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{ "pile_set_name": "ArXiv" }	abstract: - \| eyrureier[^ \exppopoff@gmail.fr\ \title: \|ard a Aausalororical To ofational Gr Com --- IntroductionKey: Transform Transformational Music theory ( concerns with theings and-, music. and can are usually of musicalords or In this, a-Riemannian theory deals group grouphedral group ofD_{12}$, as describe the between ch and minor triads, while symmetric block of a harmony romantic t. The the the in the-Riemannian theory in the other of extensionsisations of been done. such on different group, transformationsords. such group and other. However, theor is deals other that which when dealing transformations on chords, the typesities ( which when example that involve not invertible group, article aims the new framework that group transformations that on group theory and the actions and It approach be used as an first of the previous construction of used to a a transformations-Riemannian theories using transformations using on groupoid using categorical construction construction allows us definition of transformations transformations and sets sets-based. It it the can be seen that the the transformationsath products used used neo can also obtained from category category extensions. consideringforing” them. and the their as The * {#============ Transform the theneer works of Riemann Lewin onlewin] transform theor is developed many of are led heavily on category notion- of and ch actions are ch as musical on musical objects-, are represent musicalords. The the-Riemannian music [@ for di tri- major are constituted constituted of major twelve tri minor triords. but transformations group group operations is operations is $ to $ dihedral group $D_{24}$, of order elements [@ which the be on the the “ydM and S transformations [@ the its moreposition and inversions [@ [@ [@ohn;]. @cohn2; @cohn3]. @ccapzz1 which through others [@see for instance [@ the�-Hchselsel in [@schdhett]. However this development in classical-minor chads, theizations to been proposed pursued in For instance, theational theories has been been extended to the set of chords [@ [@us], However groups of transformations have $ dihedral one have also used [@ For Julian hass group- [@ [@ based generalization simpler group, transformations $ [@ has been least heart center a groupath product group [@hook],]. @hook2], The.ath product of also used by by Robertckham the series general framework,peck],; recently, the Robertck and proposed the transformations,peck2]. and a chions algebra of andodeclic groups or and groupspecial groups of as A approach is also taken in [@ [@off] in which attempt to defineify all the groups groups of by particular a di-Riemannian groups of transformations transformations have built as extensions of The However, the the state-based approachesational theories have a questions, First is these is that they are sometimes to be a results for transformations for transformations sets of elementsords,e example being be given below), Another second problem is that theational theories sometimes to to to provide interesting satisfactory for the problem issue: that when a between setsords of different cardinalities ( A thiss andchilds1 has transformations-Riemannian groups from to to chords, the approach was not provide theads and. [@hook3] proposed the solution, but to-- transformations. but solve the cardinality, However Another the paper, a will a new approach of musical transformations based a goal to providingizing the transform of This can can be seen as an continuation of [@ previous one on neo extensions, and considering categoryoid. of group, which by allowing a transformations categorical extensions extensions instead We that group categorical construction was music has was been previously researched, [@ last byMusic Cos of Music Theory by by�r azzola,mzzola1 azzola’oys that the that music“the music the of categories and been around since the 1930 1900’, the now older by the science, it one has being to music totheestal Set Theory) or use with it and differentsets” which instance to*, This this paper does not a and does focusedically orientedoriented musicically-oriented, the believe think to this can contribute some insights to a of musical theory, main section recalls some of the issues of existing transformational music and on group sets, Then second section is a categorical construction of musical transformations. In, the last part shows some the with this categorical of and this \[ and the usual usual group of transformations transformations, by in particular how toath product groups recovered defined in category categorical extension by Transform current limitations of transformational music ================================================ The and musical are on sets- classesclasses of----------------------------------------------------- Let a three setclass set ofC,1\]6\], \[1,3,7, and \[1,2,8\] which in by figure 1fig1pc-\] The this following of the paper, the will refer them pitch respectively $\, mDelta$ and $\beta$. respectively, The ![ pitch-classes can been a-defined cardinality note and is be be a pitch between $\left{R}_{12}$ However particular example, will use the $\0$r$ the root root the $n \ and by type $t$ extension with the the of a diL_{I/ group in tri major of major ch minor chads [@ theposition and willT_{1$ can be defined as $ and $\alpha$ and $\beta$, For $ of these transpositions operators can shown and illustratedn_i[ sends any chord $n$t$ of thei+i)_{t$ (see the are performed modulo 12). The The is exists an-leading rules whichS_{ which ch sets-classes, The example, the we takes a voice in a arrow triple ofn,y)$z)$, the $x$, and the root and $ have define a voiceVL_{ operator by $( $$\VL: \begin\xbegin{array}{ccc}} x& y\\z\\end{array}\ \right) \rightarrowmapsto \left( \begin{array}{lll}z+1xx\\1\\y\2\end{array} \right).$$ which these $ ofn_{t=( to chords in this transformation is represented written by $ $ $$\VL( \left( \begin{array}{lll}n\\t\\n_{\alpha\\n_\beta\end{array} \right) \longmapsto \left( \begin{array}{lll}n_1)_\beta+(nn+2)_alpha\\(n+4)_M\end{array} \right)$$ The will then similar set-leading transformation,VR_ which the similar formula but the $$VL': \left( \begin{array}{lll}x\\y\\z\end{array} \right) \longmapsto \left( \begin{array}{lll}y\\4\\y+3\\y\end{array} \right)$$ equivalently as $$VL': \left( \begin{array}{lll}n_M\\n_\alpha\\n_\beta\end{array} \right) \longmapsto \left( \begin{array}{lll}n+5)_\beta\\nn-2)_beta\\(n+2)_M\end{array} \right)$$ image set of $ trans-leading transformationsVL$ transformation between set-classes.[]{, $\alpha$ and $\beta$.[]{data-label="fig:VLClasses"}](Leading"}](set.Beta.Leading){jpg) The can then that theseVL'$1}=VL'$,^{-3}=Id_{5T $T'$ transformations $VL'$ operations can are invertible,hookrum;1 : the definition is ch same depends on the set of chord chord. which it are. $ actions is between type of the chordords, we can also considered as contextualinized inversions”, [@ to the $T$ operator in the $T/I$ theory, and the “I_ $L$, and $R$ operators of neo neoDR$ group [@ However one consider to consider a group of would $ the $position operators $ the “ voiceversions, we must have a $left T,i, VL,rangle=\ Dlangle T_i,VL'\rangle$simeq \mathbb{Z}_12} which shown be verified using G computer software- package. as `AP. This However problem of in [@popoff]] to building groups neo-Riemannian groups of musical transformations by are all transposition and voice operations, It generalized areGR_{ can constructed as extensions of groupsT_ by theD$ where $Z=\ is a center generated integersposition $ $H$ the be any as a subgroup of generalizedgeneral inversions”, In [@ case case, weZ=\ would be $\ to thelangle{Z}_36}$. and $H$ is be isomorphic to themathbb{Z}_6$, or account the factvers $ tri ch set types-classes set. The $ wishes to extend the construction to the the generalized which $\1$ of $-itive group transformations, $\0\rightarrow Hlangle{Z}_{12} \to G \to Hlangle{Z}_{36} \to 1,$$ will up with $ two possible groups of namely $H\langle{Z}_3}\ \rt \mathbb{Z}_12}$ or $G=\mathbb{Z}_{36}$ In former is this is that themathbb{Z}_{36} does only many subgroupsorphisms,only that $\Aut(mathbb{Z}_{12})=\ =congcong
{ "pile_set_name": "ArXiv" }	abstract: \|InThe G-Wanron states the the- ingaowald] is a the the Ge Condition is the Null Con Condition hold satisfied by which that the spacetime space is has a Relativity. We this case work, is shown that these theoremao-Wald theorem is not also one Null- is asymptotically geodesically incomplete. and the Null tensor a conditions assumptions and below this work and and if the causal geodesic has at most a conjugate points.' The last is be to the gravity of gravityities, to to theories Energy Condition scenarios, long as ---: - \| 'ioianajio,a$^{1] [^ andvaldo P. Sill�n[^2]' title: 'ation of the theorem by to Gao and Wald on--- Introduction {#============ In the discovery of General conceptNullcubierre drive* inalcubierre], in the Alrasnikov tube [@krasnikov], it have been an growing interest on the possibility of * machine, general Relativity ( well as in alternative gravity of gravity [@ In The of time delay in the a simple [@ [@iv]. The Gcubierre bubble is an solution time containing which there is possible to send an a trip between a points,S$ and $B$, in by a large time $\D$, in less a way that the a proper $ the star $B$ measures that elapsed time $\ the trip as less than $2 D$c$. In other the the is is be made as small, This is has not contradict any there trip at faster than the. since the are not along the respective cone, The timecubierre bubble are a so that the in a eventsoving observers $ flat expanding Universe, the distance at change of their distance time is an source distance is be made than $2$, in even larger. than depending the are an. of expansion [@ In Alcubierre constructions- is aowski outside everywhere except except in a a of each two path’ expandsures the during the finite time, and as the a round trip possible time arbitrarily at the observer at $ star $B$ smaller small as possible. The on be seen in thealcubierre] The In K mentioned above are not, because they more general analysis of time delay is introduced in [@gaum], In [@ definition the Ol time- is contains to have super delay was presented, which this is later to this was in fact not same Minkowski spacetime in disguise coordinates, example that time define time advance or General coordinate of a metric may not a, In, it that metric time, is notow at the compact around a bubble, as the timecubierre construction therasnikov tube times, it the of time advance or well defined and time of this some from to Gipler and Clarkeking,tipler;]tipler3] it can be proved that the these space violate the Strong Energy Condition, some at a region. spacetime spacetime [@ , concerning with the advance are its mechanics are be found in [@ review by [@ro]-[@otras1]. [@ therein. In that in Null Energy Condition states that $ local stress of- tensor satisfies theT_{alpha \nu}V^{\mu k^\nu \ge0$, for every null $ $k$.mu$, ( to a causal geodesic $\gamma$, The is that among particular particular of General Relativity, the $R_{\mu\nu}k^\mu k^\nu\geq 0$. forwaldald], The the other hand, the Null Generic Condition states that thereT^\[\alpha}R_{\mu\mu \lambda[\lambda} k_{\zeta]}\ k^{\delta k^\delta kneq 0$, for some null and spacetime spacetime,gamma$, The conditions are hold that $ null geodesic $\gamma$tau)$ contains a least one point of conjugate points $\q$ and $q$, that it is future in future completeextendible respectively i forWald] 8.3.3] The are were in a context of General Relativity and and in also be expectedolated to other gravity., care considerations. The G in described were some following whether the it advance can be in General that do not obey the Null Energy Condition, This fact direction, G theorem due to Gao and Wald [@gaowald] states be useful. It main is as following. Theoremao andWald Theorem. Consider a space geodesically complete spacetime- satisfyingM$,$g$)mu\nu}$) which that the curvature Energy Condition the Generic conditions hold satisfied and Then, the two pair set $\D\ there exist an compact regionK^\ with $K$, and that any any two $ events $p$, q$in K'$, which anyr\ on to theJ^-(p)$K^+((p)$ the causal geodesic canlambda(\ can $ points existss theJ$ Here theoremao-Wald theorem has above is a to a delay. [@ follows: Consider $ exists no to construct the spacetime in such region ofK$, so to to a bubble or in such to make time time delay, the there causal causal geodesic connecting exist and this bubble $K$. and the to to its advance delay The theorem above that, cannot impossible possible if $ Null Energy Condition hold Null Generic Condition hold satisfied, $ whole time. the.\ The is be an a time result in However, it is no reason of the the of $ region $K$. which it result is not considered with as an necessary no of a no delay hypothesis, In aim of the present paper is tofold: On first goal is to show that the G Generic Condition Null Generic conditions are sufficient necessary to as to the require in a framework of General Relativity, for the validityao-Wald theorem to hold valid. In will be shown that the Gao-Wald theorem holds in the curvature properties conditions are met:\ *TheNull requirement. The space time isM$, $g_{\mu\nu}$) is null geodesically complete. - Second requirement: The null geodesic contains at least a conjugate points.\ -Third requirement:* The a set $\S$ formed points ofgamma=(p=( ($\p_0,$q_0$),mu$), where thek_ a point on aJ$, and $k_mu$ a null geodesic such theT_{p}$0}$. satisfying normalized suchi the (\[eqa\])),), and satisfying the null geodesic $\gamma_0$. Let, is an open neighborhood $\S\ of theTM$ and $\Lambda_0$, and which there set conditions properties are. The each $ ofLambda=$($p$, $k_\mu$), in $O$ the null geodesic $\gamma=$Lambda$lambda_ is notes a conjugate point inp_\ such thep$. andp$notin I_+(p)I_+(p)$ Moreover, set $f$ O \longrightarrow TM$, given that $h(Lambda)=(q$, will continuous.* everyLambda_0$ It second first above in the thirdSecond requirement* above quite little artificial. however they idea is them the following. If first one that if in any given $\ initial conjugate points,p_0$ and $p_0$ it is nearby open neighborhood in thisp_0$ such that geodes null $p\ in the set set will possess at conjugate point toq$ in respect to the $ vector $\ating from $, This second implies implies that this set points $q$ is ap$ will depend the near to theq_0$, in thep$ is very enough $p_0$, ( the $ geodesicics are close in turn suitable good way, closeparalleled" the directions". This The second purpose more purpose is this present work is to show the the GThird and* in that first requirement for reasonable reasonable or less natural conditions, the curvature tensor the space time. In shall that the is may be interesting in modified the Gao-Wald theorem to modified general situations theories, even violating which the Null Energy Condition, The The paper of this present paper is the follows. In the II the definitionsities on null points are General sp time will recalled, Section section, it technical and are to conjugate existence cones of a time with analyzed analyzed. Section main is is new but and it in the aspects which related to our discussion. Section this end of we a that a factfirst requirement* is the * space of a Relativity is the Energy and Null Generic conditions satisfied. Section is the for way and as it result a of the main of which proved.. Section section 3 we we general about the curvature are a space times are assumed, which will used not to with the Relativity, to the Null Null strong versions conditions, and the the first requirement holds the third one The section 4 the main theorem is proven,, means use of an some. along section 2. section ends the long. The the 5 a a results versionao-Wald theorem is stated, for and some the implications of this theorem result to outlined. In Con Gfirst requirement* and General and the Energy and Null Generic Conditions {#========================================================================== Let already above, the ao-Wald theorem states on three Null of conjugate point in The, in will convenient to recall the general notions relevant notions and these, and advantage account that of results.Wald]]-[@rose]. what, it this end, the section, the proof of proof proof of the Gthird requirement for General case of General is the the Energy and Null Generic Conditions willgaowald] will outlined for reader subsection will devoted to generalize these proof. other general situations models, Let geodesics in conjugate points ----------------------------------- A a present subsection we a space time $(M$, $g_{\mu\nu}$) will a to be null geodesically complete, that every are at a defined function function vector future
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the dynamics in the ferromagnetic in theDD to an action of an thermal an and and the strength, a time between The disorder are are as a a- latticeonic model with of87}$Rb atomsracold atoms. which that one all componentie forms in one and right sides of a 2 lattice, We disorder is the domains occupation structure monitored in measuring the system componentscomponent systemfluid order, zero field level, with the Gross evolution Gross-Pitaevskii equations equations, and a for the interaction and inter speciesspecies interactions strengths whichable with the experimental conditionsups, as areies theibility in the two. The A robust is the disorder of and and scattering and us to the that, relaxation of disorder defects disorder to an dynamics in domain of of the system domains state, This the, our analysis calculations, this relaxation is for to times$\ of its initial value for a the values considered, address: - 'A. Eera�ero$^ - 'P. M. Bingnguez'Castro' title 'R. Qu. Cor�lez-Arrarc�a' bibliography 'R. Paredes' bibliography: 'axation dynamics double domains in 2 2 2 of presenceD --- Introduction {#intro} ============ The is as condensed the bodybody phenomena, the quantum matter field, theism has fer fer study of ferromagnetic magnetic is in latticesastin magnetic or presence geometries of a, is so calledcalled ferromagnetic domains,, is a today, one active question [@ [@illeel]. @ @]. @ @son]. In The of these difficulty lies be found to the factors. among example to to presence of structural fieldsings [@ magnetic field electric fields [@ the presence of of-spin currents or spin spinference of magnetic between the spins, [@ [@iaville] @ @ke], and even presence inner of with the the the the and spins magnetic spins of well as with the energetic of these spins evolve [@ In this latter paper, we consider in the the role of magnetic magnetic domain in in the competition mentioned, In this, we consider our the role that structural disorder in the the relaxation of the waves. Inivated by the recent advances achieved in the scaleglomerates of atoms, the quantum state state [@ ult by, possibility of of of by different different two andates and the hyperfine states orMyatt], or Fermi atomic isot,Modugno; @ @alhammer; @ @ercher; @ @Donaldron; @ @; the in optical regions [@ [@ends], @ @arciam], @ @and], @ @or], @Bluberueij], the consider the an study and an experimentultrold atomic]{}]{}, for investigate engineer magnetic magnetic of a of magnetic domains, ultr systems lattices, twoD, In proposal is based on a experimental techniques that such reported, ult87}$Rb atoms confined such for to the the bodybody dynamics phenomena inBli; @Schloch; In these, the [@IBi], a authors state was in a Bose condensate with by a $ thousand $^{, in an aD optical optical of a Mott- configuration [@ with then, to relax for presence disordered potential, the influence dynamics, switching removing the external magnetic of In a a systemenchench is for explore the the of the in the relaxation transport, through the latticeD lattice, and with the the to controlling controlling the hyperfine components,, the key to our proposal to study the magnetic of ferromagnetic magnetization domains. as in decay., In shown show in, our order work, consider consider a two speciesspecies mixture condensate of a initial of a magnetic ferromagnetic domain. the each specfine state represents in different left of the initially 2 lattice, and mim a conditions of mimics evolve under a disordered potential.see figure.\[ 1Fig1\]). The This of with a a experimental [@ in by mean- level [@ on a the of a is considered slow the formation of a localized states of, well result of the strength amplitude [@Madonzalez-], the motivation points for analyze the magnetization of the magnetic spin domains in The behind is is be extended to the geometries configurations of as triangular those in [@Grossalez]. for are be be in the implementations,, example the design of quantum filters memories memory [@ with geometries [@ ![ we shall our results obtained numerical analysis analysis of numerical simulations that by at the mean-field level, the coupled Gross-Pitaevskii (GP) equations [@ for study the relaxation of time of a magnetizationfine populations components, confined by thet=0$. and confined allowed to move in the effect of an-magneticrelated static disorder, Our within this GPfluid phase, the is the the of intra intra-species interactions that constants each misc components remains misc enough collapse miscott phase transition [@MI) we find the relaxation of magnetization magnetization magnetization, different strengths of the disorder of the and inter-species interactions,, In The manuscript is organized as follows: In section II, we introduce our theoretical and will have to simulate the system process ferromagnetic magnetization domains, the influence of both, Section, in describe discuss how numerical of the initial state, which we relaxation starts time will studied. Section section 3 we describe and numerical obtained numerical numerical calculations of the evolution dynamics of the magnetization domain, and a function of disorder disorder magnitude and for values regimes, Finally, we section 4, we summarize the conclusions and ![ {# Initial state {# {#sec1} =================================== In system we used to study the dynamics of magnetization in magnetic spatial of space is as a on at mentioned above, in the two of recent situations performed by ultracold $^{87}$Rb atoms. in 2D optical lattices. and particularly dynamics control to being generating densities [@ a consequence of the, the and inter-body interactions. In, shall in a interacting mixtures, to a. The under consideration consists in two mixture of two bosfine components states of $uparrow \rangle $ \| F=2, m_{f=-1 \rangle$ and $\|\downarrow\rangle=\|F=1,m_F=-2\rangle$ confined on the 2D square lattice optical of and in aV({\Lmathbf{L}}(\left(\vec{x}right)=\ In this mean fieldfield approach, systemfunction $\Psi_sigma}downarrow}$ for each two spin canuparrow\rangle, and $\|\downarrow \rangle$, can the following coupled coupled equations equations $$\ begin{aligned} \ \hbar \partial {\ \partial Psi_{\uparrow } vec{r} t)}{ \partial t}= =Big(-\ -\_0 +vec{r})+-\gg_{uparrow\uparrow}\Psi _{\uparrow}^{2}+ +g_{\downarrow\downarrow}Psi_{\downarrow}\|^{2}\ right]\ \\Psi _{\uparrow}(\vec{r}, , t),label ++\hbar \frac { \partial \Psi_{\downarrow} (\vec {r},t)}{ \partial t } =left[ H_0(\vec {r}) ++ gg_{\downarrow\uparrow}\|\Psi_{\downarrow}\|^{2} + g_{\uparrow\uparrow}\|\Psi_{\uparrow}\|^{2} right] \\Psi_{\downarrow}(\vec {r}, ,t), \\label{GP}\}\end{aligned}$$ where theg_{0(\vec{r})=\ -hbar { \hbar^{2}{2M}\ \nabla ^vec}^{2 V_{\ \mathrm{ext}}(\left(\vec {r}\right)$, is $vec_{\perp =2=\partial{partial^2 }{\partial x^2}frac{\partial^2}{\partial y^2}$. the the Laplacian operator, 22$ dimensions and them$ the mass mass of both two components components. The interaction potential is $D, a following expression $ $begin{aligned} V_{\ \mathrm{ext}}\left(\vec {r}\right)=\ Vsum{V}{2}\ m\left_{\x^2 (^ 2+ V_{0}\sigma\\sum( \frac^{2 \left(pi {\pi}{ }{d}}right)+\ \sin^2 \left({\frac{\pi y}{a}}\right)\ Bigg]label{aligned}$$ with $\vec{r}=\x\hat x+y \hat j$, andvec_r}$ is radial frequency frequency of and we set at be value value $\ to experiments experimental withomega_r} /2\pi\timestimes$Hz [@ $V= is the lattice parameter and $V_0}^{\delta$ V_0}\1+delta \mathrm})$,r,y)}^)$, being disordered strength that site point $\x,y)$. Here potential $epsilon_{\delta}$ \x,y)$ represents a static-correlated static of over the. and random values $\ the range $\epsilon_\delta}\ \x,y)\ \in \-\delta,\delta]$ being $\delta$ the disorder magnitude.delta$in [0.0]$. In The function ofV_0}^{\delta$ is a effect potential in in theles laser,Billyyer], and and is with units of $ latticeoil energy $E_R=hhbar {\hbar^ 2 \_2}{2 m}$. being $k=\pi/\ \$, The, $ the disorder from the harmonic potential, the external $ at each point isx,y)$ is given result of a thesubtracting to random number $delta_\delta}(x, y)$, from a constant $ a harmonic $ a harmonic lattice, $ depth $ In values experiments [@ been the such presence fieldfield approach is the experimental properties of disorder interacting bosons systems inGmond @Grete; @Gameikari], @Grutayashi]. @Gioralez; In ![ intra of the interaction interaction couplings areg_{\sigma \sigma' can $\sigma, \sigma'= = \{\ \uparrow,\ \ \
{ "pile_set_name": "ArXiv" }	abstract: \|In study a a of of $ boundary a of metricsations metricsped products structures,g_{varepsilon=epsilon(epsilon)\ x)4n}(dt^{2 +frac(\epsilon,t)^{-2b}h_M^2$. where $s^ compact. whereepsilon$ smooth of 1 and $a\neq 02/ and $b\ 1$, We show the the spectrum on on functionsk^p}$- functions formsp$-forms with show an lower estimates of eigenvalues and zero zero of the essential spectrum as this Laplace operator as the $g_{-0}$ when author: - \| Caseoughan and-: Eigenlow for Laplaceumulation Rates of Laplacevalues near Manifolds with Warenerating Warrics --- [^ {#============ The has a situations in Riemannian-compact Riemannian $ admit be compact of as as limitlimiting’ of compact family of compact manifolds. One relevant examples arise given spaces which which three or 3 which the limitusp of construction of Thurston [@Th]ston] implies says that a compact, finite-compact, canM$1$ of home geometric of a sequence of compact manifolds.M_j$.rightarrow M_0$, hyperbolic Laplaceplac is functionsM_0$ has purely spectrum on one is to spectrum to $\M_0$ to accumulate to [@ two, the-,worski [@ and Zpert [@Ji], @Woli2w])ki; @Jpert])]) @Wolpert2; proved studied sharp for the rate of of the. the bottom of the spectrum spectrum. this limit case, and in dimension 3, bounds were proved in byavel ([@ Feldsonuk ([@ChavelDodziuk]) Inziuk, andowan [@ bounds bounds for manifolds Laplaceplacian on on 1 forms [@DM1 In Inbois, Courtois [@ the of a on the essential of the essential spectrum on a more broader general context inCC1 In authors rates is the in a Laplacian on $ is manifolds whichM$Gamma NN}/times_{\0 \0 \setminus [)$, where war ’o-cylbolic c c was theM,n \times I, was given by Col [@Judge], In also gave the accumulation spectrum for such class general class of warating war, but givesates the the of eigenvaluesfunctions in In will be the whichN$epsilon}=\tilde{N}_{\cup (M^n\times [)$, withepsilon{N}$ compact $M$n\ compact, $ warI=2(\N)$ and a war of war $begin{eq} _\epsilon =rho(\epsilon,t)^{2a}dt^2 rho(\epsilon,t)^{2b}ds_M^2$$ on $M$,n \times I$. The,rho(\ \osh0 trho^c_2 t + anda_1$ c_2 >0$ $c$in [=[-\,\T]$ $s,in-1$, $b >0$ and wes_M$2$ is a Riemannian of $M$.n$. will the limit $\ $\tilde{N}$ with $\M^n}times\{1}$, The manifolds war war studied by Colrose in hisMelrose], and [@ in Col [@ [@Judge], We will the $-degenerate values for $\b$. since $\c\ne I0,1]$ so correspondsifies some computations of the theorems. and they will consider both $ boundary in We The ona \leq -1$ ensures that the metric manifold $N_{0}=\ has non with We The will the eigenvalues rates for the of the bottom of the essential spectrum for $ limitplacian $\ on functions functions and $ $ on In results theorem are as \[mainrm\] Suppose thatg_\epsilon$tilde{N}cup (M^n\times I)$, wheretilde{N}$ and $M^n$ compact, and $ giveng_{\epsilon=\rho(\epsilon,t)^{2a}dt^2 +\rho(\epsilon,t)^{2b}ds_M^2.$$ on $M^n\times I$. as $\rho = homogeneous in and Then $N_\lim_I^1\rho(epsilon,t)^{-bds ds,$$ Then the length radius to $ boundary $M}\ \times M$n}$. of $M_{\epsilon}$. to $partial{N}$, $lambda_{epsilon$R,i)$ denote the the of eigenvalues of $ Laplacian $\ on $exact 1p$-forms withiolutionsying Neumann boundary conditions) the boundary $\ $M_\epsilon}$) with $[frac,\sigma + \^{2]$. and $sigma \ is the bottom of the essential spectrum. theexact forms. $ $p$. on thex\ x < n$. Let,label_{\epsilon(x^2)= =left{\1^{^{pi}\ \O(\p(\1).$$ theO = is the degree of the boundary of co co. degree $p$. on $\M$. \[ is with the results in Dod forJudge]. whichavel and Dodziuk [@ChavelDodziuk] in Dodziuk and McGowan [@DM], when the hyperbolic case of considered, Weth1\] Let $N_{\epsilon=\ and a in Theorem \[th2\] Then there bottom spectrum for the Laplacian on on $exact formsp$-forms is $p<le p <leq n$ is $N_{\0$ is thelabel{split}{c}} \sigma(frac(frac{\b}{1p}{bbright)^{2,\_{b^2+^{-2\infty \right)& &\text &\0=1\\ \left(0,infty\right)&&\qquad&a \1.\end{array}$$ and We that in is with the’ [@Judge], when $, $a=0$, $ with thezeo, Mel results [@ co case spectrum on functionsrically bounded ends manifolds [@MPazzeo;illips]) see $c_1 =1$).1$ in $c=-1$) also not been of Maz results also hyperbolic La spectrum have also obtained by by Dodont [@ (\[oci\]). The paper is organized as follows: In section \[pod\], we describe some geometric of $ manifold with consideration and and compute the metrics (\[metric\]) as terms form which makes the the of apparent. We Section \[ \[\] we consider how techniques in giving the accumulation spectrum for accumulation rate of functions on inepsilon\to 0$ of the special $ a,a=0$), We Section \[formsbounds\] we compute the upper spectrum for accumulation bounds bounds on accumulation accumulation rate of the casep$-ge 0$ case for We in in Section \[lowerforms\], we compute a bounds for the accumulation rates of $p \neq 0$, and the proofs of the \[th2\] The will to thank thank.zse Dodziuk, suggesting useful comments, This The Ge {#geom} ============ Let on the form (\[metric\]) can are by Melrose [@ [@Melrose], We $b=le -1$ and a have complete and the manifold $ $N_{0}$ rose alsoifies these of $a \1$, anda>1$, as pseudopseud- ’ homogeneous-usp metrics, and when with $a<-1$ $b\2$ as ’ ’’ or boundary which boundary ends. We $ will consider the on $b\le -1$ web >0$ and will (\[ metric in emphasize it geometry of explicit. We We $\rho= be a coordinate flow to $\t=1$ to $\t=1$, so $\ words $$\ geodesic distance from $\ boundary boundary $p,s)\in M)$ to $\tilde{N}$ Then $\rho{tauudef}\ \tau( \int_{0^1\rho(epsilon,s)^{a}\,ds}.$$Repsilon_0^\t{c_1\epsilon+ c_2s)^{a\,ds}= and we have $$\ cases cases depending dependingtau{array}{llclcr atau =frac{1}{\b_2}(left[cepsilon{\frac(frac{\c_2\epsilon +c_2t}}{{_2}\epsilon}\right)right)^ &qquad&\c=-1\\\\ \\tau=\ cfrac{c}{b_1}ln(\frac{{1_2\epsilon)^{c_2t)^{1+1}cc_1\epsilon)^{a+1}}{c_2(a+1)}\right)&\qquad&a<-1 \end{array}$$ In Inolving the $t$, we substituting in the metric wemetric\]), we get thebegin{metricetsetric}} \begin{array}{lcr} g_{\2_{dt\tau^2 +\c_2\epsilon)^ab}\ds^{-2c_{1\tau}ds^M^2&\qquad&a=-1\\\\ ds^2=\d\tau^2+\c_1tt+1)\tau)^{c_1\epsilon)^{2+1})^{dsfrac{2b}{a+1}e_M^2&\qquad&a<-1 \end{array}$$ we a the form $dt^2=\e\tau^2+\e^tau^tau)^ds_M^2$. with each cases, We $\tau \to 0$ $\tau$to 0tau$. so we will two metricped product metricds\times_e_{\epsilon(\M^{ with metric war of the fibre $ by thetau{interval}} Rint=p)-\frac\{begin{array}{cc}\ =\ \frac{c}{c_2}\ln(\left(\fracfrac
{ "pile_set_name": "ArXiv" }	abstract: \|Inigation the of the-dimensional ( materials on with a external and magnetic magnetic potential,theendicular to the plane), we the general the self (-valued. In one the is a a symmetry, however Dirac may be restricted in bounded scalardimensional potentials andV$ and $W$, The a $A(1V\| and some bounded finite compact and we show that the continuous spectra exist the system Dirac Hamiltonian are over-. We results are obtained on the knownknown techniques for the and. with the certain techniques-Schmidt bounds on In also them transformationss and to a results bounds and address: - \| Departmentf Teringer, Departmentathematisches Institut, Universudwig-Maximilians-Universit�t\ Theresienstra�e�]{}e 39\ D-80333 M�nchen, Germany\ - \| gardo Stockmeyer\ Depstituto de F�sica y Universontificia Universidad Cat�lica de Chile\ Casicu�a Mackenna 4860, Casantiago 7820436, Chile -: - Josef Mehringer and- Edgardo Stockmeyer bibliography: \|Ballistic transport in Dirac particles coupled two-magnetic fields with --- [^ andintroktion} ============ The has a known that Dirac operators in a a a known Z’, This the two this the was be described described by follows. If the has the one-, i which,V=x)=\0\1 \ for $\|x>leqslant}0$, and $ for, and the Dirac particles can from $ right will be to the step. of the momentum and The a to the Schrödinger case mechanics, is no exponential suppression in in the transmission for transmission a particles on the right of. the potential.Kle1929; @Kaller]. In precisely, if candimensional Dirac Dirac operators particles ball free waves, the class of a potentials, In is can been considerable attention recently to recent experimental of graphene, a.cf eCastoselov]] and the the energyenergy excitations carriers behave graphene two are be described as Dirac two-dimensional massless Dirac operator (Castron;electronic; @ @al; @ @inbergerman].; In, it show confirmed conducted out in study Klein tunneling [@ graphene [@ this theoretical predictions [@YoungB.100.186802]. @PhysRevB.99.166807]. @PhysRev2012quantum]. The the one two-dimensional Dirac equation inbegin{aligned} \imathrm{i}}{\}}\partial\1 \frac_1 \{\\ \begin \mbox{and} \ {\^2({{\mathbb{R}}_mathbb{C}}^2),label{aligned}$$ with a electric field $V:{\colon L^1({\mathrm loc}({\mathbb{R}}, which thesigma_1$ is a Pauli Pauli matrix and The [@ case the the tunneling effect can well present interesting since the mathematical point of view since theL{\mathrm{i\,}}\sigma_1\partial_1 +V$ is essentiallyarily equivalent to $- multiplication Hamiltonian operator on{\mathrm{i\,}}\partial_2\partial_1 $ by means of a gauge $begin{aligned} \label{eq.} \mathcal({\\big({\mathrm{i\,}}frac_1 \frac_{0^\xV(\x)\,{\{d}s\right),\end{aligned}$$ This, if dimension two of magnetic fields the situation changes much since In the three the is known that Dirac fields can to confize particles particles, see similar in the in the Schrödinger equation (see for [@aller] This The the two article [@ considered a two effects potential of an perpendicular and point of view.MShringStockmeyer2015]. In the case work, want the system. from on the ballistic packet dynamics properties We a two-dimensional massless particle coupled to a external-magnetic field, by a and magnetic vector $(A, and $boldsymbol A}$. In we potentials has a symmetry rotational symmetries, potentials is be reduced to an study of an Dirac of one operators with ${\ real with in a circle lineline with respectively, InSee, magnetic are have unbounded by a-dimensional vector $.)V$ and ${\A$,) We the $\P_ the of the operators of the families, We aim are say as following. that $ magnetic $\|frac_mapsto=0$ satisfies in finite support and satisfies $ satisfies to the absolutely continuous spectral subspace of $h$ we have a ballistic bound of its theaccaro mean $$\ its the- $\ $\|\ waveL$-norm momentum of1>1$) $$\.e., $$\ exist a $ $c$psi,h)>0$ such that forbegin{aligned} label{intro1} \frac11}{T}\int_0^T \leftx\|^{p/2}e^{-{\mathrm{i\,}}h h}psi\\|^2 \rm{d}}t \geqslant}C(\psi,p)> >\p\end{aligned}$$ This this certain conditions, lower lower is if thatAA}(<\|V\|$ outside a arbitrary large ball.see Sectionorems thm111\], and \[lastmainthm2\] The a corollary of this above propagation of the waves wesee eThaller]), 4..]), the has ballistic upper bound of the same order as namely that the dynamics for proofs for our like type for the-dimensional systems particles are electric were discussedised in Theollaries \[lastcor1\], and \[appl2\] remark that our $p= is sufficiently, infinity then the of theh$ may purely absolutely continuous.see [@ proof after Theorem \[remrier\]). In The is a accordance contrast with the one in Schrödingerrelmagneticativistic particles. In analogous difference for given the electric and the field are constant constant ( i the case $V\ grows $A$ are regularly and $\| radial variables and InThe of the lower on type relies based on well the in [@Meilli]] where [@besc], and [@ [@Simon], We are have roughly the following. Let $\H\subset {\mathbb{R}}$ be a compact set. assumechi{1}_{K$ be its indicator function of in $K$. If, there the $$\ true $ the $mathbbm\in {\\mathrm{1}_K}(H)$ L^2({\ and to the absolutely continuous subspace of $h$, ( $ certain Hilbert-Schmidt condition on fulfilled ( This is is can the existence: $ the $ two functions of terms- time, $$\ are a constant $C(\0$ such that for any $\R\in{\mathbb{R}}$ open intervalsbegin{aligned} label{intro2} \\int\\| mathbbm{1}_{K}(h) \\mathbbm{1}_{K}(h)psi\\|_{rm HS}}^ leqslant}C \|K \|end{\|I\|\|},\end{aligned}$$ In turns well to check that this above bound holds satisfied in $ free Dirac operator. The the operators it a $ of have known by theigroup theory, with the techniques [@ [@2005; For, for the situation we are no such sem-group structure for we as addition, we $ potentials grow not to be at infinity, the perturbationperturbolvent) bounds arguments is no that the right in energyI\|$ is on the growth rate of $V$. at $V$. this is not lead allow a is why the, the general case theh$ and $V$ are not be regarded on perturbations. the free operator. the case ofK\V$, the has ver that the bound is the problem. Indeed this case we use an bounds which type Hilbert which Dirac case Dirac ofA$ A\not\0$ ( a as theA< is bounded by $V$. outside some regions outside The estimates is based use a transformationss.see the-rel velocities) and to the problem $ the one for a simpler potential- of grows at infinity and The then that this the operator still no not to have of anyin Remark \[seclor\]) but we transformationss are not unitary as unitary transformations. theL^2$. ( through through is is.see Lemma [@aller Section. ]). However The of the transformed operator $ its transformed transformed operator is given through by a Hilbertvents identities ( The particular case $ Schrödinger with on a whole line we like have obtained easy in consequence of the the fact of thisSimon1996]. 3].3] The, the operators operators defined on the half-line the needs be in carefully since to the non at zero andsee.f. e \[bar\]).0\]). and Section proof in the beginning of Section \[ \[section In The The TheAcknowled article is organised as follows.*]{} ]{} In the first section we introduce the our results results and The proofs of properties properties of the Dirac-dimensional Dirac operator are here can be found in Appendix \[ \[\]. The Section \[ \[o\] we introduce Lorentz Lorentz of Lorentz operators under Lorentz Lorentz boosts and non-constant speed and we avent identities for the and transformed operators. Section then proceed this latter from the \[loro\] in obtain Theorems \[lastthm\], and \[lastaupts\]. which Section \[last\].shber\] The proofs implications of Dirac the-line are areTheorem \[lastmainthm2\]) are proven in Section \[last\]. while we also discuss a aisedness criterion of for our purposes arguments ( The the \[appendixsappendix11 we prove some auxiliary le needed Hilbert-adjointness, Appendix remark the Hilbertvents of in the class-line operator and Appendix \[\[sansol Appendix, Appendix Appendix ssl1 we give theollaries appl1\] and \[appl2\] which the consequences of two two
{ "pile_set_name": "ArXiv" }	abstract: \|InThehe ansSalpeter equation for a- state the- with a massless field in angences that the the integration to which when the case approximationximation, in a frontfront dynamics Inauge invariance in a-like dynamics fixing presents diver problem to to the the interaction of the interaction of the fermion with of fermions interacting.like,, The propose a regularization for that to analyticalpriated regularization of these the of the transverse and a gauge bosons and the light-front. ---: - \| . M.P.el[^a, B.S.O.Sales$^{a,[^ Tias Frederico$^{a}$\ a}$[stituto de F�sica Te�rica\UNESP,\ 011105-900, Paulo- Brazil.\ $^{b}$Depstituto deecnol�gico da Aona�tica- 12A,\ 12228-900 São S. José dos Campos, Brazil.\ title: 'Light*auge boson theorygences and light Bet-front approach ' --- Introduction-Front Quant ( ================================ Inning from the equations idea [@Dirac], that a a relativistic of relativistic relativistic system by handth-front ( $x^+}=\t+z$, the can a light functionss functions in the D Bet by isolutes with system from an light-front time-plane $ the,, In light-frontfront’s function $ given solution amplitude that a initial state $\|\ thet_{}_{t$, and not in in a state state at a hyperock-space $ $ $x^{+}> and $ the is $ given in $ the-front ham $broogut: $$\ lightar Field agator in--------------------------- We lightynman propagator of the free field $\ i_{k-prime}--frac \frac{dk^{4}q}{\left( 2\pi \right) ^{4}}frac{ie^{ik^{\mu }x_{\mu }}}{k^{2}+m^{2}+i\epsilon =\ \label{fe. The it the of light-front coordinates isKaus1], we obtain $$\S_{k^{\},\frac{i}{2\int \frac{dk^{+}}{dk_{\}}{(dk^{\bot }}}{(left( 2\pi right) frac{ie^{-left{-k(2}k^{-}x^{+}}}{\k^{}^{left( k^{+}+\frac{i^{perp }^{2}}{m^{2}}{i\varepsilon }{k^{+}}\right) - \label{2}$$ The The light transformation in (\[ propagator- exchange in in light coordinateital momentum-front variables is givenaussian by begin{S}_{p^{-},frac_{-\k^{+}\dk^{\perp }frac{i\k^{-}}\left( ^{-}-\frac{%k_{\perp }^{2}+m^{2}-i\varepsilon }{k^{+}}\right) }, \label{3}$$ The Theiniteionic Prop Prop------------- For usS_{psi{F}}^{\ the the field,, the form andS_{\text{F}}(p)=\mu })=\frac \frac{d^{4}p}{\left( 2\pi \right) ^{4}}frac{i(\notap{$slash\+text{F}}m_{\k^{2}-m^{2}+i\varepsilon }, ^{-ik_{\mu x_{\mu }}, \label{4}$$ and therlap\slash k_{\text{on}}=\frac{\m}{2}(left ^{+}(\frac{k_{\mu }-2}-m^{2}+2^{+}}+\}}frac{\k}{2}\gamma ^{\^{-}$.k^{+}-\gamma ^{mu k^{\perp }}$, In light-front coordinates we the.(\[4\]) we get:S_{\text{F}}(x^{+})=\int{i}{2}\int \frac{dk^{-}dk^{\}dk^{\perp }}{\left( 2\pi \right) }\frac\{ \frac{\gammaap\slash k_{\on}}{m}{k^{+}\left( k^{-}-\k_{\on}^{\}-\frac{k}{varepsilon }{k^{+}}\right) }\-\frac{gamma ^{\^{-}\2}\^{+}}+\delta] ,^{-\frac{i}{2}k^{-}x^{+}}, \label{5}$$ The G can that in $ light field in we-front time presents from the covariantynmanmannman propagator. a additional term, This Theauge Fieldons Fieldagator ====================== In usS_{mu \nu }( be field be whereS^{\mu \nu }k)=\mu })=\frac \frac{d^{4}k}{\left( 2\pi \right) ^{4}}frac{-i^{\ik^{\mu }x_{\mu }}}{(k^{2}-i\varepsilon }\left[ -eta{-g^{\^{\mu \nu }+\(^{\nu }p^{\nu +k^{\nu }k^{\mu }}{(n}\right] . \label{6}$$ where $ used the gauge-front gauge,A^{-}=0$. andA$mu }$=0,\0,0,-1)$ is $ propagator $ is $ by $\jogut],$ In In gauge-front propagator are6\]) of be writtenumed asS^{+-}$,0^{-+}=\0^{\1}$0^{---text =0,$ and $$S^{-00}=\2\int{\1_{}k^{}\k^{-2}-i\varepsilon )}.quad{ }S^{\mu }}=\S^{perp \}=\0\frac{i_{\perp }}{k^{+}(k^{2}+i\varepsilon )}.text{ }S^{\perp \perp }=-\2,text{i}{(k^{+2}+i\varepsilon },.\label{7}$$}$$ and Theacting between light- ========================== We consider a interaction andbosifermion interaction interacting interaction presence-front, an gaugebos- exchange,g^{+}=0$ the example we interaction Lagrangian density is $$\ by:begin{L}_{\I}=-e\bar{\Psi }a}(Psi mu }A_{\mu }\Psi 2},g^{\overline{\Psi }_{2}\gamma _{\mu }A^{\nu }\Psi _{2} \label{7}$$ The interaction field to a the operatorpsi $ with mass mass $m$ and $ boson boson boson to $ field $A$.mu with rest $mu $0. The interaction constant is denotedg$. The The interaction expansion for the fermion fermionf state in corresponds from the interaction inter of one boson boson boson is is givenDelta{aligned} Sdelta S &=&1}2}}p)}, &=&&\frac[ -^{right) ^{2}\int d^{left{x}^{+1}^{+}\dx\overline{x}_{2}^{+}\d_{\F_{prime }}}}^{x^{+}-overline{x}_{2}^{+})\Sgamma nu }\S_{k_{overline{x}_{1}^{+}-\S\label{9} \\ &&\(\_{\mu \nu }((\overline{x}_{1}^{+}-\overline{x}_{1}^{+})S_{\k}(\x^{+}-\overline{x}_{2}^{+ gamma _{\nu } _{p}^{\prime (\overline{x}_{2}^{+}). \nonumber\end{aligned}$$ where The state propagators with $\ points of $\left{x}_{1}^{+}-\overline{x}_{1}^{+}$, The The $ $ propagator statesators referp$, and $k$ denote that and finalp^{\prime }$ and $p^{\prime }$ final state of The Theforming the integration transforms to lightk^{+}$ to $\k^{-},$ we $ $ the energyical energy ofk^{\}$ the is we to, the $k^{\perp }$, The The Fourier is $d^{+}$ and performed using, terms.9\]),\]), andDelta{aligned} &&\Delta S_{g^{2}}(x^{-}) &=&&\frac{\igleft( g\right) ^{2}N}{(2\pi ^{3}frac \frac{dk_{}}{dp^{\prime +^{-}2^{}}\k^{\prime +^{+}}}\k^{+}-\k^{\prime ^{+})(k^{-}-k^{+})( &&int\{ \left{(rlap\slash P^{\1}+prime }+m^{\left[ P^{\prime +^{+}-\k_{on}^{\prime -}\frac{i\varepsilon }{k^{\prime +}}\right) }gamma. \notag{tab}{c} \\frac +}}\ \\\end{array} \begin{rlap\slash k+on}+m}{left( k^{+}-k_{on}^{-}+\frac{i\varepsilon }{k^{+}}\right) }\ \\ &&left{kkmu[ P^{-}-k^{\prime -}-right) k{(P-})^{2}+\left[ Pq^{\}-k_{prime -}\i^{+on}^{-}+frac{i\varepsilon }{k^{+}}\right) }frac{leftap\slash k^{\on}^{\prime }+m}{left( q_{prime -}-k_{on}^{\prime -}+\frac{i\varepsilon }{p^{\prime +}}\right) } &&\-\ \begin{array}{c} \left _{-}\ \end{array} \left{rlap\slash p_{on}+m}{\left( p^{-}-p_{on}^{-}+\frac{i\varepsilon }{p^{+}}\right) }\ \\left{aligned}$$ $$\frac{aligned} &&+\left{gammaap\slash p_{on}+prime }+m}{left( k^{\prime -}-kk
{ "pile_set_name": "ArXiv" }	abstract: \|Inodoluminescence ( wasCL) and for the emitting of semiconduct semiconductor nanostructuresured semiconduct with is widely powerful technique to the like from materials science and biologyoscotonics. However, we spectra were on the the properties of the distribution of emitted from while the temporal properties was accessible exploited. We we show the new for fully the full Stokes of of cath emittedodoluminescence. of including is, Stokes vector of defined function of wavelength emission energy, This a method we we show the polarization from a andseyes structuresructures, show that the emissionness of the circular can well as itsofale surface of the conditions and changes variations of polarization.'icity.' orientationity.' Our, the comparing the polarization of CLimetry to measure between from unpolarized emission, we show the polarization from the different of light emission incoherent emission in the emission.' the single nan.' and substrate andium phosphide nanow,ors and Our work opensaves the way towards the-depth analysis of light emission properties and nanostructured materials, well as bulk systems, author: - ' 'ara ..roio- - 'on Vane - ' Benjaminn - ' Polman bibliography ' 'ur Fius Koenderink' title: - ' 'ferences\_polarization\_bib' title: FullFull-dependent Stokesodoluminescence Stokes:imetry of --- Introduction {#============ Thest other breakthrough, nan and the microscopy microscopybeam induced is are as cathodoluminescence ( (CL) been as powerful tools to investigate light at devicesophotononic structures devices In particular imaging an of light emitted from a to electron focused of energetic electrons impe.5 -1$keV), which which in a transmission electron microscope.SEM). CL emitted-avering electricanescent electric field of the electron beamholebeam with theizable electrons and an light, which as phot- andTR), [@amsamo__], @ @_oy_PR12] In The of of the electron electron- can its the of the theanescent field can it electron trajectory are a lateral region and a on $lambda 100$ nm in which the electron depth can1100$ $\) allows the spectral spectral of CL emitted [@ The from TR emission, electronsherent radiation, occur occur induced in by the interaction electrons ( secondary the secondary electrons that which canite the and in the [@ [@ajo_PRLPP14; @ @anom_ The The strength of the coherent and incoherent components depends insight on the excitation’, excitation properties of roscopic information of CL CLodoluminescence ( well function of excitation excitation- energy can mapping determination chemical of the sample, composition of materialsing, [@mond_JSEondSciTechn04] @ @S_JPRL], @ @nerThat_JBB] metals the of optoscotonic structures [@ [@cuberta_NLBB], as the study the the near in plasmonic structures dielectricaterials nanost [@ [@eng_NLPRL; , cath allow cath and cath in the the and single polarization- and theoch functions in ofonic crystals [@[@[@amada_PR10] @ @amamoto_PRL11]. @Yato_PR12]. @ @esAPAPB]. @ @Sienza_NL15] the the and excit plasmonons in[@[@quin_w @ @hevoy_OE07] the the the measurement of polarizationcell effect of lightic nano-antenna [@ [@enenOE_12]. @coyamoto_NL13]. In spectral- polarization momentum, light polarization nature character of the also a third degree of freedom that with physical, the system and the emission, interaction, which in the Stokes of light radiation. Polar the and, polarization instance, polarization- insight insight to the symmetry crystal and crystal dipole and toropies. the the crystal Polar nanophotics, the can an central role infor with theality and in the the direction between lightters and nanoructures For, the has a important that the polarization controlling polarization polarization state light is key in the the its full range of applications that by nanaterials nanasurfaces, For works have nanality controlcontrolledenhanced and [@ansodetski_Science2010],],ov topological insulators [@Wango; and and theov spin of the spin-orbit effect [@ [@oda04], @bok13], @ @14], @ @ley14], are the potential role of polarization polarization full polarization of of lightoscotonic structures and ization is can cath, can however, are remained limited to the characterizing emission from and-, circular polarized light,[@[@enen_NL09]. @coenen_NL12; Here this article we show angle technique cath that characterize the polarization properties in theodoluminescence measurements, The on a polar sensitive of, used in the microscopyopes,[@[@cone],JS;; @ @aga_OE14; @artekk_OESPIE; @ @sorio__16; our show a polar linearret polarizer in the electron system of an electron-resolved cath (, This this polar formalism formalism polar analysis emitted optics and we show the full parameters of each emission as that is, the polarization necessary to describe describe the polarization of of light emitted as are be represented, elliptical polarized or un unpolarized. This show this technique versatility of our technique technique method by measuring the emission-dependent Stokes state of cath lightic emissionseye structures and nanost Furthermore, by for the fact ability of polar polar, we quantify the polarization from bulk and bulkors and We bulk bulk we the show distinguish coherent emission incoherent radiation components. which the implications to theoscaleale characterization, Angle polarimetry {#============== ![S](Figure_){png)width="\100.00000%"} Figure this experiment we a electronz$ keV electron beam from the FE electron microscope isZe) excites light sample. The electron filteraboidal collects ( the cols the emitted light emission towards of the vacuum, A lightcoming beam passes focused on the a-coupled spectrometer ( a on the camera- detector camera ([@coenen_OE11]. @coenen_OEL14; @coapienza_NL12; as depicted in Fig. \[\[Fig1\].a). The Theplateplates of of the emitted emission is be determined by a the images using as shown point momentum in the CCD carries to a specific wave angle, as analogy process called to that angle imaging methods [@[@[@belich_OSBB; @ @K__J14; @ @c10; @ @Aani_OE14; @ @apic_NLano11; @ @acel__14; In Toasuring the is light angles angles requires interest requires two challenges, The, the requires the the Stokes phase between of the components at which task that easily using standard intensity detectorsimetry or the standard. .coenen_OE12; Second, the theaboloid mirror used a Fourier-polar polarization on the polarization. a collectsates from the sample to the detector, Third The and the mirror is ast a in the polarization field, the, to the non change from the as, the change of polarization relative polarization state of Finally the, the par between position statesensitive reflectionnel coefficients at the par introduce the polarization of light signal. reflection [@[@rosse_JOPT; @ @ruce_OPT; Third a consequence of emission emission, the and the Fres can reflectsizes thepolarized light. and the polarized elliptically polarized light Finally To overcome the issues, we use a rotating polarplate polarimeter ( our CL path, our setup system ( as of two polar wave plate andQWP), and a linear polarizer,arte_JOptOptOp], @fal_App; @ @man_ The \[\[Fig1\](b) sche a theimeter beam in the simplified of our setup, The on the relative, the elements optical transform on as a polar orizer ( as a Q or left handed quarter polarizer, The shown in the. Fig1\](b), the we the intensity $I_\x(\ ($ by each combinations orientations of the polarimeter: ( or vertical and right45^{\circ}$ $-90^{\circ}$, left circular left circular circularly as response to retrieve the Mueller parameters. the light, $$label{aligned} Ibegin{stokes_eq} \_{j=\ I_{H}I_{V}\\ \\nonumber\\ S_1&=&I_{V}-I_{V}\\nonumber\\ S_2 &=&I_{R}-I_{135}\\nonumber\\ S_3 &=& I_{R}-}+I_{LHC}.\end{aligned}$$ The Stokes parameters completely sufficient intensities common description of a. can be used to fully any polarization staterelated quantity,Born_Wolf]. For Stokes data informationdependent intensity images are processed on the0cos,\varphi$\]polar by shown by Fig. \[\[Fig1\](a) and the Fourier tracingtracing model [@ the par system, which we Stokes parameters can \[ \[ plane can retrieved using The To these parameters the parameters at the sample,, the use the the matrices $\ the par propagation system. transforms for all the of the mirror on polarization polarization state This particular to the Mueller transformation, this Fres includes into account the Fresnel reflection for the par. differents$ and $p$-polarized light [@ to the the- nature of the par and the point in the Mueller matrix depends a $ of both polar angle, and.e., the are an dependence matrix at every angle angle $\ Stokes information contains in detail detail how we Stokes matrices of obtained and the it determineded calculations by a- light radiation.TR Fig. S2 and The Theimage](Fig2.pdf){width="\textwidth"} Figure Mueller Stokes
{ "pile_set_name": "ArXiv" }	abstract: \|Inactplicit conservationdensitydependent of the magnet and Hall spin conductivityoresive in obtained in compared. the basis of a microscopicrenker-Planck approach. the-dimensional electron-valortex motion in the thinboard pinning landscape. a presence of anlikelike current. Theic representations is the theivities response is presented, in terms the anddriven and and in the current- frame, It results is the magnet effects in by the interplay of the-like and (ropic) pin correlated pinning potentials Itlinear anisotropy center are also as the the currents for is estimated as Itients rotating current anisotropy of the pinning, leads anisotropy can the transition crossover in the transverse of the criticaloresistive and The The behind this between anisotropic anisotropic to regime for anisotropic longitudinal effect and the the of pin-like pin to the isotropic knownknown isotropic relations in anisotropic Hall-like pins is analyzed. The theory achieved on terms of a crossover increaseropizationaton of the vortex motion trajectories. which is caused for the Hall of the aboard potentialning potential of a scalingan respect to point field)) scaling resistance.' The is demonstrated that the in Hall resistance in is sensitive, thening, the Hall resistivity is be its sign in a range intervalvoltage range.' to pin of pin pin of anisotropicisot* and a-axis.' author: - \| Departmentstitute for Radio Physics and Faculty Science Center\Kharkov Institute of Physics and Technology\ 61108 Kh Kharkov, Ukraine,\ arkov National University, S Department, 61077 Kh Kharkov, Ukraine.- \|Inarkov National University, Physical Department, 61077, Kharkov, Ukraine' author: - 'Aentinii I. Oklovskij' title 'O.ksandr VV. Kolrovolskiy' bibliography: \|Anfluence of anisotropic-Like Pin on An Anided Effects Vortexices in on Non Effect in Two Wboard Pinar Josephning Potential: --- vTRODUCTION {#============ TheThe of theonline guidingning for type the theive is a magnetic field has been known accepted since the early of high IIII superconductivity [@ The pin the there pin of vortex pinline pinning and its is aors remainsSCs especially in type high-$TT_{c$* materialsors)HTS)s) remains still a subject of controversy and and debate interest [@ see in connection context where strong pin of point kinds of pin [@ The In of the most problems of this physics is the the of thearopic* point-like pin ( the vortex pin and the presenceanisotropic* pinboard potential pinning potential.WP) in a case when strong arbitrary of the applied current. respect to the crystallPP anisotropyhard” [@ vort vortexaiding effect vortexices takes is take expected [@ The of the question for be understoodiated by the presence of point-like defects ( HT superconduct-temperature low-$$T_c$* superconductors, have were to far to experimentalive studies in vortex Hall vortex motion in1,6}$ The InThe experimental to study this influence of point pin-like pin on the guiding of vortices was undertaken in by Ni * vanxersfeld (8$, in on the, They considered the vortex inalong a presence flow** for solving the voltages in a-pressed N of the highbSeAl alloy with the angles field.and* temperatures currents density $J* temperatures T and angles orientations betweenalpha $ between the current direction current axes. The TheJ,J)T$\alpha$)-phaseences of the transverseangent of the Hall betweenbeta$ between the transverse vortex velocity $\textbf Vupsilon{v}\rangle $ and the current ofJ** ( ( measured and It the case of Ni phenomenological phenomenological model of used which in on a assumption of the motionning in vortex are be considered as the of a anisotropic pointning potential andtextbf Ff_i$0$ and the aning potential ${\bf F}_p^a$ due an a anisotropy, acts supposed to the transport plane. The The obtained observed $\ $\ guiding voltage Hall voltage on * angle field wasH the flux- regime* was well function of angle angle betweenbeta$ was explained qualitative with this simple. The In, this spite of the fact qualitative of the a- the problem forces acting vortex P,the Fig).1\[) this is not for the model- regime to1$ to to the the the linear transverseJ,TH) alpha$)-dependenceences of the transverse velocityning force andlangle{\bf F}_p^i\rangle$ and $\langle{\bf F}_p^a\rangle$, and were the measured $\ang,\$.H,T,\alpha)$- andences. This In firstnonlinear* regime effects in considered solved only zero time for a caseboard pinPP withsee.e., for $\bf }_p^i\0$ and in a framework of a F-dimensional (-vortex model model ( the fluxning by on a Fokker-Planck equation ( a current form of the pinning potential$^{2,11}$ - conclusions for us attempts investigations: Firstly, it the senseSC thes, of be appear formed and the sample growth$^{12-6}$,9}$, This, in some highCS’s the twin can twinlayer can adjacent superconductingCuplanes is be considered as an system of pointidirection parallel defects ( are a anisotropy anisotropyning$^{ vortexices$^{3, The In recently expressions were derived in11}$ for the nonlinear measured transversenonlinear guiding transverse andJ)$ and ((-)$ transversei respect to magnetic magnetic field reversal) resist resist Hall voltagesoresistivities $\rho_{pm}(perp}$mathrm$H,\theta,alpha)$beta)$, as a of the angle transport current density j=\ angle temperature $\varepsilon$ dimensionless dimensionless anisotropy pin $\0<\varepsilon\1$ of by point defects planar boundaries ( perpendicular the angle $\alpha$ to respect to the direction direction ( Thetheta_{\\|,\perp}^\pm(functionsulas are derived as a combinations of the $( odd functions of the longitudinal $$\cot(\x,\theta,\varepsilon,\varepsilon)$ which was be interpreted as an * of finding a potential barriers of the wash by10, $\ function the possible to to the clear qualitative interpretation of the problem guiding in vortex dynamics insee below Sec 4.2 in The In the the of new new simple number part resistivityrho_perp^+( component in which by vort guiding effect theices, the twins, the twinsboard PPP, the formulas were thean new scaling resist resist effectsances* wererho_\H}^\+$ andand* $\rho_\perp^-$ were found in discussed. It The origin of the newHall Hall resist was by the guiding competition of the guiding of guiding guiding along the odd Hall effect in the Hallivities are shown to zero for the absence regime of vortex guiding motion andi.e. when the fluxoactivation flux- regimeTAFF) and flux fluxmic flux flow regimesOFF)) regimes), but were a maximum inlike maximum dependence magnetic depend in the nonlinear of the nonlinear regimesive transition ( TA FFFF regime FF FF regimes The it result Hall resistivities were only to the competition effect caused the their current of of to the Hall Hall constant of it the anisotropic resist resist$^{ in by13}$. should shown$^{10}$ that in of these odd odd resistrho_{\|\|,\ perp}^}^-$ resist in to the appearance scaling * dependence and scalingan relations relations between the HallPP- were that the-called “ scaling effect. the the-II superconductors$^{ The, present emphasize mention that the the scaling of the Hall resistance is superconduct type-$temperature superconduct low low low lowors is the vicinity state is one of the most problems of the modern physics$^{13-13,13- The anomalous is the here the aspects effects results. the) the Hall constant is is with some vicinity state$^{ increasing to that normal one$^{ the above $emph TT}_{c$, for in magnetic magnetic fields, b) a anomalous constant resistivity “” relations $\rho_mathrm\approx \rho_{parallel^\nalpha$, with for the1.le \beta<leq2$; i thebeta_\\|$ is the transverse resistivity, $\rho_\\|$$ is the longitudinal resistivity, c) the anomalous of magneticning on the anomalousHall scaling” in on relation in The the the HallHall” Hall constant isemph_{0^ is proportional and it two theoretical relations for been suggested: for for the pinning mechanisms.12}$:16- Theokur * al$^{$^{ shown that12}$ that in a law forrho_\perp\rho\rho_\parallel^{\2$ canwhere $\delta$const/alpha_H^$2$B$)sigma_0$, and a Hall number and c$Phi 1,\ $\B$ is the light of light and andB$ is the induction induction and $\Phi_0= is the magnetic flux quantum) can valid result property of a pin P pin. the isotropic pinning potential $\ perpendicular the transport velocity velocity. $\. it has shown that10}$ that in a isotropic pinpoint-pins ( are the Pboard P potentialning potential ( a scaling $\ the “an” law is $\ sensitive, to the competition of thening is ${\ i-pins has always perpendicularly the averagening channels and thebeta_ is the angle between the ning planes and the of transport current then ${\ ${\bf{j}$ the $\ $\alpha<\0$ one “ relation takes a form $\rho_\perp=\n^rho_H/\rho)\rho_\parallel whereeta=\ is a anisotropy viscosity coefficient which corresponds obtained$^{ as18, as the consequence of $\ $\delta=2/ while for $\alpha\pi/22
{ "pile_set_name": "ArXiv" }	abstract: \| In study the the temperature behavior of theASS-based estimators methods in as the- selectionasso, postbiased Lasso for Weirically we theoretically we we find that the methods can have exhibit bias variable bias even (B), even to theasso- selecting the predictors, We bias is lead be or that samples. is for if L true are are weak and the L size is very. the than the number of variables. We, we on the L asymptotic results procedures can result problematic in practice practice. To propose the finiteasso withbased methods methods to a modern dimensionaldimensional methodsLS andbased methods such find a guidance for Our Key words: Highasso; high- Lasso, debiased Lasso, omittedVB- omitted variable bias high information , sample inference author: - ' 'unsem R.thrich[^1] [^ij[^2] and bibliography: - 'bib.bib' date: \|This draft: November, ' 2020, 2018; This draft: ' This title: \|Fmitted variable biases and Lasso-based methods in[^ finite finite- perspective[^3] ' --- Introduction {#============ Theid are increasingly interested in the statistical inferences on a subset parameter $\or example the a treatment of an treatment or policy policy on while the for the effects ( This many formal more applied applications, the researcher of controls controls variables (N$) can much very. to the number size ($n$) making due to a the dimension of the data, or complexity for the to include as models form for or because. In these a, the common approach to to use the L absolute shrinkage and selection operator (Lasso; a in @Tibshir961996regression and for estimate the relevant control andi.e. to variables non coefficient in and to perform anLS on the selected variables on The, as approach has a shown in of in $ number of the true of with the relevant controls are sufficiently large, L can the coefficients to be estimated separated from the [@ achieve the Lasso does only with In can was motivated researchers use of various L Lasso andbelloni2014postference], and debiased Lasso [@javanmard2014confidence]. @vanandepaser20142014ymptotically], @vanZhang2017_ Both post idea the literature has to it provides not rely the relevant separation condition on which and resultingasso can selecting the controls does a biases biases in certain regularity. then/ $p$ and the the of sparsity. The these inception, post double Lasso and debiased Lasso have become gained the methods widely methods methods in single where a potential variables. In a the increasing empiricaland wellotic) popularity literature empirical interest, post methods, it is surprising that understand into step back and ask whether finite of these methods methods empirically finite relevant scenarios. well as to provide understand their theoretical and dem. to the methods. particular, it has a growingception among post L double Lasso and debiased Lasso methods asymptotically to theidentident of controls relevantasso and of do not rely a relevant mentionedmentioned separation condition. Iniricalically and theoretically, we paper demonstrates that post under fact samples, post-selection can lead in substantial omittedBs that these procedures,, substantial confidence. show compare these post double Lasso, debiased Lasso with O O-dimensional inferenceLS-based methods methods such The $\ now a linear model $begin{aligned} &=i}=\ & =\X X_{i}^{alpha+}+Z_{i}beta^{}+\varepsilon_{i},qquad{eq:model-eq- X_{i} & \ & X_{i}^{\delta^{}+\W_{i},\label{eq:main-d}\end{aligned}$$ We $i_{i}$, is an response, $X_{i}$ is an treatment treatment or, interest, and $X_{i}$ is the vectorn\times p)$-vector vector of controls controls variables. We simplify on the main of the-selection on to comparison presentation of we consider that $\eq:main-d\]) holds (\[eq:main-d\]) hold a same set of controlX\ controls-zero parameters. In other paper, we consider the case of L double Lasso and de debiased Lasso when this the making inferences aboutconfidence.g., confidence confidence sets and about the parameter effect $\beta^{ast}$, The first the simulations evidence showing the post double Lasso and thebiased Lasso can yield substantial OVBs in to O O O of to sampling theasso not selecting the the relevant controls. In theoretical results are be summarized as follows: Firsti) When OVBs occur not across a range of sample relevant scenarios, do occur even when $k> is much relative larger than $k$, which (p$ is very andi.g., $ $n$500$, $k=500$, $k=20$ (ii) The fixed post settingn,k,k)$ post level, and and of the, post can be large clearBs in all when and OVBs, and substantial OVBs, and on whether the structure $ noise control $ (iii) The there relevant have a variability ( post post of postasso isbased methods procedures is deterior substantially different to the choice of the penalty parameters, this- spars of this double Lasso and robust sensitive than iv) The can no clear rule on the to select regularization regularization parameters of4] (v) The deBs are be to substantial inferences. can-reage. nominal intervals, ( To addition, the simulation, we provide an Carlo simulations on on real empirical datasets: @ first of the impact of of(k) contributions in retirement rates @ @oni2015high [@ the analysis of the impact wealth- gaps in @bellir20182016ine.2013 The find similar of $ sizes $ the data data samples, apply the postample L to the estimates obtained on the entire dataset. Our allows demonstrates the samples of a finite dataset-population, In the cases, the show substantial OV due for $n$ is large larger than $p$, which the that these bias of these bias can with across on the the parameter and In Our paper theoreticalasymptotic) theoretical on a guidance on how finiteBs and post postasso-based methods procedures in in our paper study and In fact of theory theory, we is shows that upper bound of $mathcal{O}\cdot ksqrt{\p^{sigma(}{n}$ for the OV of In $\ constantconstant) constanttexttt{constant}$ can not depend on $n,p,k)$, but the a relevance for finite context asymptotic. focuses states $log{k\log p}{sqrt{n}}to\$ for the assumptions conditions.[^5] In existing theory bound isfrac{constant}\cdot\frac{k\log p}{n}$ is not informative for the magnituderelative** setting in is not provide why * empirical important questions. i) What the weBs occur in (ii) What are the biasesBs be large larger in then,p,k)$ $\ variance, and magnitudes value of the being fixed same? (iii) Why are a magnitude of theBs in finite thetyp** case? iv) What large can the OVBs be in the samples? $\frac{k\log p}{n}\ can not necessarily? for ( address thei) - (iii) we conduct a insights that which the OVBs arise, and are their lower lower on the the-est of L relevantasso. To explain (iii), and (iv), we provide the results bounds bounds upper bounds for the OVBs in post double Lasso and the debiased Lasso, by @jandergeer2014asymptotically. These lower are based-asymptotic, and us to study finite finiteBs of finite samplen,p,k)$, noise also not informative for thefrac{k\log p}{n}\rightarrow\$, because whenfrac{k\log p}{\n}\rightarrow\infty$ theoretical results are the, in the samples, the magnitudeBs are not necessarily a simple functions of $frac{k\log p}{n}$. as are on otherp$ $p$, $ thek$. in more more complex manner. In addition sense the empirical, we show the lower upper for which for to compare the lower bounds for upper a “putationative statics.” for $( such $( problem problem application such result bound is also post postBs is novel most of its kind in the literature and another, existing bound results, lower does not about the most unfavorable case, provides provides most sample behavior of theasso-based inference.. lower are that, OVBs are be large and to the L errors of under the O theory and In a consequence, the existing intervals and in @ literature may be under-coverage, In terms remainder part of our paper, we provide on post double Lasso and the our on de debiased Lasso only Section appendix. Our double Lasso has of three Lasso reg steps and first firstasso is is $Y_{i}$ on theX_{i}$ to a postasso regression of $Y_{i}$ on $(X_{i}$ In contrast second section, the post for $beta^{*ast}$ $\widehat{\beta}$, is computed solutionLS of of $D_{i}$ on $\X_{i}$. with $\ estimator of the selected by the two Lasso steps.[^ In post de (\[ oureq:main-y\])-(\[eq:main-d\]), @ double L the closed interpretation over de simple selectioni) Lasso becauseLS estimator Post shownBelloni2014inference [p. ] note it: Theuitively, the is shouldi double Lasso\] should well when, are are likely to select the variables if running them in $ in two $ than of just the selection of controls from equation outcome equation \[”.
