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0705.1171.txt \|@word consider:4 funct:1 neigborhood:1 proposition:6 generalize:1 follow:1 disk:4 whose:1 2n0:3 depend:1 equivalence:1 uniqueness:1 th:1 under:2 choice:1 corollary:2 cofinite:2 every:9 compacta:2 dim:4 annihilated:1 riemann:3 louis:1 leave:1 solved:1 vector:1 small:1 anal:1 neighborhood:6 second:3 oneto:1 linear:3 even:2 appear:2 section:6 uniform:2 coefficient:3 degree:1 respectively:2 equations:1 obtained:1 suitable:1 quotient:1 via:1 decrease:1 annihilator:1 subalgebras:1 unit:2 derivatives:3 use:1 proceed:1 prove:3 positive:1 contains:4 finally:1 call:1 therefore:8 indiana:1 more:1 gamelin:2 particular:1 must:5 science:2 work:1 codimension:16 root:1 example:1 proof:6 figure:2 conversely:1 lemma:6 rather:1 means:2 how:1 pair:2 parameter:1 map:14 algebra:30 may:2 max:1 earlier:1 mapping:2 fa:1 multiplication:1 transitive:1 light:1 st:1 so:9 decreasing:1 representation:2 order:11 restriction:1 over:1 satisfied:1 paper:2 existence:1 satisfies:1 its:3 group:1 singular:2 la:1 jim:1 actually:1 derivative:2 into:3 maximal:2 cusp:30 non:2 parabola:5 surrounds:1 rotations:1 inductively:1 they:2 now:2 february:1 stabilize:1 always:1 university:1 sufficiently:1 iff:1 each:9 cusps:9 2n:15 side:1 2j:1 mean:4 en:6 neil:5 eh:4 related:1 shown:1 unital:1 furthermore:1 since:3 induces:2 mccarthy:2 looking:2 contained:1 jolla:1 formula:1 get:1 induced:1 occurs:1 math:3 foundation:2 theory:3 homeomorphism:2 california:1 univalent:2 put:1 ord:11 definition:1 agler:2 βn:1 onto:3 βj:1 first:3 origin:6 singleton:1 unimodular:1 multiplying:1 directly:1 open:3 paulsen:1 given:2 hyperbolic:1 introduction:1 system:1 πr:2 their:1 john:1 holomorphic:6 exactly:1 required:1 authors:1 coefficients:3 finitely:1 namely:1 w2:2 pre:1 shrinks:1 generalization:1 say:7 seen:1 any:2 zero:2 min:1 self:1 ideas:1 note:1 ideal:1 square:1 sufficiency:1 singh:1 shall:9 petals:1 automorphism:1 remarks:1 parametrize:1 χr:2 neighborhoods:2 coincides:1 codimensional:3 points:3 χn:1 χk:3 saying:1 show:4 supported:5 spaces:1 relation:2 d2:1 find:1 principal:1 analytic:2 only:7 summarizing:2 local:3 preliminaries:1 do:1 di:1 michigan:1 between:1 closure:1 arxiv:1 fixed:1 satisfy:1 moduli:2 set:6 exists:1 national:2 connections:2 see:4 result:1 w1:3 concern:1 surfaces:1 away:1 functionals:1 dms:2 bruno:1 simplest:1 αi:1 invariant:2 αj:1 αm:2 pictured:1 αn:5 terms:1 vanishing:1 topology:2 both:3 essentially:1 agree:1 connection:5 cod:11 context:1 comes:1 con:11 cj:1 cn:8 point:7 simple:16 continuation:1 corresponds:1 dimensional:1 adjoining:1 polynomial:2 moreover:2 throughout:1 san:1 pr:1 locally:5 three:1 algebras:4 biholomorphic:2 define:5 arises:1 corresponding:2 quantities:1 sufficient:1 maps:4 observe:1 curves:1 c2:5 c1:3 c0:2 those:1 c4:1 p2:4 p1:4 will:3 suppose:2 aij:1 property:1 petal:5 ii:1 vr:3 primitives:1 containing:1 grant:2 same:2 another:1 proved:1 finite:9 subalgebra:6 embedding:2 diego:1 hand:1 v1:12 