 rev:14 research:1 increase:1 induced:2 ref:3 shows:3 foundation:1 working:1 goto:1 interactions:1 8b:2 cheong:5 8a:1 quite:2 approaches:2 put:1 rises:1 hc2:14 hc1:24 βs:5 radaelli:2 transition:24 v2:1 times:1 turn:2 plane:16 place:6 hence:1 neglect:1 first:13 origin:1 symmetry:1 number:2 reaches:1 spiral:20 xz:1 xy:11 reached:1 electronic:1 taniguchi:1 given:14 temperature:5 revival:1 introduction:1 leading:2 eqs:12 their:1 cooling:1 appl:1 too:1 frame:1 gives:4 tfe:3 continuous:3 park:4 part:4 hur:2 focusing:1 than:12 cosθ:1 approximation:1 argyriou:1 zero:3 limiting:1 collinear:21 determined:2 str:1 were:1 russia:1 result:6 iwasa:1 mater:1 qualitatively:2 seen:4 orders:4 lie:1 angle:10 ferroelectricity:10 depending:2 jxy:33 mechanism:3 polarization:6 majority:1 materials:5 take:2 bilinear:1 play:1 electric:8 connected:1 phase:41 abe:1 considered:3 clear:2 flop:1 stronger:1 uri:1 ramirez:2 electrons:1 physics:1 lying:1 balatsky:2 show:3 supported:1 solutions:4 find:7 ground:2 giant:1 based:1 ba0:1 state:2 should:6 only:8 moriya:1 helix:2 hope:1 do:1 goes:2 vajk:1 expectation:3 satisfied:1 ones:2 dy:2 rmno3:2 approach:3 arxiv:1 paper:2 antiferromagnetic:3 exists:3 sensitivity:1 observed:1 yildirim:2 see:3 sec:4 devices:1 best:1 phases:6 compounds:5 nuclear:1 paraelectric:4 enough:7 between:11 frustrated:2 notice:1 recently:3 jz:27 nature:2 js:2 incommensurate:7 key:1 analyzed:1 configuration:1 discontinuous:3 cos:14 last:2 entin:2 many:1 taking:2 equal:5 zeeman:1 etc:1 dated:1 jonas:1 regimes:2 expression:1 finds:1 comes:1 among:2 co:1 opposition:1 point:2 address:1 corresponds:1 grants:1 moreover:2 basing:1 zimmermann:1 due:2 been:5 describes:1 interest:2 anomaly:1 fig:15 6a:2 direction:3 corresponding:6 sergienko:1 quantities:1 kenzelmann:2 demand:2 c2:2 c1:5 spin:18 present:3 case:8 exception:1 novel:1 pacs:1 solid:1 estimations:1 appearance:1 value:7 while:1 mostovoy:2 eij:3 phenomenological:1 thus:3 vm:1 iv:3 ii:9 cant:1 cond:3 ni3:1 conical:1 rfbr:1 different:2 grant:1 things:1 lett:8 same:2 chapon:2 unity:3 complex:1 nagaosa:2 dimensionless:1 several:1 neutron:1 higher:1 used:1 imply:1 upon:1 effect:2 possible:1 moment:5 harris:5 kim:1 lower:5 modes:1 scenario:1 programs:1 minimize:1 analysis:3 solids:1 without:2 tokura:2 model:2 thd:1 arising:1 mfa:5 ferroelectrics:2 proposed:3 being:1 superconductors:1 2jz:4 onset:3 density:1 regarded:1 lattice:4 treatment:1 easy:1 role:2 saturation:3 depends:2 easily:3 term:1 cf:1 smallness:1 increases:1 canted:1 using:8 qualitative:3 separately:2 eel:1 unstable:1 become:2 tbmno3:2 collective:1 spins:18 sketch:2 right:3 classical:4 some:2 begin:1 experiments:1 respect:1 ferroelectric:7 nonzero:1 gradually:2 describing:2 lead:5 footing:1 sr1:1 o8:1 o5:1 o4:3 minimization:1 equivalent:1 each:3 perpendicular:2 expansion:1 yamasaki:1 found:7 properties:3 about:1 ferromagnetic:3 coexist:1 sri:2 discussed:5 dependence:1 o:4 reduced:1 a2:1 wohlman:2 coexists:1 efforts:2 introduced:1 into:6 within:7 ahn:1 three:1 down:1 because:1 proportional:1 nowadays:1 elastic:2 aharony:2 indispensable:1 there:11 canting:1 start:2 cauchy:1 frustration:4 was:2 function:3 form:8 hs:1 arima:2 but:2 displacement:2 ho:1 russian:3 hc:4 line:12 he:1 directed:3 lynn:1 made:2 instructive:1 whether:1 characteristic:1 maximum:2 us:6 work:1 below:6 ui:1 critical:4 planes:1 fluctuations:2 similar:1 expect:1 strongly:1 constant:5 certain:1 abstract:1 influence:1 6b:2 metals:1 denote:2 fabricating:1 fiebig:1 ing:1 regime:3 functions:1 no:1 dashed:1 whereas:1 when:4 detail:1 field:35 other:3 electrical:1 recognition:1 nu:1 conclusion:2 noncollinear:4 ru:1 ui2:1 sharma:1 structure:7 correlated:1 implies:1 coupling:14 assume:1 together:1 time:1 4b:3 4c:5 4a:1 |
0704.3661.txt |@word represent:1 concept:1 sci:1 consider:5 scratch:1 concern:1 results:1 leads:2 tripartite:1 commute:1 preserves:1 equivalence:2 tr:1 young:1 under:2 crest:1 worth:1 norm:1 division:1 supported:1 advantage:1 very:1 choice:1 every:1 difference:3 condition:4 entire:2 school:1 tra:2 notes:1 trb:1 tre:1 eve:11 large:1 smaller:1 deutsch:1 direct:2 feasibility:2 imply:1 cost:1 further:1 what:2 errors:6 bb:34 sum:1 version:3 conduct:2 shared:1 public:4 contrast:1 satisfy:2 ρab:18 respectively:1 machikaneyama:1 never:1 here:5 understanding:1 adachi:1 mes:1 alone:1 σaa:20 standard:2 vbb:1 popescu:1 resulting:4 provable:1 bob:25 postponed:1 options:1 pp:1 tasks:4 useful:1 projection:1 extra:15 apr:1 merely:2 aimed:1 achievable:3 apply:4 use:2 asymptotic:2 would:2 prove:7 next:2 classically:1 depicted:2 call:2 therefore:1 more:1 successful:1 share:1 about:1 cooperate:1 particular:1 must:2 ρa:1 springer:1 onig:1 ρe:11 science:3 work:1 resources:1 following:6 example:1 unconditional:2 proof:6 control:10 claim:1 stated:1 calculation:1 bennett:1 distillation:18 states:2 numbers:2 want:1 allowed:2 uaa:4 uac:7 information:1 end:2 goal:1 provide:1 holds:1 write:1 unitaries:1 ent:4 pure:1 significance:1 instead:1 simplicity:1 de:1 may:2 after:9 tries:3 produce:3 data:1 third:1 whenever:1 quantify:1 grant:1 purification:1 rather:1 ones:1 so:1 allow:1 taking:1 definitions:1 order:2 operations:1 restriction:3 executed:1 help:1 over:7 choose:5 held:1 paper:1 through:2 japan:2 fidelity:2 its:4 before:3 interesting:1 imperfection:6 actually:1 lect:1 production:1 systems:7 alter:1 them:1 seeking:1 matches:1 ekert:1 yc:2 qab:2 fig:4 introduce:1 number:1 they:9 φi:4 yq:6 now:4 nor:1 execute:1 university:1 inequality:1 transmitted:1 each:1 renner:1 macchiavello:1 formulate:1 map:1 doing:1 ed:4 osaka:2 related:3 ex:1 measure:3 quantum:15 operation:6 eq:7 really:1 secretly:1 shown:1 space:1 restricted:1 since:5 rev:5 hayden:1 math:1 shows:3 monotone:1 given:2 undo:1 quite:1 approaches:1 jozsa:2 additional:1 definition:2 prepare:3 created:1 could:1 feasible:1 terhal:1 place:1 hence:9 onto:3 first:3 vaa:1 symmetry:1 omitted:1 powerful:1 primary:8 ρabe:12 done:3 construct:2 another:1 carry:2 message:1 precisely:1 size:3 guess:1 necessarily:1 indicate:1 leading:2 system:9 least:1 their:2 assumption:1 observations:1 statement:1 wootters:1 final:4 speaking:1 gives:2 tool:2 exactly:2 proving:2 took:1 copy:1 than:2 distance:2 fuchs:1 require:2 see:3 distill:1 project:1 exclusive:1 were:1 outcome:2 comput:1 saitama:1 argument:1 conjugate:6 need:1 seen:1 any:1 contents:2 sat:1 subsystems:1 τab:2 τac:2 efficient:1 latter:1 ideal:1 without:2 take:1 many:1 channel:20 kawaguchi:1 fundamental:1 trace:3 opposite:2 tallies:1 measures:6 pair:2 measured:1 class:1 qkd:6 kd:6 considered:1 clear:1 detectors:1 drive:1 bipartite:1 proceedings:1 principle:1 physics:1 fact:3 shor:1 show:7 random:1 implying:1 relation:1 dimension:1 trivial:2 find:1 just:1 explain:1 written:2 should:2 only:2 going:1 local:2 achieve:2 dn:2 do:2 his:1 triangle:1 invoke:1 dd:1 scientists:1 overall:1 cannot:1 subscript:1 secondary:9 resource:2 course:1 conditions:1 arxiv:1 yield:2 qi:2 view:1 apparatuses:1 requirement:1 exists:3 j0:2 toyonaka:1 namely:4 discarding:1 existence:2 discussions:1 close:4 satisfies:2 clarifies:2 preparation:1 satisfying:1 ways:1 tcc:1 state:35 between:10 neither:1 approach:4 controllability:1 available:1 comparable:1 recently:1 ability:1 complementary:9 key:27 observable:11 essentially:3 cor:2 σc:5 freely:1 σa:6 against:2 connection:1 lo:1 distinction:2 whole:1 aa:2 jj:2 point:2 unexpectedly:1 corresponds:1 insist:1 applicability:1 wider:1 cr:1 masato:1 considering:1 ensures:1 described:2 basis:3 addition:1 three:1 been:1 secret:3 combined:1 ph:7 define:6 direction:2 enable:1 corresponding:1 both:4 quantities:2 sufficient:1 subspace:1 gen:1 coherent:2 oppenheim:2 coherently:2 demand:1 ebit:4 maximally:5 protocols:6 pacs:1 value:2 choices:2 will:1 while:2 suppose:2 error:4 aid:1 0x:14 opt:1 unitary:3 thus:1 ii:17 ij:9 supremum:1 different:5 authenticated:1 author:1 perform:1 same:7 imoto:2 quant:7 arguments:1 distilled:4 party:1 ac:6 independent:1 used:1 cptp:1 hand:2 uses:1 entanglement:17 edp:4 task:10 scenario:11 possessed:1 well:1 roughly:1 obviously:1 materials:2 stating:1 latest:1 restore:1 abilities:1 protocol:29 proposed:1 being:1 captures:1 obtain:1 photonic:1 sources:1 thanks:2 using:9 alternative:6 yamamoto:2 yet:1 regarded:1 characterization:1 potential:1 lett:4 easy:1 theorem:14 eigenstate:5 real:2 koashi:5 decomposed:1 possible:7 entangled:5 distillable:14 sanpera:1 immediately:1 bit:10 unique:1 mod:1 δz:19 helpful:1 δx:17 follows:6 mext:1 conducts:1 alice:26 collect:1 yields:2 arbitrary:1 output:2 security:10 preskill:2 because:2 often:3 classical:21 back:1 specified:1 complementarity:13 proofs:1 lead:2 everything:1 does:1 steps:1 run:1 power:2 bc:2 equivalent:3 communicate:3 agreement:1 mayers:2 graaf:1 hilbert:1 limitation:1 actual:1 carried:2 extension:1 tracing:1 theorems:3 practical:2 mutually:1 extensions:1 obeys:1 discard:1 complimentary:1 slightly:2 presence:1 communication:17 into:1 bound:1 copies:1 retaining:1 parties:3 refined:1 van:1 log:15 her:1 few:1 strictly:3 there:7 reduction:1 signifies:1 low:1 was:3 naturally:1 form:3 smolin:1 regard:1 but:5 understandable:1 hb:2 remote:1 ha:4 true:2 enlarging:1 he:6 applying:3 horodecki:7 whether:2 up:2 us:4 record:2 operationally:1 ud:1 distribution:1 ua:3 called:1 mechanics:1 pii:1 pij:3 ab:17 proved:1 defined:6 stronger:2 disclosing:1 meaningless:1 ous:1 engineering:2 proves:1 chau:1 ing:2 physical:1 pω:3 no:8 whereas:1 when:2 virtual:4 graduate:1 application:2 other:4 department:1 out:5 concerning:2 nice:1 divincenzo:1 prepared:1 meaning:1 ubc:5 variable:1 implies:7 auxiliary:2 assume:5 requires:1 required:1 together:1 cpy:12 time:1 observables:4 decoherence:2 starting:2 once:1 |
0704.3663.txt |@word limited:2 consider:12 rev:18 magnetic:2 focus:1 gy:1 chiao:1 leads:2 known:1 fout:2 expressions:1 gk:3 scr:1 simon:2 subjected:1 technique:1 supported:1 finally:2 γh:1 present:3 analogous:1 elektron:1 1j:2 activities:1 doped:2 amplitudes:2 advantage:1 kraus:1 very:1 role:1 tends:2 conditions:2 results:5 gou:1 electron:1 refractive:5 resonant:8 specific:3 difference:2 condition:5 incoherent:2 presented:2 positions:1 t2:27 solution:3 t1:6 large:2 vector:4 small:2 optics:1 noted:5 fleischhauer:4 polzik:2 application:2 work:1 zh:1 antinodes:1 ohlsson:1 maximization:4 direct:1 pulse:38 approximation:2 rate:2 substituting:3 implemented:1 zp:31 leakage:1 repeaters:1 linear:2 spectral:3 index:5 interatomic:2 section:1 dephasing:2 uniform:1 current:1 matsko:1 optimization:3 above:2 replaced:2 increasing:3 consisting:1 thin:2 coefficient:2 full:1 ms:4 fiz:1 respectively:3 error:1 here:11 atoms:9 free:1 groups:1 address:1 directions:3 based:3 along:5 sherson:1 equations:2 obtained:2 ref:1 incoming:9 numerator:1 institute:1 root:2 vectors:2 allows:2 host:2 eberly:1 periodic:1 rareearth:1 usually:4 resonance:1 narrow:4 involves:2 useful:4 divide:1 stray:1 slices:2 apr:1 conclude:1 planar:1 emptied:1 vac:3 singlephoton:2 electromagnetically:1 aimed:2 welch:1 apply:2 counts:1 total:10 unit:1 eiωt:1 use:2 additive:1 takes:2 would:1 prove:1 sake:1 contains:2 moiseev:4 few:1 sample:6 program:1 therefore:6 memory:10 taken:1 themselves:1 type:2 until:1 more:2 separated:1 flat:1 successful:1 becomes:3 operators:1 apparent:1 emission:8 gorshkov:2 possession:1 carrying:1 impulse:7 varying:1 corresponding:6 hole:1 iv:1 iii:2 high:3 account:3 ma:1 equation:2 when:5 modified:1 london:3 alexey:1 ere:1 macrophysics:1 temperatures:2 transparency:1 following:4 spontaneous:6 example:5 performed:1 control:3 ions:2 calculation:1 expanding:1 arise:1 organized:1 involve:1 numbers:1 allowed:1 axis:4 information:8 needs:1 end:5 straightforward:1 carriers:2 rather:1 feature:1 write:4 located:1 criterion:2 adjacent:1 opt:5 instead:4 ensemble:6 chaneli:1 profile:1 simplicity:1 lan:1 de:1 may:12 after:3 derived:1 minimized:1 substitute:1 applications:1 snr:3 wave:17 response:10 short:5 effective:1 emit:1 negligibly:1 light:7 author:1 explicit:2 correspond:1 provide:1 so:5 allow:1 suggest:1 tittel:2 retrieval:9 typical:3 restriction:1 schwartz:1 developed:3 pointed:1 mainly:2 cook:1 paper:3 pulses:10 filters:3 during:3 satisfies:2 linewidth:3 its:5 before:3 geometrical:1 group:1 symmetry:1 ln:1 unity:2 scully:3 writing:7 absence:1 fig:6 sørensen:2 main:2 fin:25 them:5 return:1 mølmer:1 material:3 evolution:1 matsukevich:1 oll:8 emf:1 effects:2 optimal:18 front:1 now:3 hall:1 inhomogeneously:2 matched:2 easily:1 term:3 hereafter:1 ribordy:1 characterizes:1 university:1 level:3 sufficiently:1 inequality:1 mode:1 each:6 found:1 lλ:1 side:2 characterized:1 referred:1 homogeneous:4 schemes:1 ei:3 significantly:1 dωk:1 proposals:1 energy:6 reduce:1 julsgaard:1 inhomogeneous:1 frequency:7 static:1 expect:1 combining:1 quantum:26 our:2 approximated:2 transitions:6 eq:18 out:6 maximizes:2 ru:1 shown:3 rp:2 impurity:1 space:2 since:3 interference:2 fx:1 acting:1 hill:1 i0:1 print:1 induced:1 cause:1 rj:4 theory:5 retrieved:2 sio5:2 pumping:1 possibility:1 mapping:1 absorbed:1 approaches:1 york:4 besides:3 put:1 region:1 beginning:1 definition:1 interaction:5 created:8 suter:2 starts:1 transition:10 times:1 length:2 transfer:4 uses:1 teor:1 approaching:1 onto:1 lumin:2 first:6 there:2 features:2 probability:14 omitted:1 offresonant:1 number:2 echo:1 kuzmich:1 approximately:1 another:3 4d2:1 thick:3 electronic:1 given:4 destructive:1 introduction:2 eqs:5 1k:2 system:21 least:2 reconstructed:1 statement:1 burst:1 white:2 scheme:10 structures:1 store:1 gives:1 elaboration:1 nilsson:5 ity:1 academy:1 reversed:7 exactly:1 transverse:1 ix:1 part:2 suitability:1 manipulation:4 than:7 population:1 tonoise:1 distance:4 colleagues:1 polarized:1 determines:1 iteration:2 see:5 reconstructing:1 states:21 determined:3 modulators:1 amplitude:9 were:2 macfarlane:2 enables:1 russia:1 result:4 raman:1 aˇsek:1 lines:2 kennedy:1 mind:1 argument:1 regime:1 say:1 2t1:5 manner:1 2t2:5 seen:1 demonstration:1 any:1 numerics:1 rostovtsev:1 zero:1 once:1 lim:2 latter:3 able:1 isolated:1 polarization:1 sciences:1 materials:3 square:2 take:1 εk:4 online:3 finding:1 negligible:1 moscow:1 absorbtion:2 annihilation:1 pryde:2 electric:1 trace:1 opposite:4 goldman:1 denominator:1 systems:2 impurities:1 most:2 optimized:1 regular:2 pr3:1 device:2 burnham:1 measured:1 kc:1 eksp:1 reduces:1 considered:4 calculated:1 broadened:9 metal:1 order:5 kr:9 optical:7 kw:6 principle:2 exp:7 αx:5 fact:1 quantity:1 precise:1 intensity:1 show:1 absorbing:4 detection:2 authors:1 dipole:3 rotating:1 superradiant:3 earth:1 thickness:1 d2:2 find:1 ground:2 ratio:10 ensembles:1 implementation:1 distributed:3 written:5 should:11 moments:1 only:9 explicitly:1 factor:2 employed:1 over:1 achieve:1 regularly:1 do:1 goes:1 means:3 simplest:1 kind:2 law:1 ones:2 dz:1 preparing:1 reversal:1 new:4 reconstruct:1 dt:5 processes:3 amid:1 radar:1 fields:2 arxiv:2 summary:1 intervals:1 through:6 qk:1 view:1 ik0:1 reference:1 achieved:3 signs:1 j1:2 packet:11 observed:1 namely:1 sec:2 devices:2 enhanced:1 discussions:1 terms:1 fidelity:1 techniques:3 preparation:3 phases:1 y2:2 interacting:1 manson:2 subsequent:1 αz:1 sites:1 propagates:2 crisp:1 state:25 jth:1 envelopes:2 between:2 prentice:1 reading:2 approach:4 αl:17 timevarying:1 wide:1 grained:1 recently:1 creating:1 relative:1 nature:3 qubits:2 emitted:4 efficiency:11 vanishing:1 windows:1 extent:1 analyzed:1 yelin:1 jetp:1 suppressed:4 distribution:4 thank:1 concentrated:1 both:1 providing:1 last:3 many:1 taking:3 equal:5 quantization:1 fulfilled:1 april:1 connection:1 dated:1 context:4 0j:2 mean:1 whole:2 experimental:2 among:1 relevant:1 point:1 simple:1 relaxation:2 corresponds:4 zubairy:1 dimensional:1 homogeneously:7 decreases:1 kocharovskaya:1 moreover:2 indefinite:1 considering:2 broadening:1 described:1 sangouard:1 second:3 source:1 addition:1 create:1 radiative:1 due:4 been:3 shortening:1 much:4 slowly:2 coarse:1 basic:2 expected:2 ph:2 empty:1 define:2 life:3 controlled:1 proakis:1 coherence:1 photon:38 krausz:1 coherent:6 lift:1 recalled:2 external:3 c3:1 denote:1 spin:1 former:1 those:4 case:15 multi:1 laser:3 eit:1 kazan:1 pacs:1 solid:3 value:7 transformation:1 will:5 technical:1 near:2 proves:2 suppose:1 promising:2 situation:1 eik:1 pits:1 procedure:5 ras:1 bin:2 cylinder:1 larger:4 almost:4 reproducibility:1 sellars:2 thus:1 non:2 according:1 ii:2 reads:2 im:1 cone:1 crystals:1 k0:5 acknowledgments:1 capture:1 different:3 pis:1 propagation:6 media:1 radiation:4 cross:1 same:6 clearly:1 8πs:1 stimulated:1 quant:2 digital:1 several:2 exponential:2 used:6 peaks:3 i1:1 comprehensive:1 numerical:1 upon:2 hand:7 ion:1 moment:20 edges:1 moving:1 collinear:1 changing:2 normalization:4 fourier:1 schr:1 modes:3 minimize:2 expression:1 semiclass:1 well:4 knc:1 analysis:1 obviously:1 academic:1 without:1 coordinate:4 position:1 model:1 cryogenic:1 proposed:3 being:1 generally:1 half:1 obtain:8 shape:18 stored:7 atomic:35 world:1 followed:1 macroscopic:2 previous:1 oriented:1 ham:1 zoller:1 density:12 absorption:15 photons:6 bell:1 except:1 signals:2 color:3 interested:1 lett:6 versa:1 input:5 excited:4 generalized:1 identical:4 depends:1 read:6 spatial:4 possible:7 period:1 dark:1 outcoming:1 background:2 vacuum:2 press:1 using:13 mod:1 loss:4 necessary:4 like:1 shaped:1 contradict:1 signal:16 performing:1 diffraction:1 shapes:1 communications:2 mhz:1 follows:5 completely:1 output:6 hyperfine:3 collective:10 spins:1 therein:1 parity:1 right:3 wavepackets:1 classical:4 sequence:1 discontinuities:1 fresnel:1 creation:5 some:8 back:2 respect:2 duration:3 eze:1 extended:7 erator:1 scales:1 provided:5 slice:9 dense:6 broadband:1 electromagnetic:3 integration:1 comments:1 instantaneous:1 does:1 provides:1 assuming:2 stefan:1 bessel:2 kozhekin:1 process:2 noise:12 power:1 arbitrary:1 bj:2 perpendicular:1 forming:2 linewidths:1 notably:1 setups:1 step:1 afzelius:1 zibrov:2 although:1 mcgraw:1 standpoint:2 optimize:1 about:2 works:2 rare:1 commun:3 discussed:4 dependence:1 o:3 briegel:1 involving:1 presidium:1 neighbor:1 introduced:1 consequently:2 op:1 eisaman:1 cambridge:1 real:2 burning:1 scattering:2 communication:2 into:10 within:3 numerically:1 h4:1 three:2 down:2 phase:8 en:1 references:1 operator:1 fiur:1 pabs:1 additional:1 prepare:2 assumed:2 initial:3 question:1 long:1 width:1 describes:1 low:2 terminates:2 series:1 forward:6 was:5 function:19 medium:22 form:3 phenomena:1 subradiant:19 but:4 volume:6 atom:3 russian:1 line:10 highest:1 true:1 coupling:1 directed:2 begins:1 tarasov:1 made:1 applying:2 embedded:1 kessel:1 lukin:5 characteristic:1 inside:1 dω:2 maximum:11 quantitatively:1 ur:1 crystal:1 below:3 converted:1 limit:4 pl:1 pumped:1 problem:1 andr:3 called:1 gisin:4 strongly:1 bearing:1 cirac:3 constant:3 defined:1 detectors:1 ak:2 direction:3 general:3 oscillations:1 single:20 replica:5 wavelength:3 lifetime:1 hamiltonian:1 physical:1 functions:2 compared:4 us:3 dotted:1 no:2 dashed:2 whereas:1 storage:19 detail:1 field:18 other:7 detected:2 papers:1 np:12 jenkins:1 igk:1 conclusion:1 optically:11 picture:1 kinds:1 superposition:1 excitation:8 uniformly:2 odinger:1 generated:1 peak:5 describing:1 structure:1 zbinden:1 fk:7 implies:1 longer:2 vice:1 assume:7 cauchy:1 dτ:10 interval:1 packets:2 depth:1 time:34 far:1 iωt:3 decoherence:1 backward:1 having:2 4a:2 |
0704.3664.txt |@word limited:1 partial:1 consider:15 squared:4 global:6 results:10 leads:1 gf:2 ginzburg:5 maxima:3 follow:1 faster:1 contributions:1 scp:5 devoted:1 λij:3 certainly:1 depend:1 calculate:2 a19:2 presents:1 v12:4 charge:3 okada:1 negativity:1 th:1 stable:1 kanemura:1 include:1 tc:1 ta:1 eigenstate:2 very:10 keeping:1 diminish:1 choice:2 mixing:3 kasai:1 bubbles:4 difference:12 continued:1 condition:20 dolgopolov:1 plot:4 presented:2 t4:3 mb:4 t2:30 scalar:4 t1:9 large:3 item:1 convenience:1 small:11 eigenvalues:2 m212:32 m211:42 upper:2 strongly:3 slower:1 zi:9 10b:2 10a:1 sin2:3 direct:2 sign:3 approximation:5 second:12 corner:1 further:1 odd:2 ues:1 theory:1 even:7 established:2 what:2 appear:1 rate:1 opaque:1 giving:1 sum:6 m33:3 near:3 current:1 version:1 above:3 new:2 acknowledgments:1 contrast:1 satisfy:1 subdivided:1 simultaneously:2 lee:1 degree:3 modify:2 equals:2 here:11 haber:4 ei:6 illustration:2 lex:1 ratio:2 extrema:72 equations:21 appears:3 change:10 z3:6 obtained:18 search:1 sobolev:1 wesley:1 institute:1 study:5 studied:1 allows:4 guide:1 extremes:1 pick:2 usually:1 opinion:1 changes:2 relation:2 y12:1 uniquely:3 via:9 useful:7 classification:4 danger:1 vii:8 distance:1 expect:1 improbable:1 ma2:8 cβ:2 apply:1 total:1 d72:2 derivatives:2 use:3 takes:1 would:1 d75:1 positive:12 contains:3 quasi:1 next:1 scenarios:1 almost:2 nucl:1 approach:4 therefore:23 m2:28 type:17 2y3:3 today:1 more:7 separated:2 coupled:1 degeneracies:1 h1:1 becomes:5 operators:4 ti:4 corrected:1 vi2:3 appendix:4 particular:5 known:2 cases:3 iii:2 origin:1 must:9 states:21 account:3 ma:4 quartic:1 2yi:1 equation:13 constraint:7 mi:2 mh:31 rκ:1 reproduce:1 itself:1 values:25 rewritten:2 freedom:2 following:2 modifies:1 barroso:2 spontaneous:1 example:2 history:2 omit:1 cosmological:1 give:1 calculation:2 preserving:1 ann:1 high:2 effectively:1 minimum:44 14b:1 numbers:2 degenerate:5 allowed:3 tan:4 quark:1 axis:4 goal:1 discussion:8 breaking:5 feature:1 write:1 nontrivial:1 pure:1 answer:1 acta:1 guarantee:1 parameter:2 sin:5 profile:1 alternative:1 express:3 description:6 14c:1 after:6 m2ij:4 santos:3 applications:1 plane:3 summarize:2 data:2 types:6 realized:9 short:2 natural:3 effective:1 higgs:41 light:1 sartori:1 explicit:7 correspond:2 su:1 cosmology:2 cannot:10 so:8 sect:11 sm:3 definitions:2 vapor:1 order:8 exotic:1 neglect:1 14a:2 hierarchy:3 developed:1 lsm:2 choose:2 characteristic:1 presence:1 report:1 paper:3 including:1 2v:1 statistical:2 left:5 mentioned:5 kinetic:2 y2:55 its:7 ech:6 features:5 regions:2 derive:1 group:3 decay:1 energies:10 interesting:2 37c:1 37b:2 vicinity:1 lh:3 shifts:1 parts:2 fig:5 renormalizable:1 hidden:1 main:6 might:1 ly:2 yi:38 them:2 yj:1 gibbs:7 combination:1 ya:1 hunter:1 processes:1 introduce:1 break:1 bang:2 effects:6 they:3 1b:1 rotation:1 now:8 hepph:3 discuss:8 2t:3 easily:3 term:11 finite:1 cpviolating:1 university:1 2z:1 realistic:1 inequality:3 2a:2 2b:1 fields:16 found:4 constraints:3 homogeneous:1 domain:3 en:3 24a:3 novosibirsk:2 24b:2 colder:1 energy:27 kane:1 idea:2 related:3 t3:21 isospin:2 ex:1 quantum:1 our:16 happen:2 transitions:7 eq:14 special:1 out:2 rt:7 matrix:15 part:1 space:5 since:5 lagrangian:9 research:1 particles:3 re:3 v13:1 parameterization:1 ref:1 ri:3 shows:5 39b:1 39a:1 earlier:1 linear:5 interactions:1 b37:1 mechanisms:1 diagonal:3 standard:3 reason:2 perturbation:2 formation:1 besides:2 ecp:9 intermediate:1 estimate:1 nie:1 generate:1 forbids:1 additional:5 definition:2 interaction:6 r2:9 could:1 transition:6 m21:1 m22:3 place:1 massive:4 arccos:1 corrections:9 degeneracy:4 think:1 colliders:1 first:12 xj:1 xi:20 vacua:3 symmetry:42 variables:1 xa:1 sinβ:1 number:4 exact:3 obeying:1 done:1 fast:1 another:4 precisely:1 horizontal:1 illustrate:1 given:9 toy:7 temperature:5 similarly:1 introduction:1 eqs:4 system:20 1a:1 their:6 cooling:4 2hdm:8 fermions:4 calculations:1 realization:8 scheme:1 final:1 observations:2 dolan:1 statement:1 electroweak:7 ix:2 weakly:6 davidson:1 cosβ:1 authors:1 x2:9 x3:9 x1:8 than:7 coefficients:3 relative:1 kind:1 determines:2 sectors:1 accordance:6 too:3 tree:2 depends:2 modified:1 preparation:1 matter:3 future:4 doubly:3 tion:1 gives:10 boson:7 russia:1 motivation:1 sb:4 false:1 generality:2 rewrite:3 correction:3 modern:2 mind:2 vn2:1 need:1 seen:2 constrained:2 orders:1 relatively:1 mii:3 mij:1 zero:1 depending:2 efficient:4 latter:7 ideas:1 mechanism:1 note:8 mix:1 potential:105 ex2:1 generalized:1 reparametrization:4 degenerated:3 transparent:1 realizes:6 added:1 electric:2 normal:1 any:1 versa:2 systems:1 most:5 preliminary:2 phase:22 why:2 mh1:1 don:1 considered:8 calculated:1 coincides:1 higgses:1 ext:9 points:12 opposite:1 quadratic:3 subgroup:1 physics:3 section:1 fact:2 quantity:9 sector:5 phenomenon:1 isosinglet:1 violation:15 text:1 supported:1 notations:2 russian:1 gauge:4 solutions:14 d9:1 carefully:1 substituting:1 rough:1 determined:5 find:4 impact:1 finally:1 based:1 parameters:28 situations:1 written:11 should:1 jan:1 only:24 explicitly:9 positively:2 2m12:1 factor:3 local:5 extremum:153 perturbations:7 equilibrium:1 do:2 zeldovich:1 notation:1 means:5 dependent:1 dubinin:1 between:9 expectation:1 valente:1 satisfied:2 ones:1 words:2 despite:1 combinations:1 during:7 2mh:1 admissible:1 gray:1 evolution:6 introduced:1 x21:1 arxiv:1 kobzarev:1 investigate:1 softly:8 cf:2 contain:2 analytical:1 fixed:3 doublet:3 looks:1 2y2:1 set:3 exists:10 κm:1 violated:1 signs:1 respect:1 up:5 observed:2 y1:65 see:19 a1a:1 result:1 supercooled:1 discussions:1 y3:41 phases:3 satisfying:1 inequalities:6 subsequent:1 positivity:8 definite:3 thankful:1 artificial:1 label:3 symmetric:5 state:30 won:1 various:1 simplest:3 subscript:3 reading:1 conditions:14 x23:1 x22:1 preserve:2 terms:13 maximums:1 vertical:1 nature:1 comp:1 weak:5 however:4 vanishing:2 distinguish:2 jetp:1 come:1 both:2 cos:13 limits:2 many:6 taking:3 according:4 multiloop:1 etc:3 present:4 sβ:2 kastening:1 masses:11 cos2:1 among:3 ch:7 point:20 simple:6 period:1 parametrization:2 m11:2 directions:1 m12:8 non:1 coordinates:2 polynomial:7 rph:4 cp:51 factors:3 pseudoscalar:3 considering:1 slavnov:1 described:3 differs:1 basis:2 addition:3 radiative:4 due:4 been:1 z1:5 describes:10 complicated:1 z2:20 basic:2 expected:1 substraction:1 ph:9 tan2:1 define:4 v23:1 v22:4 direction:3 corresponding:4 deeper:2 scalars:1 quantities:11 sufficient:3 photon:3 essentially:1 tential:1 observe:1 2ij:1 former:1 those:3 case:60 heavier:1 look:3 frozen:1 conserved:1 value:8 spontaneously:6 will:4 cern:1 while:6 viii:2 aij:3 eii:7 aid:2 property:2 region:6 loop:6 identical:2 changed:4 a4:1 vg:1 phenomenological:1 vi:4 violating:11 vn:1 iv:2 ii:41 reads:1 good:1 vt:1 ewsb:13 fermion:1 currents:1 rfbr:1 different:26 develop:1 sov:1 ewc:7 arguments:1 lett:3 same:2 check:2 φa:1 φb:2 complex:8 split:1 widely:1 φi:20 φj:2 φk:3 solution:15 higher:4 independent:6 used:2 cubic:1 isodoublets:1 numerical:1 upon:1 hand:3 v0:5 v1:18 v2:30 v4:19 purpose:1 changing:1 opportunity:1 electromagnetism:2 lower:2 correspondent:1 nevertheless:1 studies:2 well:3 walls:4 analysis:6 scpv:30 rii:3 without:5 components:2 position:1 model:25 otherwise:1 parametric:1 dimension:2 charged:42 distances:2 proposed:1 minima:10 moments:1 generally:3 21a:2 obtain:12 product:1 transforms:2 using:4 differentiation:2 λi:6 speed:2 candidate:1 ny:1 yu:1 extra:2 seems:2 except:1 wall:4 realize:3 m222:40 unambiguously:1 transformed:3 attractive:1 easy:3 theorem:1 diagonalization:1 guarantees:1 mh2:3 transformation:6 5c:1 take:1 real:26 polonica:1 yukawa:6 around:1 fate:1 iξ:2 big:2 φ0i:1 possible:13 corresponds:2 early:3 inflation:2 21b:1 vacuum:42 world:3 λai:1 unique:1 rephasing:4 domains:3 formal:1 loss:2 massless:1 necessary:12 like:7 workshop:1 eew:3 adiabatic:1 unnecessary:1 substitution:1 specific:2 grants:1 either:3 arbitrary:5 become:4 works:1 soft:3 qualitative:1 replacement:1 2iξ:2 parity:2 right:6 old:1 often:2 deal:3 sequence:1 obliged:1 some:14 a16:1 sher:1 examples:1 nondiagonal:1 a10:1 nonzero:1 provided:1 ferreira:2 a13:1 isoscalar:1 fourth:1 quarks:1 a8a:1 eiξ:3 does:3 decomposition:3 eliminate:1 provides:1 y22:1 analyzed:1 minimal:3 limitations:1 destroys:1 varying:1 obey:5 minimization:3 simultaneous:1 krawczyk:3 retains:1 equivalent:1 each:10 37a:2 silva:1 expansion:1 disappeared:1 broken:7 evolve:1 polynomials:1 2m:1 mssm:4 imaginary:2 properties:7 stage:3 comparison:3 about:2 d74:1 extension:2 saddle:12 universe:17 discussed:13 dependence:2 o:2 reduced:1 2y1:2 range:5 a2:1 obeys:1 mixed:1 mean:3 ivanov:4 okun:2 nsh:1 goldstone:1 conserving:22 rev:10 statements:1 accompanied:1 h3:1 into:8 within:4 integral:1 hypercharge:1 negative:6 κr:2 pair:2 2v1:3 deshpande:1 references:1 determine:3 2v4:1 operator:4 proportional:1 methods:1 argumentation:1 arrow:1 hep:9 classical:2 m4:1 there:6 transform:1 long:2 start:1 conservation:3 bosons:4 way:2 series:1 was:6 naturally:2 lowest:3 interrelation:5 complete:1 form:46 enough:2 but:5 neutral:36 construction:1 goals:2 scales:1 larger:1 elimination:1 line:1 violate:1 coupling:1 absent:2 explaining:1 flavour:1 whether:1 selects:1 variations:1 maximum:3 us:3 below:7 limit:3 fluctuations:2 problem:1 λji:1 similar:3 called:2 isospace:1 detailed:1 interval:2 constant:1 directly:1 addison:1 defined:3 describe:5 influence:1 determinant:3 general:18 single:2 exist:7 subtraction:1 a12:1 a1b:2 dawson:1 ew:10 physical:6 incorrect:1 functions:1 thermodynamical:1 no:7 allow:7 when:4 detail:1 invalid:1 reality:3 rewriting:2 field:10 other:12 details:2 papers:1 mathematics:1 gunion:3 confine:1 realizability:1 conclusion:2 a15:1 picture:6 briefly:2 elements:1 a11:3 generates:1 accidental:2 separate:2 models:1 po2:1 problems:2 a18:2 variation:5 much:1 a3:1 important:8 a5:5 allowing:2 a7:1 a6:1 a9:3 structure:1 auxiliary:2 vice:2 assume:1 cauchy:1 4t:1 cpc:23 together:3 having:2 equivalently:1 mass:27 time:3 moreover:4 4b:3 original:1 4a:2 |
0704.3666.txt |@word limited:1 consider:2 switched:1 caused:3 results:1 research:1 takesue:1 sch:1 21st:1 eligible:1 γr:6 concerned:1 disturbances:1 tr:2 environment:4 charge:9 does:2 tj:1 present:1 th:2 andreev:15 ın:1 kσ:1 case:1 kρ:8 yurkevich:1 far:4 n3c:1 harmonics:2 wave:3 electron:8 zaitsev:1 affect:3 difference:4 matrices:3 condition:3 treating:1 believed:1 disturb:4 gˆa:1 level:1 ref:1 tanh:1 large:4 vector:1 τˆi:1 small:1 shows:1 oscillation:1 hori:1 consistent:1 cosh:1 past:1 widened:1 zero:7 chen:1 further:1 odd:4 spectral:5 will:2 ˆr:1 appear:1 rate:1 ˆz:1 expressed:2 current:19 above:1 net:2 method:1 movement:1 satisfy:1 lee:2 ranged:2 respectively:1 here:7 okubo:1 odintsov:2 reported:1 holistic:1 kurihara:2 mes:1 excess:2 overestimates:1 consideration:1 sind:1 microstruct:1 equations:1 appears:1 superconductor:1 obtained:1 waseda:2 clarendon:1 shift:1 study:1 studied:1 action:3 ponomarenko:1 plotted:1 golden:1 useful:1 convolution:1 esteve:1 explained:1 replace:1 1st:1 summation:1 apply:1 unit:1 recurrence:1 use:2 exciting:1 asymptotic:1 jpn:3 quasi:1 giamarchi:1 sports:1 program:1 therefore:1 averaging:1 taken:1 scope:1 ψa:4 type:1 reflects:2 more:1 novotny:1 lesovik:1 known:2 hold:1 ρa:2 states:1 account:1 tokyo:1 tunnel:1 science:3 equation:2 work:6 holelike:1 values:1 temperatures:1 transparency:2 following:2 im:2 modifies:1 numbers:1 claim:1 renormalization:4 figure:1 process:1 high:1 indicates:5 performed:1 gorbatov:1 counting:1 occur:1 junctions:4 absolute:1 influenced:1 needs:1 predominantly:1 2cm:1 acts:1 cosh2:1 how:1 parameter:1 charging:1 simplicity:2 levy:1 goldbart:2 mat:1 illustrate:1 after:2 derived:1 mendez:1 corrections:2 4th:1 waves:2 law:2 parallel:1 quasiclassical:3 collective:1 liquid:3 grant:1 correspond:1 think:1 cannot:1 green:4 correlation:3 caux:2 order:3 egger:1 s0:3 over:4 soc:3 kong:1 thermal:2 experiments:2 through:5 experimentally:1 japan:2 still:1 excitations:5 its:1 before:1 perfect:1 ld:1 thank:1 decay:2 interesting:1 affleck:1 exhibits:1 lt:1 τz:4 systems:4 into:2 zagoskin:2 them:3 good:1 affected:2 combination:1 safi:1 fig:1 number:5 scaling:1 framework:1 repulsive:7 effects:1 they:3 focus:2 oxford:1 yeyati:1 yu:3 hall:1 2t:3 easily:1 february:1 dirac:1 hereafter:1 university:2 drop:2 2ev:1 sugiyama:1 2e:1 l0:3 l1:3 2l:1 found:5 2i:1 energy:10 enables:1 reduce:1 gaussian:2 used:1 inhomogeneous:1 frequency:6 quantum:4 our:1 ev:16 eq:3 siano:1 out:1 gogolin:1 superposing:1 matrix:1 3rd:1 gradient:1 βm:4 gˆp:2 since:3 lagrangian:1 denotes:2 gˆ:7 δρa:1 performs:1 induced:2 forth:1 math:2 predicted:1 takayanagi:1 interactions:14 free:3 hubbard:1 statistics:2 term:1 besides:2 camino:1 e2:3 interaction:1 chiral:2 ministry:1 argument:1 transition:1 keep:1 length:3 grishin:1 2c:1 hence:1 moving:2 neglect:2 origin:2 probability:2 quasiparticle:4 timeindependent:1 disregarded:1 approximate:1 channels:1 urbina:1 long:5 suspended:1 open:1 separation:1 given:2 temperature:1 capacitance:2 system:1 approximately:2 indicate:1 intermediate:1 stephan:1 1d:8 πt:2 leggett:3 exponents:1 fermions:1 shifted:2 keldysh:1 part:7 simulate:1 authors:1 focusing:1 representing:1 reflection:3 approximation:2 kind:1 slack:1 showed:1 transferred:1 correlators:1 future:1 amplitude:3 were:1 gives:1 treated:1 exhibit:1 lowest:1 fashion:1 apers:1 rewrite:1 fluctuation:3 spectrum:1 alike:1 levitov:1 qualitatively:1 need:1 τˆz:2 sandwiched:1 belzig:1 convenient:1 metallic:1 ideal:1 potential:1 so:3 scatterings:1 averin:3 even:3 play:1 acquire:1 multiple:4 normal:1 compress:1 singlet:2 algebraic:1 said:1 connected:2 kanda:1 pair:2 luttinger:2 segment:1 jørgensen:1 dai:1 exponent:2 kb:1 lerner:1 considered:1 average:5 flow:1 hermele:1 physica:1 electrons:3 reflections:10 clean:1 schulz:1 velocity:2 usual:2 physics:4 lying:2 incorporate:1 shot:5 somewhat:1 show:3 supported:1 kupriyanov:1 injected:2 relation:1 solutions:1 find:2 decade:1 takane:1 indicator:1 studying:1 parameters:1 situations:1 written:2 should:1 only:7 explicitly:1 factor:1 integrable:1 oct:1 do:3 means:1 dependent:1 dc:3 ones:1 during:1 procedures:1 gen:1 becomes:1 adiabatically:3 processes:2 volkov:1 bar:1 densities:2 fields:3 arxiv:1 summary:1 investigate:3 common:1 including:1 fixed:1 interference:2 atomic:1 enhances:1 set:3 electrodes:6 implies:1 physically:1 correlations:2 zaikin:1 kasumov:2 culture:1 see:2 individual:1 result:2 enhanced:1 existence:1 discussions:1 recently:2 electrode:2 caldeira:3 wire:1 probable:1 macroscopic:1 exchange:1 definite:1 tend:1 αa:1 state:1 various:1 stratonovich:1 between:8 limit:4 boundary:3 approach:1 across:3 terms:2 reproduced:1 nature:2 originated:1 interfaces:9 weak:2 however:3 disturbance:1 carbon:1 configuration:1 suppressed:1 uσ:1 abruptly:1 essentially:2 stages:1 many:2 region:5 infinitely:1 sensitive:1 coe:1 dated:1 retarded:2 akazaki:1 comes:1 tll:29 gueron:1 relevant:1 sinh:2 cm:4 point:2 effective:1 period:1 2nd:1 dimensional:4 oshikawa:1 moreover:1 narrowed:1 throughout:1 jetp:2 described:1 tomonaga:1 uρ:3 due:2 been:1 mart:1 int:2 describes:3 treat:1 dtdx:1 refael:1 choose:1 direction:1 resultant:1 quantities:2 θa:4 σi:3 gap:2 bulk:1 θs:2 general:1 spin:5 those:1 selforganization:1 applied:1 inhibit:3 critical:1 josephson:17 pacs:1 superlattices:1 employ:1 while:1 suppose:1 behavior:1 tunneling:4 taking:1 identical:1 ivf:1 changed:1 vf:3 century:1 characteristics:2 deblock:2 thus:2 non:1 rasmussen:1 superconducting:8 bias:2 cond:1 il:1 owes:1 junction:1 avf:1 technology:1 fermion:1 disappear:2 different:2 φs:3 verified:1 σz:1 renormalize:1 φa:3 noninteracting:1 pauli:1 kawabata:1 ichev:1 eilenberger:2 independent:2 investigated:3 dǫ:2 i0:1 effect:11 hand:4 conductors:1 purpose:1 potentials:2 infinite:1 lev:2 off:3 modes:1 scenario:1 charges:1 restricted:1 modeled:1 well:2 contact:2 mod:1 consistency:1 firstly:1 model:3 dimension:2 left:4 maslov:3 being:2 proximity:2 golubov:1 superconductors:8 obtain:1 saleur:1 voltage:5 integer:1 uller:1 relaxations:2 scattering:2 λm:1 previous:1 cut:1 reulet:2 density:14 education:2 internal:4 lett:10 hekking:2 role:1 openings:1 hat:1 momentum:1 supercurrent:6 fluctuating:4 marcus:1 couple:1 possible:1 corresponds:1 increases:1 inhibition:1 cnts:2 press:1 using:1 advanced:2 formal:1 loss:1 like:1 particle:2 reduces:1 adiabatic:2 yields:1 inter:1 reduced:1 because:5 exposed:2 some:2 back:3 bouchiat:2 rodero:1 oscillations:5 extended:1 ourselves:1 provided:1 shinjuku:1 cooper:2 integration:1 comments:1 behave:1 provides:1 assuming:2 gapless:1 morpurgo:1 propagating:2 measuring:1 noise:10 power:3 each:2 oscillating:1 disregard:1 although:3 2m:1 falls:1 stage:1 stone:2 extension:1 theirs:1 discussed:1 o:3 essential:1 addition:2 range:2 act:3 titov:2 introduced:1 lindelof:1 microscopic:1 takeda:1 rev:25 ferrier:1 presence:1 kuznetsov:1 spreading:1 within:2 integral:1 functional:2 down:1 phase:15 right:3 accounts:1 sov:3 operator:1 proportional:1 theoretically:2 cuevas:1 rows:2 additional:1 assumed:2 transform:1 specifically:1 start:1 quanta:1 low:10 crucially:1 forward:1 was:3 gˆk:2 function:3 considerably:1 kane:1 2vf:1 form:2 dok:1 denoting:1 but:2 reminds:1 properly:1 link:2 nanotubes:1 delta:1 sustained:1 dissipative:1 longer:1 absent:1 compute:1 2πd:1 prevents:1 transmits:1 up:1 us:2 grove:1 below:1 owing:1 fermi:5 2πt:2 boldface:1 fluctuations:15 problem:1 pm:4 similar:2 calculated:2 strongly:1 ac:8 rightly:1 defined:2 metal:1 influence:2 deep:1 denote:2 single:1 reservoirs:2 partly:1 hamiltonian:1 regime:2 functions:6 compared:2 susumu:1 no:2 cos:2 whereas:3 nc:2 when:2 field:2 other:5 electrical:1 re:1 spatial:1 department:1 shimizu:1 coherence:8 exp:1 superconductivity:4 fazio:2 center:1 problems:2 commutator:1 peak:2 suppression:1 fisher:2 structure:1 correlated:2 subdivision:1 auxiliary:2 coulomb:2 assume:1 dτ:1 holes:1 rule:1 mass:1 time:4 serious:1 |
0704.3667.txt |@word slope:4 gravities:1 consider:1 results:2 leads:1 scalar:2 generalize:1 computation:2 edu:1 follow:4 roots:2 research:1 ward:5 whose:2 certainly:1 inverse:1 schomerus:1 equivalence:5 a19:2 interactions:1 tn:1 charge:8 program:2 dijkgraaf:1 those:3 th:21 under:3 include:4 norm:3 division:5 amplitudes:4 string:96 returning:1 very:1 differently:1 unfamiliar:2 choice:2 b261:1 witten:3 emphasized:1 matrices:4 condition:6 paton:1 schwarz:2 34b:1 level:10 ref:11 t2:1 solution:1 large:4 convenience:1 indices:1 eigenvalues:1 application:1 zn:5 rom2f:1 zi:12 orientifold:4 foundation:1 10b:1 10c:2 10a:1 direct:1 sign:1 zero:3 pass:1 further:6 cft:18 expressions:1 canonical:1 spectral:8 ˆu:3 ˆv:1 giving:1 d2:1 section:3 selected:1 d3:1 current:2 suspect:1 fractional:5 3c:4 new:10 3a:6 ˆl:6 acknowledgments:1 contrast:1 satisfy:5 full:2 led:1 respectively:3 component:3 residual:1 here:14 understanding:2 intercept:1 groups:1 berkeley:3 active:1 quite:1 equations:2 appears:1 z2:4 z3:2 obtained:4 renormalization:1 institute:1 study:3 studied:3 dixon:2 leaving:1 suggests:1 periodic:1 resulting:1 permutation:9 action:3 resonance:6 ganor:2 involves:1 via:1 although:3 extra:2 9a:1 9c:1 9b:2 unitarity:1 visible:2 total:1 establish:1 unit:1 virasoro:12 use:2 quasi:1 asymptotic:2 usa:1 remains:1 contains:2 negative:2 substitutions:1 dimensionful:3 linear:2 going:1 mysterious:2 generators:6 type:6 theoretical:1 diagrams:1 more:5 untwisted:23 duality:3 relax:1 appending:1 operators:14 emission:7 clue:1 borisov:1 appendix:4 particular:13 known:4 cases:1 iii:1 must:5 high:4 science:1 work:2 theories:7 labeled:1 regions:1 era:1 following:10 dec:1 example:3 zj:5 wang:4 give:1 permutations:1 generically:4 states:8 archetypal:3 dxi:1 arise:1 verlinde:4 mcgreevy:1 information:1 polchinski:1 turn:1 discussion:3 holds:1 xˆ:1 b91:1 zn3:1 resolution:1 fourth:1 ordinary:16 sin:1 either:1 alternative:1 de:4 description:7 algebra:9 may:6 after:1 derived:1 different:1 reflect:1 consequence:2 bear:1 multiplication:1 evaluations:1 types:1 realized:1 introduced:1 sectors:16 gimon:1 computations:2 spectra:5 explicit:3 correspond:1 su:1 element:1 perhaps:1 sagnotti:1 so:6 fundamental:1 friedan:1 polyakov:1 order:4 gµν:1 petkou:1 b500:1 dx:1 gauges:2 indeed:5 stability:2 course:2 paper:6 including:5 cuts:1 differs:1 still:1 refs:8 orbifold:65 dun:2 group:2 thank:1 ln:1 interesting:1 fix:1 affine:4 coordinates:2 lu:1 degrees:2 systems:14 martinec:1 τu:10 defining:2 deformation:1 xl0:1 non:7 than:1 rising:1 dai:1 primary:1 b274:1 half:11 now:5 b279:1 discuss:1 mystery:1 channels:1 february:1 electrostatic:1 university:3 presented:1 hepth:1 mode:5 l0:4 irreducible:2 crossing:2 found:3 2n:2 2i:1 mean:1 subsystem:1 tensor:1 series:2 energy:6 product:1 related:1 used:2 factorization:1 subsec:1 laboratory:1 eq:21 aˆ2:4 pullback:1 shown:2 matrix:15 space:5 obers:4 moding:1 since:1 rev:6 u2i:1 schweigert:2 gˆ:33 geom:1 conjectured:1 b282:1 mξ:1 evaluation:4 correct:2 math:2 shows:1 orbifolds:37 aˆn:6 trajectories:1 theory:20 lawrence:1 8b:1 8a:1 free:7 standard:8 clarify:2 california:3 approach:1 beginning:2 universally:1 b33:1 interaction:1 derivation:4 language:1 geometry:3 persists:1 keep:1 ordering:1 place:1 hence:3 first:5 xj:1 reversing:4 xi:1 xn:1 symmetry:3 horava:2 variables:2 number:2 twisted:86 restrict:1 philosophical:1 reflects:1 57a:1 relations:2 another:1 reached:1 precisely:1 open:61 koba:1 triality:1 given:5 sheet:9 periodicity:1 similarly:1 introduction:2 leading:2 eqs:6 b28:1 system:11 construct:1 1a:6 their:2 1c:5 1b:8 1e:2 1d:1 kµ:1 realization:1 behaved:1 1l:1 gives:3 rabinovici:1 shell:7 statement:1 klemm:1 serve:1 part:2 somewhat:2 kept:1 july:1 x1:1 sˆ:1 connections:1 uτ1:1 target:2 automorphic:1 cyclic:3 lepowsky:1 tree:6 second:1 final:2 hamidi:1 matter:4 classes:1 pairwise:1 amplitude:3 were:1 perturbative:1 exhibit:1 twisting:1 sees:1 7b:1 7a:1 nuovo:2 ann:2 corrigan:1 mind:1 spectrum:4 generalization:2 20d:1 qualitatively:1 need:3 seen:1 leigh:1 null:1 any:5 contents:1 lie:2 wilson:1 constructions:2 helfgott:8 studying:1 latter:2 ruegg:2 gravity:1 note:2 generalized:1 green:1 text:4 channel:1 even:4 begin:3 towards:1 multiple:2 normal:1 consistency:1 most:1 automorphism:2 representation:5 reducible:4 class:4 appear:1 tν:1 consequences:1 ki:1 later:1 graphs:5 talk:1 exp:4 harvey:1 kz:1 physics:5 fact:5 sector:22 phenomenon:1 show:3 jµ:10 supported:1 halpern:23 attempts:1 relation:8 fermions:2 analogue:1 trivial:1 find:3 ground:6 boundaries:2 finally:1 ratio:3 office:2 dividing:1 commutators:2 state:14 should:3 only:6 explicitly:1 candidates:1 reducibility:2 constant:1 dn:4 abelian:4 notation:3 dependent:1 wagner:1 between:5 trees:12 pions:1 ones:1 reversal:2 3b:10 during:1 dt:1 learned:1 schoutens:1 processes:1 fields:3 arxiv:1 expansions:2 doubled:2 twice:2 contain:2 embryonic:1 shapiro:1 set:1 physically:1 cimento:2 national:2 relative:2 see:8 wzw:8 sec:1 result:3 discussions:1 inequivalent:1 correlators:2 theoretic:2 brst:3 clarifies:1 phases:1 qµ:2 interacting:14 ostensibly:1 nuclear:1 lovelace:1 shenker:1 symmetric:3 αc:4 determined:1 identification:2 permutes:1 closed:30 regge:10 ui:2 boundary:1 conditions:12 emissions:1 terms:2 horizontally:1 neveu:1 analogues:1 however:4 operative:1 reproduces:1 comm:2 2αc:1 key:1 clues:1 suppressed:1 tensors:1 both:6 cos:1 last:2 ˆa2:2 many:5 region:1 equal:1 contract:1 b245:1 embedding:1 faces:1 finds:2 among:2 point:2 simple:8 each:3 superstring:1 pole:1 simply:1 conjugation:1 bν:2 branes:1 considering:1 commutative:1 puts:1 basis:1 addition:1 trajectory:1 copies:1 been:4 z1:3 int:12 production:2 change:2 basic:1 expected:2 combine:1 borders:1 prototype:1 reggeized:2 imt:1 quark:2 corresponding:3 reaction:1 quantities:5 sufficient:2 essentially:2 cambridge:1 bulk:2 understand:1 systematic:1 prescription:2 mandelstam:2 present:4 case:6 twist:2 schmidt:1 eit:1 appearance:1 evaluated:1 will:12 fubini:2 while:3 behavior:2 du2:1 conformal:7 a20:1 tµ:3 orientation:50 simons:1 ki2:1 metric:2 formulation:1 encouragement:1 iv:1 ii:3 examined:1 b327:1 dual:8 currents:2 chern:1 confirmed:1 decoupling:2 italy:1 grant:1 halfinteger:2 things:1 cross:1 same:10 clearly:1 pomeron:1 emphasize:2 pauli:1 cargese:2 according:1 dimensionless:4 constructed:3 subalgebra:2 higher:4 extended:23 unconventional:6 trivially:1 bonus:1 boosted:1 decompactified:1 siegel:1 director:1 running:1 off:4 modes:2 no:1 well:7 thorn:2 moded:11 without:1 reexpressed:1 components:1 sets:1 model:8 dimension:1 left:1 summer:1 evslin:3 when:1 boer:4 obtain:4 actions:1 cˆ:27 underlying:1 world:9 facts:1 momenta:8 yet:1 multiples:4 previous:3 speculate:1 conclusions:2 surprises:1 extends:1 lett:4 theorem:1 iπ:5 mod:13 5a:1 transformation:1 momentum:2 5b:1 identical:2 2t:6 nielsen:1 easily:1 read:1 evaluate:2 showing:3 comparing:1 early:1 boost:1 five:1 know:1 brunner:1 press:1 integer:12 sharpened:1 helpful:2 b109:1 fractionally:1 like:1 precise:1 aˆν:1 follows:4 28b:1 freericks:1 automorphisms:4 remind:2 δm:8 byproduct:1 arbitrary:1 jˆ:1 gauge:2 replacement:1 kiritsis:1 parity:2 npoint:1 because:2 methods:3 a14:1 a64:1 some:5 understood:2 linearly:1 examples:4 moreover:1 orientifolds:9 matching:1 provided:2 dimensions:1 deac02:1 though:2 mesons:1 critical:5 eliminate:1 imply:1 2a:5 2b:7 rep:1 vertex:23 equivalent:13 2c:1 conventional:7 eiπ:2 ple:1 chiralities:1 substitution:1 coset:2 properties:3 transformations:1 about:3 central:7 would:2 algebraic:1 freedom:2 fairlie:2 discussed:5 factors:1 o:2 dzn:4 u3:1 act:1 constraints:1 bardakci:4 jν:2 computational:1 presence:1 unbounded:1 integral:3 three:1 down:1 nothing:1 references:1 einstein:1 operator:15 prefactors:1 bosonic:10 letts:2 hep:21 additional:2 few:1 vafa:3 assumed:1 there:4 nucl:9 specifically:1 u2:7 conservation:1 slopes:5 was:7 propagator:5 function:1 form:11 unoriented:3 but:7 hoped:1 construction:13 aµ:2 contractions:1 removed:1 algebras:1 pion:1 whether:1 dz2:2 up:1 us:2 tell:1 below:2 un:1 limit:2 today:1 uj:1 define:1 called:3 strongly:1 fractions:1 associated:2 defined:1 certain:2 abstract:1 tsou:1 chan:2 general:13 dξ:1 exist:2 our:11 identities:6 simplest:1 physical:20 lim:4 d4:2 nn:12 variety:1 whereas:1 nd:1 detail:2 field:10 other:5 remarks:1 special:1 b10:1 papers:1 department:2 conclusion:4 a15:2 picture:2 a17:1 a16:1 a13:1 gross:1 models:4 uniformly:1 a18:3 a1:1 commutator:1 important:1 a4:1 additionally:1 included:1 µu:1 structure:5 fundamentally:1 ghost:1 littlejohn:1 using:2 veneziano:5 4t:6 required:1 original:2 correspondingly:1 mass:5 time:4 4b:5 strings:20 4a:5 |