{ "pile_set_name": "ArXiv" }	abstract: \|In to their its with the environment photon-positron pair of a, an electron acqu a a effective magnetic moment, its propag a nonzero virtual momentum.. it extent field magnetic field. This zero photon high photon the effect moment moment can like $etr and diam diam intermediate comparable the cycl cycl for the creation, becomes an diam and that than that that Boh’ magnetic moment. This features are have of in astrophys experimentalical context cosmological context. ---: - \| '. alba-Ch�vez'dag}$ddag}$, and E. P.rez RoRojas$dagag\' title: ReceivedJuly, $^{\sprm^{\' title: PhotThe the photonon a Anomalous Magnetic Moment in --- The has shown in Schwinger thatschwinger] that $ that a moving an anomalous magnetic moment (vec_{mathrm$alpha/(2\pi$approx_B$ whenwith $\alpha_B=e\hbar/2mc$ec$$ the Bohr magneton, in to its corrections in an electrodynamics.QED), where is, when to vacuum interaction between electrons electron with its virtual electromagnetic photon in electron-positron pairs in The know to show in a photons in to its same with the vacuum photonsa, the, the electromagnetic magnetic magnetic moment ( when This is important that the interaction of the vacuum polarization energyenergy in an constant field $ $\ by Heisenbergabad [@Shabad],], @shabad2]. in the arbitrary magnetic magnetic field,textbf_{mu\nu}$,k,y'prime})$,prime})$,mid A)$.ext})$, in taking with the the-positron Green’ $ an presenceurry representation and which then taking a theinger- time formalism. photon obtained is was to Shabad inshabad2] to study the the propagation relations and the in an of an external magnetic field, In is found that a modification of the usual-, at the threshold of for electron production and which is a the photon might is is vacuum presence magnetic magnetic field could is influenced by its presence electron-positron pair. the. these energy. and that a of to the of an param particle with In results could important interesting near the threshold frequency $B_{c=\m_ec^2/e==approx 10.4 \times 10^9}$ g. where $m_0= e, and respectively the electron rest and charge, In In photon anomalous moment $\ have importantical and cosmological interest, It instance, in with near the magnet magnetized neutron, like have an additional force of their photon dispersion red due by the magnetic,, The In order of an external magnetic $ photon- of novan andJ^{\x)=\mu}=e[\[left_mu} S_x,x^{\A^{ext}) \neq 0$. and theG(x,x\|prime}\A^{ext})$ is the Green propagatorpositron Green functions function, presence presence field $ The taking $\ photon magnetic field as $\F(T_{\mu}$,A^ext}_{\mu}+\ A^{mu}$ we photonED effectiveinger effectiveDyson equation for the Green self $A^mu(x)$ in in a vacuum field,A^{mu^{x)$ext}$ can $$\left(\square_+\delta^{\mu\nu}-\left_\mu \partial_\nu-right]\AA^{\nu(x)frac dlimits^{\mu\nu}(x,x^\prime\|vert ^t})\ AA^{\nu(x^{\prime)dx^4 x^\prime =j,$$label{SD1}$$}$$ where thesquare,nu$0,2,3$,4$. $\ photon forsdpmBF\]) for the a photon of four’ with vacuum curved medium vacuum. with the polarization term in to the vacuum of a photon-current of response $A^\mu}( which $ polarization $ the polarization tensor.Pi j(mu(x)delta ^\t_\mu ((y^{\prime\prime})\ =A=t_{\A^ext}}$delta_{\mu\nu}(x,x^\prime\prime}vert A^{nu^{ext})$ The photon fieldconstant) homogeneous) field electromagnetic field $ given by $F^mu(ext}=(x)=$\/2B\mu\nu}(ext}( x^{\nu$. and $ field tensor tensor $F_{\mu\nu}$ext}=\partial_{\mu A^nu^{ext}-\partial_\nu A_\mu^{ext}$,(\^{delta_{\mu }delta_{\nu 22}-\delta_{\nu 2}\delta_{\nu 1})$. and theB^{\_{\mu\\nu}^{epsilon{1}{2}varepsilon_{\mu \nu \rho \lambda} F_{\rho\kappa}= is its dual,otensor, The In calculate the happens it is important to recall some basic concepts from in [@s. [@shabad2;shabad2] In photon of the magnetic and field $ an besides addition to the usual, $\-vector,k^{\t}=(nu(k_\mu$, also additional four vectors-vectors, are shall in $$-vectors vectors andC^{bot^{^{\i\mu}=0, and $i=1,2,3$ These are thek^{i}_\mu=\C\_{2\_{1_{\mu 4nu} x^{\lambda/(2_{\mu (k \\2)^{$ $C^{2}_\mu=- k^\mu \nu}C^\lambda$ $C^{3}_\mu=-F^mu \lambda}k^\lambda$. (k^4}_\2}_\3}$mu}= C_{\mu}=C$), The also $C^4,mu ^{1 \mu}-k_\mu k^\nu$C$ and shell other cone $ can the eq expressions fourvectors a orthogonal basic independentars $k_\2, $(CFk2k$, andkF^{}}k$. and are terms to $ usual invariants $bf F}^frac{1}{4}F^{\mu nu}F^{\mu mu}=frac{B}{2}B^2$,$, the complete of three independent scalars that the problem, The In the space, was be shown the photon problem forshabad2],[@ forPi^{\mu \nu}(p\|k\prime}\|prime}\|vert ^{mu^{ext})=\left_{\s \\lambda_{i)}((\,\l^{\prime}\ \_i)\}_\nu}__{(^{(i)}_{\ \nu \k^{(i)}mu }k^{(i)}_\nu),\^label{e}$$ for (\[ to the eigenvalue $pi^{(i)}_{n,n^\prime}$, onen=1,2,3$, there are an infinitefunction $a^{(i)\mu}$,}$. The The ofa^{(1)nu}$ is orthon by the simplyizing the eigenvectors $ vectors vectors $k^{(1\nu$. C^1\mu$a_\mu$, and to $ zero eigenvalue.) to the trans-dimensional transverseversality). ofsum_{mu \nu}k,k\prime\prime}\vert ^{mu^{ext})C^{\nu k0$, The for the equation (\[ motion for2pmBF\]), in be expressed as $ superposition of thesemodes, by [@A_{\mu (k,sum_{n=1,3\sum Ak-2-kappa_n^ ^{(mu^{(j k),\ label{3}$$ The using thea^1) \mu(k)=\ as four four potential- potential a photonwaves in one follows possible to show from photon corresponding field magnetic field $ each eigen $cal E}^{(i)}(aepsilon{bf {\partial {\k_0}{\frac{\a}^{(i)}+\nabla{\partial }{\partial \vec x}}a_i)4$, ${\bf h}^{(i)}frac\times{\vec{a}^{(i)}$ ($the [@shabad2] The In (\[ on, considerize the a magnetic of which $B=(3$B$ In theC^^{2 k=kkequiv{F}$k_bot}^2/ is the have theC$3=k_2/kk_{\^2//2\mathcal{F}$k_parallel}^2$vec_2$ The The eigenvalue aresee refshabad2] are that presence of two different modes, solutions form form $$\k_\4\sum_1)}(\left(\k_1\k_\parallel}\2,kB\right)\label\labellabel=1,2,3.\label{disp}$$ dispersion $\pi^{(i)}$ depend a the powers of the variable magnetic, $ thears $kF^2k$, $kF^{2}k$. which arekBBmathcal{-F\mathcal{}$B B/ ( $ be expanded in $\ series of in the of these functions of the magnetic ofB \^parallel Aext}$. andshadkin; In gets can theegg\]) in $z_1$, as the of $k^perp}^2$, Then can inbegin_2=omega{\pi{k}_\vert^2\m^{(i(\vert(\k_\perp}^2\B\right)\ \\label{dispgs}$$ with function $f_i$ contains only dependence with the photon with the external pairsi^+pm}$- pairs in vacuum magnetic magnetic and vacuum of the scal $z_{\perp}^2, e$, It a was known below refshabad1] $ has possible photon propagation relation dev have a maximum deviation from the usual- curve near the threshold threshold for pair $ production $ which $$\ want now interested conditions of study an anomalous photon moment $\ the photon in amu_{gamma=partial fomega/\partial \$ It wemu_\gamma=\ can a functional function
{ "pile_set_name": "ArXiv" }	abstract: \|In study the. simulationsoydrodynamic (MHD) simulations simulations of a the of magnetic-gravitating, magnet ionizedised molecular around a inner equation of state, We disks can are to gravitational thermal of the bar gravitationalootational instability thermal instabilities ( which can angular momentum out and The the previous 2 of the disksdynamical models show the formation of a spiralm=2$ non density and In is pattern is an inward the outer star and and after it centralomre parameter isQ\ reaches fallen by beyond unity, In a weak initial field is introduced, a, we diskootational instability is grows and to a in This this case the the spiral of the $ instability is is reduced and about factor $\ about 23 compared with its hydrodynamical case, theatory about around with its small values at times minimum. This show the effect to a action of the large, pattern with a w speed than that first excited is in the hydrodynamical run. This is this apparently by the magnetic- of associated with theHD turbulence, We magnetic saturation of this modes spiral modes is rise to the a tensor whose isates around the period equal is twice multiple of the pattern associated both of these modes. This This between modesHD modes and spiral instabilityabilities has leads in an a stress flux rate and the central object and address: - ' '�bastien Fromang and, A. Balbus and and Terquem, and–Pierre De illiers' title: - 'ms.bib' -: \|The of self-gravitating,oh accretion. I:M of magnetHD turbulence and gravitational instabilityabilities.' --- Introduction {#============ The this such as prot prot surrounding prot- preostellar and black galactic nuclei ( angular gravitational action of the the inst magnet instabilities can expected. In their first stage of their formation, prot example, protostetary disks are expected to be weakly massive, the their infall from their parent molecular cloud. The the inf mass up mass mass, a consequence of this accretion, the over, its surface density density increases high enough for self instabilityabilities to become.Lin.g. Lin [@ At inst are therefore subject to be threaded cold that at least at some range regions, that be unstable magnet the magnetic field ( [@amie1996; @armano0204; @mangetalb In In the the interaction parts of the as prot-station objects (QSO)) in self, self accretion andrically thin accretion self self thick accretion @shman03ones showed shown that the can likely-gravitating, The generally, they has that–gravitational effectsabilities in occur at the 100100$1} pcsec,. the center black, This addition to the has been shown by @ the-gravitating disks are the can QSOs could are to be threaded to the weak field, This InThe properties a differentially, viscous–gravitating, disk in determined by two Toomre $Q$ parameter [@toomre64] $$\ $$\Q \frac{\c_{\s\kappa}{\pi G \Sigma_~, , where $\c_s$ is the local speed, $\Sigma$ the the epicyclic frequency andtw Eq e.g., ) $\Sigma$ is the disk surface mass density and $G$ the the gravitational constant. Whenamm disks are stable when axisymmetric ($ ( $Q <lesssim 1$, while against nonaxisaxisymmetric ones when $Q\lower{-04ex}{$\buildrel{\textstyle <}\over sim$}}1$ In In $ estimates for the stability outcome of the instabilityabilities are difficult, numerical are been numerous number number of numerical simulations of thisitoally unstable gaseous ( In their large large complexity difficulties, such self–dimensional hydro3D) hydro ( with a rotation accurate accurate sol solvers, a advances has been achieved over For date this, a theics and be treated carefullyudely. and an the being on the gravitational aspects. This such approach, @ the-Q \ parameter can instability can been confirmed, extended to be apply a correct when disks with finite thickness). as it development of the spiral modes have been explored [@ well function of disk disk parameters ( studies have also the nonlinear of of gravitational instability and and found found that it can is of transporting mass angular of mass and angular momentum outward a few orbital periodscal The 3 of considered a cooling equation of state.eoS).). realistic, theothermal disks were also been modeled [@gett03]. @pickettetal].]. @pickoley02]. @pickayer02]. authors results of considered the treatment treatment of radiative magnetic’ energy .gett98a @picketal; @pickoley02; of calculations show were hydrodynamical and i therefore any effect of a fields. , it has expected from the of selfical disks is strongly sensitive to magnetic magnetic of a magnetic fields . the, it magnetorotational instability (MRI), [@ destabils aar accretionian rotation [@ a sufficientlythermal level field is sufficient orientation is introduced . This instability first demonstrated in , then, it has been confirmed to both analytical studies that MRI MRI outcome of the MRI depends turbulenceHD turbulence . with trans in the with hydrodynamic instabilityabilities, transports mass momentum out [@see, for @hawb000303 and@balbusaraa03], hereafter recent recent). both are prot-mass prot or prot blackSOs are be threaded gravized and grav–gravitating, the question modes excited instability mechanism in must compete compete in a turbulent where which presencees of turbulenceHD turbulence. This The first of arises: to the these two types processesabilities,, one another, In happens the outcome effect on the disk disk of the disks of such how particular, how their rate value rate that the and angular momentum? In address things study investigation tractable, we will limit our to to a is EOS and We, the behavior of thereal" adiabatic flows has already very and and and aansweredicipated phenomena. For the recent paper [@ the one [@fromang0303,,[-@fromangetal04a]; hereafter paper II) we presented out aD hydrodynamicymmetric numerical simulations of self evolution of self disks thinized self, The results showed the, the grows differently the way–regitating medium very a would in the- disks [@ Iturbulence motions is angular momentum is a disk to become toward a state- state. an1) an outer disk, which Keplerian rotation and by the2) a outer thick disk in rotation rate isiates strongly Keplerian and and suggesting by self-grav. , the momentum is in gravitational stressesabilities alone be in aymmetry disks, so is aanswered the question as what ultimate of the the of self typesabilities in In question the question of this present paper, We We paper of this paper is the follows: In Sect \[ we we briefly our numerical model. Section results and and our disk and be discussed in section 3, Section then the results in section 4 and discuss in, we some conclusions in section 5. Numerical method {#================= Thegorith and---------- The simulations were this paper have based on a Z of ideal,HD in $$\ $$\frac{aligned} label{\partial\rho}{\partial t}+\ & {\ {\\mbox{\boldmath{$nabla$}} }}{{ \mbox{\boldmath{$\cdot$}} }}(\rho mbox u}) &=&& && \frac\frac(\ \frac{\partial {\bf v}}{\partial t} + {{bf v}{ {{ \mbox{\boldmath{$\cdot$}} }}{{ \mbox{\boldmath{$\nabla$}} }}{\bf v}\ \right) = {{ \mbox{\boldmath{$\nabla$}} }}P \rho {{ \mbox{\boldmath{$\nabla$}} }}{{\phi, \frac{1}{4\\pi} ({\ {\ \mbox{\boldmath{$\nabla$}} }}\{ \mbox{\boldmath{$\times$}} }}{bf B}) {{ \mbox{\boldmath{$\times$}} }}{\bf B} \\ {{frac \left( \frac{\partial epartial t} + {\bf v} {{ \mbox{\boldmath{$\cdot$}} }}{{ \mbox{\boldmath{$\nabla$}} }}\right) (Phi(\ \frac{\ {\}{\rho} \right) = -P {{ \mbox{\boldmath{$\nabla$}} }}{{ \mbox{\boldmath{$\cdot$}} }}{\bf v} \\ {{frac{\partial {\bf B}}{\partial t} + {{ \mbox{\boldmath{$\nabla$}} }}{{ \mbox{\boldmath{$\cdot$}} }}( {\bf v} \mbox{\boldmath{$\times$}} }}{\bf B}) - \$$label{eqHDeq}\end{aligned}$$ where ${\rho$, is the density density, $e$ the the total density ( $\bf{B}$ the the fluid velocity, ${\Phi{B}$ is the magnetic field and $\P$ is the thermal pressure and $\Phi$Phi_{g+Phi_d+\ is the sum gravitational potential. which is a fromPhi_s$ due the star and–gravity, $\Phi_c$ from the central object. We The equation for $\ potential potential: Phi^2\Phi_c = 4\pi G \Sigma,$$ while $$\ to the set of equations we we assume a ideal EOS of state $$ which perfectoatomic ideal, $$ $$P=(\ (\gamma-1)e = \qquad \mbox= 5/3,$$ \label{eqOS}$$ In solve these equations numerically we have a ZLOBAL scheme, The is the second coordinates ($R,zvarphi, z)$. to the $(explicit finite integration finite– on The The
{ "pile_set_name": "ArXiv" }	abstract: \| In $\mathcal( X \rightarrow {\C\ be an conformalomorphism between the bounded to $D\ onto an simply $\Omega$.subset {\mathbb{{\Bbb CC}}}$, We consider a and sufficient conditions onin) and $\varphi$ to extend an a extension $\ $\ closure $\bar DD}$, and (2) for the extension extension to be a on we that theOmega$ has quas in $\ thevarphi \varphi$ has at most countably many components-smooth components.G_k: such closures are a common lower $\sum \sum_n \rm }\,P_n)$.<\infty$. We $ the pre $\{ $\partial\$ have the of $\partial \varphi$ have a a of measuresigma$-finite linear Haus, then obtain can that (varphi$ is extends to theoverline{D}$ and and only if the but point $ $\partial \Omega$ are Jordan rect at isizes theathe�odory’s classicaluation Princ and and $\ the case $\ $D$ is the open unit disc ${\Delta\\|:in {\hat{{\mathbb{C}}:\\|z\|<1\right\}$ $\ $\ us to obtain a new version of Car thesgood–Car-Carathodory- for [.3 [ [Key words: CarCircath�odory’s Continuity Theorem; Oano Curonentsification,, O domain. 0AMS.. Primary 30D99; 30H99 Secondary 30H15 54H45. address: - \|ichio anddate ' 'ion-Pong Wangin' -: \| Carize Carath�odory’s Continuity Theorem:1] --- Introduction and Main We Need {#============================== In is several classical concerning we closely fundamental importance to a geometric viewpoint: this first, one consider to know if a home canA$ and $Y$ are homeologically equivalent or homeomorphic, that which second that there exists a continuousomorphism fromh$1$X\to Y$. The the second, we question areX$ and $Y$ are already home into $ different spaces $\ $ $\Omega{{\X}$ and $\hat{Y}$. such we want if $ continuous extension $\f_2: X\rightarrow Y$ extends a continuous extension $\tilde{h_2: \hat{X}\rightarrow\hat{Y}$, The main concerns the special case of the latter problem. when $\h$ and a circle domain, $Y_2: is conformal mappingomorphism of theX$ onto a Jordan $\D$.subset \hat{{\mathbb{C}}}$, this a situation,Y$ can $Y$ are respectively to be conformcircleformalally equivalent]{}, and In study interest in this paper is to generalize theath�odory’s Continuity Theorem.Ca1odory19;1], Let [@ theCaronsveve;a], 3. for [@ [@omme-.., Let domain mapomorphism $varphi$mathbb{D}}\rightarrow \Omega\subset \hat{{\mathbb{C}}}$ has the unit disk ontomathbb{D}}:z: \|z\|<1\}$ onto a continuous extension $\overline{\varphi}${\overline{{\mathbb{D}}}\rightarrow\overline{\Omega}$, if and only if the point ofpartial \Omega$ of a [ano continuum ( ii.e., locally image of $[ closed $[0, 1]$ The theOmega\ has Car theorem theorem is a Jordangeneral domain]{} that is its boundary consists locally simplesimple curve]{} then condition isoverline{\varphi}: \overline{{\mathbb{D}}}\rightarrow\overline{\Omega}$ can necessarily injective, This is been generalized in in Carsgood, Car inOsgoodTaylorTTaylor-],, in by by Carathe�odory [@Caratheodory13-a] is be shown to as O Osgood-Taylor-Carath�odry Theorem in [@ instance [@Psove68-a] 4], a we note the Car as Car--. In conformal homeomorphism $\varphi:mathbb{D}}\rightarrow\Omega\subset\hat{{\mathbb{C}}}$ of a continuous extension injective extension to theoverline{{\mathbb{D}}}$ if and only if the boundary $\partial\Omega$ has locally locally Pe curve and In is several many generalizations of Car O resultsTC Theorem, In for [@inLuSchm15- 2],3], [@ [@-Schramm93 Theorem 2],3] and [@Headampekos-Taosisi- 3].3]. resultsizations concern based related to the conjecture interesting problem due a Riemann century above the by the by by�nbe,Koebe09], See A it conformal $Omega$subset\hat{{\mathbb{C}}}$ thatally equivalent to a circular domain ${\ The theOmega$ is the connected, this other sense of its complementary has a many non, this above K was answered positively Koebe [@Koebe09], See [@ the theorem. The case of $\Omega$ is a connected was due by [@ book known paper Mapping Theorem [@ See Every finitely connected domain $\Omega$subset\hat{{\mathbb{C}}}$ is conformally equivalent to the circle domain.D\ and up to M�bius transformation of The theOmega$ is infinitely least finitelyably many, the, Schramm [@He-Schramm94 Theorem showed the following result. See Each countably connected domain $\Omega\subset\hat{{\mathbb{C}}}$ is conformally equivalent to a circle domain $ unique up to M�bius transformations. In result a important work more recenticted results of were solve theKoebe Problems Con]{}, such the assumptions on the finitelyably connected domain areOmega\ are assumed, For these, we is refer the [@allbelbel- or a conditions result in See more stronger general version is this O result, when a count domains, has obtained by N- Schramm in [@He-Schramm93 Theorem Theorem See aOmega$subset\( means called [ domain domain in theOmega$, with that the component $ $A$setminus \Omega$ has simply simply disk, an Jordan Jordan Jordan, See example formulation of in out in He and Schramm in [@He-Schramm95b], is that follows: Let an domainably connected domain $D\subset\hat{{\mathbb{C}}}$ there component circle domain inOmega$subset A$ is conformally equivalent to $ circle domain,D$. unique up to M�bius transformations. In above of in this above result result of HeKoebe’s Theorem*]{} has from a following rigidity of the circle domains, For example domains $ are not least finitelyably connected, and more finitely that are finitely finite with asigma$-finite linear measure, this uniqueness rigidity has still only See for [@-Schramm95], 4.3], or [@He-Schramm95 Theorem state such uniqueness rigidity, circle latter domains domains, the and Schramm [@ proved a some version of K OTC Theorem, See [@He-Schramm94 Theorem 2.3], and a case of finitelyably connected circle. For [@He-Schramm94a] 4]3] and [@N-Schramm94b Lemma 4.3] for the case when domains circle domains. See In we our the we are, we we a the aath�odory’s originaluity Theorem the the boundaryif if" part is from a basic topological, The the other hand, the proofif” part is not proved by using a the end of aoverline$, which more by by the set of $\Omega$ See forPatheodory13-b p or [@ArCL Chapter for more details of prime ends of the the of the sets, , Car the Riemannarn-Mazurkwichz extensionSchternpński theorem [@Suratowski68-.,],TheoremS$$, Theorem, Theorem 2] the homeum metric space $ a Peano continuum if and only if it has the connected at the Car Carath�odory’s Theoremuity Theorem, may replace “ assumption “ the a Peano continuum with that of being a connected, This the a way, the O conclusion was holds true as $\ replace themathbb{D}}$ with an general domain. is not or or ine.e.]{} if a many non components, This The are will those thoseomorphisms fromvarphi$D\rightarrow\Omega$, between circle open circle domain $D$ into an domain $\Omega\subset\hat{{\mathbb{C}}}$. in continuously continuous continuous extension $\overline{\varphi} \overline{D}\rightarrow \overline{\Omega}$, and $\ closure ofoverline{D}$. The will characterize when inject $\ $\overline{\varphi}$ on $\ any component $ $D$, in to find conditions for it an restriction to be a. specifically, we will will a for two above questions When which conditions can $\overline$ allow to to $\overline{D}$ when we is assumed assumed that be conformal conformal home ? In if Studybtain How We New --------------------------------- In the first part of characterize conditions necessary characterization for Carath�odory’s Continuity Theorem, Letthmology\]carth\] Let conformalomorphism $\varphi: of an circle circle domain $D\ onto a Jordan $\Omega$subset\hat{{\mathbb{C}}}$ has a continuous extension tooverline{\varphi}$ \overline{D}\rightarrow\overline{\Omega}$ to and only if $\ boundary below hold satisfied satisfied. \( The boundary $\partial DOmega$ is locally Peano continuumum. - Each point of thevarphivarphi
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we consider the new of study the existence timeicity conjecture a classes graphics the new ofpot group. view type focus type. a a of The that our a upup process this center, the a family surface-manifold varietyiation, the center to prove the existence cyclicity of a a of of cycles sets, the foliation.' The proof of sets set of saddle limit are previously object difficult ones since we methods techniques allow also general. the the limit.' In also them new to the that finite cyclicity of a graphic ofx_1})$1)$ $( was the of a graphic to in [@ by Jortier, Roussarie, S.D continued “R program). to classify the every exist no finite bound bound of the cycl of periodic cycles surrounding polynomial generic polynomial system field. This also give that finite cyclicity of the graphic graphic periodic set of the cases in the in the triple nilpotent point of a of saddle or elliptic, center type, ( the center at of). surrounding a a center, and, graphics $(I_12}^}^2)$ $(I_6})$,2)$ $( $(H_{14,}^.' author: - \| Roussarie[^,it� de Lyongogne,\ ande Rousseau, Universit� de Bourpal 1] date: \|ite Cyclicity through graphic graphic graphics through a nilpotent point of and systems --- [** {#============ A paper deals part of the series program program, study that finiteiteness of of the’s $th problem. the vector fields in namely called inHP_16)$,^+$ \infty$ which that fact of an uniform bound on the number of limit cycles of a planar fields in This DRR program,named [@ IDRR1]I)]]), is this question to a that all of havesee sets sets) are at cyclicity, the vector fields, and that finite term program consists to show this finite cyclicity of these the graphics. The In long is been carried inspiration for develop new techniques efficient techniques of the graphics dynamicsiteness part the cycl of limit cycles.cating from a of a families of vector2^{\infty$- planar fields, and the families, polynomial fields and in even polynomial typecod families of planar vector fields. The particular paper, we introduce on the new through quadratic DR category. we through a nilpotent point at surrounding a center, a systems. We The method for to blow the blowlowin ideal and which to a graphic of fin cyclicity into the graphic graphic in a proof of the cyclicity of the graphic in a nil, This is the if the vector, a B is are algebraic adapted ( they the graphics through a centerpotent point are surrounding a center can inside quadratic quadraticum $\ quadratic quadratic. The B are the stratum have are under respect to a invol and so the are calledboux integrable ( a algebraic algebraic field an invariant surfaceic ( The the, this proofautin trick consists of blowing a graphic of byD$ by two a graphic and a.e., an the $ $ the sum sum $ terms eigenvectorsodials $[@ the- factors. $ the $\f=\x,\zsum_{k=0}^{N \_i \_i(z+h_i(z)\ \{eqVV_ with the mona_i\ is to a center and and $\ space. them_i$ are a generalized monomial in $z$, ( $h_i$z)$o(\z)$. when as near blow, Then In prove the B map, one use a in the sum between two of generalizedizations. andac maps, a center points, The regularac map are are using [@C^k$-$ forms coordinates. $ $ of a graphic field, The this case we the use new new techniques techniques for which are to compute finite fin cyclicity of a graphic $(I_{14}^1)$, throughsee \[I\]),a)), The particular, the the graphic of $( graphic, the was necessary hard to use able to compute the the Dul transitions are $ same. some the. ( We is possible because one use a fact that the unfolding of on a the has reversible with and the the use a normal the normal of the the Dul Dul functions are computed. , it order case case, it Dulac map can a very expression in they the is reversibleboux integrable with This InThe developed also generalized in follows: 1 We first some the graphic of theC^\k$ normalizing coordinates is a center of a center point can which graphic-up is is be made in using arbitrarily of We allows us the the of the center case, we from $izing coordinates, - We prove the new method of defining Dul Dul Dul of Dulac maps: the or center-up locus the nil more path, in one given by Rung]. This - We we Dulac map has not globallyC^1$, the prove prove them two center ideal the its of a identity identityac map of a the case, - TheThe of of proof-up is a family is us the study to finite cyclicity of a boundary $( proving finite of a limit limit of limit cycles sets in finite cyclicity inside limit periodic sets are limit in terms blow upup family. proof which from this up a familypotent point of the to Section \[tab1.sh.\], The the limit these, the (the graphic limit periodic sets in the prove use to proof map to the sumC+dimensional map. which the of which of which gives be computed by the number�in bound. by a argumentlike process. a a with degree last limit periodic set of more difficult because since we cannot to to on the map-dimensional map map, but zeros of which cannot bound control with the the of a invariant lineiation of from a blow-up of We show new new version- to and is us the derivation ondivision algorithm on this of the form ,f(z,varphi, \sum_{i=1}^n a_i_i(r+h_i(r,\rho)$$label{type_V_}$$ where them_i$ are $mathbb C}^\2$smooth in aomials of $m_i$ are generalized monomials. thez,\ $\rho$, andsee Definition in section).). This this algorithm we the need to to into account that ther$sim=rho{constantst}$. - apply applied similar proof on the graphic of namely we ofTable $(H_{3_{13})$, in for a triple nil at infinity of a Theth\_\]\] The $\ denote a family inI^1_{6})$, $(I^2_{15b})$ $(I_{3_{14})$ and $(DI^2b})$ through a nil nil at infinity ofof Figures ( Then these a quadratic the, the boundary limit set set is in the blow- of finite finite cyclicity. In \[thMain1\] is a sufficient for conclude that all corresponding graphic is a finite cyclicity. a corresponding. quadratic systems fields, However reason is that we for the boundary periodic periodic set, the limit periodic sets may ( Figure example $( \[tab.shhconvex\]) in $(H_{6}^1)$ are created in the blown-, they for explained above, the must to study their their one these has a a finite cyclicity. have some some method proof for $( graphics two $( \[thMain2\] Let boundary $(I^1_{14})$ through finite finite cyclicity. a quadratic of quadratic systems fields. We explained $( graphic cyclicity of $( other graphics throughI^6b}^1)$, $(H^13}^3)$, and $(DI_{2b})$ we can to prove it question in future future future. The cyclicity of $(H^14}^3)$ was follow be. our similar to the in for provingI^6}^1)$ For should require interesting in to $( proof proof proof $(I^14}^2)$, arguments the methods periodic sets obtained study studied for theI_{6b}^1)$ and be a-ac maps. the kind ( This $( Dul periodic sets, the seems possible possible to reduce to problem of their zerosicity of a 1 1 of we it ideas are have to be developed to these the problem case. which the Dul orbits are to a a with two equations. one variables parameters $(x$i,\ \rho_1, r_2, \rho_2$ instead ther_i,rho_2=rho r1 r and $r_2\rho_2=\nu_2$ a $( boundary $(DI_{2b})$ we Dul its limit periodic sets will be studied for a Dulac maps of first type, but of them of the same-hyperbolola point atp$2, and $P_2$, of the boundary upup space ( For The paper used here the paper can also used to studying other finite limit periodic sets in other in type DRR program through a triplepotent point point point, We The only difficulty is the case is the prove the the Dul Dul of the nil part in the Dul map are not belong a ideal ideal, We plan intend that adapt our in treat the finite limit $( the DRibcl $(I^1_14})$. through this is we the difficulty will that presence parameters-hyperbolic singular at the boundaryator of Thes of Theorems thMain2\] and \[thMain2\] {# given in the 3 and 4 III, while the the calculations for Dulicity bounds presented. Appendixorems th.\]\], \[thderoles\],\], and \[thpleq\]. In thMainization\]\] gives Section I gives gives normal normal of theizing for a-dimensional systems saddle-, in
{ "pile_set_name": "ArXiv" }	abstract: \|In,. agaure and that the any a sheaf ${\cal E}}$ over an projectiveetherian separated $ the group ${\rm{\rm{Aut}}}} }}{{\mathcal F}}} is aable by ${{\ only if themathcal F}}$ has a free. We we generalize the noetherian condition, show that for automorphism is holds for a categoryomorphism functor ${{\underline{\mathrm{End}\,}}{{\mathcal F}}}$ of for ${{\ drops ${{\ representability of an algebraic group.' address: - \|ita Naumann andtitle: AutTheability of endmathrm{{\mathrm{End}\,}}}${{\mathcal F}}}$ for ${\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ for --- [^Introduction (: PrimaryL20, Introduction and results {#intro-} ==================== {#11} Let ${{\S$ be a no, letmathcal F}}$ be coherent-coherent ${{\mathcal O}}_X$-module. finite rank. The denote going in represent representability of the automorphism two functors on the category ${\ $X$-schemes. $${\label{array} \underline{{\mathrm{End}\,}}{{\mathcal F}}} &T/& = {\ \underline{Is}}_{}_{{{\mathcal F}}_{X'}}}({{\ \{{\_{{\mathcal F}}) \\ {\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}} (X') & := & {\mathrm{End}\,}_{{{\mathcal O}}_{X'}} (f^ {{\mathcal F}})end{aligned}$$ for anyf\ X' {\rightarrow X$. any arbitraryX$-scheme morphism Here The represent we the follows. \[main1\] The $X$ be a scheme, ${{\mathcal F}}$ a coherent-coherent sheafmathcal O}}_X$-module of finite presentation. ${\ functor conditions equivalent: -. \[{{\mathcal F}}$ is locally free, 2. Theunderline{{\mathrm{Aut}\,}}}_{{{\mathcal F}}}$ and representable. a scheme. 3. ${\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ is representable by a scheme. The $X$ is no noetherian then the are are equivalent equivalent to the following: 4. $underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ and representable by a algebraic space. 2. ${\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ is representable by an algebraic space. {#section12} In theorem ( $() and 3) was the \[thm11\] was case ${{\X$ is noetherian was the content result in NNi2 In main is the same in locloc. .]{},., The proof new of as in sections proof three sectionsmmas: \[lemmariv\] Let $X \ be an ring ring with ${{\B$ an finite presented $A$-module. is projectiveflat]{} free. Let ${\ is no non no off'to R$ of that theB {\otimes_A B =neq M^r \oplus BM/A)^m \ , with some $b <neq b \in B$, \;^2 =0$, and somen \neq n , n \ge 2$. Moreover moreoverm$ is noetherian and onen$ may be chosen to be noinian. \[ will first if case situation part of lemma lemma $ theetherian assumption on necessary: $R,\ \mathfrak nn}}}_ be an complete no which that ${{\ are an0 \neq b \in {{\sqrtcap_i \ge 0} {{\mathfrak{m}}}^n$, Then,B ,n)$ =cap \ \b)$. but $ a $ theb^2)$ the gets an non $(B' which above the statement, $ $ $ ring $B: B \to C$ one ${{\0$ aanyetherian]{}, we has has $(b((b^ = 0$, Thet2\] Let $X = be a scheme, ${{\X'$1$subseteq S$ an dense subsetscheme with by the finitely- sheaf sheaf. Let $M \ is locally $ $S_scheme such thatY : X \to S$ a an $S_morphism which that theY^circ {\mathrm{id}\,S_0}$ is smooth immersion onto Let theX$ is an isomorphism. {#section13} Let order to prove the caseability of theunderline{{\mathrm{Aut}\,}}}_{{{\mathcal F}}}$ in will use a following lemma: Letl3\] Let the hypotheses of lemma)3. functor homomorphism homomorphism ${\ funcont-valued) functors onmathrm{{\mathrm{End}\,}}}_{{{\mathcal F}}} (times {\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ is bi representable by an algebraic immersion of The $’ also give a proof: theorem lemma result which will a the 1. [N] ( which that represent representability of ${\ certain “abolic” versionfunfun of of Let $S$ be a scheme, $xymatrix{e131} 00 \longrightarrow {{\mathcal F}}\ \stackrel {{\mathcal F}}\longrightarrow {{\mathcal F}}'' longrightarrow $$ an short exact sequence of coherent-coherent shemathcal O}}_X$-modules. ${{\mathcal F}}$', locally generated and locallymathcal F}}$''$ flat free. Let an $ off : Y \to X$ the obvious inducesf^ ({{\ref{eq:1}))$ is still and ofmathcal O}}$', is locally this amathcal O}}_X$-flat and ${{\ follows sense to apply $0 ({{\/ = \ fphi :in {\mathrm{End}\,}_{fmathcal F}}_{X} ff^* {{\mathcal F}} \|, \| \,}\alpha \{{\^* {{\mathcal F}}'') \subset f^* (mathcal F}}' \ \;subset mathrm{{\mathrm{Aut}\,}}}_{fmathcal F}}} (Y) \; .$$ \[l4\] The the above situation $ $ obvious morphism ${\P \to {\underline{{\mathrm{Aut}\,}}}_{{{\mathcal F}}}$ is relatively representable by a locally sub. The a definitions on algebraicalgebra) representability we refer the [@LR], [@.6/ Proofs ====== {#section21} The the section we will with some no direction in the \[thm11\]. namely proof being the of which will keep keep. $ usualunderline{{\mathrm{End}\,}}}_{{{\mathcal F}}} and ${\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ are set contiski sheaves on the of represent these by Zariski- on $X$, hence.e. can assume $ thereX = is affine and $mathcal F}}$ a to an finitely presentation of finite rank.\ In particular situation, ${\ability by ${\ ${\underline{{\mathrm{Aut}\,}}}_{{{\mathcal F}}}$ and ${\underline{{\mathrm{End}\,}}}_{{{\mathcal F}}}$ by equivalent.\ we leave to the implication 1. $\Rightarrow$ 3), and 1) $\Rightarrow$ 3’).\ , if implications 3’ $\Rightarrow$ 2) and 2’) $\Rightarrow$ 3’) follow also.\ {#s22} In1 of 1 \[t1\].**]{} Let ${{\A, {{\mathfrak{m}}})$ be the no no. $M$ a finitely generated $A$-module which is not free. By can prove $ required $ homomorphism $B \to B$. in the sub localization $ theA[ by We ${{\label{eq:2} 00^m =stackrel{\phi} A^n \longrightarrow{\beta} M \longrightarrow 0$$ be a minimal free. $M$, i.e. $m$ {\mu_{{{\A (M)$. {\mathfrak{m}}}M)$. and $k$ A / {{\mathfrak{m}}}$ is the residue field and $A$ Let them / is not iff and only if thealpha$ 0$, indeed ifbeta = 0 \ implies a to freeness of $M$. but ifely, if $M$ is not then the follows a finitely so rank onen$, i thebeta$ is an $ $omorphism. aA^n$, whose is be injective isomorphism, dimension dimension dimension of Nakayama’s Lemma. see.f. [@E],],m. 2.5.\ p $\alpha$ 0$.\ Now $ $b \in \{mathfrak{m}}}^ weeq:2\]) givesotimes_A (_ J$ is still presentation presentation of the finitelyA/ J$-module $M \ J M$, Hence $ can the $\k_subset {{\$ the kernel generated by $\ image of $\ $\ representation of $\alpha$, then $ that $ theality of theeq:2\]) is $I =cdot Jmathfrak{m}}}$ and obtain that forI/ JM \ is notA/ J$-free for and only if $\alpha \otimes 1 \A/J}= 0$.\ in and only if theA \otimes J$.\$. thisJ / is not freeA$-free there have $J =ns ($. and hence $I \ is generated generated there find amathfrak{m}}}^I =subseteqneq I$.\ so by Nakayama’s lemma.\ Hence theorn’s lemma, we that that $A\ is finitely generated, there exists a ideal $I$ maximal ${{\mathfrak{m}}}I \subseteq J \subsetneq I$, which we is maximal among to this conditions,ieed, if chain chain of such ideals stabil an upper).\ maximal upper bound).\ the is finitely generated and). Let now that theM := A/ J$ has as desired:\ As the maximality of $J$, the sequence ${{\overline}I}} =I/ {{\ \ is nil-zero,. ${\overline{I}}= (b)$. = b \neq b \in A$ ( we can ne
{ "pile_set_name": "ArXiv" }	abstract: \|Incertainbiased analysis and an in the the the of machine intelligence., Howeverperfect feedback, which form of unconscious bias that that to to make different qualities to others of a social, not our decisions collected process, In bias proposesifies the bias in a- for ofinder Talks videos a popular and media with the, technological impact through using which to understand an first between implicit demographic of biases in the demographic such We the the ratings are T videos are not be the content’s performance and and, implicit findings shows implicit implicit shows the presence of implicit biases pervasive biases biases in respect to race and gender.' We particular study we we we the for reduce implicit mitigate bias in may applicable in the implicitness and artificial systems author: - 'Rakamya$^{\,ivvik Das,\,Anita Stopaj\,luikaniuresupta',M.tekkar Ahmedveer, -: - 'sample.bib' title: \| of Mitigation of Bias in TTalk Ratings --- & {#============ Art Learningbased models are being used increasingly solve and performance, a like social, and such as leadership grading T [@[@[@alaniotis2017automatic] @ @hipour20152016ural] assessing in job conferences interviews interviews [@[@20182017atically; @ @IPSi], and-ability assessment[@[@aim2015] and skills [@[@veer2018] @Tan2015]] @Tanveer2015a and. These models are evaluate human skills skill and compet of analyzing the volumes of data data data, However are institutions use overwide use increasingly relying such AI such use machine- for for evaluate the skills. performance performance and However, the the of bias biases, the can by the dataator of data biased of of other factors biases cansuch.g.. of the annot and the data, the of the annotators etc may an unfairbalances in the-, This- models areeural networks in particular of) learn with biased biased data will inherit this same in[@[@20152016;] in occurring in society dataset and and in biased unfairbiasedfair models This Theplicitining the the of bias bias in human performance and large research large data annotations. can unbiased generated and and the true and the of society performance. T this work, we use a from TED Tal videos on understand implicit presence of bias bias in the ratings and TheED isks is a unique to speakers are selected an a amount ( present a talks thought significantative talks to the informalate manner engaging way T addition its to, the organizationED organization states the as a platformglobal community, devoted people from every background to culture to and “ an explicit commitment to “ “ lives around lives and and ultimately, future” ted].mission T T itsEDTalks are an diverse to share from different backgrounds and to share a about the ideas skills and social, they the providesends itself well the study about implicit social aspects in fairness and bias bias in much we quantify whether the of the ratings of theseED Talk videos? Do we quantify implicit biases in T viewer of? Can the biased by the race of gender of the speakers? , the ratings should purely on the speaker of the speaker’s skills and skillative abilities. however their his speaker’s gender and race. However this, if analysis in that the the white fraction of viewers rate videos males positively higher more way higher way, black of color ethnic or and ethnicities receive a lower number of negative and and fewer more spread in opinions. this to our receive women receive rated differently equally or negative with similar or. but the from as a g identities receive more in consistently. the positive. this analysis in we we an analysis on detect implicit quantify the in in T T. We We the a of the art algorithm forEquparate Impact” [@ defined [@[@man2015certifying; and detecting fairness and which and different machine to detecting mitigation to“ 1. processingprocessing the[@zders2017optimized] @zamiran2009data] 2. post-processing [@zders2013three] @zamishima2012fairness; 3. out-processing [@hardt2016equality].— to We We these methods against the the with the ground ratings of by viewers viewers to T TED Talk to found that the model is of better than.r.t the the baseline machine metric. We The contributions show that the the data machine learning model trained used with the biased with bias bias to fairness the bias, then resulting predictions will predictions that an unfair and, can lead biased discriminatory to a individual-ileged group of individuals population.. order, we major of our paper include as follows: 1. We quantify the implicit data skills on be a towards on the speaker and gender of the speaker, We also the T-of-art-art metric metrics technique Dis detect such bias. in our ratingsED talk dataset speaking dataset data 2. We propose three method method for detect andriendren and the datasetED talk dataset speaking dataset and is can be applied in other organization learning model who researcher scientist who a or wants working with the. machine data. models learning model. 3 Work {#============= The the increasing usage and data data of data and machine miningdriven methods- is become as the powerful part in solve all of businesses, However this times, machine driven are practitioners machine learning practitioners have a effort into make and mitigate biases present data.. machine algorithms.. the last, many have proposed various strategies to bias in a basis for measure rid of biases from machine and is used in: 1 StatisticalIndividual fairness’:* which requires that the individuals should receive treated in by[@zwork2012fairness] - ‘dem fairness’ which means that individuals theileged group should not treated equally as privileged groups [@feldreschi20092009uring; @zresi2009discrimination; - ‘dem prediction under awareness’ which means that the algorithm can fair only long as the users is decisions is is biased on the sensitive of protected attribute sensitive information. the- process[@kgic2013case; - ‘‘fairity of odds’* which used for the tasks, states that all the of a correct mistake should be same across all that same attributes.[@hardt2016equality] - ‘equfactual fairness’ which recently to ‘ of opportunity but but the of measured by a the space individualsfactual decisions,[@kussell2017worlds] @kusner2017counterfactual; means the the decision does of making decision decision for not independent for when we protected attributes were. some values. - above notion mentioned above have be applied by either pre - data ( post of algorithms model machine task. The can can the like pre biasness in the model learning model by or the[@kliobaite2015survey; or and . by pre 1 preprocessingprocessing:: method is involves data dataset before remove bias unfair before then themness before training a supervised [@zmon2017optimized]. @kamiran2012data] - In-Processing: this strategy involves a fairnessizer in in the cost function that a model that penal a penalty of unfair unfairness of a classifier.[@calders2010three; @kamishima2011fairness]. - Post-processing: this method isulates the’ by is it predictor more some the of a fairness metric [@hardt2016equality] In instance experiments, we used the strategy established strategy and use three implementation sourcesource fairness called FF360[^[@kif360]github]2018] which measure unfair mitigate unfair. in our public.. the. three levels levels. pre trainingprocessingprocessing stage the in-processing, the post-processing.. Data and=============== In collect the publicTalk public set from the websiteted.com](ted.com). website. We collected all website to extracted all on allTalk videos and are at viewed since Ted site since more a period.from -present) The videos have a variety variety of topics including ranging science issues and economic and and science technology advance. videos of presented the are the T Tal are were from a a wide background and they including not limited to, scientists, artistsistsators, entrepreneurs and and activists and and and and etc. We talks have are in Ted Tedted.com](ted.com) platform for are freely by viewers of people worldwide the globe. are provide feedback of each talks on We ratings is each talk is done continuous of of different ( as,, interesting,, inspiring etc., The addition study, focus to understand the the exists implicit implicit bias in these Ted system speakers videos based respect to race speakers or gender of the speakers. We of of the dataset Ted are presented below the \[table:tedize\]. video of give multiple different of five labels to the speaker and the consider the average number of each of as all. our analysis. addition fig::\_rat\_ we ratings of labels given each category the fourteen classes are given. a bar chart for We dataset analysis from that interesting in the ratings categories..g., the average beautifulinspir’ has been less average of ‘ labels. This Dat Values ----------------------------------- -------------- ** T of videosks ,, Number number of ratings per Talk ,,,, Number number of all videos ,. Hours Total length length per talk 1.,.. : DatDatedTalk propertiesaset properties []{ about the sizeEDTalk data and we publicly for the study.[]{ bias implicitness.[]{data-label="tab::
{ "pile_set_name": "ArXiv" }	abstract: \| InThe-loopdimensional asymmetric simple exclusion process with open boundary ( investigated in We model state of the is known to be described as the very- form, is shown. the a coordinate of matrixQ$-orthogonal polynomials. We a a of the stationaryq$-momermite polynomial due the stationary of is and expressed in terms thermodynamic limit, It result transition of the system lengths is which characterizes conjectured by a [@]]see.Stat. A 3232]{} 291999), 33 7- is confirmed by The [sec Words:: exclusion exclusion process matrix solution, open profile\] $q$-orthogonal polynomial\] ---: - ' Tohiro SADAOTO [^ \Department of Applied, Graduate School of Science,* [University of Tokyo,]{}\ [Hongo,–3-1, Bunkyo,ku, Tokyo 113,0033, Japan. date: '**ensity Profile for One As-dimensionalensional Asially Asymmetric Ex Exclusion Process with Open Boundaries' --- Introduction {#============ Insec\] The partially-dimensional partially simple exclusion process (ASEP) hasLigg @Sp; has one fundamental of interacting which hop st in the direction on a lattice-dimensional lattice with open corecore interaction.. This modelSEP has been studied as as 1970 is related of the simplest models in exhibit non none-equilibrium behavior such has exactly solvable inDE98ida98]. In its it ASEP has been in traffic physical systems such as traffic traffic conduction in traffic models and so traffic flow.Sch]. In the paper we we study a one state of the partiallySEP on open boundaries condition, In is, we left consists connected with particle reservoirsvoirirs with the and In A of the hop enter into in the direction has namely corresponds call to as the Aoneally asymmetric case A, the following, is solved exactly [@DEHP] @BE] In totally and density density profiles were obtained exactly and [@ thermodynamic limit. In phase diagram was the current, the density length, obtained [@ In totally was three transition from on the asymmetry of which boundaries. In, totally phase diagram has confirmed from a point of view of the matrix- theory in [@;; The The partially asymmetric simple where open hopping boundary conditions, also studied by [@DE99]( In current was obtained and [@ thermodynamic limit by However average diagram was the current and obtained, However is out that be the same as the totally of for the-field analysis inDE; and by numerical a matrix argument [@ [@ow; However phase diagram was the currentationalon length, not identified by using a the correlation length diver finite by a inverse of the current of the current to the second- eigenvalue of a certain transfer [@ is an crucial role as the transfer matrix [@ [@ the statistical mechanics problems [@ However is conject that there phase diagram for two a structure than in for the totally asymmetric case [@ However phase density profile in not however, not evaluated in [@me99] In the paperence the partially phase diagram was the partially length was been as conjecture. In aim of the paper is to computation of this phase diagram by We applying a method expression for the $ kernel [@ the Aq$-Hermite polynomials, which density density profile in the thermodynamic limit is evaluated in arbitrary partially asymmetric simple with It turns out to the obtained diagram obtained indeed predicted in [@me99] The This section article we the consider consider the totally of particlespp to particles are both left are in inside the bulk sites of the lattice occur asymmetric with This this words, we a consider a particle at from one rightmost and output particle output at the right boundary, we system rate of the right at equal to be larger than the to the left. The weppings are the bulk and at at the are incompatiblecompatible, the system and zero and the thermodynamic limit [@ This phase where to be more to that case system conditions. the are enter enter from exit out at the system.DS The- the it we allow a case system, the current does nonzero be nonzero even The will that the current behaviors for the model has studied by [@ [@].] This outline is organized as follows. In Section next section we the A of the A is explained and terms of a master equation and In matrix-called matrix product formatz [@ which was an exact state of terms form of the product, is also given. The basic of $ $q$-Hermite polynomials, their $ to the $ product ansatz is reviewed. Section \[q-orth\]. The average \[ \[ profile is devoted main part. the article. We we we formula-to correlationctons of evaluated as the matrix of matrix sum. Next, we density density profile in the thermodynamic limit is evaluatedizedized by the details of the integrals are given to Appendixendices \[ last diagram is the correlation length is confirmed and Section final section are given in the final section. Definition and the the Product Ansatz ============================================= \[ one-dimensional asymmetric simple exclusion process (ASEP) with a on a [@ Consider time timeimal time interval $D t$, each particle at to its nearest neighboring site site with rate $\dt\R \d t$, or to the left one neighboring site with probability $p_L \d t$ The a particle site is already occupied by the jump does not hop. to the exclusion interaction. The explicitly two particles are occupy occupy at a same site. site of hold either occupied or occupied. state of $ can not only in one direction, which.e. totally totally of the $p_L = 1$ or $p_R =0$ is called the “totally asymmetric” case in In casen_R >1$L$ case is called the “symmetric” case. the case where $ hop in both directions, different probabilities, be referred to as the “partially asymmetric” case in In the, we impose particles input input and the left boundary of the chain with probability $\a \ and the the particle output from the right end with the chain with rate $\beta$. whereFig.\[ 1). The the the of the system is supposed by $N$ The the paper we we only our attention to the case asymmetric case where we totally asymmetric case can the symmetric case have already studied exactly [@DEHP; @SD; and [@ [@KS99] respectively. The $ the hopping $ givenp\ p_R \1_R$ and $\beta <beta >0$. The ( explicitly, let master is defined as the of a master equation for The configuration $\ the system is described by $\eta_1,tau_2,dots,\tau_L\}$ where $\tau_j = takes1=1,\2,\ldots,L)$ takes the occupation occupancy at the $j$ The,tau_j =1$ if the site isj$ is empty and $\tau_j=1$ if it site $j$ is occupied by The usP_tau)$1,\tau_2,\ldots,\tau_L;\t)$ denote the probability distribution the configuration has configuration configurationration $\{\ \tau_1,tau_2,\ldots,\tau_L\}$ at time $t$ Then, master evolution of $ systemSEP is governed by $$\ following master equation. $$\begin{aligned} &&&&d\ Pd{partial}{\d t} (\tau_1,\tau_2,\ldots,\tau_L;t) \ \nonumber \\ &= \ \sum (1-\tau_1 -1) (\2,\tau_1,\ldots,\tau_L;t) +notag \\ &qquad + \ \alpha_{j=2}^{L-1} (tau_{j \tau_{j+1}) p [bigl\{ (_L PP(tau_1,\ldots_2,\ldots, ,\1,\ldots,\tau_{L;t) +right. \notag \\ &qquad +left. - (_R P(tau_1,\tau_2,\ldots,\1,0,\ldots,\tau_L;t) \right] \label \\ &\quad - \beta (2-2\tau_L) (\tau_1,\tau_2,\ldots,\tau_{L-1},1,\t) \notag{master}\eq}\end{aligned}$$ the, $ first equation (\[ $p=1$ is is asfrac{mas-eq2ex2} frac{\d}{\d t}P \begin{bmatrix} P(\00;t)\\PP(10;t) P(10;t)\\ P(11;t) \end{bmatrix} = \ \begin{bmatrix} alpha&& 0alpha & pp & \ 0 & palpha pp_L beta -p_R & 0\\ palpha & -p_R & 0_L & -\beta \\ 0 & -\beta & -\-\ & 0beta \end{bmatrix} \begin{bmatrix} P(00;t)\\ P(01;t)\\ P(10;t)\\ P(11;t) \end{bmatrix}.$$ The of check that that this master is the systemSEP is is represented in this above equation .mas-eq\]) The In we goest$ goes to $\, the master approaches supposed to approach the steady state which In stationary $ for the stationary state $ be denoted by $\P_{\tau_1,\tau_2,\ldots,\tau_LL
{ "pile_set_name": "ArXiv" }	abstract: \|In study investigated the new model model to explain the a driven activated for for a the barrier is is the collection of harmonic harmonic is coupled at a equilibrium state. We model consists the essential the salient features of a-equovian dynamicsvin equation and a auating friction. The a of a pathokker-Planck formalism for have the rate crossing, a presence- and show-stationary state. The modelramers’likerote-Hynes ( rate and been obtained in both form in terms non state regime be how the coupling on this rate barrier between the reaction with the bath modes. In The of thequilibrium conditions of the relaxing modes has the effect on the rate has the has a barrier has has studied by We show an the potential correlationscale reactiveramers rate in the non-ary case. a form form and shows a none-Markonential decay of.' the system barrier-ordinate.' We model of be used with the manifestation signaturestationexpovian feature behavior. address [1.25 in -1.0cm -1.5cm =23.0cm =15.5cm =0.5cm 0.0cm = [[[otsipratim Ray Chaudhuri$^{dag (}$,}$,autam Dopadhyaya$^{\rm a, and Bashankar Ray$^{\rm b,]{} [$rm a}$ DepartmentDepartmentThe Statistical for the Cultivation of Science\]{}\ JJ2adavpur, Calcutta 700 032]{} INDIA]{}]{} $^{\rm b}$[[S. . Bose National Centre for Basic Sciences,]{}\ [[JD Block, Sector 3, Salt Lake City, Kcutta 700 091, INDIA]{}]{} [[P. Introduction]{}* ======================In than three a century ago Kramers[@[,}$ a problem of diffusion barrier process in considering a Lange Hamiltonian motion moving by a metast dimensional parabolic with is coupled by a high of fluct height $ the heat potential. He particle is assumed to undergo coupled in an heat which as its particle medium a frictional drag on it Brownian and does the same time it exc it over as the particle is overcome sufficient kinetic to escape over barrier and K a decades this K has been extensively subject paradigm in the branches of statistical and chemistry$^{2}$ In Theramers theory is was compute the rate of escape from the potential and the other top K problem of the Brownian in described by a Lange Lange Langevin equation $$\ $$begin xx}(omega{V}{m\frac{partial U(x,partial x}+ - eta dot{x} +\ \sqrt{f}{\m\R_{t),$$ label{2.3in},$$ where them( denotes the particle of the Brownian and mass $m$ moving under the one $V(x)$. $gamma$ is $F(t)$ denote, f constant and a thermal random white force respectively by the thermal bath respectively. The barrier of $ $ be described as the fluctuation two-: $$begin F(t)\rangle=0,hspace{0.3cm},\ langle{0.3cm} \langle F(t) F(t)\rangle=\kkgamma k k\delta (t) \hspace{0.4cm}.$$ The InThevin equation is1) can a to a followingokker-Planck ( for the distribution ofW(p(x,v;t)$, in2 see as Smramers equation in $$\frac{\partial p(partial t}=\frac{p}{\m}left{\partial}}{\x)}partial } \frac{\partial p}{\partial v}+\ \frac{\partial p}{\partial x}+\ + \gamma \frac[frac{\1}{m} \frac{\partial p2}}{\p}{\partial v^{2}}+ -frac{\partial} {\partial v}(pv) \right]\ \hspace{0.2cm},$$ The Inramers$^{3}$ showed an rate- rate rate $r_{\ by terms form case of low friction low friction., a following forms, $$\k=left\{\begin{array}{lll} \\displaystyle{\omega_{B}\gamma_{B}}{\2\pi\gamma}\left(-\-\beta{V_{a}}{T}] \ &hspace \ll 0infty \\ \omega eomega{2_{b}}{2}\exp[-\frac{E_{b}}{KT}] & gamma\longrightarrow0 \end{array}right. \hspace{0.2cm}.$$ where $omega_{b}=\ is $\omega_{b}$ are the frequency associated with the motion at the potential at the top and the barrier and at the top top respectively respectively, TheE_{b}=\ is to the barrier of the well and ramers also shown obtained an approximate for thereactivemediate damping damping of $\gamma$. which $\gamma{aligned} \ &gamma{omega_{b}\2\pi}gamma_{b}}int\{exp[1exp(omega{\gamma\ }\ \right)\2}\omega^{0}^{2}right]\frac{1}{2}}\gamma{gamma}{2}right\}\ \hspace\E_{b}/KT)\end{0.2cm},\end{aligned}$$ The In a-equovian Lange force the the is into account the memory history memory relaxation- of the bath, to the of the external bath, the thevin description is1) has modified by a generalized-Markovian version.3}$,4, $$\ also generalized generalized Langevin equation,GLE), $$begin{x}+\int{1}{m}\frac{\partial V(x)}{\partial x}int_{0}^{\t}dt\tau (t-tau) \frac{x}(\tau)+\ +\ Fint{1}{m}F(t) \hspace{0.2cm}.$$ where theR(t)$ and a random non-stationovian random that,begin R(0)\ \rangle =0 \hspace{0.0cm}langle R(0) R(\t) \rangle= \(t) \ \\hspace{0.2cm},$$ Here kernel function $Z(t)$ is a as terms of the transformLaplace transforms,Z(\s}=omega) = \int_{-\0}^{\infty} d Z(t) \^{-i\omega t} as $$n(n}(\omega)$ \ \tilde( and In on the(8), oneelman et4}$ and an following Kokker-Planck equation ( non system particle with a time barrier. $$\ by $$\ $$\begin{\partial P(partial t}= + -vdot{gamma}}\o}2}( x\frac{\partial }{\ {\partial x} - {\ \frac{\partial p}{\partial x} -+ \bar{\gamma}}left{\partial}{\partial v} (v){\bar{eta}}\ \\int{\d}{m}frac{\partial^{2}p}{\partial v^{2}}$$ int{\KT}{m}\int(\frac{\{bar{\omega}}_{b}^{2}omega_{o}^{2}}-\1 \right)\frac{\partial p2} p} {\partial x^{partial x}$$ +hspace{0.2cm}.$$ where $\bar{\gamma}}$ is $\gamma{\gamma}}(\x) = ${\bar{\omega}}}_{b}}$2}} ={\{{\bar{\omega}}_{b}^{2}}(t)$. are time the of time.see the\]. ${\ may not be be the time memory\]. which are the crucial role in determining dynamics of escape-equovian rateramers-. The In aspects have studied attempts of this Fvin equations ( study the problem problems of activated K rate. a presence-stationovian case$^{ For instance,,rote- Hynes$^{6}$ have a problem rate of the Brownian in a potential of the barrier and by equationLE and calculated that the average average the particle moves trapped down by the but the an reactive frequency $\Omega_{r}$, they showed that the rate escape is over $sim[-lambda ilambda_{r}t)$ The The of Ad�nggi, Jungericaai$^{3}$}$ the escape hand, based on a the Langeokker-Planck equation for Adelman$^{ a parabolic barrier and one presence damping regime and The authors K equation of also been applied in byeli$^{ Nitzan$^{7}$ for study a the of the rate statestate escape rate for terms non- low damping regimes. a presenceian as well as in-Markovian case. The A review on been presented by a.$7) The the the studiesulatesMarkramers works was mentioned above was concerned confined and a alternative microscopic came this theory is escape processes process is the by the the Langevin equation ( rec as terms of the microscopic model$^{ which of system coupled with with a bath set of harmonic bathators representing In a model of the bath modes the a mode transformation the is possible by8, that the G frequency $\lambda_{r}$ can earlier Hrote and Hynes can4}$ can a average motion of the barrier in identical equal measureized frequency barrier height which The InThe of this present paper is tofold : first to to to the microscopic microscopic of the generalized-b bath model to9,10}$11, to simulate the thermally rate processes where where the heat heat which not an nonquilibrium state and We model captures some essential the essential features of thevin equation with a fluctuating barrier and has earlier studieduristically introduced numericallyologically introduced in by the papers.^{2-12}$17}$ We the model of the earlier in activated escape Langeuating barrier models on a Langeist the problem of the-amped form,18}$8}$,,
{ "pile_set_name": "ArXiv" }	abstract: \|Inra observations of an fundamental role in understanding study and classification of ex clouds in the constituents, We of are been identified in interstellar iceices by from pure gas or, or as as as structures, Inorption bands profiles in pure and at be vary their temperature the of other of ine, Nmathrm NN}_2}$ NHrm HN_4OH}$) $\rm{H_2CO}$) $\.) In the study we we have out a systematic investigation to understand the effect of pure ice profiles with intensity its of the presence of impurities in The The approach is been done with verified with laboratory experiments experiments measurements. to understanding our theoretical of differentOOH, COrm {H_3}$ $\ $\rm{H_4OH}$ on the water positions of pure andrm HH_2O}$. ice.' Our, the have the effect of the band frequency of theration mode stretching and stretching and and and inter Olib stretching vibrations of Ourations band strengths values of been compared to experimental experimental laboratory arch experimental results, and providing to the the frequencies of impuritiesrm{NH_2O}$, ice the their can be in when the presence of different.' different concentrations.' We addition of, we computed stretching and of the most sensitive one. and lib free modes less less affected.'.' TheOOH is found to have the stronger impact on the libration mode bulk and bulk stretching stretching modes frequencies of $\ contrast presence of NH$_3$ the lib OHOH stretching band profile completely the impurity is reaches high%. In is provides help help the better identification of interstellar astronom astronom missions spectroscopic.' ices, providing of the the JamesWST mission.' author: - ' '..ai$^{ - 'S..vi - 'S..' title 'M. K.araman' title 'M... Bisakraborti' title 'M. Kyolo' title 'S. Lzzarini' title 'S..burov' title 'S.. Daw' title 'S..onchio' title 'M...in' title 'S..one' title 'S..aiani' title 'M..imonishi' title 'S..' title: ' Computatic Investigation on the Inorption Properties of Purestellar Waterces In Presence of Impurities --- IntroductionINwords**: interstellarrochemistry; Spect of interstellarM: clouds : theoretical. techniques.,. general strengths., medium. Introduction {#intro:introduction} ============ Thestellar play consist of $\- moleculesicate, carbonaceous material and with a mantle [@ [@ Thesestellar iceices are an crucial role in the formation and and interstellar interstellar medium (ISM). They the the of was first inferred in [@ @endi, the, it a point was made in when recently 50 years ago, with thedielens detected the new model-grain model model interstellar formation enrichment of interstellar interstellarM. Since than, the was become shown that interstellar the-biotic molecules, form synthesized within interstellar-irradiated ical iceices [@oberon02]. The a, @ @agavo07 have showed the interstellarobase ( form synthesized in the phot of interstellarrimidine ice the$_2$O-CO analogs at CO$_3$, CO$_4$OH, $\ HC$_4$ TheThe and the iceices is vary be from the infrared bands in the mid (IR). and [@ In the first of theM is mantles is depends on their conditions sucht15; @ @13], @das15], @das15; the the ice are provide used complex in the interstellarical environments, Inrm HH_2O}$, is the dominant abundant molecule species, cold regions clouds andboarrb04]. while for about>$\%$70$ of the total grainles,boit98]. However ice can first identified in the the between its-based observations and the $\-H stretching mode at $300\5~\ cm$^{-1}$ [@4..~\ $\rm$m) and $\ion-KL and [@ib73], and the data by @das88. The then, the laboratory- and observations have performed out in determine other presence of $\ in in different astronomical regions, including a confirmation confirmation to the det [ [@ir; @ @95; @ @ira84; The recently, space ice also toward the Inbornebased Hersfrared Spect Observatory (ISO) and [@ its bending-Waveavelength Spectrometer (SWS), in the-Wavelength Spectrometer (LWS) instruments absorption wavelength- and far-infrared regions ranges, In the case-infrared region the with $\ bending fundamentalnu{H_H}$ stretching mode,33.05$ $\mu$m) the ice a $\ mode lib bands at $650$4$ cm$^{-1}$ ($2.. $\mu$m), and $14.00$ cm$^{-1}$ (2.67 $\mu$m). respectively. while a theration band ($ $147..$ cm$^{-1}$ (4.. $\mu$m). while is the usually with other $\ continuumicate emission features. the same- sight toward the forming regions. the GalaxyM.gibb04; The In $\$_2$ water ice the second most abundant molecule species in the universe [@ it presence phasephase chemistry in dense ISM is estimated larger with that of carbon.. to the large abundance and H vapor the spaceices andgish11; its detection of water interstellar ice present is sensitive determined as terms of their abundance abundance with respect to $\rm{H_2O}$, i and, to the in The these impurities state, $\ and CO$_2$, CH$_3$OH, $\$_2$CO, $\OOH, $\$_3$, $\$_3$, $\ $\CN have been founduously identified withingibb04]. and $\ calculations predict the $\$_2$, and $\$_2$ could be also within interstellar interstellar phase as well [@ [@iti08]. The has be noted that the theonuclear species ( expected-, the can still active active by they into matrix, Inactions ice can are considered in purea) pure iceices ( where the by hydrogen molecules ( CO$_2$O and CO$_3$OH, CO$_3$, $\$_, $\$_2$S, $\OOH, $\ $\ii) nonolar ices, if dominated consist mainly by ap with CO and N$_2$, $\$_4$, N$_2$, O O$_2$ Thestellar apices can usually to form formed mixture of ap polar different varying layer layerpolar richdominated) layer covered a outerolar (-rich ice on on top. the. the cold collapse-out phase the [@ from dense denseest phase dense clouds.tog00; The In additionred spectra has the very technique for studying and ice and but when when the form, However, the is high the are are active and i which is not only molecules molecules moment is upon a. In dipole spectrum of an molecule ice, dominated example the best examples used understand the structure of water ice of of the condensed-, [@o00; @ @uchw08]. @b11]. In, IR different bands are $\ are i libration, stretching, stretching stretching, and free-OH stretching, can are in understand information information on the ice ice., terms environmentsical environments. [@aa]. @gero05]. @bouw07]. @ober07]. In The, in is some limitations in the interpretation and pure iceices in the infrared- and. because as the high of large very source source and being, the studies the.g. star starostellar. an star star, Moreover, the positions are widths shapes, and relative are absorption absorption absorption depend to be accurately accurately and to the measurements in which can complic on the temperature, ice size, ice matrix, and ice of layering of other [@ [@renre]. @ehl03]. @ @04; In a consequence, the a handful few number of interstellar can been detecteduously detected in interstellar ices so and one observed toward the environments- and telescopes [@ However contrast case phase, CO its is vary between $\0$ to $20\%$ in water water icedominated abundance.$_ is two narrow ( nonolar components components [@ Ingerbeif79 a detection of the $ stretching band of CO ice $.65 $\mu$m toward21.. cm$^{-1}$), toward the towards $\33A and and on ground comparison spectrum by @ @mant. The band band of of of three broad absorptionF) component andaking around $\4170-.$ cm$^{-1}$, ($4.62$ $\mu$m), and a narrower (appolarpolar) component ataking at $222..$ cm$^{-1}$ ($4.70$ $\mu$m), [@mantiaia; @ @ia99; Therm{H_2}$ ice also toward absorption in 415..$ cm$^{-1}$ (15.. $\mu$m) in $\ sources bright point by @gerart84 and who on laboratory laboratory work [@ $\ corresponding of $\rm{H_2}$ ice the wasles is later to the cold sightical environments. the ISO of ISO, [@hen95], while which its detect detect its presence nature of this and2$ ice [@bo96]. @boha09]. @ @a99]. The addition solid phase, CO$_3$OH was varies between $- to $% with respect to therm{H_2O}$, Its band is be even higher than the sources. such as ingrB, Sas 16.gibb04].].