v2:11 purpose:1 necessity:1 thought:1 thm:3 contact:5 sets:1 dimension:1 rest:1 except:3 theorem:5 real:1 evaluate:1 background:1 integer:1 unique:5 follows:3 arbitrary:1 because:2 sequence:1 some:12 proper:4 dense:1 dimensions:1 equivalent:4 expansion:1 restrictive:1 injective:4 integers:2 cn0:2 most:2 o:23 2k:2 primitive:11 inclusion:1 h2:8 image:3 h1:8 washington:1 functional:4 lies:1 right:1 references:1 support:1 there:19 u1:2 u2:2 way:1 was:1 function:7 form:3 hr:3 triangular:1 but:3 hn:1 repeatedly:1 convergence:2 partially:2 applying:1 wish:1 attached:1 up:1 us:2 un:8 distribution:1 called:1 zeroes:3 taylor:4 constant:2 ag:1 defined:3 ah:6 abstract:1 aj:2 general:1 globally:3 single:1 ni:1 functions:6 no:4 when:2 vanishes:2 other:1 denote:2 polynomials:2 a1:5 generated:1 a2:3 bounded:2 sides:1 algebraic:4 assume:2 space:4 modules:1 missouri:1 n0:8 starting:1

0705.1172.txt \|@word proposition:7 precise:1 internat:1 partial:2 dx:2 proposed:1 fa:1 results:4 course:1 wiener:7 spaces:12 london:1 solutions:4 immediately:2 letters:1 consider:1 compact:2 whose:1 derive:2 based:1 chosen:1 theorem:2 basel:1 editors:1 actually:2 forms:1 only:1 contractible:1 equipped:1 set:1 hamiltonians:2 dn:1 do:2 delhi:1 chennai:1 invoke:1 very:3 advances:2 de:12 db:1 choice:1 early:1 corollary:2 every:2 they:2 new:1 jacob:1 using:4 dt:2 unique:3 matrices:1 discuss:2 dp:2 krishna:1 february:1 covering:2 turns:2 university:3 arxiv:2 expansions:1 solution:1 factorization:1 separately:1 theory:1 paper:2 l2:2 each:2 indices:1 2n:2 notes:1 asymptotic:1 view:1 mathematical:2 weyl:4 modulo:1 methods:1 classical:2 maurice:1 det:3 leray:1 some:1 back:1 lp:4 radha:1 see:3 investigated:1 thangavelu:1 result:4 arg:1 quantum:5 terms:2 forthcoming:1 out:2 cambridge:3 index:3 flp:3 matrix:2 space:1 continuity:1 µw:3 since:1 lagrangian:2 consequence:1 research:1 symmetric:1 modulation:2 written:2 determined:1 geom:1 above:1 formula:1 rn:2 proc:1 sp2:1 math:2 differential:2 publishers:1 college:1 guillemin:1 recently:1 linear:1 amalgam:7 arbitrary:1 however:2 standard:1 translated:1 groups:3 represented:1 group:9 estimate:2 quite:1 equations:3 properties:2 simpler:1 obtained:1 definition:1 about:1 algebraic:1 technical:1 study:4 prove:2 maslov:5 wavelets:1 quantization:1 motion:1 deserves:1 allied:1 symplectic:5 action:1 inst:1 introduced:1 auser:1 mechanics:4 locally:2 real:1 projection:1 metaplectic:11 claim:1 press:3 ca:2 corresponds:1 demazure:1 will:1 unitary:2 references:1 france:1 operator:5 nicola:8 writing:1 follows:2 necessarily:1 lq:7 exists:1 strasbourg:1 their:4 introduction:1 come:1 continuous:1 there:3 rcp:1 due:1 been:1 imperial:1 hamilton:1 few:2 faithfully:1 quadratic:4 therefore:1 way:1 series:1 ph:1 topology:1 type:1 ann:1 vienna:1 function:1 etrie:1 grenoble:1 corresponding:1 complete:1 newtonian:1 integers:1 remark:2 operators:9 exactly:1 analyse:1 odinger:9 validity:2 principles:1 berlin:1 related:1 studied:1 particular:1 lifting:1 subseries:1 