0704.3668.txt |@word represent:2 now:2 evidence:1 consider:5 pointing:1 gp:2 lagrangian:2 green:1 lack:1 results:24 kernphysik:2 four:2 scalar:30 gd:10 gb:2 c2:2 go:1 follow:1 expressions:3 contributions:27 weakly:1 issues:1 periments:1 certainly:1 terms:3 calculate:1 collisions:2 graph:5 concerned:1 tr:1 deutsche:1 former:2 charge:2 indicate:1 those:17 th:15 under:4 analogous:1 te:1 worth:2 kν:1 ingredient:1 kσ:1 applied:1 belonging:1 amplitudes:5 advantage:1 g0:1 very:8 ously:1 focus:2 sons:1 figs:1 mixing:3 mrtn:1 difference:6 matrices:1 satz:2 leads:3 blaschke:1 facilitate:1 presented:7 issue:2 pacs:1 proposals:1 pearce:1 occurs:1 large:8 solid:5 vector:12 progress:1 lv:1 indices:2 shows:1 cnpq:1 concluded:1 upper:2 work:3 tem:1 consistent:1 estimates:2 prediction:2 literature:2 culations:1 approximation:5 second:3 design:1 gn:3 qualitatively:2 dynamics:3 nefediev:1 panda:3 quite:2 canonical:1 even:6 mu:2 what:4 plays:1 stands:1 brackets:1 section:17 while:5 expressed:1 find:1 version:1 above:4 obvious:2 d1:1 3g:2 consisting:1 mp:3 body:1 pictorially:1 agreement:1 full:9 exchange:54 mechanisms:1 mizutani:1 cal:1 component:4 here:15 understanding:2 behaviour:1 following:2 gm:1 mev:25 excess:7 alone:2 based:11 strong:4 equations:1 satisfy:1 change:4 deduced:1 box:5 instituto:1 antisymmetric:1 weinstein:1 receive:2 involved:1 study:10 larger:10 expression:4 simultaneous:1 resulting:4 pictorial:1 action:2 flavour:1 changes:4 almost:1 involves:2 composed:3 via:2 besides:1 apr:1 pling:1 kudryavtsev:1 sign:1 sizeable:1 gluon:17 depicted:1 thews:1 cassing:1 meson:65 propagators:1 bra:1 use:11 ψy:3 would:5 remains:3 ψp:1 contains:2 anda:1 predictions:5 properties:2 scenarios:3 calculation:4 nucl:22 derivation:4 kinematics:1 therefore:8 qcd:1 taken:5 means:1 panel:3 type:3 eral:1 diagrams:11 more:10 attractive:2 treated:1 pretty:1 operators:3 aware:1 primarily:1 appendix:5 basically:2 particular:3 known:6 cases:1 pieces:2 spinspin:1 exch:1 must:1 me:1 involve:4 account:6 include:2 mc:2 mb:16 equation:3 tremendously:1 mi:1 mk:3 mj:2 reproduce:1 mv:2 values:9 achieve:1 ms:1 mr:7 already:3 making:1 ulf:1 example:4 subnuclear:1 numbers:2 meant:2 indicated:1 klempt:1 process:2 relativistic:1 cited:1 table:9 kρ:2 dependence:1 states:11 indicates:1 assumptions:1 caused:2 performed:1 want:5 dominant:1 standard:2 mn:10 dfg:1 occur:1 forms:4 crucial:2 information:2 hoc:1 provide:2 discussion:2 holds:1 hoffmann:1 evidently:2 far:3 hot:1 influences:2 kondratyuk:1 ordinary:7 parameter:2 dominance:2 simplicity:1 product:1 kroll:1 description:3 may:2 reaction:3 derived:5 fb:1 produce:1 fd:1 waves:1 date:2 summarize:1 wave:7 data:2 fm:4 constants:17 curve:5 stress:1 short:7 attempt:1 outline:1 effective:8 martins:1 ss:2 light:5 sp:1 explicit:2 correspond:1 su:29 rather:2 si:4 wavy:1 so:6 sect:2 writing:1 paulista:1 representation:3 subsequently:1 acknowledges:1 order:17 typical:1 integrated:1 least:2 nucleon:6 developed:3 over:7 insight:1 mainly:1 soon:1 produced:1 course:1 experiments:1 through:3 argued:1 ffe:1 still:1 excitations:1 its:8 before:1 supplemented:1 group:8 manuscript:1 decay:1 energies:5 interesting:2 masses:10 solving:2 boson:2 qgp:3 late:1 resort:1 quarkonia:1 production:3 degrees:5 systems:4 lp:2 covered:1 main:4 emphasize:2 tja:1 them:5 good:2 motivated:1 obtaining:1 outlined:1 practice:1 regarding:1 number:1 mention:2 repulsive:3 effects:1 they:1 4παs:1 multidimensional:1 inelastic:1 discuss:2 overlap:1 term:1 indeed:5 fully:1 speth:3 forschungszentrum:1 financially:1 magnitude:4 bonn:3 reasonable:1 tributions:1 found:6 universit:1 difficult:1 constraints:5 heavy:4 reactions:1 ei:1 tify:1 hadronic:4 list:1 energy:8 revised:1 reduce:1 gaussian:4 related:1 rafelski:1 antiprotons:2 used:11 isospin:10 ex:2 entering:1 measure:1 eu:2 laboratory:2 operation:1 transitions:1 eq:8 special:1 really:1 shown:6 gv:1 matrix:2 pannel:1 space:5 mq:4 furthermore:1 since:5 interference:2 particles:3 re:1 nominal:1 mα:1 reader:1 how:2 illustrate:1 ref:12 charmonia:1 common:1 plet:1 theory:2 interactions:11 b3:2 ecm:10 ısica:1 little:2 free:4 quark:42 difficulty:1 ramos:1 formation:2 members:1 kinematical:1 antiquark:3 e4:2 estimate:2 e1:2 e3:2 e2:2 parametrized:1 interaction:69 chiral:1 widths:1 could:3 times:1 βd:9 strange:2 signature:1 consequence:1 hadrons:9 nußallee:1 first:5 origin:1 major:1 simplifies:1 features:5 symmetry:19 relate:2 vqq:8 hilbert:1 reflected:1 channels:7 ranges:1 smaller:7 done:2 specifically:4 another:1 tsushima:1 impossible:1 precisely:1 open:3 size:3 interchange:3 given:20 perturbation:2 temperature:1 needed:1 introduction:1 unknown:3 eqs:1 πn:1 system:22 construct:1 their:8 intermediate:6 ulich:14 too:4 calculations:2 1i:4 ordered:2 scheme:2 relations:3 low:3 shell:2 pect:1 kµ:1 cope:1 ch:1 baryon:18 exactly:1 forschungsgemeinschaft:1 sizable:1 assumption:4 part:13 α2n:4 somewhat:3 authors:1 oge:18 constituent:1 theorie:1 ψn:9 than:12 specify:2 center:1 distance:1 kind:1 1j:4 determines:2 sectors:1 pamplona:1 was:10 require:1 iteration:2 see:5 bi:6 matter:2 determined:2 contrary:1 assume:1 amplitude:3 were:1 hanhart:1 solely:1 acquisition:1 exhibit:2 function:4 kotulla:1 lines:4 urgently:1 mind:1 curves:4 departure:1 dash:1 say:1 substantial:1 mishra:1 interacting:1 need:2 ogy:1 constrained:1 krel:2 clearly:1 viewed:1 strength:2 genuine:7 zero:4 sj:4 efficient:1 latter:4 interferes:1 mechanism:2 predominantly:3 note:9 k2:4 empirically:3 potential:10 generalized:1 analogy:3 antiquarks:1 finding:1 new:1 similiar:2 strengths:1 channel:17 tensor:1 drastically:2 matinyan:1 play:3 added:1 kalashnikova:1 investigations:2 collaboration:1 who:1 unitarized:1 philosophy:1 cosy:2 singlet:3 most:3 involving:7 charm:4 plan:1 significant:1 definitions:1 phase:6 iterate:1 analytically:3 inserted:1 αt:1 parametrize:1 don:1 reduces:1 surprising:1 considered:7 clear:1 later:1 detectors:1 kn:58 graphs:4 reflecting:1 tpr:1 r25:1 constrain:1 differ:1 physics:1 notion:1 fact:2 sector:7 thomas:1 pd:2 simulate:3 show:5 text:2 supported:3 anyway:1 obtains:2 ki:2 attempts:2 2g:3 relation:1 threshold:9 substituting:1 rough:2 d2:2 d3:3 d0:1 orica:1 impact:1 capes:1 q2:1 ratio:2 knowledge:2 parameters:6 less:2 state:2 should:10 only:14 going:1 black:1 screening:1 ambiguity:1 factor:7 employed:3 helmholtz:1 importantly:1 combinatorial:1 dn:96 do:2 predict:1 dm:2 handle:1 gev:3 notation:2 get:3 dependent:1 vmb:2 dd:2 de:2 db:1 ko:4 da:1 inclusion:1 responding:1 listed:3 closely:1 exchanges:3 report:1 measured:1 respectively:1 averaged:1 ds:4 differentiating:1 krewald:1 liu:1 processes:8 technical:1 md:10 strahlen:1 exchanged:6 arxiv:24 yield:1 summary:2 twice:2 investigate:2 paper:10 predicted:7 though:1 including:3 fixed:2 krein:3 doublet:2 view:3 deuteron:1 ignored:1 constructing:2 fair:1 achieved:1 comparable:1 lett:3 richer:1 observed:1 mentioned:3 namely:4 individual:1 introduced:1 result:6 enhanced:1 integrating:1 close:6 bielich:1 momenta:2 best:1 subject:1 brazil:1 project:1 αs:2 said:1 qµ:7 extend:1 february:1 ph:9 pattern:2 review:3 ranged:3 8παs:1 dipole:1 tend:1 written:3 interrelated:1 various:4 sura:1 hopefully:1 invariant:1 αn:3 available:2 ends:1 recently:1 3mi:1 jz:1 nature:1 uller:3 screen:1 however:6 agencies:1 meißner:2 enters:1 hypothesis:3 extent:1 exploratory:1 lb:1 conthe:1 come:2 concentrated:1 received:1 essentially:1 monopole:1 prescription:3 keep:1 σc:3 many:2 taking:1 uncertainty:3 equal:1 contract:2 quantization:2 sensitive:1 negative:1 und:1 straint:1 exceeds:1 pdf:1 contribution:9 summarizing:1 whole:1 regarded:1 experimental:3 con:1 strongly:2 ci:1 relevant:3 a2:2 necessary:1 holinde:4 color:3 overview:1 lagrangians:6 each:3 unitarization:1 corresponds:2 dimensional:2 represented:1 simply:1 conjugation:1 iterations:2 golubeva:1 cancel:1 moreover:1 actually:1 pseudoscalar:4 ct:1 sensible:1 finally:1 described:4 analogies:1 gation:1 arises:1 due:18 been:2 defined:3 reduction:3 much:10 combined:2 interest:4 expected:2 microscopic:2 utilizing:4 pn:1 annihilating:1 fig:16 obtained:8 adopted:1 corresponding:16 kaon:4 questionable:1 quantities:1 formed:1 coincides:2 cor:1 angles:1 c3:2 cou:1 despite:1 general:5 spin:16 spirit:2 present:11 c4:2 case:16 p3:1 look:1 unlike:2 developing:1 contexts:1 warrant:1 reliable:1 groeling:2 empirical:1 value:7 will:8 invoking:1 near:3 cannot:1 situation:2 di:2 flavianet:1 c1:8 couplings:8 k1:4 versus:1 vc:2 k3:1 played:1 phenomenological:2 vi:5 refs:5 thus:10 matsui:1 ii:1 vq:5 confining:1 fn:4 insensitive:1 zhang:1 φp:10 different:10 φs:3 annals:1 grant:3 lengths:1 suggest:1 make:2 cross:32 same:18 any:5 paulo:1 shifts:6 parts:2 arguments:2 discussed:2 several:3 infer:1 prerequisite:1 higher:6 fairly:1 investigated:1 http:1 rescattering:2 estadual:1 appreciably:1 numerical:1 upon:1 effect:2 hand:4 sys:1 ion:1 viewing:2 barnes:4 internal:1 potentials:4 sibirtsev:3 build:1 invariance:1 reference:1 recent:5 relies:1 lower:2 estimation:1 off:3 whose:1 scenario:9 studies:3 preceeding:1 ingredients:2 well:3 roughly:6 obviously:1 concrete:2 epj:1 comes:1 spectator:1 simulated:1 gsi:2 quantitative:1 model:43 lin:3 usual:1 quack:1 alluded:1 linked:1 being:4 nd:2 fock:1 λc:4 λb:1 λa:2 unclear:3 thorough:1 multiplet:1 flavor:5 scattering:3 λm:1 adding:1 schweiger:1 cut:1 dissociation:1 density:1 teraction:2 qν:1 seems:1 ideal:2 veiga:1 gies:1 vij:4 add:1 k0:1 suppressed:1 treatment:2 easy:1 constant:9 eur:2 extensive:1 heavier:2 plasma:1 transformation:1 momentum:5 take:4 evaluation:1 around:3 rev:13 iγ:1 absence:1 possible:3 cf:5 possibly:2 increases:2 swanson:3 using:8 rhic:3 dard:1 machleidt:1 appearing:2 like:4 particle:1 sizes:1 follows:2 qualitative:2 extremely:1 specific:2 ate:1 integrals:3 always:1 rearrangement:1 become:1 nucleons:5 essential:1 4mn:1 deconfined:1 therein:1 parity:1 www:1 because:8 methods:1 after:3 structed:1 creation:1 some:6 back:1 b4:2 born:7 b1:4 b2:2 respect:3 extended:1 hofmann:1 reasons:1 happens:2 provided:5 scale:1 dense:1 both:2 lead:2 lippmann:3 stronger:1 resonances:1 quarks:11 sfb:1 fapesp:1 comments:1 mesons:31 does:2 meaningful:1 assuming:5 mesonic:2 refer:1 bα:1 denominator:1 a506:1 rep:1 rua:1 conventional:1 broken:1 although:1 refers:2 between:4 hadron:1 simpler:1 comparison:2 about:7 works:1 actual:2 working:2 extension:1 interestingly:1 freedom:2 bmbf:1 accepts:1 factors:6 addition:2 range:7 restoration:1 repulsion:1 germany:3 vdn:2 consequently:1 fortunately:1 ηc:2 hep:9 facility:2 into:7 within:6 integral:3 bound:3 three:7 vss:2 references:2 determine:1 baryons:1 consecutively:1 next:1 significantly:2 a3:4 uncertainties:1 acknowledgements:1 institut:2 additional:4 elastic:1 anticommutation:1 assumed:5 support:1 there:9 question:1 alleged:1 long:4 width:2 accordingly:1 noting:1 editor:1 way:2 brazilian:1 fer:1 sections:20 strict:2 opens:1 etc:1 lowest:2 medium:5 complete:2 form:11 funds:1 differences:2 but:19 jlab:1 repeated:1 construction:1 schaffner:1 kaidalov:1 line:3 durso:1 true:1 a1:7 hyperon:1 summing:1 charmed:11 made:3 coefficients:1 pion:1 whether:1 characteristic:1 caution:1 dω:7 up:3 us:6 ur:2 ωi:3 kk:1 marginally:2 spectroscopy:1 sum:3 σtot:8 demonstrate:2 stages:1 similar:4 average:2 expect:1 detailed:1 associated:1 ad:1 ln:6 ai:10 likewise:2 abstract:1 contribute:1 influence:1 ao:1 vertices:10 quantum:2 single:4 haidenbauer:15 transi:1 interchanged:1 our:14 lutz:3 universidade:1 physical:2 resonating:1 again:2 functions:4 compared:5 completeness:2 dotted:5 no:7 dashed:4 d4:2 when:6 detail:2 schwinger:3 field:2 other:10 role:5 details:1 better:1 out:1 tia:1 picture:2 briefly:1 elster:1 models:7 coning:1 vertex:5 variation:1 includes:1 qρ:2 a0:3 qσ:1 important:4 a4:2 suppression:4 included:1 structure:7 feasible:1 ago:1 correlated:6 implies:1 coupling:31 coulomb:8 practically:4 dφ:1 vg0:1 required:6 cally:1 pseudo:1 governed:1 dρ:2 equivalently:1 implied:1 mass:11 lying:1 time:5 observables:1 tolos:1 original:4 once:2 |
0704.3669.txt |@word gt:3 consider:1 remarkable:1 alg:1 results:10 invent:2 proposition:15 ga:1 edu:1 consists:1 atlanta:1 compact:2 whose:5 inverse:1 depend:3 chinese:1 γs:10 equivalence:1 γt:4 uniqueness:2 adically:2 th:10 γb:4 γa:3 presentation:2 conjecture:1 stanton:1 straightforward:1 very:1 bilinear:1 choice:1 unizh:1 corollary:5 witten:5 every:21 entries:3 affect:1 associated:2 exact:1 look:1 identity:1 school:1 induced:1 obvious:1 irreducible:1 list:1 solution:4 t1:2 discrete:1 convenience:1 interchanging:1 eigenvalues:1 evr:1 gruyter:1 rozansky:1 zn:2 smaller:3 says:2 renormalized:1 direct:2 sign:1 matrices:1 zero:6 further:2 melvin:1 odd:26 theory:2 even:10 established:1 sud:1 appear:2 invertible:3 d2:2 sum:15 3k:1 version:1 above:8 basic:1 new:2 increasing:1 method:11 completion:10 christian:13 d1:2 respectively:2 component:6 here:8 refinement:2 groups:1 address:4 along:2 bk:3 obtained:19 sending:3 colored:7 splitting:1 institute:2 study:2 studied:1 allows:2 spheres:13 winterthurerstrasse:1 action:1 bp:1 adopting:1 suitable:1 studies:1 pairings:4 uniquely:1 via:2 classification:1 apr:1 explained:1 diagonalizable:1 assertion:1 generality:1 hellas:2 apply:1 topics:1 unit:3 use:3 takes:2 zip:2 prove:3 recalling:1 positive:5 contains:1 negative:2 next:7 distinct:1 few:1 m1:5 therefore:1 taken:1 means:1 type:4 theoretical:1 more:6 separated:1 compositio:1 operators:1 lε:5 carrying:1 particular:3 known:6 projective:3 cases:1 hold:2 iii:2 analogous:1 must:2 account:1 isomorphism:1 sphere:7 recall:9 equation:5 mn:15 modified:1 ρr:2 values:5 following:14 converts:1 flc:2 trans:1 root:37 example:4 beliakova:13 f0:1 claim:2 compare:3 figure:3 stated:1 calculation:1 organized:1 turaev:6 numbers:3 sense:3 dennis:1 needs:1 s3:1 s2:1 discussion:1 holds:3 bretagne:1 how:1 adjacent:7 parameter:2 specializations:1 simplicity:2 product:1 rise:1 fu:5 singular:2 may:1 max:7 after:4 bki:6 hence:10 adic:1 date:1 fk:11 fl:4 fn:16 natural:3 third:2 lemmas:1 su:12 element:7 sk:18 wishes:1 so:17 sn:5 sl:2 definitions:2 order:33 renormalize:1 dx:1 indeed:3 over:4 mainly:1 soc:1 paper:9 through:1 mentioned:5 existence:1 its:5 roots:16 τn:1 le:16 lb:12 summands:2 thang:12 fix:5 forms:1 wrt:6 parts:1 choose:2 mail:3 main:4 might:1 arguments:1 non:9 usa:1 murakami:7 introduce:2 fr:1 mention:1 now:4 bigger:1 february:1 finite:4 2p:1 2r:2 invariants:62 identified:1 2z:10 universita:1 l2:4 l0:4 each:5 2l:1 2n:12 2i:10 2k:30 subset:2 domain:1 square:8 cyclotomic:14 map:12 series:21 hypergeometric:2 reduce:1 idea:1 related:1 sears:2 extended:1 poincare:1 combining:1 quantum:60 our:7 χil:2 eq:4 shown:1 dominates:1 rp:9 acknowledgment:1 space:2 restricted:1 furthermore:1 since:8 denotes:1 replacing:3 acting:1 geom:1 ra:14 rational:7 reader:1 denoted:4 formula:9 i41:1 evaluation:9 math:12 shows:2 earlier:1 linear:4 diagonal:7 quite:1 lmo:1 put:2 ord:14 remainder:1 definition:2 derivation:1 applications:2 phrases:1 just:1 atk:1 consequence:4 first:15 knots:5 pairing:10 variables:2 xa:1 number:8 linking:16 restrict:1 dominating:6 relations:1 modulo:4 ring:17 precisely:3 open:1 subring:1 coprime:1 interchange:1 given:4 similarly:1 introduction:2 system:1 construct:3 their:16 assumption:1 normalization:2 statement:1 recent:1 structures:2 gives:2 addition:2 proving:1 japanese:1 part:13 authors:1 copy:1 than:4 coefficients:4 determines:4 divisible:9 i31:1 see:13 roberts:1 τm:58 determined:7 pairwise:1 supposed:1 powers:1 perturbative:3 carlitz:2 ann:1 argument:2 say:1 vn1:1 zu:2 need:3 any:27 depending:1 lim:5 responsible:1 lii:1 lij:4 converges:1 oriented:7 sciences:1 k1:1 k0:3 coincide:1 formulas:6 trefoil:1 towards:1 unknot:2 centre:1 vnm:1 denominator:3 most:1 connected:10 plan:1 significant:1 multiply:1 class:4 kb:2 laurent:3 consequences:2 considered:1 kj:1 ki:36 phil:1 stronger:2 km:1 proceedings:1 quadratic:1 skein:1 section:9 fact:1 χh:1 precise:2 show:8 contemporary:1 kawauchi:1 spaces:1 relation:1 substituting:2 trivial:4 principal:1 homology:19 divisibility:1 dividing:1 behind:1 should:1 lemma:7 only:12 generators:4 summarizing:1 rich:2 factor:1 do:1 dk:2 notation:3 get:10 embeds:1 express:3 congruent:1 ones:1 framing:19 words:2 consecutive:1 compute:2 aλ:16 prime:17 arxiv:1 qa:1 qb:3 common:1 switzerland:1 blanchet:14 fixed:1 surgeries:3 topol:1 set:23 signify:1 constructing:1 exists:12 j4:1 module:1 j3:1 depends:3 result:10 surgery:17 concern:1 irp:2 rims:1 rings:3 symmetric:2 written:2 proof:17 various:1 closed:4 between:3 invariant:53 terms:2 adding:1 ju:1 jp:2 however:3 jl:12 ramif:1 derive:2 2pe:1 key:1 jk:4 recherche:1 group:2 topology:6 restrictions:1 gasper:1 last:1 universit:1 σc:10 many:1 taking:3 called:5 present:1 embedding:2 comm:1 whole:3 otherwise:3 ck:10 cj:3 ci:5 ch:2 co:2 cm:2 cl:8 simple:3 others:3 cohomology:2 framings:5 rahman:1 dimensional:2 ab:1 polynomial:19 respect:4 throughout:2 torsion:2 gratitude:1 ps:2 strong:1 abelian:1 commutative:1 second:1 fu1:2 pz:1 simplification:1 three:3 sl2:2 workshop:1 combined:1 pd:1 pe:6 universal:1 define:18 γb1:2 corresponding:1 concerning:4 georgia:1 coincides:2 observe:4 recalled:1 c1:2 denote:3 spin:21 manifolds:12 divisor:1 case:10 replaces:1 splits:2 value:1 remaining:2 will:4 while:1 suppose:30 property:1 computed:3 orientation:1 portugal:1 thus:2 them:1 vn:1 ii:2 ohtsuki:14 im:58 technology:1 whitehead:2 different:1 φs:4 author:2 belong:1 same:4 clearly:2 masbaum:2 unity:40 complex:3 split:11 φi:2 proved:2 defines:3 φm:4 φn:6 used:3 http:2 assigns:1 ni:13 publ:1 effectively:1 infinite:5 totally:1 expand:1 subgroups:1 numbered:1 gauss:2 well:5 helv:1 de:3 without:1 greatest:1 components:15 entry:2 dimension:1 left:2 unified:35 internat:1 manifold:10 proposed:1 among:1 generally:3 resp:3 rest:1 transforms:4 integer:10 previous:3 note:14 infinitely:1 wall:1 add:1 terminating:1 easy:6 theorem:28 diagonalization:1 semigroup:1 formal:4 transformation:2 loss:1 kirby:1 evaluate:2 sums:3 know:1 knot:10 using:4 ams:1 unique:9 mod:18 lˆe:4 reshetikhin:5 semi:1 follows:18 e01:3 collect:1 yields:1 either:2 always:2 multiplicative:2 become:1 classes:2 because:2 sequence:4 some:3 pacific:1 algebraically:10 ideals:1 deduce:1 γsn:2 examples:2 moreover:6 proofs:1 provided:1 univ:1 avoid:1 everything:1 does:4 provides:1 proc:1 tk:9 anna:13 conference:2 run:2 power:7 kyoto:1 l1:5 expansion:8 γs2:2 cambrige:1 binomial:2 shifting:1 although:2 described:1 imaginary:1 properties:1 injective:6 proceed:3 integers:6 habiro:27 algebraic:3 cohomological:12 numerator:2 o:1 fl1:1 a2:2 fl0:1 subsection:1 cofinal:1 block:2 mathematical:1 primitive:2 statements:2 orders:2 into:8 h1:10 integral:10 isomorphic:2 framed:8 pair:2 right:1 references:1 inverting:1 determine:2 operator:4 refined:12 france:1 weight:1 institut:1 completions:3 her:1 3k2:1 refinements:24 there:24 transform:19 appl:1 low:2 ed:1 was:7 function:1 kojima:1 form:4 regard:1 but:2 volume:1 calgary:1 gatech:1 construction:4 link:20 true:1 he:1 directed:1 integrality:11 applying:4 azn:1 whether:2 characteristic:3 variations:1 us:16 below:3 converted:1 limit:1 problem:1 similar:1 laplace:24 taylor:9 ordered:2 links:1 computing:1 defined:19 certain:2 abstract:1 χi:1 proven:1 general:2 twist:1 modify:1 exist:2 interchanged:1 ax:1 funchal:1 constructed:1 again:2 nk:2 nm:14 no:1 mathematik:1 when:6 ne:2 handed:1 application:1 other:2 mathematics:2 mathem:2 elements:4 ubs:1 polynomials:2 generated:2 important:3 structure:8 matrix:6 jones:9 implies:6 assume:8 factors:1 together:1 4j:1 4k:2 n1:15 n2:3 |
0704.3670.txt |@word consider:1 caused:1 astron:1 dynamic:1 focus:1 roy:1 scalar:11 statefinder:42 edu:2 consists:1 issues:1 gr:10 whose:1 const:1 calculate:1 sahni:5 caldwell:2 supported:1 γm:24 rabcd:2 zhang:11 very:2 results:1 interpreting:1 difference:2 exact:1 school:1 cause:3 anisotropy:1 guo:2 cmb:1 coordinate:2 braneworld:1 sin2:2 past:2 pass:1 qualitatively:1 wmap:1 index:1 3x:2 g22:1 section:3 dr2:2 current:4 bdt:1 experiment:1 increasing:3 acknowledgments:1 contrast:2 satisfy:1 evolving:3 justification:1 respectively:13 component:1 here:2 following:1 china:2 jcap:2 diagnostic:4 equations:6 2x2:8 study:2 studied:4 ωtotal:1 b611:1 chang:5 suitable:1 makes:1 attractor:24 via:2 spatially:3 apr:1 vii:1 decrease:1 apply:4 total:2 plot:3 use:1 figure:10 contains:1 negative:1 scenarios:1 linear:1 means:1 type:1 more:2 flat:6 liddle:1 th:4 clearly:2 dxµ:1 apparent:1 pairs:2 curvature:2 known:2 lcdm:7 iii:2 zimdahl:1 logarithm:2 kaluza:1 equation:11 work:4 ρm:8 theories:1 wands:1 values:4 believed:1 clarendon:1 wang:4 cosmological:10 give:1 ds2:1 carroll:1 high:2 indicates:1 chin:1 numbers:1 sense:1 copeland:1 b594:2 end:2 discussion:2 get:2 ping:3 regions:1 far:4 speeding:1 instead:1 parameter:35 after:1 sami:1 diagram:15 plane:6 geometrical:1 meaningful:1 short:1 dynamical:1 effective:1 light:1 correspond:2 element:1 accelerated:1 so:6 pay:1 order:1 g11:1 zlatev:2 essence:1 course:1 paper:2 including:1 hypersurface:1 satisfies:2 its:1 before:1 perfect:3 ln:22 d37:1 solving:1 starobinsky:3 li:5 forms:1 fig:24 clusters:1 versus:5 non:1 good:1 differentiated:1 introduce:1 scaling:1 bang:1 singularity:1 yu:1 discuss:1 represents:4 term:1 holographic:1 invariants:1 university:1 2b:2 each:2 found:6 characterized:1 differential:1 energy:23 solution:24 our:3 differ:1 es:1 standard:3 living:1 space:2 rep:1 since:1 rev:16 qc:10 denotes:2 increase:3 dominated:4 rel:2 induced:3 ref:7 shows:1 i2:1 theory:1 ast:1 galaxies:1 given:3 quite:3 hubble:1 interaction:1 r2:2 geometry:1 could:2 cosmic:2 motion:1 quintessence:27 exponentially:1 hence:1 think:1 there:5 variables:1 transform:1 xy:2 xin:1 another:2 size:1 surveys:1 introduction:1 saini:2 system:3 relations:1 indicate:2 assumption:1 observations:2 dt2:2 wilkinson:1 recovered:1 alam:2 differentiate:3 somewhat:1 authors:3 x2:20 than:1 distance:1 determines:1 see:7 matter:8 future:7 speaking:1 behaviors:1 dalian:2 rab:3 dynamically:1 dθ2:2 curves:17 b560:1 seen:2 seem:1 cosmology:1 tells:1 viewed:1 acceleration:1 ratra:2 able:1 liu:21 potential:5 spergel:1 εg:1 εb:1 alleviate:1 though:1 most:2 involving:1 steinhardt:3 pair:4 class:2 interacting:1 forever:2 observation:1 considered:1 gµν:5 exp:1 left:4 physics:1 deceleration:11 selected:7 pope:1 show:4 probe:1 implying:1 solutions:11 d9:1 astrophys:4 fine:4 find:3 chaplygin:1 parameters:17 baryonic:1 should:4 only:1 3h:6 candidates:2 factor:3 employed:1 g00:1 hope:1 klein:1 meanwhile:1 contracts:1 kamionkowski:1 rept:1 fluid:3 cannot:1 nearly:1 dy:1 dv:1 ds:1 prime:2 reveal:1 evolution:8 densities:2 nicely:1 approach:1 arxiv:1 grav:2 summary:1 investigate:1 through:3 fixed:2 ricci:2 depends:1 close:1 paul:1 uν:1 tensor:5 pavon:1 d59:1 state:7 various:1 between:4 ωm:2 overduin:1 conditions:1 d57:1 notice:1 moschella:1 nature:1 complement:1 attention:1 however:3 vanishing:1 jetp:1 autonomous:2 regular:1 both:1 many:3 region:2 hao:5 wu:2 attributed:1 figures:5 exhibit:1 cn:2 point:2 corresponds:1 dimensional:5 dependent:1 respect:2 late:4 unusual:1 tuning:4 trajectory:1 locally:1 three:2 been:11 int:9 much:2 frw:2 ph:30 dut:1 ann:1 empty:1 pm:6 dots:4 corresponding:2 tµν:11 gas:1 precision:1 gen:1 dave:1 tνµ:2 derivative:2 present:4 mashhoon:2 applied:1 attractors:1 supernovae:1 pacs:1 appearance:1 will:12 while:5 piao:2 a20:4 a21:2 a22:1 tµ:2 gorini:1 almost:1 vi:1 metric:3 thus:1 dxν:1 rip:5 iv:2 ii:3 middle:2 reads:1 ia:1 technology:2 turner:1 d14:4 d15:1 different:12 author:1 higherdimensional:1 make:1 same:2 any:1 parts:1 quant:1 widely:1 rνµ:1 dimensionless:1 finite:1 evolve:6 satellite:1 weinberg:2 i1:1 i3:1 trajectories:7 effect:1 v0:1 purpose:1 student:1 dadhich:1 changing:1 kamenshchik:1 recent:1 scenario:10 changes:1 well:2 analysis:1 without:2 rosati:1 components:5 firstly:1 model:36 usual:1 manifold:3 just:1 less:1 being:1 obtain:1 using:2 campbell:2 alternative:1 previous:3 candidate:1 density:6 guaranteed:1 lett:16 theorem:1 5d:19 mod:17 momentum:3 tests:1 insensitive:1 increased:1 eigenvalue:1 big:10 possible:1 dark:17 five:5 mon:1 background:1 vacuum:2 world:2 8πg:1 singh:1 apart:1 g33:1 helpful:1 follows:2 accelerating:1 liko:1 arbitrary:1 works:2 shed:1 right:4 successfully:1 some:1 bounce:7 deduce:1 pφ:3 accelerate:2 b2:2 proper:3 wesson:7 anisotropies:1 scale:2 describing:1 dimensions:2 kr2:2 avoid:1 microwave:2 critical:2 assuming:1 minimal:1 locate:4 scientific:1 d70:1 expansion:3 pressure:3 padmanabhan:1 lixin:1 about:1 universe:19 discussed:4 a2:10 plus:1 d68:2 quintom:1 d64:1 d67:3 introduced:2 consequently:1 optoelectronic:1 xu:13 soc:1 decreased:1 redshift:6 h2:1 nsf:1 lies:2 references:1 determine:1 einstein:5 nunes:1 hep:5 assumed:2 initial:1 72k:1 occupy:1 conservation:1 analyze:1 was:4 form:2 brane:1 but:2 astro:30 line:1 proposal:1 wφ:3 embedded:2 supp:1 up:1 us:1 dφ:1 below:1 limit:1 problem:4 define:2 called:1 aa:2 ab:2 constant:4 conserves:1 defined:1 ah:1 influence:1 relates:1 constructed:2 phantom:29 functions:1 no:1 uµ:1 generally:2 ng:1 field:23 other:5 theor:1 deviation:1 peebles:2 kinds:1 10x2:4 models:14 resembles:1 a19:1 θdφ2:2 important:1 variable:9 a8:1 independently:1 coupling:1 assume:1 dτ:1 interval:8 time:13 4d:11 laws:1 expands:1 |
0704.3671.txt |@word replacing:1 outlining:1 cot:1 jason:1 consider:6 similarity:2 magnetic:15 altland:1 results:8 four:16 ρji:3 ρjj:1 rezayi:1 overlap:1 grateful:1 dirty:1 consists:2 follow:2 gm:4 3a0:1 contributions:1 hole:6 localized:1 devoted:1 whose:4 2ie:1 calculate:6 zone:1 f2p:5 c7:1 band:2 flavor:1 c6:1 finally:9 helps:1 th:2 under:1 td:1 fermionic:5 worth:3 indicating:1 case:19 belonging:1 straightforward:3 without:1 very:5 morais:3 rise:3 springer:2 atoms:3 splitting:1 electron:31 difficult:3 inequivalent:1 affect:1 difference:1 matrices:2 condition:2 treating:1 illustrated:2 level:38 turns:1 pacs:1 ri:1 large:2 discrete:5 vector:4 rj:1 guiding:2 small:10 relation:5 dubonos:1 degeneracy:5 concluded:1 application:1 smaller:1 findings:1 renormalized:3 consistent:1 morozov:1 sign:3 approximation:3 fold:2 second:1 displays:1 zz:1 concludes:1 zu:1 defining:3 estimated:3 expressions:12 substitute:1 canonical:3 blue:1 index:2 what:1 hexagonal:1 adds:1 appear:1 rd2:3 moessner:1 section:8 associate:2 ǫq:2 expressed:1 uniform:1 cell:1 kun:1 version:1 above:19 fractional:1 new:6 ˆj:1 contributes:1 cn:3 method:7 filled:9 satisfy:2 quenched:1 agreement:3 full:1 simultaneously:1 eig:1 degree:1 respectively:15 l1:1 component:5 here:24 bi:39 eqt:1 replacements:1 them:1 expansion:3 mes:1 others:3 directions:1 standard:1 table:2 appears:1 change:1 obtained:9 great:1 generalizing:1 novoselov:2 institute:1 involved:2 study:17 vectors:2 allows:2 yˆ:1 stiffnesses:2 suggests:1 resulting:1 negative:1 stiffness:4 situations:1 action:1 resonance:1 fourier:8 changes:2 involves:1 patrick:1 examining:1 via:2 useful:3 projection:1 extra:4 vb:2 katsnelson:1 highly:5 addressed:1 vec:1 texture:1 connection:1 apply:3 total:15 tools:1 unit:3 gaas:6 ando:1 asymptotic:1 would:3 distinct:7 positive:2 contains:2 charge:11 next:3 scenarios:1 phenomenological:1 sample:2 ψi:1 call:1 therefore:14 iαk:2 taken:1 type:3 theoretical:2 corners:1 more:11 separated:1 introducing:1 spinors:1 formally:1 lkx:1 definition:1 clearly:1 solitons:1 operators:66 stable:1 pfm:5 odinger:3 fjp:2 unstable:1 berlin:1 appendix:13 short:1 particular:5 cases:3 hold:3 iii:3 analogous:2 spinpolarized:1 pseudospin:68 states:10 account:2 include:2 quartic:1 vq:4 ρi:2 equation:1 fiµ:4 girvin:1 modified:3 paragraph:1 values:3 theirs:1 following:11 arrive:1 address:1 performed:1 νt:7 radius:4 want:1 give:2 calculation:3 expanding:4 organized:1 desenvolvimento:1 involve:3 indicates:2 covalent:1 minimum:1 numbers:1 degenerate:7 ǫc:7 tan:2 onio:1 dfg:1 occur:1 simple:2 yang:2 counterpart:4 respective:4 ib:5 soc:1 carriers:1 describes:4 discussion:3 breaking:10 arrangement:1 write:1 how:3 ator:1 subject:1 eisenstein:1 simplifies:1 gate:1 2deg:4 verlag:1 parameter:1 sin:26 mat:1 algebra:9 may:8 sp2:1 after:3 derived:24 lengthy:1 collection:1 kallin:1 corrections:1 levi:1 plane:2 designed:1 physik:1 representations:2 wave:9 concentrating:1 response:1 lifting:1 sz:15 realized:7 sx:2 branches:16 effective:20 sets:2 slightly:1 counter:1 lines:3 correspond:6 su:43 like:4 si:3 so:5 allow:1 representation:26 sa:1 acknowledges:1 order:6 c2:1 brillouin:1 neto:2 wavelengths:1 six:2 pinczuk:1 developed:4 pointed:1 displayed:1 satisfied:1 stability:2 bounding:2 experiments:1 through:2 2v:1 argued:3 existence:1 kinetic:1 still:2 excitations:40 its:7 before:3 gµb:2 fip:4 derive:5 longitudinal:2 located:1 energies:2 interesting:1 zˆ:5 lm:3 methodology:2 boson:92 writing:1 complex:3 degrees:6 systems:4 lp:1 lq:90 main:1 might:11 alter:1 weber:1 emphasize:1 qhs:2 non:4 schematic:4 combination:1 propose:1 outlined:1 greiner:1 fig:11 operator:21 landau:44 break:1 framework:1 effects:4 they:3 qhe:9 nov:1 now:12 discuss:2 group:2 pz:23 easily:3 term:18 netherlands:1 indeed:11 hereafter:1 lies:1 publication:2 fully:1 university:1 hamiltonian:18 ibµ:1 filling:8 l2:3 mode:1 2b:1 each:16 2l:2 found:2 universit:1 quarter:4 2i:3 characterized:6 2k:1 spinor:6 lifted:2 en:1 ei:6 directly:1 weight:1 doing:1 energy:42 ferromagnetism:3 ρi1:2 related:16 eb:2 constitute:1 bosonization:14 2πe2:1 isospin:3 interplay:1 ez:33 quantum:47 our:9 ev:6 eq:52 ep:19 special:1 out:5 emerges:1 shown:4 ezawa:1 matrix:1 factors:10 types:1 restricted:5 tors:1 rev:20 projected:8 research:1 increase:1 eiq:8 socalled:3 reader:4 formula:1 ref:21 occurs:2 red:1 shows:3 fermi:2 wiley:1 turning:1 theory:4 interactions:2 diagonal:1 ρis:5 quite:5 completely:6 ρii:11 york:1 dynamics:1 ρij:12 modify:4 estimate:1 bilayer:5 e2:9 longrange:1 degeneracies:1 isy:2 interaction:22 derivation:2 language:2 created:3 could:1 transition:1 lederer:1 creates:1 ordering:2 length:2 calculating:2 consequence:3 3a20:1 configurations:1 condensate:1 first:3 origin:1 major:1 excitonic:1 symmetry:14 laguerre:1 brazil:1 hausdorff:1 number:6 theoretische:1 restrict:1 obeying:1 xy:1 done:2 approximately:5 another:1 uli:1 carry:1 ulpicher:1 electronic:6 tively:1 pfeiffer:1 passes:1 given:27 necessarily:1 termined:1 rewritten:1 needed:1 introduction:4 eqs:16 system:22 relations:11 indicate:2 nian:1 paramagnetic:2 listed:1 flavors:1 f1s:2 f1p:5 scheme:5 iap:1 ias:1 gives:1 mentioning:3 preserved:2 calculations:3 asymmetric:2 explanation:1 incompressible:1 task:1 larger:3 part:9 favorable:2 focusing:2 kept:1 than:4 andre:1 kind:3 polarized:7 ben:1 scenario:2 showed:5 favors:3 hirayama:1 plateaus:4 final:1 annihilation:6 matter:1 determined:1 bilayers:1 str:1 were:4 exp:4 treated:2 antiskyrmion:4 perturbative:3 hz:2 sp:1 sees:1 jiang:2 igor:1 firsov:1 spectrum:2 generalization:2 deutsche:1 already:2 ordered:1 undoped:1 levitov:1 conjugate:2 need:1 seem:1 their:6 gusynin:3 sk:11 smallest:2 zero:1 depending:2 studying:1 latter:4 able:1 ideas:1 mechanism:2 metallic:1 polarization:1 majority:1 ideal:1 lifts:1 generalized:2 analogy:1 online:4 schematically:1 tightbinding:1 honeycomb:3 circles:1 even:1 play:1 continuous:8 beyond:2 electric:2 normal:4 twodimensional:2 who:2 singlet:2 sfm:9 germany:1 ht:3 comparing:1 sb:2 pair:4 tracy:1 analytically:2 measured:3 commutation:4 exact:1 soliton:1 zeitler:1 consequences:1 considered:4 calculated:7 sometimes:2 implications:1 points:6 electrons:12 principle:2 clean:2 narrow:1 iaµ:3 abanin:3 physics:1 sum:1 fact:15 dou:1 tron:1 show:20 doped:1 angstroms:1 tecnol:1 nφ:62 lee:1 cdw:1 gauge:1 3u:1 civita:1 substituting:3 careful:1 3t:1 d2:8 agrees:4 ground:11 gaps:2 based:3 just:4 parameters:4 zhang:2 commutators:1 distributed:1 written:6 topological:11 should:20 only:14 explicitly:3 generators:1 factor:6 employed:2 equally:2 go:1 preliminaries:1 do:2 predict:1 goes:1 vary:2 de:1 expectation:3 twocomponent:1 hib:2 ones:3 iǫabc:1 words:1 iqy:2 symmetries:2 represented:1 kindly:1 description:1 processes:2 simons:1 qt:3 ρ1s:3 introduced:1 upper:1 fields:1 secs:2 arxiv:2 expansions:5 4u1:2 summary:2 paper:2 qe:3 mapped:2 qi:7 guinea:1 fixed:1 ρ1i:2 ql:2 voltage:1 magneton:1 requirement:1 set:8 questions:1 reference:8 edited:1 delicate:1 condensed:1 arrives:1 richer:1 observed:3 namely:5 sec:12 result:3 discussions:1 terms:26 satisfies:1 conductivity:2 αq:25 instance:6 phases:12 bjσ:1 interacting:8 nuclear:1 review:1 nature:2 circulating:1 symmetric:1 kumada:1 state:45 future:1 between:12 invariant:8 mathematical:1 previous:7 approach:2 µb:1 eigenˆ:1 deferred:1 notice:7 muraki:1 recently:5 leonid:1 sections:3 spacing:2 restricting:1 weak:1 however:4 a20:1 concentrate:3 orbitals:3 wq:11 h0b:3 subspace:1 bose:2 ferromagnet:1 distribution:1 suggested:2 both:6 cos:28 bogoliubov:1 2n:1 limits:2 ıfico:1 region:3 conclusions:1 c5:1 equal:5 zeeman:6 agree:1 f2s:2 σz:1 σy:1 σx:1 context:1 ρ0s:6 contribution:1 expression:4 haldane:1 cos2:1 comment:1 mechanics:1 reduce:3 relevant:2 co:3 0b:4 cm:5 point:4 color:4 smith:2 das:2 excess:1 eic:1 corresponds:7 leon:1 hvf:1 dimensional:3 analyzed:5 simply:1 confirmed:1 carbon:4 polynomial:1 respect:5 nacional:1 considering:3 ps:3 unusual:1 strong:2 described:8 perspectives:1 nomura:1 basis:4 addition:4 west:1 create:1 due:12 been:1 tesla:1 cient:1 pa:3 slowly:1 treat:1 applying:1 proposal:1 sarma:2 define:4 concentrated:2 corresponding:4 constitutes:1 cyclotron:1 concerning:2 resistance:1 ik:1 gap:4 bulk:1 coherent:3 qx:2 determination:1 c3:2 last:1 c1:1 presented:8 spin:79 former:3 present:2 alicea:11 applied:4 ǫb:2 geim:2 reciprocal:1 developing:1 frozen:1 σxy:2 diagonalizations:1 expanded:2 ij:1 value:6 ǫl:5 will:19 ǫr:2 while:8 replaced:2 behavior:5 aid:4 hybridization:1 taking:2 procedure:4 grigorieva:1 remembering:1 layer:4 unitary:1 vf:1 jpn:1 iq:23 graphene:23 sondhi:5 binding:1 site:9 iv:2 ii:15 characterize:1 reads:5 focus:2 cond:1 il:2 formulae:1 08b:1 fn:6 c0:1 vanish:2 ie:8 fermion:6 underlining:1 samples:1 arovas:5 ωi:4 different:8 develop:1 grant:1 goerbig:4 acknowledgments:1 make:1 lett:7 same:15 any:2 matthew:1 noninteracting:7 arguments:1 pauli:2 modification:1 v1:5 catalysis:1 finite:2 higher:3 hermiticity:1 independent:7 used:6 unconventional:1 see:24 ni:2 i0:2 numerical:1 effect:6 u0:33 noticing:1 average:2 levels:14 moving:1 introduce:1 kim:2 respec:1 2u0:9 2u1:6 recent:1 eigenvectors:4 lower:2 elec:1 schr:3 center:2 hopping:1 mention:2 minimize:1 studies:3 usual:3 well:12 analysis:9 bohr:1 academic:1 edge:2 utrecht:2 components:6 convenient:1 firstly:3 entry:1 model:47 dmitry:1 2πl2:2 charged:8 λq:1 background:1 proposed:13 halperin:1 skyrmion:19 half:4 ci:2 c4:1 underlying:1 situation:4 atomic:3 predicts:1 using:3 ogico:1 uller:1 momenta:1 scattering:2 underline:1 captured:1 heterostructures:6 adding:3 conjugates:3 preprint:1 arfken:1 corroborated:1 density:60 similarities:3 workers:2 scales:5 seems:1 hall:47 macdonald:2 lattice:10 add:1 potential:15 dielectric:2 easy:1 constant:5 remaining:1 momentum:6 take:2 identical:1 spinless:2 aspects:1 around:5 read:2 caldeira:4 breaks:3 disagreement:1 possible:9 smallness:1 varies:1 know:1 similarly:1 vacuum:6 press:1 integer:3 moreover:3 apart:4 semiclassical:7 semi:1 particle:9 follows:4 performing:1 δr:1 δq:22 separately:2 private:1 δj:8 either:4 δi:22 anti:1 disorder:3 reduced:3 icµ:1 δa:1 function:2 because:13 functional:7 cones:1 stormer:2 creation:7 some:5 oln:2 b4:14 understood:3 b1:24 b2:18 b3:20 neglecting:2 ourselves:1 transport:1 specific:2 shovkovy:1 describing:2 dimensions:1 lead:1 opposite:1 2nφ:11 per:2 does:8 linearly:1 provides:2 assuming:4 gapless:1 steps:2 bessel:1 conselho:1 ωik:1 refer:5 hsb:7 destroys:1 obey:3 sheng:2 ǫabc:1 equivalent:1 ntype:1 perpendicular:6 bj:3 broken:1 display:1 although:4 positions:1 condense:1 approximating:1 postponed:1 hilbert:1 hamilto:1 about:1 postbus:1 ok:1 ferromagnetic:5 a0:13 freedom:7 discussed:7 ρ2s:3 o:13 excitons:3 range:1 repulsion:7 stand:1 neighbor:1 mixed:18 connected:1 replacement:2 skyrmions:16 hi:5 considerations:4 primitive:3 cambridge:1 presence:3 communication:1 into:12 within:11 f112:2 bound:3 three:11 down:4 phase:37 hermitian:5 castro:2 determine:1 einstein:2 elementary:10 financial:1 bosonic:15 methods:1 uncertainties:1 institut:1 area:1 support:1 there:4 u1:22 transform:8 long:7 dispersion:7 start:6 quadratic:5 bosons:14 physicists:1 way:1 valley:3 was:13 assumes:5 combined:1 lowest:35 tight:1 form:16 compressible:1 smith1:1 constituted:1 triangular:7 but:6 hu:3 neutral:11 properly:1 miransky:1 atom:1 hb:2 hc:2 cnpq:1 arranged:2 b5:1 whether:1 antiferromagnetic:1 uw:1 lqx:1 up:3 us:15 ur:1 nearest:1 below:2 projecting:1 limit:13 tensor:1 spielman:1 fluctuations:2 problem:1 similar:10 called:3 uc:1 expect:2 detailed:5 sharapov:2 later:2 associated:1 defined:16 model2:1 describe:3 influence:1 karlhede:3 general:3 peres:1 dirac:11 single:3 sublattices:6 interchanged:1 wavelength:3 hcoul:3 formalism:10 regime:6 again:8 compared:2 no:2 balents:1 whereas:3 when:13 sublattice:3 pp:1 field:12 nz:5 other:1 role:1 details:4 branch:7 herbut:2 massless:1 lk:7 conclude:2 briefly:3 kinds:5 generates:1 excitation:13 bility:1 models:3 gas:3 includes:3 commutator:6 important:4 fisher:9 kivelson:1 structure:5 independently:1 condensation:1 implies:6 longer:2 coulomb:7 assume:6 4b:1 baker:1 space:3 interpenetrating:1 rxx:1 carrying:1 hashimoto:1 yoshioka:1 starting:3 original:1 once:2 |
0704.3673.txt |@word neighbors:1 gu:1 consider:1 remarkable:1 similarity:1 gupta:1 caused:5 results:4 ruyter:1 leads:2 ohta:1 grateful:1 edu:1 consists:1 research:1 layers:2 careful:1 calculate:1 re:1 technique:1 vs:1 include:3 tc:6 distorts:1 random:1 amplitudes:1 advantage:2 g0:6 mierzejewski:1 wave:12 electron:2 fan:1 experimentally:1 illustrated:1 level:1 positions:6 tanh:1 large:1 adjust:2 sacks:1 small:1 enhance:1 interstitials:1 smaller:2 disordered:1 oscillation:1 neal:1 consistent:3 sponse:1 direct:2 displays:2 chen:1 qualitatively:1 copenhagen:2 linear:1 bdg:2 cˆj:2 appear:3 nano:1 cˆi:2 giving:1 3t:1 cell:1 consistently:1 experiment:3 above:2 hull:1 beasley:1 new:7 learned:1 increasing:1 agreement:3 led:1 lee:3 exchange:1 respectively:3 modify:1 here:4 atoms:4 following:3 mev:3 smearing:1 along:1 strong:1 equations:2 appears:2 change:3 obtained:2 apical:3 institute:1 study:1 periodic:4 resulting:5 scenario:1 changes:2 iσ:3 investigate:1 scales:2 apr:1 inducing:1 merely:1 visible:2 modulated:3 summation:1 tools:1 unit:2 conventional:5 eye:1 usa:2 remains:1 positive:1 wiped:1 cˆiσ:1 substitutions:1 examination:1 therefore:5 distortions:1 taken:1 type:3 theoretical:5 possible:1 more:3 tohyama:1 hoffman:1 mismatch:1 site:1 spielman:1 vn:3 particular:1 known:1 aligned:1 effort:1 takayama:1 insights:1 sample:1 ma:1 science:3 work:2 modified:1 obstacle:1 hope:1 believed:1 sinusoidal:3 nearest:2 14t:2 wang:1 sinusoidally:1 dependence:1 high:4 assumptions:1 performed:2 axis:1 information:5 andersen:6 goal:2 provide:2 bonds:1 raveau:1 chemical:1 located:1 pure:2 answer:1 optimal:1 parameter:3 displacements:10 modulations:3 simplicity:2 mat:5 may:3 advice:1 philosophy:1 spot:1 davis:4 plane:6 fits:1 fi:4 fj:1 data:6 response:1 constants:1 short:1 effective:3 sr:1 yielding:1 melikyan:4 chief:1 maintain:2 so:1 sm:20 correlation:5 subsequently:1 order:7 typical:1 ding:1 kugler:1 numbers:1 indeed:1 over:2 vary:3 years:1 experiments:3 through:2 thesis:1 argued:1 existence:1 still:1 its:4 selfconsistent:1 le:2 fit:1 brian:1 hirschfeld:5 better:1 microscopic:2 fig:23 cren:1 main:1 might:1 easier:1 versus:10 eventually:2 good:1 thereby:1 material:2 regarding:1 effects:4 they:1 compound:1 bogoliubov:1 now:1 yu:2 discuss:1 structural:3 2t:1 february:1 oxygen:4 james:1 university:5 hamiltonian:3 barton:1 identified:1 2d:1 sufficiently:2 cˆjσ:1 2a:1 each:3 renner:1 found:3 characterized:2 bond:1 homogeneous:3 square:1 map:1 energy:3 idea:1 related:1 inhomogeneous:1 conductance:1 decays:1 microscopy:1 encouragement:1 measurement:1 wavelength:1 eq:3 es:1 out:3 shown:3 impurity:4 space:4 since:3 induces:1 cuprate:2 rz:1 denotes:1 modulation:7 induced:3 ref:3 integrated:1 shows:2 after:1 theory:2 interactions:1 disagree:1 possibility:3 difficulty:1 reason:1 complicated:1 york:1 dopants:3 generate:2 interaction:4 saha:1 could:1 florida:3 length:3 produce:1 leading:1 hence:1 view:1 neglect:1 first:2 origin:4 already:1 fischer:1 relate:2 improving:1 done:1 reached:1 clarity:1 electronic:3 size:1 given:1 1t:1 twenty:1 histograms:1 system:6 approximately:2 too:1 calculations:4 ordered:1 structures:1 maggio:1 centered:1 φsm:17 authors:1 than:3 cheng:1 distance:6 third:1 showed:1 stm:2 marshall:1 states:1 determined:4 yang:1 amplitude:10 were:2 providing:3 engelbrecht:1 exhibit:1 maekawa:1 defect:1 substantial:1 close:1 need:1 seen:4 ldos:2 obviously:1 any:2 ray:6 traditionally:1 convenient:1 self:2 able:5 complexity:1 incentive:1 note:2 extracted:1 empirically:1 potential:12 online:3 performance:1 stoichiometry:1 channel:3 aprile:1 sure:1 fundamental:1 opposite:1 track:1 who:1 systems:1 ishigaki:1 most:1 assault:1 significant:2 position:1 phase:15 acknowledgements:1 measured:3 deviations:1 minimum:1 considered:1 neighboring:1 average:9 labbe:1 points:1 electrons:1 principle:3 exp:1 oxygens:2 izquierdo:1 physics:3 notion:1 fact:2 precise:1 phenomenon:2 show:6 doped:2 page:2 discovered:1 bright:1 jepsen:1 agrees:1 current:1 slow:1 onoda:1 parameters:4 should:9 only:1 abell:1 pairing:15 ambiguity:1 he:1 local:14 pointed:1 achieve:1 dk:1 klein:1 di:1 rotated:1 de:1 overall:2 preferred:1 universitetsparken:1 nearly:1 words:1 probably:1 dv:1 net:1 bagley:1 runs:1 denmark:1 arxiv:1 remove:1 greene:1 optimally:2 contain:1 including:2 supr:1 approaching:1 scanning:2 set:2 computed:1 fascinating:1 unpublished:1 correlations:4 respect:1 maximum:1 relative:3 arb:1 result:1 enhanced:1 recently:3 observed:1 statistically:1 closer:1 phases:1 vertical:1 ways:1 sites:2 yet:1 state:1 various:2 use:2 between:6 without:1 progress:2 approach:2 discovery:1 available:2 chamon:1 terms:1 reproduced:2 extend:1 nature:2 spacing:1 sts:3 weak:3 bscco:5 incommensurate:1 extent:1 hudson:2 striated:2 delivering:1 distribution:1 originates:1 suggested:1 both:5 cos:1 region:1 conclusions:1 thinking:1 dated:1 hwang:1 experimental:12 con:1 mcelroy:5 among:2 presumably:1 point:1 color:3 anti:1 16t:1 doping:1 cu:4 described:1 basis:1 addition:2 fournier:1 due:2 been:5 screened:3 much:3 expected:1 degrees:2 ph:1 choose:1 enable:1 corresponding:5 sufficient:1 coherence:3 incommensurability:1 precision:2 qsm:2 gap:23 gao:2 nunner:8 acta:2 presented:1 irrelevant:1 spirit:1 present:6 case:5 exponential:1 pacs:1 ij:7 empirical:1 value:4 remaining:1 will:3 near:3 behavior:1 tunneling:2 couplings:2 primacy:1 phenomenological:2 vi:2 ris:3 surface:1 coppens:2 strain:2 superconducting:6 itself:2 cond:5 howald:1 lengths:1 suggest:1 make:1 same:3 highlighted:1 units:2 several:1 asano:1 pan:1 independent:1 used:2 http:1 peaks:1 trivially:1 dasgupta:2 upon:1 effect:1 hand:1 v0:1 insulating:1 strength:2 dopant:10 center:2 hopping:3 studies:1 modeled:1 well:2 roughly:1 analysis:5 bohr:1 materials:3 solve:1 comes:1 coordinate:2 quantitative:3 model:4 researchers:1 usual:1 cuprates:1 uchida:3 less:1 gainesville:1 accurate:1 superconductors:1 obtain:2 cˆ:3 via:1 identify:1 atomic:10 yamamoto:1 ithaca:1 modulate:4 rapid:1 interstitial:2 density:2 cornell:2 5t:3 wavevector:1 lattice:7 ska:1 lett:5 samples:1 diagonalization:1 input:5 extensive:1 mod:1 unprecedented:1 match:1 real:3 bio:1 around:1 rev:14 term:2 early:1 hpc:1 background:1 using:2 essential:1 like:1 geballe:1 eisaki:3 diffraction:1 niels:1 manifest:2 consensus:1 integrals:1 fully:1 δg:1 disorder:6 reasonably:1 because:1 methods:1 sleight:1 successfully:1 understood:1 avila:1 specified:1 oscillations:1 nonzero:2 ignore:1 fov:4 scale:3 lead:1 measurements:3 interlayer:1 per:1 does:3 landscape:1 provides:1 assuming:2 refer:1 bf:1 hammond:1 ufl:1 wavefunctions:1 bi:5 kan:1 cryst:2 although:2 plots:1 intense:1 comparison:1 about:2 actual:1 would:1 oh:1 λsm:2 discussed:1 sro:1 o:7 simulation:1 range:2 neighbor:1 introduced:1 own:1 moss:1 madhavan:1 into:1 within:1 berthod:1 pair:7 en:2 determine:3 kapitulnik:2 gennes:1 statistics:1 additional:1 assumed:3 there:2 question:1 appl:1 low:1 way:2 conceivable:1 was:3 gij:5 izumi:1 form:2 cuo2:4 hs:1 smolin:1 muromachi:1 but:7 histogram:10 deville:1 repeated:1 construction:1 link:1 sled:1 true:1 partially:1 made:1 zhu:1 evident:2 deficiency:1 levin:1 cells:1 variations:2 up:1 crystal:1 below:1 un:3 fermi:1 spectroscopy:2 fluctuations:1 problem:3 stages:1 similar:5 display:2 ab:2 associated:5 computing:1 defined:1 certain:1 mckinnon:2 eom:1 our:3 accounting:1 eigensystem:1 perovskite:1 compared:2 no:1 extract:1 when:2 detail:1 ng:1 field:4 other:5 tij:1 spatial:1 department:2 correlates:1 slezak:6 forcing:1 conclusion:1 draw:1 pavarini:2 superconductivity:1 initio:2 subramanian:1 variation:1 generated:1 asensio:1 peak:3 included:1 structure:1 lang:2 correlated:1 coupling:4 coulomb:2 assume:1 required:2 holes:1 together:1 phonon:1 nextnearest:1 4k:1 remarked:1 bcs:1 |
0704.3674.txt |@word concept:1 sci:2 consider:10 similarity:1 induces:1 equalities:4 global:2 nikita:1 results:1 jcjc:1 c3:2 h45:1 proposition:22 generalize:1 computation:1 c2:1 consists:2 follow:1 primes:1 research:2 reasoning:1 soc:2 looking:1 γy:2 inverse:2 depend:1 calculate:4 paris:3 b42:1 dp:1 tn:2 finally:2 tk:4 th:1 under:1 aux:1 h8:1 hints:1 g7:1 p2:2 conjecture:21 tabachnikov:1 g3:2 g1:1 g0:4 far:1 than:1 straße:1 g9:2 choice:1 wishes:1 every:14 fractal:1 o5:3 34d:1 e36:1 randomness:1 immediately:1 presented:1 induction:3 t4:1 applicable:1 t1:9 deals:2 solved:1 k6:1 settle:2 c33:1 18g:1 small:4 eigenvalues:3 c32:1 inspection:1 round:7 11e:1 mn:5 h41:1 periodicity:27 b27:1 b26:1 b25:1 direct:1 literature:1 b20:1 past:1 second:2 hungary:1 further:2 dynamics:6 linear:2 even:1 3y:22 errors:6 plays:1 stands:26 iterating:1 morse:5 d2:42 assisted:1 l0:1 d3:19 polygonal:4 steiner:23 aperiodic:34 3o:1 3n:15 above:2 fractional:1 increasing:1 method:6 shallit:1 satisfy:1 κn:4 b37:1 l32:1 degree:2 exchange:3 respectively:16 bifurcation:2 equals:1 here:3 behaviour:1 l20:1 l23:1 γx:6 z8:1 z9:2 l27:1 l26:1 19e:1 path:1 κv:2 z0:2 εn:4 z2:4 z3:2 digits:1 remark:5 suitably:1 shift:1 study:2 allows:1 h0:4 periodic:42 survey:2 d52:1 action:4 hospitality:1 postponed:1 involves:1 golden:5 29e:1 classification:1 f1:2 discontinuous:3 inducing:3 arithmetical:1 planar:20 scaled:13 ask:2 apply:1 d10:2 b349:1 unit:3 f5:1 goetz:4 use:5 quasi:1 takes:1 prove:3 remains:1 positive:2 abbreviations:1 negative:2 e0:3 few:1 depicted:1 m1:7 therefore:19 m2:4 theoretical:2 more:3 introducing:1 elliptic:1 becomes:1 k0:3 refrain:1 appendix:7 intermediate:1 basically:1 dessins:1 particular:4 g4:2 cases:9 hold:1 easiest:1 must:1 h19:1 none:1 word:2 h6:1 dep:1 science:2 work:1 h14:1 h16:1 values:7 nonlinear:1 following:25 primitive:3 trans:2 proof:27 f0:1 b17:1 vivaldi:14 o3:2 f4:1 conf:1 figure:67 f7:2 process:1 december:1 organized:1 g5:1 high:1 assumptions:2 numbers:1 c19:1 dj:1 yγ:1 times:3 reprove:1 k4:1 b14:1 end:2 goal:2 eng:2 provide:1 int:3 discussion:1 get:1 dκ:1 feature:1 write:1 maps:30 nontrivial:1 pseudo:1 fourth:1 dg:2 instead:1 b15:1 o1:1 map:45 fr:1 de:8 irrational:2 sˆ1:8 may:2 max:3 orbits:4 b486:1 tresser:2 consequence:1 plane:2 inst:3 faculty:1 date:1 representations:1 summarize:1 g8:1 shigeki:1 recursive:1 dσn:1 short:2 natural:1 dynamical:5 third:1 computations:1 author:3 lines:10 su:1 sk:1 i20:1 complexity:1 davies:1 sn:6 alphabet:1 necklace:1 representation:1 order:5 haus:1 holds:9 o0:3 help:1 september:1 hugh:1 di:2 satisfied:9 60th:1 professors:1 course:1 paper:5 filters:4 differs:1 japan:1 satisfies:8 i27:1 ieee:1 its:2 l215:1 e16:1 tˆm:7 l114:1 le:1 symmetry:4 tˆk:6 la:1 chosen:1 fix:2 affine:27 tori:1 coordinates:1 systems:7 version:1 tˆu:6 morphismes:1 main:2 decades:1 into:15 s1:13 eventually:2 non:3 ℓp:7 return:25 university:3 pentagons:1 wolfgang:1 inductively:5 h7:2 scaling:10 h25:1 they:1 acta:1 l30:1 c14:1 rotation:3 now:5 s0:2 easily:5 term:1 finite:15 ℓj:5 nationale:1 hamiltonian:2 2x:17 2y:20 2d:1 cowie:1 l35:1 dk:4 b11:1 each:2 found:2 2n:21 higher:2 out:1 tˆ3:8 mean:5 heavy:1 domain:8 square:1 24a:1 another:1 24b:1 ed:1 idea:1 related:1 10g:2 contracting:1 m0:1 extended:2 aust:1 combining:1 tˆ:176 our:8 σ2n:1 description:1 rt:2 arguments:1 shown:4 matrix:1 admissible:1 rounding:1 furthermore:3 since:27 crucial:1 chaos:6 denotes:8 content:1 e42:1 d21:1 rational:8 reader:3 c34:1 postpone:2 suffices:2 d16:1 math:9 shows:23 foundation:1 numerical:1 b38:1 theory:4 associate:1 b36:1 contain:2 b30:1 b31:1 b32:1 standard:1 difficulty:1 completely:2 e9:3 e8:2 members:1 put:1 e4:4 e7:1 e6:2 l37:1 asn:1 e3:2 e2:3 definition:3 dl1:2 v1:35 geometry:1 computers:2 lossless:1 v2:15 mahler:2 filter:1 length:8 adic:4 c23:1 hopeless:1 circuit:1 hence:15 exhibited:1 first:24 h44:1 already:1 zah:3 o10:1 u1:44 dσ:1 coding:2 number:4 ℓk:25 instances:1 l34:1 multiplying:1 done:1 approximately:1 ℓm:11 l31:1 precisely:1 open:6 zas:3 l38:1 l39:1 given:14 checked:1 courbe:1 similarly:3 introduction:1 urbanachampaign:1 c0:5 system:1 construct:1 their:6 horst:1 statement:1 z5:1 scheme:1 structures:1 exponents:1 williams:1 gives:5 a31:1 arith:1 grant:2 za:8 part:8 l33:1 authors:2 za2:1 za3:1 entropy:1 e21:1 finitely:4 kind:2 sc:1 showed:2 was:6 approximations:1 i30:1 grey:1 express:1 determined:2 were:1 jussieu:1 treated:1 f8:2 e5:2 e28:1 ann:1 argument:2 generalization:1 lin:1 20a:1 smaller:2 ℓn:4 anr:1 conjugate:2 need:1 i18:1 apparently:1 clearly:2 viewed:1 f9:1 lie:3 h29:1 h28:1 b77:1 min:3 efficient:1 self:4 billiards:5 h21:1 ideas:1 converges:2 note:11 k2:4 maxh:3 cantor:2 k7:1 take:1 εk:1 εj:2 k9:1 l115:1 l112:1 l113:1 l110:1 l111:1 lectures:1 cnrs:1 appl:3 investigations:1 denominator:2 birkh:1 surv:1 algebraic:5 petrov:1 ˆs:1 eight:1 letter:1 remarks:3 d14:1 phd:1 parametrize:1 observation:2 nonlinearity:6 torus:3 partition:5 countably:1 kn:8 points:83 i15:1 exp:2 physics:1 section:23 fact:2 b45:1 emerging:1 radix:3 b40:1 12f:1 show:11 l28:1 supported:2 large:3 relation:1 drawings:1 d8:9 d9:9 d6:9 d7:8 d4:13 d5:9 trivial:1 find:1 d0:62 d1:83 e19:1 e18:1 based:1 parameters:1 e10:1 e13:1 basel:1 e14:1 topological:1 should:1 lemma:12 only:23 explicitly:1 stability:3 factor:1 partially:1 interested:1 b29:1 sur:1 characterization:2 do:5 dl:2 his:1 triangle:1 σ1n:1 cubic:2 exceptional:1 df:2 syst:4 dd:1 between:4 db:17 stripes:2 da:20 3x:32 famous:1 dyn:3 dz:3 words:3 lattices:1 symmetrically:1 du:1 ds:1 κk:1 dq:2 prime:2 gray:2 graz:1 exhibiting:1 5h:1 fields:1 arxiv:1 i11:1 ˆm:1 woess:1 circuits:1 i6:2 mapped:1 fixed:4 automatic:1 set:36 thesis:1 exists:9 sep:1 national:1 subtracting:1 j0:2 box:1 observed:1 see:13 computer:3 close:1 b13:1 dµ:4 satisfying:5 inequalities:1 dn:2 subsequent:1 currently:1 i10:1 symmetric:2 web:1 written:1 classes:1 closed:1 simplest:1 invariant:1 boundary:1 mono:1 conditions:13 grabner:1 choose:7 h10:1 endt:1 extend:2 tables:1 originated:1 attention:1 jp:1 however:3 e15:1 wu:1 hypothesis:2 french:1 key:1 distinguish:1 article:1 amer:1 come:2 thank:1 c22:1 both:1 cos:9 universit:1 last:2 σn:13 sierpinski:1 many:5 ill:1 c29:1 according:1 dl3:2 propagation:1 connection:1 objects:1 figures:2 symplectic:1 embedding:2 l25:1 l24:1 arbitrarily:1 dm:2 d13:2 point:16 cc:1 overview:1 l211:1 period:19 l213:1 l212:1 dimensional:2 z4:2 cy:1 ashwin:2 decreases:1 sequences:7 respect:2 24e:1 h13:1 z6:2 bλ:1 code:1 c31:1 transformations:2 piecewise:32 trajectory:24 l21:1 three:3 z1:2 hitting:1 ely:1 much:1 interest:1 ah:15 pk:1 prototype:1 pn:1 abstract:1 empty:1 define:6 obtained:1 ergodic:4 i13:1 corresponding:3 sˆ:37 sawtooth:1 sufficient:3 dℓ:58 gutkin:2 dates:1 else:5 h30:1 fractals:3 observe:2 understand:1 bull:1 liafa:3 c26:1 c1:2 evidence:1 dh:4 c6:2 present:2 c4:2 case:24 e43:1 p0:1 p1:8 e46:2 look:1 u1n:2 propositions:1 c25:1 aip:1 will:1 euclidean:1 near:1 dν:1 suppose:5 2b:3 involved:1 situation:2 revisited:1 2k:4 c28:1 k1:4 a20:1 a21:1 seven:1 a23:1 k3:2 l22:1 played:2 almost:2 metric:1 dι:1 thus:6 concatenation:1 equal:1 ii:1 characterize:1 dual:5 vw:2 chambers:1 13g:1 thue:5 20b:1 inf:1 debrecen:2 acknowledgments:1 different:5 dε:2 verified:1 d11:1 considerable:1 sensitive:1 lengths:12 suggest:1 make:1 i23:1 i24:1 i25:1 same:2 dγ:18 c12:1 parts:9 split:6 proved:6 dα:48 composition:1 isometries:2 difficult:1 i9:1 calculation:1 used:2 pisot:1 trivially:2 i1:2 i0:6 i3:1 trajectories:9 i5:2 i4:3 i7:2 hand:3 h32:1 domains:9 moment:1 h36:1 auser:1 h34:1 koch:1 i12:1 h38:1 von:1 e32:1 fourier:1 off:8 center:5 possibly:2 c66:1 i2:1 e30:1 well:13 obviously:1 concrete:1 without:1 c5:2 sets:18 very:1 i2a:1 model:2 drawing:1 niigata:3 left:1 next:1 isometric:1 quoted:1 λy:1 allouche:3 obtain:24 valuable:1 isolated:1 thanks:1 using:4 e38:1 l29:1 previous:1 εm:1 conjugates:2 family:1 ny:1 conclude:2 seems:2 except:1 dc:1 e27:1 lattice:1 add:1 setting:3 lett:1 easy:2 theorem:37 role:3 extensive:1 mod:15 5a:1 remaining:6 generalized:1 real:1 c11:1 agence:1 possible:3 cf:1 several:4 five:1 21a:1 λak:7 integer:8 21k:1 occurring:1 attila:1 k8:1 necessary:1 isosceles:1 d12:1 follows:9 reduces:1 diderot:1 l36:1 f2:1 separately:1 triadic:1 steps:1 hung:1 b19:1 essential:1 melville:1 mathematical:1 i21:1 because:2 sequence:7 e22:1 some:49 back:2 b5:2 deduce:1 b7:2 b0:6 b1:3 b2:4 paragraphs:1 oscillations:2 a11:3 proofs:2 hungarian:1 b9:1 transport:2 i22:1 24h:1 possibilities:1 scale:1 l18:1 l19:1 l14:1 l15:1 l16:1 l17:1 l10:1 l11:1 l12:1 l13:1 does:1 exposition:1 provides:1 o8:1 o7:1 o6:1 allowing:1 o4:1 proc:1 o2:1 minimal:15 refer:2 γak:2 birthday:1 run:1 scientific:1 power:1 tˆ4:5 s13:2 s12:2 expansion:2 s14:1 substitution:5 relating:1 properties:2 injective:1 franco:1 a14:1 france:1 commun:3 tiling:1 o:8 simulation:1 j1:1 a2:6 greatly:1 akiyama:25 germany:1 suggestions:1 tˆ2:5 morphism:2 ıde:1 considerations:1 discretization:1 letters:1 image:2 rotations:6 ιk:1 h4:1 due:1 lies:2 as0:2 references:2 determine:6 bijective:1 substitutions:1 pentagon:2 area:1 recherche:1 support:1 there:11 question:1 lond:1 long:1 u2:13 accordingly:1 quadratic:5 sections:1 naturally:2 complete:1 form:1 b39:1 but:11 hu:1 hk:1 cedex:1 overflow:3 true:4 adler:2 h22:1 especially:1 iterates:2 u12:2 sidorov:1 partitioned:4 embedded:1 whether:1 completes:1 up:6 until:2 discretized:3 below:1 limit:2 d20:1 a13:1 russ:1 problem:5 similar:4 clear:1 b22:1 ac:1 phil:1 constant:7 links:1 defined:3 certain:23 ak:14 b3:4 linearity:1 e1:1 general:3 dξ:1 proves:2 exist:5 dλ:1 ιp:1 dζ:19 dη:5 dδ:1 az:1 dβ:49 check:2 constructed:1 again:6 codes:2 e33:1 polygon:1 no:8 c20:1 whereas:1 chua:2 illinois:1 field:1 disjoint:1 other:21 lowenstein:8 details:2 digital:5 department:1 mathematics:1 nr:1 ns:1 arithmetic:1 nice:1 a15:1 picture:1 a17:1 denote:1 calculating:1 a12:1 h37:1 preceding:2 time:3 a18:1 25g:1 a1:4 a0:9 a3:4 important:1 a5:11 a4:3 a7:1 a6:1 a9:1 honour:1 structure:1 implies:6 anomalous:1 dψ:1 dω:1 assume:3 dχ:4 i17:1 i16:1 modules:1 orbit:3 dπ:1 dρ:1 4n:25 c8:1 lying:1 dl2:2 resembles:1 determination:2 dϕ:2 having:1 dϑ:5 |