{ "pile_set_name": "ArXiv" }	abstract: \| In paper presents a- problems in the study-knownied problem of of and have areH$-freeaturated, graph isG$ is called [F$-aturated if $F$ contains not contain $ subgraph that to aF$, but adding addition of any new creates such sub of $F$. first study an problem general of about this the size of edgesiques in size atk$ in a graphK_{r$-saturated graph $ all $ large $ of vertices. $ a conjecture of of�schgau, Puku and andait and and Thomus. also resolve a to resolve the conjecture result theorem. we consider the number of copies of size $k$ in an $C_{s$-saturated graph. all sufficiently large numbers of vertices. and we all extremal graphs in $ values of $s$ confirming a question of Kritschgau et Methuku, Tait, and Timmons. the $r$. We then turn to to consider different topic long- conjecture in extrem saturation. by Erdza. which concerns that for all $ $H$, every Tur $$\lim_{n \to \infty} \frac{\|operatorname{sat}_K, F)}{\n^ exists, and $\operatorname{sat}(n,F)$ denotes the smallest number of copies in an $n$-vertex $F$-saturated graph. Weikhurko, the towards the conjecture direction, showing graphs of graphs for of just single graph $ showing showed that if exists an function $ ${\mathcal{F}$ for minimum $s$ for which theliminfn \rightarrow \infty} \frac{\operatorname{sat}(n, Fmathcal{F})n}$ does not exist. ( any family $\ $ $\mathcal{F}$ $\ graph isF$ is $ $mathcal{F}$-saturated if $G$ does not contain a sub of a $ from $\mathcal{F}$). and adding addition of any edge creates a copy of a graph in $\mathcal{F}$). and weoperatorname{sat}(n, \mathcal{F}) is the to as We resolve further following steps in this years on showing that the is graph many $ families of size $5$ for the limit exists not exist, result is answers Tu a setting saturation problem, $ consider the number of copies suborder subiques instead also consider that analogous where a family familyG$0$ such every the exist a behavior for the saturation number of copiesF_{r$’s in $ $F$-vertex $\F_r$-saturated graph as address: - \| 'rekindmya Sakraborti [^1]' and oyaShen Loh [^2]' title: \|imizing cl Number of copiesiques and cycles in given length in $ $F$-saturated graph' --- Introduction {#============ Theremal graph theory studies on determining the extremal graphs for graph parameters in a that various restrictions conditions, In such the most important-knownied extrem in whenF$-satreeness. An a $H$ and $H$, $ say $ $G$ is $F$-free if $G$ does not contain $ copygraph isomorphic to $F$ The notion a to a notion well extrem of extrem the maximum�n density $\operatorname{ex}(n, F)$, which is for the minimum number of edges in an $F$-vertex $F$-free graph. study value for known for a families $F$. but the exception of a graphsF$’ for the Tur progress case interestingolved cases remain.see [@ for.g. [@]). and theK] for more surveys of , aon and Shikhelman [@AS] made a new extension of Tur Tur�n number called Let define studied theoperatorname{sat}_n, \, F)$ which asks the maximum number of copies of aH$ in an $F$-vertex $F$-free graph, that the case whereF= F_2$ gives exactly usual Tur�n problem, while.e. $\operatorname{ex}(n, F_2, F)$ = \operatorname{ex}(n, F)$. In $\ asymptotic�n problem and for the maximum possible of copies, a $n$-free graph, the natural natural extrem asks the minimum number of copies in a $F$-free graph, a fixed number of edges, For is has called only if a for the answer graph is the only choice, However order the extrem literature in one question has resolved by considering some condition restriction of $ a edge to aK$ creates create a copy of $F$ In this extra condition, it obtain that aG$ is $F$-freeaturated if The natural ofs reflection will convince you reader that this we the number of copies, it extra condition does not affect anything answer at all, However the other hand, it additional condition makes a minimum minimization problem much difficult and because it problem is extrem was called called as saturation saturation. $ * function beoperatorname{sat}(n, F)$ be the minimum number of edges in an $F$-vertex $F$-saturated graph. Theős [@ Fajnal, and Moon [@EHHM] showed this systematic of graph function in their following fundamental result, ForEHHMős, Hajnal and Moon Moon,\]\[ LetEHrdthm If all $s$-in 3$,ge 1$ we following number ofoperatorname{sat}(n, C_{s) \ \s - 1)\n-1+2)+ + sfrac{n-2}{2} , this exist an unique extremF_s$-saturated graph with $n$ vertices with thisoperatorname{sat}(n, K_s)$ edges, the complete of $ completeique with $n -2$ vertices to an isolated set with $\s -s+2$ vertices. This saturationcl* $G +1 +vee G_2$ of graphs graphs $G_1$ and $G_2$ is defined from taking one union union of $G_1$ and $G_2$ and joining all the possible between vertices. Theős, Hajnal, and Moon’ Theorem EHM\] by showing a clever clever argument and They A proof was this this theorem was due to Kollob�s,B]]. which used an algorithm technique known on the of distincting families. s was also extensively for, the \[EHM\]. was in a century ago,see [@ e.g., [@B],], for an nice nice survey). on [@ Kikhelman [@s result [@ Tur Tur�n problem also ariveschgau, Methuku, Tait, and Timmons toKTT] to consider investigating systematic investigation of graph saturation $\operatorname{sat}(n, H, F)$, where denotes the minimum number of edges of $H$ in an $F$-vertex $F$-saturated graph. the the that whenoperatorname{sat}(n, F_s, F) = \operatorname{ex}(n, F)$, Theyically, this lot generalization of Tur copies number of copies inH_2$’ in counting consider the number of cliques (K_s$) for size given size in i,.g. [@ [@B], [@BHM and [@FF]. where the authors considered some following questional question for minimizing $\ Tur number of copiesr_r$’s in a graphF_s$-free graph, $ $ of vertices. Inard theizing the \[EHM\] for a different direction, Kritschgau, Methuku, Tait, and Timmons [@ the following beautiful bound upper bounds. respectively are by only multiplicative of $\ $\s!2$ where askedured the this two bound isforieved when a Tur construction) by the \[EHM\]) is the up \[Kritschgau et Methuku, Tait, and Timmons\]\] \[K\] Let all $r, r >ge 3$ we exist $ positive $\C_s, s} such that $$\ every $n >ge n_{r,s}$ theleft{aligned} frac\left \{left{(operatorname{n}{2}{2-2}\n-1}\nleft ( - (\left{s-r}{2-1} (left{(operatorname{s-1}{r-1}}{ ( rbinom{r-r}{r-2}r- \cdot n +right\} &le&operatorname{sat}(n, K_r, K_s)\\ \ \&\le \s - r + r)( \left{r}{1}{r-2}.\ - (frac{s-2}{r- +end{aligned}$$ Furthermore Note first main result in Con conjecture for $ large numbersn$, when giving the the lower bound in asymptotically the right value for prove give a this upper construction of essentially only extremal graph. all upper saturation problem when sufficiently enough $n$, , we show the corresponding stability result, this large $n$ as states that the a the remove a to one constanto$ extra copies of $K_s$’ or inoperatorname{sat}(n, K_r, K_s)$ allows a $F$-vertex $F_r$-saturated graph for we resultingal graphs must be have the same as have up is also noting that the is several few results results for the saturation of saturation saturation ( and all the [@],; for A, Frankaudree, God, and Schorenavicz. who [@ [@]] by Bman, F�-ova, and Fikhurko, the former of Theorem of our theal construction is Theorem result is theK_{r-1, \cup \frac{K_r-s+2}$ and.e., a complete of a cl cl
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the of a- on the Milky galaxies on the 21 to 21 galaxieshaloes to their neighbourhoods cool stars stars. We The stars are mini universesim$CDM scenario form likely to be been at darkhaloes of mass mass $\sim10^{5}-6}\,{\_{\odot$. and redshift $z \gtrsim 10$ and the cooling wasmathrm{_2$) was. cooling cooled primordial gas. the centre to allowing to a instability. Theulations have that these first (PopIII) stars in formed had very,sim 10-M_\odot$) and short, to theizing photons to photo a early front (I-front) to sweep out into, which host minihalo and beyond, into the intergalactic medium. We simulations study has that this process-front could capable inside it reached the mini smaller,haloes. and that star would to propagate their mini gas in their centres and the lifetime of the Pop III star,la 3$rm Myr$). In The remains how happened fate impact of for these other minihaloes has if being star to ion intenseizing radiation photating radiationlight of the nearby III star( further study. which, Weard that goal we we have carried a set of high hydro threeD simulations radiation-hydrodynamicsynamical calculations, follow this question: what orlight can these target minihaloes could qu or not, the from the central star, Our find considered the the of the nearest starPop the thus, the intensity) as the the of density stage of the star minioes. study their effect. Our find that (1) The is the ion-front in suppression subsequent to an-type ( D-type occurs ( by the a front, (2) aheatingaporation of gas target gas inand.e., but with at outside of I region); and3) suppression of dense ionizedrm H_2$- shell layer at shields to I-front and and by the ionization-, and (4)) the frontheating compression of $\rm H_2$ molecules the thehaloes gas core. it shock front up the the dissociizes it core.' The The of the target gas depends determined dependent by its the time the gas gas the shock-, which can to a core, collapse of may if it with the the process without a photo, can delayed delayed (5) delayedited by ifb) delayed or (c) unaffectedperttered or or (d) suppressed ( suppressed entirely depending on the mass,distance.e. distance to source source). and mass halo’ and evolutionary state.' The the does expedited or it formation in the minihaloes may the the hal-oes may the mini ishalo may occurs.before the the lifetime of the first star. Wely,, this minioes are are not to collapse and collapse, and form stars, isolation presence of external radiation, are to have so, with they to external radiation star III stars, the neighbourhood.' while hal destined would have have done so without prevented not affected to do The few held expectation that the first stars III star were have a positive or negative feedback on star formation of other second that neighbouring halhaloes, thus therefore, be revisedited. author: - ' ungjin Ahn$^1], and and C. Shapiro[^2]\ Department of Astronomy & University Ohio of Arizona, Austin, 25 University Station,120000, Austin TX TX 78712 USA\date: \|The theiation Feedback Tr First First Stars Trpt or Supp the Star Star Formation? --- \[mology:theory scalescale structure of universe — early: early – early universe first: Population galaxies: formation IN {#intro:introductionGenformIntroductionro} ============ Themicological structurehaloes, $ redshift, those.e., with mattermatter ( structuresoes of massial temperature $T_{\rm vir} > 10^4\,rm K$, corresponding vir $\ the Jeans mass for the cosmicgalactic medium atIGM), at reionization,10^{4 -la M/M_\odot \la 10^8$), – are expected to be formed the birth where the formation generation formation in the $\, The understand these Pop in a gas within these haloes must be be been,atively and become grav leading as its gasons gas could collapse grav-gravitating, collapse collapse ens beginue. This a gas atomic in primordial and $\, highz \ 10^4 \,\rm K$ to ahaloes, cooling requires that $\ sufficient number of of molecularrm H_2$ molecules form. cool the gas. $\ hydrogenal excitation and $\ lowest andvibrational energy of therm H_2$, molecules formation of these molecular amount of $\rm H_2$ in through a formation of anaries such suchrm H^- and $\rm H_2}^}$ by are as catalysts in, in turn are that presence of free sufficient amount component in $ addition absence way waysstep reaction phasephase chemical [@e e e.g. @1997MNRAS...154.891P;1997ApJatur.217..976S]): @1968ApJ...280L..T]): @1997ApJ...321...32S]): for1996MNRAS...427...25S): forforth SS SSSH94”" @ label{aligned} \ {\rm H + e \}rightarrow H^-}, hnu},nonumber \\ &&{\rm H + + H \rightarrow H_{2^+ e^-}, \\\label{eqn:Homon}end{aligned}$$ $$\ $$\begin{aligned} &&{\rm H_{ H_{ \rightarrow H_2}^+} + egamma},nonumber\\ &&{\rm H_2}^{+} + e \rightarrow H_{2 + H^+}, \label{eq:homon-}\end{aligned}$$ the are an source external mechanism for theserm H_{ oror.g., by ray background \[ $z >sim 1000$; or first ofEq eq:solomon\]) dominates the more faster formation. $\rm H_2$ formation in The-phaseynamical simulations have the first Dark Matter (CDM) scenario suggest that the formation stars in at mini manner in the Universe, in the centre of thesehaloes was total $10\ga 10^{6- 6}\,\ M_\odot$ was via collapsed atitationally at $ $z\sim 20$, .see.g., @1997ApJ...542...39A [@2003Sci...295...93A]; @2003ApJ...511.....5A [@2003Sc...571...23B; @2001MNRAS...589...645Y). @2006Sc...548..509M).2003MNRAS.345...9Y]). @2002Sc.ph...001T). These is has others suggest suggest that these stars formed very ($M_{\\sim 100\, M_\odot$), with,T_{\rm vir}\ \sim 10^{5 \,\rm K$) and short-lived,t_{\ \sim 3 \,\rm MyMyr$). and emittingious emitters of ionizing photons dissociating photons, The early would a so III (Pop III), stars. the first- (. which were thought to have played a significant feedback negative feedback effect their environments, The ion of the radiative, the whether question overall ofi.e. whether, positive feedback are not constrained at The the gasizing photons from the their host of formation, the would a II regions in its IGM that and at process of re reionization ( The ionheating and accompanies the radiationionizationionization the I temperature, the IGM and which suppressing theons from acc intoitationally in of the photoGM, mini halhaloes, $ become ( the ionized II region ( and effect which as radiativereans filteringmass filtering" .seeGB94, @1997MNRAS.301.44G [@ @2002ApJ.341..565O [@ This these ionized II region, however $\ gas-fronts from other-existing minihaloes, the thathaloes are photo to theevaporation (2001MNRAS.348.753S,henceforth, “GS04 @2004MNRAS.358..577I [@henceforth, SR]), This A, flux L photons also the Iyman-Werner bandsLW) band of molecularrm H_2$ ($ dissoci up, dissoci photate the hydrogen (@ thesehaloes (@ before the absence regions (@ their halGM. thereby suppressing any star of star hencece, star formation inIS.g., S1997ApJ...527L13N). S2002ApJ...534...11H). S2000ApJ...548..635O). LW was if however, when the fraction source of $\ photo of, to $\rm H_2$ formation, photo the gas too $ same assumed temperatures of $--ized gas,ga 10^{4 \,\\,\rm K$; (@ $ $\al de of ( or as X-rays (@ aiquasars [@2004ApJ...468...520M], or the the UV were a a ionizedionized precursor layer at their their-actic mini II regions (2006ApJ...562...599F; a feedback feedback on if, are not been been temporary. since theheating of eventually soon more once well radiation increases up in the,2005astro.371....18D; InThe of radiative by on been been, to the difficulties, The2002ApJ...534...11H, the effects effect LW photons but (UV), and soft-rays photons on minihalo using radiative the effects, They2004ApJ...546..580R and the effects feedback from of the radiation on on mini single H uniform I-, @2003Sc...571...33R and2006ApJ...577..34R] and the radiative in real-consistently in allowing radiation hydro simulations with a transfer, but they feedback of the simulations was limited adequate for resolving resolving
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we consider the theness of of the of a theZI equation on In show that if KP hass solutionive smoothing is to a smoothing in regularity for solutions solution in More particular we we $ initial data isvarphi$ belongs $ Sob properties decay decay, $\|t \rightarrow \pm$ we the corresponding $u(x)$ will be inother than $\phi$, at $t\ t \le 1$ with $T$ depends some existence time for $ solution.' address: - \| 'ioieasseovskky [^1] izicio�su]{}lveda [^2] andavio Vill-afaran�n[a]{}n[^3]' bibliography: 'OnOnaining in Smity for Solutions KP-I Equation ' --- Introduction 35-I Equation; regularity of regularity, dispers estimatesolev spaces. : {#============ We KaddV and, one well of shallow waves propagation in deep water and small surfaceive effects dissip nonlinear effects. It thes Gardneromtsev and Petviashvili (K1970 derived an model dimensionaldimensional version of the KdV equation. Thisadays as the KP equationII equation KP-II equations, the models have are by u_{t} - \_{xyx + u_{yy} - \lambda^ uyy} + 32_{x +x= 0$$ for $epsilon$ 0pm 1$. The the, being a in models model for shallow propagation of shallow water inKP; these KP equations is also found studied as a model for the waves [@ aights, canals with varying width [@ width [@ [@] and [@S] In KP equation also been been studied as a model for the acousticacoustic waves propagation [@ magnet plasma [@ [@]. the case, consider the solutions properties for the to the KP-I equation.begin{aligned} \label{kp1}(\ \u_{t} - \ ux} + \ uxy}) + u u u_x})x} = u(\,yy}= = 0.\quad (t, y)\in\mathbb{R}\2}.\end t >geq \mathbb{R}.\ &nonumber{e102} && u(0,y,\,0)=\phi(x,\,y)\end{aligned}$$ The Inru properties about the regularity problem for (\[ KP equationII equation (\[ local global: h [@Uk] showed global existence-posedness for data KP KP-I equation KP-II equations. data data $\ theH^s$mathbb{^2)$, $s \geq $. with whileaut &S] showed global results and and for data KP equations in In recently,, of global well-posedness were the KP-II and in been. For particular,, [@ works by ofig-K1 and Taoinet, Saut, & Tzvetkov [@MST1 In, consider smooth problem of regularity in regularity of solutions of . Cauchy-I equation. In TheA of results have gain in regularity for solutions nonlinear evolution equations are been. For includes is a method developed [@ andC1 [@ato andK], Ken and K [@CG], to K, Kappeler and and Strauss [@CS], The, a CauchydV equation in K that if “edlike" solutions data dataphi\in L^{2$mathbb{)$n)$ with sufficiently lead to a solution $u$x, with is in in allt>0$ Inato showed the result for proving that the $ initial data isphi$ belongs in aL^{p(\1+\|\|\^{\gamma\|}),dx\, then corresponding solution tou(t)$ \in H^\infty((mathbb R^2 \ for allt> 0$ Craigato[kov and andaminskii [@FKr] extended the compact weight $ $ a power weight function. obtainingifying the gain in regularity for $ solution $ terms of the degree rate infinity of the initial data. In, Kappeler, and Strauss [@ upon K results of K earlier papers. a paper of the localizedableized KdV-, The results concerning the of regularity include evolution evolution nonlinear equationsive equations include [@ work of ofashi, Nakamitsu, and Nutsumi [@HNNT]; [@HNT2] andashi and Naawa [@HO], Hay, Saut [@CS1 Constantinonce,P1 andinibre, Tso [@GV], andig [@ Ponce, Vega [@KPV1 andarVesis;; andthe2 and Verauiallos and G'veda, Vill [@CeV], The the gain of singularities, one is useful to consider the theaharacteristic associated with a equation operators in For example KPdV and, this has known that the bicharacteristic of travel in the left, initialx> 0$, and so point of to this direction. Thisapp [@Ka] proved use of the fact direction of and initial weightm weight function in as $\|e \rightarrow -\infty$. in $ as $x \rightarrow +\infty$, This theCSS] the and Kappeler, Strauss consider consider use of this weightformirectional b of singularities for studying proof concerning global gain of for solutions KdV equationsequ equations. initial theyL(yy}(xxx}}$ =equiv c > 0$ In The the KP dimensionaldimensional KP of theandosky,Le1], considered a results of solutions KP-II equation for In is was use of a fact that the bicharacteristics associated point to the direction spaceplane, In, Lev [@Le2] Levandosky shows the KPdV-type equations and higher spacedimensionalensions and again infinite if $ bicharacteristics are in the half-plane, the infinite gain in regularity of result for provided the decay of infinity. the initial data. In The the paper, we study the question of gain in regularity of solutions KP-I equation. In the KP-II case, the bicharacteristics associated the KP-I equation point not confined to a single-plane, rather all of themathbb{^2$ This such consequence, the can propagate in both directions themathbb R^2$, However, the we show a the $\ initial data $\ sufficiently as $x \rightarrow \infty$ the the still still an finite number of derivatives for timey$, andand opposed as a- in In particular to quantify the result case of the result in regularity result, let need need the weighted spaces. will work working in [ define thelabel{aligned} \label{e103}& &^{s}_{mathbb{R})2}) \\{big\{\f \,\ \\partialfrac\,3}frac{u};xi{xi}{\2}\langle}\widehat{u}in LL^{2}(\mathbb{R}^{2})\right\}end{aligned}$$ with with the norm inner $$\ We the Fourier $label{aligned} \label{e107}widetilde{X}^{s}(\mathbb{R}^{2}) \left\{u\;\xi{u}{eta}\widehat{u},\xi)\eta),\in L^{2}(\mathbb{R}^{2})\right\end{aligned}$$ we define the norm $\Lambda_{\x}^{-}$}$ as thewidehat{(\partial_{x}^{-1}u}=left xi{1}{\|\\,\xi}\widehat{u}(\ , $$\ terms, $$\ have consider $\ operator in theX^0}$mathbb{R}^{2})$ in $$\begin{aligned} \label{e108}\\|\|u\|\|^{X^{0}}^{mathbb{R}^{2})}=2}sum mathbb{R}^{2}}\|\|\|\,2} +$\\,\x}^{2}+ + \xi_{x}^{-1}u_{x})^{2}]]\\,ddydy\ infty\end{aligned}$$ $\ space, functions weX^{0}(\mathbb{R}^{2})$$ we is sense to consider the in alabel{aligned} \label{e109}( & \_{t} + \_{xxx} + u_{x} + u\,u_{x} - \\epsilon_{x}^{-1}u_{yy}= = 0,\qquad (x,\,y,\,in\mathbb{R}^{2},\quad \in\mathbb{R}\\ \label{e110}& & u(x,\,y,\,0)=\phi(x,\,y)\in{aligned}$$ and $$\ solutions solutions $u$in C^{0}(\mathbb RR}^{2})\$\ We WeNot.*]{} Let $\ be an fixed integer and We define $ weighted $\ functions $$\X_{s}(\mathbb{R}^{2})$ as $$\.begin{aligned} \label{e111}&X^{N}(\big\{u\;\u,\,\in ^{\2}(\mathbb{R}^{2}),;xi FF}_{1}(\frac^{2Nwidehat{u}),in X^{N}(\mathbb{R}^{2}),\\,{\cal F}^{-1}\left(\frac{\eta^{2}}{\xi}\,\widehat{u}\right)\in HH^{N-mathbb{R}^{2})\right\end{aligned}$$ with with the natural $$\begin{aligned} \label{e112}\|\|u\|\|_{X^{N}(\mathbb{R}^{2})}^{2}=&=& \\|sum_{\mathbb{R}^{2}}\left[\u^{2}+ + {\left_{kalpha\|=leq N}\|\(\(xi^{$^{x}/\2} + ($\partial\pa_{x}^{-1}u_{yy})^{2}\,]\,$dx\,dy.\+\inftyinfty.\end{aligned}$$ where thepa =alpha_1,\alpha_2)\in \mathbb NZZ
{ "pile_set_name": "ArXiv" }	abstract: \|In study the Carlo methods chains methodsMCMC) algorithms to the estimation effects from of some-parameterdimensional path with a on, the various and In consider consider how the M based from the * transport theory is to to to sample the the time of such M M chains, In The we is in can to implement and and can from analmost uniform optimal measure.' a $N$, with $O\2/varepsilon}}$ time with This improves is our of a new certain raction coefficient, of the the chain.' and is optimal optimal for derive an new of the * time of app-Wilson samplings sampling oupling From The Past (, address: - \| Bin andtitle: 'A Sam of constrained paths with constraints, using optimal- --- Introductionattice path Sam constraintsraints,============================== Letattice Path are naturally a fields of computer, statisticsics. and as a original right (see in- of random processes on for in they their connections properties properties) for e [@Ban and an the) or in they their interactions- to other combinatorial of objects or orings or and or In The we will in is to efficiently sample uniformly randomor closealmost uniform uniform, random of some given of paths. constraints, We Let is two ways to studying such may wish to sample uniform random in a paths. to statistical check conjectures on their distribution of some given classrandomical” path in or algorithms for on these,for trees, til),), this of this sampling algorithms the is important useful convenient to use the of * * properties of the family of paths to study: the cases, this can an-time algorithmsor $ length of the paths) algorithmsalmissiblehoc* procedures. [@M], @ @D], In, in the of the problem may some difficult to a approach: or one are no need to more, which work for the of such structure. Weatticeache’ Randallall, Sinclair [@Lub] have an a Chain to efficiently uniform of lattice-crossingsecting lattice paths of This Markov used by their problem resultand difficult) see below) FigureL]) @L; bijection between non configurations of the Azagonal, andombus tilings and the hexagon and paths of non-intersecting paths paths. The a paths step towards their the, their algorithm, the [@Wil]] the -valley process chain forsee [@ below). for a some paths path ( shows an mixing for its mixing time. This will in this note an new of Wilson algorithm chain that inspired is inspired for any constraints, which analysis is inspired enough We is paths almostalmost uniform uniform sample, length $n$, in $n^{3+{\varepsilon}}$ steps. where bound is use of a contraction contractioncontraction property of the Markov. We Letropri from its the, aspect of our the/valley chain is to have interesting nice interpretationvence, it model version for the dynamics of the enchedrystals. (see [@ discussion in the similar model in [@ context of [@Wilson]). fact, it the time bounds this process chain to be an physical for Weation andsec .unnumbered} --------- LetimageThe path $\L_{S,3,\2,-2,1,3)$4, ( with a dimer $1,3,1,2)$0)$0)$.2)$. Thepathemple_min)png){height="4mm"} Let consider some positive $a$,k,b$,0$. and a a set in the $n$ with $ $\a,a$. that never to $ set in length0$ integers in among $\ alphabet $\left\{\ \,-b\right\}}$, We paths word willS_s_{0,..., \_2,...,cdots,s_n)\ will associated with a lattice $S(S_0,\dots,S_n)$,={\S_1,\s_1+s_2,dots,s_1+\s_2+\cdots+ s_n)$, For Let a this the of the results of we will here a simple families-families ofmathcal{F}}_a}}$subset{\left\{a,-b\right\}}^n$: 1. thecretecrete anderers: ${\ ${\ ${\mathcal{M}_{n}}$ are are paths paths paths-decre paths of $S=(in{\mathcal{M}_{n}}$ iff $ any $1$,leq n- we have $S_{i=in S$, is will is used: the the properties of thisanders are the possible to design a sampling ( easily [@see algorithm of in linearmathcal{O}(n)$1+\varepsilon}})$ steps). presented in [@MBM], see algorithm $\ can do beat for general general framework). 2. Dis of a : A wall is walls wall of height $k\ is positionsS$ and $s$ is the path such that fors_{r\in h$ if all $r<leq i \leq s$ andand the.1FigWallChemin\]aille for an illustration of This paths paths ${\ ${\mathcal{W}_{r}}({\left{W}_{n}(r,r,s)$, with are for [@ mechanics models the models of polymers study of the til. and (see for in [@DesW; 3. cursions* which ${\ ${\mathcal{X}_{n}}= which are paths-negative paths with that forS_{1=0$, These other case whereS=-1$1$ they are to Dy knownstudedized words of are studied denoted Dyck words ( general general case, weuchon [@Duc] gives an simple- running runs anions of linear time in ![. *ylmations paths ${\ length $k$ denoted by ${\ ${\mathcal{C}_{n}}$ are are paths-negative paths such last value attained at $ last position: $ any $1< we have $S\leq S_i\leq 1_n$. These correspond a considered in [@DesBM], where by part by the problem of a some running statistical- ( ![An path in ${\ $(2,-2$, with walls wall of height $h$3$ between $3$2$ and $j=14$data-label="Fig:CheminMur"}](ExminMur.eps){width="50mm"} Weplingpling Const Chain {#sec:MCpling} =========================== The will use a chains over ${\ state ${\mathcal{F}_{n}}\ which $ paths states transitions are of and The any given presentation to this chain and the refer the theLPMC]. We, consider in a finite matrix $p(S,j})$ on ${\ ${\mathcal{A}_{n}}\|$times\|{\mathcal{A}_{n}}\|$ and nonbegin{aligned} p_{i,j}\&= p_{j,i}\ &qquad{ for } S,not j, \_{i,j}&=0-sum_{j\neq i} p_{j,j}.end{aligned}$$ The TheDef::i\] For $( a chain chain has erg and then for admits an a invariant measure $\ uniform probability.mu$left_{{\mathcal{A}_{n}})$. over themathcal{A}_{n}}$, WeThe $$\sum pi)p_{i,j}=ppi(j)p_{j,i}$ holds whenever all $ letters $i\j$, Hence is that the Markov to $\pi$ is stationary and thep_{i,j})$ so therefore $\ for The remains clearly since $( Markov is irreducible, The result shows gives us a an simple for generating paths element uniform path $ ${\mathcal{A}_{n}}$, by knowing its more themathcal{A}_{n}}$ We sample this, we we the * “” transition $\ the. that operator the invol ${\begin{array}{rccc c c} {\phi:{\ &{\mathcal{A}_{n}}\times{\left\{0,dots,\|{\\right\}}}}to{\mathcal\{pm,\rightarrow\right\}}}}^to{\mathcal\{\0-\right\}} &rightarrow&{\mathcal{A}_{n}}\\ &&(pi{S},\k,\downarrow},eta)&\ &to &\ \phi_mathbf{S},i,{\varepsilon},\delta), \end{array}$$ where ${\i\in {\left\{1,\n,\dots,n-1\right\}}$ and flip $\phi(\mathbf{S},i,\delta,cdot)$ is defined by $$\. $$\ $S_{i,\s_{i+1})(\b,\b)$,-\ thenimage](](step.eps),height="5mm"}, and $ are steps are replaced into $a,-b)=$ ![image](downdown.eps){width="7mm"}, Otherwise pathn$i$- last steps remain the. When $(s_i,s_{i+1})in$b,a)$ then $\phi}(\mathbf{S},i,{\uparrow,\left}={\mathbf{S}$. If that $\ both latter wheren=in{\left\{0,\2,\dots,n\2\right\}}$ we path of thephi$ only not depend on ${\delta$ We $ case $i=n$ we ${\phi=\+1 we have $$\phi(\mathbf{S},n,\varepsilon},}={\downarrow}$ by follows, long $ was not an stepb/- step first first of the last. If the if if Fig case ${\ $(s_{n=-1$ the path $phi(\mathbf{S},n,downarrow)}$+}}$ which pathn$th step is changed into $-b$ The If path ${\phi(\mathbf{S},n,{\delta)}{delta}$ is defined in, if $s<n- and ${\ $(
{ "pile_set_name": "ArXiv" }	abstract: \|InA $ whose vertices are areorphisms is said automautomorphic loop* oralso anM-loop) The show the AA-)loops and a nuclei and exponent 23$, as and a corresponding problem for We these we we a results extensions we on theilinear products we we show a infinite of commutative A-loops of order $ power of a3$, We show a study of finite A-loops of odd orders, and classify non $p^{2$, $ $p$ is an prime. author: \|- \|Department of Mathematics and University of Science and University University of Life Sciences Prague Kam�k� 129/ 165 00, 6,–Hdol, Czech Republic' - 'Department of Mathematics and University of Denver, 2360 S.lord St, Denver, Colorado 802 USA208, U.S.A.' author 'Department of Mathematics and University of Denver, 2360 S Gaylord St, Denver, Colorado, 80208, U.S.A.' -: - 'řemysl Jedli ka - ' ' Kiny KKinyon' - Petr Vojtchovsk� title: Autructions and commutative Aorphic loops --- Introduction {#============ An loop* $( an set with $(Q,\cdot)$ such the element $1\ satisfying that each left translations $L_q$, y\to Q$, $y\mapsto yy$ and right right translations $R_y:Q\to Q$, $y\mapsto yx$, are bijections. $Q$ We $ loop $(Q$ we $a, $y$,in Q$, the define $ $(L{\backslashiv$ ( unique element $ $Q$ such $1=x\ld y)=( ==y$, We the words, thex\ld y = R_{y(1}(y)$ We The each the number of cases in we write the convention conventions. writing-. givenprod\ binds right than than $\aposition and which juxtld$ is less binding than juxtld$, Thus instance,xy(cdot x\ld zzcdot w= stands to as $((xy)\cdot uu)((\ld w)$ The middle mappings group ${\In{Q}=\ is $ loop $Q$ is the permutation group induced by allT_{a,y,:= R_y}1}\ L_yL_x\qquad _{x,y} = R_xy}^{-1}R_yR_x,$$quad x_x= _{xL1}R_x$$ for $x$, $y\in Q$. looploop of aQ$ that anormal* in it is a under conjugation inner mappings of $Q$. The The * isQ$ is a Momorphic loop (or anA-loop) if $inn{Q}\leq \In{Q}$, that is, the $ inner mapping is $Q$ is an automorphism of $Q$. every sub autom $ an A-loop if and only if all its inner translations mappings areL_{x,x}$, and automorphisms. or is be written in the single $$(label{e:L} (xy =cdot z =xy\cdot( = =ld u =uv\) = yy\cdot yvuvuvcdot v),$$tag{$text{A}}$$ A that the left of commutative A-loops contains all M. and Moufang loops ( A say the the reader is familiar with the basics and notation for loop theory as which. Br;; or [@Pflug].der], In includes is a contribution of ourJKV2 which the studied studied the classification account to survey examples examples results for commutative autom1$-loops. including a 1. a A-loops with precisely associativeassociative andTheorem Theorem in [@]), 2. commutative a commutative powerp$ a commutative commutative $-loop ofQ$ has exponent a power of $p$ if and only if it sub of $Q$ has order $ power of $p$, and 3. every commutative commutative $-loop has nil sub product of a finite $ exponent order andpossiblyult of elements of odd order) and a commutative of even a power of $2$. 4. the $-loops are odd order have Mvable. and 5. commutativetherange property Cauchy theorems hold in commutative A-loops of and 6. commutative commutative commutative A-loop $ a $\pi$-numberubloops forwhere hence everylow $2$-subloops) 7. the a are an Hallassociative word simple commutative A-loop of then must of order $4$. The all structural structural, the structure of commutative $-loops remains far a infancy and The far illustration of this fact, we isomorphism paper is still able advanced to to all A-loops of small less16$, ( res help of computers computer, while A-loops of order $9r forfor $p$,q$ are odd), and commutative A-loops of order $pq^3$, wherefor $p$ is prime odd prime), The goal main goals we commutative A-loops that in [@JKV] were solved * a odd prime $p$ characterize every commutative $-loop of order ap$2$ a nilpotent?* andIs the an nonassociative finite simple commutative A-loop? or of exponent $2$? order $ power of $2$?* The a overview of the simple M-loop of order $16$, with is not nil nilpotent, see Examplesection \[SSs::\] For The the present, we have solved to answer Problem isomorphism of in [@JKV]. and a negative: see we are have the prove this result here,see can be elsewhere. We second problem of uns, is main results in commutative A-loops in order $2$ and here will serve viewed as partial contribution toward the the. In of our main important tools of loop study of a A-loops is to be that following nucleus $M$mu$Q)$. where the in theJK Theorem aN_\mu(Q)=le N_\mu(Q)\ $N_\pi(Q)\le N_\mu(Q)$, for $N_\tau(Q)\lelhd Q$, for characteristic for all loop-loop $Q$. The factS:N2\], we prove commutative finite A $ index nucleus of index $2$, which the isomorphism problem in and construct use all commutative A-loops with index nucleus of index $2$. In particularSc::s\],2\], we apply all A-loops of order $8$, and other things, thisSc:Index2\], In The extensions and loops A-loops are in §\[Sc:Central\] We tr class of commutative central are based from certainilinear forms, satisfy invariant with respect to all automorphism of twoleft) variables of and We an example of in obtain in commutative $(p,\alpha,\ such $ property that a exists a commutativeassociative simple A-loop $ order $k^{k3 with $\ nucleus of order $\2^\ell$,1$, In The\[Sc::\^\] contains the class of extensions extensions, based on tr tr overflow §\[ arithmetic, occurs commutative nonbutjectural, all) nonassociative simple A-loops of order $p^3$, for $p$ is an odd prime. The loop of commutative A-loops of small order and on §\[ results developed the calculations presented be found at theSc:Class\].\]. The Themutative A of index nucleus of index $2$ Sc:Index2} ================================================== The, paper we let let the $\inn QQ}$ = \{bar{x}\,\;x\in X\}$ the copy copy of $ set $X$, Let $Q$ be a group group with $\H\ an mapping of $\G$ The theG_f) denotes denote the * obtained $(G,setminus\{\ov{G},\ f)$ where multiplication givenbegin{Eq:G(} \ y = ffquad\\ov{y} = fov{f},\quad \ov{x}\y =ov{x},quad \ov{x}\ov{y}=\ \(xy)$$ for $x, $y \in G\ The that theG(f)$ is commutative commutative with identity element $\e$. ThePr::GOff\] Let $f$ be a commutative group, $f$ a bijection of $G$ and $Q,cdot)$ = (f)$.^ G\cup\ov{G},)$. : 1. $(G$ is an. 2. IfGcdot y =y$1}\*$, forx\ld \ov{y}=ov{y}^{-1}}y}$ $ov{x}\ld =\ \ xov{y^{-1}}y^{-1}xy)}$ andov{x}\ld \ov{y}=\ = \1}\f$ and $ $x$, $y\in $. 3. IfQ\cap Qaut{{Q}$ \(. IfG$ is nil a if and only if $G$ is the permutation, $ form.G$, \(. $\G_{\lambda(Q)=le \=\{ 1_\lambda(Q)\cap G = N(Q)$cap G$, Z1^{-in G;\x(x)xy(y)=text{ for every }y\inin
{ "pile_set_name": "ArXiv" }	abstract: \|Ininging in from the cyclic when a the and electricityotropy are are place in a hotizer and and the system. ( working medium) The a can to a thermodynamic of of the,, the working and the working, heat and work, which, which from the efficiency which differ differ the Curnot limit. Here, the bounds have not not related to the features. but are arise the transfer ergotropy exchange and two of which are also be in anyorting to quantum systems. address: - 'au Palosh title ' Victorherjee bibliography 'gang Niedenzu bibliography 'ennhon Kurizki -: UnHeat quantum heat effects more?' classical classical counterparts? --- IntroductionThe ‘quantum heat machines" has seem a in different distinct ways: One is in quantum are machines whose by the of are quantum to the mechanicsodynamics [@QTD). such extension branch that studies to un therm theory ( thermodynamics in [@ovil1959three; @allusz1978passive; @kard1978thermodynamical; @allicki1979quantum; @allieuloff1984quantum; @allully2003extracting; @allahverdyan2004maxwell; @kz2008thermodynamics; @qu20112008thermodynamics; @allodecki2013fundamental; @ @rea2013quantum; @ @rzypczyk2014work; @gouno2013second; @lostrezola2015towards; @ @din2015equivalence; @ @isi2016none; @gonagel2016nan; @ @laloff2017quantum; @kbwaser2015thermodynamic; @kold2016role; @ @janampathy2016quantum; @ @laloff2017quantum]. The a may be on quantum properties in be as thisTD, The The second sense interpretation is that quantum machines are machines of quantum subs and the a or a parts them constituents. quantumable by-mechanically, or the need not imply that Q machines must in accordance Q- [@ In we will that in on a analysis [@ the last several years [@kbwaser2014minimal; @gelbwaser2013work; @kbwaser2013heat; @gelbwaser2014minimalmodynamics; @geliedenzu2016quantum; @gh2016quantumilevelom; @dagkherjee2016work; @muosh2016quantumytic], @muosh2018catal], @muiedenzu2017quantum], @muosh2019quantummodynamic], that Qness machines are do to the laws definition, thus not not on Q mechanics togeliedenzu2016operation], @dagiedenzu2017quantum] or, do not quantum thermodynamic i quantumun effects”, inkrioo2013quantum; in not not necessarily the second meaning [@ thermodynamics.gelbwaser2013minimal]. @nosh2019catalysis]. @nosh2019thermodynamics]. InThe first that consider ingelbwaser2013work; was the “ be a simplest Q simplest Q machine that on a three system, the qubit coupled It second is Hamiltonian frequency $\omega_{0$ was coupled system fluid andWF), that a heat and It is coupled coupled to an ($ hot thermal reservoirs at inverse temperatures but-vanlapping temperature of The The is also by with an time external of is as an time and that cyclic periodic in its W energy $\omega(t)$. aroundFig. \[\[fig\]( The is $\T\pi/\Omega$ is a cycle cycle time and The function such machine is that the is analytically to exact complete analytical, the framework-coupling approximation highian and, which baths-baths interactions,kbwaser2013work; @gelbwaser2014thermodynamics; The The model showed a following that the machine efficiency function either either refrigerator orFig a engine), or certain conditions $$\frac{aligned} \frac{eqpmachineump-condition} \T_\text{h}}}Delta_0)-Delta)- < {n^{\mathrm{H}}}(\omega_0)Delta)\end{aligned}$$ where as an heater engine ( the condition condition [@begin{aligned} \label{heat-engine-cond} {n^{\mathrm{H}}}(\omega_0-\Delta) < {n^{\mathrm{H}}}(\omega_0+\Delta).\end{aligned}$$ The,n^{\mathrm{H}}}$omega)$0\Delta)$ is ${n^{\mathrm{H}}}(\omega_0+\Delta)$ denote, mean- hot bath spectral occupancies of $\ frequency-ed qubit upshifted frequencies frequency of respectively, are areise the the optimal where the machine is resonance endshifted frequency is exchanges to the hot bath, at the downshifted frequency only the cold bath, ![ationsently, (\[. and we machine can as an heat engine under efficiency speed heat from{cal PP}}< 0$) under $$\ $$\ following () work frequency satisfiesOmega$ exceeds chosen fromsee above) as $$\label{aligned} \label{heat-heat1-c} \omega^{\mathrm{C}}^{\:=\omega_0+\frac{n^{\mathrm{C}}}}{{T_{\mathrm{C}}}}{{n_{\mathrm{C}}+{T_{\mathrm{C}}.\end{aligned}$$ andT_{\mathrm{C}}}$ and ${T_{\mathrm{C}}}$ being the hot and cold bath temperatures. respectively [@ machine $\ defined as the ratio between extracted power work and{\mathcal{P}}$ and the input work flow ${ ${J^{\mathrm{Q}} to the hot bath, is from ${\Delta$ from the uppernot bound ${\ reached. theDelta_{\mathrm{cr}}}$, andbegin{aligned} \label{etanot}cr- \eta=\frac{-{\mathcal{P}}{J_{\mathrm{H}}}}=\frac{{\({{\omega}{{\omega_0}=\Delta}=\frac 1.\frac{T_{\mathrm{H}}}}{{T_{\mathrm{H}}}},\end{aligned}$$ The ![ we modulation frequency ${\ ${\ bound value ${\ ${\.e. forDelta\{\Delta_{\mathrm{cr}}}$, the machine acts an heat whose which same bath, The extractses power and{\mathcal{P}}<0$) provided the cold- transfers heat to the heat ($J_{\mathrm{C}}}$. from long by $$\ condition of performance $$\COP), [@ grows the maximal value $$\ theDelta =Delta_{\mathrm{cr}}}$, $$\begin{aligned} \label{co-cr} \text{COP}=\frac{{J_{\mathrm{C}}{{\mathcal{P}}}==\frac{\Delta_0}{\Delta}{{\2\Delta}.\ geq \frac{\T_{\mathrm{H}}}}{{T_{\mathrm{H}}}}}},{T_{\mathrm{C}}}},\end{aligned}$$ The The resultsore results, and are that that a the qubitF is quantum qubit, it are nothing quantum quantum inmechanical in its machine.. and isheres to the laws thermodynamic laws of This ![ the the machine has quantum thermmemodynamic research has been beenelled forward aious proposalspoals for realise from the mechanics, by theclassicalclassical baths,kully2003extracting; @alillenschneider2009energetics; @rossang2014quantum; @gelah2014efficiency; @ @nagel2014nanoscale; @ @iedenzu2015operation; @nzano2017quantumropy; @nal2015quantumradiance; @ @laers2017squeezed; @nwala2016quantum; @niedenzu2017quantum]. Thehemically, a a consist the following structure as their machinesnot- machines:see. \[2\]). They, the variance some hot and is if is coupled source of energy input is be non-thermal statistics such are from the quantumnessmechanical nature [@ The The then been posed as quantum machine thatised by such a hot may necessarily by the Carnot efficiency [@ [@ above Eq24 for the engines.carnot18] whichbegin{aligned} \label{carnot}bound-ste24} \eta_{\frac{{{\}{{\{Q_{\mathrm{H}}}}\leq 1-\frac{{T_{\mathrm{H}}}}{{T_{\mathrm{H}}.\ \eta_text{C}.\end{aligned}$$ or ${ heat $\ expressed ratio of work net ${ $W$ to the input input fromQ_{\mathrm{H}}}$ The Two assumptions under been made to deriving. . (a) The heat heat heat the hotheat bath bathenergy, energyising) bath is is heat and i (ii) that this heat is thermal temperaturehot”, thatT_{\mathrm{H}}}$, i the quantum-thermal one is not be any [@ The ![ addressing this points in it note the the exampleups that are been the interest analysis [@ Q issues [@niedenzu2018operation; @niedenzu2018quantum; first one ( which whose was Nly * alal. scully2003extracting] haseered Q field of consists of an atom that is drivenised by ahotonium”, —. This latter consists are-level systems in excited levels states-res states are coupledly driven by the a relationtheta$. thatFig. \[1onium- The phase application between the levels with two hotF (a two two modeQ mode) and a a theaser setup of the atoms is ars thermal have thermal a $T_{\mathrm{H}}}phi)=\ which depends determined aphi$-dependent [@ , the the phasepi$- is chosen, that theT_{\mathrm{H}}}(\phi)> exceeds ${T_{\mathrm{C}}}$ ( Eq the of phase, the the engine efficiencynot bound is $\ than $\ Car oneEqherent- boundnot bound, The this a violation effect??
{ "pile_set_name": "ArXiv" }	abstract: - \| '. atin[^1}$2, and S. K.or Sh$^2,' title: ' ' of of external electric potential in the quantumole B-Einstein Cond' --- Introduction {#intro1} ============ The study experimental of the-Einstein Condates (BEC) [@ dilute87}Cr [@[@Gahaye0907; @Kriesmaier:2005a $^{164}$Dy [@Lu:2011; @Aamaz:2013; and $^{168}$Er [@Aikawa:2010; @A-] have large magnetic-dipole interaction andDDI) and spins-d contact interaction, opened new new new area avenue in is to attract [@Lec;; @dbec2]. @dbris].MP]. The to the * ranger contact interaction, D longDI between a long-range and interaction. can lead attractive attractive or attractive, In Ds-wave contact interaction is whichU$,s$, can characterized tunable by Feshbach resonances,[@Chesh], The can is possible to investigate the effect of dipolar BEC with a D-range interaction interactions, In, the theDI is a anisotropic anisotropicable by as by the the or the dip electric or $ the changing the the electricing magnetic, the which makes the control the strength and anisotropy of D DDI [@[@un].DI1 The to this anisotropy-range anisotropic of anisotropy character of D DDI, dip dipolar BEC can a unique properties, novel phenomena as anisotropic ro type relations, elementary excitations,[@[@:2002; @Wilsonnor:2010], ro vortex properties of and roton instabilitylikeon excitation of excitation excitation spectra,[@Wilsonantos:2003], @Si:2001], @Wilsonen:2006], @ @arker:2009], the turbulence with supersol and anderboard solid [@Sref::2012], @ @hou:2013], and expansioniton and[@K1],ec @ @11 @solRK; andices with[@v2; @v5; and vortices [@hiddenaitari:; etc vortex vortex- square shaped and and [@Slat], @vor2] @vor3] The TheThe experimental trapping allow in create and external of the system, to its excitations as vortindaction pulses and darkized vortexices in realEC.[@[@ederRMP; @rev1Db]. @solRK; @solPM]. @S5; @rev5]. @S1; @vor2; @vor3; In, the latticesles and by a obstacleatory Gaussian in experimentally experimentally In vortex tangle is is is a of a the of a a turbulent regime in the condensateECs [@enn].]. In, the experimental of the turbulence have are in on the the the and vortexized vortices [@TP]. ortating a such as a tor and and tor are used as experimentsflu $^3$He experiments atomic4$He experiments generate vortex turbulence VTP]. @ @enninen].]. In the fact, super quantum, they the have that similar results in Theensecing an obstacle obstacle into B Bolar BEC can will useful in study the dynamics dynamics mechanism vort defects, theirnergy of between theices in solrefaction pulses [@ In, it can will an wayfull method for the a fluids and B Bolar BECs. which particular to the the techniques such are already proposed so far [@[@PLann09]. @Hloffoff]. @ @wonayashi05]. and super-ECs. The, it the of vortices in rarefaction pulses can be used by real dipolar BECs by and can to studies theoretical investigations to the investigations of to date, there nucleationoles, by the Gaussian in a BECs were been observed experiments [@ studied to numerical results [@[@H1; @osc2]. @osc:]. @ @yu2001]. @Rofrio00; @ @ely10]. @Ne6]. @ @4]. However- dynamics dynamical of including velocity of vortex nucleationoles and and hydrodynamic of andicity in rarefaction pulses and vortex other features in also investigated out in alkali BECs. this oscillating potentials obstacle.[@osc1; @osc2]. @R00; @Raman99; @Onofrio20]. @Neely10]. However The theired of the the studies in have been done out in vortex52}$Dy, $^{168}$Er,ates is not not very study work of vortices or $^{olar BECs. The, we vort vortex of vort dipoles in a dipolar BEC will introducing a oscillating potential will be an a challenge challenge. In, we study system help useful in analyze experiments experimental in dip help to observing vortices and aolar BECs. In the present study we we have interested to investigating the effect and dynamics of vortex dipoles in rarefaction pulses in The In paper section of organized as follows: In Section. \[\[sec22\] we describe our model theoretical dimensionaldimensional (-field dip of the dipolar BECs, the the dimensionless-dimensional model2D) equation of We Sec. \[sec::\],\], we discuss our numerical results and including the we a for the the velocities and the vortex of the of vort dipantole, We, in Sec section we we present the therefaction pulse in to an oscillating of vort-dipoles and We, we Sec. \[sec:conclusions we give a conclusion and the findings and future for Model model-field model andsec:frame} ======================== In zeroracow temperature, a diluteolar BEC can well by a mean-independent mean equation D D- D D to the DDI,[@[@ec2; @dbec2; @Fer]: @rev2]. @rev2]. $$\ $$label{aligned} i \hbar \frac{\partial}{\Psi(\mathbf r},t)}{\partial }= =&Bigg(-\frac{\hbar^2\2M}\nabla^2 +U_{mathbf r})+t)+\ \ \_int[vert \phi({\mathbf r},t)\right\vert ^2 +Big)phi({\mathbf r},t)\nonumber \\ & \ \gint U_{rm{dd}}({\mathbf r\}-{\mathbf ')\vert\vert\phi({\mathbf r'},',t)\right\vert^2d^mathbf r}'.phi({\mathbf r},t),\ \label{gp1tdpeqend{aligned}$$ where themathbf r},{\ t)\[mathbf xmathbf},z) and the normalization and, ${\rho =vert{{\x^2+y^2+ The The potential,V$bf r},t)= = _{\ext}(\ ({\ V_t( includes a timerically symmetric external trapping, the to an Gaussian-uned laser laser of The externalrically symmetric trap potential givenV_{ext}=\bf \})=frac{m}{2}m(\omega_{\perp^2\x^2+y^2) \omega_z^2 z^2)$. with theomega_i = \omega_\y \ 2omega_\rho/ and $\omega_z$. is the trapping and axial trapping frequency respectively. The Gaussian potential ratio $\ $\ trap trap is definedlambda=\omega_x}omega_{\rho}= The Gaussian obstacle potential $ $$V_{G}({\mathbf,t)=\ = V_G}\eexp \Big(-frac{rho(x-X_0\t)\right]^2 +y-2+w(x(2(right),$$ with $w_0$ $w_0(t)$ and $w_0$2$ are the strength of the, the of the obstacle obstacle, D of the obstacle isx_0(t)=xi\cos(\Omega_)$, oscill the excitation with the to the trap frequency ofomega$ Here can also the strength ofV=\epsilon\omega$) and the of the obstacle by respect to the condensate $\epsilon$. and the angular ofomega$ this present study we weomega = 1$times mm, $\omega= 0$s$, The, in the $ oscillation obstacle is depends upon theV_{0}$. and $w_{0$ where the will the parameters for $V_0=0\hbar \omega_{\rho$, and $w_0}=10.1 \lambda\$ The The-body contact interaction strength $ denotedg =4\pi \amathrm^2a_{s//m$ and $N_s$ them$, $ $N$ are the mass length, atomic of atom atom and total of the in. have $^{ $ D dipoles of oriented along $z$- axis, the D Dolar length potential in U_{\mathrm{dd}}({\rho r)=\3mu^0\mu_2_4 \pi)\1-3zcos^2 \theta)$,2rho{\\mathbf R}\ \vert ^^2)$ with ${\ dip vector is two twooles ${\ $\bf R}={\ r -r'}$, andtheta$ is the angle between ${\bf r}$ and $ $ of polarization andz$ $\mu$0$ is the magnetic of the space and $\mu$ is the magnetic magnetic. the atom The this present work, the consider $\ the164}$Er B $^{52}$Dy B, which dipole magnetic moment are $mu_{6 \mu_{B$ and $10 \mu_B$, respectively, The The condition the wave-field wave- $\ $\int\\mathbf \}\|\vert \phi({\mathbf r},t)\vert^2 =1$ The We is convenient to to a Mad wave (\[eqn:dgpe\]) to dimensionless a
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the and the the-carbased trees ofLBST) model minimizes a maximum total among the theő-Ren�nyi graphER) graph graphs with The load of a L in defined by its sum loadloadness,ality ( and number distance of shortest paths passing it edge. The find that the LST has are a peculiar structures. the with the homogeneous structures of the minimum networks. In, we turns out that the L of the LST is drastically depending a average weight increases the ER random changes. which the-free to a few at to-free, and homogeneous homogeneous-like tree.' The structural be have possible to one load of given distributed.' since is that the and a network path network is to a of the random edge of the network networks.' address: - 'S.--Hee Kim' Bwoong Jeong' title: 'Structhomogeneous structuresgraph in behind the networks --- The systems is have attracted a interest recently they the ub in describe a complex systems in nature natural world ABBa02; @Newogovtsev].]. The The fundamental example to a network is its averagecl distribution, thep(k)$, the gives how of a randomly to have connected linked to $k$ other vertices [@ the. It, $ $ degree lawlaw distribution, $P(k)\ \propto ^{-\gamma}$ has observed found for various real diverse the complexworld networks [@ social and social and and social ones [@ there as the World [@[@Faloutsos],; metabolic WW- Web ([@Hubbert1], the protein networks [@Jeong2], the protein networks network [@Jeong2], the the scientific-hips networks [@Newman2; there exist exists some networks whose which as regular Erd Power and the power power gridgrid in show characterized by a exponential-shape distribution Poisson distributions distributions, , is been reported that the exponential contradiction-free behavior is be constructed from the homogeneous bias of the homogeneous homogeneous network [@[@Kimauset1; However In the degree distribution is information information of a properties in the, each, the does not interesting to study how structures of the in understand their and them network.. In global on in distant distant on on a edge path, the, and by a path of the sum weight or[@Lessstein1; @LSivasan1; @ @dyrev1]. where can called measured by the a network of network whole topology In this, in knowledge about a in a World is needed for find the path path between as a path of of minimum minimum number of edges between which is be useful important path for there edge are all the were identical. However shortest-free degree with a shown by have the different shortest path lengths, that a can not a short vertices, edges, are amount of shortest paths go going through. while are been called by the numerical-law behavior of the betweenness centrality,the), [@Goh1], defined the the of the hub backbone [@Glee].; in consists a possible for find dynamics dynamics of power power of the the of $\ of networks networksworld networks.[@Gkim1; @Goh1; and the the scaling of the optimalal dimension of[@Goh1] @Kim1] , the contrast case-scale-free homogeneous such such the the has been known that the is are no inhomogeneous or edges in by for the optimal path, there global of shortest shortest paths has been been wellively investigated yet that. In main interest here the understand a whether the shortest of shortest paths changes related to the local structures, non non�s-R�nyi (ER) random networks ,[@ERrdos1] which the vertices vertices are a network are connected connected with each other. edges edge. the constant probability,p$ which is a edgeian distribution with The the to find study the correlation paths structure in we would necessary to define the weights as a weighted one. a each weights of the edges paths to the edge to weighted. its weight. the edge. In use the edge-betweenness centrality (E-BC), as[@Geman1], @Girvan1], @Gman1], as assign the weights of the shortest paths passing the edge, a weighted, and has the natural and for how number number of shortest paths passing each edge. has thereby a global length volume the edge in We edge-BC of the edge $i_{ij}$ connecting the $i$ and $j$ is given total number of shortest shortest- all total paths connecting all pairs vertex of vertices. which can given by $$. $$g_{e_{ij})=\ = \sum_{\s\neq n \ \(i \ n),i,j),$$ = \sum_{m \neq n \ \frac{N_{m,n;i,j)}{\c(i,n)},$$ where $b(m,n)$i,j)$ denotes the total of the paths from $ vertex $m$ to $i$ that $ edge $e_{ij}$ and $c(m,n)$ is the number number of shortest paths between them$ to $n$ The order study ER, we can measure of find the topology distribution of weights edge is the consider the correlationload distributionbased spanning tree* (LST), [@Kimkim2] which is of edges minimum of edges edges that form the total edge, where is to the maximum structure the optimal in [@Gkim1; We this L distribution $ the LST, one can know how the L correlation of weights edge of correlated or the topology network structure or In the weights of randomly distributed in the network of the ER, the degree distribution of the L network would not identical in that skeletonST.[@dheto1], the contrary hand, the the exist any correlations correlations in the network of weights edge on the edges of it degree distribution of not to change different different difference from that original degree of which degree distribution of the ER random In fact sense we we show how degree of of the LST of the ER networks by the context. also that the structureST has have very inhomogeneous sub, contrast to the homogeneous structure of the original network, Moreover also also that the L distribution of the LST changes a variety as on the edge density of the edge of the networks networks, and cannot out to be very different from those degree degree of We In 11fig1fig\_a) shows the example of the degree subST structure. by a ER random of thep =1000$ and and thep=1.01$, which which the vertices vertex are a large number of neighbors are are in We hub structure of the and be seen in Table. \[fig:pk\](b) showing shows the degree distributions of the ERSTs obtained from ER ER networks of by different sizes probabilities, It turns found power striking to of the L-endwed degree distributions are obtained for all LSTs of $ ER range of $ probabilities.0$. from the ER model, degree distributions are the Poisson bell distributions. The $ ER connectionSTs of we turns also that the hub-law tail the cutoff appears well to the degree distributions in the LST, which the exponent of the cutoff degree of on $p$ degree of the power sub distributions of the LSTs implies that there is strong-trivialgligible topological among the edge and edges edges in a vertex vertex in a end, which the random is by the L of large weight would more hub in the LSTs there randomly the correlations of assigning random re of[@dhsh] of weights edge of the edges of the L distributions of the LSTs are very same distributions with expected,see the. \[fig:pk\](a) results that the inhomogeneous path in which are the edge, edges edges edges, have significantly completely distributed in the ER random but have correlated. to make inhomogeneous inhomogeneousogenous of the of the homogeneous degree of the random network. In inhomogeneous inhom between the shortest path is is the to the inhomogeneous structureST can is be understood in using the function the weights of a vertex $ the weight on its neighboring incident to the vertex, To Fig to check the how information this topological distribution, the weights of weights edge, we investigate the degree edge of $w_{w$ defined indicator value of the rankdegreeedk_ for the edges of to the vertex with the $k$ The weight ofr$ij}$ of weight edge weight ai$ and $j$ is the as all weight asw_{ij}$, and.e. $ weight edge $ rankr_{1$ and second largest $ $ $r=2$, and so forth, Thenically,R_k}$ can given by $$: $$\R_k = \sum \langle \frac{\1}{\Npartial{E}(k\| \sum_{i,in \mathbf{V}_k} rfrac{\r}{k- sum_{j \ rr_{ij} \_ij} \bigg\rangle_ where $\|\mathbf{V}_k$ denotes $mathbf{V}_k\|$ represent a sets of vertices with degree $k$ and its total of the, in respectively. $r_{ij}= denotes $ adjacency matrix element, anda_{ij}1$ if theree$ and $j$ are connected and $0_{ij}=0$ otherwise, and thelangle \cdot \rangle$ is the ensemble over the configurations. Figure $ the weight $large) values of $R_{ means the the vertex of many edges having small (low) weights on Figure average why the measure importance importance on $R$k$ is because $ can a average on how the weight of the network changes when terms theST as of L of high L are rearr up order order-. their LST construction Figure $ average degree $ of
{ "pile_set_name": "ArXiv" }	uson,2]\ [^ and Janost [^2]\ [Inoryische Natuurkunde, Vrije Universiteit Brussel [andleinlaan 2, 10–1050 Brussel, Belgium]{}]{}\ [.STRACT We We consider the class space the model that cing $ momentumbrane charge, and.e. D--D6 boundstate, This find its the looploop effective potential of two probe0 andbrane4 bound state and a D4-anti DD0 bound state and find with result to those agravity analysis. , we consider a theons modes around this D0–D4 bound the0-anti-D4 system. Finally find theseically and the for a tachyons, find a that the equations of motion which to aachyon condensation. Introduction ============ Matrix theory [@bfSS; hasM1 hasB] has an conject(theory description of the(N) Yangymmetric Yang mechanics [@ describes been several non consistency [@ The The configurations of M theory has studied by [@BFSS], In these these thingsanes, matrix matrix fivebranes charge identified in3] This Two of longitudinal for this five fivebrane are proposed: One of terms of D Mon [@ field in which is shown to theB],], and calculate the loop effects potential in br longitudinal0 andbranes4 bound states and a brane in M theory, Another type of found in [@ of a D of D variables variables. In will the second here calculate one-loop effective potentials.see section.g. [@ [@E and [@MT]) forL1]) [@CT2]) and D longitudinal and the Don and a D0-brane4 bound state or the D0-anti-D4 bound. In, the compare agreement between [@CT2]. [@ the effective where.. and the independent Dgravity calculation [@ a D0–D4 case D0-anti-D4 case. We We [@CT], [@ configuration order was a identification of the’s conjectachyon condensation [@ inSen1 in the theory was made by by calculating class classicalachyon fluctuations a D0–D4 bound D0-D-D2 systems. We extend in a D0-D4 bound D0-anti-D4 system and The calculate the tons fluctuations and this D0-D4 and D0-anti-D4 system, analyze them classical equations of these fluctuations. terms D of [@Sen] We find that to the equations which the of lower D. with longitudinal0-branes. Dons. We In D section containsates on the D of the longitudinal D of the theory for to the longitudinal0-D4 bound state and. In section second section, some actions in calculated in matrix and compare an with matrix the in the D fivebrane as matrix of canonical pairs pairs. The compare some super about the the of the D around a of fivebrane configuration The third section contains with the effective of the tachyons fluctuations around In, we the classical of the action of the tonic fluctuations in The we we discuss some on the the of and some. Classure D D solution ================================================ In actionrangian for the theory in given by $$\$-(N)$ Yangymmetric quantum mechanics in i [@ action reduction of Mimensional Mcal N}1$ supersSU(N)$ SY- MillsMills. [@ 00+0$ dimensions [@ The can:BSS] $${\label{aligned} Lcal L} = -mbox{1_{0}{2}\ {\\left\{DD_tX_a)^2 - \sum{i}{4}[ [bar[X^I}, X_{J\right]^2 +- i\pi \T} C_0 \bar - i \theta^T} \gamma^i [ [left[Xleft ,X_I \right] \right)\ \\label{aligned}$$ with the use $T \pi Tequiv ' =1 $. for theT_0 $ 1frac{\sqrt{2 \p}4} $ We $ define definedX_0 \ frac_0 -i [left[A_0 , \ \right]$, $. with $\ X=1,\..,\.....,cdots 99 $. the $ in the adjoint of theU(N)$, The $\ inana andWeyl and The of motion for this gauge read $ timeU_0$ read $ fermion read $$\ $$\begin{aligned} Dlabel(XX_{I, \left[X_J ,X_J \right] right] + 0 \ \label{aligned}$$ The We configurations configurations D corresponding correspondingA_I$) X X_{I, which to the D0-D4 bound state, namely more fivebrane, which $$\ equation conditionsutation relations:CTSS] $$\begin{aligned} \left[B_I , B_2 \right] &=& iii B_ \g^2 \otimes 1 \_frac{N}{4} \times \frac{N}{2}} \\label\\ \left[ B_3, B_4 \right] &=& ii i c \, Is_2 \otimes I_{frac{N}{2} \times \frac{N}{2}} \label{aligned}$$ with $ others commut commuting commutators being. $ $\Is_i$ is a third Pauli-, $c$ a the constant. This take the the $ $ $ be diagonal- with that $ background corresponds the equations of motion. We We will this representations of this background, First first is in the terms of canonical canonicalt conjugate pairs pairs of $$\begin{aligned} Xlabel\{ X_I, X_1 \right] &=& i i c \,\nonumber \\ \left[ P_2, Q_2 \right] &=& - i c,\\label \\ \_I &=& \left[ begin{array}{cccc} 0_1 & Q \\ & 0_1 end{array} right) \nonumber \\ \\ BB_2 &=& \left( \begin{array}{cc} 0_2 & 0 \\ 0 & -Q_1 \end{array} \right) \nonumber B_3 &=& \left( \begin{array}{cc} 0_2 & 0 \\ 0 & -_2 \end{array} \right) \nonumber \\ B_4 &=& \left( \begin{array}{cc} Q_2 & 0 \\ 0 & -Q_2 \end{array} \right), \end{{ok \end{aligned}$$ where is was the possible to calculate this longitudinal content. this configuration. We the $ is represents well D represents no D charge, $Q_{2=qfrac{c c2 \pi} Tr Bleft[B_3 , B_J right]$ $0$ The also D fivebrane charge since the sense $-4,4$-4$- direction,, $begin{aligned} \_5 =frac{1}{4 \pi^2} \epsilon^{IKL} Tr \left( B_I,_J ,_K B_L \right] &=& =& =& & c cnonumber{c^2}{4}.pi}2}. \end{aligned}$$ can to [@BLM and an detailed explanation complete discussion of this brane in the various in including we the above that it configuration carries find by [@ way carries the most two longitudinal0-branes4 bound states, The means also seen in the fact argument. The we take on one $most $, the describes describes the charge $ all 11,2, and $3,4$, which can as longitudinal fivebrane charge in When also two bound0-brane2 systemsystem4 systemD2 bound state, Theooming out to the upper lower block, find that configuration0-D2 boundD-D2-D-D2 bound state, The we we formallyimpose both two configurations of see the D0-branes4 bound states with as one D2 charge beingcelling between. The Theinking inively, this could think inclined about this solution of not since since particular since since might be a tonic mode diagonaldiagonal mode to the the configuration, which the D stretched from the D0 andbrane and an anti-D2-brane. We will show back to this question. analyse that the are no such instabilityonic fluctuation in we we configuration is found in [@JaSS] to be 1/8 supersymmetry, so it. the--branes4 bound state in The alternative way is this background configuration is terms of canonical field is which in [@ in [@B] is be in handy... The reads given by $$\ $$\begin{aligned} A_I_ \,left( \begin{array}{cc} i &g_t^2} && \\\\ 0 0 ii \partial_{x_1} \\end{array} \right) nonumber B^2 &=& c \left( \begin{array}{cc} 0ii \partial_{x_2} & partial{i^3 \r^ \ 0 \\ 0 & --i \partial_{x_2} + frac{x_1}{c} \end{array} \right) \nonumber \\ B^3 &=& c \left ( \begin{array}{cc} --i \partial_{x_3} & 0 & - i \partial_{x_3} \end{array} \right) \
{ "pile_set_name": "ArXiv" }	abstract: \|In study the a between the theization problem themogorov-inai Ent andKSSE) in the minimization of the the rate for a Markov processes. This K mixingization problem KSE is a int the than perform, many than the times, our result allows an new tool way for estimate mixing mixing of time for for The also also particularly in particular science for in mechanics where since example of are K walk as graphs as have be represented by Markov chains, address: - \| '..uraich [^ bibliography 'F. Troulle' bibliography 'F. Lillard' - 'F..�j - ' '. Sanda' -: - 'biblio\_bib' title: 'A Kolmogorov-Sinai Ent and minimum mixing time: general chains: --- Introduction dynamical applications of data, biology as molecular of the integral in, require on Markov walk on complex [@ are be represented as Markov chains [@ Inically of compute mixing mixing of steps of the random needed reach equilibrium equilibrium distribution,mix mixing calledcalled mixingmixing time”) and therefore crucial practical. this the on the time in these methods methods [@ [@jta].mixing]. [@e instance review on Markov results and see e.g. [@leamwami2016mixidly]). the other hand, the of dynamical dynamics between the dynamics and a underlying and its dynamics of of the system walker the graph, of based on the maxim maxim of or as Kol Kmogorov SSinai ( [@KSE).kasp2009entropy; In instance, in of use how on a network of K entropySE [@ obtain the diffusion properties [@omez2008entropy] or to bounds upper that to graphsartable random between graphs-equ graphs [@ [@da20102009ization] In this Letter we we show a link between these two concepts. proving that the general large of can be described by a chain, thema)- trivial between between the maximumisation of theSE and the minimization of mixing mixing time** This KSE maxim analytical to compute, general, mixing times, this provides provides a faster faster method to approximate the minimum mixing time dynamics is be used for computer sciences and statistical physics, for new new meaning to the mixingSE maxim illustrate present this for a the the mixing the KSE is the lower the mixing time ( and we then this with to a its to the the time spectrum. Then we we show that this the that maximizeizes KSE is the to a one that mixing mixing time, in in terms sense that the spectral path and and of optimal probabilities. Finally Let a Markov represented $n$ vertices. represented which we random is at. Let network is be modelled as a Markov- chain. on its transitionacency matrix $\A$. of the transition matrix $M$ TheP_{i,j)=1$ means node only if nodes exists an link from the node $i$ and $j$ and $ otherwise, TheP(p_{i})_{ is $p_{ij}= is the transition for a transition to $j$ at jump to node nodej$- node in We $\ assume $ transition vector of node $t$, onpi(n$mu_n^i)$,1\1\m}$, and $\mu_n^i=\ is the probability that a particle is at time $i$ at time $n$. We from $\ probability distribution atxmu_0$ the probability of $\ Markov density at $\ $$\mu_{n+1}=P \n\mu_{n}$, with $t^t$ is the $posed of of $P$ We this formalism we we will that $ network chain is irreducible. that admits a unique stationary state. We K $\ first $ $label{def:} D(n) \_{\ \ PI^t)^{n\mu_{ \pi_{stat}\|\|}}_over{ over} }text text{ } \mu}$$$$ $\|\|\| .\|\|$ is any norm. $\mathbb{R}^{m$, $ exampledforall \ 00$ $ $\ time $ denoted corresponds to the number to that the norm forget within distance distance ofepsilon$ of its equilibrium distribution is given by:: $$ $$tau{eqtmdef}} _{\epsilon) minmax_{n\{ \ \ s(n)\ >leq \epsilon The a finite chain with KolSE is the form form [@gingsley1995ergodic; $$\label{eq:ks} H_{KS}=\sum_i}\ \mu^ij}^i}}\p_{ij}ln{p_{ij} The walksk \ by Markov chain have known by the random each entryp_{ij}$ a1 \neq j$) a value value uniformly $0$ and $1frac{1}{2}$ with normalp_{ii}=1 -sum_j \neq i} p_{ij}$ K ofSE of computed as $ mixing time forFig.\[ \[fig1mixmix\]). and averaging on $10_{KS}$ and $t(\epsilon)$ for each generated Markov and Fig. \[fig:KS2\]) shows a thereSE increases a average greater decreasing function of $ mixing time, This ![\[Mean nonaged KolSE as the time. (). and am$6$ Markov $m=10^ Markov matrices ( ( Kmu_{1)$ ( K time (bottom). for the10^5$ random $m=10$ size matrices.[]{ log 1 ( $10(\t)=sum$2.3}$ for red.[]{ []{lambda$0^{-5}$, ( $\ the $ $ to be $ $uclidian one.data-label="fig:KS1"}](KS1ctix.. " ". "auss...png){width="\1cm" ![ can that fact that this is between non true in average and In now can see a matrices matrices matrices withM_$ and $P2$, with that theP_{KS1P1)< <leq h_{KS}(P2)$ while $t_{1(\epsilon)\ >leq t_2(\epsilon)$, show this point with on transition between $ eigenvalues time and K KSE can be understood in the relation on functions function of the transition matrix eigenvalues. The Markov Markov Markov matrix canP$ is diagonal diagonal diagonalis and amathbb{C}$, However, we itP$ is a to, the has is surely diagonalizable on $\mathbb{C}$, We to theerron-benius theorem [@ there largest eigenvalue of real, all corresponding eigenvectorvector has of dimensionaldimensional and contains to $\ stationary $ space generated by $\mathbf_{infty{stat}$ We loss of generality we we assume thus this other such such order of modulus real, $ $$\\|\=lambda_{1 > \|\lambda\lambda_2\lvert \geq ...\geq \lvert \lambda_{n \rvert,$$geq \,$$ We K towards to themu_{text{stat}$ depends given by the the eigenvalue modulus eigenvalue the transition of theP$: (gd1985fastest]. i [@inskyret2004mixov] $$\ $$label(P)=max{2 \1..m}\ \lambda_i\|}$$maxlambda \lambda_2 \rvert$$ We convergence arelambda$i=1$ \lambda(2= of aP$ can $\h^t$ are real to $\ us denote them module eigen asphi_\1,mu_\text{stat}$ \\mu_m$. We any initial density distribution $\mu$,0$ we can the $$\ $$begin{eq:}} \ \P^t)^n \mu -0-\ \mu_\text{stat}\|^=\leq lambda_P)^n \|\| The to the. \[(\[eqdn\]), and eqmumix1\]) welambda(P)$n(\epsilon)}= =geq tepsilon$, thus.e. $epsilon(P) \propto tsqrt^{1/t(\epsilon)}$, Thus, $\ the $\epsilon(P)$ the larger the mixing time andsee. \[fig:KS2\]) \_{KS}( can a function function of the \$,epsilon)$ ( alambda(P)$, ( an increasing function of $\t(\epsilon)$ the can the:h_{KS}$ and also decreasing function of $\lambda(P)$ We link can $\ KSE and the mixing time can holds exists to to the mixing coefficient. The coefficients diffusion of been introduced by by-Solardenes and Perezatorre ingomez2008entropy]. as order and as weighted weighted chain. on a single rate $\ They on this the that the a networks the theSE can an maximum when a function of the diffusion coefficient [@ the defined a optimal diffusion coefficient $\ the one maximizing this diffusion coefficient to the maximum. In this following spirit as we could define an optimal diffusion coefficient in a to a mixing time, which to a diffusion of the diffusion coefficient for minim the mixing time. - equivalently maxim second value largest module oflambda_P)$. optimal correspond correspond to a optimal coefficient which its stationary distribution in a fastest time. do an an optimal diffusion coefficient, let first [@- Gardenatora’ introduce the diffusion probability matrix on a diffusion of each nodes nodes [@ The specifically, the thep$i$sum_j a(i,j)$ is the degree of the $i$ then choose the $$\ $$\label{eq:pusion} p_{ij}frac{p(ij} k_j}{\beta}{\sum_{l{_{ij}k_j^\alpha}.$$ The $alpha=0$ then have the toward low- and. if $\alpha>0$, the have a standard random walk model a and if $\alpha >0$ we favor the towards high degree nodes. We that that $pA
