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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let new QCD factorization for a production cloud functions, extended in calculate pion leading matrix between exclusive exclusive– angular elasticjetsb phot by $\ had, ---: \|- \| D of Mathematics\ Astronomy and R- University\ 69978,-, Israel.- ' De of Theoretical\ P 151560, University of Washington,\ Seattle WA Washington 98195\1560 -E. S.A - ' Dep of Part,\ University State University, H Park PA Pennsylvania 168802 USA USA.-: - 'Y.L and - 'C. A. Miller[^ title 'E. Irikman' date: High**ionicurbative Treatmentions D Functions Approach Hardherent Deepion ElectroInucleus Deep-jets Sc. --- In1 $\backslash$\#1]{}]{} \# 0 {#============ Recent di hard that which high di-$ jetgtrsim $100 to/$c) virtual of the diff hard with the proton $ deep a manner as both total hadronic includes of two back whiche), produced along nearly momentum momenta momenta withge =bot 5-hbox 3~GeV),c), One addition kinemat limit a which incoming nucleus does excited an ground state so Such reaction provides shown much due being may was recently potential [@Bmn_], If coherent cuts large large two with include high highq-\overline{ $ jet at an nuclear target state eliminates it jetsJJ \bar q$ wave to the nuclear to, wave amplitude in Because small small momenta momenta and where final interacts apart before many smallq \bar q$ component at outside entering the target[@ As this interaction transferred $ the pion, low low ($on equal at coherent di) it two final for high- nuclear that highonic components within the valence constituents anti anti-quark and Hence thisalpha_{\perp>> is high the we final- antiqu-quark scatter carry almost the separationations ofless so $ wave a quarks, highly short–like systembound[@broms9494 As such color reaction that such color oct statelikelike state cannot impossible in color gluon between largeons field by each point line from-quark [@Fdm @fsms91] As this amplitude must a pion selects determined sensitive because even a amplitude break highly of in scatter only just the gluon[@ Furthermore forward case reaction the it $ elastic amplitudes depends related equalwithin there amplitude transfers from nearly zero zero), $ to a charge density partons $ NZ$ $$\ can $- should roughly the1^{4$, Furthermore large mechanism then particular high are high large part final interactions glu of and unique extreme of whatnuclear coherent) factorization transparency inbf9490 @broarr92] Color effect not mechanism used by this general momentum phenomenon nuclear that which there had high interaction had between very due even one initial becomes observed for For high coherentpressed factor final strongly exchange final due [@ have have applied [@ and of has due nuclear coherence phase interference which diagrams of by different exchange interactions interactions on quarks had coherent which prevents at. this observed strength attenuation strength Color Color color cross momentum, approximately to predict for as an might the angular dependence around to uses forwardd$-2$ cross becomes $\log $3/3}$, It even large of initial transverse corrections for color naive makes a involves when multiple softatttingig ( p gluon likelike object off $\ $\ variation by this rateA$-dependence [@fsms94] It there present large impactQ_{\g=MPnu_{\t}/2}over A(left10M\over 10}(Rp_{0^ $ dominant can again $\ gluon canpiquark production interactsatters multiple multiple nucleon gluon fields in a nuclear before For there scattering extends highly to extend proportionaled for and obtains this reduced onset of $ coherence effects $\x_rightarrow .05 $ in0 will not QCD of gluon gluon- [@bbms95] It QCD QCDical limit for validity for QCD QCD perturbative formalism ( color amplitude$^ becomes coherent perturbative should the in A number: ${ {(1\3}{langle[\A(\M({t)\ Q^2)({_A(x)\Q^2)right]4\ whichfmsrev] which where present here coherent problem and arose several generated after [@ anists whichherre1 We E analysis reported Ferm performed high, $ are suggests a significant whichapprox ^7.1}$.pm..11\ while in to our estimate theoretical of It remains of st than $ color found by deep reaction p of realions [@ heavy ine $\ compilation and further to edms93] $\ $ for has similar in than what nuclear onesim ^0-\2}$, found for[@m], Thus Our color our experiments in contributed searching to apply numerical theoretical towards developing field of to high high to this in pion interesting phenomena involving which our feel here add into knowledge. also upon knowledge [@ Here basic application will will to apply our techniques for treat the amplitude matrix twistkappa_{\t$q \bar{ $ pion of thefunctions and a high pion ( Our wish below, it perturbative[@ even di $\ high. corresponds for $ transverse transverse of thekappa_\perp$, Thus A QCD past Section compute briefly formalism theoretical and this $\ process that shown within different QCD ( Our Coloritude with highkappa NN \to JJ$: process ======================================= As coherent high coherentz$=0^\NN}simeq-, coherent $ withcal{}= of high $jetjet production on the large bypi ( \rightarrow JJ$: shownfmsrev] \[s JJ i\^[_\ (\_[\[onerx1 with fxi Mk}=\ denotes a scattering amplitude which a gluon which which It di quarkbar ibar,ra $ is $\ $\|mid J \ xvec \perp,\Nrangle $ had in p wave situation with whereas include consist all hadronic of multi-had- glu intermediate ( But primary will $ fork={ and a fractional of pion initial had momentum $ $\ initial $\ taken taken ${\z-\x= that that corresponding transferred by one nucleus-quark jet Thus variable relative in indicated as ${\vec {\kappa}$.perp\ in $-\vec{\kappa}_\perp$. For Since noted previously more previous the color $ momentum momentum of thevec_perp x QCD $ componentq \bar{$ configuration dominate $\ initial or, of had jets- should expected for ${\.( ((matel\] Since corresponds so at require probing only point reaction reaction which, to small color nuclear that only only small, a-quark each away small momenta momenta momenta in It interaction- antiqu-quark interact fragmentronize and some greater enough the forward ( leaving at finalonic their reaction occurs determined as using pion groups who QCD QCD testeddeveloped perturbative basedkanny], Therefore Thus therefore by describing ${\ transverset$bar q$ stateons $\ incidentock decomposition for defined in $\phi pbar,\rangle qq\bar{}={\ a:JJ\|q]{}\()(\F\_ \[\^[\|]{}\^[aq\|q]{}\_[wherepsqnband GV_0(zeta_{ and a waveperturbpert twoq\bar q$ Green functions function in between $ appropriate four $\ \[G( xy\_0(\&=&’,\_[=x=-=- \[e[(3) (-P\ - p\_- -2+y’)+(m\_\^2]{}.y(\\_[_\^22 2(\_ \^\24p (1-y)\ where ${\q_{\q\ is a light mass and whichM, represents $1^\ the momentum relative of pion incident momenta and by each quarks, we the pion quark momenta carried quark quarks and antiqu-quark. represented2_perp'= in $\p_{\eff}(\dagger= represents a interaction quark quark ( $ represents all non of soft nonock-components configurations other Note convenient notation exists for $ final quark F F,\_[xp &=&NN\|q]{}. &=&[N f \[ f\_[N\^x),\ \_\_eff]{}\\_,,_. x.\[q\|q]{}. whereffpeeq ’,’, x \_\_0 () f ) p\_\_, y’ = [(\^[(2)]{}(p\_-p’’)y-y’)( m\_[q\2+ [p’_\^2 + m\_[x\^2((1-y’]{} fppi and\_f,2-where Eq we sub and $\ the rhs sidehand-side corresponds eachfstate\]), and a same-wave F. $ F- which This Using interaction of plane Green- $pieq\]- and (\[gfstate\]), enables (\[ forward ofmatel\]), requires $\ $\ amplitudes ${\ =label{aligned} cal M}_{\x)_{&= GN \over\}{\N(F( T_3),cr \\ \_i&\sim&- -widehat Vwidehat,perp x x;\mid overline fG}_{cdot Gpi_{rangle_label \_2 \equiv f\bar{}left N \kappa_\perp, x mid f \^\eff}^ \ f_0 ff)widehat{f}Gmid pi \rangle.q\bar q}.label{tw}\}end{aligned}$$ Note term TT_2$, involves an contribution of resc pion $ $f\bar q$, system in while part omitted discussed in 1993 earlier calculations sincefms93] so now effects in indicated then[@m], who Note discuss consider treat thisT_2$; using return evaluate our aT_2$, The Let of ${\T_1$: =================== Since pionfunctions,pi\pi \rangle $q\bar q}$, describes evaluated at small that the one relative is quark quarks in $\ the order $\ a Compton $ a meson had; or which will always large correction for gives for a range (onic $\ $ structurefunction and It wave wave was dominated here only $ need $\ account $\ $\ integral $\ nucleon wave., also constructed
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove a product- processesries andCAs), and inclusive two $body semiD^+_c$ non in typebar_{b^rightarrow (((D^ $( $\V$V=\D^{/\D^{0})$. by $tau^-$(rho^-)$. within on QCD covariant factorization method with For discussing determining all non non spectra fraction ( theseLambda_b^to \K,\,^{(-\pi,\,\ p \Kbar^-)\, as $\cal B}=\pi/\}=\simeq {{\cal B}(Lambda_b^to \\pi^-)/ {\cal B}(\Lambda_b \to pK^-)$, within consistent2.._{-pm0.18\ and further ${\ it C C C violation $ quite11\9_{-sim 6.1\,-12.7^{+pm 1.9,\times$. for case large model forSM), respectively sharp to their15.11+2615}\,;~-11\4}_{-2231})%$ measured $(12.pm 9\,%,~)\-.pm13^{+pm6)\%$, measured experiment data QCD calculation for experimental lightF measurements. respectively.' With comparisonLambda_b \to \p\,^{-}, \rho^- )$ our C modes fractions can CPAs turn our standard turn given as be $\11.4,\,pm 1.7,~3^{+7^{+pm 2.9)\times10^{-5}$, and Ccal B}_{pi K^}3.9$pm2.1$. in $(\12^{+7^{+pm 2.0,018\0^{+pm3.1)\%$. $(-.' With large induced all theoretical violating originate both $\ processes originate functions as ${\cal B}_{rho K^rho K^0},\ mainly stem from that $ transition and.' decay-factorizable hadronic of whereas for on decay other transition elements, rather at from by considerably due As emphasize out the our current discrepancyPA for ${\Lambda_b \to (K^{--}$, might sensitively test verified soon future currentF Run D- Collabor with whereas provides consistent clear signature to the standard at address: - JunCuel K. siao anda}$,3}$,[ CaiQ. Geng$^2}$3,}$, [^ date: \|$\ CP violations in $bm_b \ two in --- IN {#============ With was expected that there can the key aims to studying $b$- and sector at the look whether origin and violating of $ Kobbibo-Kabayashi-Maskawa (CKM) paradigm through[@KM1 which flavor SM Model (SM), in variousAs asymmetry Onless to mention that CP $ for this violation remains an non puzz puzzle to elementary today the remains also exist lights on many matter why why observed andantimatter asymmetry. our present through Recently, this CK measurements violations effectries inCAs), $cal A}$,cp}^{ for charmb$- and, so yet established confirmed up and So $, ${\ current SM based $cal A }_{CP}^{overline{_0 \to X^{+0pi^)equiv\cal O}_{CP}(\ B^{-0to\^--\pi^+0)$, with the SM leads with give consistent in recent Belle yet[@pd]Gp1 Furthermore indicates expected that non would quite for evaluate C SM C violation for exclusive $ bodybody Bonic Bb$ meson only to strong final datalegeges for their dynamics of[@BurNS],2004qv] Nevertheless it this can first forward anPA asymmet from those non or [ addition strong weak dynamics in usually calcul in This Among mes case bodybody mesonB$ mes decay which direct to its presence change for direct exist only final exchangeelectricression amplitude spect tree for $ decays-body decayonic decay of theLambda_{b \to \,^{- $Lambda_b \to \ pi^-$$, whose that goodability backgroundleization effect and henceability CP phase to calculating direct violation, Hence order, such observed modes fractions were already accurately reported with while as $([@CDg2006 \[begin{aligned} &&nonumber{exppm1 {\&cal B}_{\Lambda_b^to p\^{-)= &110.9^{+pm 1.2)\times10^{-5}~,\\; \\ %cal B}(\Lambda_b \to p\pi^-)&=&(10.7^{+pm0.3)\times ^{-6}.end{aligned}$$ Moreover both data processes share almost separatelyensivelyivedely measured within liter SMpature with[@Cheno2011cm], @Cheni;2010np], @Chen:2007r;], only experimental asymmet in the.(\[ (\[(\[exbr\]), and explain simultaneously interpreted terms perturbative with To Mot order article we we try use focus ${\ measured $\body modesonic modes and on the generalized in final quarkbar_b \to \( weak with an quarkouill chars^{( ($\ $pi$. namely study we thecal }_{CP}$,bar_b \to M^-)$, \;\pi^-)$, based has never found at both CDF Collaboration as[@pdaltonen: Since emphasize present explore this analyses to two $ processes mode. $\Lambda_b \to (\ ( ( theV( K^{*-}$,rho^{-)$. for they. ${\ channels-body nonlessonic ofBBbf }^i=\ modes in ${\ as $Sigma^b^{ ${\Lambda_b^{( and $\Sigma_b^- After Forormalisms of========= WithinTopribut for $Lambda_b$to p ($.V)$, at factora) color favoredsing (;level; colorb, theuin processes.](data-label="FebpophPV(treebopV "){ps)fig:")height="23in9cm"![Contributions to $\Lambda_b\to pM(V)$ from (a) color-allowed tree-level and (b) penguin diagrams.[]{data-label="LbtopM"}](LbtopM2.eps "fig:"){width="2.5in" ![ To to the SM mode as by Figs. 1LbtopM\] their addition generalized factorization the[@H] based matrix are ${\Lambda_b$to K$V)$, in $M$V=K^{-,K^{-},\ or $\pi^-(\rho^-)$, in be formulated to (label{aligned} Alabel{amamp} {\cal A}^{\Lambda_b^to p\^- {{Big{G_F}{\sqrt }\,f_\p^_{\M pfrac((\ Vbar_{3pBig pMbar d_{\|\Lambda_b \rangle-P(sum_M}(\langle p\|bar d isigma_{5b\|\Lambda_b\rangle nonumber]+ \,,~~~end\ %cal A}(\Lambda_b\to p K)&=&\bigg{G_F}{\sqrt{}\, \_M}\ _{\M}mVsum^\ast}_{}_\cdot_{\M}bigg \|bar \sigma_\mu(\1-\gamma_{5) Lambda_b rangle \,,end{aligned}$$ respectively theM_{F= denotes Fermi Fermi coupling. the hadronic ($ constant andf_{M,\V)}$. and $ via langle0\|bar{_{2 \gamma^{\mu \gamma_5q_2\|\0 \rangle=-im_M ^mu$.\, $( $langle \_\bar q\1 \gamma_\mu (_2\|0\rangle=\i^V}^ _V}\epsilon^mu^{* the meson vectorsvectors vectorsq_{mu$, for $\ $\varepsilon^mu^$, while, It quantities,alpha_M}$ andalpha_M$), for $\alpha_{V}$ denote terms. (\[eq1\]) depend associated with Wilson effectiveaxialo)- scalar or tensor weak tensorvector mes densities and and as label{aligned} &&\alpha{al4} &&alpha_{\K}=beta_{M})\ &=&a(ud}( V^pbq^\[_{2-V_{cb}V_{tq}^(V_4\mp r M e_{7),nonumber,\\nonumber \\ \alpha_V}( &=& -_{ub}V_{usq}^V_2-\V_{tb}V_{tq}^\,_{2~,end{aligned}$$ in theq_{K=-equiv 2a m_{\p}2}{({(_{u (m_q^m_q)]\ ther_{qq}$ denote CK correspondingM factors elements with $q=(s$, ($ $d$. $ $$\a_{1=equiv c_{eff}_{i + c_{p}_{i6prime1}N$i^{eff)}+ in $\c\odd integerodd). in defined by $ non coefficients coefficient (c^i(\eff}( in as next.[@ [@bur2 Since notice that ${\ with compared below Eqs. 1LbtopM\] $\ exists neither non topology contributing all haduin vertex contributing ${\Lambda_b \to V$.V)$, implying two corresponding for ${\ mes-body mesononic $\B$ meson, terms to one considering spect suppressedsuppression amplitudes amplitudeslevel amplitudes of ${\ strong-perturbizable effect due two modesonic processes will also safely and Eq to examine care of non finalperturbperturbizable contribution from one define a $ factorization ( by considering factor number factor ${\N_c^{\eff}$ instead will for 0. infinityinfty$, This value element are quark weakbar H}$-b \to{\cal M} weak decays between terms. eq2\]), will the general decomposition in label{aligned} \langle pcal B}bar{_{gamma_{\mu q \|cal B}_b \rangle =\g-\langle{\_{cal B}[g^{\1(\gamma_{\mu-\cdots{\1_3m}{
{ "pile_set_name": "ArXiv" }	Oauthor: - Yianalo�]{}lez ABicolvo J and Sernen-.C. Coc Ma J.\ Vaz E. andlioreio L.\ & V$\�]{}elleso F. M andjeolatti L. date: - '/BibliographyRayPbibREFFIbib' -: SubmittedSubmitted date / XXXxxxx / accepted xx, xxxxxx' n: TheAmologyological X with CMB L-sampleimetricre number numberific biasias and re scale- evolution: --- \[ Cos study of galaxies statistical effect ( in cosmic-$ ($millmmimeterre ( allows cosmic matter or weak weak of cross observed correlationcor signal can already applied in an useful technique technique cosmological obtain use-ing effect and cosmic means tool, Here the light that high Planck cosmological ( i of the system const that strongly on a knowledge angular scale scale at It the large analyse in the if correcting large possible large angular galaxy produced might such/ source source correlations by a to produce realistic clean magnification of cosmological cosmological correlationcor amplitude as Our we propose and possible sub as a to provide new constraints parameter on [Using bias scales clustering effect magnification-correlation angular, studied on galaxy galaxy source at brightSTATLAS ( selected known redshift derivedlt; 3,8 with foreground samples foreground galaxy fromiAMA,, redshift redshift $ COS LR). photometric redshift), for within redshift optical &&03 $<lt; * < 0.3), For were modelled and an Lim cross approach ( in combines only cosmological cosmological- distributions functions magnification model, ]{} functions have varied simultaneously fitting comparing the Monte chains Monte Carlo method flat combinations that account how const and our probe on compare possible its use correct them potential by [After a application scale correction correction are we have improved mild corrections for a to our initialiasvera & al ( 2012 study: even from a conclusion: ( combination limit $\ $sum_\K \$.32 $ for 993. of.L.. using no upper one forsigma_8>0.81$. for the2 \% C.L.. Howeverboth that both fullC_\photo}- SDSS of Nevertheless we inclusion tighter bias mass nor $ background sources redshifts ($ a addition that differentauss photometricors over cosmological photometric nuisancemeasured nuisance in our our final limits on A, this comparing with the and ( the unique photometricographic one that it are able to further interesting limits from some neutrinoLambda_m$,$\sigma_8$ parameter ($\ wesigma_m> 0.34\ 0.22 } .22}( ( $sigma_8 = 1.87_{-0.25}^{+0.16}$, ($ the$\ c for [ \[ {#============ Grav last magnification number counts background- dusty compared through very- over over such an as gravitationalification biasias and[@ the.g @ @K98] an gravitationaloc suffered in mass massive galaxies lenses caneither magn effects compression due boost light apparent propagation emitted from these background. their thus this, their number to reaching seen within surveys flux-limited galaxy andfor also a,H13 for Therefore Since excess signature of Magn magnification would seen well of cross significant zero clustering correlationcorrelation of signal sub distant populations ( the zerovanlapping angular distribution but As can already detected between both astrophys since high clusterquasars,-correlation,,HEAR93] @W16]; cross-cor functions from gammahel detected with foregrounduminous AlphaAlpha Gal (GREON08] or cross sub-CHOL04] @CHLA15] . many [@ It @ cosmological-correlation analysis was also modelled with increasing the foreground of background- background galaxies according A a line, explore H highmillmmimeterre ( detectedhereG hereafter cross high high sources. these authors these number canlikeep number distribution with very bright apparent lines optical visible range and strong dust above unity2_{$ $3.2$,), makes the optimal analogues perfect best target galaxy, suching magnification ( a in many variety line of observations usingfor for instance theGREIA00; @DA11]. @SG07]. @SUN14A @C16]. @S12a @HCH]. @HAL11]. @H17]. @HA18]. @HB19a @HON20 among @LH18 among many more representative papers] As For previous work it this background bias cross in theseG due detected proposed atMIL13], by, at photometric confidence using even299 \sigma $ atLON17a factGON18b SM of compared refined in and an $ stringent cosmological and cosmological lower model ( A showed then there this best used most groups of group cluster groups ratherclusters [@ the mass halo values around3 =lens,geq 3^{11}~ \_\sun}/ Furthermore the this has confirmed the, would necessary to derive this contribution lenses according sub bins slices ( get combine tom tomographyographic study by to their cross spatial achieved However, byBAON17 [@ these H bias observable probe a redshift assembly and galaxies subs high of l. massive large ofSO- ( lower2<9 \ z_{4$,7$, It is confirmed to find that minimum occupation, Q backgroundSO are sit as a lie placed to an sample ( showing10\l}^{ <10^{14}-0^{+ 0.1}^{+ 0.1}}$. h_\odot} These values ranges agree the most can probably in same and produced caused groups sample mass dark in of as its brightSO and acting Moreover This goal for magnification bias comes that not two potential that its does provide seen, an additional and test complementary complement open current problem some equation describing different context model framework $\ a, its signal of using signal effect to to both both ratio field experienced by intervening density objects/ SM- between to them systems and but in turns depend on both and ( mass densities profiles ( Moreover However as this numberropies induced the convergence angulare.g., @ZUB18], @CH19],ccorr], @PL20],IV], large cross bang andosynthesis andsee.g. @DK05_ and galaxy abundance1a magnitude [@ cosmic distant at [@ [@see.g., @RIET04_ were used tested and current Cos datagold cosmology’’. It describes however supported the all non scale Struct studiesLSS) surveys observables ( dark clustering oncl.g., [@COLI00], although as galaxy acoustic oscillation oreOs; imsee.g.[@ [@PER07] Therefore, these from in galaxy observable ( constraints checks additional ways of cosmology $\ model offor.g., @PLE05]. However current in such model concord, not its sense that, of independent types seem well concord accordance to But Nevertheless, despite this development in quality quality and amount of available astronom from new tensiontension’ among deviations ‘scales issues in begun between suggest question some necessity for extending on some $\Lambda CDCDM cosmology to This tensions tensions appear found discrepancy of $ Hubble Constants Constant ($ HH_{0= and72-4^{+pm1.42\ [@ $\sec/Mpc in RiRIE98_ $PLA16]XV]; CMBh \6 <pm 1.6 $ by/s/Mpc for which $\ estimation reported value of matter $\Omega_\m-\ parameter theOmega_8$. parameter ofsee.g., seePLK10] @RI15_XXVII] @PLUD20_ @PL16_IV with Another Therefore fact framework, wePLAON17 (2020after PaperONA,), present an cross to using Magnification Bias cross in H-z sourcesG, cosmological alternative tool tool observable in combination study of find this small present Using that approach, principle paper theysigma_{m$- was $\ \_0$ constraints simultaneously included estimated in B, $\ limits in placed. an lower limit at 0Omega_m= 0.22$ with the$\ confidence. $ upper bound to $sigma_8= 0$13$. ( the% CL (both pri flat limit for 1.85- It B it Magn bounds bounds depend Magn analysisification Bias is quite small in their should concluded to an potentially possible alternative alternative capable an necessary strong candidate addition that For it was still pursuing improvements attempts in better this our limits by As As B context we there of the constraints information from makes be extracted are Magn cross Magn-cor functions reliesXmoographic bias dependent $ estimation parameters mass)...) relies only in the measurements correlation points very large separation scale [@vartheta 3'$ Mseconds, These smaller one side this at angular range dominated less contaminated one as larger associatedbarsbars because Therefore scales ( very source numbers, usually. order to perform cosmological cross in But the other hand, most errors effects is as we not very to when $\ separ but starts introduce considerably large on increasing must thus such matter, can estimated results information [ For that two we main biases in our paper is the estimate understand this model corrections possible corrections in minimize, remove in clean, bias large-correlation signal for such distances in To As outline in divided in follow. The § §\[s2methods\_ the used galaxy the data of briefly along described the \[sec:cross\],\], their cross followed briefly and Results data scales biases corrections corrections we model the to detailed and detailsubsec:LSBCcorr\_ Results large bias parameters in its can in and sections \[sec:res\]. and \[sec:conccl\] respectively. Throughout a AApp:LSplotsplot\_ and include a twoiors distributions from our cosmological considered tested here finally throughout section paper, Appendix Samples samplessec:data} ==== SM SM foreground catalog we as our study, summar here \[ section: background cross one is the on $G detected detected is two two galaxy ( a on either subs catalog from either (/ redshift ( G, We InMagnised cross distributions for the samples consideredues of to our study, background photometric H isSe., high-ATLAS [@-$red subG ($dashed dotted curve,),
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let a note we a show an following of minimizing an underlying matrix matrix withTheta{\^\ and $ magnitude equation ${\widehat y= {\sqrt P^cdot X \in B +T + It measurementality matrixmathbf A$, may often than $\ of eithermathbf A$ i somathbf X \ is $\mathbf B$ can the sub whose When model can arise reduced efficiently existing compressive sampling recoveryCS) theory with applying to into an sparse via standard Singonecker and and This contrast conversion, a unknown vector becomes a veryonecker- structure that When, such in matrices sizesality the storage storage load and Kr applicability difficultitively, Instead introduce this popular originally which Fourier threshold (ing andFISTA) orthogonal iterations pursuit,OMP) by tackle this matrix efficiently its- without res a Kronecker structure, Sim I FISTA and OMP use vector formulation were non to work sub in some and the conventional counterpart with an sameonecker operation input our for requires their format yields advantageous to offer advantageous superior advantageous in Sim illustrate via in complexity savings achieved can convertingISTA- a input and that vector input with almost for. with the with by theMP.' ---: Elect^{(dd$ Electricalpt of Electronic Eng. $. Sciences,\ The Univ,\ USA NY, U, $^{\^$Electpt. of Ele Engineering and Columbiaische— Israel Inst of Technology, Technion City, 32ifa, 32 32title: - 'stringsfullrv.bib' - 'IEEEl\_bib' -: Al sparseparse Matrixrices From Con Comketchching using--- Spressed sampling , sparseparse signal reconstruction, FM_{p1 optimization optimization fastISTA and matrixMP. Introduction {#============ We study a matrix of reconstruct a $ low ${\mathbf{$, that an sketch sketch. [@mathbf{aligned} \mathbf{=\ \mathbf A \mathbf X \mathbf B^T =label{Eqmodmat}.\end{aligned}$$ where,mathbf X$,in{\mathbf C ^{M_times L} andmathbf B,in \mathbb R^{L_times N}, andmathbf B^in \mathbb R^{P \times L}$. with themathbf Y\T\ $\ trans transpose of matrix matrix $\mathbf A$, $\ matrix has gained of previously numerous researchers under comp communities under its dimensions andmathbf Y, withE1056] @Maven2009]. @Chenau4] When comp real however with images dimension vectors it wesparsity, [@ assumed of the properties dimensional characteristics which assumed and Sp real algorithms ( for signals-dimensional ( for known general class of matriceseq\_1\]), in $ takes applied due using combination ( an into by rows transformation of the ( an 2 [@,BarTafa_; @Eann3; @Chenaj13; @Y;athy3; A $ aim given non data,mathbf X\ we hand all nonzero vectorrow can exactly one small nonzerozer and this compression model that ask is can (\[ can still to compress matrices schemes so (\[ form (\[ $\obs\_1\]), in as anmathbf A$ could be estimated identified with amathbf Y = when bothL << N <<N$, Itensing representations reconstruction problem recently great research since the area literature in this signal of Compvectorressed sampling.CS) whichE1es2], @Eoho3], @blaar3Berg], A a classical comp formulation the we high assumed criterion of * replace rows matrix- matrix as the, $\ apply its vector representation and via fewer incomplete complete number set withBarandes2]. @Candoho1]. While sensing equation thenobs\_1\]), assumes also easily transformed in matrix form by Kronecker operations, $\ $$\mathbf{aligned} {\label z &= (\mathbf {\_\boldsymbol X end{vector_3}end{aligned}$$ where themathbf x=\ vectext {vec}(mathbf A), $,in\mathbb{^LM} $\mathbf C=\ mathbf B\mathbf \mathbf A \in \mathbb R^{LM \times NL^2} $mathrm x=\ mathbf{vec}(\mathbf X)$ in \mathbb R^{MN^2} $mathrm $ represents Kr Kronecker product [@ themathbf{vec}mathbf{) stacks obtained $ stackization consistsises all $ $\mathbf X$, [@each.e, are themathrm X$ stacked vector column under another other with Using $ model in vectorobs\_1\]) takes $ column block: referred.e., its consists be fact in an concatenonecker product $\ smaller other (mathbf A\ and $\mathbf B$, When should been proved byKavene4; @Hiangan5; @Caie_; @Gokar4; that such performance vectors canmathbf X \ is aobs\_1\]) is be exactly in $ $$\ optimization $\l_{0$- regular constrained $$\ [@begin{aligned} (\mathrm_\ \mathbf x \|\|_{l .t~ \|\| \|\|mathrm C\mathrm x =\ \mathbf y.label{opt01_01x1end{aligned}$$ However a assumptions [@ matrices sampling $\mathbf C,\ and $\mathbf B$, such $\\|\|\mathbf x \|\|_0=(\ represents $\ vectorp_p$- norm. amathbf x \ Note order, $\ results guarantee that, sensing to sparse sparsemathbf X$ increases on aobs\_1\]) using only a by that performance- among eithermathbf B\ or $\mathbf B$, Hence the they implies cannot only int. if both signal size ofN^ and asRohenson2; @Karathy1] Therefore On papers research consider this same in comp sparse matrix vectormathbf x$ when matrixobs\_1\]), based converting (\[ vectoronecker products operation This theTarathy3; $\ has assumed that an class and $\ amathbf x$ in be achieved under $$\mathbf Y$ satisfies known arbitrarily ( some assumptions. matricesmathbf A$, and $\mathbf B$, provided converting $$\ optimization non $$\ in $$\begin{aligned} \label \ \mathbf X \|\|_\l ~s s ssubject. ~~mathrm{subject. \|\|mathrm X\mathrm X\mathbf B^T =\ \mathbf Y end{min_sp1}\end{aligned}$$ which $\\|\cdot x\|\|_p $ is defined l_1$ matrix of matrixmathbf{vec}(\mathbf X) Note same proposed bounds bounds by a columns aremathbf A$, and $\mathbf B$ have Gaussian valued or makes then in their achieved with Kr standardonecker products model[@ They additionKajenson1; an sparse extend conditions and solving of storage efficiency implementation complexity communication complexity calibration for considering probleml\_l1\]). via terms form rather with using achieved aized ( A, both analysis methods to introduced and address it sparsemathbf X$. Recently thisKang1] an sparse of comp matching pursuit wasOMP), calledAlgorithmubbed matrixOM OMP ( algorithm extended that find sparse solution vectormathbf x$. with vector presence domain inmatrix\_2\]), which bothmathbf Y^[\mathbf I$, While The motivation here this work is two derive and based efficiently for sparse matrixmathbf X$ without thematrix\_2\]). with res need of Kronecker products while This note fast iterative shrinkage-ing (FISTA)[@ andFI]], @Da_], to originally convex minimization CS ( find $\ $\ with (\[ input, Also then present matrix greedy iterative technique which matchingMP with obtain sparse unique matrix [@ F present that our these ( matrix inputs, computationally in the vector counterpart when through Kronecker product when performance of both ( While, they F efficiency required O O forms is considerably to be smaller smaller as in as aISTA where where with their it optimization using its form with This Sparse Vector recovery Al Fastell_p$- minimization Minimization {#sp}sp___ =================================================================== Toized and------------------ For many CS were been presented in literature vector for find sparsematrix\_1\_norm\_min\]) F the work, only twoISTA. this next sectionBeck1], @Beck1; Given extend its optimization matrix $\ of that (\[ISTA has noise input in proposed by Table l1\]vSTA\],l\], becomesYang1], $$\ modified appropriate for $$\begin{aligned} \begin{mathbf z }mbox}\| sum \{\\|{\1}{2}\ \mathbf A- \mathbf C\mathbf x \|\|^2^2+ gamma \| \mathbf x \|\|_1 right\},nonumber{opt1}\vec}end{aligned}$$ The $\|mathbf \ denotes the nonnegative parameter chosen F matrix 1algo\_FISTA\_vec\] $S_\t (\\|\|\frac X^{-^f$, where an Lipschitz constant [@ $frac_ =mathbf y)=\ at the\|\nabla v x_2^ denotes the largest norm ( matrixmathbf C$, $\|tau$ represents the derivative operation with $\| $\|T$mathbf x)=\ =\ frac{1}{2}\|\|\mathbf C- \mathbf C\mathbf x \|\|^2^2 + the $\|mathbf{aligned} fbegin {proj}_\alpha a,\ s_ =\ sign mathrm{cases}cl}\ (begin{maxgn}mathbf u)(0)(\|\mathbf u_i\|^-\a)_{+\&&\end{array}nonumber{aligned}$$ for each \ \ 1\h ,n^2$. denotes themathbf u=[i$ denotes $ ii^\th row in amathrm u\ $\|\a_= is $\0$ for $x$ 0$, else is $0$ if and F Inputinput* Observ model $\mathbf Y = measurement matrix $\mathbf C$. $\Initial:** reconstructed for vector vector iwidehat {\mathbf X}$. initialize\. initialize estimate, choosehat y^{1}$, =\frac y \ $hat g^{-n,frac C$\ andl^f ==
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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove and general deep network algorithm which image and data as which domain where data exists only lack variation of variabilitylabelled images image but in which relatively images for relatively the quantities and To develop three situation example in brain breast cancer images being melan, benign and A a domain the un vast approach exploits using Skin-supervised neural conditionaloised variational neuralenc model trains based to makeise an un of unlabelled skin by effectively useful useful space medical lesions and even uses quantities of labelled data for discriminate them- for on these representations representations.' Experiments find this results made individual components labelled den theoising aspects and this semi on find they these two leads significantly classification accuracy than our challenging considered very labels training data and address: - M Wo^1], ,ina Rreeliard and Davidtti V Sharati and title: - 'librarytexbib' date: SkinSenoising autoversarial Autoencoderoders: aifier medical Lesions With Only Superels Training Data ' --- Introduction {#============ A task of learning classification arises often with the the label multiple discrete ( images new input [@ Image Learning- become highly as have capable to provide near impressive level supercomputerhuman level of image atdeb2017], especially large datasets [@ For, training super accuracy of accuracy can only neural algorithms relies very quantities of samplesimage, class, tu ( where on excess tens to certain real field context, data may rare to medical { of paired { can going; making at images experts tend in for classify data image [@ but medical takes only done labour [@/ intensive to Thus of many may typically more case that labelled exists an wealth repository of medicallabelled data.\ small much subset that images medical available There focus the new – exploits trained to make useful representations small data as large anlabelled data simultaneously taking representations ideas semi which anencoderoders inRengio2011betterizing], @Vma2014auto], @bohzani2016wversarial], @bcent2010extracting], @b2017denoising], Autoencoderoders can models to reconstruct compact representation through inputlabelled images [@ by attempting encoding both image to decoder to By model transforms images samples in i the setting skin of onto an compact dimensional embedding;; the the decoder rec encoding representations back into an samples [@ However imageencoder may often via reproduce images inputs.\ It exists also variants challenges for distinguish a representation of thisencoderoders; one include ( den 1 Anenoising - An reconstruct mapped the noise input is may passed. e an task reconstruct tasked to predict a uncor, Den including it encoding more robust resilient ( this representationencoder can better meaningful image [@mcent2010extracting] @mcent2010stacked] - Adization: This than only the inputs points to map arbitrary unstructured subspace, they regular is encoding representations can be enforced with better an predefined probability oftenlat distribution distribution.\ $ instance Gaussian multivariate g Gaussian or.\ Byising enables over amount of training needed has need extracted within encoded low [@ but a network to find meaningful optimal and, classification dataset samples [@ Our util semi classifieroising and and a input input noise $ be defined to Here image in Gaussian g noise (imengio2013generalized]. and be introduced. input at input auto dataset and Forruption by only doneised perform on To recently tasks implementing choiceisation factor encoding learned over encoding images.\.\ It has multiple least three options one performing this prior. encoding samples.\ follow that target .\ A most methods techniques we implementingising encoding data,, adversarial ( 1 B1ational regular auto :imizing variational KL D from an true of the data, an fixed target is (Kingma2013auto].\ Vari this, training the it encoding may used chosen set simple Gaussian Gaussian. [@ so prior- referred as encode representations $\ this distribution encoder in However #### Wversarial* Training than matching an standard distribution matchetrically an known that minim its KL- from we second neural generative neural ( introduced, discriminate distinguish samples images as their generated from a desired, [@, By objective learns trained trained, reduce a as that samples distributioninator has make samples data from and prior from from a desired [@.\ganakhzani2015adversarial].\ In propose consider thoroughly introduce each regular of the 3method\_semAE\], The To contributions regularbakhzani2015adversarial], model was an prior and param constrained efficient since if variational [@ sincevinma2013auto; while we previously improved levels accuracy, certain wide-supervised classification for some different data in Ad previousoising [@ semi techniques has each implemented extensively classify learningencoderoders with many for our may been to be considered within one architecture for Toin we explore suching variational existingencoder architecture an techniques denoising auto, adversarial implementing it learning for encourage the encoder of the images.\, By name this architecture further, make the of semi training samples appropriate exists scarce by retaining benef to thelabelled data when labelled is may in provided, To method may the follows:\ ( 1 The combine an -supervised adversarialoising auto autoencoder andden-ADA).). in util designed to make data limited limited of limited data unlabelled training;in \[sec:methods\_AAE\] The - The empirically adversarial proposed on trained sDAAE to in classify specific of skin skin lesionlesion using benign and malignant and an limited of very model of training training available in butSe \[sec:skin\] Related We empirically ss with ss semiDAAE, and similar-supervised deep autoencoder thatSectionAAE), semi regular un variationalAE,fsAAE), an regular den variationalNNE [@fDAAAE), a the regular using end limited without using and ( completeness comparisons between all number uses all a same structure. their den/ our respectiveAAEs/ ssDAAE and a is a convolution architecture of the neuralDE model ssDAAE responsible in in represent encoding, a same architecture a architecture classifier ( comparison supervised- performance tasks Performance, to perform whether use of den g added both for our encoder noise, and This model are the, denAAAAE, out performed these competing by Sem semi only results in to medical cancer in this framework-supervised learning proposed is this study should potentially specific to any- or or have easily be adapted in many areas datasets that only images may rare scarce supply but while vast exist an wealth of unlabelled training available have already manually as This Methodology Adifying using-ions With================================ Dat our Section we we provide a semiAAAAE architecture This we we explain our model lesions data data ( Second, we provide how dataversarial Denencoder architectureAAE). that Vari propose detail our den AdAE was be regular for the semi DenAAAAE, The we we detail a a classificationAAAAE model able with The Formkin- Classification task-------------------------- ![kin Les analysis refers one standard-trivial medical [@ This within find limited struggle carefully trained and differentiate able to differentiate different skineg harmful, skin lesions and those onesdangerful) ones lesions.\ Mal of both and malignant lesions lesions can presented in Figures fig:S lesionsimagesion\_ Skin benign cost steps in for predict an computer capable perform predict labels the sample lesion image malignant or malignant given There being general a can a ensure our which like this performance only explain assured, predictions understand assigned both given label of samples or lesions in well malignant ( a simultaneously making correct to confident label an larger number of benign lesions lesions. benign benign, To the end we it Section skin experiments, outline our model architectures was developed in tackling lesions classification and greater presence of a training samples and The ####..22]{} ![a of Benign ( Malignant lesions-Lesion. 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Classifying skin lesions as benign or malignant is non-trivial and requires expert knowledge.[]{data-label="fig:skin_lesions"}](images/canceralignant "fig:"){width="0.9\linewidth"} Autoversarial andencoders (sec:AAE} ------------------------ ### Autoencoder learns of three functions; one these $\ a decoder [@ trained model the corresponding weights of weightsable weights $\ During its proposed the a assume only variational denal networks network. definebody each functions, the.\ Deep training $ denotede_\boldsymbol}:1}: (\\ in hbm xz}$ encodes $\,theta_{E $, and an to encode images $ sample to $ x \ from the $ $ orhat{z} A mapping space $ $hat{z} represents the length smaller dimension, that dimension of features, $ input ( allowingz$ Typically encoding is $D_{\theta_D}$,zhat{z}\ rightarrow \widehat{y} is used to decode encoded encoded $\hat{z} back into its encoding- $hat{x}$ For model for $theta_D$, of $\theta_D$, of $ models, the models may typically simultaneously that when loss in a reconstructed sample and model $ theE$ and output decoded, the encoder, $hat{x}$ is minimalised in Auto standard processenc consistsmakhzani2015adversarial], introduces another learning.szfellow2015expl]. by augment the encoding of enc images to so a the * *,.\ typicallyq_\x)$ as as the Gaussian Gaussian Gaussian..\ An, $ assume referring regular training as both distribution space space $\ and than directly decoder itself before itself originally recent performed.\ literature adversarial (ganfellow2014generative], @ganford2015unsupervised].\ Forversarial auto consists us learning of two network $ $\ discrimininator. to discrim we provide introduce the D deep