0704.3675.txt |@word limited:3 baganoff:5 l163:1 consists:2 consider:4 whose:1 fronts:1 calculate:3 auf:1 under:1 magnetic:1 summarizes:1 rise:1 connects:5 summarized:1 school:1 solution:2 vector:2 force:1 10o:3 consistent:4 surrounding:3 second:6 estimated:2 even:2 errors:1 blum:2 supplied:1 above:3 new:2 tips:1 shocks:1 never:1 residual:1 here:8 reported:5 represented:2 interpret:2 obtained:13 study:4 procedure:2 ne4:19 suitable:1 ne2:1 ne3:6 ne1:7 diameter:1 projection:3 explained:3 moran:1 total:3 plot:1 would:10 negative:2 kinematics:2 therefore:15 distortions:2 type:1 until:1 curvature:1 hofmann:2 warm:1 vpm:3 hole:16 aligned:4 must:5 mm:1 work:6 itself:4 springel:1 example:1 mezger:1 give:6 keep:3 absolute:2 feature:39 far:1 hot:4 answer:1 vf2:1 vollmer:11 description:1 earlier:2 confirmed:2 diagram:1 spectrometer:1 lenzen:3 correlation:6 order:22 wind:36 interpretation:4 over:3 before:1 connec:1 fit:4 destroyed:2 fig:42 shear:1 them:8 hawthorn:1 affected:1 combination:3 band:53 effects:1 they:18 represents:6 brightness:2 40o:1 routines:2 bonn:2 arrow:2 each:4 side:3 mean:3 series:4 displacement:1 extract:3 gradient:2 quantify:1 particles:4 re:2 linear:4 free:2 standard:2 formation:4 estimate:4 created:1 ism:7 onto:8 already:5 features:35 clear:3 another:2 ulpicher:1 he:11 similarly:2 approximately:15 needed:1 rates:1 too:1 inflow:1 centered:2 serabyn:1 binned:1 western:6 distance:7 matteo:1 likely:2 classes:1 tion:1 acquisition:1 mini:41 rao:1 ram:2 seen:6 seem:1 tells:3 ray:2 latter:1 responsible:4 isolated:1 oriented:2 fitting:3 2006a:4 forces:1 2006b:3 blue:4 germany:2 coil:1 acknowledgements:1 genzel:28 histograms:1 calculated:5 flow:9 inferred:1 sum:1 fitted:3 rayleigh:1 labels:1 infrared:7 colors:1 radio:14 northeast:4 proposed:4 explain:9 x7:15 judged:1 g00:2 do:3 klein:1 di:1 de:1 preferred:1 thatte:1 despite:1 report:3 runs:1 bar:7 covering:1 bad:1 vlos:1 reference:6 detection:2 depends:1 radius:4 result:5 fail:1 best:1 subject:1 away:2 irs:29 µm:5 drawn:1 approach:1 discovery:1 terms:1 nature:9 confusion:1 weak:2 however:6 extent:6 contamination:1 suggested:1 received:1 uncertainty:6 against:1 uni:1 contribution:4 argue:1 presumably:1 16c:3 grazing:1 conference:1 basis:1 three:5 been:10 extraction:4 much:5 interest:2 basic:1 25o:1 concerning:3 chile:1 spie:2 brightening:1 cygni:1 applied:1 originate:1 excited:1 near:1 suppose:1 gerhard:1 leaves:1 launched:2 ir:1 ii:4 interacts:1 containing:5 najarro:2 perform:1 border:1 clearly:7 complex:3 split:1 filtered:3 several:3 european:1 evolve:1 milky:4 hand:3 hartigan:2 nir:6 adopting:1 scenario:5 contact:2 dominating:3 left:4 unified:1 quoted:1 mie:1 epochs:9 identify:5 scattering:1 yet:1 previous:3 lacombe:1 had:1 eckart:30 wright:4 5o:2 transformed:6 east:7 brandner:2 l83:1 possible:13 possibly:5 boxes:4 indicative:1 background:10 radioastronomie:1 advanced:1 wavelenght:1 northward:2 adiabatic:1 salim:1 successfully:2 oln:2 escape:3 contaminating:1 dense:2 normal:1 cnd:17 hst:1 nicmos:1 losing:9 properties:4 meyer:9 anomalous:1 o:2 plus:1 slightly:4 considerations:1 faint:2 presence:4 rotations:1 down:1 lies:1 right:4 methods:2 compression:1 support:1 initial:1 approximate:3 width:5 collimated:17 way:5 resulted:2 was:13 medium:3 form:5 forming:1 magnitude:3 imprs:1 arrays:1 inside:2 maximum:3 devices:1 originating:5 moore:1 abstract:1 evidence:6 simulations:1 regime:1 no:9 whereas:1 when:2 ne:8 role:1 depoy:1 test:1 picture:1 models:2 uniformly:1 irs2:1 variable:1 jones:2 longer:2 bullet:4 assume:5 together:3 time:4 overplotted:1 leads:1 ward:1 layers:1 arcsec:7 inverse:1 technique:1 finally:1 marks:5 southwest:7 frequencies:1 geometrical:1 orientations:1 exact:2 presented:10 prevent:1 insignificant:3 measurable:3 sign:3 appear:1 axes:1 current:3 international:1 falling:1 filled:1 dem:1 supporting:1 agreement:8 along:17 appears:1 box:6 dusty:2 shift:1 studied:1 marrone:2 commonly:1 bow:10 diolaiti:3 inducing:1 marked:3 filaments:82 achtermann:1 planck:2 positive:3 suppl:1 perp:1 yusef:25 theoretical:2 diagrams:2 apparent:1 envelope:1 casey:1 appendix:9 clumpy:1 cases:3 rotational:2 collision:1 labeled:1 values:6 following:2 stream:2 predict:1 sample:4 performed:7 distinguishable:1 occur:1 divided:2 range:1 positional:3 map:3 mas:9 substructure:1 information:3 may:20 max:2 southern:7 produce:3 data:19 supersonic:1 dynamical:2 sw:8 ghz:1 ionized:8 so:4 representation:1 wavelengths:3 indeed:1 pointed:1 mainly:1 years:2 stability:1 motions:31 still:3 observational:4 derive:3 thank:1 how:2 interesting:2 vicinity:2 forms:1 mail:1 main:8 non:1 gray:1 disentangled:1 discuss:6 nor:1 name:1 arrows:6 instabilities:1 quarter:1 kband:2 significantly:1 populated:1 ed:6 gaussian:2 challenges:1 wavelength:2 crowding:2 shown:7 jackson:2 space:1 furthermore:1 formula:1 squares:1 shows:12 theory:1 mechanisms:3 possibility:3 besides:1 widths:1 motion:57 place:1 massive:5 swing:1 first:9 origin:2 symmetry:4 transform:1 fast:3 directly:2 ring:1 angular:4 size:5 given:7 structured:1 indicate:1 cooling:1 white:2 structures:11 fraction:1 asymmetric:1 continuous:1 astrophysics:3 zadeh:25 x3:12 x1:6 x6:3 than:16 x4:2 x5:4 cologne:1 l41:1 duschl:12 were:16 quataert:2 pre:1 san:1 correction:3 locations:2 allen:4 any:3 20o:2 unsuitable:1 note:4 potential:9 take:1 coincide:1 opposite:3 probes:1 especially:2 eisenhauer:5 average:2 later:2 drive:1 show:15 atom:1 friction:1 bright:8 ground:1 ratio:1 enough:3 only:11 black:19 thompson:1 helmholtz:1 get:2 ssw:1 designated:1 cannot:6 reveal:1 summary:2 bautz:1 relative:3 concern:1 surfaces:2 fails:1 invoked:1 label:1 behind:2 between:13 across:2 notice:4 august:1 concentrate:1 analyzed:2 pixels:1 concentrated:1 outflows:2 many:1 region:9 according:3 comes:1 stretched:1 associated:23 coker:3 west:9 mark:3 odel:14 combined:2 geis:1 breugel:1 direction:17 chan:2 formed:7 grayscale:1 observe:1 diffuse:2 those:9 sound:1 50o:1 profiles:1 orientation:5 discrepancy:1 cluster:14 l159:1 vesc:1 ambient:2 loosing:1 rouan:2 different:12 etc:1 l121:1 same:10 shifts:1 epoch:10 sams:1 investigated:1 maeda:1 kelvin:1 lutz:2 drives:1 driven:1 harris:1 changing:1 validate:3 largely:2 roughly:1 without:1 components:4 coordinate:5 model:14 tional:1 charged:1 beloborodov:8 rest:4 ekers:1 speed:1 conclude:1 seems:1 except:2 samples:2 around:8 psf:4 dark:1 confined:2 using:10 accepted:2 velocities:12 facing:2 either:1 gezari:1 respect:5 images:33 imager:1 provided:1 dimensions:3 confirm:1 cavity:19 kms:4 refer:1 process:2 power:1 convincing:1 equivalent:2 refers:1 comparison:10 central:35 discussed:6 stand:1 naos:2 image:30 references:3 determine:3 strip:1 burton:5 wade:1 area:6 assumed:2 astrometric:1 there:11 dispersion:2 low:8 stars:48 viscous:1 complete:1 jun:1 mnras:8 technologies:1 perpendicularly:2 embedded:5 usten:2 agree:2 connect:1 strongly:1 taylor:1 ak:1 describe:2 moved:1 deep:1 au:1 lifetime:1 moves:1 e38:1 field:10 valid:1 spatial:1 deviation:3 drift:5 includes:4 important:1 peak:2 60o:1 brandt:1 tanner:3 accretes:2 mass:17 8µm:1 accreted:3 resolution:11 original:3 arcsec2:2 represent:7 surrounded:1 sch:15 pointing:2 caused:1 astron:2 lacy:3 disk:27 preserves:1 tail:1 nodes:1 case:6 belonging:1 mpc:3 straightforward:1 very:4 translations:1 difference:9 list:1 large:6 small:6 past:1 rate:1 pass:4 further:2 what:1 sub:5 beattie:1 section:13 drifting:3 version:2 method:4 compresses:1 full:2 component:11 behaviour:1 stipend:1 directions:3 strong:6 observing:1 allows:1 amount:3 published:2 narrow:8 elongated:5 imaging:3 goss:11 wardle:4 via:5 layer:2 extinction:7 eddington:1 takes:2 contains:5 taken:3 more:7 flat:1 biretta:1 vl:4 corrected:2 emission:26 keplerian:7 known:1 none:2 herrnstein:2 examined:1 nine:1 viehmann:5 dec:10 compare:3 stated:3 pushed:1 arise:1 sharp:1 axis:8 influenced:2 needs:1 rather:5 maps:4 sellgren:1 galactic:32 derived:8 orbits:8 plane:21 fe:1 coming:2 choice:1 short:1 crowded:1 e29:1 negligible:1 thermal:4 paper:1 through:4 existence:2 its:5 adios:1 l71:1 actually:5 detected:6 φc:1 travelling:1 might:1 good:3 propose:3 naco:5 yr:5 easily:2 pc2:1 2d:2 radial:4 2l:1 found:2 universit:1 energy:2 hard:1 positioned:1 extended:6 expect:1 measurement:1 thick:2 really:1 divide:1 since:5 projected:6 research:2 dominated:3 issue:1 asp:4 offsets:5 rieke:4 backer:1 reason:3 brightest:4 nayakshin:1 inspection:1 just:2 conducted:1 consequence:5 upper:2 maillard:3 number:10 done:3 construct:1 bland:1 harbours:1 passes:1 unexplained:1 temperature:1 jet:6 introduction:3 interact:1 least:3 assumption:3 calculations:3 dfg:1 molecular:3 smoothed:1 observations:17 shifted:3 imprinted:1 part:10 bower:2 authors:3 observatory:1 aims:1 determined:3 str:1 toward:6 randomly:1 cometary:4 concentration:1 orders:1 lie:1 l95:1 extracted:3 finding:1 play:1 towards:7 koeln:1 quote:1 reach:1 most:17 significant:8 measured:6 torus:2 coincides:3 km:18 ks:19 starfinder:2 optical:1 velocity:25 physics:1 particularly:2 scattered:2 find:6 markoff:5 northern:51 less:8 distributed:1 being:6 factor:6 circle:3 his:1 dominant:1 notation:1 polarized:4 during:2 alexander:2 resolve:1 continuum:7 arxiv:1 investigate:2 common:3 inefficient:1 scoville:4 bars:2 set:2 astrometry:1 see:26 close:11 contour:2 lee:1 probable:1 various:1 probably:7 available:2 recently:2 spectroscopic:1 incident:2 zylka:2 distinguish:1 both:14 context:3 point:4 simple:3 smith:1 corresponds:1 dimensional:3 simply:2 described:1 due:14 pc:5 reduction:1 pa:4 collected:1 ph:1 lived:1 gas:32 precision:1 determination:1 systematic:1 grains:3 solid:1 reliable:3 while:10 behavior:1 error:4 sw1:1 sw3:2 sw2:1 sw4:2 sw7:7 melia:9 vol:2 apjl:7 rim:2 confining:1 ric:1 overlayed:1 shorter:1 emphasize:1 relatively:1 higher:4 used:8 levels:1 moving:5 purpose:1 yuan:5 recent:3 lower:9 analysis:5 paumard:24 edge:7 moultaka:1 distances:1 shape:12 alignment:1 conclusions:2 source:12 transformation:10 showing:1 emanating:1 apj:32 imposed:1 aitken:5 shaped:3 follows:3 signal:1 disks:1 flux:3 indication:1 alignments:1 sketch:2 often:1 begelman:2 some:19 back:1 hartmann:1 stolovy:2 sight:4 30o:5 30e:1 scale:2 l15:1 measurements:18 connecting:2 proc:2 inclination:4 run:1 bh:1 perpendicular:13 br:5 plots:1 intense:1 idl:2 into:9 within:19 integral:1 primarily:2 frames:9 wn9:1 ellipse:1 uncertainties:3 institut:2 question:1 long:1 moseley:1 ut4:2 analyze:1 sections:3 filamentary:5 filed:1 line:26 characteristic:1 uv:1 up:4 us:5 ur:1 spectroscopy:2 planes:1 highlight:1 similar:8 called:3 ordered:1 puget:1 defined:3 influence:1 single:4 parsec:10 amounts:2 dashed:1 excitation:1 generated:2 sides:4 structure:11 correlated:1 implies:2 required:2 diffraction:3 orbit:4 broad:1 having:1 once:2 code:2 rousset:3 results:15 existing:1 winds:5 contributions:2 centers:1 compact:5 young:1 granular:1 contours:1 include:4 indicating:1 vla:1 wavy:1 continued:1 vlt:5 entire:3 positions:11 shock:16 try:1 ofpe:1 optics:4 noted:1 smaller:2 zu:1 dynamics:1 universities:1 assisted:1 zhao:5 consistently:1 3d:1 body:1 chose:1 respectively:2 l23:1 l22:1 consideration:1 nachr:2 involved:1 larger:5 suggests:3 resulting:5 shaded:2 composed:1 geballe:1 ugel:1 scaled:1 limb:1 clockwise:5 loop:1 next:1 few:6 themselves:1 hydro:1 becomes:2 inclined:2 gendron:2 iii:1 account:4 crosses:2 thin:39 pichon:1 calculation:2 high:15 streamer:2 tan:1 hydrogen:3 regions:1 located:17 varies:1 filament:19 martins:1 light:5 counter:1 lines:4 correspond:3 allow:1 christopher:1 discussion:2 enet:6 produces:1 astronomical:2 move:1 symbols:1 including:2 krabbe:6 mentioned:2 fwhm:2 galaxy:7 contaminated:2 outer:1 hornstein:1 chosen:2 temporal:1 previously:4 bonaccini:3 pixel:9 eastward:3 material:17 subtraction:1 rotation:2 outlines:1 february:1 preclude:1 traced:1 identified:3 morris:10 kpc:2 l1:1 elston:1 astroph:1 related:1 variety:1 measure:4 our:19 out:9 matrix:1 cws:4 messenger:1 adaptive:5 supports:3 red:1 completely:2 70o:1 3kt:1 interaction:12 geometry:3 could:28 times:1 isotropic:4 biting:1 south:10 manuscript:1 blown:4 reaches:1 l33:2 observer:3 unknown:2 pott:3 system:11 cuadra:2 roche:1 their:20 accretion:12 final:2 shell:1 explanation:3 lists:1 july:1 observed:15 submitted:1 roberts:9 lesch:1 providing:2 westward:4 becklin:2 curved:5 constrained:1 apparently:1 linked:1 instrumentation:1 angle:14 able:2 mid:1 mechanism:1 arm:46 polarization:9 highvelocity:1 gravita:1 connected:2 but:11 preliminary:1 sfb:1 class:3 volume:4 subtracted:3 neutral:1 graphs:1 fowler:1 fact:4 text:4 supported:3 12n:1 rotating:3 purely:2 subtracting:1 postulates:1 based:5 knowledge:1 should:3 candidates:2 arcseconds:8 postulated:2 conica:2 local:1 means:1 overall:5 beam:2 ones:1 words:1 denominated:3 bondi:2 produced:3 processes:1 densities:1 16µm:1 luminosity:1 reid:3 contain:4 view:1 enhances:1 computed:1 expel:1 frame:5 turbulent:1 intensity:4 enhanced:1 luminous:1 closer:1 interacting:1 nuclear:1 southward:1 favor:1 identification:2 routine:1 physikalisches:1 neither:1 comparable:1 opening:5 hypothesis:1 key:1 probing:1 taking:3 equal:1 april:1 streams:1 passing:2 blandford:2 detailed:2 unclear:2 cm:3 cl:6 nonspherical:1 deflected:1 table:9 kinematic:4 addition:2 trajectory:1 outflow:41 corresponding:8 bulk:2 ao:1 ours:1 c1:1 ott:9 present:11 multi:1 appearance:6 value:3 will:5 sgra:78 gredel:1 vb:1 vf:1 almost:3 vk:4 thus:5 surface:3 vr:3 vs:2 ph1:1 hyland:2 orbital:1 cross:11 parts:2 northwest:4 schematic:1 largest:1 units:1 gets:1 infer:1 raymond:1 effect:1 dust:33 expand:1 destruction:1 ashley:1 center:43 modeled:1 well:16 residuals:1 redshifted:1 sets:2 position:35 heavily:1 proximity:1 sources:16 distant:1 paul:1 christou:1 density:4 ghez:7 supply:1 sky:12 add:1 vα:6 vδ:6 prominent:2 loss:4 displaced:1 like:3 lost:1 sizes:1 alternatively:1 become:1 indications:1 because:1 phenomena:1 convex:3 proper:58 supportive:1 demonstrates:1 avoid:1 overlap:1 does:4 masked:1 assuming:2 eso:5 vs2:1 noise:1 slight:1 journal:1 stellar:32 pressure:3 although:2 offset:6 supermassive:2 panel:3 about:9 actual:2 carried:4 universe:1 software:1 h2:7 interstellar:1 dataset:1 weighted:1 rigaut:1 van:1 additional:3 h92α:3 spiral:24 smoothing:2 describes:1 inner:5 function:2 north:7 overlapping:1 astro:1 repeated:1 ho:3 highest:1 falcke:9 partially:5 whether:1 levin:7 gravitational:6 smooth:3 placed:1 below:2 limit:6 demonstrate:2 distribution:2 radiatively:1 display:1 lobes:15 circum:1 compared:2 calibration:1 detail:2 collimation:1 other:6 riaf:1 predominant:4 conclusion:1 francisco:1 star:11 june:1 bundle:1 gatley:5 additionally:5 astronomy:3 portion:1 mosaics:1 |
0704.3676.txt |@word represent:9 gt:4 caused:1 results:22 four:1 generalize:1 gl:11 contributions:2 b380:1 bremsstrahlung:10 depend:1 ℜp:1 0gev:1 program:1 present:8 include:1 division:1 very:9 dokl:1 figs:3 difference:1 presented:2 t2:2 solved:3 vector:1 small:2 guy:4 noted:2 jhep:3 yaffe:2 htl:1 arnold:2 further:1 estimated:1 quite:1 subscripts:1 section:2 laurence:2 above:1 method:13 coefficient:5 full:2 ibid:1 here:1 reported:3 address:2 represented:3 along:2 strong:6 equations:7 obtained:2 search:1 colored:1 suitably:1 study:2 studied:2 p2:9 resulting:1 suitable:2 studies:1 cancellation:1 plotted:4 useful:1 extra:1 apr:1 integrations:1 gluon:5 redefining:1 research:1 select:1 flavors:1 use:3 tabulated:1 nucl:2 therefore:6 taken:1 diagrams:1 more:2 bhabha:1 emission:32 cases:2 iii:1 md:2 integrating:1 sastry:1 equation:2 work:7 mh:1 cat:5 labeled:2 values:20 temperatures:7 cal:2 following:3 trans:2 my:1 example:1 f0:8 imπ:1 figure:17 process:3 india:1 high:4 numbers:1 occur:1 needs:2 six:3 regions:1 instead:1 parameter:1 fr:1 ladder:1 earlier:1 derived:1 hence:1 coming:1 fits:9 rameters:1 law:1 data:2 constants:2 dynamical:9 sensitive:1 lines:4 κeff:1 definitions:1 order:2 superscript:1 over:3 itb:1 symbols:11 thermal:1 paper:1 including:1 mentioned:7 cola:1 gta:6 gtb:5 derive:1 longitudinal:8 traxler:1 fit:7 ln:1 gti:2 qgp:5 forms:3 parts:3 fig:15 hidden:1 defining:1 versus:10 good:5 cea:1 ya:1 obtaining:1 landau:3 scaling:1 suryanarayana:3 effects:8 they:1 now:1 represents:1 finite:1 thankful:1 merge:2 found:1 energy:6 hard:1 extended:1 loops:1 our:1 eq:41 shown:9 superscripts:1 quality:1 robert:1 rev:4 cancels:1 denotes:1 m2d:4 formula:3 gov:1 integrated:2 red:17 shows:2 after:1 mechanisms:1 ors:1 quark:5 ααs:1 moore:4 generate:9 e2:3 r0:10 applications:1 qred:13 virtuality:1 corrections:2 first:1 already:1 xl:12 variables:7 xd:2 multiplying:1 approximately:1 q02:2 xp:1 electronic:2 xt:16 given:27 temperature:5 similarly:2 eqs:17 behaves:1 construct:1 their:2 rates:7 calculations:4 articles:1 variational:1 exponents:1 aurenche:7 akad:1 transverse:10 part:14 b337:1 x2:12 x3:4 x0:5 x1:7 coefficients:3 eq0:1 barc:1 annihilation:1 determined:3 were:4 distinguished:1 result:1 exhibit:1 ane:1 ious:1 dp0:3 curves:4 need:2 seen:2 apparently:1 any:4 depending:3 c75:1 mechanism:1 polarization:15 fitting:1 generalized:7 thoma:1 strengths:6 circles:3 blue:2 pomeranchuk:3 centre:1 aws:12 involving:1 formulae:2 marie:1 probes:1 observation:1 considered:2 calculated:5 adopt:1 lpm:8 physics:1 fitted:4 quantity:1 show:3 text:2 labels:5 colors:1 xd4:1 solutions:1 keywords:1 d4:1 d2:4 q0:47 q2:30 based:1 parameters:11 mumbai:1 should:3 only:4 black:1 factor:4 integrate:1 virtual:6 dn:2 do:1 get:2 ssr:2 gef:34 during:1 processes:5 x21:1 arxiv:2 acknowledgments:1 nauk:1 t02:1 qk:1 fixed:4 2p0:1 requirement:1 set:2 reference:1 observed:2 see:3 p20:3 violet:1 recently:1 αs:27 tensor:14 nuclear:1 various:7 cooperation:1 between:1 progress:1 approach:4 d56:1 terms:5 qt0:2 missing:1 however:3 bose:1 braaten:1 tensors:1 essentially:1 ilb:1 region:1 equal:1 energies:4 figures:2 retarded:4 com:1 experimental:1 relevant:1 simple:3 cb:3 dimensional:1 iterations:4 ct:1 considering:2 addition:1 three:1 been:3 pa:1 interest:1 ph:10 define:4 dilepton:5 corresponding:2 quantities:6 photon:35 precision:1 demand:1 1gev:2 ruuskanen:1 those:1 case:3 p0:28 p1:9 pacs:1 solid:10 empirical:14 value:2 transformation:5 will:1 replaced:1 momentum:2 ultra:1 loop:2 phenomenological:5 thus:1 ii:1 im:7 different:14 circumventing:1 same:1 complex:1 units:1 dimensionless:6 several:1 higher:2 used:4 http:1 altherr:1 v1:1 levels:1 delicate:1 c67:1 well:2 without:1 solve:1 components:3 jean:1 arising:1 r02:3 proposed:1 obtain:2 atomic:1 tilde:3 zaraket:1 previous:2 except:1 improvement:1 color:1 transformed:3 plasma:8 remaining:2 match:1 real:2 rµ:8 thermalized:1 phenomenology:1 amy:2 using:14 necessary:1 alternatively:1 δe:2 soft:1 reduced:7 www:1 because:2 methods:1 namely:1 trends:1 debye:1 peter:2 25gev:3 provided:2 truncate:1 electromagnetic:1 integration:1 overlap:1 gelis:3 power:2 agreement:4 πred:2 plots:2 imaginary:11 includes:2 comparison:3 discussed:1 range:1 misleading:1 introduced:1 slightly:1 spht:1 into:2 integral:3 functional:3 pisarski:1 parton:2 einstein:1 hep:10 transfer:1 there:1 transform:1 lop:1 low:5 way:1 var:1 was:4 function:32 but:1 highest:1 especially:1 made:2 variations:1 cil:2 below:1 limit:1 cit:2 distribution:1 similar:1 clear:1 mtd:1 detailed:1 constant:5 choosing:1 defined:6 contribute:1 am:1 cbl:2 general:1 single:1 cbt:3 formalism:1 distributions:5 functions:18 compared:2 nc:3 when:2 nf:6 migdal:4 other:1 details:3 sponding:1 conclusion:1 deviation:1 calculating:1 αem:1 yahoo:1 generated:3 important:1 variable:10 coupling:12 wife:1 required:5 curve:7 mass:5 having:2 |
0704.3678.txt |@word limited:3 positions:1 surrounded:1 consider:3 remarkable:1 omont:2 caused:2 global:2 results:10 existing:4 four:2 code:4 broader:1 stochastically:1 constants:1 disk:99 optical:2 layers:3 arcsec:12 certainly:1 terms:2 calculate:1 paris:1 assumptions:1 should:2 young:1 send:1 protostars:1 presents:1 2004b:5 2004a:10 program:2 av:1 those:4 under:2 include:1 puffs:1 mixte:1 very:19 rise:1 cardelli:2 atoms:1 focus:2 prusti:6 electron:1 crosses:1 every:1 figs:1 atmospheric:1 emphasized:1 evaporation:2 vlt:3 cool:1 mathis:3 17th:1 chamaeleon:1 solves:1 experiencing:1 radii:4 correct:3 large:19 especially:1 small:6 optics:1 keene:1 upper:3 too:1 smaller:1 thin:1 exposed:1 bution:1 direct:1 goldreich:4 approximation:1 surrounding:2 likely:4 noise:3 chopping:2 profiles:2 further:1 implemented:1 carlo:2 targets:1 ionized:1 spectral:4 index:4 abundant:1 appear:2 nano:1 section:6 near:4 agrees:1 consistently:1 version:2 sur:1 goes:1 new:4 increasing:2 method:1 movement:1 compact:1 full:8 ms:3 degree:2 whose:2 here:5 understanding:2 behaviour:1 reported:2 explore:1 kamp:1 midinfrared:1 excess:4 ratio:4 along:3 strong:16 bode:1 appears:3 change:1 deduced:2 settling:1 great:1 thirty:1 bouwman:1 shift:2 drs:1 larger:6 allows:2 reason:1 commonly:1 hydrostatic:6 astrophysique:3 suggests:1 amount:1 resulting:2 chang:1 narrow:1 studies:1 composed:1 via:1 spatially:2 ratios:1 scales:1 apr:1 vii:1 while:1 magnitude:1 ugel:1 brought:1 visible:4 puffed:4 issue:1 illumination:1 total:3 planck:1 unit:2 predicted:9 use:3 charge:3 takes:1 photospheric:1 intense:1 visir:22 depth:1 predictions:9 france:4 tauri:2 few:4 camera:1 therefore:3 taken:8 survive:2 associated:1 25th:1 type:1 tell:1 today:1 more:8 vrba:1 flat:2 diamond:3 started:1 neglected:1 inclined:4 envelope:1 emission:45 tested:1 transient:1 transiently:6 normalized:2 particular:1 haebe:2 r0:2 monte:2 1µm:1 must:3 abundance:6 md:1 account:3 recombination:1 apjl:4 science:2 points:2 work:2 intercepted:1 reproduce:1 minimum:3 values:2 temperatures:2 den:9 believed:1 making:1 l129:1 equilibrium:9 example:5 decoupled:2 compare:6 weaker:1 strenghts:1 figure:4 give:1 process:1 thermally:4 flaring:15 organized:1 high:2 pinte:2 slit:1 mixture:1 performed:1 tab:1 palla:1 keep:2 hydrogen:2 species:1 absolute:1 information:1 needs:1 siv:9 january:1 boekel:4 divided:1 get:1 feature:15 occur:1 regions:6 located:3 varies:1 adjacent:15 strom:1 distri:1 parameter:2 simplicity:1 mas:5 impinging:1 description:1 seds:4 max:1 waters:5 after:2 variant:1 confirmed:1 millimeter:1 shukla:1 coming:1 date:3 spectrometer:1 law:3 data:11 grow:1 hotter:2 ene:2 intriguing:1 short:3 boeing:1 third:2 beam:1 following:2 pontoppidan:3 spectra:7 geometries:1 ledoux:1 rather:2 si:1 cannot:1 so:2 sect:6 decreasing:2 obvious:1 increase:1 order:9 typical:1 integrated:1 evolutionary:1 interpretation:1 closely:1 reservoir:1 produces:4 laboratory:2 indeed:3 over:3 insight:1 dullemond:21 meter:1 installed:1 thermal:12 paper:9 including:2 filters:4 affect:3 cold:1 still:1 fwhm:9 its:5 observational:2 shorter:1 some:4 group:1 evans:1 fit:3 how:2 chosen:1 interesting:2 hot:1 hydrogenation:3 circumstellar:7 detected:1 primordial:1 degrees:1 fig:12 annual:1 mail:1 main:3 image:10 versus:1 measurement:1 non:2 good:6 fourth:1 cea:2 material:4 band:15 effects:1 they:7 half:3 now:1 discuss:1 above:2 represents:2 february:2 itself:1 vibrational:1 offline:1 fully:3 classified:1 sufficiently:1 tielens:1 coagulation:2 nodding:2 mode:7 each:5 found:6 universit:1 quarter:1 characterized:2 constraints:4 individually:1 neii:3 telescope:1 energy:5 conditions:1 reduce:1 related:1 solution:1 constitute:1 extended:15 yvette:1 measure:1 quantum:1 wavelength:13 extract:1 standard:6 shown:1 rq:1 space:3 furthermore:3 since:6 particles:4 re:1 dsm:1 dominated:3 reflection:1 laboratoire:1 adaptive:1 induced:1 cause:1 perrin:2 red:1 shows:9 hendecourt:1 state:2 derived:1 several:5 mechanisms:1 given:3 free:2 quite:2 completely:1 formation:2 imaging:7 van:17 estimate:1 hand:4 telescopes:2 natta:5 silicate:20 geometry:5 midplane:2 could:12 inferred:1 r9:1 times:1 filter:12 iso:7 isotropic:1 bjorkman:1 assumed:1 iras:2 undergo:1 south:7 first:5 chopped:1 meeus:3 already:4 features:25 manuscript:1 rms:1 waves:1 hydrogenated:2 number:2 reaches:1 references:1 djie:2 fh:3 reflects:1 done:1 adopted:2 another:1 thick:6 fluxes:4 open:2 angular:2 size:8 little:1 temperature:4 service:1 width:2 introduction:1 revealed:1 winter:1 night:1 franco:1 system:4 least:2 their:1 intermediate:3 sheu:3 observations:23 1h:1 molecular:1 structures:1 final:1 ias:1 low:2 way:1 mostly:2 centered:2 part:7 l33:1 tef:2 authors:1 surprising:1 weintraub:2 than:8 positively:1 population:2 distance:5 parts:1 observatory:1 determines:1 morever:2 intensity:5 aims:1 matter:1 individual:2 submm:1 amplitude:1 were:12 geometrically:1 providing:1 spatiale:1 pre:3 function:2 astrophys:1 basically:1 radmc:2 emits:1 spectrum:6 kastner:1 waelkens:3 astrophysical:1 unlikely:2 seen:1 constrained:1 any:2 dapnia:1 lie:1 strength:2 angle:3 flared:15 astronomie:1 rout:1 able:5 mid:12 apj:6 situated:2 note:4 majority:1 fitting:1 absorbed:2 take:7 online:1 photosphere:1 davies:2 detector:2 silicates:2 specifying:1 even:2 play:1 experienced:1 lagage:17 object:7 reach:3 justify:1 extending:1 doucet:13 errors:2 germany:1 comparisons:1 measured:3 ujf:1 lee:2 observation:2 radiating:1 won:1 considered:2 calculated:6 adopt:2 stronger:2 neutral:1 32l:2 mjy:3 kr:1 mrn:1 accounted:2 principle:1 wesselius:1 chiang:4 constrain:4 shadowed:2 physics:3 review:1 dot:1 slope:1 jonkheid:1 particularly:1 phenomenon:1 show:4 detection:1 probe:1 degrades:1 infrared:7 mnras:1 bright:1 superimposed:1 convolved:2 rough:1 longer:2 find:1 ground:1 symmetric:1 photoionisation:1 finally:8 based:10 knowledge:2 parameters:8 destruction:1 true:1 explain:3 behind:1 peculiar:1 launhardt:2 only:7 wood:1 black:2 molecules:1 factor:1 emitting:1 columns:1 centrally:2 briefly:1 do:6 cube:2 triangle:1 tracers:1 bonds:1 beams:1 de:3 soon:1 aim:2 ones:3 photoelectric:1 words:2 probably:3 nanodiamond:1 unfortunately:1 reveal:1 processes:2 resolve:1 continuum:23 wavelengths:2 luminosity:1 arxiv:1 median:1 suggested:1 summary:3 stored:1 common:3 through:1 implication:1 kilkenny:1 view:1 hydrocarbons:1 irradiation:2 reference:6 burst:5 bary:1 variations:1 sensitivity:2 geometrical:2 emergent:1 module:2 freeze:1 observed:20 see:13 sed:11 radius:11 result:3 close:3 forthcoming:1 best:2 gmail:1 closer:8 exploited:1 pictures:2 away:3 nebula:4 underline:1 µm:50 enough:3 smallest:1 identification:1 correctly:1 between:13 tens:1 progress:1 boundary:1 timmi2:1 wide:1 available:1 gives:1 abundances:1 various:1 recently:3 jy:1 vertical:1 weak:3 however:2 rapidly:1 spectroscopic:5 clayton:1 reproduces:2 cut:3 hypothesis:4 key:2 contamination:2 outer:9 reappears:1 hundreds:1 come:1 pixels:2 paranal:5 both:5 recherche:1 toward:1 hillenbrand:4 region:12 density:3 heating:1 comparaison:1 objects:4 grain:3 receives:1 absorption:2 requests:1 com:1 comes:1 nearby:2 reside:2 among:2 extent:1 habart:9 point:2 simple:6 corresponds:1 l213:1 height:6 kerckhoven:4 nearir:1 carbon:8 table:3 li:3 graphite:2 enard:1 considering:1 5m:2 atmosphere:1 chopper:1 described:2 decoupling:2 instrument:2 addition:4 west:9 radiative:6 due:7 been:9 pc:4 reduction:1 much:8 slowly:1 treat:1 interest:1 expected:1 kalas:1 ph:1 extreme:1 closed:1 siebenmorgen:3 obtained:7 direction:9 enable:1 ancker:9 deeper:1 testi:1 concerning:6 coherence:1 gas:5 essentially:1 modelling:1 determination:1 external:1 chile:1 astron:1 evidence:2 myr:1 former:2 present:6 case:6 extracted:1 microns:2 fur:1 look:8 grains:25 developing:1 isolated:1 originate:1 budget:1 value:3 pixel:3 will:8 dominik:14 fiducial:1 intercepts:1 exist:1 study:2 va:1 layer:1 stretching:1 pahs:23 coupled:2 almost:2 ir:19 thus:1 them:3 surface:15 equal:3 rin:3 middle:1 rim:7 henning:2 nordsieck:1 different:7 walch:1 l55:1 multiphoton:1 graham:1 radiation:6 cross:2 same:8 clearly:2 equiped:1 attributing:1 became:1 pah:54 constructed:1 events:1 excited:1 calculation:1 used:7 peaks:1 pah2:4 absorb:1 blue:2 upon:1 effect:3 coralie:1 possible:3 moment:1 bastien:1 dust:18 contribution:2 recent:1 acke:5 lower:2 modes:3 mention:1 nevertheless:1 disappears:1 well:4 thought:1 directly:2 duchˆ:2 modelled:1 does:2 sets:1 position:1 model:48 chemistry:1 arising:1 self:2 left:6 bending:1 construct:1 halfmaximum:1 proposed:1 less:4 photo:2 rest:1 quarters:2 sources:1 shape:3 underlying:3 thanks:1 predicts:3 turbulence:3 augments:1 uller:1 scattering:2 yet:2 previous:5 settles:1 rapid:1 preprint:1 cm:1 farther:1 conclusions:2 irradiated:2 photons:1 brightness:3 hae:6 passive:3 source:4 add:2 other:4 east:9 heidelberg:2 match:1 tests:1 photometric:2 around:16 checking:1 bands:4 showing:1 bib:1 polycyclic:1 dark:1 tracks:2 press:1 using:5 shadow:4 grenoble:2 wings:1 psf:8 vertically:3 like:3 sizes:1 follows:3 signal:2 disks:14 specific:1 flux:9 either:2 confront:1 rate:2 qualitative:1 whittet:3 opacity:2 because:5 methods:1 classical:1 sequence:3 affects:1 herbig:10 dimensional:1 cnrs:2 added:1 sight:3 respect:1 images:13 indirect:1 guess:1 reasons:2 scale:5 dimensions:1 umr:2 broad:1 measurements:1 vibrations:1 cloud:1 assuming:2 eso:3 cerro:1 inclination:1 airmass:1 run:1 power:2 molecule:1 equivalent:1 processing:1 agreement:10 stellar:10 pressure:3 confrontation:1 although:1 2m:1 drawn:1 properties:5 panel:2 comparison:1 about:5 photometry:2 central:10 would:4 extension:6 most:9 discussed:2 dependence:1 o:3 ism:2 range:3 mixed:1 bond:1 seeing:7 computes:1 presence:3 fraction:3 instruments:1 into:4 within:3 interstellar:2 down:1 appropriate:1 right:4 rising:1 decrease:1 determine:1 heated:11 elementary:2 orsay:1 significantly:1 uncertainties:1 institut:2 comparing:5 reynaud:1 transfer:6 support:3 there:3 convincing:1 montecarlo:1 long:4 class:1 gif:1 l133:1 gaz:1 inner:16 stars:21 astrophysics:2 slopes:1 was:4 naturally:1 hz:1 compensate:1 underestimated:1 medium:1 north:7 hs:5 hp:1 differences:2 analyse:2 but:9 sophisticated:1 astro:1 draine:4 cedex:1 jones:2 solar:1 convolving:1 counterparts:1 groundbased:1 line:12 nodded:1 sws:2 hd:31 partially:1 rumpl:1 made:7 absence:4 kurucz:2 whether:1 characteristic:1 uv:1 attached:1 up:13 us:1 prep:1 weidenschilling:2 template:4 frequency:1 limit:3 emissions:1 distribution:13 similar:4 emit:2 expect:1 strongly:1 peaking:1 pantin:2 ae:10 defined:1 abstract:1 describe:4 influence:1 general:2 globally:1 single:2 au:23 planets:1 our:12 orders:1 corresponding:2 moves:1 distributions:1 check:1 physical:4 compared:5 no:3 asymmetry:1 dashed:5 whereas:3 nc:2 when:3 detail:1 aromatic:7 field:4 interested:2 role:1 details:2 spatial:17 extinction:1 out:2 acceptable:2 optically:7 perpendicular:1 star:28 excitation:1 models:7 mismatch:1 tjin:3 june:1 includes:1 a0:1 important:1 peak:1 included:3 complications:1 moreover:3 astronomy:1 diamonds:1 structure:16 exposure:2 offprint:1 independently:1 coupling:1 algorithm:1 assume:1 age:1 confirm:1 diffraction:7 saclay:1 fuv:2 siess:1 warm:2 mass:8 fact:3 time:6 far:1 resolution:5 original:1 once:2 |
0704.3679.txt |@word consider:2 caused:1 astron:2 dynamic:1 results:3 extensively:1 leads:1 roy:1 scalar:9 entropy:2 gr:5 kratochvil:1 sahni:2 caldwell:3 rel:1 behave:1 those:1 th:7 tegmark:2 presently:1 zhang:2 very:1 onemli:1 rise:1 choice:1 interpreting:1 guo:1 mp4:4 solved:2 convenience:1 enclosing:1 small:1 mp2:5 cmp:1 employing:1 garnavich:1 riess:1 cosn:12 sin2:1 cosh:1 setare:6 astrophys:3 zero:1 dynamics:3 b535:1 substitute:3 established:1 hde:5 find:4 3h:1 above:3 3c:3 filled:1 coefficient:2 evolving:1 iran:1 lee:1 respectively:3 never:1 here:2 provides:1 sinn:4 sinh:1 investigating:1 ratio:1 equations:1 change:1 box:1 inspired:1 studied:4 contradiction:1 suggests:1 action:1 jackiw:2 bertolami:1 scales:3 apr:1 vio:1 ipm:1 total:2 establish:1 planck:1 d73:1 use:2 d71:1 commun:1 remains:1 positive:3 negative:2 sitter:2 therefore:3 expanding:1 robertson:1 type:2 theoretical:1 more:1 flat:6 tsujikawa:2 bennett:1 6c:1 apparent:2 curvature:6 hole:2 linder:1 zimdahl:1 must:2 comoving:1 science:1 equation:11 ρm:7 theories:1 3mp2:5 values:1 mp:6 universe:19 following:6 field:14 example:1 thooft:1 claim:2 wang:4 cosmological:5 relativistic:1 arise:1 weinberg:1 states:1 sphere:1 sense:1 bonet:1 copeland:1 fischler:2 rays:1 provide:1 write:1 parameter:2 sin:1 simplicity:1 description:1 kahya:1 may:1 sami:2 consequence:1 data:1 short:1 dynamical:1 effective:4 su:1 element:1 accelerated:2 so:2 fundamental:1 definitions:1 order:2 evolutionary:1 dx:1 pointed:1 mainly:1 soc:1 paper:4 mentioned:1 kinetic:2 its:3 huterer:1 derive:2 ln:1 interesting:2 starobinsky:2 li:3 late:1 degrees:3 mail:1 h0:2 correspondence:5 non:2 pressureless:1 framework:1 souza:1 b574:1 now:6 yu:1 barrow:1 easily:4 term:2 ωk0:2 university:1 hepth:1 inequality:1 l3:1 reasonable:1 radial:1 2h:2 homogeneous:1 energy:41 related:2 literature:2 grav:1 combining:1 quantum:4 our:2 eq:2 event:9 out:1 emerges:1 shown:3 space:3 since:3 rev:14 denotes:2 lapuente:1 dominated:2 ra:1 emerged:1 rh:22 math:2 theory:4 free:1 gumjudpai:1 dω2:1 definition:2 hubble:2 r1:5 ds2:1 excluding:1 times:1 hence:1 first:1 origin:1 initial:1 features:1 relate:1 number:1 2a6:2 directly:1 open:1 size:4 given:5 rewritten:1 introduction:2 eqs:7 saini:1 system:5 assumption:1 observations:4 dt2:1 white:1 behaved:1 gives:2 alam:1 b235:1 distance:2 showed:1 see:3 viollier:1 matter:6 future:3 b575:1 derivative:1 pasquier:3 intriguingly:1 cohen:2 argument:1 sen:1 turner:1 null:1 acceleration:1 strength:1 ratra:1 convenient:1 mechanism:1 chiba:1 instance:2 potential:5 take:1 kaplan:1 linde:1 play:1 bordemann:1 steinhardt:2 measured:2 why:1 fair:1 considered:1 saturate:1 kr:2 points:1 principle:3 fact:2 show:1 implying:1 relation:2 d9:1 carefully:1 debate:1 chaplygin:15 based:2 should:1 only:2 black:2 factor:3 local:1 perlmutter:1 ruiz:1 do:1 shmakova:1 get:4 vary:1 de:8 fluid:3 ρcr:4 aγ:5 words:1 reconstruct:2 dr:2 gen:1 evolution:1 arxiv:1 mon:1 qc:5 experiments:1 view:1 shapiro:1 set:1 reference:1 frame:1 observed:1 depends:1 radius:2 result:1 3c4:1 lna:2 violates:1 3c2:3 attempting:1 review:1 pavon:1 tend:1 state:5 difficulties:1 cooray:1 closed:3 between:6 limit:1 gonsalves:1 approach:1 nature:1 supernova:1 sola:1 huang:1 motivations:1 odintsov:6 cos:1 many:1 taking:4 conclusions:1 according:4 candidates:1 adapted:1 sloth:1 relevant:1 moschella:3 point:1 simple:2 coincidence:1 elizalde:1 constant:11 ogawa:1 branes:1 considering:3 described:1 basis:1 due:1 been:3 int:1 polychronakos:1 frw:4 interest:1 ah:1 expected:1 6c4:1 ph:4 ann:1 define:1 obtained:1 direction:1 arises:1 gas:12 dave:1 cosmology:5 c2:2 present:5 case:7 reliable:1 value:2 will:3 while:2 replaced:1 situation:2 gorini:1 ir:9 thus:2 surface:1 b511:1 obeying:1 reads:1 ia:1 conserve:1 different:1 l53:1 suggest:2 same:1 reconstructed:1 widely:1 largest:1 dimensionless:1 investigated:1 hand:1 phy:1 kim:1 dust:1 kamenshchik:3 recent:1 task:1 off:12 scenario:2 well:1 remain:1 solve:1 studying:1 undertaken:1 model:10 possesses:1 usual:1 proposed:4 obtain:6 infeld:1 jcap:4 cut:12 density:17 hoppe:1 nojiri:6 lett:23 outermost:1 possible:2 dark:26 holographic:24 unification:1 know:1 using:7 unique:1 8πg:1 mod:2 like:2 particle:1 accelerating:1 separately:1 abdalla:1 either:1 pereira:1 exceed:1 because:4 people:1 some:4 born:1 pφ:1 respect:1 proper:1 hannestad:1 scale:3 lead:1 bento:1 myung:2 integration:1 does:2 noor:1 inserting:1 2c:3 expansion:2 pressure:3 hsu:3 bilic:2 a0:2 instantaneously:1 freedom:3 discussed:3 o:3 compatible:2 greatly:1 horizon:14 consequently:1 d62:1 raised:1 almeida:1 h2:1 into:3 within:1 bound:1 suppl:1 references:1 determine:1 wλ:2 hep:7 area:1 there:3 long:1 conservation:1 fabris:1 way:1 hooft:1 was:4 lowe:1 form:3 forming:1 but:1 hu:1 astro:4 tupper:2 bazeia:2 hl:1 ling:1 line:1 uv:2 ωk:9 decays:1 ωm:4 problem:7 similar:2 gong:1 associated:2 defined:2 certain:2 abstract:1 describe:3 single:1 ar:1 friedmann:4 compared:1 susskind:4 when:5 application:1 other:3 role:1 capozziello:1 department:1 b641:1 b642:2 easther:1 b644:1 peebles:1 models:2 enqvist:1 replace:1 ωm0:3 a2:2 a6:9 variable:1 b317:1 implies:1 assume:1 required:1 eos:1 implied:1 mass:2 nelson:1 time:4 walker:1 |
0704.3680.txt |@word aln:1 extrapolated:1 illustrates:1 interference:1 magnetic:9 lack:1 rod:1 resistance:2 bhatt:1 four:1 follow:1 cases:1 localized:2 dimensionality:5 longstanding:1 technique:1 supported:2 quasi:1 does:1 present:1 under:12 tf:6 lh:3 cm2:7 indicating:5 applied:2 random:1 far:1 dynamic:1 kω:1 assuming:1 n3d:7 keeping:1 results:4 oxides:3 electron:24 crosses:1 ultraviolet:3 khmel:2 uwe:1 leads:1 hikita:1 level:1 deficient:1 anisotropy:1 hussey:1 t2:1 t0:2 large:5 small:4 sano:1 shows:6 tshuler:2 related:1 hasegawa:2 smaller:3 compensated:1 l2h:2 consistent:3 estimates:1 sign:2 approximation:2 zero:2 pass:2 rigorous:1 further:1 estimated:3 lmin:2 scientific:1 even:2 trapping:1 giving:1 localization:15 near:4 supplied:1 uniform:1 current:1 above:3 new:2 increasing:2 ever:1 semicond:1 contrast:2 thin:1 coefficient:3 edited:2 agreement:1 full:1 lee:2 degree:1 fiz:2 eksp:2 spacing:1 here:1 atoms:1 reported:3 srtio3:26 inverse:1 relaxation:2 dewar:1 path:2 strong:1 appears:1 logarithmic:2 deduced:2 great:1 oxford:2 study:2 larger:2 allows:2 reason:1 suggests:1 resulting:1 licciardello:1 suitable:2 studies:1 york:2 ovadyahu:1 mobility:19 apr:1 semiconductors:5 plenum:1 highly:3 illumination:20 triscone:1 planck:1 kobayashi:1 predicted:5 shirai:1 conventional:4 figure:7 would:1 positive:2 until:1 charge:1 sports:1 fet:2 regel:2 m0:1 taken:3 asahi:1 reflects:1 more:1 smeared:1 zh:2 clearly:2 becomes:1 apparent:1 about:2 normalized:1 varying:8 known:1 hole:2 iv:1 iii:1 potential:1 states:2 account:1 recombination:1 ma:1 room:1 tokyo:3 science:4 equation:2 work:1 mi:8 mk:1 mw:2 lorentz:1 values:2 three:7 ms:1 following:1 mott:9 performed:1 control:1 indicated:5 give:1 neglected:1 o2p:1 sample:13 indicates:2 minimum:7 caused:1 numbers:1 degenerate:1 sharp:2 chapman:1 absolute:1 motion:1 lumin:1 varied:2 carriers:1 rather:3 discussion:1 feature:2 chemical:1 how:1 lamp:1 criterion:4 gate:1 films:1 profile:2 fr:1 description:1 may:7 magnetotransport:2 fz:1 after:1 minimized:1 diagram:1 takenaka:1 mag:1 photoluminescence:1 geometrical:2 revealed:1 response:2 curve:2 short:3 effective:6 light:19 spectra:1 correspond:2 mannhart:1 beyer:1 sons:1 so:1 inhomogeneity:3 decreasing:5 american:1 order:6 typical:4 wavelengths:1 over:2 competing:1 solids:1 thermal:1 including:1 filters:3 ity:1 unfavorable:1 japan:4 suffer:1 before:2 thomas:1 longitudinal:4 thank:1 decay:1 2e2:1 interesting:1 fix:1 vicinity:1 exhibits:3 absence:3 systems:4 insulator:4 mail:1 deformation:1 eventually:1 acknowledgments:1 good:1 affected:1 universality:1 material:2 investigated:1 landau:1 band:5 penetration:7 effects:3 eµ:1 inelastic:3 hall:8 dielectric:5 oxygen:2 university:3 drop:4 magnitude:4 transmitted:1 2a:1 reasonable:1 katsumoto:1 characterized:1 mean:2 heavy:1 el:1 bridging:1 square:1 eh:1 generation:2 ed:2 energy:5 nea:1 used:4 abrahams:3 conductance:7 owing:2 σ2d:3 measurement:4 wavelength:16 approximated:2 transitions:2 extract:1 repulsive:1 mat:1 magnet:1 shown:7 furthermore:1 crucial:1 projected:1 research:1 semiconductor:2 modulation:1 investigation:1 dominated:1 suggesting:1 induced:1 ref:2 occurs:2 chemically:1 fiber:1 ecc:1 theory:2 interactions:2 free:3 standard:1 approaches:1 threedimensional:1 imaging:1 nakamura:1 estimate:3 e2:7 pairs:1 interaction:3 ministry:1 geometry:8 transition:11 imry:1 filter:1 length:2 teor:2 diminishes:1 eqs:1 note:1 enhances:1 grade:1 number:1 xe:1 fujimori:1 defects:2 another:3 reached:2 precisely:2 electronic:10 given:3 sheet:11 temperature:25 indicate:1 introduction:2 data:6 πh:4 hν:1 photoconductivity:1 system:5 parallel:1 their:2 furuuchi:1 milligan:1 john:1 ranging:1 gives:4 correlations:1 trapped:1 relative:1 continuous:1 wiley:1 immediate:1 transverse:2 optical:7 jp:1 maintaining:1 than:9 diffusion:3 wide:1 third:1 measured:1 intensity:23 str:1 were:5 bare:1 larkin:3 treated:1 descriptions:1 exhibit:1 lowest:3 modulating:1 izumi:1 correction:6 measure:1 crossover:3 in2:1 cyclotron:1 analysis:2 qualitatively:2 kikuchi:1 komori:1 any:2 strength:2 partly:1 lin:1 agency:1 lǫ:2 mechanism:1 metallic:5 chiba:2 high:6 materials:4 take:1 analogy:1 online:7 techniques:1 blunt:1 kawaguchi:1 transistor:1 electric:3 opposite:1 correlation:2 reach:1 most:1 satisfying:2 significant:1 tanaka:1 extremely:2 nagaoka:1 kf:5 neighboring:1 ramakrishnan:1 phil:1 metal:7 inoue:1 proceedings:2 points:1 electrons:9 physics:1 wavenumber:1 2m0:2 show:1 violation:1 doped:6 scattered:1 purely:1 expressed:2 threshold:1 rough:1 thickness:10 kravchenko:1 gefen:1 o:1 feng:1 based:2 onoda:1 spite:1 conduction:4 controls:1 should:3 terminal:1 only:3 going:1 corresponds:3 screening:3 equipped:1 employed:1 equilibrium:1 characterization:1 do:1 dominant:3 dependent:9 dc:1 magnetoresistance:35 cannot:1 nonequilibrium:1 despite:1 report:2 takahashi:2 densities:1 arxiv:1 shape:2 remove:1 tuned:1 investigate:1 common:1 though:1 tunes:1 through:1 force:1 irradiation:1 attenuated:1 enabled:1 semiquantitative:1 observed:19 culture:1 namely:2 electrostatic:1 radius:2 result:2 discussions:2 close:3 conductivity:18 wire:1 exponent:1 nondegenerate:2 subsequent:2 takagi:3 bias:1 tend:1 µm:1 state:5 inset:1 between:3 fermi:4 justified:1 across:2 grabner:1 comparable:2 terms:3 responses:1 extend:1 nature:2 importance:1 commercial:1 weak:14 however:4 efficiency:1 incident:1 jetp:2 distribution:1 originates:1 suggested:1 both:1 paalanen:1 σc:2 many:1 taking:1 conclusions:1 according:1 ln:5 aronov:2 context:1 irradiated:1 exceeds:1 contribution:1 estimation:2 hwang:1 experimental:1 originating:1 relevant:1 co:3 cm:22 point:1 color:7 address:1 resistivity:2 2nd:2 dimensional:18 directions:1 decreases:1 doping:5 crystalline:1 considering:1 tuning:4 geometries:7 source:1 addition:4 due:4 been:10 screened:1 reduction:1 much:7 basic:1 anisotropic:2 cohen:1 fig:18 imada:1 controlled:2 gas:1 kashiwa:2 gap:3 bulk:1 observe:1 determination:1 coherently:1 stems:1 those:2 case:4 pacs:1 solid:2 chap:2 value:6 lesser:1 while:7 behavior:12 cox:1 aid:1 london:2 layer:3 jpn:4 almost:1 exceptionally:1 ir:4 thus:1 surface:12 n2d:19 ii:1 characterize:1 superconducting:1 examined:1 cond:1 lifetime:2 technology:2 fermion:1 increased:2 orbital:1 confirmed:1 pis:1 grant:1 suggest:1 radiation:1 lett:5 same:1 orders:2 shorter:4 unity:2 noninteracting:1 nagaosa:1 schematic:1 units:1 finite:1 higher:3 extended:2 imply:1 tufte:1 effect:6 hand:1 driven:1 insulating:1 changing:3 tune:1 recent:1 numbered:3 lower:3 weakly:1 framework:1 nevertheless:1 no:2 well:1 roughly:1 undoped:2 bohr:1 observations:1 edge:1 tokura:2 dashed:2 quantitative:1 ju:1 dimension:1 edwards:1 ferroelectrics:1 rosenbaum:1 just:2 less:1 nd:2 hikami:1 press:3 bandwidth:1 immediately:1 facts:1 localize:1 alternative:1 scattering:1 onset:2 uniformity:1 zastrow:1 density:18 absorption:4 regarded:1 conclude:1 seems:2 fitting:2 lattice:2 other:1 attractive:1 samples:3 identical:1 saturation:1 around:3 disappearance:1 bands:2 sarachik:1 period:1 increases:3 varies:1 indicative:1 vacuum:1 clustered:1 using:3 roach:1 altshuler:1 moreover:1 advanced:2 mod:2 generated:1 confine:1 necessary:1 helpful:1 follows:1 separately:1 history:1 completely:1 output:1 disorder:2 reduced:6 permittivity:1 belyaev:1 function:6 satisfactory:2 because:9 methods:1 exposed:1 successfully:1 okamoto:1 understood:3 suppl:1 respect:1 transport:7 conventionally:1 recently:1 dimensions:3 contacts:1 magnetoconductance:1 avoid:1 measurements:7 exceeding:1 pell:1 critical:7 tends:1 prog:2 o3:1 demonstrated:1 conference:2 dimensionally:1 2b:1 obscures:1 use:1 clarendon:1 bw:1 variation:3 although:5 francis:1 properties:8 conducting:3 carried:1 smolensky:1 kawasaki:1 dependence:8 pe2:1 range:6 carrier:17 greatly:1 2k:8 consequently:2 schroder:1 soc:3 rev:13 polished:1 previously:3 pergamon:1 into:2 within:3 ahn:1 steady:3 negative:10 down:4 device:1 sov:1 elementary:1 factor:1 theoretically:5 intrinsic:2 k19:1 there:1 long:2 anderson:1 appl:2 low:8 way:1 cairo:2 tunability:1 was:10 therefore:1 questionable:1 considerably:1 medium:1 illuminated:1 photogenerated:3 adjusting:2 but:2 expected:4 neutral:1 mm3:1 ioffe:2 attainable:1 line:2 true:1 longer:1 absent:1 made:1 stanford:1 characteristic:4 vacancies:1 variations:1 maximum:1 us:1 different:1 below:1 limit:1 continuously:1 problem:1 panels:1 similar:3 strongly:3 ac:1 taylor:1 constant:15 defined:1 ah:3 contribute:1 metals:1 photoexcitation:1 globally:1 single:4 µh:1 our:4 crystals:5 education:1 regime:4 discrepancy:2 ev:1 nm:46 variety:1 asymmetry:1 eq:2 nb:1 nc:6 when:8 ne:1 field:15 valid:1 electrical:1 details:1 department:2 out:2 optically:1 perpendicular:1 generates:1 resembles:1 bundle:1 lens:1 bonding:1 structure:1 gao:1 correlated:3 faster:1 typically:1 holes:3 theor:1 depth:8 confinement:1 mass:3 fact:3 time:3 international:1 |
0704.3681.txt |@word represent:1 now:3 partial:3 consider:1 remarkable:2 similarity:2 czerny:2 global:5 dynamic:13 primed:1 esz:4 indicates:4 roy:14 scalar:4 selection:3 subtle:1 kato:3 go:1 sci:1 gm:14 conservative:1 reasoning:1 compact:2 whose:5 dimensionality:2 referring:1 indices:1 equivalence:3 finally:2 does:5 afshordi:2 stable:5 include:1 toropin:2 worth:2 carried:3 sound:3 linearising:2 advantage:2 very:15 dispense:1 account:2 choice:6 govern:1 affect:1 fractal:35 condition:23 common:1 clouds:1 immediately:1 presented:1 cause:1 tex:1 selfconsistently:1 t2:2 solution:32 large:2 admissible:1 delivered:1 race:1 guiding:1 subscript:2 small:4 relation:2 inspection:2 noted:2 nowak:2 favoured:1 theuns:6 mn:1 force:1 radial:3 miller:1 consistent:1 direct:6 pasj:2 feasibility:4 astrophys:1 rate:7 asp:1 enclosed:2 surface:1 pass:4 rigorous:1 further:2 dynamics:8 conclusion:1 aptly:1 substitute:1 approached:1 even:5 established:2 what:10 nonlinear:6 sub:1 chicago:2 imagined:1 exactly:6 favour:3 expressed:2 uniform:2 reminiscent:1 anywhere:1 absolute:1 procedure:1 fractional:10 judicious:1 new:3 falling:1 appeal:1 ever:1 tarasov:2 exercise:4 3d:5 satisfy:1 evolving:2 full:2 simultaneously:1 astrophysicists:1 respectively:6 inviscid:2 vol:1 here:5 understanding:2 behaviour:6 reported:2 deposition:1 inverse:2 near:1 sink:1 physically:3 represented:1 accretion:29 along:2 quite:6 equations:31 implicit:1 logarithmic:2 q4:3 obtained:6 great:1 stark:1 suitably:1 institute:1 akr:1 study:6 studied:2 allows:1 completely:3 reports:2 later:2 tempting:1 primacy:2 turolla:1 published:1 dickey:1 california:1 linearised:11 studies:3 plotted:3 goss:1 technique:2 followed:3 scales:9 differentiating:1 explained:1 kuiper:1 conjecturing:1 assertion:1 scaled:7 rφ:2 wagoner:2 should:6 armed:1 select:2 readily:1 derivatives:1 use:4 barab:2 dǫ2:5 would:14 dǫ1:3 remains:2 positive:1 chechetkin:1 negative:1 next:1 comparing:1 doubt:1 therefore:10 expanding:1 taken:1 conservation:1 obstacle:1 type:3 theoretical:1 today:1 more:15 diamond:1 said:3 started:1 becomes:8 company:1 under:11 theory:1 needed:1 carrying:2 clumpy:1 labelled:2 particular:8 known:2 actual:1 hole:10 burkert:3 must:2 md:2 keeping:2 crosses:2 ma:1 sphere:2 science:1 equation:66 work:4 theories:1 recast:2 remain:1 infinitesimal:4 values:9 evolved:1 concepts:1 believed:1 making:2 sets:2 root:2 vary:1 fulfillment:1 f0:11 continuity:3 ready:1 metrical:1 infalling:2 figure:4 give:10 process:2 relativistic:2 sense:1 india:2 purposes:1 involve:3 effectively:3 minimum:3 something:1 arise:1 velusamy:1 isothermal:1 times:1 evidently:2 world:1 inflows:5 successful:1 vanish:1 end:1 straightforward:1 rather:1 following:1 discussion:1 romanova:1 vc2:3 fortunate:1 makes:3 far:3 varies:1 criterion:4 stinebring:1 es:1 instead:1 ordinary:2 axis:1 parameter:4 conceived:1 isotropic:2 suffer:1 wave:1 especial:1 incorporated:1 v02:4 may:10 earlier:3 derived:6 ostriker:2 hence:2 independent:1 plane:2 preferred:1 ω2n:2 barotropic:1 cambridge:6 requirements:1 perturbing:1 law:2 meaningful:1 grow:1 constants:1 curve:2 supersonic:2 short:2 natural:1 dynamical:8 effective:3 elmegreen:2 negligibly:1 light:3 approximation:1 author:1 explicit:5 exhibited:2 greek:1 so:6 increasing:1 fundamental:3 kovalenko:2 obvious:1 increase:1 scintillation:1 order:5 michel:2 recognised:3 evolutionary:2 interpretation:1 help:4 indeed:2 over:7 insight:3 closeness:2 soon:1 stability:9 course:2 already:1 through:22 2v:2 preliminary:2 argued:1 existence:1 still:3 its:9 roots:3 before:1 perfect:1 respect:3 style:1 derive:2 outer:7 bonazzola:3 chandrasekhar:2 how:1 chosen:5 petterson:7 klessen:2 relativity:1 vicinity:1 coordinates:2 actually:3 forms:1 platform:1 absence:1 stanley:2 systems:2 total:5 derivative:1 main:1 might:3 overcome:1 correspondence:1 freeman:1 non:4 contention:3 reveal:2 matches:1 bernoulli:1 amenable:1 processes:4 number:5 newman:2 framework:2 effects:5 they:2 das:11 oxford:2 conformity:3 malec:2 yu:1 3dimensional:1 temporal:5 possess:1 heithausen:2 february:2 finite:3 rendering:1 conspicuous:1 zampieri:2 university:7 identified:1 applied:2 cowie:2 magnitude:1 mode:1 reasonable:1 each:3 well:2 acoustic:8 entirely:5 higher:5 side:3 lorentzian:1 accretor:10 homogeneous:1 differential:7 determine:4 evolve:3 fixes:1 iucaa:1 reduce:1 principles:2 related:2 ornsson:1 astrophysical:9 static:2 perspective:1 impossible:1 quantum:2 gµν:5 approximated:1 extract:1 event:2 special:1 description:2 stands:2 shown:10 network:1 driving:2 space:10 gradient:2 res:1 since:4 induces:1 chaos:3 research:2 rd:1 seriously:1 prescribing:1 ren:2 hill:2 emerged:1 rc:24 ble:1 issue:2 integrated:1 shows:6 after:8 linear:8 l205:1 frank:2 bodenheimer:1 divergence:1 little:1 free:3 standard:3 curved:2 analytical:4 reason:2 salient:1 deliver:1 term:1 besides:1 eigenvalues:2 noticeably:1 intermediate:1 asi:2 δa:1 goswami:2 combes:2 log:2 v0:15 pune:2 retained:1 regarding:3 geometry:3 starts:1 could:5 hyperbolic:1 but:9 plot:6 used:2 david:6 motion:6 thing:1 length:14 place:1 massive:2 ism:5 consequence:2 bate:2 support:1 first:12 origin:6 raine:1 initial:6 features:4 render:1 lovelace:1 variables:3 primary:2 exact:2 smaller:3 done:2 least:2 directly:1 robust:2 carry:2 reached:2 difficulty:2 bensch:1 horizontal:2 affords:1 constructing:1 given:17 perturbation:11 discussed:3 requirement:1 their:2 introduction:3 data:1 top:2 tata:1 system:25 construct:2 anyone:1 indicate:1 perturbations:3 1e:1 observations:2 autonomous:5 biased:1 ballistic:1 o:1 scheme:1 sensitivity:2 speaking:2 inflow:5 shifted:1 prone:1 4r:1 liang:1 prescribed:1 wang:1 visser:5 continuous:10 minute:1 immediate:2 wisdom:1 appreciation:1 assumption:2 part:3 jordan:4 too:2 somewhat:2 fall:1 resistance:1 undoubtedly:1 than:5 coefficients:1 character:1 distance:5 kind:5 molecular:1 abramowicz:2 second:1 limiting:1 kργ:1 matter:9 determined:2 represents:1 were:3 gives:3 solely:1 perturbative:11 kazhdan:2 questionable:1 entail:1 shu:2 lines:1 unchanged:1 conventional:1 mind:1 argument:2 curves:6 latter:1 separatrices:3 close:3 perault:1 seen:3 bohr:2 orders:1 viewed:2 relatively:1 numerics:1 affairs:1 angle:1 newtonian:9 regime:2 efficient:1 convenient:1 self:2 gravity:8 mechanism:3 note:1 extracted:2 potential:12 take:3 simplified:3 simplifications:1 objective:1 concern:1 buff:2 towards:5 ray:15 allow:1 centre:3 whole:2 object:2 dilute:1 l171:1 birkh:1 logarithmically:1 most:1 invoked:1 connected:2 printed:1 position:1 phase:4 kaz:1 analytically:1 cases:1 why:1 grave:1 mach:4 latex:2 deviations:2 kg:1 especially:3 fluids:1 considered:2 markovic:2 clear:2 adopt:1 flow:42 drive:1 ρvr:3 2gm:2 kr:1 hints:1 properly:2 rev:2 wind:3 exp:3 velocity:21 effect:1 left:2 physics:9 section:2 fact:14 debnath:2 precise:4 incorporate:1 parker:3 apj:20 bj:1 crs:3 authors:1 fukue:2 foregoing:2 implying:1 solving:2 radio:1 solutions:27 king:1 zaslavsky:2 analogue:2 fine:1 principal:2 q1:4 larson:2 q3:6 q2:6 ambient:1 knowledge:1 parameters:2 explain:1 written:1 moncrief:2 terminal:2 only:12 going:4 black:10 factor:3 integrate:1 identification:1 falgarone:7 accretors:1 local:2 scientists:1 regularly:1 do:1 above:1 get:1 dependent:6 familiar:1 express:2 fluid:10 pave:1 truly:1 inclusion:1 2f:1 cannot:2 nonequilibrium:1 words:1 drawn:1 dv:3 dt:2 silk:3 dr:10 bondi:10 dp:1 builds:1 prime:1 matsumoto:2 evolution:21 switched:1 continuum:6 axford:2 typeset:1 numerous:1 linearity:1 arxiv:1 choudhuri:2 method:1 bag:2 investigate:1 discs:1 differencing:2 hydrodynamic:1 puget:3 levin:1 semelin:2 extended:1 fixed:9 okazaki:1 view:2 fledged:1 shedding:1 set:6 computed:1 achieved:1 imitate:1 national:1 saddle:9 turbulent:1 bears:1 mentioned:1 see:2 justification:2 radius:8 result:9 successive:1 versus:1 portrait:4 midst:1 bhattacharjee:7 incorporating:1 subject:1 closer:1 appear:1 aros:4 exponent:2 intersecting:1 away:1 irrotational:1 symmetric:14 state:16 classes:1 various:4 between:4 invariant:1 boundary:20 reading:1 approach:7 justified:1 observational:1 accord:1 terms:10 vertical:1 nature:10 weak:1 notion:1 points:12 however:8 york:1 key:1 interface:1 configuration:2 come:2 problem:5 lc:5 both:11 stages:3 prescription:3 limits:1 outflows:2 many:5 ill:1 density:9 according:2 against:3 auser:1 sensitive:2 context:2 interesting:3 asplund:1 passing:2 argue:2 expression:3 regarded:1 otherwise:1 seminal:1 comparative:1 relevant:2 extent:1 prepared:1 point:34 simple:3 smith:4 vain:1 others:3 corresponds:4 whatever:1 chakrabarti:5 dimensional:1 concluding:1 taylor:1 simply:1 decreases:1 consideration:1 addisonwesley:1 associated:4 lies:1 worthwhile:1 considering:1 described:3 tuning:1 simplification:1 three:1 been:44 faithfully:1 much:7 combined:1 interest:2 certain:1 expected:4 ph:1 extreme:1 acta:1 derives:2 fig:7 led:1 field:15 aj:1 general:10 versa:1 restricted:1 quantities:1 gas:3 precision:2 solitons:1 bulk:1 fractals:1 understand:3 external:2 angles:1 astron:1 c2:3 plasmas:1 maximally:2 altered:1 present:1 case:12 intriguing:1 wins:1 look:1 straight:1 appearance:1 nski:4 value:12 remaining:1 will:67 while:8 replaced:1 euler:2 rigour:1 heyvaerts:2 stutzki:1 situation:1 revisited:1 balance:1 taking:2 launched:1 engineers:1 a20:3 real:1 generate:4 larger:2 coupled:3 almost:1 characteristics:1 metric:4 them:2 encouragement:1 ii:1 scaling:1 itself:6 headway:1 ganeshkhind:2 accounting:1 claimed:2 ernet:1 worry:1 greater:1 eremin:2 different:4 governing:1 verified:1 propagation:3 generic:1 suggest:2 make:8 secondorder:1 cross:3 same:9 any:11 another:3 arguments:5 pressureless:2 several:1 borne:2 difficult:1 status:3 fairly:1 readjustment:1 literature:1 slightly:1 solved:1 trivially:1 everett:1 numerical:14 upon:3 drives:1 flows:13 hand:4 driven:2 v2:5 a2c:2 moving:1 hydrodynamics:2 infinite:1 frequently:2 invariance:1 adopting:2 nityananda:1 mentioning:1 blumenthal:2 lower:1 task:1 nevertheless:2 safely:2 underlies:1 polytropic:5 investigation:1 roughly:1 analysis:6 obviously:1 without:1 solve:2 greatest:3 mathews:2 studying:2 accreting:5 model:7 arising:1 dimension:10 preference:1 spherical:4 restore:1 universally:1 lesser:2 just:2 among:1 being:13 generally:1 mandelbrot:2 necessitate:1 rest:1 astronomica:1 underlying:3 aspect:2 spherically:13 differentiation:2 simi:1 mastichiadis:2 speed:6 reduced:1 cut:1 transonic:35 infinitely:3 absorption:1 ease:1 had:5 parametrization:1 selfsimilar:2 boston:1 suddenly:1 other:5 extends:1 treatment:3 easy:5 pair:1 necessarily:1 mandal:4 apart:1 transformation:2 momentum:1 details:2 identical:2 sonic:9 saturation:3 fluctuating:1 aspects:2 analogy:1 appreciated:3 easily:3 read:1 hint:1 dropping:1 decomposed:1 possible:12 early:3 possibly:2 indicative:1 mon:1 background:2 selects:1 press:5 using:8 progresses:1 formal:1 chengalur:1 modifications:1 necessary:3 like:3 lost:1 δv:1 confront:1 facets:1 adiabatic:1 δr:1 manifest:1 separately:1 flux:1 titarchuk:4 yields:1 either:6 integrals:6 always:2 become:2 inter:1 stationary:21 essential:1 ncra:1 lends:1 mathematical:13 erault:2 shed:1 right:4 classical:2 begelman:2 realisability:1 some:8 back:3 chaudhury:2 understood:3 linearly:1 growth:6 choosing:1 specified:1 proper:2 multiple:1 strogatz:4 apparent:2 infall:2 pronounced:2 ρdv:1 scale:9 describing:1 lead:2 αa2:2 establish:1 measurements:1 integration:11 comments:1 manipulations:1 critical:20 eliminate:1 conclusions:2 stressed:1 unstable:1 closely:3 demonstrated:3 refer:1 lowest:1 gratitude:1 paczy:4 denominator:1 run:1 scientific:1 power:2 2q1:1 seconds:3 journal:2 arbitrary:3 analysed:1 expansion:1 stellar:2 pressure:8 olsen:1 powerlaw:1 although:2 found:2 losing:1 khan:1 post:2 crossing:1 properties:8 publishing:1 about:5 works:1 central:2 working:1 anything:1 tsuribe:2 2ct:3 novikov:1 kylafis:2 brinkmann:2 numerator:1 dependence:4 realistic:1 langer:2 range:3 involving:2 greatly:1 horizon:7 trajectory:1 mean:2 consequently:1 therein:1 soc:1 rendered:1 letters:1 presence:1 into:5 within:3 integral:4 interstellar:3 nonperturbatively:1 due:2 down:4 nothing:2 appropriate:1 because:4 references:2 paper:1 stellingwerf:2 paradigmatic:1 import:1 imposed:3 tifr:1 significantly:2 acknowledgements:1 forwarded:2 fields:2 area:1 normalised:1 suffice:1 there:6 transform:1 long:1 accordingly:1 grasping:1 inner:2 way:2 labelling:1 astrophysics:5 was:2 energy:7 opposed:2 function:8 slope:4 medium:34 complete:2 form:15 attempted:1 denoting:2 umemura:1 jul:1 astro:1 2vr:3 cloud:1 hierarchical:2 gain:1 mnras:14 line:2 trying:1 true:1 themselves:1 partially:1 volume:1 singapore:1 made:8 applying:1 gravitating:1 evident:1 q21:2 characteristic:3 gravitational:3 vice:1 up:1 nasa:1 placed:1 below:1 books:1 limit:6 embedded:1 approaches:1 fluctuations:2 distribution:2 define:1 similar:1 display:1 regimes:1 mechanics:2 bearing:1 ac:1 alembertian:1 constant:10 arnab:1 mindful:1 ln:5 defined:1 steady:9 abstract:1 combining:1 influence:4 evidence:3 migenes:1 au:2 km:1 file:2 simulations:1 qiu:1 balazs:2 conic:1 happen:1 sarkar:2 physical:15 again:2 no:4 fixing:1 when:7 rs:5 subsonic:1 wiita:2 application:1 conditions:12 remarks:1 crovisier:2 spatial:2 test:1 mathematics:1 out:9 realisable:1 principle:2 deviation:3 picture:2 elements:1 star:2 quantitative:1 lend:1 bottom:1 inherently:1 helpful:1 a0:2 a2:5 graphically:1 variable:3 astronomy:1 gets:1 structure:7 matrix:4 l65:1 tailored:1 implies:3 faster:1 calls:1 practically:1 corresponding:2 dτ:7 required:1 pseudo:2 indirectly:1 equivalently:1 ascertained:1 implied:1 mass:10 lying:2 time:24 everywhere:1 starting:1 having:4 once:3 |