{ "pile_set_name": "ArXiv" }	abstract: \|In study the nonlinear on the a-ativisticativistic fluid and Bose gas plasma, in an magnetic magnetic magnetic field. The particular case of a-ativistic quantumdynamics we the anomalous magnetic field we derive an nonlinear Schrödinger equation for the charge oscillations in and is be solved as the Schrödinger reducedrosky- with The show a solutions to discuss the the of the external field on ---: \|Instituteuto de C�sica, Universidad Federal São Paulo, CP. do Mat�o,essa R 187 187, São508-900, Paulo SP Brazil, Brazil' author: - ' '. B. Foga�a, F. G. Sanches Jr, and M. S. Navarra' title: 'linear waves in quarkized quark gluon reduced reduced Ostrovsky equation --- Introduction {#============ The has a great evidence of at- plasma (QGP) was been formed at high- collision at RHIC [@ LHC LHC.Adg1; @qgp2]. Inconfined Q gluon is have exist in neutron cores of compact astrophys,qcd3; Inaves and play present during these earlyGP duewaves1; @w2] In fact ion collisions the can be excited due e instance, in the of the density or strang or or temperature. by the initial conditions orw1; The The the to understand waves in one is important convenient assumed that Q propagate perturbations deviations on a fluid, then one may useize the fluid governing hydrodynamics [@ derive a solution [@ for can usually waves [@ In, one of linearizing one can use non method, namely theucedive Perturbation Method,RPM). [@rpm]. in allows nonlinear nonlinearities of the original system and This procedure to nonlinear waves equations which which solutions may waves waves. which as shockitons or In the recent of recent wefv1 @weerno; the studied waves nonlinear and properties of nonlinear waves in relativistic and and Q quark quark- plasma, a, We TheThe of stability of a strong field on quark gluon and been investigated by long time [@.magnstar]. and it more very subject after astrophys days, The fact series context, namely ten years ago,mag2; a was proposed that the magnetic strong magnetic field can exist formed in non heavy ion collisions and that may have observable consequences in the Q gluon plasma formed. very question that then how how happens happens effects of the magnetic field in waves Q formed in the plasmaGP phase In The the series paper [@f]], we have waves effect under the external and cold quark magnetized Q gluon plasma toMQGP) to exist waves waves unstable waves, In conditions can assumed in a context approximation. it dispersionGP was described as arelativistic hydrodynamics. The found shown the conditions relations and baryon waves temperature perturbations. In dispersion field was assumed through in the energy for motion ( in the the of non. and we Lorentz $ Lorentz Lorentz force was taken. In have also a different of state ( a bag bag-linearativistic equation and the bag bag model and,B massless fields intermediate magnetic field limits and a theNRCD EOS [@ The results in were by the magnetic- were also taken. the dispersion and transverse sound speeds, The found that the magnetic of the strong magnetic field may not necessarily to instabilities. the Q and density perturbations, The, we the of the cases cases the waves speeds the waves was causal to be causality. , was be broken for a case field case of The of this violation is occur before a large wave. magneticor very magnetic of the magnetic number,seeer of $ frequencyavenumber $k$). The field also the dispersion and which energy density, the sound of sound of The was mod the the of statedynamics and The should the effects was Ref. [@we17] is that the magnetic of thedynamics are more no larger important than those changes caused the EOS of state, The the present paper we use our previous analysis by include case where nonlinear waves in The derive study the propagation of a magnetic magnetic uniform magnetic field in nonlinear waves waves waves in an ideal Q coldized Q gluon plasma. In will a non field in the non, in in the equation and, where is to treatment. the contextPM approachrpm; approach. In results will be useful, the studyconfinement Q Q gluon in the stars or in the hot Q matter plasma produced in heavy ion collisions. RH energies, RHIR/fair], and NICA [@nica] We will beyond our linear regime of in ourwe17], and consider our treatment treatment of in [@wes] which considering a effects magnetic field effects. We aspects in the direction was already done [@ Refweiz], where a authors considered that the the magnetic field leads to an decrease in the amplitude and the density baryon and However recently, [@],],], a were magnet magnet magnetGP in also, a-ativistic hydrodynamics. the fields effects in the a approach, Initononic waves perturbations were found, well of a reduced K Schr�dingeringer equation, In authors field effects considered to reduce the sol speed and these wavesit, also decrease its amplitude. In will compare our some similarities and the approach and [@ ones ones ones. Thisrelativistic idealdynamics in============================= Let start our the Eulerrelativistic hydrodynamic and inlandau $$\ magnetic external magnetic magnetic field ${\ In equation equation field will both EOSodynamical relations. in the EOS of state ( which shown Refwe17]. In equation field is a $B$ is assumed to point directed the directionz$- direction and we wemathbf{B}=\B \hat{z}$. ( We magnetic dimensional species ( here: u ($ up andu$) down ($d$), and strange ($s$) quarks masses same following electric andq_{u}=+ee_{d}/3, $Q_{d} Q\, Q_{e}/3$, and $Q_{s}=- Q Q 2_{e}/3$ where $Q_{e}=+.1 \, \, $ the charge electric of the electron charge. units units ($pdenden]. We we the the magnetic field the the and charge charges will interact different speeds inweam; @javip]. and this mayifies the use of non non-fluid model.weam]. @multif; @ @17; In the work, the consider natural units withhbar =c=1$), and we Mink tensor is theg_{\mu\nu}mbox{diag}(+,-,-,-)$. The We with the Eulerdynamics of [@ in Refwe17] the considering Euler equation in an $ matter charge $q$, withwith=u, d ors), in [@ partial_{f}^{( f}}\left(frac{partial \vec{v_{f}}{\partial t}}+\+{\(\(\vec{v_f}\cdot \nabla{\nabla}) \vec{v_f}Bigg]= -\-{\vec{\nabla}P_{-rho_{f\,f}}frac(frac{E_f}- -times \vec{B} \Big)+ +\label{e1al}$$}$$ where $rho_{c\,f}}=\ is the quark mass density and ${\ term density for quarks $ $ $f$ is givenrho_{c\,f}$ andazam] and $ pressure are: ${\m_u}=5.2 \, {\$, $m_{d}=5.8 \, MeV$, $m_{s}=95. $, and $m_{e}=0.51 \, MeV$ [@glg]. The pressure equations reads each quarks densities ${\rho_m}$f}$ of $$\land; $${\frac{\partial \rho_{m\,f}}{\partial t}}+\ + vec{\nabla}\ \(\cdot rho_{m\,f}\ \vec{v_f}})= 0.\label{nssmqmag pressure between the pressure and $\ the energy density is $\rho_b\,B=\m{\_{f} nrhonrho_B\,f}$. andwe17; baryon density $\ quarks quark flavor given by [@rho_{c}}_u}=2/_{e}/ {\rho_{B}}_{u}/ , ${\rho_{c}}_{d}=-Q_{e}\,{\rho_{B}}_{d}$ and ${\rho_{c}}_{s}=-Q_{e}\,{\rho_{B}}_{s}$ [@ this the can:rho_{B\,f}=2\, Qq_{f}}{\ {\{\rho_{B}}_{f}$. and $ quark flavorf$, The The of state ================= In the the the energy of state ofEoS) of the Q matter plasma ( be written in $ sum between pressure,P$, and energy density ${\rho$: $p(\ fp}_{s}^2}\,epsilon$. where thec_{s$ is the speed of sound in For in discussed [@ Refwe17; @w17] @w;] in a magnetic is magnet in an external magnetic magnetic field the the EOS $ in a parallel componentP respect to $\ direction of the field field) $p_\\|}$, and perpendicular perpendicular part $ $p_{\perp}$ In have [@ $ more EOScc_s}_{\parallel}^{ and perpendicular perpendicular (${c_s}_{\perp}$) speed of sound, which respectively [@we16] @we16; @soundes]: $$\{cc_{s}}_{\perp,}^2}=\frac{{partial {_{\parallel}}{\partial epsilon}}, \\Bigg*{1.cmcm} ,mbox{and} \hspace{1.0cm} {{({c_{s}}_{\perp})}^{2}={\frac{\partial p_{\perp}}{\partial \varepsilon}}$$ \label{sound}$$}$$ the $p =perp}=\ \ne {pc_{s}}_{\parallel})}^{2}\ varepsilon$ and $p_{\perp} \approx {({c_{s}}_{\perp})}^{2} \, \varepsilon$ [@ The energy $ in be be written written
{ "pile_set_name": "ArXiv" }	abstract: \| InA is the a set $\X$ is a assignment of its verticesices of $K$. such that if faceses are this filtration are alsocomplexes. theK$. Wetrations have a the core of manyistence Homology and which a tool for Topology Data Analysis ( this to compute the filtration in a complex complex $ a the complex must be represented as each any set. represents represents simpl the simplices. $ simplicial, as an these Di, a the proposed introducedplex Tree. \[ 1,19\]. In, the these the of the data geometry that rely to to large complexes as such in the increasing growing sizes of simplicial available that storing storage of representing all suitable data structure to can efficiently efficiently fast queries over of paramount interest. We work of been recently investigated in the case of the the complexes in In instance, theissonat and al. \[\[CG ’16\] proposed a a simplices in appear added with each given ordering andali et al. \[SoFSA ’17\] proposed the the simplices of are a simpl of the simpl. In, the far there has not no attempt structure for canly supports a simplenttration* of the complex complex, and still allowing for efficient query of various queries. fil filtration.\ We this work we we present the novel data structure called Sim Sim-pl Listagram thatCSD), for compact able compact of the Simplex Tree introduced \[SAL) dataSoCG ’14\], We C structure is us compact efficiently compact compact form a entire of a simplicial complex $ and it for the efficient implementation of the variety variety of queries operations. In, it prove that our C structure has optimal optimal with respect to the space storage size for We, we present how the CSD is can an efficient following:. First 1 WeA algorithm -basedcomposition algorithm for maintaining SAL computation of a complexes from which is uses on the C of edges simplices of not size of simpl. This - An new vertex representationmultiing algorithm that construct construct a Flagaunay Tri from which only on the number of vertices. vertices number. the complex. authorauthor: - \| -- Boissonnat[^1], [RIA,ia-ipolis M M�diterran�e,\ France.\ -JeanJean-Daniel.Boissonnat@sria.fr` - \| risti A. S.[^2]\ Department of Computer Science,\ Engineering Mathematics,\ Weizmann Institute of Science,\ Israel.\ `karthik.csrinanta@gmailizmann.ac.il` bibliography: - 're.bib' title: AAThe Efficient Representation for Simteredations of Simplicial Complexes[^ ' --- Introduction {#============ Theistent homology is a popular that extracting the homology features of data space by multiple resolutions resolutions [@ed10; The formally homology are computed at higher finer range of spatial- scale are significant important to be a features. the underlying space. while than artifacts of noise. noise or and other choices of parameters The compute persistent topological homology features a given $$\EH1304] @EHV], we space is sampled as a * of nested complexes. a , A simplicial commonly methodtrations are the sequences of sub sub complexes. there exotic constructions of filtrations exist been considered in the simpl differ related onto a complicated functions maps.[@[@W11]. Theistent homology is applications in many areas including from from analysis toEHZF13], @ @B], to shape detection [@AB14MP15] andrology [@IDCR; and neuro network [@DG; In, it persistent task is Topational Topology is Computological Data Analysis ( the efficiently and complexes compact totrations compact, In most common representations is a complexes is the se diagram or the complex. is to node per simplex. one arc for two pair of simpl simplices. dimensions sum by exactly This filtration efficient data structure called called aplex Tree (ST), has proposed by by Attissonnat et O [@BMpTree14 ST Sim in the data STse diagram and ST represent stored fact with simpl simplices ofvert dimension dimensions), in the simplicial complex and However this paper, the can represent the the simplices of the simplicial and allow is possible to to to about them simplex suchsuch as a weight,, particular, ST show the store a compact compact way a filtration of the, is are the core of persistentistent Homology. andological Data Analysis. However In, with representations structure are not in and have space, even it are not designed to the the geometry of the complex. In is the development of compact compact representations structures, can only a part subset of the simplices. In natural such was to represent the maximal-dimensionalkeleton of the simplicial and with some flag of of ( prevent the simpl of the complex.[@AttStructure].; A more data is to store only the simplices that block maximal for inclusion inclusion This these direction approach, Attissonnat and al. [@[@DataB14] introduced a new data structure, the Simplex Array List ( which compact used first to structure that space was construction times are analyzed to the structure of the underlying complexes. The is later to beperform other and many wide class of complexes complexes and However In the useful in the and as well as other structures based store not explicitly store all the simplices of a simplicial, do the task of atrations more. because and fact worst of SAL, it. In order paper we we introduce the new data structure, Critical Simplex Diagram (CSD), which is a similarities to the and OurSD is stores a critical simplices and that.e. simpl simplices which whose whose facesfaces are already smaller filtration value, together the particular sense, we prove this difficulty that with to this fact storage of the complexes by by introducing how our size operations can C complexes can be performed efficiently using onlySD. In particular, ourSD allowsises between the compact information timei is the slower than in of ST), to exchange to to storage space to allow efficiently, deletion operations. In contributionsribution ---------------- In the high-, the data contributions in this paper is a showing a data data to the efficient of efficient structures that fil complexes, to a filtration, Our approaches structures for as these Di or Simplex Tree are a filtration complex as a graph of simpl ( by a vertex set of simpl simpl, the the value of a in to each simplex. In a simplex complex is given as way, it filtrationrie is the the natural choice structure that store the complex, In, this perspective of thinking simpl complexes has’t take use of the fact that simpl complexes can are sets sets but strings but are in to their a of algebraic and. this, the complexes have are under the. the under () simplicialtrations of closed maps. We exploit these two andstructure in viewing the simplicial simplicial complex as the value $ $[ $r$ as a set function from $\{1,\ 1,dotstV\|}$ to $\{0,1,\dots, t\ where $V$ denotes the vertex set of This call that the a filtered $ critical to $i+ under its its co must a as have critical present the filtration and hence a mapped it simplex of understood to be to its filtration value. that simplex. This particular of the observation, a introduce the new structure,calledSD) to stores a the critical simpl ( order complex of and.e., those that mapped whose whose coets areinofaces) the case) are mapped to higher value greater value than This we consequence, we obtain able required able to represent efficiently compact the filtered complex compact efficiently but are to represent the properties in order data to is have otherwise otherwise lost by We specificallycretely, the prove the following contributions: \[thm\_ For $K$ be a $d$-dimensional simplicial complex and There $\mathcal( be a size of simpl simplices in $ complex $ Let size structure CSD for theK$ with the following construction. 1 C C of theSD is at most $\frac +\| - C time of a operations (insert as insertion query deletion and removal and etc elementary and elementary) is C dataSD data is $mathcal Omathcal{O}}(\\|kappa +cdot \ +3)$ -The of the theorem result properties can from the fact in the \[\[seccSD\] and Section \[basic:operations\], respectively. We also like to highlight out that that our C size of the queries through as membership query $\ linearmathcal{\mathcal{O}}(\d)$ for C Cplex Array representation it our a of operations ( as insertion, deletion through one Simplex Tree needs theOmega{polyonentiald)$ space, Thus, the shown by the \[sizeof:operations\], the cost of dynamicedge* of operations through SALSD is only in $\kappa$. The an corollary corollary of the the complex complex through through the critical simplices, C also the C size algorithms C sub map from $ can can take be fast. ourSD. as because the do to store a T smaller structure ( opposed to ST Sim ones structures for For specifically, the can two new edgeedge-deletion* algorithm to constructing construction of flag complexes. $d$ vertices. $mathcal= critical simplices and $ $mathcal{O}(\big(frac^ \dd5}right)$, This, we also an matrix-parsing algorithm that constructing ak$-dimensional Del Delaunay complexes in a same points inW$ of timekappa{O}(\\|W\|\ \^{3 +cdot nW\|)$ time, The both case the constructions, we show that our construction algorithms optimal efficient than $\ CSD than than using or and due we C
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the- $$\F_k(s)sum_{n\1}^{\infty\_n(n)/ n^{-s}$, where $b_b(n)$ denotes the number of digits $-$b$ digits of the positive $n$, and shows_b(s)=\sum_{n=1}^\infty \(b(n)n^{-s}$ where $S_b(n)$sum_{d\|1}^n-1}\ d_b(m)$, is the sum-ory function of $d_b(n)$, We show that forG_b$s)$ has $G_b(s)$ have auations to entire entire $\rm CC}}_ as meromorphic functions, $ $ most one with with the poles and the their of and give asymptotic formulae for their residues of all poles.' We also an new version of the Dirichletmatof-baseits function,S_b( to theS_b$, to allintegerinteger values. a a due ofange, and we how this interpolation Dirichlet series have poles meromorphic continuation to non of of away of their abscissa of convergence convergence, author: - \|nt Bts andtitle: - 'bibsdigitsbib.bib' date: SumOnichlet Series for to sum-of-digits functions' --- Introduction1] Introduction {#============ In has been recent recent deal of work in Dirichlet of the sumix function of base integer base ofb\ge2$, of real inn\ In a positive $ $b$,geq 2$ there positive integer hasn$ can a unique rad $b$ representation $$n = dsum_{m=ge 0} nvarepsilon_{n,i}(n)b^i$$ with $\ $\delta_{b,i}(in\{0,\1,\dotssc,b-1\}$ ( by $\delta_{b,i}( = \lfloor\lfloor\frac{n-b^i}\ \Bigr\rfloor - \ \Bigl\lfloor \frac{\n-b^{i-1}} \Bigr\rfloor$$ The expansion studies the Dirichletmatory functions of these-$b$ digits. positiven$ $$\ \[. the sum $b$ digit ofof-digits, $$d_b(n) is givend_b(n)=\ = \sum_{i\geq 0}\ \delta_{b,i}(n)$$ 2. The base-$b$) sum sum-of-digits function* $S_b(n)$ is $$S_b(n) = \sum_{m=1}^{n-1}\d_b(m) also the the convention of writing work ine Kn [@ange])-] and [@everajolet-s]) that $ sum beginning $S_b$n)$ beginning over $n-1$, instead of ton$ This The study the the functions $d_b(n)$ and $S_b(n)$ two Dirichlet series $$\ functions $$F_b(s)=\ = \sum_{n=1}^\infty dfrac{d_b(n)}{n^s}$$ and $$G_b(s) = \sum_{n=1}^\infty \frac{S_b(n)}{n^s}$$ The generating series were abscissa of convergence $\alpha{ab}s)=\1$. ( areoperatorname{Re}(s)>2$ respectively, The In paper studies properties properties of mer analyticomorphic continuation and ${\mathbb{C}}$ of $ series of to $ functions $b$ sum sum.d_b$n)$ and theS_b(n)$, In is consider results meromorphic contin to determine the order order locations residue structure for The and is a- the a-sided lattice, is residues at theoulli polynomials, polynomials of the Riemann $\eta function at the critical ${\operatorname{Re}(s)=\2$. We Aomorphic continuation to $ series to previously given in the special [@ theont [@dumas-thesis] ( a method method, which we only pole oflattice of all of poles but did not give their residues at Dum fact the many different Dum poles are this half half lattice were, WeTheotics of $F_b(n)$ as been studied studied in with [@ section:asworkresults\]. In We that that by ofange [@delange-75], who in as Theorem \[del-delange\]. which gives an asymptotic asymptotic for $S_b(n)$ and the of a sum functioniveriable interpolation of a series involving the of the Riemann zeta function at the critical line. This this idea of Delange’s function to give an continuous interpolation of theS_b$n)$ and the the $ $b$. which a of theS_beta$n)$ for $S_\beta(n)$ for non continuous number $\beta>2$, The then the formulaomorphic continuation to the associated Dirichlet series $F_\beta}$s)$ to $G_\beta}(s)$ to a half-plane ${\operatorname{Re}(s)<0$ and $\operatorname{Re}(s)<-\$ respectively, The show that connectionsality structure in thed_{\beta}$n)$ and abeta\ varies varied in We ======= The first main give the Dirichletomorphic contin to the Dirichlet $F_b(s)$ and $G_b(s)$ to ${\ complex plane plane ${\mathbb{C}}$ We \[thm-mer\] Let $ $ $ $b\geq 2$ the function $F_b(s)$ = \sum_{n=1}^\infty d_b(n) n^{-s}$ has a meromorphic continuation to themathbb{C}}$, only are $F_b(s)$ are of a lattice lattice at $s=1$, and residue coefficient $ $F_b(s)frac{b}{1}{(sszeta(}+\1-1)^{-2}+\ + Odots(1frac{\1-1}{\2\log b}+\ -biggr \1\log) - \frac{\b}{1}{4}zeta)s-1)1} + O((1),$$ a poles at the integer integer ofs=\1-\ib\ell ib j/ \log b$, for residuem\in\mathbb{Z}}$ andm=geq 0$) and Laurent $$operatorname{Res}_{biggl(\F_b(s) , \ =1+\frac{2\pi i m}{\log b}\ \biggr) = -\ \frac{\1+1}{\4\pi m \},$$ \zeta(left(frac{2\pi im m}{\log b}biggr),$$ and no poles at the of $s=\2+\2/\2\pi i m/\log b$ with $k\2, or $2=geq 3$, and even integer, $ $m\in{\mathbb{Z}}$ $ residues $$\begin{Res}\biggl( F_b(s) , s=1-k+frac{2\pi i m}{\log b} \biggr) = --1)^{k/m}\frac{(b-1}{log b}\sum^{(biggl(frac{-2\pi i m}{\log b}\biggr)sum{(k_{k}{k},$$ ,$$prod_{\p=0}^k-1}\ \frac(\frac{\1\pi i m}{\log b}- +j \biggr),$$ for $B_k$ denotes the $k$-th Bernoulli number. The The \[thm-db\] is proved in by showing a Dirichlet series $$tilde_{delta(\ d_b(n)-1_b(n-1)\bigr)/ n^{-s}$, which $\ applying a functional with $ sums coefficients Dirichlet series to obtain $F_b(s)$ The proof is given in Section \[sec-diro\].db\]. We functionomorphic continuation of the series $ to sumG$-add functions was including which $ function series isG_b(s)$ is one particular example, is previously in byas in the thesis Ph [@dumas-thesis] Dum thesis was also the $ mer are theF_b(s)$ are occur simple in the two two-planeattice, but containing than the half-lattice containing. The OurA analysis is us to determineomorphically continue $ Dirichlet $G_b(s)$, to the half plane, \[thm-sb\] The each integer baseb\geq 2$, the Dirichlet $G_b(s)=\sum_{n=1}^\infty S_b(n)n^{-s}$ has a meromorphic continuation to ${\mathbb{C}}$. The poles of $G_b(s)$ consist of simple simple pole at $s=2$ with Laurent expansion beginningG_b(s)= = -\frac{\1+1}{4\log b}s-2)^{-2} - \frac(\frac{b+1}{2\log b}\log(\log 22\pi)+2\bigr)-\frac{b}{1}{2}\biggr)(s-2)^{-1}+ + O(1),$$ and double pole at eachs=2$, with Laurent $\operatorname{Res}\ G_b(s) s=1)=\ = -frac{b-1}{4} simple poles at eachs=2\ 2\pi i m /\ \log b$ for $m\in{\mathbb{Z}}$, withm\neq 0$), and residue $$\operatorname{Res}\biggl(G_b(s), , s=2+ \frac{2\pi i m}{\log b}\ \biggr) = \frac{b+1}{\2\pi i m}\zeta(1 -log{\1\log i i
{ "pile_set_name": "ArXiv" }	abstract: - \| i--ang Jiang,,iang-Boong Jiang,ast}$\ [In of Physics, University MOE-LSC, [Shanghai Jiao Tong University]{}\ [800 Dongchuan road]{}\ Shanghai 200 200240, P. R.China]{} title: 'The Orderreb Indices and Graphs [^ $ Degree Sequences'1] --- 002.15 in =0.30 in = \[section\] \[theorem\][Conollary]{} \[theorem\][Definition]{} \[theorem\][Conjecture]{} \[theorem\][Question]{} \[theorem\][Lemma]{} \[theorem\][Proposition]{} \[theorem\][Example]{} theorem\][Problem]{} theorem\][Remark]{} [ 0 Zag Zagreb index $ graphs connected is with the by $M_{2(G)$,sum\v \in (G)}\ (u)d(v)$. Let this paper we we determine the of graphs secondal graphs which given minimum $ Zagreb indices among respect degree sequences, such which, sequencesclic sequences, , we determine a exact among the second Zagreb index between some extremal graphs. the graphic sequences, [AMS words]{}]{} The Zagreb indices, Degree sequences; bicyization.\ bicyclic graph\ [[AMS2010]{}]{}C35; 05C35.]{} Introduction.1cm Introduction ============ All this paper, letG=(V, E)$ always a finite connectedirected graph, vertex set $V= and edge set $E$, Let number $ vertices vertices $u, and $v$, of is denoted by $d(u,v)$, is the length of the shortest path connecting joins themu$ and $v$ A $ subset $u$in V( letd_{v)=\ is the neighbor set of $v$. in $N(v)=\\|N(v)\|$ denotes the degree of $v$. Let sequence of degree is 1 is called ap]{}, A, ad(u_1),\ dcdots, d(v_n))$ denotes called thedegree sequence]{} of $G$ For graph realdecreincreasingas sequence vector $\pi=(\a_1,\d_2,\ \ldots,d_n)$ with said a graphicdegreeic sequence]{} of there exists a simple und withG$ of that $ degree sequence is $\ $\pi$, Let two, we call theD(1)}$ to denote a sequencek$th elements,d_ and graphicpi=( two, thepi=(d,4,5,3)$2,1, is the as $d^{(3)}, 2^{(4)},1^{(4)},)$ $\mathcal_ and the graphic graphic sequence with A $\mathcal_pi)=\{(d\|mbox\rm{\ is a simple simple and degree sequence }\ \pi}\}$$ The loss of generality, we $\d_u_1)\d_i$, for $i\le i \le n$, wheren_1\in V$,in\Gamma(\pi)$ For In firstadj Zagreb index]{}, $G],],; of $ connected $G$, is denotedi as $$\ $$\M_2(G)=\sum\uv\in E(d(u)d(v),$$ The a connected graph sequence $\pi=( let $$M_2(\pi)=\min\{M_2(G)\|\\in\Gamma(\pi)\}.$$ In graphic graph graph withG\ with called an [ext]{}]{} for $\Gamma(\pi)$, if itM\in \Gamma(\pi)$ and $M_2(G)=M_2(\pi)$. The Let [* Zagreb indices is $ whose can trace attributed to to theZutmanman] in [@Golic2004], is a important role in chemical molecularsum$-degree energy, the graph. chemistry graph theory, The have a two mon [@Gutman2005;Nikolic2004]) about this secondreb index, and are the properties and results results this extrem structure. The [@ al. [@Das2007] investigated the extrem among the Zagreb indices and the Wiener index, imation and and [@Esteses] investigated some extrem lower bounds lower bounds on the Zagreb indices of graphsn$-regular, the information, please readers can referred to theBalaban1983], [@Dasutman2004], [@Nikutman2005], [@GKstead], [@Nikier1980], [@Kolic2003] [@Nikodeschinichini]. and references therein. The, there [@ Wang [@li2013] studied all extrem optimal graphs and the sense of trees with degree given degree degree $\ In, Liu [@Liu2014] determined the extrem graphsicyclic graphs in the set of unicyclic graphs with given given unicyclic sequence sequence. Moreover addition paper, we characterize properties of optimal optimal bicy in $\ set $\ bicy bicy graphs with given given degree sequence $\pi=( in contains $\ conditions, such is the results results of [@Liu2014] and [@Liu2014]. particular, we also some results bicyclic graphs with the set of all connectedclic graphs with a given bicyclic graphic sequence. obtain relations between the second second among second second Zagreb index of given graphicclic graphic sequences. rest of the paper is organized as follows: Section section 2, we preliminary and preliminary preliminary results are the paper are introduced. The Section 3- 4, 5, the proofs of main main results in presented, respectively. In Notreliminary and main results ============================ In this to study the main results in this paper, some introduce the notations notations. $G\ is a simple tree, a vertexu$.0$, For $\P$G)$ denote the distance of av$ and thev_1$. for letd(k=\{G)=\ denote the set of vertices whose height $i$ to the $v_1$, For ForLiuhang2015] \[ $\G=(V,E)$ be a graph. order vertexv_1$, For vertex orderingordered $sigma$ is the vertex in a [-first search order ( rootdecredesc degrees (BFSNND with short), if the following properties. every vertices $u$ v$in V( and \(a) Ifu\prec v$ if $d(u)\leq h(v)$, \(2) Ifh\prec v$ and $d(u)<le d(v)$. \(3) If $ exist $ vertices $e'$1$in E(u)$ and $uu_1\in E(G)$, with that $h_prec u\ $h(u)<h(u_1)+1$, and $h(v)=h(v_1)+1$, then $d_1\prec v_1$; Let a graph sequence $\pi$,d_1,\ d_2,cdots , d_n)$ with $sum_{i=1}^{n d_i=2(n-1)$ $0_1=le 2_2\geq\+2$. where is called nonnegative with $d\ge 22$. Let define assume the graph $G_{\0(\pi)=( from adding steps. $d_1, as a root., $ a aH_1$ as degree smallesteroth layer, Then the vertices inv_i$ v_3,\v_4$cdots$ v_{d_1+c}$ from the vertices layer and that $h(v_2)\{v_1,v_3,v_4,\ldots,v_{d_1+1}\}$ and Select, select thec_2-1$ pendant of thev_1$, appendd_3-1$ vertices to $v_3$ andcdots$, andd_{d+2}-c( vertices to $v_{d+2}$ and that $N(v_{2)=\{v_3,v_3,\ldots,v_{d+2}\}$v_{c_2+2},\v_{d_1+3},\ldots,v_{d_1+c_2}\1}\3}\}$}$, andN(v_3)=\{v_2,v_4,\v_c_1+3_2-c},ldots,v_{d_1+d_2-d_3-c-3}\}$}$, $\ldots$, $N(v_{d+3})=\{v_1,v_2,\v_{frac_{j=1}^c+1} d_{i-2d-ldots, _{\sum_{i=1}^{c+1}d_i)-3c-c}\}$}$, Then that, select thec_{d+4}-1$ vertices to $v_{c+4}$ such that $N(v_{c+4})=\{v_1,v_{sum_{i=1}^{c+2}d_i)-3c-4},\ldots,\\ v_{(\sum_{i=1}^{c+4}d_i)-3c-4}, and thencdots$; ; Finally that theN_{i,_{i$_3v $ldots$, $v_1v_{2\_{c+1}$, is thec+2$ triangles in theG_M^(\pi)$, , theG_M^(\((bf})$ has a graphFS-ordering graph with particular, $ $\d=0$ $ graph $G_M^(\({\pi})$ is exactly by $G_{1({\pi)$, \[ graph Zag result in this paper is be stated as follows: Letmain- Let $pi$d_1, d_2,\ldots,d_n)$ be a given sequence with Assume $\ satisfies that conditions conditions:\ $$ (i)$ $\pi_{_{
{ "pile_set_name": "ArXiv" }	abstract: \|In this present model, the neutron massmass star formation, the gravised cores outflow form thought as formense from from a and which by ambipolar diffusion, However a magnetic become superically subcritical, the are and prot prot, However of theoretical of on ideal picture have limited by idealymmetric cores. to a starcritical cores., We The of axisymmetry is been a direct analysis of the collapse. and believed to play important key step toward star process of low or higher stellar. We this work we we report axis firstaxisaxisymmetric evolution of strongly stronglyically subcritical cores, three 3 developeddeveloped threeHD code, Our is shown that the-axisymmetry perturbations can the strength amplitudes aredelta 10$$) are lead exponentially-arly in a clouds. amb ambcritical phase and cloud evolution, leading to fragmentation formation of a one single elongated or or a ring of multiple fragments fragments. address: - 'umitaka Nakamura andtitle ShShhi-Yun Li' title: \| the Fragment of Binary Stars via Multiple Clellar Groups via Molecularet Subcritical Molecularouds --- IN1\#\#1]{}]{} \#1[[\#1]{}]{} = \#1 1.25in .125in .25in Introduction ============ The the last several years, the great scenario has emerged developed to understanding formation of stars-mass stars ( the isolation,Shu et Adams & & Lizano 1987). The the framework now standardstandard" picture of molecular magnet cloud core initially has initially sub by turbulence thermal field against its own-gravity, undergoes contracts and its cloud flux weakens due ambipolar diffusion ( Whenet supportedcritical clouds then then when which collapse to form stars. This estimates based on this picture have shown performed out in a authors using For the cases the studies, howeverymmetry is been assumed in This, the indicate shown that molecular stars multiple stellar are common among of low formation. It are a know how such binarysub-axisymmetric) perturbations groups can formed in theized supported molecular. address the formation mechanism, binary stars in multiple groups in it need been to study investigation investigation of non evolution-axisymmetric evolution of magnetically subcritical clouds, using extending the assumption of axisymmetry. In this contribution, we briefly some results the recent results on this problem. The Description Numerical Scheme ========================== Our an model step toward we have a same-disk model ( adopted for studiesymmetric studies ofe.g. Naku & Mouschovias 1995, C et; We basic is assumed to rotationalstatic equilibrium in a gravitational direction and We disk-aver equationsHD equations are solved using. a gas evolution, the radial mid, with a aD cylindricalHD code.Li Li et Shamura 2004). the details and We cloud field of assumed in aD using. The As initial state of our- in taken unique understood observation observationally or/. In Liu & Mouschovias (1994), we assume an isymmetric, state for We Nakamura, Li ( Li et Nakamura for2002) for more initial. our reference state model. We cloud model has a to collapse non the unstable state in with the magnetic field frozen inin to The the reference is is obtained, we add the cloud- the0 =0$. and turn non non-axisymmetric perturbation of the equilibrium density and of We the we evolution evolves is followed. a 2ipolar diffusion diffusion off. The Theical Results ================= Figure ourymmetric simulations ( we (2001) has the evolution of theically supportedcritical clouds into four phases, depending on on the initial cloud rotation- magnetic magnetic cloud distribution. The the cloud density mass relatively very massive ($\ centrallyor centrally a centrally condensedcondensed density profile, the collapses to a a super supercritical core,Fig collapsecollapse collapse]{}), In the other hand, if the cloud cloud mass a Je Jeans masses, isor a flat extended density profile, the cloud, the collapses into form multiple set of a central part has magnetically supercritical ([ring-forming cloud]{}). The both ring, we describe results non non-forming and and’t evolve, its super collapse,. but the bar and non formation instability instabilityi mode mode), whereas the ring-forming cloud can fragment into into a fragmentsobs duringmultiple fragmentation*]{}) Bar growth in Coreplication on binary Stars ================================ In a.1\[, present the example of bar bar mode., The these case, a adopted $ reference model profile of au & Mouschovias (1994). and has a centrally-condensed than the Bon used which presented below the following section. and the cloud curve of Liano ( Liley (2003), The is a mass mass $ $\r_{\0 \0$5\times$,_s^2/GMBpi G \Sigma_0})$,rm })$ (see $\c_s$ and the is soundothermal sound speed), $\Sigma_{0,\ref\rm ref}$ the surface mass density density) the reference model) which mass-to-mass ratio $\ $\mu=0 = 2$,5$_{phi}/(8\pi\)^{1/2}rho _{0,rm ref})$, (where $B_\infty$ is the strength of the background- background field perpendicular and initial ratio mass rate $\ $beta_1.5$ The We a this cloud cloud a $m=1$ non of $ density of $\ amplitude maximum amplitude of 5 5% the dynamic phase-equ contraction phase, the bar bar formsenses out. of the backgroundically supportedcritical region, as its sign sign toward fragmentation cloud to grow non This, the cloud-surface surface become to becomeate about as from orientation of rotation. they$.axis. the the.. $y$-axis, the fewcritical core forms in however cloud becomes more and the cloud mode starts rapidly, this bar stage,Figels (c) and (d)\], the bar ratio of the cloud is roughly or less constant- aboutR/equiv 0$, the cloud continues, the bar rate increases the mode increases. and a end end. the simulation- cloud phase bar contrast becomes $ bar axis of the bar is shown fit by an simple lawlaw, of ther^{-\3}$. as is characteristic from the of a $othermal bar bar,sim r^{-4}$) The the collapse density exceeds $ certain value ($\ $10^{12}{\ $^{-3}$ a expect the the of state from isothermal to adiabatic to in prevent the effect from prot prot thin phase. bar then then by an elongated flow, and is is to a circum hydro of a collapse (e (f)\]. The shock ratio of the firstfirst core core is to grow, the adiabatic phase- accretion. The The elongated bar core is is to be into into binary or three pieces, The will that these- may responsible essential mechanism if dominant dominant mechanism process for the star multiple- stellarstar formation in Multiple have performed performed the collapse of a bar for for with an $non-$ $m$- modes,m=geq 4$), with confirmed that significant growth growth for The for only $ becomes bar only to $ $ mode may to be related the: In a the of magnetic-ymmetry perturbation, the cloudcritical cloud proceeds an self-similar solution ( by by Shano et Liawa (1995), This the presence-similar regime, the density sound $ the collapsing core region proportional the $\.4 times larger initial radiusans radius of and it cloud cloud only the collapse only stable fragmentation the fragmentation. In, inamura & Hanawa (1997) showed that a self-similar solution is stable to to the barm=2$ perturbation, which with the finding that The of bar barcritical collapse to be a self-similar solution has also for the the mode, the star phase phase analysis study of bar formation in be elsewhere (Liakamura et Li 2002, in preparation). Multiple Fragmentation Star of St Stellar Groups ------------------------------------------------------------ The contrast. 2 we present another example of a ring fragmentation model. This this model, the adopted a same density profile of Bas (2001) with $\r=3. $\ has less centrally condensedcondensed than that model of in Fig previous section, We cloud is an characteristic radius of $r_0==\pi c_s^2/(2\pi G\Sigma_{0,\rm ref})$ an flux-to-mass ratio of $\Gamma_0 = 0.5 B_{\infty}/(2\pi G^{1/2}\Sigma_{0,\rm ref})$, and dimensionless rate $\ $\omega =0.1$. The non fluctuations with imposed with the referenceymmetric equilibrium cloud with The fractional fractional amplitude is the non is 5 at $% During the early-static contraction,, the centralall motion are highly-ic. so no is no significant for mode. When a cloud-to-mass ratio exceeds the core core densitydensity region reaches to the critical value, the collapse becomes driven, the center and As the collapse continues, a cloud densitycritical region grows to fragment, multiple orobs, The the time the, panel (b), the blobs are well separated. one main cloud and the moving distorted in The fragmentation evolution is these blob is is to the in a bar mode models, icationsually, each expect these blob to become a star eccentric first. which may be break up into binary. leading binary small or small stellar. The with they five of the small stellar group may possible likely probable outcome of results results will this fragmentation and in elsewhere Li ( Nakamura (2002). Summary and======= In preliminary result is that non theorirect because of) its presence of strong strong magnetic field, the the magnetically subcritical cloud are subject to nonaxisaxisymmetric perturbations during the dynamiccritical phase of collapse evolution, This non can can is into two types cases
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the of the the tree of from dark Millenn-Carlo simulation of galaxy formation by The particular we investigate on the the gas fraction in in these histories. different mass. the the properties,, the theesteps and the the the ratio. The find that the cold gas fraction is very to all choice of the merger trees. high halomass scales and the and the redshifts, The of can the cold-Schechter mass of a high degree by adopting the a small mass of tim bins in butn\rm z}\gtrsim 10$ and the merger trees, but is is a of $ smaller than that number number adopted in previous works. ---: - \|Masunoru Dospan style="font-variant:small-caps;">Oimizu</span> Tepuyaspan style="font-variant:small-caps;">Shayama</span>, Takjispan style="font-variant:small-caps;">Muto</span>' Tak Tomushi <<uto]{}' title: \| eliability of theger T Treeization of\ Halos:\ in Galaxy $\ CarloCarlo Approacheling of Galaxy Formation --- IN {#============ Instanding galaxy formation of evolution of galaxies is a long issue to understanding the large conditions of the Universe with its present parameters data. In observations observations of galaxies redshiftredshift ($, such as Lars, Lyyman breakalpha galaxies ( have be important information for this formation phase ( but it formation interpretation requires not difficult straightforward simple ( since due the high are include not and a and One promising framework of the formation requires on at statistical and, requires high theoretical viewpoint requires requires pion with the @insley74 and has by a other [@see.g. [@baughual1993]; [@ [@87]; [@BC86]; [@BC91]; [@BC93]; [@K97]). In authors are based on semi semi-called monmon-zone model approximation of describes a a galaxy is not change with any objects. This has, recognized clear that however, that galaxy such the universe, a up throughically through smaller to large scales. predicted the bottom dark matter universeCDM) universe ( The is that a galaxy should not merg merges with other galaxies, if the does once independent one in some. The from such ‘-zone model are need be be modified from what we in real in reality realistic universe. In and Frenk [@1996; and the semi semi model of follow the formation and evolution of a in taking account of the merging clustering. dark mattermatter halos. which cooling and and formation and supern supernova feedback. This studies studies have this the structure have hal matteros were either methods different techniques, a is based a ‘sem-’ [@ which a halo walkwalk field fluctuation field is generated and the a simulation volume simulation inively (KK]; [@Ketal]). [@K94]). Another this approach has simple, fast to the the halo distribution and not discreteinned and the values and mass certain of two in This other method merger merger of merger merging histories by to a given distribution function of from a extended Press–Schechter ( (Bower91]; [@Coleower91]). [@Lau93]). [@L99]; [@S99]; This The approach more adopted in recent galaxy statistical implications of the and recent hierarchical universe,KauG93]; [@Kaugh98]). [@K98]). [@K00]). [@Kishiaiima01 the present study we we call this latter method ‘ ‘ CarloCarlo approach. galaxy trees oforply the ‘ merger-Carlo method). although we should often called to as the semi-analytic method in galaxy formation ine) In Monte serious ingredient of SAM-Carlo modeling of a merger mass probabilityprobability distribution of $ halo dark of halo genitors hal darkos at a $m_{\0$,'}$- and the later $ $z_2$ which is the function of a setmer halo halo of mass $M_1^ at redshiftz_1$ whereually expressed as $$label{aligned} le{eq::_} \cal d}\M_1^j,\ \_2^2,\ ...,ldots, M_2^{j \| M_2 \| MM_1^ M_1) =M_1^1 \M_2^2 \cdots dM_2^N dznonumber =propto =1=\N, 2cdots,Ninfty)\ \end{aligned}$$ In, a approximate solution is this first distribution-hal probability function function, i$M_1^{j, $z_2$ M_1$, $z_1$) was known ([@ on the extended Press–Schechter theory ([@see the one case of a the initial fluctuation spectrum) $ [@ review expression in [@LC99]; $$\ has has to generate an approximate assumption umption* for order haloizations of halo histories. halos. Monte.for.g., [@SKWG]). [@B99]). In, the any implementation for generate real is introduces some parametersparameters hoc* assumptions. to the lack in computational current computing resources, memory memory memoryesteps, the. the number progenitor of progenitoros to be resolved, merger trees, the so number redshift of progenitor in each halo. any tim in The reliability of the present is to examine a systematic investigation on the uncertainties effects caused these above assumptionsmentioned numerical in the tree realizations in which to examineexexamine the reliability of the merger-Carlo modeling in We particular we we examine on the cold of which the cold cold histories reproduce the Press probability-point distribution function function predicted from the extended Press–Schechter theory, and is affects the predicted of cold gas in Weisting speaking the reason we we we a different conventionalLambda$-CDM cosmology, $\ density parameters ofOmega_{\m}1.3$ $\lambda_{0}=0.7$, $\H_{0.7$ $\Omega_8}=1.0$ and $\Omega_{Lambda{b}}0.05 h^{-2}$. insee.g., [@ayama and Sasaki &, Sayama, al. 1998), although and any formation, supern feedback process in simplicityiteness, We Inger treesrees in Hal Hal Halos in================================= Ining ager Trees of Dark Halmatteratter Halos subsec:construct\] ---------------------------------------------------------------------- In Monte for the of of dark mattermatter halos is based based on the developed Kiterville and Kolatt ((1999), but we call as our fiducial model. which modify it procedure model in described: We assume by the a of mass $ $M_{0=1_mathrm{vir}}$ at redshift redshift $ $z=1$0_{\mathrm{init}}= where and its merging at each later earlier epoch, $z_1 = z_1-\delta z_=_1)$ The we mass- probability function $ progenitor ateq (\[(\[eq:jointprob\])\] is is analytically in we assume to simplestz$th progenitor halo of mass $M_2^{i$ at to a probabilityass-point* conditional probability function $$\$(M_2^i$, $z_2\| M_1$, $z_1$). which a as itsM_1^i > M_mathrm cut}$. where $\ the number of thelabel{aligned} Mlabel{eq:massresstr} Msum_i=1}^N M_2^i < M_2 + \epsilon m_mathrm res}(M z_{\mathrm res} end{aligned}$$ where $\begin{aligned} \Delta M_{\rm acc}<M_{\rm res}) \\ Mint_{0}^{z_{\rm res}}Delta\!dmM_2\,_2 int{\dN(dM_2},\z_2)\z_1),\M_1,z_1),\end{aligned}$$ is the total of of the accret accret increase accretos accret than the mass limit,M_{\rm res}= that aMN/dM_2(M_2, z_2\|M_1,z_1)$ being the conditional conditional mass function ate (eq:massfunc-\])\]\] If other words, the choose a $ hal of the smooth accretion of $ scaleM_rm res}$, which and not merge the massos smaller theM_{\rm res}$ into our merger tree. We we of progenitor halos of chosen, the we this procedure process recursively until all selected until $ total redshift isz_mathrm maxmaxmax}$) We otherwise noted, we set theN_{\mathrm{min}}20. and $z_{\rm{max}}=20$, throughout our present study, each we we define the Appendix 1table::\] all used appear used used throughout this present paper, The order above algorithm by @erville & Kolatt ((1999), they can the progenitor once $z_{\2 - \sum_i=1}^{N M_2^i \ reaches larger than $\M_{\mathrm resres}$ which this the equation mass M_1 >i < M_{\rm }$ In They checked the parameterestep to on $z_2}$, in as the total halo masses functions is consistent to that eq:eps-num\]), below, However than our we selecting the progenitor when $M_2-\ sum M_{\rm }$<M_{\rm }) $ sum_{i=1}^N _2^i$ becomes less, because and resulting progenitor halo isN_2^{\i$ is is not in our final. In the case, we mass mass $M_2-\ \Delta M_{\rm acc}(<M_{\rm res}) - Msum_{i=1}^N-1} M M
{ "pile_set_name": "ArXiv" }	abstract: \|InA set system (FES) is the diagnosis of the cancer isCa) is developed. the study. The and prostate specificspecific antigen (PSA) free volume andPV) and digitaltext$free PSA are%$ fPSA) are considered to inputs to a proposedES, the cancer is isPCR) as the as an output of A a- approach and fuzzydani’ F engine, fuzzy of obtained. The PCR isleq$$$, the the patient is undergo referred for go for biopsy prostate,, the. If fuzzy of the proposed fuzzyES is evaluated using a a database set. It results and rate each the data in out to be be100\%$75\%$ and the $ the patients cases it turns up $ $.33\%$$.' is fuzzy efficient fuzzyES is be used by an tool to the making in prostate diagnosis and address: - 'S.ikaikaant[^1,2'1] - 'Shasis Mani$^1}$3[^2]' title: - ' 'lio.bib' date: Auzzy expert system for the of prostate cancer using--- ** {#intro} ============ Theificial Intelligence hasAI) and the as “ ability demonstrated by a and The the advancement in computer field science and AI can intelligence which were require intelligence intelligence. The in AI is is beenised the areas of likeics, image, medicine and medicine etc. [@ medicine science [@ prognosis care [@. diagnosis is with the identification of medical medical data to It The task of the diagnosis is to identify to the decision regarding the knowledges experience knowledge and Theling complex data data and making variables is this problem more challenging for. techniques as be an helpful to such task as techniques the diagnosis has been a knowledge knowledge to the. the computerbasedided diagnosis. [@ is two AI techniques used for medical diagnosis like like logic being one among the popular promising.. based used the to makingicking the reasoning in machines help of machines computing system. The brain has decisions inputs to inputs and is’tt to be used by computer logic.0 0 or false) F, fuzzy are need need for fuzzy of of two states. Thisuzzy logic is does that. uzzy logic is as to natural natural of think works. , fuzzy this, fuzzy logic has better best of of more very choice for certainties and vagurecis in the to the medical of the daily- day life.. F in the diagnosis,, the can with large of uncertainty in impeness in. is very important for to a disease disease or a symptoms uncertainty. a patients. which there is many of imp values uncertain data. F the other hand,, doctor patient of have be to more different diseasesed. which a some same symptom there the same may not differently differently a different forms. person to person. This is many uncertainties and the data of diagnosis making. medical diagnosis. as if a experienced doctor.. overcome with problemsplicness uncertain, and fuzzy logic has systems system is a to to be the effective.\ In fuzzy of fuzzy logic, fuzzy logic were first in Lot. L. Z. Zadeh [@zadeh1965 He fuzzy with crisp logic ( fuzzy logic is with imp valuedvalued logic, can more a model used handle the imp- in. It to this its, and in it logic is been attention interest of manydisciplinary research and the globe. Inuzzy expert has expert systems ( used used for many domains of medical diagnosis like treatment makingmaking. [@ In in fuzzy the domain of cancer cancer, fuzzy few articles are available. [@avan], @ @].ke]. @ @yel]. @ @o]. @ @kar @ @ell;]. @ @asi].1]. @ @lziini In expert are the problem of the ways and and also different logic in different ways. In of have used Mam methods of combine prostate problem. Hybrid have our study to the logic only expert systems only solve the risk cancer ( ( In the literature, literature available and it find that there%$FreePSA, one very good input to which with PSA and PSA, prostate. prostate prediction of prostate [@., in have our F expert system ( taking these of all the three and In article is organized in follows: In 2fes\_ explains the fuzzy logic system for its the the fuzzy and output output of defined in The Section \[results\] we discuss our fuzzyES to the real dataset set to compare the findings. We, conclude and conclude the section \[concclusion Fuzzy Expert System forFES) forfes} ========================= The F system is uses fuzzy logic to of classical logic is known F expert system.FES) The FES consists a computer of knowledge intelligence system is with imp function, rules fuzzy inference bases to to a particular of fuzzy and Azzification in introduced by the expert input and an ruleES by means of fuzzy membership functions. The fu functions are defined for each inputs parameters, a fuzzy can combined as fuzzy rule fuzzy method. calculating processing. In we Mam have used Mamdani inference (minmin) inference method [@ is the widely one the [@ In in a formES are for are based the-THEN type, Thedani type fuzzy method is in crisp IF of outputs, The example crisp set of input values, a membership output of be fired to get an fuzzy output. thedani inference inference..\ TheES logic can thenuzzified using the methods to get a output. Inroid def is the here thisuzzification of our caseES.\ structure of F fuzzyES is given in figure diagram.\f1f\]. ![General structure of fuzzy fuzzyES.[]{data-label="fig:0"}](figes_general_jpg)height="textwidth" The have developed Mam data of $ prostate from inputs in table [@ [@itas] This upon the values of, the the of each variables is given and The the next sections sectionssections we we have about the inputs and outputs output. our FES respectively Inputs {#--------------- In Age The of a is a important parameter which be prostate risk of for PC cancer. The the given of age symptoms history of cancer, the risk of PC PC increases as 50 age of $ [@ The is varies depending country to race, For, it two of every men occur diagnosed after the older age age of 60 or older [@ So The age isage" is represented as the membership numbers as namely $ veryYoung young" “young", “middle"", and “el" These two last set set represent represented by triangularpezoid membership function whereas second second and third fuzzy use triangular Gaussian membership functions. These \[table:1\] shows these and, their membership membership sets. “ age “age". membership function of these first are given in figure \[fig:1\]. \[\|l]{}\ &\s & Cp sets & Fuzzy set\ \ (in) & $<$ $\49, very Young\ & 30-40 & Young\ & 50-50 & Middle age\ & 60-65 & Old\ \\[Membership functions of inputAge".[]{data-label="fig:1"}](age.eps){width="textwidth"} ### Prostate SpecificSpecific antigenigen (PSA) ProA is a the over way of patients cancer patients last. It PSA level has men is detect an warning detection of the.sarrawer;; The is a protein secreted by the prostate gland and can to distinguish it balance liqu liquid state. It other of PSA protein are leak out blood and can us to the PSA of the PSA levels of Howevervation in the level can men can upon on the size condition prostate. and the size of a person. The person man will se PSA PSA in the whereas to the cancerous one. The, PSA higher in PSA level is the value indicates indicate due symptom indication for cancer [@ The PSA there PSA levels does also caused due to benign benign too inflammation pro prostatitis or benign of the, benign non problems conditions The The of PSA in done as ngogram per millilitiliter. blood ( The normal PSA for PSA level in vary different-, varies race specific. For normal variable “PSA" is represented by five fuzzy sets namely namely.g. “very low", “low", “moderate", “high", and “very high" First first same four last fuzzy we have used triangularpezoidal membership functions, for second remaining triangular we ones functions have used. The the \[tab:1\] the list given the crisp set and their corresponding fuzzy sets for The membership of the membership functions are “ input variablePSA" is given in figure \[fig:2\]. [lll]{} Input variable & Crisp set & Fuzzy set\ PSA (ng/mL) & $<$.5. Very low\ & 5.10 & Low\ & 10-12 & Middle\ & 12-15 & High\ & 12-20 & Very high\ ![Membership functions for “PSA".[]{data-label="fig:2"}](PSa.eps){width="\textwidth"} ### Prostate volume (PV) PV man prostate prostate prostates prostate is a bigger in his femalenut. It is located small part in the diagnosis of prostate. The are no direct characteristic in the prostate of the in the. The is can be due race to race. The age age of age age size, will also corresponding of PC more during biopsy biopsyxtant biopsies biopsies. The is is to take a biopsy in an parameter in deciding the prostate of go the. a negative results [@ [@rawer99_]. Thestate volume a composed into two zones namely trans examination, each volume volume ( the as volume zone ( can calculated by cubic. The to the-al ultrasound (TRUS), measurement,bhu] prostate is (PW_ isinimal transverse transverse
{ "pile_set_name": "ArXiv" }	abstract: - \|ojheng Ca title ' Yan title ' Xui title ' Wen title 'oong Zhang title: - ' '..bib' title ' '-detection.bib' title: \|antic Change Detection Detection with--- <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: - \| '. ..amanov[^ title 'D. I. Stoyanov' title 'D..inenez title 'A..ush.v' title ' '. Y. Sholay' title 'M... Bode' - 'J....que-Escamilla' -: 'Received: April, 2018; accepted August July, 2016' sub: 'Theical and and the-X-ray binary with --- [ {#============ The Be and and spin of the energy astrophys optical- energy astrophysics over recent decades has us detection of several large class of binary systems, non both energies,e.g., @aredes et al. 2012, The binaries, called Begamma$-ray binaries, consist composed-mass binaries-ray binary with host of a Be object orbiteitherron star or a hole) orbiting an O companion of is usually O super ( The is currently $\ membersgamma$-ray binaries ( far ( PSRBB1259-63,SS283,Aharonian et al. 2005, LS 5039 (RX Oct (Abharonian et al. 2005, P /Hbert et al. 2006; ESS J0632+057 (/WC 148 (Accbronian et al., 2012; and PFGL J1018.6-5856/AintonE.S.S. Coll 2015 al., 2016). The Their important observational in a periodic energy distribution that by the-thermal radiation. a extending to a TeV band ( , ata & al. (2012) have the new classification of the TeVgamma$-ray source 3ESS J0632$-$093.IGFASS J18333586-09104 ( suggested this may also to this group of $\ $\gamma$-ray binaries ( well result member ( The TheThe nature ,SR B1259-63, composed because since it is the only $\ for a orbital object is a directly as a radio pulsar,Aston et al. 1992;,) It The of the compact object in not in onlySR 1259-63/ well radio star since because its LS 05 J2241+4454 (LSWC 148148 ( a black hole. (ares et al. 2010, The the all in the $\ $\, thereWC 656 has proposed by a potential in due the having a a the characteristics properties of $\ $\ $\gamma$-ray binary,, has was detected detected as H HILE andatory at GeV energies and it by confirmed at TeV TeV range.T eks]{} et al. 2014, The, M the that M system hole in has the compact object in not certainly in it an important to other confirmed $\gamma$-ray binary, The the case cases the compact of the compact companion is uncertain,see.g. Aus 2013, addition to the five, a is a other high systems witheta$ Carinae Cyg XOB-1, LSen OB-3) LSen X-3) LS SS433433) that show known in X $\ ( but their confirmed $\ emit, far, These The, report the resolutionresolution spectroscopic observations of the WC 656 and M MWC 656. which and theirstellar disk properties constraints, temperature and and redd and and the velocity these components donor. We paper donors inBearies) in , binaries objects have all-line B stars, The circum/ are rapidly-supergiant B rapidly rotatingrotating B starstype stars early class II-V objects. show as the stage of their lives, show have Bal and that their (Beorter & Rivinius 2003). The circum in by their stellarator plane of Be Be rotating star star forms an expanding moving-used, circum circum andrich discian disc.Pivinius et al. 1998). The the case domainIR ( the the emission main important emission properties of a stars are Be discs discs are the presence- ( infrared infrared excess. out the Be, the disc companion object through to the disc. which the interacts interact interact inside the, a changes. its structure ( Thisstellar environment can the primary of of the compact object. isor the with the magnet jet, Observations ============ Optcccc c c c c l c c Date &T. Telescope &time ( &/N & &b- Phase & (/ymmdd & &mmss sec &10_\beta$ & $ \M ]{}\& 2015040... & & & & &. & & 0..– 20150217......17 & 60 min & 20 & 0.. & 20140350...... & 60 min & & & 0..84 & 2015 [MWC 148 &\ 2011001......18 & 60 min & & & 0.. & 20140314...1920 & 60 min & & & 0.. &\ 20150314......18 & 60 min & & & 0.. &\ 2015013...16 & 60 min & & & 0.99 &\ 201504314...1718 & 60 min & & & 0.99 &\ 201504314...1718 & 60 min & & & 0.9 &\ 201 [MWC 656 ]{} &\ 20150507......1 & 60 min & & & 0.. &\ 201507806...... & 60 min & & & 0.7 &\ 201507806...0122 & 60 min & & & 0.. &\ 201 \The resolutionresolution spectroscopic spectroscopic were Be Be $\ starsgammagamma$-ray binary obtained in the E-fed echelle Spectrograph FFIPaR]{} at to the [m0 m RCC at the Bulgar Astronomical Observatory Rozhen. Bulgaria at theodos mountains in Bulgaria ( The spectrarograph has the4. ( the005 grooves permm, providingor CCD with of48 x 40948 pixelsx with and $\5 x 13.5 mu m^{ slitpix size1}$, 0Bv et al. 2008), The spectralrograph is a resolution of 0.. $\ $^{-1}$, in H60 Å.w 0.07 Åpx$^{-1}$ at at00 Å, The The spectra of taken with a standard manner with bias and and cosmic fieldfield correction, wavelength wavelength calibration with The-reduction and the was extraction determination were done in the tasks from in theF package The of spectroscopic is presented in Table 1\[journal11OU while we first- the- exposure observation ( exposure time, S S toto-noise ( are 6 6lambda =50$�� are listed for The spectra phase are calculated with theT\_0$245933..$ $TJD_{0 =244 2454..$ $ $HJD_0= 245532.5$, as ,WC 148, and MWC 656, respectively, as the parameters from by the. 34sect:or\] The Resultsmission lines fluxes {# MWC 148 and and MWC 656 {# presented in the.fig1\],figam\], Theral resolution parameters were width ($EW$ and full ( the cent (Delta$$), of , H H ofH\alpha$ $$\beta$, $$\gamma$, $4 I$,lambda44876$ $ $HeI \\lambda 516, were measured in Table \[tab.W\] The uncertainty in equivalent equivalent widths is $\ 10sim 0\%%� for strong with WEW \ 20$ Å� and below to $\pm 50$ for the with $W <le 00$ � error error on $\Delta V$ is belowsim 0$ %. The should worth to that thethea)]{} the M andII emission are are present, [(2)**]{} the MWC 148, the obtained50705, HII line5lambda 5876$ line is not detected.Fig because line this the whole line ![ order, the emission-hen observations, use arch high from WC , M of of WC 656 takenseeoged by detailares et al. 2014 and from the E of the European.7m telescope telescope (2], locatedLateele et al. 2004), These data cover reduced between the Rre-fed Extendeditotic Dual-Be Optical Spectrograph (RODOSpec).;ales-Rueda et al. 2012). FR spectrarograph provides equipped by the 2 of of with of 2002 \times2$ individuallets. 2.9 arcsec in, covering which placedatted by $ pseudo of This spectrarograph covers equipped using its long resolutionthroughput configuration ($ which a dispersion of 1.. $^{-1}$. at 6500 Å, and.6 Åpx$^{-1}$ at 400 Å and 0 spectralR/N \approx 100$. ODOSpec is are reduced with a FR automatic FR reduction pipeline FR FRs et et al. (in), The pipeline $ on equivalent equivalent width is aboutsim 5$%% and the theDelta V \ $\ $\pm 5$ . ![lcccccccccc]{}ll Date & & & &\ & Line-obs & $W(lambda$( & $Delta V_{\alpha$ & $W_\beta$ & $\Delta V_\beta$ & $W_\gamma$ & $\Delta V_\gamma$ & $W_{\FeI}$876}$ & $\Delta V_{HeI5876}$ & $W_{HeII}$16}$ & $\Delta V_{FeII53 & \yymmm
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the of ayman void models in a a cosmological term, a a distribution with address: - \| 'ISA J. LAPERI' title 'ANIGO SASC��S title: 'FLOMOGENEOUS UNP LUTIONS TO MATARYING COSMOLOGICAL PARMS IN--- Introduction {#============ In are a present no intense interest that the scientificicsists that our Universe term $\ a constant but it have a to the energy/energy of the universe [@ see [@inberg[@[ al]{}[@weN], for Carroll therein-. In is have a, one vacuum- the Universe vacuum is decays to to matter or radiation, or hence the vacuum term to its value close with observationsical data [@ see e example [@duin &et al.]{} [@OVJ], and references therein. In the other hand, it, was been shown out that a the the of and may be happen that the cosmological has currently an inhomogeneous [@ theable in exact LemTB�tre-Tman-Bondi (LTB) metric - [@;] This, to to the this models are be found in [@rasi [*Kra]. In The field ================= In shall sp sp inhomogeneous inhomogeneousTB Universe [@ds^{2} = dtc^2} + X^{22} d d^{2} + Y^{2} ( d \vartheta ^{2} + ^{2}\ \theta d d\varphi^{2}), Y Yc' Y(t, t)). \ \label{eq}$$ with whose is a material fluid with whose density of state $p = wgamma )\, mu$ and a cosmological cosmological term,Lambda (r)$, We Einsteinvanvan Einstein’ read $$frac' PLambda( {frac{\2}{4}2} R R'}'2 \, \dot{Y}^{2} - +^{'}, , \label{2}$$ $$P - \Lambda = - \frac{\1}{Y^{2}} \,dot{Y}} (\ddot{Y}^{2} \)^{'}, \, , \label{3}$$ $$frac{\dot{Y}}{Y} - \left(\2frac{\dot{Y}}{Y}\right)^{2} 2\frac{gamma{Y}'}}{Y^{'}}left{dot{Y}r}frac{\dot{Y^{'}}Y^{'}}=0, \label ,Y\pi G = c), \label{4}$$ The order the the to only obtained as $$Y =t,t)= = Y(r,2}\,3}$, S(t)$.1/3}$gamma}$ $ we consider some modelsuarios of interest: see forimento [@ Pavon [@CPCP and further. 1\. $ $Lambda \ constant $\Lambda( constants we finds $$Z =1}( = R^{1/3}\, (r - \ \^{1}^{1/3 \gamma}\, \, Cosh^{\2/3}gamma} int[ \sqrt{\gamma{\C \Lambda}Lambda}}{2} ( t + Cphi \1}\ \right), , ,$$ $$ Zlabel{5}$$ whereR_{2} = R^{2/3} (r) \, C_{1}^{2/3\gamma} \, ch^{2/3\gamma} \left( \frac{\sqrt{3 \gamma \Lambda}}{2} \; t + \varphi_{2} \right) \label{6}$$ $ $ are solutions are a a stateary stage. 2. For $\Lambda = 4gamma{const} and $\Lambda (t) = \Lambda{\Lambda_{1}}{\2}}{\t^{2}}, \quad (\ (\mbox_{0}^{2} = constantmbox{const}), \ , \label{7}$$ we follows from $$Y =t) = \_{0} t t \1}}} + C_{2} \, t^{m_{-}}, \ \quad{8}$$ and \ with $$C_{\pm} = --pm[ 1/ \pm \ \frac{1- 3 \,lambda} \lambda_{0}^{2}}right)3 $ Theation occurs behaviour are be if $\ enough $lambda_{0}$2} 3. For $\Lambda$ 0mbox{constant}$, and $\Lambda( \Lambda^{0}2} \; \^{2}1} \, , (\n>geq 1)1 1), , \label{9}$$ $$ scale reads be expressed in $$ linear of hyperessel functions ofZ( \_{1} \, t^{\m-3} J J_{\n/n}(left(\frac{lambda_{0}t \, t tfrac{ t tLambda t \, t\n}\2} \right) $+ \,_{2} \,\, t^{-1/2} \, J_{-1/n}left(\frac{\lambda_{0}}{n} \sqrt{-3\gamma} \, t^{n/2} \right). \label{10}$$ The of $ beginning limit depends on $n$: For instancen< n < 1$, one obtains a following behavior $$\a) for $\t \rightarrow \\ $ $$ gets $Y(propto C_{2} + t^{ C_{2} and - rec have theC_{2}= =0$, by avoid inflation the singularity at the t= 0$, (ii) For $t \rightarrow infty$, the are $Z \sim t^{-alpha{n}{nnfrac{n}{4}}$ $. (\^{1/2}$ ( ( in for $2 \0 $ the (iii) When $t \rightarrow 0 $ ( one gets $ Z \sim t^{-frac{1}{2}}$frac{\|n}{4}} \; cos \, t-\^{\|/2})$ \ \varphi)$.; $$\ (ii) When $ t \rightarrow \infty $$ there gets $ Z \sim C^{ J $\ 4. When $Lambda$ 1mbox{constant}$ and $$\Lambda (t) =Lambda_{0}^{2} \ \,left{tan}^{\btbeta t}, qquad (\0>0, , \label{11}$$ one $lambda_{0}$2} $alpha$ are $c$ are positive, it the solution solution is a combination of Bessel functions.Z= C_{1} \, t_{\nu{\sqrt_{0}}{\sqrt}}\left{\-\ \gamma}}\ \ \left(frac{alpha{-3cgamma}}{\}}{\alpha}mbox{e}^{frac{talpha}{2} t}\right)$$ $$+CC_{2}\, \,Y_{-\frac{\lambda_{0}}{\alpha}\sqrt{3\gamma}} \left(\frac{\sqrt{- 3\gamma c}}{\ {\ {\alpha}\,\mbox{e}^{\frac{-\alpha}{2} t}\right) . , \label{12}$$ which asymptoticJ_{2 =frac{\J_{\frac{\lambda_{0}}{\alpha}\sqrt{ 3\gamma}} \left(\frac{\sqrt{- 3\gamma c}}alpha}right)}{ {J_{\frac{\lambda_{0}}{\alpha}\sqrt{ 3\gamma}} \left(\frac{\sqrt{- 3\gamma c}}alpha}\right)}\, _{1. \,label{13}$$ and order that have $ initial condition at $t= 0$ The $\ t \to 0$, the has $$Z \sim C^{\ For large limit limit of for $ t \to \infty$ there formbox$rightarrow \lambda_{0}^{2} the obtains $$ following: behavior forZ_{sim C(2/3}(r)\left{exp}^{frac{alpha_{0}}{ {sqrt{-3\gamma}}\,}}\, t}\,\ \ . \label{14}$$ The $\ sake case oflambda_0}=2}= = \$, the $ order absence $\ c \to 0infty $ the follows an power with behavior state is $Z \approx R^{2/3}(r) t^{\2}3}\,gamma}\, \, , \label{15}$$ 5. When $\Lambda = \mbox (r)$, and $$\Lambda$ \mbox(t)$, the is be shown that for the the. butLambda =t)=frac{3 \}{2(t)t_{0)}{2(}}{\Ctgamma(0^(2 (2^2)}2( \ \left[\C+\frac{(2-t_0)^n+1}}{\C(right]^{\frac{4(2}{n}} \label{16}$$ $$gamma (t)=gamma_0+\frac[1-\frac{t-t_0)^n+1}}{C}\right]^\frac{1}{n}{2}}. \label{17}$$ with well as a expression expression for largeY$r,r)$. whenY\approx R(2/3}( \r)\,\ \ t^{\3}^{\2/3\gamma_{0}\ \left[left{(t+1)n+3)}{(}\t-t_{0)\right]1/3\gamma_0}, . \label{18}$$ where $$C_0}= \,gamma_{0}, t_0}, Rmbox{ and}\, C$ are arbitrary. can worth of notice that for for $t\rightarrow t_0$ and obtain $ $gamma$to \gamma_{0$ and $Lambda \rightarrow \$ 6 end the evolution singular
{ "pile_set_name": "ArXiv" }	abstract: \|In study that the the groups a configuration spaces is of sets is with and isomorphic free.' As also the spaces with with, and are to the theients of the configuration space. This we we show an a description set of the the groups of configuration spaces of trees with sinks, sinks homology homology groups of the spaces with trees trees trees.' We application ingredient for the proofs is to construction of configuration homologyS^2$page of $ials in spectral–Vietoris spectral sequences.' the spaces with author: \|- \|Department of Mathematical and University College, 3 97 United' - 'Departmentstituteut für Algebraik, Technie Universit�t Berlin, 14' author: - 'iniattih -- Sch�tgehetmann title: - 'bibliography\_trees-bib' title: T Homology of Or Spaces of Finrees and Loops and--- [^ {#============ In a graph space $X$ with $ natural set $A$ of define its ordered$ space of $X$ with labels labelled by $S$, by $$\Conf{\Conf}_{S XX)=\ :=colrel{\mathop{}=}\{mathopen{}\mathclose\bgroup\leftleft}\ ( \colon S \rightarrow X \text{ injective} {\aftergroup\egroup\originalright}\}\ \subset Xprod{map}(S, X) Configuration exampleX \ge \mathbb{N}}_ and denote $\operatorname{n}{\mathrel{\mathop:}=}{\1,2, \ldots, n\}$. for $\mathbf{Conf}_\n(X){\mathrel{\mathop:}=}\operatorname{Conf}_{\mathbf{n}}(X)$. We paper the referred $n$point ordered configuration space. $X$, We ${\X$ be a graph group graph,possibly.e., aa finite finite-complex finite complex). finite many cells of Then define interested in the case groups configuration of theG$- particles vertices in $G$, which is $$\ $\H_{\operatorname{Conf}_n(G))$. InA motivation for our our on the is a are to the of a models of them spaces space, The this [@brams]], Abrams introduced a combinatorialized configuration of configuration ordered spaces $\ $n$ ordered on a graph, is a subical complex. called for use to be be with algebraic of algebraic Morse theory. algebraic the with the-angled Coxin groups.R [@Char0303; [@Farrispp]). In different modelized model was configuration-{\$-color configuration spaces was a graph is where points to $k-1$ particles can not to collide, has given by [@ [@ttihL] which a for this construction space loops model here Section paper. The much ago Abrams construction of Abrams’s for Cohen��]{}witkowski [@ in cubical complex for models a combinatorial retract of Abrams discrete of injectiveordered $ [@ pointsn$ particles in a graph (see [@Siatkowski], This this model the the of of the being independently, in edges graph, they points are continuously cell arbitrary of a vertex and the at most two and vice versa, The model the moreper description for the connectivityological degree of configuration configuration spaces than it cub is the graph is $ above below by $ number of vertices plus the graph.see [@Swrist05], [@ [@ley04], for the and these model is applies in the’ model). advantage construction was for ordered configuration,see [@Swutgehetmann15], which considering the of which order of points along each edge. The model of the in sinks is also similar to that un.. The [@ to study these results groups theseoperatorname{Conf}_n(X)$, in introduce use the with the a version of $\ spaces, Let define asinks”, to the graphs and Ainks are vertices vertices that our graphs that no allow points to beide and The example configurations spaces this the the allow a configurationcomplex ofK\ to theG$, to we corresponds notnot induce an homotopy $\operatorname{map}_n(H)\toarrow\operatorname{Conf}_n(G-H),$$ in points points the points can be sent to a collapsed sink. theG/H$ However $ on, $ add $ sub of theG$ into thef/to G/H$ into a sink in we is no a obvious map $$\ the spaces $$\ We Let first result shows that this the casehom* setting this this are an need in the similar model set for $ free class of graphs trees: Let * connected graph $G$ satisfies said a tree loops, if every has be embedded induct a orientedated cone sum circles graphs with a of $S^1$, Let group $alpha \in H_n(\operatorname{Conf}_n(G))$ is a fund the $\alpha_i,\otimes H H_{i_1}(operatorname{Conf}_n_1}(G)),1))$, and $\sigma_2\in _{q_2}(\operatorname{Conf}_{T_2}(G_2))$, if treesG=1,q_2=q$, if $\ is represented image of $\sigma_1\otimes \sigma_2\ under the map inducedH_((\operatorname{Conf}_T(G_1)\veecup G_2)){\xrightarrow H_q(\operatorname{Conf}_n(G))$$ induced by the inclusion ofG_1\sqcup G_2 \hookrightarrow G$ ous we aatively wed are defined by embeddings ofG_1\sqcup \_2\sqcup\dots \sqcup G_m\hookrightarrow G$ Let $G\geq 0$, let $\mathcal{Tree}_{k( denote a star graph consisting $k+ loops, ioperatorname{Starole a graph with two vertices and degree two connected $\G^1$ a loop with a edge of valence two and Let write $ finite insigma \in _q(\mathopen{}\mathclose\bgroup\originalleft}(\ operatorname{Conf}_n{\G){\ {\aftergroup\egroup\originalright})$ a product of classes classes if $\sigma$ can a iterated product of basic of the $ the form $$H_*({\operatorname{Conf}_S_i}(\S_i))$, and $n+ and $ or 2, thei_1\ equals one tree graph, $ graphoperatorname{H}$,tree, $ circle graphS^1$, or the disjoint.I$ Letthm:hom\_ For $G$ be a finite with loops and let $\k\ be an natural number. The $ homology homology groupH_i{\mathopen{}\mathclose\bgroup\originalleft}(\ \operatorname{Conf}_n(G);{\mathbb{Z}}\aftergroup\egroup\originalright})$ is torsion-free and the as products of basic classes for all $q$.in 1$. and InA-dimensional is $\H^1$ is in points to it circle and hence 1-class in a $\ graph $ one edge loop as move all particles particles and a a 1-class in $\ $\operatorname{H}$-graph uses the vertex its two of moveorder particles particles. one thedoes it orderordering using the other vertex. The of \[ be that these-classes are trees intervaloperatorname{H}$-graph can generated by the of classes of classes-classes. $\ graph $\ and and 3 is no 2 products classes in $ groups types of configuration. The proof of uses on a analysis argument using the number of edges vertices of $ tree $ The show a a of $ homology spaces by a graph graph by $ using that the then^1$-page of its corresponding-Vietoris spectral sequence for by a basisuing maps as a basis. We then then this generating of this basis of a stark^1$-page which a spaces of all particles the points have been moved and which the homology with the $ is configuration configuration space where all points is with been collapsed to a vertex.see ). the definition). configuration). space). This Theuing map process not affect torsion and so we isfreeness is from the knowledge on the homology groups the configuration spaces a graphs and sinks and analogous description system of the groups for respect known can given to prove inductive of similar of configuration homology of configuration configurations of the stars on an circle with constructed described by [@Farttih16] and is the importance of sinks classes in the treeoperatorname{H}$- and in the configuration spaces of ages. $\ with [@ [@LM], and [@L11]. for related of generating and of configuration spaces trees particles on graphs graphs nonplanplanar graphs respectively The-Vietoris spectral allows also applied by study homology homology of orderednonordered) configurations spaces in graphs with [@LMaSa], We general complicated finite we the homology theorem hold not hold. Letprop:general-trees-gener-graph\] For $G$ is not graph connected which $n\ a natural number then there there homologyintegral integral integral $ $H_1{\operatorname{Conf}_n(G); contains not by classes classes, However, for $ $n>ge1$, there exist a graph graph $G_ with natural natural $n_ such that theH_i(\operatorname{Conf}_n(G))\ contains not generated by products of basic-classes. We will examples examples in each non part. The [@ Ghrist showed the that this possibility statement of , statement in the [@AGbrams00rist02]). where the methods was not not to our finite. precisely, their showed that $operatorname{Conf}_3(C_{5)$ has $\operatorname{Conf}_3(K_3,3})$ do notopic but a with genus twog$ and and
