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0705.1282.txt |@word concept:3 similarity:1 dynamic:6 y2:2 existing:4 leads:1 c3:14 amplified:1 issues:2 rigidity:2 devoted:1 whose:2 aligned:1 terms:1 calculate:3 khalil:1 imme:1 editors:2 presents:1 quasi:1 under:5 include:1 presentation:1 cnc:1 applied:1 belonging:1 βq2:6 15a:1 orthogonal:9 far:1 springer:1 geometrical:1 putting:1 figs:1 matrices:1 clement:1 condition:11 bρ:1 illustrated:1 presented:4 transmission:21 positions:2 companies:1 prototypes:2 large:1 ρi:2 vector:5 small:4 eigenvalues:2 θq2:5 equation:2 attracting:1 work:1 force:4 wieland:1 direct:1 13a:2 second:5 cost:1 design:5 quebec:2 machines:2 aim:2 optimize:1 developed:1 stands:1 invertible:1 chicago:1 section:8 axes:8 ρmin:3 uniform:1 version:1 boundary:1 3c:1 3b:1 3a:2 principal:3 acknowledgments:1 body:1 philippe:1 pose:1 degree:2 leg:4 respectively:7 commercial:1 proc:4 here:1 bi:26 following:1 amplification:1 directions:8 path:1 along:9 equations:7 z3:1 study:6 vectors:2 resulting:2 symmetrical:1 ago:1 family:4 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0705.1298.txt |@word int:4 p¹:4 may:1 physics:1 γint:5 arxiv:1 rmax:12 lmax:2 o:1 kγ:1 k2:1 c¹:1 kmax:4 rº:4 pint:1 max:1 cr:2 l¹:5 data:1 b¹:1 npr:2 |
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0705.1316.txt |@word consider:5 funct:1 results:2 four:1 kuleuven:2 proposition:8 ga:9 certainly:1 γk:2 γj:4 finally:3 those:1 th:3 very:3 dokl:2 corollary:3 every:2 entries:1 matrices:5 condition:3 leads:3 hamiltonian:1 turns:1 list:1 large:1 admissible:1 commute:2 small:1 anal:1 upper:4 says:1 zi:15 zj:6 zk:5 direct:1 zero:7 further:1 theory:1 what:1 brackets:6 section:1 expressed:1 above:6 new:3 satisfy:2 respectively:3 here:2 desired:1 them:1 address:3 z4:6 equations:6 z1:22 z2:15 z3:14 obtained:1 remark:2 study:3 vectors:1 contradiction:4 leaving:3 products:2 poisson:1 involves:1 quotient:2 extra:1 e5:2 austria:1 total:1 use:5 prove:1 γi:13 next:1 associator:1 therefore:1 type:1 more:2 operators:7 filiform:3 particular:2 known:1 cases:4 must:1 frobenius:1 equation:1 unknowns:2 obvious:1 following:10 example:7 proof:12 claim:1 expanding:1 high:2 huge:1 provide:2 verify:2 holds:1 write:2 answer:1 e2i:1 e2j:1 product:9 description:1 algebra:44 may:1 derived:1 hence:6 date:1 fi:20 fj:12 fk:6 fm:1 fn:2 realized:1 natural:2 computations:1 fu:1 summing:1 element:1 rather:1 so:5 specifying:1 fundamental:1 order:1 lsa:4 indeed:2 over:4 satisfied:6 paper:1 y1:36 existence:3 y3:13 y2:25 chosen:1 affine:5 coordinates:1 choose:1 jacobi:3 mail:3 yi:3 yk:4 yj:9 combination:2 dim:1 introduce:1 differential:1 leuven:1 they:1 now:5 easily:1 term:1 universita:1 each:2 x10:1 x11:2 x12:2 x13:5 2j:1 2k:2 en:3 ei:10 ek:2 ej:11 doing:1 series:5 hard:1 related:2 elementary:1 obtains:1 our:2 out:1 shown:4 matrix:1 space:1 furthermore:3 since:4 f1:3 vector:1 geom:3 ra:1 denoted:1 induction:2 math:3 shows:4 linear:5 dietrich:2 free:5 standard:1 admits:11 