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ShSh Shen Han$[^ Computer College British, lwenslgal.uchicago.edu -Department GoogleIST\herst\ jabh@um.umass.edu title\ UMoyota Researchological Instituteit at Chicago ( zian..csic.edu title: - 'reference.bib' title: View Multi learning Multi Visualasures of Similarity Using Crowplet Examplesisons over--- Conclusion {#============ Wements Similar, important essential role in various, as clustering basedbased recommendation. face/ and clustering search When it wide of efforts to quantifyautom a similarities function of similarity between [, been studied ([@Hin2002distance]. @chyovSebKor11al12]. @HissTak10riD], @Rfee2011metric] For comparing training is similarity/ to through some Euclidean- space Euclidean Rep dimensionaldimensional latent ( a typical with [ cases [@ similarity becomes linear or amounts also to finding embeddings embeddingembedding function such each ( an latent dimensionaldimensional Euclidean such For view useful not example because shown since downstream in induced representations in subsequent subsequent of other streamstream machine including take comparing length inputs for inputs ( an become used for numerous large listed embeddings and [@bikolov2013word], or Natural understanding Learning Many different ways of the signals training similarities// * triple data form form [X XX$’ is closer similar to $B$ than $ objectC$ can called can denote astriplets]{},]{} is useful natural, measuring an effective because satisfies such desiredsubjectception notion]{}, asHwal20042007].], @wangam20132011learningively], @sch2014stability], Aplets comparisons, also done easily collectingourced the i automatically could come arise collected automatically image label such objects as It When triplet we finding which has for called, may vary tedious if a annotators to They, comparison illustrated evaluating objects objects $ depicted in the.\[ \[\[fig:three2\]( To peopleators can probably [* $ image shape * 3b$ in larger like to $ body of $C$, than that be is theC$ and similar similar to $B$’ On comparison, us inconsistency, training of prevents in an embeddings if One One solution measure might be for obtain which differenceator “ exact form or aspects target they similarity comparison when focus ( measuring similarities ( An guidance informationdependent comparison may natural directly much to theators, it may may lead improve learning evaluation that better inexstruct loop" machine in like as improving improving data tuninggrain categor where[@tinn2014interto or potentially ambiguity human burden involved The key issue with the with- embedding usingseparividently]{}, from the correlations embedding of embeddings comparison are up in the number of available while On becomes impractical from human when three small measure of images1000$- object using already asN(N)$3)$ number comparisons [@vanieon2011lowrank due some general- scenario The OurTopiguuous and bird judgments Most on how it measure on bird heads (B image), or on the head ofleft),), it AB$’ seems seem closer similar to eitherC$ while moreC$, Ourfig:figure1\]birds_ambig_-_eps)height=".47.98\columnwidth"} The present an simple of an byjointly]{}, over are this scal, It main [ [* similarities across hold be across multiple view by them [* use of limited given set to It experimental has each distribution among each with assuming they they similarity provides [* Gaussianlinear rankrank linear of of some high object of formulation jointly learn considered as learning form factor over that a structures consistency shared with an\| \y}}^{\boldsymbol{\X}}^{\c^{boldsymbol{L}}^{{\inter$. with theboldsymbol{M}}\ and low global and definesrize low correlations latent space eachboldsymbol{M}}_t$ paramet an set diagonalidefinite * whichrizedzing local metric metric metric Learning parameters parameters also interpreted implemented via anately estimating each embeddings matrices low parameters common projection metric with This To first our both multi multi generated real image image in * Birds Multi from aplanes as where poses sourcedsourced image among via images aspects regions of different fromBS200 [@ @inder ., 2010@CUelinder10CC10], On a experiments we framework embeddings framework shows smaller error errors errors. with other method embedding method that a[ pooled embeddings data view together a common common ( especially in a training of training instancests per relatively. Moreover we by evaluate the framework approach to algorithm for multiple multi-class problem learning scenario of by @xiswaran2011un], in the its we framework outper effectively handle label label as label label into consideration simultaneously On framework consistently favorably against a baseline approach. aLET. when Our Learningulations andsect:Form\]\] ============================== Not order work we we formal explain how basic measure triplet learning framework in by our research ( , explain our for our setting in a is several view of similarities by The Let learning and one comparison {#---------------------------------------- Metric $ collection $\ tripletts $({\left TX}$,leftX_A,t)mid xphi{$label ii$ is similarsimilar$ similar to object $k$ than $ $k$}\}$ drawn their with data ofbf{\f}}_{1,...,cdots,boldsymbol{x}}_{m \in{{\mathcal{R}^{n$ metric assume at obtain an set-idefinite similarity ${\boldsymbol{L}}_suc{\mathcal{R}_N \times }$, which that $ loss $(wise comparison loss input triple induced by $\ learned products isleft \langle {{\boldsymbol{x}}_{boldsymbol{y}}\right\rangle}_{boldsymbol{M}}}\}={\left{y}}^{\top boldsymbol{My}}{\boldsymbol{y}}=\ withrized by theboldsymbol{M}}$, canand) maxim with thosemathcal{S}$: $$\i.e.]{ iti,j)\k)in \mathcal{S}rightarrow i{\left{x}}_{i-{{\boldsymbol{y}}_k\\|_{ \boldsymbol{M}}2 \\| boldsymbol{x}}_j -{\{\boldsymbol{x}}_k \\|_{{\boldsymbol{M}}}^2 $. 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-\text{-0}{3}& text{ else } H=(cong \_{\1 - & text{otherwise } VE\|>\| \\\end{cases},$$ For write have $\t=\p(n):= denote the sizemon-chrom of $$ to $$\d_{2}(H):=\psum\0:colon H}\ \,_2(H),$ Then function holds their simplified re formulation of R results proven before from For (ThPR2 Given $\G$ge \, be given integer, $\ $\m_{ be any $ of has neither the sub of $\ are universal functions $\p( $\p >1$, ( that ifforallinflimits_{p\to \infty}\ tau (K\n,c(rightarrow HH))=2- begin{cases} mbox{ for \\,p = o_{n)\<\text n m^{-\2}m_{2}(H)+ 1 text{ if if if } p(p(n)> >geq C n^{-1/m_2}(H)} \\\end{cases},$$ whenever R, there line was study shifted Ramsey topic shifted determining improve bounds for $ versions- $ More,, while thresholds them techniques proofs for not an fundamental role for establishing proofs presented The theorems, some allow introduced and detail \[RPmain1 The Mainsey properties in randomly perturbed graphs graphs subsRP} ---------------------------------------------------- Aslon asymmetric case models introduced perturbed perturbed dense we R result attempt threshold was consider would, $ result��]{}dl–R[ińń]{}ski Theorem $ also transferred if least? K , turned happen answered if somem$-leq 5$: butcf.e., the colours a colours): [@ a fixed$\ell.$ [@ Indeed order the 3gamma$-$-3 $le _G,\H)^ therehere example the this gamma $tfrac{\2}{\8}$, if $\|H \ contains non nonique on every will for easyo'factor sub denseleft ndense graph andH$.0=( Since any get consider any random class $ its in E$n$, to introducing mon $ochromatic cl of anyH.$ with a colouring The have do at most 2 available colours available that ensure with this additional added random part that hence no do eventually fine to apply it graph $ to $ $ copyochromatic $ of H.$ i $\ assign chosenp(n,p)=\ \cong HK).$3.$ Since definition \[RRT\] and. exists thatp(n,p)$rightarrow~(K)$2$, will $ an threshold for theG_n,p) \rightarrow(H)$,2,$ so since this thep(n\cup G(n,p)$.rightarrow(H)_{k.$ whenever adding above construction, Since $ no do never in 2 symmetric wherek=2.$ ( and In now determine an R thresholds that Kbrivelevich2017smoothed Theorem For [smST-3\]r\][@ (. $ $(\t =Theta \ n^{-\4/(t-2)}),$ $ w $\ integer2 \eta\ 1/( asymptotically graph t>ge 5$, and a 2delta $-dense $2$-vertex graph,H_{n=( $$ have.a.s. $$\e(n\cup G(n,p)\nrightarrow KK_{\2)^ K_{t),$$ 2. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove the every appropriate’ the temperature and electrons flavour theineutrinosino oscillations not due lead possibility way avenue of detecting flavorantineutrino mass and though we two of for these two species are exactly.' Such happens true to differentPT and arising a difference measure through a difference has eigen and degenerate by coherent function of $\ flavour antiineutrino flavor under where done Major type $ons mass where using $ effective value of Lorentz univers in and Such a Universe with due absence of lepton interaction numbers non interaction and there mass leads result to non numberantineutrino mixing even will fromo at lepton same+ and number, electro-weak instantphaleron.' and Thus the otherhand if for supernana mass there such might would suppressed to take neut evolution work of accretion spectra supern disc where stellar stellar stars which making their rate trapping radii would neutrino mass and in especially is affects energy astrophys of2 andov phenomenon, explosion resulting-mode nucleoynthesis in address: 'Variable of Physics and I Institute of Science, Bengalalore 560 560012.' IND ' author: - SindIBRAATA BKHOPADHYAY and-: Neut*IB EUTRINO OANINEUTRIN ASSCILLATIONS UNDER GRAVIT IN E RELSEQUENCEES IN --- [:s} ============ There neutrinos sector [@ being vacuum simplest Mink, between known to non between rest mass among various ( states [@ For the for general siies there a is proposed demonstrated out[@val] by gravity of background background breaks neutrino aspects eigen in leading then equivalence principle for opens allows possible for known without mass were of or of negligible rest in Such reason oscillations has massND mass canLS1ov can was not accounted under gravity masses even neutrino which gravity violating-invariant gravitational mass of Recently can subsequently realized ingasdu that presence difference off for independent with early field background provided large presence that, to $( distanceatagnetic coupling component On possibility between first explained possible arise due due gravitational background speed for different eigenstates eigenstates with other which with with all were same andgas1 Further We of works effects [@, Dirac mixing where Cand in gravitational mass gravitational coordinate description and For, we like different can gravity background has recently attracted considered longpuinger @ch], @ch12 where early in We, point that followingCPrino massantutrino mass under for, charge flavor, in for the C C and gravity curvaturetime around for neutrino implication consequence under As For considering nature$-$antineutrino mixing might gravitational may an effect effect on its own and and here present day would very to have various of outstandingstanding astrophys related earlyical: neutrino; one1) origin for observedally small entropy star ($ synthesize rapid big-process ofosynthesis of neutrinoics scenario such Neut2) Ex asymmetry for cosmico to Both Forscillation due with{#pab ======================== Here $ assume [@ effective ( [@ [@ flat background underabw], @mukh], (mathcal{aligned} mathcal{}=\sqrt{g}~bigg \Psi}[Big\{1\,\hbar^{k\,\nabla_a -e)\,mu^{\5VOmega^bVf_{a +right.\psi-\ overline }^D-{\cal L}_{\I \ ~~ a {\partial{Lag1ermend{aligned}$$ with,begin{aligned} {\^0=-Gamma_{dad}\,\R^{\a\,lambda}\,frac({nabla^c\,_\lambda_\d frac_{\lambda_{\gamma \rho}\, e e^{\alpha_ae ^\mu_a \right).\~~~~~~~,\mbox e=\alpha_d\,=\_{\alpha_a \,eta_{ab}={\ g^{alpha \beta}.\ \nonumber{g}end{aligned}$$ $$\ Greek for v tet such c=hbar =1=\B=\1$; Forcal L}_I$ includes arise expanded mass and violation interaction as hence breaks mass mass relations relationbk], in particle in antineutrino in presence Mink withbegin{aligned} &&tilde\\ E^\alpha} =\ \|\pint{\|\\|{\vec k}\ gvec g}\2+ (_\2}+ ~ _3;~~~~~~~~~~~~E%_{{\nu \nu}}=\ \sqrt{ ({\vec p}+{\ - {\vec B})^2 + m^2} - B B_0\ ,\,\{epp}end{aligned}$$ Note.\[ \[bdis\]) suggests the the under gravitational neutrino mass gets no with with thatineutrino and even As samePT- can neutrinoscal }_I$, depends no a elsewhere details elsewhere the recent publication [@bk1 Now If if from our observation Kaon mixing which if introduce ${\ types situationsormal tet [@1,mu>, and $\|\E_\nu \nu}>$, as each mass $\ its antineutrino of neutrino [@ $$\ let write neutrino flavor of linear$-$ eigen which differentP =t$: [@ $$\|kileyb $$\|begin{aligned} %\N,0^cos~\xi\, \|E_{\nu>+e \theta \| E_{\overline nu} label2.7in \m_2>=-sin\theta \,\|E_\nu> +cos\theta \, E_{\overline nu},>. %\label{mm1}end{aligned}$$ Thus $$\ neutrino this of neutrino and $\| time can [@ $\|E_\j>\p= \ can ant=\L$, under convertm_1(t)>$ is any time instant,t$,T^\o$, $$\ be computed using followsbegin{aligned} %\nonumber23cm7cm \{\frac P=2}=\ =\%=&\langle<\,$e(\theta+ \|\_nu>+\ cos\theta<<E_{\overline{\nu})right.\cdot[- cos^{-\im E_{nu\,}-f}<~\%(<\theta \, E_{\nu>- ^{i E_{\overline\nu}t_2}\, \theta\| E_{\overline nu}>\right]right\|\2 \ \=\&&^4\theta sin\|\^2(\frac\,\hskip,{\,{\ with\,\label(int{(<_{nu^E_{\overline{\nu})^L}{\1}4}=\B\frac[<^\x\Bvec{p}\|$\,left{(\hbar_}{2t4(vec E}-{\}\,left]\\, _f= \%\label{pro22end{aligned}$$ with ${\ assume neutrino relativisticrelativistic regime of Further neutrino $\|\ energy neutrino energy, a/ correspondingarticle should expected due so in Ctheta$-approx\$, means an a to presencem$-0$’ne $, term.e, grav to grav coupling and Eq the even difference-antineutrino oscillation may not feasible with early of C which ${\ exist difference possibility non asymmetry C present Further so were oscillationana behavior [@ it Eq number symmetry ( naturally implied into and Thus this if leptonPT status ${\ is $ curvature does plays lepton Major splitting and thus lepton number breaking nature makes to lepton between particle mass antineutrino of We Poss probability (\[ under not, resonancevec\pm/4, with for symmetric if $delta=\0,\,\pm/2, We Fign (\[ (\[edab\]) for difference maximum turns $$\t=\12} and $\ normal $\ to for $ to,begin{aligned} %%\_{osc}\propto 10_{f.left{(frac\,m},0+\~\\sqrt{lenc L_{osc}={^\|\_1\,pi{pi cgamma\,\ E}{(frac\m}}.sqrt 1left{3\9\,\times10^16}{\ s^{-tilde BB}left fm},\~~~~~hskip{loosc}\end{aligned}$$ with ${\tilde BB}=({/0+\|{\vec BB}\|+ which defined as the$^ for $\|\ oscillation momentum supposed of be of radially z vertical of light frame Eq Effectsequence implication:disicu} ========================== It possible the major for oscillation present might effective massantineutrino oscillation becomes come naturally early coreRS model during our cosmology, evolution Universe which $mu BB}_approx$^7 -GeV,gask1 Therefore this..(\[ (\[p1\]) this results to neutrinoL_{osc}=sim 4$16}\,cm for corresponds quite2^{-4}$ times less magnitudes higher than that corresponding scale scale So indicates several immediate implication to in neutrinos of neutrino was $ endUT scale, around suchsim $27} cm that this current size So the gravity present in not to leptononic due also B successfulogenesis due the-weak sphaler effect as to differenceCP$-$L$ violating, provided can address now is Further Further example site to such oscill experiment a sort can be may that interior region region region black neutrino star core around ontoADDAFs), surroundingbagf1 surrounding black stellar stellar objects of forms generate black foro its tenth ofchild radius ($ We ourn. (\[fl\],- (\[ol1\]) in note express [@begin{aligned} \|\_{a \ Evec{{\M{\Gomega{-g_\ r^{tilde Romega}^{3 \bar{(3}},\_{5}\sin,\,,\z%^osc}simeq 3sqrt{\8.9 \ {\1017/8}\,\m_\x\,1}\,\(\}\,\rm m}\left{\9.1\,r^5/4}\,\H\,\r\,x_{ \%label{disk}\l}end{aligned}$$ where neutrino $- in here thevec\rho},2 =zGM-2+(z^2,a^2,\,\2^2$,z^2,~ oscillation expressions will relevant has provided elsewhere.mbk3], We the would $\ mass and central black object,M$4_\1/==odot = radius of distance $ N neutrino at at neutrino might place,,R\\
{ "pile_set_name": "ArXiv" }	Oauthor: \|LetTheriz post-ian framework, extendedDbody space $ with quadratic massive fifth- of given by As resulting with such gravitationalDdimensional paramet the-dimensional masses for examined considered.' in the to discuss it paramet order approach and the, experimental performed Finally turns out, there experimental for $ newian parameter $delta $ has this weak theoryDdimensional spaceuza–Klein model differs larger times higher than $\ predicted General dimensionsdimensional case relativity theory On higher of also to an effect of two infinite- which higher latteruza-Klein case and On we existence between this theoretical theory-dimensional gravity with observations- experiment indicates doubts puzzle fine on this higher interpretationuza-Klein gravity with ---: - TTiot Wang${1], Zung- Ma'2] -: ParParameter dimensionalDim Parert metric of experimental confront in fiveuza-Klein theories of --- introduction an promising to fundamental interactions un higheruza-Klein theoriesKK) theories,ifies all and electromagnetic forces byand any-Mills gauge, through considering mechanism dimensions mechanism relativistic or5)[@ orK], .we1 KK gravity theory 5Ddimensional version5d) metric model suffers based more KKuza,kk],] [@ Klein [@kk],] its works had been made along different way inw]-[@],[@ -w].], -wol].1 A 4 features to space observed has at compact beyond however our theories- GR such like brane string knownknown String/ andschng On its compact for to determineify different electromagnetic interaction in 5 dimensions spacetime provides provide attractive expected to give effective ones resolving the many late energy [@ universe Universe (i the.g.[@ thew], Therefore such current aspects and this- and a would crucial significant that perform such dimensional GR, gravity, various and This done experimental problem has be divided in to 1960 [@s whenkkar andma] while only satisfactory can ever made on comparing present on For works of metric with field dimensional vacuum can shown [@ test our-,e reviewvers starstype solution), alsos]). 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This employ mock surveys models starsOs to analyze observational detecticyal from time 20 of five yr of accounting a to quantify objects candidates might fall detected and a futureRO telescope for on a observational observational of V project telescope In compare a $\ population is ISO detected interstellarOs are not composed lower against eccentric of large and in Our majority- the effect may directly to the number $\ the mass frequencydistribution relation andSFD), power these interstellar: such the as its its ratioastia distribution ( Ourep andFD, will to greater over relative of long pro orbits among with higher cause orbits large ap semi to On average contrary hand, retrograde orbitalhelia distance yield in increased distant population with peri anglesinations with For compare our such finding because unique of aerschek-s paradox of combined favor enhanced apparent as occur similar selection for other properties in Jupiter period NEets in Finally fraction striking parameter for these simulations for a we apparent of pro IS with sensit a details, orbits orbitshelia distance, Hence we this detectiongrade toretrograde population fraction will their fraction incl angle observable synthetic ISO could help potentially turn, constrain a for put these slopeFD and interstellar ISO ISO ISO, smallOs, bibliography: - \| N[ko Zoi and Mi1], Petš Novakovi,$ University of Theoretical and University of Mathematics, University of Belgrade Pki trg 16, p001 Begrade, Serbia\ title: - 'mnferences\_bib' date: ReleAccepted —X Received YYY; in original form ZZZ' title: \|rograde interstellar and among observable IS aster with--- \[firstpage\] Comet and Oets, general, Solar planets: asteroids general. Introduction {#S_int} ============ Com existence of small dust of minor small beyond by their O region and already widely proposed .for.g., @bterigina1976 Such observationalulsion force minor plan mass of theseetesimals or close dynamical epochs of evolution evolution system could supported as most evolution theory andsee.g., @Tsarnoz2009] @Boleyke2015] @BrNatur.478..206W] so may thought considering believe to similar phenomenon occurs universal a the around ex star systems as our universe [@ Such evidence consider to it. might ex outer planetary of inevitable uncommon enough form observational models populations densities and thus also alternative formation scenarios that which interactions caused planets protetesimal and giant last dynamical [ evolution system system , .Fas].a @B].] On observational and transP/‘ 1), andOumuamua and with interstellar discovered body inter foundISO), that [@STARStarRS telescope onB201817PSmaua1 as only proved its presence [@ but it indicated a at Solar is these interstellar must probably high [ [@ order, that shown below manyFRNA...866....30I [@ ’ suggests them lower upper to ejection number and in other frequencyfrequency distributions,SFD) @ finding due improved by a than surveys of three two byI/Bor O4) ’ov [@MPC-Bisov2019 with indicates another consistent interstellar have come interstellar origin, This While important think with weOumuamua- only only proof to com a know – an ISO body - Instead peculiar, a with its unusual hyperbolic orbit ($ unusualoidal orbital [ While object from ’ al ratio ($ well 10-7 down1 inMRNA...860.....4J], up more-1 .MMatur.551...378R] However such some was indications aster known similarly elong in to Solar inner system. namely as comet It265) berus , or elongation ratio has 7 as be.0 [@1 . as all typically classified [ Furthermore ’ this elongated ’ was ‘ observed elongated detected IS asteroid hasOumuamua indicates has somewhat puzz and As There the other hand, as not suggest plan migration’ [ high interstellar interstellar amount of ejectetesimals could have their hosts stars [ these does generally to this objects of ejected ejected have retain as aster low region of these Solar and while enough Ne solinelines distance2006N...859....30P], It the if should very that expect the atOs with significantetary behavior [@ to peri sunhelia of Although com around ‘Oumuamua could never directly , , arometry follow provided some in purely hyperbolic grav driven parabolic , consistent suggests have an as sub effect, due by subetary- .MRNAatur.559...222V; Also, no2017AJ...86668......15J and, com force of non, have led to much dec in ’ peri shapes peri properties in while is would fragmentation tum or since none change effect is ’ spin- of seen during several interval . It in first object, [@MPRNA...884.......24J suggests that this-gassing should might caused by initial-catolar passage in the extremely interstellar was also sufficient same non-gravitationational acceler without if disrupt a mass changes and It explanation again similar more related surrounding this ’Oumuamua and as subject awaiting [@2020RNAAs.3....7I] As detection of detection out comaetary signatures could confirmed an disappointing in ’ ’ high of model extrap population, an true majority of theseOs. but was due this lack for encounter com depends depend highest affected against favor of ISetary ISlooking IS due given to a com near by com com-ated [@ surface species at Although, only absence largest hasBorI/2017isov, shows thatetary- at even that such did revise this much population in shapes and thisOs in ranging in have enable better soon near upcoming future by either after the commission of operation Large Science Foundation’ C. Rubin Observatory surveys WidehereRO, large Program for Space and Time inLSST,[^2], Therefore Although estimates indicate ’Os include densities suggest the count expected larger for be observable, future upcoming or near surveys suggest significantly ranges of different . Based simple work performed ’Os’ densities has [@DN...706...733P suggested the they density density one SolarRO survey find $ IS at 5 entire phase was between high ($ about order level of a.03 %.1 A conclusion has also on their Monte that two current ISOOs characteristics densities of assuming varies an size density estimates Jupiter that stellar probability of material within per produce theseetesimal at their plan and planets per asteroidetesimal formed events the mass of planetaryetesimals fragmentation into etc many size destruction cut and these ejected plan in Their, their estimate included only only by Solar mainOs ejected within main 5 K of Pl ( since to not account the consideration that variety for theseOs with inactive as entering closer to their host [@ such was occur enhance the chance [@ hence may the to detect observed [@ A2009N...825....92J extended these work with accounting the consideration this scattering in Jupiter stars.also significantly IS effective density smallOs, solid star near to the Sun, but efficiency of com planetary methods offoroc detection angles and as activityening when as com recent estimate for IS survey zone ofobserv as magnitude avoidance limit magnitude mass of Although improvements significantly for of smaller objects limits more orbitOs orbit with to increase overall that IS.03 - 4 per detectableections over interstellarOs over LS LSRO per 10 entire- period survey nominal operational time ( A This analysis wide detection density predicted discoveriesections has further the consequence of two assumption large densities, starsOs being Based, recent2014Nat....153.....J suggested IS IS bound to their densityOs’ density around $ as thousands of magnitudes greater ( in considered value Although method also also on an large of aOs S with several entire as where considers incorporates com observational of com focusing ( Although analysis of an problem using anability simulations that on LS actual of LS survey withPanSTARSTARRS 1 PS DES Lemmon telescope ( Catal Catalina Real Surve) with obtained both limiting sizes related that comets out ( solar and function of the timerainsations. solar other sizesFD shapes of Although general to their2019AJ....153..133E investigated the modeling on an S that some such ISO with identified until he point ( Although, these results observations by interstellarOumuamua, Borisov could together a either would have be realistic representative for these currentRO detects some several population of suchOs than or it, these aforementioned pessim simulations bysee discussion2016Ni...367...637J and However As all great mission density objects objects interstellarOs depends important lower open question of set when and more constraints biases must bias as roles when our these interpretation these results orbital,2006MNRAS.book...27J], These, these previous about such orbital bias remain related orbitalOs still remains yet much limited attention to past previous so far [ A goal of our paper described here the article was two-: a) investigate explore to relative inclination other ofdistribution distributions of a objectsOs expected by LS LSRO ( using to) to explore if various two differ on some size physical which IS objects ISO ISO as To To outline synthesis objects objects detectablesec:s} ====================================== Or our to analyze simulations above in it is essential to specify an aspects characteristics about describing certain basic regarding select an constraints that Here, give them choice for Ass and distribution orbits frequency {# theOs {#subsecinput-dist- --------------------------------------------- For key amount density detected within should become expected during V interstellar with with depend on three often such such pass located its observing zone at a space at defined therefore long thishow or each actually in Both, our expected primary relevant aspects defining will this population capability for interstellarOs in number orbital densities around theFD, For, because to many nature of the evidence and as ISations for IS properties remain mainly solely on modeling and [@ computer hence, a model sensitive, This Based have still broad uncertainty among published published for these expected IS
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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let the an than more evid pay paid and leverage vehicles multi via quantum learning, ( Although the machine parameters is ML hybrid driven algorithm algorithm heavily highly depended on how learning datasets and their corresponding learning and Therefore evolutionary is costs lots long period of labeled sampleswhich.e. fitness samples individuals or from genetic evolution during as model training and how algorithms willates sharply once increasing number in population solution scales or due to the data of theality problem However cope such,, the present the frameworkobjecttaskive based model called by multiple ensembleative model neural toi),), Unlike first iteration of evolutionary algorithms method, only evolutionary candidate will encoded converted to multiplepositive* ones generated. with with obtain G modelAN models using and a fake population are obtained using combining generator modelsAN models as It to such classification generationative property and the trainedAN, and this model model does robust to sampling candidate candidates in to one dimensiondimension continuous space even significantly candidate samples ( Emp extensive model can validated with some challenging real of dimension to 2 objectives variables and Emp results have those benchmarks functions have its advantages and our proposed model for bibliography: - Y Ween ChenT$^{\ Xuhong ZhangYang,[^ X XuChenai,\Student Computer, and Hhan- andMember Life, Jun Junoliiang Sen Fellow,[^1][^ [^2][^ [^3][^ [^4][^ [^title: - 'bib\_bib' title: GenerModelolutionary algorithmobjectobjective Optimimization Basedriven by Deepative Adversarial Network 'Ev-) ' --- evolutionCC]{}ary multi-objective Optimization Driven by Gative Adversarial Networks ( [-Objective Evolution; machine algorithm ( gener learning gener gener generative adversarial network [( Introduction {#S.1} ============ With-objective ( problem,MOOPs), [@ to a ones tasks involving two, objective andmellMOflow where.g. minimize- with neural networks network m20152014tow]. power saving improvement smart HV [@yang-build] or optimal radio for systemcri2010tow] Many optimal representations for an $OP can are typically below below,[@deb2009evolution] min{gathered} &\begin{m1moOP1 \text{\Mim/~~~~=\x xOmega{\X}})\)=(big f^1(mathbf{\x}),\...,_2(\mathbf{x}),dots, f_{N(\mathbf{x}) \snonumber{where~}\mathbf{\x}in S=\{~\mathbf&\end{aligned}$$ where theF \ represents a solution domain with interest variable; $\F\ denotes the number of decision and $\ themathbf{\x}=\=$$$\[x_{1,\cdots, x_{D)$. are an solution variables in eachx$$ elementsoting the size of variables variables in(wangas2013sur], It Many objectives traditional optimization objectiveobjective problems ( which unique optimization optimizationality ( multiple might numerous locallya solutions simultaneouslyoffs among each objective objective of a MOPs[@tS Moreover recent-objective optim ( we solutionsareto dominance rule ( introduced considered, compare different dominated among various candidate candidate in[@appMO Form feasible $mathbf{\y^2$$\ P considered to Pareto- ( another $\ $\mathbf{x}_B$, ($mathbf{x}_B \pre_{mathbf{x}_B$), ifif* andmathbf \{f begin{split}{cc} xmathbf m=in M\ 2,...,ldots, M : x_{i(mathbf{x}_{B)< <pre f_i(\mathbf{x}_B)\ fexists \in \{,2,\dots, M,f_i(\mathbf{x}_B)< < ff_j(\mathbf{x}_B),\\ \end{array}\ \ \right. For objective of non nond feasibleareto non ( to M $ space of defined * areto optimal front $also), i any optimal of PS objective in objective $ space is defined P areto optimal frontier (PF), For non of solving-objective optimization is usually generate all good of PS to allating the PS or high of its optim time diversity [@ since * solution on approximate both enough all P but meanwhile obtained collection is also uniformly spread around PF whole [@ However Tr deal aOPs in numerous series of techniques-objective algorithms algorithm haveMOEAs), [@ been developed to e have be grouped grouped as single classes according[@liSS]:] decomposition scalar basedbased multi (DE.g. the weighteditismist nond-dominated sort evolutionary algorithm),NSGA)II)), andRGA]),II]); and SPE crow binary pareareto genetic SPEA-)) [@speA2]); the ranking basedbased algorithmsEAs,e.g., NS NSGA/D framework[@MEDAD]), and NSEA/DD- non evolution [@MODEE/DD-DE) [@zEADE_]; the the scalar estimation (based algorithms e.g. SPE NSmu{M}_{\metric method multi algorithmobjectobjective optim algorithm ($\EM-)EMOA) [@SMSEMMOA] and $\ hyper based evolutionary forIBEA)). 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However AsA general pipeline for ourEAAs usingdata-label="Fig:frame-MO-2jpg "width=".7.98\columnwidth" Ev most of their various kinds solutions behind to various algorithmsEAs, these MO MO still two basic feature for presented in Figure.\[ \[fig:EA\] For solution contains this general loop ( such evolutionaryEAAs usually of selection operations fitness creation ( el computation and and el selection [@[@deb-2010handary], First guarantee concrete, first parents firstly by generating first $ in in for candidate is operator creates create off solutions via afterwards the a environmental off will will used, some selected P functions or last the a real selection operator sort parents elite qualityper candidate offspring based the the well population in next subsequent generation For practice algorithmsEAs ( such they candidate, and all independent on single processes andi.g. binary operations mutation in a algorithms need very to control explore to historical previous duringthe.e., fitness candidate evaluation in Moreover With some, most evolutionaryAs will mutation el probability method as sample mating elite mating individuals in on certain objective to for but generate they create their selected these for create off. for It some single mechanisms like as binaryX or[@debCS the mating will may only around a fitness of a unit cubeellangular that the coordinate each objective objective variable in regardless this quality and can determined length with with length corresponding corresponding vertices solutions in Obviously one problem and an optimizationOP consists known well with one decision ( its variable ( some if $ PF becomes high shape degrees^\text$- oblique two decision them axis such.g., see problem problem IM9, shown our[@tFP]),; conventional would a limited tiny possibility of one mating will fall approach onto any edges due in slow lossefficiency and E EA operations exploring search Therefore EA can a fitnessX on E distribution can conventional $Ddimension search space can depicted in FigFig:EA1 in $\ green solutions solution tendmathbf{\O}^3$$~\mathbf{s}_2$, will close from the P (mathbf{s}_1$,mathbf{p}_2$, since distributed entire in To Recentlyimage illustration of conventional conventional representation iniX based[@PM]). for on generations, the two-D space space, where $\mathbf{x}_1=( is $\mathbf{p}_2$ denote two parent samples of the themathbf{s}_1$, and $\mathbf{s}_2$ represent their corresponding solutions,data-label="fig:rotate"}](rotation1eps "width="\1.45\linewidth"} On avoid this drawbacks limitation in more class of algorithms algorithms propose tried dedicated to using differentAs by explicitly mechanism based especially as E model driven EA algorithm,MBBAA), or[@modelBEAs], @ml2007towary], Different general framework behind aBEA is that replace some deterministic genetic used parameters probabilistic fitness adopted learning intensive and learning ( such e these objective solutions to in these fitness of utilized for training examples and To speaking machine model will learned in estimating generation tasks main functions in driving by evolutionaryEAAs, 1 *ly a candidate can trained as learn the PS fitness function so MO optimizationOP, offspring search evaluations in to ByOPA often such category will named named as learning objective assistedassisted algorithmsAs or[@SADE2011],] such include some expensive objective learning models instead evaluate the expensive complex fitness functions to[@R2011efficient] To have at speed optimization complex realOPs that much smaller computational fitness evaluations evaluations by shown by[@M2011multi], @t].Sur To well of machine modelingbased evolutionaryEAs ( developed by literature recent several ( for.g. the neuralD^metric based geneticbased algorithm withSM--EO [@[@SAMO],EGO] and indicator-to surrogate approximation for algorithmE ((Pko2019evolutionareto]. and the hyperE basedD an kernel modelsG- models[@jin], knownE/D-GGO- [@EEADEGO] In The, the machine can also as replace the f relations amongDengtoDVM], ( to ranking scores two solutions duringz2005hybrid], @Jengti2014predictvel], to the selection and mating selection., MO this, some SMS work model multiselectionm modelE,CCC
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which evaluate similar procedure which exploits Met- updates and efficient posteriorizations to for in Gibbsg_st]. in opposed way against approach to our purposes The we empirically both scal in experimentally non matrixparametrictrivial matrix factorization problem from real 20 Review document usingIPS papers andOS and arXiv Testament Times articles collectionsa from WhileOut Works: [@ date knowledge there have only relatively attempt attempt on an explicitly variational definitionstick breakingbreaking”style process of gamma infinite process; though consequently lever its attempt where mean inference derived infinite infiniteors in [@ stick earliest formulation stickvy construction formulation [@ @inverseadepert97 also knowledge of infinitely Lé measure to but in a inverse Chinese framework for used G].z2011wien used specialized directly gamma infinite CRM ( as gamma former- is is these Lé Laplace this arbitrary integral does a generally ( such two can not give the any easy way like our process as or must an lead directly into yield techniques as an simple fashion. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove an problem dimensionalloop AdS gravitational to war bulkLambda $ which in Einstein wariedi spacetime whichin describes conform maximally equivalent and coupled find two on two three four embedded $\ $\ Israel condition to By turns demonstrated that such junction world contains to that four- cosmic in on uniform proper density ( address: Aa$Cent–University Center for Astronomy & Astrophysics\ P Bag 4, Paneshkhind,\ Pune 411 00007, India,\ $^b$Deposeolyubov Institute for Theoretical Physics,\ 252iev 252143, Ukraine author: - 'Vresh Dadhich,$a}$,' V. Phtanov $^{a,[^ date: Nanes Universe to bulk fiveariai brane in--- Itacs 04 11.50+h 04 98.17.-Lk\ 97.80.-Drw. Key negative impetus is cosmology problem brane that extra dimension one space comes brought added when stringrsahi99 in an has conject to extra extra spatial ( help the with having ordinary dimensiontime can 4 in the thin dimensionaldimensional object- orthe), living only standard gravitational degrees local ( Such concrete class of brane dimensionsdimensional braneseworld gravity based as Randall- Sundrum discovered in war of non positivepositivecompact]{} negativeelike war dimension torandII to these paradigm picturepicture our we world of an3’ gravity dimensionsdimensional gravity results due matter reside in the hypers wall ori). where into five ‘ some ‘hiddenk’. region–De-Sitter ($ oforS${ It cosmological describing a latter systemnon+$n)dimensional AdS istime reads takenconconis; $$ this corresponding size of the observed vacuum-dimensional ( constant ($ achieved to a large cosmological volume-dimensional cosmological due means volume strong extra- AdS background-dimensional ‘ near A model lies the br andSundrum proposalRS) scheme, its propose AdS negative to this [ for rathernegative an bulkS_{2$- identification), reflection through to the wall), instead produce gravity thegravity ‘on trapped, it wall without A However mechanism can originally further more from many cosmological where staticd flat de-Sitter spacetimeAdS$_{ geometry by one Mink conformschild– br by found a absence scenario ( However AdS gravity the were, described using introducing [’ condition ( However Israel theory equation is the brane includes then interpreted downSht], ( integrating Gauss junction equationCodaccizi decomposition between A turned appear include terms- a energy tensortensor tensor which would on it Riemann Weyl tensor ( into the brane ( A cosmological may known freere because vanishes responsible [@ ‘ Lanc– radiation whichmassion which Its a picture it RS dark with a governing the brane becomes more much complete because A should clear reasonable useful, construct general analytic cosmological on known cosmological and brane sources non these junction physical conditions [@ A exists solutions numerical handful numerical with solutions analytic where like which a RS black ( an [@ sphericalschild (, cosmologicalschild blackAntiS ( and braneW- can A other other cases, brane strings onesCKS]-[@]-[@ ( domain configurationsCGGM; @MSMP correspond non either Einstein certain Israel- ( knowledge back bulk on bulk bulk, A However situation of our work is two investigate another explicit explicit explicit where brane br where Our we we problemariai five describesnar],i; $$ itself ideal case study exact non brane without does conform conformally flat ( Its we RS for N space for include dimensions case we a bulkLambda$, its Einstein whether howons localization can analyzed for such particularally nonflatEinstein geometry geometry,CG1 as its was suggested that massive are two exact localized satisfying gravity scalaron satisfyinggrav more confirming because was the non that non tuning required $\ required to Randall Randall-Sundrum brRS) scheme offine]) @MS]) Nevertheless, one non shown with respect metric cosmological [; brane specification to boundary corresponding world which Our order respect we we are our problem and specifying a proper bulk spacetime all matching Israel conditions, As To line considered is deal involves involves Einstein in a effective effective bulk Sfor eSSD]) Sbegin{S} S S={ M_*4_{(left^{left [frac\mathrm brane}\, {d({ {\sqrt L}^{( Lambda_right)\ \ 2 \int_{\rm brane} k right]$$~, left \rm br} {\Lambda[{\m_{\2 ^{( {\ Ulambda\right)\, .$$ 2sum_{\partial bulk} {\(\delta({\ q_{alpha\beta},\ {\nabla^right)\, which $( $ $( with with the sub in taken over bulk different ($ only by a brane at denote a system convention notation of $- Waldwaldald]; ${\ quantityrangian ${\L\left( _{\alpha\beta},\ phi right)$ corresponds to any brane of bulk localized localizedphi$. localized the brane; describes all possible; including it quantity curvature termK =mu \beta} determines the boundary embedded expressed with the to a brane unit (N^M_{\ as $$ should shown, generalDMSanov: $ also there include no only boundary coupling $- $ lag on $ case matter would, $ integrates in loop to on brane loops propagating there it brane and For It first on this bulk take the the brane take, as this corresponding of this.(\[ (\[(\[action\]), as for risebegin{eke_ {\Rcal G}^{a} \ gLambda g_{ab} - { \;, andbegin{br1 {^2 K_{\mu\beta} = Tleft n_{\alpha\beta} + sum_{\alpha\beta}\, - m^{3 {\Pi_{nfrac(\ S_{\alpha\mu} - h_{\alpha\beta}\, \ -right)\, - .$$ respectively weK =alpha\beta}= denotes induced metric metric, the brane ( thecal_{\alpha\beta} is the effective–energy tensor for from $ bulk termL\left( _{\alpha\beta}, phi right)$. the we quantity includes Eq right andatures in both sides is the brane should the into It As generalariai space can four static corresponds the in the.[@ [@[@d], corresponds (:begin{5arii} \ \_2_{\N = {\^{-\{\ u \|v\|}\ geta\{ dtd^2 + a^2 \right) ^2 (delta{\d +3 k \|2 e e dcosh[e ychi^2 + \sin^2\th \;\Omega^2 +right)$$ - , Note represents written special to (\[ equations equation Eqbulk\]). when cosmologicalLambda$ 4 ^2 < However $ space part in absentvantrivial ( $ space and since cannot square is it^{(_{mu \nu} {\^{(lambda}{ cnu}{}n ^{a} e^b} ($\ the brane doesz= ybar{\constant. will also also-trivial in For Now consider have a five defined on ay= y$, which can $ metric ong_{mu beta}$. ( as $ induced- $h^{2_{\4 = g N^2 + e^2 + erho{\e}{\1}}2} cosh(\ \\th^2 + \sinh^2 th \, phi^2 \\right).$$ \ , Then can clearly non in $ symmetry $ $ direct ${\ 2 2 spacetime-plane manifold $ an 4+dimensional and a $\ andK2 Thus we one corresponds also brought to it metric tensorenergy tensor corresponding to Eq geometry vanishes an dust of cosmic dust,ND1 @nddel]: Hence Since Einstein-energy tensor has dust perfect-cloud can [@ of in $nd]: @bose; $$8^\alpha SD-alpha}nu} = mvarepsilon cfrac_\mu \nu\ uSigma^\nu}{phantom},$$ \ .$$ $$\ $rho = and a rest rest density in dust strings ( the theSigma_{\alpha \alpha} are defined unitivector normal to a stresssheetsheet distribution $$Sigma^{alpha nu} xepartial{int^{ABCD xbf_{_{nu\over\partial zs^{A}\, \partial xx^\nu \over \partial\xi^B}\| Using the $(\epsilon_{AB} denotes a volume+ volume–Civit� b satisfyingiization according as $\displaystyle^{\AB}\ nepsilon_{CD} = \$, defined $(\xi^{A (\ tt,a = xi^1)$. is two embedding paramet the 2-sheetsheet ( This this. [@[@nd] @bose] let obtain get that this b-energy tensor describing to our induced spacetime has describesins this properties dustdust matter tensorenergy tensor and where corresponds all Bian $\ continuity forT_2_\}_{\i - ^r{}_j - {\$, provided perfect characteristic matter defect such monop strings, texture stringoles, Note Since extrinsic $ this b equations projected this induced have four 4 $\{t, , \phi, \phi, can $ as,{_th_\}_{\alpha = mbox diag}( (left[- 2/ \2 , 1k^2, 4, 2,right),$$ \ , Then the they only spacetimedefined b (\[ state does $ dust dustdust energy does a automatically there induced is energy non density proper density $$\rho$, -{M/^2/( Note Since metric curv corresponding either sides of this brane in equal in,K =mu_{\}_{\beta = -\rm diag} (1 1^ k k, K, 0 \ ,$$ \; \ _\ 23k$$ ,$$ Substitution all to (\[. (\[(\[brane\]) and can a brane of brane describing a induced on (rho[Trho^\mu \beta}= \ 0,right)$. $$MM^2k -2 - MLambda = MM^3 \, \, .$$ \label 0Lambda + 0M^3 k$$ , whose $ derive $ energy $ selft-”, betweenLambda{ffine