level:1 kashiwara:1 appear:1 usefulness:2 double:1 equation:9 oscillator:1 depends:1 aim:1 geometry:1 coll:1 classes:2 obvious:1 mp:6 applies:1 following:1 exist:1 similar:1 proof:4 f0:4 gosson:10 larger:1 associated:1 abelian:2 vol:1 cover:1 abstract:1 thus:3 1980s:1 regularity:4 associates:1 im:1 analysis:1 conf:1 ax:1 hamiltonian:2 orders:1 feichtinger:9 lie:1 different:1 january:1 holds:1 fourier:1 bremen:1 note:1 dependent:2 report:1 mathematics:1 flow:1 techniques:1 parameter:2 mit:1 conclusion:1 r2n:1 product:2 literature:1 cocycles:1 algebra:1 may:1 symbol:2 wiley:1 birkh:1 applications:4 connected:1 immediate:1 representation:5 remarks:1 pages:1 structure:2 recent:1 short:1 schr:9 consequences:2 assume:2 sp:9 well:1 eom:1 vch:1 cordero:8 mass:2 ege:1 sternberg:1 time:2 claims:1 physics:2 fact:1 subgroup:1

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0705.1193.txt \|@word represent:3 evidence:1 chain:2 maximum:1 rev:9 magnetic:1 global:1 desirable:1 amplifies:2 yellow:1 leads:22 circuitry:2 divalent:1 edu:1 consists:1 sci:1 negf:3 soc:1 whose:1 simon:1 depend:2 νth:1 palladium:1 vardeny:1 res:1 environment:2 charge:5 device:25 thiol:1 henderson:1 kσ:2 nσ:7 hibbs:1 ckσ:2 g0:4 very:1 amplifier:1 connects:1 wave:1 hybridize:1 electron:14 novel:1 every:1 entries:1 difference:3 continued:1 4ev:3 ibm:1 treating:1 illustrated:1 aσ:2 vibrational:1 presented:1 transmission:11 ref:5 pacs:1 solution:1 integrated:2 large:4 discrete:1 kondo:1 progress:1 science:2 small:3 nos:1 shows:2 configurations:3 upper:1 smaller:1 foundation:1 consistent:3 parameterization:1 estimates:1 direct:2 fold:3 second:6 street:1 dissipation:1 traveling:1 500k:1 qualitatively:1 chem:7 even:1 tang:1 plays:1 mσ:2 iterating:1 incompatible:2 ohno:2 section:4 current:22 public:1 bipolar:1 above:1 values:2 tips:1 increasing:2 method:3 contrast:1 condensed:1 full:2 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0705.1194.txt \|@word magnetically:1 concept:2 consider:4 chinese:2 caused:1 magnetic:11 results:5 gg:1 mirage:1 remarkably:1 causes:1 calculate:2 subjected:1 quasi:2 under:3 cm3:1 inject:1 applied:1 supported:1 straightforward:2 outside:1 very:1 geometrical:1 resonant:1 experimentally:3 condition:1 look:1 illustrated:1 exits:1 level:8 positions:1 solution:2 large:1 vector:1 path:4 optics:6 fleischhauer:2 upper:1 smaller:4 consistent:3 ωac:2 ωab:2 approximation:3 zero:1 traveling:1 7th:1 further:3 linear:9 even:2 index:8 nonlinear:1 trapping:1 sun:1 butterworthheinemann:1 while:3 expressed:1 uniform:1 current:1 lights:1 experiment:13 above:4 lifshitz:1 new:2 method:2 filled:1 respectively:5 here:1 atoms:4 following:1 china:2 sinh:2 irrespective:1 consideration:1 along:7 strong:3 equations:1 obtained:3 undeflected:2 inhomogenous:1 institute:2 incidents:1 study:1 studied:3 allows:1 characterizing:1 resonance:3 makes:2 via:1 spatially:2 explained:4 aphy:1 electromagnetically:2 stern:1 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0705.1195.txt \|@word convolute:2 secondly:2 quarks:5 gs:12 consider:5 qian:1 depends:1 forbidden:7 φp2:2 results:14 2c1:6 four:2 ali:1 expressions:3 contributions:15 seemed:1 devoted:1 whose:3 glimpse:1 depend:1 calculate:5 concerned:6 technique:1 tr:72 finally:1 program:1 those:1 4nc:33 exit:1 include:2 kν:8 divergent:2 p2:107 supported:1 amplitudes:21 q2ρ:2 far:3 b153:1 account:1 induce:1 splitting:1 endpoint:2 ultraviolet:1 iup:1 difference:4 logarithmically:1 categories:1 treating:1 trj:12 level:5 cause:3 mb:2 guo:1 large:2 vector:4 dealt:1 scadron:1 noted:3 upper:2 smaller:4 consistent:2 prediction:2 literature:5 sign:1 approximation:1 rate:6 lepage:1 denner:3 correlator:3 further:3 estimated:2 d4:28 theory:1 even:5 section:3 expressed:2 current:1 tkm:2 above:8 obvious:2 brambilla:1 acknowledgments:1 contrast:1 hebei:1 full:1 escaping:1 reliably:1 respectively:16 here:2 ozi:15 believed:1 mev:35 china:3 free:1 based:4 strong:1 appears:1 logarithmic:1 extreme:1 obtained:3 remark:1 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0705.1203.txt \|@word secondly:2 homomorphism:3 consider:12 funct:1 pairing:10 bull:1 focus:1 scalar:4 proposition:21 grateful:1 consists:3 partial:3 remarkably:1 denotes:1 ıs:1 gˆ:59 tn:32 γi:6 tj:2 preserved:1 γm:4 ti:6 ebres:2 analogous:2 include:1 applied:5 provides:3 straightforward:2 orthogonal:6 choice:2 corollary:17 valued:1 every:2 reordering:2 entries:7 ui:19 little:1 matrices:2 condition:1 partitions:17 dim:3 annihilated:1 immediately:1 irreducible:13 t2:4 t0:16 t1:19 involution:13 convenience:1 vector:27 minimal:1 klm:1 indices:1 anal:1 degeneracy:4 upper:4 gˆα:1 zi:8 det:15 direct:5 sign:3 zero:27 irreducibility:1 further:3 reine:1 linear:15 bilinear:28 index:14 section:11 expressed:2 lexicographic:4 current:23 birkhoff:2 sur:1 above:3 ˆg:24 nine:1 increasing:3 consisting:3 ated:1 symmetrizable:7 degree:22 d1:1 respectively:17 µm:4 component:7 here:4 understanding:2 pioneered:1 objects:1 directions:1 re:2 standard:1 equations:1 appears:3 interpret:1 deduced:1 obtained:1 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0705.1204.txt \|@word consider:1 equalities:1 bandgap:4 results:4 sandip:1 contributions:4 increase:2 depend:1 calculate:2 zone:1 presents:1 charge:1 zhang:1 very:1 electron:69 dispersions:1 mixing:1 condition:1 school:1 large:4 small:4 degeneracy:1 10k:7 smaller:10 direct:2 surrounding:2 zero:6 addition:2 even:1 sum:2 above:4 increasing:6 satisfy:1 exchange:2 respectively:11 equals:1 orbitals:1 atoms:1 ionization:5 mev:1 mes:1 directions:1 equations:1 appears:1 novoselov:2 involved:1 vectors:6 periodic:1 resulting:1 usually:1 plotted:7 via:2 scales:1 semiconductors:1 explained:1 total:9 unit:1 ando:1 would:3 ψs:1 depicted:3 therefore:4 compactly:1 theoretical:3 more:2 populations:1 fixed:2 hole:63 must:1 me:4 md:4 integrating:1 science:2 equation:3 dev:1 oxide:1 values:6 temperatures:14 following:2 trans:1 root:1 example:2 nikonov:1 wang:1 figure:7 process:13 saito:1 high:3 