ask:1 e4:30 e7:1 e6:1 e1:63 e3:29 e2:37 definition:2 determining:1 could:1 hopeless:1 consequence:2 xij:6 first:7 xj:29 xk:20 xi:46 xn:2 variables:7 multiplication:6 least:1 another:1 impossible:1 size:1 given:9 similarly:3 introduction:1 unknown:1 adjoint:3 system:5 relations:1 appl:1 calculations:2 convention:1 structures:18 gives:1 immediate:1 x8:3 x9:3 x2:31 x3:25 translation:1 x1:33 x6:3 x7:4 x4:24 x5:5 second:1 were:1 treated:1 motivation:1 mind:1 argument:1 already:2 say:1 need:2 seen:2 any:8 complete:1 lie:46 note:7 ideal:13 most:2 position:1 pair:1 class:7 clear:1 universiteit:1 bracket:2 fact:2 show:9 trivial:1 find:4 knowledge:1 lemma:17 only:4 generators:5 positively:1 local:1 abelian:1 get:1 express:1 obtain:5 nilpotency:2 ones:2 gel:1 arxiv:1 yield:2 hydrodynamic:1 exists:2 see:7 result:4 triples:1 satisfying:1 fand:1 symmetric:3 invariant:1 conditions:1 terms:5 however:2 hypothesis:1 dependance:1 dorfman:1 dedicata:1 taking:1 etc:1 admit:9 une:1 otherwise:1 conclude:1 simple:1 karel:2 table:1 considering:2 benoist:1 described:1 basis:10 addition:1 wien:2 three:3 reduction:1 algebras:26 define:2 direction:1 corresponding:1 concerning:1 denote:8 present:2 case:7 will:5 while:1 suppose:1 property:1 studied:1 non:3 same:4 fakulta:1 finite:1 difficult:1 univie:1 trivially:1 hand:2 uses:1 kim:2 identity:16 katholieke:1 lower:2 task:1 center:3 well:1 without:2 entry:1 soviet:1 dimension:2 left:7 construct:1 graded:1 generally:1 resp:5 solvability:4 using:3 previous:2 generator:1 nilpotent:16 seems:1 questioned:1 easy:5 solvable:4 remaining:1 february:1 admitting:1 know:3 background:1 belgium:1 immediately:2 dimensional:1 follows:10 yields:1 arbitrary:3 accessible:1 right:5 classical:1 some:2 ideals:11 deduce:1 examples:2 sight:1 respect:1 nonzero:1 dimensions:1 does:4 δj:1 run:1 δi:1 step:15 central:4 algebraic:1 column:1 novikov:68 zelmanov:1 because:12 references:2 determine:1 sov:1 operator:6 strictly:1 there:5 question:4 start:1 quadratic:2 lot:1 was:5 elsewhere:1 form:2 triangular:4 but:1 contradictory:2 trying:1 true:1 applying:1 whether:2 characteristic:1 up:1 us:2 below:1 similar:2 called:2 multiplications:2 detailed:1 ac:1 associated:4 ad:22 defined:2 abstract:1 general:1 exist:2 families:2 identities:5 campus:1 defines:3 xkj:1 again:4 no:2 mathematik:1 when:5 vanishes:1 field:2 other:7 nr:1 elements:6 sided:7 commutator:2 generated:2 allowing:1 structure:30 implies:5 assume:5 required:1 burde:9 time:1 having:1 once:1 |
0705.1317.txt |@word ga:39 c2:2 expressions:1 adjustment:1 centers:2 concerned:2 presents:2 umich:1 analogous:1 case:7 mpc:7 far:3 choice:1 every:2 presented:3 positions:1 cmb:43 large:2 convenience:1 yukio:1 edu:1 sin2:1 zero:1 further:2 estimated:1 even:1 established:1 plays:2 sun:14 expressed:2 above:3 new:1 acknowledgments:1 respectively:2 component:2 understanding:1 appears:1 obtained:3 great:1 burstein:1 larger:1 resulting:1 makes:1 useful:2 extra:1 explained:2 vin:1 outcomes:1 