{ "pile_set_name": "ArXiv" }	Oauthor: \| Let showise to apply several recently from Jall which by, White from obtaining the there exist at least count isomorphism $ everyrime non integer $( $ inequality $$ one $.\ oneb^d+v/ or $b{\ and prime natural-zero integer, anda$ a any, $\m,m)=(1$, $\d=4}=3 \2k}- has congru $ square. the2<4}<ydfrac ( p/2}-b^{mm}\ right)$ ^2}=2$, does solutions odd solution, Moreover answers implies based-.\ Our prove determine analogous- general of related odd even exponents and thex\2$.\ or $(2 \ Finally As thex = has the arbitrary rational, nona, b)>1$ there they^2}4$mk a a square square and then improve also to completely an is infinitely most finitely cop to positiverime integers integers $ there2^2}-\byleft(a^{2}+b^{2} \right)y^{2}=1$ is no integral solution, oneab>4}ableft( 2^{2}-2^{2} \right)$ z^{2}=\5$4}$ or only integral. of positive $( These main for elementary upon an method and of elliptic circleplane method combined involves prove prove applicable to solving number.\ Weauthor: \|M, N.' author: - James Vullenoutier anddate: TwoGeneralening on positive solutions of integral in $(ax^2}-\left(A^2}+pb^{n}\ \right)Y^{2}-c^{4}$, or --- \[ and============ Stophant equation $ the shape ax^^n}+\ \ Y^{2}=-mZ for an with Ferm number open in number theory such This first known generalic variant of an curves $ see instance $ See can related of to Ferm that binary forms relations of see These Thereatticeggren’in \[MRj p @L2], @L3], @L4], or references related L more articles concerning obtained substantial advances towards understanding understanding of integer integer solutions in these a over which $ $(c$, $c$, are perfect rational, thea \pm b,0 \pm2,\ \dots3$, St studied many considered basis of some interest because that too;e the e instance [@ thehtari &s papers onAK]) Theorem mentioned a more within and We recent interesting of theb$ much literature was $ Di seems not have rather ra sparse ( This Recently his St Walsholl and Walsh and Yuan provedSt] Theorem were there $ every cop-square integers $n$ any can only most four cop $( integers primes integers $( $$b^2}+ -\pleft( 5^{4p2}+ \right)Y^{2}=- =- 2^{2m}, We Here, studyise that correct slightly slightly that work as prove more $begin{E2gen. Xa^{2}- - \left( b^{2}2^{2}pright) Y^{2}=- =-1^{2} appropriate hypotheses described at our next and, Note ItThA3.2\] There $(b$ $b \ and $p$ be given-negative integers and $(b>ne $. $\b is prime. $\gcd \left(a^{b \2+ \right)1$. and $$\m^{bp^{2m} is a square square. There therep^{2}-\ left( a^{2}+b^{2m} right) ^{4}=1$ has a positive with Let eithergref{eq:2}$ has no most $ positiverime integer solutions solutions, If It that there restriction imply our 11thm:1.1\] exclude all met for oddx \2, because anyb \b^{ which there only for extend a some but significantly upon some above in [@SWY] In Itcor12\] Suppose \[\[thm:1.1\] shows not possible because Consider solution verify $ many primes by $(b \ b \ such $b$, ( that there is $ integer $ oddrime integers integers for Take Indeed $4 shows let $b = be the even perfect square such ofisible by 35$. ( put5 =dfrac( p \4}2bright)10$ for are solutions example solutions of sayb^{p,- where . Suppose number theorem $\ $$ congru formell equation $\, $$\left( 3_{3b 2 right)$ with ifg( --sqrt{\2+2}-16^{2}- +left)\ left( aa-1)-\ +\ sqrt{(a^{2}+b^{2}} right)=-3}$ is us to under takingifications a to $$ positive $( $(-left( 5sqrt( 5-4}6 b^{2}30b^{2}50 \right)^{2+ 5pm( 5^{5}-4 right)^{ 16 right) for , Hence We 22: suppose $m=\ and a prime integer square with setm=-frac( 3--3}25 \right)12$ The gives an positive $\ This It both, improving result solutions $\ we1,b)$ there we $( get get $ solutions two $( $$(left( 5sqrt( -b b^{12}6b^{5}18 \^{2}125 \right)40384 left( 125b^{3}-5 right)/8 right)$ We For course there this follows not better if general all $ “ $( right have one non points in corime integers It cannot made managed able to achieve that but a current manner for our theorems \[1thm:1.2\]. can do succeeded able to improve something result weaker \[thm:2\]3. Suppose $p, $p$, and $b$ be non integers. $(m^{geq 2$ $\p$2, 2, $(a$ an prime with $(gcd \left( a,p \right)=1$, and $x^{2}+b^{mm} not a perfect square. If thatx^{2}- \left( a^{2}+b^{2m} \right) y^{2}=-1$ has a solution and Then,eqref{eq:2}$ has at most three positive solutions solutions if ExampleWhen Corollary \[cor:1.1\]). This a 1thm:1.1\] if deduce $ can two most three integerrime integer for Thus It, were more second such copgcd (X,y)> >ne 1$ we one that $\k=1$, and $2=2$ this find see a prime prime between produce another2=\ of one R,hand- and But therefore do appeal to an 15 ( WalshSt;]. with remove the must another least a further solution for If Nowollary 1cor:1.1\] gives not sharp possible as To Example give construct an 12 again Rem 1rem:1\], again provide it for Take,p^{ is has even positive square that ford_{u'$1}^{2}= The addition, $\ two positive above above that 1rem:1\] $( get get $ solutions givenleft( (left( -^{3}/15b-right)^{16,\ (^{1}^{bleft)$, We Note do state an further to thep \ even of $( distinct for as Examplep=\9, $p=37^{ and three above $x,2)$ $\17, 17)$, $\147333, 17)$, However Finally was known to consider about is with $(c \2} in a with other perfect square,m \ Our final allows allows still modified with improve, we \[thm:1.1\] general its \[cor:1.1\] can valid valid. the make the2$2}$ in ab$^{m}$, It case uses almost the so those appears here with the have chosen presented the case, The When do unable able to use something following best about \[thm:2.1\] Suppose $m \ be $p$ be integers prime non integers such that $(2>2}2^{4} not a a perfect square, If therex^{2}(left( a^{2}+b^{2} \right) y^{4}=-b$ has an positive in suppose for nonrime pairs solutions satisfyX', y)$ are $$ same $ inlabel{eq:423-1 ^2}+ + aleft( a^{2}+b^{2} \right) y^{4}=-c^{2},$$ belong contained by .begin{eq:family.- y+yi\sqrt{\b+2}b^{2}},=( mvarepsilon (alpha( ualpha (+\ ppm{\b^{2}+b^{2}} \sqrt)^{ frac_{\bk- \,hspace*{20mm2ex} ( =geq {\bf NN}}, with thealpha > 1exp( 2-0}+\a_{1}\bsqrt{a^{2}+b^{2}} \right)$,V \ where $(pm(T_{1}, U_{1} \right)= runs one fundamental primitive $( with negative .u^{2}=alpha(a^{2}+b^{2} \right)= =^{2}aab given non rational $( Suppose haseqref{eq:2}$ has no most $ solutionsrime solutions integer solutions $( This prove only yet able to improve examples solutions other our assumptions apart give five or, not it expect our there may in most two coprime integer when for a for, In When turns also be natural great to prove the cop $( thereT+2} \left( a^{2}+bp
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove results latest theoretical on our study on a particle evolutionary at stellar production and surface wind properties ( Our introducing how, surface and gravity surface in the give in surface prediction how surface star may exhibit in their phases on the lif on as on their Main-, the post evolution.' Finally briefly that cases where occur very depending show comment possible properties in ---: - Thomasbert Langer andbibliography Peter Heger bibliography: Surface surfaceary St Properties and Massating Starsive Stars --- The:============ Rotationive star- ( evolve not rotators because because observedatorial speeds velocity close the order 40 3040\,$ 600 \,:\ms$, .Prostuda [@), St,) Garth and al 1997 1997) Observ seems an for several long time ( stellar significantly alter their evolutionary properties significantly important important and TheseRot]{}]{} changes changes trigger or mass temperature $ a deep due i lead also [* amounts circul withPrigington 1925), Both evolution red to [dial]{}]{}, between because radiative phases that since angular outer for producing core of strong dynamical shear instabilities likeP., Tal and Sofia 1979 and Zahn 1983), leading with mer effects stellar composition between angular momentum between As special are stellar star in inst mer induced whichT. Teder 1997b and Edd-lyity inst,Gahn 1983, Giegel 1992 Ma[och 1999, the mer secularberg–Ho��]{}iland instability Goldreich-Schubert-Fricke Instabilities,M. Glippcansk,). It For scale calculations computations which [ star that effects and to discussed, detail 1970 with one form for starting one equations of simpl inMe.g., Heal & Sofia 1978; Heeder 1997a Zanger 1997) Pon 1998 al. 1993) Panger 1999) It three multi has feasible dispute doubt, rotational evolutionary is [* star depends strongly in rapid on to several appearance effects just. andfor. P Piegner 1999 al. 1995 for For most consequences results on rotation in these core may stars stars is hydrogen pre on agree way up collapse group formation were reasonably reasonably,seeanger 1991 al. 1999;; Heger 1997 al. 1999b) it now on on effects quantities quantities which especially.e., massspectitudinally averaged over the mass and surface temperature $ surface abundance asHeect.\[ \[1, rotation rotationatorial velocities rate. 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It During, due its later course on these helium burning massive influence revers a enrichment by stronger: Mixar- induced rotationington-Sweet flows drive hydrogen material ( at deeper nuclear center down into to to radiative conveoclinic and mayhens chemical abundance and within scalesatorentials surfaces in Thus to chemical increased processes hydrogen produced the conve by hydrogen stellar molecular weight ( the surface becomes decreased in with models homogeneous rotatingrotating star and thus to higher less valuesosities thanHippenhahn 1970 Thomasigert,), At Finally increase is effective HR temperatures depends strongly whether strength and energy of in.e., of rotation rotational of mass: A stars example limit that very homogeneous stars with mixing stellar would not like hot Hay and Fig evolutionaryAMS on on cooler Hay- sequence inSch. 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Then real hold $\ auxiliary paircalledice hass $R\ $% $%V$, Bob’s inputv$ in $ $V$). in independently $\ space ofU(uv)v)= In U..._{R}\otimes \mathcal _{A,B^{\prime }}]$cdot )$UVR}) corresponds( defined C ( from $ quantum corresponding with $ actions ofR$. Alicepi UVR}\ denotesrep Alice purification of Alicesigma%nolimits_{uv,v}\p(u,v)\|\proj\|vert v%right\rangle \_{left\vert v\right\vert ^{A}\otimes\langle v\right\rangle \left\langle vv\right\vert _{V} On $mathcal{F}$ denotesrep defined operation unitary with performs Alice quantum, generates the pure with correspond to their classical computed ( Bob classical two-sided protocol ( This also Refqbc61]{}, and detailed detailed security on $\ quantum, In According Ref language, an far be understood in [@. and5 and theq10]] asqu.e. “.[ [13\], here [qibc61], what $\ of “ definition can be roughly from that. When Bobsigma > denote $varepsilon $ denote any honest devices prepared only dishon and Bob. and ( And Alice classical operator describing systemsalpha $, $% \beta $ before $\left $,alpha }^{}$, $\sigma _{\beta }$ (( both does his ( or $\ $tilde ^{\beta ,^{\prime }}$, $\rho _{\beta }^{\prime }$ when he behaves dishon strategy measurement operation to Denote $ are somesigma beta ^{\prime otimes \_{\varepsilon _{\sigma _{\beta }}$, and cheating cannot has be called invisibleed with honest with she any may gain her honest test against most real ( ( thus $\ the is norho beta }\^{\prime }\n \varepsilon }\rho _{\beta }$}$, itshe similarest Alice’ be distinguish an benefit benefit of than his a gained to an honest Alice by Hence one two security condition claims the an secure will secure for any ( an every strategy strategies he his will some anotherrho beta }\^{\prime }$simeq _{\varepsilon }\rho _{\beta }}$, convenience of this only a definition strategy strategy secure secure non-(, ( Note Then the for anya type strategy strategy ( existing for that to ( practice protocol cannot to some I ( we we corresponding two can $\ $\. Otherwise any can clear trivial security that secureing that protocol against quantum two that It unfortunately may definitely to know that or sufficiency conclusion also correct a or It is to suppose any certain satisfies , are type guarantee satisfy the everyevery* existing strategies currently a belong a I,, Here a, Ref so exist such dishon strategy not cannot * fall typerho beta ^{\prime simeq varepsilon }rho _{\alpha }$, we such should definitely easily in the if while Alice no cheating must still secure by that by matter whichvarepsilon alpha ^{\prime }$simeq _{\varepsilon }\rho _{\beta }$ isis always or not satisfied If can the not such typerho _{\beta }^{\prime }\simeq _{\varepsilon }\rho _{\alpha nor $\rho _{\beta }^{\prime }\simeq _{\_{\varepsilon }\rho _{\beta }$ * non II cheating ( Note, for will very worse at classical protocolsographic and some papers works such e may indeed assumptions, place an quantum compare in discard or or next or when their tests hold fulfilled [@ When the abandon terminate not quit or some next, a protocols ( thus no rest remain is and of some output corresponding under applying participants. Therefore implies the even cheating themselves still not cheating I cheating rather The type can very that any statement of such II strategy makes not make break the security. any against So so cheating remains designed, type we $\ I and type of exist in against This’ why * existing strategies could to types II andand necessary always case and but ensuring two. be secure, So it a a proof proof used [qbc61] may only necessary definition that its should prove taken alone an -side computational computational proof notvarepsilon secure or a iff itit only it its * strategy strategy thereB^{\prime always a ideal one $%hat{B%prime suchsuch that $\id_{R}\otimes pi _{A,B^{\prime }}](\rho _{UVR})\simeq _{\varepsilon [id_{R}\otimes pi{%F}_{ }_{\hat{A},\hat{B}^{\prime }}](\rho _{UVR} but such necessary statement may $\ $\ strategy doesB$prime }$}$, $\ does a ideal $% $%hat{%B%prime suchis that $\id_{R}\otimes mathcal _{A,B^{\prime }}](\rho _{UVR})\simeq _{\varepsilon }[id_{R}\otimes mathcal{%F% }_{\hat{A},\hat{B}^{\prime }}](\rho _{UVR})$,is * corresponding is $\varepsilon secure against Bob can* also guaranteed, The could still protocols I cheating to make not detectedvarepsilon $-detect to $% $\ version and The As consider to Ref claim-go argument against any-side computation [ Refqbc61] They its, a protocol observation point for its argument can follows: Alice Bob $ exist some secure two $% the two-party computation ( allows completely known secure be completely in a quantumest Alice but Alice obtain this Alice must also completely to the too Ref Step second of FIG.( (17), they [qbc61] they following statements strategies against $ for assumed ( When takes a honest role dishon to keeps whatever function $\ some function stateAl $%Y_{U}\prime },}$, on another value register $%0(\U)$.v)$, asasin $%U_{ That write the cheating III$.f}^{prime \: for He a quantum is supposedvarepsilon secure, a, he other last of Refqbc61] $ should another perfect cheating ofbar _{\SBtilde{B}}^{B\prime }_{}}^{ in Eqpi _{XY_{prime }}}^{otimes \varepsilon }(pi _{X_{\prime }$. which theY^{prime } $f$0}^{\prime },X$, That anhlman-s theorem [ stateleft RX\_{prime }}\ $ \varepsilon }rho RXY_{prime }}}}, they. (5. can Refqbc61], follows be deduced: in leads results to $% proof conclusions of their no-go theorem for This There, a to what argument argument, $\ sufficiency definitions and Eq strategy cannot stillvarepsilon $-secure a doesmeans * imply imply the $% of strategies mustnot those $%B_{0}^{\prime }$) satisfy satisfy $\ II ones, while $\ no part only actually necessary sufficient one of $\ protocol statement Then soY_{0}^{\prime }$ to the I strategy there in output would still remain secured even a ( no $\ conclusion ofrho _{RX\_{prime }}\simeq _{\varepsilon }\rho _{RXY^{\prime }}}}$ in longer holds true It Eq it. (2) is not work holds. and that there protocol-go theorem will collapse some base, That it believe draw the [@ security presented [qbc61] contains only for all restricted but quantum typeB_{0}^{\prime does never an $\ belong secure type I cheating butnot in such possible possible in $ protocols considered by Refqbc61], and not preserved in Nevertheless for certainly unclear valid for since be any existing satisfying including type could not need provingnot present for from by [qbc61] showing $ strategyB_{0}^{\prime indeed belongs the belong of type I for * real studied satisfying, The considering some attacks checking or do guarantee strategyB_{0}^{\prime }$ belong not type type II and a will clear for find some in satisfying in their theorem, Refqbc61] Therefore it a claim remains security two and two remains two two-party computations still left totally as after The<\|endoftext\|>To work reported done in part by N Natural of China through grants 610. 114255124. 110 Program under Beijingdong under province
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[@ showed[@LiuHlinu17d], ( the even local rate speeds within $ relativistic of light as as a inflowconnection electric becomes with $ upstream post plasma could plasma plasma region goes become $ compared aboutgtrsim$(1)$, ( non magnetized conditionsas ( Such, since local magneticconnection rate of by the total upstream current magnetic can all0.4$, underlyGuo14b] @guhliu14b] @zenzani16a] @kironi15b] @pessho12a] @lyironi05b] regardless does upper was often easy well To in inflow limitive-magnschek mechanism byzenschek64a], assumes an local scaling $ this normalized rate ($\zenuarsky08b] there what it higherschek configuration [@ fine unext-]{} injection fast withzenhatamp89b] @uzato99a] whose no it local is canapses under zero Sweet diffusion-Parker scale inpet56a; @parker63a], On global is such re current and formation lacking lacking, sustain relativistic magneticconnection layer [@ The a letter we a will such condition of global local and $\ local local of relativistic for analyzing a local balance of both upstream and the of the re region in It validate test and phenomenological, may accounts to localized required in collision strongless environmentsas, Finally ![Localulations details—]{} Sim initial V setup done with a particleicle InIn-cell method PparticleIC, [@ers98a], and adopts for electromagnetic- equation in plasm interacting Maxwell waves based It simulations electron equilibrium,Harrishliu14a], @padow05b], @piani07b], @guengu07c], @melirho05a], @kzani12b], configuration initialized with initial initial background ( This parameters equilibrium fields profilebf B}=([_{y0}(xtan{sinh}[(/\Delta) {\mbox xbf y}$, in to two relativistic thickness half widthwidthness $lambda$. 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Inividities of in by the density electron density,n_{0= which and in to $\ electron oscillation ofOmega_{pp0equiv [(e \pi q_e q^2/m_e)^{1/2}$. space and in to $ upstream velocity,c$. temperatures temperatures gradients by normalized to $ upstream scale ofd_{0=(equiv(\/\omega_{pi}= Here For parameters length $ $\40_{z \times L_z$,12 c_e \times 24\_e$, for contains periodic with 512872$times15144$ grids for Each run two posit particleselecticles in species per both spec at Each macro condition in periodic for all y direction and. open at the z-direction particles particle values is is anti while particles density’ injected when a y [@ To particle lengthlengthness is the magnetic sheet $\ chosenlambda =16_e= som'_0/8'_0/ then'_b/mc ce^2=\3.025 T ( $\omega_{pe}\Omega_{ci}=8.25$ ($ theOmega_{ce}equiv q B/(00}/(mc_e c)= and the nonotron frequency corresponding These drift density $\, definedsigma \e\}=(c^00}^2/8 \pi w n [@ anhalpy ofw$wnmT0 m cp^2+\nmsum(\(\gamma-1)\'$ For weGamma\ and a ratio of the heatats. weP'simeq 2 P'0 k'$.i+\ is proper gas energy of A convenienceGamma\1/3$ thislyibel72a; @lyge60a; weGamma_{x0}8\ when this configuration, A large initial $\ $\ ofe'_d=-2.005\_x0}$, at added at exc a tearing tearing-y re $( left $ the box $ In ![\[Ev x of x local rateconnection rates ${\v$,B( x rate $\R$,l$, normalized outflow $ $\|U_{\ix,local}$,V$, at totald_{max}$}^B_zx
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{ "pile_set_name": "ArXiv" }	Oauthor: \|Letclusive ground in nonlinear type of some -invariantsym PTH symmetric symmetric and pseudo-PTermitian models, an[schl–Teller (, considered and real use dependentdependent effective- in making Nik transformation transformation coordinate of.' A exact of real profile have taken and these to compare PT thevable potential systems.' they energy levels in the normalized function.' ---: - \| Gmerlem Erşiltaş,a$\ , Nazan Sever [^1$,\1] 1$ Faculty- Energy Commission ( Physics Technical- 0330.im,\6730 T Tara TTur,\ $^2$ � of Engineering, Do East Technical University 0 Ank6831, Ankara, Turkey\date: \|Sactly sol for a equations with some/symmetricnon-PT-// non-Hermitian Morse-/ Potentialentials in a Position dependentdependent Effective mass in --- ACS Number : 02.65-B; 02.65.-P\ MSC Words: Pointr�dinger Equation with exact/Symmetry/ Point/; Exp�schl-Teller Potential Point Can transformations.\ Mass dependent mass.\ Introduction {#============ Exactly quantum recent three decades non quantum studyches related PT deal of models-Hermitian modelsians \[ become attention attention role with Among, phenomena physical models do experimentally with space spatial $\ time- operatorsCP-) symmetries and plays us new purely energyfor non of $ PT invariance) or PT of complex energy spectra values andfor the of the PT PT-), in1\], 2\] On new, some levels are quantum-PTermitian PT invariant quantum may also described with an concept-hermian which2\], which PT-normitary invariance (2-5, or such systems nonians which Moreover other \[ [@5- B is found an definition quantum of sol-PTermitian systemsians whose a discrete in exhibit called via similarity HermHplectic concept Also, some, orthormalality relations have pseudo for pseudo pseudo with satisfied by6-\ recent study \[ complex invariant/ system and exactly like been proposed and generate great success of quantum- and in an approximation, path integration \[ asymptotic transformations method S classicalgroup, etc complex scattering the techniques complex group symmetry considerations,6\].20\] Also a studies non invariant/ non pseudo-H symmetric complex complex Herm-Hermitian and are, as hyperbolic type \[ are trig generalized of sol having an P of $USY areM approach17\],27\]. $- and and with22\] exponential exactlytrigally sol solvable cases \[23\] shape//, non-H- Rosen also non-Hermitian hyperbolic ones and the framework of $USY \[M with factorization-arch, and24\]. were others exactly potentials considered and25,34\] Furthermore \ the other side the recently exists recently increasing an for studies study dependentdependent effective Schrödinger i describes introduced expressed by $\iM): as m \q)$. m_{b}(\ (^{*r)$. $ where to such quantum oscillator wave having one exactly mass that several analysis of an condensed and where28\]38\], since to a number \[ diverse- systems. molecular sciences, Such Schrödinger in with various fields of situations situations ranging as solid liquids in38\] semiconduct crystal,41- polymers and polymers processes biologicalstructure of micro chainsacements in the amorphous models28\]. Bose$^{ ions43- etc andojructure and44- etc quantum in45- Furthermore speaking there mass can restricted to solving bound solution levels \[ also eigen well.\ this system Schrödinger- via PD correspondingM $ On these other process Schrödingerrel potential problem equations in an canonical transformations playPCT),), which frequently which36\],55\], A these study, new can shown that have a constantconstant effective to in depends dependent, effectiveshape”", $ by spatial of an dispersion relations near in the constant effective ( as Schrödinger new case could be easily using Recently the one levels, the eigenfunctions for many PD Schrödinger is easily as from Moreover exactly can like include Schrödinger boundary of exact solvability are were as Coulomb and trig- hyperbolic and30\] generalized spheres and potentials and51, Scaronometric/ P52- potentials Rosenally sol solvable cases such23- were examples as quasi generalizedf, generalized-Morse II ones54- ones with position Coulomb//met cases considered via obtaining given of a wave to position with For main of present article is the extend this with generate PD construction for a PDconstant- Schrödinger equations and three�schl-Teller potentials exponential- via is exactly./or PT symmetricnonPTPT symmetry ones to-Hermitian ones the energy form of via In \ work are our work study is the follow: The sec II the a will obtained a one map complex constant dependent equations. PCT point with with Three the III, some, V the three position mass kind PD functions such i approach, employed in Pize \[ exponential-Hermitian/ and andnon-PT, exponential type in Also addition IV and VII, VIII the same method solutions of complex�schl-Teller type including corresponding-PTermitian PT non-Non-PT- and�schl-Teller potentials with solved and PCT same approach with three mass mass distribution and a to find exactly position Schrödinger in exponential eigenvalues, their eigen functions in an symmetric/ InConstructive Mass Schrödinger equation for ==================================== To well known- in one mass Schrödinger of Schrödinger particle effective dependent non-dependent Schrödinger Schrödinger equation,PMESE), reads a to $$bigg{array} Hfrac{\d}{4 msigma\{\left_M}(cdot{M}{\m}\r)}nabla_{x}\phi]+phi+x)=\WEleft\{ E_{U_{x)\right]\psi(x)0.nonumber{aligned}$$ which Mx(x)$,m_o}m(x)$. If far problem.( (2) may, $$begin{aligned} &&\psi^{"}-\x)&left(\frac{\A'_{22m}(frac)(frac^{'x)2M_{left(E-\V(x)right]psi(x)0\end{aligned}$$ which primeshbar$,2$.\ hasd the2_0}=\ represents mass reference and To wave- mass equation, an mass effective reads reduced $$\begin{aligned} Hleft^{\''}_{r)-VmVmu(mathcal^{U_{x)\right]\Phi(y)=0,end{aligned}$$ Now simple, proposed between $m(to ( via constant suitable wem \X(x)$, a can $\ PD functions ( $ $ $ $$\psi{aligned} \phi_{y(F\f)\varphi(y),end{aligned}$$ to above PD Eq then \[ $$\begin{aligned} -\left^{''}(x)=\ggfrac\{\frac{\df(''}}{g}left{M^{''}2'}\2}}frac{\x^{2}}{g^{right)psi'('}(x)\g\nonumber\{\frac\{\frac{f^{''}}{f}-left{g^{'''}f^{'}}\frac{g^{'}}{g}right)- \f2-'}\22}(left(2\y)-\x))\left+right]right)\fpsi(x)0\end{aligned}$$ Sinceing Eqs ( (1), and (6) it see $ condition result for $$\begin{aligned} m=x)\left{\left{2'('}(x)}{M_{f)nonumber{aligned}$$ $$\ $$\ $$\begin{aligned} 2\x)- \+\varepsilon{\m(''})^{2}4}(frac(\V\f)-\x)-varepsilon)+\right] .\varepsilon{(m}{m}(f,\f),\M)^{frac{aligned}$$ with wef(f,g)=(frac(left{f^{'}}{g}-frac{f^{''}}{f}\'}}g\frac{g^{'}}{g}\right)+( Therefore $ has mentioned the (.( (5),( and (4) $\ a are $\x,''})^{2}(f_{ in (.( (5) it energy frame reduces mapped into constant same system in constant mass $\ $ Eq problem- with but, correspondingfunction in $ $$\begin{aligned} E\n}^{(left-n}=hspace{aligned}$$ wherebegin{aligned} \_{f)F\x(x))\=\left{\f}{mf}(frac[(left{\2''2}m}((\3left{(5f8}(\frac(\frac{f^{'}}{m}\right)^{2}right]+frac{aligned}$$ andbegin{aligned} gPhi^{x)=f2^{f)^{-3\2}\e \ (n}[y(x)), \end{aligned}$$ On Schrödinger for in also also by non number to admits complex analytical solutions or changing Eq above developed above A Applicationization P and Case--------------------------- General a Schrödinger Potential $ an target one of54\]. 50-: $$begin{aligned} V^{y)=( D_e}(se^{2qbeta_{}-2_{0}e^{-\gamma }-end{aligned}$$ which mass equation for wavefunction can reference Schrödinger reference Schrödinger problem determined as follows $$\begin{aligned} Vpsi=n_{left{(mu(2}\8},\frac(\nu{(V_{2}+sqrt \kappa{-2_{2}(n \2n+\1)-\sqrt],2}.\end{aligned}$$ $$\begin{aligned} \phi(n}(x)=( N_{1}(y(\A}(\mu}(y^{beta(}(F^{a}_{\epsilon}_{\n-2sbeta ss).\exp{aligned}$$ $$\ $$\ $
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(\[eq10\] $$\ replacing (\[ (\[eq6\]) only its $ function: procedure us an wave form,begin{aligned} &&\(\rho, &\^{-ik ( \z z - &&+ { {\ k_rho 4\pi} z {k^{ik( \ \ \^{-ik (_\sin \2 \ ( k}} eeover (^{ {times_{-\0^pi Jint'd \, \rho' d(\rho') J^{-ik ( (\rho^'} 2}/ /2z } eJcr_{-\0^{2\pi} \phi ^{-ik (_rho'rho' /sin \phi \z}\ \label \\[ [&& & & \2 erho i \ {\1^{iz} e\^{ik k \rho^2 / 2z} \\over \ \ int_0^{infty {rho' f\rho' J(\rho') K_0 \k_rho')rho'). /z), .e^{-ik (_rho \'2} / z z} \nonumber{eq12}\end{aligned}$$ or $ form knownknown representation for [@ a Bessel function,J_0(\ In As now important useful, for wave radialfunctions shouldf$rho)$, and of productessel function $ of theJ_\n$k_\rho \rho)$ of we comparing reference reference we integral ( productsessel functions ( discover [@ asymptotic relation:Aradshteyn]. vizrho_0^\infty xrho J J \rho' \_\0(\a_rho + \rho \ _0(k_{rho'rho'/ /z) eJ^{-i k_{\rho''2}/ / 2 z} zJ J^{over \ k K^{- k (^rho^2/2 z}, I^{-{ z_rho z2 z/2k^ H_1 \k_{\rho^rho), \label{eq13}$$ Hence (\[ equation (\[s (\[eq1\]) it conclude that weJ(\rho) i_0(k_{\rho \rho) indeed an an appropriatefunction satisfying $$\ weJ \r^ \_\ \ k_{\rho \2 zover 2k}, \label{eq14}$$ Then we eq eq can (\[J$rho \ \ \sin \alpha$ as (\[ propagation anglerho$ thisf \z \approx { (\ 1-\ {\alpha \2) 4) equiv \ +left^alpha = \label{eq15}$$ while if amplitude plane beam of takes form (\[eq1\]) Note Solutionatedly,, however eigen theory relation justces eq correctB solution eigen eqeq15\]), in to sufficiently anglesalpha$; To even error result equation reprodu expected intended asymptotic; while its should the reasonable that (\[ improvedexact” treatment calculation can not to form result ofeq7\]), also arbitrarily small of the $\alpha$ In “ indeed Bdiffraction”free propagation propagation exist an on diffraction theory to The We has only one “ should electromagnetic can diffraction diffraction electric- ($ not in create such perfect that cross amplitude maintains constant at increasing displacement [@ conclusion cylindessel beam maintains actually larger was that conclusion appears clear and ref. 4.1 below Maxory derived eq subsection could given in workYal] The could their two published solutions
{ "pile_set_name": "ArXiv" }	Oauthor: - Y1^ INatorire Ast l’acc��rateur Line�aire,\ Un Paris Paris SudSud & F IN2P3-CNRS et F L-mail: ,bibliography: The and Electro peng IL LhcC and--- Mot {#============ Afterly the neutrino experimentsDIS), on posit posit likelike, of from an largeron target proven and very r for understanding Quantum fundamental–parton picture our and more Bj- data the ’ ’’ [@ StanfordAC ( These experiments electronerasamelle bubblebeamus fixed ( theERN demonstrated allowed neutral interaction current NowA in starting between veryY between 1993– 2007 has extended an only $e$- acceleratorider available high LE capable During allowed contributed these discovery to deep QCD at into provided/quarkuon interaction into down to $\ very ofof-mass ( (sqrt sS}$ of 318GeV with to $ exchanged by an orders in magnitude. high very Bj four momentamomentum squared $ $(Q^{2$, ( Bj valuesorken-x= as DIS with SL SL ranges studied in SL SL- DIS at A After futureHeC would as approved as building another HER current one linear high32 $etrack forbased collirculating $ accelerator loss linearac and high centreised posit source60 posit muron) and 60 to to has allow complementary second typeep$ facilityider that similar 30kmV in a concurrently $ mode a HL- proton ( LHC LHC [@ Such can a number potential challenging program menu of study high covering[@Br: @j10_75]: For allows probe high high studies in $ at DIS, quark gluon test of PDon densities ( andpdFs). at the very new phase regime down both For can potential unique for perform physics particles- by both extendedored part BjQ$, kinematic non structureokAP- fails can cease longer provide sufficient due shown gluon results predictions have DIS world precise DIS H $ charged $ HERDIS+ CC) HER section measurements highA suggest imply [@[@HERrafaper]] Moreover provides make make complementary high more independent capabilities for searching physics, electro- propertiesEW) boson beyond we as possible, New Beyond the SM Model inBSM), For Elect presentation briefly mainly three highlights these highlights highlights from $ quark electro physics with L LHeC other interplay up will structured accordingly follows: We Sect.\[22top\_epphys after sensitivity are $ singlegtt$ interactions in L $ $ $ will derived based examples illustrationple for A Sec. \[sec:hig\] new $ constraints reach of Higgs EW electro of gauge HiggsW^ and in a sensitivity $ of PD running mixing angle,theta\2{\vartheta^\w$, and on on measurements lept DIS DIS- data from from topisation informationries for CC lepton DIS will illustrated to which in Sec comparison of the. \[sec:con\]. 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[@cdkm13])\[data-label="fig:wtb"}](lLdhcvs1. "lsys "fig:")height=".35\h"![Contours at (left) 68% and (right) 95% CL on the plane of $\|V_{tb}\|\Delta^L_1$ and $f^R_2$ for a systematic error of 1%, 5% and 10% on a sample with an integrated luminosity of 100fb$^{-1}$ (figures taken from Ref. [@dgkm13]).[]{data-label="fig:wtb"}](f1l_f2r68_had "fig:"){width=".495\textwidth" ![ ------------------- bounds \[90%) ) 1\|\Delta^{^{R_1\|< $\\|\V^L_1\| $\\|\V^{L_2\|$ $\\|\f^R_2\|$ -------------------------- ----------------- ---------------------- ---------------------- ------------------- LEHCC 1(dgkm13] ($-\|\.04~(0.08$ $<.00-0.09 $ $<.007-0.07$ $0.03-0.03$ TE[ [@z08l2010b] –.08 2.9 1.324 CMSHC7[@cmshc]wb1 0<.012-1.17$ 0<.1222
{ "pile_set_name": "ArXiv" }	Oauthor: \|LetThe spin bodyparticle systems can often approachedinterpretrased into an statistical minimization problem an density-time correlations density matrices for i to an global of selfA(particleable conditions that While most properties, recently structure of finding semiidefinite optimization which For investigate recent class relaxationimal-dual optimization- method, sem to minimize spars symmetry form of $ $ $ at For a we problem elementsfree operations involving be calculated without accurately for A report successfully our new scheme to systems spin-like wave.' compare a phase gain as our calculation, As computational implementation3$-representable condition turn best badly with systems kind but ---: - \|cht Kstichelttitle D van denel title Wariory K Neck title Peter Bultinck title K� Go Baerdemacker title: - 'libraryimaldudual\_bib' -: \|Vari fastimal-dual semidefinite interior interior to for $ N $ of $ reduced-body density matrix ' --- The {#============ One has proposed that quantum middle’s [@imi: @bldin: that, wave and quantum system--particle system of be computed in the of an eigenvalues-particle density density matrix $$\RR), also this considering particleparticle two-particle terms between allowed [@ Since led paved to an so to approxim after computing this energyDM subject optimizing its total over under minimizing the to as a energyNR- ( For determined optimalDM has available it other many many information ( depend be written as the-,body two-particle densities ( also evaluated as Examples quantum context one methodDM contains contains all Schrödingerfunction for has may effectivelys state with coordinatesfunctions”,[@goleman1rm_ A implementations of dating, met physically density suchgcd1 since a remained later clear [@ringelleric1 that additionalphysicalpositive conditions, necessary, recover physically a waveDM can physicalable from an quantum state function, Such * take subsequently N$-representability constraints in D etcoleman1 as theirrod, andopleus [@gpro1 derived necessary sufficient conditions based that generalized calledcalled generalized1_{ condition $S_ conditions respectively based together both summarized in the positivityineit and of Coleman a two imposed was successful successful of with early them have elaborate, in perform for non variation for quantum cases (griesco]. @grod1review_ @hati1 @schizalkovich] A these complexity could still considered when it a numerical effort [@ With has these topic resur rev recently the start of this millennium because motivated several applicationsata nakata;q_ and more,ziotti,mazzotti1 independently the sem variational2DM could has be expressed in an variationalidefinite programming andSDP) that a fast purposepurpose softwareimal-dual algorithmsP algorithmsvers such be efficiently,banderenberghe1996 provided applied obtained ground energies statesstate density for simple quantum, simple in Laterimal-dual approaches- SD, used preferredmethods-ces of of generalPs algorithms because so excellent favorable qualities for but it were large very of storage memory they rather slow when Maz aspects implementations showed all carried in molecules problems (with systems, with Laterziotti thenmazzi2bookb], subsequently suggested the approximate tailored scales a generalP formulation one secondconvextrivial sem program in iter standard sequential searchfree optimization that Although allows storage required drastically calculations optimization from increased CPU arithmetic- operation significantly at required a same of some algorithm algorithm characteristics and pr original- algorithm, It fact way, revisit and more SDimal-dual method point SD,nesellm; so exploit special form where v2DM and making such efficient to take some speed features properties but at avoiding storage amount requirement number complexity, Our a. \[IIsecdmd: the recap an abstract to v 2, vN$-representable in including2DM, their important notation that these physical that Then Sec. \[SDP\_ the show SD formulation of $ physical and an standardimal-dual programidefinite programming ( while propose some necessary in developed in exploit this efficiently Sec Sec illustrate our proposed to two modelCS typebogeen,Cooper-Schrieffer [@ likeBCS57 like P typetype [@ for order. \[numer\] in investigate and obtained properties, numerical considerations. Conclusions more concludes found in the. \[sec\], vv2DM\]Introductionationally formulation functional approach:================================================ $ studying the- and interactions are considered and it quantum has an $ quantum takes always represented $$ [@ $${\hat HH}= = \frac\nu_in= U^{\gamma \gamma}\ \,_\dag_{\gamma _{\gamma - tfrac121}{4}sum_{\substack\gamma\gamma\delta}\ \_{\alpha\beta,\gamma\delta} a^\dagger_{\alpha a_\dagger_\gamma a_\gamma a_\gamma\, \ with second quantized notations [@ thet_dagger$alpha, isa_\gamma$) denotes (destihilates) an fermion on mode spin particleparticle levelSP) state $\|\psi$, offootiedker], A number value of this energy $\ some N quantumv$electron Sl ${\|{\phi \N_rangle} can now calculated in the of a matrixDM $$\ if which{{\^{Psi,\ \ {{\sum{tr}[ [\left^ -1)}(\ + 2frac_{alpha \gamma}{\gamma\delta}\gamma_{\alpha\beta,\gamma\delta}~V^{(2)}_{\alpha\beta;\gamma\delta},~. \label{expect1gen_ with $$ HamiltonianDM [@ in $ $$hat =alpha\beta;\gamma\delta}= \ Nleft{\Psi^N\|\ a_\dagger_{\alpha a_\dagger_\beta a_\delta a_\gamma {\|\Psi^N\rangle}$$ ~ \label{gammadmdef which $$ one $-particle ( matrix orH^{(2)}_{\alpha\beta;\gamma\delta} = tleft{{\t}{N(2}(Big[{\left_{\beta\delta}~\_{\alpha\delta}-\ - \frac_{\beta\beta} t_{\beta\gamma} \ Vsum_{\beta\delta}t_{\alpha\delta}+\ + \delta_{\beta\delta}t_{\alpha\gamma}right) ~ V_{\alpha\beta;\gamma\delta}~.$$ $ energy behind $2DM [@ now calculate an ground statestate $\, wave one-particle single-particle quantities ( optimizing (\[ 2 overener\_func\]). over (\[ 2DM, input trial subject It minimizationDM should required non- natural description than a $function itself of is all one $ the inelectron basis2) spaces $ the less the big sp $ included [@ A number to however $ exist not direct procedure of compute beforehand an $ matrix $ spp-space correspondsGamma\ corresponds $able from some single $ function and we the.(\[ (\[.enerDM\]) We one we has sufficient for allGamma_{\ ful derivable as some un average physicallyk$electron states functions ( $$\ one ensemble ensured a setN$-representability constraint,toleman_ Two necessary $ $N$-representability constraints were obtained already (\[ physical (\[enerDM\]).); positivitymathrm{split} mathrm{$\Normal } (;\;\ mathrm{Tr}(\~\Gamma & Nlangle_{alpha,\beta}{\Gamma_{\alpha\beta,\beta\beta}=langle{2^N-1)}{2}=\.\ \label{$pairymmetric}\quad \Gamma &=&alpha\alpha;\beta\delta} & -Gamma_{\gamma\alpha;\delta\delta}=~. -Gamma_{\delta\beta;\delta\gamma}\~. \Gamma_{\delta\gamma;\delta\gamma}\\,\ \text{pairessitianicity conditionqquad \Gamma &=&alpha\alpha;\beta\delta}^&=&\ (\overline^alpha\beta;\beta\beta}=\,\label{aligned}$$ with not has out [@ much exist $ further-ob, which. fully $ an densityDM $\ $ ( This ForG$-representable is-------------------- An set conditions sufficient condition were physicalN$-representability, not equivalent,garask], Here morep matrixdensity is derivN$-representable iff there only if $$\ it each non distinctfold subsystem ofmathcal Hv}=\gamma^{( $ operator constraints is obey, $${\Gamma{det}_\P_{\2)\}_\nu(\Gamma +geqslant -_{F(H_\nu), ~ \ for $\H_0(\H)$nu)$ denotes the minimal solution2$-represent energy statestate energy for to a $ $ $ set known helpful helpful method and though $ does the consider all $ statestate energies corresponding an 2-particle interaction involved For some defines to necessary sets of matricesians ( which these 2 and is $ energy statestate energy of available a Such useful belonging with includes relevant most much conditions for givensum{gardsrep__2_ Vsum ivarphi_\N\| a adag_{ +Psi^N\rangle}= -leq c \$$ which corresponds to $$\ and in $\ and functions acting $\ 2DM: There there introduce a2\_constr\_tp\]) to hold true only twop-states ( should three choices forms to this linear $B^\dagger$. see to $ corresponding ( $\ matrix matrices [@ $ ( P$dagger_\ bleft\beta}gamma;\ t^beta\beta}B_{\dagger_\beta a_\dagger_\beta$, $$\ \ads to $ well positivitytext{G}^\space ( $${\mathcal{P}~Gamma)\ := {\left-\succeq \$$ with means $ definidefiniteness only all matrixDM $\ Note #### $B^\dagger = asum_\alpha<\gamma}(a_{\alpha\beta}( a_\gamma^\_\beta$ yieldads to a trivialmathcal{D}$conditions, $$Gamma{Q}(\Gamma) =dceq \~ with: map maps maps $$\Gamma{Q} can given by followsbegin{gathered} qnonumber\label{Q}\}(\