0704.3682.txt |@word limited:1 hickox:2 consider:1 pointing:1 magnetic:2 luminosities:2 results:3 rxte:1 gx:7 advices:1 helped:1 munari:1 per:2 coincidence:3 edu:3 sct:5 disk:1 hole:1 overplotted:1 compact:7 fits:1 1rxs:1 send:1 supported:1 finally:1 program:1 spain:1 excluded:1 ti:1 atlas:1 braga:1 indicating:3 2mass:2 loon:1 belonging:4 v11:1 made:3 returning:1 far:1 santangelo:1 reader:1 mg:1 focus:1 cavaliere:1 sensitivity:1 difference:2 matrices:1 paradijs:2 entire:1 school:1 gsfc:2 stiening:1 apjs:3 presented:2 heasarc:5 positions:2 standards:1 large:1 cooke:2 second:1 small:2 inspection:1 der:2 shed:1 servers:1 cgi:1 strongly:2 smaller:1 computation:2 periodicity:3 deutsch:2 trend:1 so17:1 porb:1 direct:1 pasj:1 past:1 surrounding:1 likely:9 noise:3 timescales:2 displays:2 spectrograph:1 multiwavelength:3 download:1 further:2 observatories:1 spectral:21 index:3 what:1 ccd:1 appear:1 section:1 axes:1 while:1 expressed:1 overwhelmed:1 mv:1 giommi:1 above:3 flowing:1 new:13 change:1 bird:8 temperatures:1 elsner:1 full:1 led:1 dwarf:2 degree:1 atel:1 respectively:1 l1:2 iraf:2 here:2 hundreds:2 hours:2 ibis:9 explore:2 objects:7 galileo:1 ratio:1 along:2 corbet:5 observing:1 galilei:1 box:6 lomb:1 mattana:2 dividing:1 study:3 larger:1 funded:1 experience:1 suggests:3 accomplished:1 periodic:3 survey:4 usually:1 narrow:1 changes:1 amati:2 sci:1 2006c:2 composed:3 emerge:1 reprocessing:1 via:5 useful:2 secure:1 campaign:1 africa:3 marked:1 apj:18 frame:1 energies:1 counts:1 total:2 univ:2 estimate:2 cloud:2 readily:1 use:5 feb:1 stream:1 usa:2 levine:2 sake:1 timeaveraged:1 quasi:1 barycentric:1 france:2 m5:1 m4:1 wood:1 examination:1 therefore:4 crab:1 m2:7 taken:2 type:21 marginally:1 more:8 flat:1 cusumano:2 hensberge:1 composite:1 company:2 apparent:2 corrected:2 emission:12 improve:1 pspin:2 payne:1 tomasella:2 malina:1 investigation:1 particular:2 known:5 actual:3 cases:1 mounted:1 iii:9 cocco:2 earth:1 high:3 account:2 science:4 setup:1 work:3 doxsey:1 tomov:1 erg:11 del:1 three:1 evolved:2 smear:1 growing:2 under:1 dec:2 could:1 usno:3 turnshek:3 narayan:1 compare:1 radcliffe:2 figure:1 give:1 process:1 longterm:1 suggestions:1 spectrophotometry:1 states:1 indicates:1 slit:1 minimum:1 kenyon:1 performed:8 allowed:2 exclude:1 counting:1 hydrogen:2 simple:2 axis:1 information:3 rays:3 monitoring:1 straightforward:1 rather:4 discussion:2 means:2 feature:2 hampshire:1 positional:3 located:4 hardness:2 bassani:5 instead:1 flow:2 absolute:1 parameter:4 classify:1 profile:1 predehl:2 galactic:4 description:4 book:1 modulation:2 strohmayer:1 after:2 processing:1 containing:1 caldb:3 mns:1 spectum:1 united:1 jablonski:1 fe:2 mag:3 coming:2 winkler:2 law:2 data:25 parallel:2 curve:5 stress:1 short:4 physical:3 outline:1 pulsations:1 martins:1 light:10 spectra:4 lines:4 paizis:2 vieira:1 verbunt:1 cannot:2 so:1 sect:5 allow:1 african:2 order:3 wind:7 typical:10 horne:2 instabilities:1 pulsed:2 interpretation:1 help:1 indeed:5 astronomical:5 meter:1 years:1 produced:3 timing:1 thermal:2 paper:5 through:1 statistical:2 telluric:3 lx:4 its:11 galaxy:1 before:1 aj:2 sciences:1 position:4 probability:3 fit:9 acknowledge:1 he:1 temporal:1 facility:1 encompasses:1 l77:1 coordinates:4 late:1 detected:5 degrees:1 systems:9 bevington:2 stephen:3 stemming:1 main:4 pixel:1 archival:1 misalignment:1 them:2 good:1 combination:1 christian:1 press:3 docs:1 simbad:1 hunter:2 investigated:1 break:1 band:12 course:1 effects:3 they:1 satellites:1 fiume:3 rotation:1 now:2 day:1 association:1 term:7 several:2 den:2 galloway:5 fully:2 university:3 level:3 events:2 lowmass:1 kpc:5 follow:1 mode:2 denmark:1 found:10 dennis:1 erratic:1 characterized:3 accretor:3 afforded:2 bruzual:1 square:1 financial:1 telescope:5 series:1 energy:3 hard:4 reduce:1 bolometric:1 intercalibration:1 xrtpipeline:1 hosted:1 laboratory:1 ev:1 event:2 out:2 19m:2 shown:1 nss:1 mauro:1 3rd:1 twice:1 periodicities:4 quality:2 furthermore:1 since:1 rev:1 dss:1 research:2 increase:1 may:5 contained:1 nominal:2 dominated:1 ra:2 wide:2 istituto:2 formula:1 gov:2 supports:1 red:3 shows:5 foundation:1 classification:1 asp:2 theory:1 romano:2 fisica:2 standard:2 completely:1 base:1 brightest:1 besides:1 usual:1 org:1 asi:2 shotnoise:1 beginning:1 l131:1 inhomogeneities:2 r0:3 ltt:1 geometry:2 intersystem:1 cosmic:1 days:4 times:3 counterpart:6 produce:2 barbier:2 undergo:1 onto:2 anonymous:1 south:5 first:4 does:1 features:5 manuscript:1 upper:2 aperiodic:1 kt0:1 number:2 bazzano:1 references:2 peculiarity:1 stsci:2 skrutskie:2 western:1 fluxes:1 sutherland:1 angular:1 size:4 given:4 checked:1 ten:1 strasbourg:1 similarly:1 introduction:1 bologna:2 top:1 structured:1 pspc:1 system:11 adopted:1 response:1 roche:4 their:3 accretion:9 observations:19 consistent:3 normalization:1 white:1 ribeiro:1 isdc:1 ranging:2 inner:1 dolan:1 progr:1 fraction:1 centered:1 duration:1 continuous:1 park:1 persson:1 mn:1 optical:26 frascati:1 values:1 authors:1 suntzeff:2 july:2 believe:1 than:7 l9:1 distance:6 kind:1 observatory:3 l49:1 measured:1 rate:3 final:1 project:1 matter:2 determined:4 characteristics:2 iron:1 were:8 kte:1 amount:1 providing:1 russia:1 hz:1 accounted:1 correction:4 giancarlo:1 spectrum:29 curves:3 peculiar:1 say:1 substantial:2 astrophysical:1 perri:1 cleaned:1 seen:4 null:1 clearly:1 ray:76 gives:1 kunieda:1 broadly:1 latter:1 note:3 liu:2 fitting:2 positionally:1 2006a:6 take:1 analogy:1 kaplan:6 finding:3 donor:1 detector:1 simultaneity:1 explanation:1 palazzi:2 rebinned:1 gunn:3 markwardt:1 test:1 centre:2 cutri:1 correlation:1 blackburn:2 did:2 most:4 errors:1 germany:1 wavelengths:1 significant:1 accreting:14 remarks:1 coded:3 inserted:1 class:2 pulsars:1 southampton:2 redistribution:1 constructed:1 especially:1 koyama:2 into:2 later:1 metal:1 binned:1 km:2 pasp:3 ks:4 part:1 verlag:1 davey:1 leahy:1 fosso:1 conservatively:1 foschini:1 latest:1 physics:1 width:2 fact:5 space:1 shot:2 intensity:1 show:3 kaper:2 text:4 random:3 bin:1 infrared:3 rotating:2 bright:3 lewin:5 cds:1 superimposed:1 ftools:3 find:1 fifth:2 xmm:1 giant:13 based:1 nevertheless:1 parameters:4 explain:1 state:2 should:4 jan:1 brighter:2 only:9 ancillary:1 black:1 equipped:1 emitting:2 circle:8 partially:1 thousands:1 pointed:4 ser:2 do:1 over:3 di:7 overall:1 ones:1 nearly:1 words:1 report:1 during:2 onboard:2 averaged:5 barlow:1 blends:1 secondary:3 following:5 evolution:2 continuum:1 countries:1 luminosity:8 arxiv:1 method:2 deconvolved:1 garcia:2 optimally:1 andrei:1 processed:1 activity:1 switzerland:1 frequency:1 view:1 intervening:2 reveals:1 computed:2 fair:1 attenuated:1 acquired:1 national:2 hα:3 astrometry:1 hosting:3 observed:1 mentioned:1 see:18 decided:1 radius:4 result:2 operated:2 close:1 masetti:33 best:6 invoked:1 interacting:1 extragalactic:1 tucson:1 cd:1 enough:2 future:2 identification:1 alignment:1 between:10 limit:2 geometric:2 discovery:1 available:10 variability:7 comparable:1 attention:1 recently:1 spectroscopy:1 nature:3 component:1 momentum:1 emitted:3 however:7 acknowledgements:1 spectroscopic:1 hill:3 york:2 rapid:1 irradiation:1 windows:1 key:1 kev:34 swift:11 thank:2 suggested:1 received:1 prescription:1 concentrated:1 reported:8 region:3 uncertainty:3 cool:1 according:3 contract:1 display:1 takeuchi:1 april:2 ferrigno:2 xspec:2 aura:1 absorption:11 behaviour:2 requests:1 whole:1 synoptic:1 comes:1 grounds:1 among:2 ch:1 16h:2 cm:4 characterization:1 color:1 aschenbach:1 ca:2 barthelmy:1 narrower:1 period:3 community:1 2nd:1 maintained:1 non:1 wider:1 table:15 throughout:1 cu:1 chakrabarty:5 better:3 strong:1 described:5 goldwurm:2 ubertini:2 instrument:2 equivalent:1 seed:2 absence:2 been:1 extraction:1 reduction:4 pa:1 slowly:2 combined:1 likewise:1 collected:4 ph:2 pi:1 fig:11 firm:1 obtained:12 atlases:1 referee:1 partly:1 deeper:1 both:8 sufficient:1 photon:2 search:3 uncommon:1 falanga:1 inaf:4 otz:1 confinement:1 determination:2 stems:1 suspected:1 evidence:2 spin:4 present:3 reddening:1 case:4 extracted:5 cassegrain:1 bevilacqua:1 ricker:1 empirical:1 density:1 hayes:1 will:6 near:4 intro:1 confidently:2 reliably:1 error:11 procedure:2 jacoby:4 identical:1 planets:1 courvoisier:1 linked:1 metre:1 av:2 thus:9 site:1 surface:2 iv:1 ii:2 bias:1 properties:1 conf:2 voges:2 comments:1 orbital:2 binary:13 different:1 italy:4 shaw:1 campana:1 grant:1 suggest:2 l223:1 radiation:1 cross:1 same:3 any:7 member:2 dal:3 unity:1 html:1 evaluate:1 l141:1 relatively:1 infer:1 neutron:3 ibvs:1 satellite:1 used:4 http:5 ni:1 baliunas:1 effect:2 companion:4 v0:3 v2:1 v5:1 variance:1 lebrun:3 tighter:1 task:3 scargle:1 center:1 malizia:3 database:1 pennsylvania:1 studies:1 poland:1 calibration:4 well:2 spent:1 analysis:12 thought:1 severe:1 residuals:2 arnaud:2 roma:2 comparisons:1 model:10 binaries:8 l105:1 left:2 spherical:5 noao:1 salvo:1 ratios:1 quoted:1 less:1 being:1 accurate:2 newton:1 obtain:2 boller:1 sources:9 shape:1 intervals:1 atomic:1 sguera:2 facts:1 co:1 nousek:1 spectrophotometric:1 captured:1 moretti:2 davidsen:2 aiming:1 timescale:1 conclusions:2 hamuy:3 photons:2 sky:2 capabilities:1 improvement:1 signals:1 source:35 tio:1 pile:2 board:2 grating:1 absorbed:2 craine:1 east:1 plasma:4 match:1 gave:1 kingdom:1 isgri:7 march:1 around:7 alternatively:1 bands:5 showing:1 2006b:9 psf:1 possible:3 psd:3 caps:1 possibly:5 wavelength:2 grid:2 background:3 xrt:30 rns:1 using:18 accepted:1 moreover:1 wings:2 theor:1 like:1 follows:1 signal:1 schmitt:2 chincarini:2 klis:2 flux:3 titarchuk:5 individuals:1 indication:2 night:1 mcgraw:1 pereira:2 soft:7 cui:1 stryker:2 segreto:1 barnes:1 satisfactory:1 right:1 often:1 sequence:1 czech:1 comptonization:8 heuvel:2 some:1 springer:1 mtype:1 j2000:2 molina:1 suppl:1 sight:1 cr:1 oscillations:1 bins:1 little:1 orlandini:3 pinpoint:1 collect:2 symbiotic:12 l17:1 subclass:6 saao:3 magnitude:5 centroid:1 cutler:2 esa:2 assuming:8 eso:1 chandra:1 subtracted:1 l65:1 participation:1 inclination:1 bd:1 bowyer:1 object:17 ba:1 power:3 seconds:4 rosat:6 each:2 bh:1 confidence:3 stellar:5 host:1 lamps:1 although:2 kallman:1 refers:1 primini:1 intense:1 jacobi:1 comparison:1 pipeline:1 rare:3 package:4 column:4 freedom:1 months:2 ranges:2 chance:4 o:1 nagase:2 compatible:2 maiorano:1 carries:2 a2:3 latetype:1 farinelli:1 connected:2 introduced:1 slightly:1 obs:1 software:4 david:1 cambridge:4 presence:4 instruments:2 image:3 within:8 integral:10 interstellar:3 due:7 gehrels:2 accounts:1 determine:1 mcclintock:1 accumulated:1 rembold:1 next:3 significantly:1 uncertainties:2 statistics:4 van:7 log:2 area:2 extremely:1 support:1 long:5 spaziale:2 dispersion:1 start:2 low:4 stars:10 ed:3 astrophysics:2 unige:1 was:28 leray:1 m0:1 files:1 lang:5 medium:1 north:1 form:1 annulus:1 attempted:1 jun:1 but:6 histogram:1 astro:2 neutral:1 solar:1 cosmica:2 line:6 tiengo:2 observation:4 count:1 sokoloski:1 october:1 rejection:1 ut:2 burrows:3 variations:1 up:6 us:3 lmxb:2 considered:4 below:1 converted:1 those:5 hand:1 lmxbs:6 fluctuations:1 distribution:2 value:2 similar:4 called:1 detailed:1 interval:2 associated:2 factor:2 pinpointed:1 mask:1 abstract:1 describe:2 assumption:2 covers:1 general:2 pix:1 balmer:1 single:1 ar:1 tawara:1 file:1 our:3 arrival:1 corresponding:1 moves:1 archive:2 inc:1 nh:2 again:1 extending:2 compared:1 igr:39 no:10 zand:2 capalbi:1 generally:1 detail:1 field:8 other:5 republic:1 details:3 digital:1 jaschek:4 1bj:1 ns:18 concerning:1 gaining:1 polar:1 draw:2 star:17 ftp:4 astrofisica:2 symbol:1 time:11 frontera:1 dof:2 pointings:4 heathcote:1 generated:1 important:2 coverage:3 variable:1 astronomy:3 range:2 needed:1 exposure:1 offprint:1 implies:1 assume:1 starting:1 odds:1 4u:14 accretes:3 orbit:1 together:1 having:2 ducati:2 inset:2 nasa:3 mass:6 resembles:1 walker:1 resolution:3 gobetti:1 |
0704.3683.txt |@word represent:2 code:8 homomorphism:1 consider:8 tsev:1 varying:1 results:2 unchanged:1 four:3 gf:5 mile:1 computation:1 c2:1 consists:4 follow:2 decisions:1 issues:1 row:7 extra:1 whose:2 4ns:1 combinatorial:2 graph:14 deterministic:2 ladner:1 grohe:6 tq:11 languages:3 reductions:1 finally:4 rg:6 restriction:1 lanford:1 th:4 ti:3 hermann:5 assumption:3 undirected:2 tc:1 sorkin:2 applied:6 conjecture:2 random:1 advantage:1 g0:2 very:2 reader:1 dobrushin:1 induce:1 focus:3 corollary:7 endpoint:1 every:38 entries:4 ln:1 papadimitriou:1 condition:3 partitions:1 entire:1 school:2 squares:1 immediately:1 hamiltonian:2 positions:2 notes:1 integrating:1 solution:3 fewer:2 t1:19 deals:1 assignments:1 proposition:1 phase:1 interpolating:1 generalises:2 indices:6 shows:1 equation:6 configurations:10 prevent:1 smaller:1 zh:10 zi:3 lecture:2 consistent:1 d3:2 literature:1 zero:11 valiant:1 gn:1 further:2 odd:2 linear:12 even:2 index:9 what:1 sub:1 complexities:1 ni:3 sum:7 expressed:7 find:6 version:5 above:7 asz:2 replaced:5 contributes:2 journal:6 satisfy:1 full:1 αii:2 degree:1 component:3 csps:3 here:9 understanding:1 leeds:2 evaluates:1 represented:3 equations:6 appears:2 z2:1 obtained:2 hell:2 technical:1 study:2 vectors:2 allows:2 colourings:2 through:1 ignoring:3 pinning:11 resulting:1 permutation:3 usually:1 conveniently:1 makes:1 inherits:1 named:1 equivalence:14 useful:12 projection:8 txi:2 ix:6 wij:1 logical:1 interpolate:1 boolean:11 pp:3 summation:1 apply:1 tools:1 linearly:1 use:17 would:4 prove:5 distinct:9 positive:14 contains:6 ej:2 negative:11 automata:1 eds:1 call:2 therefore:5 paterson:1 contradicted:1 scope:12 associated:1 dalmau:2 theoretical:1 minor:1 more:2 integers:1 greenhill:3 acceptable:1 about:3 appendix:4 wi1:4 particular:4 known:4 foundations:1 cases:4 adequate:1 tx1:1 must:10 high:1 springer:1 valued:2 word:2 r2:12 weighting:1 science:4 h12:1 mi:3 unknowns:1 λj:1 values:7 learn:1 following:13 example:11 proof:26 f2:11 want:1 jerrum:3 permutations:3 purposes:1 ann:1 pieces:1 involve:1 effectively:1 assumptions:1 walsh:1 numbers:4 employs:1 allowed:1 scheduling:1 spanning:1 counting:22 44th:1 simple:3 dk:2 information:1 partial:1 end:1 goal:2 rather:2 divided:1 di:1 feature:1 machine:2 maps:1 nontrivial:2 pair:1 pure:14 instead:2 csp:142 fp:22 fq:11 product:23 proc:3 algebra:1 may:15 turing:4 earlier:3 derived:4 mapping:1 factored:1 applications:1 membership:1 fc:2 snp:1 cambridge:1 arities:1 mal:1 constants:1 acyclic:1 natural:1 imply:1 computations:1 combining:1 winkler:1 correspond:1 think:1 like:8 provide:2 complexity:24 so:38 allow:1 sc:1 definitions:2 first:11 bipartite:4 operations:1 exclusive:1 least:2 words:1 ith:1 summands:2 indeed:1 over:7 xh:2 course:1 paper:8 london:2 same:16 statistical:4 y1:7 existence:1 satisfies:3 jℓ:1 ieee:1 its:12 multigraphs:1 write:1 derive:1 group:3 how:1 chosen:2 interesting:2 fix:1 affine:60 li:6 forms:1 choose:6 main:3 defining:1 setting:3 yi:1 denominators:1 non:17 good:1 fourth:1 outlined:1 inductively:1 finish:3 framework:8 g1:1 ls2:1 they:8 symposium:2 oxford:1 now:19 nor:2 easily:1 inversion:3 stated:2 homomorphisms:8 2k:1 university:5 level:1 identified:1 2z:2 obius:3 possibilities:1 sufficiently:1 iff:5 each:15 wγ:2 repeating:1 side:1 2j:3 constraints:19 subset:6 domain:15 weighted:26 another:2 weight:19 dichotomy:13 series:3 creignou:6 hard:39 reduce:2 idea:3 related:4 applicable:1 used:9 computable:4 t0:30 measure:1 our:9 happen:1 transitions:1 extract:1 reduct:1 special:3 out:1 leave:1 shown:4 matrix:11 factors:1 restricted:1 furthermore:2 since:44 induces:1 denotes:2 replacing:2 rf:63 vector:4 rational:10 conjectured:3 denoted:1 formula:2 get:4 induced:2 induction:7 rk:2 theory:5 interactions:1 monotone:1 hardness:6 contain:2 1s:2 quite:1 demanding:1 put:1 org:2 e1:2 definition:3 r1:9 language:11 r3:3 determining:2 could:2 programming:2 feasible:1 ordering:1 length:1 preprocessing:2 place:1 assumed:3 hence:5 existential:1 onto:7 assign:2 colouring:1 xj:2 xk:9 major:2 xi:10 xn:1 symmetry:3 xm:2 u1:11 variables:52 cj:3 number:18 rank:7 xe:6 restrict:4 instances:5 done:3 construct:5 directly:1 type:16 xq:3 open:1 size:7 given:21 necessarily:1 checked:1 minimality:1 changing:1 similarly:5 introduction:2 xik:5 πh:1 πi:14 system:4 relations:6 their:1 intermediate:1 statement:2 ary:2 handbook:1 siam:3 potts:4 behaved:1 recovered:1 gives:5 discussion:1 tuple:18 recursively:1 exactly:5 proving:1 technique:2 arity:23 parsimonious:1 somewhat:1 x2:1 x1:13 iη:5 than:5 coefficients:1 zγ:6 wii:3 target:1 showed:1 structures:2 require:2 tree:1 depends:1 modelled:2 project:1 aat:1 classes:12 contrary:1 posets:1 were:2 ruelle:1 w2:4 seminal:1 idempotent:1 false:1 generality:6 contradict:1 lines:2 cohen:2 turned:1 argument:4 say:15 goldberg:4 need:4 elsevier:1 element:2 any:30 viewed:6 elsewhere:1 depending:1 convenient:3 h21:1 si:2 h22:1 note:25 sciences:1 without:7 take:6 algorithms:3 tool:1 rationals:1 towards:1 unless:2 though:2 gξ:2 denominator:1 evaluation:1 monadic:1 algebraic:2 regular:1 connected:7 amongst:1 position:3 reducible:1 accepting:1 probabilistic:1 class:20 kc:4 give:9 observation:3 clear:1 later:2 vertices:1 order:5 graphs:5 symmetrically:1 krokhin:2 typically:1 notion:1 fact:3 directed:1 simulate:6 show:10 characterisation:3 queen:1 purely:1 fγ:2 relation:34 solutions:7 trivial:2 agrees:1 subtracting:1 copies:2 indicator:1 coloring:1 inductive:1 schwartz:3 dividing:1 less:2 written:2 incidence:1 completes:1 lemma:57 only:12 abs:2 reducibility:2 inherited:1 employed:1 constant:11 interested:1 columns:14 do:7 intractable:1 intersect:1 notation:4 means:5 cannot:3 simulated:3 closely:1 new:14 applying:4 hij:1 assigned:2 addition:1 resource:1 arxiv:3 comprising:1 remove:2 method:1 inputs:1 mapped:1 scott:2 tutte:1 fixed:5 valid:2 view:4 fi:10 set:32 computed:2 exists:5 intelligence:2 testing:1 j1:2 observed:2 see:12 computer:4 leslie:1 result:8 w1:3 w0:9 triples:1 subject:1 satisfying:6 welsh:1 uλ:16 xi1:5 purpose:1 clearing:1 representatives:1 artificial:2 symmetric:14 halves:1 state:2 between:4 pairwise:3 neither:1 conditions:4 yk:7 wf:2 zippel:1 attention:2 terms:4 wa:2 complementary:1 originated:1 restricting:1 analogues:1 however:3 jr:2 khanna:1 ji:1 key:1 distinguish:1 article:1 configuration:9 bulatov:8 h11:1 restrictions:1 essentially:1 10th:1 avoid:2 many:5 iℓ:6 annual:2 according:1 constructed:1 april:1 connection:1 colloquium:1 context:5 section:2 hσ:1 contribution:3 argue:2 adapted:1 ll:1 otherwise:16 ck:4 generalisation:2 ci:3 relevant:1 brightwell:1 conclude:1 cc:2 corresponds:5 sampling:1 satisfaction:14 active:1 vardi:2 simply:1 polynomial:16 respect:1 throughout:1 second:1 most:6 pq:2 asks:2 monthly:1 beek:1 three:5 been:4 mark:1 ai:5 reduction:6 cauchy:1 9jt:1 combined:2 ph:1 pn:1 mary:1 empty:1 differently:1 addison:1 direction:1 liverpool:2 corresponding:8 both:3 formed:3 subspace:2 σi:3 modelling:2 finished:3 observe:1 occurrences:1 representative:1 c3:1 checkable:1 c1:5 general:7 those:4 case:34 classifications:1 look:1 unweighted:6 datalog:1 harder:1 single:5 value:12 will:26 deferred:1 reliability:1 suppose:20 none:3 applies:1 situation:2 property:2 leaves:1 a20:1 identical:1 vc:17 vol:1 vi:1 thus:19 them:1 vn:7 equal:4 disjoint:1 yj:1 bij:3 jeavons:2 binary:6 different:4 recover:1 etc:1 make:3 determinant:2 enumeration:2 clearly:3 arguments:1 gibbs:1 finite:4 independent:3 investigated:1 http:2 trivially:2 i1:1 optimisation:1 πir:2 u0:1 hand:2 v0:5 v1:12 v2:3 edges:1 v4:3 v5:3 recall:2 ab:1 identity:2 simulates:4 polymorphism:1 weakly:2 mention:1 colour:2 parameterised:3 well:4 obviously:2 edge:5 machinery:2 components:1 sets:4 hγ:1 entry:3 model:6 paradigm:1 arising:1 just:5 among:1 being:8 identically:1 obtain:3 rest:1 unary:8 yq:3 underlying:6 using:13 λk:1 txk:1 λi:13 studying:1 yet:1 captured:1 contradicting:1 adding:4 πj:2 cut:2 instance:47 point:1 had:2 except:6 assignment:1 sometimes:1 possibly:2 appeared:1 add:6 tuples:6 extends:2 association:2 easy:3 theorem:25 neˇsetˇril:2 input:1 apart:1 solvable:1 remaining:2 bisection:1 real:4 acta:1 enumerator:7 satisfiability:6 evaluate:5 showing:1 possible:1 decidable:1 department:1 know:2 press:4 integer:7 gr:1 formal:1 loss:6 modifications:1 necessary:1 helpful:1 identifying:1 follows:16 reduces:1 specific:1 hypergraphs:1 either:6 sparse:1 martin:1 become:1 introduce:5 δc:8 terminology:2 mathematical:2 parity:1 because:11 33rd:1 often:1 classical:6 sequence:5 tells:1 3bx:1 some:13 cs:3 include:1 table:4 multiple:1 proofs:1 tj:2 nonzero:1 solving:1 cooper:2 feder:2 xv:3 sudan:1 broad:1 decision:9 cosets:1 does:11 select:1 provides:1 assuming:1 respects:1 straightforward:1 minimal:2 core:3 schaefer:5 power:1 deleted:1 vertex:2 equivalent:2 arbitrary:4 bi:2 bj:1 wesley:1 step:2 leftover:1 xγ1:1 properties:2 inapproximability:1 simpler:2 constrains:1 y0:3 limitation:1 disequality:14 ferromagnetic:1 constraint:58 column:11 soft:1 completing:2 meaning:1 acm:2 summarise:1 practical:1 remains:1 range:8 involving:8 ensure:1 discard:3 referred:2 road:1 em:1 a0:2 computational:8 lms:1 dichotomies:1 previously:3 subclasses:1 into:7 within:2 due:1 equality:5 appropriate:1 square:1 references:1 determine:5 operator:1 proportional:3 rossi:1 rows:4 van:1 deal:1 area:1 removing:1 support:18 there:29 question:1 approximate:1 fast:1 u2:5 start:3 lov:2 way:2 xγk:1 was:7 naturally:4 function:91 complete:19 form:3 believe:1 converse:1 jun:1 but:20 taken:1 hh:3 construction:2 don:1 true:1 wγ1:2 kf:2 established:1 absent:1 partitioning:1 wmi:1 compute:7 versions:1 whether:6 antiferromagnetic:1 uw:3 up:1 us:4 variant:1 below:7 verification:1 uk:6 problem:32 define:6 similar:6 called:3 uc:12 detailed:1 partition:34 proved:4 computing:28 defined:8 certain:2 abstract:1 aj:1 generating:3 textbook:1 denote:13 chap:1 arises:2 relates:1 identities:1 check:1 knots:1 defines:1 nh:1 again:3 functions:26 completeness:2 no:5 whereas:1 mathematica:1 when:6 build:1 other:12 np:10 constraining:1 elements:3 expressible:1 problems:32 ensured:2 a1:3 oracle:4 generated:1 important:2 bounded:2 ising:2 eval:12 n1:4 variable:8 generalized:1 singleton:1 structure:2 implies:2 lead:1 algorithm:4 assume:10 physics:4 american:1 l69:1 original:1 vq:2 hungarica:1 weights:5 time:11 dyer:4 international:1 having:3 once:2 |
0704.3684.txt |@word limited:4 similarity:1 rev:11 magnetic:22 excellent:1 splitting:4 leads:2 pulsing:1 consists:2 alt:1 assembled:2 increase:3 depend:1 technique:2 environment:1 charge:3 prolonging:1 under:3 ingredient:1 case:6 probe:12 advantage:1 song:1 very:3 rise:1 account:1 results:3 indication:1 electron:30 fal:1 fall:1 resonant:1 experimentally:1 1s:1 exact:3 petroff:2 minute:1 modulator:2 presented:3 knight:1 prolonged:1 magnet:2 minimal:1 science:1 small:3 govorov:1 optics:2 warburton:2 nccr:1 upper:1 smaller:1 kowalik:1 findings:1 pulse:8 sign:1 equation:1 surrounding:4 second:2 compensates:1 timescales:3 pass:1 further:7 dynamics:14 estimated:2 spectral:4 nonlinear:1 plays:1 christ:2 clock:1 sun:1 assistance:1 bl:1 waiting:4 experiment:8 increasing:1 degree:5 exchange:1 respectively:2 residual:12 here:2 understanding:3 condmat:3 asymmetry:1 operating:1 separation:1 relaxation:1 active:1 path:1 along:1 µev:7 taylor:1 interpret:1 obtained:5 sending:1 great:1 bext:12 institute:1 shift:2 study:6 studied:5 allows:1 commonly:1 resulting:13 slowed:1 makes:2 via:2 followed:2 projection:1 τdecay:22 semiconductors:1 private:1 highly:1 addressed:1 buildup:14 apply:1 counts:1 total:1 gaas:6 use:1 russell:1 would:3 distinct:1 positive:1 vg:1 negative:1 few:6 krebs:2 abragam:1 milliseconds:2 more:5 separated:3 comparison:1 relevant:2 stable:2 emission:3 site:1 transient:2 controlling:1 qds:4 varying:3 cases:1 aligned:1 producing:1 sample:7 keeping:2 recombination:4 karrai:2 decouples:1 setup:1 work:4 modified:1 mt:9 remain:1 values:1 splittings:1 ms:21 following:1 address:1 performed:2 control:2 superlattice:1 figure:1 acousto:1 states:1 indicates:2 his:1 numbers:2 conversely:2 depolarizing:3 axis:1 information:1 respective:3 varied:1 verify:1 dalgarno:1 zhang:1 feature:1 varies:1 gate:12 strong:1 charging:1 blocks:1 lai:3 flip:3 aom:6 after:2 confirmed:1 collection:1 diagram:1 produce:1 snr:4 fe:1 fits:1 spectrometer:3 photoluminescence:2 revealed:2 maletinsky:3 efficiently:1 urbaszek:3 short:2 dynamical:2 effective:2 light:8 yielding:2 perform:2 switch:2 ones:1 allow:1 correlation:1 ingaas:2 order:11 serving:1 feedback:2 reservoir:4 indeed:2 over:2 crosstalk:1 confirm:1 stability:1 course:1 experiments:5 through:2 jaynes:1 its:5 before:2 thank:2 fit:4 decay:37 interesting:3 exhibits:1 actually:1 absence:5 permanent:1 degrees:1 systems:1 communication:1 might:2 pixel:1 non:2 mechanisms:2 propose:1 material:1 tartakovskii:1 functional:1 band:1 effects:4 half:1 oxford:1 now:3 discuss:1 fields:6 antiparallel:1 february:1 several:1 fully:1 imamoglu:4 micro:1 magnitude:5 reasonable:1 each:1 inherent:1 difficult:2 referred:1 ohmic:1 another:1 hundred:1 energy:4 principles:1 inhomogeneous:1 investigated:1 measure:2 quantum:6 our:7 differ:1 es:1 mat:1 shown:7 ejecting:2 factors:1 furthermore:1 since:3 crucial:1 semiconductor:1 posteriori:1 mediated:5 rb:1 maximized:1 electronics:1 induced:3 cause:3 badolato:3 red:3 shows:5 barrier:1 interactions:4 gammon:3 overhauser:1 pumping:2 minimized:1 clarify:2 polarize:1 dependencies:1 formation:1 lab:2 shi:1 van:1 estimate:2 finite:1 card:1 pairs:1 interaction:3 singlet:1 created:1 dip:1 could:4 times:4 creates:2 length:3 hence:1 parallel:1 onto:2 assign:1 first:3 already:1 features:1 coding:2 number:1 randomized:1 long:2 directly:1 open:3 angular:1 given:2 likely:2 width:1 data:6 top:1 amsterdam:1 system:14 ω2e:1 their:3 cooling:3 sweep:1 molecular:1 kov:1 deflects:1 trapped:1 giedke:2 park:2 braun:1 optical:4 differentiate:1 than:3 positively:1 maximizing:1 diffusion:2 observed:6 polarized:10 holland:1 roles:1 rate:9 limiting:1 preparation:1 determined:3 were:5 negatively:1 acquisition:1 extracting:1 addressing:1 predicts:1 curves:5 correspond:1 enforces:2 events:1 orders:1 zero:4 efficient:4 studying:2 self:2 able:3 isolated:5 polarization:11 high:1 calibrated:1 take:1 online:3 switching:6 channel:1 unperturbed:1 even:2 though:1 reach:2 impurities:1 most:1 cummings:1 device:1 paget:1 marie:2 measured:4 deviations:2 don:1 surprising:1 average:2 flop:3 ko:1 neutral:2 alas:1 electrons:1 mechanical:3 left:2 physics:1 dot:3 drastically:1 spaced:1 intensity:3 show:3 gerardot:2 doped:1 dependant:1 rough:1 longer:1 find:2 ground:1 szymanska:1 finally:1 ratio:1 knowledge:2 parameters:4 conduction:1 state:7 supported:1 should:1 only:1 version:1 black:3 brown:3 factor:1 acknowledge:1 local:1 do:1 slows:1 dominant:1 get:1 secular:2 beam:3 synchronization:1 despite:1 timing:2 during:3 processes:1 switched:3 substrate:1 schottky:1 conditions:1 arxiv:1 garcia:1 investigate:2 qd:39 mapped:1 switzerland:1 pulses:12 fixed:4 voltage:14 reveals:1 questions:1 electrodes:1 achieved:2 maximum:1 detection:1 depends:1 individual:5 discussions:1 close:2 best:1 points:2 ways:1 nuclear:55 currently:1 dipole:8 µs:4 µm:1 pump:8 depolarization:11 closed:1 between:6 paramagnetic:1 spectrometers:1 terms:3 creating:1 opening:1 jp:1 however:6 merkulov:2 key:1 distinguish:1 dependance:4 τel:2 suppressed:2 pixels:1 both:4 limits:1 many:1 taking:1 la:1 equal:1 zeeman:3 figures:1 dated:1 eth:1 argue:1 experimental:5 nearby:1 ch:2 jitter:1 groups:1 timescale:5 simple:2 smith:1 excess:1 corresponds:2 directions:1 cirac:2 anti:1 adding:1 sequences:3 fruitful:1 suppressing:1 skolnick:1 pq:1 described:1 wright:1 create:2 due:8 been:8 detuning:1 much:2 slowly:1 expected:1 fry:1 pl:7 fig:11 dots:1 direction:2 controlled:2 suppress:1 coherence:1 amand:2 precision:1 bulk:3 coherent:1 dramatic:1 determination:2 external:11 systematic:1 stems:1 spin:43 present:4 applied:2 exponential:6 pacs:1 solid:1 value:3 remaining:1 will:1 while:9 behavior:1 property:1 layer:1 larger:1 orientation:2 coupled:4 almost:1 thus:5 surprisingly:2 strain:1 superconducting:1 bias:1 cond:1 seen:1 conserve:1 around:1 grown:1 different:2 anymore:1 lengths:2 lett:5 same:3 any:1 complex:2 schematic:1 physical:1 composition:1 higher:2 independent:1 used:5 see:1 complemented:1 blue:3 effect:2 hand:1 inhomogeneities:1 katzer:2 insulating:1 levels:1 urich:1 changing:1 onggerberg:1 paredes:1 off:1 center:1 voisin:2 charges:1 studies:1 well:6 analysis:1 without:1 sets:2 ccd:3 model:2 latter:1 charged:2 when:1 obtain:2 snow:2 distinguishing:1 underlying:1 atomic:1 aspect:1 facts:1 co:2 previous:3 letting:1 note:1 secondly:1 zoller:1 density:1 help:1 apr:1 plateau:1 excited:1 momentum:1 identical:1 saturation:1 increased:2 couple:1 possible:5 period:2 tunnelling:2 indicative:1 helicity:3 vacuum:1 press:1 using:3 color:5 loss:1 bistable:1 necessary:1 like:4 semi:1 kennedy:3 signal:1 performing:1 serves:1 nanoscience:1 shutter:5 collect:1 yields:1 become:1 hyperfine:3 reduced:1 spins:12 accessible:1 exposed:1 back:2 sight:1 duration:1 indirect:2 scale:3 represent:1 excitation:16 lead:4 contacts:1 cavity:1 measurements:7 exceeding:1 meier:1 ensemble:1 straightforward:1 demonstrated:2 measuring:2 noise:1 reaching:1 seconds:4 2c:1 clarendon:1 host:1 found:1 exciting:1 t1e:2 island:1 o:7 rosen:2 islands:1 mean:1 os:12 block:1 presence:6 previously:2 ωe:6 into:2 within:1 bound:1 down:1 appropriate:1 weighted:1 capped:1 accumulated:1 computer:1 additional:1 comparing:2 removing:1 support:1 initial:1 fast:3 quadrupolar:2 tind:2 low:1 way:1 was:6 efros:2 function:3 north:1 magnetism:1 removes:1 but:1 lemaitre:2 compensating:1 repeated:1 ethz:1 hc:1 line:5 faster:2 timated:1 made:1 applying:1 prolongation:1 epitaxy:1 lukin:1 up:5 us:2 placed:1 fluctuations:1 distribution:1 similar:1 nature:1 detailed:1 interval:1 constant:4 minutes:2 measurement:3 influence:1 doesn:1 denote:1 single:8 periods:1 lifetime:3 regime:2 bnuc:8 again:3 compared:3 nm:4 no:3 amounts:1 exciton:5 coish:3 percent:1 detail:1 field:23 other:1 role:4 digital:1 ns:2 optically:2 picture:1 calculating:1 depolarize:2 a2:1 allowing:1 suppression:1 variable:1 skiba:1 coupling:2 corresponding:5 korenev:1 required:2 curve:1 governed:1 inset:2 observe:2 fact:2 time:26 nuclei:12 resolution:2 |
0704.3685.txt |@word roberts:3 concept:1 partial:3 sch:15 chinese:1 represent:2 crucial:1 magnetic:32 results:4 leads:8 diss:1 perturbations:5 primes:2 disk:1 plasmas:1 consider:9 layers:3 whose:2 c0:4 const:1 zone:2 should:1 environment:4 does:6 under:2 stabilizing:2 include:2 indicating:1 mpg:1 conjecture:2 adiabatic:1 goossens:8 straightforward:1 orthogonal:1 frequencies:4 kω:4 conditions:3 urel:10 wave:24 dimensionalized:2 mps:1 resonant:2 affect:4 difference:2 exact:1 condition:11 trigger:1 four:2 intersections:1 uph:10 presented:1 turns:1 criterion:5 solution:3 damped:2 large:1 vector:7 phase:4 instantaneous:1 upper:4 unexpected:1 force:8 direct:1 b20:2 approximation:4 surrounding:3 second:2 alfv:12 dissipation:6 tangential:3 further:3 dynamics:3 amplified:2 even:1 index:1 what:1 adds:1 appear:1 rate:4 section:2 http:1 near:2 expressed:1 uniform:5 consistently:1 cheng:2 obvious:1 harbors:1 3d:1 coefficient:1 full:3 respectively:5 never:1 component:5 here:10 behaviour:1 growing:3 q2:3 galilean:3 directions:1 aerodynamic:2 along:14 equations:2 appears:1 change:2 obtained:1 deriving:1 covers:1 geophys:3 study:2 studied:4 approaches:2 through:1 gravitationally:2 suggests:2 resulting:6 domains:1 changes:2 prints:1 projection:1 cairns:3 apr:1 apj:3 ma2:8 decrease:1 viz:1 apply:1 total:2 planck:1 unit:2 readily:2 derivatives:4 silva:2 takes:1 would:1 remains:1 positive:7 negative:11 γh:4 call:1 therefore:3 criteria:8 taken:3 associated:1 type:6 entails:1 reflects:1 untwisted:1 introducing:2 compensated:2 formally:1 comparison:1 started:1 becomes:8 stable:2 keplerian:1 correspondingly:1 normalized:2 particular:2 cases:3 aligned:3 iii:2 circumstances:1 account:4 ma:23 pursue:1 equation:5 work:2 oscillator:1 modified:1 values:4 thin:12 astrophys:3 following:4 example:2 decoupled:2 ρe0:5 compare:1 schmitt:9 indicated:4 give:4 process:5 discussed:3 hydrodynamic:1 organized:1 high:2 indicates:3 caution:1 numbers:5 prograde:2 keep:2 reynolds:1 axis:1 normalize:1 vanish:2 provide:2 antiparallel:3 discussion:1 s0:5 write:1 varies:1 pair:3 surpasses:1 parameter:6 sin:1 tension:2 mas:11 description:1 may:2 max:1 use:1 derived:3 treatments:1 hence:1 plane:1 waves:19 cambridge:1 horizontal:1 parallel:4 branches:2 accelerates:1 third:1 ss:1 lines:3 element:6 en0:7 maintain:1 so:16 sect:4 vertically:1 order:5 holds:1 reversal:2 developed:1 thresholds:1 vary:1 katlenburg:1 stability:22 thermal:1 paper:8 frequency:6 thesis:1 differs:1 existence:1 kinetic:1 still:2 its:8 roots:1 before:1 satya:2 longitudinal:12 symmetry:1 chandrasekhar:2 chosen:2 nection:1 exhibits:1 writing:2 forms:1 owe:1 parts:9 fig:17 marks:1 mail:1 hidden:1 main:1 setting:1 shear:2 non:10 motivated:1 lindau:1 evolution:1 framework:3 effects:9 they:3 front:1 rotation:1 now:7 discuss:2 nor:1 ks0:2 represents:2 term:8 2p:1 name:1 always:4 university:3 equlibrium:1 arrows:2 2d:1 sufficiently:2 mode:26 toroidal:3 instabilities:15 crossing:1 instability:83 universit:1 higher:1 2h:1 side:1 upward:3 en:6 nondimensionalized:1 significantly:2 independent:6 series:6 energy:13 displacement:7 related:3 astrophysical:3 static:4 expect:1 ξˆn:1 separating:1 our:11 eq:37 out:6 batchelor:2 shown:9 u2a:14 driving:1 furthermore:1 since:3 lagrangian:1 denotes:1 re:1 investigation:1 dominated:2 kelvinhelmholtz:3 induced:17 supports:1 occurs:1 red:1 shows:10 doppler:1 linear:11 mechanisms:2 possibility:3 reason:2 proportionality:1 habilitationsschrift:1 imagine:1 put:1 institut:1 estimate:1 phd:1 definition:1 pairs:3 derivation:1 could:1 similarly:1 used:1 linearized:5 motion:6 length:3 u20:9 exponentially:1 consequence:1 hollweg:3 speeds:2 first:7 simplifies:1 manuscript:1 number:7 restrict:1 smaller:1 fast:1 another:1 carry:2 illustrating:1 thick:3 kolesnikov:5 given:19 perturbation:3 temperature:1 their:3 introduction:2 leading:4 eqs:5 behaves:1 system:10 realistically:1 indicate:4 accretion:1 rates:1 4ma:1 iau:1 structures:3 gives:4 shifted:1 way:1 wavelength:10 reversed:1 incompressible:1 transverse:15 assumption:1 part:9 authors:1 sign:8 than:4 coefficients:1 diffusion:1 relative:10 kind:1 critically:1 require:1 see:6 aims:1 preparation:1 determined:1 stratified:12 amplitude:1 identical:3 treated:2 iωt:2 rae:2 derivative:1 merging:1 unchanged:1 holzwarth:13 already:4 binormal:3 qualitatively:1 curved:2 achterberg:7 ray:2 acceleration:11 prohibits:1 strength:1 zero:7 depending:1 words:1 latter:1 davies:2 mechanism:3 zaninetti:1 onset:7 k2:5 ideal:4 internal:4 square:1 take:1 forces:1 neither:1 schematically:1 new:1 2001a:2 2001b:1 dissipationless:2 normal:15 siphon:1 most:3 ulmschneider:1 connected:3 but:4 significant:1 contrasts:1 segment:2 mach:10 consequences:2 considered:5 sometimes:1 flow:45 kr:1 yang:1 ferrari:2 exp:4 mechanical:1 velocity:33 tubes:20 undular:1 wavenumber:1 precise:1 parker:20 show:3 text:1 enic:9 friction:45 rotating:2 relation:15 solutions:3 threshold:4 spruit:8 trivial:1 find:6 2ma:3 slow:1 ratio:3 parameters:2 conduction:1 true:1 blue:1 reverses:1 surroundings:1 only:6 black:1 subsection:1 factor:6 helmholtz:24 amplifying:1 equilibrium:14 do:3 goes:5 means:1 mainly:1 de:2 fluid:5 inclusion:2 dyn:3 cannot:1 closely:1 altogether:1 dt:4 heats:1 symbols:1 processes:2 densities:2 fields:2 arxiv:2 choudhuri:2 photosphere:1 contrast:1 including:3 gravitational:3 approaching:1 set:2 questions:1 reference:7 publishers:1 frame:8 trussoni:1 flip:1 zones:7 depends:3 arc:3 radius:1 result:7 enhanced:6 ballegooijen:6 satisfies:1 instance:1 et0:12 brunt:2 subsequent:1 propagates:1 pressures:1 outside:3 various:2 envelopes:1 between:5 crude:1 ui:7 ais:2 approach:1 multiplied:1 terms:2 vertical:5 nature:5 importance:1 lel:1 attention:1 eb0:4 jets:2 jetp:1 inertia:5 originates:1 both:4 c21:2 reverse:1 outflows:1 biquadratic:1 similar:2 taking:1 density:1 equal:1 against:2 fulfilled:1 propagation:3 connection:1 context:2 retrograde:3 exceeds:1 0k:1 expression:2 ansatz:3 arbitrarily:2 relevant:4 co:1 simple:2 corresponds:4 height:2 dimensional:1 simply:3 invariant:2 respect:6 buoyancy:5 considers:1 considering:4 better:1 described:3 transformations:2 basis:2 addition:1 three:3 been:8 describes:1 combined:2 interest:1 figure:2 ph:3 define:2 dots:2 direction:12 corresponding:7 quantities:2 concerning:1 excite:1 osin:2 external:17 systematic:1 decreased:1 c3:2 c2:2 c1:11 denote:1 irrelevant:2 case:40 exponential:2 contexts:1 straight:7 appearance:2 value:9 will:4 while:9 volin:1 harmonic:1 behavior:1 balance:3 stenflo:1 procedure:1 real:12 vectors:2 coupled:2 thus:3 dubious:1 ii:8 expressions:2 commonly:1 exterior:3 seen:1 convection:10 undulatory:3 different:1 verified:2 perform:1 solely:2 format:1 radiation:1 cross:1 same:7 any:2 member:1 complex:2 potentially:1 schematic:1 modification:1 finite:4 erdelyi:1 difficult:1 development:1 con1:1 extended:1 infinity:1 kelvin:24 numerical:6 effect:13 flows:13 hand:2 driven:7 action:1 changing:1 2u0:7 sonnensystemforschung:1 upturn:1 lower:9 mech:1 modes:15 keeping:1 largely:1 well:1 roughly:1 analysis:8 academic:1 without:4 components:4 sets:6 quantitative:1 left:1 unified:2 being:1 when:4 guided:1 obtain:4 rest:6 detail:3 oxford:2 underlying:1 identify:1 transforms:1 predicts:1 merge:2 destabilize:1 speed:5 previous:3 note:4 analoguous:1 conclusions:3 absorption:2 excites:1 character:2 potential:1 extends:1 treatment:4 gwdg:1 relevance:2 grow:1 plasma:6 transformation:4 frenet:1 sub:2 lacking:1 easily:1 iα:3 replaced:1 sakurai:1 february:2 cf:5 galilei:2 possibly:1 background:4 press:2 using:2 apart:1 atmospheres:1 loss:1 necessary:1 like:3 follows:2 mhd:3 velocities:3 specific:1 flux:63 continue:1 unstable:17 completely:1 become:8 stationary:1 depend:1 sketch:1 traced:1 methods:1 namely:1 some:1 back:1 understood:1 growth:5 b0:2 oscillations:1 ourselves:1 dc0:2 1996a:3 provided:3 scale:2 describing:1 lead:2 bottom:1 nakariakov:3 tube:55 exceeding:2 insertis:5 critical:14 provides:2 eso:1 moreno:5 propagating:3 restoring:1 inserting:5 reasonable:1 elucidate:2 equivalent:3 each:3 perpendicular:6 stellar:11 pressure:7 symp:1 although:2 imaginary:11 properties:3 earlier:1 panel:4 stokes:3 about:1 actual:1 carried:3 decelerates:1 overstability:3 pe0:2 dependence:3 o:1 range:3 a2:1 plus:1 mixed:1 germany:2 consequently:2 other:7 hydromagnetic:1 perturbed:4 ξˆt:2 statements:1 presence:5 previously:1 into:13 within:2 stratification:10 sol:4 included:3 right:2 references:1 raises:1 determine:1 unstratified:2 proportional:2 van:6 additional:1 assumed:2 suffice:1 there:1 question:1 u0:26 long:3 dispersion:11 collimated:1 quadratic:4 low:4 stars:1 ed:1 astrophysics:3 was:2 damping:3 function:4 medium:19 4q2:1 form:6 becoming:2 regard:1 removes:1 ussler:15 ρi0:6 astro:2 neutral:2 1996b:2 solar:1 larger:2 mnras:2 line:7 dξn:1 dissipative:10 faster:1 directed:1 dma:8 made:1 applying:1 embedded:2 whether:1 inside:2 ωt:2 quantitatively:1 ur:1 dordrecht:1 below:3 owing:3 limit:9 marginally:1 uk:1 ue:9 problem:1 ua:8 called:2 detailed:1 constant:4 ad:1 up:1 defined:1 abstract:1 measure:1 deep:1 general:3 ap:1 exist:1 governed:1 simulations:6 ottingen:2 formalism:1 physical:6 again:1 functions:2 dotted:2 no:2 dashed:4 storage:8 leftward:3 handed:1 field:5 andries:5 branch:4 papers:1 snapshot:1 theor:1 sufficient:1 kluwer:1 met:1 star:1 excitation:1 gas:4 preceding:1 curvature:1 ξt:4 much:1 a1:3 drag:7 important:3 validity:1 ξn:19 pi0:2 ξb:2 astronomy:2 narayanan:2 structure:2 undisturbed:2 dω:6 assume:4 confirm:1 curve:1 interiors:1 together:1 appendix:2 mass:6 fact:10 time:3 walker:2 backward:19 requires:2 |
0704.3686.txt |@word monte:4 cosines:2 partial:1 consider:7 illustrates:2 global:4 edn:1 results:8 month:1 steve:1 disturbance:2 proposition:20 computation:2 edu:3 consists:2 follow:1 chair:1 research:4 alp:1 emily:1 compact:1 bassett:2 preserves:2 depend:2 calculate:1 iii:3 deterministic:1 finally:1 program:1 those:1 th:12 stochastic:2 include:1 edgeworth:1 worth:1 norm:5 case:13 random:7 very:4 fas:1 confounding:1 recursively:2 trigonometric:3 denoted:3 sons:1 fan:2 affect:1 trouble:1 bringing:1 condition:1 chernozhukov:4 northwestern:1 squares:2 presented:1 knight:2 notes:3 mimics:1 applicable:1 ri:1 leave:1 vector:9 math:1 fourier:23 indices:2 anal:1 shows:6 smaller:3 neighborhood:1 dealing:2 estimates:65 measurable:8 approximation:24 second:5 design:3 value:3 infimum:3 further:3 estimated:4 carlo:4 victor:1 even:1 index:14 what:3 errors:4 plays:1 rate:1 chicago:1 complexities:1 fine:1 section:15 expressed:1 uniform:2 cell:3 ˆb:4 version:2 poles:1 above:7 illustrations:1 new:1 net:3 increasing:43 method:13 satisfy:4 multivariate:33 focuses:1 transportation:1 smoothing:2 degree:2 atel:1 respectively:7 error:34 equals:1 here:2 delivering:1 andrews:2 ratio:3 along:12 strong:4 table:9 ordinary:2 obtained:6 interscience:1 noticeable:1 bu:2 institute:1 study:1 economics:3 through:1 resulting:6 permutation:1 suitable:1 changes:1 biometric:3 sines:2 useful:4 classification:1 apr:1 basel:1 hardy:2 specifics:1 rπ:2 org:2 apply:2 rkn:1 total:2 tools:1 select:2 standing:1 plot:8 use:5 andreas:1 takes:2 would:2 prove:1 distinct:1 positive:1 motivate:1 normal:1 next:1 comparing:1 asses:1 therefore:7 taken:3 themselves:1 rearranging:2 theoretical:3 more:6 sort:2 rearrange:1 initial:2 rearrangements:22 everywhere:4 virtue:1 particular:3 known:1 cases:1 producing:2 capturing:1 must:1 me:1 high:1 springer:1 quartic:7 integrating:2 f0m:3 science:2 des:1 values:11 three:2 following:14 root:1 example:18 proof:19 f0:66 claim:8 expansions:1 wand:2 stated:6 process:15 december:1 sense:2 organized:1 sample:9 unbiased:1 lorentz:4 pulling:1 performed:1 arise:1 exclude:1 simul:1 absolute:1 information:1 needs:1 requirements:2 provide:5 discussion:1 holds:2 carries:1 regions:2 how:3 holland:1 answer:1 optimal:1 centimeters:1 parameter:2 fs:1 may:2 after:3 derived:1 mapping:4 collection:3 tractability:2 applications:1 mesh:2 ff:6 coming:1 improving:2 evaluations:1 choice:1 data:10 fm:5 constants:1 induction:2 natural:2 four:6 replication:1 whenever:4 lpr:5 acknowledged:2 yielding:1 trevor:1 element:5 hypotheses:1 complexity:2 so:3 decreasing:2 every:1 order:2 operations:1 dx:30 produces:4 indeed:1 over:10 nonparametric:13 years:1 course:1 paper:8 london:3 statistical:2 cole:2 its:14 figure:10 write:1 quantifies:1 monotonicity:12 thank:1 fit:2 chosen:1 interesting:1 fix:1 solving:1 better:1 choose:1 lp:20 mail:3 main:2 health:3 arguments:12 yi:7 cef:15 non:11 good:2 greater:2 entire:1 matches:1 bernoulli:1 males:1 evolution:1 number:5 resolve:1 equidistant:2 they:2 own:1 sorted:2 products:1 mimicking:1 discuss:2 wiley:3 bahadur:1 february:1 several:2 equality:1 splines:11 always:5 university:5 composition:2 fπ:5 submodular:4 inequality:25 each:17 crossing:1 repeating:1 mean:9 subset:6 harm:2 square:1 directly:1 weight:1 doing:1 series:18 ηp:9 fitting:1 related:2 slowdown:1 society:1 extended:1 measure:7 our:3 operation:4 special:1 out:1 gallant:2 shown:5 dominates:2 factors:1 quantify:4 furthermore:6 since:3 induces:1 denotes:4 rd:2 specifications:1 participants:1 dominated:1 performs:1 sloan:1 size:2 issue:1 correct:1 rj:2 statist:3 foundation:3 earlier:1 linear:9 monotone:12 standard:1 difficulty:1 completely:1 york:1 costas:1 estimate:69 monographs:2 generate:2 definition:1 uiuc:1 r2:2 created:1 impose:1 times:3 ordering:4 econometrics:3 produce:3 πk:2 consequence:1 castle:1 think:1 first:10 xj:36 xi:8 features:2 probability:6 strengthened:1 third:1 primary:1 xd:16 approximate:4 restrict:1 date:1 improvements:2 done:1 least:6 another:2 precisely:1 quality:1 fj:2 illustrate:5 given:17 necessarily:5 reference:4 πd:2 introduction:2 unknown:3 system:1 approximately:1 their:15 assumption:1 rates:2 alfred:1 white:1 variational:1 final:1 interests:1 georgetown:1 relationship:3 asymmetric:1 completed:1 exactly:1 accurately:3 lists:1 direct:3 part:22 because:1 x0:9 x1:1 than:15 population:1 observed:1 hundred:1 target:25 approximations:2 see:6 smoothed:1 states:2 future:1 doubly:1 fˆ:65 tion:1 providing:4 perspective:1 conseil:1 comput:1 displays:1 generality:1 nutrition:1 boston:1 cohen:1 ages:2 argument:12 curves:13 chapman:2 say:1 emphasizing:1 need:2 constrained:2 seek:1 any:16 seminar:1 extremal:1 generalizes:1 piecewise:1 computationally:2 rearranged:50 zero:2 min:2 convenient:2 latter:4 r3:1 note:1 rearranges:1 subjects:1 2006a:3 take:2 2006b:2 resembling:1 2d:1 coincide:1 techniques:3 mit:5 accuracy:1 surfaces:1 begin:1 added:2 unless:2 though:1 price:1 dette:5 chart:4 birkh:1 metrics:3 fℓ:5 gallagher:1 immediate:1 representation:1 measured:2 model:1 tensor:1 give:2 demonstrating:1 year:1 average:35 implications:1 kn:1 lpo:15 replications:4 points:9 hoboken:1 notion:2 fact:2 slope:1 rejoinder:1 efficiency:1 show:10 reductions:2 charles:1 pkn:3 find:3 neuchˆ:1 based:5 parameters:3 much:1 distributed:1 19th:1 should:6 only:2 aperiodic:1 subsection:2 integrate:1 partially:1 local:13 hall:2 nj:1 do:5 intractable:1 american:1 triangle:1 establishes:3 notation:2 means:1 dependent:1 express:1 expectation:6 closely:1 ones:1 words:1 report:7 applying:3 du:4 secondary:1 processes:1 appeal:2 argmin:1 qy:7 areas:1 arxiv:3 median:1 yield:2 summary:2 whether:1 intervals:1 roger:1 common:12 sankhy:1 qf:1 including:1 implication:1 fixed:1 econometric:1 kernel:18 requirement:2 set:10 computed:2 exists:2 med:1 national:4 regressor:3 topics:1 relative:2 namely:7 individual:6 college:1 result:2 arg:2 sen:2 limiting:1 contour:3 best:1 subject:2 closer:8 draws:2 inequalities:5 away:3 enough:1 various:2 john:1 between:1 conditions:1 across:2 available:6 terms:2 extend:2 dxj:4 weak:9 deliver:1 however:1 wi:3 ltd:1 gratefully:2 harvard:3 po:1 key:1 separately:2 amer:1 condi:1 distribution:6 improve:5 both:8 essentially:1 outcome:1 improved:5 tractable:3 many:4 taking:5 density:4 equal:6 rπ1:1 semiparametric:1 improves:7 figures:1 context:1 variance:2 estimation:23 com:2 among:2 point:2 simple:7 effective:1 specification:1 height:38 dimensional:8 ii:3 simply:2 polynomial:14 moreover:9 ucl:1 panel:6 forms:1 pp:2 villani:2 transformations:1 basis:4 monthly:1 buja:1 quantile:71 due:2 been:2 strategy:1 reduction:4 describes:1 asymptotics:1 basic:2 collected:1 pk:1 cqp:16 ann:3 define:4 box:1 describe:1 corresponding:4 molchanov:1 restrictions:1 sufficient:1 theorem:1 body:1 andrew:1 modelling:1 func:1 demand:1 last:1 general:4 present:2 applied:5 subsets:1 might:1 experiment:2 empirical:13 evaluated:2 employ:1 while:3 optimization:2 suppose:9 applies:1 property:7 fernandez:4 inherits:1 larger:1 century:1 almost:5 averaging:2 eral:1 thus:9 them:3 discrepancy:1 iv:1 helped:1 ilya:1 bias:1 comparative:1 technology:1 regression:20 sequentially:1 different:8 author:1 generic:1 cross:1 same:5 parts:2 manski:1 widely:1 survey:1 finite:4 shao:2 conflict:1 status:1 independent:2 clear:1 used:6 columbia:1 raymond:1 cubic:4 numerical:2 upon:4 monotonic:24 disturbances:1 asymptotic:2 auser:1 infinite:1 cqf:9 recent:1 weakly:22 center:2 studies:1 depending:2 well:2 analysis:10 patterns:1 without:2 residuals:1 components:1 qǫ:1 tional:1 parametric:1 dimension:6 left:2 krob:1 being:3 generally:1 obtain:3 press:1 bandwidth:1 underlying:1 transforms:3 simsek:1 integer:1 inference:1 yes:1 graduate:1 univariate:11 λn:2 previous:3 letting:1 tables:1 now:4 application:4 cornell:1 wei:3 olya:1 royal:1 except:1 improvement:8 attractive:2 samples:1 propositions:1 sectional:1 transformation:1 match:1 cornish:1 conclude:2 possibly:2 working:2 quantiles:2 know:1 knot:1 silverman:2 using:12 ams:1 unique:1 koenker:8 loss:4 sorting:10 like:1 follows:14 reduces:3 strictly:3 pol:2 specific:1 continue:1 steps:1 either:5 fixes:1 characterizes:1 ivan:1 become:1 interestingly:1 portnoy:3 mathematical:1 www:4 right:2 often:3 classical:2 sequence:6 conditional:33 some:6 draw:1 econometrica:2 handbooks:1 born:1 growth:10 examples:2 respect:8 indirect:1 proofs:2 orderings:4 chaudhuri:2 provided:1 vol:5 throughout:1 describing:1 dimensions:3 avoid:1 measurements:1 recorded:1 mines:1 comments:1 providence:1 does:2 provides:1 yields:1 imply:2 sixteen:1 measures:1 location:2 equivalent:2 l1:1 illustration:2 rearrangement:73 twenty:1 plots:2 approximating:1 properties:9 proceed:1 constrains:1 integers:1 stone:2 pere:3 extension:1 months:1 discussed:1 dependence:1 o:1 simulation:4 range:1 estimator:4 plus:1 theory:1 eight:1 constraints:1 consequently:1 explicit:2 op:3 converging:1 soc:1 computational:6 into:3 obtaining:1 functional:2 charts:10 submodularity:1 en:1 references:2 determine:1 estimators:4 operator:5 amsterdam:1 reducing:1 technol:1 spline:2 methods:25 statistics:8 additional:1 val:4 support:2 there:5 transform:2 specifically:2 u2:1 strict:5 exchanging:1 quadratic:1 handbook:1 way:6 ed:1 analyze:2 naturally:4 function:73 considerably:1 north:1 form:7 offer:1 but:3 repeated:1 hastie:1 gain:3 flexible:12 convergence:5 delivers:1 highest:1 true:9 newey:2 he:6 infinity:1 consist:2 bandwidths:1 differentiable:1 fˆ0:1 considered:4 below:3 economic:1 limit:3 continuously:1 locally:8 problem:9 panels:7 similar:5 called:1 econom:1 constant:3 computing:3 defined:3 likewise:1 abstract:1 specified:1 ssrn:2 denote:7 littlewood:2 single:1 proves:1 exist:4 lya:1 ind:1 inf:6 work:2 distributions:1 again:1 functions:30 us:4 no:2 when:4 ng:2 grouped:1 other:9 role:1 holding:1 becomes:1 department:3 mathematics:1 nonmonotonic:1 conclusion:2 deviation:1 stat:5 elements:4 pronounced:1 models:1 problems:1 polynomials:1 includes:1 rise:1 important:2 bounded:9 massachusetts:1 ubc:1 variable:9 fisher:1 normality:2 sides:1 ramsay:2 jones:2 implies:3 described:1 assume:1 age:64 interval:3 curve:4 having:1 cambridge:1 mass:2 gijbels:2 moshe:1 original:64 evenly:1 |