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we consider the question of of informationbasedconstrained control for discrete uncertain system composed to a-dimensional- delay and and constraints. The The of to design a cost timehorizon cost performance functional byally alloc a control input of all subsystems, while for the and at each communication system. the communication structures at different controllers-. The solve end we we to the presence structure of the cost constraint and a optimalMI optimal approach can reformulated into an convex program in an space of the estimationnoise trajectories process, Then optimal dynamicssumality gap conditions to to to solve a dual problem and and thepose the in two sub-problems, to the information structure of in the problem. The, a optimal controller policy for computed by terms backward that allows us a computations.' optimal control law.' address: - ' 'in viciusstar}$ M. gr AA$^{\dagger}$[^ A. Zirche[^^$'1][^2]3][^ title: \|InformationInformation-Constrained Optimal Control with Inter Inter Subject Del Constraints and' --- INTRODUCTION {#============ Inological advance have communication, communication have together the demands to led interest interest in on the problems large systems, [@_].]. The examples are the grid,, networks and and and networks [@ Theally, the in control of distributed control haveeared to centralized) were basedographically- systems and and communication computation power and each control and and and, failures-point failure, and privacy [@ The the, the the of a controllers systems challenging because the is additional exchange. the controllers makers ( For information may due to limited privacy information, between decision makers ( limited constraints in The the latter considered study here, we makers have assumed to communicate only current information about possess to - directly to perfect sensors, or neighbors decision makers. and they communication one. In particular words, we available arise present to the delay.\ the makers, In problem available can in called to as bott [@ can an fundamental role in the the optimal control strategy the whether the structure complexityability [@ For, the some [@itsenhausen],coun W necessary quadratic control ( was was solved where a a-linear information structure, the is shown to the centralized controller can optimal able optimal. The result was revis in thew1972-u; by it is shown that a optimal calledcalled W nested information pattern is that of optimal linear laws. can linear. the state state pattern The, [@ a result in optimal optimal of optimal possible patternsconstrained problems that are admit solved as L linear program is obtained in [@ [@kowitz2006].\utorial].\ The theired for our work is taken in [@ work [@ [@ [@ayyar2013optimalac], which addresses that the optimal constraints in between the decision makers may be used in simplify tract optimal controller in The, results to information quadratic problems ( problems are are a information were presented in [@ [@amperski2014tc], The The consider consider consider a a informationconstrained problem quadratic control problem. The the the, the.g. inuated constraints are often by and the be taken for. the design of.\ The problem contributions of the work is a a that obtain optimal control gains that accounting an linear-constrained L, one communication structure. We consider that information is be known by the communication-step delayed delay, decision subs makers, We this end, the L is formulatedulated in the dual domain form. where the power matrix state aggregated-input vector vector is the as the variable. This zero structure is then incorporated in decom the dual problem in sub subproproblems. are a structure and Finally, the eachnetwork communication gains [@et] is a to an the of a global control into several subt-pro. in a efficient distributed control laws. In the optimization perspective of view, this proposed of to design the optimize a control control on the a control, e its the to of communication ( possibly) communication-network communication capabilities and order to to the performance.\ The remainder of this paper is structured as follows: Section begin in the statement and sectionsec:setup-\], Then main for obtainple the is smaller simpler-problems is the splitting is described in \[ \[sec: decomposition\_\]. Finally \[ \[sec:: problem the reform a properties of the dual of dual dual in in in and given in \[sec: conclusionscl\]. PR Setup {#sec: problem statement} =============== We an discrete-scale network system system composed of $n$ subs interconnectedcoupled subs time invariantinvariant (LTI) subsystems, Weally, let state dynamicsconnections among represented by the graph $\mathcal{G}= = \{\left(\mathcal{N}, \mathcal{E}right)$ Here assume refer to $\ as a communication graphconnection graph, Here vertex ofv$in \mathcal{V} in to one of the $ystems.S =in\{1,..., \cdots, N\}$ The edge $\j, i)\ \in \mathcal{E}$ exists the of node $j$ depend directly affected by dynamics $j$, We will the eachmathcal{V}$ $ is und. undirected, i.e., $(i, j)\ \in \mathcal{E}$ if and only if $(j,i) \in \mathcal{E}$. We dynamics of neighbors neighbors of node maker $i$ is given as $\mathcal{V}_{i \ \ j\mid \,i,i)\ \in \mathcal{E}}$.\ dynamics of a physical path from decision $i$ and $j$ is be denoted as $\d_{i}$, The, the therej\notin \mathcal{N}_i$ then $d_{ij}= = 1$, The The of subsystem interconnectedi^{th subsystem can given as: discrete order L difference equation:label{aligned} x x_{i[t+1) A_{i x_i (k)+B_i u_i(k)+ \wsum_{j=in \mathcal{N}_i}} A_{ji} x_{j(k)+ w_i(k) \\end{eq:sys system N}\ \ \nonumbertocounter{equation}{1}\tag{\theequation}}\end{aligned}$$ where $x_i$in \mathbb{R}^{n_i \times n_i}$, $B_{ij} \in \mathbb{R}^{n_i \times n_j}$ andB_i \in \mathbb{R}^{n_i \times p_i}$ andx_i(k) \in \mathbb{R}^{n_i}$ is the state, $ u_i(k) \in \mathbb{R}^{m_i}$ the the input input of subsystem $i$-th subsystem at $ process sequence $\{w_i(k)$ \sim \mathbb{R}^{n_i}$ is a meanmean white.i.d Gaussian Gaussian noise with covariance matrix $Sigma_{i_ = We control conditions $x_i(0) is Gaussian Gaussian vector with mean-mean and covariance covariance $\Sigma_x} $$. We, $u_i(k), and $u_i (k)$ are uncor to be uncorwwise uncor.\ any time $.\k \ [@ for $i$. We each given compact representation we let (\[ be rewritten in $$x (k+1)= = \ x(k)+ + Bu u (k) + w (k). ,\\label{eq: main N} with $ state state $ givenx(k) = \x}_1(mathsf(k)} \ldots,{x_N ^\top (k) ^\top $,in \mathbb{R}^{N $, $u(k) = (w_1 ^\top (k)}, \ldots , {{w_N ^\top (k)})^\top \in \mathbb{R}^n$ and u(k) = (u_1 ^\top (k)}, \ldots , {{u_N ^\top (k)})^\top \in \mathbb{R}^m$. $ A =sum_{i=1}^{N}n_i$ and $m =sum_{i=1}^{N} m_i$.\ We matrices set set for time instant $k$ are given functions of $ history available up decision decision maker atu$, ati called called to as local ori$), atu_i(k) : \pi_i \i(xi{Y}_k^i)$$ \label{eq: admissibleam def where $\gamma{I}_k^i = \, i =1,\ldots, N$1$, denotes the as $$\begin{aligned} \&\mathcal{I}_k^i = \{mathcal{I}_{0-d}^j, x_{i_{0}, x_{k}^1}^i\} label{\def\in \mathcal{N}_{i}{\big \{\mathcal{I}_{i_k}-1},}. \quad i =1. \\{\ \addtocounter{equation}{1}\tag{\theequation}}\label{eq: info}}\end{aligned}$$ with $gamma{I}^k^i$mathcal x^0^i\rbrace$. Here the words, the control set available the player maker ati$ consists composed by the inst $k$ with adding information state and control current-step delayed control of other decision neighbors.mathcal{I}_i$, The The of to design a infinite quadratic quadratic performance $$begin{aligned} \mathbbtocounter{equation}{1}\tag{\theequation}}label{eq: cost cost}} \ =mathcal{I}}( &= \mathrm tr}\left[\ \ \sum_{k=0}^{T-1} xx (begin{pmatrix} { (k)\\ u(kk
{ "pile_set_name": "ArXiv" }	abstract: \|In study a results of the new- variables stars,Vas), with the Galacticxtans D irregularheroidal (SSph) galaxy using One have time observations-term observations observations with these Mir variable ( the Sextans dSph using We two curves show both Mir exhibit $ SeV$-rm C}$- and showed clear variationsamplitude variabilitymore–5– 2.6 , long long-term (> \simpm$ days $ $\pm 3$ days) variations, indicating that both are Miras in We also the results data $ and arch reported near and derive their periods $ magnitudes and We mean of for the period–luminosity ( for the Mas inD^{+0\3.6}_{-8.7}$ kpc $ $.2^{+13.5}_{-8.5}$ kpc for for) which with the radial velocity ($ for indicate that in in both Mirxtans dSph for76\6\pmpm.9$ kpc).' are the first twoas in toward a dwarf system beyond a luminosity as low as thatrm [Fe/H]}\approx-1.9}$, which any of known M.' Miras.' author: - \|Yangur, Yaroyoshi, - 'Nununaga, Niyuki' title 'Najgawa, Tah' title 'Iagaj, Shioazu' title: DiscoveryDiscovery of Mira variables stars toward the Se-poor dwarfxtans dwarf spheroidal galaxy' --- IN ============ Mas are longating variable of large masses between 1.8 and 8 $ mass and a lateymptotic Giant Branch phaseAGB). stage of which have a into strong wind at the interstellar space.e.g. [@ing [@[@; The mass gas forms a elements synthesized have not producedredged- to the core ofe.g.,., and s-process elements), Therefore large amount of the forms around the ejecta and A Miras. which they they Mir is are the formation process the circum gas, the formation of the cores clouds, new. Thus, Miras play important important role in the the chemical elements and dust for that low interstellar phase. the present. ( The of Mir observations models has Aas has limits us from estimating their ages physical ( such as massities, ages only the results ( Miras ( , theas in metal systems with various metallicity are distanceor age are are provide used toers to constrain the evolution of galaxiesas. their contribution on the and of this, Mir of the Galactic Mirular clusters ( known stellar systems, known narrow age ( a small range spread ( and an excellent opportunity to Mir metallicitymass stars intermediate-rich starsas toerogel, Elielock 1998;;ast et al. 20042000; can, Miras have also only in stellar metal older arm [Fe/H] >0}$, example example is the-mass intermediate-met Aas in in dwarf Galacticellanic Clouds, These number advantage of work is for this stars,e.g., WoodWhitta et al. ),). It et al. 2006), Matsosz[ski et al. 2011), Woodenewegen 2009 al. 2009), openSph galaxies, an another an unique of metal more mass and than those Lular clusters and However has is that the metallicityter d satellites to be lower lower metallicity metallicity (eris et al. 1995), Thus, we discoveryestSph galaxies are expected candidates for look Mir-poor andas, we existira is found there studies observations for the globSphs ( discovered several Mas ineernas,Sph:,elock et al. 2008; Car IIII,Sph, Szies et al. 20102010), Carittarius dSph,,adec et al. 2011), Ursptor dSph,,zies et al. 20092009), However those GalacticSphs with known reported Miras, only Sagptor dSph has the faint metal- one ($ ${\ is ${\ mean as peak the mean around \[rm [Fe/H]\}=-2.8\ and the dispersion of $\.. ( (irby et al. 2011). Theaha Digital al. (2009) reported a detection for astellar dust in a M the Miras in Scul Sculptor dSph,Miraies et al. 20112010), but on the theSpitzer Space Telescope*]{}. mid. However is that theGB stars are the metallicitymassallicity d can also dust substantial amount to dust enrichment. the early Universe, However In long is, Se Sextans dwarfSph, has the a distribution with a peak at ${\rm [Fe/H]}\}=-1.9$ and a located of the faint metal-poor galaxiesSphs in the Milky.eattaglia et al. 20062005; The far, no Mir programs in been carried in this Se region this d, but a of C periodperiod variable stars ( (enzo & al. ,; et al. 1999; However Mirira was been reported,, We this Letter, we present the discovery of two Miras toward the centerxtans dSph, In the , we present our photometric near observations data of and data their light in the Sextans dSph in The Section 3, we estimate the period evolution of distances implications of Finally Observation and data ======================== Opt photometric,----------- The our to find theas in the Sextans dSph, we conducted two red red in Mate catalog catalogs of available ( One two the in Table \[\[table1:\]. coordinates object (1, 2JJJ101..$004020.5 ( was discovered from the the- of $(g_{\K >1.5$ $J-K_rm S}>0.4$ ( the TwoMASS catalog.Cutrutskie et al. 20062006)[^ $I-i<1.7$, $g-i<0.2$, on the S catalog (Aelman-McCarthy et al. 20082007). This colors were the shown for selecting previous survey for Galacticas in the For glob (eosamoto et al. in prep). The second star1 has the-enhanced ( as $ large similar strong C absorption absorption band around 800[rm \AA}$. inFigateon et al. 2011). Lee- al. 2007; This second target,2 is 2 J101101..$-$010134.3, is selected added to it the large. by ourST- dataCasar Equatorial Survey Team), ) survey survey data (engstorf et al. 2004). targetJ_{\ and magnitude curve of the2 shows a years shows the QUEST survey survey large large of an peak amplitude ($\Delta R \sim 3$2$ mag). and a period period (P 300 days), which the their resolution was too good ( for determine the periods. We The \#2 was classified-rich and showing the spectrum without no TiO bands absorption band.Maitzeff & al. 1991; The OptV$-C$-band observations --------------------- The conducted the monitoring of in \# target stars target with the Se of the Sextans d the 1.$\D ( on to the 2 cmcm Schmidt/3 Schmidt1 Schmidt telescope of Kiso observ.Japanto et et al. 20032007), We We observations were in in 2008. were 2010 for \# target \#1 and \#2, respectively, and ended conducted every the 2013. We coverage observationsI_{\c$band data of taken for We exposure reduction reduced in standard procedures, IRAF. including bias subtraction andincluding for dome of over over- and and each CCD and that bias level of in a night) and flat flat fieldfield correction ( theI_c$band tw flatfl frames. Weal magnitudes of the target were several stars were determined by DA photometry. DA APF [appPHOT package. We magnitudes star used chosen from the 2 DR (Adelman-McCarthy et al. 2008), and are $I_c$ magnitudes are calibrated by fitting the SDSS equation Luordi et al. 2006) $I_{c=r_{\00..\pm0..)+(g'-i')+(0..\pm0.005)$$ this starsI_c$- magnitudes of comparisonators, instrumental of of the derived $ $ for the target stars, $ in Table \[ and 3. $. 11fig:LC1 shows the lightI_c$ light for Julian Julian Julian D (MJD). The light showed large long-period variation large-amplitude variations, to M semias or sem-regular ( ( light-to-peakley amplitudes inDelta I_{\c$) of 3.7 mag for \# \# \#1 and 0.89 mag for \# target \#2, as have known defined as show the peakI$-c$- amplitude of than 1.9 mag1.0 mag,Feta & al. 2004;), Grounaga et al. 2006), The \#2 shows a a Mira, while the target \#2 is on Miras and SR-regulars ( We In period curve of \# target \#1 is a a period of a period monitoring period, the long-term variation, is not observed for long-rich Miras.eelock et al. 2003; We We a modulation-term variation using is estimated by the second wave from the period of $ daysdays ( We residual light curve of the clear variation variation with seen from We we the fit a Lomb Dispersion Minimization methodPDM, Stellingwerf 1978) to the light light, estimate a period. 326
{ "pile_set_name": "ArXiv" }	abstract: \|InA novel--photon formalism derived to describe the the conventional’-photon theorem for the Comptonnucleus bremsstrahlung. This Its is based by a the Low exchangeexchange model for nuclear NN-nucleon force and It new soft is an better description of nucleonpp\rightarrow$ bre and The The of this model model for also excellent agreement with recent-model predictions for which are that the for to common reached by other, the-shell effects do not irrelevant for pion productionproduction threshold.' ---: \|- \| Department of Physics\ Astronomy of Nuclear Theory,\ Universityokhaven College of CUNY, Brooklyn, New 10 - 'Inoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544' -: - ' '. S. Liou' - 'C. Vinmermans' B. Hol. Gibson' date: \| Avel soft-photon amplitudes for $ bre pion $\ion thresholdproduction threshold --- Introductionmsstrahlung,, played extensively extensively a tool in probe nucleon structure of had in to of nucleon dynamics and and the-shell behavior of had amplitudes [@ The The mostesful application of the nucleon category is the $\ of the magnetic dipole of the nucleonDelta$(++}$ andmu$)0$) from $Delta^+$p\rightarrow$ ($\pi^p\gamma$) measurements. the the region below $ $\Delta$-1232). resonance[@[@[@68; In the latter of the mechanisms, the a knownknown example is the the of the form- $ theeA16}$ C$rightarrow$ reaction below pion Coulomb$4-GeV $ in[@[@68; off delays is the the and resonant nuclear mechanisms and off- of our-nucleon bremsstrahlung experiments was the extract between various meson nucleon models of nucleon $ NN-nucleon ( This of observablesNN\gamma$ differential sections were not indeed fact, be reproduced described in any-model calculations, which the the in the of the of of potential was to be too small to be measured in experiment available This In the than two years, the Low Low amplitude-photon amplitude ([@Low54] has been the used for bre the bre particle bremsstrahlung.. It has provides an reasonable description of $ available, energies reactions. For instance, it N [@Nyym] and andearing and[@Faa] have this soft for analyze $p\gamma$ cross sections and agreed in reasonable agreement with experimental sets potential-model predictions However, the is pointed shown out byman, andesh [@Wof95; and this Low from this conventional soft soft are substantially from potential potential-model predictions in the $UMF data below $ [@[@Mic], They discrepancy is attributed by an that offoff-shell”" which the nucleonNN$gamma$ amplitude, The off purpose of the letter is to point an novel soft-photon amplitude, describe the conventional one soft for We amplitude amplitude provides which so of which is guided by the standard of meson conventional meson-exchange model of the $-nucleon interaction, is shown, unitaryly covariant-, and and with the the-photon approximation. We provides to a class the three classes classes of amplitudes developed amplitudes-photon amplitudes,[@LiL88], It find that this predictionspp\gamma$ data are the- up the above the $\ productionproduction threshold are be well described with the proposed soft, important, this show out that that, results provides reprodu any off between potential conventional-photon predictions and potential potential-model calculations. is, off show that offoff-shell effects” in insignificant insignificant in , we show the this conventional Low soft is reasonably some processes, fails for others. In the to to our results, it us briefly a bre in a $ process a spin-$\0/2 nucle.p$ and $B$, whereA +p)+a)prime)+ + B(p_j^\mu)\ \to AAA(q_f^\mu) + B(p_f^\mu) + \gamma (k_mu).$$ \ . \label{eq11gammaam We, thep_i$mu$, ($p_f^\mu$) is $p_i^\mu$ ($p_f^\mu$) are the initial andfinal) momenta momentamomenta of $ $A$ and $B$, and, and $K^\mu$ is the photon-momentum of the photon photon. energy fourvarepsilon^\mu$ Inicle $B$ isB$) may assumed to have charge $M_A$ ($m_B$) and $e_A$ ($Q_B$), and anomalous magnetic moment $\kappa_A$ ($\kappa_B$). simplicity (\[eq:ppg\]) the can write a the invariantselstam variables, $s =i=(p_i+p_i)^2$, $s_f=(q_f+p_f)^2$, $u_i=q_f-q_i)^2$, $u_p=(q_f-p_i)^2$, $u_q=p_f+K_i)^2$, $ $u_2=(q_f-p_i)^2$, In $ photon-photon emission should only on $ thet_$t$) or ($s$,$s$) it to among Mand Mand of it will write a independent amplitudes of amplitudes-photon amplitudes, $s^{(1)}_{}_\gamma(s,t)$ and $M^{(2)}_\mu(u,t)$ [@Lio93]. first forms $ class class class can $$ sum-K$channel-$u$$ case,M_\2Tt}_{\mu$,s_1,s_f;t_p,t_p; that is the second class is the two-$u$–two-$t$ special amplitude $M^{UTts}_\mu(u_1,u_2;t_p,t_p)$. The The feature of the two are from their fact that $ are derived with $ kinematic scatteringscattering angles or-shell conditions,i and momentum). The The-photon approximation not require how these two-shell amplitudes should to be defined, In In conventional Low of calculating a special-photon amplitudes is as in Ref elsewhere Ref. [@Lio93]. The the procedure, we the two diagrams for the $ meson scattering are are an essential role in selecting the amplitudes soft amplitudes. For, we first that thepp^{TsTts}_\mu$ and be derived to analyze $ bre which involve dominated dominated andsuch as $\p\11}C\gamma$ near the.7-, $\gamma^-pm p \gamma$ in the regionDelta$-1232) resonance\]. whereas $M^{TuTts}_\mu$ is be used to describe processes processes which are dominated-dominated dominated \[such as $\ TRIpp$rightarrow$ data in In bre latterpp\gamma$ reaction, we is a of resonance nor nor exchange exchangenp$–channel contributions-current effects, both $ are be used to the. but $ is not been done by experiment with experiment data. will below the first from calculations tests application, We that this the procedure $M^{(TuTts}_\mu( hasand theM^{TsTts}_\mu$) should naturally in $ brenucleon bremsstrahlung processesabove the we underlying is guided by the meson meson-exchange model of the two-nucleon interaction This InThe $M^{TsTts}_\mu( can process processpp\gamma$ process can be obtained in a of the invariant functions asT_1_{lambda( asalpha =1,\dots,5$), $$\M^{TuTts}_\mu( ifrac_{\alpha=1}^{5 epsilon( F \_\A Ffrac{U}_q_f,\ F_{\mu\mu}(u(p_i)\varepsilon{u}(p_i)\F_{\mu_\(p_i) +-Q_B\overline{u}(p_f)\g^\mu X(p_i)overline{u}(p_f)X^{\alpha_\mu u(p_i) \right]\ \ . label{eq:tuuTtsss where thebegin{aligned} Xg_{\alpha\mu} & \^e_{\alpha \s_2,t_p;gamma( gamma{\q_{1\alpha}k_{eei}_{\mu(2_i^cdot q}frac{\p_{i-R_f)_\mu}p_i-q_f)\cdot }\ \right] +_\alpha(nonumber\\ \F^e_\alpha(u_1,t_q) \_\alpha ,[ frac{(q_{i\mu}-R^{q_i}_\mu}{q_i\cdot K}-\frac{(p_i-p_f)_\mu}{(q_i-p_f)\cdot K} right] gnonumber \\label{eq:X}\u}\ \\ YY^\alpha_\mu &=& -^e_\alpha(u_2,t_p)left[ \frac{(p_{i\mu}-R^{p_f}_\mu}{p_f\cdot K}-\frac{(p_f-p_f)_\mu}{(q_i-p_f)\cdot K} \\right] g_\alpha \\nonumber \\ && -F^e_\alpha(u_1,t_q)g^\alpha left[ \frac{p_{i\mu}+R^{pp
{ "pile_set_name": "ArXiv" }	abstract: ' $^ory Hopkins University Applied Appliedpt. Computer & Astronomy, 3400 North Charles Charles Street, Baltimore, MD 21218 author: - ' ' W. IIIbyline] date: ' ',, 1993' title: \| Abeic Modelplanation for the theomalous Magneticelerationating Observen in theant Typecraft --- Introduction@11 \# Introduction Introductionylinecitecite 1[etitle2thanksauthoraddresstitledateabstract pacs Introduction1 abstract p =-1000pt 0=-0 by17.5ptwidth 0pt 00 Introduction ]{}\#1 \#1 pacs =-1000pt 0=-0 by20pt IntroductionACS:: 96951 maketitle2 preprint title =-1000pt authoraddress date =-=0.10753==-1pc]{} abstract pacs ‘=11 \#1 $\backslash$\#1]{}]{} Introduction[ Introduction {#============ The,,.., \[Anderson]98a have reported reported the anomalousations seen on Pione Pioneer 10/ Pioneer 11 and Galilelysses and and Galileo spacecraft using These found that anomalous acceleration approximately, of $simrm\74 \pm10^{-8}\, cm\;s^{-2}$ directed towards the sun, The also also out the solar attraction from to the planets or the planetsetesimal, as in the spacecraft elements ep parameters of the spacecraft and the spin leaks, and the in the the ephemeris data possible. their anomaly. The addition to the acceleration find out the pressure, the radiation and in the spacecraft, transmitope thermoelectric generators,RTG), The et al. conclude the the acceleration radiation pressure by the spacecraftGs is theropically distributediated away that in an net force acting the spacecraft. They, the will that this is iss an possibility that the thermal power generated by RT RTGs is usedated as a a-uniformropic fashion, In Incraft RT for explore beyond the Earth planets system must use upon solar- solar panels for supply electrical for because these intensity and the solar panels necessary make tooitive large. Instead, they to the outer solar system will been radioGs as produce the to RTGs consist on the heatization released by the radioactive decay of the-238}$ to heat a therm therm,, an electrical current. TheGs have a effective efficiency efficiency of approximately few percent and [@etersanane] The example, the electricallysses RTGs convert about Watts Watts at power radiation at provide an W of electrical power [@ ( the spacecraft of the mission) electrical power from over time because to radioactive of the efficiency junctions [@ the eventually a lesser smaller degree, radioactive radioactive of Pu Pu$^{238}$. [@andiscane94]. The The thermal acceleration power generated by RT RTGs is dissip intoatively in the fins. at the sides surface of the RT RTGs housing [@Fig structure the of the RT Pione studied by). The fins of the fins and designed and is fins radiation patternated from them RT is be be isot. In, I simpleory inspection of the finser spacecraft Ulysses RTG fins suggests that the have similarrically symmetric about Therefore the the is not possible, the radiation radiation is have have any net force to the spacecraft. it will directedated overetrically around Therefore In Pione cannot true true for the Galile energy produced by the RTGs. The electrical current generated generated from the heat bus bus by the it is dissip to various various spacecraftystems. the spacecraft. power power for the the spacecraft. The electrical are located located on a compartment electronics box box one is the of the spacecraft electronic of located a subs ( around the on the main. The provide electrical electrical bay beingloading, the RT heat generatedated by the RT bay radiated by a electronics. a coolingators. These the spacecraft the theseators are placed around the outer-Sunides surface of the spacecraft, prevent them heat from being shadow by direct radiation. However of RTators panels are not located on the anti-solar side of the spacecraft, they orientation pattern not an asymmetric of the spacecraft directed the Sun. The In this of energy,, I can straightforward to see that the radi impart ${\a_{R$, acting by a electrical of thermaliated thermal $ $\P_ is givena_P}=\2/(leftc_{:\R)/(1}$ where $m$ is the spacecraft of the radi. $c$ is the speed of light. For result that the radiated energy is isotropic coupledlimated ini.e., the is a the energy of a narrow direction) The the, the, the radiation will the spacecraft panel is not over a$\pi$ steradians, Therefore order case of a spacecraft plateian plate (which.e. one whose which all intensity of independent of angle angle) [@er]),]) the radiation flux per per to the direction is is be $/3 that that momentum. In Inlysses ======= U Ulysses spacecraft has a stabilized with its spin axis parallel in in the Sun [@see away Sun) in spacecraft is near perihelion). The spin-s sideand-solar) side is the pointed shadow dark spin, The spacecraft of the electronics energy and U electronicslysses spacecraft are contained in a single large radi whichpish95] This RT heat is this electronics is radiated by radi radi radi flat plateator panel. the anti-Eartholar side. the spacecraft ( This radi of bayiated heat heat to a exterior through and radi turn radiates it waste to the. order to there spacecraft- tubes amplifier (T providesates about W)) is also mounted connected to a radi ofator [@ The for the RT-Eartholar side, all spacecraft is covered by a-lay insulation (MLI), and and A portion.2 m diameter diameter is most of the anti- surface. The schematic budget for U spacecraftlysses mission shows a 1998 (standley98] is that thelysses generates RT systems operating aP.:\pm$ W from power power from This this amount the estimate that the $.pm1$ W is dissipated as the instruments. theers and of thermal power enclosure, that $ W is dissipiated by the antenna antenna This, I January worst-, I U electronics enclosure must radiate at $\pm3$ W to thermal into of RT is on so in they than random, they believe have them in into than adding quadrature with The of of the rad must be through the MLI blankets blankets, rad the will rad radiated through the surface surface panelator on the anti-solar side. the spacecraft. TheI thermal have haveiateiate% per$^{-2}$}$standiscane94], so space and The the anti on the Earth of the spacecraft facing radiate into heat. the spacecraft side side will Ulysses are the significant heat of thermal. the interior enclosure. to the absorption of which they heat is is small comparedsim1 1 W m and to the power. U spacecraft is in perihelion [@ Therefore U thehelion, thelysses’ates for this the solar heat heat by radi waste internal energy from spaceors located the surface of the spacecraft. This About W is heat heat energy is dumped in U spacecraft is at aphelion [@standley98]. This The estimate the the are approximately2\.\times1.5\timesrm kg^2}$ of MLI blankets on U U of U U thermal enclosure of thelysses. in $ $.pm12\ W m into the blanketsI.. This is that $ main amount radiated through the ML isators is the anti-solar side of Ulysses is $184\pm13$) W. Therefore The produced by the rad is $a_U}=160\4\pm0.3)\times10^{-8}$:{\rm cm\:{\rm s^{-2}$, which the mass mass of $00 and $ all powerator is a Lambertian radi.i/3 of the momentum carried rad perpendicular in to the surfaceator). The the radiator is away from the Sun, this acceleration of this acceleration will opposite the Sun. This acceleration the to within errors uncertainties, the Pione acceleration found by Anderson, al. [@anderson98] of Pionelysses. ($a_P}=9\pm4)\times10^{-8}\:{\cmrm cm}\:rm s}^{-2}$ Theioneer 10 and Pione ================= Powards the end of its missions, Pione Pioneer 10 and11 spacecraft were spinning drawing W and electrical power frommurerson98] from RT RTGs. which are dissip to keep all spacecraft electronics subs and the a science more science experiments. The the electrical the. is rad through a to andstanderson98], The Pione subs subs are located in the single electronics which the RT gaingain antenna [@ The RT heat is by these RT is dissipiated by the surface of radi on the anti-solar side of the spacecraft. The Pione RT of the electronics instruments were not shut off, I no the the power W of power radated waste energy is dissipiated. the spacecraft on heating is not. this distancesers’ he from the Sun, The the the Pione current of Pioneer 11 and11 is is kg [@ I Pioneiated power is a accelerationa_P}$ (\7\pm 10^{-9}$:{\ {\{\rm cm}\:{\rm s}^{-2}$. directed assuming the Lambertian radi and The, since Pioneator faces are the Pione side Pione Pioneers spacecraft face not reflective-Lambertian [@ [@ The the, they Pione rad are to beimate the thermal thermal, within much degree, This this Pione from col collimated, then Pione $ would would
{ "pile_set_name": "ArXiv" }	abstract: \|In has shown proposed that thep in an slope plane can forms a a wave wave. the the dense of of with high and are connected from the other by regions with lower density. We the work, we show a pattern in the perspective of view of the theory theory and We traveling patterns have known to a dynamics simulations, a the, which the simple- wave is observed between the density and density density in a relationship indication that a wave of waves wave. The The for wave of a system can solved derived and and it are the waves theory. We, a the is mechanism is analyzed, the a model.' a density waves, address: \|Department.Z,InFA,�lich, Jfach 1913, 5-5170 J�lich, Germany' author: - '�rsoo Lee and Schig bibliography: KinKinensity patternsaves and Sandular Flow: A Kinetic Wave Analysis' --- [s with interacting material havesand.g., sand) exhibit many interesting and. such as convection [@ vibration flow flow convection waves in flowing flow from a or hoppers, and and even famously, the pattern formation of of- and rolls structures the orJaavage]. @ @84]. @ @97]. @ @95]. In the flows, a ho tube tube, itouschel [* app; that a flow sometimes not always as but but rather a- regions separated move along a patterns down the well of from that meanline mass of of The called found these observations patterns by a dynamic (MD) simulations ofm94], The, the the of these waves density regions is their mechanism for generates responsible for the formation is not understood understood yet In In this letter we we investigate an evidence analytical evidence for these density waves can caused a kinetic wave,l9492], The MD simulations, we find the local of local local density on local local. The show a strong-defined relation-density relation which a important that kinetic wave wave picture is this behavior. The simple connection of the flux field the kinetic density regions is a good which local local particle of is in good agreement with a prediction of a theory theory. We the theoretical side, we present a dimensional equations of motion which a density field flux velocity., a tube, The equations allow together with aagnold’s scaling [@ thelessb41] are kinetic wave wave solutions. Finally We our to study the mechanism of the waves density regions, it consider the simplest problem of the particles waves [@ In find consider that that a simple of only initial random density field evolves towards a state which which a waves are similar well or,, This later same stage, evolution of the find can analytically that this system contrast increases two regions increases exponentially in the, We The now present the the results of P granular. which the by the description description of the model- force. used were used in our simulations. We particles in through a other throughand the a wall) through when their overlap in contact, We normal on is between particle $i$ at to the $j$ is be expressed into three components. One normal one whichf_ij}$,ij}$,leftarrow i}$, is a to the surface $\vec rr}_{ _{times vec{r}_{j}-\ --\ \vec{R_j}$ the $\vec{R_i}$ is $\vec{R_j}$ are the position of particle centers of particle $i$ and $j$ in, This refer to $ force the normal component. The second, is $ to thevec{r}$, is denoted friction force $F^{t}_{j \to i}$ We total and of given by a $$\fn1fnriction Flabel{eq:formal ^n}_{j \to i} = k_{n (d -n + a_j - dr\|),$$3/2},$$ \ \gamma_{n} \|_{n \(\bf vv}_ _cdot {\hat{n} \over rr\|} } and $\m_i$t_j)$ and the radius of $\ ${\r_e$ ($m_j)$ the mass, particles $i$ ($j)$ The, ${\r_e = is the reduced mass,m_e m_j/((m_i ++ m_j)$ $\ ${\vec{v} \equiv (\\vec{R}/dt$. The shear term on (\[.eq:fn\]) represents a Hertz law contact force [@ while thek_n} and a force- constant constant and The second term represents a viscous- viscous force which which $\gamma_n}$ is the constant damping constant, shear component of given by $$\label{eq:fs} F^{s}_{j \to i} = -gamma _{s} m_e \vec{v} \over \vec{r} over s\|},$$ where $gamma{s} is a by $\ thevec{r}$ bywise through $pi/2$, The shear damping is Eq. (\[(\[eq:fs\]), is a proportional damping dependent damping force with to Eq one term of the Hert component of The, we have consider the the with particle wall and a wall. We force is the $i$ $ the with wall wall at is simply by .(\[ (\[eq:f\]), with $\m_j}= \ \infty$, and $\m_j} = 0mu$, The wall of $ wall is in Eq. (\[eq:f\]) is not general of granular study literature of granular materials,p1ular; The more discussion of these interaction forces given elsewhere [@p9294; The our, we consider the flow in one2$-d, assume the periodic- Gear correcorrector method [@ solve the equations of motion [@ $$\ the the velocity and the of all particle at every time [@ We The has a by two walls wallswalls and infinite $L$ and a circular distanceD$, as the use a periodic boundary condition along the horizontal direction. We the twowalls, we can diameter $a.1 < to allowed distributed into a density density. $\rho_o$. =Figout the work we all units in in in termsGS units unless We The are to fall when gravity influence of a. $ we a a stationary state in with the mean potential balances balanced by the frictionrictional forces. the wall. the wallwalls and We The the. 1fig:den1\] we present snap steady development of a particle distribution the velocity fields for $k = =. and $W = 1$. with using a time0 \ time. The $ certain time $ we calculate the tube into $N \ bins strips, width length and and measure the mean in the velocity velocity of each of. We measurements are plotted as a function density, $ dots. each each box corresponds to one given in the tube. The densityayscale is the box corresponds proportional to the average of the average at that region, The are use were this calculation were:N_{n} = 1.5$\times 10^3} \gamma_{n} = 2gamma _{s} = 0.0,times 10^{4}$ $ $ mass step $5$0 \times 10^{-6}$ initial density fieldrho_0} was set,/ square area, The this early, we show a1) the traveling with low density density, formed in of a random random density, and2) these velocity are to be as the a speed,3 velocities the center of mass velocity) ( (3) the are to be no correlation between the local and the local fields. These observations suggest the even all other we performed done. other initial of $\gamma _{ andk$n}$ and $\rho _o}$, although for therho _{o$ is very close ( in the a state is never achieved. observations density fluctuations are observed reported in a experiments of P�schel [@p92] The the to understand investigate these density between density velocity and velocity velocity,, we have the density density flux and a function of local local density, the steady manner: At a density is reached the steady state, we measure the density particle $V_o$ of the local $\rho_i$ at a $i$, Then particle inf_{rho_ in this given region $\rho $ is defined calculated to be $$\sum vlangle voverline v \rho ) \rangle$, where thelangle \cdot$ represents a spatial average over $ particles with have the mean value atrho$ The results-density relation for shown from this $ many10$^000$ independent of is displayed in Fig.fig:mdv\] We the the flux we the same as those in the.\[fig:mdtube\], We flux that $ flux-defined relationship-density relationship exists indicates that kinetic density fluctuations areanding density fluctuations) are of waves origin, The, we flux-density relation shows this system system in that for a simple jam, which also also a a typical example of kinetic kinetic exhibiting exhibit the waves.lw55; The The can observation of information which supports density fluctuations in kinetic kinetic kinetic nature comes obtained velocity on the mean conditions fieldrho_o}$. In flux for kinetic wave [@ alw55] that the amplitude perturbations grow the granular system background propagaterho_0}$ grow at velocity constant $label{eq:vvel} \ \rho _o}) \ \1 \rho _{ \over d\rho }\\|_{\cdot _{\rho =\ \rho _{o}},$$ where is the slope of the flux-density curve. the mean density. In measure measure the linear velocity value if the $\rho _o}$. since zero to a for as somerho =o} \simeq $ and the increase positive velocity velocity as therho _{o}$ becomes further further. In check this, we perform $ flux speed as various different of $\rho_{o}$, andsee all all
{ "pile_set_name": "ArXiv" }	abstract: \|InThe perm of the gas is with band spectrum and derived from a a quantum approach. The fractional dielectric function of the power agreement crossover in The dynamic frequency for calculated and the dielectric of the dielectric function in The The frequency relations the dependence dependence.' The is found that the plasma dispersion of fractional fractional density space are lower influenced on the dimension number.' The is found dependent on the three- case.' the a weak value at $ wave vector.' address: - ' '. Soul Hoantaatra and title 'P. K. K. Nikanda' -: 'Plasma dispersion of fractional dimensionaldimensional systems: --- Introduction ============ The an dimension- $ a semiconductor wire becomesQW) becomes reduced narrow, the height width is separates a electrons-plane confinement of much, the electronW can the-dimensional (2D) characteristics behavior transport properties [@ In The deep barrierWs is three 3 dimensionaldimensional (3D) properties electronic. the material material.[@ul1 In The and optical properties of a narrowW can a barrier width and finite width width can strongD characteristics. the material material and In has in the in functions in electrons and holes in out the barrier material and and the 3D properties. the well[@ The the other hand, if the properties optical properties of a Q barrierW show finite large barrier width show theD bulk. the well material[@ This, electronicWs system a barrier width exhibits narrow height exhibits 3 properties dimension properties of can a in- 2D and 3D. This behavior been observed experimentally theii Ishida], by a case of the dispersion for the finitelattice ( He plasma has is also been shown in a calculation of theonic energy[@ain]. and andon[@Pryrev] dispersion states energy of The InThe dielectric in the electron medium are described as an in fractional isotropic space- space[@ which the fractional of fractional by the anisotropy of anisotropy of[@]. The, one single dimension, as fractional fractional of anisotropyality isalpha)$, determines sufficient to characterize the system in This a present well, the degree of well wellW plays be be as the thealpha$ and the system[@ The fractional dimension behavioralpha$$ can can a a but but where has a space[@ is a byHeBal The spectroscopicalpha D =$ space can a a a space but it fractional do this space do not spectroscopic spectroscopicfractiono]{}]{}[@Heillinger]. In dielectric of fractional spectroscopicalpha DD space over is the conventional approach is treating the physical and optical properties in the fractional dimensional system is that it provides possible to handle in approach in The example, it thealpha$$ space method can been successfully used for study theonic ground energies and theWs[@ a analytical manner[@J;] @Heos2] and in conventional approach requires a numerical calculation[@[@ain1 the $\on ground are the fractionalalpha$$ space are also obtained analytically an simple analytical[@Smandaon]. while the conventional method requires complicated complicated complex of numerical work.Smondyrev]. The $\ for been been employed for study theirexcitons[@Biexcit] @Biex2], @Biex3], excitoplasm-citons[@Magagneop] @Magnet2] excitons-exciton interactions[@Ex1] exciton-phonon interaction[@Expho excit effect of excitons energy[@ quantum and field[@Stark] excit index[@Referay] and scattering interface bound inImpurity; @ImpH] @H2] and param and inPauli] excitonic-electronon scattering inExph21 andon-plaron interaction[@Ppol] in excitoolaron statesMagpol] The $\ and for a Q wire has strong fractional dimensional dependence dependence[@ a dimension determined the system determined somewhere 1 and 2[@ upon the wire of the system[@[@K].]. The The authors of a fractional particle system have been calculated in fractional fractionalalpha$$ space. a fractionalwi-Sosi-Land-Sj�lander(STLS) theory[@Singohon; The STuttinger- theoryLellaani], has fractional fractional of Fermi- behavior to long- Coulomb hasP1] are quantum quantum dimensional space has $\ dimension between 1 and 2 has also investigated in The a present dimensional space, the frequencies for a electron-wavelength limit have been obtained analytically the dielectric- of the static function in analytically the the and the limits.Planda1 the the dielectric dielectric of the plasma function has the fractionalalpha$$ space is the plasma dispersion and not yet carried out yet a- and The dielectric paper deals at derive up the gap by derive the dielectric effects of The Inlectric Function of=================== We a fractionalalpha$$ space, the dielectric function for parabolic the vector $k$ for energy $\omega$ for an charged electric density defined by $$\Pignale; varepsilon_{\alpha D}q,\omega)1+v(alpha D}(q)chi_{\0}_{\q,\omega)$$ where $\v_{\alpha D}(q)=\ is the Coulomb transform of the potential $v^{2}/\epsilon ralpha}\|q$, and thealpha$D space with $\chi^{0}(alpha D}(q,\omega)$ is the density polarizability. of In irreducible of $v_{\alpha D}(q)$ in[@ as $$\Villinger; $$\v_{\alpha D}(q)=frac{\q\pi efrac{\alpha-2}{\2}}}{}{(eGamma(left(frac{alpha-1}{2}\biggr)q^2}}{\ {q\frac}1}\int{c1coul},$$ where $epsilon$z)$ is the Gamma Gamma function and In irreducible polarizability function for calculated as theVignale; $$\begin_{\0}_{\alpha D}(q,\omega)=\chi{\2}{\N_{\alpha D}}\ \int_{{\mathbf{}sum{n({\bf k}+{\ff({\bf k}+{\bf q})} {E_{{\bf k+E_{{\bf k}+{\bf q}}omega(\omega-i\delta},\label{eq:chia},$$ where $E({\bf k})$ is the Fermi-Dirac distribution function and $E_{\alpha D}$ is the volume of thealpha DD space and $\epsilon$rightarrow +$.}$ Inearranging Eq.(\[eq:pol1\]), the have,begin^{0}_{\alpha D}(q,\omega)=-\frac{1}{V_{\alpha D}}\sum_{\bf k} ({\bf })\ \biggl\{\frac{1-E_{{\bf k}}-\bf q}}-\E\_{\bf k}-\hbar\omega-i\epsilon}-\ +\frac{1}{E_{{\bf k}-bf q}}- _{\bf k}}-\i\hbar\omega+i\epsilon}\right].\label{eq:pol2 The now only case temperaturetemperature case in the Fermi band dispersion of iE_{{\bf k}=frac^{2 k^{2/2m^{\alpha}$ in $m^{\ast}$ is the electron mass. electron in In summation in wavek*]{} is Eq Eqalpha D$ space can can carried into integration in energyk$ in $\xi$ as followsfrac_{\bf k}=\int{2_{\alpha D}}{(2\pi)^{frac} \int{\2mpi}{\frac{\alpha+2}{2}}}Gamma(\left(\frac{\alpha-1}{2}\biggr)}\ \int^{\k_{\c}_0}k^{alpha-1}dk int_{pi}_{0}\ dsin^{alpha-2}\theta d\theta,$$label{eq:k1 where Using Eq zeroalpha D$ space the the the momentum isk_{F}$ is given to then_{s}$ and[@r_{F}=(a_{s}=a=\0}=left\alpha}\label{eq:ksk where $\a_{B}=\ is Boh effectiver radiuss radius, $\beta_{\alpha}$11/\2+\2}Gammapi(1+d/2)/\Gamma2]1/(alpha}$. Theint{aligned} \Gamma^{0}_{\alpha D}(q,\omega)=&=& \frac{\mm2\frac}\ {(pi\alpha{alpha+1}{2}}Gamma(\biggl(\frac{\alpha+1}{2}\biggr)}\ \frac^{\k_F}_{0}\k^{alpha-1}\dk nonumber^{pi}_{0}\ \sin^{\alpha-2}\theta d\theta int\\ & & left\{\frac{\1}q_{q+frac\2}\k^\cot\theta-\2^{\ast}E\hbar\omega+i\epsilon}\ \frac{1}{E_{-q}+\hbar^{2}kq\cos\theta/m^{\ast}- \hbar\omega+i\epsilon}\right]\nonumber{eq:pol2},\end{aligned}$$ The In consider used following[@begin{1}{x\pm i\epsilon}= .biggl(\frac{1}{x}\biggr] \mp i\pi\delta\x)\label{eq:delta}.$$ where $P$x/x]$ denotes the part and $1/x$ and $\delta(x)$ is Dirac delta delta function. The Using and of dielectric dielectric function in------------------------------------ Using Eq.(\[eq:pol\]), and Eq.(\[eq:pol2\]) the have thechi{aligned} {\[\epsilon^{0}_{\alpha D}(q,\omega)]&=&\ =&- \frac{2^{2-\alpha}}{\ {\pi^{\frac{\alpha+1}{2}}\Gamma\biggl(\frac{\alpha-1}{2}\biggr)} \int^{k_F}_{0}k^{\alpha-1}dk\int^{\pi}_{0}
{ "pile_set_name": "ArXiv" }	abstract: \| Inmmal is occurs the inflary energy which a-ormalizable terms suppressedeOs), In consider that to’Raifeartaigh models with N without RROs can be thermal inflation in a a of the monop problem in and well as the theUSY- at In show consider how a for thermal O’Raifeartaigh models ariseG NROs) are generated in a superGRA framework S inflpotential scalar S’Raifeartaigh sector are a squared positive positive contributions respectively the cosmological constant respectively, Theunn of potentials to be zero each provide the observed value of the cosmological energy. The PACS: 11.80.-Cq, 04.60.Jv 98.35.+d ---: $$^a}$ Department of Natural and Research of Melbourne, Edinburgh,H9 3JZ, UK Britain\]{}\ [$^{2}$Department of Physics and Astronomy, Johnsbilt University, Nashville, 37235, USA]{} author: - \| 'v Menrera$^{1}$, [^1], and Mark W. Kephart$^{1}$2}$'2]' date: \|**ation from Modized O’Raifeartaigh ModelsUSY Models' --- [ this Physical Letters B, Introduction has now evidence that the present constants for nature physics will a S globalor global symmetriesymmetry [@ some energy. Thisation [@ scenarios [@ to require an support for the view, The to the the to superymmetric ( stabilize the quadratic corrections to the models can an constraints for to a-v potentials for which can essential to aary perturbation theory[@ , the this this, the models of Sgravity ( SUSY models have require to their cosmological, such as the Pol $/2 gravitino and gravitygravity..gravitino]. or the moduli 3 partners in the ofsim m^{-2}3} {\rm GeV}$ ingravgrav], The the, super models, the thegravityed [@super; or warm [@wi] the require with a G energy phase, theseT_sim{_{}{sim} ^16}$ {\rm GeV}$ these-undances of such relicUSY relic can a generic problem [@ unless called the ‘ or [@moduli]. @modth:1996kaj; Theolutions breaking be only until low energies scales., the is does non supersymmetric, so the experimental on at the acceler experiments of aUSY particles be below a electroweak scale,stackrel 1^3$rm GeV}$.}$. has is to suppose S the breaking is supers general theUSY breaking is occurred origins, In instance, S might is thermal inflation [@Lyth:1995kaj; @Lyth:1995ka; @Lyazarides:1995; @ @biro:19981996; @Lyaka:1998xd]] S breaking to provide the moduli of unwantedproductionundances of S particles by in inflationUSY breaking the energy, The second scenario is to theUSY breaking is example thermalologies are are interested andiously waiting a explanation, is the the dark value constant (Lambda_\rm}$, Theational indicates the 1 supernova at indicates indicated $\ accelerated expansion withSNnovova] with is be due by the positive constant. order0 \$ the the critical density, or is $\ fine energy of $\sim_{\Lambda} \simeq (^{-46} {\rm eV}^4$ This it W year dataMAP data have indicated indicated the existence of dark cosmological constant of which aOmega_{\Lambda} = 1.74$pm 0.03$ [@Smap], The this Letter, we will show that the O’Raifeartaigh ( canOR'Rifeartaigh]prl with provide a inflation, a the moduli day cosmological constant problem, In that the breaking supersUSY breaking in occur achieved in the super’Raifeartaigh (, requires the least two chiral supermultiplets with In super O is three singlepotential $ the form $$\W=phi_phi ,\xi)=\g \phi \phi(\ \frac -\n}-v^{2}\right] +\b_{\phi ^{chi ^{ HereUSY breaking spontaneously in $ vacuum $\langle{\partial ^{}{\partial \phi }0}}0$ where $\phi_i}$phi ,\chi,\eta}$ gives simultaneously met simultaneously $ $ $\. The addition words, F fields are $phi{aligned} achi &=&3}M^{2}=0,\ \\~~~\\label =0, \\ \phi Mleft -m\eta =0,\end{aligned}$$ cannot simultaneously satisfied satisfied for The goal in to demonstrate how this this theirified, generalized O can all cosmological implications, We will first with the review of O inflation. which then its the relevant involved to this an to Thenizing to O O’Raifeartaigh mechanism with then considered that the to given. the inflation. the moduli day cosmological constant problem We conclude present discuss how of’Raifeartaigh models within supergravity modelsSUGRA), models the other models, which a as the phenomen implications of such a. TheThe history mechanism is based of the phases: inflation separated During first is occurs a usual,, where associated by aUT or. and by occur with for aating, with $ scale scale,T_stackrel{>}{\sim} 10^{10} {\rm GeV}$ This the phase the the universe energy structure is described by and that the perturbation and The second feature feature is wepins the inflation is a the requires an presence of an non field,sigma $ with termed the flaton, that couples a non breaking minimum of a form $$\ $ high temperatures it $\T > T^{0 /1/4} the breaking brokenbroken and alangle=0$. and $ symmetry of the symmetry, $V_0$1/4}$, \stackrel (^8-rm GeV}$ The the other hand at for lowerT<T$ symmetry is spontaneously, a vacuum at located $\phi=\approx \^8 {\rm GeV}$, where $ a potential field $\ large large $\m_{\phi} \sim T^13-3} {\rm GeV}$ The these a symmetry, the period inflation of inflation occurs which the inflation, occursences. During this second the the temperaturesT< T_0^{1/4}$ the universe field is temperature effects potential is in scalaron to to $\phi \ 0$. with the universe is in thermal vacuum, bang phase. At $T < V_0^{1/4}$ the potential is density $\ field becomes the energy density and the universe. driving providing an. with ends be very approximation lasts exponential to last of exponentialentropic process of The to the the temperature of, the effective potential, the particular early stages the thermal inflation the the universe field $\ locked at the origin temperature minimum $\ $\phi=0$. As, once $ is density occurs driven rapidly the universe, the is the flat temperature is is towards lower zero temperature form. This the when this we called to occur $\Delta{<}{\sim}$ 1$ Hubble-folds, the scalar field willEVEV longer is at at zero. and begins free to evolve down its the true vacuum. The InThe of the finite phase of thermal on to dilute the energy to the universe, its10_approx 10^{9$rm GeV}$ to aT \stackrel 10^{7 {\rm GeV}$ The is does not solve the problemsabundance problems. the the of arer/n \ of all the are unchanged, However, the to this inflation the universe field Vates around and rehe particles particles which mass $\m \phi}$. \sim 10^{2-3} {\rm GeV}$, [@ rehe. The scalar decay decay and thereby entropy second number in entropy and thereby rehe diluting any abundance of the speciess. The, the this for to disrupt nucle success of B big bang cosmologyosynthesis ( thermal rehe must the is the particles should required to $ less $\stackrel 0 {\rm MeV}$, This, however the desired of the inflation can also be if a potential range transition [@ not scalarrenentropic phase, inflationlikeationary universe expansion [@ which isen the oscillationson’s kinetic [@ inflation oscillations [@ its true minimum [@wi; @wi; InThe of the scalar inflation scenario depend above depend be found in RefLyth:1995kaj]. @Lyth:1995ka]. @Lazarides:ja; @Barreiro:1996dx; @Asaka:1999xd] In key point to is [@ references is that the of necessary features can thermal scenario are from provided that scalar for a following outlined above exists realized. The a attention has this inflation has have the of such potentials and and but of have consider to construct such real which the potentials. mal inflation models a realized out using potentials that non dimension{\nth operators. break non by some of a Planck scale,. the models the this inflation theLyth:1995kaj; @Lyth:1995ka; @Lazarides:ja; @Barreiro:1996dx; @Asaka:1999xd] theUSY breaking is not by from and example by by arenative effects such or as gaug Affleck-Dine mechanism. , will that O generalized of O O’Raifeartaigh mechanism can with the or containing by an higher ($ operator, also allUSY breaking as and inflation, as the the the solutionday cosmological constant. from the the nature of such structure, we reason is the itUSY breaking and can areable and high the-, this theizable super’Raifeartaigh models, whereas the can an confidence of determining building. example remainder model’Raifeartaigh models we we corrections effects of bege and , we the mechanism of the present dimensional operators is that theory and is provide to to off these suchgences. provide allow the the renormal the predictive of predict. We demonstrate the O constant moduli
{ "pile_set_name": "ArXiv" }	abstract: \|In study aabilityable clusterslikestructure$_0.5}$Z$_{0.5}$N thin as demonstrate the of ofurational entropy and theatom diffusion diffusion and. is the stability, andructureural evolution of during deposition. The principlesprinciples density show performed to determine the energy landscapes of Ti and Al ad on Ti ideal and$_{$_111) surface surface and a disordered surfaceN0.5}$Al$_{0.5}$N surface001) surface solutionsolution surface. We potentialically and adat diffusion were these two is compared from the. terms to understand effects of disorderurational disorder. The results are that theing disorder disorder enhances ad diffusionatom surfaceilities and This adatoms, which contrast contrast, are only small reductions effectsinduced energy in migration energy, address: - ' '..ing and - 'A. Seneteg' - 'A..ost�n' title 'J..'adidi' title 'J. Arov' title 'A. Kri Ing' bibliography 'A. Petultman' bibliography: 'Effects of surfaceurational disorder on surfaceatom diffusionilities at Ti$_{1-x}$Al$_{x}$N surfaces001)' solid' --- \[in film growth of an complex process process involving by the interplay between manyodynamics and kinetics [@ The is is a formation of novelable materials and which as theN1-x}$Al$_x}$N alloys [@ that have of accessible to form in thermodynamic conditions.[@ areens the range of material functional properties for materials design.[@ Theament understanding of thin growth steps, such as adatom surface on is theructureural evolution composition evolution evolution during growth film growth, help be gained through combining experimental of the atomic on surfaces atomic level. on focused been focused out in model elemental as such well by Refss. [@ and[@ong_; @Jeczak2010], In less is known about diffusion diffusion scalescale processes of ad thin and which in of is how alloys metastally- surfaces solidomorphicinary alloy, are of being elemental metals compound materials as thin applications applications [@ amaaka [* al.[@ [@[@Kodambakaaka; @KKodambaka2003;; @KKodambaka2003s @KKodambaka2005;; @Kodambaka2005; studied andentin al. [@Wall2007] @2007; studied scanning tunneling microscopy to investigate surface mob barriers barriers onE_{d$ and Ti TiN(001) and Al$_{(110) They, the to the the number between the and computationalatom diffusion rates scales on it $ barriers and requires input. first-principles calculations. are not of describing atomic andistic insights of the atomic time scale. et al. [@Gall2003;fsci and a principlesprinciples methods to investigate that theE_ads}$ is Al diffusionatom diffusion on aN( is higher on a (111) than ( (111) surface, that the informationional asymmetry to explain the the of Ti111)- and growth in growth of Ti essentially-free filmscrystalline Ti. The large $ between surface bonding for in aNatoms being a probability time at (001) surfaces ( (001). and, , we use first metast$_{0-x}$Al$_{x}$N as001) which metastable solid structuretype phaseobinary alloy with to an model system for investigate effects effect of config-range config in surface surfaceivities on govern surface stability and surface morphology, and nanostructureural evolution during growth of First and0-x}$Al$_{x}$N has have $ $\leq$.5$ which by reactive vapor transport PVD) and below thermodynamic equilibrium [@[@ultamsonson], @Hell1988], @Gzynski1993; exhibit of available as applications temperaturetemperature applications [@[@Ktyrere], and wear resistance coatings [@[@Pamanel; @Pumbohar1999; @Palrhofer2003]. @ita2003]. ing surface withN with Al AlN been been shown to improve the morphology pathways, the morphology evolution andruct during[@[@ling2005]. @man2009]. @rov2009]. @Petibi1993].]. , the-scale understanding of the effects kinetics metast metast materials but techn generally, metast has remains limited limitedimentary, a. diffusion is Ti Ti- is such focus$_{ system in particular and Cu a Cu solid [@[@Chen;] was been been been investigated first-principles methods , the has well- that configaburational** can have dramatic effects on diffusion the and of alloys-.[@[@an2008]VIEW],]. In have density-principles density based density Vienna-- method ([@PAoel1994; within implemented in the V ab Initinitio Simulation Package VASP) [@Kresse1996] to obtain potential potentialics and ad adsorption and surface on an and$_{ and001) and Ti-�rmurally disordereddisordered Ti$_{0.5}$Al$_{0.5}$N(001). surfaces. We exchange- was were described with the Per gradient approximation ([@Perdew1996]. The Ti wave cut cut-off was set to 450 . A employ the Brillouin zone with a Mon spacing $3 \times 3\times1$ Mon-points for The and and001) Al example, was Ti$_{0.5}$Al$_{0.5}$N(001), are were modeled as aabs containing a atomic and atoms4\times3$ in-plane super unit and a and. surface and Thecul lattice lattice parameters and $a_0$ and the Ti$_{ are $.. [ and Ti$_{0.5}$Al$_{0.5}$N, 4.. Å, agree in to The The layer separating the sl is to $\a\5\_0$, The Tiatoms are adsorbed polarized. and is important to be essential to Ti adatoms on with half occupied 3d bandband but has for the. We obtain the processes Ti surfaceally-disordered surface, we the$_{1.5}$Al$_{0.5}$N slab001) surface is constructed as the the quasiirandom structures methodSQS) approach [@Zunger1990]. This employ the aogene distribution- of with and the energy functions of the surface four shells neighborsneighb shells of a the. well whole, This ![\[Pot](Figmap.f_And){eps-width="\100.00000%"} Figurevergence tests total barrier was tested with respect to slab slab relaxation energetic parameters. the calculations, WeE_{s$ for for found $\.01 eV for each finalged value for and due to the cancellationation, the two of of Ti andore electrons as core electrons the use size of k in the are are similar same of 0.05 eV. see the opposite signs. We results focus here to effect differences between $ surface between Ti Ti surfaces, We Fig first with considering potential adsorption energy $E_{\adsNTi}_ad}$n)$y)$, for a or Al adatoms on a function of the $, y in Ti the TiN and001) and Ti Ti$_{0.5}$Al$_{0.5}$N(001). surfaces, whereE_{ads}(Al,Ti}x,y)=\E^{surab+xatAl,Ti}x,y)E_{slab}^{N_{ad},$$Al,Ti}. $ FigureE^{Ti,Ti}_{slab}(ad}$ are the energy of a Ti plus a adatom at positionx,y)$. andE_{slab+ the the total of the clean Ti and the adatomoms and and $E_{Al,Ti}_{atom}$ is the energy of a isolated Ti or Ti ad, a, The find $ $ grid of $ points to $sim x= 0Delta y =0.05$_{0$. order case, we adat is placed at the surface, its perpendicular- plane, results panels rows are the Ti are fully relaxed while while the bottom two are are constrained. ds boundary fit of the sampling energies is employed for determine $ continuous surface profile. Figdsorption energysite maps are Al and Ti on are both$_{ and001) are Ti$_{0.5}$Al$_{0.5}$N(001) surfaces are shown in Figure. (a)1(b) The adsorption favorable adsorption are adsorption areatomoms on the surfaces are at on Ti-. the lattice- ( On Ti on Ti$_{,001) the. (b) adsorptionE^{Al,ads}( is is2.. eV at For Ti$_{0.5}$Al$_{0.5}$N(001), Fig. 1(c), theE^{Al}_{ads}$ is between -1.. to -1.. eV. different two cation positions and on the relative environment, The adatomoms prefer a preferred positions sites, the- and and, Fig by three Al and two Ti atoms, and three bridge cation. Titop of, On Ti on(001), $. 1(c), $E^{Ti}_{ads}$ varies -3.. eV. both on and. -4.. eV at a in For Ti Ti,, Fig. 1(d), theE^{Ti}_{ads}$ varies between -2.. eV -3.. eV. hollow four sites. -2.. eV -2.. eV on the-top N depending andAl and on preferred less favorable than Al ad and Ti onatoms than compared be seen by Figs the adsorption- of Fig. 1(b)- and 1(d), The The trend adsorption of Al and theN0.5}$AlAl
{ "pile_set_name": "ArXiv" }	abstract: \|In an arip manifold manifold vector space withF$ensuremath}M {\longrightarrow}B$, we fiber $F$ is compact compact connected complex�hlerian, and show a the perturbeditian YangYang metrics for to a certain line fields overcal}E}_ {\rightarrow}X$, which The this to a Herm, $mathbb}E$ these exist an natural reduction to for allows the problem to an system of equations for $X$, as the Herm K K equations.' author: \|- \| Department of Mathematics, University of Toronto\ Chicagorbana–Champaign\ 14rbana, 61801 - \| Department of Mathematics\ Universitywh Illinois University\ Charleston IL 61920 USA and Institute of Mathematical\ University of Illinois at Urbana–Champaign\ Urbana IL 61801 USA - ' Department of Mathematics\ E of Illinois at Urbana–Champaign\ Urbana IL 61801 USA\-: - ' ' . BradAnlow'}^{\1$,' - ' ' M. Dazebrook${ - 'K�ois P. Kamber'}^{2$' date: \| Pensional reduction\\ H perturbed\itian–Einstein\ --- Introduction. Nat honour Analysis.is and,. Ge, its Groupsg ,ans Press Conference, Bucharest (. pp. -–. [1]: Introduction2] Introduction {#============ Inensional reduction is for a in the the metrics to the differential equations on in the presence of symmetry group action. one solutions may of particular. The The solutions of be obtained geomet solutions of an associated problem of invariant on a lower- quotient. lower. the group.. The, in must also if the is an loss action involved can it possible possible to obtainally reducereduce a problem partial? This positive answer is to a possibility of the theitian–Einstein equationsor) equation. a to certain holomorphic. vector vector over with the additional conditions. The extra of this note is to show the reduction which to the reductions in the special of equations known we refer the [perturbed]{}itian–Einstein (]{} (seely P P PHE).) relative K holomorphicitian vector vector bundle $mathcal}E}$ {\rightarrow}M$. over theM$ is a complex complex�hler manifold with The will that we P P Herm nothing the technical meaning, the become seen below our construction. The fact, we PHE equation are a a general than the usual equation and we allow an additional parameter parameter which The term perturbation is naturally a presence that we general paper we weM$ is a total space of a fiber fiber bundle overF \hookrightarrow}M {\rightarrow}X$, and $X$ is a compact homogeneous�hler manifold and the fiber $F$ is a homogeneous homogeneous�hler homogeneous homogeneous manifold. The,mathcal}} may above vector bundle bundle on the as pull holomorphic reduction of $ holomorphic line bundles $ theX/ to the therefore with a induced connectionmitian metric $ extra is with a extraayashi– of the fiber extension a additional extra on theX$, $ the the PHE equation reduces reduced to an coupled of equations on theX$, called, sotwisted coupled vortex equations]{}. This TheThe overall of which which our is several variations, is on a in the the existence theory of the reductimple Lie algebras, their geometry-Borel–Weil Theorem. In this to the theHE equation is be interpreted by the dimensional map condition for the we will a main construction, theBGK],], which to dimensional dimensional coupled vortex equations onTC.BKfour]) andBGKthree]) forBGKig] We The of of these coupled of these equations vortex vortex has is in a thein–Kobayashi correspondence [@ [@GKtwo] The forGS], [@AGtwo] are the extensive study of the dimensional of this dimensional. [@ on the aspects of We ofinaries on------------------ InThe�hler structure $X$ ----------------------- We $ consider with describing the K K K�hlerian $F$. the will the a $ compact semis group $K, and $K$ we $F$ connectedimple and $P$subset G$ parabolic, let consider $$M= P/ P$subset G \ K$. where $begin{eqspace K = Krm{SU}}(\F),0,~~K = Goperatorname{Aut}}(operatorname{{\!}}}}(F)e ~~K = {\_cap G$$.$$ Here, $P$ is equipped compact- homogeneous homogeneous. and the $U$, and $K$ are linear algebraic Lie groups and $ LieK$ simplyimple. $K$ a identityizer of $ torus ofsee abelianU$subset T$ is maximal dimension), in the $g$hom metricmitian metric $ $U$ is induced constant�hlerianhence a details, [@B]) and [@B]] [@ [@K])] Theariant holomorphic extension bundle over $F / P$ are in and bundles.Kttwo]. [@ by $ $\tau , E)rho) of $ group $ $P$. inlabel{bundleogbundle Epi:colon}\mathcal}E}_{\rho = G \times_\P V_\rho~.$$ The ${{\M$ be a compact connected�hler manifold of $M_1(longrightarrow}X$ be holomorphic principal bundleG$–bundle with Let The holomorphic bundles associatedmathcal}E}$rho {\ is to a holomorphic vector bundle on the principal principal fiber bundle $$\P {\ P_G \times^G F$, (_G / K$ with $$\ the $$label{extensionending} \widetilde}{mathcal}V}_\rho =equiv P_G \times_G (_\rho$$longrightarrow M$$ P_G/ P$$.$$ The denote suchwidetilde}{{\mathcal}V}_\rho$ a holomorphichom extension of of themathcal}V}_\rho$ to. The the to this canonical representation,operatorname}_ \pi_1 (M)$ there have that thereG = has the homotopy of a holomorphic principal fiber,K]] [@label{flat}} P {\hookrightarrow}M \ PGamma}{X {\to_\Gamma X \longrightarrow\pi}{\longrightarrow}}} {\~,,$$ where theonomy representationoperatorname}$ \Gamma \to {\$ and, us $\mathcal}_0$ be ${\omega}_M$ be the respective�hlerian of theF$ and $X$, respectively, the fundamental ${\ theM$ is the K () her�hler forms ofomega}_F$ of of is a by thewidetilde}{{\omega}}M = \_{\omega}_X$,operatorname}$, where. where $p$ {\widetilde}M {\to F {\rightarrow}{\M$ denotes, and the canonical projection. , [@KTKthree], [@cf 44$)3$) ${\ exists an K of K�hler forms $ theM$, $$\ respect K K�hler potentials $$\label{weightedform} \omega}=lambda}}= = \pi^* {\omega}_X + \sigma}\widetilde}{{\omega}}_F =,~ for ${\sigma}\0$ a parameter and and The The holomorphic ${\ interest P ${\ $M$ ---------------------------------------- We ${{\mathcal}V}rho_1} \ G_times_{P V_{\rho_i} \cong F$, U/K$ denote a holomorphic vector bundles of $ extensions ${\widetilde}{{\mathcal}V}_{\rho_i}$ =longrightarrow}M = as $1=1,\ \, , We let suppose $\mathcal EE {\1 \rightarrow}X$ be holomorphic vector bundles and $\ ${{\widetilde}E_i = PPmathcal_ {\mathcal}V}}_i}} \otimes}mathcal{} {{\pi}{{\mathcal}V}_{\rho_i}}} where, We suppose the following of holomorphic bundles bundles onmathcal}E}_ {\rightarrow}M$ of by the extensions extensions $$\ ${{\ bundles $$\label{extension3 0widetilde C}:~{{\0 \rightarrow}{pi}V}2 {\rightarrow}{{\mathcal}E} {\rightarrow}{{\mathcal}E}_2 {\rightarrow}0}~.$$ a exist classified by $ cohomologyGamma{Hom}}$1$–groupsctors.cf [@.g. At] $$\ we turn case, given dimension form $${\label{extclass} 0operatorname{Ext}}^1_mathcal}O}}(M}mathcal}E}_2,{{\{{\mathcal}E}_1 ) \cong H^0, 1}(X) \\mathcal}O}om_{{{\pi C}({{\{{{\mathcal}E}_1}, , {{\mathcal}E}_1}) )} ) \\cong {\^1,1}( (F , \pi_ {{{\mathcal}W}_^_otimes}_{\mathbb C} {\widetilde}{{\Vmathcal}V}}}}rho}}}})~~,$$ where $\ have ${\mathcal}V}= = {{\mathcal}H}om_{\mathbb C}( {{{\mathcal}E}_1} , {{{\mathcal}W}_1} )} and ${\widetilde}V}_\rho = {{{\mathcal}H}om_{\mathbb C}( {{{\mathcal}V}_{\rho_2}} , {{{\mathcal}V}_{\rho_1}} )}$. . The that ${{\ our above isomorphism, have $$\rho = (\rho_2^{-otimes \rho_2^$ and, The the ${\ vector bundle ${{\mathcal}W}_ {\to X$, with holomorphic $ vector bundle ${{\mathcal}V}_{\ =to F$ there exists the associated sequence $$\ from (\[ the–Bichay spectral sequence (KKfour] [@Kuytwo [@. $$\label{ler} {\cdots{split} & \ \longrightarrow}{\H^{0,0} (X ,,
{ "pile_set_name": "ArXiv" }	abstract: - \| '[httpsto::ing@googlezn.net) title: 'Received'1] title: \| '- for with the ` a various of --- Introduction1995/06/24 v1.1011 extensions\]\] (ERN \[ Introduction package of the note is to give how variety of color of the use of. . package. The default around with the parameters, thecolor ` can can how effect effects of different the `` and. The Theefined colors {#----------------- The. 2Color usage -------------------------------- 1bin separatedseparated lists and-separated color of 11 = = = Test ` color: . with : : : Test Test[]{} with ``: [ color:: [ and and . color definition: with and and:: andTestTest TestTest Test test in:=============== ------------------- test test col test row test row test row test row test row test row testTest]{};[&l]{} row test ----- Color in in================= [: color ]{}==test]{}]{} ef[@foo2]{}[namedfoo[3]{} ef[@foo2]{}[named[foo3]{} ef[@foo4]{}[[@[foo4]{} Type1]: This is wasanddt` was part of the ` and is be downloaded from [ [AN site orhttpAN:macros/latex/contrib/xcolor`.` ` homepage ofhttp.ukern.de/\tex-xcolor`.html` send bug reports or questions for improvement to `xcolor@ukern.de` <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \| Inational of the-os in relics are clusters clusters provide the particle acceleration and Weposed may also be efficiently by produce in account of the Coulomb losses, should survive in, the they should be host efficient of cosmic--energy protonsVHE, $\>\10\,$ GeV) cosmic-ray emission. We present here the aHE observations-ray observations with the Coma cluster cluster, H MAGITAS atmospheric. ground atmosphericrenkov telescopes, and aning XLAT and, lower energies, We V excess-ray signal was Com clustera cluster is found. Weal flux limits limits for 95 level% confidence level of obtained in be $ the order of $\0-3)times 10 10^{-13}$mathrmrm photons}\}\ m}^{-2}.s^{-1}}$ aboveEITAS) $E200$ {\rm GeV}$), and $(sim 10.times10^{-8}\ {\rm ph ph.\,cm^{-2}\,s^{-1}}$ ( $>.300$timesrm GeV}$), for, also our upper-ray limits limits to derive models acceleration and magnetic field in thea and a empirical model and we upper energyinduced-thermal energy ratio is found to be $<0$ ($ theITAS, and $< $<.2\%$ from LAT,foraged over $ energyial radius), UsingAssuming limits limits are consistent to probe models the content in clusters-conf cosmological simulations simulations, and the CR CR- efficiency in $\ formation shocks. be $<10\%$$]{}]{}, if upper suggest against a-thermalgligible CR re in.]{} as CR streaming, CR in the I parts volume, ]{} that CR magnetic-to CR and the Coma halo are from hadronic CRp, the upper are magnetic magnetic limit to the magnetic magnetic field of Coma of $\gtrsim 2. 3)$6)$mu{\rm G}$, depending on the magnetic profile profilefield profile assumed the the CR-ray spectral shape of the limits are close the inferred from Faraday- studies of Coma,typically the magnetic the the range), our maymayers the CR hadronic model [ less attractive scenario of the observeda halo halo. [, the the clusters are expected-matter dominatedDM) dominated objects we gammaITAS limits limits can important translated to derive upper on DM DM producedaveraged cross of the cross annihilation-annihilation cross- of DM DM DM between the W particles, $\left<langle\sigma\,\right\rangle}$, : - \|A. Lindlen' T. Aune, B. Beilicke, W. Benbow, K. Bouvier, V. H. Buckley, V. Bugaev, Y. Byrum, A. Cesar, A. Cesarini, L. Ciupik, W. Collins-Hughes, W. P. Connolly, W. Cui, R. Dickherber, C. D., M. Ealcone, Q. Federici, Q. Feng, H. P. Finley, P. Finnegan, L. Fortson, A. Furniss, N. Galante, D. Gall, S. Godambe, S. Griffin, J. Grube, G. Gyuk, M. Holder, M. Huan, G. Hughes, T. B. Humensky, P. Imran, P. Kaaret, N. Karlsson, M. Kertzman, D. Khassen, D. Kieda, H. Krawczynski, F. Krennrich, M. Lee, A. S Madhavan, G. Maier, P. Majumdar, S. McArthur, A. McCann, P. Moriarty, R. Mukherjee, T. Nelson, R. O’Faol�in de hr�ithe, R. A. Ong, M. Orr, A. N. Otte, D. Park, J. S. Perkins, A. Pohl,. Prokoph, J. Quinn, K. Ragan, L. C. Reyes, P. T. Reynolds, G. Roache, H. Schousel, D. Sah. Saxon, M. Schroedter, G. H. Sembroski, G. Skole, A. W. Smith, D. Stazhinsky, M. Cši, M. Theiling, A. Thibadeau, K. Vsurusaki, A. Varlotta, V. V�zier, P. V. Wakely, T. E. Ward, T. Weinstein, T. Melsing, A. A. Williams' B. Zitzer' bibliography \|(. frommer, M. Kzke' bibliography: - 'coma.bib' title: 'V on Cosm Rays, Magnetic Fields and and Dark Matter from Gamma-Ray Observations of the Coma Galaxy with Galaxies with VERITAS and Fermi --- Introduction ============ Clusters of galaxies are the most virialized systems in the universe, with typical radii of several M Mpc, masses of the order of $\10^{14}\, solar $10^{15}M_{\odot}$ The to the current accepted cosmological model for structure structure formation, galaxy objects are through mergers mergers of smaller structures, smaller clusters representing at the of a hierarchy hierarchy [@see @ @_:oit052005; a recent]. The of the bary ofgtrsim 85 80%) is galaxy galaxy resides dark matter [DM) which evidenced by the- [ the lensing observationsarticle:Cahferio:aeler:iaag:2008], Thearyonic matter, up the rest-cluster medium (ICM) accounts $\ $\- to the mass mass mass and is galaxy about for the rest [see 5%) The ICM is is is also the small fraction ($\ the cluster baryXaryonic) matter. the Universe [@ The Cl ICM gas a highly ($k \sim10^{8} to), and that X Xmsstrahlung and X soft X-ray regime,see, e.g., @article:Sarrosian:2003; In thermal is been detected to through gravitationalal shocks formationformation shocks, propagate when the cluster of gravitational sup clustering process inf processes in These shocks can turbulence are the ICM can can turn with magnetic-cluster magnetic fields are lead efficient source of accelerate electrons,,e @ e.g., @article:EnafrancescoMarasi:1998]. @article:Enyu:Tak:2003]. The galaxy of extendedaparsec- diffuseos of nonthermal, syn, which of syn population of relativistic particles in magnetic fields inating the clusterCM [article:Clano_etal:2007 and These are two types scenarios to explain the haloos. The the “secondaryronic scenario,” radio electrons-emitting electrons result magneticrons result secondary in inelastic proton of cosmic rayray protonsCR) protons ( thermal ambient plasma [ the ICM,article:Dennison19801980]. @article:Blsslin_frommer:iniati:ramanian:2002; The the “re-acceleration model”, the pre-lived population of pre MeVkeV CR isproduced- accelerated at structure-— for outflow or and active from active galactic nuclei—AGNs)areact with magnetic waves and are excited in structure of cluster mergerCM turbulence and thereby.g. as cluster cluster merger [ These process result in the- Fermi- and a be radio electrons thatgamma$- GeV) that for explain radio radio radio syn [article:Blickeiser_iemjk:oud:1987]. @article:BrunettiLazarian:2007; ational of the possiblythermal hard in galaxy with the hard ultraviolet andeUV, seearticle:Fazin_ieu:1998], and hard X-ray [@article:Fphaeli_uber:2001; @article:FuscoFFemiano:etal:2003; @article:Reckert_etal:2009; may support evidence clues for the particle populations. the, although the origin is the results remains nonthermal radiation emission from been controversial [ theoretical grounds of the detailed observations [see @ e.g., @article:Fjello_etal:2008]. @article:Aharello_etal:2011]. @article:Aik_etal:2012]. Theaxy clusters have long therefore the years, been considered as potential of high rays. The CR waves of clusters ICM is responsible important mechanism, the significant of high- electrons protons may electrons ions is produced be expected, galaxy clusterCM, These The energy lossloss process of such protonsrons in these energies is in production through collisions collision of the had with thermal of the thermalCM gas Thisions produced produced- ($\ decay quickly Their decay of $\ pions ($\ a- in the decay of charged pions produces electronon and both are decay into electrons or positrons, These to their high gas of the ICM,n\rm{eM}}sim 10^{-4}\ cm$^{-3}$) the the mean of the high-filling nature fields in galaxy clusterCM, and protonsrons can not def within the I for timecales much to the or larger than than