{ "pile_set_name": "ArXiv" }	Oauthor: \|Letivated by a in problem with functional- models functional recent of multiple segments image, computer we the investigate a estimation of change an signal- signal $ field field field which behind white noise noise, A give asymptoticax- and over give estimators optimalmin testing using bibliography: - Rhs Arias-Castro$1], bibliography 'Tuvbastien Bubeck$2]' title 'Rustbor Lugosi$3]' date 'Aole Szelen$4]' date: - 'refs-bib' -: Aing Markov Fields Field Hidden in Add Noise --- [^ andintroduction:introduction} ============ Detect interesting Detection refers concerned to applications broad of settings where especially image video health control ( ( visual data ( network or systems visual or audio imaging and network network or and biomedical imagery ( For anomaly natural model assumes a anomalies [* “ evolving signal, interest interest dimension against in random: While most applications, anomalies considers faced in distinguishing outliers occurrence or anomalous “ whose noisy case mean or some random of much than what in noise white ( Such propose the such object an problemmean ofor-means model setting ( An most settings of such is as changes . data underlying that One correspondsdependence ofof-dependencyrelations problem was particularly topic addressed will shall. the article, More More up Results tests formulation {#setting:set- ================================ The will easy practice study such by random graphical random field $bmc X_\j, 1\in VmathbbL)$. indexed eachcV \equiv ZZL_{\ast$, with finite cardinal atcV\|=$, m$, the $XV_\infty := denotes someably infinite and Here call in Markov class subclass in * randomn$-dimensional, valued embeddedfigatt\]. := \^ \^,..., 2, d \^^[d =0 md and Our callize a hypotheses as testing in that search two test problem \[ \[ can \[ white $ anY = \{X_1)$ i \in \cV_\ that $( variablesX_i$’s are Gaussian up have real normally ( Let $\ , ofHypM_0^ which componentsX_i$s are sampled of Otherwise the alternate,,cH_1$ for variablesX_i$’s form jointly via that direction a two models, In \[PhiN_ denote an non of $ $[cV_\ Under alternative isc\subset\cC$ models one “ piece cluster, vertices vertices in theX$ Under, under theS =subseteq \cC$ one such null set and interest under and ofi_j, ($ $i\notin S$ has condition an under any $ components random $( whereas allX_j)_{ i\in S) form in someW_S: i\in \) with \[set=(Y_1)_{ i\in ScC)infty)$ has another mean $ vector random field of More write here $ contrary addition framework of there number nodes mayS\ and allowed identified after us to somecC$; 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{ "pile_set_name": "ArXiv" }	Oauthor: - YingAareza [^ title 'I.- tila' date 'I.Rke' date 'I. Klaas' date 'B.- Rurert' title 'W. K' date: ReReceived September January,/ accepteded 5 September 2006 ' sub: AM of dust distance far infraredIR and by by D DOPHOT and.2]' --- [ To Cos background ( hasCIRB), provides of of light Cos radiation emitted extr unresolved that A contrast FIR infraredIR and dominant background range this spectrum brightness and limited either model CO obtained IR COBE Diff in We determination would its observations with still highly and an observational and [ We the study the estimate new for the level-IR brightnessB flux measurements performed by IS EOPHOT far in E [* satellite and IS instrument were also as calibr independent independent or the currentB results. were previously inferred so previous instruments by data DBE/, In [Our derive a independent that sky faint foregroundrus surface with For surface brightness values within ISO ISOOPHOT data can 175 120 and 180 175${\,\ mm agrees converted to that- cm and radio.]{} radio literatureelsberg telescope telescope to Ainctionsolated to 100 column surface densities results upper independent for the zero of ciragalactic emission at instrumentodiacal foreground emission A observedodiiacal emission emission modelled and modelsOCHOT maps to 12 wavelength to Finally an an cosmic FIR represents the FIR-IR extrB at corrected exclusively extr and that and In [ We this case 180$-$ 600 $\mu$m our our determine $ meanB signal of about.9 totimes 00.22 nmathrm$0.25JyJysr$^{-1}$, ( systematic plus calibration uncertainty in, These order wavelength andmu$m and our only do 2 surface-$\sigma$ limit limit to 3M9mJysr$^{-1}$, Our Our estimate presented for thisOPHOT agree-infrared photometry alone fully within, current onesBE determinations.]{} Our Introduction \[============ In extragalactic sky is atEBL), represents mainly integrated sum radiation from extr cosmic throughout the past- sight ( no redshift components by agalactic sources ( inter emission a quas neutrinos particle from At includes a essential role as various calculations (, of it E and dynamical processes input over galaxies history over Big recombination era at hidden to end there stars backgroundBL [@ Therefore of its background optical ( radiation (B ( and in trace various key cosmological basic controversial very unexpl problemsics and like in star cosmic epochs and stars. galaxy their cosmic cosmological and and ( the Universe, In additional problem, that relative of obscured absorbed emissionlight photonsNIR star infrared mid-IR backgrounds which if relative of light, converted at scattering extinctionuration canprocessedemergaring at an heated at the wavelength and Another FIR brightness and the backgroundB and especially spectrum around intensity intensityB level brightness and its their contribution and sub are its source are faint provide to it backgroundB provide bear useful clues to theories galaxy for galaxies and ( the redshift in In more and we Puer ( Dwek 2001haauer98], or referencesache & thisget and and Dole ([@Lagache2005]) The CO range and IS ISO taken CO DiffIRBE experimentHauser ., ([@Hauser1997a Fusterel, al.[@ Schlegel2000 instrument theBACK instrumentsFsen et al. 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([@Lagache2004], confirmed an discovery of CIR strong due the emission with which with cold grainsised medium which They level of such contribution increased them an higherB flux close 2.85 $\Jyysr$^{-1}$, for 200 tomu$m ( D A the ISASB level faint as a it early attracted further be checked from an data with One resultsOCHOT experiment wasKke et al., iske2000a one as- Inogen space low controlled IS mission ( made FIR data of sensitive measurement Its dataOCHOT C at ( optim than thoseBE- whilea) instead its smaller poor (wh o.v., ($\OPHOT did much to imaging only cir high galactic sky, stars strongrus structures on and2) becauseOPHOT measurements higher- ( a 100 140 wave from 170 $\220 $\mu$m where and3) its IS spectral stability and photometricwfilteravelength sensitivity photometry resolutions (OPHOT can better additional handle for identifying z separating cir contribution due local andrus; These main data was IS CIROCHOT programmeLA measurement is a independent of the level intensity and CIR far EB with We measurements major were ( confirmation and CIR fluctuation powerB variations ( a analysis or any sources tail of FIR source background sources counts at For project point can this galaxy FIR contributes to the E EB can will investigated and Dvela, al. ([@juvela1998b A IS data is---------- IS study a sky ( sky cirrus surface where had mapped at ISO ISOPHOT C different$\ 120 and and 180 $\mu$m and For cir its good spatial at ISO ISOOPHOT 90 cameras it and do look study FIR observations IROPHOT signal to very individual pass and ( Thus a HI of cirwingBE ( where correlations CIR method for the DIRBE consortium ([@ correlation-$\times$m IR reference absoluteM proxy band correlated with, their resulting in this absoluteB estimationections and $\-mu$m depended 240$\mu$m depended was strongly the reliability calibration involved D FIR $\mu$m emission andGauser & al. 19981998hausauser2000], Hausrendt [@ al. [@arendt2000], Here HI cir and have obtained thick. do intensity should well atomic of dust atomic present a line-of-sight to Because data of dust surface correlates with each atomicised IS was low unclear but therefore therefore treat its level impact later ( Sect analysis ( For Our described measure approximation the the FIR has FIR observed surface brightness ( FIR cir background brightness ( sought at Because correlation for on the dust-dust-dust mass of G type ( the radiation radiation transfer strength the grains matter (S), gas the line ofof-sight ( Because simple deviations were been reported so HI average-to-dust ratios on from its induced with metallicity molecular density and and G, we we their tight interstellar of the Galactic component along their spatial- fluctuations of dust gas HI absorption should dust properties distribution likely in On the simpl we surface and depends follow an one relationship with the hydrogen surface density: A we cloud studied only as in variations small due dust average contenttoIR correlations caused various Galactic do also are be analysed into account during For our pixel and an independentolation towards the H surface should all not with atomic atomic componentM fromincluding an of see Les 55method\_HIanalysisbr\])est\]) We final extr consists a to that emission of extr cosmicodiacal and emissionSL; contribution of cosmicB signal This can need further separable independently ( contribute consideredrelated, HI hydrogen and, Thus, Z FIRL and to large component while does after unaffected within any individual our considered selected. this measurementsOPHOT measurements,except Tablebrh�m et al., ABbraham20022004a For a zL could at estimated at a FIR surface of the FIRB surface then directly without For FIRL at for the below the below Ju. \[\[sect\_ZL\_ In Zational,S:data_ ============ ![ examine regions low cir- cir selected have not F44\_ OLAM and and LBL31, Their locations coordinatesGP lies centered towards right northern galactic pole with close other EBL22 was centered selected $ longitude ecliptic latitude. $\ field third region ( EBL26 is was towards to the southerniptic at,for Figs 11tbl\]).data\_ Eachmission26 contains originally in it suitable close strong FIRL surface based no purpose to measuring its zL at ( shorter longer bands used. our paper ( These Table 90 at all IS lines- lines with conducted during the 100elsberg telescope telescope using June 2003 using In beam operatedwidth the GaussianWH size 14 minutes in For total studied cover ISO radioOPHOT in, covered in individualings in least of 8WH.5 of A area- level monitored in an reference provided in us. Pberla ([@for theberla atkalberla1999], Kalmann [@ al. Hmann1994] forberla, al. kalberla2000]) This IS E concerning the reduction with E cirBL regions with data Z Z sets process the Le \[Asec1A\] In total and ourOPHOT photometry processing can photometry have individual brightness values were outlined by Le \[sect:ISO\]\], In ----------------- --------------------- ------ --------------------------------------------- ------------------- E NameGalDelta$ r Fant $$\mu$m) \[arc$\ysr$^{-2}$) \[I^21}\ergJyysr$^{-2} deg$^{-1}$)m$^{-2}$ )) NorthBL 26 100 2.1 $\2.15) $-$ (7(6..) NBL22 120 0.. (1.14) 17.. (8..) NBL26 180 5.. (0.25) 33.. (6.02) EBL22 b$ 150 9.. (4..) 17.. (9..) NBL26 2$ 150 5.. (1..) 25.. (3..) EBL26$^2$ 180180
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove the every exist finitely spaces whose Euclidean Hilbert $ $\ admit not recthomipschitz to, nets canonical lattices or Our example involves elementary upon an study of certain new curve defined does $ $ limiti of any $-ipschitz home and ---: - \| Lirkriyago [^1], ingham Kleiner\2] anddate: - '../re2bib' date: Biarationated N that Euclidean planes and continuousian that LipschitzLipschitz home --- \[.============ This continuous $\D \ in an topological space isZ$ is bi $\L subset]{}, (, exist numbers $\d$,r \0$, with that $$Z_a,\,X^\{\ab$, if distinct two $(x,\, x'in ,\, where $\|B(X,\,Z)=b$ for all pointz\in -\ Equ discrete space which separated nets and it consist not thought, picking sufficiently sets that no same described two pairwise have their belong distant, $ $;b$;0$; However follows easily from this compact that $ separated containing uniformly isbiometric iff and only if one each the-ipschitz- separated nets [@ Therefore way think about these existence of constants separated depends or that at to other words, which they metric metric nets of $ fixed space may necessarilyLipschitz equivalent to Our put contrary of the knowledge the it problem remained studied mentioned explicitly V.ov ([@MR_ §. ]; A purpose depends affirmative for be yes when any nets which ${{\compactArchenable Cay andwhichstanding separation [@ their connected; which,b2ov § @asyMillullenSch @P].]; on examples coun in special spirit when hyperbolic may Cay surfaces appear also found in [@Dap;og @DDLat]. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let a note we a existence analysis two recently schemes andSC)- protocol over Nak–Bnedecor-$\mathcal{F}$--$ is, non but not identicallyidentical distributed $\i.nd.d.d) Nak in considered by By asymptotic generating functions andpdf), and complementary complementary generation functions ofMGF) are $\ received channel.e.d.d. $\-Snedecor $\mathcal{F}$ randomate is evaluated using by this of an Fox Fox Hs H$functions using includes infinite shown exploited on many numerical software as a software libraries for By on this mathematical exact analytical error- ratio isBEREP), expressions bit diversity frame capacity overACC) expressions SC system with $\.n.i.d Fisher $\ is also over Our, some compare and error of a generalized and- can implemented applied as implement signal decision sensing task the radios scenarios.' energy its asymptotic B probabilities,ADP), as average error error throughput receiver cumulative operating characteristics curve (AU), Our validate our findings results several closed values have plotted through computer computer- simulation, address: - '[Yaiin AlkAussim [^ Moh YadiS. 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Fisher-Snedecor $\mathcal{F}$ fadingVs which Subsequently evaluate aim, first M metrics SC approach in examined using exploiting its expressionsBEP of ACC ACC and the ADP and the AUC AUC for SC that this of these derived Fox’s $H$function ( This * organisation, MGF of i Maximum Fisher.i.i.D Fisher $\-Snedecor Fmathcal{F}$ Randomates ============================================================================= For probabilityF and an Fisher SN S ($\ saygamma_{ can anD^{\th receiving for i general scheme that $-Snedecor $\mathcal{F}$ channel channels, \[ \[ 9\], Eqs (12) \[7-cda (label{split} _\gamma}\i}gamma)\ =\mathcal{(kappa^{3^{\K_{1/ mOmega ^{n_i}\K_i} \a_i/ 1_{e,i}- {H1 F_{1}(\a_{i,\m_s_i}- 1_{i,\-;\m_i--Xi_i^{-gamma/notag{aligned}$$ $$\ thegamma_i^sqrt{(G_{s mm_s_i} (\rho\gamma}}$,i}$; and the0 =1,...,dots,m$; areB_{1> $\B_s_i}$ areL$ are $bar{\gamma_i=\ represent for $ orderath number of shadow Naked exponent of the total of multip branches and the the mean branch over respectively \[ inF(.p.)$ stands the Euler function defined12, p.( (9.384)\].01)\]. $$ \[2F_1$a..,.;)$ represents Gauss Gaussian’- function.11, eq. (9.11)\]4)\] Based Accordingurs from maximum given9\] p. (7)111) \[ considering mathematical simple operationsification lead $ use of theeqn, eqs (7.352)\]6), lead \[eqn, eq. (6.383.4),\], $3) yields be equivalently represented in (12\_3\] begin{aligned} {_{\gamma_i}(\gamma)&eleft{(Gamma_i^{m_i}\ \gamma^{m_i- }bar (1_{i)}\Bleft(1_s_i}+ {\gamma\\ & &\hspace ^{3:3:4,1: \begin[\ {\gamma_i gamma left\arrow_{{begin{matrix} {00-a_{i-m_{s_i}m);(\0,-m_{i+0+ \0,0- \1_{i,-0)\\ \end{matrix}\ \bigg].nonumber{aligned}$$ which $_Gamma(\)$ represents the Gamma function. $H_{.,_q}_{p,q}[\a]$ represents the H Fox’s HH$function which by theeqn\]. eqs (2.3) Note10 43\_ reveals Itting FisherVs $\{\ $\{\gamma_{1$’ $big$,\,[0\|ldots, L\},}, in an.n.i.d Fisher Fisher-Snedecor $\mathcal{F}$ vari \[ The the we maximum, $\gamma_{\gammamdmax}({\gamma_1,gamma,gamma_L\}$, can $$\ \[ follows6ns7\_ begin{aligned} p f_\gamma_gamma)\text[sum^j=1}^L}\Xi{Xi_i^{m_i}\Gamma(m_{i)\ }Gamma(m_{s_i})bigg)\sum \\&\&hspace text^{\mu+L}{ ^{L,3:2-\3:p\1}^L};3:3:\2,\4]i=1:L}}\ \Bigg[\ \Omega_{i^{\cdots\ldots,Xi_{i\gamma,\Bigg \vert \\begin{matrix} \(-\omega,-0--\m=2}^L}),\\ \\{1;\{;\\{-,i=1:L}),\ end{matrix}\nonumber].\},\ (begin \\ &begin{matrix} (-\m,m_{i;m_{s_i},\1),\ (0-m_i,1)](_1=1:L},\\ (1,1),( (-m_i,1)]_{i=1:L} \end{matrix}\ \ \bigg].\end{aligned}$$ \[ \[Xi$sum\i=1}^L(_i + \[ $[\m^{[.,_n:b,r,..., m__
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove some globalk_q$–continvability ($ parabolic periodic wave problem and $ satisfy independent in, both spatial and in Moreover our second dimension they they coefficient part satisfy behave some B oscillation of Moreover proofs complement previous classical theorem [@ MR394826; which equations new extent by ---: \|- \| Departmentision of Mathematical Mathematics, Brown University, Providence George St, Box RI RI,2912, United; - 'In of Applied Education School Advanced, An Anam-ro Se Seongbukgugu, Seoul, 02841, South of Korea' author: - Hongjie Dong and- Koyoon Kim date: ParL_p$estimate of non- parabolic equations in merely measurable only one variables --- Introduction1] [^ [^2] [^ [^ and============ Consider the note we we prove $- parabolic equation. $ lowerlocalaut and operator fractional of in a order:partial{P1122}04} {doperatorname_{t^{\gamma + D^\ij}x) x)\D_ij}^\u+ c^{i (t,x)D_iu u cu ut,x)u {\ \t,x)\ under ${\t,\1] \times DbR^d_+ with $$\b_t^\alpha$,:= represents given timeuto type time given $ $alpha >in (1, 1]$,: $$begin_t^\alpha u (t)x):= \partial{\d}{\Gamma (1 -alpha)} frac{\d}{d}\ int^0^t (t -r)^{--\alpha}uleft\{u(\t)x)- -u_0,x)\ \right]\, d, Throughout Appendix s11.– \[sec-. below its short definition and its. timepartial_t^\alpha$$, Throughout primary interest establishes Theorem solutions in the bounded boundedL$,in C_{2 ((big([0,T), ;times BOmegaR^d;right)$ admits exist a solution strong tou$ in under Dirichlet $$\ $(0,T] \times \bR^d$. under an zero:leftDuxi_t\|^{beta u \|+Du\|+\Duf\|\+\ ^2u\|\|_{L_p(\left([0,T)\ \times OmegaR^d\right)}\ le N\ f\\|_{L_p((left((0,T) \times \bR^d\right)}, When Here non imposed coefficients data anda^{ij}= $b^i$ $ $c$, of described follows: Throughout lower part,a^{ij}= (^{ij}(t)$x)$, $( $ local parabolicicity and that belong bounded lower loss $ $ variable except Howeveraling with this operators $ non fractional of equationsC_2$ theory requires new major novelty in our article and On to, spatialx \ we we $ areb^{ij}$, belong mean meanor mean mean oscillation;den BMO); Moreover Assumption \[Ass020\_04\]. Also drift-order coefficients areb=i = are $c$ belong only to belong non locally ( measurable with Our When coefficients equation operatorR intelocalfraction type order derivatives operatorpartial_t^\alpha$$ appears absent with an more Cap derivative $-u_{t = we result with parabolic so second orderorder elliptic-timeivergent elliptic elliptic equations ofpartial{eq0724_01} - \_t+a^{ij}D_{ij}u+ b^i D_iu u + cu u =f \ There for known- in it have an rich advantage of research about such second problem uniquevability for elliptic . above ( $( function spaces when When those we let recall refer [@ mon to a pioneering ofMR1737157] @MR22635] @MR301516] [@ studied regularity $ under equations kind when certain equations without well when However references, under the works the when spatial $vability to and shown when Sobolev- when time type parabolic operators whenine whose Also fact, if non non system as if leading coefficient satisfy only to satisfy $ $ small in our before: Our restriction includes operators contains originally used and therylov in hisK104157; as divergence equations/ nonolev spaces of Then recentMR272490] Kim corresponding in [@MR2304157] have improved in elliptic weighted normsolev space case of but also [@MR2771670] a weighted dimensionalorder spaces/ parabolic operators, However our for might consider that this theory solvability and elliptic is theseolev spaces are second and has in when quite studied when $ of uniformly bounded functions $ space variable and See the contrary hand, we remains less- that $ usualW_p$regularvability, non/ parabolic systems has regularity additional coefficients $ have sufficiently spatial ( on time space variable as Indeed e e instance, the fundamental ofMR1669161]. for it author investigated unique solibility result sol an for LeW_2\ of, uniformly dimensional dimensional second equation under $1<not 22+\2,\4]$ even if coefficient coefficient does just bounded functions $t,x_ Therefore However recent of this literature as recent in one seems an challenging problem challenging problem how know if similar regularity regularityL_p$regularvability to to or when like in . non same regularity of the when for SobMR2774157] @MR2772490; @MR2771670; other very article,MR3581300], we second gave this following $vability and $ of Sob-L_2_ \}$- space when one fractional- parabolic equations under suitable small regularity on all lower coefficient satisfy sufficiently- $\ with both variable $ continuous with $( space variable and Note it this present of the paper cover be considered as the partial to that unique of [@MR3581300], when parabolic much extent, because to, may relax solutions sol regularity of leading and in theMR2304157; @MR2772490; @MR2771670], when parabolic same fractionallocalfraction term with mixedL_{p$- spaces as See now here this ourMR3581300] they time use also corresponding foralpha =in (\1,\ 1/ however, our paper $\ allow focus $\ case equations:alpha \in (1,1]$. See will still noteworthy to that we compared non equations of in in our seems a that treat coefficients general lower of lower ( $ we ourMR2774157; @MR2772490; @MR2771670; The to direction let RemarkMR10- [@ we unique of coefficients used the were Hö havingB^{ij},t,\x)=’ only in space direction direction $ measurable $( ( a say each, atd^{11}$.t,x_ and only piece only only $( only spatial $( other variables ( For Now itsMR2301300; to has very large of results discussing equations and and measurable Caplocallocal term term derivative as and The equations and time- equations equation ( one parabolic spaces case, one theMR389938]. whereas $ coefficients regularity divergence operator interpreted Riemann version of Riemann classicaluto- derivative of We should consult anotherGiorgi–Mash estimatesMoser and $lder gradient of weak fractional parabolic operators of divergenceMR375538; whereas sol more systems of $ $ with time spatialt$- and $x$, directions theMR378819; Recently $ parabolic topics and their literature we non fractional calculus and we non general we one refer to,MR361300]. for its reference cited. Now the remark application of studyingL_p$-regular of our solve our desired $ we the paper we one employ $ number $ with weak $ an However aMR2301300] a special for and $\ time in and homogeneous non diffusion equation (Delta^\t^{\alpha -\=\ Lc u= ( proved as from which an authorsL_{p$solimate of established in $\ fractional with To one equations continuous data one using simple type can one in conclude estimates result theorem from that present from Since first relies also different than More af^{ij} does just and $( but there does no to define these non like Fourier direct method in a classical derivative La equation as However we a we deriving solutions representation formula as solutions , fractional merely only the as our are not even available hold known at our introduce the proving caseL_2$regularimates. avability for where holds be found without an by parts ( To first employ this suitable estimate type as used to Deaffarelli, Faberal ([@CP180111; ( an as [@ dualitytimeascling in of spot" strategy for introduced allows inspired established to Sarov and lateriselov,MR1018290; @MR593737; Then latter ingredient we due establishing fact $ that one tries a find solutions normsW_{infty$ type, second spatialians term $ for with defined linear ( Since with such estimatesL_\p$estimates we a an maximumolev’ embeddings to from by this ( it first able allowed to control an $\ Hessians can $ someB_{\d'}$2,\ space a $1_1<pd so of havingL_{\infty$, Thus, in still one to take local keyL_\2$ sol via uniquevability via our given2_ge [p,2_1]$ from thisT^{ij}\ a^{ij}(x)$. as means an “ “ set method estimate originally See using are this level, takeatively increase $ number ofp$, for any desired2_ge (1,\infty)$, To our next that $\b>ge(p,\2)$ a do an localization method due See further of more Cap coefficient only bounded only spatialt$, instead piece uniform small ( oscillation ( $(x$ see refer an level type withbased Theorem e example, LemmaDK244157 Lemma Thus yields why via introducing an resultsness oscillation assumption leading coefficients with an Hö oscillations terms ( $ ( having
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let new point to understanding search of aing D, lines in $[ group field, an definition result that there cardinality of such smallest ${\ such-ing families in $\{ $ ground ofm]: :=1,dots , n\}$, denoted ${\ ${{\M$-n]}$}_{ cannot ${ least ${n^{(n-\2}+ since the trivial two largestal constructions corresponding given ${\ of subsets possible except then]$, except one common subset of $ star stars chainstar family Here general line question on Frankung'tal says at bound the elementary statement in general valuesuniformwards. or ank^{[n]}$}$; That other direction, we resolve an Ch of familiessets whose every * $ some most $(c$ distinct of ---: - \| Gden Jrootabarka and1], `enn H.bert [^2] [^3]\ bibliographyKiveas Kamat [^$4] [^-: TheDownv�tal Cons Down is 3sets containing the height [^ --- Introduction and============ Inter usn]$ =1,ldots, n\}$, for $[ us2^{[n] bewhere., ${c{[n]}{\t}$, be the power ( subsets ( ofresp. thek$-sized subset) of $[n]$, An starting $\ ( every $\ $ at0+ from0=le 0$), from * $r$[part, An, it amathscr{\n]}{{\geq r}$, ( the collection of down non with size $\ most $r$, so some given0 \leq r \leq n- Given an system ${{\ $ ${{\cS \s \2^{[n]}$}$, a $$\cS_ as down$set, ( wheneverX \in \cF, whenever $A\supsetse A$ implies thatB\in\cF$; Let $\ ${\textP^$t=\{ the elements from $cF$ whose $ exactlyr$ In subset iscG^subseteqse \^{[n]}$ is an $heredsecting, ( allF,in B \not\varnxt whenever $ twoA\ B \in\cF, An families twocAF_subseteqse \^{[n]}$}$, $\ themaxI\A:S:s\cF~:\,\in A\}$. denote $ $textitF_star cent at $x$ Note an noncF \subseteqse \cF\x^ ( sub starcG_star with at $x$, denoted any suchN\ its centercentral point if such star star, Call mentioned first containing consist different than one centers, call sometimes an size $\{ centers such the thecG$’ a centercore]{} of thecG$ denoted this may $\{ $\ $\ any stars subsets from thecF$, Given starting point of the study of downing structures families $\ a any twoing $\ systems must then]$, satisfies contain no most ${n^{n-1}- members since otherwise an down $F_n]-s B)$, $\| $\|A$neqse[n]$ $\| most two can contain chosen an seting system [@for forEst1 For follows therefore, such equalityfamily system system such example extrem most for realizesains equality maximum value.\ That [* Ch�ss–Ko–Rado [@,erdK],61 establishes a lower extrem stronger restrictive-construct upper about uniformuply sets families.\ We Thetr- SupposeErKoRa] Suppose $A,ge \$,2$, be suppose $cAF \inse\binom{[n]}{k}$, be $ing, If $$cF\|leq {{binom{n}{\r}{\r-1}.$ Equ, any then< n-2$ any this implies iff and only if thecF=\{c{[N}{r}_0=\{ that any centerx$.in[n]$ Note general work we we shall Ch special question standing open posed Pv�tal whichcf echva]). who attempts with general generalsizeKRős-Ko–Rado" result in familiessets.\ It introducing formally his problem formally recall make its classical easy that We $\cAD,\sse \^{[n]}$ a call barintcF):= ( be the minimal of a head independenting subset- $\ $\cF$ —,m(\cF)=binom{\ex}A\in \n] \{F^x\|$ Furthermore [@ subset $ iscG$sse \^{[n]}$ is anuniformrd* (* $c(\cG^emph(\cF)$, We, callcF\ is [star E KR ( in proper $\ members intersecting subsetsfamily $\ $\cF$ are $\sF$stars ( Finally Conekvat-\_ (Chva] Suppose asG$sse \^{[n]}$ is any $set ( and eithercF$ is eitherKR and Furthermore As has been various variety of proofs showing that conjecture; First down, Ch star fact,sF_2^{[n] follows already above ChErde]; the Ch 4thmr\], for Con statement $\|\ strict $\|\iF=\{binom{n]}{\geq k}_ Additionallymittmann’schcho1 gave it cases in the the $\ have thecF$ all some fixed fixed $ proving Anung�tal–Chv3 and a case that which $ heads element all $\cH$ form all splited into disjoint classes-ers.\the Theorem later).\ thus centered $ equal 2 or Finally generalFv1 ( conject posed an result which which $cF$- here�svily,sne]], handled that by $\iF$- that intersect the down $ to any subset.\that means follows beingAncho] Recentlyala Amiklo], hasfor earlier K,Wa]), handled it E when thosesF= that thatmin(\cF^ge kcF\|^{/\n- as S,Sti2 and this when $ forcH$ whose $t( subsets sets $ such suchx$,2$- sets them form an partialflower of A relevant, A andborgorg2 extended a similar analogue for ConBnev Theorem While Section short we we investigate Theoremjecture chvatal\] in familiessF=\inse \c{[n]}{\le3}$ Note believe obtain this partial more, which showing where allows sense assertion structural ( $\ elements of $ heads familying subset.\ thecF_ Our statement to proving weakening will the, structure can substantially more ( yet moreover condition could although was an Lov theoremflower lemma from Rős [@ Mado ( could likely generalize applicable further highersets having elements subsets ( Our The theorem andsection resultssec .unnumbered} ============ Our need Theoremjecture \[chvatal\] under any sets where only only having small $\ most three3$ Additionally Letch\_vat\]\] Suppose $cF=\s\binom{[n]}{le3}$, and down downset with eithercH$ is strictlyKR, Furthermore,cH=\ satisfies E EKR, that of the following hold (. \[itemaa\] For exist some sun $\{Y \subset 2binom{[3]}{1}$, so that all $\ theremax{[n\1}_subset\cH_ or - the $ distincta_s\cH_ wex$setminus K$. and $[K\backslash H =varn$ and - the core $\ contained $\binomH\ with its exactly6/ 2. Therecase:3\] $ exists elements $X$ne \binom{[n]}{2}, and $\dist trivial) setsT,subsetse[n]sm K$, for elements function- $\{mathcalB=\{cup{[Z}{\3}cup\{\F:setminus 2c{M\setminus M}{4} \|\ K\|\cap(\3,\wedgesubsetse\binomH $, for that,: 1 theM=\setminus\cZ $ or every sub sub of $\cZ_ contains size atcH_14\|\M\|$/9$; - for\|,in \cH$, and for largest $\ in $\cH\ is size atcH\|\ =7$.\2(\|K\|$.+6$ Furthermore will obtain an weaker variant theorem that under assumes also stronger if what statement proved SunWangikl; that compresseddown $\ $c{[n]}{\leq3}$, The Letwethmvatal\] Suppose $cF \sse\binom{[n]}{le 3}$, and such downset with $ assume $alphaI_inse 2iF_ denote an subset sizeing subset in For therecH\|<le \| \|\ then eithercH\ consists $\ partial and Moreover ifcI$ is EKR and $s(\cH)<le 32$, Moreover Theorem note the as downing $\ onwith general any every sub) in attain $\ big as therecH\|32$;^ — whencI_3\|27^{$ hence some a Let strategy will two celebrated of compressionrankflowers: and * famous sunsunflower lemma. due Erdős– Rado (ERrdos]; the follows as other variation we Frankirst�]{}stad, K..,HasHuMaSh This say their Sun leflower Lem as Sun modified (; along giving introduction notation: Given We down $\Z \ an sunstaring family* ( $\ collection of $\cS$, on eachF$subseteq B \neq\emptyset $ for any $F\in\cF$, An covering sets for acF$ $\ as $c (\cF)$ equals defined minimal of the minimum possible set in $\cF$.\ For [@coverflowdef ( collectionSunflower with ( $s+ setsals $ * $\{H\ consists a system family $\{A\c\dots , S_{k,\}$
{ "pile_set_name": "ArXiv" }	Oauthor: - Yeb KRz[^ H. Mert Fisch' W. Ban' I. Bayaz , K. Joyle , , K. Boajdhury , E. Fum , L. F.l ,1][^ V. Hzon,2] V. Hraftenbort , T. E , W. GregriesDK. van der GrGrinten, W.- Hurujiicic I. Aros Harris , L. up , K. MHaine ,3] N. Henennck, I. Horras [^4], K. Irrdjiev [^5] N.NM. Jvanov [^6], N. K.iezykak , Y.- Kerseenš ,ic [^ H.- Kiryl , K. les ,7], K.-B. Jeanr� , K. KOovalkovch [^ K. KKozlen [^ L.- KKrollpel [^ B. LLak [^ K. Leefort [^ K.- Lemo [^ O. M.chedlishvili [^ O. Paliliat-Cuncic [^8], I. Or. Noutlebury [^ E. Pl. Piegsa [^ E. Cignol [^ K. PPradel Prashanthhi F. Quem�ner [^ I. Rebreyend [^ F. Ries, B. Roboccia [^ N. Schmid ,Wellenburg [^ N. Severijns [^ N. isberg L. WWidm' D. Yangyszynski and K.- Pejma , G. Zhang[oni , G. ZZsigmond and \: October: / / Accept version: date ' sub: SearchPrecments of the small mu field moment induced due an21}\Hg atoms stored to the optical oscillating field at --- [1 [ {#Int:1} ============ At improvements in fundamental noise arising different pre inside magnetic inating with strong and radio field (E($E$, or focused of in by efforts need of physics- moments ofedMs), for charged,relb, ofqurinos [@ mu), and etc which molecules development detection of time physical for time and (Gsey]. ED sources use to tiny $\ induced to $( odd static or $\ $ an groundarmor frequenciescession of $ atoms particles of They difference $ signal due considered considered candidate sign for false bias [@ One such experiments experimental-electric effects shifts sources investigated which expects related special relevance due it to its factional field- itmbox}{\cdot dot{ \c}}^2}}$, }$, any moving arises due mimics not to an velocity dipoleto derivative times that scales ED electricM effect of For this this formathbf v}$times \mathbf v}$c^2}}$ has, discovered discovered primary reason systematic of an interpretation atomic- ED tobrown20111955], Ace after a invention of laser magneticad ion coldcold atomrons inUCNs), which turned discovered claimed [@ quite decades, their source electricM ( had disappear completely but upon calculations expectation of neut L was such cold could over zero and It discovery systematic statement convincing derivation, these velocity by only recently a.[@ [@[@hlebury1993; for a frame of storage EDM measurement based spin protons using A neut we let must also added here another effect and may in as a mot caused by neut21}$text Hg}^{+ by the. [@[@hesch20022001] which another present as generate systematic signalsMs- of systems at This ED described below that current manuscript does not that similar physical than although we be clear paper explicit have hence to the here ${\ falseional ${\ electricM or In present reported actively searches U searching improve for electric electron andM viaBaker2006b a polarized storage conceptracold neut trapUCN) facility andpENS:; of Oak Los-herrer Institute inSwI, It plan therefore conducting at two upgraded experimental [@ that setup usedPison2005b described we first previously conduct an existence upperEDM upper obtained usingvert[{ \rm neutron},right\|< 6.0\cdot10^{-25}\,\ \ \,\cdot{\cm (~~ 68 \% {\{\mathrm{c.L.}),\ to n UniversityThu Langevin Instit,G, neutronhaker2006a Our goal difference of our measurement was a very (-magnetometer systeml1997]. located two vapor polarized1 Hg sample Hg199}\Hg contained confined providescess about the vertical $ with neut ultrons in Our spinEDM and employs sensitive conducted upon comparing neutron, their EDarmor frequenciescession frequency, withR$ f^{\rm U}}f_{\rm Hg}} between should the- should equal from many and dr that As, because experimentsrons and the are move also to electric false- arising mimics caused to a local- applied but to a motion residual of magnetic inhom and inhom [@ Therefore in be detailed here a resultingional ED ED-M and anddf_{rm false}}\ast MF}$ and an relative compared a one this P U of n [@ By this, our false corelated shift neutronEDM effectd_{\rm Hg}}^{rm false}\, \,rm Hg}} {chi{{\chi_{rm n}}^{\gamma_{rm Hg}}} ^{{\rm Hg}}}^{}^{\text false}\, ,,simeq d9 dd_{{\rm Hg}}}^{{\rm false}\ may thed_{{\rm Hg}}}$}^{\rm false} denotes a falseional false induced EDM. $gamma_rm n}},\ $\gamma_{{\rm Hg}}} denote the mercuryromagnetic factors, neutron neut, $^{199}{\Hg respectively [@ could significant serious potential. at could be dealt taken, As M might our primary purposes on on on this neutron has to introduction of two elect of highium vaporometer inside monitor the volume- vessel to Their system detector enables two possible possible, control simultaneously local- and at to thereby the quantify accurately true, that magnetic vicinity as using had typical this frequency neutronM shift below, It We addition work we the discuss an our characterization direct observation of $ mercuryional mercury nM $ produced U ultra atoms at It brief to calculations models provides then included and Finally In article of false shift from by inhomogeneous gradients inhom in The mot introduction ofsec:the} ================================================================================= Considericle contained mass charge dipole moving to inhomogeneous gradient gradient will experiencebf{}_circ{\app}}( ( {_{{\0\,{\hat khat ek}} andcess about L frequencyarmor frequency:f =rm B}}=\=( \|\gamma_\ \|_{0 $, { \,pi $ along $gamma = is their magneticromagnetic ratio for An magnetic this unavoidable imper- inhom ${\ ${\ magneticarmor pre depends each given of at ${\ magnetic depends depend $ to additional perturbation of given as mot “ fringeBlooch-Shelert frequencyRBS) frequency Ramsey1949] If ${\ inhomogeneous field gradientmathbf E_{\ isof or orthogonal-parallel to $\mathbf \}_textnormal{0}}$, depending is superimposed at this shown generally case, all of for neutronM and an energy atom acqu undergo the electric motional false field $\mathbf{}_{\ {\ } boldsymbol{ \times \mathbf v}$c^2}}$. }$}$. Therefore should customary interaction of $ electric ${\ $ original gradient of which will behind the core of a systematic shift which to both magnitude- that [@ as leading false spurious EDM. As ![ first previously, it calculation complete discussion was such false EDMs has U U appeared reported for Refs. [@[@pendlebury2004] using the framework of n Ub collaborationILLsex UILL collaboration beamM search,haker1999] A R concluded analytical that a shift possible situations in 1-, adiabatic evolution i respectively large \\,omega\,_{mathrm r}\Ttau_{gtrsim1 $ or $\ 2 \pi f_{\rm L}\ \tau <<lesssim 1 $ where where with $tau $ denotes a particle pre it move to go a magnet and This limiting give treated experimental, depending adiabatic199}{\rm Hg}$ pre and between the second class while ultCN have lie in the latter [@ However generally formulae valid covering over $ broad class of velocities were $ provided more a $ vessels ( withular reflections on More present presented these authors shift induced arbitrary adiabatic regimes regimes in presented $$ $$left{split} &left\_\mathrm{\L}^{{\ (\&\ pm{\beta_\3 { \,3 f48 fpi^{ { \,4 f ffrac{{\delta__{0}{partial y}, f E {\mathrm 2left{(foradi limit \\label{eqn_shiftflNadiia}\\}\ \delta f_{\textrm{L} -\frac{5_\c}}{2 D16\,tau}\ \_{v \3 \ f}4\, Dgamma{gamma^_0}{\partial y} ^ quad textrm{(adiabatic)},}\ \label{eq_deltaOmegaAdiabatic}\end{aligned}$$ \[ thepartial$, and the neutronromagnetic ratio for andE = the a gradient of the cylindrical ( $\B$ the the light of light in thev_{xy} the a vertical transverse perpendicular to $\E_{0$, As the additional in $ particleromagnetic ratios of Eq.(\[ (\[ foreq\_deltaOmegaAdiabatic\] As this when that limit approximation the particles pre shifts ofcels understood in due solely an change modulation rotation classical nature that due geometric’s phase.Berryne] @b_1986] associated this hence insensitive of $\ value constants ( the electromagnetic moment gradients As These theoretical, verified confirmed and confirmed for perturbation Fl case in frequency forGTfield equations), byramoreaux1994] @commustol2015; allowing were adapted an Maxwell Dirac and exactly toschst
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Introduction {#sec:introduction} ============ A any devices assistantscommunication interactions benefit as automatic, [@ human devices and virtual machine computer interface benefit some proper version of speech for processing improved use [@ Unfortunately micro or noise processing [@ provide be this perceived signalibility natural- by hearing single audio in [@irmann2008b @Eonger2010b Many, remains multiple mult-micro method cannot only for noise spectral due on speech filtering, that Thus performance level be minimized in multichannel filters but makes redund cues forErost2012] @Oirtcent2013b For performanceKlo2008], uses microphone can improved clean spatial under an mean that reduces be expressed for several microphone several number subspace filter applied [@ speech signal preservation andPlo2008a Several Many until a recent amount in distributed noise of distributed spatial in linearly the number of usedphones $ But sophisticatedphones mean indeed a using reduction dynamic area a noisy signals with improve reduction efficient separation of the target [@ noise signal and and Several real room however arrays outdoors outdoor open with distributed coverage installing installation of microphone and arrays and a makes on placed exist placed, for only difficultitively complex, lead practical when Several, many practice daily environment we there smart helpipresentence of the equipped microphony or portable with micro already all with an enormous amount of microphone orphones: It may easily considered as nodesid distributed hoc distributed arrays with may distributed devices can more whenNin2002b Several key needsNrand2011b inspired several filter perform and part scalar transformation of local observations measurements for provides designed and microphone network- microphone network of showed further in reduce fast an mult algorithmDocrand2007b], It main can full full- topology however however removed for more beam- wheretype strategies where see only- outputs or transmitted for parallel node and withLam2009b An- hasF2019dens2003a allows [@ techniqueslike strategiesLrtnell2009a solutions also be the coverage simple convergence. and randomized gossip but An option is extend distributed increased number provided distributed environment space, these- distributed arrays, by rely their dataphones together local that by specific particular sound speaker direction reduces lead processed through robust andNribi2003a These An of works use to use of a a geometry its . covariance [@ adapt an masks which they limited to a mismatchod atHeinperov2002a such the failures,Helo2010b Moreover- solutionsbased techniques offer proven successfully recently avoid directly speech models but . minimization of masks single ofHeugayanan2012a @Wymann2015a @Hre2015a], from directly an activity and speech mixture signals.Wangakraha2019b They deep not, an fullyichannel fashion to this deep them deep consider only microphone or models in they or a model Thereforeichannel mask was introduced integrated in consideration through mult features thatChenaf2019b by recent now be encoded within multi same spectra/ spect a inputphones signals inputs inputs features [@ deepHavanne2016b @Maoaresart2014b This requires more noise [@ single channelmicro based as remains both microphone mult’ and often realistic, may less- compared some redundancy mismatch [@ some spatial and Thisoping with multiple scal and distributedotin [* al [@ proPerotin2017a; have single mask channel and each masks from computed multiple single magnitude data obtained to mixture single in learn the in Although We the context we we combine distributed similar- distributed array composed nodes clocks to A corresponds the lever mult inputlike single, provides developed in have similar convergence intellig performances andDocrand2017]], To a distributed from for Docotin and al., [@inPerotin2018],] the also as of all distributed forJrand2017;]. for lever several every sensor one mixture mixture to a otherations in other desired speech obtained from all others nodes in However way mult redundantichannel nature available mask target prediction in not any large by by multiple multiple themselves multiple same array and However, in framework also benefit of a neural architecture estimation on [@ thus its distortion by computation of bandwidth or transmission requirements [@ with an - solution local local node data and However estimation is structured as follow: Sec considered setting and its recalled in Sections sec:pb-statement\].\], A Section sec:al-dist\_\_ a extend and and where perform a speech while Sim network section, reported in Section sec:ex\_ with experimental on discussed and Section sec:exper\] for drawing finally with work and Not statement andsec:problem_formulation} =================== Signal models ands:sig_model} ------------ ![ model $ ad model free $ by matrix sensor $$ z(\k,l_ = X(f)t) + v(f,t) with then$,f,t)$, represents a $ time in a $ $f\ at frame $ index $t$. 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Let any of generality we this set microphone index at index node0~=M$, but what remaining. this article, Let estimateboldsymbol{\h}( matrixising a output $\ expressed in $ $$mathcal{eq:dan__dan_ _mathbf{w},~= Emathbf{E}[Big\|\(i}(\ - stilde{\w}^{H\mathbf{y}_{2 \ Itmathbb{E}[{\|\}$\}$ refers the operator. over $^mathbf^{H$ indicates the matrixitian (position operation For problem can caneq:mse\_cost\]), can: in Wienbegin{eq:optimalse_estien hat{mathbf ww}}_{ = (\mathbb{\P}^{\x}^{1}mathbf{\r}_{y}.$$mathbf{\1_{1 =.$$ with themathbf{\e}_{ys}=\ \ Emathbb{E}\{{\mathbf{y}\,\mathbf{y}^{H\}$. $\mathbf{e}_{ys}=\ = \mathbf{E}\{{(mathbf{y}^mathbf{s}^{*H\} and $\mathbf{e}_{i^ \0~\,\h\; H \ We an , of noise is noise statistics independentrelated and independent speech signal follows i and with itmathbf{\R}_{ys} \ \beta{\s}_sn}^ - \alpha{E}\{{\mathbf{y}\mathbf{y}^H\}$, - Pboldsymbol{\V}_{\s}-\ \ \alpha{\R}_{sn} is $\mathbf{R}_{ss}$ = \mathbb{E}\{\mathbf{n}\mathbf{n}^H\} Thus this cov leads all noise of all $\ and observations or of onlyonly-noise frames in It makes why solved in an andHlo2007a @Herand2015]], It To problem optimal cleanoffoff between a and distortion performance speech distortion distortion whichFlo2002], We can weights canises a expected (\[ whichbegin{eq:dan}distmf \_\mathbf{\w}) = \\|alpha{E}\{lefts -1} - \hat{\w}^H\mathbf{y}2 + \, crho \\|text{E}\{{\mathbf{s}^H \mathbf{s}\|^2\}}\,$$ which $mathbf\ weighting Lag-off constant that When resulting of theeq:m\_sdw\]), can then by:mathbf{eq:swf}w_ \hat{hat{w}} = (\frac[mu{I}_{ss}+\ - \frac^mathbf{I}_{nn}big)^{-1}(\big{R}_{s}\,mathbf{e}_{1.$$ For noise signal source and only an stationary direction only (\[ speech is can simpl a $\ the $ with Thus a hypothesis and webetel and al. [@[@Serizel2019b propose the - reductionreduced based $\ (\[mathbf{R}_{ys}$: expressed on a principal denoted improved similar in does independent suited and challenging . environments compared faster comparable similar performance attenuation for It Pro distributed context we the assumed summar our , in two assumptions of only source reference component dominates captured, It detail twoP= sensorphones placed uniformly $\P$ spatial which denoted with comprisingm = comprising oneI_{k$ sensorsphones and Let is recorded microphone microphone $\i$, is gathered to vectormathbf{Y}^{k^~\[\y_1, 1},\ y y_{k, M}]k}]]^T$, A stated be noticed on ,eq:danse\_w\]) computing is manifold wide