0704.3687.txt |@word d2:12 d1:17 aº:4 ln:2 tn:1 γj:1 γi:13 γn:23 di:6 zº:1 arxiv:1 t2:5 t1:5 l1:2 tγ1:10 2j:1 zm:3 zn:14 en:4 β2i:1 sep:1 α2i:1 dº:2 w2:12 w1:7 αi1:1 αi2:1 qº:1 math:1 αij:4 wi:1 e1:1 z2:15 zjn:1 tº:1 f2n:5 oa:1 βi:1 l¹:1 ci:1 xy:1 ei1:3 f1n:5 zk:5 u1:2 u0:2 u2:2 m1:3 m3:3 m2:3 pk:6 pn:1 hp:1 α1i:1 hi:2 aµ:1 x2:8 x1:8 p1:1 det:5 nº:1 ui:1 eik:3 hp1:1 vi:1 kn:2 ik:1 id:12 lim:11 enj:2 g0:3 k2:29 k1:114 k0:9 hpn:1 φi:3 tγ2:7 φn:19 mº:2 i1:1 xº:1 v1:7 v2:12 β1i:1 fjn:3 tγi:8 pº:2 kj:1 ki:6 p¹:4 tγ:24 en1:4 en2:4 exp:2 |
0704.3688.txt |@word wedge:1 represent:1 consider:3 remarkable:1 hats:1 lack:1 anticommutation:1 produce:1 dynasty:1 four:2 commute:2 comments:3 grateful:2 edu:1 osc:5 disk:2 regularize:3 b268:1 careful:1 calculate:11 γs:6 γr:1 technique:2 tr:6 languages:1 charge:2 th:9 under:4 γe:3 divergent:4 ǫab:3 b181:1 supported:3 string:79 very:2 misunderstanding:1 results:3 non:2 witten:12 formula:1 logarithmically:2 difference:2 matrices:27 condition:1 look:1 identity:8 bn:1 solves:1 presented:7 did:1 issue:1 notes:1 itep:1 solution:5 reminding:1 discrete:16 vector:4 ghosts:3 regularizations:7 eigenvalues:3 barbara:1 concluded:1 jhep:16 zn:11 unexpected:2 oscillation:1 foundation:1 mi:2 erler:2 factorization:2 divergencies:2 cosh:3 zero:7 cft:1 odd:2 linear:1 even:2 established:1 kinetic:1 developed:1 stands:2 ambiguities:1 section:9 ρs:4 version:2 above:6 connected:1 χab:3 contrast:1 coefficient:5 full:1 respectively:2 realizations:1 neveu:1 equals:1 answers:2 tachyons:1 inverse:1 sinh:2 represented:1 constructive:1 taylor:4 appears:1 z2:3 z3:32 obtained:1 search:1 didn:1 antisymmetric:4 exemplified:1 algebra:4 institute:2 study:1 vectors:3 φr:7 products:2 uβα:2 published:1 action:6 complicated:3 suitable:1 changes:1 limz:1 via:4 useful:3 figure:2 extra:1 ls:1 logarithmic:1 f3:1 b341:1 anomalies:1 total:3 bra:3 virasoro:2 use:13 graphs:1 usc:1 takes:3 would:4 prove:4 ψr:6 ca2:1 contains:1 chooses:1 next:5 comparing:1 nucl:13 explicitly:2 call:2 therefore:10 det:23 associated:1 theoretical:1 diagrams:1 more:3 nondegenerated:1 brings:1 operators:8 apparent:1 kn:8 appendix:3 normalized:1 excellent:1 known:1 iii:1 fermionic:21 states:1 account:4 potting:1 equation:3 βs:2 oscillator:7 ik:7 theories:2 γr2:3 labeled:1 fock:3 obvious:1 shelton:1 krs:7 following:27 nonsingular:1 singularities:1 example:2 numbers:1 f1:1 f2:1 omit:1 νs:1 give:3 calculation:14 introduces:1 organized:1 ψrp:2 cation:1 lorentz:1 performed:5 story:1 ψra:2 βr2:4 βr1:3 guarantee:1 needs:1 krk:1 provide:4 discussion:3 acts:3 enm:1 enn:6 write:2 how:2 nontrivial:1 pure:1 answer:1 greatly:1 simplicity:2 product:14 rept:1 description:2 singular:4 critics:1 oscillators:2 act:1 southern:1 regularization:16 ψr2:3 consequence:1 φs:16 coming:1 multiplication:5 representations:2 choice:1 revealed:1 fn:2 stress:2 drop:1 gluing:2 sectors:4 read:1 kroyter:6 explicit:1 sv:2 st:2 their:2 rather:1 giryavets:4 cannot:1 so:6 keeps:1 friedan:2 definitions:1 order:4 superscript:1 breaking:1 jevicki:1 help:2 schwartz:1 enter:1 diagonalizes:1 indeed:1 spectral:9 rpp:2 produced:1 rrs:6 paper:4 through:4 looks:1 preliminary:1 mentioned:1 satisfies:2 steklov:1 its:3 features:3 unlucky:1 style:1 group:1 thank:1 sν:1 superstrings:1 ln:2 interesting:2 d34:1 solving:1 conjugation:1 actually:1 zubarev:2 complex:1 choose:3 lovelace:1 main:6 defining:6 transparently:1 arguments:1 correspondence:1 them:2 explanation:1 thereby:3 ya:9 integral:5 uhl:1 practice:3 fig:6 introduce:4 break:1 sψ:2 b271:1 they:8 half:2 singularity:1 now:3 discuss:3 nor:1 represents:2 gets:5 dirac:1 2s:3 university:2 level:4 backgrounds:1 maccaferri:2 tra:1 mode:3 l0:1 l1:1 found:4 2n:1 konechny:2 2i:1 constraints:1 schemes:5 weight:1 map:2 principles:1 vsft:1 expect:2 measure:3 our:8 mapping:3 transitions:1 eq:3 πs:1 special:5 out:1 ru:3 matrix:17 space:4 since:2 rev:3 douglas:1 acting:2 performs:1 got:10 δrs:1 b283:1 ref:1 correct:1 math:3 b287:1 benjamin:1 kαγ:1 turning:1 theory:40 1p:4 ψr1:2 midpoint:2 diagonal:9 free:1 standard:2 small:1 reason:2 moeller:2 california:1 marino:1 put:1 tadpoles:1 derivation:2 βr:2 v1:46 geometry:1 zwiebach:5 could:1 transition:2 counterpart:1 unitarity:2 plane:3 place:1 hence:7 b450:1 first:4 origin:2 already:1 xn:10 vacua:6 tachyon:3 variables:1 potentials:1 number:1 exact:1 fits:1 multiplying:1 simplified:1 relations:29 another:4 president:1 ways:1 open:10 several:1 1q:3 πr:1 given:10 perturbation:1 checked:3 rewritten:1 start:2 introduction:3 data:1 cheremushkinskaya:1 system:1 construct:2 1a:2 needed:1 1c:2 1b:2 a2n:6 calculations:20 realization:1 scheme:4 1m:3 exponents:2 speaking:1 gives:7 commutativity:1 academy:1 moscow:4 continuous:7 realized:3 direct:1 part:13 b337:1 natural:1 coefficients:4 b303:1 legs:1 superghost:9 approximations:2 bonora:2 see:9 annihilation:1 matter:18 determined:1 were:6 ssft:5 toward:1 russia:2 decompose:1 perturbative:1 function:8 sees:1 rewrite:2 lines:1 topics:1 argument:1 say:1 ras:2 any:1 contents:1 built:2 convenient:3 self:1 1d:2 able:2 note:5 sciences:1 k1:6 absorbed:1 build:3 analogy:1 δnm:2 lhs:2 associativity:3 formulas:1 play:1 exactly:2 trace:1 index:2 sft:6 sl:1 metrics:1 λr:4 representation:11 multiply:1 analytically:8 commutation:2 gorbachev:1 constructed:2 considered:2 calculated:5 uκ:1 vertices:46 sx:1 typeset:1 irp:1 points:1 rastelli:3 exp:50 µt:4 usual:3 physics:3 notion:1 fact:2 sector:26 medvedev:6 hyper:1 bosonized:1 show:5 nσ:1 notations:3 berkovits:1 relation:34 sliver:1 keywords:1 diverge:1 d2:1 find:1 make:1 feng:2 explain:1 produces:1 state:2 should:2 jan:1 analytic:2 only:2 bases:4 generators:1 positively:1 factor:9 vkl:1 constant:2 he:2 lim:5 v1x:1 notation:3 get:11 spurious:1 samuel:2 liu:1 ones:3 words:1 probably:1 dw:1 boundary:1 coth:1 crs:1 extract:1 determinants:1 densities:3 fields:11 arxiv:2 remove:2 method:6 fuchs:5 investigate:1 satisfy:3 bars:1 set:1 schwimmer:1 kishimoto:1 j0:1 yost:1 cremmer:1 trick:1 namely:3 result:6 discussions:1 sen:2 brst:1 subject:1 appear:1 hilbert:1 still:1 eigenfunctions:3 kl:3 nondegenerate:3 pictures:7 review:3 irs:8 shenker:1 µs:5 tend:1 symmetric:3 written:4 various:1 closed:1 between:13 invariant:4 neither:1 conditions:7 vrs:13 terms:2 initially:1 component:2 however:1 moyal:6 here:12 key:1 vrk:1 koshelev:2 ket:4 suggested:7 both:6 cos:1 fit:2 b296:1 many:1 taking:5 b517:1 equal:2 demanded:1 γβm:1 anomalous:1 etc:1 figures:1 determinated:1 b293:1 expression:7 finds:1 experimental:1 rpq:2 aa:6 ch:1 δab:2 conclude:2 simple:2 ca:1 v2x:4 cf:1 dimensional:3 superstring:13 preitschopf:2 diverges:2 anti:1 eva:1 moreover:3 branes:1 considering:1 pp:7 pq:12 tuning:1 second:1 basis:55 decent:2 three:3 been:4 mark:1 frs:1 ai:1 workshop:1 change:2 expected:1 schiappa:1 κs:1 anomaly:4 universal:2 define:4 generating:1 arises:1 corresponding:4 truncations:3 ψp2:1 concerning:1 subscripts:1 subspace:3 spectrum:1 noncommutative:2 external:1 general:4 present:1 case:6 p1:6 manes:2 tanh:3 means:1 appearance:4 value:1 will:6 suppose:1 euler:1 intas:1 situation:1 property:1 conformal:8 procedure:1 exponent:1 redefinitions:1 characteristics:1 ir:2 thus:4 vm:6 vn:16 iv:8 ii:2 reads:5 itself:1 im:1 peskin:1 ic:17 id:1 rfbr:1 different:20 a1n:1 descent:45 squareintegrable:1 grant:3 perform:1 realizing:1 same:6 φa:16 unity:2 parts:5 descend:1 universality:1 modification:1 finite:7 φn:1 difficult:2 used:7 infinity:1 cubic:3 numerical:6 effect:1 v0:2 usually:1 v2:38 v3:14 uses:3 symmetrical:1 infinite:5 changing:6 invariance:2 supersymmetry:1 normalization:9 eigenvectors:2 modes:4 ingredients:2 well:3 analysis:1 obviously:1 thought:1 b276:1 consistency:2 coordinate:1 dimension:2 left:2 λs:2 vˆn:10 just:1 less:1 being:1 b240:1 rest:1 ellwood:2 integer:1 alternative:1 previous:1 adding:1 unique:2 preprint:1 generator:1 density:6 iψ:1 add:1 other:3 ohmori:2 lett:7 easy:6 uαβ:10 transformation:4 momentum:1 take:1 real:7 iκ:2 aspects:2 marcus:2 checking:1 evaluate:8 harmonic:1 know:1 background:1 vacuum:7 using:13 vˆ4:2 vˆ3:16 vˆ2:5 vˆ1:20 mod:2 meaning:1 theor:2 like:5 performing:2 δr:6 specific:3 remind:3 integrals:2 arbitrary:5 tower:4 reduced:1 mathematical:2 right:3 neumann:22 γr1:3 some:5 back:1 regularized:9 towards:1 b1:3 sight:1 respect:1 santos:1 nonzero:1 separately:4 demonstrates:1 avoid:1 novelty:1 overlap:6 critical:1 decomposition:2 unit:2 cnm:1 rhs:1 refer:1 obey:1 bc:7 11m:1 equivalent:2 each:3 agreement:1 expansion:2 γs2:1 bs:2 imaginary:1 super:2 properties:3 integers:1 kinematical:1 working:1 freedom:1 discussed:1 dependence:1 angeles:1 srs:2 cancelation:1 stand:1 done:1 positive:1 discard:1 nsh:1 generalized:1 eφ:4 nonequivalent:1 martinec:1 into:10 within:1 numerically:1 functional:1 due:4 nothing:1 because:2 references:1 scherer:1 strip:1 operator:24 nsr:1 bosonic:21 physical:1 methods:2 aref:2 kαβ:6 acknowledgements:1 hep:9 log:40 few:1 indispensable:1 there:8 question:1 transform:1 los:1 quadratic:2 inner:4 way:2 ψn:3 analyze:1 was:22 treat:2 lowest:1 creation:1 form:30 enough:1 hs:2 but:5 formalisms:1 goals:1 cαβ:9 russian:2 true:1 ψs:10 truncation:6 absent:1 made:2 happen:1 leclair:1 characteristic:1 inside:1 uq:4 up:10 us:8 work:3 below:3 belov:9 spectroscopy:1 russ:1 problem:1 called:3 poincare:1 detailed:1 ab:25 proved:1 moore:1 defined:10 abstract:1 determinant:3 doesn:1 denote:2 referee:2 dκ:23 rule:1 formulation:7 exist:1 formalism:3 check:12 defines:2 arefeva:8 functions:2 completeness:1 nm:11 vαβ:6 no:3 rychkov:2 b179:1 generally:1 rs:3 field:53 interested:1 role:1 details:1 papers:1 department:2 ohta:1 ns:6 conclusion:2 picture:14 elements:4 star:10 gross:1 urs:7 vertex:40 polynomials:1 a1:8 chance:1 important:2 qφ:1 b316:1 b317:2 astronomy:1 sides:2 structure:4 okuyama:1 ghost:19 condensation:1 factorized:4 assume:1 thorn:3 factors:11 interacting:4 together:2 strings:1 delta:1 fresh:1 weights:1 n1:3 n3:1 starting:1 having:1 covariant:1 |
0704.3689.txt |@word represent:1 partial:8 consider:1 remarkable:1 secondly:1 iib:2 results:6 four:1 zhong:1 entropy:6 per:8 consists:1 contributions:1 gi:9 particles:7 depend:1 calculate:6 iii:2 shanghai:1 charge:1 th:1 include:2 tc:4 brown:2 lations:1 song:3 very:2 focus:1 figs:1 summarized:2 difference:1 condition:3 presented:1 applicable:1 t0:3 large:1 tsushima:1 convenience:1 small:2 exhibits:1 raha:2 degeneracy:1 employing:3 dealing:1 consistent:3 direct:2 second:2 qmc:2 canonical:1 even:1 will:13 g22:1 stands:1 g20:1 section:3 brief:2 expressed:2 d3:4 current:1 consistently:3 3n:4 above:5 new:7 satisfy:4 lee:1 ibid:2 exchange:1 respectively:12 never:2 modify:2 equals:1 mev:8 china:4 others:4 consideration:1 along:6 quite:1 equations:1 change:2 box:1 great:1 g19:1 study:4 studied:1 completely:1 bf:1 su1:1 adopting:1 suitable:2 changes:2 uniquely:1 emerge:3 extra:7 apr:1 limt:2 addressed:1 meson:1 establish:1 market:1 derivatives:7 use:5 refers:2 takes:1 positive:2 negative:5 next:1 discrepancies:2 calculation:6 nucl:3 m1:3 qcd:2 taken:3 theoretical:3 diagrams:3 more:2 introducing:1 g16:1 composite:1 becomes:5 reversible:7 iia:1 far:1 particular:1 known:1 effort:1 must:6 me:3 evolves:1 account:2 c47:1 ning:3 equation:2 work:3 mi:11 modified:1 ms0:4 labeled:1 values:2 temperatures:3 ms:2 following:3 arrive:1 example:7 beijing:1 weaker:1 wang:6 figure:2 give:8 process:11 neglected:1 saito:1 states:1 ia:8 numbers:1 yang:2 needs:1 siu:1 discussion:1 get:2 chemical:2 how:4 instead:4 thermodynamic:2 after:1 treatments:27 produce:1 benvenuto:2 law:3 fm:7 mao:1 shortcomings:1 attempt:1 shiomi:1 liquid:1 ss:2 explicit:1 summing:1 su:18 so:2 fundamental:2 definitions:1 order:2 nucleon:2 differences:1 satisfied:2 years:1 produced:1 course:1 experiments:1 through:2 differs:1 satisfies:3 still:5 its:1 regions:2 ln:4 masses:9 boson:1 peng:3 permanent:2 choose:2 derivative:7 transparently:2 fig:12 scaling:1 repulsive:1 effects:5 qhd:1 now:1 yu:2 discuss:2 term:7 finite:4 neutrality:1 b374:1 university:1 hamiltonian:3 νe:1 bonn:1 reasonable:1 each:2 found:1 constraints:1 energy:32 related:1 sinha:1 used:1 our:21 happen:1 thermo:1 eq:20 out:1 ru:1 shown:8 keng:1 mq:2 since:3 rev:20 research:1 increase:1 similarly:1 europhys:1 m2i:3 formula:7 ref:11 correct:3 theory:1 given:1 free:6 quark:13 difficulty:3 reason:1 besides:1 imagine:1 e6:1 e0:2 interaction:3 derivation:1 transition:1 keep:2 corrections:1 programme:1 first:6 third:3 variables:2 number:3 antiquark:1 done:2 directly:3 ying:1 illustrate:3 differ:1 temperature:36 their:6 introduction:1 eqs:4 system:26 relations:4 needed:1 calculations:3 lugones:2 baryon:17 b394:1 part:3 b334:1 authors:5 150mev:1 than:1 kind:4 effective:6 zero:3 matter:4 determined:4 supposed:1 behaviors:2 function:15 lines:5 unchanged:1 argument:3 curves:7 correspond:1 say:1 b520:1 categorized:1 qian:4 confirms:1 dynamics:1 jour:1 studying:2 self:4 gkt:1 mechanism:1 polarization:2 internal:3 zou:2 antiquarks:2 added:2 sm:3 serot:1 though:1 collaboration:1 systems:4 rho:3 formulae:4 pair:1 acknowledgements:1 why:1 appear:1 considered:1 clear:1 partition:2 stronger:1 feynman:1 points:3 principle:1 exp:4 fowler:2 chiang:2 physics:1 sum:1 fact:3 quantity:1 ambiguities:1 thomas:1 weiner:1 show:6 supported:1 relation:6 find:5 based:8 ensembles:1 parameters:1 chong:1 explain:1 nnπ:1 only:4 explicitly:1 ambiguity:2 factor:1 employed:1 helmholtz:1 hope:3 equilibrium:14 do:3 predict:1 zhao:1 dk:3 ermion:1 means:4 dependent:20 cannot:3 dt:1 dose:1 dp:1 unfortunately:1 densities:2 conditions:1 arxiv:1 µ2i:2 remove:1 summary:4 investigate:1 paper:1 including:1 fixed:3 50mev:2 national:1 depends:4 sec:2 result:1 definitely:1 µu:1 nuclear:2 review:1 definite:2 µs:1 state:15 difficulties:1 µi:26 between:3 µe:1 µd:1 approach:1 luo:1 various:1 terms:11 confusion:1 attention:1 weak:1 wu:1 hypothesis:2 come:1 suggested:6 both:3 last:1 many:12 region:2 according:2 called:1 etc:2 argue:1 expression:2 experimental:2 nnsf:1 comment:1 cj:1 ci:4 cn:1 point:2 simple:1 address:2 corresponds:1 ce:1 anti:1 decreases:1 table:5 cp:1 cv:1 chakrabarty:2 due:4 been:12 treat:2 goes:2 basic:2 fudan:2 attractive:1 obtained:4 direction:1 corresponding:2 quantities:17 gas:1 gao:3 c9:1 confinement:2 former:1 present:4 pacs:1 solid:5 ǫi:8 nd:2 value:1 enthalpy:1 employ:2 while:2 replaced:1 overcome:1 pdv:2 property:1 couplings:1 3nb:6 almost:1 ne:1 refs:3 herein:1 iv:2 ii:2 reads:2 vs:4 df:1 ic:8 ib:7 different:21 suggest:2 make:3 lett:10 same:6 tells:1 read:1 strange:2 arguments:1 gibbs:3 several:2 conflict:1 independent:2 extended:2 infinity:1 see:1 numerical:1 effect:9 phy:1 uses:1 characters:1 potentials:2 b491:1 lower:1 makes:2 well:1 obviously:3 comes:2 lim:2 model:18 usual:4 they:7 just:1 generally:2 obtain:2 reviewed:1 using:1 flavor:1 previous:4 density:59 had:5 wen:1 thermodynamics:12 add:5 potential:12 treatment:35 extensive:2 5f:1 momentum:1 gave:1 identical:2 saturation:4 rules:1 capacities:1 increases:2 know:1 vacuum:6 world:1 accepted:1 mod:1 particle:10 contradict:1 reduces:1 eβ:1 arbitrary:2 become:5 chinese:1 nucleons:1 obstruct:1 because:10 methods:1 shen:1 calculated:1 b0:6 ccast:1 provided:1 total:3 confirm:1 avoid:1 quarks:4 comments:2 mesons:2 refer:1 claimed:1 indicated:1 jennings:1 pressure:13 although:2 stay:1 properties:2 comparison:2 b358:1 inter:1 constraint:6 discussed:1 dependence:2 o:3 introduced:3 considerations:1 significant:2 into:3 integral:2 three:3 phase:1 right:2 references:2 c56:2 c54:1 c53:1 additional:5 jin:1 few:2 tendencies:1 there:3 c59:1 dispersion:7 low:1 lot:1 was:2 sdt:2 medium:21 zhang:6 m2:2 but:10 volume:1 failure:1 heat:1 contradictory:1 nb0:1 line:5 removed:1 hyperon:1 coupling:1 made:1 characteristic:2 inside:1 variations:1 up:1 us:2 ωa:2 problem:3 similar:1 agree:1 ac:1 later:1 constant:3 abstract:1 hatsuda:2 general:1 exist:1 gorenstein:1 laboratory:1 physical:2 ni:15 functions:9 ev:1 thermodynamical:40 nn:1 no:5 dashed:2 nb:50 when:6 detail:1 field:1 other:10 department:1 ns:2 nu:2 conclusion:1 draw:1 zheng:2 kinds:2 models:1 vertex:1 includes:1 deriving:1 important:1 sqm:4 omega:1 ago:1 longer:1 pion:1 dω:1 walecka:1 together:2 mimic:2 mass:26 n0:4 serious:2 |
0704.3690.txt |@word gv:2 homomorphism:24 consider:26 chain:15 bellaterra:1 reiten:1 global:2 splitting:4 invent:1 proposition:60 comments:1 jenda:1 consists:4 follow:3 gm:1 denotes:13 preenvelope:7 gi:2 row:1 devoted:1 inverse:13 fits:2 transactions:1 hereby:2 tv:1 gorenstein:1 prin:1 tr:4 tq:2 properly:2 kβ:2 finally:7 indicate:3 spain:1 th:2 under:19 syzygy:1 analogous:1 nonsplit:1 presentation:2 adapt:2 p2:1 conjecture:8 departament:1 orthogonal:1 very:2 regional:1 dell:2 results:12 non:4 implicit:2 corollary:35 every:73 continued:1 categories:2 identity:1 trm:1 etudes:1 presented:104 turns:1 t2:1 solution:2 t0:1 t1:1 discrete:1 vector:1 announced:1 el:1 envelopes:2 society:2 gruyter:3 programme:1 strongly:1 ρj:1 zi:8 submodules:19 cohomologique:1 q1i:3 discover:1 approximation:1 go:1 second:3 huα:7 gn:6 further:25 preinjective:2 canonical:39 even:1 will:19 addt:5 filtration:5 appear:8 tipo:1 section:19 hereditary:9 universitat:1 version:2 en:4 above:8 new:8 increasing:1 consisting:9 satisfy:6 hn0:3 notions:3 respectively:10 component:4 jointly:1 understanding:1 following:64 q2:4 ext2r:1 mathe:1 groups:5 situation:2 xβ:5 xα:15 observing:1 preprojective:10 interpret:3 deduced:1 obtained:6 remark:11 ˇt:1 tx:7 covers:1 study:7 studied:5 allows:5 host:1 contradiction:3 propostion:2 products:5 uβα:48 domains:5 hospitality:2 studi:1 suitable:1 explain:1 sci:1 quotient:2 equivalence:2 useful:2 subcategory:1 family:20 f1:15 apr:1 torsionfree:1 herzog:2 limi:1 apply:7 des:1 tools:1 ıa:2 use:8 proceed:5 baer:22 prove:19 sake:2 positive:3 contains:5 visit:1 kα:3 properties:16 distributing:1 few:1 linear:1 subsumed:1 therefore:10 criteria:2 taken:2 associated:1 quotients:1 type:16 theoretical:1 more:3 duals:2 flat:17 almost:6 symposia:1 multiplying:1 duality:8 initiated:1 lim1:3 projectivity:1 berlin:2 correspondingly:2 particular:15 known:3 projective:27 cogenerated:7 hold:10 iii:9 easiest:1 must:2 account:1 isomorphism:6 defines:1 contradicts:1 recall:6 setup:1 work:9 mi:11 lukas:1 ordinals:1 mv:2 ms:2 mr:8 canonically:5 im:1 ın:1 example:21 proof:70 f0:1 claim:13 f2:10 f3:2 dung:3 give:9 endc:4 organized:1 belonging:6 scand:1 topic:2 kaplansky:7 assumptions:1 want:1 sense:1 extir:1 mn:1 information:1 uab:1 end:5 provide:8 verify:5 discussion:2 means:12 american:2 revisit:1 write:10 maps:10 pura:1 criterion:3 pure:84 answer:1 instead:1 map:48 product:5 algebre:1 mat:3 algebra:11 may:1 after:1 derived:1 containing:1 diagram:23 applications:6 birthday:1 inst:1 date:1 verified:1 fj:3 choice:3 arch:1 fm:2 fn:37 rmodule:2 short:5 natural:8 imply:4 joint:1 yielding:1 element:12 hypotheses:1 filtrations:3 so:44 sn:16 allow:2 definitions:1 bimodule:7 order:1 contrary:1 fα:128 fβ:24 hom:4 interpretation:1 words:4 september:1 indeed:3 over:25 insight:1 satisfied:4 balanced:1 years:1 functorial:1 course:6 paper:8 through:13 mentioned:1 existence:1 satisfies:23 its:11 before:2 perfect:3 finita:1 ıc:1 group:4 thank:1 imf:1 summands:6 exact:26 fix:14 solving:2 weaker:1 li:3 corollaire:1 continue:1 condition:36 torr:5 mail:2 main:1 image:1 semisimple:9 split:25 them:2 good:3 motivated:1 auto:1 inductively:2 introduce:4 garc:2 mention:1 they:7 uα0:9 now:24 discuss:3 developments:1 interrelationship:1 february:1 several:3 tensoring:4 name:1 homomorphisms:10 lies:1 always:5 raynaud:8 identified:1 establishing:1 applied:1 iff:3 semisimplicity:5 behaves:1 each:12 found:1 universit:3 difficult:1 characterized:4 subset:2 ordinal:5 domain:7 adjointness:1 telescope:2 independent:1 quiver:1 idea:3 related:6 t3:1 ext1r:16 reader:2 investigated:1 interplay:1 undertake:1 year:1 our:21 eom:1 special:2 out:4 category:1 shown:6 dominates:43 monographs:1 matrix:28 rr:1 factors:12 restricted:1 furthermore:5 since:33 induces:3 research:3 replacing:2 contained:5 mα:46 ra:1 wide:1 mβ:17 denoted:2 rm:2 rn:15 induced:5 induction:3 ri:2 math:15 shows:6 mτ:1 representations:2 sented:1 turning:1 theory:10 goodearl:2 platitude:1 denoting:1 clarifies:1 surveys:1 free:15 shelah:1 noma:1 york:2 habilitationsschrift:1 azumaya:5 wanted:2 beginning:1 compositions:1 irreducible:1 additional:1 definition:20 pairs:21 fixed:1 lix:1 r1:2 language:1 anchez:1 geometry:1 rule:1 similarly:3 keep:1 tor:3 length:1 cycles:1 consequence:3 projection:3 qn:4 first:21 mittag:181 xk:4 qki:1 already:3 xn:6 xm:1 bijection:1 radical:1 possessing:1 number:1 rank:1 restrict:1 clear:7 employing:1 dominating:9 relations:1 another:2 fi:3 crit:1 trans:1 ring:33 precisely:7 appl:3 illustrate:1 given:11 etrie:1 e1:4 πg:1 start:3 introduction:1 πi:2 system:68 construct:3 their:4 assumption:9 observations:2 statement:26 pairwise:1 ordered:1 recent:1 final:1 gives:2 commutativity:3 m0:11 relationship:6 tool:1 continuous:1 proving:3 direct:111 hut:1 part:5 univ:1 push:2 authors:4 x2:1 gluing:1 translation:2 believe:1 completes:1 xj:9 finitely:141 monomorphisms:1 kind:1 showed:1 cyclic:5 holds:10 lying:1 approximations:1 uαn:6 see:38 cotorsion:59 project:2 classes:9 uβ0:5 implication:10 monomorphism:31 were:1 providing:1 treated:2 pre:1 motivation:1 fashion:1 rend:2 auslander:1 mind:1 argument:3 endomorphism:11 say:15 ringel:2 need:9 seen:1 recover:1 any:132 contents:1 functors:1 apparent:1 zero:8 homological:3 lim:105 latter:5 εv:2 milano:1 thorough:1 tensor:1 note:18 instance:1 k1:1 εn:3 take:9 xi:13 hfm:3 coincide:1 techniques:1 εa:4 hfl:2 towards:2 sm:1 trace:1 investigations:4 arguing:1 1this:1 sets:2 systems:3 birkh:1 algebraic:2 ker:118 kα0:2 connected:1 but:8 honor:1 preliminary:2 pair:45 plays:1 acknowledgements:1 intrinsic:1 class:104 es:1 s0:1 fji:1 reduces:1 consequences:1 considered:2 kj:1 ki:8 later:2 stronger:3 kn:1 dimension:8 countable:14 ext:3 hi:6 subfunctor:1 usual:1 notion:6 fact:12 repeatedly:1 precise:1 show:21 rings:8 converse:10 supported:3 implying:1 fγ:3 asserts:1 definable:1 decompositions:1 trivial:3 find:3 q1:7 iq:1 x1:7 inductive:1 proposed:1 representation:6 enough:5 lemma:67 only:59 going:3 specify:1 bundles:1 employed:1 padova:3 local:8 hopf:1 abelian:8 inclusions:1 ϕx:1 notation:5 di:10 dekker:1 uncountable:1 de:9 tilting:32 enochs:1 aim:3 aβ:2 rest:2 closely:1 progress:1 during:1 he:1 interpreted:2 gen:1 gem:1 gel:9 closure:5 erents:1 bel:1 sγ:9 approach:1 arxiv:1 whether:3 investigate:4 she:2 pointed:9 qi:65 london:2 qk:60 qj:4 discussing:1 kiel:1 crm:2 kernel:4 moduli:2 set:40 progetto:1 exists:53 hβ:4 hγ:1 hα:4 module:253 relative:9 differs:1 finiteness:3 alg:1 result:11 corre:1 discussions:1 close:2 sem:2 analog:1 subject:1 eres:1 fails:4 said:9 fαn:6 twosided:1 tackling:1 uε:1 uδ:1 uα:46 representatives:1 uγ:3 uβ:54 written:3 determined:1 chosen:1 closed:23 between:8 αi:1 invariant:1 enjoys:1 conditions:43 αn:12 hence:38 notice:4 endr:3 terms:11 extend:1 fis:1 ext1z:1 restricting:2 focus:1 fuchs:4 vanishing:7 endb:2 hypothesis:12 here:2 key:2 subgroup:8 amer:2 k1i:1 topology:2 both:2 javier:1 last:4 reverse:2 limits:6 desired:4 vun:1 many:1 taking:3 kji:4 according:2 edgar:1 fulfilled:1 etc:1 improves:1 colloquium:1 context:2 logic:1 coh:1 fα0:10 sα:8 matema:1 detailed:1 relevant:1 globale:1 characterization:12 address:2 cf:9 dimensional:6 pm:1 simply:1 bα:13 bβ:7 sequences:2 moreover:29 bidual:1 throughout:3 hvt:3 torsion:24 considering:3 lidia:24 commutative:21 basis:2 union:4 locally:29 due:3 been:2 strategy:1 ai:5 faithfully:1 belongs:15 combined:1 certain:6 gent:1 algebras:7 pn:2 pl:1 choose:7 surjective:6 ements:1 generating:6 walter:1 corresponding:4 ranging:1 commutes:5 countably:36 fund:1 observe:9 modr:3 systematic:1 bull:1 garcia:1 general:3 spirit:1 present:2 case:15 p3:1 p1:1 splits:3 subsets:1 developing:2 contexts:1 ǫi:6 ǫh:2 remaining:1 employ:2 contemp:1 while:5 suppose:1 behavior:3 applies:2 indecomposable:6 revisited:2 property:17 inspired:5 ini:1 satisfying:6 epimorphism:13 thus:21 vm:1 vn:16 ii:23 characterize:2 ij:4 vt:3 dual:8 aspects:1 noetherian:11 whitehead:1 different:2 italy:3 author:2 journal:2 arguments:1 belong:4 same:1 unity:1 pac:1 viewed:1 filtered:9 finite:47 composition:3 european:1 development:1 qji:1 used:3 embedding:4 trivially:1 ni:5 i0:2 sequel:1 dgi:1 hand:1 v0:1 uses:2 eklof:1 infinite:11 artinian:1 interested:1 totally:1 kαi:8 reference:1 subgroups:31 relies:1 suffices:2 kni:1 no:5 well:6 salce:1 morphisms:2 obviously:1 academic:3 directly:2 components:1 pursued:1 model:1 arising:3 gruson:8 left:69 forum:3 gelfand:1 fαi:4 just:2 theorems:1 being:6 resp:1 obtain:14 valuable:1 detail:1 via:2 drinfeld:2 thanks:2 sabbatical:1 immediately:5 griffith:1 previous:7 oriented:2 submodule:25 preprint:3 classification:1 integer:1 field:2 hℓ:4 auser:1 conclude:14 character:6 ideal:1 add:13 hn2:2 corollaries:1 easy:1 theorem:54 stable:1 atomicity:1 transformation:5 book:1 evaluation:2 tβ:2 showing:2 sums:19 term:6 vα:2 vβ:3 descending:1 know:12 insubria:2 press:3 using:4 ascending:4 mod:71 trlifaj:6 necessary:1 like:4 huisgen:1 follows:37 fβi:1 ha:6 sparsity:1 intertwines:1 yields:5 either:3 arbitrary:3 stationary:147 aβ0:1 terminology:4 mathematical:3 copies:1 right:155 methods:1 classical:2 sequence:27 homt:1 successfully:1 some:20 catalunya:1 homr:78 homs:29 deduce:14 elements:2 examples:7 choosing:1 respect:41 soc:4 teoria:1 nonzero:3 provided:15 vol:2 recently:1 bottom:1 establish:1 shall:6 annr:1 per:1 coker:4 does:1 decomposition:1 summand:4 assuming:1 prod:4 proc:2 cogenerator:3 refer:1 specializing:1 q2i:3 equivalent:41 view:2 bi:12 bj:20 how:1 step:5 leffler:181 br:6 zimmermann:13 relating:3 injectivity:8 injective:73 artin:1 about:1 faisceaux:1 would:1 most:3 facchini:4 discussed:1 o:1 reduced:1 dually:3 regular:1 extensions:5 publ:1 ti:1 introduced:4 slightly:1 cofinal:1 morphism:13 exactly:1 raised:3 statements:44 inclusion:15 h2:2 subclasses:1 into:4 h1:2 integral:1 isomorphic:14 εe:3 three:4 remarks:2 because:14 references:1 determine:1 bijective:1 infer:5 next:4 rows:1 degli:2 homz:2 her:1 comparing:1 spending:1 there:106 question:5 long:1 tame:3 strict:80 sary:1 universita:1 way:3 m1:1 was:13 naturally:1 complete:7 form:9 basic:1 hv:54 ht:3 hu:36 hj:1 etude:1 construction:2 hn:15 functor:6 solved:1 hm:10 hc:1 algebraically:1 true:20 partially:2 directed:6 made:2 applying:6 ebrique:1 versions:3 recerca:1 ut:4 inside:1 maximum:2 us:19 hni:6 below:1 un:5 limit:19 grothendieck:2 sum:5 observation:2 problem:5 define:2 similar:2 called:12 asensio:1 originating:1 adopt:3 proved:1 defined:11 focussing:1 abstract:1 combining:2 proven:1 denote:21 single:2 proves:1 exist:16 together:5 relates:1 hautes:1 tα:3 commuting:1 check:1 constructed:3 cotilting:12 again:5 nj:1 qβ:25 completeness:3 stationarity:3 index:1 when:16 hnm:3 hn1:3 application:4 other:8 role:1 details:1 sponding:1 phism:1 mathematics:4 pi:8 conclusion:1 happens:1 expositions:1 generalitat:1 generates:1 remains:3 setting:6 problems:2 visits:1 stay:1 a1:10 a0:2 generated:84 important:5 bounded:2 validity:1 included:1 implies:21 informatica:1 described:1 assume:47 established:1 modules:354 barcelona:3 original:1 equivalently:1 bazzoni:6 n0:1 n1:4 n2:2 resolution:1 having:7 |
0704.3691.txt |@word limited:1 consider:1 tiator:1 wiik:1 rev:30 global:1 focus:1 existing:2 leads:1 facilities:1 parameterization:1 remarkably:1 excluded:1 contributions:11 issues:2 depend:1 re:7 isobar:4 γr:2 γp:1 γv:2 horn:1 those:3 th:3 stable:1 kλ:2 include:1 worth:1 mpf:1 klempt:1 amplitudes:9 performs:2 advantage:1 parameterize:1 very:3 rise:1 none:1 choice:4 interpreting:1 resonant:6 condition:1 carman:1 entire:1 obvious:1 impressive:1 lenske:1 level:4 turns:2 large:2 vector:1 small:3 refer:1 challenge:1 employing:1 lightest:1 unpolarized:1 sign:3 past:1 likely:1 hyde:1 displays:1 further:4 dynamics:4 implemented:2 quite:1 theory:1 residue:1 established:1 what:1 errors:1 const:1 appear:1 gk:1 sum:3 interactions:1 mentioned:1 saphir:3 current:3 consistently:1 above:3 8qq:1 method:1 contrast:1 pioneering:1 impact:1 full:9 lee:1 degree:1 exchange:5 respectively:3 unobserved:1 favourably:1 here:1 asymmetry:1 mev:3 a627:1 possibility:1 groups:1 address:1 ghent:2 along:2 strong:4 appears:1 obtained:4 search:1 fwo:1 spite:1 study:3 typically:1 example:1 suggests:1 accomplished:1 σtt:2 contr:4 resonance:22 suitable:1 involves:1 capstick:2 useful:3 although:2 explained:1 natural:1 private:1 mess:1 meson:3 propagators:3 cloud:1 use:4 would:1 covariant:1 contains:2 predictions:2 eyn:1 discrepancies:1 few:4 nucl:6 taken:1 drechsel:1 type:1 theoretical:1 diagrams:5 more:5 separated:3 optimizing:1 duality:3 successful:1 acceptable:2 effect:1 particular:1 hypernuclear:1 insights:1 high:12 account:1 avoiding:1 originally:1 averaged:1 modified:1 reproduce:4 values:6 mr:2 following:2 παk:4 mx:2 performed:1 nikonov:1 compare:3 reasonably:2 figure:5 give:1 process:4 cimento:1 suggestions:1 involve:1 numbers:1 council:1 qq2:1 σlt:7 standard:3 counting:3 guarantee:1 information:1 respective:1 united:1 provide:3 s0:2 regions:1 how:2 sr:10 pure:2 sarantsev:1 opt:1 instead:2 firmly:1 parameter:2 sin:2 description:14 replacing:1 demonstrates:1 photoproduction:11 after:5 variant:7 diagram:1 modest:1 produce:2 spectacularly:1 fk:1 data:41 response:2 constants:2 kreuzer:1 λ2k:1 electroproduction:12 effective:6 light:1 quoted:1 sensitive:1 lines:2 correspond:3 rather:1 negligible:1 order:2 complementary:1 typical:1 reproduced:2 breaking:1 superimposing:1 ϕk:1 nucleon:1 developed:2 over:3 insight:1 displayed:1 years:2 cambridge:2 including:4 differs:1 its:6 before:4 supplemented:2 le:1 rapidly:1 fit:5 energies:3 interesting:2 fix:1 gtk:7 d33:3 better:3 absence:1 production:4 degrees:1 fig:12 eur:6 non:1 good:2 affected:2 combination:1 was:9 unclear:1 hinting:1 evolution:5 introduce:1 framework:3 p13:5 effects:1 cst:6 nor:2 pz:6 represents:3 february:1 finite:2 gev2:3 university:4 vanderhaeghen:5 identified:1 magnitude:1 bonn:5 reasonable:2 each:2 found:8 difficult:1 reproducing:2 em:3 reactions:2 differential:7 significantly:1 arbitrariness:1 hadronic:3 energy:14 ef:1 reduce:2 gaussian:2 related:1 conventions:2 ex:1 reached:2 quantum:1 our:5 beyond:1 eq:2 out:6 shown:6 dominates:1 m2x:2 factors:7 furthermore:2 since:1 lagrangian:3 m2r:3 research:2 particles:1 may:4 contained:2 plaguing:1 dominated:1 emerged:1 m2k:3 newly:2 ref:15 reconciled:1 red:1 shows:2 linear:1 ryckebusch:10 free:3 quark:3 approaches:4 hep:1 estimate:2 rutherford:1 definition:1 interaction:2 readjusting:2 could:4 impose:1 βx:2 david:1 turn:1 flanders:1 leading:1 onto:1 first:1 major:1 already:1 sinclair:1 powerful:1 number:5 linking:1 channels:4 multiplying:1 least:1 carry:1 impossible:1 quality:2 angular:1 given:1 smaller:1 indicate:1 introduction:2 unknown:1 achieved:1 adopted:1 zegers:1 their:4 intermediate:1 listed:1 calculations:2 structures:1 final:6 williams:1 denominators:1 cauteren:6 option:2 ch:1 baryon:2 tool:1 acquire:1 s31:2 eliminates:1 rejected:1 transverse:1 released:2 assumption:1 part:1 too:1 constituent:3 believe:1 than:6 cosθ:5 anisovich:1 accordance:1 double:3 metsch:2 tree:4 transferred:3 submitted:2 janssen:5 project:1 states:6 determined:2 amplitude:14 were:9 identical:1 elaborate:1 providing:1 solely:1 exhibit:3 function:2 motivation:1 remained:1 turned:2 spectrum:2 curves:5 qualitatively:2 need:1 elsevier:1 constrained:3 any:5 relatively:3 gky:1 issue:1 angle:1 triggered:1 efficient:1 studying:1 latter:3 able:2 mechanism:1 polarization:3 extracted:4 fitting:4 potential:1 thoma:1 performance:1 subject:1 juli:1 channel:18 blue:1 electric:1 collaboration:12 most:4 photoinduced:1 letter:1 unmeasured:1 phase:5 future:1 extremely:1 petry:2 known:1 considered:1 clear:3 adopt:1 vertices:2 g12:1 traditional:2 feynman:5 yang:1 exp:1 databases:1 chiang:2 constrain:1 spin3:1 physics:2 section:6 fitted:2 selection:5 unseparated:5 supported:1 dependences:1 longitudinal:1 rotating:5 gauge:1 stepping:1 fine:3 find:2 schmid:1 partonic:1 q2:13 based:1 mosel:1 parameters:13 much:1 state:9 should:1 jan:1 only:5 usov:1 candidates:1 summarizing:1 factor:2 scholten:1 employed:1 pointed:1 do:1 dominant:1 gev:28 di:1 between:3 quantified:1 assumed:4 preferred:1 beam:1 remedy:1 ones:1 negative:2 words:1 new:2 combinations:1 dw:1 neither:2 processes:6 bradford:2 arxiv:1 yield:2 glasgow:2 optimally:1 contain:2 release:1 through:2 predictive:2 set:2 signify:1 computed:7 fair:2 sep:1 subatomic:1 lifetimes:1 observed:1 argued:1 individual:1 result:5 fail:1 optimum:2 best:4 kaonic:2 roberts:2 phases:1 tensor:3 shupe:1 αx:6 currently:1 dipole:2 favor:1 written:1 readjusted:1 various:4 regge:25 progress:1 αk:6 approach:5 email:1 µb:10 available:2 comparable:2 iπα:1 terms:2 nonresonant:2 missing:13 however:5 supports:2 equals:1 reproduces:1 ji:1 key:1 group:1 overestimated:1 comparably:1 suggested:1 both:7 essentially:1 σl:13 region:12 against:2 chosen:1 pdg:1 contribution:6 σt:19 rpr:62 conclude:1 lagrangians:3 addressing:1 proton:2 quinn:1 table:11 highenergy:1 second:1 pr:1 pp:1 described:2 tuning:2 cqm:5 addition:1 trajectory:9 px:6 three:1 been:8 strategy:5 mart:4 imr:1 combined:4 ireland:5 expected:1 gent:1 reggeized:4 lett:5 peaking:2 θk:7 reggeon:1 corresponding:2 reaction:7 concerning:1 elsa:1 photon:1 precision:1 leps:2 fund:1 otz:1 observe:1 angles:1 spin:6 present:2 case:2 saghai:2 pacs:1 will:2 while:3 λres:2 match:1 behavior:3 applies:1 situation:1 property:1 couplings:9 procedure:1 real:1 seven:1 vogel:1 coupled:2 phenomenological:1 characteristics:1 refs:7 thus:1 itself:1 dual:1 discarded:1 vanish:1 different:1 az:1 d13:18 acknowledgments:1 radiation:1 cross:12 same:4 clearly:2 member:1 tchannel:1 strange:1 dotted:1 widely:1 several:2 higher:2 development:1 responses:1 used:5 trajectories:6 differing:1 hand:2 running:1 user:1 opportunity:1 six:2 tune:1 recent:3 lower:1 elec:1 center:1 ampl:1 database:1 failing:1 well:1 analysis:3 without:3 components:2 dashed:3 comparisons:1 model:31 schm:1 whereas:4 preference:1 stringent:1 proposed:2 heavily:1 photo:3 obtain:2 press:2 shape:2 relevant:1 thorough:1 using:8 λk:2 flavor:1 scattering:2 yet:2 previous:1 adding:1 renewed:1 preprint:1 conclusions:2 ideal:1 kretzschmar:1 wright:2 other:2 treatment:1 input:1 momentum:1 kingdom:1 around:1 appreciated:1 rules:1 phenomenology:1 results:9 term:4 test:1 indicative:1 helicity:1 background:24 belgium:1 world:1 variants:16 unique:1 nuovo:1 apart:2 necessary:2 dq2:1 follows:1 tabakin:1 specific:1 either:5 reduced:1 poor:1 laget:4 spring:1 remarking:1 rot:11 born:2 trends:1 respect:1 cotanch:1 gvk:1 scale:1 describing:1 lead:2 electromagnetic:7 measurements:1 mesons:1 dipoles:1 provides:2 assuming:2 propagating:1 demonstrated:1 dolen:1 bg:6 scientific:1 power:2 s11:3 agreement:2 ratios:1 substitution:1 p33:3 analyses:1 p31:3 properties:1 graal:3 comparison:2 stone:1 kinematical:2 freedom:1 dependence:2 o:1 essential:2 remains:1 range:1 plus:3 efforts:1 introduced:1 slightly:1 kaons:1 cutoff:3 artefact:1 a754:1 previously:1 communication:1 into:4 within:2 collins:1 parameterizing:1 dataset:2 undetermined:1 references:1 primarily:1 exchanges:2 guidal:5 clas:11 van:6 additional:1 possible:1 comparing:1 measured:3 ugent:1 there:1 question:1 specifically:2 width:1 conservation:2 low:1 way:1 resulted:1 sections:6 propagator:4 assumes:1 lowest:2 considerably:3 interest:1 form:7 bennhold:2 but:1 forward:4 recoil:1 underestimates:1 p11:16 implies:1 line:1 considerable:1 understood:1 variations:1 tan2:1 work:3 note:1 naµ:1 grasp:1 embed:1 monopole:1 nature:1 strongly:3 constant:4 computing:1 defined:1 certain:2 abstract:1 describe:2 proven:1 manley:1 single:3 deem:2 formalism:1 worse:1 constructed:6 again:1 functions:2 compared:2 nn:1 no:1 cos:9 ωlab:4 kaon:2 when:5 envisaged:1 overshoots:1 field:3 supplementing:1 valid:1 compares:2 parameterizations:2 department:1 deviate:1 conclusion:2 gaining:1 boyarski:1 models:9 vertex:1 important:1 ky:6 structure:1 merten:1 jlab:1 regime:1 coupling:4 dω:2 assume:2 veneziano:2 required:3 dσ:2 governed:1 mass:6 lying:1 resonances:13 observables:14 heide:1 original:1 once:1 |
0704.3692.txt |@word represent:1 positions:1 gt:6 partial:1 consider:2 σt2:9 particular:1 brownian:6 results:9 gg:1 horsthemke:1 consists:2 anggi:5 expressions:1 research:1 localized:1 scr:1 particles:16 u3:1 depend:5 calculate:1 kurtosis:5 subjected:1 deterministic:1 passage:1 presents:1 comtet:1 charge:1 does:4 under:3 breach:1 nori:1 xtk:2 divergent:1 p2:3 supported:1 g2:2 advantage:2 very:3 assuming:3 keeping:1 dunlap:2 valued:1 stays:1 ma:1 exact:4 condition:10 illustrated:1 exponential:3 ref:1 t5:1 solution:5 large:5 excellence:1 demonstrated:2 small:8 zhu:1 challenge:1 glassy:1 force:13 disordered:3 findings:4 zk:2 dealing:1 direct:3 cosh:2 jump:1 zero:4 street:1 further:3 dynamics:5 odd:2 theory:4 even:4 plays:1 advantageous:1 brackets:1 sum:1 effort:1 issues:1 above:4 new:1 3g:2 method:3 satisfy:1 quenched:9 full:2 respectively:4 realizations:3 equals:1 here:6 red:1 sinh:3 represented:2 path:4 standard:1 equations:2 appears:1 z2:5 z3:9 ukraine:1 gnedenko:1 difficulty:1 technical:1 study:4 studied:3 commonly:1 resulting:2 usually:1 fourier:5 limz:2 via:3 useful:2 family:1 mobility:1 integrations:1 limt:2 expect:1 inequality:1 summation:1 counts:1 total:7 unit:2 readily:2 gu3:1 use:4 asymptotic:6 commun:1 probabilities:2 positive:3 contains:6 finally:2 few:1 depicted:4 monotonically:1 therefore:5 centre:1 characteristics:3 borkovec:1 nanosystems:1 type:1 until:1 today:1 more:3 hu:1 initial:4 berlin:1 appendix:4 normalized:1 varying:3 known:2 cases:1 iii:2 capturing:1 obeying:1 account:4 lengths:3 defines:2 permits:1 setup:1 salas:1 values:4 im:1 example:1 def:1 performed:1 compare:1 workstations:1 give:1 calculation:2 organized:1 sample:5 effectively:1 assumptions:1 numbers:1 want:1 allowed:1 ds1:1 νk:2 absolute:1 end:1 carriers:1 provide:1 verify:1 travel:1 holds:5 s5:1 s4:1 located:1 nontrivial:1 overbar:1 parameter:5 ensemble:1 belongs:1 description:1 singular:9 may:1 max:1 derived:6 different:2 residues:1 physik:2 cambridge:1 summarize:1 forschungsgemeinschaft:1 short:1 dynamical:1 effective:5 light:1 explicit:4 deutsche:1 st:2 sj:22 complexity:1 so:6 sn:8 decreasing:2 definitions:2 acknowledges:1 equation:8 s3:1 interpretation:1 help:2 kampen:1 indeed:1 over:10 move:1 displayed:1 choose:1 dichotomous:7 produced:1 thermal:1 paper:2 through:3 statistical:5 mentioned:1 existence:2 s2m:2 its:7 before:2 perfect:1 s2:2 2λf:8 derive:3 chosen:2 interesting:1 varies:1 decreases:1 complex:1 systems:4 constitutes:1 bin:3 main:5 marchesoni:2 possessing:1 s1:4 maximal:1 non:4 dsn:2 integral:14 outlined:1 processes:1 introduce:3 framework:1 walls:1 effects:4 yu:2 transparent:1 xt2:2 2t:1 represents:1 several:1 dirac:1 name:1 verifying:1 university:2 arrows:1 2g:10 golosov:1 reasonable:1 each:1 2m:12 universit:2 characterized:3 mean:1 domain:4 scheidl:1 financial:1 weight:3 doing:1 series:3 reduce:1 gaussian:12 t3:3 constitute:1 internal:1 used:3 ey:1 ex:1 magnets:1 measure:1 eu:1 our:13 eq:11 special:1 mat:1 rt:2 space:2 res:8 rep:2 since:3 rev:9 denotes:3 diffusive:1 re:2 dsj:4 formula:5 induced:2 evaluation:1 occurs:1 math:2 lopatin:1 linear:8 kostur:1 f2:1 quite:1 nth:1 approaches:2 york:1 van:1 bouchaud:2 rewritten:1 definition:3 derivation:1 determining:1 could:1 transition:1 ds2:1 times:15 motion:4 length:2 exponentially:1 consequence:3 probab:1 first:8 origin:1 xk:1 already:1 features:1 probability:62 variables:2 number:3 reaches:1 approximate:1 unexpected:1 specifically:3 brychkov:1 precisely:1 angular:1 xt:42 size:2 passes:1 given:5 temperature:5 similarly:1 introduction:1 eqs:6 prudnikov:1 amsterdam:2 system:3 their:2 appl:2 calculations:1 inconvenient:1 ranging:1 discussion:1 excellent:1 kolmogorov:1 augsburg:2 exactly:1 blatter:1 part:11 x0:3 sign:1 white:1 diffusion:5 ratchets:1 quantitative:1 succeeded:1 showed:2 accordance:2 marichev:1 second:2 limiting:1 project:1 matter:1 enables:1 collecting:1 acknowledged:1 ann:2 modern:1 turned:1 randomly:1 mater:1 any:1 numerics:1 paths:5 depict:1 efficient:1 studying:2 latter:1 converges:1 note:3 potential:9 take:1 online:1 objective:2 tool:1 gη:5 formulas:2 towards:1 though:1 logarithmic:1 correlation:1 georges:2 most:2 regular:4 germany:1 but:2 representation:9 analytically:4 sfb:1 class:1 chemistry:1 especially:2 considered:2 average:7 physica:1 order:6 points:1 principle:1 exp:2 velocity:7 physics:2 fact:4 quantity:2 slope:1 thomas:1 intensity:2 show:3 german:1 random:20 relation:4 substituting:3 talkner:1 find:4 o:2 slow:1 based:1 knowledge:2 parameters:2 distributed:3 written:4 elucidated:1 analytic:1 only:4 explicitly:1 employed:1 do:2 insight:1 dominant:1 dk:1 means:1 dependent:5 express:2 straightforwardly:1 ones:2 dz:7 dx:4 during:1 du:6 ds:7 holland:1 evolution:9 densities:1 conditions:2 arxiv:1 doussal:2 yield:1 3f:1 investigate:1 analytical:5 fixed:1 generations:1 view:1 coefficient:3 set:2 exists:2 national:1 testing:1 differs:1 see:7 sec:5 result:7 successive:1 w0:8 versus:3 iu:3 contour:2 best:2 tend:1 state:1 proof:1 between:1 geometric:1 reading:1 approach:4 luo:1 terms:3 statistically:1 vertical:1 wn:10 however:1 gratefully:1 le:2 magn:2 key:1 distribution:6 concentrated:1 both:4 last:2 repeating:1 limits:1 many:1 taking:3 conclusions:1 according:9 contract:1 etc:1 layered:1 variance:2 contribution:2 expression:2 otherwise:1 exhibit:1 point:2 simple:3 asymptotically:2 dislocations:1 dimensional:4 z4:5 initiative:2 leads:1 moreover:3 theoretical:1 ct:1 nim:1 pt:48 piecewise:6 addition:2 been:3 z1:9 much:2 slowly:2 change:1 interest:1 basic:1 expected:1 fig:11 obtained:7 arises:2 corresponding:4 quantities:3 residue:1 gao:1 stochastic:1 external:3 general:1 former:1 those:2 case:10 p0:1 p1:3 being:1 pacs:1 solid:1 value:1 will:1 deferred:1 while:2 pressed:1 behavior:11 ku:2 procedure:2 real:1 iz:21 almost:3 vi:2 refs:1 thus:5 iv:2 ii:4 characterize:1 ik:1 bias:1 cond:1 ia:8 mod:1 acknowledgments:1 containing:3 φt:12 propagation:1 perform:2 media:2 gaussianity:1 same:4 wherein:1 ya:1 parts:2 emphasize:2 schematic:1 dimensionless:5 finite:4 grows:2 independent:3 literature:1 infinity:1 singapore:3 numerical:9 unimodal:1 hand:1 driven:5 moment:3 deff:9 necessity:1 changing:1 normalization:3 gordon:1 mech:1 no:4 well:5 analysis:1 obtaining:1 solids:2 solve:2 monthus:1 lim:1 coordinate:8 position:2 model:5 σt:9 arising:1 usual:1 λs:2 popescu:1 moments:6 superconductors:1 obtain:6 valuable:1 teff:1 intervals:10 λg:9 λf:9 summed:1 spatially:1 denisov:4 density:53 extra:1 reimann:1 evidences:1 corroborates:1 setting:1 transformed:1 lett:3 easy:1 theorem:3 republic:1 5g:1 prominent:1 solvable:1 identical:1 rules:1 sums:2 iη:19 test:1 increases:2 divergence:1 using:5 apart:1 overdamped:7 scaled:1 counterintuitive:1 like:1 particle:16 follows:3 reduces:1 velocities:1 yields:4 either:1 integrals:4 arbitrary:2 disorder:12 essential:1 because:5 methods:1 classical:1 vortices:1 brito:1 some:1 b4:2 b5:2 b6:2 b1:2 b2:2 b3:2 transport:1 a10:1 nonzero:1 vol:1 s2j:2 describing:2 collaborative:1 eiη:1 avoid:1 normal:5 langevin:3 integration:5 equal:2 tends:4 kenkre:2 minimal:2 averaging:1 biased:1 noise:4 seconds:1 elucidate:2 jumps:3 agreement:2 expansion:1 notably:1 wesley:1 step:1 depinning:1 plots:1 refers:1 properties:4 simpler:1 central:2 interestingly:1 anomalous:1 dependence:1 recognized:1 simulation:4 practical:1 remains:1 carrier:1 other:2 computational:1 final:2 into:8 within:2 numerically:2 interstellar:1 lies:1 appropriate:1 right:1 elementary:1 proportional:1 munich:1 often:1 a3:1 vinokur:2 institut:1 assumed:1 support:2 there:1 transform:1 long:10 start:2 accordingly:2 describes:1 low:1 way:2 slopes:1 was:1 sinai:2 a2:1 function:26 scale:1 north:1 form:16 phenomena:1 jul:1 histogram:5 properly:1 gain:1 line:1 true:1 made:1 applying:2 appendixes:1 characteristic:5 inside:1 up:3 us:1 ur:1 placed:1 below:1 exerts:1 limit:5 ωn:7 horner:1 problem:1 similar:1 calculated:6 obtains:1 strongly:1 ac:1 required:1 constant:5 astumian:1 addison:1 defined:2 certain:2 abstract:1 describe:1 denote:1 together:1 simulations:3 dη:6 moves:2 distributions:3 spends:1 physical:1 functions:4 compared:2 variety:1 when:3 detail:3 field:2 valid:1 role:1 details:1 department:1 out:2 conclusion:1 deviation:2 stat:1 atsstraße:1 calculating:4 condens:1 a1:1 generated:1 important:1 allowing:1 variable:1 needed:1 implies:1 auxiliary:1 algorithm:1 assume:2 interval:10 governed:1 investigated:1 time:31 |