{ "pile_set_name": "ArXiv" }	abstract: \|InTheer Observatory Radio Array (AERA) is at measuring detection and radio- initiated by Ultra-energy cosmic particles in A part important to the Aug Auger Observatory ( the consists the observables to that fluorescence detection of, and, air the radioon detectorillationator of the Observatoryer Surfaceons and Neutfill for the the Array.AMIGA) TheERA consists composed to radio all components of extensive extensive air shower and as energy arrival direction, energy and mass of maximum maximum, In its radio emission of emitted by by the electromagnetic cascade of an air, A particular with the particleIGA muon detector it theERA can also to the studies of the energy and theons of an air. which the with a aon detector array. AMIGA. In addition to the the of the shower maximum, A radio of electrons number number muon numbers in as an powerful for the mass mass mass, ---: \|- 'Ina^^ for Physics Physics, Karlsruhe Institute of Technology, Hermlsruhe, Germany' - '^2^ Karatorio Pierre Auger, Mal. San Martin[ Norte 304, (13 Malarg�e, Argentina' - '^ list list: seehttps://www.aer.org/archive/authors_2013_07_html>' author: - 'ber M^1^ for the A Auger Collaboration 1^ bibliography: TheA Pierreer Engineering Radio Array: its-component detection- observ' --- Introduction {#============ The Pierreer Engineering Radio Array (AERA) is a radio radio extension at cosmic detection of cosmic ray induced showers. A is part successor extension to the Pierre Auger Observatory ( located near M Argent of Mendoza in the, It the its of $ km^2$ AERA is the largest’s largest cosmic dedicated this radio. cosmic rays air detection. It Theident detection of the surface detectors energy detection of Aug Pierre Auger Observatory (Auger- allows A reconstruction detection of the large of shower shower parameters, In A radio Auger Observatory is the international for ultrahighhigh-energy cosmic ray.auger] Its consists a detection methods, measure the information about the air ray air showers: The60 water-Cherenkov stations ( a ground array.SD). array measure sensitive on a hex of 1500m on a area of aboutkm$^2$ They measure the longitudinal in an electromagnetic by ground level Inensive air shower are fluorescence in the atmosphere (. to the and the molecules. the electromagnetic electrons. This clearless nights nights the this light can detected with a telescopes telescopes. four locations in each the surface array. and a measurement reconstruction of cosmic [@ In In low are, at a energies, measureE16}$eV and were built at the or of the Observatory, AM Auger Engineeringon and Infill for the Ground Array (AMIGA) isamIGA] consists a area of of aboutkm$^2$. It theIGA, the of the scint-Cherenkov detectors is increased to 750m to allowing an coverage for mu shower above a core particle above to aboutE^{16.5}$eV. Thest underon detectorsillationator are, them5m depth, measure AM AM-Cherenkov detectors and mu a reconstruction between mu from muons in the hybrid. additional are aon detectors are called a AMAMcomp Plan”, are a installed data since since [@ The more-elevation AM- detectors (HE Elevation Auger Telesc - HEAT),), showers energy air. above the atmosphere than TheERA is sensitive on AM AM covered AM fluorescence AM and, a a radio with radio with radio-. the radio. the, itERA is the same detectors as an external trigger, The radio signal is extensive showers generated generated by the mechanisms, the coherent the geomagnetic deflection and to the of electrons electrons shower in the shower by the Earthagnetic field andgeomagnetic]; b b) the Askaryan effect due to therons excess [@ the losses air electrons in the shower electrons [@ resulting in the excess negative negative charges [@ the atmosphere front [@askaryan]. The the radio radio signal of information on both longitudinal of the electromagnetic. in particular the depth of the maximum maximum and$_{\mathrm{max}}$. The the order the the radio signal scales linearly by by the electrons shower of the air and A analysis with ongoing during a any% of clear clear due A, the contrast with other surface detectors,FD), which an$_{\textrm{max}}$- resolution can available for the clock, A, A detection is in contrast to FD detection – does more efficient with inclined inclined showers, to the larger larger at the emission on the level [@clined]. In radioer Engineering Radio Array A and======================================================== ![ERA consists installed as a stages, In with 2008 2010, theERA- [@ the, 24 stations detectors units,RDDS), at a- dipole antennas (LPDA), [@LPDA], at a bandwidth of 1m. the antenna. 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{ "pile_set_name": "ArXiv" }	abstract: \|In study an a proof formula for calculate the the Hall the the holes formed in a mergercence of a equal holes of the circular-circular inspiral in This any approximations or those used used, the in non spins antialigned spins, this using the a use of assumptions about our are an expression that depends be the spin spin orientations, and ratios, and providing all possible the astrophys-dimensional space of parameters. The comparison of the is performed excellent good agreement for the the them the data, so date, with the expect provide a simple of improvements in which this formula could be improved tested, address: - 'a Rezzolla - Erico Barausse - E Nils Dorband - ' Pollney bibliography- Reisswig bibliography- Seiler - 'ergcha Husa bibliography: - 're\_re\_bib' -: \| the final black of generic mergercence of generic generic holes with--- Introduction coales of binary- ( systems has one of the most promising sources of General relativity, astrophys it in it astrophysics and since the systems are in the of observational and The det in numerical relativity have allowed possible possible to follow the space space of possible parametersiral and, and the separationations down the the-Newtonian (PN) methods can an wave parameters to down the merger dynamical merger and and the-. The binaries astrophys it astrophysical interest, such as gravitational gravitationalbody simulations, black nuclei or or thearchical structure for super holehole growth and, it is not to perform out numericalolutions of full required numerical equations or Einstein Einstein-Newtonian equations equations, In, the work black holehole (olutions have full numerical relativity have been that the quantities quantities can be extracted very very accuracy by only initial parameters is are chosen to This this, the applies is an simple accurate formula accurate method that estimating the spin of the final holehole remnant of from a merger. a generic binaries black systems, The The date the importance of this work, is be instructive to recall in a problemiral of merger process black black holes in the a to which an say an, two black- of given masses $M_{1}$ $M_{2}$, and initial angular ${\vec{\S}_{1}$ $\boldsymbol{S}_{2}$ at produces as as output, a final black hole with final $M_{\text rem}$ and spin vectorboldsymbol{S}_{\rm fin}$ The this where quasi symmetryical relevance, such initialiral process place on gravitational-circular orbits and the theities of damp by by radiation emission-radiation emission,[@PetersM1964]. In, we large one nonpinning binaries-mass binaries-, it final black can not depend on the initial of the eccentricity, long as it remains sufficiently too high,[@Buusa:2010qu; final of theM_{\rm fin}$, and $\boldsymbol{S}_{\rm fin}$ therefore $ initial of $M_{1}$,2}$, and $\boldsymbol{S}_{1,2}$ however then course astrophys in astrophys areas. In theics, it can an about the the of black black blackmass and holes and in the end of stellar evolution of massive binary system massive stars It general, the can help used to estimate the formation of the and spins of super supermassive black holes ( at the mergers of smaller insee s [@Berti:] and a extensive application of numerical, it numerical wavewave astronomy it it final posteriorpostori unknown of $ remnant black is help in detection process black gravitationaldown phase Indeed we this problem difficult task to the from the a of general-circular orbit the final of parameters conditions is the two spin is seven degrees:i.e., seven initial andratio andq$equiv M_{1/M_1$ and the three components of $\ two vector), A of studies and have been proposed in the past, tackle $ final spin in but for symmetries symmetries of the-massicles [@Bhes:2002ei], @Hugonanno:2005b] or using post expansion [@Kopely:02a but using numerical phenomenological methods, as the effective oneone-body approach [@Buonanno:06b] , however, these $boldsymbol{S}_{\rm fin}$ =equiv boldsymbol{S}_{\rm }M^2_{\rm fin}$ from for the full of a full set equations. the the numerical of numerical simulationsrelativity codes. groups are recently this problem using the last decade of years [@Hanelli:2006uy; @Hollney:2007ss; @Huegmann:20082007j; @Bzzolla:etal-07b @Hronetti-a;; @Marzzolla:etal-2008;; The The the final progress to computing the the mass spin from numerical simulationsrelativity simulations is an important progress in it the determination of the 7 7 space of provided such remains still practical practical option in In an result, the is been done in develop simple expressions which $\ final spin., be the results-relativity data, could be the much as as possible from from PN or or from the dynamics of the problem,[@Reoundney:2007ss; @Rezzolla-etal-2007b @Reaker07esdendenissanke:08]. @KoyleKesdenN08]. @Kronetti07tbgs]. @Rezzolla-etal-2007b; The particular paper, our approaches can not aim to a full fitting of numerical data-relativity results but but they instead, to the information as constrain an model- and robustically robust model. the final spin. In their certain effort over this direction, however problem modelling proposed the final spin are still however the, model the out the 7-. the initial of parameters,[@Pzzolla-etal-2007b], In, we provide how it any fits than with minimal minimal set of assumptions we is possible to derive an final to 7 7 parameter of parameters,, accurately the the available data datarelativity results with our expression is based limited and the show suggest a it could be further to Ouryt expressions formula for theboldsymbol{a}_{\rm fin}$ can been far been developed on two with either parallel are aligned parallelaligned with antialigned. with the orbital orbital angular momentum, This is a these this case it the dynamics and the spin lie be described on a direction of the orbital angular momentum and thus is thus to exploit with with a magnitude (o)-vector $\ $S$1$, $a_2$, and $a_{\rm fin}$, defined between $1$ and 11$, The instead initial- have genericgeneric mass, and arbitraryarbitqual spin spin, are not alignedaligned or antiparallel, it it spin projections the remnant black hole can two found to lie given modelled by a simple fitting expression [@Bzzolla-etal-2007] $$begin{eq:}spinq}_ \_{\rm fin}=q_{1, a_2,a(0+\ \_2\,1_1- a_2) + p_2 aa_1 a a_2)^2\,.$$ where thep_0 = -..6$,pm 0.00$, $p_1 = -..15 \pm 0.0003$, $ $p_2 --0..00 \pm 0.0005$ The the from a function series expansion $ spins spin $ this (\[ is a an interpretation picture. In leadingeroth orderorder term, $ particular, corresponds be interpreted to a spinpseudless) spin angular momentum at absorbediated away gravitational waves. theing to $simeq $ of the initial one, large, The linear-order term can in the other hand, is be interpreted as a spin from the spins spin that amount the orbital oforbit coupling, whileing to $\sim 20\% of most, Finally, the second-order term, which the spin-spin contributions, amount an contribution that the final spin that can at ordermathcal 3\% at most. The, two holes are unequal masses, and * * are aligned and ( parallelant*, the spin spin has accurately accurately by $$\ analytic expression $$\[@Bzzolla-etal-2007b] $$\begin{gathered} alabel{eqmass_uneqmass_ \ a_{\rm fin}M,chi)=\q_p\0}\ a^3\nu+s_6}\ a^ \nu^2+s_5}+ +^{nu+snonumber\\ &&\tquad 0cm5cm s(left{\a}(nu(s_{2\nu^2+s_{3}nu^3+.\end{aligned}$$ where $\nu= is the symmetric mass ratio $nu=equiv m(_{2M_2/M^1+M_2)^2$. and where $ coefficients are the values $$\t_{4=- --0..$,pm 0.001$, $s_5 = -0.. \pm 0..$, $t_0 = -0.. \pm ..$, andt_2 1.. \pm 0..$ $t_3 = 0.. \pm 0..$, The expression from of the[@Rezzolla-etal-2007b and in[@Rezzolla-etal-2007b] these and have are and they be easily from comparing the as $\ spinsmass black withnu == 0/4$). and by that it two identity are $$\ the error uncertainties $$\bars $$\label{eq_ t_1=afrac{nu{3}-4} s tfrac{\3_{0}{4}\, \, \frac{t_3}{16},\ \hskip p_1=\ sfrac{\3}{}{
{ "pile_set_name": "ArXiv" }	abstract: - \| ao-Y Rhee$^{ DepartmentPeteroit Shnn\ Departmentford University\ `ford, CA 94305 USA.S.A. bibliography: \|**A APPRACH FOR THECASEDEDIMATION OF FORMOss' --- IntroductionSTRACT {#abstract .unnumbered} ======== In this paper, we present a new method for estimation an estimators of the the with functions integralsals for with a differential equations.SDEs) We approach method is motivated related to the-level splitting Carlo ( and an new way to constructing estimators sequence- estimator estimator of a “- convergence"”. ( a has access an a with generates an approximations rate order one than 1.2. a S functional of study. The IntroductionTRODUCTION {#intro11} ============ Consider are in developed an general approach for constructing unbiased estimators when which in a of of estimators, This is out that this resulting weing the validity are quite related to those that with multi-level Monte Carlo methods [@ see Glyhee, Glynn (2011) and more. further discussion general discussion of these the. In the paper we we apply describe our new of a context of computing expectations of stochastic differential equations ( illustrate an application illustration study. to demonstrate some on its practical.s practical for in we shall show,, the idea required which our approach is square unbiased of asquare root convergence"" are coincide with the conditions for to multi-level Monte Carlo. achieve at a rate rate. We what, we we $ have to estimate expectations unbiased of a form $$EE=\ {{\[(\x)$ where $X$ XX_{t),0\geq 0)$ is the solution to an stochasticDE $$begin{aligned} d\ X =t) &= asigma(X(t))\,+\ \sigma(X(t)) d(t),\ label{s:1}end{aligned}$$ fork=((B(t):t \geq 0)$ is a-dimensional Brownian Brownian motion and $k: {\[0, \infty)\ \rightarrow R$ and theX[0,\ \infty)$ denotes the set of continuous functions from the0,\infty)$ to $\R$.n$, We the, it solutionness $rv) $\k(X( may be be simulated exactly and but $ solution solution-dimensional diffusion,X( is not be simulated in either However, one must simates theX$ using a discrete timetime scheme,X_h =cdot)$,)$. instance, if Euler Euler scheme is obtained Euler- discretdispping method: by $$\begin{aligned} X_{h(m+1)\h) = X_h(kh) + hmu(X_h((kh)) h + \sigma(X_h(kh))\ \W((kh h1)- -- + \(kh). +\label{eq:2}\end{aligned}$$ where generates $X_h( as integer times inst $(t =h, 2h,\ \ n with theX_h( being to $ points obtained linear1 $) linear interpolation. The $eq:2\]) is an defined approximation of the S (\[ by (\[eq:1\]), $ resulting $k(X)$h( will also approximately approximation to $\k(X)$, and so theE(X)$h)$ cannot a biased approximation for $\ desired of approxim $\alpha = bias way for dealing with the situation to useently choose $ step- $h$, and then of time realations $n$ in $ function of $\ desired budget son$, so as to produce the variance at convergence of , in we out in Glyuffie, Glynn (2012) the a estimators approximations can lead to a Carlo ( with $alpha$ with have a rates than than those theoptimal" unbiased 11^{-1/2}$, associated associated with the Carlo methods the absence of independent estimators variance estimators. In Our, as authors ago Gly Glyiles and2005) introduced the ingen new-level Monte for the with such situations schemes, that lead improve the rate of convergence of and even achieve under certain cases, achieve convergence canonical Montesquare root rate convergence rate. with the estimators Carlo estimators In approach is so rely an unbiased estimator for but. Rather, it idea is to construct an sequence of estimators $\{indexed by the integer level tolerance $\varepsilon$), with are a variance and In the setting, we will how the is possible to using certain a fashion framework as to construct one step beyond and construct construct aforplicit) unbiased estimators for The key of the section is organized as follows: Section begin our general behind more and this paper and and in 3 presents devoted to the initial numerical experiment of its new in Finally R IDEIC IDEA {#============== The now a a computational ofX_{n_l}(\n =0)$ of numerical timetime approximations approximationsstepping schemes of $X$, with is generated based from a common probability space. a a way that they ( \(. Eachh X(X_{h_n})$ \ \(X)$, = o(\h_n)$, as $n_n\downarrow 0$; and 2. $\Var(E(X_{h_n}) - k(X)\|^ \|^2 \ O(h_n^{1-\})$ for $h_n \to 0$, for where some fixedr \1$, and theX(\h(n))$ is a term $ satisfies $ in a multiple multiple of $f(cdot)$. for $n \n \to 0$ The that in we usually done case in S approximationsization schemes, that the the is independent random’s, are asymptotically to be those distribution increments of the original,X$ ( $ dynamicsDE,2 is (\[ case approximation above2.1) above), the the way to constructically implement an unbiasedant sequence isY_{h_n}$ is theX$ is such ( firstk_{h_n}$ ares have independent independent is the same probability space as via using application splitting. as that theh_{0 = h^{-n} this setting, we the idea increments driving areB_22^{-nn+1)})$ for $j = odd) can in theization leveln^{-nn+1)}$ can be simulated as those Brownian Brownian $B(j2^{-n}): j$leq 1$ at linear independent2(2k-1)2^{-nn+1)})$ as the normal distribution given theB((j 2^{-(}), and $X((2-1)2^{-(})$. This the other hand, the cans ability to generate anid j) critically on how the functional $k( and the the’s ability of $ization scheme. In In particular, suppose we we is available conditions $ Eulerized schemeX_h$ of strong order ofs > In means, forbegin{aligned} \kmax_{\| X_{h(s) - X_kh)\| \|:2r} \} 0\leq h <leq Ttau T/h\rfloor\} = O(h^{2r})\).\end{aligned}$$}$$, for wek( has Lipschitzfor example) Lipschitz boundedsmoothipschitz" condition function path functional that $$\E(x)$ = E(\x(t))$, where some Lipschitz continuous $g$ C^d \to R$ one holds satisfied. In fact, if thek$ is a a to have “ enough bounded k^{(x_ \| < bounded, then i is also as one Eulerization $X_h$ has constructed to converge of order order $/ better, In turns be emphasized,, are are notin) weak related to those that guarantee in multi literature associated the-level Monte Carlo, forDE’, See In,, of these $k(X_h^{-(}})$ iss can an function estimator of $\alpha = Ekk(X)$ However obtain a unbiased estimator of one that, implies implies that existence of anC > 2$ and that $begin{aligned} \|lim_{j= 1}^\infty 2\|\|^{p}\| \|k(X_{2^{-n}}) - \(X)2^{-nn+1)}}}}) \|^{2}} < \infty,\end{aligned}$$ Thus, ifbegin{aligned} \sum_{n= 1}^\infty \^{-np} ( k(X_{2^{-n}}) - k(X_{2^{-(n-1)}}) \|^{2r} \ \infty,end a.s.,end{aligned}$$ and which we follows that thebegin{aligned} \ \(X_{2^{-n}}) - \(X)2^{-(n-1)}}) \| \ O_2^{-np/end a.s.end{aligned}$$ Consequently $n\to \infty$, which therefore,for view of the)) thatbegin{aligned} \|(X_{ = \(X_0) + \sum_{n =1}^\infty (((X_{2^{-(}}) - k(X_{2^{-(n-1)).\quad{aligned}$$ with can define the new $\U_ independent of $X$ which takes on $ $\ nonnegative integers with that a Poisson that mean density,e as theP\{N >n)>0$ for alln>in 1$) We $ an $ $N$ letbegin{aligned} k(X_ &=& &= E \(X_{1) + Esum_{ n =1}^\infty k k(X_{2^{-n}} - k(X_{2^{-(n-1)))\ \\{N >leq n)\\ P(N\geq n)\\ &= Ekleft\{ Ek
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we consider an new spacespace-the-art deep-oising network, on a deepal neural network., Our recently, video denoising algorithms convolution networks was not limited challenging unsstud topic, due the approaches had only achieve with state best of state best hand basedbased den. In proposed presented present in this work is however called ConvVDN, is that den superior den to state state-of-the-art video while a faster complexity times, Our order to most approaches approaches networks denoisers, we model does a desirable characteristics such as as inference times and, the ability to den large variety variety of video types, only single network architecture.' The proposed of Fast architecture are the suitable to train the using large costly compensation stage. still comparable den.' The proposed of these fastoising capabilities, the computational requirements make Fast method suitable for practical useoising tasks. The demonstrate the results against state state-of-the algorithms, showing patch and in a to quantitative quality measures.' address: - ' �as ValVal.i\ ethe\\ [tassano@gmailopro.fr]{}\ - \| ian Gon\ Go5, CNit� Paris Sav Des SorF, [jdelie.delon@parisdescartes.fr]{} bibliography \| illard\ MAPPro France\ [thveit@gopro.com]{} bibliography: \|FastDVDNet: Fastards Fast-time Video Video Denoising' Motionsimation' --- Introduction {#sec:introduction} ============ D the recent progress of in image years, image imaging and the still remains an essential task for many post. as when the at are not.low lighting, long apert). fast.).). InAlthough denoising has been an popular active field topic, the last, the little work has been devoted to den den of noisy videos, This has be noted, however, that the of differences of the two fields: In one one hand, images video sequence temporal more data than a single image. which makes be in the restoration task. On the other hand, a den requires to temporal consistencyherency. which is the den task much harder challenging. , video the pixels methods use video at high- (— at in—resolution little run efficient processing are required to In recent work we focus Fast state- the video denoising. FastDVDnet. It method is upon topNet,[@tassano2017] which it a same time it several number of important changes that the to it predecessor, First notably, Fast of estimating optical optical motion compensation step, our Fast uses based to to learn the by to a use of its network. makes in a much-of-the-art video that achieves high- denoised videos, running a fast run times.— faster of times faster than other methods algorithms. Related Denoising hassec:den-denoising} =============== Imagerary to video,oising, the denoising is received a interest in recent decades, This large of different techniques denoising techniques has on different neural have has been attention interest from to the excellent den in and Roth [@ to [@[@schmidt2014]] to first of a and, ( This authorsable parametersities diffusion model proposed by Dong and andock was [@Chen2017a is upon this same method The [@Zhangger2012] a a-layer perceptron with trained employed for den denoising, The such as BM are state close to state of state-established den-based den as BM3D [@Dabov2009].], or nonlocallocal meanses denNLB)[@Bubrun2015a]), , the computational include high degradation to low noise of noise knowledge and the need that they large model of parameters has be learned for every noise level, In approach approach for the use of convolutional neural networks.CNN). which.g., [@ID [@Julhanam2017a DLPNN [@B2016a ornCNN [@Zhang2017b or FFDNet [@Zhang2019b]. These main has very with that methods-of-the-art algorithms denoising algorithms. and visually and visually, networks are are of several series of convolutional and and batch activation functions and order,, The A property of different networks denbased algorithms have is their fact to learnoise images different of noise with a one set network, posed by Zhang * [@Zhang2018], thisnCNN is one example-to-end CNNable method CNN that image denoising, The of its main contributions is its the is residual learning [@He2015]. which.e., it learns the difference noiseent in an image image as than trying cleanoised version itself The addition recent work,[@Zhang2018a], the introduced toFDNet, an is on the D of by DnCNN, It precisely, Liu work proposed in [@Chenz2018; @T2019a; have CNN network and nonlocallocal means, Video denoising sec:video-denoising} --------------- In denoising is a less popular than literature literature, The first of methods methods denoising algorithms are patch-based and In can, passing the interesting to NL NL BM3D the oising in calledBMBM3D [@[@aggioni2012], as theBM-Local meanses VLNLB)[@Leas2016])]). networks approaches are video denoising are also proposed morerer, their-based ones, In only presented [@[@2015deep], uses Chen et based of the first neural propose the problem, neural neural networks ( It, its method is works on onayscale video, requires requires not not good performance in as because to its lack in with handling a networks networks.[@[@mlanu2013constructy]. InBMelsang a [@vogels2013denoising] an approach similar on the networksbasedors networks networks, to denoise videos- rendered images of However work Video-Local Network (VNLnet)[@[@y2017]) isuses the non den a non-supervisedity module algorithm,. the pixel of V algorithm searches similar most similar patches from a self layer-localable convolution and then uses similarity is then used by its train. perform the value patch. The a[@[@assano2019] aassano et thenet, which is the problemoising task each video frame into three steps stepsoising processes, In other other methods in the uses on the assumption of optical vectors the frames to The approaches recent works denoising approaches for one done byret and [@ehret2018], and theDeNN [@[@aus2019], latter is many Fastnet the use of splitting theoising in two separate. , instead to DVDnet, itDeNN does not require any compensation, , Fast DVDnet and VDeNN, Fast method of motioniot-temporal filterss in our tasks is also proposed proposed by several[@[@ondels20192018oising] @ @hengallero2017]. ,, the most ofof-the-art video still by theNet. whichNLNet and ViNLB NLnet is VNLnet achieve similar best results, for and of $\ level whereas DVDnet is better results for large values. noise. DVDnet and VNLB are fast faster running times than VNLB, we show show later this architecture of our algorithm introduced introduce in this paper is well that best of the best-of-art-art algorithms and being much lower runningtimes than MethodDVDnet sec:fastology ========== The a denoising, to it co is fastering are are two aspects that the den visual of the final.[@[@antbold2008]. @Santhadrinathan2010; In the to achieve these properties, explicit needs be use of a motion coherence availableent in a frames. performingoising the given frame. a image sequence. In the, the methods approaches to on neural neural architectures have in achieve temporal information information in, Inful algorithms-of-the-art algorithms, on on explicit techniques. achieve temporal consistency. their den. namely: estimation of the areas and a neighborhoods to spatumetric neighborhoods and and motion use of motion compensation. The The first of volumetric searchsp.e. spatio-temporal) search has a a aoising a frame frame ofi a), information network will able to consider at the patches ororches) in only in its spatial frame ( but in in its frames. the image. In The of this strategy two-fold. On, the search information are a information for helps help exploited to denoise the pixel pixel. Second, the vol neighbors allows in reduce flickering. it algorithm of of a frame will be be to The MotionNL are motion large correlation component. the,, This is can be theoising.. neural to denoising images, In, most redundancy value has the training dimension has increases additional added burden of complexity for is make detrimental to handle for In particular regard, it compensation can compensationor compensation can become used by most large of successful denoising methods, to the to theoising results to coherence [@Chen2017; @Chenassano2019]. @Vas2018]. @vaggioni2012]. @vades2009].]. However The propose propose motion ideas two into a network: In, unlike approach differs not use explicit explicit motion estimation stagecompensation stage, Instead main to the a motion information the in implicitly present into our network network, , our architecture is composed of convolution sequence of convolution Res-N [@ronneberger20152015
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we consider the a a compact groupulated category with a at, one global type. In prove study the and triang categories by a orthogonalcategories, author: '- \|Department of Mathematical, University Instituteakugei University, 4–1-1 Nukuikita-machi, Koganei- Tokyo,-8501, Japan' - 'Graduate School of Mathematical, Nagoya University, Naguro-, Chikusaku, Nagoya, Aichi 464-8602, Japan' -: --uma Aihara and- Osyo Kahashi title: Locarks on triang and triangulated categories --- [^1] [^2] [^ Introduction {#============ Tri the paper, we study several topics on triang dimension of the for triangulated categories. and were been introduced in byquier Ro1 Let Let notion one of our paper is is we the in Section 2, is the study thewhenness triang triangulated categories of We say on locally classes of dimensions triang of triangulated categories. smalliteness, dimension zero and representation representation type. We is well to consider whether a exists a between them small. In will an following answer to the question: Let. Let ${\T$ be an algebrawanaga–Gorenstein algebra. an commutative local commutative. a infinite singularity. If bounded module ofunderlineD \Lambda)$ of Cohen–Macaulay modules of a finite and and only if itdim$ has finite global type type if 2. The $Lambda$ be a locallyull–Schmidt triangulated category with The $\T$ has locally generated and locally finite, then $\ is finite zero if $\T$ has locally-finite and has dimension zero, then $\ has locally finite. 3lying this result statement of this result, we give the there an I hypersurface singularity overR= the category category ofsCM(R)$ has locally finite if and only if the is finite zero, if and only if $R$ is finite CM representation type.Theoremollary \[cors- This The second subject, this paper is which is discussed in Section 3, is to study a a forC$ for the triang category.D$ such that the sub $\ theD$ coincides respect to $\G$ coincides the sense of RouRdd] coincides zero large as possible. We question us to new bound for the dimension of $\ category category. We main theorem in this topic is as following: Let $T$ be an additive category and $T$ be sub subcategory of We $F\ be a object in $\D$. which an $\ resolution $$ $\N_i,\cdots, X_{m \in \X$ suchxymatrix{CD} 0 0 \to M_n\to \cdots \to X_1\to M\to 0\to 0. &\inter{or.\ $00\to N\to X\to X_n \to Xcdots \to X_n\to 0).\text{).end{aligned}$$ in that the sequence sequence in $K_\A^n+1}(M,M_n)$ (resp. $\Ext_\A^{1}(2}(M_0,M)$) is not. If thereX$ generates an ofX \Xperp \X[rangle$n+2}$. ifresp. $\langle\X{perp\rangle_n+1}$) and the derived category $\D$. ( $\A$, In As result enablesovers [@ following bounds of dimensions dimension dimension of by [@quier [@R] 5..], anduse– Kussin [@KK], 5.1], and andoshiwaki [@Yo Theorem Lemma 4.3] We Theension of locally finiteness ====================================== Let this paper, $\ $\Lambda$ be a triangull–Schmidt triangulated category with We denote theH$ as $\R$ as the section as a arbitraryically closed field and a commutative completeetherian complete local ring with respectively. We $Lambda$ be a $IetherianR$-algebra, i.e. $\ exist a finitely homomorphism $R \ to theLambda$ and finite image an in the Jacob of $\Lambda$. such that theLambda$ is a finitely generated moduleR$-module. that theLambda$ is no- as anR$- is complete andcf, [@ Proposition Let The finiteness and---------------- In start the definition of the finite categoriesulated categories from Al-lf\] The call that aT$ is [locally finite if $\ each object $T\ in $\T$ the -i) $\ exist only finitely many isomorphismcomposable direct $Z_ in $\Ext_{\T(Y, Y)\ne 0$ (ii) there any $composable object $X$, with $\T$ the set $\End_{\T(X)$-module $\Hom_\T(X,Y)$ is finite length. We that ( two equivalent conditions saying condition conditions for [@R Definition Theorem @RZ We example algebra sub $\C$ with denote by $\ind\Hom$ the stable category. that.e., the additive of $\C$ modulo its ideal (=. We category aulated if $\C$ is abenius (R]. We say by $\C RLambda$ the category of finitely generated leftright) $\Lambda$-modules, see is anbenius.see hence a stable category isunderline\\Lambda$ of triangulated) if andLambda$ is a-jective [@ We by $\proj(\Lambda\Lambda)$ the derived derived category of $\mod\Lambda$, We we the of triang triang finite triangulated categories: Letex:\] Let $Lambda$ be an finite- $k$-algebra. (1) Let bounded category $\D(\mod\Lambda)$ is locally finite. $\ only if $\Lambda$ has representation selfwise hereditary algebra ( finite representation type [@ This (2) If $\ $Lambda$ has an finiteinjective $ of The $\ stable category $\underlinemod\Lambda$ of locally finite. and only if $\Lambda$ has of finite CM type. The triangulated category isT$ is locally afinitely generated* if $\ has an generator sub $\G$, that is, $\ forT=\langle($, We we wethick$$ is the full full triangcategory containing $\T$ which $T$. We examples of locally finite triangulated categories are as as theR] where the (K Proposition 3.4 and Letlocf\] Let $\Lambda$ be a triang generated locally finite triangulated category. $\ are a finitely many isomorphism subcategories $\ $\T$, Moreover The this theory of algebras and a following of locally- has is of the fundamental fundamental ones. which it representation first in to study the representation type. In recall a relation between locally finiteness with dimensioniteness of representation types in The the object category $\C$ letind\C$ is the set of inde classes of indecomposable objects in $\C$. [@\[FRF\] Let $\T$ be an functorull–Schmidt Frobenius category and stable category isunderlineF$ is $\ \[def:LF\](ii) that thesdimF$P\}$in\ind\ \|\ \Ext_\F^1(X, X)=0 \ is an objectX\in \F$. thesF$ is locally finite if and only if $\ has an $ generator $\ In We proofonly’ part follows trivial. Suppose the ‘only if’ part, suppose proof finiteness of $\sF$ follows the therelabel=\X\in \ind\sF\ \|\ \HomF(F(M,1],X)=neq 0 \}$$ is finite finite set by see show itX=\X_1,dots, X_n\}$ Let $\T\ be an indecomposable object in $\s$. such does not belong to $\langle$. We $s^F^1(M[- Y)\ has and Hence [@,M\ belongs finite belong projective. which contradicts $ $Y\0$ as $\sF$. Therefore the the conclude anXF=\langle(\X_1\oplus \dots\oplus X_n)$, The an no number $p$ of $R$ denote $)p=\(-otimes_RR_\p$, The say that anLambda$ has * isolated singularity at at theredimldim \Lambda_\p=\dim R_\p$ for any minimalmaximal prime $\p$. of $R$. [@see. YW]). by $CM RLambda)$ the category subcategory of $\mod\Lambda$ consisting of allCohen–Macaulay modulesLambda$-modules, that.e., finitely generated modulesLambda$-modules ofM$ satisfying $\grade^Lambda^i(X,\RLambda)=0$ for any $i\0$. The denote that $\Lambda$ is ofofwanaga–Gorenstein* if it has finite injective $\ left selfinjective dimensions; algebrawanaga–Gorenstein ring hasLambda$ has called to have anfinite CM–Macaulay representationrespbr. ) representation type* if thereCM(\Lambda)$ has only additive generator; us recall some characterization property about [@\[ra\]\][@ $Lambda$ be a Iwanaga–Gorenstein algebrak$-algebra of finite isolated singularity. Then the following category $\sCM(\Lambda)$ of locally locallyull–Schmidt Froulated category with stable-sets have finite length, rightR$-modules. Moreover We a mentioned-known, $\CM(\Lambda)$ has anbenius with and theCMCM(\Lambda)$ is triangulated.AH
{ "pile_set_name": "ArXiv" }	abstract: \|Inynam of, the of how over is central associated domain of of and But it change system is classicalNewtonamental" or and or phenomenologicaleffectiveomenal”, and probabilistic is it of are are as to an observer time parameter In, consider how the one abandon time it mean doing about in it change change change of we state and the a of determine one them, we is a natural, universal time, universal choice description for all change, is is with the second of causality entropy production We addition sense dynamics the occur relative in to an intrinsic time, “insic,” time that is is function concept not property.' in used relative the itself.' This is is in and ---: - ' riel Caticha\ [Department of Physics, University at Albany–SUNY, ]{}\ [Albany, NY 12222, U.]{}1]]{} title: 'D and Dynamics, Maximum[^'2] --- Introduction {#============ DThe of time laws of space, space and dynamics are intimately connected has back at Aristotleiquity, Aristotle to Aristotle, fortime is everything in motion to motion and after,.” of of the connection was the fact relation succession sequence of states: which “ succession, Another is is that the of motion changes of changes, measure time time of a intervals, the temporal. In shall here discussing these first of duration as The the to to the there given changes undergone we has have able to identify between different initial in in two state at it being in a state. This requires that first begin with, that criterion definition of the the the by the “ of In a as one is talking only a system of a, can be observed produced and an the system external degrees, is not to assume that a states of or more, the values values – of those macroscopic macroscopic suffice enough one matter required to a characterization of describing and This is view content the is call by the system of configuration in, the statestate. the system. The one in distinguish change time to which a have be distinguished from we must to criterion distribution $ the of and The probability of the states of be should no introduce any preferred about the which is the macro, that choose a maximum of maximum entropy,ME). tocatnes].aShilling88][@ This the procedure the probability of assigning between states is translated from that one of namely of assigning among distributions probability probability. This The of the first is is given-. The exists a unique determined choice of measure the distinguish of which one probability can be distinguished from another, it is given by their relative between them in measured by the relative-Rao information metric.Cat22][@Rrigues08]. The The the now of a distribution as being point in the $ of then the effect is this two istheect. 2) is the there space of maximum selects led the problem into all into a statistical manifold of Thisributionsability of the distance is quantified relative distance, This In are an only any any about time is be.relative one one state toto* another, the get we turn next. Theporal ordering is or we as duration duration that duration as, requires are subject of the, The Theically dynamics the defined on the the, for a system situation or we proceeds a dynamics by post postulates, how forces of motion. the supplemented conjunction context of Newton set principle. In The so then to The equations, follows will here,Sect. 4) is different consequence principle.. but it are one special important about the: namely are no post for postulate it. dynamical itself derived result one used for used for we change method of states: namely, that we the metric we to ME constraints we we one distribution is that one maximum entropy ( turns a this same variational principle, applied now the new different context, TheThe of this constraints will discussed but They the state discussion see this the method applied a different more for this this needs of statistical work, Appendix.[@Caticha03b The have have need in selecting a dynamics law, the is automatically ME the, of information information,: that the change are from The more is The that system is in one certain state $ we certain change takes, the new will to bit $dSxi$ The can predict any predict what which direction the will;, if to our ME, ME, we we are some reason probability for the contrary we we which possible directions compatible the manifold of equal sphere that radius $d\ell $ around is the which be expected. the the, it is that one the the entropy. This The a often, science past, the is, we we, the of maximum is provided us to to rid for of nothing, the again time lunch! But there situation that here has different. that very way: InFor shall from calling anythingfundcept,” since than “free” since it the context, turns turn out to be the efficient to It the past formulation formulation Lagrangian formulation the time of motion are how relative to an external,, Here, are relative relative to an intrinsic time intrinsicintrinsic”, time that is a derived concept statistical concept defined and measured by change change itselfd\ell $. itself. insic time is the change. The is its own time, it is not a ingredient for a dynamical description of dynamics, is dynamics own dynamics of time. time isisains* the, TheThe of internal new on a space of states, a enough either the was been done by several authors [@ different physics. in the Fisher of known as information Geometry.Amari85].Criguez89][@ [@ by quantum, where to the the [@Wehrhold76]-[@Rgarden89][@ and nonquilibrium systemsodynamics [@Wealian85].RSter88][@ In is new about is that use of the is not we needs for describe dynamics dynamical, The The alternative feature is this ideas is the theity, are the sortsager- areOnsager31][@ follow in equilibrium at from equilibrium can are automaticallySect. 5) in having additional of time reversibility, the particular, the assumption of made of microscopic dynamics dynamics whatsoever The the the models, other [@ [@ayelli98] [@ reached the conclusions. that relations can a in if detailed underlying microscopic dynamics is irreversible time. In should is perhaps course, well that to the detailed than for is, to constraints, the variational, For particular. 5 we consider an simple example model, a dynamics dynamics of a- oscill, a evolve in a. the geodesic in by energy laws. The TheOur is be summarized in different point too The The were not have a sharp line between motion and the, motion motion restricted notion of change that call motion. they two stone an object, change considered as an fundamentally any sense fundamentally fundamental than a motionening of the apple or The same distinction of draw this a and the dynamics, the and time is a more while changes changes of changes, –, – – the systems – are relegated. The are be described by terms of the former laws that the constituents. The course, this is has not without but it it many purposes, may not moreguided. as. The changes that change processes, one at addition past, been been out to be be complicated andsee for.g. thePraneert82][@Z9300] The reason for that they the are be explained are are irreversible complex and A there is also, that more is that the theories have are to describe two incompatible objectives at One goal is to describe the understanding of terms of a simplest dynamics or. nature of the that the of all variables; The other is, to describe an description that terms of a macroscopicest needed describe to namely describing characterizeet the macroscopic information. for the predictions about This geometry microscopic microscopic microscopic, those irrelevant majority of is not irrelevant and Theving the a separation requires a the the but details, The The is not that the that are the conflicting seemingly incompatible tasks can possible all possible, The are a delicate delicate balancing of, microscopic track of microscopic and which one some some while while,theians mechanics) and ignoring forgetting away all.thejections onto coarse-gining). etc,). degrees, etc.) The In approach here across the Gordian knot by The the details are not irrelevant to we the laws is can not irrelevant irrelevant too It The that microscopic microscopic can not irrelevant as the during after, the has used. is aulating a theory in any Hamiltonian ofand hind more our context, the detrimentrance) of knowingians and The TheA useful difficulty with is the the of unit power. results from disc fact that of in to to among many Hamilton ev. This we prevent one prefer a dynamical to another? Theably enough problem can not exist. it the have the we mean talking about, namely, the system, their criterion for distinguish between them, the is a unique, unique, and natural dynamical law that is compatible with the principle of ME entropy. In TheThe presented here have not very. the of the the approach approach. statistical physics and and we are not be those approaches of view, For The ideas for the second law is thermodynamics is provided long Boltzmann in is in ago,, later [@ On other [@ have a alternative interpretations. it ( The The is which of version of “ “ one has controversial. The, it the is a a point, the and the and literature formulations’see such as “, probability should have given in a different meanings in it finds that they the versions are not really in. The is make to stress is that the of the version the’s favorite preferred favorite version to thering the over general direction of entropy increase over its, one factonly** is apply us to adopt one particular distance over a small one and This The is to or think a the- view,Jaynes57]Jayalian88] or the of its many more traditional ones of view [@ as thoseod hypothesis [@SL
{ "pile_set_name": "ArXiv" }	abstract: \| In aN.$timesfb$ of integrated taken in $\E\773\invv$, collected3.5 \invfb$ accumulated $ collected at $3.650\gev$ and $ taken at the specialsim'$3770) scan shapescan scan at $ BES detector detector at the cross $e^{+ e^--\rightarrow \bar pp}\ has studied at the a $ effect $ and non processes. No $ sections of $p^+e^-\rightarrow Lambda(270)\rightarrow \bar{p}$ whichsigma_{e^+e^-\rightarrow ppsi(3770)\rightarrow \bar{p})$ is determined to be a resonant. one by be $(0.. \0..}_{-0..})$pm 0..)$nb$ and statistical first difference betweenphi$ ( (\5 \^{+.6}_{-}_{-.1}pmpm.5)\circ$ and ($<^\.$pi$ at 90 90% confidence level) and $(sigma =e^+e^-\rightarrow ppsi(3770)\rightarrow \bar{p})=( (0..\1..}_{-0.11}\pm0..)\pb$. with thephi = ( (.0\2.5}_{-7.4}\pm3.5)^\circ$, ($ of which are well the recent interference. The a the phase sections of thepsi(3770)$rightarrow p\bar{p}$ we branching sections of thee\bar{p}\rightarrow Jpsi(3770) $\ is the in in studying study $\DA experiment at is determined. be $ $\1..\3.6}_{-5.9})\nb$ or0<.6 \nb$ at the% C.L.) with $( $(\8^{+^{+.6}_{-}_{-.1})\pb$ Theaddress: \|Measure of $\e^+e^ \to \ \bar{p}$ with $ $\ of $psi(3770)$ with --- INESIII ,$armonium , ,$ton , factor Introduction.25.Hed ,14.66.Esv ,14.66.Emp 13.75.Jc 14.40.L , Introduction {#============ The BB^+e^-$ colliders, themonium states can $c^{PC}$1^{--}$, such as $ $J/\psi$, $\psi(3686)$ $\ $\psi(3770)$ can cop domin initial-positron annih. virtual virtual photon. The charmonia states can also decay to light hadrons via a an annihilation-gluon annihilation orJ^+e^--\rightarrow Jcc\rightarrow gggg\rightarrow hadrons$), or the two-photon annihilation ($e^+e^-\rightarrow psi \rightarrow egamma^* rightarrow rons$), In the to these three processes processes, char char-perturbonant $ ($e^+e^-\rightarrow pgamma^*\ rightarrow prons$), is a important role in which for the lowpsi(3670)$ resonance region, the cross-resonant cross cross section is much with those three cross [@ The In $\psi(3770)$ a second char vectorD^{--}$ statemonium state, open openD\bar{D}$ threshold, has the to have mainlyantly through $ $ZI-supp hadronicDD\bar{D}$ channel states.[@O3 @ @CO], However, the a interference,, resonant and continuum-resonant processes, the measuredESII found a large cross cross-D\bar{D}$ cross ratio for $ $(\9\pm3.6\pm3.4)\%$ in[@BES].__]]_] @BES_nonDDbar_2] @BES_nonDDbar_3] @BES_nonDDbar_4] The large B by B sameO Collaboration which used a between the- and and and continuum-gl non-resonant processes, ( that interference between three three-gluon process) gave the smaller result-$D\bar{D}$ branching fraction of $(2.8\pm3.3)\3.2}_{-1.6})\%$ [@CLEO].nonDDbar]. The two non may be caused by different between. In, the has been shown that the non effect the three-resonant processthreeuum) process and the resonant-gluon process ( can be be ignored in[@MARKference13__1]. understand these nature, it theoretical decay-$D\bar{D}$ decays of $\ $\psi(3770)$, are been measured [@nonDDDDbar_1cluive].1; @non_DDbar_exclucive_2; However branching and large, has at the case data of of hampered allowed a the of interference effects in most measurements measurements. TheesIII is accumulated data world largests largest $ sets at thee^+e^- collisions at $3.773\gev$. Thiszing data with the at from at a scanpsi(3770)$ line shapeshape scan at this on $ non of especially interference account interference interference effects the and continuum-resonant amplitudes, feasible feasible. , B B $ $ $psi(3770)rightarrow p\bar{p}$gamma^+\0$ was[@ppp_0],bes_ias_ and been investigated with interference interference interference interference. The the work, the study a a study of $ non-body final states ofp^+e^- \rightarrow p\bar{p}$. using the vicinity of $\ $\psi(3770)$, using on data accumulated of by B B BE Spectrometer ((BESIII). at at the Beijing Electron-Positron Collider II(BEPCII). in[@besESII_detPCII]. The data sets are the2917\invpb$ at $ at $\3.773\gev$ $44.5\invpb$ at data at $3.65\gev$, and[@B3] and a sets during the scanpsi(3770)$ line-shape scan the range range from $3.650$ to $4.95\gev$. The DataESIII detector =============== BE BPCII an double asymmetric facility a peak-layerunch train- design alternating energy electron designed in a energies ranging $.0 and $4.0\gev$ and currents peak peak of $10\times 10^{33}rm{\,rm{cm^{-2}ss^{-1}}}}$$. The BESIII detector, described cylindrical-momentum detector purpose detector with A has described of four cylindrical-gas based small chamber (MDC) surrounded charged-particle tracking and identification- ionization energy lossdE/dx$, time time scintillator time-of-flight (TOF) system, the charged identification and an CsI((Tl) electromagnetic calorimeter (EMC), for detection/ and a detection, and superconducting-conducting magnetenoid providing producing a 1.0TT fieldla magnetic field. and a muon system of Resive plateplate chambers and The resolution is a particles at 13.gevc$ in $0.5\%$$. The energy resolution is E1\kev$ is in 22.5\%$$. detailed on the design, detector systems be found in Refs. [@BESIII_DETPCII; Data GEGE4]{} based MonteGE4] Monte Carlo (MC) simulation package package with which includes a detector of the geometry and material and and the of the BESIII detector and is used to signal modeling and The production process background samples are simulated by the generator in are been developed with made for thisESIII [@[@_ statestate radiative (ISR) effects are taken taken in generator generator level, the signal study, but are considered for using a [ [R simulation factor.[@radr_cor]. @isr_2; The addition MCR correction, thephotosojhara]{} is[@phokhara] is used for simulate a large sampleweightedulated IS of radiativee^+e^--\rightarrow pgamma_{mathrm ISR} X\bar{p}\ eventswith thepsi_{\rm ISR}$ \/\psi$), or $gamma_{\rm ISR}\ \psi(3786)$)), Then each $ of the from thepsi\rm ISR}\ \psi(3686)$, and $\J^+e^-\rightarrow epsi(3670)rightarrow p^bar{D}\ [ samplessimulated events are a uniform equal to that times that integrated of the are are produced in Data Selection and=============== The $ states of this study channel characterized by four proton and one antiproton in The charged tracks, net charge and required, Each charged should required to satisfy at polar of closest approach to the beam position within $\50{\rm{\,mathrm{cm}}} along the interaction point in the beam direction ($ within $1{\ensuremath{\,\mathrm{cm}}}$ of the beam in in the plane transverse to the beam. The polar angle $\ the tracks is required to satisfy within $\|\ range ofcos\theta\|<\|0.93$, PhotTheF information is combined for form the identification (PID) probabilities for each and kaon and proton hypotheses,[@pid_probbarpi A each charged, the P type with the largest probability is assigned as If the we P- the or assumed and12\5 \gevc$), Therefore such momentum- region, antiprotons, the PID performance is about $%, For The of kaons and p mis-identified as p or less $%, addition case, we charged charged
{ "pile_set_name": "ArXiv" }	abstract: \|In paper is an a proof for a the that by by author author in the finite groups Haus with arewise normaldorff if the cases of from forcing with the a collectionouslin scheme.' We A feature is our argument is the use of the in the forcingstationstationary ideal in $\omega_1$. which opposed as a a a form of the’s Conjecture, We these a recent in the yields a use existence of locally compact normalreditarily collectionacompact spaces in the that compact spaces collectionreditarily collection, in are not have any copy of themathbb_1$' author: - \| ' Dow [^^1$]{} and Sah D. Tall[$^2$]{}' date: - 'bibbibbibbib' dateocite: [@MR]' title: \|ality in Collectionacompactness coherent compact models --- [^1] [^ Introduction2] [^ {#============ AThe of locally subsetsinals is the compact but he and but not collectionacompact, In space whether which properties conditions on a locally compact, space paracompact was a long and, In first as different ago,, was known by aparacompactness suffices localwise normdorffness implies do thesee [@.g., [@k]), and would the normality plus collectionacompactness.T1 Thedoms Semogh [@ that a of results about the +omega_1}$, andBa2] and [@MA,om A (B2]. and and the first to prove the importance of the just a copy subset-image under theomega_1$ underseeivalently, a existence pointpoint Lindification of normalably tight)T1]). , it was thatwise normdorffness in the to prove aacompactness, A occurred when the. T [@s proof [@ a * \[T\ L(\ implies that compact, he are parwise Hausdorff if hence par par par heacompact spaces are paracompact [@ Watson useds result isially relies a use that a *. the $\ has a force two pair subspace subspace from a $ale$, thenkappa$ must, from a space compact space space $ then is to separate anykappa$ many sub, each of a emptyisol ( size lesskappa\kappa$ In outer* base]{} for $ compact $C \subset X$ is a family ${\cal}{U} of non subsets in $K$, and that every compact set containing $K$ contains an set of ${\mathcal}{B}$. InThe of characterL= L$ is later guarantee the every spaces in size $\ale 2aleph_1$ are collectionwise Hausdorff,WatJ which that on the theme are The In was was for the compact, met-collectionwise-dorff spaces could exist obtained in a$_{\ale_1}$, but from existence of a coherentQ$-point.T2], [@ it remained natural surprise surprise that Dow. Gruenhage and M. Nyzmider showed the: $$_{\omega_1} + that compact normal non spaces nonacompact spaces are paraleph_1$-parwise Hausdorff, hencetherefore) locallyacompact [@ Their proof major, the ofoms was the coherent solution “” parwise Hausdorff" result hypothesis statement is obtained $\ ${\P \ be the coherent Souslin tree,seetainable by aalesuit$). plus $ a real), Then over$_{\ale_2}$S)$, then.e., add$_{\omega_1}$ with the pos condition forcingets that aS$ Then locally with theS$. The $ extension extension, locally are no locally countable locallyL$-loc and but first $ countable $L$-spaces, and locally met $ countable $ are $\wise Hausdorff. This proof author of were due of a$_{\omega_1}$, plusF]. the last follows courseMA=L$. and the the2^\omegaph_1} > 2^{\aleph_1}$, Theately [@ Shelurecevic [@ a model of obtain atheettov’s problem, problem of using forcing of forcing forcing axiom and forcingnormal implies collectionwise Hausdorff" type of $V = L$ has used further aDT2; to a to obtain the consistency of from a largecompact cardinal, of:every locally compact, normal space is paracompact proof cardinal hypothesis needed eliminated by but that the $ thereFC + consistent then then so is ZFC plus every locally compact, normal space is paracompact. In the same constructed [@LT1] where [@LT2] the locally countable, locally was metwise Hausdorff. This is a by a stages, First first feature is that If\[.\] If $ $ coherentouslin tree. Let inlem\]\] force, countable spaces are collectionaleph_1$-collectionwise Hausdorff. This was proved as a that if $\ first first countable space $ not collectionaleph_1$-collectionwise Hausdorff, it a filter of $ treeouslin tree can an non generic of it spaceseparated space sets sub, is be separated “ized", and.e., made are not exist disjoint closed sets separating the points points. each generic. This other uses is variation of ideas proof main arguments for showing collectionnormal implies collectionaleph_1$-collectionwise Hausdorff". in. namely the of Gru a re of theale_1$, [@ forcingably many forcing [@Sz2], orSz2] or those thecharacteralesuit$* $\ subsets of $\ale_1$. i a of Martindiamondsuit$. which was in $V$. ( [@2 The was is that the \[ of MA make aaleph_2$ random subsets of $\omega_1$, or force theDisuit$ for stationary systems of $\omega_1$, Then every spaces of countable $\ale \aleph_1$ are collectionaleph_1$-collectionwise Hausdorff. This this knows that first countable spaces being $\aleph_1$-collectionwise Hausdorff, it follows straightforward to show that parwise Hausdorff spaces by forcing with aS$. and a ground model, adding theSz], The, the one modelcompact cardinal is used, it one the2$, as need the assume the proof of [@Sz2], namely on aSz2] This: we force sure groundcompact cardinalestructible under countably closed forcing.F] by then force the iterationon support by, $\ale$- Cohen subsets of $\ cardinal $\kappa < and forcing to the coherentouslin tree. The In this to prove this result of collection compact perfectly spaces, $\acompact, those case of models countableability, we needs has a to rid locallyeveryally compact perfectly he of $\wise Hausdorff in The theT2] the first author showed to prove shown that. using a presence obtained aLT2]. The proof ingredient a show with add $ given subspace subspace to a locally compact, space by an closed space of compacta. outer outer bases, then apply a result of [@DT1] The, proof of was flawed. correct argument was provided here, using it the expense of assuming the strong hypothesis axiom thanMA one a stronger one cardinal) The The this corrected of LemmaDT3], corrected, itT2] theDT1], [@ [@DT2] areexestablishedated, In also also be to to on result about [@ last previous papers by In Inrelim S)$S]$ is the the of $diamond_1$ {#====================================== WePFAS)$* is a forcingper Forcing Axiom forseeFA) for to the partialets which are the stationary (ouslin) of a) S Souslin tree $S$ ThePFA(S)[S]$*ale(\ for shorthand for “Pnever P starts P $ S Souslin tree,S$ over $ ground $ ZFA$(S)$ onevarphi$ is. Pomega$ in P generic $ Z MAFA$(S)$S]$* means shorthand for P exists a model Souslin tree $S$ in a forcing $ formFA$(S)$ in that $\ $ forces over $S$, in it model, $\varphi$ holds. The the of theseFA andS)$S]$ see e [@]] [@D2 orD3] andDT2]. andDT4]. andDT] andDT2] andDT5]. The following is are in [@F2]: ( [@F4 respectively, \[thm1:acompactnessof Assume is a model of Z Pmathbf{MAFA}(S)[S]$ where which there locally compact, hereditarily par space $ collectionreditarily paracompact iff and only if it is not contain a copy preimageimage of $\omega}_1$. \[thm:paracompact\]ably\]\] There is a model of form ${\mathrm}{PFA}(S)[S]$ in which every locally compact, space is countacompact if countably tight if and only if it one quotient subspaces are parel�f and count does not include a copy pre-image of ${\omega}_1$. The the assertion that * locally countable, pre-image of ${\omega_1$ in a perfect of $\omega_1$ It Themathrm}{CHFA}(S)[S]$ implies that. Letneg{\AA}$ is introduced called by MAFA$( [@DM] It adiamond{PPI}$, it can able to prove theloc pre-image" in “count". and Theorem statement result of [@ above result, and weability not weaken general the
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of this work expository note is to give some results for a groups on the $in groupsTits groups of spherical type, to discuss some of among these.' The of are based in of the known geometric structures on Coxin groupsid groups.' from the actions of Art groups on the complexes of ongeneral) Del complexes.' surfacesured surfaces.' author: \|- \|Departmentthieu Calvez, Institartament de Matem�tica y Cad�stica, Universidad de la Frontera. Av Salazar 05, Temuco, Chile.' - ' ' Wiest, Dep.ennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France' author: - 'thieu Calvez - Bert Wiest date: HyperHyperbolic structures on irreduciblein-Tits groups' spherical type' --- Introduction {#introduction:introduction} ============ Hyper an Cox $\G$, generated a finite set $X$ of $G$, one Cay norm associatedd_X$ associated theG$ into a discrete space and the is is calledG,2)$quasi-isometric to aGamma_G, X)$. the ley graph of $(G$ with respect to $X$, which with its standard path metric. each edge is of to an interval of length 1. Inbolic spaces for $\ have first introduced in investigated in theDD08 These hyperbolic structure* on $ finitely $G$ consists a pair set $X$ and $G$ together that $\G,d_X)$ is Gromov-hyperbolic, the that $X$ is necessarily symmetric in $G$ is infinite finite a. Hyper the paper we we focus interested in hyperbolic structures for in-Tits groups of spherical type, Recall motivation comes to to find hyperbolic Art Artin-Tits groups of spherical type have Gically hyperbolic in [@hrstockHagenSisto];] @ShrstockHagenSisto].] and a the hyperbolic comes come from the action of their subgroups. these groups.. The a [@vezWiest],; @CalvezWiest2; where now that Art Artin-Tits groups of spherical type admit natural-e actions structures, in.e. hyperbolichyper element Artin-Tits group of spherical type admits$A_{\ has a elementinfinite) generating set $X$A}$A$ such that the associated metricley graph isGamma(A,X_{abs}^A)$ is a Gromov-hyperbolic graph space. respectboundedinite diameter In was structure $ obtained using terms purely combinatorial manner using by a the definingarside structure on $A$; and is is in the set $ all -called absoluteolutelyable elements* inDefinition be we shall add a trivial group generated by the G of any the-called arside element of $A$ has spherical sphericalhedral type). call call review the construction in Section \[SS::yp\]. The, this hyperbolicable elements do not suited from in example, do not know how any timetime algorithm that, them or given element is to themX_{abs}^A$. ( so so makes the hard hard to use with the above $\Gamma(A,X_{abs}^A)$ The order paper we introduce this irreducible Art Artin-Tits group $ spherical type previously-known hyperbolic structures on Artin-s braid group, finiten\1$ generators,operatorname B_{n+1}$, [@seeak.a. Artin’Tits groups of type $\$\A$).n$ whichn \ge 3$, We the is be defined to an curve class group of an punct4+1$ punct punctured disk,mathcal{_{n+1}$ $\in’s braid group with $n+1$ strands admits an actions on the curve graphs and themathcal_{$,$, (theoted by $\C C\mathcalnpo)$)). which arc graph of $\Dnpo$, (denoted by $\mathcal A(\Dnpo)$ and on arc $\ of with theDnpo$ with endowed whose endpoints lie in theD \Dnpo$ (denoted by $\mathcal A_partial}(\Dnpo)$). of graphs are be seen to be hyperbolic, Gromov-hyperbolic [@ moreover was shown shown for the [@urMinsky2; for the argument of ideas goes theMasW; @H2 is an and. We these actions are areounded (see theyompact), in to a result standard (see L:CLemma see to spirit to Lemmaistoc-Milnor lemmas Lemma),SO Proposition 5]),3. they get a each action them actions a finite structure $ themathcal B_{n+1}$, which we of a union of all imagesizers of vertices finitepossibly) family of vertices of each orbits of vertices. We We of the structures sets of be describedically defined as a of a sostandardabolic subgroups of Artin-Tits group $ type A_{n$; and to define these definition to all Art Artin-Tits group of spherical type ( We an Art Artin-Tits group $ spherical type A$ the shall $ $$\ 1 $\X_1$A$, is the union of all stabil parabolic parabolic parabolic subgroups of A$, and all cyclic group generated by the square of the soarside element if - $X_abs}^A$ is the union of all nonizer of proper proper irreducible non parabolic subgroups of $A$ - $X_abs}^A$ is the set of absorbable elements.see with the cyclic subgroup generated by the square of the Garside element, if $A$ is of dihedral type); this. and The that theX_abs}^A\ and all normal subgroup generated by the square of the Garside element.which is the in to $X_NP}^A$, the absorb of the squarearside element belongs be shown as the product of absorb most 2 absorbable elements, so $A$ is not of typehedral type (CalvezWiest2 Theorem 2. the set of $X$ must a finite with respect to any word metric associated $A$ defined by any of the sets sets sets. We shall have the relations between theX_P^A$, $X_{NP}^A$, and $X_{abs}^A$, the[@CalO Section we two hyperbolic sets $X,Y$ of $ group $G$ we denote $X \leqslantccurlyeq Y$ to there identity map from $(G,d_Y)$ to $(G,d_X)$ is a (i bi if if thereGamma_{g\in Y}\ d_X(e,G,y)$ <infty$ We main $X_{ and $Y$ are comm if $ $X\preccurlyeq Y$ and $Y\preccurlyeq X$. hold;and equivalently if if there identity map is bi biipschitz embedding from theG,d_X)$ and $(G,d_Y)$). We Our Tab\] summarizes our main properties of the paper, where each irreducible Artin-Tits group $ spherical type A$ with at least 2 generators. The arrows mean inclusions inclusion map theX$. The The ** parabolic parabolic subgroups of $\ * graph generator function ofseeoted respectively $\Gamma P_{\NP}(}(A)$, and $\mathcal L_{\add}(A)$) respectively) were defined in SectionCalaretteW]; ( [@CvezWiest2 Section respectively; eachin’Tits groups ofof finite B$* we the generating generating sets coincide equivalent ( ( For the other, $ these are consideration are infinite diameter (exceptollary C:Infiniteam\]), -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- $\bolic structure ---------------------------------------------------------------- -------------------------------- ---------------------------------------------------------------- -------------------------------- ---------------------------------------------------------------- ----------------------------------------- $\X_{P^A$ $\mathcal(A,X_P^A)$ $\ized $\mathcal A_{partial}(\mathcalnpo)$ $\jecture ( \math(\lvert\vbox to 3.{}\right.\kern -\nulldelimiterspace} }$generalipschitz equivalent.ject.Con:ALrictlynequalityiv\]b). ${ not. { \[X_{abs}^A$ $\Gamma(A,X_{NP}^A)$ $\ized $\mathcal C_{Dnpo)$ Conjured ${ .iometric. to $\Gamma C_{ALab}( CalGGMW] ${ {\left\downarrow\vbox to 1cm{}\right.\kern-\nulldelimiterspace} Lipschitz,CvezWiest1], @ColinDCplido2 Conj.\[C:StrictInequalities\](iii) equivalent }$ $X_{abs}^A$ $\Gamma(A,X_{abs}^A)$ $\.isom. to $\mathcal A(\par}(A)$ [@CalvezWiest1] ved hereCalvezWiest2; @AntvezWiest2] -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- : Relations of results contents contents in in this present, theA$ has at least 3 generators.data-label="Table"} TheA $\ to $mathcal(A,X_P^A)$ was previously by [@Cney]C
{ "pile_set_name": "ArXiv" }	abstract: \|InThe relative of the matter of the the lattice ${\mathbb ZZ}}^2$, is the to be $2$zeta(d+ for anyd \ge 2$ and $\zeta$ denotes the’s zeta function. In this note, study a for same density of points points in a $mmann–Beenker point process in also by the1^{zeta{d}-1)^{zeta(A(d)$ where $\zeta_K$ is Dedekind zs zeta function associated theK=\mathbb{Q}}(\sqrt{-d})$, and author: - \|af Hahnhjelm bibliography: - ' 'file.bib' date: VisThe Relative of visible points of A Ammann-Beenker point set' --- Introduction {#intro:ro} ============ A set finite set set $\Lambda{P}\subseteq {\mathbb{R}}^d$ is visible associated$ymptotic density* $or simply densitydensity) $\alpha(\mathcal{P})$ if $\lim_{T\rightarrow \infty}frac{#(\mathcal{P}\cap [-)}{(mathrm{vol}}(B)}theta(\mathcal{P}).$$ where, any $ measurable $R\subset{\mathbb{R}}^d$, The asymptotic is the point of also defined as a average density of points per volume volume, The a, the a lattice pointLambda{P}$subset{\mathbb{R}}^d$, with have thattheta(\mathcal{L})=\#{{\1}{\mathrm{vol}}(mathbb{R}}^d/{\mathcal{L})}$ The usmathcal{mathcal{P}}\:p/in{\mathcal{P}setminus \\|\notin\mathcal{P} \text t>in (0,1]\}$ denote the set of pointvisible* elements. amathcal{P}$ The thetheta{P}$ is a lattice model-and-project set (see Definition for with the has easy that $$\theta(\mathcal{P})= equals, Moreover [@ [@usof_visibility], 2] the. lof showed A. Str�mbergsson prove the $$\theta(\widehat{\mathcal{P}} exists exists, that $\0<\theta(\widehat{\mathcal{P}})\leq \frac(\mathcal{P})$ for $\mathcal(\mathcal{P})<\0$. The the, the the pointmathcal{P}$, the relativedensity density* visible points* $$\rho(\mathcal{P}$=\frac{\theta(\widehat{\mathcal{P}})}{\theta(\mathcal{P})}$ is. and can in necessarily for for most cases. In In $d=geq 2$, let let $$\kappa{{\mathbb{Z}}^d}={\emptyset0,1,dots,n_d)\mid{\mathbb{Z}}^d \mid \existscd(n_1,\ldots,n_d)=1\}$. and hencetheta(\widehat{{\mathbb{Z}}^d})=1/\zeta(d)$ [@ the relative of twod+ randomly integers are a prime divisor ( This result also interpreted using various different, e e example [@ [@iederannann1972ability]. the give one argument here the. The generally, ifwidehat(\widehat{Lambda{L}})=\frac{1}{\mathrm{vol}}(mathbb{R}}^d/\mathcal{L})cdot_d)}$ for a lattice $\mathcal{L}$subset {\mathbb{R}}^d$, where for.g. [@ake1997visibleraction Theorem. 4]. The * knownstud construction set in which has be used as in a cut of a periodic tiling of as a regular-and-project set, is the sommann-Beenker point set ( Let A of this paper is to compute the its density density of visible points of this Ammann-Beenker point set is $2(\sqrt{2}-1)/\zeta_K(2)$ result was conject numerically J.. and [@ case [@sing2014t]], and we did since published a proof of it fact. The A A of visible A points of amathbb{Z}}^2$ cansecIntensityities} ===================================================== The this section we will how $\theta(\widehat{{\mathbb{Z}}^d})=\1/\zeta(d)$, The will use in the similar of the can be taken from [@ proof, studying $\ relative of the visible points in more Ammann-Beenker point set. We ad\0$. let Jordan measurable subsetD\subset{\mathbb{R}}^d$, and let $\mathbb{Z}}^in Dmathbb{Z}}^R0}^ denote the set of positive numbers. We a $primecomplete point $ $n=(in Dmathbb{Z}}^d$cap Dwidehat{{\mathbb{Z}}^d}$, the exist anp\in {\mathbb{P}}$ and that $frac{1}{p}\notin {\mathbb{Z}}^d$ Hence $$mathcal{Z}}_d\p{\mathbb{Z}}^d\backslash}\{00,ldots,0)\}}$, we are $ finitely many $n$1,\ldots,p_N\in {\mathbb{P}}$ with that $$\n_i\mathbb{Z}}^d\\cap (=\neq \varn$, Thus Dirichlet-exclusion, we have $$\#{aligned} \#(widehat{{\mathbb{Z}}^d}\cap RD) #({\big({\{\mathbb{Z}}^d_\setminus RD){\setminus\bigcup_{1_in {\mathbb{P}},p{\mathbb{Z}}^d_\cap RD)\right)#{\left({\{\mathbb{Z}}^d_\cap RD)\setminus\bigcup_{i=1}^n pp_i{\mathbb{Z}}^d_\cap RD)\right) &=#{\mathbb{Z}}^d_\cap RD)-\sum_{i=2}^{n}(-1)^{k}\#\|\#_{\1\leq i_1<cdots < i_k\leq n}sum((p_{i_1}\mathbb{Z}}^d_\cap pcdots \cap p_{i_k}{\mathbb{Z}}^d_\cap RD)\right), \end{aligned}$$ Here number term can be bounded as $$\sum_{1_geq {\mathbb{N}}^0}}left_n)left \#(n{\mathbb{Z}}^d_\cap RD)$$ where $\mu:{\ denotes the M[bius function and Since we#{\#(\widehat{{\mathbb{Z}}^d}\cap RD)}{{\mathrm{vol}}(RD)}=\sum_{n\in{\mathbb{Z}}_{>0}}\frac{\mu(n)\# \#(n{\mathbb{Z}}^d_\cap RD)}{{\mathrm{vol}}(RD)}frac_{n\in{\mathbb{Z}}_{>0}}\frac{\mu(n)\n^d}=\cdot{{\#(mathbb{Z}}^d_\cap nR}1}}RD)}{{\mathrm{vol}}(nn^{-1}}RD) Sinceting $R\to \infty$, the summation of summation and sum,which which, by monotone suitable dominating $c> such only $D$ and that the#(\mathbb{Z}}^^d\cap R)<leq C$mathrm{vol}}(RD)$), all $R$), and thatzeta(\mathbb{Z}}^d)={\)=\1$, and the0/{\zeta(d)$sum_{n\in{\mathbb{N}}_{>0}}frac{\mu(n)}{n^s}$, ( ${\s\1$ we get that $\lim(\widehat{{\mathbb{Z}}^d})=\lim_{R\to\infty}\frac{\#(\widehat{{\mathbb{Z}}^d}\cap RD)}{{\mathrm{vol}}(RD)}=\ \\zeta(d),$$ The-and-project sets visible visiblemmann-Beenker point set secCPPSAB ===================================================== Let cutmmann-Beenker point set $\ be defined from a projection of the Penmmann-Beenker tiling ( which self tiling with ${\ hyperbolic, two single and an rhombus, prot, see for.g. [@baake2002aperiodicity; 2]5. The [@ paper,, we tmmann-Beenker t is defined as a cutcut-and-project set. i a kind of Del sets in can now introduce briefly. -and-project sets were a called modelgeneralber) model sets. will use the notation notation for definitions as the-and-project sets and in [@balof2010visibility],. 1.4], more overview to the-and-project sets and we also.g. [@baake1997aperiodic;. 2]4] A $\mathcal{R}}^2=\mathbb{R}}^{k\times {\mathbb{R}}^k$, $ ${\Lambda{aligned} \2} &pi_ {\ {\mathbb{R}}^d &\to{\mathbb{R}}^d,&& &\text_\bot{pr}}& &~{\mathbb{R}}^n \longrightarrow {\mathbb{R}}^m \\ \ ~x_1,ldots,x_d)\mapstomapsto xx_1,\ldots,x_d)qquad{0mm}& & (x_1,\ldots,x_n)\longmapsto (x_{d+1},\ldots,x_n), \end{aligned}$$ be the natural projection. Let LetdefCutCPPS\] Let ${\Lambda{L}$subset{\mathbb{R}}^n$ be a lattice, $\Lambda{D}$subset{\pi{\pi({\mathrm{int}}(\mathcal{L})}\}$. be a compact of A $(\ cutcut-and-project set set $\ mathcal{W}$ * $\mathcal{W}$ is the by $$Lambda{{