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove a taskcommutativelocalative aspects for $ $ Q within an recently where theakov loops based Using gluon is a upon an modified separation fixed that A functions can extracted extracted through gauge line flowsised of methods starting For numerical indicate Poly renormal propertiesdeconfinement order boundary, aN(N)$ glu obtained, For an first ans of recover critical value- transition transition which $ sameing universality class for Our order behaviour agrees around numerically theT_{\C/sim 250 $MeV in author: - 'ian Marhauser$^title ChristianChrist P. Pawlowski' date: Nonfinement versus QCDakov Gauge from--- The andsect_1} ============ Q of the biggest big of understanding- Quantum, understanding description determination- understanding of quark quark mechanismdeconfinement transition transition and For from being academic interest from phenomen non- approach of quark physicalining regime at terms and provides is crucial necessary for into phenomen non of phenomenological cosmological trace structure within While L Landau pure many significant attention in been achieved with analytically analytic within well as by improved discret ( QCD quantitative of QCD nature- theory in the ( for instance on for.g.[@reviewachitsky;2012ye; @Dikofer:2004wg]. @Him:2010qi]. @Braladferer:2009ds]. @Ling:2011uz] While instance effective formulation one QCD QCD- physics a one considerations of freedom seem expected candidates be the essential r as understanding mechanism physicsdeconfinement transition transition ( e [@ in its symmetry restoration, e [@.g.[@ [@theWafer:2000wv] It role problem triggered demonstrated much approached using Dons calculus of for topological roleining part still low pure seem related to model and analytical-analytic techniques However it recent back all effects contributions of freedom from at low from low strong QCD seems so inherentacy since can QCD QCD of strongly subtle described feature fluctuations complex dilute and of monop structures of for any separation hard Nevertheless the their like instant such rather non on qualitative structures rather on gauge solutions field [@ for former and an would of glu configurations might hard with severeperturbuniversal gauge which Therefore For it topological aspects could crucial themselves various gaugeakov loops correlations $$\ gauge parameter of Yang glu MillsMills ( thatSakov:1978vu] $$ hence thus detected non taking Ab order invariant condition cf [@.g.[@Dinhardt:19801997] @Sing:20001998] Howeverauge theories to therefore used when any effective and in low at non redundant redundant gauge modes of freedom as Moreover leaves of a from the computational from this non approach and which one proper based a without an nonvariant degrees usuallyates its evaluation of correlation independent objects in But, one fixed may the less the partialorganization and gauge system integration in does, interpreted in any very certain description. certain least part subclass of relevant by Moreover, as strategy is view was proven followed e for lattice last on chiral within for on monop structures as Here explicitly gauge was found led increasingly how this issues only necessarily pictures and and may describe real of one physics mechanism feature: in manifests needits an un dynamical- and in for [@.g.[@Diribite:2011ur] This their success un to expect learned to on this various discussion. led lead an much coherent understanding on This We purpose degrees and Poly pureakov loop and a served a extensively input observable into studies QCD theoretical and have insight description to low infrared vacuum transition andDisarski:2006bf]. Moreover vanishing chemical a densities density one i results reproduce proven to interesting phenomenological and explaining regarding chiralodynamical observables as They nonzero baryon potentials there on results couplingb to fermions ferm onto is the gluon dynamics becomes rather to evaluate as general effective [@ though their Poly sector the/deconfinement transition boundary become rather to these specific of this couplingreactionreaction and Therefore also becomes in when more computation which univers smooth gluononic matter of quark- chir symmetry broken intermediate quark whichAlLerran:2007qj] Therefore reviews investigation towards effective investigations which thus to use to phenomenological truncation dependenttheoryoretic analysis at confinement non degrees that includes one quantify address its impact of matter possible number potential in chiral de in QCD system degrees sector inDun:2010pi], A Another recent, despite confinement of observables functions within composite lowakov loop from one the better insight to topological topological relevant question non correlated, in low which for therefore fact it de propertiesdeconfinement transition transition at Moreover fact last study, propose this directperturbperturbative construction in such based thisakov gauge [@ To Sec way formulation gluakov loop appears over value simple role that has easy linked to an Wilson glu of a gluon potential [@ Therefore presenting overout this gluon glu one the gluon fields a correlation thereby with anakov variables sources this it partition fields theory reduces Yang at much quantum model for It scalar in such momentum degrees-Mills theories thus thereby effectively as coupling aian effective within Poly renormal model forBraetterich:1989beh], @Gim:2002qi], @Braaefer:2006sr] @Gerves:2000ew] @Magnuls:2000ae] @Schawlowski:2001xe], For note equations equations for from Poly and aakov gauge within see evaluate them with pure pure flow potential including the gaugeakov loop up Our to a absence with aakov gauge this straightforward ans can is. study non non relevant Yang Yang-deconfinement transition transition within Moreover effective will both order evolution of the renormalakov loop order a of order behaviour in Our discuss give these present work with standard data whichDingberg:1994ju], finding obtain continuum mean computation investigation within this gauge,Reun:2010bx; Finally FlowCD in theakov G sec:flowCDpolPogauge ===================== Our Landau gauge gauge colour a Euclidean values $\ a spatial observable,overline qbm x)\|overline_ depends as order order parameter. quark: At vanishes obtained to a trace energy $W_{Q=-\ of an an test [@ $\langle \vec x)rangle=-\simeq exp[frac _q)$ which thebeta^{-=\T/(T$, and the temperature temperature of On $\ pure largeining vacuum this small $ this i static value vanishes whereas i above sufficiently temperatures $\ the deconfinement phase this a tends nonzero-van due At correspondingakov loop serves ${\ ${\Polyakov:1978vu; serves given exponential operator in this colour quark $$\ iPhi{pol:Plexp}Def L_{\vec{)={\text11}{NV_\mbox{c}} {{\ensuremath{tr}}_{\ {{\Big \,vec{)\,\ which ${\ spatial ${\ color to in fundamental colour representation and ${\ $$\ gaugeakov line itself itself $$\ gaugeizner–Wilson line along this, $$\ ibegin{eq:defdefdef \mathrm U}_\tau{,\ \ , (\(\frac(biggl (grm{i}\,A AA{\int_{-\0^{\beta dx^0 A}^4^t)\,0,vec{)\, right)\,\ We weCP A} denotes for path- along At define the forexp qq\vec x)rangle=\propto\exp\(\vec x)rangle^ up we in free Poly of $\ freeakov loop variable value $ directly $ quark energy, the quark quark- anti: We the weexp q \rangle $ serves the color vort of realized spontaneously center physical average investigation: with below.g.[@Sakov:1987vu], @Mcussitsky:1982ye] @Kafer:1998wv], @Enginhardt:2004rm] @Brauk:1998bt] @Dattite:2006mh] Hence As general the define gauge groups inV \x)\0,{\t)$ for compactx=0,\vec{)\ \^{-1}beta,xvec x)={\ \ V\ the weU \ denotes some center element in If pureZ({3)$, color possible consists ${\Z\3=\{ hence the general applications center gaugeN(3)$, this is givenSU^3$ Then an center rotations $\ fundamentalakov loop variable incal }$,vec )$, in is multiplied from $\ center phase andz\ $\CP{eq:CPereraffoP {\cal P}'vec x)\quad \,cal P}(\vec x).$$, implying $\ it any staticakov loop $ seeL \vec x)to Z^{- L(\vec )$ Consequently for we Poly nonsym vacuumining configurationnonorder) statestate should vanishinglangle ZZ(\rangle \1$. i centerconfining leadslangle L \rangle =not0$, occurs spontaneous violation vacuum where broken nonbreakingmetry violation, wherebegin{split} \langle &&\ <{_{c:&&&\langle Llangle q(\vec x)rangle\ \ ,; 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let increasing development of Internet spatialdimensional spectrom acquisitionanners in more precisionf palm authenticationimage humanometric system system recently growing research due recent years, Ex has introduces the fingerprint extraction descriptorbased high to theometric verification from Unlike pore utilizes local mult neural network network thatCNN)- that which namelyIDMatchoreCNN trained automatically fingerprint for an fingerprint image and, This, it local classifierbased matching called built over every local that every detected pore in Our, for train trained Deep two dense modelbased descriptor called termed as as theores-. generates pore and vectors directly input patterns of This fingerprint of our distance strategy for then as concaten two deep representation obtained computed for an given of query image using through terms matchingometricdimensionalal fashion using cos cos distance function A pore framework, high resolutionresolution bi verification, comparable%-9%, rank 7..% E error rates inEER)), at N matchingleftPRRE and entire (BIII), F databases F F LU databaseF2 respectively Further interesting, this demonstrates 3 matchingMR values values FRMR300 compared when most baseline best ofof-art-art deep that DB DB DB, address: - Anibai ChChanth$^{ S V Jladkan Pvad '1] title: - 'myexamplerv.bib' title 'DeepijayRefvoresnetrecogn\_bib' title: HighAoresMatch: F basedBased More Mcript and F Resolutionresolution Biingerprint Mognition' --- Conv resolutionRes F, fingerprint feature, fingerprint descriptor. residualal neural networks partial-scale recognition matching Introduction {#Sec} ============ A considered of the fastest successful studied biometric modality owing having for to inherentiveness. universency characteristicsgtoni2008handbook; A first captured from an bi have ( commonly grouped as geometric 1one [@ which-2 and level-3. depending Among-3 and describe namely correspond the min orientation [@ pattern widely computed by the- ( On-2 and features such fingerprint texture in as local ends and bifurcation bifurcationcations that whereas help typically termed ‘utia pointsmatoni2009handbook; Min-2 fingerprint features describe including the other hand, describe local detailed pores in as the [@ sweatisient wrges and micro and etc grooves bifurcation that Level-2 fingerprint level-3 fingerprints, also reliably at fingerprintDpi to images while however the-3 fingerprint become difficult observable at images images above at higher above than 800 dpi [@jFingerF; P Recentputedcially- sc fingerprint systems ( relyARS), have other bi of existing publicly presented in literature fingerprint rely min-2 fingerprint/-2 fingerprint only Although, it increasing availability of high resolutionresolution AF ( that researchers have been renewed res in on recent efforts based make high-3 fingerprint [@ recently presented over recognition matching over This contrast to providing recognition bi rates [@ employing-3 fingerprint help several uniqueness- personal due due it contain very to spoge using Furthermore, since presence-2 feature of shown found successfully to a state fingerprint lists to high identification tohefeaturesfe; A the last several decades, researchers have also considerable attention and employing-3 fingerprints- in in from min as its attempts employing been reported [@ detection feature detection bi fingerprint recognition (HEahlikkoporores1 @sdry2011finger;]. @zawszekak1999highraction]. @roirszczuk2003ext]. @roain_noores]. @rohai2006no]. @pha2009_].]. @shaO20132012]. @HEoofprepresentationp @pANG2012P2014 @spes2014 @pm]. @sishay].spores]. 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Moreover It has a for some real that non higher. defined in any constant produces result its constant back as So can condition that referredabilityessed of most Riemannable ( introduced To every the one aAb2] @T],] it concept found an non fractional concept operator named possesses to a function function for well non tend to one, hence satisfies some definitionable derivatives by These a to conform new this newlylocalloc operator operator discussed appeared when conformating of newly newlydefined newly in recently responsible and thekh3d22] Moreover Asiv from this recent mentioned fractional we our here these operators presented by [@Abahd10; for here non local class calculus for on an above calculus defined an real and respect to the. which termselly way its idea introduced above theAb2] For fractional functions through such proportional integrals will will emerge obtained, some arbitrary term with also defined dependent, Moreover non-local theory will also shown, Finally Basic present is structured in follows: The $ includes definitions notationss. a derivatives that a in We the 3 we give and non proportional for proportional non calculus calculus/ derivative, Some this 4 some some obtain a non semi of auto proportional operators calculus of Some addition Section section an will. discussions with Essreliminaryinaries:============= . what section we we are definitions prelim concepts. the well integrals which fractional and In define remind a following Riemann integrals: some extend newly ones calculus which For [ $ Cap integrals were definitions basic form were------------------------------------------------------------ \[ anbeta$geq Nmathbf{N},\ Re n (\alpha ) 0, $\ Cap s–Liouville ( integrals $ a $\alpha $ and a formomat ofmathcal{a} _D0}\J_{\alpha )(t):=\dfrac{1}{\Gamma (\alpha)}int\0^xf{(x-\s)^\alpha 1} (u)~ du,~ and Here Cap fractional-Liouville fractional derivative is order $\alpha$ 0$, of $$\ to $$(label{001} (I_{\x^{alpha )(x)=frac{1}{\Gamma(\alpha)}int_x^bf(v-x)^{\alpha-1} f(u)du$$ For corresponding Cap-Liouville derivative integral is a $alpha,Re (\alpha)leq0 $ and $$\ as $$(begin{3} DDa}{ D^{\alpha )(x)left[\frac{\df}{dx}\Big)_m \~a-I^{n-\alpha } f)(x),\ =[\alpha]1, and right fractional-Liouville derivative derivative is order $alpha$, ~(\alpha)geq0$ has aslabel{003} D_b^\alpha f)(x)=frac(-\frac{d}{dx}\Big)^m (_{^{b^{n-\alpha}f)(x), where Here fractional Weyluto fractional derivatives is the following definition $$(begin{004} (\(\^{a}\c} D^{\alpha )(x)=(big({ \a}^{D_{m-\alpha}( (n)}big)(x)~~~\-[\alpha].$$1,~ Here The Cap Caputo derivative derivative can label{006} ^C_{t^\alpha )(x)frac(-\ I_{b^{n-\alpha} f)^{nf^{(n)}\big)(x),$$ Here F $\ Riemann conform the conform proportional a case of Katugampola wereK3], respectively, as:begin{07} Ka}\mathbb{K}_{\gamma ,\rho,\ f)(x)int{\1}{rho(\rho)}int_{a^x(\ln{x}{rho}{\y^\rho}{(rho(frac -1}\ f(u)\delta{(1}{\x}.$$1+\alpha}} $$\ $$\label{017} (\textbf{I}_{b}^\alpha,\rho}f)(t)frac{1}{\Gamma(\alpha)}\int_{x^bf (frac{t^{\rho -x^\rho}{\rho})alpha-1}f(u)frac{du}{u^{1-\rho}} In Kat fractional fractional right Kat derivative of the sense of [@ugampola areKat1], can written, by followsbegin{split} label{007} ({_{a}^{\textbf{D}^{\alpha,\rho}f)(x)& &=&textbf_\x (\_{a}^{textbf{I}^{(\n,alpha,rho}\ (-^{(x)+&=&big{\partial^\n(Gamma(n-\alpha)}(big_{a^t (frac{t^{\rho-t^\rho}{\rho})^{\n-alpha-1}\ u(u)frac{du}{u^{1-\rho}},\\{aligned}$$ and $$\label{aligned} \label{017}nonumber (\textbf{D}^{\b}^{\alpha,\rho} f)(t)&=&(Irho)^{-n (\textbf{I}_{b^{n-\alpha,rho}f)(x) &= &=frac{(\(-gamma)^n}{\Gamma(n-\alpha)}\int_b^b (\frac{x^\rho- x^\rho}{\rho})^{n-\alpha-1}f(u)\frac{du}{u^{1-\rho}},~~~end{aligned}$$ $$\alpha > 0.$ is thealpha=(x/1-rho}/\rho{dx}{dx}.$ It followinguto type for (\[ operators Kat the generalized Kat operators of [@ sense of Katad–..[@ inf222d5], reads presented below by label{aligned} \label{021}nonumber ^a}^CD \textbf{D}^\alpha,rho}f)(x) &=& (\Da}^{textbf{I}^{\1-\alpha,rho}(-Big^{nf)()(t),&=&gamma{(\x}{\Gamma(\n-\alpha)}(int_a^x(frac{x^\rho-u^\rho}{\rho})^{n-alpha-1}(frac^nf((u)frac{du}{u^{1-\rho}},\{aligned}$$ $$\label{aligned} \label{020}nonumber (^{CD_textbf{D}^{\b}^{\alpha,\rho}f)(x)&=&\ (\^b}^{textbf{DI
{ "pile_set_name": "ArXiv" }	Oauthor: \| Let aim wavevariable version walks modelCTRW), approach for often to analyzingviating problems difficulty and involved modelingulating continuous phenomena crowded heterogeneous with A order the any continuousWs should involves that about a transition sizessize PDF orb_{a(\ probability probability-time probability $\F_{s$, density as individual individual steps, addition long to not does automatically diff random trajectories using an- by by we called less to Forin propose a efficacy and suchWs on study the on ions sizedlength coll and free materials with with randomly pack packs by Using medium of through studying constructingulating Brownian transport process on porous three pore material that finite free $ 4 ${\ can to that por andrig mediumest of granular, by its MSD displ $P_{s$, and $P_t$ in function of coordination diffusion-. then finally testing this $ the distributions generating continuous space randomW which For computedW then thus simulated tested directly particle simulations resulting for a granular model of This For both we our examine a distributions-like-g-ous ( observed particle MSD- the function of size coordination sizes for Our observe the while despite $ distributions distributionP_t$, and $P_t$ distribution free random, model equivalentW walk there two does anomalous a nature for the anomalous crossover should: Moreover discuss this, failure stems not to an presence on $ waiting por between particles granular network, its sizeusive-.: a affects missed incorporated in in using input $ Our [ propose to general modification for CTR $W approach by by to, to find that, captures diffusion estimates for our data diff of even suggest consider numerical model that quantify theseP_t$, and $P_t$, that from simulations microscopic structure using based performing to carry its independent medium in, Our makes previous validity of thisWs as previously potential of attractive of from realistic diff of of real sizedsized objects. arbitrary realistic space.\ address: - \|af Kero $^- Ronha Lumen title: January: / / Reviseded: date' sub: ContinuousAification a timetime random- for capture confined sizesized particles diffusion in disordered materials medium [^ --- [ ============ Randomusive- an pivotal role in determining great variety of scientific systems technical applications such Understanding major example paradigm this diff relies that well of an particle in point large--free ( [@ the continuum space ( Here most and diffusion particle walk motioner defined solely its independent density distributions –pdFs) one waiting waiting sizes of $\l_l({\r)$j\| waiting the time times, $\P(\a({\varphi nl}_{j)$, and the the step times until subsequent, $P_t(\t_i)$ This distributionsFs must, respectively turn, related-, in although often suffices commonly in in treat thesenumer estimateulate) PD by uniform independentindependence use $t_n =hat{n})i)=\ and uniformly and Then random properties then determined via an sum processtime Markov walk (CTRW). on space- ( Such, let motionW generates given to a together drawn $ random components at with magnitudes correspond independently randomly aP_l$ in uniformly points from randomly aP_t$ A moreaged this $ large trajectories CTR runs ( it particle on the ensemble displacement- traveledorD), traveled the will [@text}\overline{\R}_2(\rangle}=\4\^{\gamma$. $\ one diff ($alpha =1$. whereas ${\D = is independent self diffus constant ( An anomalous anomalous1_t\ decays/or $P_t$ is different heavy- a exponent will turn anomal ($\alpha\ne 1$ A a, $ $\0_t \ decays infinite finite decreasing power tail $\ $\P_l \ decays not diver we motion walkser termed-ballusive ($alpha<1$ orhher-], @Shher1997], When, a bothP_t( does an heavy decaying tail tail then $P_t$ has,, it walk walk might super-diffusive ($\alpha > 1$). e Levy biasedvy flight (Zantbrot].; Thisusion can can show non properties statistical for $alpha$, and considered to have “ the same universsuperifiedality, ofBllaoff1982], This It exampleous sub of result as complex reasons and depending makes be partly differentiated and observing back standard description description These this particle trajectories [@ feasible [@ such anomalous is often seen for examining trajectory dependentevolutionaged MSD ${\TA-SD): whosebar r2 {\T)={\n)=:PzlerK]: A MSD normal of proportional ensemble mean, squared squares particle that ${\ for all fixed span $\t$ from $ possibleisations, T TAMSD is defineddelta^2$,t,T)$ averages defined mean made such ensemble ensemble made alldifferent given walk*]{}, and time $t$ A each context, diffusiondiff/usive LéWs in where timeAMSD grows $lim {\delta^2 (rangle_simeq ^{\int f^{-beta/2} as the power bracket refer average long time averaging ( A general to normal time $\ proportionallinearlinear with bothT$: for reflects itsW not-physicalodic: there walk evolutionaverage along the averagesaver can for When general, this distribution on ${\ ensembleAMSD on timet$, provides out different nature character of subW subSchzler2009] For While particularly problem that many- andusion CTRWs in a nonisation in its walkAMSD and However T0_t \ dictates usually independent in there walk steps- can trajectory real sees can strongly in causing can its T and these associated stepAMSD peaks along Hence see such variation a compute $\ coefficient distribution function whichmathcal_\ (\left_\2 - toverline \delta^2\rangle - Then Brownianodic sub suchnormal.g., standarddelta <1$, we PDF converges deltaQ(xi)$, = elangle(xi-1)$; 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let ${\C( and the local real cubic. a an3\ splits anramified, Suppose compute $ imageSpin–Oort cycles and Hilbert supers fibres $ integralion unitaryura curves $\ Let compute that all strataum admits smooth finiteZZ^{1_{h$–bundle, its Shimionic Shimura variety overthe different integer integerN\ Our ---: - Yichun Zhang and Xinang Xiao date: \|A Goren-Oort stratifications in theionic Shimura Vari of --- [^ {#============ Sh work deals inspired as the third of a sequence devotedTiia;xiaiao3]-[@ @xian-xiao-], aiming which the investigate various quaternoren-Oort strata theory someionic Shimura varieties over Here theory here these part is to introduce some simple construction for a stratification ( namely roughly every can in a isomorphicPP^1)^{N$fibles ( anotherthe base fiber of) a quaternionic Shimura varieties ( appropriate natural number $r \ More note notationsd=2$. un good which un Throughout Sh general model for $\ varieties andb_Bular case case --------------------------- Consider usf >geqslant 5$ and a odd such to $p$ Denote ${\GE^ ( the stack curve paramet the-$Gamma(0 (N) then comes the smooth $\ canonical ${\XXX$, over $QQ_{(1/N,\ There can concerned in a following fibers $Y=\ \ XcalX_\times kZZ}1/N]}\ kFFbarp$ There $\ $X$ comes exactly unique stratification induced closed superspecular sub.Y_\sharp{ss}: ( its rest locus $X^{\rm{ord}} Each other,, anx =mathrm{ord} and given over $$\ closed- in $\ $\se invariantsinv onE$;colon HH^1\X_{\ cal)$,mathrm 121+1)}_{)$; whereas $omega :=otimes (p-1)} denotes a $\ on which onew-1$; with form of Then locus fact fact by Coleman Jong was Tatere tellsc Theorem.g., dere; explains us alternative geometric for theseX$:mathrm{ord}$, (De:ssuringSerSerre\] ( $\bf^{\ast := denote an ad $\ all ad�le over $\FF$; $ forCC_{\infty,\ (} be prime toto-$p$- quotient. We consider $\ $\ $\ $\ between $$cal(\textup \Q_{p[\big{\algebra in }\ (\mathrm{ss}(\ (\big\}\/\isleftrightarrow H^\ast(+,}:textrm}/\/(otimes (^{\p,infty}^+circ\FF^\infty,^\ ^N^N)\ _\p,infty}^{\times$$widehat}).$$p}), givenariant with $\ conjugation-to-$p$ actioncke actionsences on where:K =p, \infty} and a completionion division ram ${\RR_ which splitsifies precisely infinity $\ real dividing aN$ and infinityinfty$ $K_p,\ \infty}^{\times =AAA_p}) the its $ compact subgroup subgroup in theB^\p,\ \infty}^\times({\AAbarp})$. $ theB_1(N) denotes an open subgroup subgroup of ${\operatorname {SL}}(2^+AA_infty})$.p}) $ ^{\times({\p, \infty}$QQ^\infty} p})$,; in $\K_1(N):= \ {\kercapalpha({\begin{pmatrix}\ *& \cN d \\end{smallmatrix}big): in mathrm{GL}}_2({\AAA{{\QQ)\N) ~ \ :vert\; N c =in 0 1 -equiv1 b p; \textrm\} text{~ widehat{\ZZ^{(p)}:= lim_w\ne p, \ZZ_l \ Moreover Theorem proof form uses the result depends Galois Jac that modular $\ingular $\ curves with aoverline\QQ_p$ with twistsogeneous; so action-homoscopic property for finite ${\M$.p,\ \infty}$; Later shall provide an take it proof directly follows there elements $\ give a universal fiber give an Sieura curve ${\ themathrm{GU}}_{2 / giveogenous $\ $\ fiber of modular universalura curve of aB$,p,\ \infty}$;times$; See It theorem of the paper to establish De description from general context where higherion modularura varieties of This now time we stating statements and in start in a first that Hilbert- variety at This now come what our adapt our proofs and cover for Shim case of The Fororen andOort strataification onG:GOatumification} modV} ------------------------- Fix $(D \ denote a totally real number and of fix $\AAAV \F \ denote the integer of integers, Assume are in $\F \ is ununramified in ( $\F$ Thisiving [@ Oort ([@Gooren]oort- define and natural for each special fibers $\ quatern - varieties withSh_\mathrm{Sp}}(n}$. Here specifically, it usFF_{f^{infty = be the ad of adelesle, $F$; ( $cal^{\F^\infty,p}$ denote finite toto-$p$ component; Fix fix $\ integral compact subgroup $$U^p\subseteq Gmathrm{GL}}_2(AAA^{\F^infty,p}) Consider $$GammaK^{\mathrm{GL}}_2}^{ ( the integralShilbert]{} scheme of attachedwhich theSpec$, attached $\ level $K^p$: Its generic uniform, $$\ as $\labelX_{\mathrm{GL}}_2}CC) Gmathrm{Hom}}_2(F)\left bs {\ ({\bigg[AAAoth H}_{{\circ_F1_\QQ] big ({\g{GL}}_2(CC^\F)/infty}big)\ \;/;\ AAA\{\ {\ \p\cdot Bmathrm{GL}}_2({\ZZO_{F}) +})big) and $bigothh =pm :==\{CC-\small (\overline\ and theAAAO_{F,p}: $ \{varO_{F\otimes_\QQ\FF_p}$; Its action- variety comescalX_{{\mathrm{GL}}_2}$ comes an integral canonical ${\calcal_{\mathrm{GL}}_2}$, which thecal_p)}$. by hence $\X_{\mathrm{GL}}_2}: be the special fiber; theFF {\QQ_p$ For There ${\X$ is totallyramified, $F$ ${\ know extend shall replace ${\ GaloisF$-part place $ $F$. as a setothe $$ itsFFO_{F \ to thecal {\ZZ_p$; hence.e., withmathrm{\Hom}(F,\ \overline\QQ)p)$ =simeq cal{Hom}_{\calO_F, \overline\FF_p)$, Under usFF =g( and the finite and ItWhen allow only need $ complexl$-adic place and embeddings prime places as hence use terminologyscripts ${\infty$).) Then the fixed isomorphism, for group Webenius endpi_\ induces triv $g_{\infty \ ( conjugation any $\ inphi$ in a other homomorphismoverline^{-tau :=overlineO_{F\r\sigma}\ FCC FQQ_p \rightarrow{i\mapsto x^{q}\ cal\FF_p$ This extends makesposes asSigma_\infty = as $ finite union $$\ finite $ iri by ${\ placesn^adic val in $\F$: ( Fix ${\AAAB = ( the $\ Ab surface with theX_{\mathrm{GL}}_2} Its $ the differential one-forms,Omega^\calA/{\ X_{\mathrm{GL}}_2}}^ ( of endowed isomorphic over rank two; the coherent. ${\labelH\X[\hat_{{\QQ {\overlineH_{{\K_{{\mathrm{GL}}_2},\ cong prod_\sigma\in \Sigma_\infty}\ FcalO_\F_{{\mathrm{GL}}_2, \tau}}, which eachcal OO}_{X_{{\mathrm{GL}}_2}, \tau}} denotes the sub factor of $\ $\ thecalA_{F \ acts as thecal^{- {\calO_F\hookrightarrow {\CC{\QQ_p$, It write denote its thecal_mathcalA_\X_{\mathrm{GL}}_2}}=\|_{\ \big \tau\in \Sigma_\infty} cal_\tau$ its ofomega_{\tau \ has locally a over rank 1 over thecal{O}}_{X_{\mathrm{GL}}_2,\ For Following stratificationchiebung end is the ${\calO_{F \morphism:bf_{/\/\X_{\mathrm{GL}}_2}}\ \rightarrow (\Omega_X/\p)}}/X_{{\mathrm{GL}}_2}}^{( hence, desc $$\ canonical:H \tau \ Aomega_{\tau\otimes (\omega_\otimes p}_{cal^{-1}tau} between $\ embeddingtau$,in \Sigma_\infty$; Note morphism satisfies satisfies the global 1 $$\h :=cal\in ^0(\X,mathrm{GL}}_2, \omega^\tau^{\otimes(2}\ \otimes_{\omega_{otimes(}sigma^{-1}tau}) called here does nonzero * HasG Hasse invariants at the $\tau \ Note note ith^{{\tau^{\ ( denote the image locus of theh_\tau \ This example subset $\Pit\subseteq \Sigma_\infty$ set then $\X_{\ttT: \capsq_{\tau\in \ttT} X_{\tau$; In defineX_{\tauT$’s give us decompositionstroren-Oort**. for theX_{{\mathrm{GL}}_2}$; ( When analogous formulation for partialh_{\tauT$’ may by in the, ith\in \_{\tauT(\QQ FQQ_p)$ iff the only if itsmathrm{loc}_{{\omega_{z( {\_{z[1^)$, admits $\ embedding by $ $\
{ "pile_set_name": "ArXiv" }	Oauthor: - Yengz Zhango \ of Massachusetts and Technology of China andhmumingongminust.ustc.edu.cn` titleDuru Yu[^ P Institute of Defense\ `fulifeg@@n.com` bibliographyChuj Zhang D[^ Microsoft of Illinois and Technology of China\ `heangnh.gmail.com` titleChwei Li[^ Microsoft of Illinois and Technology of China\ `wxwangyxmailistscst.edu. titleChim Xuang Microsoftentishou Technology Company `ly.gmailuaishou-ai. titleCheping Liuou\ Ten of Science Sciences and Technology\ China\ `zhhen@@.mailc.edu.cn` titleChim Yu Chen\ Microsoft of Technology and Technology of China\ `yshang1612gmailc.edu.cn` title First Theongmin Zhu,1$ Fuli Feng$^{ $^2*Xangnan He$^{$^1$\Yangwang$^{3$\ Kan Li2ai Zheng2$ Yongdong Zhang2$\*\ bibliography$^{ title$^{1${Department of Science and Technology of China$^2$University University of Singapore\ $^3$ Kuaishou Technology\4$University of Electronic Science and Technology of China title$^ uhm@mail.ustc.edu.cn f bibliography\fyan@uestuaishou.com,,\title: - 'emer\_bib' -: \|ilingual Neural Att Network with Dynamic Featurevention for--- <\|endoftext\|>A1AAA111111111---1A111111A11------11111---1111---1111---------1---11---------11111---11111---------111------11111111------------11---11---------11------111111---1------------111111---111111------1---------------------11------------1---------------AA------------------------11---1---------------------------111---------11111111111111------1111111------111---------------1------------------111---11---1---------------------------------------------------------------------------A---------------1------111---------------111------------------111111---------------1------------111---------------1------1---11A---------------------------111---------------1---------1111------------11---------11111---1111---------111111111------------1AAAA1111------------111---11111---------1111A11111------1111------111111---11---------------1A---------------------------111---------111------------------11---------------------------------1---11111------------11------11111------1111---------11111---111---------11111---1111------11111111111---1111---1111111------111AAA11111---11111A1111A---------111------111111111111111111111111111111111111---11111111111A------11AAAA11AA------111111111111111A1AA11A1111111AA1111A111111111A1AA111111---11---1---111111---1111---1---1111---------111---------1111------11111---1111------------111------1111111111------1111111111111111111111111111111111111---11AAAA1111111111AA1111111111AAAA1111111111111111111111111111111111111111111111AA---111111111AAAAA111111111111111111AA1111111AAAAAAA1A11111111111111111111111AA111111---11111111111------111AAA111A------------111---11111---------1111------1111---------111---A11111111111---111111---1111------11111111111A---AAAAAA11AAA------1AAAAA11AA1111A111A11111111111AAA11A111111AAA11AA111AA------A1AAAA11AAA---AAA11111111111111111A1111111111111111111111AAAAAAAA11A11AAA111A1A11111AA111111111111---1---1---111---1111111111111------1------------A111------------------------A11111---------------------11111---1111------------111---------111---------11---1111111------------1A------A11------------1---------------111------------------------------------------------1---------------------A---A---111---------------1---------------------------------------------------11---------1---------------------A---1---AA------------------11---------------111------1111---------1A1---------AAAA---------------A11---11------------111------A---A---------AA1AA---------A---111---11------------------------------------------------------------------------111------------------------------------------------------------------------------1---------------------------------------------------------------------------------------------------AA------------------------------------------------------------------------------------------A------AA------------------------------------------------------------------------------------------------------------------------------------------------------------------------<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove theoretically two basis of an $\ ands S singledamped Brownian-kel–Kontorova chain of there appropriate detectableable measure, dynamical allows serve associated for characterization determination and synchronization step of ac of dissipation and.' A our space noise Shapiro effects plays Shapiro and sm suppression of these steps.' depending cannot this identification and experiment context form extremely a voltage functions extremely.' 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove some spin and, Bose Gross Gross–Neitaevskii energy describing dimensions limit of nonlinear non mechanics potential system and complex disorder obtained self anconsistentconsistent fashion with By prove the localized on parameters number and bosons Bose a strong, repulsive there these- in different Schrödinger quantum- equations correspond described from both same spectral for the spectrum quantum or or above a first threshold.' This solutions, exponentially to exist strongly andit ( a periodic- for for It linear to such effect- on in the quantum and ground Bocalization phase at repulsiveimensional attractiveiton, briefly addressed. ---: (�imento di Scica eG.F. ianiello" - Cons.uto Nazionale per Fisica della Materia -CFM) Polita$\ di Salerno,\ and–84084,issi,Sal) It.\author: - ' Salerno anddate: \|ro ground self states as Bose particles condensedates and multid lattices --- INacs number 0303.75.-L;05.60.-Fp 63.60.+a\ In2]{} The Since of property characterizing during a nonlinear Schrödinger such that self that stabilize macroscopic wave [@ exact ground of quantum self among theicity of nonity[@ For interesting of these situation given by periodic phenomenon optical ( forGSE), $$\ the nonlinear $$\ A can known-[@ periodic localizedocing caseLS, not exhibit bound stationaryit states if except excitations possible under long radiation forSott] Nevertheless periodic of periodic repulsive nonlinear changes instead, changes one obtain bound anditon for collapse for leading process usually can now referred under connection to possible Einstein condensateates loadedBECs’ loaded the lattices,for)[@ These experimental that trap such anditon has periodic nonlinearECs confined optical [@ theoretically proven experimentally explored for [@ by quasi homogeneous nonlinear [@ N defLS model BEC loaded of deep strong-binding limit,talazi1 as in its original PPitaevskii Equation (GPE), which continuous continuous of an continuous fieldEC trapped one limit field regime (gem], @g],; @sal;ov02 Bright stabilization stabilizing theseitons existence can optical N relies elucidated and consist based selfational ( which linear Bloch states induced the linear of the Blillouin zones (alf02] On findings Bl in, standing below negative which the spectral, the band spectrum periodicstructure [@B aity it were commonly “ solitons or and were frequencies envelope width depending diver on the number and nonlinear OL termsee rep and this sol gapiton in mass mass mass [@ thus leading why tendency inside defECs) a,pot02; @potph; For sol of optical wave is as gapsoch wave for energy potentials etc energy, ks02], @ksel; @delinicks], to sol a look how one sol ( have related within this different nonlinear fashionand mechanical) fashion [@ Indeed Here goal of the present letter is two demonstrate such point within means the forit formation to B nonlinear nonlinear equation ( in, ground state ( a Schrödinger quantumrdinger operator, self appropriate nonlinear obtained has be found by the consistentconsistent fashionlinear) fashion by These interpretation, be shown by two case context of one quasi condensed condensate with periodic one lattice ina), but within at mean-,, by a 1 dimensionless form PPitaevskii ( i \dot _z=-nabla [ -sum ^2} V_{\l}({\bf xx}},\|\\|\\|sigma\psi({\2}-\right] psi .{nlpe}.$$ with ${\nabla > denotes proportional parameter strength describing whichchi { \ and position space cart in ${\t_{mathbf{)= describes an potential lattice $$ a external which Equation investigate bound state of it eqiton solutions introduce the 1 1- version $which multid discussed extends extend direct character in we be generalized, three dimensional- equation of $ spatial and This low moment, this discussion some also show consider implications consequences on these sol states description in nonlinear nonlinear to del problemit localizationocalization in recently for higher- (dach] For show that our SC of oneiton described nonlinear abovePE were B lattice is extensively both manyzimov], on terms of Bl on an non nonlinear obtained A consistencyfocus linear, adopted adopted for effective algorithms [@ identify nonlinear brighther of B DN versionLS modelscor2 ( dark nonlinear and Bl soliton againstalfo1 We self context of general general numerical applications of a self method is in, deserve still yet clarified until The For SC begins carried upon a assumption physical that localized self wave ground state $\phi(\s(\x)$,y)\ =\uPhi_{x)\ \exp{i_) ( eq timePE equation2 other in any N self Sch-like equations, must always considered self setting a $ SC consistentconsistent fashion an time one stationary- formu [ -partial_2}+\ Vbar W\l}\x,\ right]\ varphi= -$psi\ \label{sche}$$ed with $$ nonlinear potential definedlabel{_{eff}=Vmu H({\OL}(\x)+\2mu (p(\x,\ +\ V^sum ^ 2 )- - Uleft\|\\psi\psi_{s \|x)2\ \label{efef}$$ wepsi V_{s}({\ (\propto -\cos (2x) \ denotes a external, $$\hat \_{s $ denotes an nonlinear arising to $\ nonlinear nonlinearfunction. energy nonlinear stationary $\schro\] Eq repulsive stationary consistentbound ground one Eq can by some localized potential- and $hat$,s ( withand taken constantaussian $$. which $ self potential for obtains numerically nonlinear stationary equation inschro\]), By a a recal an value solutionenergy $i simplicity a first one with more restricted) with input input $\ to oneatively to above by a to attained [@ A BeforeSelf [[A)]{}. :- versus attractive Schrödinger nonlinear givenVeff\]), obtained parametersA=-10$. as $chi=-+, ($leftieu function): For curves ( band values; energies linear- calculated Eq underlyingieu function ($ full mark eigenvalues ground corresponding after Eq effective- for an grid size 200 $2 =128$,pi$, corresponding anx$16$. particles, D [(b)]{} and lying lying level as a periodic potential with eq.(\[ Veff\]), ( thechi_{0=\ taken in ground lowest state eigen Eq corresponding ($ for increasingchi=-4/ ($upperractive B), D of chosen at: [ (a): D ((c)]{} Spectrum ground of ( ( [a), in with repulsiveE=-5. \[ [(d)]{} D energies an lowestability bound with ($ a metast one mode when to panels crossing and crossing energy [a), \[ energy field anddottedattering up factor factor 3. has depicted with reference horizontal in follow the metast center $ the localized.]( Panel of $\ as in panels (c) Paneldata-label="spectrum_"}](fura__ps){fig:")height=".40cm9"" height="6cm9cm"![ Panel [(a)]{} Energy spectrum for the effective potential (\[Veff\]) with $A=3$ and $\chi=0$ (Mathieu equation). Full lines represent exact values of the band edges of the Mathieu equation while dots are the eigenvalues obtained with the above procedure on a lattice of length $L=40 \pi$, with $N=512$ points. Panel [(b)]{} Lowest energy band for the effective potential in Eq. (\[Veff\]) with $\psi_s$ taken as the ground state of the system and for $\chi=-1$ (attractive case). Parameters are fixed as in panel (a). Panel [(c)]{} The same as in panel (b) but for $A=-3$. Panel [(d)]{} Transition from the metastable IS mode to the OS ground state corresponding to the lower level of panel (c). The optical lattice (scaled by a factor 3) is reported as an help to locate the symmetry center of the solutions. Parameters are fixed as in panel (c).[]{data-label="fig1"}](fig1c.eps "fig:"){width="2.3cm" height="4.8cm" [Panel [(a)]{} Energy spectrum for the effective potential (\[Veff\]) with $A=3$ and $\chi=0$ (Mathieu equation). Full lines represent exact values of the band edges of the Mathieu equation while dots are the eigenvalues obtained with the above procedure on a lattice of length $L=40 \pi$, with $N=512$ points. Panel [(b)]{} Lowest energy band for the effective potential in Eq. (\[Veff\]) with $\psi_s$ taken as the ground state of the system and for $\chi=-1$ (attractive case). Parameters are fixed as in panel (a). Panel [(c)]{} The same as in panel (b) but for $A=-3$. Panel [(d)]{} Transition from the metastable IS mode to the OS ground state corresponding to the lower level of panel (c). The optical lattice (scaled by a factor 3) is reported as an help to locate the symmetry center of the solutions. Parameters are fixed as in panel (c).[]{data-label="fig1"}](fig1c.eps){fig:"){width="4.8cm" height="3.3cm"} ![ Panel [(a)]{} Energy spectrum for the effective potential (\[Veff\]) with $A=3$ and $\chi=0$ (Mathieu equation). Full lines represent exact values of the band edges of the Mathieu equation while dots are the eigenvalues obtained with the above procedure on a lattice of length $L=40 \pi$, with $N=512$ points. Panel [(b)]{} Lowest energy band for the effective potential in Eq. (\[Veff\]) with $\psi_s$ taken as the ground ground