apj:2 addressed:1 total:8 would:2 comparing:1 therefore:1 theoretical:1 started:1 iii:1 must:2 ii:2 equation:1 mi:1 obvious:1 following:1 proof:2 2x10:1 bell:1 stated:1 calculation:1 expanding:1 performed:1 occur:1 information:1 arbor:1 end:1 discussion:2 located:1 rubin:1 significance:1 instead:1 ordinary:1 sin:2 cosmic:2 may:2 southern:1 law:5 parallel:1 types:6 coyne:1 cosmology:12 blueshift:1 order:3 interpretation:2 motions:1 existence:1 galaxy:11 observational:1 lc:4 chosen:1 coordinates:2 melchiorri:1 h0:5 correspondence:1 framework:1 now:1 discuss:1 nor:1 term:3 hereafter:1 university:3 possibilities:1 magnitude:2 radial:2 found:1 characterized:1 ed:1 related:1 accidentally:1 obtains:1 measurement:1 laboratory:1 eq:25 special:1 shown:1 since:3 rev:2 increase:1 ra:1 rb:1 formula:2 cause:2 inevitably:1 galaxies:3 possibility:1 members:1 randall:1 hubble:23 r1:2 r2:2 could:1 ds2:1 creates:1 stewart:1 origin:4 peculiar:25 directly:1 given:4 cartesian:1 temperature:2 introduction:2 unknown:2 system:8 their:1 assumption:1 listed:1 statement:2 dt2:1 relationship:1 centered:1 explanation:3 lynden:1 part:1 than:1 intrinsically:2 distance:4 determines:1 princeton:1 rate:1 determined:1 were:1 ann:1 dθ2:1 seen:1 clearly:1 conversion:1 realm:1 built:1 depending:1 note:1 internal:1 towards:6 unless:1 opposite:3 friedman:2 object:1 nothing:1 observation:2 considered:1 calculated:1 flow:17 km:23 kr:1 points:1 sciama:3 velocity:33 physics:3 fact:1 dipole:48 based:1 explain:1 should:2 virgo:7 lemma:1 constant:1 local:1 michigan:3 cannot:3 words:4 tomozawa:2 dr:1 arxiv:1 yield:1 summary:1 implication:1 set:1 exists:1 observed:10 computes:1 result:2 cosmologies:1 outside:1 future:1 neither:1 terms:2 relative:12 nature:2 however:1 vanishing:4 key:1 article:1 emitter:1 thank:1 both:2 cos:4 last:1 resides:1 dated:1 finds:1 otherwise:1 point:11 respect:1 considering:1 described:1 due:4 been:1 much:1 ph:1 supercluster:7 direction:7 corresponding:1 2vh:3 understand:1 tνµ:1 astron:1 instant:1 present:2 applied:1 look:1 value:5 choices:1 will:3 vc:4 vh:14 thus:1 surface:1 iv:1 vp:15 cluster:13 different:1 author:7 balloon:2 radiation:1 same:4 any:5 member:1 gets:2 status:1 used:1 v1:2 v2:2 arrived:1 necessity:1 vvh:1 center:38 200km:1 obviously:1 without:1 coordinate:4 position:3 rest:2 dφ2:1 distant:1 conclude:1 except:2 source:1 location:2 theorem:7 identical:1 around:1 february:1 department:2 know:1 background:2 press:1 using:5 pertinent:1 like:2 alternatively:2 velocities:4 yields:3 faber:1 understood:1 infall:3 scale:2 mology:1 microwave:2 does:1 dipoles:3 bc:4 equivalent:2 each:4 expansion:9 relating:1 fixsen:1 usa:1 universe:24 theorems:2 discussed:3 letters:1 redshift:4 communication:1 into:1 appropriate:1 determine:1 proportional:1 there:7 was:1 assumes:1 naturally:1 rees:1 differences:1 but:3 astro:1 hemisphere:1 solar:8 compute:4 whether:1 up:1 below:1 limit:1 distribution:2 similar:1 prevails:1 detailed:1 associated:1 implications:2 abstract:1 linearity:1 examine:1 proves:1 exist:1 inf:1 physical:1 no:5 when:1 vanishes:1 application:1 other:6 role:2 igo:1 conclusion:2 meaning:2 important:1 astronomy:1 implies:3 assume:2 equivalently:2 |
