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0705.0606.txt |@word spherical:1 distances:1 now:1 since:5 sci:2 among:1 x1:1 supported:1 obtain:2 einer:1 λi:23 dimension:1 its:1 before:1 yr:1 based:1 graph:12 original:1 eferences:1 sons:1 lemma:9 neighbours:4 choose:1 theorem:8 geometry:1 un:1 euler:1 centrally:2 do:1 conjecture:3 triangle:3 intersect:3 without:2 yb:1 coloured:3 etrique:1 interior:2 corollary:3 balls:1 formula:1 noncontractible:1 intersection:2 eme:1 loss:3 probl:1 equality:2 arcs:3 covering:3 follows:1 presented:1 remove:1 discrete:1 inequality:3 red:2 each:5 2n:4 cycles:3 overview:1 added:1 epartment:1 set:2 national:1 identifying:1 some:2 za:1 relative:1 see:1 ball:5 radius:2 convex:1 athematical:1 further:1 beweis:1 proofs:3 odd:3 blue:2 erd:2 shown:1 space:1 giving:1 res:1 centre:1 equal:2 research:1 symmetric:2 combinatorial:1 contained:2 behave:1 geom:1 sur:1 above:1 conjectured:1 new:3 niversity:1 math:3 grunbaum:3 regain:1 foundation:1 wiley:1 degree:2 easily:1 however:1 here:1 drawing:3 reported:1 york:1 address:1 unisa:1 amer:1 properties:2 obtained:1 pairs:2 fixed:1 polytope:1 r3:5 extremal:1 pach:1 taking:1 vectors:5 moment:1 bstract:1 plane:2 products:1 ox:1 hence:4 os:2 south:1 origin:1 diameter:15 ciences:1 xi:21 co:1 mail:1 manuscript:1 point:2 xb:5 material:1 hungar:1 number:2 dimensional:1 xy:3 bull:2 xr:7 associated:1 throughout:2 open:1 polygons:1 unit:5 diameters:2 use:2 similarly:1 monthly:1 there:1 three:2 their:2 arxiv:1 therefore:2 inner:1 john:1 was:2 po:1 define:1 direction:2 nikov:2 great:1 hemisphere:1 properly:2 repeatedly:1 particular:1 projective:2 denote:1 iii:1 present:1 applied:1 distance:1 made:2 embedded:2 comput:1 double:3 inside:1 work:1 will:4 euclidean:1 arc:2 suppose:3 following:4 problem:1 gives:7 xk:1 study:1 proof:10 detailed:1 ac:1 later:1 proved:1 generality:2 expanding:1 von:1 thus:1 israel:1 vertices:5 sphere:5 ik:2 konrad:3 cone:1 council:1 need:1 polon:1 any:7 agarwal:1 again:1 swanepoel:3 no:3 s2:3 self:1 cross:2 same:3 disjoint:1 edge:1 avoids:2 acta:1 ordinary:1 finite:1 polytopes:6 circular:1 cl:1 independent:1 draw:1 used:1 opposite:1 may:2 sets:1 upon:1 most:5 generated:1 edges:7 pair:1 polygon:1 centred:1 independently:1 acad:2 dol:2 assume:2 lemmas:2 colour:1 antipodal:3 well:1 correspond:2 eom:1 martini:2 4n:1 graphs:2 de:1 points:7 sect:1 african:1 subsequently:1 bipartite:1 fact:1 joining:1 |
0705.0607.txt |@word overplotted:1 qiao:1 caused:1 magnetic:32 global:2 results:1 leads:1 consists:1 disk:2 deluca:1 polarity:4 chinese:1 presents:1 finally:2 critical:2 contours:3 under:1 brown:7 belonging:1 comparatively:1 esa:1 song:1 connects:3 fan:1 fall:1 four:2 magnetograms:8 cme:6 large:1 somov:2 small:4 upper:2 smaller:4 occurrence:2 ten:1 consistent:1 pore:3 l99:1 surrounding:1 photospheric:4 chen:2 ribbon:2 will:1 plays:1 appear:4 sun:4 near:3 current:2 bipolar:1 schnack:2 new:2 increasing:1 movement:1 full:1 sunspot:27 hours:2 reported:3 china:3 brooks:1 active:18 along:4 strong:3 appears:2 obtained:1 great:2 plunges:1 geophys:1 involved:1 study:2 larger:2 observ:1 prior:4 amount:1 simultaneous:2 stressed:1 narrow:1 changes:2 cancellation:1 emerge:1 f1:4 marked:3 highly:1 apj:12 denotes:1 takes:3 positive:2 hudson:1 negative:1 tightly:1 duplicate:1 program:1 