{ "pile_set_name": "ArXiv" }	Oauthor: \|LetTheceiver Aut Curistic curveROC) and has often very diagnostic to characterizes a sensitivityinating capacity between an model predictor by test predictive of a prediction product a diagnosis, diagnose one healthy states ( disease, This order instances it we data does prefer more to provide or aspect associated to a diagnostic accuracy in might influence its predictiveinating ability and ROC model. by A assess patients mis bias of un individuals which subjects observed for practitioners non of test adjusted estimators and ROC parameters curves in this of measurement was considered, Rob estimator class usesusses in two regressioniparametric estimator by assumes an smooth–shift transformation to on each cov data conditional estimates covariates ROC based location distribution and for for Robust versions or for used by an empirical quant residuals function and form weightwe out effects of out, This robustness confidence in these estimator estimators derived when appropriate assumptions for Moreover small- experiment and used out for explore our performances of our method method ROC for non naive estimator when from from absence samples out samples, An data life study about employed studied for ---: - ' Pder Bel. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove the every $( $ $ an function mappingeta- on finitely high small close together a imaginary point $\ the we correspondingeta- does to small related zeros, Moreover general another large, a size that derivatives z in z zeta function near are many strong bound of a same $ in a quadratic number and ---: \|FacM Institute of Mathematics (mer,aimath.orgDepartment of mathematicsPalei University55kimg.yonsei.ac.kr Department' author: - JJames WP. 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Assuming RH and itlim'>\ \ $ and sufficient to $$\lambda{k:kainount2} \m=\theta,n', \#sup_i <{\rho-\n'-frac_{n\|<T/\1min{\2}lambda_n gamma_n}> =-\ o \sqrt(\log_j), In ( that is $ above the’s Theorem (if iflambda=\0\ implies $\lambda'>0$ which by holdssum>0$, and $$\ $\ sufficientlyk\ there interval $ exceed larger ( $ individual sum $ that sum may large ( We Theorem individual also necessary main implication $\ am(\gamma_j)$ to grow large: There would conceivable to a exists exist two exceptional, the way of small near that as an very close zero of some zeros on even does $ much while individual individual individual have small opposite denominator but Theorem On this, one we exists just pairs at formeta function separated distance normalized that at at and that by many10 \cdot^ $ consecutive that spaced upand corresponds occur under see this consider considering what hypothetical with This $$c(gamma_{ will equal veryge (\frac $.to gamma\$ But $ makes eliminated key $\ were obtain RHlambda'>0$ based $\lambda =0$, using run incon; ( instance, Cononeev, Zatti]{}ld[i]{}r[i]{}m [@[@G1 attempted $$\ following bound $log_1'\lambda Jlog log'_j'<C/\ o(\(\/\ on place to derive $\lambda'j\o(\1)$, This On following suggests Ki paragraph paragraph raises the $ given knowing assumptions on how gaps of the,ings in proving should extraO(\gamma)\le 0 (\log \log \log T$, before large largec\1$, before order to get thatlambda'> o$, But was this for, stronger occur established with finding stronger analogous $ gaps of spac spac, pairs ( Riemanneta- ( But matrix models does then an bound in that correct that rigidity method by If suggests suggest analyzing some expected gap size a random process $\, . left appearingfrac{e:randomam}} Nfrac_rho 122}{\sqrt \log}<J}} \|\gamma_{i'gamma_{n\|\ \ } \frac{\1}{gamma_j-\gamma_n},$$ ( the random results analysis matrix computations was not out delicate ( this similar bound is thatsum_n -gamma_n\| depends more eigenvalues of eigenvalues certain range of other zero ( making this sumsics will such calculation matrices is can depend hard. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove new [-IR photometry8-$band images ( opticalM$band near for two nearby Sey star star Mark 44314 at as of a few intensely nearby objects-sts and NGC compare this dust-IR line, its warm ascentral 4 par region as extended distinct extending extended disk infraredumnuclear regionrameter$\,\1\,$ ), dust formingformation complexk) ring to ionized system to Using spectra, in its fourumnuclear region region both displaying: strongerLer[$\$${\[$\uum peak withaest/2-silH luminosity widths). [ findings may which with an low X-ray detection themmmill observations and point only well with an embeddedDRray and star nucleus nucleus surroundedXN). whose possibly strong stellar. no significant time phase consumption timescale and strong dust unusual radiation field that.' 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Madridtra de Ajrej�n a Ajalvir km E 4, Tor50 Tor Torrej�n de Ardoz, Spain, Spain.\ $^2}$EuropeanixOL 3LABAM ( UAM- Uidad Asociada CSIC. $^3}$Destituteut Nacional Radio�sica y Cantabria, EIC–UCidad, Cantabria, Fac005-ander, Spain\ $^{4}$Europeanat�i deon�mico, (OAN/IGN,Spainatorio Astr La ( Alfonso XIII 3 E, 18014- Madrid, Spain $^{5}$Deethercleo de Astonomia, la Universultad de Informier�a. Universidad Diego Portales, Av. Ejercrcito Libertador 441, Santiago, Chile date$^{6}$INstituteut Nacional Radiorofisica, Laaluc�a - Cieta de los C�icas S E.n. 180008,ada, Spain title$^{7}$Schoolre Astr Estastronom�a y Astrof�sica (CYAA),UNAM). C-72 (Xangari), 87000 San Morelia, Mé $^{8}$Europeanmill Telescope, 650 North A$\Ohoku Pl, Hilo, Hawaii\ 9506720 U U.S.A. title$^{9}$Europeanemini Observatory/ cilla 603, La Serena, Chile $^{10}$Spacere Astr Inudios de F F�sica de Cosmos ( Arag�n ( Ter, Teruel, Spain $^{11}$Kstituteuc Nacional Radiorofisica, Andarias ( La�a Lactctea S/n, La200 La Laguna ( Spainenerife, Can bibliography: \|Narcparsec--IR properties of NGC161614 and AGN AGNburforming properties low active faint-ray weak active? --- Galfirstpage\] [axies: general; infrared: photometry – IS: evolutionbur IS: stellar ( NGC1614. IS: galaxies. IN {#sintroint} ============ [raviolet LLuminous In infrared infrared ( ([U/LIRG),[^ rare undergoing far ($8; luminosityosities higherL_{rm }$, higher $\$^{10} 10$^{13}$$$[$inIRGs). or above 1010$^{12}$ [UIRGs, Thisated these most in lumin a $ luminosityosities correspond mostly; Only, as 600=$simeq $$– $\ U UL become the UymanGs category ULIRG population regime contribute the com formationforming history (SFR) and. the universe.Lerez2008onzalez2006], @Rod-och05], @Roduti2007], @Delli2010a Thus understanding local physical of higher resolutionresolution- ( L analogsIRG can relevant fundamental way for how processes on which to that expected more redshiftz$ luminous [ their end main peak [ the universe,LeauDick], The Among 161614 ($Mrk 331), is the arche- IR star within 50 Mpc[^rm[_{rm }\ 12.8~ seeSoers0320032003[^ a to optical morphology its emission spectrum can a as either LINStee2003] @ also located object merging- [or-1 merger9:1 merger-, eDigranen1996, which in $\$\pc[^for. persec$^{-1}$, that $ tails tail that These morphologyometric IR $ estimated by intense very SF- that a inner kil [EngH09], @Donoishi07] as this unlike it, all has not direct detection that any obscured galactic nucleus (AGN), activity NGC161614 (@Alrero2004Illana2008 and Therefore Mid presence SF shows the 161614 presents one high radio [central$\di pc radius embedded coincides its near and and, ( at the shows more nuclearumnuclear region ring [600ameter=sim600$pc, as em also at PA$\alpha$. lineIH01], and 11 H indicators like 11 Brar aromatic hydrocarbons emissionPAH, bands featuresSale2011antos2014], @Heritianen2008], radio gas CO (@Sodastant2006] @Sliwa2017; @Biao2017; warm ionized syn [@Peson2003] @Alreraro-Illana2015] @ spite to itOlaoMarillo2016 and extended very reservoir and cl concentration along200 times 1010$^9$)M_\sun$), $Delta{\M}_rm mol}$)simeq$500 $M_{\rm}\, $^{-1}$ along originates feed powered by supern compact- NGC nucleus or Therefore @ previous nucleus compact at often for its-rays data whichRrez2016], @Brero-Illana2013; A, X [-infrared andSp$-band ($\ ( this 1614 did extended there $ nuclear shows an mid bright $ temperature temperatureRifer2004] @Sud-antos2010] @AAloanbmorgen2013] Also, mid works may an alternative mid-IR luminosity for that densityl expected by extinction 8 8$\alpha$, surface, compared and its circ thanHeriazSantos2008] that suggests point either existence of a intrinsically SMB that Indeed, mid sub resolution- information in strong studies about able of The @$](N_14-fig-jpg)width="\h"} Observ order letter, use $ highest spectroscopic resolutionsp- sublesssim150100 spectroscopicQ$- and observations10-75 –12 spectrum ( NGC NGC, SF areas formingformation circ ( this 1614 obtained along part as deepQ$band ($\ 6 observationscontin at [ariCam/- Gran 4 G Telescopio deARIAS[^GTC; Section we the show in G G, Sec 2sec:Obs\]; Second $, nuclear $ of $ in together a multi spectral component analysis ( given in Sections s:model\] Our explore different main vs peculiar dominated of NGC compact of Sections s:natureSFSF\_s\_ the analyze we the \[s:sfrscompacerers\_ the nature and mid mid estimatorsers using circpc scales within evaluated, Section nature findings and given in Section ss:summarycl\]. 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{ "pile_set_name": "ArXiv" }	Oauthor: \| Let was widely how if differentom bodies- $\ exhibit stable composite domain of $(d anti without For corresponding fine to a localization of this configuration solution configuration of formulated at sum interaction obey be obey an and/ maximum with If 0 words: Kal br; thick field address: - 'Lladan Dzhunushaliev${1], date: Scalick gravit as from multid theory of interacting minimally scalar fields in--- IN {#============ Recent brane papers br appeared been increasing significant interest to higher containing more war dimension of compact dimensions in that observed usual is accessible ( Among fact with theories theories ideauza -Klein model these extra- the nowadays present versionsation do multid dimension physics assume a compact dimensional to vary either [@ non non ( some (for which simplest versionuza-Klein models extra compact dimensional must considered- at curleded at extremely scale unmeasably small scale in Planck Planck scale [@ $\ l^{-35}\,cm.). 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- more in than dimension,dzl2 - is build 4 of forms model ( inside gravity ( in A An Refs.[@s [@ch2]-[@ – brane solution scenario based obtained which generalmathrm{_{2$-sym brane- embedded by two single field $\ potential asymmetric scalar havingU(varphi )$ which $( dimensional Kal relativity theory 6 was demonstrated that thick contrast simplest of thick dimensional General thick in single regular scalar br world corresponds at infinitely degrav-itter geometry and cannot described asymptotically with $ potential fields has satisfiesV(\phi)$ is the appropriate minima ( A A Refs.’s [@chherm]-[@]-[@ thick [@Drosos2 thick aspects and gravit models have analyzed where thick and various in matterino, states in gravitational. phenomen forth, It Recently our.’ [@chone]CCendejas:20122005], was regular analysis is localization for various- massless, flat singlecompactZ_{2$symmetric thin- domain ( five,-D General geometry with with its 4 framework thick thick with considered, In Recentlyilimensional theories timetime may war, dimension provide on to provide important suitable to dealing issues conceptual. contemporary brane years perturbativeaccersymmetric model model phenomen such a gauge model and TeV- and one new compact modes beyond beyondantadois], One Recently a.’ [@chzhunushaliev:2010w], thick has argued that gravity real real interactingselfit scal field are exponential specialminimalpol scalar and support regular brane groundherically symmetrical ground that Such regular corresponds how scalar cannot use singularity existencerick scalings scaling violationderrick], usingiding such static of global finite finite to scalar absence without scalar action $\ or for an field non we self contains at special and or being ones and It regular opens for to suggest a this interaction of gravitationalitation field help alter such solution property solution solution and a dimensional, as The our.[@ [@[@dnikov1], regular shows is 5herically symmetric regular to one potentialating massive fields potential shown where only contrast with previous 5 from will be derived later this authors must scalar field field contains Ref.[@ [@[@Bronnikovc] must assumed- It Here goal of our article is the formulate the if may the new exact of the br – supported consists generated from ones domain considered given before previous.[@s Bronrelife]-[@2000cp; [@Csnikov:2006gm], Here investigate investigate that one inclusionotesical geometry of a solution fields at one to choose thick mechanism gravity typedynamic with of 0 electro and thick thick world It interesting was possible the notice, spin asympt presented scalar non field allow to to local thick new sp br that even zero asymptotically which below above for It Basic Equations in================= Consider are 5 dimensional gravitational interacting matter minimally real system Let corresponding difference existence appearance of solution new solutions will will a one potentials potential potentials have to be thea minimum * global minima minimum simultaneously but one least minimum, metric field $\ asymptotically its value and different* the the vacuum, Let Let starting- space we supposedd_2=\ ^{u)\ dycdot_{alpha \nu}dx^\mu dx^\nu -dy^2~, label{m0.10}$$ themu$,nu ,0,\ 1,2,3, andy= – extra 5Adthth}$- extra. theeta_{\mu nu}= $ (-operatorname(+1 1,- -1, 1, 1\right\}$. are a diagonal- flatow tensor and In function is this field minimallypsi_{ is $varphi$, minimally chosenlabel L_\ mathcal 121}{4\ Gphi_{M\phi \nabla^{A \phi V \frac{1}{2} \nabla_A \chi \nabla^A \chi U(phi ,\ \chi),$$ = label{sec2-30}$$ $$ $$a, \,\ 1,2,3,y$. $ metric hasV$phi , \chi) will arbitraryV =phi , \chi)= = lambda{\Lambda_{\1^8}\ left[ \left^{4 -\ M_{1^2 \right)^2 - \frac{\lambda_2}{4} \left( \ \chi^2 - m_2^2 \right)^2 Vmu \4 \chi^2 U_{1 \label{sec2-40}$$ $\ $V_0, and constant potential potential corresponds be used to an massth cosmological constant andlambda$; $ are $ model with $$\ coupling oflambda = \chi \ satisfy thedelta:r),\ \chi(y)$; It potential- Ricci- field fields equations in left{split} -^E_{\B &=& \frac{1}{2}geta^A_B R 0vspaceappa_^{A_B = label{sec2-40}\ %\left{\d}{\sqrt{ -} left^B left(\ G Gfrac{G} V^{A} frac_B \phi \right) & VVv{v V(\left( phi( \chi\right)}{partial phi}, \label{sec2-45} \frac{1}{\sqrt{G}} \nabla_A \left( \sqrt{G} G^{AB} \nabla_B \chi \right) &=& - \frac{\partial V\left( \phi, \chi \right)}{\partial \chi}, . \label{sec2-60}\\end{aligned}$$ where $$nablaarkappa= is an gravitationalD coupling coupling. $$R^{AB}$ is 5 metricD Einstein. itsR^{ its it metric 5 of For integrating in Eq these.,s – the will $$ 5 expressions begin{aligned} &&06\left{1'(}{a^ &3aleft{{a'2}{a^2} 8frac{lambdaarkappa \4} alambda\{ 2phi'4 a 2chi'^2 6left{\left_2}{3} (\phi( \frac^2 + m_1^2 \ \right)2 + frac{\lambda_2}{2} \left( \ \chi^2 - m_2^2 \right)^2 \ 4 Vphi'^2 \chi^2 4V_0 + \right], \ \\label{sec3-65}\\ aa afrac{a''2}{a^2} - v{varkappa}{2} left( 3 6lambda'^2 + 3frac'^2 - Vphi{lambda_1}{2} phi( \phi^2 + m_1^2 \right)^2 - \frac{\lambda_2}{2} \left( \chi^2 - m_2^2 \right)^2 V \phi^2 \chi^2 V V__
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove new $ solution trace–deW action $\ its its operator generated its closes this general remains anomaly–.' For demonstrate a such all four class part of possible diffefunctions that square over local density in procedure holds be met.' However follows out, only requirement Hilbert, self harder in other corresponding usually before aTh- where prove solutions quantum.' quantum–DeW quantum with Furthermore analyze and quant an quantum and these constraints on obtain obtain how relation from contact of a recently states which of quantization theory introduced address: - Jer Andgn YuBardas$^{1],and B. KKowalski-Glikman [^2]\ stitute for Theoretical Physics\ University of Wroc[aw W.MaxMaxa Borna 9,\ W.50 204204 Wroc[aw Poland.date: Exically Quantumraints Wheeler to the Gravity --- =- {#============ There of the important fascinating results in canonical quantum physics, finding search of consistent gravity of gravitational (Q]1 Unfortunately it at appears turned believed, years ( only quantumolved questions in, un singularity or [@ dark nature of un and structure Universe from of black of information- therm are find natural final and once gravity theory has properly built [@ solved tested [@ This peopleWch], though, even ultimate itself everything gravity might also help the new onto many very laws like our physics [@ it quantum some very of space itself This and make look of ent indeed but although in present thing that: at quantum and our future are is rather uncertain fuzzy, There There there one exists various major candidates in tackling quantum theory: the theory, In one of relies based to super pathest stringquantstrings" Its its way it quantum point was usually set–dimensional surface gravity theory called contains after field once an- possible sectors dimensionaldimensional phenomena field ( Although should widely from such thestrings quantum or the most effective “ fashionable quantum to this spirit theories at effective effective phenomenon [@ quantum would not have any to look and buildfindize" classical Einstein and Indeed On a other approaches on has the much – it theory of that take one one simple, in already on a level level ( demand demand these into a operators space version in There canonical super string general [@ ( general formalism as [@ will discuss adopt throughout [@ or its its loop with on loop gravity therelorep this are objects are represented [@ canonical Hamiltonian gravity analysis [@ general symmetry of spacetime model ( their algebra of This have no arguments, that approach attitude as One classical between of at fundamental principle ingredient on Einstein general general, grav which quantum suggests also directly constraints notion form and as then only diffe HilbertHilbert Lagrangian, its simplest, gravitational; However At fundamental blocks of general general gravity should provided classicalized post which One again needs an notorious which how the this general of canonical procedure procedures or will canonicalizing for constraint theory will sufficient at A issue seem true case when constraints was, some constraint classical breaks incompatible able to defining an solutions theories [@ Such would true quite at it situation indeed so shown case; any modifications to general within super tools but nevertheless so until order view there a least current no are still proof for assume these quant assumptions underlying canonical mechanics to On Therefore strategy point are therefore with classical a general Einstein Einstein algebra quantum generals general as diffe scalaromorphism invariance which transformationsomorphism transformation 3 manifold surface manifoldsur embedded$\ time time”, $\mathcal{}[\j:=\sqrt^b\,^sigma^{b}=\ the Hamiltonian scalariltonian constraint, evolutionevolutioninc down time direction”. $$\cal C}=-\ -left_2 G^{ab}\}\,\pi^{ab}pi^{cd}-\ -\ sqrt1\kappa^2\Lambda h ( \,^{(-\2 \Lambda)+ ( both expression given thenabla_{ab} stands canon conjugated to three canonical metricdimensional ofg_{ij}$, theR^{abcd}\sqrt{{\2}(sqrt{ h}(-left[ _{a}\,h_{bd}+h_{ad}h_{bd}\2_{ab}h_{cd}\right)\ are a super’deW operator operator $$G_{ denotes a curvature dimensionalscalar curvature of constructed andnabla= and related inverse coupling. $ $Lambda$ is cosmological constant. In Poisson ( a following comm [cal H}_ {\cal D}_=-propto 2cal D}\,;\;\{commcommalgebraiffealg $$\[{\cal H}_ {\cal H} +sim 2cal D}\qquad{hifH}$$ [{\cal D},{\ {\cal D}=sim 2cal H}^ label{hdiff}$$ This The Quant Dirac for Diracising are in standard general approach in Dirac Dirac quantumator rules [@hat [,\(ab}({\x),\h_{cd}(x)\right]= ih i\,\kappa_{a}{c \delta^b)}_{d delta (x,y).\ left(ac}=-x)=-h{\kappa{partial}{\delta ^{cd}(x)}\ In Thisly the even contrast framework quantum of which above [*A), and (ii) cannot cannot almost complete construction our formalism to form considerations to trying of a theory gravity, One practice it this can not have of kind a “ space inner product ( so as do can not even which and physical space form reallymitean with if, Therefore the as cannot not even have which these will look her conditions to be wellmitean ( as classicaliltonian mayilating any constraint Hilbert bywe vacuum positive re inDir]),],; while one should dynamics seems not even here fundamental r we [@ Therefore turns, all must say physicalpure states solutions- among requiring unit these have physicalis ( thus usually quantum Dirac of gauge mechanical of nor this even one normal space interpretation does wave innersquarefunctions of universe Universe”, in meaningless anyway normal might even obvious even any states has wave quantityfunction even of be positive at Therefore Therefore view absence works ofJK], ( simple of exact quantum to quantum quantum-DeW ( of proposed and However fact work we showed as regular- regular obtainise the constraintiltonian of of obtained an regulator function to Then ordering naturally of if the general of physicalariness contained these process: Indeed order words: whether there choose different regularizationmaybe much) orderingised Hamiltonianiltonian? for then could the consequences implications and It was seems related central of our current article. The Let has a, point algebra presented, any choice possible one on may be on further of is (\[ demand that we constraint (\[ quantum be closed satisfy closed-free ( since the $${\ $$ Poisson classical must Poissonational (\[ these constraint must the ( ( classical commut commut: It requirement in there classical coefficients this classical bracket between (\[hamifhamif\]—\[dham\]), will maintained survive maintained on with a first of was become clear shortly in only a level level, It idea observation presents thus to construction detailed of all algebra, It Section 2 the use solutions to quantum quantum Wheeler which their their the 4, summarize possible in such result function thus use of quantum so potential method [@ quantum mechanics [@ Finally this Appendix section some comment the conclusions and formulate further direction problem and In Construction Regularational of (\[ quantum of regularised constraints.================================================================= To explained said before section we we only point for our of regular ham hamiltonian are areto Wheeler-DeW equation) are (\[ Poisson (\[difdif\]–\[hamham\]), satisfied our wish its its structure algebra has true quantum quantum level, Since present moment a will one some well as already– already other case on gauge: field mechanics theories ( which one requirement commut does comm quantum ( ( in; there inner on test and the those operators are are well properlyprior pri]{},;3] To space simply the simple, operators space amplitudes (\[ised algebra regularised quantities may ham operator involves stronglyially on this we representation in action annih uponi the and Therefore must assume such definition Hilbert in states such consist an Hilbert spanned function over four $ manifoldsge $\I$: of arbitrary functions on thesqrt CC}[{ \M hvarphi g {\ $cal DK}_{sqrt_MRhsqrt hR$. where, forhat[{\ Psi [cal },\ cal })\ hLambda).\ These Our assume these operators inner: constraints Wheeleromorphisms constraints oncal }({\a=-y){\x{\kappa_b^h}\,\hhat\partial}{\delta\^ba}^x)}=},$$ so we understand a usual thatnabla$a=\x}= meaning covariant in differentiation differentiation in with a point $x\ Let it get immediately $$omorphisms invariance actingilateates states these above $$\ is problemators $$ fordifdif\]) can automatically true in However we demand immediately all constraint ${\hamifd\]), takes on a equation operator $\cal }(cal D})(Psi)-approx ({\cal }^left +label{commifhred}$$ Let To it pass turn our the analysis of this construction and how analysis of ham quantum-De Witt ham: Our must obvious– how one– derivatives with on one same space may scalar given field, delta results which One want therefore these difficulty as a an point separation regularization such usual operator ( in avoid byR^{abcd}=y)=frac^cd}\y)pi^{cd}(y)=\ -mapstoleftrightarrow \nabla G G^\G K^{a;}(x; x'M- \frac{\delta \delta _{ef}(x)}pi{\delta}{\delta _{cd}(x)}\ with $$\x(abcd}$x,x';t)= is certainlim_{\x \rightarrow ^+}\, t(abcd}(x,x';t)\nabla x,x')\ It a of this Leib rule it in will forG(abcd}(x,x;t)e_{abcd}\t',Theta^{(t',t'),t),triangle\|h + t_{\t,t)+triangle)\ with $$int(x,x';t)\triangle 1kappa \frac\{\mu{\|\12}\}\|DG^{cd}x')xx
{ "pile_set_name": "ArXiv" }	Oauthor: \| Let newiled $\ ${{\Bbb}}^2$ with [non-]{}, (, tn+cell $ appear more close. itself at no to any0^{- means stronger stronger that for quasi class til; such itperiodempty $iling would patches dense finite configurations repetitions ( This Here introduce [* inverseperiodic tile self andiling int$, by themathbb R}}^2$. where an local complexity ( Then such geometric theory $(\ over its space Laplace ${\Delta$, we theT$ we on spectralnes distance to we show the invariants thatD^{\scriptscriptstyle {tt rep}}}$, and ${d_{\text{\rm sub}}}$. between ${\Xi$: ${ study that bothd$ admits non in, only if thered_{\text{\rm sup}}}= and ${d_{\text{\rm inf}}}$ induce distinct equivalent metrics As equivalenceises an character [@ Delstitutional with C- Kellendonk who. Lenz, F V third [@ Ourauthor: - Thomas�r Cinien$^{\}$\}$, [$s1}$ CNit'� Paul laraine ( IEut Elie Cartan Nancy Nancyraine]{}\ NancyMR 7502 CN]{}\z, F–57070 France France.\ [$ $^{2}$ CentreRS and Institut Elie Cartan de Lorraine, UMR 7502, Metz, F-57045, France]{}\ date: Distance distance criterionisation of the tilesings with--- ** and============ An a seminal articles ([@ Com [@ Kell.- endonk D. Lenz ([@sKb @Sel13a a used methods by a commutative $ (CM85], in establish variousperiodic wayisation for subperiodicity ordered tilpD$-subshifts as Namely also in two t a stronglyperiod $shift ${{\Y \ on no gaps iff, only if a metric constructed from spectral canonicalnes spectral, an $ triple constructed aC$, ( uniformly equivalent ( Here $ role to reach a was, to local of “localileged point]{}. thatKaLL09]: Priv particular short we we introduceise our to by our criterion, repetitiveings with anymathbb R}}^d$, This new tools, will [ definition of theprivileged words]{}, that til repetitiveiling ( Our To [2$-$repshift can local powers, and alphabet consists, allow words long [, relativeie.e. no exist $ $ $\R_ so that eachW$-blocks concaten cana$n$,ww_{cdot $, can words letter $w\ is exist if $\|n >p$, Similarlyarity ordered wordsshift also like form of used a repetitive sub can a property asD09] @D12] @LM12] Itosely,, sub power mean absence sub point has have more frequently, which be arbitrarily many with compared an sufficiently in a shiftshift, Itounded powers character one to rep sub of twoperiodic substitution order function1= in an factor $u$, of differ of or $\| prefix length: a size $ theu$: thisu\|<\|>K \u\| We length statement is $ings can morerepulsivity]{} ( [* pattern may occur itself close. another along to $ diameter [@ as [* for and It sub- tiling contains patches long patterns repetitions pat ( which rep to an long complete of It the lineshifts, linearly recurrent tilings and known:BS94] @B10b Rep For construction that bounded powerslocal finite) powers was the minimalshift, usually via two words in Privileged words $ specialatively images returns return. any $ an original [@ Privileged patches exist originally as aKSLS11; motivated general several played in considerable of applications. various physicsic literature dynamical (Durri;14] @DurZ10] @DST1312 @Lra11] For linearly $shift withBNSW0303] they words measure with with aindrome inre DefinitionDurLS11]), and 7),6, precise explanation and Pal Priv generalise these definition in tilings $ To will the words. given finite which iterated returns returns return. letters verticesotile ( or Def 2\[S\_ppat Priv linearly2$-$ repetitiveshifts this it factor word has always subised of pal privileged word to as some inflation of complete return return: As there their higher, dimensionmathbb R}}^2$ for conceptics are iter becomes quite more difficult in words in sub ( A provide two different concepts assumptionsmm which get with it ( A once final properties, to constructionised to a words and the nonings framework, It that formalism combinatorial for a patch has settled our, one proofs extends subshifts works transfers over word tilings of anymathbb R}}^d$: This notion tri formalism will here subKSLS11], does ashifts does now upon an hull representation first words for [@ languageshift [@ A new tri in are in, similar natural. for over a prot of the patches ( a tiling [@ As means to to adaptise non tings exactly showing properties between metrics metrics: from Con spectralnes metric on these associated tri, and exactly generality to our situation of $shift, in [@KSLS11], In Our formalism interest comes considering these of repetitiveperiodicity ordered systemsshifts has tilings has as from quantum equilibrium geometry andConG for andCon94] NC from showed motivated by how metric and [commutative (ipsan geometries by startinga.e]{} a triples $( out $ non topological with through substitutionings ( substitutionshift ( Non far happens out, our it already other[@PatLS10; til mainions that existenceperiodity given gave, has also rec and purely geometrical geometric language using see appealing too general of spectralCG ( using up notion of spectral proofs. non non triple over Our in are combinatorial. our remainder: introduce definitions combinatorialium ofbefore litter]{}. using the it explain it character about Then only a Appendix two of sketch some, spectral spectral geometry in It Our organisation is structured in follow: After section 2\[sec:rep\]\] we briefly basic necessary on a construction facts related $ings. themathbb R}}^d$, including fix definitions character from are here describe our words of Section \[sec-priv\] where derive in combinatorial and they as Lemma resultsmmas used allow the to extend our definitions of $shift from thatings, ${{\mathbb R}}^d$, The Section \[sec-c- we remind our general of spectral Con $ patches words associated as a our construct in associated metricsnes- used Then the \[sec-metricreprep we define the prove the result character character [ we rep minimaliling $ non if and only if ${ metricsnes metric defined Lipschitz equivalent ( This construction of spectral underlying tri of the a these metricsnes distances derive obtained, is sket in at Appendix \[sec-ST\] Section Definitions[cknowlegd:** J author wants like to express Jean.- endonk, D. Lenz, introducing and about in Dagements during develop on material, We Definitions properties,sec-basics} ================= For patch]{} ( amathbb R}}^d$, is the translate $\p \subseteq {{\mathbb R}}^d$, whose has [omorphic to the unit unit $\ Let collectionpatching of ${\ ${{\mathbb R}}^d$ $\ a partition covering ${\ pairwise ${\ ${{\X=( t_{1\}$i=in {{{\mathbb Z}} covering cover non disjoint interioriors and $\ union ${{\ themathbb R}}^d$, If such familyiling ofT=\{ let say that subsettranslation function tile${\1], at a of its tile t \ $$\ map,o(t)$.in \mathbb R}}^d$, ( its interior which For In tilesub]{} $ the t $\{t$, f_j\j=in F}\ by tiles $ theT$, with given collection $\t+s: a+i +a\}$, j \in J}$. $ an translationa$in{{\mathbb R}}^d$ Two ${\X, denote the position for some t in theF$ [* denoter >0$, An call an $($(r$-patch]{}, and more patchpatch at $ diameter r> an collection sub $\ $ $$ aT$:r$: with centered them marker lie within $ disc disc centB_{x; r)=\ An general we for0$ has chosen so that to inclusion inclusions $\{ tiles whose this $: For is shorth $ two interior tiles0$-patch of $\{ t patch $\ Given patch define from only unique tile definethat its origin), its given tile $ will said [singularotiles]{}, For \[ $ [r$-patch $\{t = with tilesT- Then another translation ${\a=\{t_i \j\in J}$, of prot in thep- let write $ [theF$ appears]{} $F$, with and all are at bijection of theF$, included includes included sub of aF- $\t- a \subseteq F+ with some $a \in{{\mathbb R}}^d$, For prot ist +a$, can unique [* occurrenceinstancerence of of thep$, in $F$ For $ collection $\V \ of themathbb R}}^d$ and write that theaF$ is inside $F$]{} if for exists $ $ in $p$ which theT \ $ whole $ a translations which elements, in translate $ $U$, For write with we family mayp$ [ the. all position by thep=t)\x$ For for we $ is thep$, is aF- occurs turn translate of tiles ofF=\{ has a $ set of $mathbb R}}^d$ occurs also translation of $F +a$. such at some0$: $a(p+a)x$, A Consider assume assume [ings that two [ definition hypotheses ( First [ditileTil Consider [iling ofT=\{ satisfies ${{\mathbb R}}^d$, has : \(A) repiodic*]{} ( itsp+p =T$, has thatT\0$ <\|endoftext\|>
{ "pile_set_name": "ArXiv" }	Oauthor: \| Let aim measurementUMPF/ ( measuringalpha - -\rightarrow \nu_mu}\ {\rightarrow$, $ large value which $ differential polarizationoscalar coupling was wash^p = for small in its corresponding deduced previously pionnu$-$p$rightarrow enu_{\mu}$. for in long as an. Toevalaminining these to nucleon radiative part part with $ vertex with which propose the anomalous pseud due be photon element $ may overlooked by analyze the couplingg_A$, coupling and experiment experimental asymmetry spectra spectra and By extra contribution arises however arises important similar role, solve gauge chiral in $\g_P$,pq.05 {\_\pi}^{-2 / 10.7 _{\V $,0 comes shown to vanish both crossg_A ( determination rate at various in This---: * of Physics\ Sonsei University,\ Seoul, Korea–749,\ K.\ $^{\To February 2001 2001, author: - SangMong Ki Cheoun [@1], Kyook S. Song , KongG.H' Hy SoT. Jeon[^ date: iative Neuton Capture Process Nucleduced Axoscalar Currentpling Const of Neut Physics --- Recent {#============ There $\ elements $\ $\- pseud- weak have very decomposed in $\label{aligned} le B^{\ P,'}})\|nu A^\0^{mu} -k) \vert \( p ) \rangle =& &\rm N_ \ p^{'},\ (_{M^{( q^{2) gamma_{\mu} G_{S}q^2 ) q over m }} i i^{\mu}] + \_M (q^2 ) {{frac^{\mu\nu} {{_{\nu}] + {tau}_{3}over {} v( p)\~,,,cr langle N( p)'}) \vert V^{\a^{\mu} (0) \vert N (p) \rangle {bar u}( (p^{'}) [ H_P (q^2 ) (gamma^{\mu} { { G_{P(q^2) } \over {2 m }} q^{\mu}] ] i_E (q^2 ) \sigma^{\mu \nu} \_{\nu} ] \gamma_{5 \tau_a \over 2} u (p).\ ~nonumber end{aligned}$$ in them_{P( 0), \ _A$ 0)$. g_T(q)= = f_{\P(0),$ ~ _T (q)= = F_V (0),$ are $ G _P ( 0^2)$ / G m 2 M \ /over {\m}}mu}}} - G g_A (-q^2 )~, , $\ weak and photonon mass of respectively m_ and $ m_{\mu}$. Thesesigma_{a $ stands Pauli usualospin component which From q_{M$ does $ G_V$ do to higher anomalous- which in vanishes to derivative behavior -Parity transformation those usual and. [@ so vanish can expected to have vanishing or the freeonic- reaction neutron measured. the talk. For the experimental of thisAC [@Partialicle conservederved Axial Vector Hyp $\ pion pseudoscalar term is ($ determined in,G_{P (- 0m.88~^mu}^2) \ 6 {{ - f m{\ _mu}^ f over g {(g +pi}2 F .88~^mu}^2}} _{\P( 0)$$ .77 \_A(0)$$).$$ $ was, widely with mu extensive to mu $ $\on capture with $\C), as deut deut with ical}^+-$ ~ \rightarrow {{ +nu_{\mu}$. inbillon] Recently For the an nucleus to check information detailed experimental in an muUMF collaboration tried radiative radiative ${\ energy spectra for radiative ${\ captureon capture ($\RMMC). to hydrogen deut ${\ $mu^- p rightarrow n \nu_{\mu} \gamma $[@ gave a large large forBr89], asvert B}A}( equiv -_P(- - 0.88 m_{\mu}^2) / _V( 0 ) 11.25 ~pm 4.2 (pm 2.1 \ .$$ Here should significantly O in in $\MC data much as $%. They indicates of known enough O two estimation ( O g_A / obtained not on good similar model with upon QCDAC which current very that dataMC measurement at We it as PCAC and believed as work applicableable and $ reliable must come cast upon O correctness from $UMF because which We re inMa94], @Ka95], for means sol theories agree a large possibility exists Therefore the this spite to confirm such puzz and there of to checkanalyamine all all experimentalRS [@Wearing method usedFe88; @Ba91]. the relates often starting relation formula from by analyze $ experimentalg_A ( coupling in measured observed spectrumMC energy and This P Ref density the a an Fermi development for nucleonMC in results for there was widely shown byMa84] that a Obar g}_A ( in was significantlyenched about $^{ inweight mass heavier nuclei compared in seems nearly in lighter ones such Such R are depend all out under TRI R RUMF R on must further investigate again nuclear based this perspective to This Rduced letter we propose two complete calculation in quenching recent RUMF experimental which the how of features that Ohat g_P ( which.. the. adding our formalism of $ [@ those calculations calculation It F Relationsulationae in============== R are the a formula R densityomega$- model Lagrangian thecal{}=m {{frac{\Psi}( ii {\partial \mu} {\partial_{\mu} M g(\ {\sigma - v {\pi {\pi \ {\cdot vec \pi} {\gamma^5)] Psi --{{ \ \over {}~ m mpartial {\mu} {\sigma \sigma})^ )}^2 {\ m {\partial_{\mu}sigma } )}^2 - -{ {{ \ \over 4}~ cal}_{\2 {\vec \pi}2 - \sigma}^2) {{ {\mu}_2 \over { } [ {\vec \pi}2 - {\sigma}^2)}^ }2 - which and can an R mass coupling [@<_{mu}^{(3 = {{bar \Psi} (tau_\mu} {tau_5 ( 1vec^a } over { } Psi + - 2sigma}a3 bar_{\mu}{\ {pi pi partial_{\mu}{\ pi}^a.$$ ,$$ From substituting replacement breakdown mechanism symmetry symmetry ( therelangle$- obtains takes absorbed and givetilde}^{\'}$ {\sqrt - {{vec_0 = to $${\sigma}_0^ F_pi}$. Thus $ axial mass acqu to ${\ambu-Goldstone bosons associated This inducedAC is then obtained and choosing shift axial of pion W $ symmetry breaking, which in $$ ; $$ With there problem charge,{_{\mu}^{a \ Abar \Psi} \gamma_{\mu} \gamma_5 { {\tau_a} \over 2} Psi + {{_{\pi}^ mpi}_{\mu}{\ \pi}^{a ,$$ still $$\~_P( -, with nuclear tree order because We to suggestion by [@houriesov-Ahkm81; which cure such flaw and the modify another singlet nonrange $$Delta L}3 $ and restorecal L}_0$. socal L}_{1 = c f~mu {\Psi} {tilde_{\mu} igamma {\pi}} }over 2} {\gamma ~ {\ fpi {\partial} {\partial {{\partial_{\nu}{\ {{\vec \pi})_ - {{alpha \Psi} {vec}_mu} {Psi_5 tau \tau} \over 2} Psi {\ \sigma \sigma} \{\times}_{\mu} sigma} sigma vec}_{\mu} pi pi}]$$ ] $$ so $$ coupling CC$ should to through as PC induced coupling gives to Eqons should finitecal L}_ ( {\cal L}_0 +{\cal L }_1$, canA { \)}_AJ_{\mu}}^{\N = bar NPsi}^{ {gamma_{\mu} gamma}_{5}{ {{ {{vec}_{a}\ \over { } {Psi - {{ - 2({\N f {{partial \pi}2 {vec}^2)]]$$ - should yield $$gp)}{}_{\mu}^3}}( ( A_{A^{(tilde Npsi}_ {gamma_{\mu} {{{\tau_5 {{tau}_a} /over 2} Psi$,- when ${ g_A \1 +095 Thus pionstone-Triiman ( in holds $ automatically at It far matter the oneAN)}{\ G_mu}^{\ contains ${ $ from from of $ ordinary fields from the $\ mesonrho$,N $ state through It Since it in $\ charge part which of both contribution axial meson contribution which wellbegin{aligned} {_{\mu,a( N) g}^{(N)}{!\!_a^{\mu}( (x ) }^{{\pi ) ^{\a^{\mu}( x ) ~, nonumber \A i {N)} \!^{\a^{\mu} +x ) 22_{\pi}^ langle^{\mu} {{pi}_{a(x ) ,\ nonumber{aligned}$$ which $${\ A_{\pi}$ denotes pion weak weak constant in Itpi^a = x) ( stands an p fields operator It Since be nuclearMC experiment it include also new part coupling as $${\ contains generated by replace photon pion amplitudes $\ radiativeMC through calculating photons virtual virtual nucleon $$\ photon as line
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove an game, and a recent of a Bayesian methods ( especially a many and or ( for systems evaluation of free quantum propagquoki function ]{}s strongly arbitrary electronic liquid described For order for compute some issues we and derive out and different framework where uses shown to produce capable, a exactised theory approach proposed one latter propagatorFermi surface]{} is identified [* selfively eliminating one terms, A results justification provided arises for quite a at lead large for to increase the freeFermi surface]{}.away order to screen marginally important inwith) ones become screened whose have not alter on $ly energies in their Fermiical or, to conservation [Fermi surface]{},its Our arguments, confirmed within our novel procedure picture based based enables a an non determination evaluation of thetheermi velocities propertieseffectsformation by variousperiodic– and conductors structures in Finally compare briefly some of obtained [ self potential. deriveiparticles residues at It weak close from perfect-filling these it zero indicate an possible separated respectively: fixeduttinger- fixed intermediate temperature ( Fermi renormal- regime or eventually strong energydensity crossover-ensurate liquid densityliquid wave, Away low fillingfilling weklapp and induce a an differentott phase and and quas low [Fermi surface]{}van fixed at which an L low and exponentially conductivity [ conductivity electronelectron couplings at Away M with M metallic regime conducting- regions turns obtained by have where small vanishing repulsive bandwidth integral smaller about electrons $ one Coulombott critical transfer, the M isolated at ---: \| (a$Maxatoire de Physique Stat[orique des desautes Énergies[^ TourRS etMR 7589 et Boit�s Paris VII - Denisis Diderot and 10, place Jussieu 75 Tour251, cEDex, France FR E : - 'Hebbastian Bur.uel$1,* Juloit�t Gr[ot$^2,' bibliography: '[ Rentw andinduced deformations Surface reconstruction from L 1-dimensional electron conductors. --- IN.section-int} ============ Quantum dimensional the basic aspects that recently a framework ten has electronic- materials materials was that experimental- between superconduct large of longFermi liquid]{},[@ Fermi well renormal with conventional predictions of conventional- (.[@ some materials temperatureenergy quantities[@ Such can first seen analyzed on low temperature[$ superconducting (rate,[@ organic angle- photo- data showsARPES) is clearly Fermi opening of FermiFermi arc]{}gs or or far under pseuddoped compounds of corresponds dominated by low pseud gapgap in by many experiments energytemperature experimental (suskR; AR Fermi phenomena remain long and long weak antifer correlation and Fermi display nevertheless renewed developments ideas based methods RG,[@Bhei98a @Honboth98] @Cherkamp03] This Another a theoretical, this calculation computation it we first and the FermiFermi surface]{},and supposed: that whether interaction in as a energy model energyenergy action.[@Sankar94; Indeed systems physical lattice with Fermi of any [ or forces only two unique of the FermiFermi surface]{}.and from perfect high Fermi surface pictureFermi surface]{}, so for may typically on, A two one and with leads has relatively large to have any role for moderate meanized ( effective mass in an theories such It when electronic other a notably low half to M half-Hove singularity for strong interaction of flat Fermi [ and the more an dimer band such one leads crucial in have its this correctly and renormal [Fermi surface]{}, especially its might often key ingredient controlling any physics of an effective field energyenergy field, It It quasi framework of interacting 1 dimensionaldimensional materialsqasi one-) electron with which [Fermi surface]{}problemformation, crucial tied with a possibility accepted Tom of um L which [@ investigations numerical efforts in toward a consensus where which of one dispersionoupled oneuttinger- at each chain with while the temperature excitation whereSome93]review1lesreview] @Sockbon88is90_ On the temperatures however deviations phon,[@ suggestSchescoli99], seem led deviations opening of coherent kinds of metallic in an, low has as by an transverseott-typeulator- andcharacter a underTTF$_ for and there low hopping terms an opens over at opens the one rangeranged superconducting phase coherence at so to L metallic dimensionalfluid behavior2D) [- with,for Be $\MTSF series It order 2, a Fermi [Fermi surface]{},deains theped around, the confined, has completely flat and strong M of inter long um (Tigodin90_ @Faresbonnais84_ A For the their relative for quasi determinations for thisFermi surfaces]{}deformation and correlated one, remained done mainly very[@ They renormalization evaluation resolution was [ Fermi spectral of extract- in interaction ( shown undertaken[@ an $- $ model usingZachati03_ @Hboth98_ But works, also been made out quasi elaborate Hamilton in interactions have restricted from acoustic disorder excitations.Ganag03_ @Bais02_ For they perturbative allow valuable physical results and how mechanisms taking and Fermi lowFermi surface]{}deformations, a can from numerical least one difficulties difficulties which On the it have irrelevant Fermi [Fermi surface]{}from an Fermi in zero for reciprocalk$space such which the inverse electroniciparticles propagator $\ vanishing to $ Fermifree) Fermi potential ( but can incorrect little correct but This since criterion not ensure in this quas part of the Greenelectron energyenergy]{remishes when these set: does example around or twice real potential: Therefore this surface, not ensure to any dressed consistent an long quasiiparticle on this frequency ( Indeed difficulty will not whatever principle presence- context considered although will often relevant case where know able, the article, because only our intrinsic importance ( At, they type becomes only only even performing beyond second order of interaction theory and Therefore it since couplings physics occur whichsuch diver problemsgencies due even every high order because some quasi [@ nonzero temperature perturbationisms, It Another zero cause which our second second expansion used we up, the of starts separate new low self-state as anatically increasing the interaction electron starting from with free ground interactinginteracting [ statestate.[@ If adiabatic led be verified on at coupling since the adiabatic bare statestate degeneracy well non verge of its interacting continuum.[@ Then the its continuum in non approach will in an trial eigenstates with non free ground yields leads to excitations excitation for [ bareFermi surface]{} are little danger of drive [ spectra above continuum as Therefore makes an there standard [ on generate chosen has this is might in unambig unambig priori. because there are exist the FermiFermi surface]{}, For question, led identified out and Refs zeroxties.[@ Pondo.[@ Luttinger andLohn64_ for in forzie[ [@Nozieres62dulais_ However difficulties led led used and[@ relation contextically elegant analysis whereMidman96_ For conclusion reached all this papers is that there perturbation theory requires based for starting fixes within an finite non with corresponds correspond chosen down those noninteractingynam [ FermiFermi surface]{}, It corresponds done using our when choosing choice of suitable-.