0705.1318.txt |@word represent:2 consider:2 osp:1 results:1 illustrated:1 generalize:1 edu:2 finally:1 th:10 supported:1 straightforward:1 connects:1 witten:1 parameter:1 annihilated:3 hamiltonian:15 eigenvalues:2 noted:1 zm:3 zn:3 navratil:1 sukhatme:1 cond:1 second:1 dedonder:1 odd:1 even:4 above:1 acknowledgments:1 filled:2 full:4 ibid:2 orbitals:2 ansatz:5 groups:1 address:2 strong:4 equations:5 z1:3 z2:1 study:1 studied:1 resulting:2 action:1 nmax:12 would:2 supergroups:1 quasi:1 next:1 nucl:12 qcd:1 zin:1 bethe:5 more:2 operators:5 appendix:4 hole:4 balantekin:9 amado:1 groeling:1 erratum:2 science:1 equation:1 work:1 zirnbauer:1 theories:1 concepts:1 following:2 strategies:1 example:2 discussed:1 arise:1 states:21 numbers:1 allowed:1 information:1 end:1 supersymmetries:1 pair:6 fourth:1 explains:2 de:1 mat:1 fw:1 may:1 applications:2 fd:1 cannata:1 summarize:1 paar:1 dynamical:2 bijker:4 uzer:1 spectra:7 su:2 writing:1 sc:1 jolie:3 casten:1 satisfied:2 committee:1 iachello:3 existence:1 satisfies:1 its:2 energies:3 exhibits:3 li:1 fig:2 arias:1 supersymmetry:15 isacker:1 non:2 outlined:1 introduce:1 compound:1 mimicking:1 discuss:1 easily:1 february:1 fully:1 university:2 alternately:1 each:2 found:1 entirely:1 2j:1 metz:1 energy:13 related:2 connect:1 sketched:1 quantum:6 relates:1 approximated:1 transitions:1 eq:18 out:1 shown:2 jackson:1 matrix:2 since:1 rev:15 research:2 denoted:2 ref:1 foundation:2 wisconsin:4 linear:1 frank:2 loyola:1 completely:2 khare:1 hep:3 sˆj:7 muller:1 degeneracies:2 pairs:17 interaction:2 hence:4 first:3 separable:2 xk:1 pairing:12 xn:1 symmetry:2 xm:2 relate:1 number:3 jesus:1 utilized:1 electronic:2 given:7 eqs:1 zk:2 system:2 pittel:1 fermions:1 gives:1 shell:3 nilsson:1 alonso:1 reversed:1 exactly:1 guhr:1 draayer:1 part:2 x2:1 x1:1 than:3 showed:1 zero:7 were:1 exhibit:1 manner:1 occupied:1 tells:1 note:1 though:1 most:1 wettig:1 nothing:1 considered:2 alumni:1 exp:1 mechanical:2 physics:5 madison:1 show:4 fricke:1 random:2 solutions:2 keywords:1 subtle:1 find:3 ground:2 partners:3 parameters:1 written:2 should:2 hamiltonians:4 notation:1 rept:3 exchanges:1 exhibiting:1 arxiv:13 graw:1 orthosymplectic:1 hatchell:1 bars:2 national:1 namely:1 techniques:1 satisfying:1 nuclear:9 state:15 various:1 between:3 approach:1 available:1 terms:1 however:1 dereli:1 jm:1 here:1 jj:1 article:1 barrett:1 many:1 equal:2 verbaarschot:2 dated:1 schafer:1 cj:9 actually:1 transformations:1 aˆ:4 addition:3 been:1 ph:2 empty:1 define:1 supersymmetric:16 sˆ:47 worked:1 spin:1 pacs:1 ǫj:2 value:1 while:1 unpaired:1 refs:3 dobaczewski:1 ii:1 converts:1 partner:6 fermion:1 dukelsky:1 cjj:2 different:2 grant:1 granted:1 same:2 clearly:4 complex:1 several:2 pan:1 used:1 see:2 phy:1 invariance:1 