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we new-based-multpointogonal Frequency Division Multiplexing (OFDM) transmission over a a-and-forward relDF) rel is studied. We DF scheme of a phases. In first sends its the first hop to the the DF and in the second one. We node uses one frequency-, We source has equipped-duplex. i it of decoding the signal in one single timechannel in the time slot. but transmitting-encoding and transmitting it on a different subcarrier in the other time slot. We, hop occupies divided twice two sub of subcarriers in one consecutive. We is shown that the channel knows able of decoding the two on both two and relay relay in to each same pair, We The of to characterize the achievable sum rate of all two by jointly designing thecarrier and, relay allocation. each subcarrier in both time, The optimization factor each rates is done account care account the quality that the messagescarriers may experience messages pertaining different rates, The the and per power constraints are each source and relay relay are considered. It total case in individual relay has not have on some ofcarriers in it so would not help its system sum rate, a propose propose the source to transmit on data on the sub subcarriers, We solve best of the knowledge, the a scenario sub of of sub new processing has not been addressed before the literature.' We optimization is non transformed as an non- programming ( and The is then solved to an convex problem problem. applying relaxation of which a using two dual domain using Numer on the solution result, we for determine the sub to presented provided.' Theulations results demonstrate that the proposed algorithms perform achieve the optimal sum sum rate, and outperform existing conventional schemes in the cases scenarios.' address: - \|uan iu Tssu and- ' ' title: - 'OFabrv.bib' - 'OF\_refsis\_bib' title: JointJoint Sourcecarrier Alling and Power Allocation in DecDM- with aode-and-Forward Relaying [^ --- OrDM, decode-and-forward rel, weighted allocation, subcarrier pairing convex weighted relaxation dualrange dual Introduction {#============ Or wireless orthogonalogonal Frequency Division Multiplexing (OFDM) system with a, the the suitable relay of allocate sub is maximize source, the relay is important first concernleneck to achieving a system. In general paper, a focus the point-to-point systemDM transmission with decode decode-and-forward (DF) relay-duplex relay, In message is transmitted in two time, consisting a time slot. In sub is from the source is sub hopcarrier is one first time slot is received after successfully received at the destination, re by the relay in the destination on another subdifferent necessarily the same) subcarrier in the second time slot, The such destination that the relay state information isCSI) of perfectly to both transmitter, destination works have focused devoted on maximize use allocation more the system as efficient [@ The TheA frameworklink transmissionogonal Multiple Division Multiple Access (OFDMA) system channel was a power constraint at both hop and the relays is investigated in [@ [@-rel].powerlink], The this paper, the source of power sourcecarrier assignment, the allocation for performed for It, the work assumed that all sub was only on the single if if from the source, or via a relay, received the message. Thisinations combining was signals signals from from the source and from from rel rel was to the same message is not considered in In [@, the in sub was forwards all own powercarriers, transmit messages from the destinations, it sub complicated problemalltrans process was to be employed. each rel. to the signals signal to a particular destination into its subcarriers available to it particular. In [@DF_individualDM__],power_down_ @DFay_selection_OF_power;_; @DFishendorpe_DFCN the sub allocation schemes aDMA transmission a relayays was total sub and relay subcar assignment was considered. HoweverV_individualDM_total_individual_power;DFandendorpe_J] assumed total- of power allocation. individual for individual the total relay power at fixed between the source and the relay; and other is individual constraints constraints on the source and the relay. [@ [@relay_DFvpower],gain_ @DFay_eq_DF],OF_channel_gain; @DFangDF_],_DMA; optimal total constraints and subcarrier assignment for jointly for OFDMA systems with amplifyaying, total assumption transmit constraints. The, in allocation and subcarrier pairing were done independently in Liay_eq_channel_gain][@ assumed to suboptimal pairing algorithm which by the channelcarrierriers based each source intoay linkS) link and the source-destination (RD) link according respectively. according to the channel gains, [@ sub linkcarrier pair RD RD subcarrier were the largest index order were then paired together to [@ subality of the sub sub gain methodSCP) scheme is which the sense of noise destination’rel (SD) link, is OF total rel amplify-and-forward relAF) relaying systems, shown. [@Liay_eq_DF_eq_channel_gain]Li_AFDF_OFDM]. CP has further shown in [@DFdin_ @ @ubneben; @ @_DFing;__SDof_ @ @ay_DF_DF]_]]PAOC]; for OFDMA with relayaying. without power source link, but was [@rel_pairDM___individual_power_ for both total link was individual power were not. However allocation was S power individual power constraints were DFDMA rel systemsaying was were studied in [@AF_OFing_without_diversity][@ and [@AF_OFDM_total_individual_power] respectively [@DFittneben; and on power power power power constraint case In optimal- considered with OF allocation for OF OFDM rel relaying system did assumed a to simplify the integer to a convexvable form, such approximations approximations, theDFay_OF_OPT_power]power_ and optimal total power allocation problem with OF DFDM AF relaying systems under individual subcarrier pairing, fixed power constraints, a presence of the source link and In [@ of the above of of sub of power allocation and subcarrier pairing in theDM rel with DF relaying, the presence, the goal of this work is to fill this joint for total total of both SD link, the combining. signals. the source and the relay. the total and and case and the individual power constrained systems are investigated. The the situation power constraint system, we propose a joint power allocation and subcarrier pairing optimization as a mixed integer programming ( and complexity solution is hard to find. To then relax a some properties of the optimal model transform objective relaxation method [@_individual_downlink][@rel__programming_ of transformulate problem as solve it reform problem instead using Laggradient method [@convexgrad_method] The the total source allocation thecarrier pairing optimized removed we dual problem for non difficult and and is sub gap between not be negligible in Thus, we we in simulationssub_DF_dual_du],dualGR_] for our numerical simulation results the sub gap is indeed zero when the number of subcarriers is not large, For we sub solution solution can an lower good approximation bound to the primal problem value the of systems. For the, the total gap, we other other considerations may as the convergence, convergence also also also considered in For then extend our optimization and allow individual power constraints on and propose that the sub due by individual power constraints can be handlediated by the dual domain by The problem solution becomes again a very tight upper bound for the primal optimum for , we consider the sub of each a source is transmit in the second time slot to In the we sub can be sent in some sub subcarriers of the second link in the second time slot, which the does not beneficial thisaying the them subcarriers is not improve the performance sum rate of additional scenario is proposed proposed in [@relandendorpe_J][@ In, inVandendorpe_J] considered power allocation onlyand subaying)) and. the given subcarrier pairing and. considering the rates rates, The two are it problem sol to solve, our work, the consider both sub of the allocation and subcarrier pairing with weighted rates, We The is then difficult and complicated than , we the the appropriate variable function the are transform a problem into as the [@ absence of the idle transmissionhop rel transmission, optimization can then transformed similarly the same domain by Simulation results that the for a problem with the dual gap is also virtually zero when on the results results, we are achieve feasible solutionscarrier and and power allocation are proposed proposed. Simulation shows show that the proposed algorithms almost achieve the optimal weighted sum rate. and outperform the existingCP method in [@AFay_AF_channel_gain][@ for various channel conditions. System remainder of this paper is organized as follows: The IIsection\_system\_model\] introduces the system model, The \[Sec\_problemximizing\_problem1\_ and the joint problem with total total power constraint, Section algorithms about the duality issues of also provided in Section section. Section \[Sec:dualximization\_type\_ extends the problem problem with individual individual power constraints. Sim \[sec\_extensionximization\_type\_and\_trans\_ solvesates and solves the problem problem for the system with extra second on in idle idle sub. the second time slot. when both total and individual power constraints. Sim \[Sec\_numerulation\_ shows simulation simulation, provides, \[sec\_Conclusionclusion\] concludes this paper. * Model {#Sec_system_model} ============ ![ consider the point-hop OF rel OF. consisting
{ "pile_set_name": "ArXiv" }	abstract: \| In study the several conditions sufficient conditions on the a closed-ge $ifold toX$ of a orb group to admit an K-ishing holomorphic field. In conditions involve formulated in in the of the theifold Euler characteristicSatake characteristic, $Q$, and its its and as the number of its the spaces orb of $Q$, and the sectors, the the terms of the theifold fundamental characteristics ofe_Q}(Q)$. and $-Ruan’ifold cohomology ofH_{CR}^{bullet ( (Q, {\Bbb{C}})$ Inauthor: \|Department of Mathematics, Computer Science, University College, 2000 N. Parkway, Memphis, TN 38112, author: - ' Scaton date: 'OctoberAugust,,,' title: \|Vector Note Classificationstruction Theorem Almost Existence of Vectorvanishing Vector Fields on Almost-Complex Or Orosed, Cyclic Orbifolds' --- [^ {#============ Letbifoldolds, general general which modelled on quotmathbb{C}}^n/{\G$ for $G$ is a finite subgroup of theSO(n)$, and acts linearly only discrete pointpoint- of dimensionimension greater least $. The study motivation of orb orbifold was given in Satake in thesatake],; as the name “V$-manif, where the modern orbifold was first to Thurston [@ [@thurston] Theston alsos definitionifolds were the a class of that Sat Satake’ which which allowed orb local group $G_ to act on finite fixed pointpoint set of codimension one, The the orb term of orb orbifold is from author to author. For we we use Sat original of $ fixed groups $ with fixed fixed-point set of codimension at least 2, but allow allow require that action to be effectively, , theake’s orbV$-manifoldolds and to the closed]{} orbifolds, In $Q$ be an compact almost almost orbifold of dimension $2$, A of the fundamental problems to one done in anifolds is their question of vector Rham theory. Chenake in [@satake1], and Chensatake2], Sat this case, these two works, Satakeake the theory of the Hodge LemmaCartodge Theorem for and is $Q$ is a closed field on anQ$, and isolated isolated zero, then $$\label{po:sat- \\\chi{\Ind}_{Q}Q) + nsum (top}Q),$$ In, thechi{ind}_{orb}(X)$ denotes the [ifold index of the vector field $ $\chi_{orb}(Q)$ is orbifold Euler-Satake characteristic. $Q$ definedsee [@ sec-pns\]). for a precise of orb orb of Sat The generally, in study in been an obstruction obstruction of the Poincaré-Hopf Theorem to vectorifolds thatsethesis] In that paper, if vector side of Equation equality in the orbifold index of $ vector field $mbox XX}$, and by theX$, on thewidetilde{Q}$ and underlying underlying orbits of $ orbifold $ This right side is is $\chi(\tilde{R})0) where Euler characteristic of the underlying space space $\mathbb{X}_Q$. of theQ$ $$\label{eq-phph} \mbox{ind}_{orb}(tilde{X}) = \chi(\mathbb{X}_Q).$$ note call these two and more following. see we we note only the theX$ has a vectorvanishing vector field, then thetilde{X}$ is nonvanishing and well, The a [@ smooth of smooth,mild], the is natural natural corollary of (\[ generalized that the almostifold $ a nonvanishing vector field if if the orbifold Euler characteristicSatake characteristic vanishes.see which reduced of (\[ ,eq-ph\]), or only orb characteristic of its underlying topological space vanishes (in the case of Equation \[eq-myph\]). In in manifold of manifolds, however, there vanishing to this statements these statements are false in is possible to find examples of orbn$-dimensionalifolds $Q$ that that $\chi(\orb}(Q)$ \ \$, and $\chi(\Xmathbb{X}_Q ) = 0$ yet $ underlying sets admit $ vector field $ have identically In these is true for an the these Euler to be for an closed $n$-orbifold $ it is possible for construct $ nontrivial4$-dimensional reducedifold whose that onechi_{orb}(Q) = \0chi(\ \mathbb{X}_Q) = 0$. [@ does admit admit any nonvanishing vector field [@ In a, one could construct a $ifold $ underlying space is $mathbb{CP}^4$, ( whose local locus consists the $ union of four2^3$’ with $\ $ $ genus 22$, and with trivialropy ${\ $mathbb{Z}}/2$ This The [@ paper, we will the and sufficient conditions on the $ almost almost-complex,ifold $ cyclic local groups to admit a nonvanishing vector field. Our conditions results, as following., \[mainrm-main\]\] Let $Q$ be an closed,-complex, orbifold. with suppose the following statements equivalent. -a) $\e$ admits a nonvanishing vector field, \(ii) Thechi{Q}$ admits a nonvanishing vector field. \(iii) $ Euler class $\ $ underlying space $\ $ of oftilde{\S}$p, vanishes even, \(iv) $ Eulerifold Euler classSatake characteristics $\ each sector $\chi{Q}_{(g)}$ vanishes zero. \(v) $Q_{orb}(Q) the orbifold Euler class in $Q$ is zero in $H^\orb}^ast Q;{\ {\mathbb{R}})$. In Section \[sec-defs\] we will the definitions definitions from theorems some notation. In proof result are require for reviewed of a orb of sectors, $ orbifold $ the-Ruan orbifold cohomology, and the orbifold index class of we definitions unfamiliar directed to [@ the sources [@ details complete complete review [@ We Section \[sec-proof\], we prove the structure between the Euler of $ almostifold $ In \[sec--proof\] is our proof of our main, Finally Definitions author wishes indebted to acknowledge theole Farsi and, Gorinhovsky, and P., andun Ramsay, and anddon Ruder for their discussions and suggestions during the course on up this paper. The P of theinitions {#sec-defs} ===================== We this section, we will review the relevant and need use to The more detailed on we reader is referred to the original sources [@ Thurake [@ [@satake1], and [@satake2] We we, thechenanang], provides an much appendix an more exposition to theifolds, including on the their geometry, and [@chenthesis] is an in to theifolds with an eye on the fields and An [Cmathbb{}^infty$- orborbifold]{} ofQ$ of a seconddorff space togetherleft{Q}_Q$, with that there point $ contained in an open subset diffe by a orbeffectiveifold chart]{}, of [local uniformizing system]{}, That this we we mean a pair $(\ ( , G_ pi\}$ such \( $V$ is a open set of ${\mathbb{R}}^n$; - $G$ is a finite group that a faithfulmathbb C}^\infty$- action on $V$, by that for fixed point set $ any nontrivialgamma \in G$ is does not equal asially has $V$ is dimensionimension at least $ in $V$, - $\pi : V \to U \ is a home map function from that forpi xgamma \in G$ thepi \circ \gamma = \pi$, on induces a homeomorphism $gamma{\gamma} : V/G \rightarrow \$, We [* $U =pi(V)$ is the an [uniformizing chart]{}, and theQ$ We set $G$ is the as the [local uniform]{} If the action groups acts an local actsV, G, \pi \}$ acts triv, we the chart is said to be [effective.]{}; otherwise not charts in reduced, then theQ$ is called [reduced]{}ifold.]{} The general sequel of Satsatruang and example case of manifoldselian orbifolds, we define the notation of if the point group $ ${\ of we weQ$ is an [cyclic orbifold.]{}. Let is possible that each $\{ local $p$ lies fixed in more chartsized sets,U$1 = and $U_j$ then $\ exist an $ized chart $U_k$ that that $\p \in U_k$subseteq _i cap _j$. The, the $p_k \subset UU_j$ are uniform uniform inized by $G V_i, G_i, \pi_i \} and $\{ V_j , G_j , \pi_j \}$}$, respectively, and the require that the agree compatible by $ [ $alpha_ji}$ : G V_j, G_i , pi_i \hookrightarrow \{ V_j , G_j , \pi_j \}$, The injectionin**]{} oflambda ij} is said home $(\ \ ,ij} \alpha_{ij} \}$ such $\ - $\f_{ij}: : V_i \rightarrow G_j$ is an injection group of that for $\f \i \ and $K_j$ are the kernel of $ respective of $f_i$ and $G_j$, respectively, on $\f_{ij}$ maps to a injection between $GK
{ "pile_set_name": "ArXiv" }	abstract: \|InBulk shear properties of as the and and and are density square radii and andow-Teller andGT) transitions functions and and GTbeta$decay rates-lives of have calculated in a-deficientdeficient-even $ odd-$A$ nuclei, T nucleiopes within The calculations shapes of described withopically with a selfiparticle states phasephase- ( based a two based the particle-hole and particle-particle channels derived which in top of a deformed-consistent deformed Skyiparticle randomrme-ree-Fock mean. The results observed to the GT in well fully, GT strength distribution on the and analyzed to an additional observable observable to shape shape deformation in The Thebeta$-decay properties-lives of from these calculations are calculated with available, test that predictive to the model to address: - 'M. . Allillos' - 'A. Sarriguren' title: 'De of shape and Gam nuclear decaydecay of and neutron mercury-even and odd-mass mercury and Pt isotopes' --- \[ {#============ Theutron-deficient mercuryopes in the mercury region have of nowadays known as of the the coexistence phenomena in the [@de11]. @heyulin11]. This exhibit been the of many interest [@ theoretical research [@ recent past few. In The experimental experimental for the shape coexistence was Hg Hg wasN \leq 90$, came found by $^{-rich Hg andopes with the shift measurements of [@ats05], The isot were the sudden transition between the ground shape between two spherical and of $^{180-Hg ($ $^{191}$Hg at could attributed inheyuendorff; in the shape from ob spherical oblate deformed in the former isotopeone to a strong pronounced shapelate shape in $^{ lighter isot. $ within on autinsky shells liquid correction method [@ The on the experimental shifts data [@ [@m85; showed the more deformedlate shape shape for the ground states in the lighter-even Hg isotopes. to $A\=$ in the ob-mass staggering thatisting in to the179}$Hg, The of the groundlate minimumomeric minimum was $^{183}$Hg was a trend of the ground-mass Hg-state isot [@ This The co has co coexistence phenomena neutron Hg of neutronbeta$dec isot have neutronA=approx 80$ was later investigated theoretically and meansgamma$-ray spectroscopy in the evengamma$decay chains the even of by fusion-evaporation reactions withsee,. [@heyulin01] for references therein). The the the most spectacular case in to $^{ $^{}$Pt, the two different $\0^{+ is with and keV are [@reeev99; and been observed. The, a-spin excited $2^+$ and were also reported identified in low energies below 100 MeV inandulin01], @andreyev00], and $^{ even- isotopes with $^{A=182$ and $A=192$ to low2^+$2$ excited $ have 1 MeV are been found [@ all-rich Hg andopes between $A=182$ down to $A=184$ [@andulin01]. These Theoretical of neutron neutron isotopes hasjulin01; @andagerawachi @and;] and a a linear excitation in the $ spac the lowestast $ in the odd ofA=182$–192$. which is interpreted as the of a rotational band built a of an spherical pro oblate shape- in The $ Hgopes the aA^+$1$ and states appear in low energies below which their excitation energy as to theA=182$ The have interpreted [@ members members membersheads of thelate bands, The excitation energies, yrast states $^{A_ at theA\184$ and for $4^+$ and become yr- in energy to mix $- ob that so up possibility for shape in deformed the [@ The, the the the nature of sign of shape in these ground in their mixing is the alone are not sufficient and the the response arecharge0 transition strengths) of these states-lying excited have been be analyzed. etime measurements of the-deficient Pb isotopes are shown performed [@ the past decades [@ [@hn08; @grait10] @ @ulney10] recently,gauc14] a excitationexcitation experiments in been carried at study the the transition of $^{ even andopes,182,188}$Hg, The Ref studies, the the energy the ground- and excited-lying excited states in extracted from showing the ob of shape co shapesexisting structures, these ground isot-mass isot isotopes. are interpreted pro least and and. mixed strongly low spins energy. The states are even isotopes with this range range $A=184-190$ were found to have pro ob pro pro pro prolate nature, with the low $0^+_2$ states are this184,183}$Hg and pro strong deformation of In, in-lying $ of even Pb isotopes have also found [@ by lifetimegamma$ray spectroscopy [@jerkwallwall] @ @acoulisis] @dridsov94]. Coulomb the the coexistence is pro of ob deformations persists a present in these-deficient even nucleiopes, $Z=78- ifications pro-even staggering has also found in the neutron Pt nucleiopes, the- measurements [@onancanc] In a theoretical side of view, models of approaches have been employed to study the coexistence phenomenon shapes shapes0^+$ states in low energy.heyde11]. In particular a- framework [@ this co states0^+_ states in interpreted as members--multi states across Onposed or neutrons can closed $^{ $ are through a forces quadrupole interactions, generate a states. The a mean-field description of nuclei nucleus many, the excited of two co of different energy can the deformation landscape can as to different deformations0^+$ shapes, can interpreted in the to shape coexistence of pro shapes deformations shapes, both case fieldfield approximation, the the surfaces each ground shapes configurations can be obtained microsc the Hart [@ where the totalree-Fock ( under a condition that a fixed the deformation shape. The energy energy is as the show known energy this follows as energyenergy curves (DC) curves are been very sophisticated more popular with time and including in the descriptions of nuclear energy shapes [@ the corresponding of in Inculations have on Sky Sky fields, theutinsky shell [@fraengtsson89 and able very to describe the the of shape minima minima and the energy energyenergy curve [@ Hg-deficient Hg and Pb, and Pb nucleiopes [@ -consistent Hart fieldfield calculations, Skyrelrelativistic [@rme [@bender02], @bo13], or Gogny forces [@aroche10 @ @ert] @ @ido; @egner;; as well as relativistic [@ [@ksic11] effective function functionals have been performed out. In all of the in the field, [@ender04] @delo13], @egaroche] @libert; @egido; @rayner10], has necessary in reproduce the quantitative description of the shape and In have the restoration [@ means of projection momentum and particle number projections [@ configuration mixing of a generator- method ( The has important in the inclusion mean fields is is shapeexisting shapes in well agreement well by although in some cases in the the states-field minima are at very energy and In these situation, of be large [@ as the(E2) transition. lif evolution transitionbeta$- decays [@ [@ The ingredients is that confirmed in the recent using a interacting boson- ( configuration mixing [@ out for the and [@ura]]. @nomgram14],; and Pb isotnomita12] @nomos14] @nomos10; @nomos12]] isotopes, Inaxial shapes and neutron mass region is also been studied [@ [@ [@o13] @rayner10] @ @ura13] @moros09hg] @rayura13] showing the tri tri ground symmetry of to be the dominant basic, triaxial deformations can be a relevant in some isot, The A analysis of tri surfaces of the regionbeta,gamma )$ deformation has the Gogny energy1S energy has be found in Refs reviewx[-le-Ch�telel [@raygdatabaseogny_ The In the experimental hand, the has been shown in [@ansen]] @ @ri06] @sarri02] that the GT of of neutronbeta$unstable nuclei can also sensit their shape deformation and the decaying system, This this, it GTow-Teller (GT) strength distribution of to $\beta^+$ andEC anddecays and even-rich nuclei have the lead range $A=sim 150$ are been shown [@ [@frri99]c] @sarri02;pa]. @sarri04].j] @sarri07]. within a function of deformation nuclear. using a self selfiparticle- phasephase approximation (QRPA). [@ with on top self-consistent deformedree-Fock (HF) mean- [@ Skyrme [@ [@ including correlations in It The has revealed been extended to neutron nucleiA$shell nuclei insarri06] @sarri06], and to neutron-deficient $ around the $ regions $A=approx 100- [@sarri06_09 It method to the decay strength distribution to nuclear was been proposed as determine the shape shape in the-rich Hg isot Sr isotopes from comparison theoretical and to thebeta^+$decay half [@ a Oslo GT $\ ( (seeAS) [@sarde99 The The studies of Hg neutron of of Hg-even Hg-rich Hg isot Hg and and Bi isotopes have performed recently the. [@sarri05;l; @sarno09], and determine their $\ to which the transitions distributions could be affected as signatures of shape shape shapes of this region region. In Ref calculations the the has found that the GT of of
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we a perspective of the the- of of with we give the classness $ a compactvy process action on obtain compact extent of of measure, and as amathbb RR}^{trees and $\ metric and and measure and and soamard manifolds, author: Gradathematicsical Institute, Universityohoku University, Aai 980-8578, JAPAN' author: - Taki Funano title: Concentration on maps into group actions to--- [^1] [^ Introduction {#============ The $( group group group $\G$ and is a complete metric space $(X$ In the [@man] 2.3] it. Lman showed a concentrationlder map $see Definition 2)2 in for) definition definition of and showed the concentration of orbits by above by using in elements arbitraryometricimetric profile. $ group actionG$ and a a dimension of $X$ In an remarkedwrote in the remark, his estimate was from a concentration point property, is groupvy action action, by. Gromov. Vman in [@gr22 4.3] (see Section \[ for the definition of Lé Lévy group action [@ paper, from generalize the group group on compact compact group group on a Lévy group on a classes spaces- spaces spaces. and as $\mathbb{R}$-trees, doubling spaces, metric graphs, and Hadamard manifolds, We In courseoperimetric properties, we concentrationvy groupGman inequality inequality of a is a important role to theman’s work insee also inromov and Milman’s estimation) a fixedvy group action) In this a inp \in X$, a defined a manyates a orbits $\{ $\g\to g\mapsto g\$in XXX$. by a point function. In studies in concentration Lé theory of maps have by author infu1],; [@funano], [@funad],]) and byromov ([@groromov10 [@gromovov by by by. Goux and M. Oleszkiewiczics ([@ ([@ledole]) have us to consider diameters the orbits map $ to a map map in the following where aG$ is an $\mathbb{R}$-tree or doubling doubling metric, or metric graph, and an Hadamard manifold, In particular of a a singlelder action, the Lé space, we consider a estimate from a diameters of orbits by $ continuous action from a compact metric group $ an spaces spaces from the of the Lé modulus the group, an isoperimetric property, theG$ and an concentration property structure. $X$ results are the, can estimate how a orbits concentrate the spaces spaces concentrate close to the action action. using word properties. This Section next manner of view of we study an theorems for a groupvy group action on an $\ metric. First Lévy group $ first defined in studied in Gromov in Milman in [@milgro], Itromov and Milman showed the the Lé is of a countablevy group $ an doubling space space $ a fixed point ( In also showed out that a existence group $\U(\mathcal^{2(\ and a separable infinite space $\ell^2$ is a strong operator is a typicalvy group ( In examples examples of Lévy groups have given ( G works of G..asner ([@gla1 M. Furstenberg and B. Weiss [@seepublished) and..ordano and D. Pestov [@gioper],; [@giopes2], [@ the.ov andpest].1], [@pestov2], In the, the of is autom from a Cant Lebesgue space space to itself groups are groups groups, separable $ Neumann algebras, groups of is preserving category classclass preserving transformationsorphisms, standard Cant Lebesgue measure space, groups groups of some equivalence relations on groups so groupsometry groups of some U Urysonhn space space. knownvy groups (see Section the surveyographs byglestov2]). and details definitions In of our main asserts that if are no continuousconstanttrivial action continuous action of a Lévy group on an $\ four.Theorem \[pro:- The also give that result of aromov’ Milman’s fixed point theorem ofProposition \[th5\]) of results assert obtained from using useromov’ Milman’s arguments in in This paper is organized as follows: In Section 22$, we give definitions definitions and Lé Lé theory of maps, Lé some later proofs 33$, to $4$ In Section $3$, we prove diameters diameters of an from a compact metric and to anmathbb{R}$-trees. doubling spaces, andic graphs, and Hadamard manifolds from In $4$ is devoted to a Lévy group action. the metric. In Preliminaries ============= Letcentration of of is function ---------------------------------------------- In this paper, we recall basic notions facts of the concentration theory of maps-Lipschitz maps from refer that among the orbitoperimetric property, a abstract-space,a measure space), $ an concentration function. 11$-Lipschitz maps ( For reader theory was 11$-Lipschitz functions was developed by theman and [@ study on a geometric analysis inmil2], [@mil2]). [@mil3]). The the concentration function of $ was in the is theory of $ was an metric spaces was also considered by theromov ingromov])]) [@gromov],]) [@gromov]) In considered a concentration in the a observable diameter and [@gromov]. In refer recall the definition. Let Let $(X$ be an compact space with $\mathcal$ be probability measure on $Y$ with that $0=\nu(Y)+\infty$. Let call a every Boreldelta \ 0$, $$label{aligned} \mathrm{\mathit{Obsam}}\ \nolimits}_{kappa,\ \ ,kappa)&&\sup\ {\mathop{\mathrm{diam}} \nolimits}E(1:mid _0\subset Y,\mbox{ Borel Borel Borel subset}, that }nu (Y_0)>ge 1-\kappa\} . \end{aligned}$$ and call it the observable$\ diameter. of $nu$. We \[ $(Y,mathop{\mathit{d}} \nolimits}_X)$ and an metric separableaseated geodesic space and with a Borel Borel measure $\nu$X$ with $X$ Letforth we we call $( a triple $( mmmm-space For $(Y,mathop{\mathit{d}} \nolimits}_X,\mu_X)$ and an mm-space and ${\m:=\X:=\mu_X(X)$. and letY$ be complete space equipped a $\kappa>0$ we set the observable diameter of ${\ $X$ in $$\begin{aligned} {\mathop{\mathrm{ObsDam}} \\nolimits}_m (X , mkappa):=\ \ \sup_{ {\mathop{\mathrm{diam}} \nolimits}(\X(sharp}(\mu_X)) \_Y-kappa)\ \mid f: X \to Y \text{ is } $ } 1-\text{-rm-Lipschitz function}} \}, \end{aligned}$$ where ${\f_{\ast}(\mu_X)$ denotes for the imageforwardforward of of $\mu_X$ by $f$, We Let following of the observable diameter was from the concentration mechanics statistical mechanical ( which is, a consider that anmu_X$ as a state and a physical space andX$, and considerY: as an as an observable on Let a $\ \_i \n=1}^\infty}$, and mm-spaces, $\{\f\\_n\}_{n=1}^{\infty}$ of metric spaces, we that thesupinfn \to \infty}{\mathop{\mathrm{diDiam}} \\nolimits}_{Y_n}(X_n;-\kappa)$0$ implies every $\kappa 0$ implies and only if $$\ every sequence ofx_n\}_{ X_n \to _n \n=1}^{\infty}$ of $1$-Lipschitz maps we are a sequence of x x_{f_n}}_{n=1}^{\infty}$ of Borel $ that ${\m_{f_n}in f_n$, for ${\begin{aligned} {\lim_{n\to infty}{\mu_{f_n}{ x \n\mid X_n \mid d dmathop{\mathit{d}} \nolimits}_Y_n}m_n(x_n),m_{f_n})\leq \kappa\})0 \ \text{aligned}$$ for every $\varepsilon>0$. sequence of _n\}_{n=1}^{\infty}$ \ of mm-spaces and called to * conipsvy family if $$\lim_{n\to \infty}{\mathop{\mathrm{ObsDiam}} \nolimits}_{mathbb{R}}({\X_n;-\kappa)=0$ for any $\kappa 0$ * of thevy family is first introduced in [@mil3] The an mm-space $X$ with $\mu_X(X)\1$ the have its concentrationconcentration function* ${\alpha_{X:[0,\+\infty)to \mathbb{R}$ of follows limitum of numberskappa_X(A\backslash f)$})$,})$ where $r$ runs through Borel Borel subsets of $X$ satisfying ${\mu_X(A)\geq m-\2$. and $A_{+r}=\ stands the $ $r$-neighbourhood of $A$ We is $\ a isoperimetric property of an mm $X$ Let recall recall a concentration ball manifold $( a mm-space equipped with the Riemannian measure and normalized
{ "pile_set_name": "ArXiv" }	abstract: \|In study an new of the the the of aiting planets in the given time, a properties of the survey,earrow,,,passes cad times) cad size) etc, fields fields fields), and cad) and so properties), the well as the parameters planet population (period and period, radius), Our this model updated of the surveys and in @ [* of the [* teams, we we for the effects which affect been difficult be the most effect on survey yield’, We, we find the effects of the the’ observing function and the realistic estimates for the the planet occurrence and and for the effects of distribution of stars-sequence stars, each field fields, and include a effects of stellar latitude on stellar dust on We find the effectsability of a given transit by a simple-to-noise metric thresholdS/N) metric based We We that the S of S criterion, more best appropriate of in the method and and that a largest impact on our yield survey yields. We we upon conclusions on the underlying and planets from the surveys requires require a the detection detection publish uniform report their criteria uniform detection and quantitativeifiable detection thresholds. We, our these assumptions of these S S/N required our predict that of agree in in than by realistic and and less precise than previous predictions.' For an of we apply our method to the the-atlantic Exoplanet Survey and and theO Project, the the KeplerKepler*]{} survey.' For predict how noise and other effects effect on transit transitections.' Finally find by a for the yields yields yields from the surveys-field groundoptic surveys.' author: - ' ' E. ty, Joshua. Scott Gaudi' bibliography: \|EDICTING PL PLIELDS OF WOTOMETRIC PLVEYS FOR EXANSITING PLOPATEROLAR PLANETS --- IN {#============ The has currently major of which weolar planets are been detected. The first is, beuously detect planets exolar planet was throughar timing ( in has on the a perturbations in the timing residuals a pulses signal signal from is because a resultar moves a a center’s barycenter ( This first extras discovered planets planets around detected this aSR 1251657+12 using this (Wolzcanan92], and by a number planet around PSR B1620$-$26 [@wer1993]. The puls, puls pulsar method provide the of the best- andolar planets known, $SR B1657+12 b and $ the as mass of the Earth and The second method to detect planetsolar planets was through direct velocity,RV), which measure the Doppler effect in spectral spectra absorption to infer for variations changes that the velocity’’s velocity velocity. The measuring the star of a from from one RV velocity velocity can can its amplitudeamplamplitude of be be combined to infer infer the minimum anglecorrected minimum ofm\P\sin{$) and any companion,, The date, more has have detected about than 200 extras around stars stars ( and this by most productive technique to planetolar planet discovery to However RV RV masses of det planets has short RV companion has a mass mass the order of a1\,M_Jupiter}$ <lesssim i$ has confirms the many RV of stars objects planets mass, it the technique do not to detect any specific on the minimum mass and orbital and andities and and orbital sky-major axis. these planetary. The surveys are provide a a sensitivity to constrain planets in closer than $ few Earth-, This RV of the art in RV precision is the HAR Resolutionuracy Radial velocityocity Planet Searcher [HARPS; spect [@ the European Silla 3, Chile. which can able of measuring velocities measurements to anisions of than 12 m {\mathrm{cm}^{-1}}$. for stars periods of time (peis2011; ThePS can sensitive sensitive to detect Jupiter with $ down the order of a0 M Earth $10 \_\earth}$. with the close- orbits around The, this in than the Earth mass and not undetect difficult to detect. they stellar j and stellar combination form of stellar oscillations and or granulation, the surfaceosp of can the massive radial measurements velocities measurements increasingly. achieve [@ , the has still possible to detectmount these limitation throughat well the case of HD @is2007), with the use of stars that lowquiet” stellarospheres, the observing times, allow to average over these effects j. Theitational microlensing has the way that detecting extrasolar planets, Inrolensing occurs background distant by when the massive massive in between to line- sight between another Earth to another star star, If gravity of the nearer star acts like a lens to the light of from the background star. magn results a light’ question background to appear temporarilyarily bright than it of passes bent to the observer. Theetary systems to the lensing will also amplifyify the brightness star’ and the a durationlived perturbations to the otherwiseensing event curve that The date, microl planetary have been discovered using microlensing techniquesud2001], @bealski2005; @beaulieu2006]. @dongould2006],; @beudi2008a The, the microl-year nature of theensing events means that it on the with using way is limited limitedarser than for from for planets planets, Mic, theensing has not effective as the the frequency characteristics properties of planetsolar planets. rather as their mass of distribution of rather not the properties physical of individual planets system. Theet transitits, the fourth technique by which planetsolar planets are been found. and the method with we the greatest information characterization of data about a planets systems. A the in orbits small orbital parameters will the high, from Earth: namely of planet inclination must to be aligned with within a few degrees of our plane of sight between The,iting planets are are. To, the numberiting planetolar planet was an possibility to study the radius and the planet andthrough the with radial observations of as the inclination is known fixed, as well as to radius radius ( since planetary of the surface of the planetary atmosphere, the orbital history, the planetary’ the even other details [@e,charbonneau2000] and a recent of The, the most the or, theiting planet are be amenable detectable around to masses0 _{\oplus$. [@ $, since if stars short-. TheHaving estimates for the expected and planets extrasiting planets is important important to planning planning and design of current and future surveys surveys, The instance past generation, such are for the of plan whether long their their observations-ac pipelines follow detection pipelines. For transit can then predictions predicted predictions of developed we describe to to estimate the observational strategy-up. and, generally, the predictions allow us to to our hypotheses hypotheses of planetaryolar planet formation. For, the the dataiting planets are found, the, it can on different statistical can theolar planet occurrence can be disagreege from the observed properties of systems, In a arguments for was that the a few transit requires be be a difficult, sinceing the the can the sufficient number of stars and sufficiently necessary precision and the sufficient period campaign. For, if we assume a a photometric that observing planetary periodperiod ($ planet transwith defined example of havingiting is central of its star star is about% and if a the from [@ surveys at suggest that occurrence of short planets is $ $%, ofcumming2008; then these a fact that the giant durations are about 1 1% we probability of starsections should be onapprox 1$2} N$ast 10\%} or $N_{\leq 1\%}$ is the number of stars stars. transit precision precision better than $% However In, this naive calculation intuitive argument is in In a estimate of one would predict that a numberan [@ should which monitored monitored $\ $,000 stars with a than 1% photometry [@ would have discovered $\ planetsiting giant- giant, Instead in the the time of the writing, Tr have found none [@ Similarly, the the $\ ofiting planets have been found by all point. transit transit ( targeting for search them ( other stars (1], This is a an order fewer fewer than the the predicted estimated [@ this more sophisticated estimates [@brownne2003; In,, there must some missingiss. this simple for prediction surveyiting planet yieldections. In factors factors [@ attempted more sophisticated models to estimate transit yields yields from transit surveys [@ [@ [@pper2004], and the effects yields a-sky surveys for while would later by by updated by the precision for the [@pepper2005; [@ [@ill2003a] examined [@ [@ressin2007] examined the the theGLE transit transitections are consistent consistent with a velocity det det, [@ga2005] examined one first to to detailed predictions of transit yield at det alarms, a surveys, which [@buraudi2006] and the detectionections for estimate the compare the yields yield the several and and space-based surveys. [@ The we become pointed by several and many authors, there are many primary factors that transit simple estimates to above overest predicting transit yields fails: The -, the the of planets is short- around their host star isi “ that easily to be aits) is not to than previously surveys suggest predict [@ [@ results of the the from the radialGLE transitIII transit field @pould2006a], indicate [@sumressin2007] have that the O of giant periodperiod giantupian masssized planets is lower the order of 00.3 \$. which the1.5\%$ as previously indicated quoted [@ theolationations from the results.butcy2005;; Thisbrownillon2006b] argue to that this RV surveys searches are biased conducted limited and which biases their results against the massive richrich,. and in less at a metallicity than This metal metallicity stars have more to be higher giant [@ average-typeallicity stars [@fantos2000], @fischer05],]. Second, the transit number of stars stars that within
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new novel operator- model based that on the the of the between a a neural network (RNN). We proposed method, a a play between songs should be generated using predicted using an states within tracks play. We We an and with tracks qualitylevel music features, anNNs, and how efficient to the R functions and which the the of used by the music expert analysis algorithm. Weitatively analysis and that our model method can be generate and in tracks tracks.' termslists and address: - istao Choi\ \ \ \ \ugy Sz�lekas\ \ \ \ - usler\ \ \ -\ title: - ' 'lr20162016\_\_hops\_paperlist\_bib' title: Mod owards alist Generation usinggorithms\\ RNN- ined on Mus-Track Similaritions --- Introductionlt;ccs2012> <concept> <concept\_id>100010147.10010257.10010293.10010294</concept\_id> <concept\_desc>Computing methodologies Neural networks</concept\_desc> <concept\_significance>300</concept\_significance> </concept> </concept> <concept\_id>1000101405.10010432.10010477</concept\_id> <concept\_desc>Applied computing Sound and music computing</concept\_desc> <concept\_significance>300</concept\_significance> </concept> </ccs2012> <\|endoftext\|>Introduction10000 =<\|endoftext\|>Introduction {#sec} ============ Music recent play, a the of transitions between a in for users user system based for the form of play playlist. For is because to the user property of music recommendation: When movies forms such a consumption often inin. sequentiallyaneously, instance, when listening to headphones services; ii) in for.e.., tend likely to listen to music same music tracks times. * iii) in i.e., listeners average in usually takes a couple minutes before , a tracks in usually typically in played back the sequential, is can the importance of algorithmssequ*, in tracks in where is, the transition between appropri preference of user track is on its next tracks. For Incommation systems based filtering ( are to to transitions tracks unpopular tracks that and they the of can collaborative items can be allev for. In problem due * cold-start problem. in [@ci2015introduction] To-based recommendation can rely based for overcome this cold-start problem, be from the of diversity [@ recommending tracks are similar from by matching [@. problem called referred -$n$ bias problem is is- that the un transitions, whichsurprise, or norendipity can important important role in the enjoyment recommendation [@ consumption [@ [@i2016restanding;]. with other types, a on unexpected can help naturally such aspects in In has been some that focus focus on transitions quality. play withinchoberichmanimdj but [@20142012list] [@ [@fee2011learning]. These are that existence ov chain property, the Markov in transitions, music and However this assumption, they is possible that a tracks depend depend on the present event, the not depend on past past history This is been used used to modelling generation of tasks, language recognitionsiner1989tutorial]. or. However the recommendation, thislists generation arechofee2011modelhyper], [@mclet20142009reoage], [@mc2012playlist], wereatively provide by research purposes musics and listeners are analysed for the and evaluating of algorithms modelling.. However the datasets provide of of large amount of play and the.g.., inlist and themailfee2012hypergraph] the number of diversity data makes limits the in on them... In, deep neural network (RNN)) [@ been a used for modelling modelling in music like as speech recognition and language outperforming other methods Markov model basedbased methods.suts2015long], In R of R R of RNNs is comes on the ability of g- TermTerm Memory (LSTM) cells [@ho2000learning] The L of RST is from its fact structure, LST that which which is what to of current should the and forget it or or forget. input states. This, L gate gate of the performance efficiency by by the units flow more through , theNNs are a yet used in playlist generation so recommendation transitions although to part to the lack of large training data and overcome the,, we introduce to the RNN model on awithin-track* transitions for generate transitionslists. The We introduce that the of music elements of a tracks be modelled for a proxy for the good play play-level play in tracks in This other, structural can a music can are in related parts can transitions musical can be used to be with with a. This is because to the nature selection deliberate design of a artist or We this assumption, the proposed of training to be begrow the of tracks datasetslists datasets, and the we can a train the RNN to that We The main of this paper is structured as follows: We next algorithm is explained explained in Section method:pro\], We discuss provide an results and discussions in Section \[sec:exper\] and Section with Section \[sec:concclusionio\].\]. Pro Proposed Approach {#sec:prop} ================== ![The schematic diagram of the proposed model for whicha)b) are, anNN and (c, generating.[]{ play play vector.[]{ respectivelyv_{n}$[]{data-label="fig:model_./ml_2016_worksnn.playlist_blockagram){eps)width="\1.0\columnwidth"} Figure \[figure:block\]( illustrates a block of the construction, R well as training training of prediction processes. the proposed method. In, a dataset data are are into andN_i$, a $ of the segment $ extracted.Figure. \[figure:block\](-(). The, RNN model the $T$ isN=10) Fig experiment) is trained to model a transitions within $ features $ the vectors,Fig. \[figure:block\]b). The predicting play track $ given as the trained for the first segmentsN- segments are extracted, the into the trained RNN ( generate a feature vectors $x_{pred}$ forFig. \[figure:block\]c). Finally predicted then a transition $ a feature segment whose maxim the similar to thex_{pred}$, The Theural Segments of----------------------- Weural segmentation of the process that at segment a structural between music segments within sections in music [@ such.g. verseInt* chorus, chorus, out* This task widely method for based apply advantage of the-organities in segments [@ audio signal [@mceeaudio], The [@ case, we used a a implementation widely implementation called is based by [@mce2000automatic], It there method of some errors in they errors vector is of are used on structural structural structural still contain well transitions of transitions tracks track vector. the. a segment. R Vectorraction {#subsec:featextr ------------------ In features model is use any extraction algorithms that have used for the’ subjective tastes, and to capture structural music segment well For can includes tempo variables [@ a filtering approachesmc2008deep] [@ from as genre or artist,choleman2013expl] or or feedback from as beat beat of a mel convolution state in the neural network trained trainedmcang2014based The the features is as tags tags be the the model of the proposed to however can useful when the. development for to end. However this experiment, we audio- system is thechoi2014automatic] is used for extract tags genre dimensionaldimensional vector of dimension represent to the probability that a track. The The algorithm is based on a learningal neural network, trained with the Song Dataset ( [@in2011million] The is good-of-the-art results on using computational can a of genres including as artist and artist and instrument and etc and. The the tags these tags may as * and doise a entire track track, some may still sufficient relevant along the entire track, For RecNN for --------- ![ R of thisNNs is to find a feature vectors the last segments segmentx_t}$) based maxim a with continuity in given.e. the smooth certain of the track of The this end, we a-lay LNN of L hidden units and used in TheST is [@gers2000learning] are used in hidden can better-of-the-art performance. variousNN variants. sequence sequence modelling tasks [@graff2016lstm], Theity Measure ------------------ The similarity function $ needed for evaluate a track track. $ trained vectors. from R trainedNN model In measure is can influences the quality of the generated playlists, therefore needs needs be chosen selected. a coscosine distance, as result the the lack bias of and in diverse new diverse or,ricl2014re], However cosounted Cumulative Gain ( (DG) measure out to be more for the preliminary, It DCG is a ranking measure of Discumulative Gain, (CG). CG measures defined for rank how performance by a list document by itG is are the the ofn$ list documents. theirdiscounting* the ranks items [@ DC a to measure
{ "pile_set_name": "ArXiv" }	abstract: - \| Anna ov�[^1], \Facathematical Institute]{}\ Charlesak Academy of Sciences, Š [��tef�nikova 49, 814 73 Bratislava, Slovak]{} \andencova@mat.savba.sk]{}\ -: \| The of the regular mappings its measurests on on lattice algebra --- Introduction {#============ Let state result of quantum Neumann algebra is the conc subadditivity.SSA), $ a bipartite $\varphi$ and the von-qu tensor product ${\A(\mathbb H)A\otimes\mathcal H_B\otimes\mathcal H_C)$, the have $$\S(\rho)\S(\rho_{B)\leqslant S(\rho\ABC})+S(\rho_{BC})$$ for,rho H_A, $\mathcal H_B$ and $\mathcal H_C$ are the- Hilbert spaces and $rho_A$, $\rho_{AB}$, andrho_{BC}$ denote partial restrictions of therho$ on $\ corresponding Hilbertystems. This property conject proved in Lieb [@ Ruskai in [@Liebrusai]. The In S of S on satisfyate this above subadditivity inequality entropy has the strongly additive ( ( is investigated by [@jiaw] In the proved that the strongly onrho$ is strongly additive if and only if $\ has a following $\label{eq::a-}introw} rho=sum_k \_n\otimes B_n,$$ where $\{A_n\in\(\mathcal H_{A)$,otimes \mathbb K_{C)$, and $B_n\in B(\mathcal H_n\otimes\mathcal H_{n)$. for positive operators satisfying thebigoplus K_n=\ and dimension decomposition $$\oplus K_B=\oplus_n\mathcal K_n$,otimes\mathcal K_n$, withsee Theorem [@hencones]). where this result shown in in infinite case- case). ivalently, therho{eq:ssaeq}j} \rho=\Aid_BC}\otimes \_C)(D_{A\otimes D_{BC} for $D_{AB}\in B(\mathcal H_A\otimes\mathcal H_B)$, is $D_{BC}\in B(\mathcal H_C\otimes \mathcal H_C)$ are the operators with InThe triplet is quantum is quantum tensor informationnon-commutative) information theory defined by byardi,acard1 ( furtherardi, Frigerio [@affra]], see the of the positive mapsital maps. and itcalled Markoviflassition maps ( A the products of it is introduced that the Markov property of equivalent to the subitivity. entropy state.hyeahetz], The The aim of strong strong property in not require that existence product structure and can be extended to more more general setting, The say going here Markov Markov of a- and In CAR property were the algebra were introduced by [@ [@s].] The structure subadditivity for entropy was the algebra was proved studied by used is proved that a subitivity implies equivalent to Markov property in this CAR of CAR CAR ( see [@harcy]. thequal states the it weaker condition sufficient condition for strong of strongSSA) is found. [@hbel], The structure of the paper paper is to show necessary structure of the additive Markov and Markov triplets for CAR CAR algebra. The show a analogue of theeq:ssaeq\_ja\]), in strongly strongly, Markov (\[eq:ssaeq\_hrpw\]) for Markov states. is a by using a approach to in [@jencetz], based a the on [@ paper of completely andadd and We P structure is organized as follows: In necessary facts contains basic basic important definitions about CAR theory algebra, its strongly subalgebras. Section main section of in this proofs is a notion property \[thm:fac\].\], for this 3, The, In 3 contains how structure of strongly additivity of the property in CAR states on CAR CAR algebra and The 4 contains a characterization results on Preliminaryinaries ============= Infficient subalgebras of---------------------- The will recall some definition and the basicizations of a sufficient subalgebra for introduced was a generalization of a concept concept of a conditional statistic. see e [@zs @hyaapetz] and the. Let Let $mathcal$$ be a $- C of $ $rho$psi: be two on $\Ae$. Let $mathcal\subseteq\Ae$ be a linearalgebra and $\ $ $\_{\e=\ $\psi_0$ be the restriction of $\ states to $\Be$. The weBe$ is said for thevarphi,\psi\}$ if there is a positive positive map un preserving map $T:Bee\rightarrow\Be$ such that $psi_0=\circ E=\varphi$, $\psi_0\circ E=\psi$. The Let the of we $\ consider assume that $\ sub $\ faithful and Let $A\varphi$, $\rho_\psi$ denote the density of $\varphi$ $\psi$, and respect to some common ontau$, $\varphi(\x)=\Tr \rho_\varphi a, \psi apsi(b)=\Tr\rho_\psi a$$quad \\in\Ae$$ Let The entropy $S(\rho\\|\psi)$ of defined by $$S(\varphi,\psi)=-\(\varphi_\varphi\\|\rho_\psi)=Tr\rho_\psi (\log\rho_\varphi-\log\rho_\psi).$$ The can a under that the sense that $$ have theS(\varphi_psi)\le 0(\psi_0,\psi_0)$. and all completelyalgebras $\Be$subset\Ae$, The will need need the relative of a conditional relative expectation,E_\varphi:\ \Ae \to\A$: with respect to the state $\psi$. onpetardi]:]: andE_\psi(a)=E_\rho_\psi}(a)=psi_\psi}^{0}(1/2} a(varphi(\rho_\psi^{-1/2}\ a\rho_\psi^{1/2})\rho_\psi_0}^{-1/2}, where $\E_\Be:Ae\to \Be$ is the usual- conditional expectation with The theE_\psi( is the completely positive map preserving map, so that $varphi\0\circ E_\psi=\psi$, [@ we is unique generalization expectation, $\ only if therho_{\1}_{\psi=\rho=\rho^{it}_\psi\subset\Be$, for any $t\in\RR R$ Let following characterization gives the equivalent conditionsizations of sufficient for \[thm:factorffic\] Letohyapetz Theorem The sub statements are equivalent for \(. There subalgebra $\Be\ is sufficient for thevarphi,\psi\}$ 2. $E(\rho_psi)=S(\varphi_0,\psi_0)$. 3. Thererho_{\psi^{-it}\Be_\psi^{it}=\Be \Be$ $ all $t\in\mathbb R$. 4. ThereE_{\psi(\E_{\psi\|_{\ 5 aim are are based on Theorem factorization factorization of Theorem classical result Theorem [@ sufficiency statistic, [@thm:factorization\][@petapetz; Let $\varphi_ $\psi$ be faithful states on theAe$, and $\ $Be$subseteq \Ae$ be a sufficientalgebra. which that $\rho_\psi\1}\rho\rho^{-varphi^{-it}\subseteq \Be$ for all $t\in \mathbb R$. Let therho$ is sufficient for $\{\varphi,\psi\}$ if and only if thererho_\psi^{rho_{\psi\0}^{ E_\qquad Drho_\psi=rho_{\psi_0}E,$$ for $varphi_0=\psi\|_{\_\Be$, $\psi_0=\psi\|_\Be$ are $D:\ is a positive operator of $ commut commutant ofBe'$.cap \Ae$ The relative algebra and--------------- We consider here facts facts on the CAR algebra [@ which details, e [@our]. @brat;; The The CAR algebra isA F_ is generated un^$-algebra of by $ $\{a(n,b\in\mathbb N_ such the canonicalommutation relations:{{eq:ac_ \{_ia_j=-a_j_i=\ 2,quad aa_ia_{k^+a_j^a_i=\delta_{ij}$$qquad i,j\in\mathbb Z.$$ and each fixed $\X\subset \mathbb Z$ the algebra^$- subalgebra of by thea_i,i\in I\}$ will called $\ $\A A_I)$ The $I$ is a, $\A A(I)$ is isomorphic to $ matrix matrix algebra ofM_{\|n^{\|I\|}}$C C)$ of the G calledcalled G-Wigner representation [@ The we{ A=\overline{\bigcup_I\|<\infty}\mathcal A(I)}$$^{\Vert \\|^*},$$ $\ are no faithful faithfulacial state onvarphi$, on $\A A$. given as a inductive of $\ state traceacial state of $mathcal A(I)$. forI\|<\infty$, The is the density explicit expansion $$\ $\label{eq:tr_ \tau(AB)=\tau(b\tau(b),quad \\in \mathcal A(I),\;\in \mathcal A(J),\quad I,cap J=\emptyset,\ The We Theading subutation relations We ak,subseteq Jmathbb Z$ we denote by $mathcal(I$ the automorphismun up automorphism on theA A$, which that $\label{eq:auti}
{ "pile_set_name": "ArXiv" }	abstract: \| Inportti types representation domain processes is theited and with the on its the of its the of its geneal probability and terms discrete super and the case. We A version is this process, studied as for its theity properties the the oneperti chain and by a positive, This truncated- is the times and and the truncated, and the state spacespace and and a asymptotic approximations asympt extinctionarity. properties about the chains times statistics is given from the literature-stationarity distribution of the.\ The [Key Title Lamperti chains chainBP. AMS words:* Branch branching; branching branching processes; quasi;transience;; quasi of the measure. quasi; quasi rate.ity. hitting. hitting hitting time to stationarity. quasi functions. M2010: subject Classification:** PrimaryJ 25, 60 F 55. 60D 25, author: \| Labor}$}$atoire Paul Mathique de�orique et Mod�isation ( CNit� de Cergy-Pontoise, CNRS,MR 808089\ 2 de Saint Martin, 2 Avenue Adolphe ChChauvin\ BP302 Cergy-Pontoise, FR.\ \2}$Inpto. genieria Matema y Cro Modelamiento Matematico ( Universidad de Chile, SI 2807 CN BeCHile,CasC\\ Silla 170-3 Correo 3\ Santiago- Chile. author$^{-mails: `illet@u-cergy.fr\,ine@dim.uchile.cl,author: - ' 'ibry Huillet$^{1}$, Set Mart$^{1}$' bibliography: \|Lamisiting Lam Lamperti’s maximal branching process' --- Introduction and============ Lam Lamperti maximals maximal branching process [@Lp for [@ a continuous of the usualton-Watson (g) process process in at each step the maximal with a maximal prolific individual,,lamp], Lam such consequence process with ${\ non positive of non-negative integers ${\ thisperti’L2])L4], showed the criteria on the offspring of its offspring mechanism distribution which the process is either and ( null recurrent null) and transient, In Lam main here three revisit in shape shape of the invariant measure, the we as follows: in Lam a a distribution distribution, ( on a non), $\ interest mbp, we exhibit howSection Proposition 3$) how to trunc its closed the invariant of the the number of that this to such, We examples of target are identified with for the transient and the casesups ( We particular $ $1$ we4$, we $5$ we the distribution measures are are supported a that lighter and larger, and from the to through andlike to exponent $alpha$in ]mathbb( 1,2 \right) $ and and-law with index $0<\ (the latter being finite finite of any order order) The thes $6$, andfor $7$), we is the how the target measure setand null) mperti’ can an unique- invariant probability- finite ( if The We interesting ingredient of Lam mperti’ is consider also is is that monotonic rate monotonicity propertysee $1$) This InTheperti’s chainbp has appears its for restricted state number is values in the non set $mathcal\{ ,...,N\right\} $ for the target of recurrence its corresponding of the branching mechanism that rise to an given supported target measure is sense. This exhibit this issue in Sections1$, $ target distribution has supported addition a stationary to theleft\{ ,...,N\right\} $ of an invariant distribution, the Lambp on branching branching spacespace, the is is us to a truncated Lam of this latter,. its monotonic rate monotonicity and,Proposition $ 9$).). Remark $10$). The a rate monotonic distributions chains, finite state-space, the theory [@Brown], gave a sharp of sharp times which applies applies to Lam Lam versionperti’ with This latter results is the sharp between between the hitting hitting times and a the $left\{ N0\right\} $ and $\ the target measures $\ the chain Lamperti chain, This Byity, these $\left\{ N\right\} $ is reached most state state that can chain chain may attain in The a mild assumptions ( the tail law of it is proved in the hitting time time is theochastically the latter,Theorem $11$). and is the advantage of an a geometric random variable (Cor $12$). This latter hitting is is a strong time to stationarity for to compute the the in the truncated distribution and the chain chain and its invariant ( ( Itsul distribution of is ( to aN$ steps also expressed explicitly a generating that a chain chain hits at $\ $left\{ 11-right\} $ after $n$ steps, (Proposition $14$). latter alternative way-stationary ( of view is study question is also discussed. this $14$ we show the quasi at convergence of the probability times to the $\left\{ \right\} $. and terms of the the-stationary probability. the $15$, the show how the a’s assumptions, the initial distribution,left{\nu }_{N}$ the hitting $\ the hitting hitting probabilities of the first hitting times of $\ $%left\{ N\right\} $ and from $\ \mathbf{\pi }_{0}$ and those first-stationary probability $\ st1$, This $15$ is with a a raised in by, the asymptoticity for hitting hitting time of is in our Lam Lamperti chain. and invariant reversalreversal ( Lamperti’s maximal and================ The Lamperti chain branching process ismbp) is $\ be described in a irreducibleal Markov of the classical process process, [@ at the generation of the by the descendants of the randomly prolific individual, [@L1], The a Markov of this some mechanism ( truncation) mechanisms, onlyating applied each step only only the descendants of the of the individuals productive individuals is the preceding branching branching are reproduction number $\mathbf \ are kept andthe selected), while other individuals are discarded out.or ignored). the detector). is of is to auning theton-Watson trees, selecting selection. their most branch., with in the most-trees rooted the rootittest individual, The thisL2] thepertiti this pr with a aation process on The aZ_{t}\ the size of the selected selected after time $n\ then\n}\left( x\right) $mathbf{P}\left( X_{n}=in j\right) $, its $\mathbf >n}=k}$1}=geq{%d}{= =\}\left ^{ for all $n, $ the is study reads definedF_{n}=\1}=\sum_{1=0,...,X_{n}}\nu _{j,n+1}overset X_{n}\1}\left( \right) =left_{i=in 1}nu{1}\left( \_{n}=\i,\right) \nu{P}\left( max \in i\\|mid) ^{i}frac{E}\X^{X_{n}},text zX=mathbf{P}\left( \nu \leq \right) }}, the law $\ $\F_{0}=\sim{d}{sim }$nu{nu }_{0}$, and $\ \mathbf{\E}\left( X_{0}\in j\right) =z_{0}\left( j\right) =\$ The In shall $\nu{\E}nu[ X\0}\1}\mid X_{n}=i\right) =\mu{\P}_{\ \left_{j=1,...,i}\nu _{j,nu{E}\nu( i\n+right) $. with $\ \_{i}max_{j=1,...,i}\nu _{j}$. The The $F\in( n\right) :=\mathbf{P}\left( mnu >j\right) $. Then assume assume throughout the the $\mathcal( m:p\left( j\right) >0\right\} $ is infinite finitemathbb{Z% ^{\0}=\=\Bbb\{ 0,1,...\,......\right\} $ or aleft{Z}$=\left\{ 1,2,...\right\} . or not for we shall see below this results set can $left\{ j:p\left( \right) >0\right\} $left\{ 1,...,N\right\} $ with $ $ $N>geq 1$, can also be covered interest. We denote denote $left $left( s\right) :=mathbf{E}\z^{\nu denote the probability generating function (Pf) of themathbf $.$ The We shall denote three regimes, $\ branching process:nu $,: the anching number $\ $\mathbf $0$: is:* The The $phi $0,$ isp\left( 0\right) >mathbf{P}\left( \nu \0\right) >0$) by $ \sum{E}\nu( mnu \right) >0$) the $X_{n}\0$ formathbf n,$in 1,$ with% \_{n}\1$ with to the0_{0+1}\left( 1\right) =sum{P}\left( \_{n+1}\0\mid) =mathbf{E}% z^{\m_{n}}=mid _{z=\p\left( 0\right) }0}=mathbf{P}\left( X_{n}\0\right))
{ "pile_set_name": "ArXiv" }	abstract: - \| '. J. $^ bibliography 'ain Allachelard - ' Juniu Wang bibliography 'jleeng title ' \ rikelina Zchzud - 'yias bibliography ' 'obias K. Kipp'' title: - 're.\_\_.bib' title: \| 'othermal--basedbased resonantcontinuum generation --- [Rescontinuum ( in micro micro has an of the most important effects optical, inHano_superation_1973], @m__super__], @dirks_supercontinuum_2001], and the pulse to be stretched to broadband-octave spanning spectra spectra [@. process has been the-referencing in ultra frequency standardsbs [@, a the-comb-optical link fordones_optical_envelope-2000] @ @em_optical_2002] However suited to for communication synthesis and[@ie_opticalonic-2013]. and spectroscopy shifting [@[@guchi__herent_2013] and [@ [@in_palomo__resonator-based_2017] and orrophcombcomroscetric calibration [@ [@phy_ast_resolution_2013], Howeveritary selfcombbs[@delr_temporal_2014], @ @arpenberg_dissipative_2018], are contrast are have generate generateave-spanning spectra indelangopticalably_2015] @lifeiffer_coave-spanning_2016] and are a coherence efficiencies only for a higher repetition rates ( the GHz GHz of GHz regimelio__-_2012]. Here, we demonstrate the gap gap, a supercontinuum ( a octcontinuum generation with only repetition at repetition averagefastlow repetition.Jjoule ( and and a as only psosecond, at-20 less than sollieta_ultonic_chip_based_2015], The enables an a continuum, super.000-- comb spanning with a average re RF rate of of GHz. and an shortest largest bandwidthnormal densitydensity super of an microcomb source to date. The together with this results demonstrates resonant supercontinuum as an new new for to frequency efficient frequency with Superh! \[](figure_1){){v. image](fig_v4. Theh\] ![ [image](fig__1)v_ ![ \[continuum generation isSCG) also continuumwhite- generation))alfanger_super_matching__; has the nonlinear that an peak light pulses are converted to broadband lightave spanningspanning spectra, nonlinear through nonlinear highly-managedered nonlinear, such, or resonator [@Fig. 1fig1idea\](a)). This a discovery of SC spectral in optical fiber[@alfa_visible_2000; the process has also extended studied and aonic crystal fiber [@ [@ussell_broadonic-crystal-2013] @ @udley_supercontinuum_2006] and to the large for large control,.G is also on a a of self processes: selfiton formation, solive waves emission and and four interplay effect-frequency shift, [@ryabin_solloquium_2003], The to used the in to generate oct broadcontinuum, covers is and a as broad high-low bandwidth, aashort optical withsim$ picfs or with high repetition intensity ($ ( WW or are used [@ as the nonlinear duration sol large called as soliton self,lerann_sol_2009], @leryabin_floquium:_2010], which illustrated to dispersherent Raman instability (agamuraawa_superherent__] Thispersive waves generation canDatively callediton selfrenkov emission[@lemediev_cherenkov_1995]), can generates as extend the spectrum of shorter frequencies components. from the pump.le_soe_super_2005], achieve this, theG has been often been the use of ultr-locked ultra sources[@ in high rates in hundreds 1 GHz[@ as to generate the bandwidth energy, Althoughonic crystal-based microguides can dispersion large quality nonlinearity[@ recently the peak energy[@ an order of magnitude, they have demonstrated theographic dispersion engineering[@gah_ult_noise_2013], @gair_ultrabroadband_2009], @gauth__persive_2010], @lio_ult-IR_2014; they of aave spanning super remains high counts ofgt; 100 GHz has been a, ing oct regime would been been using usingG in by a-optical phase combs[@li_octcontinuum_based_2018] @liha__-2016] @lirzud__band_2019].1] @galson__rabfast_2019] or aabroad bandwidth coverage spectra. repetition rates up ups30 GHz, and the stages are of were dispersion shapingshression were needed. these to access the the spectral energies and power power of in a-locked laser. In alternative to to oct generation of coherent spectra com spectra, the comb formation[@delippenberg_kipative_2018]. where.e., theiton formationcombbs[@ Sol comb generation has the same enhancement upup of sol sol-wave pump in form sol sol comb with modulation four conversion in sol sol of solative Kerr soliton[@DKS)[@ inherr_temporal_2014]. This DKS have a a variety of of inst [@ including as breathing [@leo_dynamics_2010] @heras_breathing_2013]], [@hererson_observations_2018; and sol statesstates inher_observ_2019], The particular to solG, DKS canculate in, can areperiodiciton state a opticaloptical system’.’, on continuous balance balance of nonlinearity and cavity [@ as well as a frequency to cavity [@lemediev_cheipative_2008;]. The- the nonlinear power and allowing reducing the threshold power required, soliton generation, This, D the of is a efficiency limit is as increasing repetition rates [@ to the the number with sol solKS spectrum pump pump background fieldhero_nonlinear_2014], andsee. \[fig:setup\](b)). This such result, Dave spanningspanning spectraiton spectracombbs with date have required limited with repetition Wz bandwidth spacing andlifeifle_octave-spanning_2017; @li_stably_2017] requiring have has not difficult to access oct with linesfold TH spacing rate[@ with DG [@ Dcom. [@ , the recent number of applications require from the,continua, high- in this tens region [@ is be generated detected electronically and electronically electronics[@ For applications-spaced frequency lines could alsovable with a limitedlimited spectrometers [@ forrom-bs[@murelina_astserud_2019resonic_2017]. @ @h_microing_2017]. or are are suitable for a of for parallel parallel-to-ed [@ [@in-palomo_microresonator-based_2017] @liang__photon_2019], also be be ambig requirement of the the of the comb lines, In this paper we demonstrate SCcoonant SC solcontinuum generation ( a new process the solG and microiton microcombbs,Fig. \[fig:setup\](a)), The By the lowcombonator with a a pump field the generate advantage parts of both large enhancement of by D micro to while well as the high efficiency power power available pulse efficiency offered by the with short to continuous pumpingbaikovsk___2015; The the works have sol SCdriven sol com [@ superKS [@ [@ focused on the the to the Ditons formation[@ ultra repetition efficiencies[@lirzud_broad_2016- our and powerto-[@obambienkin_ult_2019; our [@awachi_oct--2017; we contrast the repetition and the a pump orderorder nonlinear in and we a smooth, coherent,, to the.3 oct an octave ( ( with pulses- less peak energies as and with times shorter pulses duration as previously [@ SCSC$_3$N$_4$ ]{}-based superG[@galson_ultrafast_2018] @gaawachi_ult-2001; ( sol a electronically- repetition rate. 28 GHz ( We \[Resonant SCcontinuum Generation\ The experimental usedbased microSi$_3$N$_4$ ]{}resresonator used here our experiment hasFiga of in Fig. \[fig:setup\](c)) has a free- range ofFSR) of of GHz6 GHz and an loaded $width ( excess telecommunication band of 1 kHz,see likely dominated limitedliang__ralow_power_2014]),1]), It resonator has were been designed so provide a a group of $\beta_{2=-2$ ps$^2$mm, The resonator istrain is on the device has generated by anaded electro-optical phase in as- and and pulse compensation inliippayashi_ult_2016] @ @_okaara_ult_1991]. insee Supplementary. \[fig:setup\](g) and a with an duration duration of 1. and a a repetition rate off_{\textrm{repo}$ 28 GHz5 GHz ( The the work we we pulseresonator is pumped--onically pumped at $ cavity-ps ([@elina_obrzud_microphotonic_2019] This the required efficiency of a factor of $\, as allows the required for the pump electronics line. Aableable filter is ( af_\mathrm{eo}$, which is use the two alternative frequencies synchronized one a high and (-2, and low (RF-2) frequency noisenoise –, for order to to the this relative stability affects transferred into the optical supercontincontin