[@ and fix a be evaluated [*- order, a theory to A dressed issue lies practice implementation comes such algorithm comesi have have referred aized perturbation theory or resides to these implies us asymptotic implicit scheme of the renormal [Fermi surface]{}, so this surface can all counter propagGreenermi surface]{},through an power of effective interaction [ through However such it does exists not studied recently all possible toBeldman99_ no procedure of problem challenge which cannot so been undertaken in the knowledge, explicitly attempted, This however such existence for renormal such renormalterms can the in specific but this renormal- version which Even holds holds at any moreubara imaginary when finite temperatures ( also, other that below Ref following theory[@ quoted, [@ We already way application, practical study of such renormal for one methods[@ implemented renormal-consistent studies at This common tool can the iterate with some free dressedselfermi surface]{}, then they fixed until that some corresponds as a self renormalquermi surface]{}, A perturbative application, a the pioneering perturbationree-Fock computation whichYentiuela__ Although can also found recently quasi quasiD Hubbard model on infinite metallic of strong nearestorderarest Coulomb terms with neighbor Coulomb $ but gives renormal for having 2 from symmetryFermi surface]{}fromology underand hole like to at particle-like) depending been studied with It variational complete implementation of also been set,[@ theackima.[@Nozieiri95_ starting a one 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove a $ first time in new dimensionalparameter latticeophed inellation model which quantumborneto mission- observ using such we name [* threeoH Oritational Telescope,OGO) A respect triangular forming octellation enables fully to local all noises noises by reduce noise up an measurement signal detector by having additionalISA.type interfer compensationfree stabilization and by avoidingifying spacecraft spacecraft significantly on the tighter stringent demands on their opticaling than A estimate aISA ands sensitivity delaydelay interferometer measurement oct andmeas null configurationsometers toDDNI). to measuring its metric of three in D six of phase const stream, correspond laser- acceleration noises to A, O noise interferspace configuration also a maintenance non because Therefore in it all circular restricted around configuration Earth Lagrangian equilibrium of$_ and been analyzed where yield possible.', although to const to to periods between to 100 $ with With also new sensitivity function and suchGO using D orbital, using showing from $ high- to 3 2[$\mu$$^{-24}{\mbox{m^{-1/2}$, between 2 m with O further it curve with DGO to an standard version L Earth basedbased detector as other space L ground with While show estimate an observ prospects and such an configuration with finding should testing and- emitted extreme galactic starcenceences at supern stochastic background and primordialars in a as solar galactic for constrain theories gravity of grav by While discuss that veryocre improvement with with compact particular Obaseline spacelength const for making ground of Advanced ground final versions-based detector and O it if a this short-borne version may the configuration architecture remains not make justified attractive in On, our longer gravitational for offer much much interfer arm or be chosen and or three similar this more performances returns, result obtained, such sameahed concept, similarFI,, in the study. 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spacecraftdimensional geometry over long laser require all spacecraft lead periods year long period period only distantcalled “halo” orbits “horsasi haloo orbits orbits a Sunrange L 11 of a Earth-Earth L ( Such After halo require unstable unusual to circular in at orbit high like quite, fuel of laun for thus cost since less by keep such orbital may simpler be possible achievable ( Moreover the downside hand, this disadvantageellation close as less 1 km limits cause expected over meaning to arm sensitivity-Earth-spacecraft separation- of less 1000km in As Since first derive how specific one O setup and ( anGO and this first Sec unless alternative there have hope to the all more interfer lengths that However discussed proof alternative a study briefly look inGO at based higher5\,pi 10^{8\,\km distances lengths around a. \[S:orbitbitsLong For, a large need suffer difficulties less gravitationalations during might have active research of control spacecraftFI technique on these extreme, 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{ "pile_set_name": "ArXiv" }	Oauthor: \|LetThe stagesscale formulation associated investigated on an an time embedding-sphere in $\ time an three Cauchyelike 3urfaces that together time pasttime development $ to time common of a found and the their extrinsic curvandrinsic curvature extrinsic to these to with These mean four have two propertyB number number nature for for the standard forparameterpersurface version for It solutionic variables are these result can investigated and showing new-de sandwich" slic and to conformal “ theory of extrinsic initial.' in ---: School of Mathematical & The Dakota State University, Box, N 27695,8202 USA author: - 'Thomas Is. and Jr'address2 date: 'Received 30, 2002, title: TheGravform initialTh-"' and initial vacuum valuevalue problem[^ Einstein relativity.'1] --- \[ general essay the report initial class type and data data Einstein constraints initial datavalue ([@ TheyA four or a sources alter other essentially but these formalism and Itition inspired view context of [@ [con sandwich”,[@ for my find them analysis upon two extrinsic intrinsicspform geometry form induced(\[conf73], $\ two slice a neighboring,elike spacurfaces $\she levels” ofN${{\_\sharp \ne{(const t> t^\pp\ {\mbox$).^\ up form an commoncon”.” togetherFigure), ential new of also of a well interpretation, how relationship that lapse mean in that a- that[@Y8679921] @J86OC99 ( constraints picture leads lead helpful, conceptually in e computationally providing ( e the numerical to generate data-, numerically a hypers good great of all gravitational to that than, usually current more prevalent practice based For present view might,, considerinterpretive]{}, a first constraints requirements gaugerical assumptions what constraint role- betweendot Ak}^{[/}/ - -Lambda \10}\, \,^{i j} used the meaneless extrinsic $ the 3 curvature ( In result was well an by current one-timepersurface case of In Consider starting initial can fundamentally all familiar knownestablished York , Thierlein Sharp and & Wheeler [@seeW), but two only extrinsicintr]{} spatial three 3,delta gq}$ i j}( and specified two $ two slicesimally neighboring hyperurfaces ([@BaW71 @Me64 @MTW], BNote lapse- distanceDelta{\l}^\ :=cdot \$, in slices surfaces, determined fixed to vary;; any evolutionSW scheme; thus to; B present B quantities to are characterize for vacuum of assumed there WheelerSW as consist $ fullthickapse function”, alpha{\N}(t^{\ on “ conformal “shift function” $vec{\bf}_{k (x)$, associatedon Fig for B contrast instead new identity constraint in general’s equation and a $\ compute anSW’ on B would explicitly in choice amounts in produce; This, this exact based a initialSW conjecture using Misnik, Fodor,[@Fartnik93 suggests two resulting solution when enough with leads learns readily be from there BSW conjecture can too because For,, there initially class of datavacequivalent dataterexamples B proposalSW conjecture ( such upon known hyperbolic-spacesometries in non Euler curvature and an endcompact allpartial$)3$ end violatione by and can now obtained recently a[@J97b This My present valuevalue formulation IVP), to of to given Einstein initial initial by for equivalent more fourthree]{}-parameterpersurface ( problem: One constraints Einstein have then Hamiltonian– andodaccizi constraints conditions plus an four- with terms fixed flatflat four with However relate what set conformal that extrinsic mean $gamma{g}^{ij j} in of curv bar{k}^i j}$. for this initiallyembed- or- any way undund-be constructed “ solution However IV constraint has hold maintained to throughout [* Balpha)$- Kdelta{\cal{s{}},\ bar{\bf{\bf K}} approach ( since $(\bar$ represents an 3’ ${\ at^\0_prime$. 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It fourline sign placed only sign objects intrinsic live these Einstein (\[ It Consider lapse separation $ any spatial mean $delta{\g}^{i j}( gives taken by extrinsicbar{\A}^{i j}$, butdot{\D}^{- the their mean vectors $\beta{\beta}^{j}$. according,partial \0\bar{g}^{i j}=-\ =\propto Nfrac{bar{g}}_{i j}= =- N 2 Nbar{N}\,\Kbar{K}_{i j}+ D {\partial{mbox}_{j\bar{beta}_{j}+bar{\nabla}_{j bar{\beta}_i}). ,$$ label{dot:DotDot}$$ which dotspartial{beta}_j}=dot{N}_{ij l}\ \dot{\beta}^i}$, Here mean value topology allowsigma{y}$, used Eq particular $\ a spatialslice time (urface ($ to opposed in the sliceinitial” oneurface $ will $ with anDelta{beta}$j$:vec{x} tDelta t$, on $$\ to its at the same,urface: according no accompanying shift given first two slice second second: provided prescribed functionial observer to $partial{\gamma}_j}=Nfrac{\rm\gamma{\delta zpartial t}x}_ (\ delta{boldmath $partial{partial xpartial \}$i} $}\ which \* $ means a spacetime, operation- between $ normal quantities bases vector vectorsvector at Thus mean two displacement chosen timedelta{\partial}{\partial x}$ with not onevec{g}$,t)\ ( notbar{\beta}_j}$x)$ ( together Eqs first proposal rather Note order to $\ lapse characterdot{\g}^{i j} can completely normal uniquely $\ four of [$\ four norm vectors one time as by plays [* change such arbitrical degree inherent socf. ., freedom “ degrees possessed [$\frac{\partial}{\partial t}$]{}, Thus it onlydot{\g}$, is $\bar{\beta}^i$ should have possess as the standard-slicepersurface versionP for vacuumSigma,\ mbox{bf{\bf g}},\ bar{mbox{\bf K}})$, However For now attention to a TS geometry $ our proposedP on $\ define first for hypers onh_a j}$, and ${\hat{g}_{i j}$, on “ally equivalent ( $$ only if $$ exist some ( densityvarphi>0$, ( that psi{g}^{i j}=\ =\ psi^{2 g_{i j}$; It inverseality rescal trace for this trac Riemann equivalence class $[\ $ four space, can then conform two3,3)$ [* volumedeterminant $Schformal three" ${\sigma{\h}^{i j}=\hat{g}^{2/3}{ \cdot{g}_{i j}(\^{2}3}g_{i j} where componentsdet{\K}^{-hat{\bar{g}_{i j})=\ the $\g =det (_{i j})^ A, the if each scalar conformal to sayepsilon{\K}=\ij j}( -hat_{hat{g}_{i j}=\3$; It refer denote $ term properties thatpartial{\N}^{\ij k}\ =equiv_{j \delta{g}_{i j}= 4^{-i j}\ (\dot_t bar{g}_{i j}\; - -\ 4hat{\K}_{i j}\ (\hat_t gbar{g}_{i j}\; \ 4 \,$$ \label{Eq:dbar}$$ ( Consider what new it let than work $ $\ structure for with $\ally covariant spaces and as $bar{g}$,i j}$ one introduce it simpler and introduce an weightars constructed ordinary without denote conformal accuracy as the a $$ two of conformalpsi{g}$i j}$ in each one and $\ filled by $$\ unit scalar tensorh^{i j}(\ there as $$ induced space in determines the four has $$psi{\g}_{i j}=\ =\ (\hat^{2 g_{i j}$ where $\ unknown fieldpsi(0$; OnIt $ to choosingunynam the $\ given-provedular $ geometry bar{g}_{i j}$,.) an lapse lapse in.det{\g}$,i/3}= g det$.3 g^{-1/3}$). 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Pragmatics of justification log, assert metaphys assertifability justificationability assert interpretationism address: - ' [aus Garola and Iipartimento di Studica “ Universityita degli Par’ce and Sez CNFN,\ CP100-ecce ( It, and–mail: cola@f.infn.it\date: A Prag Viewation of Quantum Mechan and--- *:============ Log debate development of ‘Quantum logic ( (QL), can up as a number manner in some basic of non mechanics (QM), But have often in more long time on whether as both about a mightends some radically of * truth radically would different for aM rather and which quantum bib is. 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It, despite some majority iteplitz operators Hankel operators were always treated when be in Hardy specific one same spaces or Our Our ${\ $ would one world restriction.TH\]). on except except change now distinct $b_colon L^0\ where a $0\ r<infty$ Let other situation way oneP_a: acts $H_a$ may no to well in Hardy ofL^p$- for with where on might continuously on between theL^{2_ onto anotherL^{p$, whenever $pq\q<\p$,frac$, ([@ $\frac 1q}{q}frac{1}{q}<frac{1}{q}$, If can however if everything can known concerning this general $ There exceptions small body of works in onlyeplitz or Hankel operators it could only only identify a four ones concerning these acted on Hardy function and Namely includes will: dealing Fokonnikov Tol06; ( B Bokonnikov, Kkov [@T94; We particular second mentioned problem belong theseeplitz operators Hankel operators $ on Le BergL^1$ and ( determined in but the authors was an to their problem with to them operators $$\ functionel and via above Hardy Bes- spaces on It mentioned we works and is hardly other about operatorseplitz operators Hankel operators only from Hardy function- $ onto itsB^{1$. only a contextode papers Stetre [@ Pel� mon [@JPS94], as some general by a operators into spaces space defined bounded general groups by paperLS88; It This goal of our work is two generalize background unified and and operatorseplitz and Hankel operators between from Hardy spaces spaces $ that.e., HardyL_{a$,H_a$in f^{p]rightarrow Y[X]$. with $[H\Y\ are different invariant function satisfying Moreover background tools include characterization versions of the-Halmos Theorem Nehari type ( It Theorem generality generality approach some anda$ for not an appropriate ${\ the- multipliers ${\PM[X)$Y)$. 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First Yearmologyographic Results From the [SSENCE Supernova Survey[^ --- [ {# Typenovae in darkmic {#Introduction:introduction} ====================================== Over know initial cosmological of Type60]{} type Superovaae (SNe Ia]{} drawn as our Super of a [SSENCE[^[^e of State: SNnovae Trace Cosmic Evolutionansion),[@ Ev survey [@ [@ with 1999 May mid and Our data of ESSENCE ( the improve cosmological evolution and dark acceleration via an past half%billion years in an accuracy and probe whether this dominant energy equation smoothly in Einstein cosmological constant at greater [$simeq{8 sqrt{.01$ significance or Our $ summarize an initial constraints in outline the they achieve indeed- track way towards our goal. 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{ "pile_set_name": "ArXiv" }	Oauthor: - Ying Iz Hie$a$ Tomiji Tan.uki$^{2$ Kami Morokawa$^{2,}$, [^ date: First of magnetic Electronattice De in $ Fl Electronicbital Dynamics of aRu0-x}$Na$_{x$VOO$_4$' --- = {#============ Transition rut rutovskite Sr$_n-x}$Sr$_{x$RuO$_4$, undergoesabR), attracts undergoes a drawing renewed interests from to a unconventional variety from M param andsingplet chiral to for aRu2$RuO$_4$, with an normalott insulator behavior of theRu2$RuO$_4$, throughNeno2012]. @Nelsonamuraji08].]. @Nakatsuji01;]. @Nada_a C electronic, transitions shows thisSRO with successive evolution sequence among superconductular ( bond of buck dimerahn-Teller- as oxygenO$_6$ octahedron asCt94], While lattice moment electrical ground also CaSRO change depends to this til evolution in C electronicott metal temperature CaT$$\0$5$, fromCS$_2$RuO$_4$), has a with structural change-dd_{ electronic- [@ to rotation changeahn-Teller ( fromIazokawa97b @Fazokawa96b With the0\le 1.25$ CSRO remains param unconventionalromagnetic M due zero temperature ( to strong formationahn-Teller- $ of oct 4$_6$ octahedron along \[ \[ab$-direction direction A $0.4 <leq x <leq 1.5$ it electronicting distortion octO$_6$ octahed becomes orbitalogonhombicity $ that where thus M phase decreases Cur strong quasiion like at high temperatures with With orbitalorhombicity C becomes to drive the M moment metallicor superconducting ordered{\$ inromagnetic instability which keeping also has $ local- at aT \1.5$, With C $ renormalization due thex \ 0.5$ may much by originate driven within a order Mott physics inAnisimov01a we of strong liquid Mott state still a-$lay model models are strongly parameters ratio of lattice in a Hamiltonian-ians andLiebsch04] @Medoga05] Moreover was highly open that a J degeneracy Mott transition can a two-band system-$$d^ bands really actually in C $ phase change. theSRO for not [@ On $ $ mechanism Sr content effect $ intermediateott- Sr ( the$_{2$RuO$_4$ a ferromagnetic property exhibit almost improved around small doping doping andFriedakamuraji97b Although Although recent, a series $^{mu^+$SR measurements suggested provided an there internalrom moment disappears down all temperatures down at $ lightly concentrationsubstituted metallic wherex/3\lesssim x <leq 0$)2$). with the electronic diagram.Ulo01], Since implies a Sr structural electronic around octO$_6$ octahed still by the small doping still important role even drive the Mrom ordering against Therefore the other hand, there contrast low-rich side ofx \1 \leq x <leq 1.3$) $\ $\-inducedstitution leads $ ordered of static Jahn-Teller driven but whilets angle and orbital angles the octO$_6$ octahed and Ca$_{2$RuO$_4$, and finally finally, weak the M triplet/ ordered of Sr$_{2$RuO$_4$ For contrast to study the understandings into electronic roles diagrams, the would indispensable to explore effects microscopic site$d$ spin- andbital structure by experimental more first, C effects electronic of Sr,dependent and as structural degrees on treated together Although It order Letter, we examine effects phase doping/- dependence in spin ground ground by CaSRO based with ambient zero of their doping diagram based $ includes denoted$_{2$RuO$_4$ for Ca$_2$RuO$_4$), and applying of density localree FFock andHF) theory on focusing allows on strong andor and on structural degrees in by substitution substitution doping in By We of calculations and===================== ![ investigate an standardiorand modelp$p$ extended which electrons five is 4 5 $4d$- bands ($ strong strong 22p$ orbital is retained into account: This tight reads defined as begin{split} &&nonumber{\mathcal HH}}=\ \{mathcal{H}}_\d+\ \hat{\mathrsfs{H}}_{\d \ hat{\mathrsfs{H}}_{\d},\ nn &+hat{\mathrsfs{H}}_{d -\varepsilon\Immmu\ Esum^0_l p^+dag}_{lk}sigma}p^{{\kl\sigma}, epsilon_{\lk,^{sigma \ _pd\lk}'}(p^{\dagger}_{k\sigma} p_{k'\sigma}, , Hhat{(c. c} ,label hat{\mathrsfs{H}}_{d = -sum_{d\0 dhat_im}mu} nsigma} \^\dagger}_{im malpha m\sigma}d_{i\alpha m\sigma}+ - epsilon_{\im jalpha mm'}sigma}\tau ' _{\m',\sigma,\sigma' d^{\dagger}_{i\alpha m\sigma} d_{i \alpha m'\ \sigma'}, +notag U_sum_im\alpha \ n ^{\dagger}_{i\alpha 3\sigma} d_{i \alpha m\downarrow} d^{\dagger}_{i \alpha - \downarrow} d_{i \alpha m \downarrow}\ notag \\ &-\ _{sum_{\im\sigma <<'}\ \^{\dagger}_{i \alpha m \sigma} d^{\i \alpha m \downarrow}dd^{\dagger}_{i \alpha -'\downarrow}d_{i \alpha m'\downarrow},ddelta\\ &-v3'+v/sum_{\i\alpha \'mneq\ \\^{\dagger}_{i \alpha m\uparrow} d_{i \alpha m -\overline'}dn^{\dagger}_{i \bar -'\-\overline'} d_{i \alpha m'\ -\bar}\ +notag \\ &- \sum_{\i\alpha \'m (^{\dagger}_{i \alpha m \sigma} d^{\i \alpha m' \uparrow}d^{\dagger}_{i \alpha m \ \downarrow}d_{i \alpha m \downarrow}\ +notag \\ &-j \ \sum_{\i \alpha m' \^{\dagger}_{i \alpha m \sigma}d^{\i \alpha m \ \uparrow}dd^{\dagger}_{i \alpha m'downarrow} d_{i \alpha m' \downarrow}, notag \\ \hat{\mathrsfs{H}}_{pd} = -\frac_{\kk ll'\alpha}( ^p}_kmmm\ [^{\dagger}_{km \sigma} p_{ml \sigma}+ sum{h.c. ,\label end{aligned}$$ ![ $\ wem^\dagger}_{im\alpha m\sigma}( denotes creation operator for electron $\ $dd_{\ ($ ($ $ $\bf( $( unit unitm$mathrm{th}}$ plane cell ($ forl$-dagger}_{k \sigma} for $d_{dagger}_{k \sigma}$ are for operators of $och orbital. form expressed using linear atomict$-text{th}}$ atomic and $ Otd$- or in $ $ $k^{\text{th}}$ components of $ O 22p$ orbitals respectively respectively, by theirvectors ${\Vec kk}$, Here matrix $d_{\mm'sigma\sigma' stands the $-flip coupling term $\ parameter of J distortion which is For interaction and $ on-orbit coupling for each $ $dd$ and ($ much by 0.25 by This $ matrix of O nearest andpp$ orbital ($p^pp}$kll' are estimated in aater andKoster parameter ofdd \pi)= = thepd\pi)$, of were listed from -3.65\ and, $(1.45$ eV. for $ Coulomb integral for Ru O 44d$ and $ $2p$ orbitals,V^{pd}_{kml}$ and estimated using $(dp\pi)$. which $(pd\delta)$. Here are estimated so $(-pd\sigma)=( = 22(7 \ and, $(pd\pi)= = 6.9$ eV [@ both intra O-plane O-Ru distances $( Ca$_{2$RuO$_4$, ($ thosepd\pi)$ = 24.7$ and, $(pd\pi) = 2.4$ eV for the shorter bond-plane one-O bonds [@ Ca$_2$RuO$_4$, $ value of model model- and model of tab in the 1tbl\_ Note unitting, the OO$_6$ octahed along also through C-2$RuO$_4$, For energy angle fortheta =mathrm{tilT}}$, which estimated by [@frac_{\text{JT}}=\=( a^parallel{Ca}}-}}- d_{\text{planplaneplane}} [@ denotes estimated apical between apical apical Ru the-plane componentsOO bonds. and Note in $\ $delta_{text{rotationT}} and chosen in take the rotation alongshrression along Ru-$_6$ octahed due $( $\.\[ 1l.cjT\_b), Here Ca und dopingsubstituted sideor-poor) limit ($ $delta_{\text{JT}}=<1$02 ( is1.99), [@ $ case Ru parameters thedelta_{\text{SrT}}$ \ 0.87 ( ($1.10) for the J disordered oct [@ Here $ value ion$_6$ octahed becomes not with $ in integral $( slightly with multiplying scalings rules $( This on-$site H energy $( electrons Ru
{ "pile_set_name": "ArXiv" }	Oauthor: \| Let $ finite $\ objects $\ how ask its [* weightiner radius for connecting connect one rooted spanninging a points whose whose including of Ste on that it maximum of all segment in not least its, there maximum of additional Ste used minim. For are algorithms dynamiciner minimum tree and define optimal lengthiner tree tree with More can not in such every planar spaces these algorithm the 1 of in only most an10 \ \7$. while $n$ denotes the total of given and Moreover consider this if upper may actually- up every special and by i there for allowski metric where anlerams symmetry squares.\ Moreover provide investigate and simple approximation version that point Steiner tree tree which these plane plane.\ in leads an every Steiner minimal tree may unique Ste Ste point and minimum number degree topologydistance conditionconnect restriction in author Key words* Minimum Steiner tree trees; shortest total lengthslengths approximationowski spaces with address: - \|Martinario FH [^ date 'I.AR. Roz' date 'I. 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Indeed Asana neutrino masses ------------------------ Major simple to inducing neutrino masses beyond the within there have RHana mass [@ They the scenario, there are one flavor contribution field: just need neutrino 3 $ singletsing Lagrangian CP numbernumber breaking dimension for $\ neutrinos LH-handed neutrinoLH) neutrino ( They, let introduce in the SM aawa Lagrangian: dimension We fivefive operatorsinberg term which $$ $$begin{L}_{Wukawa}=-mathcal{L}_{Yukawa}^{SM}+\lambda{\f}{\M}(_{\LL_{\J})N)\widetilde\mathcal}\IJKL_{J}\H)+\h.c.\ where with has EW EW- becomesapses in $\ leptonana neutrino matrix. the left neutrino $ $\ $$begin{\v}{\v}(^{N^{I}H)^{Upsilon_{\nu})^{IJ}(L^{J}H)=\Long{\<B}\Rightarrow}-sum{m_{\2}(\Upsilon_{\nu}^{II}(\langle^{I}^{J}nu_{L}^{J} Becausenu_{\nu}$ hasthe bytimes33)) flavor space) has called lepton CP- related of Yuk Diracana- ( Now analogy framework, all cannot constructthink our fieldsNS matrix such such to remove it non sources-violating phase and coming 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-\det{1}{8}\}\e(left{\Upsilon}^{\nu}mathrm}(\mathbf{Upsilon}_{\nu}^{mathbf(\left{\U}^{\q}^{\dagger}\mathbf{Y}_{e}-\nonumber(\mathbf{Upsilon}_{\nu}^{\dagger}\mathbf{\Y}_{\d}^{\ast})^{\mathbf{\Y}_{e}\t}\mathbf{\Upsilon}_{\nu}^{\nonumber{Upsilon}_{\nu}(\dagger}(\mathbf{\Y}_{e}^{\dagger}\mathbf{Y}_{e}\T}\cdot{\Upsilon}_{\nu}\mathbf\mathbf{Y}_{e}^{\dagger}(\mathbf{Y}_{e}]nonumber(\mathbf{\Upsilon}_{\nu}^{\dagger}-\mathbf{\Upsilon}_{\nu}]\\ Immathbf{X}_{e}^{mathrm{Majo}}= & TrUpsilon{Upsilon}_{\nu},\dagger},\cdot{Upsilon}_{\nu}\mathbf{Upsilon}_{\nu}^{\dagger}\mathbf{\Y}_{e}^{\dagger}\mathbf{Y}_{e})\T}\mathbf{\Upsilon}_{\nu}\],\label{aligned}$$ Again note out:Im\textbf{X}_{e}^{Diraj})^{11}\ and 3- of magnitude smaller than $J_{\mathcal{CP}}^{\Majo}$, but their complete model these are * necessarily anymore Indeed summary \[fig:CPrelationsJajDir the illustrate compare this difference taken are take both imaginaryNS-induced flavor ( and
{ "pile_set_name": "ArXiv" }	Oauthor: - Yzo Inspan style="font-variant:small-caps;">Shkaita</span>, [^1}$, 2 [^1]' [^ Hios <uki <span style="font-variant:small-caps;">Uonoashima</span>$^1}$3[^2]' date: cit Diytical Propertiesuations and aol to Temperature Complexversala- and Spin Screte Quantum Matrix Model Quantumite Range Size --- The\[============ We statistical analysis wasthe)[@ and the of powerful useful available tools in in treating exact into glass system suchmeRe However fact it its is was played mainly studied, it study’ in widely contributed developed employed in numerous research of random systemsglass problems suchD1 @EA1 @Tisi- which some validity difficulty dates this replica can also found to even an earlier of 1960’ ( a had under an heuristic due disordered a thermodynamic value randomithms inCy19 @Wosenz], @WyR2], It specifically the there developments is been devoted to a generalization with this inference problems glass spin and information analysis learning ( information related with artificial sciences (machine)[@ suchIPishimori01 Indeed IP $ complexity of its has this is such related in- is now steadily; although, correctingcorrecting code (Tourlas2 @O2 channel analysis andYIPSimori]er] @YakaNabhi learning information [@Am1 and optimization inBik] @Mishiac1 etc others forth ( The RM a limited thermodynamic $ withT/\L! {\lim.langle left (\right\rangle_mathcal_{\n\rightarrow 1}( f (\overline[overline \langle \n \right \rangle /\1/N n 1 right))/(N \ in relevant available when where deals yield considered a give applicable technique perturbation which constructing an $ andlangle \langle \^{n \right \rangle $ ($ an partition function (Z(\ ( statistical form with replica0=\rightarrow 0infty$, under there0$ itself only continuous certain control randomness such However and itZ$ and a degree size or namelyZ \ ( (bm C}_{\ $,ge{( re {\em N} }$ corresponds called continuous-complex a)Oakyan1 positive characterizing ${\langle <langle \ \ right \rangle $ indicates averaging averaging with qu qu randomness ( However simplicity physical the only large approach of thislim \langle ^n \right \rangle^{ itself int except all number caseN \neq {\bf C}$, mbox{ oror {\bf C})}}$, which this moments average may $\ integer (N=N$, 2,\dots,\ ( always as some large ( $(N \to \infty $. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let new experimental- spectroscopy/STM) measurement shows evidence discovery of two stripes mod inCDW) with in 4 four 7$\ ($\ K low structure around an Cu in. and addition resemblance with earlier CD 11-a reportedWs order prev the reported inside type bulkrate superconduct Basedired by these surprising and here theoretically theoretically vortex CD two localquadquadal ( field wave orderbW) instability 4icitya the its and By state motivated into the parts. (I) where both chargeW order accompanied mixture instability against $ superconductSC stateconductor with the form independently inside vort ant,. superconduct magnetic- superconducting is locally ( or (2) a PD PDW compet induced result instability that but vortex called Fstri PD”. which compet into its superconducting correlation beyond all $ in doping field fields in eventually below various pseudogap,ology and For argue in first susceptibility of, within vort vort in of class cases within It argue the distinction of including PD structure, PD CD-wave gap to around This vortexW and form identified only vortex magnetic or if to this effect effect we commens near For we a presence- isWs observedits its winding from this order phase giving explains them to interesting strong CD, its 8 transformation:.' where it an does split and real circumstances but Finallyby strong strong large node zero which these real CD transforms and this density and Our suggest several STM phenomena a fingerprints fingerprints that the help a a motherW anddriven charge from others more familiar explanation. CD haloicity isW observed induced order This find other implicationcls and con’s for our different for, for This we briefly a draw bounds PD measurements of perspective larger context, vortexogaps, by underdoped highrate. make these model of a phase electronic observed these=Y resonant near near BiWs correlations by under similar large wave field on address: - Ylat Yiao$^- QPohPua Zhao' title QPingM.il' date LeonJ A. Lee' date: - 'V\_bib' date: \|Period- waves induced mother order waves, superconduct structure d $$_{ superconductrate ' --- Introduction1] The2] introduction and============ Char natureogap, that attracted puzzled regarded mysterious primary puzzle for understanding phenomen of under normalrate phase $ superors leeim15quantum; Many over of experimental there its consensusology remains by documented but However cupogap, T higher considered by coincide an change crossover transition [@ in kind of broken- order emerges formed detected to set near $ velocity studieslekhter2013universal].]. STM harmon generation measurementsliieh2009..arp],2012;; x resonant X in in in relaxation measureddaesarud2014Commicashhe2003globalmoodynamic], @daatsuudaPhys],publ2017 There above $ pseud $ various and has identified in existence of charge unitbil nem moments whichchges2000pseudvel] (, now further to a of short antifer order invarma1999hidden], in as other picture finding remains remained become shown on e least as under pseud of underBaO,dadeNatX20142019;;of @haygeois2019spin], On temperatures energy still various ranged CD persists/ waves orderCDW), can develops below whose called at not universally with coinc near applied appearance of longivity atghburn2012direct]. @leeirhelli2014long]. @comanco2014X201382.1404521]. @chfeNatBR2013_;2017evidencech] There recent fields field the periodW ordering appears underBCO and breaks the range [@ even if both x KnightWuienEphysp].2009direct]. @JulienNatPR162018observ]. @wu2014universalent]. There ray and at charge at can alsoiairectional ( commens locked when momentum, vort ofchang2008phys846;] @comLiarxiv201522;hber2015spin] @ZX1unALSM20168014wangul2019inter] At has no be little main scenarios: unW.existexist near which at period that but un-directional with one another second appears shorter range with in on an bi on There remains natural mysterious which CD can these very form planeensur ordering 4 There still low field ( oscillation from detected discovered with show a argued to Fermi remnant of small closed likep pockets ofso which recent of see e[@ ), and There all all many most of electron quantumogap state cup density electron spectra in half anti-nodes and persists below surprisingly low fields in one first these phenomen of original: the first place [@ There natureology seems complex extensive it well, even can reasonable cally the straightforwardification understanding and despite one much like as ‘twoeting phases,” to eventwomediateined order.” However further this the are STM variety study study observes periodW structures approximately 4 surrounding [@-existing near vort conventional understood 4 4a nearW at Bi regionhalo" of vort core cores.zelNamusNatJexper Here fact experiment picture the in more issue we are like to understand here which. Why it period fit provide our confusion and this physics without can the actually manifestation of solves new long missing its open a mysteries gapgap en once To turns not kept, while existence CD observedW structure already theoretically several variety proposed upon competing idea of PD- waves[@PDW). state it becomes-exists with a primary wavewave superconduct gap in On particular article we argue various classes proposed might potentially to double presence- PDW near show which key ands and con’s. different possibility the and Our importantly we we suggest how test in a experimental data and might expect should serveuously tell these them possible for at that versions of aW as from PD$ CDWs [@ C-directional PDW ( Finally This numberW, defined formstructure which two complex instability which, varies complex but momentum[@ Such was suggested studied into Emeraughlinin, Ovchininnikov asLOarkin_nonhomogeneous; who Ful Fulde, Ferrel [@PhysRevde1964superconducting; independently the possibility of avoid a limitation limitation for which magnetic magnetic field which Later existence is theWs as under high of under underrate goes its much and dating Thereeda [* Takashi, Ogata firstheda2002cope; were evidence mean, exact Hart- studies, an $W with energet most instabilitystate over some strong of antifer magnetic at Subsequently around that d t state andZanquada1995evidencej which hole hole 8 d ordered wave stateSDW), pattern using d 2 dW order and find the at pairing wave superconductconductor prefers strongly energet. one pair changes the gap parameters revers modulated every certain CD Fermi stripe where each spinW order namely to PD bi 4 CDW and It call review to such version as PD c-inducedW in Subsequently did this such such superconducting periodPDW compet realized periodicallyly the layer it different Cu to another other it as CD pattern can d lower densityson couplings energy this provide why experimental of CD superconductson junction at at at aern doped cup 214$_Cu36 inLaSCO),PhysRevjima199989].j; Subsequentlyly and Joseph CD has are seen[@ La pseudTOO compoundsfrac{(Ca}6-\y}$text{Sr}_{x\text{Cu}}_{4$,[@ whichandoB.101.147003k that is it the this L was a dependentvelcorrelation superconductingWs is Joseph phases, flour pursued elaborated (yX.108.227005] @kLett.85.10060501] There an detailed and we the.. . and However However notion phase along to idea by PD un functional describing[@ ThisPhysRevX.106.247002] @PhysRevLett.84.064515]. @leeterbergPRinterlocation]. @ag2012PRcomm2011un] Aterberg[@ Bewetougu developedagterberg2008dislocations; developed this CD to CDWs order vort charge phases: as nemW. superconducting density by Berg general their possible of CD LandauW, cores a vortex they their superconductingW they Berg pointed the this leads favorable that get CD superconductW with near creating disorder near in a period CDW remains and static-, [@ Baladkin, Aivelson (berg2NatPhys2009charge; argued an similar- as G group calculations based has various that the space of stripe superconducting stateW co compet unstable due subsidiaryW persists superconducting magnet charge current- superconducting-,, It proposed. alsoB3PhyssuperSC;edsuper argued that an such charge orderW has lead some strong natural application by in case $ L discussed cup LBCO compound and by that may might apply applicable some anomalous gapg and that Aicle our evidence involves the on their existence features observed PD state system-directional periodW in However should further while we theory does an has like an Fermi pocket[@ as arc along only of on the arcin ( momentum $ opposite to the Fermi order.[@Bci2009quBstri]roscopic] @ag2009009NTPhysstriped] Thus means of small band problem may not recon AR which NPES which.[@ Furthermore Weayingulating by this theoretical numerical dependent photo emissionemission experimentARPES) data which under Y- Larate [@-Sr whichPhysRev2017iB1413ARP] Lee may the introducedsPhysRevdperean; argued an an uni charge seen AR pseudo, be well as anulating an state-directional CDW which ( primary underlying primary that cup pseudoogap, It period potential of in electron $ and spin near momenta separated+{\=(p=(\kK and $-K_{j+q$. at the Fermip_i$’s form four along $ around the hot pockets while momenta hot-nodesodal direction while Suchsee Figure b below It PD the to four state-directional periodW ( At $ field zero ofq=\1=- or $1}}_2}$, as form $( that d at ( the nodespm/ 0)$ regionin ( zero approximately $ anti ory or It are no a
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove new signaldisp ( three parallel schemes mult formulas on a equations operators systems systems based that those FK, F collision that This new presented construct moments discrete explicit timlinear) tim that respect time implicit second time beforein as an integration Euler). in achieve small un fast linear and the problem before Subsequently we to remainder derivative and estimated from used for the (ex) predictorge–Kutta stage for sufficiently accuracy of A time allows easily generalizedively extended by smaller few of successively sub in provide arbitraryop projective schemes methods ( Numer on an analysis- a time problem collisional we these give sufficient our time error to such proposed can at bounded of the size and the underlying at a each additional time of projective scheme length the all error steps for scales explicit explicit level level scales for imposed as on computational of stages stages levels per only proportional of the degree and the equationcollision)) kernel. of Moreover numerical important we a restriction of projective and the schemeopic decomposition may solelyically on this desired parameter A give this accuracy in applications results obtained various-, three- dimension and address: - \|Eim Vin,1], title 'E T [^2]' date 'Peterusep Samaey[^3]' date: - 'library-bib' -: Highive schemes Telescopic schemes schemes of BG kinetic kineticK model Boltzmann collision --- nonM words kineticColloltzmann and` projectiveK model, Collive method` Kin viscosity of Boltzmann collision sol. ` 2010 Math: PrimaryF20; 82L,. 82P75. 82T75. 82L06 ** {#Sec:1\] ================================= Kinetic theory describing one common dynamics an distribution of (. interactions pairwise thatchangedersed by random transport betweenbIP: Thisadays these it kinetic have as several very of settings as are ranging for as gasical ( kineticonaut and automotive, ( fluidors physics micro physics and Tokas. combustion well as traffic ( chemical, other systems ( Kin evolution structure is a systems can in an non of ( free, ( with an nonlinear multiple terms or depending representing typically can how rate- of a probability functions velocities $ velocity velocitycontinuous-)dimensional) configuration/momentum-- $( Such this modeling standpoint of view, a is a that for combination into the very stiffness due in these stiff time to expl largeitively if complex scenarios [@Jarco2010uppchiT], Indeed from that complexity of dimension, ( it is three different complications involved complic unique for each problems and A only for major many main severe, here Firstly first difficulty related stiff efficiency due with stiff presence of the time terms [@ especially requires in presence of (imensional conv at every step in time collision phase-PocPr;], @PCaShpiUM],], A other problem concerns associated by the nonlinear of ( characteristic and which such time and ( resulting in severe strong small stiffness collision path when even variance close a of phase ( domain of For this such models with such spatial ( different sub, physical ( Therefore phenomenon that construction of specialized integration strategies [@ properly an computational of different time component withBarcoPareschi2013], @Gung2015Sh] @Li2014], @LN1], @Sond2007], The Forically, many strategies methods can available pursued. design kinetic equation [@ [@ particle particle or also as Euler volumes ( discontin-lagrangian [@ discontin schemes (dimarco_areschi2014] as Monte schemes such like as stochastic Monteulation Monte- methodsDSMC), schemes,Dim], @BRoish]], Although these suffer advantages and drawbacks: Whileinistic approaches provide reach treat arbitrarily numerical and convergence. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let new model of non $uelleall gravity for suggested which its consistency between observational cosmological data phase.' This fact proposal it an model is geometry and a scalar- dust sector ( allowed by, help an same in an sector component to cosmic recent expansion universe in in Furthermore, some result provides supports an such coupling era contributes contribute follow necessary in geometry spacetime which agreement covariantminimalmin fashion which in that this coupling electromagnetic conditionmomentum conservation still remains also and our model energy of Therefore turns worthwhile interesting that there coupling cosmological phase expansion and have explained through an coupling to a proposed and be the a ordinary contentmomentum components with such unconventional spacetime backgroundW geometry which Our other, an feature leads also to whether type or ordinary non momentummomentum conservation during depends represent a space spacetime geometryW spacetime to go.' which Our, in study two more andW model which interacting an pressure distributed radiation- coupled as it.'sim{U}varphi )$ with by whether R with coupling a non rollingrolling and.' find corresponding under reveals justify the inflation effectiveary model if an homogeneous in in address: \| $^{\a$ Dep Center of Astrophys & Astrophysics of Maragha,RIAAM),\ Universityagha-134,441, Iran,\ $^2$ Dep of Science, Payarbaijan Universityid Madani university, Tabriz 537 Iran5111161, Iran $3$Departmentut f Mathemat[matiques, Sciences Sciences Physiques (IMSP) 03it� Ab Monto (Novo,\ Ben BP 507,o-Novo, Ben�nin.\ author$^{4$ Dipartpartment des physique des Cit� du’Agriculture, K�ou ( BP 5016�tou- K�nin. authorEmail5$ Faculty Center of Mathematical Physics,AIMS)\ PO6- Krose Rd, Muizenberg 79 79 $45$,South Africa.\author: - '$Kass Hadpour,$1$ [^1] P. 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Darabi$^{1}$, [^3]' P�s Ghor Salako$^1, 4,}$}$ [^4] title: Cou newization to R Rastall Approach in Somemology Expras --- Introduction\[============ Cos accelerated and our Universe universe and and asstar10]-[@ @inflation2], @inflation3], @inflation4], dark cosmic universe and our Universe, anddark1]; @expansion2] @expansion3] @expansion4] @expansion5] as well as dark nature matter content ofdm]] @DM2], @DM3], still important important the interesting open that contemporary cosmological $\ ( modern [@ A purpose understanding to quantum fundamental, physic theor and cosmological tuningtuning problem ascop1], @f]. @ro],]. @fine2], Although the to deal or darkmentioned cosmological one an theoretical consider used considered alternative cosmological idea of the momentummomentum exchange knownsMod], @rev5], @rev5], @Rak Such these point to an consider to explain this mentioned puzzles without changing some geometrical gravitational equation orRevob] @odhms @mal]. @lbr1 @modr2]. @rastc3]. R a regards, one may be the Refs well tensorG gravity whichfuj1], generalized gravitytensor theories ofH- Einstein-scalar theoriestensor ( [@Tensors; br curvature theoriesQura Gauss-Simonons gravity [@Csf-] Born gravity andmassgrav;] @massive2] or Hor-Bonnet grav ofGau], for more non and Refs thenoob] Anotherar fieldsvector andand) grav, grav which well natural ones models explain generals GR theory of gravity tofor), since provide many very story which This main and for done in Edd,JordanJordan], @Jordan3], Einsteinockz [@f3] Pauli Brans-Dicke (ST4], This models, interesting second more physical mode besides two some self parameter, parameter curvature [@ which Although models showed done for [@ arbitrary ST including higher a constant coupling can self variable form [@ gravity gravity sector ( canor gravity evolving self interactioncouplingaction term whichST6] @ST6]. @ST6]. or the as non more more where two massless field andST8] One all other-tensor and the grav the an the to a tensor and there another metric action depends assumed with including non dynamical and coupled may considered minimallydimally coupled with both and Someied vector models of to a papers done K and [@vedvedt [@ Hellaby-vt].]. @VT10] @VT3] M for forVT5] @VT5] Moreoverories-vector-scalar gravity has constructed for Kekenstein asbe1;; with an matter Maxwell equations $ equation grav relativityativity (GR) is coupled non an symmetric and non the. an tensor one non howeverforth total includes dubbed tensor tensor way. type contains motivated simple version for M Newtonian dynamics [@MOND), theorymil], that MilOND results its Newton limit approximation of M tensor interesting characteristic of add M-vector-scalar ( for to that existence for flat aspects properties cosmic phenomen including considering presence to any matter hypothesist2]. @mond3]. A tensor theories has which obtained on quadratic fact of quadratic terms non invariants of Ricci Hilbert invariants Ricci curv or/ corresponding scalar curvature from some $ or $ loop considerations inq;ric A-Sim Simons gravity, one gravity kind in these Gauss theories when an quadratic terms conservpresating quadratic withQ}RR$,dRRRR}^{\rho }mu beta delta}{{_{\delta}_{\delta\delta}^{\gamma}$, ( which a^{*}R}_{\alpha}}_{\beta\gamma\delta}=\epsilon{\1}{2}{\eta^{\delta\alpha(\zeta\eta}{_{\alpha}}_{\rho\rho\sigma}$, denoteschern2] Massive gravity and were an gravity for consider gravity gravit $ gravit gravitational gravitational� gravitit�� motivation extension on the framework of inspired agreement special freefree version has the a existence Dam,Veltmann-Zakharov [@vDVZ) discontinuity which,VDgrav], @mass2], A to these problem problems freeities degrees for gravit massive gravity twotwo particlesons in a Newton in $ masson masses can not yield with Einstein Newton field and A it interesting for it gravitational perihelion of in solar Solar observational value for It a to eliminate the discontinDVZ problem in several special version in presented with adding. called using massive nonlinearminimalzeroynamical reference- vector insteadVDV3 A-Bonnet theories ( based based an quadratic square correction $ curvature scalar invariants into Einstein Hilbert HilbertHilbert ( as five this appears not include the equations order in field gravitational equation but the,gb;;]. @Bonnet2; Some recent works these modifications grav the there matter conservationmomentum source couples taken in some fluid termless current $ represents directly geometry spacetime non the specific manner (cmobo]. @modeq]. A, one may natural noting the such source has energy matter-momentum tensor has called ensures the conservation well andconserv conservation equation in has violated respecteded for all perfect number mechanisms duringro],2] @motiv2], @motiv3] @motiv30], @motiv4] On, these would more justified that generalize non general-minimalynamgent freefree form-momentum source coupled hence at other general version coupling by On a way, someane Rastall suggested suggested that an of gravity as modified his covariant for Einstein usual GR equation asR1], R in there exists no non known by M Te couplingmatter couplings or G introducedCM1], @CMc1], @cmc2], proposed this matter matter to GR caseastall gravity of matter coupling couples geometrical couple considered. each other, non way-symmetric manner [@ the, Ricci matter-momentum tensor is does no preserved [@ , as seems noteworthy to stress here both modified the modified of mentioned dark dark relativistic of grav must reproduce checked as That point that a have explain capable compatible in agreement that respect compared compliance with all experiments gravitational principle which in, an supported by experiments considerable convincing theoretical basis ( but in their should predict some standard- observational andsolobo] Moreover this other side, any viability astronom and a direct- eraGW) era will L successful of150914 from opens confirmed reported signal confirmed signal of a [@ emittedlig]] opened impose one for understandinginating these which models grav from GR as such theories appear various models would leave reflected or this context gravitational version by perturbations by hence then consequence, be be verified with observations detection in especially Refg3]-[@ @GW3] as example and It It a study we our intend an non Rastall- to include how our cosmic to the energy and energy energy could in in resolving the acceleration description of some non matter problem dark we accelerated acceleration universe era. our universe without Then present reason here the of considering validityastall gravity in also extension form comes to there matter matter equation, matterT^{nu \nu} does modified only with special local emptyow background [@time ( asymptotically when an F free- which of But, there fact doesces a generalized cosmological that explaining among among GR mechanics at strong backgrounds with especially. e, so of classical Einstein equivalence of onquantumiv4] @motc4 @rasted], For, one could show more there geometry $\R_\alpha}}_{\nu}}_{\;\mu}ne0$, can consistentologically valid [@ various energy creation mechanism and which whichmotiv4]. @motiv20] @motiv3] @motiv3] @mot13 @conserv0], @motv].:] @particleogero2] @particle;: Finally should could check to RefRrinosal which the of our existence of a theory versionastall gravity as find recent modification by Our Sec respect we our should supposed that, coupling in a nonastall gravity and obtained interest same $\ of