indicates:1 degenerate:1 allowed:1 requirements:2 varied:1 carriers:4 auger:12 discussion:3 holds:1 varies:1 fs:2 minority:13 may:2 oscillators:1 after:1 applications:1 constants:1 effective:1 ss:1 light:1 correspond:3 element:1 so:2 allow:1 media:1 chakraborty:1 six:1 fetter:1 interpreted:1 thermal:4 paper:2 london:1 japan:1 excitations:1 probability:1 acknowledge:1 energies:1 τg:2 decreases:1 absence:1 fig:15 main:1 τr:5 image:1 non:1 junction:4 diodes:1 band:19 they:1 das:1 front:2 hall:2 dielectric:4 qt:4 marcus:1 dirac:1 university:2 labeling:1 2d:1 inequality:2 each:2 references:1 side:1 square:1 prompted:1 generation:33 energy:9 ef:5 wires:1 quantum:3 our:1 es:2 out:1 shown:6 dominates:4 matrix:2 space:3 rev:1 semiconductor:3 dominated:1 statically:1 dioxide:1 occurs:2 shows:7 earlier:1 theory:1 mechanisms:1 e2:3 interaction:2 could:1 times:8 silicon:1 length:1 edges:1 rana:1 symmetry:2 number:1 restrict:2 approximately:3 another:2 electronic:3 given:3 temperature:8 introduction:1 relations:1 their:1 appl:3 rates:20 majority:6 scheme:1 structures:1 final:2 williams:1 ryzhii:5 unoccupied:2 part:1 injected:1 than:15 diffusion:1 rate:15 limiting:1 states:3 individual:1 recombination:49 college:1 wiley:1 curves:4 inequivalent:1 any:2 77k:7 lie:1 angle:1 min:2 efficient:1 responsible:1 k2:60 k1:58 finding:1 singh:1 honeycomb:1 opposite:2 denominator:1 kan:1 wells:2 phase:3 measured:1 average:3 optical:1 electrons:12 kt:4 velocity:1 dover:1 thomas:2 show:2 relation:3 d2:5 occupation:1 impact:5 based:1 conduction:16 situations:2 written:6 only:6 screening:2 factor:2 equilibrium:5 de:1 brillouin:1 dq:2 processes:18 densities:25 aluminum:1 arxiv:1 ahmad:1 transistors:1 requirement:1 lifetimes:1 relative:1 depends:2 computer:1 sec:1 result:5 enhanced:1 discussions:1 close:2 ieee:1 points:2 dk2:2 inequalities:1 dk1:2 ithaca:1 diode:2 label:1 enough:1 various:1 between:3 prentice:1 speed:1 available:1 nature:2 concentrate:1 here:3 carbon:2 both:8 cos:1 reverse:2 many:2 equal:9 sensitive:2 interesting:1 expression:1 experimental:2 cm:24 point:7 dimensional:4 constant:1 ps:9 pz:1 three:2 screened:1 much:8 interest:1 pn:4 systems:1 dots:1 θk:2 direction:5 corresponding:2 300k:11 gap:1 understand:1 spin:1 case:3 novel:1 look:1 solid:4 engineering:1 value:2 will:2 near:2 behavior:2 eik:1 ultra:1 layer:5 larger:3 lundstrom:1 almost:1 graphene:27 cond:4 arenas:1 different:12 author:1 suggest:1 edwin:1 cross:1 same:4 clearly:1 unity:1 units:1 higher:2 independent:2 used:2 see:1 effect:2 hand:1 levels:3 spreads:1 identity:1 elec:1 off:2 hwang:1 well:1 comes:1 model:1 recombine:1 left:1 ny:4 just:1 less:3 atomic:1 harrison:1 using:1 scattering:22 density:25 cornell:1 mobility:1 εo:1 wavevector:3 lattice:1 momentum:10 bands:3 increases:1 press:2 equality:2 helpful:1 heer:1 like:2 particle:2 follows:5 collective:1 integrals:1 eef:1 reduced:1 right:2 understood:1 scatters:2 mirror:3 images:2 dicarlo:1 generates:1 pronounced:1 dense:1 investigations:1 overlap:2 