0704.3693.txt |@word inverse:1 syzygies:1 sci:1 consider:9 gq:2 pth:1 invoke:2 saves:2 results:2 existing:1 four:1 scalar:2 proposition:6 subtle:1 computation:2 originally:1 consists:1 follow:1 primes:1 gl:11 gk:1 toric:7 equivalences:1 compact:4 whose:1 certainly:9 compose:1 calculate:1 c0n:27 re:3 graph:6 equivalence:10 tr:5 goodearl:1 kγ:5 tail:3 those:3 under:5 syzygy:1 must:12 c0t:25 spec:2 norm:1 brown:5 belonging:6 global:14 comm:1 string:1 straightforward:1 g0:2 very:1 fujiki:1 discrepancy:1 reader:2 none:3 gz:1 corollary:16 replaces:1 every:24 ma:3 vls:4 1s:7 continued:6 categories:5 kui:1 annihilated:1 hilb:1 swapping:1 level:1 suffices:4 notes:3 michael:16 rainwater:1 leave:5 covering:1 convenience:2 commute:14 annihilates:3 fourier:1 small:5 c01:7 c02:15 c32:9 glued:1 round:2 elγ:1 desingularisation:3 zm:3 smaller:1 says:2 grothendieck:1 direct:3 zero:3 displays:1 surface:4 remainder:2 further:5 repetition:1 rough:1 canonical:3 aim:1 what:2 vl2:1 tensoring:2 appear:1 cover:3 giving:2 hokkaido:2 section:17 kut:15 kus:11 expressed:7 kun:9 sz:3 gi:16 reconstruction:52 sup:3 new:7 wn:2 appeal:1 s11:1 exercise:1 mp:1 y2:1 subdivided:3 full:7 respectively:1 ravenel:2 henrik:1 component:12 here:5 localisation:5 desired:2 tensors:2 objects:3 free:2 groups:3 address:1 path:27 reine:2 preprojective:7 z2:33 obtained:2 quart:1 remark:6 generalizing:1 technical:1 root:1 leaves:3 larger:2 allows:1 ku1:8 leaving:34 suggests:1 resulting:1 minimality:1 advantages:1 bookkeeping:1 studies:1 involves:2 quotient:6 via:9 useful:2 subcategory:2 aidan:1 extra:14 tensored:1 subrepresentation:2 merely:1 private:1 replace:1 ask:1 cohx:4 decrease:2 pp:2 xz1:26 resolutions:11 clockwise:5 indices:2 use:12 craw:4 ht:3 takes:3 working:1 prove:28 sake:1 positive:1 contains:10 bundles:4 only:19 ψt:2 next:6 iq:1 call:7 opposed:1 vi:2 taken:2 threefold:1 means:6 compactly:2 type:27 reflects:2 more:15 fractions:1 sons:1 duality:6 alastair:3 becomes:2 factor:1 kn:1 surjection:1 berlin:1 backwards:3 labelled:7 particular:2 known:3 projective:16 cases:2 iii:16 iain:1 keeping:2 isomorphism:10 join:1 springer:3 internet:2 recall:4 points:3 work:17 s8:1 hopf:1 quivers:2 ij:1 obvious:8 three:3 den:4 following:12 my:2 example:33 proof:39 annalen:2 claim:11 subcategories:1 quiver:21 xz2:1 process:9 arise:1 organized:1 purposes:1 ann:2 sphere:1 numbers:4 want:3 sense:7 orbits:1 mn:3 occur:1 g2:1 sis:1 information:6 siq:42 sip:50 end:6 notation:9 sit:1 provide:1 ie:9 s1:5 s0:16 american:1 s4:1 write:13 maps:9 opposite:1 answer:2 hi:17 verlag:2 sin:7 css:4 ats:3 map:32 riemenschneider:1 proc:1 description:6 ζf:1 algebra:53 may:24 tilting:8 fz:1 after:7 derived:12 containing:3 epsrc:1 diagram:26 applications:1 produce:4 courses:1 representations:8 horizontal:1 data:5 warwick:1 si3:1 si2:1 si1:3 short:3 natural:4 third:1 si4:1 whenever:2 lemmas:3 sq:1 author:1 explicit:2 summing:1 st:6 s3:1 si:2 ones:1 so:90 sn:1 sm:1 sl:9 definitions:1 typical:1 x18:1 hom:8 ith:2 summands:2 a03:1 over:9 a01:59 suppose:8 consulting:1 produced:1 course:1 paper:12 through:27 looks:1 thesis:1 existence:2 y3:3 still:3 its:8 depending:2 before:2 perfect:1 s2:2 group:15 forwards:1 singular:2 chosen:1 exact:3 characterisations:1 lj:3 actually:2 forms:2 production:1 lr:1 copies:2 radical:1 total:1 mail:1 main:1 defining:1 easier:1 split:2 correspondence:10 non:25 h1:3 return:1 greater:4 was:1 coproducts:1 a0s:7 inductively:2 noticing:1 introduce:4 tjn:2 framework:1 annz:7 a0n:12 they:5 oxford:1 singularity:15 now:44 comes:1 smoothness:1 wiley:1 structural:1 kirillov:1 represents:1 stated:2 name:2 lies:1 fixed:2 invariants:4 university:2 fonts:1 arrows:38 school:1 2z:1 possibilities:2 pda:2 theory:3 modc:1 eis95:2 arrow:8 each:16 done:11 monomials:3 side:1 exti:1 mean:3 homogeneous:7 git:1 square:9 ei:5 another:2 fairly:2 doing:1 series:9 eg:4 hard:3 reduce:1 idea:2 functor:1 inverted:2 society:1 used:1 remove:2 impossible:1 quantum:1 our:1 operation:2 patch:1 thick:1 special:15 out:6 category:4 pullback:1 space:11 furthermore:5 since:45 induces:1 forty:1 research:1 looking:2 i1:6 e1:4 vector:5 hcf:1 com:1 rb:1 max:2 lecture:3 squares:26 induction:5 correct:1 math:12 shows:6 ass:9 rational:3 i2:4 linear:1 associate:2 easily:1 singularities:15 neeman:3 lms:2 little:1 governing:1 standard:5 five:1 quick:1 approaches:1 necessarily:7 complicated:2 trick:2 rhom:1 element:4 put:1 azumaya:12 nonzerodivisor:2 hand:1 beginning:3 compositions:4 irreducible:1 encode:1 definition:20 unique:3 c03:13 benefits:1 r1:11 language:2 created:1 geometry:5 starts:1 could:3 similarly:3 maths:2 noted:1 turn:2 att:34 place:2 gordon:1 hence:26 kapranov:1 crm:1 think:1 polynomials:5 first:8 blind:1 journal:2 xi:3 graduate:2 symmetry:5 u1:4 variables:1 dynkin:5 xf:1 number:3 rank:1 leuschke:1 clear:9 xy:5 morita:1 relations:35 directly:2 xr:3 reached:1 ring:36 precisely:16 open:5 stage:1 chikusa:1 passes:1 given:8 1r:13 heads:1 1t:49 needed:2 introduction:1 mam:1 top:4 notational:2 restricts:2 construct:2 xip:19 their:5 assumption:2 xit:5 statement:3 convention:1 brevity:1 subgroups:8 behaved:1 final:2 bridgeland:2 gives:9 e0:27 a30:3 schemes:1 fraction:5 mostly:1 behind:1 relative:1 exactly:2 immediate:2 technique:1 part:2 j2:6 x2:3 x3:3 copy:1 than:4 x5:3 finitely:2 king:3 john:1 determines:2 unfortunately:1 cyclic:9 double:15 namely:2 xi0:3 xi1:1 xi2:1 determined:9 supposed:1 a40:2 geometrically:2 seamlessly:1 naturally:2 treated:1 localisations:1 pre:1 xin:10 basically:1 lines:1 cohen:19 pass:2 argument:6 correspond:2 endomorphism:13 say:2 progr:1 factorizations:1 manner:1 w0:3 dictate:1 need:10 seen:7 seem:1 macaulay:19 dimn:5 any:37 viewed:1 relatively:1 maxz:5 paths:32 generalizes:1 generic:2 minimally:1 homological:3 convenient:2 self:2 degenerates:1 ideas:1 jacobson:1 note:9 k2:23 k1:37 k0:11 k6:1 forces:3 k4:5 indexed:1 coincide:3 subject:5 εa:1 εc:2 lγ:2 surf:1 1n:9 shall:12 denoting:2 complexes:1 sets:1 reach:3 αs:4 simplify:1 ordering:1 an0:20 but:34 representation:7 nothing:1 extremely:2 class:1 involving:2 forever:1 give:17 observation:1 surprising:2 ki:20 later:2 coincides:5 vertices:16 bousfield:3 ks:38 kr:1 kq:2 kp:7 ku:1 kt:28 communication:1 camb:1 left:9 sum:8 fact:6 choose:1 precise:1 contracted:1 particularly:1 show:13 characterisation:1 labels:3 rth:1 discovered:1 purely:2 spaces:1 relation:3 nagoya:2 yoshino:1 corner:3 analogue:1 font:1 trivial:8 d0:17 ground:1 q1:3 ni:1 inductive:5 knowledge:3 x7:1 invertible:1 ishii:1 written:2 transforms:1 should:7 lemma:56 theme:1 explicitly:2 generators:1 summarizing:2 indeed:6 identification:1 local:2 a00:1 achieve:1 centrally:1 ip:26 do:9 his:1 above:37 viewpoint:1 get:5 stafford:1 db:9 soon:1 made:1 negative:1 mention:1 primeness:1 combinations:1 during:1 dt:12 geometric:1 prime:7 stability:7 regarding:3 qt:3 die:1 y8:2 xi3:1 conditions:1 schofield:4 arxiv:3 zs:1 factorization:1 summary:1 reid:2 tth:3 deploy:1 cij:4 cˆij:1 cycles:11 cii:2 view:9 kernel:17 moduli:12 set:15 ser:1 exists:3 sep:1 j4:2 hγ:18 calabi:1 j0:8 j1:9 module:13 j3:4 observed:1 vσ1:1 see:29 legacy:1 merits:1 result:11 w1:1 2jn:1 discussions:1 recently:1 theoretic:1 paul:1 best:1 techniques:4 mckay:7 αp:10 kα1:1 said:1 αt:50 ways:3 factorisation:3 rings:10 appealing:1 label:7 symmetric:1 enough:1 smallest:4 x29:1 y7:1 closed:3 between:12 αi:18 invariant:1 boundary:2 previous:7 approach:1 representability:1 αn:30 cancelling:2 ken:1 notice:4 terms:13 monomorphism:1 vertical:1 web:21 jt:19 confusion:2 cit:1 jp:72 however:8 jq:18 jn:24 wt:6 hypothesis:7 εit:2 lectures:1 εr:5 rows:1 holds:3 regular:1 pull:1 needs:1 both:8 c21:26 last:4 0t:1 always:2 many:6 equal:5 etc:5 connection:1 equidimensional:1 ils:3 bristol:1 σs:3 ws:2 argue:3 0n:1 fix:3 combinatoric:1 simples:3 generalisation:1 ci:2 relevant:1 fields:1 cm:3 point:5 reasons:2 smith:1 smashing:1 corresponds:2 2i1:1 dimensional:9 cz:1 fashion:3 differ:1 right:2 sequences:1 cancel:3 associated:17 rep:3 throughout:1 ct:29 considering:3 sensible:2 most:1 amer:2 described:1 commutative:21 second:2 hille:1 yau:1 skew:3 locally:2 due:3 been:6 z1:11 homogenous:1 yao:1 much:1 pd:11 basic:28 slodowy:1 transactions:1 algebras:22 universal:3 empty:2 define:13 surjective:2 ctt:23 direction:4 arises:1 corresponding:13 finishes:1 scalars:1 am:3 formed:1 homologically:8 search:1 else:3 2in:1 finished:1 noncommutative:3 c2:24 c1:7 general:5 duke:1 present:1 esnault:2 case:28 multi:1 p1:6 fur:1 look:1 being:1 sheaves:1 straight:1 value:3 will:4 complexity:1 aii:2 hdb:2 cannot:1 aij:4 vσ2:1 indecomposable:2 di:3 property:2 loop:1 a20:6 maximal:11 stop:2 a23:7 k3:15 ve:1 almost:1 funded:1 thus:34 them:3 vn:5 iv:1 ii:20 itself:2 vt:3 localizations:1 dual:6 claimed:1 mod:1 noetherian:4 technology:1 id:2 barcelona:1 different:1 φt:2 uσ2:1 uσ1:1 prior:3 perhaps:1 powers:1 σz:3 indistinguishable:1 same:9 clearly:5 a0r:1 unity:1 arguments:7 established:1 universality:1 φi:1 proved:3 finite:20 aˆij:1 composition:4 vasserot:1 independent:2 extended:5 http:2 localization:1 lie:3 ut:6 i0:4 i3:3 conceived:1 rail:12 i4:2 phd:1 v1:4 viewing:5 v3:2 uses:1 a0t:24 infinite:1 equipped:1 six:1 recent:1 suitable:1 off:1 kleinian:3 tjp:4 makes:2 min:1 well:8 object:1 phil:1 endc:4 concrete:1 thm:2 without:2 cohenmacaulay:3 components:1 εt:1 firstly:3 position:1 hall:1 flops:1 g1:2 dimension:19 polynomial:1 subgroup:2 universally:1 sheaf:4 op1:3 just:8 yz1:1 monomial:6 resp:2 obtain:5 rest:1 shape:2 underlying:3 thanks:2 immediately:2 facts:1 followed:1 yes:1 glue:3 yet:4 based:1 move:4 crepant:3 yr:2 preprint:1 decomposes:1 ease:2 surfaces:1 had:1 ideal:8 silver:2 simple:22 add:3 belongs:6 easy:9 theorem:24 mathematik:1 c12:1 c10:41 remaining:1 ought:1 take:8 identical:1 available:2 reflexive:3 aspects:1 k5:5 2j1:1 isomorphisms:1 read:6 showing:2 repetitions:1 sums:3 possible:2 cf:1 qj:1 grid:1 know:5 using:10 intersection:4 stable:1 advanced:1 extr:2 geometers:1 multiply:2 necessary:1 like:2 texts:1 alternatively:1 reduces:1 japan:1 robson:1 niels:1 eli:3 ignore:3 ai:2 continue:2 either:15 arbitrary:2 translated:1 become:2 li:2 mathematical:2 www:2 because:4 homx:1 methods:1 jls:4 sequence:4 thomason:1 some:65 back:1 algebraically:2 certain:2 understood:3 deduce:2 elements:4 examples:7 b2:9 respect:1 proper:2 soc:3 jli:1 homc:1 s44:1 uniqueness:5 hirzebruch:3 dimensions:2 xvi:1 grading:1 avoid:2 centre:6 angewandte:1 mukai:1 whole:1 everything:9 leap:1 does:1 a10:1 cnn:9 torsion:2 yg:1 o2:1 minimal:27 refer:4 who:1 und:1 power:1 ps:3 s13:1 equivalent:3 dictates:2 continuing:4 equality:1 expansion:5 anticlockwise:6 step:19 isn:1 bp:7 jung:3 although:1 hilbert:1 triangulated:4 properties:1 injective:1 proceed:5 1z:2 integers:1 about:3 x31:2 central:6 extension:1 algebraic:5 row:1 commun:1 kvt:21 o:6 page:2 practical:1 remains:2 gelfand:1 a2:14 ensure:1 invarianten:1 create:1 kvs:9 bath:1 considerations:1 primitive:1 rails:1 statements:1 follows:15 unbounded:2 into:7 preliminary:1 endlicher:1 isomorphic:6 locus:15 down:3 pair:2 en:4 references:1 c00:1 abel:1 mark:1 delete:2 van:4 combinatorics:2 suffice:1 there:27 question:2 u0:1 long:1 dn:1 start:2 accordingly:1 handbook:1 way:7 m1:5 sections:5 opens:2 therefore:3 function:1 head:3 toward:1 complete:3 form:1 forming:2 m2:4 ample:3 ranicki:1 encodes:1 content:1 failure:1 repeated:1 construction:3 gain:1 cycle:3 fully:1 don:1 line:11 removed:2 true:22 ωx:2 pi:2 compute:2 whether:2 characteristic:1 inside:5 smooth:7 flip:2 us:5 localised:1 un:6 ui:1 diagrams:3 uk:3 uj:1 lvn:1 similar:5 called:8 care:2 b1:7 aa:4 ac:2 required:2 supervisor:1 endx:4 ag:2 computing:1 defined:8 resolving:1 abstract:2 describe:1 condition:5 generating:1 denote:19 ar:74 exist:3 together:10 a12:29 kv1:1 ay:1 controlled:1 bergh:4 combining:1 triangles:1 constructed:3 again:10 mathematische:2 completeness:1 entirely:2 eisenbud:1 no:14 ends:1 index:14 ecole:1 when:10 reality:1 field:2 finish:1 other:7 papers:2 mathematics:4 belong:3 trobaugh:1 nice:1 picture:3 draw:4 ll:1 a11:3 generates:3 completes:1 0th:7 kvn:20 vertex:120 gluing:2 bundle:13 a1:16 generated:10 important:6 bounded:3 a4:5 a7:2 sides:1 structure:2 upwards:1 independently:2 miles:1 longer:1 algorithm:2 assume:30 starting:3 factors:9 modules:21 orbit:2 gorenstein:5 notion:1 wherever:1 begins:1 already:2 resolution:34 having:1 localising:2 once:1 |
0704.3694.txt |@word urbana:1 consider:1 rev:5 magnetic:1 particular:2 results:4 parameterization:1 follow:1 remarkably:1 reasoning:1 issues:1 whose:1 tr:14 passage:1 charge:2 tk:1 th:3 stable:1 2πm2:1 divergent:1 subtleties:1 string:5 advantage:1 very:2 wave:1 decide:1 mixing:1 exact:1 condition:1 encodes:1 hamiltonian:4 large:6 freidel:2 configurations:1 mn:5 mi:5 consistent:5 edu:3 direct:1 nair:6 ωab:1 approximation:3 second:4 further:3 dynamics:1 zw:2 established:1 expressed:1 agrees:1 experiment:1 new:1 preserved:1 full:1 here:4 understanding:1 hkn:2 separation:1 path:3 strong:1 appears:4 change:1 obtained:2 vibrating:1 ignoring:1 resulting:3 action:1 fourier:1 studies:1 useful:1 apr:1 redefinitions:1 highly:1 counts:1 propagators:1 linearly:1 derivatives:1 use:1 asymptotic:5 usa:1 covariant:3 contains:3 dimensionful:1 nucl:3 qcd:1 taken:1 det:4 type:1 theoretical:1 more:1 sort:1 formally:1 becomes:1 operators:3 δhh:2 odinger:5 curvature:1 excellent:1 known:1 must:2 involve:1 quartic:1 mm:3 equation:8 work:2 blacksburg:2 mj:1 remain:1 values:1 believed:1 example:2 performed:1 calculation:1 sense:2 share:1 states:9 numbers:2 dxi:1 allowed:2 firmly:1 straightforward:1 acts:1 pure:2 e2n:2 tension:3 transforming:2 different:2 representations:1 data:4 physical:2 momen:1 third:1 computations:1 lines:1 su:1 so:1 correlation:1 order:2 teper:2 leigh:6 constituents:1 over:2 through:2 argued:1 existence:1 kinetic:2 its:2 lg:1 masses:2 solving:1 lk:1 conjugation:2 better:1 mail:3 main:1 defining:1 non:2 good:1 introduce:2 encouraging:1 scaling:1 now:3 nos:1 term:3 university:1 identified:1 mode:1 found:5 differential:3 series:2 energy:1 computable:1 obtains:1 measure:8 quantum:1 our:5 eq:1 borne:1 canada:4 space:2 tensions:1 since:2 crucial:1 cancels:1 looking:1 may:17 dominated:2 theory:6 interactions:2 complicated:1 inconsistent:1 e0:1 lucini:1 uiuc:1 argument:1 exponentially:1 unknown:3 first:4 features:2 symmetry:1 variables:8 number:1 restrict:1 done:1 calculational:1 precisely:1 given:6 leading:2 adjoint:1 calculations:3 holomorphic:6 exactly:2 artifact:1 prediction:3 part:1 manifestation:1 constituent:2 eliminated:1 appreciated:1 distance:2 effective:1 zero:1 correlators:1 regulator:2 matter:1 determined:2 were:1 enables:1 distinguished:1 perturbative:1 symmetries:1 outstanding:1 sw:2 spectrum:7 constrained:1 orders:1 wilson:1 able:1 ideas:1 note:8 potential:1 take:2 jacobian:1 trace:1 shall:1 riccati:1 simplify:1 connected:1 amongst:1 pair:2 analytically:1 consequences:2 clear:1 coincides:1 yang:4 tech:2 principle:1 exp:2 normally:1 fact:1 quantity:1 probe:3 infrared:1 gauge:9 solutions:1 corner:3 trivial:1 find:4 ground:5 ratio:1 knowledge:1 state:8 should:1 analytic:1 only:1 explicitly:1 rich:1 factor:1 local:3 dl:1 expectation:1 hij:1 normalizable:2 regarding:1 arxiv:1 kernel:1 bars:1 set:2 j1:1 j2:2 see:3 result:5 dµ:10 concern:1 detect:1 exponent:1 review:1 definite:1 functionals:1 written:2 closed:1 simplest:1 invariant:6 available:1 terms:3 importance:1 attention:1 weak:1 however:1 jl:1 concentrate:1 tum:1 cousin:1 both:1 essentially:1 limits:1 many:1 region:1 etc:1 connection:1 casimir:1 finds:1 grounds:1 simple:2 dimensional:3 pole:1 table:2 considering:1 transformations:2 rewrite:1 been:1 reduction:1 pg:1 expected:1 determinant:1 corresponding:3 nrc:4 sufficient:1 gap:1 confinement:4 determination:2 derivative:3 spin:1 pacs:1 straight:1 will:5 cast:1 while:2 va:2 planar:1 vol:2 thus:2 vt:2 il:1 containing:1 minic:6 make:1 complex:2 grand:1 units:1 finite:3 higher:1 used:1 effect:1 possible:1 average:1 kim:2 invariance:2 g2:1 recent:1 suitable:1 schr:5 proceed:1 modeled:1 well:2 thought:2 usual:1 restore:1 quoted:1 being:2 mills:4 glueball:4 obtain:1 reality:1 yet:1 gmi:1 density:1 lattice:9 lett:5 possess:1 momentum:1 real:1 virginia:2 vacuum:2 using:1 apart:1 formal:1 like:2 particle:1 collective:1 specific:1 δm:2 δj:3 arbitrary:1 resolved:1 essential:1 δa:1 therein:1 parity:2 because:1 methods:1 namely:1 diff:2 ignore:1 dimensions:3 though:2 integration:2 contributing:1 does:2 wavefunctional:6 assuming:1 prog:1 ellipsis:3 bessel:2 demonstrated:1 power:1 equivalent:1 agreement:2 expansion:2 although:4 2m:2 takes:2 ol:4 would:3 most:1 freedom:4 act:1 consequently:1 equally:1 integral:3 functional:5 variable:1 appropriate:2 references:3 determine:2 operator:4 rely:1 hep:3 assumed:2 there:2 transform:1 low:1 hooft:1 was:1 propagator:1 asymptotics:1 function:4 form:10 regard:2 wavefunctionals:2 but:3 volume:2 collected:1 hh:1 line:1 truncation:1 greensite:1 compute:2 whether:1 wish:1 us:2 below:1 limit:2 problem:1 coordinatization:2 similar:1 agree:1 detailed:1 required:1 constant:1 ai:2 abstract:1 describe:2 general:2 karabali:6 single:2 formalism:1 trailing:2 constructed:3 tedious:1 functions:2 compared:1 no:1 generally:1 detail:1 illinois:1 field:2 other:4 details:1 spatial:3 department:3 b641:1 out:1 picture:1 apparent:1 problems:1 important:1 rising:1 included:1 structure:1 implies:3 coupling:4 physics:4 factors:1 equivalently:1 mass:6 observables:1 requires:1 strings:2 |
0704.3695.txt |@word 2kµ:1 evidence:1 consider:28 chain:1 gp:14 magnetic:14 global:1 y2:31 existing:1 four:6 arranging:1 scalar:1 rebbi:2 consists:3 follow:1 expressions:4 ward:3 row:1 whose:4 depend:2 centres:1 concerned:1 equivalence:1 tr:9 send:4 charge:25 does:2 tj:6 present:1 th:9 under:17 analogous:1 kθ:4 αe2:7 norm:1 applied:2 witten:1 2rj:4 straightforward:1 orthogonal:2 far:1 could:1 implicitly:2 rise:1 translations:4 multi:3 choice:4 falk:3 caloron:87 fall:1 δµa:1 associated:5 difference:1 matrices:11 rn:38 condition:14 identity:1 illustrated:1 y23:3 solves:3 did:1 irreducible:1 t2:12 applicable:1 d2:17 ri:2 large:61 solved:7 vector:3 math:6 b533:1 small:2 relation:1 configurations:3 periodicity:1 yaffe:1 sin2:6 prediction:1 cosh:7 located:2 zero:10 evaluated:1 chen:1 further:5 cft:1 implemented:1 zp:1 y11:5 even:2 index:1 t2k:1 t2j:4 sub:1 invertible:1 euclidean:1 diag:2 section:23 while:6 expressed:1 version:1 goes:2 new:2 method:2 satisfy:10 b666:1 q2k:4 lee:3 component:2 diagonalises:1 here:9 understanding:1 identifications:1 tangent:1 ansatz:5 groups:4 address:1 path:1 strong:1 equations:13 z1:2 change:2 differential:1 obtained:7 sending:1 algebra:1 rigorously:1 my:1 study:4 larger:1 approaches:1 marcos:1 ignoring:1 p2:4 periodic:6 resulting:2 harrington:13 t20:3 t22:9 changes:1 y10:4 y13:3 jackiw:3 via:2 limited:1 divide:1 classification:3 scales:3 natural:1 replace:1 separation:1 rφ:1 durham:2 tp:5 apply:1 total:1 tools:1 imaginary:1 unit:4 repectively:1 use:3 ellipse:4 takes:3 would:7 kinematics:1 distinct:6 xg2:1 bundles:4 predictions:2 e0:15 nucl:5 approach:2 m1:25 harland:2 reciprocity:1 m2:25 3le:1 themselves:1 type:2 tell:1 more:7 smeared:2 flat:1 duality:1 successful:1 becomes:4 ti:2 curvature:2 particular:7 known:2 cases:6 hold:1 eα:3 must:21 monopoles:49 sheds:1 recall:2 equation:23 work:2 det:1 geometry:2 remain:4 mp:3 following:6 making:5 arrive:1 root:1 example:1 proof:1 f1:3 compare:1 νp:3 figure:4 give:5 process:1 purposes:1 weinberg:1 states:1 sphere:2 t1j:6 gas:1 tan:7 t1k:1 yet:1 g2:7 d35:1 g1:7 sit:1 provide:1 discussion:1 di:1 parametrised:2 recovers:1 write:7 how:2 nyi:1 phd:2 types:1 axis:7 parameter:9 sin:38 nye:2 fp:8 map:5 product:1 description:3 singular:2 may:5 qql:1 after:1 singularities:4 dx0:2 consequence:1 plane:2 coming:1 date:2 representations:9 geometrical:1 data:79 constants:5 goal:1 λ2j:6 hartshorne:2 diagonal:2 λ2n:1 outline:1 imply:1 higgs:1 light:1 chern:1 explicit:3 correspond:2 su:33 element:1 18th:1 so:29 fundamental:1 suggest:1 representation:26 divided:1 framing:1 undo:1 jnr:6 acts:8 interpretation:6 gauges:1 atiyah:2 over:5 entries:1 encounter:1 satisfied:1 murray:3 interpreted:2 course:1 through:2 thesis:2 signs:1 mentioned:1 existence:1 satisfies:4 still:1 its:6 before:4 recalling:1 group:10 thank:1 decay:1 ln:10 interesting:3 masses:12 solving:3 translation:3 complex:5 coordinates:3 tpl:1 forms:2 lu:2 baal:6 choose:8 omitted:1 jacobi:1 easier:1 yi:1 non:19 unframed:1 combination:1 matches:1 integral:3 largest:1 dxα:1 very:1 motivates:1 they:6 sσ:1 yp:9 rotation:12 now:6 overlap:1 easily:1 2v:7 equality:1 2r:3 always:4 university:3 classified:5 identified:3 hepth:2 inequality:1 reasonable:1 each:10 found:7 2i:1 mean:1 subset:2 holonomy:11 ei:1 ek:1 ej:4 doing:1 michael:2 reduce:2 approximates:1 related:4 solution:7 used:7 static:1 expect:5 our:8 approximated:1 t1:13 πs:2 out:5 leave:1 shown:4 matrix:12 space:5 since:12 rev:8 denotes:3 acting:9 transposing:1 papers:1 formula:1 get:2 2k:2 correct:3 rj:8 shows:1 numerical:2 theory:10 derived:1 attempt:1 f2:3 standard:3 admits:1 reason:3 term:1 ǫjkl:1 eigenvalues:10 van:6 earliest:1 remainder:1 generate:1 dω2:2 e2:5 r4:5 r2:24 r3:21 perpendicular:1 poncelet:1 traceless:2 quaternions:6 turn:2 length:2 δij:1 assumed:1 hence:3 discussions:1 first:12 xj:1 xk:1 already:2 features:1 symmetry:7 bijection:1 u1:6 number:5 approximate:1 restrict:1 done:2 construct:4 another:2 ring:2 size:1 blobs:3 given:10 2fp:1 e1:3 temperature:3 start:1 introduction:1 adjoint:1 least:1 their:13 positive:1 too:1 calculations:1 bijections:1 final:1 speaking:1 gives:2 centred:1 eyes:1 completed:1 exactly:1 contribute:1 ogr:3 nahm:113 part:8 x2:23 constituent:35 x0:20 x1:9 than:4 summarise:1 e3:3 connections:1 kind:1 generalisations:1 anticipate:3 second:6 submitted:1 limiting:1 classes:1 recovered:1 were:17 sec:6 declare:1 abor:1 motivation:1 sp:4 discrete:1 generality:1 ann:1 corrigan:5 turned:1 argument:1 tends:2 winding:1 adi:3 conjugate:1 need:5 seen:2 unaffected:2 any:6 adhm:11 lie:5 genuine:1 rotations:1 lumps:4 lim:10 self:9 mills:3 b698:1 kraan:2 sciences:1 k1:1 k0:17 derek:1 take:10 tp1:1 tp0:13 interior:1 circles:1 begin:2 shall:4 measures:1 clearer:2 z2:2 most:2 said:2 eight:2 definitions:1 phase:1 acknowledgements:1 inequalities:2 fjk:1 picture:1 unequal:1 subrepresentations:2 considered:8 chosen:2 later:1 tpk:2 tpj:9 order:2 yang:3 principle:1 exp:25 analogy:1 left:6 normally:2 naively:1 fact:3 qcd:1 analysed:2 particularly:1 show:7 supported:1 nµ0:3 converge:2 purely:1 spaces:3 gauge:68 solutions:11 x3:9 substituting:1 d4:2 trivial:34 find:5 d0:1 d1:17 q1:9 q0:1 q2:5 based:2 parameters:8 implementation:2 minus:1 behind:1 topological:10 should:5 analytic:1 only:15 black:1 subsection:1 prof:1 circle:8 local:2 interested:1 triangle:1 above:4 notation:1 means:3 dg:1 overall:1 aα:3 cannot:2 dz:1 iǫabc:1 words:1 ds:6 dp:3 processes:1 densities:1 fields:3 arxiv:12 expansions:3 remove:1 consisting:1 investigate:2 intervals:5 hitchin:1 including:1 qk:13 fixed:10 ql:2 2p0:5 moduli:9 set:9 constructing:3 exists:7 sep:1 generally:1 t12:10 observed:1 y1:30 see:13 radius:2 result:1 vertices:1 terms:13 elliptic:2 jardim:1 goddard:1 points:3 satisfying:8 tensor:3 ways:3 harvey:1 review:6 rings:3 diverge:1 symmetric:23 written:1 determined:5 between:7 invariant:20 boundary:18 conditions:28 email:1 d56:1 side:1 preserve:1 notice:2 restricting:1 recently:2 planes:1 importance:1 suppose:2 attention:2 transpose:2 however:2 pseudoparticle:1 white:1 conjugates:1 comm:5 subgroup:3 article:3 valid:3 adapting:1 both:6 cos:37 2πz:1 limits:24 eigenvalue:1 iℑ:4 many:3 taking:5 infinitely:1 equal:4 laplace:1 april:1 connection:1 instanton:18 whole:1 fix:5 comes:1 cos2:1 relevant:1 sinh:6 conclude:2 simple:4 acted:1 others:1 unitary:1 period:22 chakrabarti:3 dimensional:6 taylor:3 anti:6 conjugation:1 away:1 constant:14 restriction:1 branes:1 considering:4 sensible:2 finally:2 xα:18 described:3 transformations:19 geometries:1 fairlie:4 addition:2 barry:1 locally:1 due:2 been:18 much:1 combined:1 interest:1 expected:1 ak:1 important:1 define:3 concentrated:1 relations:1 families:7 quantities:1 sufficient:1 formed:1 iµ:2 locations:9 specifically:1 calorons:135 edinburgh:1 θp:3 general:5 those:2 case:30 p0:4 p1:4 look:4 leiden:1 suitably:2 value:3 iτ:2 will:53 parametrisation:2 near:1 associates:1 replaced:2 evaluating:1 endpoints:1 2e2:1 loop:3 computed:1 studied:5 shepard:13 ip:7 thus:1 instantons:22 iw:2 ik:2 dual:8 mod:1 leaving:3 fermion:1 manton:1 compactified:1 d15:1 different:5 d17:1 mµ0:1 propagation:1 things:1 make:9 progressing:1 lett:3 same:4 clearly:1 parts:1 pauli:2 iθσ:1 products:1 finite:9 higher:2 odd:2 literature:2 infinity:11 i1:6 i2:7 effect:1 hand:4 action:31 dgp:1 edges:1 introduce:1 infinite:3 six:3 reference:2 subgroups:1 eigenvectors:1 modes:1 charges:27 studies:1 valued:2 well:3 roughly:1 thought:3 without:1 solve:3 hτ:1 sets:5 coordinate:4 position:1 dimension:4 dh1:1 usual:1 λq:1 just:4 less:3 able:3 rotated:1 obtain:3 formulated:2 drinfeld:1 transforms:4 using:7 λj:5 alternative:1 λn:1 67b:1 previous:1 letting:1 note:3 rapid:1 family:16 density:5 had:2 except:2 mathematically:1 appeared:1 setting:1 extends:1 location:4 theorem:1 tp3:2 iσ:1 practise:1 transformation:13 tp2:1 real:10 bruckman:5 asymptotically:1 around:1 depends:5 represents:1 evaluate:2 iβ:1 possible:6 spanned:5 corresponds:4 ypj:1 five:2 makes:2 integer:5 subfamily:1 stable:1 usually:1 moody:1 loss:1 like:3 follows:10 interestingly:1 either:4 arbitrary:1 rearrangement:1 essential:1 mathematical:1 kac:1 right:1 classical:3 what:1 some:17 pierre:4 examples:9 choosing:1 normalisation:2 extended:1 matching:19 reasons:1 nonzero:1 gross:1 scale:31 represent:1 swaps:1 obtaining:1 opposite:1 comments:1 aˆα:1 behave:1 t10:5 provides:2 rectangular:1 y20:3 y21:4 three:5 bogomolnyi:1 2q2:1 equivalent:4 radial:1 aj:11 agreement:1 expansion:1 interval:2 quaternion:8 substituted:1 bp:2 relating:1 refers:1 properties:2 earlier:1 simpler:1 stokes:1 thomas:2 central:1 constraint:1 column:1 freedom:1 discussed:1 o:12 posess:2 remains:1 involving:1 act:2 conformal:1 d67:1 constraints:1 skyrmions:1 automatically:1 jacques:1 localised:1 previously:3 into:5 formulae:1 numerically:1 isomorphic:1 λe1:1 framed:5 down:1 hermitian:5 because:2 references:1 determine:1 ǫijk:2 next:1 rossi:3 hep:9 removing:2 there:24 question:2 transform:22 long:2 u2:5 strict:1 way:8 hooft:5 was:9 therefore:7 function:6 yp2:1 form:11 quaternionic:3 hp:2 brane:1 hv:1 hw:1 but:7 construction:5 aµ:1 gain:1 line:2 true:2 partially:1 maximised:1 made:3 erick:1 consist:2 proceeds:1 gravitational:1 2πj:1 up:17 us:2 discarding:2 below:1 owing:1 limit:42 uk:1 sum:1 fαβ:2 demonstrate:1 monopole:56 similar:6 called:8 eigenvector:1 exact:3 ac:1 ab:1 ordered:1 resemblance:1 computing:1 defined:10 abstract:1 describe:4 am:2 proven:1 denote:11 ap:4 single:2 arises:1 exist:2 b149:1 corresponding:2 az:1 check:1 triangles:1 constructed:7 functions:5 compared:4 no:9 amounts:1 image:3 when:32 detail:3 reality:6 field:17 other:5 details:1 spatial:1 massless:6 ar:1 b645:1 conclusion:1 tionally:1 briefly:2 elements:1 kinds:1 generates:2 garland:2 subspace:5 preceding:1 d58:1 uniformly:1 stay:4 a1:9 a0:6 generated:2 a2:9 vectors:2 pisarski:1 pparc:1 rescalings:1 sides:1 dimensions:1 ago:1 χe2:4 implies:5 longer:1 assume:1 sigma:2 required:1 2e0:1 edward:1 equivalently:1 mass:1 useful:1 distinguished:1 having:2 |
0704.3697.txt |@word limited:4 func:1 similarity:1 gabrielli:6 poorly:1 calculate:8 marcos:6 paris:2 behaviours:4 γn:5 under:3 divergent:1 rise:1 figs:1 summarized:1 solution:6 vector:9 math:1 force:7 estimates:1 direct:4 approximation:17 second:8 qualitatively:1 estimated:1 even:4 errors:12 wavenumbers:4 ˆu:1 above:22 new:1 net:1 increasing:4 coefficient:1 evolving:1 never:1 here:21 reported:2 represented:1 obtained:3 study:8 wdm:4 fourier:5 changes:1 appropriately:2 9a:1 explained:3 diagonalising:2 total:3 linearly:4 derivatives:1 would:9 chooses:1 therefore:9 type:8 until:5 glass:2 warm:4 hold:1 must:3 springer:1 pursue:1 rν:1 work:1 mi:1 era:1 vlasov:7 springel:1 example:4 wang:1 indicated:4 give:5 organized:1 generically:1 degenerate:1 times:8 end:2 recovery:1 provide:2 verify:3 feature:1 recovers:3 how:10 hot:4 adjacent:2 widespread:1 4πgρ0:7 oscillatory:1 description:2 after:6 modest:1 mesh:2 summarize:2 law:2 parallel:5 attempt:2 third:7 schneider:1 maintain:1 contributes:2 correlation:7 order:22 operations:1 origin:4 interpretation:1 over:17 vary:1 before:4 fix:1 αmax:1 writing:1 better:8 fig:40 maximal:3 them:7 specifying:1 couples:1 effects:86 they:10 rµ:1 filling:1 each:12 side:9 mean:7 series:1 displacement:33 used:14 tremaine:1 quantify:5 particles:24 re:1 ri:1 numerical:11 linear:22 given:50 standard:3 proportionality:1 corrects:1 tdyn:3 iiic:1 r5:1 r3:1 starts:1 isc:1 already:4 subtlety:2 a3b:1 a3a:1 another:2 clarity:1 toy:1 periodicity:3 top:1 approximately:5 perturbations:1 observations:1 ranging:1 collapse:1 centered:4 dissipationless:2 binney:2 somewhat:3 peculiar:2 distance:10 princeton:1 approximations:1 tree:1 preparation:2 matter:10 tion:1 perturbative:10 spectrum:11 valageas:1 manner:2 seen:9 tells:1 convenient:1 latter:14 oriented:3 forces:2 shall:1 simplify:1 boltzmann:1 marie:1 observation:1 calculated:4 inferred:1 curie:1 points:8 principle:4 quantifying:7 sum:12 random:1 attempts:2 solutions:5 d3:3 resemblance:2 coefficients:2 do:9 zeldovich:7 de:3 fluid:63 runs:1 ˆk:1 heaviside:1 fields:8 analytical:1 unsurprisingly:1 observed:4 depends:9 radius:1 result:9 discussions:2 best:1 subject:2 said:1 exponent:1 away:1 artificial:1 symmetric:1 drawn:1 approach:6 splinter:2 terms:5 extend:1 nature:3 component:1 weak:1 however:12 improve:1 ranges:3 essentially:5 variance:6 contribution:5 timescale:1 applicability:1 basis:1 19a:1 mizuno:1 three:12 been:21 much:8 interest:1 expected:5 dots:1 hepp:1 quantities:7 θf:2 maximally:1 applied:7 exception:1 reciprocal:10 abrupt:2 applies:1 leaves:1 played:1 kohn:1 iv:1 ii:5 characterize:2 ik:3 cond:4 comparative:1 ic:25 id:1 make:1 dµν:3 dimensionless:2 grows:2 independent:10 laboratoire:1 trajectories:2 hand:11 suitable:1 inherit:1 rome:2 greatest:3 quantitative:3 just:12 able:1 identify:1 previous:3 enters:1 character:1 ruffo:1 spread:2 easy:1 zinit:21 5a:1 5b:2 9b:1 breaks:3 possible:3 possibly:1 background:1 isotropy:3 specific:5 steps:1 sparse:1 www:1 right:6 dense:1 umr:1 comments:3 contributing:1 plt:27 plot:7 properties:5 o:2 ensure:1 slightly:2 soc:7 bound:1 22a:1 down:8 lies:2 initial:42 approximate:6 width:3 way:2 was:2 bartelmann:1 form:5 becoming:1 differences:4 pµν:1 cedex:1 encoded:3 true:5 surprising:1 supp:1 inside:7 crystal:1 fermi:1 moore:2 abstract:1 simulations:51 dδ:1 distributions:1 regime:19 ni:2 nk:2 no:8 generally:1 vanishes:1 setting:1 role:3 test:1 models:8 felt:1 cnr:1 faster:1 assume:3 time:41 characterising:1 precedent:1 neighbors:1 precise:3 particular:7 leads:5 roy:1 microwave:1 extremities:1 inverse:1 depend:5 zone:11 finally:2 analogous:8 choice:1 orientations:2 emphasized:3 exact:6 level:1 anisotropy:18 discrete:11 upper:1 unexpected:1 plummer:1 findings:1 trend:1 appear:2 axes:4 uniform:1 current:6 goes:3 shandarin:3 realizations:1 qµν:1 understanding:2 address:1 along:1 appears:1 change:2 box:6 sending:1 shift:23 studied:8 spheres:1 poisson:3 usually:9 t20:2 studies:1 plotted:5 useful:4 convolution:2 extra:1 fbz:11 translational:1 d73:1 d75:1 predictions:1 france:1 encode:1 theoretical:13 introducing:1 validity:6 eν:1 appendix:1 everywhere:1 cases:4 insights:2 rotational:2 bouchet:1 flt:6 values:10 growing:8 making:1 numbers:2 nearest:1 figure:2 expanding:2 arise:2 conˆ:1 14b:1 refine:1 buchert:1 14a:1 evidently:2 verlag:1 regularization:3 requirements:1 discussion:8 orthogonality:1 write:1 criterion:2 pure:3 optimal:2 parameter:6 displacements:10 astropart:1 product:1 mat:4 may:15 max:12 expectation:1 applications:1 produce:3 deviates:1 grow:1 branches:1 dynamical:5 explicit:2 cosmology:7 so:8 halos:1 definitions:2 typical:10 wavelengths:2 furnished:1 indeed:17 years:1 course:4 statistical:4 cuts:1 differs:1 cold:1 thank:1 interesting:1 decreases:5 non:23 22b:1 half:3 eµ:1 now:8 discuss:9 term:17 equality:1 orthonormal:1 entirely:2 quarter:2 domain:3 en:9 significantly:4 collisionless:1 gaussian:1 manifests:1 wavelength:1 approximated:8 eq:42 emerges:1 shown:16 space:10 lagrangian:4 increase:2 collisions:2 extrapolate:1 dominate:3 correct:3 shows:2 theory:6 divergence:2 quite:4 gotz:1 unwanted:1 org:2 e2:1 derivation:3 language:1 impose:1 motion:2 neglect:1 first:22 xj:2 xi:5 symmetry:4 waves:4 transform:5 simplified:3 specifically:5 directly:2 minimizes:1 size:4 little:2 necessarily:3 indicate:2 1e:1 realization:1 white:3 gives:7 fraction:1 mostly:1 continuous:4 twopoint:1 braun:1 artifact:1 transverse:1 than:32 specify:1 l41:1 effective:2 require:1 future:1 pre:2 generality:1 correction:4 generalization:1 say:1 recover:2 saw:1 any:24 stadel:2 note:18 potential:10 take:2 coincide:1 modulus:1 discretisation:4 trace:3 opposite:1 decreasing:1 formulae:1 pair:1 analytically:4 nonlinearity:1 considered:13 average:18 ways:1 typically:8 quantity:12 slope:2 show:8 slow:1 ratio:2 proportion:1 state:2 analytic:4 only:33 explicitly:4 nyquist:8 get:1 ki:1 straightforwardly:1 dyn:2 cannot:1 summary:1 relative:7 uncorrelated:1 satisfying:1 phonons:1 sites:2 outside:6 between:13 justified:1 diagonalized:1 αn:1 densely:2 comm:1 analyzed:1 article:1 many:2 region:2 according:1 propagation:1 expression:13 comes:2 nearby:1 generalisation:1 characterization:2 sampling:4 exploit:1 constant:5 considers:2 considering:5 most:6 locally:1 cosine:2 combined:1 differently:1 direction:3 observe:1 former:4 those:15 case:34 eik:5 orientation:3 coupled:1 discrepancy:1 comoving:2 different:19 same:11 shifts:1 epoch:1 arguments:1 physical:20 investigated:2 closest:1 constraining:1 invariance:1 modes:26 macro:1 roughly:3 without:2 components:1 coordinate:1 model:8 dimension:1 being:1 when:19 scoccimarro:1 sampled:2 seems:1 instrument:1 interested:3 treatment:11 real:5 around:5 eigenvalue:5 early:5 grid:1 mon:7 using:24 particle:30 reduces:5 velocities:1 either:1 fully:7 inter:1 reduced:5 densest:1 specified:2 duration:1 sommer:1 matching:1 provided:1 extensively:1 moderate:1 refer:1 process:1 power:31 equivalent:2 notable:1 notably:8 a6a:1 a6b:1 comparison:2 package:1 discussed:10 practical:1 bertschinger:1 perturbed:6 redshift:2 numerically:8 determine:5 einstein:1 operator:1 accumulated:1 theoretically:2 log:1 strictly:2 there:12 dispersion:4 low:2 complete:1 newtonian:3 longer:2 applying:4 quantitatively:1 3t0:4 eigenvector:4 expect:3 strongly:1 taylor:1 certain:1 ak:2 describe:3 general:6 ax:1 again:2 assessing:1 completeness:1 field:24 valid:3 deviation:7 briefly:2 a1:1 a0:1 a3:1 important:3 a5:2 a4:1 a7:1 included:4 l63:1 perturbatively:1 curve:1 mass:8 starting:12 represent:1 sci:1 consider:14 pth:7 invariably:1 follow:2 expressions:7 subjected:1 stochastic:1 kν:4 subtleties:1 global:1 amplitudes:1 worse:2 straightforward:9 melott:5 very:19 induce:1 difference:2 condition:1 treating:1 evaluation:1 t2:1 t0:70 large:11 small:19 houches:1 ten:2 zero:11 further:11 amplified:3 what:6 sub:1 section:8 fractional:4 method:1 condensed:3 full:9 modify:1 behaviour:17 relaxation:1 directions:4 2kn:5 strong:2 equations:5 hdm:4 19b:1 allows:3 periodic:4 pick:1 narrow:4 via:2 followed:1 extrapolations:1 takes:2 distinct:2 contains:1 comparing:2 nucl:1 sitter:1 taken:8 more:21 corrected:2 varying:1 known:4 a5a:1 evolves:2 keeping:5 a5b:1 recall:1 equation:2 dei:1 remain:1 del:1 evolved:10 learn:1 compare:1 cosmological:38 sphere:1 minimum:2 attain:1 sense:3 axis:1 goal:1 rather:8 breaking:5 larsen:1 explains:1 ensemble:2 simplicity:1 ft:1 derived:4 corrections:5 plane:5 coming:2 fn:1 short:1 extrapolation:3 negligible:2 sect:6 ith:2 developed:4 held:1 paper:9 through:5 excitations:1 its:16 l79:1 rapidly:4 energies:1 actually:2 absence:1 microscopic:1 systems:2 might:1 good:5 return:1 anticipated:1 framework:1 easily:2 always:9 presented:1 found:3 universit:1 2h:4 characterized:2 engendered:1 generation:1 hard:1 reduce:2 kℓ:2 extended:2 yoshida:1 obtains:3 http:1 beyond:4 dominates:3 solved:1 since:6 denotes:1 dominated:6 induced:6 issue:1 occurs:3 benjamin:1 belief:2 favored:2 difficulty:1 reason:3 kˆµ:1 beginning:1 definition:1 pairs:3 eqs:7 relate:1 number:16 linking:1 done:2 takada:1 differ:1 perturbation:4 introduction:1 least:5 assumption:1 calculations:4 exponents:3 recovered:7 kµ:4 dauxois:1 immediate:1 part:3 authors:3 kind:1 kazantzidis:1 anticipate:2 smoothed:1 determined:4 contrary:1 treated:5 motivation:1 orders:1 depending:1 lim:10 self:4 k0:2 generalized:1 finding:1 aliasing:3 unperturbed:3 play:2 towards:3 measures:5 eaire:1 significant:3 nothing:1 extremely:2 kc:19 deviations:4 clear:7 sometimes:1 coincides:2 kn:36 physica:1 optical:8 velocity:4 physics:4 wavenumber:4 particularly:1 cdm:4 relation:3 carefully:1 find:1 impact:1 parameters:6 subsection:3 factor:18 dependent:4 longest:1 lattices:3 vergence:1 continuum:10 arxiv:2 common:1 set:10 sep:1 emax:11 see:35 individual:1 close:4 forthcoming:2 currently:3 smallest:1 various:2 numerous:2 recently:2 sparsely:1 initially:3 prescribe:1 both:6 last:2 context:9 arbitrarily:3 point:12 simple:28 asymptotically:2 corresponds:10 whatever:1 dimensional:3 simply:9 throughout:1 ps:38 complication:1 described:25 due:10 reduction:1 describes:7 pd:8 kronecker:1 ph:11 pm:1 interparticle:9 refered:1 precision:3 else:1 understand:4 systematic:2 plasmas:1 surveys:1 look:1 exponential:2 pacs:1 solid:2 expanded:1 ǫn:15 evaluated:1 while:14 behavior:1 error:12 bravais:1 detailed:1 vectors:8 itself:2 vanish:3 italy:2 ωn2:8 widely:3 modification:14 higher:2 literature:3 robust:1 eigenvectors:6 dark:6 analysis:5 picks:2 solids:1 edge:1 exponentials:1 parametric:2 shape:1 intervals:1 alternative:1 cut:9 conclusions:7 source:1 theorem:3 relevance:5 input:16 bin:3 appendices:1 integer:2 modifications:3 imposed:2 follows:8 continue:1 translated:1 essential:2 methods:2 some:9 pierre:1 understood:1 scale:31 describing:2 exceeding:1 couchman:1 tends:1 minimal:3 cgi:1 agreement:1 step:2 bz:2 analysing:1 integers:2 constraint:1 simulation:26 range:8 transients:1 bloch:3 computational:1 nonequivalent:1 into:6 within:2 integral:4 appropriate:2 lensing:1 moderating:1 proportional:6 clustering:4 acknowledgements:1 measured:1 question:4 long:9 analyze:1 sections:1 considerably:2 elsewhere:1 cosmics:2 ka:1 underlined:1 link:1 delta:2 considerable:1 hamana:1 gravitating:2 characteristic:6 up:19 us:9 un:10 planes:3 approaches:1 fluctuations:17 similar:3 called:1 associated:8 defined:18 surpassing:1 globally:1 quantification:3 single:1 formalism:13 defines:1 codes:2 application:4 citebase:1 deviate:1 elements:2 generated:4 structure:3 implies:3 algorithm:1 practically:2 required:1 equivalently:1 far:2 labelled:3 code:2 illustrates:2 results:21 illustrated:1 eds:13 broader:1 gm:1 contributions:3 centers:1 issues:1 send:1 include:1 wave:1 matrices:2 eigenmodes:11 manifestly:2 eigenvalues:21 noted:11 configurations:3 smaller:6 za:10 modified:1 astrophys:11 dynamics:3 λcdm:1 plays:1 analogously:2 expressed:1 3t:4 consistently:1 experiment:1 3n:4 tdisc:1 body:35 degree:1 respectively:1 spacing:10 desired:5 explore:1 les:1 separation:1 implicit:2 great:1 technical:1 involved:2 larger:10 leaving:1 suggests:1 makes:2 involves:2 formulated:1 scales:13 app:3 decrease:2 apply:5 use:9 asymptotic:5 remains:2 next:2 few:1 exhaustive:1 summarizing:1 formally:1 started:1 becomes:5 normalized:6 discreteness:72 iii:4 account:3 averaged:11 publications:1 averages:1 performed:3 control:1 calculation:5 high:2 shuffled:1 decaying:4 arrangement:1 regions:3 varies:3 instead:2 sin:2 lines:2 correspond:5 writ:1 allow:2 divided:3 bins:9 insight:1 equally:1 interpreted:1 symbols:2 spohn:1 yamaguchi:1 perfect:3 huterer:1 longitudinal:7 decay:2 chosen:7 choose:1 defining:1 greater:4 practice:4 subtraction:1 transparent:1 university:1 identified:2 sufficiently:3 magnitude:2 mode:31 crossing:29 astroph:1 related:3 elementary:1 frequency:9 static:5 interplay:1 measure:2 separating:1 our:17 matrix:7 rev:6 posteriori:1 suffices:2 integrated:1 red:24 interactions:2 completely:2 york:1 shortest:1 hubble:1 interaction:2 determining:1 could:1 frenk:1 feasible:2 length:1 davis:1 3kn:1 pines:1 barr:1 l32:1 precisely:8 system:12 their:7 final:2 commutativity:1 shell:29 exactly:5 manifestation:4 limiting:2 amplitude:14 distinguished:1 fluctuation:2 unchanged:1 galactic:1 curves:2 need:2 demonstration:1 clearly:7 acceleration:1 angle:3 studying:2 physique:1 gravity:7 mechanism:1 εn:1 accuracy:1 lectures:1 but:8 representation:1 intrinsic:2 class:1 linearized:3 volume:4 url:1 face:2 astro:11 prefactor:1 normally:1 fact:18 text:4 anyway:1 purely:7 trivial:5 q2:1 based:3 knowledge:1 tranverse:3 should:9 inherited:1 attained:1 employed:2 cube:1 means:6 familiar:2 quantified:6 ones:1 brillouin:13 collisional:4 following:3 evolution:62 conditions:9 fixes:1 fixed:17 multiplying:1 exists:1 argued:1 sylos:6 closer:1 interacting:1 attempting:1 written:8 boundary:3 comparable:2 importance:4 reproduces:2 efstathiou:1 configuration:8 distribution:7 limits:5 taking:4 equal:7 fulfilled:1 ln:4 figures:1 otherwise:1 aa:1 relevant:3 cf:1 diverges:5 respect:8 addition:1 trajectory:2 copies:1 treat:3 sµν:10 define:4 corresponding:9 sufficient:3 cos:11 astron:9 improved:1 present:7 appearance:1 value:12 will:21 inherits:1 almost:5 vi:1 thus:32 vn:10 optimistic:1 generic:2 lett:1 unity:10 parts:1 largest:9 units:6 finite:8 infer:1 infinity:4 cubic:24 effect:23 diemand:2 infinite:8 keep:1 off:9 center:1 well:20 position:1 less:6 accurate:1 identically:1 obtain:3 sources:1 underlying:1 interchangeability:1 gmj:1 density:35 lattice:80 attractive:1 diagonalization:3 tests:1 increased:3 increases:11 press:1 displaced:1 necessary:2 like:3 qualitative:3 become:8 suto:3 exhaustively:1 because:5 regularized:1 growth:11 contested:1 lead:3 avoid:2 does:6 assuming:1 demonstrated:2 limitations:2 manifesting:1 obey:1 expansion:6 offset:2 simpler:1 gained:1 about:17 universe:11 introduces:1 dependence:7 a2:3 introduced:4 discretization:6 joyce:8 additional:3 smoothing:29 citations:1 diagonalisation:1 function:21 overlapping:1 subjective:1 eb:1 made:2 evident:3 instructive:2 gravitational:3 smooth:1 placed:1 below:3 limit:71 problem:9 pin:12 universal:1 contribute:2 linearity:2 generating:2 slowing:1 denote:1 hautes:1 functions:12 compared:7 percent:2 detail:11 oai:1 envisaged:1 other:12 details:3 branch:9 conclusion:4 repeat:1 kinds:1 variation:1 labini:6 coupling:1 factors:3 rule:2 determination:2 |
0704.3698.txt |@word since:8 consider:3 results:5 gy:4 gx:11 scalar:2 gd:3 grateful:1 follow:1 chair:1 gl:1 gh:11 ihes:1 tz:18 tx:5 paris:1 technique:2 uniqueness:1 critical:5 th:1 stable:4 conjecture:2 g2:4 onishchik:1 pages:2 gz:5 corollary:1 eration:1 condition:1 dim:5 irreducible:1 notes:1 vust:1 t1:2 proposition:7 limites:1 direct:1 zero:1 further:1 theory:1 intersection:1 stands:1 section:7 analogously:2 expressed:1 sur:1 above:2 new:1 rigidity:1 consisting:2 etriques:1 codimension:1 coefficient:1 respectively:1 here:4 les:1 groups:3 address:1 xα:8 table:1 morphisms:2 obtained:1 divisor:1 gln:2 my:1 gld:2 action:2 hospitality:1 quotient:1 uniquely:1 via:1 projection:3 classification:2 apr:1 diagonalizable:2 replace:1 coinciding:3 rkg:4 equivariant:6 apply:1 establish:1 linearly:2 use:3 triples:1 takes:3 would:1 prove:2 remains:3 h0:32 visit:1 france:1 few:1 m1:5 therefore:2 reductive:1 brunswick:1 type:13 ψg:31 nauka:1 normalizer:4 said:2 under:1 flag:1 rigid:4 particular:1 known:4 projective:2 cases:2 springer:2 isomorphism:5 recall:3 des:1 pour:1 paragraph:3 stabilizer:1 following:13 root:6 example:2 stimulating:1 proof:10 claim:2 vers:1 sph:2 professor:1 procesi:2 cartan:1 so2n:1 rescaling:1 conversely:2 verlag:1 holds:3 berlin:1 maps:1 amazing:1 map:4 product:2 eductifs:1 algebra:8 may:2 earlier:1 different:3 levi:2 short:1 natural:3 varieties:9 lemmas:1 element:4 sp2n:2 so:12 sl:1 representation:1 op:1 restriction:9 acts:2 dx:1 fλ:2 satisfied:1 paper:4 through:1 yandex:1 during:1 differs:1 satisfies:1 vari:2 its:8 roots:4 le:1 group:5 thank:1 fix:1 nontrivial:2 lect:2 moebius:1 choose:7 inspecting:1 mail:1 main:1 image:1 semisimple:2 maximal:2 prime:1 number:1 now:6 smoothness:2 equality:1 invariants:1 university:3 identified:1 possibilities:2 iff:3 each:1 homogeneous:3 en:1 weight:2 ed:1 reduce:1 idea:1 related:1 extended:1 special:1 rt:1 ru:2 shown:1 space:2 involutory:1 denotes:2 combinatorial:1 vector:1 rational:1 conjectured:1 denoted:1 get:2 ri:3 math:10 foundation:1 linear:2 localization:2 possibility:1 mapping:3 base:1 put:7 publ:1 beginning:1 definition:8 equivariantly:1 phrases:1 place:3 adjoint:2 first:3 already:1 plongements:1 bijection:1 radical:1 possessing:1 xg:2 rank:3 concini:2 directly:1 open:3 given:1 πa:5 introduction:1 crossings:1 system:4 wonderful:19 statement:1 assign:1 moscow:2 exactly:2 translation:1 institution:1 dans:1 imply:1 determined:1 were:1 eriques:2 distinguished:8 argument:1 say:3 enes:1 need:2 presque:1 any:15 seminar:1 lie:8 symplectiques:1 note:9 k2:2 ideal:3 gσ:1 generalized:1 gπ:4 austr:1 gα:3 normal:2 grassman:1 algebraic:4 satisfying:1 connected:5 automorphism:1 acknowledgements:1 why:1 especially:1 considered:1 torus:2 coincides:3 dimension:1 proceedings:1 wasserman:1 xπ:12 fact:1 show:1 supported:1 spaces:2 d2:1 agrees:1 d0:1 d1:2 q0:6 cellules:1 eigenspace:1 explain:1 written:1 lemma:5 going:2 subsection:3 parabolic:5 preliminaries:1 do:1 dj:1 di:5 dg:23 de:7 ones:1 dz:4 words:1 ϕd:15 dr:3 closure:2 approach:1 arxiv:5 kernel:2 set:6 ser:1 welldefined:1 module:1 see:8 result:3 discussions:1 embeddings:6 subject:1 αr:2 review:1 symmetric:4 state:2 un:1 closed:1 αi:4 invariant:4 αk:2 conditions:3 αn:3 terms:1 however:2 key:1 2αn:1 amer:1 vinberg:1 restrictions:1 lu2:5 lu3:8 last:1 many:2 equal:1 une:1 embedding:6 eralisation:1 point:3 simple:8 demazure:15 dimensional:1 assertions:1 moreover:1 throughout:1 kernels:1 commutative:2 basis:1 due:2 sl2:1 algebras:1 montecatini:1 systems:1 corresponding:6 lu1:5 propositions:1 essentially:1 bull:1 general:2 case:10 grassmanian:1 p1:2 sln:1 rutgers:1 suppose:2 inefficiency:1 slk:1 property:1 procedure:1 thus:1 im:3 containing:8 same:2 clearly:2 finite:1 subalgebra:16 higher:1 independent:1 used:1 hand:1 subvariety:3 normalization:3 subgroups:2 no:4 components:1 english:1 stating:1 subgroup:8 spherical:16 quoted:1 thanks:1 previous:3 brion:6 preprint:6 character:4 lattice:2 tuples:1 theorem:8 gave:1 knop:7 press:1 using:1 unique:7 like:1 δx:36 follows:8 losev:6 automorphisms:3 ivan:4 immersions:1 because:1 nm1:1 some:6 algebraically:1 ideals:2 respect:1 nonzero:1 provided:4 cp:2 opposite:1 everything:1 does:1 minimal:1 compactifications:1 equivalent:1 symm:1 bk:3 bp:2 br:4 properties:2 injective:6 proceed:1 pα:2 assertion:4 whence:3 ov:1 ou:1 complimentary:1 slightly:1 morphism:12 subset:8 soc:3 cambridge:2 into:1 h1:22 isomorphic:1 luna:8 references:2 span:2 there:14 transform:1 class:1 borel:3 was:6 m0:4 function:1 complete:1 converse:1 but:2 so2:1 russian:1 espaces:1 true:2 divisors:1 partially:1 embedded:1 supp:6 characteristic:1 smooth:12 up:1 us:6 lo2:4 below:2 lo1:2 problem:1 similar:1 called:7 mechanics:1 proved:9 ag:8 defined:2 certain:2 abstract:1 describe:1 am:1 denote:13 single:1 formulation:1 check:1 qα:1 groupes:2 variety:17 commutes:1 when:3 cˆ:1 sublattice:1 ng:11 field:1 grd:3 other:1 es:2 department:1 mathematics:2 nice:1 elements:4 ξi:1 generated:1 important:1 ξd:1 implies:1 homog:1 factors:1 orbit:6 |
0704.3699.txt |@word secondly:1 concept:1 gs:8 consider:2 remarkable:1 fronsdal:1 magnetic:3 eκ:4 results:3 gg:4 eds:1 p00:1 lln:2 broader:1 edu:1 constants:2 follow:2 research:2 contributions:1 4an:2 issues:1 devoted:1 whose:3 ver:3 dα1:22 eα:6 ponomarenko:1 tr:2 pfau:1 list:1 charge:1 investigation:1 under:1 kurtsiefer:1 equalities:5 ta:1 p2:9 supported:1 g2:6 g1:7 orthogonal:3 soni:1 semidefinite:2 zachos:4 ankara:4 mps:4 summarized:1 emphasized:1 obvious:1 exponential:1 immediately:1 presented:3 pacs:1 z12:1 solution:1 involution:1 vector:1 indices:1 gauge:2 optics:4 says:1 coordinate:6 concise:1 α2i:2 direct:4 hillery:2 imply:2 perspective:1 odd:2 canonical:4 bilinear:2 established:3 plays:1 stands:1 section:15 selected:1 transforms:1 respect:2 uniform:1 current:1 en:3 localized:1 above:7 new:3 d1:6 method:3 satisfy:3 processing:2 led:1 lee:1 respectively:3 shchukin:1 here:1 understanding:2 desired:1 address:2 directions:1 laughlin:1 along:4 bk:2 observing:1 z1:6 z2:5 dp2:7 obtained:3 antisymmetric:1 parameters:3 technical:1 study:4 studied:1 simultaneous:2 products:6 poisson:1 stressed:1 action:1 adopting:1 studies:1 glu:1 king:1 projection:3 apr:1 marginal:7 why:1 analyzing:3 summation:1 δn:1 tools:1 planck:1 bound:1 derivatives:1 conventional:1 would:1 prove:2 probabilities:1 positive:11 give:1 predictions:1 next:3 comparing:2 noting:2 therefore:4 m2:1 taken:2 robertson:1 sternheimer:1 type:4 achieving:1 reflects:1 more:3 introducing:1 operators:2 itak:1 pairs:1 ip2:2 berlin:1 normalized:5 charged:1 known:4 cases:1 hold:2 iii:3 origin:3 states:20 springer:2 valued:10 mc:1 integrating:3 science:1 equation:1 work:1 glauber:3 values:6 mp:13 following:3 making:1 example:2 performed:1 claim:1 council:1 stated:2 rodriguez:1 table:1 reconstructed:1 indicates:1 minimum:3 numbers:3 degenerate:1 sense:3 2cs:2 overbar:1 information:2 goal:1 provide:2 verify:1 means:2 orthogonality:2 regions:1 how:2 pair:1 low:1 pure:2 simplifies:1 instead:3 simplicity:1 product:12 description:2 algebra:2 may:3 ladder:1 use:3 derived:4 applications:2 plane:3 designed:1 faculty:1 computation:1 types:1 o:2 diagonal:3 dα:1 third:1 read:1 light:1 lines:4 correspond:1 element:1 so:2 contributes:1 fundamental:1 z2n:1 βk:2 zℓ:1 restriction:1 holds:1 wigner:29 subsections:1 schwartz:1 indeed:2 over:4 dy:1 satisfied:1 experiments:1 mentioned:2 y2:2 its:3 write:3 revived:1 derive:2 rapidly:1 symmetry:2 δg:6 ln:1 theorem:1 pnℓ:20 lk:1 coordinates:12 better:1 wineland:1 hm:1 parts:1 itano:1 systems:1 jacobi:1 main:3 defining:6 deformation:7 correspondence:1 non:2 combination:1 yn:1 outlined:1 introduce:3 landau:10 p10:1 framework:2 onesided:1 effects:2 they:12 now:6 hall:1 eigenvalue:1 february:1 equality:5 always:1 university:2 hamiltonian:1 2y:1 2d:4 theory:1 inequality:5 mode:2 man:1 each:3 2m:3 x12:1 2i:1 associative:2 mean:1 weyl:1 another:3 series:2 energy:1 hard:1 gaussian:1 related:2 constitute:1 used:7 ey:1 combining:1 quantum:17 our:6 eq:8 special:4 out:1 shown:2 space:60 rep:3 since:3 rev:12 denotes:3 content:1 cahill:1 acting:1 qb:1 oberhettinger:1 formula:1 get:5 gov:1 integrated:1 math:8 shows:1 after:1 linear:3 bayen:1 2h0:1 2h2:1 mω:1 given:8 standard:7 admits:1 2nℓ:2 completely:1 8y:1 advantages:1 york:2 eigenvalues:2 detecting:1 e2:2 r4:14 definition:3 training:1 fixed:1 derivation:1 r2:3 r3:2 similarly:2 canceling:1 moment:1 times:1 motion:4 length:1 hence:5 βn:1 first:11 xj:7 xk:6 lichnerowicz:1 xi:11 xn:4 kim:2 probability:9 laguerre:1 describes:1 number:2 instances:1 utilized:1 autonomous:4 directly:2 electronic:2 angular:2 properties:11 cartesian:1 their:6 introduction:1 curtright:4 eqs:9 behaves:1 system:8 relations:9 obtainable:1 1d:10 calculations:5 convention:1 normalization:6 realvalued:1 structures:13 gives:5 relationship:1 tool:1 serve:1 realized:1 α1k:3 part:1 lℓ:1 x2:5 off:1 x1:2 representing:1 distance:1 determines:2 princeton:1 second:5 bondia:1 annihilation:4 computations:1 determined:1 kth:2 were:2 p21:3 18y:1 result:7 behaviors:1 aoki:1 addressing:1 rewrite:1 20y:1 explicit:2 ann:2 modern:1 generalization:1 factorizations:1 uematsu:1 conjugate:2 seen:1 concentration:1 any:5 przanowski:1 constructions:1 zero:2 depending:1 efficient:1 lim:2 latter:1 responsible:1 connell:1 note:5 sciences:1 potential:1 generalized:10 δnm:1 analogs:2 associativity:1 even:3 multiple:2 trace:2 shall:2 mlynek:1 α1i:2 who:1 most:3 involving:1 an2:1 successive:1 phase:56 measured:1 class:1 waldmann:2 eigenfunctions:2 observation:1 kk:3 bracken:1 into:1 ko:1 inferred:2 physica:1 h2m:2 bracket:4 principle:1 exp:10 mechanical:3 velocity:1 usual:2 physics:3 fact:12 pnl:5 show:7 v12:2 probe:1 relation:10 substituting:1 analogue:3 d2:3 find:1 ground:6 q1:51 henceforth:1 feng:1 q2:18 based:2 knowledge:1 dp1:4 written:1 should:1 moments:2 only:3 explicitly:1 subsection:1 equipped:1 employed:1 dereli:1 2bb:1 αki:1 dk:4 di:1 dependent:1 expectation:5 2a:12 dx:1 altogether:1 dv:14 applying:1 gen:2 prime:1 exhibiting:1 densities:14 fields:2 arxiv:3 summary:1 qa:1 investigate:1 paper:1 dodonov:1 qi:2 qk:2 4πl:1 view:6 set:3 computed:4 achieved:1 γp2:1 correlations:1 ωq1:1 ωq2:1 see:4 radius:1 descriptions:1 lnk:2 w0:22 cyclotron:4 alternative:1 best:1 appear:1 deriving:1 inequalities:2 doebner:1 consistency:1 ways:1 nuclear:1 review:1 symmetric:2 importance:1 state:32 interrelated:1 various:3 between:1 αk:4 approach:3 x22:1 p20:1 terms:4 vertical:1 nature:1 dxj:2 wn:2 w00:1 wj:1 moyal:5 γpi:1 jj:1 analyzed:3 group:1 tub:1 phasespace:2 suppressed:1 problem:2 adapting:1 both:3 last:3 2n:3 many:1 taking:4 uncertainty:26 equal:4 quantization:10 dated:1 context:3 variance:1 vourdas:1 adapted:1 among:1 anti:2 ch:1 point:3 overview:1 2na:1 qαβ:7 corresponds:3 dimensional:2 distinguish:1 simply:2 conjugation:3 cs:11 associated:2 2nq:1 throughout:1 turkey:3 forms:2 finally:4 described:2 leibnitz:2 equations:2 three:3 been:10 cauchy:2 basic:3 pj:2 pk:2 ph:2 pi:1 hardly:2 define:2 v22:2 generating:23 enable:1 corresponding:5 subscripts:1 gan:1 coherent:31 observe:2 taek:1 despite:1 present:2 case:10 wood:1 multi:1 p1:12 eβ1:1 kazan:1 developing:1 variances:3 expanded:1 value:5 will:9 while:1 suppose:1 evaluating:2 investigating:1 property:13 walther:2 unitary:1 vogel:1 vol:1 characteristics:2 vk:1 thus:1 them:3 iv:1 ii:3 reads:3 itself:1 im:1 xy:1 zhang:1 p22:2 monroe:1 around:1 cjj:2 mαβ:7 different:1 verified:1 generic:2 commuting:2 same:6 checking:1 complex:10 quant:2 emphasize:2 units:1 dimensionless:1 several:1 composition:2 higher:1 independent:2 extended:1 assigns:1 singapore:1 folland:1 i1:4 i2:3 hl2:2 hand:4 v1:2 v2:1 levels:6 moving:1 purpose:1 iv2:1 entanglement:1 identity:1 recent:2 lower:1 schr:3 center:3 p11:1 magnus:1 well:9 analysis:3 amounts:1 without:2 components:1 easily:5 firstly:2 position:1 left:4 distances:1 being:1 obtain:9 rest:1 abbreviation:1 atomic:1 integer:5 facts:1 momenta:1 speed:1 previous:1 application:3 conclude:1 had:1 zubairy:1 density:2 discuss:1 source:1 hn2:2 lett:5 easy:1 hermite:2 relevance:1 mod:3 scully:1 remaining:1 momentum:4 take:5 real:11 fairlie:2 spinless:1 eigenfunction:2 represents:2 rules:2 papers:1 term:2 harmonic:1 np:4 qj:2 nq:14 press:2 using:8 aiming:1 like:3 displaced:3 dq1:5 particle:2 follows:9 signal:1 bℓ1:1 bℓ2:1 groenewold:1 steps:1 schwarz:1 integrals:1 arbitrary:3 δf:8 become:1 pointwise:1 essential:2 mathematical:3 parity:2 right:7 classical:8 formulas:1 imaginary:2 successfully:1 some:5 calculated:1 q22:1 gilmore:1 specified:2 gracia:1 possibilities:1 describing:1 lead:1 establish:2 prog:1 refer:1 particular:1 bordemann:1 obey:3 power:5 infinitely:1 wavefunctions:2 perpendicular:1 constructive:1 step:1 substituted:1 found:6 βn1:1 nℓ:22 hilbert:1 integers:1 about:1 central:1 world:1 algebraic:2 basis:1 discussed:1 recognized:1 side:2 mutually:1 a2:1 wolf:1 stand:3 oy:1 act:1 introduced:2 perelomov:5 equally:1 ηa:1 h2:15 h0:1 integral:11 functional:4 negative:1 remarks:1 hermitian:1 wn1:2 proportional:1 additional:2 α2r:1 assumed:1 there:3 iq2:3 closedness:1 inner:6 way:5 analyze:3 was:3 q12:6 function:45 academic:1 creation:3 complete:1 form:5 forming:1 regard:1 wnl:3 displacement:7 volume:1 expected:1 construction:1 hn:2 justify:1 encoded:1 line:2 level:1 commun:1 made:1 compute:4 flato:1 characteristic:1 uv:4 smooth:2 up:3 us:4 theoretical:1 below:1 frequency:1 limit:1 planes:2 distribution:1 ix1:1 similar:9 called:2 recalling:2 mechanics:5 nnl:5 constant:3 cin:2 defined:14 ny:2 abstract:1 aj:1 influence:1 direction:3 general:4 cbs:2 scientific:2 proves:1 together:2 formulation:3 distributions:4 check:2 constructed:1 xkj:2 functions:49 nk:1 nl:1 nn:3 eα1:5 na:4 nb:2 eα2:2 when:4 vanishes:2 meekhof:1 field:2 other:5 role:1 details:2 bℓ:1 department:1 mathematics:1 acknowledgments:1 briefly:1 star:7 provided:1 sided:2 polynomials:7 odinger:3 a1:1 generated:3 important:4 n1:3 β1j:3 sides:2 structure:4 qi2:1 4e:1 implies:5 4y:4 dq2:5 rule:2 bb:2 equivalently:1 leibfried:1 mass:1 lying:1 observables:1 n2:5 2mω:1 4b:1 having:1 4a:2 |