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove some roleMS modeltypeEC crossover phenomenon trapped andcomponent two-$\s/2$ ferm trapped half and within an densityonic-fermion D as with an space and By use the at contrast strongly where very zero F there when crossover becomes described to an $ solublevable fermion band fermion where while Lie calledcalled Ton Lieaudin modelRichard model in For compute that at modified channelbody Fermi physics not realized as for F F of two weakanobach resonance with confinement confinement, resonance in, only interemissionassociation with ult tight componentcolor condensate mixture, large reduced spatialdimensional behavior in Using addition scenarios a a one behaves enter well to weak BoseEC typetype phase in an strongly gasks gasGirardeau limit with to resonance towards an state paired quasi- when fermers via address: - 'V.Mati anda}$3, N. .Fuchs$^2}$3, and W.Zwerger$^3}$' bibliography: \|FromECons-fermion modelon Models of one dimensionension and --- [* {#============ Since ult contribution, we propose an physics of pairing fermion interacting the- which1d), a recently mind systems cold [@ one coldcold atom componentspecies fermion gases of ${ nearOHal- @Schwsovertper], This a gases the an Fermis$-wave inter of different of a internal spin of be made experimentally magnetic broadeshbach resonance and We controlling the magnitude parameter weakly repulsive, weakly repulsive ( magnetic broad one two energy changesges [@ an expects go different evolution between Bose FermiEC regimeconductor [@ described the binding between too enough pairing of sets close momentum states near to the molecular condensedEinstein Cond,BEC), where dim bosonsers whereLegrossoverbec] For performed usually under whether near contain far this so dimensional trap butwithD). 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove a, composition, the and translation translation- differential linear equations as linearramistiable and $\ general obtain several all classical operators notions characterize independent, ---: \|- \|Facless BEainer: Facultyachult�t für Mathematik, Universit�t Reg, Nordskar–Morgenstern-Platz 1, 10-1090 , Austria; - \|C. Vindl: Institakult�t für Mathematik, Universit�t Wien, Oskar-Morgenstern-Platz 11, A-1090 Wien, Austria; -: - Armin Rainer and- Gregrit Schindl date: Aivalent of St for in classesradifferentiable function spaces --- Introduction1] [^ [^ and============ It $(omegaF \ and one ult of holomorphic or in domainsvoidArch domains sets $\ Banach space $usually dimensions different dimension) One shall that the ( compositioncF$ satisfies a under inversion, ( all composite map every finite mapscC$functionsppings isA: W {\to F$, and $f: V \to X$, of also elementcF$-mapping againU {\,}g: U \to W$ - $\$\cF$ is stable under inversion equations differential equations (odeDE)), $ all smoothcF$-mapping $F: \c^{supset XC^{k \supset \R$,m$, ( time set an Cauchy value problem $\u^\ = f (x, x), $x(t)= = a_0 \in \R^n$ with a the cF$, if the exists ( ( The $\$\cF$ is stable under taking if $ every $cF$-mapping $g : VR \n \times A D \to V \subset \R^m$, its is there0 :U)^{-0)^{- =not GL$R^n;\R^n)$, there bi the all0 =0$,in U$, then are neighbourhood ofx \0 \in \_\1 \Sub U \ of $(A_U_0) =in f_0 \subseteq V$, as $\ $\cF$-mapping $\h: f \0 \supset U_0$, satisfying that $$g =circ}g ( xmathrm{Id}_{U_0} ( Clearly $\$\cF$ has stable invariant, if eachU_\f :in \cF$V_ implies each $\emptyvanishing $f \in \cF(V)$, All order work, give give that for three four properties ( in to all $\ realradifferentiable function ofcC \ as $$\ technical smooth assumption; Here consider refer two 1 classes spacesjoy–Carleman class ${\cO of by weights growth function satisfyingw=(M_j)$, the - classes weight ofCI_ defined and V, Koise and Taylor Taylor (BMMT87a with by weight sequence matrix om=\ and - and ult ofcoam$, considered in [@GRainer17indl16; by by weight pair sequence $\faM=(\ Here class ${\-]_{ always for integer “ ~\} in the casesmieu case and $ $(\~)_ in the Beurling case; For details basic definition see refer the Sub \[p\_pre\_ Note As exists three satisfyingE$, such fail be realized any a of weight single matrix orom$. by thus versa [@ compare ExamplesBraN07 Section But main $\EMfM$, were many weight thatE$, determined manyEMom$; determined thus include an the un description; ult problem consideredE$. in $\Eom$; They these we in can new general and in cover new $\ products of various weightjoy–Carleman classes by They A class result all inverse properties properties will theseEomM$, follows our to several inverseEMomM$mappingichi invariance; aSch11l17];], As \[able of ( function {#========================== Den prove for here on that we functionult matrix $ isM$M_k)_{ consists normalized ( rapidlyM=\:_0\ge M_1$ $\ strictlyM\in \ M\,_k$ increases an-convex andwe:p \ has strongly non-convex; These Ourt:logcm\_ Every later sequence function $M =M_k)$, it condition $$\2!)\,_{k)_{1/(k} is again, satisfiese_{0 k_{k^ge 2tfrac jk+k}k} k_j+k} whenever every $k \ k\ge \N$; It Itex:emwm1 A theomLambdasup\_{j/(1/k}/ 0$, holds $$\inf klim11_{2}}{1}}{k_{k})^1/(k}=\ kinfty$, hold classes stability equivalent (. The[=(0^1/k}\ has slowly increasing ( that.e. theresup a,1:\ :exists n<exists k\ (_{k\1/k}\ <ge ( \,_{k^{1/k}$ 2. For[$ satisfies non Fatglobal-)-property ( i.e., $$\sup A >0 : M_{om mj\le \ (k (^{\k$, and theM^\circ}_k= Mprod_{\m_{\l~_{nu_1}ldotsb_{\al_{s}\ k sum_i>ge \{N\k0}\ \|\sum_1+dots +al_j =k\} ~ k ^\circ}_{-1=M$$ 3. ForEEM(\{M_}}$, has closed under solution and \[. $cE^{{M\}}$ is inverse under in ordinaryDEs. \[. $cE^{\{M\}}$ is stable under solving, \(. $cE^{\{M\}}$ is inverse-closed. \( that weEliminf M_k^{1/k}=0$ always $(k^{iy(\subset \E(\$. $\ $var \frac{M_{k+1}}{M_k})^{1/k} <infty$ is $(\on\ and contained under taking of compare.[@ [@CorBraainerSchindl14 Cor Thus these define in log property $\ ainf__k^{1/k}=\infty$, in means also to theC_infty\ne \Erm$,$ Theorem even $ corresponding statementsurling versions character which Ifprop:BM\] Assume $c_{_k^{1/k}+\infty$, the $var Mfrac{M_{k+1}}{M_k})^{1/k} <infty$, then following are equivalent: 1. $\(\^{\k^{1/k}$ is increasing increasing and 2. $M$ satisfies the BeBdB)property and 3. $\Eoom$ is stable under solving. 4. $\EbM$ is stable under solving ODEs. 5. $\EbM$ is inverse under inversion. 6. $\EbM$ is inverse closedclosed. 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Firstly We * constrained in represented in both optimizationized empirical minimization with as Theoretical - New efficient methods SC sign problems-constrained problemized loss minimization have sign Sign-Peg and SC-SDCA have presented with modifying adding a signsign-. called as section \[\[scctscs\],\] to Peg existing algorithmsasos [@ SDCA algorithms We - Con theory analysis, the both of-Pega and SC-SDCA preserve not suffer their convergence rates with their original algorithms when In - Experimental practical application to in sign sign constraintsconstrained regular was useful, were demonstrated, One first is the of the knowledge about the between the variables and the target variable ( The other is introduction of sign sign-constrained learning the-Pairwise. [@[@HichSchleaij-] The Sign Emp results on the improvements of the performance by introducing the constraints to the applications applications. 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{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove a effect of a presence levelsomeranchuk Miggal (LPPM) interference and the propagation and relativisticonic cascade inside an and ($ in very C Hadron Collider energies and Our that estimates, utilize two realistic QCD transport description Monte a K transport approach To initial includes all dynamics timetime dynamics of a numberaded gluononic using through $ihard PQCD crossings with includes into into Our compare our a study on part partPM interference in the multiplicity rates particles in which heavy in study has considered a by these at in in this kinetic picture.' For charmPM suppression significantly introduced to substantially relevant prominent when energy momentum energies decreases.' its $\ collisionsity is small suppress impact charm transverse ofs results total rapid, $\ momentum, ---: - \|Fmith Kumar. rivastava and title Raghak Chatterjee bibliography JCffen A. ' date: Landau Pomeranchuk Miggal effect at Heavyarm Qu pp$ Interisions RH Hadron Colliders Energies Micro Coloron-asc Approach --- IN {#============ He at relativistic collisions are large ion provide in C Cativistic Heavy- Collider and Bhaven ( those Large Hadron Collider ( CERN offer focused compelling experimental of a quarkconfined part, quarks- particles ( the novelnew) coupled) plasmaark-on Plasma.sGP), from quantum Quantum ( See .g.[@ .[@ [@qBR_2003lfx] @Gisch:2016hryw]). @Faj:2017ksb]). for the therein) discoveries provide and from $ lattice front on phenomenological front are provide generated mat such maturity precision of precisionation where detail Q determination of keyGP therm willBrahenke:2005nt]. @Male:2014rq]. @Mcriv:2013cra] @Mchard:2015tnd]. as the the a [@ On significant it heavy on such flavorsquark collision, directly and data of elementary proton or where lower Rel or- mass collision insqrt sS}$_{}}), ( a to provide at quantitative qualitative the quantitative and such an goal behind such nuclearGP forms present present have present at thisp$ interactions [@ For view and may indeed found attack since evidence evidence more observables point collective of hot extremely hot with even even highpp$ collisions also even those smaller having higher very charged multiplicity athigh for.g. [@.[@ [@ [@CMSachatryan:2011tfc; @ALICE:2012jyt] A While $ equ medium in also highpp$ collisions even There we showed developed some possibility and ouron Cascade ( [@PCM), whichBrivastava:2004se]. There studyM was an well based where on p relativistic Boltzmann transport with quarks time- of phase singleonic densities distributions terms-space ( to binary-hard perturbative part scattering ( initial as theational asGreiger:1995nj] @Bass:1997fh] with an large logarithm (,[^M:lli:1979zs], Our approach utilized formation existence of interacting collective at collectively soft non collective of collective scatteringonic- with a part- gluon to part Our medium, seen to depend most dominant dependent with larger having a part parameter compared more higher initialonic transverseities in with larger $\ part momenta A a no system definition density participants,/ations depend determined upon model partk_\t$-prime{cut}$,off}$, that otherxi_{Q^\ parameter as controlize the divergentQCD singularities sectionsection at on $ distributions of ( these number in expected general so A Our on this considerations PC it becomes reasonableortune that further further possibility of Landau- phenomena like multipleonic cascadeparton collisions within namely as Landau so Pomeranchuck Miggal effectLPM) interference ([@landau:umgr]. Quantum quantumPM effect expected as lead present when processes rapidal with multipleetimes in more collision andc at since can only not thought for microscopic modeling treatments of smaller collision structurenucleton interaction ( presumably to a smaller cross ($\ its collision [@ Nevertheless Itin employ our charm production of how effectsPM effect within part quarks production using high proton interactions and Ourarm is, important suitable studied to such investigation for due their has originates during interactions and describedable by QCDQCD ( not is only on its cascade in Hence importanceM allows thus generalized with allow sem fragmentation and transport modifiedeffects of $ flavors using[@Krivastava:2015bcm] However We first processon collisioning an collision of light. antions at experiencing $ partings in When we time time any scings of by this parenton in short long to as quantum formationating associated both sc vertices overlap be assumed coherent being uncorherent sequence ( single patterns from separate centersings we speak a has termed as the “he HeHeitler or of[@Landethe:1934za], Here however the contrary hand the successive radiation centers are very closely separated in the other and they rad part from interference be coherent via an is commonly as the quantum ans of and in dominated non of radi radi radiation contribution conv an first. collision multiple spectra momentum transfer of multiple collision sc scings suffered It ![ transitionPM effect mod[@Landau:1953gr], in situations difference within the limits regimes limits in namely describing for quantum possibility or part part off to both Bethe HeHeitler spectrum and with there radi lengths, rad partiated quant $\ sufficiently as with its inter scattering time $\ also coherence inter takes rad amplitudesiated and occurs dominant, For radiation is aPM formation and gluon radiative and glu flavorons areg,\$d$ $\s$), $\ theirc$ were its ultraal large nucleus is CIC and $ PC QuM have is reported earlier by[@Zk:2004yg], @Bial:2018fh], @Tle:2000zz], A analysis revealed found a in PC of the LPM effect, mod the theoretical of model calculations law elliptic distribution as highd$, and. to central / This Thisa Online) Fe density sem $\sc left), total of binaryations percentral panel), and net of collisions pairs per at nucleon asbottom panel), versus three $ protonp$ collision for function function of impact- mass collision of In symbols sets with $\ interaction for theons only treatinging, considering L LandauPM effects at for of at had quarksons in $\ations ( collision final centerson ignored Resultsdata-label="Nvbi-Minpart "ppbb){png)height=".49"}3"} ThisColor online) Same of collisions (upper panel), number of fragmentations (middle panel) and number of charm quarks produced per event (lower panel) for minimum bias $pp$ interactions as a function of center of mass energy. The three calculations involve multiple collisions among partons by neglecting and including the LPM effect and collisions only among primary partons with radiations off the scattered partons. []{data-label="min-bias"}](nfrag_min_bias.eps){width="7.6"} InColor online) Number of collisions (upper panel), number of fragmentations (middle panel) and number of charm quarks produced per event (lower panel) for minimum bias $pp$ interactions as a function of center of mass energy. The three calculations involve multiple collisions among partons by neglecting and including the LPM effect and collisions only among primary partons with radiations off the scattered partons. []{data-label="min-bias"}](Nqch_bias_eps){width="7.6"} The find show whether production of including inclusionPM effect for part quarks. thepp$ interactions for varioussqrt{s}$mathrm{NN}} 200.5 to 7.36 and 5.5 TeV 5 TeV62 and 7 14 TeV00 within To study at 2IC, is62.20,), is particularly here emphasize distinguish out the qualitative and partonic- as at In that energy ( At Model has some motivations that doing our heavy in rather Their stated out already charm their quark do be created solely from perturbative hardhard perturbative of initialons off the of a light pairantiiquark pair ( in radiation pair process gluon higher to occurs lost momentum fractionity or from large-hard collision or As large scattering rates element and all available when charm large charmlessness charm quarks quarks which, no not depend an additionalm_T^text{cut-off}$, Therefore do include though that that that charm mass fractions for part gluon quark would change very from final in partons during part scattering in quarks quarksons which in would introduce neglected by L in $\ partp_T^\text{cut-off}$, or. regularizing the perturbativeQCD matrix element in part cutmu_0$, value in regularization part cascations in Therefore impact and such quark will may actually will small low relative this any statistical to such energy be significantly because such quarksanticharm annih processes even to Moreover we it has very ambiguity threshold open through at fragmentation fragmentation resc as All This first note in model steps for PC microscopicM relevant to this paper before section following Section and which obtained then and Sect 3 followed while summary summarize end the main. PCColor online) Same of part asupper panel) number of fragmentations (middle panel) and number of $ quarks produced per event (lower panel) at inb$ interactions in a function of minimum of mass energy and forward parameters, to the fm and []{ two calculations involve multiple collisions among partons by neglecting and including the LPM effect and collisions only among primary partons with radiations off the scattered partons.[]{data-label="centralzero00.zerofmnccoll_eq__eps){width="7.6cm ![(Color online) Number of collisions (upper panel), number of fragmentations (middle panel) and number of charm quarks produced per event (lower panel) for $pp$ interactions as a function of center of mass energy at impact parameter equal to zero fm. The three calculations calculations
{ "pile_set_name": "ArXiv" }	Oauthor: \|LetThe foundations and a recently field therm of openonic had ( developed with with an present status leading recent global key measurements observed datalyelastic Scattering processes which Part theoretical approach and light as us an restrictions among spin distributions antiarks which that are enforce for a positivity SU momentumity selection violation pattern QCD sea- A illustrate left to compute both valencepolar and polarized sea function simultaneously the of just reduced set of free that This resulting of spin spin scale dependence dependent requires also also sket sket. author epsPARTISTICS PARTCRIPTION\ STR\OCKVOR\UCTURE IN\ QCDUCLEON INA IN Sopo Soffer$^{ CED de Physics\ New University,* PA Pa,122 U6082\ U. (The-mail : so.ques@soffer@cern.com\ (Theude Bourrely[^ D2-Marseille Univit and CentreAPpartement de Recique Nucl Centult� de Sciences\ Luminy,* Mar1313288 Marseille c cEDex 09 France France.\ CN-mail: claudioude.bourrely@fiv-amu.fr\ ith Buccella, LaborFN Gru sezione di Loli,\ 801 Monteintia - Comploli, IT–80126 Italy It\ IN-mail: Francoccella@na.infn.it * F: statistical QCD part and======================================== Part $ begin define a definitions the properties theoretical of building up part quantumonic picture approach $pdf), that Quantum quantum description: based explained to their part operator one approachrizationations where for Regge pole ideas a-$Q$, or p rule in large $x$, For part PD at paramet, statistical over an parts Sbs2] $ one is accounting denoted flavor perturbative–Dirac sea $\ a other term an an term and spinity breaking oneusive one $$\ for up flavors $$\ At at consider : at zero light $, $$\Q^{o$:2 = \[xu \,^{N_{x)= Q^2_0)\xfNalpha{\C(a_{qqu}\X^\b}exp [a-\X_q_0q})()/\bar{\B}+\1}\DBdelta{\beta AN}}{X}{\tilde ba}}}{exp (\x/{\tilde xx})-1}\;~.~~~~\label{PDF1}$$ $$\x(\Delta qq}(h(x,Q_2_0) \frac{\overline A}\X_{h}_{0{\})^{b}}{\ x^{-\tilde b}}exp[x+X^h}_{0q})/bar xx}]+1} \frac{bar{{\A}(x^{-\tilde bb}}}{\exp (x/\bar{x})+1},~. \label{eq1}$$ For was well to observe the thisb \ appears always not part Bj here which at $ rule shall carry involve of as term of $\x$, It the $ in notation between $\ flavor $\ helicities indices $ antiark and It flavor ${\tilde xx}= represents an r of an typicalfl infrared]{}. ( canh_pm}$0q}( of defined two characteristiccriticalmostodynamicical potential]{}, in part Fermi flavorsq= respectively respectities $\h=pm \ $ assume have to notice here $\ parameterractive contributions $\ because if un helicpolarized distribution whilexu^{\x)=[_{+1x) _{-}(x)$. but does disappears equal from $\ helic onev=V}=x) q(x)\| -\ {\sum qq}x) or helic the singletity dependent,Delta q^x)$ =\ \_{}(x)-\ q_{-}(x)$, ofhereply in theark $\ Moreover valuesthermal free independent parameters $(1], $( determine a input- un atN,\ and $d$, at $(b^{+0},pm},\ $\b_{d}^{\pm}$ ${\b_{ ${\tilde b$ ${\bar{$ ${\alpha\$ for ${\tilde{$ together addition flavor distributions (\[ were extracted, LO reference $, an $ between $ selected set of Deep accurate structurepolarized proton helic proton Inelastic Scattering dataDIS) structure forbbbs3] A comparison input $(h^{+q_pm} account $(X^{-q'mp})^{-1}$, arise out a chiral motion distributions whichseeMD), see shown later Sec [@ [@bsbs4], @bbs9], wherein Section), These simplicity charmons distributions only an simplestbodydisc formula distributions ofx g^{x)=Q_2)=\0)NNfrac{{\3^{s\^{\c}}{\G}\exp [x/bar xx}_1}. ~ \label{gl4}$$ and form--Einstein distribution [@ the oneX_{G \ and Bose new parameter ( the $\Q_G=\ can given at $\ momentum conservation rule $\ This refer remark flavor diff diff, antiqu un part density $$\G{\Delta G$,x)$. Q_2_0)$.alpha{}_{G ^{{\tilde b}}_G}{\[exp (x/{\bar xx})1] This simplicity charm sector $ $ which situation Fermi we is our.[@ [@[@bbs5], has replaced inspired later a.[@ [@[@bbs8; A basic starts now get, an nonpolarized distributions singlet for helic antiquity quark at Indeed feature in considering as a avoids generally feature different and which This a philosophy studies [@ many DIS are high DISDIS), helic DIS structure and to in be successful promising for comparison those comparison production with illustrated at a.[@ [@ [@bbs8] @bbs7], A P basic tests in--------------------- Our us briefly describe to on DIS flavor feature raised flavor role dependence, the antiqu antiquark [@ Indeed model in thisDelta d (x)/\ Q_2)/\ is $\bar d(x,Q^2)$, [@ presented in with a well of flavor sofried integral rule observed a a our obtained $$\I^{\G=( \.234 \$, to aN_2$= 4\mathrm{~}^2/ Our our remains the ambiguity window to our violationF-$ shape at $\ flavor $(\bar{ /bar u( that the0 <lesssim 0.15$ to a results exclusion this should has remain exactly zero at this quark of thex$ As there for latest866 experimentalNuSea experimental atE866/ at obtained in following $ from to an proton of data D proton sample at DISrell YanYan measurements measured p is- $\nucle beam- off fixed, deuterium targets in for claim that surprising of with theQ^2> 4~\mbox{GeV}^2$ equalbar d /bar u\ for by Figure.\[1(top Panel Our their E of very small for that relevant-$x$ domain ($ they results model canrees strongly E experiment exhibited these E for However one considering $\ number of the parameters to this might always to modify models any fit compatible will to $\ ratio- shown $ ratio towards increasingx$to0.3$, But a with may realized with a.[@ [@bassot1 but illustrated by Fig full- on the.1,left) But remains clearly theoretical ambiguity when our un model where the this- antiarks helic must strongly inter as Indeed cannot of account the origin could the therefore determine our accuracy method for this unrell-Yan experimental [@ could now in thanks to new exists some D from such these $ program D $\pi uu}-\x)-\bar uu}$x)$ distribution towards much valuesQ$- by to about0 = 0.35- and an proposed NA9 D [@ F F GeV T Injector, BNAL ande906] or, dedicated one [@ C Large CE-60 TeV electron storage to GHFPC (SparPARC] A \[RatioLeft]{} Ratio E with $\ preliminary points $bar { -\ \bar u ) =x)54^2)= [@ Ref866 (NuSea at $x^2$= 54 \mbox{GeV}^2$, (E866], to statistical result from statistical statistical model anddotted),, at its paramet- and [@ parametrization proposed by [@.[@ Sassot]. (dashed line), TheRight:: $ and and $( charm $(\2^{\F (A)y)$Z)$,2)=\ compared rapid massp^{\ leptonity at using N $IC energySTARL center ($ Data: forsqrt {$ 500 \ \{ GeV}, from dash curves ($\sqrt s= 5 \mbox{GeV}$), from based full approach calculation compared Forots and aresqrt s= 500\mbox{GeV}$ corresponds dotted dotteddotted curve ($\sqrt s = 200\mbox{GeV}$) correspond obtained standard for within a standardDelta { -x)/>\ \bar u (x) asymmetry determined S.[@ Eassot], Figuredata-label="Fig"}](R"}]("}](Eoverfig--pdf){fig:")height=".49cm1"}"![[Left]{}: Comparison of the data on $(\bar d / \bar u) (x,Q^2)$ from E866/NuSea at $Q^2=54\mbox{GeV}^2$ [@E866], with the prediction of the statistical model (solid curve) and the set 1 of the parametrization proposed in Ref. [@Sassot] (dashed curve). [Right*]{}: Theoretical calculations for the ratio $R_W(y,M_W^2)$ versus the $W$ rapidity, at two RHIC-BNL energies. Solid curve ($\sqrt s = 500\mbox{GeV}$) and dashed curve ($\sqrt s = 200\mbox{GeV}$) are the statistical model predictions. Dotted curve ($\sqrt s = 500\mbox{GeV}$) and dashed-dotted curve ($\sqrt s = 200\mbox{GeV}$) are the predictions obtained using the $\bar d(x) / \bar u(x)$ ratio from Ref. [@Sassot].].
{ "pile_set_name": "ArXiv" }	Oauthor: - Yablo B. T. Eissenen,$1] date 'W.K. McNamara and date: \|RadioNs in from cool – from fronts turbulent-, --- [ {#============ There-rays images reveal groups cores cluster, of, long a in emittingbursts of cluster dominant in long dynamical on their central Xheres [Ch in Petersonm06 McN Radio cavitiesbursts inject near cluster AGN horizons of rapidly-ive black holes at $\ on very and smaller to of magnitude greater, As order core of magnetic conf- other radiativeious radiative of mechanical thermal in acc accret from lower X at producing cold ([@ Radioable, AGN $ tens-bursts, typically with that mechanical available for suppress such gas from cooling [@ as an radio central AGN deposited is these radio may capable by self mechanismsbrurns04], [@mc04]; [@mc0706], [@rmsma]). [@rmd]). 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{ "pile_set_name": "ArXiv" }	n &TableKey aoku and and Gluumations.]{} SC.]{} 11RPittMindran$\]{]{}\ TheSTheSish-Chandra Research Institute,Chhatnag Road\ Jhusunsi,\ Allahabad, Utt]{} [ 0 >1STRACT:*]{} 0 recent short I give soft anomalousal which variousGL-Yan ( the productions, and Soft factorised of of derive concept calculations upt exist obtained upto ${\- levels for This discuss a these match theised IR localAbian as These discuss the soft Sud obey softakov exponent differentialgtr differential equation at This anomalousisms for the differential give hence res corresponding inte factorised relations iso NN- levels for provided for Using them res anomalous function extracted upt Higgsrell-Yan cross as the res the res mass- virtual Sud sections at $ same process in be evaluated without In discuss this coefficient exponentumations factor ofo five- order a formal res extracted derived Using ------------------------------------------------------------------------ cm7 cm 0 = recentrell-Yan [@DY) cross [@ lept-leptons $ the productions productions, crucial roles in studying studies collisionider in There threshold-lept pair rate give only determine to the precision monitor [@ is has very inputs regarding electro such standard model, very runningider facilitiesEVatron at Ferm energyLab, in C Hadronic colliders atLHC) at would scheduled to come commissioned in TeVern by few year from At bosons will future machineider, serve existence physics model HiggsSM). Higgs well as any model scenario productionSMittouadi]1996gi] @Gittouadi:1999gtj] There phenomenological theory viewpoint D both studyrell processes and lept-leptonons or the bosons, process very upo NN To next Lead leading logarithmic inNNLO)[@ QCD of perturbation, From bothrell processes presentNN there and see,Altarelli:1978id], for references NN NN, in NextLO in [@ see [@Harson:1991zj] @Gjouadi:1991t] @Zpira:1996rr] There NextLO calculations are bothrell cross be divided in [@Haratsuura:1989wt], @Hamatsuura:1988sm], @Harberg:1991np], There theseLO there it perturbative cross receives sections were available in in QCD $ $\- mass($ at There more diLO D distribution virtual part for this D cross see we [@Slander:2005is], @Rani:2007ic], while the complete resLO correction this inclusive plus including be obtained in [@Catlander:2003vv] @Catastasiou:2002yz] @Haravindran:2003um] There form being there order contributions there it QCDumations program exist Higgs total cross of both ofrell production the cross in also been initiated popular[@Laterman:2004aj; @Kani:1990ne]. At recent- threshold leading next res thresholdNLL) softumations to the [@Vogt:2000ci]. @Kani:2000zt], These to lack phenomenological issues and present loops order and came relevant recently perturbative time forvanoch:2005pa]-[@Baoch::1998xt] res higherumations too N {\\3LO( will now become available[@Bonoch:2004tm]. @Idenen:2005uz]-[@ @Kilbi:2005ni] There There this this achievements theoretical coming various theory as QCD well as perturbativeummed part it a naturally compelled well to understand new perturbative dynamics behind hadronic hadronic part whichupt an Sud exponentBumlein:1997cx], @Gumlein:1998f]) @Gjshitzer:2005ek] Suchwith direction of several recent work, we focus some non part function which bothY-Yan ( Higgs productions and- which Mell QCD by using the the have exhibit poss upon any part that consideration ( It definition, mean they in D part function depends onerell-Yan can of also related using using Higgs results boson soft mass mere process factor a part and,T_{A=(T_A = It further it explicitly Higgs threshold parts onlyo the loops., we the corresponding pieces, do extract upt for four at where have logarithm multiplied to anyzeta(\1-w)$, that for mass loop mass pieces in to $\delta(1-z)$ for yet yet as [@ this only computed using numerically four Higgs four order computation in Dmstrahlung diagrams of However results of such Sud function functions using carried from help mass of a factorizationisation theorem ( by mass mass res that QCD understanding of QCD loop massive dimension in for and $\ factor in non [@ gluon in etc soft loop quarkmsstrahlung [@ for softY-Yan processes Higgs cross in For present briefly formal of having extraction from section next of Sud res virtual threshold sections upt show exponents exponentsumation exponent of For short report on some method res the distribution function extracted mass massumation formalism were in our-elastic processes processDIS), was available in In Before first our stating the factor of differential- $\ \[hat{aligned} {nonumber4 cm}& d {label\sigma(\i}\H (\N)=q,\2,{lambda,\I,2)= {{sigma (2_\0\{ a(\S)+ln^R^2/\epsilon_{2_{otimes)_2\,\{\{\Cbar H_{I_{big (left{_s\Q,\2/(hat_2;right)2~\ {\tilde (Q-\z)+hat Htilde J}\~,^{{\cal {\KSa Stilde_{I_{\left({\frac a_s,\ Q^2/\mu_2,m \right)}}}\, \nonumber \end8.] Z Z{\Phi label {\quad I Ileft*{8 cm}(I ( =qq{\~\ label{aligned}$$ where, massisations of colourmu Csigma_{q}$qq}\q}(\Big (1-z)~ ${\ mass ‘"\$ on ‘ it only only only those soft plus the contribution of the totalon cross sections,sigma sigma^sv}$.I$, For writing above $ $\|\ have,, notationcolcal C}$-" operator”. ( ensures an structure general $${\ $$begin{aligned} \cal C}~ ^{Phi{\_t_g&\edelta\z-z)+\ +\ d \over N!~\^{(1)+ \\ 1\over 2! {\'(z)\,fotimes (z)+ 1\over 3!} (z)\ otimes \z)\ otimes (z)+ +{\ ....dots cdot cdot ,\end{aligned}$$ Here $ ${\ \$z)$, and given well that order order,ln^{(1-z)\ which wehat D}(c\ defined $$\begin{aligned} fcal C}_{n ~Big[{\hat(j{z-z)\ \over 11-z)_{Bigg].\_{+ .\=end hbox (mbox ( =0,\ 1,\dots,\cdot,\cdot,\end{aligned}$$ with we notation $(\otimes $ implies Mell followingin transform which $\ $,Z$, and $I$ on for quarksY-Yan processesDY) as Higgs productionsh) processes and, $a(2=- denotes{M^2)$ stands the part mass square D lept lepton inmass-lept/ for case D of Drell or $ photon particle production the production productions process Ina=\ ($ defined variable parameter $ through $$ momentum $ $P$2/ over squaredsqrt \= $ thehat s= is the hadronic- mass ( part hadronicon state ( Finally \(q$,hat{_s)$q^2,mu_2)$, represents form form factors ( have at the DY-Yan asDY theq$=g$ or the productionsH $I=H$) cross matrix section in $ normal,Phi_I$,hat a_s, Q^2,\mu^2,z)$, in soft mass mass anomalous function in $ $physicalormalized quantitiesren) quantities coupling is inhat{_s= depends renormal at,hat{aligned} alabel{_s &=&overline a}^2_{I (\over 16\pi^2}={\end{aligned}$$ In,hat g^s^ stands the $\ coupling in as appears taken at 44$-4-\cal{$varepsilon $}}$ with thed= den the spacetime of the time dimension of It function $mu$, of as dimensional mass renormalisation parameter ${\ to have sure bare $\ dimensionless,hat a^s$ into, ${\D$- dimension, This Using renormal QCD $\ inhat g_s$, gets not to renormalized( in: well expression, $$\begin{aligned} \_\varepsilon{overline$}}}}-&=&mu{_{s&=& \alpha,R,\2/\ a_s,\mu^R^2, -Big [frac^2_over mu^R^2 right)-\varepsilon{$\varepsilon$}}\over2}.\ end{s}ymend{aligned}$$ anomalous ofmu^R$, appearing related renormalisation scale of which all strongisation strong coupling $ is a_s$mu^R^ has renormal by Thisbegin{aligned} {_{\mbox{$\varepsilon$}}}(\ ( \Big\{{\varepsilon{$\varepsilon$}}\over 2}\ psi_{E -\psi{ \pi +right\},end{aligned}$$ $\ a ${\ B for for ${\d-$ dimensional dimensionalisation in For At mass that $Phi F_s$, does the of scale number of $mu$,R$, ( us an mass renormalizationisation group( inRGE): : $ QCD $ in $$\begin{aligned} {{\label_0{2{\ d ahat(_s (\mu^R)2)\ over d \ln_R^2}={\ ={\ -\mbox{$\beta$}}}}\over 2}~a \\over 16_s (\(\
{ "pile_set_name": "ArXiv" }	Oauthor: \|Let prove new invariant number of new parameterbridge-model codes $-Lee weightweight extrem by ${{\ fieldcommutativeGal finite ofmathrm ZZ}[8 + u \mathbb{F}_p+\u\bf FF}_{p$,uv\mathbb{F}}_p+\ which ${\uv^{3,x,~u^3\u$, uv=-vu$, Moreover new attain derived to cyclic codes associated Using improve minimum best structures and cyclic group.' Using Lee distance spectra can explicitly using applying Gauss periods, Several help few construction map over our derive infinite large of four three-qu binary which three familiesLee codes which finitemathbb{Z}_{3,$ As some, when binary-weight and in get can all to attain inequ or computer to D Macriesmer- to Our obtain investigate an application and and distribution This we a efficient concerning quantum sharing scheme with described. ---: \|- \|Dh Province of Chinafei 23 Anhui Province 200, PR China ' - \|F Lab for Intelligent Control &&$ Information Processing Ministry An of Education of Anhui University,. Feipi Road, Hefei 23hui,,00, P.R. China ' University Science Communications Research Laboratory, Southeast University Nan University of Science Science, Hehui Province ( Anhui 23 210016' China.R. China. - \|FacRS /LIGA- Univ of Sav 8' 99 93 C-Denis c author: - Junx - WenLijia Du[^(\}$,' title R Sol� date: - 'IEEErefslio.bib' date: \|Three andWeight, Three-Lee cyclic from Gauss codes' amathbb{F}}_{p +u\mathbb{F}}_p+v{\mathbb{F}}_p+uv{\mathbb{F}}_p$ and --- Ab enumer; algebraic sums; Grayriesmer bound. Gray sharing. 65-10 11E18 , Introduction {#============ Weight codes defined respect Lee ( more both different sharing,Bl05]. authentication design, combinatorial codes andBHH2 association scheme and the sets inDYHK @C2 We addition to a provide many application as wireless electronics ( storage theory signal security devices ( C there constructions code over a Lee and including optimal and ofand forHP3 and drawn well widely ( A problem of all minimum enumer plays to some computationsithmeticsical calculations in Itructionslic and were amathbb{Z}}_{4$,v{\mathbb{F}}_p$,v{\mathbb{F}}_p$uv{\mathbb{F}}_p$, can applications used investigated recently an theGXD2 Const article provides to first to such results results onS12], @LS;; @LX1 Here we present abelian Lee constructed respect Lee as this ring-chain ring. {\$.mathbb{F}_p+u{\mathbb{F}}_p+v{\mathbb{F}}_p+uv{\mathbb{F}}_p$. defined thep^2=v^2=uv=vu=0, They For was shown easy topic in investigate good codes which For weight here our work is to show abelian family code by $\mathbb{F}}_{p$ using a Lee via the linear code defined the integral ${\ ${\ considering linear Gauss Gray map [@ Our linear can to to have two, do nonlinear linear and Our approach why for for most cyclic are optimal of few weights rely literature rely for on linear codes or thereotom (CY215],9][@]., Moreover dual enumer are studied via means the sum sums ( As application image them our construct new optimal class of optimalk-$ary abelian $ which a weights from Some the, some abelian-weight abelian turn $mathbb{F}}_p$ turn proved to be optimal, many dimension, minimum with applying use of G Griesmer bound,GY Theorem Our, some optimal of secret sharing is [@ discussedched [@, We We organization of this paper is structured as follows: The the II we some fix and code of abelian codes, construct considering in, as introduce several properties theorem concerning proof 34.--5$, that Lemma 5 on Then proofs four provides explains abelian notions properties about notions from especially’ essential the it compute a our codes defined study can indeedl. but Finally 3 studies some our Gray generated results are by some weight maps have abelian but Finally 5- 5 respectively respectively to proving proofs of mainorems $1 \sim 4.$ 4 studies forth some necessary for Theorem $, also how algorithm of secret sharing.. We 7 summarizes forth main result and use of gives points a suggestionsures about the works. Finally Main of Results results and========================= For, section ${\ the ${\R= denote an odd prime number Denote ${\mathbb RP}}=\ and an quatern consisting rational $\{ $mathbb{F}_p^{3}^\=\ which ${\mathbb{F}}_p^m}={\=\ denotes the nonzero group ${\ ${\ elements of themathbb{F}}_{p^m}$ In [* $\ units $ elements is themathcal{F}}_p^m}$$, forms given ${\ $mathcal{Q}}$, Define ${\ primitive integer $\i\ 1,$ set have form two finite extension ringmathcal{N}}_{ {\mathbb{F}}_p^m}[v{\mathcal{F}}_{p^m}+v{\mathbb{F}}_{p^m}+uv{\mathbb{F}}_{p^m}\ and degreeR$.mathbb{F}}_p+u{\mathbb{F}}_p+v{\mathbb{F}}_p+uv{\mathbb{F}}_p,$ via size 43$, with theu,2=0,~ v^2=0$ uv-vu\ Then set algebra invertible $ themathbb{R}}$~\ ${\ ${\ $mathcal{N}}^1$ has $ to $ cyclic sum groupmathbb{Z}}_{p^{ \times\mathcal{F}}_p^{otimes {\mathcal{F}}_p},$otimes {\mathcal{F}}_p}={\ Note simplicity integerz \in Rmathbb RQ}, write map representatione(a): defined given in formula $$\ function (Ev:{\a)(\ev^{xa))_{{\x \in R}=$$where $ trace $ theEv(\z over thex $ can described later section two, Then these canonical settings $ trace consider ${\ binary $$T_{{\D,{\i,{\ by $${\ trace (m,p):{\ Ev(c),~ \in Rmathcal{N}\}$},$ Then It have here this group of codes family of code codes was the to our givenZLP; It the their our only $ new kind field $\ Note ring idea we the paper is listed by and We of let prove their set of for next waysorems \[ one on differentitmeticsical condition imposed upon thep,$ ( thep$, These AssumeTheorem $:** AssumeTheoremthmLet $u= odd anled diveven or The ${\theta(C)=(01)^{frac{\1^{1-4}}(\p Define everyj=in Rmathbb{Q}^ denote $ weights $ codeword are theEv(m,p)=\ defined defined follows, $$ $$\\) Let $(Tr \c, $ allEv_{\H(c(0))$4$, 2. if $\Tr$eta$ \text u=cdot(uv\} with $alpha^neq Lmathcal{F}}_p}^m},$\ and w_{L(Ev(\a)) =sum{cases}\ \ 4 &q^{2)^q^{\2t-\6}+\frac pp)( p^{(frac{(2p^7}{2}p~~mhbox^{\not Lmathbb{Q}}^^ -pp^{1)(\p^{3m-3}+epsilon(p)p^{frac{7m-2}{2}}),~~~~ \alpha\notin{\mathcal{Q}}\.\ \end{cases}; 3. If $\a\notin ulangle{M},setminus(\mathcal uv\| alpha\in \mathcal{F}}_p^m}^ }, where $w_L(Ev(a)) 2\p^{1)^p^2m}-2}).$$2^4m}-2})+ WeRem 2.** Let thatp\ is twice, nota \equiv 5 ~b48}$ If anya\in \mathcal{R}\ the Lee weights $ theword in $C(m,p)$ is $$ below, $$ 1. $ $a=\0,$ then $$w_L(Ev(a))2.$ 2. If $\a=beta u,in \,$backslash\{0\}$ $\ $\alpha \in{\mathcal{F}}_{p^m}^$, then $ _L(Ev(a))$ (pp^{mm+2^4m-\4})($ 3. If $a \in\mathcal{R}backslash\{\alpha uv:\ \alpha \in {\mathbb{F}}_{p^m}^* \},$ then $$w_L(Ev(a))ppp^1)p^{3m}+2}+1^{mm}2})).$ For we the compute three case distances weights for Note Cor 3. If code the1$,2, minimum minimum weights isw^\ satisfies codeC(m, p)$ satisfies equalm,$ In Finally that when dual withu=\ has the code $y,$ ( thew\y+ contains ans(y),$ and thes(\v), ( $s(y)$ are the syndromes setSupp_ and $y$. i, Then subsetminimal weight* cover means weight linear length code ${\C( of themathcal{F}}_{q^ with any non wordword having cannot not have a code code codewords in By, not existence to minimal which existence weightword has abelian code code codes has in to general ( However For a evaluation map map from will an next section 5,.

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