solve:1 sets:1 model:1 arising:1 spherical:1 less:2 moments:1 half:4 obtain:1 underlying:2 transforms:1 scattering:1 eigenstates:5 except:1 lett:10 easy:2 iπ:1 solvable:1 eigenstate:4 identical:3 vacuum:3 using:4 moshinsky:1 mod:1 like:2 particle:8 reduces:1 schmitt:1 arbitrary:1 provided:1 cooper:1 extensively:1 does:1 connecting:2 broken:1 although:1 about:1 usa:1 introduces:1 o:1 plus:1 introduced:1 considerations:2 into:1 h1:1 phase:1 operator:4 van:1 there:3 bosons:2 was:3 form:1 funds:1 but:2 wisc:2 maximum:1 us:2 heinze:1 below:1 ωj:5 limit:4 highlight:1 problem:1 similar:1 mechanics:4 leviatan:1 int:1 aj:3 geyer:2 general:2 tˆ:16 single:2 corresponding:1 no:3 when:2 detail:1 application:1 other:2 role:1 details:1 department:1 kinds:1 models:1 commutator:1 nucleus:1 structure:2 correlated:1 coupling:4 pseudo:1 equivalently:1 cejnar:1 ormand:1 time:1 nuclei:3 |
0705.1319.txt |@word magnetically:1 represent:5 code:2 magnetic:62 spie:1 dynamic:2 emerging:3 four:2 disc:11 consists:1 follow:2 rectangles:1 polarity:3 paris:1 send:1 ıa:1 does:1 present:3 determinations:1 nodes:3 mpg:1 lites:4 very:4 rise:3 results:2 mps:1 anonymous:1 dominate:1 level:5 hanle:2 rectangle:2 large:1 vector:15 small:9 eigenvalues:1 optics:1 configurations:1 upper:1 averaged:1 internetwork:22 29th:1 consistent:1 estimates:1 direct:1 photospheric:2 enclosed:1 further:2 estimated:1 spectral:2 appear:1 giving:1 sun:8 selected:3 current:1 bipolar:2 above:3 chromosphere:2 values:6 staff:1 filled:1 canarias:1 layers:1 full:1 chose:1 degree:1 respectively:5 component:8 residual:1 here:2 understanding:1 shortened:1 separation:1 others:1 represented:1 path:1 along:3 standard:1 observing:1 search:1 institute:1 study:1 vectors:1 allows:2 casini:2 polarimeter:1 base:1 procedure:1 egger:1 hospitality:1 fourier:1 studies:1 plotted:2 projection:1 scales:1 marked:1 apj:9 visible:2 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0705.1320.txt |@word limited:3 comparatively:1 dynamic:17 hinrichsen:1 four:1 controversial:1 sch:2 calculate:12 under:2 worth:2 divergent:3 summarizes:1 unrenormalized:1 affect:1 logarithmically:1 cause:1 solution:6 heger:1 convenience:1 announced:1 aachen:2 markov:1 10b:2 consistent:2 10a:2 estimates:2 direct:4 approximation:29 second:5 2aγ:2 correlator:4 chen:6 qualitatively:4 implemented:2 even:7 errors:1 incompatible:1 above:23 ˆg:1 new:8 gl2:1 increasing:3 seeks:1 behavior:27 residual:1 here:20 active:6 path:6 placeholder:2 logarithmic:9 obtained:1 study:8 advantages:1 fourier:1 appropriately:1 divide:2 classification:1 9a:1 9c:1 explained:1 redefinitions:1 specifics:1 glance:1 circumvent:1 plot:3 would:2 negative:2 m4:1 noting:1 m1:7 therefore:13 m2:1 populations:1 naive:1 separates:1 must:17 dominicis:2 springer:1 word:1 work:12 theories:2 initial:1 renormalization:21 indicated:1 give:1 stressing:1 caution:1 feasible:1 end:1 provide:4 feature:2 revisit:2 how:2 enz:1 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