0704.3700.txt |@word similarity:2 magnetic:237 swirls:2 andre:1 consists:1 cyprus:2 assembled:2 localized:1 whose:1 const:1 calculate:2 paris:1 presents:2 under:19 worth:1 alternating:4 downstream:1 rise:2 every:1 upstream:1 experimentally:4 nishioka:2 solver:5 squares:3 induction:2 solution:6 vector:4 force:55 specially:1 consistent:3 heterogenous:3 approximation:1 helices:1 second:8 street:4 qualitatively:1 implemented:2 even:5 established:1 hide:2 selected:1 supplied:1 above:1 zoomed:1 new:6 increasing:3 bi:1 sinks:1 grenier:1 never:2 equals:1 here:7 reported:4 obtained:9 sidewalls:17 rigorously:1 study:9 changed:2 reports:2 suitable:1 changes:10 der:1 diameter:1 projection:7 elaborated:2 explained:6 highly:1 brought:1 visible:1 total:1 unit:1 plot:16 quasi:1 would:4 negative:17 tabulated:1 occupying:1 definiteness:1 call:2 therefore:11 type:1 until:2 successful:2 brings:2 correspondingly:3 excellent:1 aligned:1 must:4 blade:5 oleg:2 already:5 my:12 example:3 mechanik:1 references:1 cited:4 organized:2 want:1 validated:2 end:2 provide:1 verify:2 how:3 ordinary:4 classify:1 sato:2 oscillatory:1 after:2 diagram:2 wrong:1 law:2 parallel:1 undesired:1 third:6 summing:1 hypotheses:1 complexity:1 green:1 decreasing:1 order:9 concurrence:1 satisfied:1 london:1 before:3 destroyed:1 differently:2 imx:3 shear:1 maximal:1 effects:4 they:8 represents:4 ekman:6 each:8 side:10 mean:1 financial:1 series:5 precedes:1 magnets:14 driving:4 gradient:7 angular:1 particles:3 re:69 rc:1 got:1 free:10 ascending:1 streamline:1 hand:2 created:2 starts:3 creates:3 tempting:1 onto:2 industrial:1 features:2 primary:1 peculiarity:2 another:3 illustrate:2 top:11 approximately:1 needed:3 observations:1 john:1 kubota:1 western:1 distance:4 showed:1 zero:5 matter:1 stratified:2 iron:1 okuda:1 solely:1 modern:1 torque:1 seen:2 seem:1 hydrodynamic:2 strength:2 thoroughly:1 latter:5 responsible:3 epm:1 2006a:8 forces:7 2006b:5 karman:4 explanation:1 davidson:5 circles:3 shall:5 viscosity:2 extending:1 regular:2 germany:2 manifested:1 redistribution:4 grove:1 calculated:2 metal:5 points:2 inaccuracies:2 calculates:1 dot:8 attempts:1 solutions:3 explain:3 topological:4 rich:1 des:1 plate:1 fluid:22 dz:3 reversal:1 despite:2 report:2 dr:3 runs:1 fields:6 twice:1 analytical:5 observes:6 zones:2 depends:2 electrostatic:13 projections:1 discussions:1 subject:2 symmetric:1 approach:8 terms:1 nature:3 weak:1 however:8 extent:1 topology:3 received:1 met:1 conclusions:1 und:1 distinction:1 con:1 height:2 gratitude:1 three:10 been:34 quickly:2 much:3 interest:1 expected:2 suppress:2 concerning:1 lavrentiev:2 coherent:2 confinement:1 applied:3 near:2 abrupt:1 applies:1 balance:2 cylinder:8 iv:1 ii:5 penetrable:1 brake:2 numerische:1 confirmed:1 occupied:1 make:2 linked:1 plates:3 dimensionless:1 several:3 grows:2 independent:2 disagreement:1 swell:1 numerical:32 kit:3 insulating:2 hydrodynamics:5 braunschweig:1 thoughts:1 kept:3 academic:1 materials:2 greatest:1 quantitative:3 possesses:1 left:3 just:4 rotated:1 thanks:1 yet:1 previous:2 visualization:1 infinitely:1 slices:4 had:1 transformed:1 easy:2 take:4 casting:3 hartman:1 posed:1 possible:9 ducts:1 descending:1 appearing:3 arbitrary:4 ha2:4 right:2 deal:1 successfully:1 bottom:11 electromagnetic:5 normal:1 olshanskii:4 bold:3 derivatives:1 yoke:1 zur:1 stokes:4 o:7 continous:1 slightly:2 automatically:1 functions:1 maxwell:1 down:1 ussr:1 neumann:1 support:1 initial:8 width:7 accordingly:1 way:5 resulted:1 was:9 lowest:1 medium:1 form:6 attempted:1 becoming:1 differences:2 absent:2 cylinders:2 hartmann:16 inside:19 attached:36 maximum:7 discretized:1 proved:1 proven:1 evidence:1 exist:1 simulations:10 distributions:2 check:1 triangles:1 constructed:2 weakened:1 no:24 whereas:1 nc:38 when:34 reality:1 ny:1 interested:1 role:7 papers:1 dipolar:1 vanished:1 models:1 preceding:1 braking:13 variable:1 regime:5 assume:1 governed:2 time:6 remarkable:1 12a:1 global:2 exceeding:1 computation:1 remarkably:1 rectangles:2 layers:14 certainly:1 dimensionality:2 zone:1 finally:7 monotonically:2 infinitesimally:1 analogous:3 notations:1 presented:9 did:5 turns:1 magnet:37 item:1 sidewall:4 abdou:2 upper:1 work:8 occurrence:1 insignificant:1 trend:1 sign:11 nonuniform:2 appear:6 axes:1 uniform:8 current:12 goes:2 falling:1 hb0:1 filled:4 satisfy:1 perpendicular:1 address:1 along:15 appears:3 change:12 box:1 incoming:1 thirty:1 institute:1 petersen:1 studied:4 mx:4 poisson:3 plotted:3 useful:1 marked:3 crisis:1 opposes:1 working:1 prove:3 positive:9 france:1 opposed:2 nicosia:1 vieweg:1 appendix:3 cases:3 sheds:1 inertial:12 flu:1 renders:1 following:10 making:1 stream:1 sense:3 2ly:2 2lx:1 allowed:1 occur:1 verlag:1 requirements:2 discussion:2 write:1 parameter:32 divides:1 map:1 staying:1 information:1 may:1 applications:2 produce:1 designed:2 data:6 stress:1 dynamical:2 pulsations:2 whenever:1 explicit:1 so:10 increase:6 typical:3 indeed:1 mainly:6 years:1 stability:11 experiments:18 cuts:6 peterson:2 still:4 noncontact:1 tendency:1 derive:2 group:2 thank:1 vicinity:2 decreases:3 forms:1 attraction:1 main:5 decades:1 non:3 within:1 views:2 evolution:1 half:5 now:4 discuss:7 nor:1 term:9 name:1 stabilize:1 corners:1 drop:3 arrows:4 instability:1 domain:1 significantly:1 revised:1 inhomogeneous:5 ey:20 proportional:1 happen:1 eq:2 shown:31 jackson:2 space:10 looking:1 investigation:3 centerline:14 correct:2 shows:16 nic:1 earlier:2 theory:3 divergence:3 pumping:2 governing:1 quite:1 dependencies:1 besides:1 e1:1 widths:2 transition:7 programming:1 motion:13 place:3 first:12 origin:2 symmetry:1 striking:1 spanwise:57 omitted:1 xz:3 xy:3 simplified:1 long:1 directly:1 carry:2 impossible:4 array:2 open:6 kolesnikov:16 size:2 given:19 checked:2 caught:1 1a:2 1b:2 dissipate:1 structures:3 speaking:1 gives:5 moscow:1 continuous:1 transverse:5 x2:2 than:14 wide:1 unfortunately:1 were:5 deutsche:1 saw:1 any:5 numerics:4 downwards:1 aside:1 note:5 potential:13 idealization:1 forming:3 channel:4 sure:1 inhomogeneity:2 opposite:2 falls:2 insets:1 algebraic:1 pair:11 analytically:5 inserted:1 magnetohydrodynamics:9 especially:2 nonlinearity:1 considered:1 later:3 steady:2 drive:1 slope:5 show:11 friction:6 discovered:2 threshold:1 corner:1 imagined:1 ratio:10 behind:7 analytic:2 only:17 helix:3 parabolic:1 over:3 moreau:2 get:2 2mx:1 2my:2 dyn:1 cannot:1 nearly:1 symmetrically:1 neither:1 secondary:2 reveal:2 bifurcation:3 discussing:1 physically:1 namely:2 impressions:1 fails:1 detect:1 review:1 boundaries:2 outside:2 between:24 geometric:3 multiplied:1 notice:1 jy:9 vertical:14 jets:2 suppressed:3 many:3 region:17 according:2 called:5 tour:1 exploit:1 moreover:9 considering:2 come:1 damping:1 borders:4 fig:93 6a:1 direction:22 formed:1 observe:3 wake:12 external:44 former:3 those:6 case:27 developing:2 streamwise:23 profiles:5 situation:3 nonstationary:1 thess:5 versus:2 coupled:1 characteristics:1 middle:28 technology:2 different:28 develop:3 coexisting:1 same:25 physical:9 extended:1 closest:2 changing:1 charges:1 roughly:2 peculiarities:5 without:5 components:2 very:3 model:12 dimension:3 being:2 aspect:1 differentiation:1 speed:1 captured:2 hint:1 except:3 wall:2 lett:2 stagnant:3 real:3 around:19 cf:2 grid:4 using:4 outlet:4 adams:1 particle:6 velocities:6 pole:2 either:3 integrals:4 characterizes:2 stationary:23 satisfactory:1 specified:1 alternates:1 provided:9 dimensions:3 confirm:3 extensively:1 critical:21 provides:1 moderate:1 refer:1 power:3 manufactured:1 equivalent:1 ratios:1 comparison:5 conducting:5 central:7 fringe:1 discussed:4 generated:4 practical:4 act:1 mixed:1 cambridge:2 numerically:8 velocimetry:2 rising:1 determine:1 area:1 assumed:2 strictly:1 there:17 start:1 low:6 slopes:3 viscous:4 assumes:1 enough:4 promote:1 ωz:23 qualitative:3 quantitatively:2 creeping:6 regimes:1 strongly:5 ohm:2 diverges:1 coordinate:1 certain:2 describe:2 general:1 together:3 gradients:2 moves:1 fill:1 again:3 deserve:1 mathematica:1 field:135 briefly:1 drift:6 important:3 bounded:1 included:1 curve:4 helically:1 resembles:1 resolution:1 original:1 externally:1 vorticity:31 consider:5 pointing:1 caused:5 lack:2 scalar:1 denotes:1 causes:1 diffusive:1 program:1 th:1 andreev:6 heterogeneity:6 far:3 supercomputer:1 removing:1 induce:9 resistance:5 difference:7 condition:6 large:5 small:8 grateful:1 fringing:1 past:17 rate:11 design:1 perspective:3 further:7 what:4 nonlinear:2 section:18 thickness:1 method:6 movement:1 devoted:1 full:2 component:13 ranges:1 directions:3 strong:11 equations:13 search:1 griebel:3 published:1 action:2 formation:2 suddenly:1 takes:3 electrostatics:1 distinct:1 contains:2 charge:1 comparing:4 taken:8 minor:1 more:5 flat:1 zeitschrift:1 diffused:1 particular:1 known:7 keeping:1 recall:2 equation:4 r3:2 remain:2 compare:1 neglected:3 states:2 minimum:4 numbers:4 arise:3 sharp:3 axis:10 influenced:7 needs:1 goal:1 rather:5 influences:1 ensemble:3 mould:1 wiley:1 derived:2 plane:15 electromotive:7 verified:1 horizontal:6 fl:6 dormy:1 negligible:1 fundamental:2 developed:3 hele:3 paper:16 through:3 signs:1 existence:4 kinetic:3 avenue:1 its:10 rapidly:1 inward:3 fruitful:1 systems:2 convective:1 jacobi:2 might:4 deformation:3 colleague:1 good:2 return:1 ya:1 walls:13 yz:2 yu:16 develops:5 easily:3 always:6 level:1 forschungszentrum:1 2d:26 found:8 universit:2 2h:3 characterized:4 referred:1 generation:5 energy:3 obtains:2 measurement:2 loops:2 solved:1 since:3 induces:2 research:3 induced:9 issue:1 occurs:2 disposition:2 earliest:1 beginning:2 generate:1 definition:3 pairs:1 technische:2 consequence:1 probability:1 feel:1 number:15 done:1 passes:2 differ:1 jet:4 introduction:4 leading:1 eddy:1 assumption:5 advection:2 calculations:3 hundred:1 shifted:1 relationship:1 incompressible:1 part:5 differentiate:2 authors:7 believe:1 center:14 diffusion:1 atomizdat:1 kind:4 scheme:2 determines:1 double:1 determined:3 intensities:4 str:2 treated:1 7b:1 electrodynamics:2 substantial:1 conjugate:1 cumbersome:1 confirms:1 paths:1 bz2:1 depending:7 self:1 extracted:1 internal:14 build:1 analogy:5 finding:1 unperturbed:1 play:3 towards:5 electric:27 rhs:1 reach:3 most:4 significant:3 nothing:2 measured:4 clear:6 kh:2 drifts:1 traditional:1 exp:2 velocity:44 barrel:2 physics:3 ncm:2 find:4 parameters:11 distributed:1 failed:1 factor:13 columns:1 dependent:3 express:1 closely:1 combinations:1 during:2 molten:1 transitional:1 arxiv:1 investigate:1 common:1 approaching:2 undergoes:1 see:38 close:5 outward:2 probable:1 dipole:7 various:4 probably:2 conditions:6 available:1 recently:7 attention:1 distinguish:1 inertia:3 both:9 last:2 reverse:25 annual:1 connection:1 retarded:1 whole:2 finds:1 experimental:15 point:7 simple:4 corresponds:4 dimensional:2 adjoining:1 indefinite:6 decline:5 described:4 due:14 reduction:1 describes:1 pf:2 referee:1 gap:13 understand:2 systematic:1 fur:1 solid:32 straight:2 bω:3 while:13 behavior:9 loop:1 styles:1 century:1 von:1 demon:1 obstacle:71 confining:1 currents:2 shaw:3 grant:1 belong:1 higher:8 used:8 reversion:3 flows:14 ρu0:1 moment:2 moving:4 necessity:1 recent:3 lower:4 consistence:1 analysis:4 obviously:1 concrete:1 magnetohydrodynamic:3 shape:2 questions:3 spatially:1 letting:1 cut:6 kluwer:1 readers:1 source:2 location:1 contrary:3 guarantees:1 showing:1 formal:1 imposed:3 shaped:10 systematically:1 follows:9 interestingly:1 manifest:1 continue:1 unstable:2 pointwise:4 essential:3 mathematical:2 sketch:2 methods:2 some:5 back:1 understood:5 trends:1 b0:7 examples:1 ijk:4 pronounced:1 gradually:1 scale:1 affects:1 measurements:1 integration:6 connecting:15 prof:1 proc:1 minimal:1 varying:4 processing:2 obscures:1 agreement:5 step:2 plots:3 bx:3 bz:37 coexist:1 simulation:9 range:4 consequently:1 computational:1 into:12 helical:6 integral:1 appropriate:1 drifted:1 institut:1 few:5 vortices:88 question:2 u0:4 fast:1 analyze:2 governs:1 properly:2 link:2 line:6 considerable:1 directed:1 uy:15 ux:32 uz:4 characteristic:5 up:5 us:7 ur:1 heterogeneous:1 fluctuations:2 similar:11 prevails:2 constant:14 defined:2 flow:158 influence:10 single:2 curl:2 defines:1 dashed:25 electrical:9 hydrodynamical:1 generates:1 problems:1 drag:2 sides:1 structure:10 ago:1 algorithm:1 practically:1 renounce:1 broad:13 inaccuracy:1 requires:2 having:2 once:1 code:1 partial:2 melts:1 results:24 fluids:4 illustrated:1 go:4 metallurgy:1 helps:1 stable:11 include:1 matrices:2 fakult:1 eigenvalues:2 originally:1 configurations:6 smaller:2 zi:1 seventies:1 jump:1 fold:4 dordrecht:1 dynamics:2 refereed:1 plays:2 access:1 experiment:5 poles:10 advected:1 3d:34 body:6 lee:2 degree:2 exchange:1 commercial:1 desired:1 objects:1 sink:1 separation:2 others:1 adjoined:3 consideration:4 extrema:5 remark:1 involved:1 larger:7 resulting:5 opinion:3 makes:1 involves:1 frictional:1 composed:1 duct:20 scaled:1 addressed:1 decrease:2 summation:1 apply:3 use:1 figure:14 remains:1 next:2 calculation:1 depicted:1 themselves:1 reflects:2 becomes:8 normalized:3 iii:2 account:1 stabilized:2 arched:1 integrating:1 averaged:1 reproduce:1 unknowns:1 stabilizes:1 angewandte:1 drops:2 performed:6 slip:6 do:1 process:1 high:15 effectively:1 lorentz:29 employs:1 reynolds:13 varied:8 decaying:1 six:11 regions:3 located:5 varies:1 instead:5 sim:2 circular:7 profile:18 physik:1 realized:4 light:1 counter:2 lines:19 correspond:3 extremal:1 allow:1 subsequently:1 dx:1 produces:2 dy:2 symbols:4 including:1 looks:1 mentioned:1 perfect:1 delay:1 revived:1 inlet:5 temporal:1 laminar:3 permanent:1 degrees:1 defining:1 lx:2 ly:11 front:2 rotation:7 university:4 sufficiently:1 magnitude:5 mode:1 electrically:4 accompanied:4 homogeneous:4 afanasyev:5 doing:1 chorin:1 product:5 related:2 frequency:1 static:1 measure:1 separating:1 our:15 transitions:1 special:3 out:9 rev:4 cause:1 clarify:1 completely:3 surely:1 york:2 interaction:28 geometry:2 times:3 length:4 navier:3 hence:4 south:2 staggered:1 reaches:2 quotation:1 acheson:2 publication:1 revealed:1 riga:1 system:12 relations:1 their:15 intermediate:2 ulich:1 longmans:1 perfectly:6 final:1 interests:1 reversed:1 exactly:1 forschungsgemeinschaft:1 arctanh:8 manifestation:2 decisive:3 steel:2 observed:14 liquid:5 geostrophic:1 limiting:1 roberts:3 providing:1 insignificance:1 result:3 enforced:2 curves:17 chapman:1 constrained:14 border:1 clearly:2 min:7 able:1 axisymmetric:2 mechanism:3 contour:3 instance:3 schematically:1 accuracy:1 who:1 why:2 stronger:3 takeuchi:2 fact:13 impression:1 12b:4 12c:1 12d:1 chances:1 rotating:9 agrees:1 ha:10 based:1 knowledge:1 should:1 desjardins:2 local:7 hall:1 means:7 ones:1 words:1 steepness:1 produced:1 streamlines:10 numerous:1 differential:1 streamlined:2 fixed:10 view:9 shedding:7 computed:3 exists:1 frame:1 turbulent:7 edition:1 intensity:10 enhanced:1 conductivity:1 closes:1 lyon:1 pattern:14 diverge:1 difficulties:1 closed:2 progress:1 boundary:9 publishers:1 ends:2 importance:1 configuration:4 problem:4 instant:1 limits:1 taking:3 equal:4 attributed:1 figures:1 passing:1 otherwise:2 detailed:1 co:2 conclude:2 basins:1 coexistence:1 respect:1 kinematic:1 trajectory:2 slowly:2 define:3 arises:3 corresponding:6 sufficient:2 miki:1 bulk:1 present:13 bifurcations:1 appearance:12 value:15 rectangular:7 will:9 layer:3 almost:2 thus:5 retarding:4 surface:2 schematic:1 largest:4 finite:3 infinity:1 upon:1 effect:12 v1:1 v2:1 infinite:1 destruction:1 mech:7 reflection:1 nevertheless:4 obstacles:1 well:16 patterns:19 mathematik:1 firstly:2 comparisons:1 arising:2 usual:1 bicgstab:1 excessive:1 less:4 obtain:1 recirculation:57 density:6 mathematically:1 reasons:2 resolved:1 increased:2 increases:7 press:2 turbulence:1 necessary:6 like:1 mhd:21 vortex:47 lose:1 become:2 works:4 soft:1 exceed:1 because:22 classical:1 smoothly:1 phenomena:2 bashforth:1 proper:2 happens:2 throughout:1 demonstrates:1 overlap:1 does:6 dipoles:4 assuming:1 demonstrated:3 conference:1 slight:2 expansion:1 pressure:5 although:1 about:7 actual:1 carried:3 extension:1 freedom:1 dependence:4 compatible:1 insufficient:1 own:1 cuevas:13 additional:3 noticed:1 inner:6 notices:1 function:2 north:2 but:12 volume:2 construction:1 goals:1 convergence:1 highest:1 made:3 compute:3 places:1 whether:5 below:4 demonstrate:1 distribution:9 stirring:3 mechanics:1 ilmenau:5 universal:1 contribute:1 denote:2 permeability:1 identities:1 approximated:1 mutual:1 compared:4 variety:2 detail:1 arctan:5 other:9 details:4 branch:1 conclusion:1 kinds:1 variation:4 stay:1 additionally:1 else:1 4y:1 starting:1 factors:4 inset:2 |
0704.3701.txt |@word remarkable:1 rev:3 magnetic:2 results:2 skin:1 follow:1 localized:1 zone:5 charge:3 under:1 worth:1 far:2 continues:1 wave:18 fall:1 difference:1 presented:1 transmission:4 diffract:1 occurs:1 optics:1 ups:1 upper:3 periodicity:1 consistent:3 prediction:1 second:2 traveling:1 grooves:1 milled:3 index:3 axes:1 near:5 thickness:1 experiment:1 judicious:1 consisting:1 supporting:1 evolving:1 evanescent:2 component:4 here:3 address:1 along:2 appears:1 interpret:1 obtained:1 shift:1 study:2 approaches:1 periodic:1 fourier:1 studies:2 apr:1 standing:5 plot:2 use:1 asymptotic:1 would:1 predictions:1 france:1 few:2 noting:1 therefore:1 themselves:1 resonator:1 separated:1 composite:4 transient:2 diffracted:1 aligned:1 evolves:1 mf:1 thio:1 thin:1 figure:2 stated:1 process:1 cited:2 slit:21 numbers:1 sharp:1 axis:1 narrowly:1 permission:2 feature:2 how:1 hot:3 adjacent:1 fr:1 ifsc:1 fx:1 broad:1 after:1 spot:1 different:1 evˆeque:1 produce:1 waves:9 choice:1 parallel:1 realized:1 light:4 sp:1 correspond:1 wavelengths:1 indeed:2 seideman:1 experiments:1 through:4 erot:1 its:1 rapidly:3 production:1 fig:6 narbonne:1 they:4 cep:1 silver:2 structural:1 easily:1 february:1 subwavelength:6 corners:2 did:2 fringes:1 transmitted:3 mode:4 found:1 universit:1 side:2 carlos:1 domain:1 directly:1 generation:3 constitute:1 measurement:1 wavelength:3 drude:1 out:2 emerges:1 shown:2 sabatier:1 space:1 quality:1 interference:1 acting:1 ref:5 correct:1 belief:1 free:1 quite:1 reason:1 launch:1 inspection:1 route:1 plane:5 first:2 initial:2 toulouse:1 channels:1 spots:2 another:2 thick:1 avenida:1 electronic:1 xie:5 structured:1 modes:5 1d:1 calculations:1 structures:4 cite:1 spp:9 centered:1 transverse:2 optical:3 authors:2 than:1 population:2 peaked:1 wide:3 showed:1 express:4 exclusive:1 amplitude:8 spectrum:1 smolyaninov:1 need:1 concentration:2 tlse:1 efficient:2 metallic:1 online:2 surfaces:1 electric:1 normal:3 incidence:1 falls:1 optimized:1 regular:1 propagate:1 significant:1 irsamc:2 phase:4 measured:3 metal:3 points:1 nanostructure:1 physics:3 fact:1 gold:3 show:2 keywords:1 dissipative:1 controls:1 factor:1 invoke:1 distance:7 de:4 report:1 polariton:1 reveal:1 evolution:1 arxiv:2 predicted:1 including:1 cycles:1 set:1 reference:4 unpublished:2 relative:1 result:3 enhanced:2 close:1 brazil:1 pattern:1 complementary:1 µm:2 between:3 vertical:1 missing:1 however:1 efficiency:1 incident:6 key:1 distinguish:1 suggested:1 both:1 essentially:1 many:1 region:1 figures:1 dated:1 refraction:2 lezec:5 experimental:2 comment:3 strongly:1 relevant:1 supply:1 simple:2 asymptotically:1 period:1 dimensional:1 simply:1 spps:3 constant:1 cavities:2 source:2 damp:2 radiative:1 due:2 been:1 expected:2 lived:1 gay:4 formed:1 ao:3 dwyer:2 pacs:1 launcher:1 originate:1 appearance:1 will:3 while:1 behavior:5 situation:1 opt:4 layer:3 played:1 refs:1 surface:32 confirmed:2 suggest:1 same:1 paulo:1 emphasize:1 finite:1 calculation:1 numerical:1 edges:2 purpose:2 lower:3 off:2 center:4 well:2 edge:1 oft:1 model:4 just:1 guided:4 paul:1 yet:1 point:2 except:1 color:2 slits:1 lett:1 grating:3 momentum:3 real:1 tests:1 around:2 showing:1 corresponds:1 using:1 moloney:2 necessary:1 shaped:1 contradict:1 unnecessary:1 either:1 martin:1 hung:1 weiner:6 permittivity:1 phenomena:1 understood:1 dimensions:1 cavity:7 demonstrates:1 propagating:1 oscillating:1 perpendicular:2 although:1 plots:2 periodically:1 about:1 anomalous:1 o:7 simulation:1 mutually:1 concentrations:1 bloch:4 presence:1 previously:1 into:3 within:3 bound:3 artifacts:1 there:1 transform:1 long:3 width:1 was:2 function:4 hx:3 illuminated:1 groove:21 but:6 illuminates:1 true:1 partially:1 evident:1 arrays:1 smooth:1 up:1 below:1 distribution:1 similar:1 originating:2 fdtd:4 required:1 associated:1 model2:1 ez:3 metals:1 evidence:2 single:2 simulations:1 universidade:1 film:2 nm:9 no:2 phonon:1 field:4 prism:1 other:1 role:1 details:1 nat:1 test:1 picture:1 excitation:1 fabry:1 structure:9 implies:1 coupling:2 factors:1 diffraction:3 depth:4 train:1 plasmon:3 time:1 |
0704.3702.txt |@word λq:1 xρ:1 zº:1 jº:2 iø:2 xφ:2 eµ:3 gc:2 λk:5 zx:2 3a0:1 d2:1 bº:1 gh:3 q1:1 lg:6 aº:1 const:1 kbl:1 µl:5 ln:77 δpn:3 bx2:1 δpk:1 e2f:1 δpi:3 bqi:4 zreg:5 tm:3 k1n:2 5k:1 µni:1 dµ2:1 tc:2 creg:2 lct:1 kπ:6 dj:3 dk:2 p0:1 dz:13 nz:1 dx:13 dy:4 dv:5 ds:1 dp:1 αj:2 2q:4 qx:1 arxiv:1 δr:1 δp:2 φm:2 δn:2 2f:1 δm:4 l2:3 δk:10 2b:3 qi:14 2m:4 2n:14 mº:19 qn:1 zl:1 zm:2 zn:2 mn:30 ezx:1 zi:18 zj:5 2x:1 ef:4 zc:2 z0m:3 dº:2 ezi:1 pτ:1 ez:1 2πn:1 zq:2 qnq:1 αp:4 mt:1 3q:1 qº:2 µq:1 n3:5 dz1:1 aji:1 2a0:8 rg:1 γout:1 µk:5 mβ:1 mq:13 rº:1 x21:1 tmn:31 ρn:1 wc:3 wb:3 wa:3 πc:1 µm:13 φb:1 2l:30 bq:6 nα:1 z0:18 z1:1 dreg:1 pβ:2 x2l:2 x2n:1 a1:1 a0:70 dzi:4 qmax:1 o:12 dzn:1 βe:1 aki:2 lº:8 γin:1 nmax:10 xk:1 ci:4 xn:6 cm:7 16k:2 apr:1 lj:1 xf:1 22b:1 2δk:3 xy:2 limn:1 wα:1 9q:1 q0:1 xq:3 22q:1 nø:1 cqi:3 mb:4 m1:35 zφ:1 πi:20 2x21:1 pb:2 pc:6 pa:3 1e:62 m0:6 m3:4 m2:4 zin:5 kº:10 λm:14 pn:2 pl:2 tm0:10 iº:8 4a0:1 x2q:1 pαβ:5 pα:3 pk:1 x2:4 x3:1 x0:9 x1:7 mδ:1 ρc:37 ke:1 dxn:1 2πi:18 3k:1 mi:49 mj:10 tnn:1 ǫr:5 nº:19 αm:3 aii:11 aik:2 aij:17 pβα:1 cq0:1 nµ:1 k1m:2 f1:2 vb:3 iz:7 πba:6 iq:4 ak:10 aj:1 aq:21 vq:2 ik:2 ij:8 cond:1 ax:2 v0k:2 dα:1 ni:10 nk:53 izk:1 nn:17 min:10 na:5 nb:5 nc:4 si:3 k2:15 k1:52 vexp:4 dm:5 nq:13 zs:1 eµ0:2 sn:5 pexp:2 stat:1 xº:1 mat:1 δm1:1 i1:2 dx3:1 dx2:1 dx1:5 kal:1 v0:10 qπ:1 a2:1 fi:1 bsb:1 kb:1 ka:1 mech:1 χs:1 knk:2 χq:2 4y:1 pº:6 kj:12 ki:38 kn:30 km:2 4n:5 kq:1 kmax:19 4k:2 exp:27 lα:1 n0:48 n1:14 n2:11 nxn:2 exz:1 |
0704.3703.txt |@word consider:3 esteve:1 magnetic:4 global:11 results:3 leads:4 go:1 expressions:2 cases:1 sch:1 depend:2 graph:2 groundstate:19 domainwall:1 under:6 include:1 advantage:2 very:1 implicitly:1 rise:1 connects:2 electron:3 rotational:2 eiλj:1 stays:1 affect:1 exact:2 hamiltonian:30 suffices:1 occurs:2 solved:1 vector:8 manifestly:5 antiferromagnetically:1 noted:1 upper:1 inconsequential:1 second:4 displays:1 further:1 dynamics:2 linear:1 even:1 developed:1 appear:1 hansson:2 sum:3 brief:1 find:4 current:1 above:7 new:1 net:1 acknowledgments:1 nakamura:2 wavefunctions:1 simultaneously:2 den:4 component:1 here:1 explore:1 governing:1 address:1 path:2 along:4 strong:6 appears:3 superconductor:24 sjz:4 sending:1 great:2 parameters:1 institute:1 involved:1 study:1 studied:1 allows:1 isolation:1 resulting:4 pick:1 demonstrates:1 relation:1 via:2 projection:2 forbid:1 hermite:2 merely:1 scaled:1 condensates:1 counts:1 total:6 plot:1 would:1 prove:1 remains:2 contains:2 negative:1 next:1 classically:1 therefore:3 taken:1 themselves:1 type:3 theoretical:1 more:4 linden:1 introducing:3 separates:1 incorporates:1 becomes:1 operators:2 factor:1 particular:1 known:6 hole:1 must:1 pseudospin:4 account:1 valued:1 science:2 der:1 modified:1 mk:1 regions:1 values:4 thin:27 caveat:1 tracing:1 following:2 trans:1 spontaneous:7 example:1 stimulating:1 challenging:1 figure:1 give:1 calculation:2 sense:1 conspire:1 states:22 indicates:1 lorentz:1 recognized:1 degenerate:1 allowed:1 tions:1 times:1 axis:7 needs:1 ferromagnetically:1 varied:1 antiparallel:1 discussion:1 breaking:17 feature:1 chemical:1 how:1 zaxis:1 before:1 instead:1 absolute:2 parameter:1 e2i:1 description:3 may:1 thermodynamic:1 after:1 mapping:2 plane:3 demonstrating:1 representations:1 excited:2 realized:3 effective:5 higgs:5 tsai:1 explicit:2 correspond:1 su:1 sj:8 maintain:1 so:1 fundamental:1 enter:1 representation:2 order:2 prefactor:1 indeed:2 over:5 course:1 experimentally:2 still:3 excitations:8 its:4 equiv:1 horizontally:1 thank:1 maps:1 chosen:1 fix:2 solving:1 writing:1 attraction:1 parts:1 meissner:2 systems:3 main:2 decades:1 split:1 non:3 motivated:1 schematic:2 rotations:2 outlined:1 material:1 break:2 electro:3 they:5 half:1 rotation:9 now:2 φj:2 easily:3 february:1 netherlands:1 fully:2 university:1 arrows:1 identified:1 filling:1 urbina:1 each:3 higher:3 2i:1 characterized:3 bond:1 goldstone:4 domain:1 square:1 another:1 generation:1 mesoscopic:1 energy:13 related:2 elementary:2 gaps:1 ex:1 magnets:1 quantum:6 our:7 mat:1 projections:3 emerges:1 shown:2 space:1 rev:11 ra:1 dutch:1 ble:1 size:3 cause:1 integrated:1 vion:1 foundation:1 fermi:1 theory:1 pseudospins:12 interactions:4 free:1 standard:1 small:3 generate:1 definition:1 pairs:7 interaction:1 ms:1 transition:1 quantummechanical:1 creates:1 massive:3 consequence:2 onto:3 polynomials:2 first:3 origin:1 there:3 pothier:1 symmetry:36 striking:1 lowenergy:1 number:3 restrict:1 xy:3 simplified:1 signifies:1 directly:2 computed:1 given:6 perturbation:1 needed:2 introduction:2 leading:1 top:1 system:4 construct:1 their:1 nian:1 unbroken:2 gives:1 collapse:1 φsj:2 exactly:4 direct:1 environmental:1 part:4 absorbs:1 than:2 coefficients:1 observed:1 kind:1 scenario:1 favors:1 andersson:2 zero:3 determined:2 doubly:1 amplitude:3 ber:1 peierls:1 function:1 symmetries:1 generality:1 contradict:1 ann:1 spectrum:29 superconducting:15 pedestrian:1 manuscript:1 manner:1 2t2:1 unaffected:1 occupied:1 any:4 strength:1 angle:6 mechanism:3 note:1 potential:8 analogy:1 hs:1 siddiqi:1 heisenberg:1 continuous:1 opposite:1 σj:3 reach:2 horsch:1 most:2 regular:1 fore:1 letter:1 sb:4 pair:12 extremely:4 kb:2 constructed:1 observation:1 consequences:1 considered:1 neighboring:2 average:2 brought:1 face:1 properly:1 electrons:6 mechanical:1 physics:2 naively:1 fact:6 quantity:2 sector:6 show:3 preperation:1 gauge:24 uniform:1 brink:4 near:2 slow:1 based:2 spite:2 should:2 jan:1 only:3 explicitly:2 disconcerting:1 acknowledge:1 local:14 do:1 dl:1 means:1 stot:1 rotated:3 overall:1 expectation:1 obtain:1 cannot:1 aδ:1 pashkin:1 combinations:1 ssb:4 evolution:1 mattis:3 continuum:1 numerous:1 arxiv:1 rotationally:1 investigate:1 contain:1 analytical:1 joyez:1 supr:1 view:1 set:4 constructing:1 exists:2 cottet:1 j2:2 maximum:3 relative:1 see:1 result:3 zaanen:4 discussions:1 recently:1 wonder:1 disjunct:1 eigenfunctions:1 possi:1 away:1 sites:3 symmetric:1 state:11 future:2 closed:1 between:10 invariant:11 diagonalized:1 approach:1 preserve:1 notice:1 terms:5 nature:1 qubits:6 weak:3 however:6 gratefully:1 extent:1 come:1 downgraded:1 observable:1 cos:1 orients:1 micnas:1 σb:2 σa:2 conclusions:1 equal:2 quantization:1 energies:1 dated:1 context:1 hσ:2 qubit:5 whole:1 comes:2 con:2 arbitrarily:1 cj:3 jj:1 timescale:5 point:3 wall:1 corresponds:3 mirroring:1 height:1 σjz:2 exploit:1 sequences:1 associated:5 considers:1 complication:2 transformations:2 lattice:2 create:1 three:1 been:1 implicit:2 much:2 combined:1 expected:2 microscopic:1 empty:1 fig:3 elitzur:4 box:5 generating:1 corresponding:2 both:3 coherence:9 gap:8 observe:1 external:5 angles:1 spin:4 present:1 case:2 align:1 appearance:1 value:2 spontaneously:3 will:6 while:2 situation:1 procedure:1 devoret:1 larger:1 coupled:1 robaszkiewicz:1 von:1 sondhi:1 thus:2 site:2 according:1 reads:1 itself:1 cond:1 vanish:1 different:3 hubbard:3 generic:1 aassime:1 make:2 lett:4 same:5 clearly:2 unity:2 complex:1 virtually:1 coworkers:1 advances:1 proved:1 finite:11 difficult:1 independent:1 formalism:1 used:2 cubic:1 absorb:1 effect:2 liquids:1 potentials:1 changing:1 invariance:3 weakly:1 modes:6 hopping:2 charges:1 expression:1 well:8 picks:1 materials:1 solve:1 experimental:2 position:1 model:7 stating:1 just:1 technological:1 being:2 superconductors:10 jeroen:1 detail:1 sources:1 underlying:1 λj:2 rotates:1 macroscopic:1 eigenstates:1 alignment:1 orderparameter:2 density:1 apr:1 other:2 treatment:2 easy:3 theorem:6 transformation:3 momentum:7 identical:2 antiferromagnets:4 around:5 evaluate:1 breaks:2 kaplan:1 posed:1 term:4 boxes:3 canted:1 using:1 unique:2 mod:2 semiclassical:4 ns:1 periment:1 particle:1 follows:2 collective:4 specific:4 flux:1 either:2 arbitrary:2 oganesyan:1 become:3 topologically:1 spins:5 because:3 classical:4 competition:1 added:1 proper:1 ourselves:1 happens:1 kaiser:1 dense:1 lead:1 electromagnetic:3 extensively:1 overlap:4 does:6 provides:1 tends:1 fom:1 ranninger:1 equivalent:1 spinwave:3 expansion:1 broken:12 reduces:2 although:1 manufacturing:1 stage:1 about:1 island:2 generated:2 o:1 reduced:1 distinct:2 range:2 nothing:1 introduced:1 consequently:1 lieb:3 presence:9 into:5 within:4 integral:1 bound:1 due:5 down:2 phase:9 jasper:1 operator:1 proportional:2 van:8 support:1 pairing:5 long:2 dispersion:1 start:1 anderson:4 describes:1 low:9 hem:4 was:1 lowest:1 form:7 governs:1 makhlin:1 leiden:4 shnirman:1 but:4 volume:5 construction:1 ec:1 removed:1 kf:1 made:2 applying:1 qualitative:1 whether:1 antiferromagnetic:3 inside:2 variations:1 up:6 us:2 antiferromagnet:4 below:1 decays:1 limit:7 σtot:3 problem:1 similar:1 strongly:1 ordered:3 computing:1 defined:4 certain:1 universal:2 direction:2 general:2 single:1 sublattices:1 wavelength:1 crystals:4 universiteit:1 check:2 physical:8 again:1 nj:4 paradox:1 no:4 amounts:2 fixing:1 whereas:2 when:2 vanishes:1 field:13 priori:1 details:1 4j:1 out:1 peschel:1 unobservable:1 conclusion:1 picture:3 formed:1 superposition:2 excitation:2 superconductivity:2 time:8 variation:1 develops:1 important:2 included:1 cooper:10 structure:1 ago:1 coupling:11 coulomb:1 requires:1 factors:1 pseudo:1 together:1 inset:1 mass:3 gapped:2 decoherence:6 resolution:1 having:1 bcs:3 |
0704.3704.txt |@word limited:2 dynamic:2 entropy:2 parameterization:2 consists:2 whose:1 calculate:8 moodley:1 presents:1 under:3 inwards:1 worth:3 updated:3 rise:1 every:3 figs:1 overcomes:1 affect:1 vast:1 publicly:1 solution:1 correct:1 vector:3 enclosing:11 markov:1 degeneracy:4 favoured:1 jhep:1 incremented:1 miller:1 consistent:9 estimates:4 approximation:7 elegant:1 second:4 estimated:9 even:15 errors:1 selected:1 above:19 new:24 increasing:8 consisting:2 simultaneously:2 never:1 here:4 met:2 active:5 obtained:11 approaches:8 ignoring:1 xiα:1 characterizing:1 complicated:2 fourier:1 changes:3 divide:2 mobility:1 highly:7 visible:2 total:5 circumvent:1 unit:4 plot:2 would:21 keith:1 negative:1 noting:3 therefore:1 assessment:1 until:8 separated:8 naive:1 curvature:1 correspondingly:1 excellent:1 must:5 springer:1 work:3 mi:5 example:6 give:1 bennett:3 implementations:1 degenerate:1 feasible:1 end:2 provide:3 feature:2 machine:1 far:4 ancestor:5 replacing:2 thermodynamic:10 after:6 attempt:4 third:3 greer:1 schneider:1 hypotheses:2 algorithms:16 decreasing:9 operate:2 order:11 operations:1 over:9 vary:2 satisfied:4 spergel:1 vastly:1 24th:1 somewhere:2 exhibits:1 better:3 fig:21 hidden:1 overcome:1 eventually:1 them:7 combination:1 tained:1 they:6 multidimensional:3 comprised:1 eigenvalue:1 mcmc:18 reasonably:2 routines:1 reasonable:3 each:99 mean:8 t2:1 cmb:1 substantially:1 laboratory:1 publically:1 restricted:1 crucial:2 re:2 assignment:1 matrices:2 linear:1 given:12 standard:14 grapes:1 estimate:9 hysteresis:1 degeneracies:13 r1:3 r2:3 created:2 starts:2 iso:13 separable:2 already:1 features:1 encouraging:1 restrict:2 another:4 illustrate:1 anyone:1 toy:23 similarly:1 top:1 approximately:1 listed:8 percentage:1 john:1 rejected:2 somewhat:1 kept:1 distance:1 target:1 showed:1 iteration:42 likely:2 kth:6 sivia:3 skilling:11 tion:2 enables:1 mini:1 fashion:1 sees:2 spectrum:1 ras:16 increment:3 seen:2 relatively:3 traditionally:1 latter:1 isolated:11 vtot:4 optimizes:1 shall:1 object:37 prohibitive:1 accurately:2 phase:4 acknowledgements:1 calculated:10 partition:4 inferred:4 points:99 principle:2 maxima:1 notion:3 dickey:1 random:7 halpern:1 arbitrariness:1 hypercube:1 hobson:17 proposed:4 ellipsoid:51 implementation:3 guidance:1 pursuing:1 adequate:1 do:7 mixture:1 dd:3 stop:1 preferred:2 dx:5 dp:1 runs:4 public:1 traversed:1 analytical:6 kolmogorov:2 detection:10 depends:3 decided:1 radius:1 w2:2 w1:2 discussions:1 subject:3 draws:2 away:1 rings:5 symmetric:3 bucher:1 simplest:1 drawn:10 tolerance:1 terms:2 extend:1 nature:2 however:18 wi:8 cut:1 extent:1 picking:2 improve:1 faced:1 received:1 uncertainty:13 against:1 jeffreys:1 hinshaw:1 variance:2 contribution:5 expense:2 com:1 con:1 height:1 wider:1 trust:1 conference:4 proceeded:1 basis:1 union:4 three:10 been:10 quickly:1 commission:1 much:3 interest:5 basic:3 expected:3 basin:1 grainge:1 dots:3 quantities:4 applied:5 occam:1 aip:1 marginalised:3 employ:1 near:1 slo:1 suppose:2 stopping:2 procedure:3 remembering:1 ii:6 containing:5 suggest:1 make:5 unnormalised:2 intersecting:7 drawback:1 potentially:3 split:1 mukherjee:6 several:3 independent:6 peaks:9 numerical:4 differing:1 hand:1 centred:2 ellipsoidal:38 shortly:1 contact:1 encounter:1 simulated:4 paradigm:1 left:2 just:8 wasteful:1 able:5 assigned:12 identify:7 yet:2 previous:5 adding:1 regarded:1 had:1 evidences:10 fortran:1 belongs:1 transformed:1 apart:1 basset:2 insensitive:1 progressed:1 possible:6 converged:1 background:7 clustered:13 progresses:4 occurring:1 performing:8 detections:1 steps:4 arbitrary:1 right:2 deal:1 successfully:3 topping:6 tutorial:1 ferreira:1 circ:3 algorithmic:1 burn:1 illustration:1 substituted:1 pogosian:1 proceed:1 accepts:1 o:5 probabilities:2 steadily:2 slightly:1 automatically:1 considerations:1 raised:1 presence:1 trotta:3 marshall:2 obtaining:1 bound:5 accommodate:1 lies:6 often:8 suffice:1 initial:7 transform:2 width:6 way:4 resulted:1 was:10 lowest:9 underestimated:1 form:4 feroz:10 differences:1 analyse:1 failure:1 verde:2 removed:1 true:12 normalising:1 inside:6 maximum:8 discarding:1 complications:1 stages:2 nonintersecting:2 adopt:1 moore:1 inclusive:1 abstract:1 evidence:93 simulations:2 adversely:1 nnt:1 distributions:16 check:2 constructed:6 nk:11 no:13 na:4 whereas:4 generally:3 ne:2 topped:2 setting:5 role:1 papers:1 test:7 nr:6 shrink:2 intend:1 savage:1 models:6 uniformly:2 update:1 variable:3 longer:2 assume:3 interval:1 together:2 time:4 n1:2 n2:2 chain:10 switched:1 global:14 integration:10 leads:2 supplement:1 computation:1 displaying:1 dimensionality:9 depend:1 technique:9 finally:6 monotonically:1 division:1 advantage:1 geometrical:1 exact:2 partitions:1 presented:7 corasaniti:1 cavendish:1 travels:1 discrete:5 upper:2 mn:1 illustrating:1 hindered:1 cost:2 curse:1 appear:2 assistance:1 uniform:7 current:7 template:1 shared:2 satisfy:2 subcluster:1 address:2 change:3 wait:1 vectors:1 trial:3 simultaneous:5 poisson:1 usually:10 plotted:2 emerge:1 inference:8 extra:1 problematic:2 flexibility:1 fake:1 additive:1 prove:2 suppl:1 nonconcave:1 live:41 criteria:3 associated:9 meyer:1 liddle:5 cases:8 trapezium:1 modified:3 values:27 cam:1 following:2 making:1 nearest:1 figure:18 smirnov:2 sample:16 incremental:1 performed:11 occur:2 verlag:1 normalize:1 fortunately:2 discussion:1 write:2 criterion:2 frequentist:1 optimal:1 parameter:37 divides:2 economy:1 map:5 product:4 may:11 needs:1 applications:8 produce:6 data:30 natural:1 outline:1 ghz:1 cosmology:2 so:17 progressively:1 representation:1 worsens:1 typical:1 indeed:9 pointed:1 wishing:1 soc:1 thomson:1 course:3 experiments:1 statistical:2 differs:1 still:6 group:1 thumb:1 how:3 decreases:4 attraction:1 constitutes:2 mail:1 main:2 non:14 introduce:3 tucker:1 tails:2 sorted:1 now:3 discuss:3 possess:3 down:4 drop:5 last:2 individually:1 el:2 weighted:1 vanishingly:2 ek:7 ed:2 gaussian:28 astrophysical:3 year:1 approximated:1 eq:1 adequately:1 neighbourhood:2 shown:8 3rd:1 space:31 increase:7 contained:8 investigation:2 gaussians:6 navigating:1 viable:2 shows:4 inevitably:1 earlier:2 theory:3 multimodality:1 possibility:5 quite:7 advantages:3 bayes:1 e1:1 e2:1 widths:1 transition:1 turn:1 place:1 wright:1 first:10 xj:4 xk:5 xi:25 xm:1 subclusters:2 parkinson:1 nested:67 xy:2 simplified:1 directly:2 impossible:1 ring:2 size:3 little:2 necessarily:1 checked:1 1a:4 returns:2 1b:2 brevity:1 gives:1 exploring:1 inefficient:4 eliminates:1 released:1 x2:1 x0:3 x1:2 than:37 coefficients:2 unfortunately:2 require:5 hypersurfaces:1 lmax:2 were:5 ann:2 occupies:1 locations:1 occupied:3 any:24 computationally:6 efficient:17 aside:1 note:5 potential:1 take:8 resembling:1 performance:3 begin:2 multiple:9 rankin:1 printed:1 sheets:1 successive:6 multiply:1 latex:1 especially:2 considered:3 average:3 later:2 steady:1 typically:5 quantity:2 slope:2 madison:1 show:5 spaces:1 feng:2 ratio:4 enough:1 only:19 trapezoidal:1 get:1 nobj:9 expectation:2 truly:1 cannot:1 nearly:1 4dimensional:1 outperform:2 yield:1 summary:1 naked:1 ignored:1 fellowships:1 bounds:5 relative:3 namely:1 differentiable:1 eliminating:1 surfaces:1 satisfying:1 ways:2 subsequent:3 review:2 colours:4 outside:3 jth:1 between:15 across:2 useful:3 jj:1 suppressed:1 σk:4 panels:1 implementing:1 many:5 region:16 according:1 σe:1 beltran:2 comes:1 among:1 characterization:1 sampling:147 iterations:10 moreover:6 considering:1 tuning:2 capable:4 locally:1 absence:1 workshop:1 gaussianity:1 formed:1 andrew:1 bayesian:32 careful:1 spirit:1 those:10 case:12 npix:1 kogut:1 engineering:1 profiles:1 ongoing:1 promising:1 situation:1 cluster:53 l51:1 different:15 develop:1 circularly:1 same:3 underestimate:1 investigated:4 edged:3 assigns:1 closest:3 trivially:1 nest:1 running:1 footprint:2 cartoon:3 implements:1 modes:29 largely:1 without:8 fixing:1 model:36 dimension:4 genovese:1 pakistan:1 being:5 when:9 ci:8 rest:2 speed:1 sampled:2 conclude:1 seems:1 except:2 improvement:2 interested:3 samples:25 heavier:1 real:11 aspects:1 around:11 represents:3 replaced:3 early:2 mon:1 using:40 innovations:2 particle:1 identifying:3 reduces:1 discarded:6 either:1 reduced:4 learning:2 rms:3 specified:2 matching:1 provided:1 dimensions:19 extensively:1 stops:2 critical:3 provides:4 refer:1 destroys:1 metropolis:20 power:1 notably:1 inherent:1 comparison:1 central:1 bimodal:1 discussed:13 practical:2 greatly:1 processor:2 cambridge:5 image:7 numerically:1 references:1 determine:7 accumulated:1 log:28 shells:1 assumed:3 there:11 dispersion:1 start:1 low:6 series:1 complete:2 jul:1 posterior:66 mnras:24 faster:2 datasets:1 applying:4 default:1 robustness:3 strongly:2 ac:1 certain:1 ak:9 describe:1 resultant:1 file:1 controlled:1 moves:5 incorrect:2 again:7 ideally:1 hybrid:2 field:2 valid:1 spatial:1 deviation:5 briefly:1 regardless:1 separate:15 nichol:1 includes:1 a1:1 cb3:1 important:4 peak:12 recognise:1 characterising:2 partitioned:4 curve:4 approxima:1 mass:2 resembles:1 once:9 starting:2 original:4 contructed:1 represent:5 monte:6 consider:9 caused:2 quadrature:1 nstep:3 former:1 tn:1 tm:1 ti:5 belonging:5 amplitudes:5 straightforward:1 very:16 supercomputer:2 ln:31 difference:4 condition:2 treating:1 17th:2 hamiltonian:1 list:2 t1:3 large:13 small:7 rk:4 20th:1 employing:1 rate:7 further:11 wmap:2 sub:39 richard:1 clock:1 section:14 2r2:1 version:1 intersect:3 method:103 contrast:1 revealing:1 full:11 behaviour:3 tracks:1 inverse:2 commonwealth:1 search:1 increments:1 allows:2 experience:2 prior:64 amount:1 narrow:6 elongated:1 via:1 suddenly:1 marginal:1 aimed:1 limon:1 detecting:4 select:1 eye:1 takes:3 distinct:5 contains:7 summarised:1 comparing:5 taken:5 minor:1 more:25 lesgourgues:1 flat:1 damtp:1 emission:1 instrumental:1 tested:1 2w2:1 particular:10 known:1 producing:2 none:1 science:1 equation:1 remain:3 evolved:2 learn:1 f0:7 compare:2 mackay:5 challenging:2 cosmological:6 accept:1 states:1 minimum:1 numbers:1 axis:1 information:8 respective:1 recursive:3 rather:5 occasionally:1 derived:2 plane:2 ff:1 fi:4 evaluations:12 negligible:1 discretisation:2 ith:3 essence:1 paper:5 through:5 suffer:1 avenue:1 its:22 style:1 rapidly:3 inward:1 actually:1 detected:5 systems:2 might:6 yk:5 good:1 propose:1 anticipated:1 framework:1 oxford:4 easily:5 always:2 level:12 radial:1 found:13 likelihoods:1 weight:3 hard:6 reduce:2 extended:1 expect:2 operation:1 beyond:5 dominates:2 since:23 projected:2 denotes:4 denoted:1 targetted:1 evaluation:10 occurs:3 difficulty:1 experimenting:1 base:2 members:2 bellido:1 kunz:1 diffuses:1 assign:2 probability:20 number:49 enlarged:11 general:9 done:2 least:4 stage:1 razor:1 differ:1 temperature:1 introduction:1 leading:2 construct:2 calculations:1 dealing:1 scheme:2 banana:1 too:2 pare:1 recursively:2 part:3 blindly:1 believe:2 inconvenient:1 peaked:1 albeit:1 determines:1 determined:2 picked:2 alongside:1 randomly:4 substantial:2 null:3 orders:1 lie:3 built:1 zero:1 refute:1 build:3 finding:4 towards:1 populate:1 inconvenience:1 reach:2 most:12 bridle:1 plan:1 significant:2 extremely:6 deviations:1 mobile:1 clear:1 coincides:1 traditional:3 wasserman:1 exp:4 usual:1 physics:1 lying:5 particularly:4 accuracies:1 authors:1 relation:1 astrophys:1 find:3 impact:3 parameters:25 inflection:1 distributed:2 factor:19 circle:3 dominant:2 goes:1 closely:3 competing:2 during:5 arxiv:3 remove:1 garcia:1 investigate:3 mclachlan:2 set:51 achieved:1 collectively:1 see:26 individual:4 sec:10 close:5 forthcoming:3 contour:15 chose:1 currently:3 smallest:2 various:2 conditions:2 knowing:1 lasenby:1 recently:2 statistically:1 missing:1 initially:2 generalised:1 both:9 paradigms:1 improved:5 barely:1 became:1 context:3 whole:1 finds:2 load:1 point:33 simple:6 corresponds:2 dimensional:16 simply:6 expensive:4 pr:23 complication:1 described:11 transformations:1 acceptance:5 due:4 lahav:1 reduction:1 pg:6 pe:1 extends:1 ph:4 pi:1 precision:2 modelling:1 determination:1 representative:1 reliable:4 expanded:6 evaluated:1 while:4 superposed:1 evaluating:4 error:17 manner:2 costly:1 approximate:2 vol:2 drawbacks:2 apjs:1 shaw:23 widely:1 modification:5 higher:17 development:1 used:16 appreciably:2 levels:3 uses:4 user:2 robust:6 eigenvectors:2 lower:1 task:2 analysis:12 hastings:1 exploits:1 lester:1 shape:1 intervals:1 λj:2 alternative:7 accepted:6 conclusions:2 source:1 ellipsoids:39 location:2 theorem:1 relevance:1 remaining:16 evaluate:2 advocate:1 bic:1 helpful:1 astrophysics:2 shaped:2 follows:13 signal:2 separately:5 continue:1 methods:71 some:34 back:1 added:1 pronounced:11 gradually:2 exceeding:1 per:5 centroid:3 tends:2 varying:3 run:4 remembered:2 processing:3 confidence:1 step:6 analysing:5 constraint:7 range:7 stuart:1 consequently:5 david:1 computational:6 into:18 within:24 integral:9 exceed:1 appropriate:4 proportional:2 ellipse:1 clustering:40 uncertainties:5 criticisms:2 statistics:2 few:6 question:1 fast:5 occupy:2 gflops:1 forward:1 sections:3 considerably:3 memory:1 hopes:1 considerable:3 partitioning:2 rejection:2 up:11 us:3 exploration:1 uk:3 sum:5 similar:5 called:1 storing:2 constant:5 defined:12 single:14 defines:1 priors:3 occasional:1 application:1 priori:1 explaining:1 calculating:6 problems:19 spatially:2 generated:2 allowing:1 independently:4 suffers:1 algorithm:55 required:19 weights:1 international:2 requires:8 having:3 evenly:1 code:2 illustrates:2 results:14 existing:4 illustrated:8 softer:1 go:1 contributions:1 centers:1 inferences:15 compact:1 intensive:2 include:1 ingredient:1 overlaps:2 continues:1 putting:1 colloquially:1 continued:2 categories:1 entire:3 michael:1 fewer:8 dealt:1 eigenvalues:4 noted:2 encloses:3 smaller:3 zi:1 jump:2 enclosed:2 insertion:1 dynamics:1 carlo:6 victor:1 consistently:6 multivariate:3 pvalues:1 respectively:9 jointly:1 desired:1 explore:2 objects:19 l29:1 consideration:3 z0:1 z1:4 z2:3 z3:1 involved:1 larger:6 suggests:1 resulting:3 bryan:4 shaded:1 makes:1 involves:1 claim:1 apj:3 decrease:3 summation:1 apply:3 analyses:2 use:17 remains:4 jarosik:1 next:3 process:11 panel:6 becomes:4 rare:1 iii:2 account:4 alim:3 challenge:1 thin:1 drops:2 dropped:1 control:1 calculation:9 high:9 effectively:3 dm:1 hereinafter:1 curving:6 sit:1 holds:1 parametrised:1 regions:8 numerous:1 elliptical:1 instead:5 nips:2 profile:2 collection:2 efficiently:6 advocated:2 counter:1 correspond:4 σe1:1 looking:1 lλ:1 produces:6 astronomical:8 move:1 interpreted:1 produced:2 including:1 mentioned:2 bunch:1 perfect:1 bridges:4 chosen:7 lj:3 li:25 estimating:3 choose:2 clusters:45 defining:6 pixel:5 mitigates:1 greater:4 outlined:7 functional:1 february:2 university:3 concave:3 identified:14 sufficiently:8 magnitude:4 transmitted:1 mode:21 l0:2 l1:1 identifies:3 constraints:2 subset:1 exacerbated:1 inputs:1 doing:1 related:1 constitute:1 fraction:4 measure:2 our:46 special:1 out:9 matrix:7 posteriors:8 rev:2 performs:5 cause:1 math:1 release:1 completely:2 york:1 likelihood:85 determining:2 could:6 times:4 length:1 explored:2 hence:15 retain:1 facilitate:1 reaches:1 improvements:2 reached:1 precisely:1 publication:1 unknown:3 their:19 final:6 testing:1 wollack:1 completed:1 exactly:2 nolta:1 skordis:1 diminish:1 unimodal:2 observed:2 submitted:3 amplitude:8 providing:2 result:12 exhibit:2 unlikely:1 need:4 curved:3 clearly:4 slosar:4 schematically:1 techniques:9 accuracy:10 unless:1 allow:3 centre:1 who:1 but:36 definitions:1 astro:4 proceedings:4 hierarchical:1 se:1 normally:1 fact:1 impression:1 selection:6 chances:1 supported:1 bring:1 based:9 knowledge:2 cache:1 should:16 dunkley:2 employed:2 local:40 achieve:3 equilibrium:1 means:50 overall:2 flattens:1 words:2 areas:4 approach:22 optimally:1 contain:2 enclose:3 fixed:1 intervening:1 available:3 requirement:1 constructing:2 exists:1 national:1 0he:1 geometrically:1 closer:2 attempting:1 tend:2 written:1 identification:6 correctly:3 allanach:2 progress:1 variability:1 efficiency:27 job:1 hypothesis:3 key:6 distribution:37 thank:2 concentrated:2 taking:2 equal:4 etc:1 girshick:2 estimation:13 safely:2 otherwise:1 ck:5 cj:4 adjusted:1 relevant:1 cl:2 walk:2 coordinates:1 table:25 cent:3 proposal:6 isolating:1 suggested:3 arises:1 corresponding:22 sufficient:2 subspace:2 bulk:3 astron:1 c2:2 c1:2 repetition:1 present:11 vanilla:1 fitzgerald:1 value:31 will:36 annual:2 almost:1 vk:6 thus:17 perhaps:2 higherdimensional:1 unity:2 parts:1 largest:2 units:4 finite:1 infer:3 difficult:5 effect:1 v2:1 off:3 neural:2 variety:1 well:15 sets:2 position:2 drawing:5 latest:1 less:6 increasingly:1 accurate:4 obtain:4 underlying:1 vπ:2 density:2 capabilities:1 combine:1 match:2 conspires:1 tests:1 increases:5 press:5 2nd:1 like:2 lost:2 sizes:1 lose:1 underestimation:1 become:1 soft:1 page:1 replacement:3 therein:1 poor:5 indications:1 because:1 classical:1 sequence:2 library:1 convex:1 proper:1 lead:2 broad:1 avoid:2 overlap:5 does:11 assuming:1 intersections:1 chains:1 demonstrated:2 l3:1 noise:12 slight:1 selecting:2 pp:4 although:4 approximating:2 simpler:2 about:2 actual:1 carried:1 extension:1 dependence:1 a2:1 introduced:3 homogeneous:1 equally:1 own:1 suited:1 previously:1 h0:9 h1:10 kmeans:1 assess:2 mrao:1 tiny:1 significantly:7 terminated:1 additional:4 function:10 eal:1 overlapping:11 volume:45 repeated:1 construction:1 heuristic:1 pk:6 convergence:3 partially:1 made:4 jaffe:1 whether:3 wish:3 smooth:1 placed:3 below:7 limit:4 demonstrate:4 problem:27 minutes:1 3mb:1 intersects:2 denote:9 multimodal:27 sibling:5 education:1 proceeds:5 functions:1 compared:5 nonetheless:2 detail:1 other:13 ellipses:1 conclusion:1 stat:1 covariance:9 enlargement:14 searches:1 factors:1 covariances:1 rule:3 cpu:1 portion:1 volumes:3 understand:1 validation:1 peiris:1 |
0704.3705.txt |@word equiprobable:1 papanikolaou:1 global:5 results:1 existing:1 four:1 eds:1 computation:7 reasoning:2 simon:2 xxii:1 knill:1 tt:1 deterministic:3 languages:1 program:2 those:1 include:2 random:2 far:1 choice:1 fall:1 popl:1 basics:1 internally:1 level:1 transmission:1 companies:1 programme:2 illustrating:1 rate:1 design:1 manipulating:1 qmc:24 implemented:1 expressive:1 incompatible:1 specification:2 nec:1 supplied:1 current:4 ˆb:1 shared:1 public:1 agreement:1 full:1 led:1 degree:1 understanding:1 explore:1 plenio:2 looping:1 represented:1 b2a:4 simulating:1 receive:1 gla:1 study:2 allows:4 ctl:1 bob:9 named:1 secure:1 apr:1 compare:1 outcomes:4 aimed:1 viz:1 apply:2 should:1 tools:1 approximating:1 select:1 clifford:2 executable:2 flaws:1 would:2 probabilities:1 dcs:3 nikolaos:1 opposed:1 scope:1 nagarajan:1 noisy:1 type:4 theoretical:1 today:1 more:1 bennett:2 operators:1 tested:1 appendix:2 particular:4 known:2 foundations:1 potential:1 must:2 high:1 science:2 work:3 emerson:1 values:2 stabilizer:8 growing:1 im:1 example:3 unconditional:3 proof:1 dedicated:1 process:6 allowed:1 implementations:1 states:9 abort:4 numbers:1 sense:1 simple:1 information:4 needs:2 end:3 clarke:1 chadha:1 id:1 symposium:1 widespread:1 brassard:2 description:1 may:2 typed:2 after:1 epsrc:2 applications:1 produce:1 designed:2 gottesman:3 cambridge:1 fi:4 data:1 types:3 efficiently:1 imply:1 algorithms:3 specifying:1 representation:4 sigact:1 order:2 operations:2 restriction:1 executed:1 produces:2 developed:3 over:1 satisfied:1 produced:1 course:1 paper:2 including:2 concurrency:1 mentioned:1 converting:1 satisfies:1 ieee:1 its:2 sigplan:1 group:3 chosen:1 interesting:2 temporal:5 forms:2 imp:1 systems:12 constitutes:1 non:6 stabilizers:1 matches:1 audenaert:2 delbourgo:1 toshiba:1 framework:1 they:3 now:1 discuss:2 developments:1 meas:1 always:1 university:3 truth:2 each:1 referred:1 stabiliser:1 list:1 principles:1 related:1 measurement:8 quantum:54 laboratory:1 ep:3 network:1 restricted:1 furthermore:1 research:1 re:1 imperative:1 statically:1 reader:2 formula:6 earlier:1 theory:1 commercially:1 reason:1 base:2 york:1 beginning:3 benefits:2 prepare:1 language:8 computers:2 programming:2 hence:1 exhibited:1 first:3 already:2 probability:3 variables:10 powerful:1 number:3 dini:1 executions:2 channels:1 directly:1 given:3 checked:3 introduction:1 system:2 their:4 checker:2 compromise:1 bits:4 final:1 implements:1 tool:12 rajagopal:1 simulate:1 authors:1 than:1 semantics:2 pointers:1 tree:2 namely:1 modelled:1 jarvis:1 project:1 future:2 enables:3 treated:1 distinguished:1 false:7 measure:1 kitaev:2 analysis:1 initialized:1 need:1 any:4 qb0:2 paths:2 built:1 note:1 ideal:1 internal:3 relies:1 online:1 new:2 channel:4 heisenberg:1 formulas:2 begin:2 towards:1 normal:2 most:1 significant:1 formulae:6 phase:1 coin:4 probabilistic:2 branching:1 especially:3 url:1 clear:1 partition:1 proceedings:5 principle:1 qbi:4 qbj:4 physics:2 section:1 fact:1 laws:1 supported:2 syntax:1 corney:1 chuang:1 expressed:4 bravyi:2 based:2 knowledge:1 implementation:2 outside:1 operational:1 only:2 bases:4 indeed:1 local:1 do:2 guarded:1 specifications:1 cryptography:7 express:1 expectation:1 cannot:1 international:4 during:1 procedures:1 him:1 enemy:1 evolution:1 settings:1 arxiv:2 glasgow:1 circuits:1 investigate:1 qb:1 common:1 qi:2 through:1 automatic:1 declared:1 set:2 honesty:1 detection:1 ancillas:1 finiteness:1 computer:1 result:7 techniques:6 preparation:2 ways:1 review:2 currently:2 justifies:1 state:12 determined:1 various:1 approach:1 checks:1 available:2 terms:1 qubits:5 analogues:1 key:3 commands:2 10th:1 flipping:3 limits:1 extracts:1 equal:2 involve:1 became:1 colloquium:1 rq:4 logic:9 qubit:11 expression:1 point:2 reasons:1 guaranteed:1 2nd:1 polynomial:1 respect:1 conference:1 ensures:1 java:1 basis:4 due:2 been:4 reduction:1 workshop:2 treat:1 interest:2 warwick:3 ph:3 choose:1 arises:1 corresponding:3 valuations:3 sufficient:1 aborts:1 nikos:2 modelling:5 declaration:1 improved:1 protocols:17 case:2 compatible:1 novel:1 developing:1 bb84:1 value:2 choices:3 will:5 while:1 evaluating:1 involved:1 determinism:2 investigating:1 property:3 launched:1 quantique:1 lightweight:1 technology:1 allocating:1 different:3 verified:1 grant:2 perform:2 same:1 quant:2 finite:1 development:1 used:4 http:1 see:3 downloads:1 counterparts:1 a2b:5 user:1 entanglement:4 simulates:1 programs:1 nevertheless:1 well:2 know:1 concrete:1 without:1 command:2 model:16 arising:1 entangled:1 gates:1 protocol:13 just:1 less:1 being:1 obtain:1 rest:1 using:9 bit:6 aaronson:1 rapid:1 ny:1 had:4 source:2 setting:2 theorem:1 input:2 hat:10 match:2 real:1 nielsen:1 checking:5 evaluate:1 possible:7 abound:1 scheduler:2 press:3 integer:2 emergence:1 execution:5 like:2 interestingly:1 alice:8 discarded:1 either:1 security:7 signal:1 www:1 methods:1 classical:6 traversing:1 matching:1 nondeterministic:1 establish:1 does:1 expressing:1 demonstrated:1 dcm:1 mateus:1 power:1 performed:1 sixth:1 journal:2 processing:1 notable:1 use:1 mayers:1 although:2 hadamard:1 described:1 analyses:1 properties:7 cnot:1 analysing:1 integers:1 about:3 actual:1 usa:1 attacks:2 acm:3 simulation:4 practical:3 mixed:1 consequently:1 automatically:2 computational:2 statements:1 communication:3 within:1 satisfactory:1 references:2 determine:2 her:1 area:1 there:3 ed:1 var:3 form:1 enough:1 basic:1 analyse:1 but:1 repeated:1 automated:2 line:1 true:17 partially:2 applying:1 whether:1 declarations:1 us:1 considered:1 verification:8 uk:3 distribution:3 mechanics:1 ac:3 ag:1 computing:1 universal:2 describe:2 general:2 eu:1 single:1 enable:1 our:3 controlled:1 floating:1 formalism:5 check:1 physical:2 gay:1 no:2 tossing:1 field:2 other:1 bool:6 details:1 department:2 conclusion:1 gaining:1 briefly:1 users:1 expressible:2 models:3 includes:1 concurrent:2 important:1 matrix:1 cryptographic:2 individual:1 assume:1 resolving:1 time:1 original:1 |