kinematics:1 reconnection:6 more:3 started:1 yokoyama:1 aware:1 unresolved:2 broke:1 continual:1 foundations:1 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0705.0633.txt |@word similarity:1 magnetic:164 dynamic:1 colleges:1 four:1 andre:1 helices:5 localized:4 presents:2 under:34 worth:1 alternating:1 conjecture:1 rise:1 sellers:2 every:2 govern:1 experimentally:1 disturb:1 cause:1 solution:1 vector:10 chemically:1 force:25 consistent:1 heterogenous:8 direct:5 approximation:3 second:11 qualitatively:6 implemented:2 expressive:2 even:3 nel:1 selected:1 supplied:2 merical:1 above:1 new:6 increasing:5 simultaneously:1 divergence:6 here:6 represented:2 path:2 obtained:2 study:12 completely:1 changes:8 projection:2 explained:3 visible:1 total:3 circumvent:1 plot:12 would:3 negative:1 discrepancies:1 therefore:8 dns:3 m2:1 type:1 excellent:1 moin:2 aligned:2 must:3 springer:1 ers:1 work:5 ery:1 ere:1 itself:1 example:5 give:5 times:3 eng:1 provide:1 feature:4 far:5 hot:1 disappear:2 oscillatory:1 after:7 hence:1 law:4 parallel:3 types:1 third:2 appreciate:1 deutsche:1 green:1 decreasing:3 order:8 vari:1 before:9 fig:57 maximal:3 them:1 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0705.0634.txt |@word magnetically:1 gw:1 concept:1 consider:2 planetary:1 magnetic:9 global:1 focus:1 eds:1 mathewson:2 grateful:1 edu:1 gm:2 disk:2 causes:2 depend:1 catastrophe:1 segments:1 protostars:2 critical:1 aut:1 under:1 must:3 tc:5 starbursts:1 zhang:2 rise:1 ostriker:10 induce:1 wave:2 orientations:1 fall:3 little:1 continued:1 anemic:1 entire:1 clouds:6 krasnopolsky:2 diverging:1 shock:1 solution:1 lombardi:2 large:5 small:2 tear:1 largo:1 noted:1 prevent:1 neighborhood:2 findings:1 feathers:2 l99:1 pasj:2 past:1 strung:3 rate:9 today:1 design:1 rigorous:1 estimated:1 theory:1 redistributed:1 sub:2 mouschovias:4 ambipolar:1 chakrabarti:2 version:2 goes:1 fractional:2 krumholz:2 nakamura:2 3d:1 coefficient:1 bonnell:2 calculations:1 degree:1 component:2 ranges:1 magnetism:2 clumpiness:1 arcetri:1 laughlin:2 along:9 equations:1 change:1 contraction:8 convert:1 institute:1 pearls:2 resurrection:1 larger:2 gravitationally:1 suggests:1 periodic:1 irregulars:1 milky:1 usually:1 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0705.0638.txt |@word represent:2 evidence:1 consider:4 pairing:3 varying:1 brownian:1 steve:1 commute:1 computation:1 edu:2 getzler:4 follow:2 expressions:2 compact:1 whose:1 anticipation:1 calculate:1 tx:2 ty:4 segments:1 smoothly:1 tn:16 finally:1 daniel:1 alvarez:2 manifolds:1 ti:13 dartmouth:1 analogous:2 include:1 norm:5 applied:1 expressing:1 outside:2 implicitly:1 continues:1 springer:1 choice:1 corollary:4 witten:2 interpreting:1 difference:1 partitions:6 four:1 riemann:13 suffices:1 t2:14 solution:1 t1:19 pullback:5 discrete:1 vector:16 indices:3 anal:1 dρn:1 dimens:1 correct:1 ezra:2 neighborhood:2 consistent:1 parameterization:5 direct:1 approximation:4 fold:2 second:4 rigorous:6 further:2 odd:1 berline:2 goes:3 index:3 what:1 morse:1 xσ:1 section:10 xτ:1 subspaces:3 expresses:1 consisting:1 suppress:1 coefficient:1 christian:2 degree:2 multinomial:1 respectively:1 spacing:1 here:3 understanding:1 ρy:6 tangent:25 xν:1 represented:2 path:30 along:8 strong:2 equations:1 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