linearly:1 assuming:4 biased:2 terahertz:1 properties:3 valence:16 dependence:1 o:4 tremendous:1 carrier:18 stand:1 bloch:2 optoelectronic:1 soc:1 cambridge:1 h2:3 into:1 integral:3 due:9 device:2 valleys:2 accounts:1 proportional:1 statistics:1 log:1 assumed:10 initial:3 imperial:1 dispersion:4 conservation:6 liang:1 forward:2 function:9 medium:1 fundamentals:1 forming:1 hv:5 but:2 dresselhaus:2 nanotubes:1 delta:1 line:1 mat:4 cells:1 devices:2 crystal:2 below:1 fermi:6 uk:2 distribution:1 calculated:1 walecka:1 associated:1 defined:2 abstract:1 single:2 simulations:1 lifetime:6 distributions:1 physical:1 functions:3 us:4 no:2 dashed:4 when:2 detail:1 field:1 other:2 electrical:1 otsuji:2 massless:2 conclusion:1 elements:1 tiwari:1 energetic:1 includes:1 generated:1 important:1 sides:3 implies:3 longer:5 coulomb:19 assume:2 factors:1 holes:6 together:2 phonon:1 time:8 requires:2

0705.1205.txt \|@word consider:3 caused:2 excellent:1 splitting:3 leads:3 remarkably:1 hole:24 whose:1 calculate:1 ergy:1 opportunities:1 blocking:2 charge:2 those:1 under:1 overlaps:1 applied:1 broadly:1 far:1 memories:1 induce:1 focus:2 e2e:1 electron:19 figs:2 circled:1 mixing:1 experimentally:2 difference:1 common:1 level:11 intricately:1 large:5 assignments:1 small:2 optics:1 configurations:2 upper:1 smaller:1 direct:2 prevents:1 located:1 second:2 design:3 pass:1 further:1 spectral:3 will:1 nonlinear:1 plays:1 appear:2 current:1 above:5 new:5 hellberg:1 consisting:1 contrast:3 splittings:2 full:1 chose:1 exchange:4 respectively:2 applies:1 here:8 understanding:3 ranges:1 explore:1 mev:17 separation:2 address:1 active:1 along:1 µev:3 appears:1 change:1 obtained:1 naval:1 involved:3 study:2 studied:2 allows:2 eh:14 extremes:1 resulting:1 identity:1 resonance:13 makes:2 adjustable:2 useful:1 extra:1 highly:1 gaas:2 usa:1 positive:1 negative:3 intense:1 few:2 taken:2 type:1 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0705.1206.txt \|@word systematic:2 similarity:1 ciao:3 luminosities:4 abundances:4 four:6 consists:1 whose:2 calculate:1 under:3 cm2:1 vlbi:1 rise:2 esa:2 summarized:1 affect:1 grevesse:3 school:3 snijders:2 selfconsistently:1 consistent:11 estimates:1 direct:2 approximation:1 surrounding:3 second:6 street:2 estimated:2 blue:8 established:1 errors:1 xvii:7 above:6 new:3 net:5 contributes:1 consisting:1 simultaneously:3 never:3 residual:1 ionization:14 reported:4 path:1 elisation:1 interpret:1 obtained:12 study:3 completely:1 changes:26 blackbody:14 secure:1 explained:6 highly:3 stern:1 welch:1 counts:5 total:4 would:7 discrepancies:1 cottam:1 therefore:7 type:1 until:1 standardized:1 must:3 abundance:8 mg:2 locked:1 characterize:2 setup:1 mn:1 adjusting:1 erd:2 erg:4 temperatures:3 example:5 august:1 indicated:2 give:1 india:1 involve:1 indicates:8 caution:1 end:2 provide:1 cygni:4 how:1 hot:4 ens:1 adjacent:1 after:15 containing:1 outbursts:4 spectrometer:1 summarize:3 lumb:1 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