0704.3706.txt |@word narsky:2 represent:1 monte:5 measurements:1 systematic:1 qian:2 luminosities:3 results:6 mrenna:1 four:2 selection:3 comments:1 consists:1 latorre:1 layers:1 increase:1 inverse:2 depend:1 caldwell:1 technique:11 editors:1 environment:1 finally:3 stable:1 nodes:3 discriminants:2 overlaps:1 activities:1 worse:2 broadly:1 very:4 pages:1 degrades:1 summarized:1 affect:1 difference:2 exact:1 tagging:44 squares:2 level:4 positions:1 large:4 zhu:1 piccione:1 noted:1 jhep:4 review:1 smaller:4 semileptonic:1 consistent:1 japanese:1 sign:1 fold:1 second:19 estimated:1 carlo:5 tev:1 contingent:1 even:2 errors:4 abazov:2 power:25 section:6 selected:3 brief:2 bdt:36 experiment:3 above:4 judicious:1 international:1 increasing:1 method:3 multivariate:2 simultaneously:1 respectively:6 leveraging:1 component:1 here:4 desired:1 tracks:22 separation:1 address:1 ratio:3 along:1 standard:2 z0:6 tn:1 box:1 search:2 splitting:1 oxford:1 leaves:1 larger:6 allows:1 flavour:1 implement:1 studies:4 involves:1 useful:1 gluons:1 instr:1 decrease:1 trained:2 resolutions:3 select:4 plot:2 would:1 commun:3 positive:1 negative:1 throw:1 scenarios:3 nucl:7 kinematics:1 therefore:2 taken:1 selects:1 more:4 extent:1 tolerated:1 under:2 benchmark:1 pairs:2 herein:1 normalized:6 studied:1 varying:1 known:1 must:1 high:5 springer:1 eden:1 mb:5 prof:1 equation:1 work:1 mh:1 minimum:6 values:3 ms:1 learn:1 following:2 clarendon:1 trans:1 cone:1 norrbin:1 figure:20 give:2 table:10 purposes:2 significances:5 sample:11 tag:6 performed:1 tan:1 axis:3 information:1 needs:1 end:2 decaying:2 σz0:2 a400:1 feature:1 b409:1 lepton:1 far:1 eywords:1 delphi:1 significance:7 absolute:1 parameter:17 lonnblad:2 description:2 schapire:2 may:5 after:5 containing:1 25k:2 fb:1 plane:1 55k:2 data:12 lhc:4 higgs:3 light:23 grant:2 lines:2 correspond:4 like:1 cascade:18 si:2 algorithms:15 decreasing:1 subsequently:1 order:5 bins:2 superscript:1 bastos:2 cowan:1 help:1 september:1 developed:1 over:1 produced:3 experiments:5 looks:1 statistical:3 left:1 mentioned:1 peterson:1 still:2 its:2 features:1 fis:1 style:1 vtb:1 group:1 thank:1 fit:3 decay:7 ln:1 boson:4 actually:1 better:9 production:4 nardulli:1 mail:2 hidden:2 supersymmetry:1 maximal:3 them:1 good:1 affected:1 greater:4 material:1 investigated:3 primary:3 abreu:1 coimbra:3 front:1 nov:1 reconstruction:12 easily:2 gets:1 always:2 university:2 presented:1 40k:2 miniboone:2 infer:1 applied:3 each:2 crossing:4 found:1 higher:4 classifier:4 characterized:1 referred:1 heavy:3 significantly:2 weight:5 independent:2 hadronic:1 energy:6 hard:3 gaussian:4 constitute:1 society:1 decays:8 ex:1 combining:1 substantially:2 meth:7 beyond:1 event:2 ru:2 shown:7 accomplish:1 network:4 furthermore:1 since:7 crucial:1 denotes:1 particles:1 forte:1 seriously:1 investigation:1 performs:1 reader:1 newly:1 gov:1 integrated:1 shows:11 abbott:1 interactions:12 differ:1 quark:4 reason:1 besides:2 boosting:3 detecting:1 likelihood:2 additional:1 training:58 interaction:1 geometry:1 widths:4 days:1 turn:1 bstract:1 instrum:5 hadrons:4 sartori:1 first:15 feed:1 there:2 yong:1 probability:1 variables:16 bagging:1 powerful:1 number:17 traveled:1 channels:2 improvements:1 done:1 fast:1 open:2 size:2 manuscript:1 given:17 jet:42 indicate:1 introduction:4 leading:3 top:8 construct:1 their:1 compromise:1 observations:1 prong:3 gives:3 sixteenth:1 para:1 abramowicz:2 obtained:6 rejected:1 transverse:13 weakly:1 differentiate:1 simulate:3 manipulation:1 horn:1 than:11 distance:7 critically:1 double:1 rate:2 discriminating:12 computer:1 yang:1 supposed:1 were:18 garrido:1 acquisition:1 result:3 comput:2 ann:35 randomly:1 outperforms:1 say:1 seen:1 any:2 contents:1 sfrh:1 implemented:1 angle:1 built:1 output:12 εu:1 able:1 note:2 liu:4 fitting:1 internal:1 lip:1 build:1 forces:1 performance:33 detector:5 miu:1 channel:1 εb:2 circles:1 lectures:1 multiple:1 though:1 track:16 collaboration:5 sets:2 most:2 optimized:1 significant:2 alabama:1 diffractive:1 deviations:1 considered:8 performances:4 average:1 saturate:3 vertices:5 typeset:1 pseudorapidity:1 points:1 ferrari:1 typical:2 typically:2 sum:2 rejections:1 sector:1 hyper:1 show:6 supported:1 tagged:3 participate:1 superimposed:3 networks:16 d0:10 impact:22 fg02:1 based:1 parameters:11 justice:1 outperform:1 distributed:1 state:1 should:1 only:2 version:1 σd0:2 a311:1 employed:2 constant:1 do:1 gev:4 degrade:2 de:1 trees:21 beam:2 words:1 determines:1 sz0:1 meir:1 secondary:17 qq:3 reading:1 bar:1 luminosity:3 arxiv:2 yield:1 acknowledgments:1 investigate:1 paper:4 architecture:1 doubles:1 cycles:1 conversions:1 predictive:1 set:4 rojo:1 intelligence:2 testing:3 observed:5 200k:2 flavours:2 individual:1 us:2 best:4 techniques:5 instance:1 fails:1 learns:1 pattern:1 away:1 artificial:18 behind:2 score:2 identification:3 between:8 invariant:2 bunch:7 approach:5 available:1 comparable:2 recently:1 vertical:3 superior:1 roe:2 however:2 efficiency:32 premise:1 contamination:3 jets:74 longitudinal:9 distribution:3 improve:4 both:5 improved:2 cot:2 region:3 b517:1 σd:2 participating:1 etc:2 σy:1 σx:1 context:1 attributes:1 key:1 conclude:1 cb:3 ca:1 others:1 batavia:1 bpd:1 exploit:1 learning:4 cs:3 respect:3 considering:1 sensible:1 pp:2 collider:7 pt:7 discriminant:1 discrimination:6 acceptance:1 radiative:1 three:5 been:6 reduction:1 describes:1 combined:1 azimuthal:1 expected:3 inefficiencies:1 topology:1 ctt:31 corresponding:3 leptonic:1 formed:1 precision:1 angles:1 decreased:2 c2:2 general:1 irrelevant:1 those:3 case:2 extracted:1 solid:10 value:5 will:2 subsample:1 while:8 threshold:4 promising:1 situation:1 study:1 procedure:5 versus:2 layer:3 sizeable:1 portugal:1 almost:1 non:1 bias:5 il:1 conf:1 mcgregor:1 id:1 increased:2 different:6 σz:3 perform:1 belong:1 radiation:1 same:2 clearly:1 reconstructed:3 improves:1 split:1 see:3 several:2 events:23 difficult:2 development:1 exhaust:1 used:11 closest:2 slac:1 boosted:18 effect:3 hand:2 parametrized:1 intersects:1 levels:2 purpose:1 frequently:1 sjostrand:1 lower:7 task:1 so:1 center:1 scenario:2 neural:18 no:4 well:1 analysis:5 obviously:1 without:11 trains:1 model:1 fermilab:1 charged:1 distances:1 proposed:1 epochs:1 valuable:1 assigned:1 subsamples:2 identify:2 regardless:1 alternative:2 scattering:3 previous:1 tables:1 cut:4 preprint:1 classification:1 conclusions:3 seems:1 exclusively:1 improvement:5 verse:1 pile:6 lett:3 samples:12 reconstructs:1 input:5 remaining:2 momentum:7 divided:1 tests:1 march:1 around:1 represents:1 corresponds:7 department:1 increases:1 freund:1 background:13 consisted:2 press:1 using:6 accepted:1 scatterings:1 advanced:1 prominent:1 displaced:2 excluding:1 particle:7 jinst:1 alternatively:1 signal:11 sizes:3 manual:1 serves:1 specific:1 yields:1 fnal:1 popular:1 experimentalists:1 conrad:1 soft:1 reduced:2 poor:1 lipc:1 because:1 methods:4 friberg:1 some:8 identified:2 specified:1 extended:1 ins:1 leaf:1 gluon:1 bottom:3 decision:19 quarks:4 extensively:1 per:3 efficiencies:9 mhz:1 moderate:1 conference:1 taggers:1 ba:1 bb:4 selecting:2 journal:1 lose:1 perpendicular:1 how:1 step:25 leptons:1 bs:3 described:3 properties:1 hadron:2 stancu:4 about:17 concretely:1 package:3 discussed:1 dependence:2 o:1 simulation:8 compatible:1 introduced:1 software:1 tecnologia:1 sd0:1 final:1 presence:1 mendelson:1 into:3 year:1 due:3 variable:1 right:1 references:1 75k:6 mrad:1 next:1 hep:1 log:2 elastic:1 assumed:1 initial:1 long:2 why:1 low:3 fraction:2 irrespective:1 smola:1 was:11 naturally:1 function:1 building:1 semileptonically:1 complete:1 form:1 enough:1 simplifications:1 differences:4 but:1 idea:1 berg:1 construction:1 goals:1 line:14 removed:1 lncs:1 made:1 rejection:19 joint:1 stanford:1 type:1 inside:2 robustness:3 up:9 signed:2 below:2 fermi:1 problem:1 panels:3 similar:1 uc:1 smeared:4 ab:2 associated:5 inclusive:1 defined:1 measurement:3 pid:5 evidence:2 separating:1 single:4 lifetime:1 doe:1 distributions:9 physical:3 machine:1 again:2 functions:6 compared:2 ingredients:1 dashed:8 nb:2 when:7 proceedings:1 other:7 compares:1 spatial:1 test:6 weights:3 optimization:1 node:1 polar:1 calculating:1 separate:2 vertex:23 variation:1 pjet:1 generated:4 important:1 pythia:1 scores:1 included:3 fisher:3 15k:3 astronomy:1 searches:2 correlated:1 algorithm:10 direct:1 physics:11 original:1 mass:5 boone:1 time:1 observables:3 resolution:8 having:1 once:1 |
0704.3707.txt |@word aguilera:1 limited:1 partial:2 crucial:1 results:7 scalar:1 poorly:2 whose:1 rameter:1 finally:2 does:3 those:1 excluded:1 stable:3 chirally:1 applied:1 g4:1 string:2 very:4 choice:2 figs:1 bubbles:3 resummations:1 level:1 issue:1 large:17 vector:2 small:11 upper:4 approximately:1 carter:2 ten:1 hics:5 10a:1 approximation:2 second:3 qualitatively:2 dynamics:3 estimated:1 even:1 aim:1 what:1 plays:1 appear:1 current:1 wiggles:1 version:1 above:2 rho:1 new:2 preserved:1 exchange:1 mω:1 here:7 mev:39 ratio:1 strong:4 respect:1 obtained:7 study:1 larger:7 ferrara:3 suggests:1 complicated:1 via:2 useful:1 extra:2 visible:1 gluon:2 condensates:1 cassing:2 meson:2 toneev:1 plot:1 use:5 takes:4 would:2 remains:1 charge:2 a750:1 scenarios:1 phenomenological:2 nucl:15 therefore:5 qcd:3 taken:2 associated:2 type:1 theoretical:2 minor:1 more:3 elliptic:1 becomes:2 tested:2 particular:2 known:4 account:3 drago:1 science:1 equation:4 fµν:1 reproduce:4 values:6 temperatures:10 following:2 dec:1 example:1 numbers:1 compare:4 wang:1 calculation:3 relativistic:1 neglected:1 purposes:1 high:1 indicates:2 performed:1 burgio:1 information:1 provide:1 torino:3 how:1 pure:1 instead:1 parameter:5 danielewicz:2 oscillatory:1 tension:4 description:1 may:1 proach:1 produce:1 incompressibility:14 fe:1 develop:1 data:2 fm:4 constants:1 attempt:1 correspond:2 su:1 dilaton:10 so:4 allow:1 taking:2 pleasure:1 order:5 lynch:1 breaking:2 ahle:1 produces:1 developed:1 mainly:1 interpreted:1 produced:2 experiments:3 through:2 existence:1 still:3 its:4 group:1 thank:1 energies:8 interesting:3 masses:2 presence:2 decreases:1 actually:1 better:1 absence:1 production:1 degrees:2 fig:11 clusters:3 main:1 eur:1 non:1 prevision:1 they:3 now:1 discuss:2 represents:1 term:1 several:2 delimiting:1 stabilize:1 always:1 alford:1 presented:1 senger:2 luca:1 found:1 universit:1 d46:1 characterized:1 mean:3 heavy:2 significantly:1 hadronic:5 energy:6 hard:2 related:1 literature:2 isospin:3 quantum:1 our:8 beyond:2 eq:1 really:2 hyp:1 shown:3 conceptually:1 since:2 lagrangian:2 rudaz:2 increase:1 collisions:2 dominated:1 blaschke:2 ref:5 c32:1 c57:1 mρ:1 8a:1 divergence:1 fisica:2 free:3 quark:9 approaches:1 formation:10 estimate:1 generate:1 definition:1 interaction:1 chiral:22 starts:1 transition:4 eoss:4 times:1 sahu:1 place:6 b458:1 corrections:1 hadrons:3 condensate:4 first:7 symmetry:10 relate:1 number:2 smaller:1 least:1 directly:1 reached:4 size:1 temperature:11 similarly:1 introduction:1 dipartimento:2 system:1 adopted:2 their:1 intermediate:7 too:4 calculations:2 stoecker:2 ranging:1 gives:1 fraction:4 asymmetric:2 baryon:3 rajagopal:1 sizable:1 a555:1 than:4 ivanov:2 was:1 fm2:1 depends:2 isovector:2 matter:10 future:2 contrary:1 were:1 perturbative:1 shrinks:1 curves:1 deconfinement:4 clearly:2 collapse:1 strength:1 studying:2 responsible:1 able:1 c74:1 instance:2 potential:2 take:1 gρ:1 modulus:8 mit:2 gω:1 play:1 serot:3 αs:1 extending:1 letter:3 phase:34 extremely:3 furnstahl:2 clear:1 adopt:2 flow:2 exp:1 link:1 left:2 typically:1 quantity:1 sector:1 show:9 purely:1 trivial:1 nucleation:2 based:4 proposed:2 parameters:1 baryonic:1 situations:1 minnesota:1 should:2 only:8 explicitly:2 gradual:1 gev:5 viewpoint:1 di:5 dependent:2 simplest:1 fluid:1 wiggle:1 liu:2 respectively:2 reveal:1 densities:21 progressive:1 fields:2 arxiv:1 beff:1 bag:5 compressibility:1 fixed:2 approaching:1 requirement:1 set:2 computed:8 fair:1 lavagno:1 papazoglou:2 sez:2 observed:1 ehrenfest:1 alessandro:1 radius:1 microscopical:1 discussions:1 precursors:1 bielich:1 fails:1 nuclear:4 participant:2 justifies:1 symmetric:3 state:4 smallest:1 various:4 between:2 invariant:1 approach:1 notice:4 reproduced:1 reproduces:1 interface:1 bondorf:1 tensors:1 suggested:3 both:5 csernai:1 limits:1 region:6 vanishing:1 ln:2 manifestations:1 planned:1 exceeds:2 inspired:1 toro:1 experimental:4 grounds:1 solving:1 simple:1 bratkovskaya:1 moreover:2 li:1 forms:1 described:1 due:9 been:6 extraction:2 reduction:2 basic:1 expected:3 ph:2 systems:1 diquark:2 rather:6 corresponding:1 kaon:1 concerning:1 bulk:8 dramatic:1 representative:1 ours:1 andrea:1 present:2 case:2 uncertain:2 pacs:1 tang:2 appearance:2 value:8 will:2 reviews:1 while:6 behavior:4 applies:1 lacey:1 couplings:1 studied:1 almost:1 refs:3 surface:3 reads:1 vs:3 vanish:1 result:1 different:2 italy:2 same:4 any:1 strange:2 pae:1 gibbs:1 finite:2 independent:1 used:5 see:2 effect:4 hand:3 ion:2 traditionally:1 necessity:1 variance:1 invariance:1 reference:1 recent:4 lower:5 scenario:3 c69:1 charges:4 c65:1 well:3 roughly:1 analysis:12 tatsumi:1 comes:1 c70:1 gsi:1 model:34 parametric:3 usual:1 c72:1 softening:15 c75:1 obtain:2 bµ:4 relevant:1 density:17 seems:1 parametrization:6 hyperons:3 lattice:2 concerns:1 lett:1 plasma:1 build:1 saturation:3 breaks:1 possible:3 increases:1 vacuum:2 using:14 like:2 g31:1 g30:1 helpful:1 signal:1 soff:1 specific:1 flux:1 unstable:2 either:1 gm3:11 mishustin:1 soft:3 indications:2 right:2 interm:1 b0:2 bν:1 indirect:1 bonanno:1 provided:1 gradually:1 scale:3 describing:1 c66:1 quarks:8 exceeding:2 per:2 critical:5 provides:2 yields:1 moderate:2 2a:1 voskresensky:1 pressure:8 grigorian:1 th:3 properties:2 hadron:2 panel:5 comparison:1 about:1 actual:1 constraint:2 freedom:2 discussed:6 dependence:3 simulation:1 practical:1 restoration:6 mixed:29 introduced:4 slightly:3 xu:1 muller:2 rev:14 significant:2 strangeness:6 facility:1 maxwell:1 into:3 within:2 glendenning:1 because:2 tiny:1 reducing:1 descriptions:1 hep:2 c52:2 comparing:1 assumed:1 there:2 c59:2 start:1 window:1 low:1 way:2 bubble:4 a2:1 function:3 form:7 bµν:3 metastable:5 forming:1 but:11 sophisticated:2 content:1 construction:1 politecnico:1 schaffner:1 c60:1 hyperon:1 partially:1 directed:2 infn:2 made:2 up:2 limit:2 marginally:1 spectroscopy:1 fluctuations:1 problem:1 panels:3 similar:2 called:3 strongly:3 constant:6 defined:1 describe:2 general:1 ap:1 conserved:5 exist:1 formalism:5 arsene:1 again:1 no:1 nb:1 when:2 field:10 other:5 role:2 rapidity:1 test:1 ns:1 conclusion:1 separate:1 models:10 generated:2 important:2 allowing:1 ellis:3 40a:2 heide:1 assume:1 sigma:1 curve:1 together:1 eos:10 impossibility:1 nuclei:2 ags:1 |
0704.3708.txt |@word consolidated:1 dynamic:1 consists:1 whose:1 γi:7 bike:1 aux:5 ontological:1 every:8 school:1 unrelated:1 commented:1 specially:3 miller:1 approximation:4 second:3 even:1 established:1 neg:2 specification:2 selected:4 reasoning:3 above:15 new:14 net:6 seeks:1 coefficient:3 mel:1 residual:1 here:15 reported:2 active:1 path:4 interpret:3 obtained:2 items:29 study:8 symmetrical:1 suitable:1 changes:2 york:9 9i:1 projection:5 replace:1 unit:1 would:2 monographs:1 motivate:1 negative:1 until:1 adjacency:3 phone:3 reversible:1 adult:16 teaching:1 must:6 me:2 springer:1 ma:5 room:1 mm:1 work:11 theories:1 transparency:1 already:1 my:17 example:20 indicated:2 organized:1 involve:4 indicates:3 caution:1 want:13 end:2 syntactic:67 inhabitants:1 feature:2 how:5 significance:1 answer:1 place:2 abstraction:8 description:1 replacing:2 after:3 lab:1 predicated:1 wrong:2 law:1 types:2 attempt:3 third:3 acknowledged:1 lost:2 hypotheses:1 complexity:8 order:11 operations:3 internalization:1 interpretation:5 over:8 nets:4 before:1 personal:3 fix:9 production:12 differently:1 weeks:1 easier:1 overcome:2 them:12 fragment:1 weakness:2 differentiated:2 they:10 structural:35 grammar:17 reasonably:1 routines:1 reasonable:3 each:3 side:1 carlos:1 dga:6 extract:3 network:57 restricted:1 crucial:1 particles:7 re:1 ajk:3 linear:4 associate:1 given:12 ramon:1 standard:3 universally:1 days:1 iso:1 tied:1 onto:1 organize:1 features:10 subtlety:1 restrict:1 adopted:2 another:6 hood:3 illustrate:1 toy:1 annotated:3 needed:3 compromise:1 too:2 corpus:17 erlbaum:1 rejected:2 begins:1 distance:1 bits:1 tree:2 project:2 matter:1 enables:5 acquisition:24 modern:3 mine:4 talking:1 manner:1 seem:6 contents:1 kohler:1 latter:2 isolated:5 forces:1 though:1 object:3 involving:8 phonological:7 don:9 vertices:1 principle:1 finitary:1 notion:1 labels:1 syntax:60 implying:1 constituent:5 keywords:1 substituting:1 make:3 ıguez:1 situations:5 semantics:1 do:15 stop:1 despite:5 dr:1 pearson:1 method:1 bag:1 linguist:1 blackwell:1 observed:5 decided:1 w2:2 w1:2 subject:6 pete:2 said:7 away:2 simplest:1 approach:7 terms:2 nature:9 wn:1 wk:5 wj:5 wi:15 wh:4 extent:2 clues:3 topology:1 essentially:1 merging:1 receiver:3 unk:5 com:3 coo:2 puts:1 basis:1 simplification:1 three:1 been:10 confident:1 interest:1 basic:4 expected:1 conversational:4 concerning:6 xxx:19 writting:1 coherent:3 lift:1 child:44 exception:1 spontaneously:1 aim:3 abrupt:1 aij:3 property:1 precede:1 procedure:5 ix:1 ii:4 characterize:2 grammars:13 conj:2 perform:6 realizing:1 clearly:8 complex:14 potentially:1 hierarchies:1 several:3 wheel:3 independent:1 hand:4 academic:1 mother:1 quantitative:1 popescu:3 sentence:20 identify:5 human:1 facts:1 lexicalized:2 yet:1 previous:2 candidate:1 similarities:1 character:2 ideal:1 affinity:1 easy:3 save:1 5a:1 designate:1 advances:1 possible:7 advanced:1 cognitive:1 morphemes:5 mit:3 specific:10 arbitrary:5 www:1 right:12 deal:2 people:2 productions:34 confusing:1 consensus:1 comments:1 everything:2 denied:1 core:4 substitutes:1 substituted:1 properties:9 takes:1 months:3 ensure:1 considerations:5 publishing:3 presence:10 sol:3 down:2 lies:1 often:3 poss:2 categorization:1 abstractions:2 combinatorics:1 intrinsic:4 support:1 fraction:1 was:4 head:7 medium:1 form:6 illuminating:1 removed:2 true:2 dordrecht:1 stages:6 computing:1 abstract:2 evidence:2 exist:1 triangles:1 nj:1 floor:3 whereas:2 generally:3 grammatical:8 role:12 tii:1 nw:2 models:3 reorganization:1 assume:10 together:1 time:4 n2:1 neighbors:4 concept:5 remarkable:2 global:16 leads:2 computation:5 morphology:2 displaying:1 milk:1 devoted:1 certainly:1 inverse:1 graph:19 editors:1 finally:5 analogous:4 string:4 choice:6 word:15 exact:1 din:1 level:8 item:6 funcional:1 unexpected:1 illustrating:1 occurrence:2 dealing:4 meanings:1 substitute:1 appear:5 inflectional:4 filler:2 goes:4 filled:1 french:1 understanding:1 address:2 alone:2 appears:2 naturalistic:6 box:3 unidentified:1 studied:2 suggestion:1 usually:2 studies:2 useful:1 logical:2 perf:2 working:3 perl:3 explicitly:3 opposed:1 criteria:51 scope:1 prep:2 pres:1 validity:1 oop:1 cases:6 effort:1 insights:1 car:2 syntactically:5 following:10 imitation:4 claim:1 figure:4 confused:1 sample:3 performed:2 exclude:1 s3:2 s2:6 discussion:1 s4:2 write:6 pure:2 speaks:1 may:1 revealed:2 annotation:7 natural:3 maybe:2 explicit:3 sv:1 provide:5 sh:1 so:7 representation:3 increase:1 talk:3 sd:4 indeed:1 mainly:4 unacceptable:1 entity:2 experiments:1 statistical:10 argued:1 still:1 thank:2 acknowledge:2 interesting:8 forms:3 main:2 non:14 bernat:1 conversations:2 evolution:4 symposium:1 now:4 discuss:1 nor:3 inversion:3 name:1 algorithmic:1 ed:1 entering:1 year:2 shown:2 space:1 furthermore:2 looking:1 contained:1 imperative:2 internet:1 suggesting:3 theory:9 cars:2 mechanisms:1 possibility:2 dependencies:3 org:1 axioms:1 derivation:1 language:37 transition:1 programming:1 thing:1 yum:1 qn:2 think:2 first:12 altmann:1 pseudocode:1 specifically:4 directly:1 generative:1 ring:2 open:5 size:11 little:1 exists:3 structured:15 returns:1 realization:1 structures:27 speaking:4 gives:1 way:6 hub:1 continuous:2 huh:1 than:4 specify:2 braine:2 connections:1 assortative:3 were:1 outcome:1 inferring:1 pre:2 pro:17 argument:1 generalization:1 say:4 recover:1 any:21 ideas:2 note:11 intends:1 potential:1 transcribed:4 take:7 performance:2 coincide:1 closer:1 trace:3 opposite:1 paid:1 successive:4 pages:1 surprising:1 considered:19 average:10 later:2 steady:1 duplication:4 quantity:1 show:1 aggressive:1 xml:6 prepositional:2 only:9 going:1 awareness:1 correctly:1 get:4 morphological:2 cannot:9 ssh:1 assignation:1 naked:1 source:3 seat:2 relative:1 namely:2 wonder:1 detect:2 enlightening:1 managing:1 lexical:29 label:1 enough:6 between:12 justified:1 reading:1 dmin:2 ji:5 analyzed:4 acquiring:2 many:10 wheels:4 utterance:8 among:10 period:1 sampling:1 learning:1 moreover:5 bizarre:2 considering:4 rebuild:1 conceptualization:1 attaching:1 combined:1 linguistic:1 wants:1 icrea:1 observe:1 external:1 careful:1 former:1 those:1 case:24 caso:1 profiles:2 situation:5 constituency:2 telephone:17 technology:1 binary:2 different:14 pat:3 alphabet:1 same:6 fixation:1 speech:5 arguments:4 document:1 status:1 finish:1 edges:2 locality:1 roughly:3 without:10 components:1 very:6 model:1 researchers:1 justify:2 being:4 when:13 captured:3 cl:1 seems:4 treatment:1 complements:1 extensive:1 real:3 aspects:1 around:1 rules:10 mor:14 mot:2 early:42 moo:1 world:1 accepted:8 ruled:1 particle:5 identifying:2 discarded:1 reidel:1 verbal:1 conditional:1 generates:1 recorded:1 extensively:1 provides:1 semantically:5 biased:1 power:1 retains:1 broken:1 ok:3 oh:3 discussed:3 generated:2 practical:2 act:7 ow:1 tape:1 cambridge:5 yyy:1 annotate:3 references:1 operator:2 conceptually:1 your:2 loc:4 log:4 distinctions:1 loi:4 hey:3 lot:1 complete:2 chaitin:1 trying:1 grasp:3 strongly:3 gone:1 ah:1 describe:4 general:3 reliability:1 file:4 walks:1 ay:1 again:1 valid:2 bollob:1 you:12 poor:2 separate:1 vertex:1 includes:2 ising:1 tackle:1 radford:1 building:7 thematic:6 barcelona:1 hello:1 quantify:1 starting:1 strings:9 semantic:6 consider:12 pointing:1 lack:4 follow:1 expressions:1 children:4 combinatorial:2 tv:1 tr:11 tp:2 program:4 present:8 th:4 nodes:10 te:1 ta:10 belonging:2 straightforward:2 far:3 verb:17 interpreting:1 decide:4 difference:1 condition:1 list:1 large:5 small:3 biological:2 neighborhood:1 harder:1 past:2 zero:2 design:3 displays:1 further:3 what:21 sub:1 section:2 brief:1 version:2 acknowledgments:2 movement:1 full:1 loose:1 component:3 behaviour:1 free:3 strong:1 via:1 analyzing:2 select:2 proceed:1 contains:2 comparing:1 taken:2 more:24 knows:1 company:3 particular:4 known:3 include:1 recall:1 det:6 dem:1 decidability:1 challenging:1 stated:1 conspire:1 accept:2 numbers:1 sense:4 phrase:8 information:6 needs:2 recursive:3 rather:2 acts:1 reject:3 mendes:1 wiley:3 mapping:3 connectivity:2 tries:1 develop:4 bloom:4 response:1 short:1 fundamental:5 phrasal:3 help:2 ith:1 hierarchy:3 developed:8 paper:8 through:3 its:17 rooted:1 fruitful:1 absence:1 systems:3 good:1 framework:3 hyams:1 oxford:3 bigger:3 easily:2 fully:1 found:5 universit:1 hard:1 idea:1 extended:1 connect:1 infinity:1 operation:1 beyond:4 really:3 psychology:4 research:3 acting:1 lawrence:1 confidence:1 difficulty:1 reason:8 members:3 put:20 beginning:4 generate:4 definition:2 pairs:1 reinforces:1 just:2 reinforced:1 sinclair:4 probability:1 encoding:1 number:9 done:1 tok:6 introduction:2 leading:3 least:3 assumption:2 part:3 authors:3 focusing:1 kind:6 determiner:6 sti:1 aims:2 dtd:1 contrary:3 supposed:1 treated:6 risky:1 motivation:1 sentences:9 constructions:1 built:4 extracted:2 internal:3 build:10 finding:1 added:2 english:38 reach:1 most:8 soriano:1 measured:1 deviations:2 clear:6 sometimes:5 3s:3 exp:1 physics:7 session:1 relation:6 networks:29 impact:1 computability:1 giant:1 parameters:2 inflection:1 his:5 famous:1 ferrer:2 during:5 him:1 contextual:1 arxiv:1 underlying:1 common:1 approaching:1 set:20 unpublished:1 see:9 arc:2 close:2 11th:1 theoretic:1 sequences:3 woo:1 verbs:5 statistically:1 complementary:1 complement:2 attention:3 competent:2 last:1 context:11 whole:4 experimental:3 point:4 simple:2 asymptotically:2 simply:4 adaptation:1 pp:5 described:3 perspectives:1 due:6 pl:1 lett:1 addison:1 great:1 gap:1 understand:2 systematic:1 demand:1 conception:1 look:9 corpora:16 receive:1 while:1 replaced:1 behavior:3 evaluates:1 advising:1 vol:3 itself:2 ready:2 belong:1 read:2 widely:1 development:5 used:4 annotator:6 uses:1 nouns:2 recent:1 database:2 analysis:12 obviously:5 edge:1 machinery:2 organization:3 parametric:3 abilities:2 intervals:1 questions:6 using:6 conclusions:1 prepositions:2 parents:1 location:2 relevance:1 format:3 showing:1 emergence:2 formal:2 utterances:17 follows:2 separately:1 translated:1 essential:1 mathematical:5 methods:1 some:40 back:2 understood:1 examples:2 decision:2 prop:2 pen:1 prog:1 minimal:2 measures:8 patient:1 agreement:3 infra:2 step:1 relating:1 cautious:1 chomsky:5 deserves:1 range:2 regular:1 consequently:1 into:9 within:4 clustering:6 statistics:31 question:5 long:4 handbook:3 analyze:2 files:1 infinitive:1 memory:1 ka:1 properly:2 link:3 russian:3 considerable:1 directed:3 intuitive:2 up:3 us:12 theoretical:5 um:1 cautiously:1 uh:1 called:5 associated:3 adults:4 defined:12 doesn:1 single:4 associates:1 denying:1 pronouns:2 nice:3 explaining:1 elements:11 clean:1 problems:1 meaning:3 structure:45 implies:3 algorithm:1 negating:1 age:4 required:1 having:1 once:5 results:2 existing:1 eds:1 go:15 contributions:2 issues:1 vacuous:2 languages:3 undirected:2 random:1 mainstream:1 unstructured:3 mixing:2 try:1 barbara:1 zn:1 imply:3 dynamics:5 index:1 plays:1 cancho:3 analogously:1 find:13 experiment:1 indef:1 degree:7 nonexistent:1 explore:3 focused:2 others:2 consideration:1 z1:3 z2:2 remark:1 technical:1 involved:1 suggests:2 makes:1 involves:1 composed:1 scales:1 apr:1 win:2 manage:6 addressed:2 apply:2 tools:1 dorogovtsev:1 use:8 chi:10 hudson:1 next:2 exhaustive:1 sort:1 formally:2 trait:1 train:3 topic:1 account:4 ride:2 assumptions:1 obvious:1 averages:1 links:7 process:10 purposes:2 pieces:1 high:1 tag:1 something:4 serial:1 rodr:1 gcc:6 ricard:1 negation:7 located:2 aft:6 instead:6 profile:1 blocks:1 singular:1 collection:2 ambiguous:3 realized:1 purely:2 computations:1 light:2 lines:1 element:4 fortunately:1 allow:2 s1:5 evolutionary:1 move:1 interpreted:4 produced:10 looks:1 mentioned:1 strikingly:1 chosen:3 lt:2 degrees:1 choose:3 bye:2 descriptive:6 python:2 practice:1 13s:1 minimalist:1 university:5 identified:6 merge:1 mode:1 traces:2 constraints:2 doing:1 ferromagnetism:1 programmed:1 related:9 society:1 measure:4 our:18 special:1 out:10 matrix:7 rev:2 socalled:2 plural:1 determiners:1 harold:1 approaches:3 surely:1 munteanu:1 likelihood:1 shortest:1 phrases:5 could:19 counterpart:1 conversation:11 length:4 derivations:1 assumed:3 there:56 manuscript:1 confuse:2 reaches:1 occurrences:1 ordering:1 data:16 behaves:1 system:14 relations:28 their:4 attack:1 intermediate:2 final:1 explanation:1 acquire:1 noun:1 bef:2 richer:1 bee:2 individual:2 need:21 turn:1 linked:4 screw:4 able:2 mechanism:1 sergi:1 truck:4 competence:2 valverde:3 connected:5 transcript:1 why:7 stronger:1 graphs:6 construction:3 constrain:1 veneziano:4 fact:4 emerging:1 selection:3 text:2 bring:2 trivial:1 pause:1 based:5 knowledge:1 should:9 terminal:1 smallest:1 candidates:1 ambiguity:1 constituents:2 employed:3 local:4 achieve:1 means:2 overall:1 ones:9 words:26 years:1 procedures:2 processes:2 trucks:1 fixed:2 view:6 computed:2 pronoun:2 operates:2 edition:1 pragmatic:1 wire:8 pattern:1 missing:11 tend:2 state:1 identification:1 closed:1 routine:2 neither:1 ends:2 sole:1 linguistics:1 no:23 key:3 users:1 thumb:1 observable:1 interpretations:2 taking:4 monograph:1 otherwise:3 detailed:1 relevant:2 co:5 conclude:3 poissonian:3 predication:4 walk:1 interface:1 universitat:1 cs:1 table:2 ct:2 addition:1 certain:1 indicators:2 proposal:1 define:11 arises:1 corresponding:3 hmm:1 spain:1 contexts:4 appearance:1 will:26 frameworks:1 hubs:4 examines:1 almost:3 thus:33 vp:8 capture:1 enumeration:1 member:6 strange:1 largest:2 units:3 finite:11 difficult:2 material:1 http:1 orth:6 infinite:3 compendium:1 off:1 reflection:2 nevertheless:1 well:11 patterns:4 oops:3 sets:1 firstly:3 usual:3 less:1 accurate:1 obtain:5 mistakes:2 adv:9 hall:3 reasons:4 newman:1 adj:2 divided:1 checking:2 term:1 know:1 press:7 like:7 success:1 sizes:1 works:7 accessible:1 because:12 classical:1 sequence:3 phenomena:8 preposition:2 peter:74 lead:2 avoid:1 does:5 assuming:4 limitations:2 selecting:1 journal:1 zipf:2 wesley:1 stage:10 about:7 rare:1 carried:1 extension:5 dependency:12 discard:2 own:1 lenght:1 functional:25 negate:1 artifacts:1 function:1 but:28 repeated:1 hierarchical:3 convergence:2 made:4 compute:6 whether:6 variations:1 below:4 projecting:1 problem:2 piece:1 display:5 jenny:1 ki:8 contribute:2 ind:1 compared:1 detail:1 other:15 marius:2 conclusion:1 variation:2 auxiliary:2 rule:2 |
0704.3709.txt |@word arcminutes:1 consider:1 distances:1 developed:1 excellent:1 obtain:1 years:1 leads:1 sources:5 paper:1 rosales:1 consists:1 abundant:1 fine:1 line:2 galaxy:2 astron:1 maps:2 paris:1 observe:1 uson:1 sky:1 coordinates:1 corresponds:1 petersburg:2 molecules:1 into:1 do:1 fig:2 distant:1 results:1 accepted:1 discovered:1 transversal:1 presented:1 university:1 arxiv:2 misidentifications:1 identified:2 radio:11 edif:1 optics:1 mean:1 upper:1 significantly:1 successfully:1 some:4 observed:2 see:2 astrophysical:1 laboratory:1 tenth:1 special:1 out:1 probable:1 space:1 measurements:1 research:1 investigation:1 identification:1 between:1 conditions:1 method:1 shows:1 bold:1 galaxies:3 agreement:1 here:1 identifications:3 objects:1 obtained:1 about:1 carried:1 many:1 taking:1 discussed:1 reason:1 russia:1 figures:1 ism:4 refraction:12 changes:1 col:1 egorova:1 first:1 major:1 cm:2 apr:1 image:1 powerful:1 number:1 coincidence:1 apj:1 aph:3 sov:1 mark:1 open:1 wada:1 illustrate:1 use:1 france:1 calculation:1 criteria:1 ph:2 was:1 correction:2 empty:2 more:3 function:2 wavelength:1 tool:1 corrected:1 nvss:3 but:1 astro:2 optical:5 particular:1 cases:1 than:1 present:1 must:1 applied:1 account:1 observatory:1 aal:1 maximum:1 value:1 frequency:1 distribution:1 mx:1 celestial:1 figure:3 mexico:1 process:1 abstract:1 our:1 blvd:1 physical:2 information:1 compared:1 end:1 same:1 field:2 epoch:1 sh:1 branch:1 department:1 percents:1 circles:1 independent:1 used:2 norman:1 optic:1 may:1 comprehensive:1 object:1 reach:1 centro:1 arcmin:1 significant:1 lower:1 calculated:2 cover:1 st:2 part:1 time:1 coordinate:3 model:3 typically:1 order:1 |
0704.3710.txt |@word represent:1 partial:1 consider:4 remarkable:1 global:1 results:2 fluids:2 proposition:6 assessment:1 expressions:1 reasoning:1 gr:2 compact:3 gases:1 depend:1 tt:5 show:1 presents:1 finally:2 tm:2 spain:1 under:2 tc:6 norm:4 sound:2 fax:1 supported:6 far:1 escudero:2 keeping:1 wave:3 corollary:1 interpreting:1 difference:1 continued:1 condition:3 implying:1 incompressible:1 shock:2 t2:6 solution:26 t0:3 t1:29 large:3 solved:1 differential:3 small:3 subindex:1 smaller:1 tel:1 direct:2 second:5 complicates:1 value:1 rigorous:2 further:1 dynamics:4 estimated:1 theory:2 spectral:2 what:4 nonlinear:5 appear:1 brackets:1 uniform:2 henceforth:1 version:1 above:2 new:2 contrast:2 full:1 respectively:1 never:1 here:1 behaviour:1 giles:1 address:1 equations:16 obtained:1 remark:2 sobolev:4 institute:1 study:2 studied:1 allows:1 contradiction:1 onwall:2 resulting:1 fourier:1 studies:1 concerned:1 boundedness:3 useful:1 apr:1 limt:1 put:1 apply:1 derivatives:2 use:4 proceed:2 would:1 prove:5 positive:2 noting:1 memory:5 compactly:5 type:3 theoretical:1 3lb:1 more:3 clearly:1 becomes:1 distribution:1 validity:1 4c3:1 known:1 hold:1 circumstances:1 account:2 indicates:1 recall:2 equation:29 work:3 modified:1 london:2 values:1 todorova:1 burnett:2 following:4 fulfill:2 example:2 proof:9 grained:1 process:2 claimed:1 performed:1 sense:1 vtt:12 rid:1 verlag:1 sir:1 united:1 requirements:1 goal:1 travel:1 get:6 very:2 derivations:1 de:1 description:4 singular:1 may:1 max:1 after:3 derived:1 ball:2 straightforwardly:1 applications:1 data:3 parallel:1 constants:2 short:1 dynamical:1 chapman:5 st:1 so:5 doklady:1 media:1 pleasure:1 order:7 wavelengths:1 holds:1 help:1 schwartz:1 developed:1 choose:2 interpreted:1 16c2:1 including:2 statistical:1 argued:1 existence:3 kinetic:3 still:1 its:4 before:2 derive:3 till:1 actually:1 lt:1 parts:4 microscopic:4 systems:1 mail:1 main:1 might:3 maximal:1 non:2 processes:1 akademii:1 sssr:1 effects:5 they:3 oxford:3 now:18 discuss:1 represents:1 term:2 finite:12 university:2 sideris:1 l4:1 vt2:17 l2:4 l3:4 l1:3 2l:1 found:2 higher:1 side:4 carlos:1 square:1 energy:3 idea:1 constitute:1 literature:1 interplay:2 measure:1 our:7 eq:19 out:2 shown:1 continuing:1 space:1 res:1 furthermore:2 rev:2 denotes:1 adapt:1 conjectured:1 dxdt:12 ref:2 integrated:1 math:4 shows:1 i2:2 linear:2 singularities:1 cowling:1 divergence:1 possibility:2 quart:1 clarify:1 formation:1 york:1 maths:1 estimate:2 e1:4 anal:1 e3:2 e2:2 integrating:4 derivation:2 r2:1 just:1 counterpart:1 turn:3 undesirable:1 navier:4 consequence:2 facilitate:1 strictly:2 first:9 major:1 already:1 xc:2 encouraging:1 cercignani:1 xx:6 done:1 relations:2 another:1 blows:2 fluxes:2 open:1 xt:1 golse:1 necessarily:1 hyperbolic:14 introduction:1 arch:1 eqs:3 least:1 their:1 perturbations:1 vxx:16 unboundedly:1 vxt:28 john:1 1d:3 saint:1 exactly:1 proving:1 mech:2 spiegel:1 appearence:1 j3:2 than:2 vxxx:12 approximations:1 modelled:1 were:1 vx3:3 vx2:12 collecting:1 rewrite:1 rao:1 spectrum:1 summing:1 chen:1 say:1 need:2 orders:1 self:1 note:3 instance:1 k1:2 take:1 resembling:1 play:1 sure:1 who:2 viscosity:1 rearrange:1 boltzmann:6 regular:1 remarks:1 later:2 flow:4 exp:6 velocity:13 physics:1 fact:7 quantity:4 disturbances:3 random:2 x2:1 solutions:5 keywords:1 tempted:1 d2:2 find:3 d1:2 knowledge:2 situations:1 ox1:1 should:1 only:2 integrate:2 partially:1 hope:1 do:2 establishes:1 notation:1 means:3 bardos:1 between:3 fluid:6 nonequilibrium:1 dx:67 dt:7 µg:3 evolution:4 continuum:1 arxiv:1 yield:1 summary:1 nauk:1 hydrodynamic:8 through:1 fixed:1 grad:1 requirement:1 set:2 constructing:1 exists:2 achieved:1 physically:1 j1:2 j2:2 maximum:1 see:5 result:10 discussions:1 prototypical:1 et1:1 exponent:1 speed:4 educaci:1 enough:5 vt3:1 hopefully:1 boundary:3 µf:2 conditions:9 µc:6 preserve:1 multiplied:1 inviscid:1 terms:2 levermore:1 extend:1 nature:1 weak:7 however:1 reproduces:1 article:1 come:1 inertia:1 suggested:2 last:3 limits:1 desired:2 taking:1 acknowledge:1 equal:1 agree:1 propagation:6 embedding:2 argue:1 rosenau:3 experimental:1 among:1 point:1 others:1 walk:1 dimensional:2 respect:5 ct:13 union:1 due:2 been:3 ja:1 cauchy:5 coarse:1 ph:1 define:3 life:1 corresponding:4 concerning:2 gas:2 fis2005:1 argument:1 understand:2 derivative:6 c2:49 c1:4 denote:1 c6:9 present:1 c4:16 case:3 k2:2 ǫg:2 rat:1 evaluated:2 ǫl:1 will:12 rests:1 while:2 suppose:3 momentum:1 exist:1 property:3 leaves:1 procedure:1 almost:1 thus:5 surprisingly:1 ii:1 regularity:2 itself:3 vt:14 cone:2 vx:14 convection:1 different:1 develop:1 suggest:1 same:2 any:1 complex:2 arguments:1 nonphysical:1 modification:4 regime:1 difficult:1 used:4 infinity:1 raymond:1 vvx:7 i1:2 i0:3 i3:2 numerical:1 effect:1 hand:4 v0:3 v1:3 hydrodynamics:3 infinite:4 ministerio:1 suitable:3 expression:3 well:1 analysis:2 burgers:11 solve:1 does:1 model:4 paradigm:1 stating:1 left:1 rarefied:1 proposed:1 being:1 accurate:1 obtain:7 turbulence:1 macroscopic:2 previous:1 blow:10 k3:2 conclusions:1 similarities:1 cl:1 sometimes:1 lett:1 easy:1 theorem:3 complements:1 euler:3 generalized:2 kingdom:1 rules:1 evaluate:2 increases:2 reads:1 know:4 press:1 using:4 projects:1 formal:1 lost:1 success:2 follows:2 signal:2 velocities:1 yields:6 arbitrary:1 interestingly:1 mathematical:2 because:2 classical:11 some:8 springer:1 regularized:1 happens:2 provided:3 footing:1 integration:2 2c2:1 inequality:14 provides:1 prof:1 proc:1 blowing:2 reaching:1 2µc:4 equivalent:1 notable:1 expansion:7 substituted:1 although:1 analyses:1 properties:5 asymptotic:2 stokes:4 conducting:1 carried:1 theorems:3 dependence:1 reduced:1 addition:2 15b:2 stand:1 ox:1 introduced:2 slightly:1 soc:1 cambridge:1 previously:1 into:3 within:1 integral:4 functional:4 hyperbolicity:5 three:1 ultrasound:1 right:5 sov:1 proportional:1 rely:1 fast:1 span:1 additional:1 support:3 there:6 transform:1 long:2 vvt:1 start:1 much:1 way:1 viscous:1 was:6 damping:1 form:1 compressible:3 but:5 heat:1 2vt:1 convergence:1 he:1 commun:1 persisting:1 fulfilling:2 characteristic:1 inside:1 up:14 us:11 ciencia:1 below:1 limit:1 critical:1 uk:1 problem:9 similar:1 called:1 supremum:1 mechanics:2 fulfills:2 ac:1 diverges:2 constant:1 certain:2 abstract:1 describe:1 proven:2 convergent:1 initial:15 controlled:1 identities:1 physical:2 again:2 paradox:1 no:2 when:1 invoking:1 application:2 role:1 nonexistence:6 hydrodynamical:1 nice:1 conclude:2 stat:1 estimation:1 models:1 problems:1 makarenko:1 15a:2 important:1 bounded:3 enskog:4 implies:5 auxiliary:1 assume:3 interval:4 together:3 time:22 walker:1 laws:1 starting:2 once:1 |
0704.3711.txt |@word concept:5 homomorphism:17 consider:7 chain:1 funct:3 bellaterra:1 alg:5 equalities:1 results:6 invent:1 gf:2 proposition:59 ice:3 projective:1 consists:3 follow:2 denotes:6 gk:7 gh:3 compact:17 whose:3 isometric:17 inverse:1 caveats:2 analytic:2 gˆ:5 bimodule:6 eα:76 equivalence:3 finally:4 umf:1 certain:2 tk:3 under:9 connecting:2 analogous:5 characterised:1 norm:9 abelian:1 applied:1 queen:1 departament:1 g2:7 g1:6 orthogonal:12 very:1 regional:1 choice:1 unitaries:1 corollary:34 valued:4 every:82 should:1 rm:2 matrices:3 rn:2 condition:5 beginning:1 ρji:8 turns:3 notes:1 list:2 solution:1 t0:41 involution:1 vector:3 o1:49 recall:6 anal:3 zn:1 smaller:1 semicontinuous:1 concise:1 sℓ:6 lecture:1 ready:1 c0:37 direct:16 surrounding:1 second:6 uk:1 infimum:1 concludes:1 further:1 linear:7 even:1 established:1 intersection:1 plays:3 appear:1 iterating:1 diag:3 section:25 goodearl:1 hereditary:8 henceforth:1 version:1 gn:3 above:31 sup:25 new:9 net:11 rigidity:5 consisting:4 contrast:1 ξi:18 xy:1 simultaneously:1 notions:6 q0:3 respectively:11 component:1 certainly:1 here:3 behaviour:1 desired:5 objects:3 them:1 groups:1 situation:2 affiliated:1 along:1 strong:2 cba:15 appears:2 morphisms:9 obtained:3 remark:11 suitably:1 involved:1 study:6 studied:5 allows:1 reason:1 contradiction:2 yˆ:3 cx:2 arens:1 qub:1 products:2 adv:1 akl:10 complicated:1 suitable:2 makes:1 ξk:1 quotient:1 uniquely:6 named:2 via:4 useful:1 subcategory:1 family:17 claim:8 apr:1 compare:2 replace:1 expect:1 ask:1 equals:1 limi:2 limn:1 topological:2 annihilator:7 apb:1 apply:3 total:1 establish:1 estimate:1 unit:3 readily:2 use:10 pointwise:1 triples:3 start:2 pere:19 prove:4 remains:2 positive:20 continuous:22 contains:18 ej:3 uniqueness:2 bimodules:1 hilbert:17 wherefore:11 noting:2 call:6 therefore:22 centre:3 m2:3 finest:1 associated:1 type:10 entails:17 more:8 taken:1 multiplying:2 said:7 started:1 becomes:4 operators:8 envelope:36 toolkit:1 needed:1 eξ:4 rigid:24 particular:9 known:7 kgh:1 cases:1 hold:3 iii:6 must:5 zi:3 springer:5 isomorphism:15 defines:2 1nn:1 ρi:3 gabriel:3 takesaki:1 work:6 cat:1 arveson:1 paragraph:1 obvious:2 concepts:2 following:35 making:4 example:17 proof:59 f1:7 f2:6 triple:1 indicated:1 give:6 process:1 discussed:1 preserving:2 ids:1 states:2 kaplansky:4 assumptions:1 reviewing:1 want:3 sense:7 mail:2 mn:24 conversely:6 ic:1 verlag:5 counterpart:1 uab:1 end:3 straightforward:2 mutually:5 provide:2 verify:4 discussion:7 holds:5 pedersen:5 aℓ:3 saito:1 evidently:1 write:4 maps:13 lam:1 vital:1 criterion:2 pure:3 answer:7 priori:1 stand:1 simplicity:1 product:8 rise:1 description:6 algebra:203 replacing:1 neat:1 suprema:1 different:6 ζn:4 diagram:2 consequence:3 ξj:2 fe:1 multiplication:4 rare:5 arch:1 compatibility:2 repeat:1 ide:1 natural:4 answers:1 imply:1 whenever:9 slightly:1 explicit:1 correspond:1 element:31 their:4 would:1 so:25 sect:1 fundamental:1 decreasing:3 representation:1 sa:11 acknowledges:1 order:14 countably:2 operations:4 restriction:4 fβ:3 acts:1 exploited:1 devote:1 indeed:17 over:10 dy:3 expects:1 murray:2 course:2 paper:6 through:2 filters:1 banach:1 existence:4 satisfies:3 still:1 its:17 before:3 massey:1 lg:1 x21:2 τj:3 lc:3 yρ:6 la:3 chosen:1 interesting:1 fix:3 writing:2 mek:1 xyx:1 para:1 continue:1 choose:6 ηn:21 asa:20 ours:1 definitely:1 image:4 s1:5 maximal:56 closure:8 non:30 good:2 ym:2 supλ:1 focus:1 yn:5 cen:1 outlined:1 introduce:8 xg:1 often:1 mention:2 yz:6 they:1 half:1 now:13 discuss:4 eξn:6 structural:1 easily:2 rocky:1 homomorphisms:2 goldstein:2 fully:1 frank:2 drop:1 identified:2 infer:2 orthonormal:10 enlargements:1 inequality:1 fα:6 each:40 found:2 entirely:1 european:1 2i:2 subset:42 int:1 en:17 ei:27 directly:1 completions:1 map:7 doing:1 ed:1 ιe:2 idea:2 related:1 eb:9 society:1 reader:1 literature:1 selfinjective:1 ex:4 combining:3 algebraists:1 our:13 happen:1 ℓa:38 neighbourhood:3 out:5 category:27 yξ:2 shown:3 matrix:3 rr:1 unital:36 spectrum:3 kummer:1 furthermore:1 since:71 crucial:3 ry:2 research:2 may:4 contained:8 omitted:1 ra:16 emerged:1 rc:1 denoted:1 formula:1 how:1 suffices:8 math:26 shows:16 i2:8 theory:8 reformulated:1 written:1 iz:3 monotone:28 limα:1 mapping:9 admits:2 atica:1 completely:35 noma:1 advantages:1 york:3 put:9 subalgebras:4 remainder:2 axa:1 edinburgh:1 definition:12 βv:2 derivation:2 fa:2 geometry:1 phrases:1 could:1 times:1 filter:9 turn:4 amodule:1 derivations:1 hence:32 uses:1 aen:1 onto:8 exhibited:1 frequent:1 first:31 separable:21 ultraweak:1 already:5 xn:13 xm:10 xb:1 u1:1 xa:4 number:2 rank:1 nested:2 ℓi:8 hι:1 un:21 relations:2 another:5 impossible:2 ring:16 precisely:4 open:54 illustrate:1 given:22 necessarily:3 embeddings:2 reference:1 categorical:2 introduction:1 unknown:1 adjoint:1 submodules:1 system:7 least:1 yij:6 xξ:2 belongs:5 assumption:12 too:1 statement:7 behaved:1 unambiguously:2 discontinuous:1 gives:2 relationship:1 tool:1 ιa:8 required:1 employ:1 part:10 j2:2 somewhat:1 authors:1 norms:1 x3:1 copy:1 undoubtedly:1 than:3 ηm:1 observed:2 kind:3 aaa:2 characterizations:1 alia:1 kaneda:2 zero:22 final:1 project:2 lim:20 elementary:1 determined:5 fm:16 monomorphism:2 were:1 mackey:1 enables:1 projections:34 pre:2 entail:1 generality:2 outstanding:1 ann:2 reduction:1 mind:1 matem:1 malabar:1 endomorphism:4 say:7 re:1 pieces:1 manner:1 close:1 need:7 seen:4 seem:1 recover:1 linked:1 relatively:1 mountain:1 depict:1 built:1 depending:1 describe:1 pursued:1 latter:4 sections:1 converges:3 note:22 instance:1 ideal:95 take:13 analogy:2 forming:1 interior:3 coincide:1 canonical:9 subscripts:1 play:2 converse:2 unless:1 uξ:9 shall:24 any:10 denoting:2 object:12 systems:2 gι:2 hw:7 most:3 regular:19 orthogonally:1 eag:1 automorphism:1 remarks:5 information:1 hu:4 class:7 rickart:3 subspaces:1 kb:11 kg:2 especially:2 considered:2 clear:5 sometimes:1 focussing:1 possesses:1 countable:13 paulsen:5 add:2 what:2 usual:1 typically:1 notion:4 fact:12 akemann:2 hyper:3 particularly:1 show:24 characterisation:1 supported:2 spain:1 functionals:1 implying:3 spaces:7 relation:7 subbimodule:1 ireland:1 subtle:1 analogue:2 uniform:1 trivial:1 find:15 pacific:1 fε:10 completion:14 o:1 46l05:1 x1:2 northern:1 ier:3 outside:1 contraction:3 separability:1 tomiyama:1 lemma:48 only:20 going:1 ambiguity:1 factor:1 identification:1 constant:2 he:8 local:21 similar:1 continuity:2 do:1 his:2 closed:103 notation:5 get:10 embeds:5 dd:2 de:5 self:2 aβ:6 negative:3 words:1 aζ:1 combinations:1 carries:1 bsa:1 aξ:3 prime:4 runs:1 increasing:12 evident:4 conditions:6 arxiv:1 yield:1 roy:1 recerca:2 berlin:1 exercise:1 contain:2 ban:8 london:9 implication:1 fixed:2 view:2 requirement:4 set:29 modulo:1 exists:16 principal:1 clopen:5 j1:2 module:38 hε:2 relative:1 ara:24 see:33 result:27 japan:4 showing:2 pi:4 subject:1 closer:1 satisfying:3 tensor:6 uλ:3 ways:1 supα:16 review:3 rings:6 representatives:1 symmetric:7 state:2 smallest:4 various:5 envelopes:19 between:22 ui:6 previous:4 approach:6 complement:3 x22:2 available:1 letting:5 bt7:1 restricting:2 recently:1 jy:1 complementary:1 importance:1 weak:1 arises:2 attention:3 measure:1 however:7 js:2 gratefully:1 vanishing:1 inclusions:4 hypothesis:9 jointly:1 key:1 multiplier:28 lb:8 ac:1 contractive:8 uρ:15 ker:3 topology:6 both:11 interpretations:1 last:5 reverse:2 complemented:1 giles:1 annihilators:3 many:4 taking:1 τi:11 equal:1 constructed:4 agree:5 etc:1 admit:2 present:1 embedding:4 inspired:1 asked:1 coincides:3 otherwise:1 unitarily:1 seminal:2 ci:3 relevant:1 cn:1 cm:3 point:2 simple:10 cb:41 ca:1 address:2 cf:6 ce:2 2nd:1 dimensional:9 ab:1 sakai:1 effros:1 xi:1 sequences:2 yi:3 respect:1 throughout:2 factors:3 kp:2 selfadjoint:1 mathieu:21 amer:2 described:3 commutative:11 wright:6 addition:1 computing:1 induces:1 due:1 nachr:1 pb:11 ai:3 faithfully:1 much:2 goes:2 basic:6 collected:1 algebras:77 pn:8 universal:5 empty:7 define:7 surjective:1 aj:1 corresponding:5 sufficient:1 propositions:2 subspace:5 essentially:5 cambridge:3 argument:16 fund:1 observe:4 understand:2 representative:6 bull:2 univers:1 general:5 fl:1 those:4 case:21 extracted:1 hξ:1 pitman:1 couple:1 look:2 subsets:16 ada:1 means:2 ij:1 strict:1 will:28 invoking:1 while:1 ar:9 suppose:25 soc:10 wild:1 investigating:1 xx:1 property:23 guide:1 procedure:2 correspondence:4 detailed:1 unitary:1 tholen:1 epimorphism:1 endowed:3 von:19 ir:6 thus:42 surprisingly:1 assertion:1 iv:2 ii:5 disjoint:6 itself:2 cone:2 dual:2 weakest:1 claimed:3 march:1 supremum:16 id:2 proc:1 pap:2 containing:16 verified:1 author:2 arguments:1 make:4 belong:4 shorten:1 same:15 clearly:5 x2:2 complex:2 emphasize:1 largest:1 proved:1 finite:31 subalgebra:19 composition:1 isometries:6 difficult:1 fairly:3 schelter:1 used:1 context:1 trivially:1 i1:15 comprehensive:1 oper:1 dgi:1 functions:6 hand:8 hulls:1 ly:5 spanned:1 infinite:5 frequently:1 yf:3 identity:26 recent:2 lower:1 weakly:1 proceed:3 studies:1 min:1 well:11 know:2 thought:1 academic:1 without:4 components:1 sets:3 factorised:1 undertaken:1 gδ:8 matema:1 cca:1 stating:3 ccc:1 left:25 isometry:14 adjointable:1 construct:3 just:1 less:2 being:2 when:4 resp:4 identically:1 obtain:27 mloc:94 press:3 unclear:1 identify:4 atomic:1 questions:1 immediately:5 krieger:1 yet:2 projection:30 begin:2 unique:25 preprint:1 classification:1 k2:2 decomposition:1 conclude:11 royal:1 k1:2 lattice:7 ruan:1 setting:4 extends:3 easy:4 theorem:76 role:5 cex:1 real:3 aspects:1 gρ:1 depends:1 isomorphisms:2 rules:1 characterise:2 decomposed:1 implications:1 possible:2 bijective:4 corresponds:1 possibly:1 five:2 partial:1 interfaces:1 using:6 accepted:1 moreover:12 wiss:2 mod:1 loss:1 injectivity:5 necessary:1 helpful:1 semi:1 identifying:2 university:1 follows:43 auto:1 belfast:2 intertwines:1 yields:9 either:1 martin:19 multiplicative:1 simply:3 canonically:4 inter:1 page:7 terminology:2 therein:1 copies:1 because:5 neumann:19 namely:1 sequence:6 universitat:1 some:38 catalunya:1 feel:1 algebraically:30 ideals:39 understood:1 elements:12 include:2 examples:3 paragraphs:1 images:1 extended:2 classes:1 provided:5 cp:1 dense:47 lead:2 univ:2 though:1 isometrically:6 per:1 does:9 exposition:1 provides:1 assuming:3 icr:3 confusion:1 intersections:1 closely:1 symbol:1 minimal:12 refer:1 considering:2 uniformly:1 equivalent:12 arbitrary:4 uj:4 bi:4 bj:4 interval:3 notably:2 submodule:13 step:1 nowhere:1 putting:1 approximating:1 bx:8 properties:13 injective:95 quotients:52 pα:13 central:2 baer:2 extension:13 enlargement:8 choi:1 aˆ:2 introduces:2 qmax:59 oa:1 essential:130 compatible:2 sake:1 whence:3 a2:7 idj:2 rule:1 idi:11 idf:1 introduced:4 consequently:11 morphism:8 vi:2 a0:12 contractions:3 convergent:1 bja:4 inclusion:7 h2:2 unbounded:1 into:23 h1:2 ηk:1 isomorphic:6 three:1 right:117 references:1 supn:1 determine:3 operator:59 alas:1 next:8 vj:4 methods:4 span:2 additional:3 ζm:6 refinements:1 support:3 there:63 question:13 approximate:18 why:1 occupy:1 pa:10 inner:3 way:3 infinitedimensional:1 was:14 gij:4 naturally:1 function:13 interrelation:1 arise:2 complete:39 form:15 enough:1 ea:2 believe:1 differences:1 agrees:4 independently:2 but:7 back:2 hk:1 hh:1 construction:12 hn:12 borel:1 basis:8 convergence:1 lectures:1 line:1 true:2 hg:2 partially:1 hamana:14 made:1 applying:8 mat:1 embedded:3 whether:5 izi:1 inside:4 up:7 us:6 um:10 supi:1 below:2 projecting:1 limit:12 iterated:1 sum:3 observation:4 locally:2 problem:3 subclasses:1 called:11 recalling:1 aa:21 irish:1 kh:12 intersects:1 ag:4 af:1 defined:11 stronger:1 abstract:1 convex:2 lanning:3 denote:25 proper:5 proves:1 exist:4 barcelona:3 aw:61 ax:16 inf:2 approximated:1 union:3 ida:1 aeα:4 again:2 extending:2 completeness:2 faithful:2 nn:1 no:6 whereas:1 generally:1 detail:2 multipliers:3 other:13 essentiality:8 details:3 normal:8 department:1 mathematics:2 lance:1 generalitat:1 completes:1 herrlich:1 sided:18 time:1 problems:3 a1:4 hausdorff:6 generated:7 important:6 bounded:39 ξm:15 ξn:29 gap:1 sides:1 structure:10 algebraic:6 implies:10 auxiliary:1 assume:10 normally:1 space:49 modules:18 agb:2 together:7 noncommutative:1 came:1 remarked:1 n0:7 introductory:1 requires:1 once:3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.