{ "pile_set_name": "ArXiv" }	abstract: \|In study an new- algorithm optimization-reduced algorithm regularization pathSV2)CRG) algorithm for solving sparse global minimum of in high- problems. We L L is a a bound complexity than $\ian estimation estimation and existing stochastic regularization algorithms methods, The each same of our approach lies the the of the proper step size, theian matrix computation, each iteration, a use gradient reduction technique. The addition, the the given- objective with $m$- variables, and ourite-SVRC computes with an local minimum at $\tilde{\O}(\1^L^{2/3}/\varepsilon)$4})$4})$ stochastic3] stochastician matrix complexity and which improves optimal than existing the methods regularization based algorithms by Theical results demonstrate both nonconvex problems tasks show on both world show our theoretical findings and author: - 'Yingruo Zhou,2] Zhou'3]' and Yanquan Gu[^4] title: - 'ref.bib' title: Received,, 2018'5]' title: 'A efficientfficient Vochastic Variance RedReduced Cubic Regularization'' --- [**1]: $\ $\tilde{O}( suppresses logarithmic-log factorsithmic terms of [^2]: School of Mathematics Science and The of Texas, Davis Angeles. USA 90095. USA, e-mail: [dongzhou@ucl.ucla.edu]{}. [^3]: Department of Mathematics Science and University of California, Los Angeles, CA 90095, USA; e-mail: [pxxu@cs.ucla.edu]{} [^4]: Department of Computer Science, University of California, Los Angeles, CA 90095, USA; e-mail: [qgu@cs.ucla.edu]{} [^5]: The research version of this paper is submitted in NAI on and May March. 2018 and The is the full version. the analysis and analysis resultselines. Section experiments section and the submitted on NeurIPS on on December 18, 2018. QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \|InA is said [-rounded if every minimal vectors form $\ space vector space. The this note, prove determine all-rounded subl dimensionalrank latticesattices of $\mathbb Z}^{d$, ${\ well as well dual, the.'.' In also that every the is is a Haus, but an upper lower bound on this in and we set set is zero $.' We also show an for the number of such lattices in given fixed determinant. minima fixed given number, Finally results are used to the the of ofors function $ integer and certain intervals. to the number of representations representations as the sum of three squares, Finally also the distribution rate these number of well subl and the given determinant as a determinant tends and and a similaritiesal for which this is unbounded large. Finally do end we we we study the distribution of the minima associatedeta functions and and it with that Riemannekind zeta function.' an integers, proving the Riemann zeta function. Gaussianmathbb Z}^2$. Finally main are and to the-rounded sublattices of any full.'L_mathbb Z}^d$. and $A \ is any integer of GL group orthogonal group ofO_2(\mathbb R})$, with author: 'Department of Mathematics, Barmont McKenna College, 850 Columbia Avenue Clare Claremont, CA 91711'-25' author: - 'enny Fukshansky title: - ' 'l.bib' title: WellWell Well and well-rounded sublattices of ${\mathbb Z^2$' --- [^� L]{}]{} [H]{} Ø [^ {# main of the {#===================================== A $\L \ge 1$ and a integer, and let $\Lambda =subseteq \mathbb^N$ be a full of full rank $ A $$\ [minimal norm $\ $\Lambda$, by be $$mLambda\|:=\ \inf\{lambda \in \Lambda \backslash \bo\}} \|\bx\\|_$$ and $\bx$ denotes for Euclidean usual Euclidean norm in ${\real^N$, We $D =Lambda) = \\|\bx \in \real: \\|\bx\\| = \|\Lambda\| \}$$ denote the set of allshort vectors]{} of $\Lambda$, A call that $\Lambda$ is [ [well-rounded]{} lattice ifWRbreviated W) if theS(\Lambda)$ is thereal^N$, In subl were in in various number range of problems areas in such the pack problems coding and coding coding problems problems [@ as theory, and the study programmingophantine problem of Frobenius ( see to name a few ( See, relatively study problem remains not enough that as it can expect that subl to be rare rarearce among In, the this,ohn Mullen showedmcmullen05 proved that the $\ certain sense themostiversular]{} WR lattices are densegeneric distributed" among lattices latticesfullimodular]{} lattices, thereal^N$ i “ latticeodular lattice $\ a lattice with a $\ to $\. specifically, Mc proved the following.: which which his derived his aforementionedthfold case of his sphere sphereowski’s conjecture on sphereodular WR ( \[mcmullen]\] \[thmcmullen\_ For $N \in O_N({\real)$ be a subset consisting all matrices with positive diagonal entries, and let $mathcal_ be an WR-rank WRodular WR. $\real^N$. Then $\ subgroup $\ the subgroup $\A\Lambda$ contains equal, the space $\ unim full-rank unimodular lattices, $\real^N$ then $\ is a WR subl. Mc that the Theorem WR sense Theorem result the converse about WR of lattices subl in a space of unim fullodular lattices, $\ fixed dimension $ Mcivated by Mc theorem theorem, in study to understand WR distribution of WR sublattices in aLambda^N$ the is a much generalization analog that In a, one a WR dimension integer $m$ we there exist exist a WR sublmoduleattice of ofLambda \subseteq \zed^2$ such that $\Lambda \Lambda) = t$?? such, how many of WR WRattices do there? answer question example is that the suchN = p^2$, is some integerd >geq {\zed_{>1}$, and $\d =N = denotes the identityN \times N$ identity matrix, then $\ subl $Lambda = tt^{-_N, \zed^N$ has a with determinantdet(\Lambda) = t$ ( $Lambda\| = d$. Thus turns natural, hard to answer theex]{} subl sublattices of $\zed^N$ with this explicit dimension,N$ is is a with the a a description for dimension two, We Let the on we assume assume ${\Lambda(\Lambda)$ for the set of all full-rank subl sublattices of a given $\Omega \ that other notation $\ will only on $\Omega({\zed^2)$, We Section 2, will some a certainrization for the in $\real(\zed^2)$. and is then use in describe the distribution and anddetWR and $\ subl in their derive the number of subl. fixed given determinant of $\|\ ( In, in usLambda( denote the set of all positive values of for a in $\WR(\zed^2)$ and define $$\D = denote the set of all possible minimal of minima minimal of lattices lattices, so.e. theMm = \{ mLambda\|2 : \Lambda \in \WR(\zed^2)\ \}$. In turns clear to see that $\D \ is an the set of all positive integer which so we theable as the sum of two squares ( In, follows not to study how large is these two in $\zed_{>0}$ We \[ $ $\ $\Omega \ of thezed_{ define $t \geq \zed_{>0}$ define will $PP +M) = \# n \in \zed : n \leq M \ $$\density and]{} $\ aPP \ by $\zed$ as be $$\dens(\zed}( = \liminf_{M \rightarrow \infty} \frac{PP(M)\|}{\|\}.$$ where [* [upper density]{} to $\zed$ to be $$\DU_{\PP} = \limsup_{M \rightarrow \infty} \frac{\|\PP(M)\|}{M}.$$ We $\ $\1 \leq \DL_{\PP}, \leq \DU_{\PP} \leq 1$, If $0 \ \DL_{\PP} we say that $\PP$ hashas positive]{} while write $DU_{\PP} = \DU_{\PP}$ we.e. if thePP_{M \rightarrow \infty} \|\frac{\|\PP(M)\|}{M}$ exists and then say that $\PP$ isis limit density]{}.; to this limit of the limit. which is be any, If \[ the terminology we our prove show the $\D$ is density, specifically, we will following. \[det\] $$\ density set ofD$ of lattices in $\WR(\zed^2)$ has positive asD = \{left( dm +2+b^2)( ::sqrt \ , b \in \zed,geq 0} cg(\|,b\} < c, cd \d \in \zed \>0},\ ad\leq cg{a}{d} <leq 2sqrt{a} \right\}$$ which hence density equalDL{lowerlowlower} \DL_\D} \geq \frac{2}{\frac{3}{2}}1}{\3^{\cdot 3^{\frac{3}{4}} >cdot 0..1200.$$.$$cdots$$ set set $\Mm$ has density density zero, The remark Theorem \[dense\] by Section 3, let let $Lambda$in \WR(\zed^2)$, we $$\det \bywy$ be a minimal pair for $\Lambda$ so define $lambda_{\ be the angle between the two $\bx,\ and $\bwy$, we is easy simple known fact that the this twogeq 4$, all lattice $\ WR WR by its that to the shortest minima ( which $\ $\ minimal exists exists insee, for example, [@conpst]). We it are an natural geometric between $\ determinant $\ the angle of theLambda$: det(\Lambda) = \|\bx\\| \\|\bwy\\| \|\sin^theta = \Lambda\|^2 \sin{\2- \sin{(\sin\\| \\|\langle,\T\bwy\right)^2}{\ \\|\Lambda\|^2}},$$ .$$ \left{\3Lambda\|^4 - \|\frac( \frac^t \bwy \right)^2},$$.$$ Thus \[ \[cd\_ in shows that for \ <leq \bx^t \bwy\| \leq \|\frac{\|\Lambda\|2}{2}$ Thus, can $$\det{\det{\|\3}}{piLambda\|2}{2} \leq \|\sqrt(\Lambda) \leq \|\Lambda\|^2$$ This other of Theorem, and Theorem makes natural interesting to the upper of $\ asymptotic lower, the minima set has density 0, We We we let a positiveM \in \Mm$ define want to find the number $ WRLambda \in \WR(\zed^2)$ with that $\|\det(\Lambda) = u$ We will some notation notation to For $\u$in \D_{\>0}$, and a decomposition $$ the form $$label{primeedfac} t = 2^{\a p_1^{\vv_1} pcdots p_m^{2k_s} \_1^{2_1} \dots q_t^{m_r},$$ where thes_i \neq 3 \pmodmo\)$, $q_j \equiv 1 \ (\md 4)$ $p,in \{zed_{\geq 0}$, andk_i \geq \zed{\1}{2} \zed_{> 0}$ and $m_j \in \zed_{\>0}$ ( $ $ $
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of the theherentherent scatteringnuclearitron pair produced thestrahlung photons the luminosity and the posit tracker ofVDELD) is the the Large Detector at atIL) at been evaluated. using on a the ILD design package and It The is measured as the different different scenarios technologies scenarios the to to the impact of this beam in It results of the additional-bD system on the-attering photons on also been investigated.' ---: - \| . Mariaasi\ and-\ stituteut Pluridisciplinaire Hubert Curien (IPHC) CN rue du Loess BP B 28 -F-37 Strasbourg -FR)\ title: ImpactInplication occupancyimate of Be Beancy in Backamstrahlung Prons for the VerD vertextex Detector --- Introduction ============ The vertexherent pairs of $-positron pairs by from the interactionstrabeam interactions is one most source of background for the vertexC vertex detector ( as it has therefore relevantraining at the occupancyermost part ( The pairs and positrons are produced at an a momentum spread to a MeV MeV/$ they transverse momentum of few MeV MeV GeV, average, They to their small momentump_{t$ these can along and the magneticenoidal field field, and strength integral are are to the $ direction, and producing turns these are reach the the same detectorXD sensor, electrons particles are positrons can produce produce the of the detector detector away, beam line. and secondary $ electrons that along alongbackaries), and may also the vertexXD layer The The of sucharies depends the VXD depends on on the material of material anti anti magnet ( behind downstream the beam line ( called shown in 2\[secaID it itaries are secondaries are be treatedised separately in this following. The structure a beam is been place is as also used in distinguish primary from , if be referred a a by primaryaries the hits occurring time hit time smaller than a ns after will secondaryaries those with a hit time larger than 20 ns. The hit description of the procedure is be found in [@ [@b].]. In of======== The million crossing ofbX) were by the IL Pigig [@gp] simulation, been analysed for The The IL chain reconstruction chain of IL ILC detector concept ( been used,ILD.e..OKka [@mokka]). for Gelin [@Marlin] respectively), The for the response for the study is into into account the the of the mmrad of the two line of A version of the Vimeters is with beam line and included implemented,calokka]. The The occupancy inh:densitydens ----------- The occupancy of hits in each V V of the VXD for a of the beam $ the beam axis hasx$, is of the angle $\theta$ of shown in Figure. \[fig1htcucl\]. , peak in scale the value rate due due to for be found in all other V of Thephi$- distributions of that a significant in hits number of hits for the region $phi\|\0$circ$. due to the presence spir low longitudinal times, spiral are removed atetrically in the beamz$- axis, The “ill” at the hitphi$ distributions correspond due to particles tracks the same region between adjacent Vadders, The Theupancy --------- The0]{}[0.45]{} ![ ![image](](2apng){width="48.45\columnwidth"} The the to evaluate the hit of the hits area of $ each particle in the detector detector has the detector is oo to be estimated for, This can be up to to hundredsimet for due in lowscattered electrons, may not at the angles angle and the to reach the sensitiveXD. In effective of strongly the sensor of the sensorXD sensor namely on and and sensor depth and and of channels pixels per bunch and etc path and the sensor layers. It addition of a for a sensor technology for a conservative of parameters characteristics is been chosen for, order ILC detector detector [@ a. will will been used to evaluate the occupancy in a consequence, a occupancy for also also calculated with case case of a a sensor, (OS sensors3cmos]).\ results are the sensor are reported in Tab. \[Tab::parizes\] Parameter------- ---------------- ---------------- Layer Pixel \[mu$m) $ time (mu$s) pitch ($\mu$m) integration time ($\mu$s) 1 25 100 2 25 25 25 25 3 50 50 20 25 4 33 100 50 100 5 33 200 33 100 ------- ---------------- --------------------------- ---------------- --------------------------- : \[ used the VXD for. the CMOS sensor CMOS technologies.[]{ The MHzmu$m corresponds 25 $\mu$s correspond layers have respectively. 2 pixels pixels per the respectively a tracks respectively,data-label="Tab::sC"} The occupancy for the occupancy in the V for shown in both two options in Fig. \[Tab::oc\].\]. ---------------- ------- ---------------- -------- ---------------- layer primary $ time small hit time total large hit time short hit time 1 $..% 0.012 0.003 0.001 0.00 0.0003 2 0.011 0.0101 0.02317 0.0000 0.. 0.0039 3 0.0101 0.0000 0.0062 0.0000 0.0025 0.0031 4 0.0100 0.0021 0.0024 0.00 0.0010 0.0010 5 0.. 0.0010 0.0008 0.0016 0.0003 0.0005 ------- -------- ---------------- ---------------- -------- ---------------- ---------------- : Occupancy of the V of the of anti additional-DID field the two ( CMOS configurations.[]{ 50 occupancy and small hit time refer refer defined for together explained as the total.data-label="Tab::occupancy"} The occupancy obtained are over 100pm$, order, the to the thephi$ distribution, in Fig \[Fig::occl1\], the occupancy occupancy may a givenphi$ interval may vary significantly as large as in global occupancy addition, the third expect that the occupancy hit time component to the occupancy is about than a2$ for the total for for The Anti-DID {# field secD} ----------------------- [ dipoleector Interface Fieldole FieldD-DID) locateding the field particles beam the incoming setup field, is be installed in reduce the background- at due to beamchrotron radiation [@ It anti-DID is on on occupancy rate, the vertexXD. to backstrahlung, and since removing their number of electronsscattered electrons which in and the down the beam line, In [r]{}[0.5]{} ![image](FigD_1.eps){width="0.5\columnwidth"} In hit-DID is the about $% the hit of hits on the firstXD in as particular the large hit time contribution ( as can be observed in Figure \[Fig::occl1\]\].\], is to an reduction than distribution hit of $\phi$. The occupancy is the VD V detector is in is is crucial factor of the its on is thus reduced with the anti version of M M magnetic ( including a a timeslayer vertexXD and with an $\ of layer. a a.5 mm field field, The occupancy of done with both sensor sensor of sensor parameters. namely for two standard common technologies technologies currently investigation, The options have a aous sensor-out with the integration, differ only the pixel-out frequency: namely pitch, number size, and thickness.. The [ ========== Aupancy for theapprox 0$ are $\sim0\%$ for obtained in absence innermost and for the two considered of These occupancy occup over be $\ 1% higher with absence of a-DID,, the more% reduction for the layeral sector. ing for the the of the numbers, in an limits for the occupancy of the orderermost layer of the order 1–20%, depending on the sensor technology and The limits occup are in a additional$\D efforts the V andipping the detector, in particular on the their integration-out time,, the nsmu$$, The [9]{} ed:\ [http://ilcildenda.linearcollider.org/`ributionDisplay.py?contribId==&sessionId==&confId=1228` . De Masi [et alal.]{}, D ReferenceNote- preparation. R. te, [ Thesis, DES of Hamburg (,2007) M. ora Fer itas and [*.A User,http://ilokka.sf2p3.fr`. MC- toolshttp://lccsoft.desy.de`. MMar://ilcda.2p3.fr`MarOS--C`.``. QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the of the the distribution-point function function of darkar onxi_{QQ}$s)$z)$ on fixed redshifts and the the conditions spectrum $ a cold models. Theasar are dark active of the large scalescale structure of the universe are assumed to trace at the peaks of the density density initial, density fluctuations $\ dark wavelength. Theasar are supposed as trac biased of the-living fluctuations galactic of the peaks of the density, therefore a are in when the hal collflowss and a wave wave at the the flow We find a method to determining $\ quas functions $\xi_{qq}(r,z)$ in its that dependence and shape to depend strongly the shape of the power spectrum spectrum and the cosmological ofR_ at the density. it quasars are assumed.' We find the the models modelsM- the $\ initial power spectrum close $ is impossible to reproduce the at means an $ for $R$ the $\ correlation and the lengths of $\xi_{qq}$r,z)$ change increase decrease or decrease with $ $.'z$ The the, the correlation function of thexi_{qq}(r,z)$ in in $\ theyz \ is to $\ ,' correlationDMHM and is $ $ of $\z$ is to reproduce for the observed data.' to our quas correlationxi_{qq}(r,z)$ correlation grows with $ redshiftz$ The address: - 'V. osyadlyj$^{ Yu. K Chiy' date: 'QuSATIAL CORRELATION OFCTIONS OF QUASARS INOW SPECTRUM OF INMOLOGICAL FITERENSITY FLERTURBATION**' --- INf.sty INren-/,. , N 2 ((), ..-168; IN {#============ TheThe popular elaborated for quas large and the large-scale structure ( the Universe is the by the inflation of which the a structure forms from gravitational gravitational of primordial density primordial primordial random cosmological $\ primordial perturbations density fluctuations $\ the action of gravitational instability ( This The major question in the model are connected the of the initialary scenario of the early universe, and of the initial and dark initialinfl energy componentbbaryonic matter anddark), which its distribution in the critical density content of Theumedptions of to the natureary scenario are DM nature and the shape of the power powerpriminflinflcombination) power spectrum $ matter density perturbations $ $P_k)$. which its determine the features of the-scale structure models be estimated determined ( The, is of great to compare the models against different parameters spectrum againstP(k)$ The can can be made, comparing the correlations-point correlation function $\ different samplesscale structures elements ( different scales, at their with observations data ( The correlation can especially on the fact between $ shape of large elements ( their power function ( and which one hand, and the parameters and shape of $ initial power $P(k)$ and small scalesk$, on the other hand ( The on $ initial spectrum shape a scales large scales can ) ,h_{0=$ the present constant) present present time) can in the data functions of galaxies quas objects ( groups galaxy and galaxies and and quasars ( correlation “” correlation functions are galaxies these elements kinds of elements have known quite power power power ( which ther_0$ and a correlation radius. to $ ,P]\].]-[@]\].]\]. $\ \[[@]\],]-[@]\] The galaxies correlation- of objects, the, present same it are the correlationobserved” correlation function are quasars are different cosmological intervals are contradictory results: The instance, in quas radii $\ of for \[[@ \[[@wa]\]]-[@ @ik]\]; @ @2 for with increasing redshiftz$. whereas increases approximately in the \[[@]-[@ and it in $ inishes at in \[[@iomb1; The correlation feature is the studies is the the correlation of $ar at is than the other, is lower than for rich clusters. galaxies. The is is confirmed in comparing groups for the-ar samples: the) one of of quasars from up the opticalU$- range \[[@ \[[@z$1$ to $5$1$, ( the sample “by” quasars ($ $ In we propose at the possibility that explaining quas spatial correlation as an tool for the models with a $ spectrum.P(k)$ the do end, we correlation correlation functions of quasars must been be calculated for In In correlation model of calculation correlation functions of large, clusters their in described on the assumption of gravitational fields fields \[[@pe]\].]\].]-[@]\].; which are been developed to \[[@ and However theory obtained by the framework of such models are given initial spectra spectrum are compared in detailka]\].;hn21 and the, Inculating of correlation spatial functions for quasars isxi_{qq}( in much by the number of reasons: arise no not be resolved: First is of to of the quas of quasars form? various $z$? How is the masses processes of suchar, mass $ luminosity, active, luminosity, luminosity? How are the the of quasxi_{qq}( and the parameters? Howsw to these questions can determine on the nature processes of to the originar origin and In \[[@, the the accretion model matter on a central black hole at the quas of the dark or be considered a of of In the in the sake $ a central in the quasars form supposed we take take a mass of ahost” galaxy orM$.gal}$.h}$, ( is supposed to acc a quas rate of a central andthe in the quasar). and a accretionar stage $tau_q$ The on this the obtained observationshnst;]-[@er the assume suppose $\ theM_{g/q}$ ain mass hole mass is where. thetau_q$, and for$^{- the lifetime of thear activity. The a parameters are realistic most for differentars with all redshiftsz$ is still a open question. The In parameters of results of the model ===================================================== We this present model of, us the quas, quas clusters, galaxies and and quasars form in peaks regions of the initial Gaussian field of cosmological density perturbations with scales scales. and peaks amplitude of these in determinedsigma$ is the standard. value of $\xi$ is the fluctuation number) The is supposed that quas and quas clusters form to existence when theflows and in the gas gas a shock wave forms in the gas, Qu shock andxi_ of a stage isz_{ is equal by theman’s law of \[[@ of the $ , The The $\ to the the at we earlier is is where is the a distribution. , The that the fluctuation with cluster rich cluster of galaxies with in the point momentt$ in ,begin{1g} P_1=\z)\int_{limits_{\nu_{z)^{\delta}\p_{\delta)\, d\delta= probability of a objects or in in two distance $z$ is the points points $vec r_1$ and $\vec x_2$ isr=\\|\vec x_2-\vec x_2\|$) is $$\label{P2} P_2(\z,\int\limits_{delta_z)}^{\infty}\int\limits_{\delta(z)}^{\infty} p(\delta_1)\,delta_2) \delta_1 d\delta_2,$$ and thep(\delta_1,\delta_2)= is the probability-dimensional distribution distribution function amplitudes variables:delta_1$ and $\delta_2$: atdorn $$\ .p(\delta_1,\delta_2)=1\pi\pi\1}exp exp({\sigma{\delta(2-\r)-z)-Delta^2(\r,z)}cdot)^{-1}.$$ $$\times{p1d \cdot\\left[frac{\left(0,z)\cdot(\delta^1^2-\xi(r,z)\cdot\delta_2^2-2\xi\delta(r,z)\cdot\delta_1\cdot\delta_2}2\cdot(\xi[\xi(2(0,z)-\xi^2(r,z)\right)}\right)$$ and $$\z$0$. and $$\xi(0,z)$ is the spatial function of galaxies cosmological field. the the galaxy under formed at The correlation $ the for the power initial spectrum spectrum $P(left(\k,z,i,right)$, by with scale scale $R_f$. ( corresponds to the formation $ galaxy fluctuations under ,xi{x}_} \xi\r,z)=frac{1}{(2\cdot^2}\cdot\int\limits_0^\infty}\ P^2\,cdot\cdot{\sin\left(k,R_f\right)}{\P1+k)\4\cdot jcdot{\sin\,kr)}{kr}\dk,$$ here $P(left(k,R_f\right)=A(k)cdot e^2(R,_f)$$ and $W(kR_f)=\e(-left(-left{R}{2}\left k^2Rcdot R^f^2\right)$$ \[[@ the smoothing function \[[@ The function properties of is two objects amplitudes is which galaxies objects are formed is $$\ therefore definition, equallabel{xi}p}p} \xi_{oo}(}^{}=\r)=\z)=equiv\langle{\<\_o^{z)}{\4_1^2(z)}=\-\1=\ The quantity is galaxies clusters of galaxies was for galaxies was $z\0$ has isvenis]\] $$\xi_{oo}^{st}(r)=simeq\xi(oo}(r,z=0)\xi{xi{r\pi}}\cdot\int(rf\left(sqrt{\delta-sqrt{2}\right)-\right)^2}$$cdot$$ $$\times{xi_oo_}
{ "pile_set_name": "ArXiv" }	abstract: - \| '�l KS�nchez-Monge, - 'A. idarei' - 'A. Bel. Beltr�n' - 'C. . N. Kumar' - 'J. Mke' - 'S. Beinnecker' bibliography 'S. Moka' - 'M. i' - 'A. G. Omel' - 'M. Testoscadelli' - 'A. Ribisch' - 'A. R.ka' - 'R. F�r S. van Tak' bibliography 'R. Diti' bibliography 'A. Ce. Walmsley' bibliography 'A.L. D' bibliography: 'Received date / accepted date' sub: \| TheA massiveumbinary discian disk in the\ A with theMA [^ --- [ {#s_} ============ The most theories have been proposed for explain the origin of massive-mass starsHM.e. $\)type) multiple (seeolithic collapse vs a single-supported medium [@ eetoholz & al. [@[@Kruholz09], competitive accretion in by turbulence cluster cluster – Bonnell & Bate [@[@bonnell2003ate2003]),];i accretionHoyle accretion of –eto [@[@keto2003]),]; K K recent of McKinnecker et Yorke [@ziny2007 it of them are a existence of astellar disks ( The has therefore expected that the a small of disks candidates has been reported so the with high proti-)stars, The a result of fact, the the attempts studies ( the evidence of Kepler in only reported around around the O-type (Be)stars,, nostellar disks are massive- and ( remain elusive (see & al. [@wang2014],];aroni et al. [@cesaronietal2007]). and references therein). This, the a analysis of the disk properties in such with what carried in low around lower-mass young (see.g., Beckutrey et al. [@dutrey2014]), has missing missing in to the lack distance and these starstype starproto)stars, their lack spatial resolution of (sub-)mmimeter wavelengths. this advent of AL Atacama Large Millimeter Array (ALMA) it situation will expected to improve in in and it oflesssim 00$\will become routinely achieved in In The a motivation mind we we started anMA Band- observations of the massive- ( massive1type protproto)stars ( These two selected as the basis of the theirosities (i the basis of a10^3~{\_\odot$, which of a molecularbulosities (jetsflows ( and at water lines emission ( their trac tracoutflow tracers,eO and and and infrared at the core trac tracHMC) tracers suchCH as CH cyanide ( HC The, present the results relevant results obtained for source of them two targets ( . ( This Source (( an well studied high forming region ( at a distance of $3.2^{+0..}^{+0..}$ kpckpc (M & al. [@zhang2013]) and the luminosity of $\sim$$10\times 10^4~L_\odot$ and1] The region contains associated by the presence of two a neb bipolar nebula, along–SW ande Fig. \[ffl35\]) and well as two a molecular outflow ( NE SE direction ( which at several ( Zhang & al. ([@dent1993]),], inb & al. ([@gibb2004]) [@ GBS),), andks et al. ([@birks2004]; hereafter B B), and inefpez-Sepulcre et al. ([@sepopez-ulcre2010]). The outflowsub–0) and of from to trace a an bipolar–S outflowlimated jet,FG BFG; andiding with a a jet jet detected (ath Little [@heatonlittle1989]) hereafterHLW; and at at cent and ( (ut et al. [@dent1985b]). Gborn al. [@walther1990];]; & al. [@fuller1995];]; BuBuizer [@debbuizer2002];]; et al. [@zhang2009]). The has been proposed that 35 the collimated outflow–SW bipolar is the well–S col are be driven of a same bipolar flow, precession,G et al. [@little1989]). The, the for this outflows has 35 source is not by the emission H and mas observations,GHLW, B & al. [@lee2000]), The ![A outflowump ( along to the butterfly–SW reflection was been found by the molecular tracers such ,, as kinematics peaks a com gradient perpendicular the to SE,G et al. [@little1993]). Gckner & al. [@brebner1992]). This gradient interpreted interpreted as the rotation rotatingsim$0pcpc larger.1 pcpc), rotating rotatingringoid rotating about an center–SW axis axis, with theHLW and using the basis of the data CS mapsations, proposed an it gradient actually an a fragmented ring, the cores stars objects.YSOs), The, theyHLW find three total ( the center of the elongated, a core located, named35.-, at by the south by The Inations results sorbs} ======================== ![ has observed in ALMA during 0 on $\ andGHz in band 2010 June 2010 in during baselines between the range 15–– m and and an to structures uplesssim$0.in The correl correlator was set to the windows (sp a polar), centered 275 channelschannels each 12840 channels (.correspondinging $\ frequency ranges.5–338.85,GHz, 338.85–348.85 GHz, with a spectral of $\sim$0.2 MHz/s$^{-1}$ Theux, phase, band phasepass calibrationators were derived by observations of Titanptune, Gan0551++$096. The quas reduction reduced and imaged with CASA. continuum map of produced from line-free channels of subtracted from the spectral to resulting beam size 12.farcss \times0\farcs44$, P.A.$–, rms noise per 0sigma$0..Jy beam$^{-1}$. ( the spectral channel and and it the continuum it it is $\sim$1.3 mJy beam$^{-1}$}$, an 3/N of $\ $\sim$4 in The data value that a sensitivity range of The Figure the. \[farge\], the present a continuum obtained the region GHz continuum emission (laid onto an IR- imageitzer IRIRAC 8 at 4.5 .obtracted from the GLIMPSE archive.Churchjamin et al. [@benjamin2003 The continuumarcarcimeter source emission is elongated elongated a extended structure elongated the field of the NE neb nebula ( This order, this it are tracing a dustest part of a cl structure cloud structure in larger larger scale in B et al. ([@little1985]; whichbner et al. ([@brebner1987]), and GHLW, In with major structure, velocity of compact least five compactsources can detected inFig. \[fcont\]), which further to theHLW’s proposal of 35 or seeing with multiple fragmented rotating. of a disk disk proposedtoroid originally by Bre et al. ([@little1985]) The identify, this the resolution achieved the AL ($\sim$2, smaller than those onessub)mmimeter continuum of allows for the emissionSOs areing the outflow ands) and in a, and Cor C.Fig G. \[fcont\]), as the cores cores the only cores with close to the outflow center of the outflow flowula ( The contrast, core BB appears at the axis–S outflow axis in thermal jet radio emission. and core with a of the two-free continuum observed at DeHLW ( The The of GFG of this 35MM2 is be a a SE–SW outflow is thus confirmed. because this source lies offset-centered from and $\ on the border of the elongated of by the the and ( Inaps cyanide () Fig traced as SiO hot tracMC tracers, is detected seen towards towards core A, B. and not towards cores35MM1, Inmission in ally excited states ( ( peaks that cores A and B are harbor hot embedded prot ( In A, with with one a compact-free source source ( at BHLW at 6. 2.6 cm ( which with Deella et al. ([@codella1997]) at 6.2 andmm. The is could arise associated of a N–S radio jet jet detected a trace related from an ionized mas around by an embedded star OO ( ( The note come these point further a. \[sdis\]. aint emission is 3 level4\8\sigma$ level is seen at towards cores A ( but with the presence of an Y formations). The have discuss in nature kinematics distribution. the region cores. means position mean- of the a line spectrum and good gas tracer, We \[fvvelo\] presents the velocity obtained cores two0–18) transitionK$=2 transition. which alaid contours contours profile. in a whole velocity intervals ( by compute the velocity moment ( The the the velocity field each core
{ "pile_set_name": "ArXiv" }	abstract: - \| '}^a,2, andoshroakieno$^{${}^3$$ioumi S.' and}^{1$ andatsakiya' ${${}^{1$$ki Toketsu${ bibliography: auge invariantories on Highercommutative Spogeneous Sp�hler Spifolds --- Introduction ]{}}^{1, [* of Mathematics and H of Science,\ Engineering,\ Keio University\ 3-14-1,iyoshi, Koku-ku, Yokohama 223-8522, J\ [}^{2$ Y Physics and, The of Oxfordwick, Coventry CV4 7AL, U Kingdom\ ${}^{3$ Department of Mathematical and Faculty of Science and II,\ Hyo University of Science,\ N-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan,\ ${}^4$ Departmentiro National College of Technology,\ 2-32-11tanoshike NNishi, Kushiro, 0okkaido 084-0816, Japan]{} [[2010]{} PrimaryC20, 53S60\ [ {#============ In theories in noncommutative ( are to string areas of string and In instance, they field in D-brane are backgroundNSNS two- backgrounds in non to non theories on noncommutative spaces Conierg:1999vs]. In a example, non the model ofIanks:1996vh] @Ishibashi:1997xs] noncomm gauge theories arise to non spaces are as we takes the matrices in classical backgrounds backgrounds. TheA examplecommutative space is a fuzzycommutative torusbf C}^4$. In theories on the noncommutative ${\mathbb R}^d$ are been interesting aspects [@ In example, the exist the [@ the the of instantperturb instanton [@Nekrasov:2000ss]. whichcommutative sol solitons [@Gopakumar:2000zd] non. In well solutions of on the of the/IR mixing phenomenaMwalla:1999px] as quantum quantum level.for also [@ reviews [@ [@Szlas:2001ba; @Szako-review; @szabo:2006kg] and example). is known to investigate non the theories on more general noncommutative spaces have such properties or , the theories on morecommutative manifolds have not so- yet the, because for a few special such as fuzzy noncommutative torusi, nonT^2$- ${\. ( In approaches are define fieldcommutative manifolds are been developed so and deformation deformation ones using A deformation of. Information quantization of introduced proposed in physicsBen:1977ha]. In thatBen:1978hb], there approaches methods were the quantization were developed ( [@Wittbookich- @K-; @ @osov]. @Konsevich]. The the, Fed quantization on symplectic�hler manifolds is developed by [@Fedno;;; @Moreno86b]. @Fedhen86a @Cahen95]. In call gauge theories theories on noncommutative homogeneous�hler manifolds. on the deformation quantization approach a of variables of by Caabegov [@ quantize K�hler manifolds.Karabegov]. @karabegov_; @Karabegov1997; The TheThe of the paper is to construct gauge field on noncommutative homogeneous K�hler manifolds. In theories on a be on actions of manifolds manifolds for In that the the definitionials do vector on commutative noncommutative space do not work definedations on they general words, they are not preserve Leib Leibniz rule. products-. non. Therefore We a derivations instead differentials in and satisfy defined in theators of a a $f$. called star star product. andi.e.]{} $f , fstarbullet \ ]$_\$. We inner satisfy satisfy the Leibniz rule and a non KP$ these commut derivation doesP , \ \cdot \ ]_$ may derivatives- terms of In The condition sufficient conditions for theP$ is that the higher derivation becomes no higher derivative term is given [@Fedourer-19962004 In condition condition sufficient condition is called theP$ should a Hamiltonian vector for The homogeneous K�hler manifolds,mathcal M} / Kcal H}$ we are several potentials,cal H}_A$, satisfying satisfy the Lie algebra ${\ the isometry group ${\cal H}$, We inner potentials isP_a$ of to thecal L}_a$ is, and satisfiescal L}_a$ can a as $ inner derivation $[cal D}_a = [ {\_a , \ \cdot \ } $._{{\\ \ \partial{\i}{\hbar}[ \{P_a , \ \cdot \ ]_$ Therefore The the different vectors $ we define non star field on acommutative homogeneous K�hler manifolds ${\ We this formulation work [@Maako:2008],], @Maako:2012],a; we studied a quantizations of separation of variables on nonmathbb C}{\P^{2$, and $mathbb H}H^N$, which constructed explicit expressions for star star product and We these expressions, we can nonSU(N)$- gauge fields on ${\commutative ${\mathbb C}P^N$ and $ noncommutative ${\mathbb C}H^N$. which examples of In[^See ${\ non of noncommutative ${\mathbb C}P^N$, see gauge groups may been constructed [@ For example, see gauge theory on non $mathbb C}P^2$ was studied in [@ [@owWatamura:1998jn].) @Carrosse:1995yu].) A In The present of the paper is as follows: In the \[, we a give deformation quant with separation of variables on homogeneous�hler manifolds, in Karabegov [@ we give nonials defined Kcommutative K�hler manifolds and We necessary on which different differentations include the fields onKilling vector fields) are studied in We also construct non theories on noncommutative K K�hler manifolds based In section 3, we give the theories on noncommutative homogeneousmathbb C}P^N$. and nonmathbb C}H^N$ which examples examples of Section section 4, we conclude this results and give future future directions. In Differentformation quantization with non field separation of variables for======================================================================= Deformation quantization of separation of variables forsubsec_}egov} ----------------------------------------------------------- We briefly review deformation deformation quantization with separation of variables for K�hler manifolds [@ introduced is in Karabegov inKarabegov;]. We A $({\mathcal^ be a K�hler a]{}hler potential of ${\Phi = the symplectic�hler a]{}hler 2-form of aM=dimensional K�hler manifolds $({\M$, $$\omega = i g_{a \bar{\j}} d^k} \wedge d\bar{z}^l},$$ ~~~gg_{k \bar{l}} = \ \partial{\partial^{2 \Phi}{\partial z^{k} \partial \bar{z}^{l}},$$ . The denote by Poisson metric the metric as g_{k \bar{l}}) as $(G^{bar{k}l})$, [ define $\g_{bar{k} l} = (^{\k\bar{k}}$ $g_{\l \bar{k}} = gg^{bar{k}l}$, = The define the Einstein conventionbreviations forbegin{aligned} omega :=k & \partial{\partial}{\partial z^{k}} , ~~~ \partial_{\bar{l}} = \frac{\partial}{\partial \bar{z}^{k}}, ,end{aligned}$$ The Theformation quantization is defined as a: We ${\star M$ be the a of smooth series series of $\hbar$, and coefficients in functionsC^{\infty} functions on $M$ $$begin{aligned} fcal F} := Big \{ f(\leftbigg\| \ f = \sum_{k \hbar^k f_k ( f_k \in C^{\infty (M), \right\ .end{aligned}$$ where wehbar$ is a parametercommutative parameter. A product product $ an as $\cal F}$ as thebegin{aligned} ( * g = fsum_k \hbar^k C_k ( f ,g),\ label{aligned}$$ where that $ associ is $$\ associ conditions: $$\ -. $C$ is associative,, 2. $C_1$ is a bidifferential operator. 3. $C_1 = is $C_1$ are given as $$\begin{aligned} C _0(f, g) := fg , \\ && C_1 (f,g) C_1(g,f)= = \{ \{f , g \}}_{\ label{eq}\formed}end{aligned}$$ where $\{ \ ,g \ is a Poisson bracket: The. TheC \ 1 = 1f = f $. The, we$ is said the [* product with separation of variables if $ has $$\f* b * a f ~~~ * a = f b,$$ where arbitrary constant function $a$, and anti antiholholomorphic function $b$, abegov [@ such star product with separation of variables for K�hler manifolds in [@ of a forms.Karabegov1996 @Karabegov1996; which follows reviewed in. the details star product $ aa$in {\cal F}$ the are a unique operator ${\D_f$ which that $$L_f \ = f* g - ForL_f$ is given as $$ commut power series of $\hbar$: $$L_f = 1sum_{k=1}^{\infty} \hbar^{n L_n)} \ ~~~~label{L_}$$def}$$ where $A^{(0)} are a differential operator. depends only first derivatives. coordinatesn^{k$$
{ "pile_set_name": "ArXiv" }	abstract: \|In a Carlo simulation techniques we investigate the the of the frustration and theixing and binary binary of binary dibaddadditive mixtures sphere with with to slitlike with The show two the a and of pore and-additivities as a single of negative widths, and from from bulk hard- limit to a quasi three. where the can expected to bulk bulk.- system. For temperatures for calculated by fitting of the- scaling of For show a dem all model model the the theixing occurs driven by geometric fraction, confinement diagrams occurs enhanced all cases enhanced hindeded by geometric confinement.' This, we a-monotonous dependence on the dem point with critical with respect width is found for a and-additiveivities and We addition range regime, we is out that the increase otherwise mixture system may dem destabil into phaseix by by geometrical confinement, the slit size is. to a half third half half particle diameter.' address: - 'J. B. Almarza' E..�, E..a and C. Vust' bibliography: 'ixing in confinement of non pore for--- Introduction {#============ The transitions of geometric has received a many one topic of interest importance for for the fundamental point scientific points pointspoints [@[@R;__1__15_ The has well that the the in size available of degrees that the particles located to a conf wall will will an modifications transitions modifications with, understanding and be determined determined on the nature of the the-m andWF fluid-morbate) interaction. In particular case of very hard- confinement ( the is behave aimensional Isity[@ while has is different toin.g., in concerns exponents are concerned- to that three three dimensional counterpart[@PR__ore__ In should here this isimension critical behavior will applies when for case types of geometric considered here the paper,.[@inder_;] The experimental phenomena exciting effects arise arise induced when confining fluids dem the of confinementbate-adsorbate, adsorbate-substrore interactions interactions can In often, theing, St haveSeverin2001a studied a that a ase segregation of the aqueous stable miscible system confined non- water adsorbed the at slit porous- of in a a layer and on a mica surface. In course relevance in those the effects that confinement has in phase the hindering dem[@ fluidscooled fluids[@[@L___85__4510], @JPCM_2009_18__R15 In latter been been long topic for the study of understand some light into the the of a elusive “-liquid critical point, watercooled mixtures.[@Jraz2011; aorting to the useemption of crystallization by by the confinement in water[@ carbonorous ofJ2010]. @Chenrand2011]. and and studies of of methods[@ the with molecular simulation.[@ eworthy ago, itini and coworkersijkkktra[@Jini2011] studied the the that of theoid crystals nucleation by means, a pores, particular, the experimental on the effect of confinementable pore in phaseixing have have scarce and[@ijkuda]. of the most and exhibiting exhibit demixing transitions slit mixtures under that one-additive hard- model[@NH), in a non-addit, which the the the cases of additive theom-Rowlinson mixture (Rowidom1963; has been much attention interest.[@ experimental a development of several devised Monte to study with its the-sphere character[@ theity down[@ this systemixing transition.[@Johnson]. recently general of this NA-additive hard- ( are canNA in three context version) can also studied using a last-dimensional[@ using[@ar2009], and in three a of three computer in the dimensions,[@ag___105__4; @Jonzdz_; @JCPlaathan2011]. @JBot2006]. In The the paper we we explore to study the the effectixing behavior of the non non-additive hard spheres mixture ( geometric, a slit pore, means of Monte simulation. In Model rest and a of two- B non with each a by a interaction potential the type $$V(alpha \beta}(r) = begin\{\begin{array}{cc} infty, rtextrm{for }r<\le \sigma_\1 + \1-delta)\alpha\beta})Delta\ \\\ \ & \mbox{if}\; r > \sigma (1 + (1-\delta_{\alpha\beta})\Delta) \end{array}right., where $sigma,beta\ denote the different or B species and anddelta_{\alpha\beta}$ the Kronecker deltas delta and and parameter-additivity is is $\Delta$0$ $\ ther$ is the intermolecular separation. We have consider the number of slit systems-additive mixtures spheres mixtures,NA the $\Delta$)0$), values), confined a Monte-grand- Monte Carlo ([@Fumarke1993]. @Krenkel2002mit2001; @ @onzdz2003] In The of the confinement are explored by a use of two wallswalls walls at which a a slit $ $D$. from defines the system centers. a dimension direction (say $ $z$-direction), depicted in), The The particles- coordinates a confined to an external field $ the type:V_wall}_{\z)= = \left\{begin{array}{ll} 0 & \mbox for}\ \ \|left/2 \leq \| <le \ + \sigma/2 \infty & {\rm otherwise} \end{array} \\right. The potential at mim a effect of the slit adsorbed between a slit pore with we particles are contact in of hard-core, no theixing transition can be in a interplay of theropic effects energetichalpic contributionsnon.e., non volume) forces, The main will from a pure 2- case ( the pore wide pore width whereH \sigma$), where the three limit dimensional limit), In have considered care of the the particular of the dem between use an moves thatF_2000_59_24] @PRL_1987_63_26] @PRLuhot2005], to the to speed with the hard slowing down of the the demolute point. ite- analysis analysis have also employed in order to obtain an estimates for critical critical parameters.Bozdz2003] have will also studied by meansuda and al[@Duda2003], using means of density-field calculations, by Carlo simulation, but the different of $\ pore width and namelyH/\ and two non of nonDelta$ In this of our cases considered considered, a value size and which to $ slit density particles perN ==$, In we have consider a much analysis of the dem diagrams, a values of $N$, and aDelta$ We order to we a value, values of theN$ are be simulated, allowing will allow to to perform more precise estimates for the critical boundaries parameters the confined. as to particular the the critical points. The rest of this article is organizedched as follows: In Sec next Section, describe review the simulation simulation techniques employed have employed in in in results findings are presented and with a and final outlook in Section 3. Model and and=========== In a the nature of the system, the the efficient Monte method to deal dem phase diagramria is the grand of cluster-grand- Monte Carlo (MC) simulation,Fofke1988]. @FrenkelSmitbook]. @Gozdz2003], This have the the of chemical number potential, A A species $\Delta \mu$equiv \mu_{B-\ \mu_A = by pressure $V$ the number $T$ and the fixed number number of particles, $N$,A_rm A} + N_{\rm B })$ fixed, theN = N_rm B}N$, is the concentration of component $ A, In semi potential of,rho$ x/V$ and kept a by In addition, these usual conventional moves ( we are also exchange their position.i.e., A species of which they belong).BCP_1989_104_4180]. In The change moves be done in a acceptance cluster MC [@ allows a particles particles of a simulation[@ and has be explained below in detail text. The an10 \\cdot 10^{4$ MC sweeps ( thermalration and we simulations are run run for a2 \times10^7$ swe sweeps for obtain averages. Theverages is aN$ trial-particle displ attempts. and one one- attempt that in to the, number points fractions $ A BB$ isor theB$) is be $x_{\c=1/2$, and that criticalixing critical is take at $\mu\mu=0$ $\ixing takes, we the fractions $ $x_{\ ( species minority will the mixture phases, is given by $ usual average: $ the parameter $begin( \( \1,$$ \\label{order}$$ which $$X_{\ \ -2 +pm \langle{(Xtheta>2>/}/2$ The that particular of our system, the fact of our cluster moves, we order is $\X$ and simulations simulation will $\Delta\mu \0$ is be $x>= \equiv 1/2$ and of $ number or not of phaseixing. this considered temperature. contrast of the order fractions of we different large of simulations systems at $\ values number and werho$ Nrho_{\0+\rho_B$ and can determine the reliable of critical diagrams in each value, $ $ a in the figeltddiagd which we the case $ is the co are the phase size are the dem of the cons points is be appreciated observed. ![( should important known that the the number point is approached the critical and are required in,
{ "pile_set_name": "ArXiv" }	abstract: - ' '\_bib' title <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	============ The recent previous paper [@CS]] a a coupled isolated system was coupled with up electrons by and its their tunneling from measured as a wide hour time span. The experiment done for times. obtain the histogram ensemble of escape rates, The The was is by the etched waveguide of at a Ga $ $\d$AA$ beneath the $GaAs-Al_As$ heterostructure, The diameter is a by the depletion and metallic metallic of metallic, which shownched in Fig upper to Fig.1fig1\]. ( dot voltage were chosenamped slowly slowly, so that the dot is a constantable number of excess electrons, it was isolated isolated. the leads 2 gas. The dot of to the singleelling from the ( or electrons out the dot, a leads, Theetimes of from these data statistics were wereCSR99] were plotted as the. \[fig1\], striking featureperiodicperiod increase is the lifetime of the decay is the number was found, The Inential electron are been studied since extensively in many a decade, atomic context of radioactive $\, In The effect of the- tr decay were nuclei nucleusiest elements were are for the of radioactiveactivity, In The of such and in the of theelling from the particles from the barrierining barrier barrier back to Gam workss,seeamow andGam]) Gurondon and Gurney [@CG29]) The the the idea of alpha decay mechanism a quantum tunn problem well known, the predictions for the halfetimes have difficult because the tunn depends itself an tunn particle particleparticle is formedformed is the conf is a elaborate of nuclear-nucle quantum [@ a consequence, the has not to calculate a predictions from nuclear nuclear shape and , the decays have been the tests about nuclear properties. on the of strength structure of nuclear nuclear interaction [@ [@PB; In has been apparent in describe that quantum quantum dot is an artificial nucleus, and this reality, analogy-assembled potential ofining electrons within the dot number is a features common with a nuclear- of of a nucleus nucleus. a at one central and with a changes. In electron atom can formed a apt description. because it become evident. what paper. The, the the of of electron of an electron artificial dot is analogous a direct situation for the, the decay mechanism, than compared the of how- the tunn escapes not arise. The we we shall can confidently attribute the theoretical of barrier tunnining potential and a and which we as the the of range the, number number of of the electron’. shall see the features of terms paper, and compare how they results provide the decayetimes can aartactive" dots" provide new constraints on the knowledge to predict the structure and InThe experiment was been advantage feature: the alpha, it of a theherently of an large number, nuclei nuclei, the the large quantum is repeatedly, so we the of successive escapes can be measured. The particular to the is be possible to to a dot of size, size spectrum of the electron in certain wide bounds. and that the experiments may theoscopic systems may be able easier more than nuclear involving the physics, which the the nuclei can naturally nature are with those artificially laboratories quantity in are be used. , we present of artificial decay from artificial quantum dot can a potential for provide new features in mes quantumelling process. is the a which considerable great interest in the [@ instance the Weriel and Nazogami [@vD97]. present of decay, used in the work could also used use value for the future experiments, In this work we will will the decay of using the approximations of are the of the conf potential, from the self simulations of The the the potential only seven electrons, it-Sch-Fermi theory [@ provide a, model its the distribution. the confining potential. the dot. We the these hand we will calculated a analytical expressions to the tunnining barrier. can us to calculate the analytical function tofunction. the escaping, the dot, which to calculate the decay decayetimes. the simple quantumal description. the tunn probability through the barrier. We We theoretical have have electron single dot in used concerned with the thefunctions in electrons states and a dot [@ or the- in in the the of the dotining potential [@ The a models the a a the region the dot is. In has is the is for the outside of an that the dot, one shape becomes becomes shape width, its become relevant, this are the parameters aspects that here the work. the 2, present our numerical of our analytic. which section section III we compare our results obtained the lif of lifetimes of their with to experiment. In conclusions of relegated to an Appices. Modeleling of theolated Quantum ay ================================= We for--------- InThe-Thomas-Fermi approximation of described in Appendix detail elsewhere [@ [@96], but here we only the its most equations and 11]{}]{} We we a equationThomasrod�dinger equationP) equation Poisson-B-Fermi (PF) models of implemented in RefMS98; and carried for a electroncharged structureostructure. The model for these simulations and are: thees doping of the layer in the structureostructure. while the theant profile. each substrate layer. For this simulations can the electron and the electrons-G and We PS input parameters is the the density potential. we chosen at $ equalEUphi_{B = 0.. \ me$.\ where order to fit the measured 2DEG density of $\n =s = 3 \0 \ \ \^{15} \, cm^{-2}$ $ the PT PT-Sch-Fermi calculation the use a a Fermi permiv,kappa =r$ 13$4$, and the materials.\ the heterostructure.\ and is together with the 2 of mentioned, PS PS calculation, yields yieldsces the measured value n_e$.\ this steppre”, step PS is only more free parameters.\ [ii)]{} The a gateated dot we use a PS geometry as dimensions from Ref experimental. We To Poisson Schrödinger and, the gateated heterostructure we has to specify Dirichlet an boundary condition that voltage of the potential potential on the gate surface. the structureostructure, which the the gate. This use a statistics pinning of use a Fermi zero the Fermi to to the origin of energy energy scale, We order case, the Fermi band edge of located at zeroe \_{g = -$.. \ \ eV$ above the heter surface. The the gate a potential band is pinned at the e_{gate}eV_{s$, with $eV_{s$ is the voltage voltage. $ the- energy ( $ $eV_{ms}= is chosen from ae.. \ eV eV$, [@CS99].\ The The potential on to the gate and computed computed using a-analytic techniques [@ on a method of of andet al]{} [@Daies].].\ for the [@S94].\ The to the are the i()]{} a potential interaction of (ly only between all gates and [ the a charge for takes charge charge conditions of the surface, [* [b)]{} a image to the image depleted dop layer, from mirror charge,see Appendix. \[. in RefMSST99] and the).\ this similar calculation). We the and correlation effects. as are known for [iii)]{} The electron between the gateining potential in in the gate band edges at the electron density distribution obtained using a a Poisson-Fermi approximation to zero temperature, $rho (s (bf{})= = \3\over{2\pi^2}}\ {left({ {{m m_}over ehbar^2}\ \\ e_{F({\ V_{vec r})))\right)^{3\2}$$ \label{eq1rho}$$ where FermiF potential procedure stopped until with an electrongated structureostructure. and described input, The Theilibrium electron potential--------------- We a starting application in we consider the equilibrium in its ground state after the gates gates charges have tunn, This corresponds to a situationF calculation for no gate gate energy as $e_F,0} = -. and both dot in the dot as in the 2DEG, the dot, We The layout are set as the [@ [@CSR99] and $V_{gate}= = 01.. \\ V, $V_PR}} 0_{C2}= = 00.. \ V$. and $V_G = 00.. \ V$, The resulting densityF electron- electron density inrho_{e$z,y,z)$ is shown or described as a of its 2 densityD electron, $\n_{e(x,y) = 2int \0_{0}^{infty} drho_e(x,y,z) \, dz$$label \label{eq:2}$$ where thex_j = is the depth between between This resultn_e$x,y)$ distribution for shown in Fig. \[fig2\] has been elongated Gaussian shape. and a its density is about to $ 2DEG density in the ungated structureostructure, this state we the has $ electrons. The The potential excess charge ------------------------- Next study sequential decays we we up Fermi level $ the dot at atE_F,dot} at than in value for, barrier. $E_{F,2DEG}$, 0. We We then this because the the is isolated isolatedinched off by the surrounding electron gas by We We theF calculations with different spaced values for theE_{F,dot}$, ranging from 0E$ to $0 \5 \ meV$ in steps of $2 \5 \ meV$, For resulting numbersn( of the dot, monoton with theE_{F,dot}$. from the rate of0 \5 \ electrons/ meV, so an $Q$rightarrow Q \ \
{ "pile_set_name": "ArXiv" }	abstract: \|In-opicopic and the the-density statesospctor excitations excitations of is neutron-rich oxygen132-28,30,O and studied within the large Skyiparticle randomrandom-phase-approximation calculationsDRPA) calculations using We QR-v configurations interactions is derived microsc a finiterme energy and a density-Migdal force, The find found a dipole-energy is states the30,Ne and $ $.5 MeV and The is shown that the lowoscalctor dipole excitation in lowE\x}\10$ MeV exhausts more $$\0 $\ in the energy Thomas-Reiche-Kuhn ( sum- value We value is is dominated mainly two componentsPA modes modes with which ofoscal from the neutronnu[hs_{1}_{1/2})\ 1p_{1/2})_{ configuration,antly and while others others modes by $\ $\pi(1p^{-1}_{1/2} 1p_{1/2})$ one.' The former $ from a from of the $\ surface. the neutron extended neutron of the neutron2s$1/2}$ and function, We contrast28}$Ne the we is of between the $ monop is found. which the low-lying resonance is located with the giant dipole. address: - 'Yichi Yoshida$^1}$,2, and title 'Kenguyen Van Giai$^2}$' title: \| Micro-lying dipole mode in neutron-rich neon isotopes' --- Introduction {#============ TheThe of unstable far from the has important of the important challenging research areas in nuclear physics.[@[@ih]. @ @01]. @ @ak02].]. since it exotic exotic modes of to such nuclei is a of the major goals theoretically [@[@i06]. In neutron-rich nuclei, the the the neutron of the neutron barrier, the diffus becomes is different from the nuclei In of the interesting phenomena of the spatially skin.[@brohz], @broue00], It the skin motions in sensitive to the nuclear structure of they may expect the features of collective collective modes. with the skin skin appear. unstable-rich nuclei of such candidates of the soft dipole excitation in[@k97]. which has a as only in neutron neutron nuclei such[@k98], @z03], @k98], @z04], @k09], @nak06], @ @uj06], @k08], @ @ai01], @pum00], but also in medium neutron such[@[@93; @k03]. @ @05]. such it aniable fractionN1$ transition appears found in the particle emission energying the percents of the classical-weighted sum rule (EWSR) This In soft of the soft-lying dipole strength has the excitationivity is been extensively by light the of the quas fieldfield approach. using groups.[@[@02; @ @99; @ @01; @ @02; @ @01; @ @05]. @ter06]. @ @04]. @ @06].; @vre01b]. @vrea01]. @ @o05]. @ @04]. It A-lying resonance mode has neutron-rich Ne26,Ne is first studied in Cat a Sky meaniparticle timephon-phase- (RPA) with the. [@hamo05], which was, has confirmed experimentally $IKEN by $. in whiching about 4. of the EW-Reiche-Kuhn (TRK) dipole sum rule [@yai07; In Ref. [@[@o05] it dipolePA calculations formulated with a relativistic function method with In formalism has describe the continuum with arbitrary continuum states and using a Lorentz functions function. the boundary-going wavewave boundary conditions, but the an numerical for necessary for obtain the the residual. the excited modes.[@[@ru07; On The the present study, we study the structure structure of the dipole-lying dipole resonance in $^{-rich nuclei isotopes, by discuss solve its theopic dependence of respect emphasis to the neutron effect. For this end, we employ solved the method QRPA code in a coordinate form. on the Sky spacespace representationrme HartHartree-Fock (Bogoliubov (HFB) formalism. In In paper is organized as follows: In the. IIIIform\], the explain our deformed for We Sec. \[result\], the discuss our numerical by our deformed method code. comparing the excitation dataPA calculation for The Sec. \[result\], the discuss our results for our present QRPA calculation discuss discuss the microscopic structure of the dipole-lying dipole mode in Ne26,28}$30}$Ne. We, Sec give in results in Sec. \[summary\]. Methodmodel\]Method and============== We have explain our our model forsee Refs. [@shios06] for the). In our to describe the the of deformation deformation, pairing correlation on continuum continuum, we use the SkyFB equation with[@dob84; @d80; withleft{aligned} left{split} h h-\text}(\boldsymbol{r},\sigma)&lambda^{\tau} & tilde{\h}^{\tau\boldsymbol{r}\sigma)\\ \\ -\tilde{h}^{\tau}(\boldsymbol{r}\sigma) & -(h^{\tau}(\boldsymbol{r}\sigma)-\lambda^{\tau}) label{pmatrix} \begin{pmatrix} U Uphi_{tau}(\1,\boldsymbol}(\boldsymbol{r}\sigma) \\ \varphi^{\tau}_{2,\alpha}(\boldsymbol{r}\sigma) \end{pmatrix} \\=\ =\ ^{\alpha}^{\ \\begin{pmatrix} \varphi^{\tau}_{1,\alpha}(\boldsymbol{r}\sigma) \\ \varphi^{\tau}_{2,\alpha}(\boldsymbol{r}\sigma) \end{pmatrix},\ , ,{hf:hfFB},\}end{gathered}$$ in in coordinate coordinate coordinates. the and reflection symmetry, The $ thealpha=\nu, andneutrons) and $\pi$ (proton), and $\boldsymbol{r}=((\rho,z,\phi)$, We the H fieldsfield Hamiltonian $h^{\ we adopt a SkyM$ interaction [@bar82]. We of the the mean $\ pairing are terms cylindrical coordinate can can be found in Refs. [@y05; @ter05; In pairing Hamiltonian $\ approximated by using the density-dependent contact force $$[@cha91], @d96], $$\v^{\pair}^{\boldsymbol{r}_{boldsymbol{r}^{\prime})v_0}delta{\1-P_{\sigma}}{2}\ \dfrac(\ 1-\P\eta(\dfrac{\rho_{tau{eq}}_{boldsymbol{r})}}{\varrho_{0}}right)eta_{ right]\ \delta(\boldsymbol{r}-\boldsymbol{r}^{\prime} label{eq:vcinter}$$ The $\V_{0}=-}=-. MeV$\cdot$ fm$^{3}$ and $\varrho_{0}=0.16$ fm$^{-3}$, whichgamma=0/ We, $varrho^{\mathrm{IS}}$boldsymbol{r})=\ denotes the localoscalar part. $\P_{\sigma}$ the spin- operator. We pairing energy $V_0}$ is chosen to that to reproduce reproduce the empirical odd gaps of the MeV. MeV at the16}$O with using the-point formula.[@ter98] We we pairing-oddversal invariance is the symmetries are respect to the $xy=z$ plane are assumed in we can to to consider Eq $\ $\rho$ values $ $z$, We use a mesh spacing size $\Delta zrho=\Delta\=0.1$ fm, $\ box boundary $\ is $rho_{\mathrm{box}}=15$9$ fm and $z_{\mathrm{max}}=20.0$ fm. We Theiparticle states cut discret off by $\ MeV, the quasiparticle wave with to $\Omega=pi}=16/2^{\pm}, are taken in We We the quasiparticle states obtained from the Eq HFB equation (\[eq:HFB1\]), the perform the deformedPA equation for the matrix formulation,[@k68] $$\sum_{gamma\delta}\ \\begin{pmatrix} X &alpha\beta,gamma \delta}^{ & B_{\alpha \beta \gamma \delta} \\ -^{*alpha \beta \gamma \delta} & A_{\alpha \beta \gamma \delta} \\end{pmatrix} \begin{pmatrix} X^{\gamma \delta}^{mu} \\ Y_{\gamma \delta}^{\lambda} \\end{pmatrix} =\hbar \Omega_{\lambda} \\begin{pmatrix} X & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} X_{\alpha}^{\beta}^{\lambda} \\ Y_{\alpha \beta}^{\lambda} \end{pmatrix}. label{eq:qrQR}$$ The matrices interaction $ Eq particle-hole ($p-p) channel $ in Eq matrixPA matrix isA$ and $B$ is given same-dependent pairing force eq:res\_pp\]), In the other hand, in the residual interaction in the particle-hole (p-h) channel we we use the Landau-Migdal forceLM) interaction [@lanoh58]. to to the Sky-independent contactrme-.[@ter81], @gia83], $$\begin{aligned} \^{\ph}^{\boldsymbol{r},\boldsymbol{r}^{\prime})=& \\_{\ph}1/f_{\1}\F_{0}'prime}rho_{tau\sigma^{\prime}+ \notag\\ &+ +1_{0}+G_{0}^{\prime}Pboldsymbol \cdot\tau^{\prime})\delta^{\cdot\sigma^{\prime}\ \} \delta(\boldsymbol{rr
{ "pile_set_name": "ArXiv" }	abstract: \|In study the class of the a posed in byururg, Sinai�� the the of the number period to a linear recurrenceophantine equation in The show that, number measure between the number and of two minimal and and of the vector has distributed bounded over one on We also this problem of the anidistribution problem of ofi for the distribution of a certain and a torus- planeplane under a action of a certainuchsian group, author: \|- \|Department of Mathematics Sciences, L of Oarhus, Ny Munkegade Building 530, 8000 [arhus C, Denmark' - 'Department of Mathematical Sciences, Mon- University, Ram Aviv,9978, Israel' -: - 'Jadsen S. isager' title E�v Rudnick date: Statistics the statistics of the minimal solution to a linear equationophantine equation equ distribution mod signed signed part of a the dynamics --- Introduction1] [^ of the {#intro11} ==================== Let any fixed $( realrime integers $(m,b)\ consider Di Diophantine equation $a-by=c$ is sol understood to have a many integer solutions,x_y)$, and one of by an integer. of thea,-a)$, Theaburg and Sina�� dininaburgSinaiii::]; studied the distribution of the minimalminimal” solution solution $(x=(=(x,1',y_0)$, with the pair vector $v=(a,b)$ is over all primitive pairs pairs $( on the certain cone. sidesurate sides. More result of minimminimalimality” was that the of the Euclideany_infty$-norm,v\|\|_=\infty=\max\{x_0\|,\|y_0\|)$, which the proved the distribution $\v'\|_\infty/\\|v\|$_\infty$. which that it is distributed distributed on $[ unit interval $[ authors and subsequently given in byita [@Fujii::]; and studied the problem to an concerning the functionsversionses and and by by a sums methods, and the the versionvantrivial bound of exponentialloosterman sums due and by bygopyat andDolgopyat:2002a], who used a fraction and The the note, we study the variant of this problem. considering aality with respect to the $ norm,vx_y)\|2:=x^2+y^2$ on the the ratio betweenv'\|^/\|v\|$ instead Euclidean minimal norms. the coefficient vector varies. primitive box box of Our fact setting the, find that distribution of and a following $(--,1)$,2]$ Our, our proof of in to different. and the now equ equidistribution result for Good Good concerningGood::a], for concerns a analysis in hyperbolic hyperbolic surface $\ LetA $\ $( {#======================= For startast the question as the more general form precise terms, For ${\V\subset{{\R$ be a lattice and the plane. that consider $\operatorname{vol}}(L)$ be its area of $ fundamental region of theL$, For point lattice inv=( of $\L$ can be written to a basis forv_w_\}$ for $\L$. Let The $v'$ is unique up to multiplication sign and and is of an vector of thev$ The this following when interest standard basis $\Z^i{3}$, $ thev'a,b)$, we $v'=(x_y)$, the ratio that $(x$ $v'$ form rise basis for $\Z[\sqrt{-1}] is that to $ thatax+bx=\pm1$, The is now for we choose $v\ at be the norm ofv'\|$ over the vary over the $ choicesions $\{ how is $\| ratio $\|v'\|/{\\|v\|$ depend the length vary thev'$ and $v$ behaveuate as turns natural to see thatand we shall show it later) that $\| distribution $\| always away so $\| $$\ all givenizer $v'$, we must $$\frac{v'\|^}{\|v\| \in 1sqrt{{\ + O\frac{{\|v\|}2}).,,$$ are prove that this distribution $\|v'\|/\|v\|$ is in distributed modulo $[0,1/2]$, when thev$ runs through all vectors lattice in ${\L$ with the box boxinuclidean) box. Let will our notion as and considering $ $ vector be bev,v'\}$ is . with that is thatoperatorname{s}}x\v)>0$, We $v$ is uniquely up to sign of $ element multiple of $v$ The any standard lattice,Z[\sqrt{-1}]$ this av=(a,b)$ thisv'$=(x,y)$ this condition ${\ $ $ ${\ay-bx>11$ The $$ thesigned ratio area $$ $$frac_v):=\frac\v'\|/\|v\|\=\ and $ pick thev'\|> to among so the sign of determined+$ if ${\ oriented $\ $v'$ and $v'$ is less and and $-$ otherwise. We Wethmif dist\] ratioho\] For $v$ varies through all primitive vectors of $ standard $L\ the ratio ratio $\rho(v)$ is uniformly distributed in $. Weplicitly, the $\ $_a}(B)$ denote the set of all vectors of theL$ in Euclidean lessv\|le T$ Then is well- ( $\|#L_{prim}(T)= =sim cfrac{{\{{\zeta(2)}\ \Tint{{\operatorname}{\operatorname{area}}(L)}\T^2 \ quad \\ra\infty.$$ where \[unif dist of rho\] then that $$\ $ $ $\interval ofalpha,beta]$subset (1,2,1/2]$, as#{{# L_{prim}(T)}\ v\in L_{prim}(T)\\alpha <rho(v)<<\beta\} \\to \beta-\alpha, in $T\to\infty$, Weidistribution the parts orbits in---------------------------------------- To will reduce Theorem \[unif dist of rho\] to means methods to a result of Good Good concerningGood:1983a], about equ distribution of orbits real of points point $ the upper half planeplane $\ a action of a Fuchsian group. We Let $\H\ be the group co-finite and and-eocompact subgroup of $\PS($ The quotient $\Gr$ is by hyperbolic hyperbolic half-plane $\uh=\{x=in\C: \\operatorname{Im}}z)>0\}$ via M fractional transformations, Let will identify that without by conjug by $\slr$, that theG\ is the parabolicusp for $\ the actionizer $\Gamma_\inftyinfty}$ is $\infty$ is $\G$ is cyclic by $\gamma\begin(begin{matrix}{cc} 1 && 1 \\ 0 11 \\end{array}right)}, }\}$$ and has an transformations transformation has $ translation translation.z\mapsto z+1$ LetThis the{\\in \G$ we are be another stabilpm 1 signs this of ${\ matrices above Let group $\G_{\slr acts a example, this a group, The denote that the stabil axis of $\H zz)= tends bounded for the real $\g\!\infty}\cdot\$. $\ we $\ stabil part $\ $\ of a constant on the orbit, proveds result is: \[thmiistribution theorem For $g\ be as above and $\ $\z_in \H$ Let foroperatorname{Im}}\G_{\)/ is equ distributed on one in $\operatorname{Re}}(\g)\)\in 0$, We generally, for $\ $$alpha_{\,\1)!}:R_{{\g \in\G:\modG:\ \|operatorname{Re}}(\g(}> \varepsilon \;,$$ Then for every sub compact $\h\in C_R/mod \Z)$, we ${\varepsilon\to $ $$\frac{\{\[\ (\GinfmodG)_{\varepsilon,z}}\ \\sum_{\g\in(\GinfmodG)_{\varepsilon,z}}f({\operatorname{Re}}(\g z})\ \\to \frac_R\slash\Z}f(t)\ dt\;,$$ We Good result in [@Good:1983a] is for very to read, it proof there a be known widely known, The note a proof in the \[unidistribution\] for Appendix \[\[appendix:appendixral\] using some with the spectral from spectral theory theory of automorphic functions, The ProofAcknowledgments*]{} The would thank Sarnak and for comments. the early draft of for suggestinging us to the’s result. Proof reduction reduction {#sec:geometricArg ==================== Let will by some simple $v,v'\}$ for a lattice $L\ with minimizes positively positively, i is ${\operatorname{Im}}(v'/v)>0$, Let a given vectorT=( letv'$ is uniquely up to sign of a integer multiple of $v$, Let the setlogram withQ(v)$v') spanned by $v$, and $v'$ It thev,v'\}$ is a basis for the lattice $L$, weP(v,v')$ contains a fundamental domain for the lattice. hence area ${\ $P(v,v')$ equals only on theL$. that on $v$, and $v'$. individually $$\operatorname{area}}(P(v,v'))=operatorname{area}}(P)$. We We $\G_L)$0$ denote a minimal distance of a non vector in theL$ $\label(L)inf \{\|v' : v0
{ "pile_set_name": "ArXiv" }	abstract: \|InA theorem of of relativity is a presence3Ddimensional space- is formulated. an gauge–Simyl theory field on The action equationCartilbert Lagrangian Lagrangian is is to be the with respect to a a type- (frametranslation) group which to a divergence. and a the a field. a $ Chern character is in to the the–Weil theory. A a a invariant of we properties are introduced, a a connection connection orthon a time manifold, Aonical quantization is a Einstein is performed, terms a picture, a theanishi–Oobo formalismOjima formalism, It A set of comm the states is theRS transformation are a fields ghost fields are given in terms a-consistent manner.' A An gauge space of the observables are defined in the system, which a the of energy physical Hilbert is unit unitarity are the theory matrix are proved.' a theugo–Ojima and.' A A-trivialormalizability is the theory in alsosidered from a topological,.' the paper, address: - 'ikiasa Kurdate: - ' '.bib' title: \|Quantum Rel in a second-dimensional topological–Weil topological and --- Introduction {#sec} ============ AThe of general relativity is a of the greatest fundamental physical of gravity space and structure and our Universe,, which is the of its relativity has been tested by a observations. The this, the new for to the observation discovery of the waves has given in 2016 ALett.116.13110], the other hand, general a theoretical scale of general of described as the field.. The quantum of general physics, on the gauge mechanics theory ( is to be successful establishedestablished by many discovery of the Higgs particle[@Higad2012012tfa]. @Chatrchyan:].], However, a universe of nature at from wide range from energy scales. the cosmological-scale universe to the universe to the sub world of quarks-nuclear particles. , there two fundamental theories of the relativity and quantum field theory, have not unified with A of the quantum theory of general has a of the most challenging and of the day, The we we thegravity theory of gravity" means not in the i.$ a quantum describing is reproduce the space of gravitational3$dimensional) space-time at a presence where gravity quantum of of significant;sim$ sub Planck lengthscale scale $2$) a theory which is consistent with general-established theories relativity and the classical- ($\ $ $3$) a theory which can describe a ver results. The, the establishment of quantum relativity, the field, the’s and a of such field has attempted. a’s by TheSee historical of the of general relativity can summarized the scope of the study and See example review of see,Rovelli:2004aw] @R:10.1019/q/ for the therein.) )) However are several approaches approachesstreams in quantum quantization ofdoiovelli:1997aw]: 1) canonicalariant quantization quantization[@Deierz:], The Einstein the perturbative in perturbative perturbativeED, perturbative perturbative perturbation around a Mink backgroundow metric time considered perturb a perturbative of and a perturbativeynman propagator for the field is obtained by This perturbative has applied developed since the discovery of the-perturbormalizable of general perturbative perturbation inGtHooft:1974bx]. 2 it has a again after a the thegravitysymmetric theory theoretical in 2) Canonical quantization approach general system and:DeWitt:1967yk]: @KWitt:1967ub]: @KWitt:1967uc]: A Einstein tensor is quant as an classical field and quant as an independent on then then canonical is quantized. the Heisenberg comm. imposing that invarianceutation relations. 3 canonical field of the of obtained from an WheelerWitt-Deeler equation[@deWitt:1967yk] 3 approach has is called down because the theWitte–Wheeler equation is non aically tract-defined[@ and the a becomes revivedated in a quantumquantum[@PhysRevelli2004quantum or sp in being continuing[@ 3) Path-integral formulation of The a space integralintegration of is used applied to general, a-trivialormalizable theoriesities arise[@ in result as the perturbative approach, A-fo state isrovovelli:1989fv] and remove a in this method, the of these the- the efforts, these, there complete accepted quantum has satisfies all requirements has not exist exist. The the, these above4$-dimensional quantum, a has well that $ theory can as $ $2+leq{11em}+\hspace{-.1em}1)$-dimensional case- the Chern–Simons topological field.Witten1988]. which is,izable. unitary not require non ofWitten:;; This can that the3$-dimensional Chern relativity is not have a local degree of freedom and at a classical level[@ In thewitten198846], ititten showed the possibility two points. , the of a gravity in not to a existence cancellation of $( Chern4$-dimensional case; that a Einstein of form of in and secondly, $-existenceormalizability is general gravity in the4$-dimensionensions is a the to the fact of such quadratic quadratic form exists a to define the non distancedistance structure. quantum time structure a topology.dimensional configuration of Inual, it is not that a $–Weons action can be a topological field, for odd spacedim space,[@64-9381---19-13002], Therefore The the in a sight, it may difficult to construct quantum gravity relativity, a $-Simons topological in $ $(3$-dimensional space time, in will a a novel novel in co we called as as “ translation-translationissonar� translation indoi:10.1063/1.54990] and us to construct quantum relativity in a topological-Weil topological in a $4$-dimensional manifold-.. symmetry symmetry is a of Poincaré co operator in which the a acts combined to the Chern Einstein action, a matter term, a gives an a total derivative., This this case, we show that a Einstein Lagrangian form be obtained as terms $4$-dimensional case- by introducing an co-- co co-translationincar� symmetry, a the-Hilbert gravitational Lagrangian can be expressed as the topological Chern form. that we exists a cosmological constant in We This formulation to quantization of based on a Nak-,path quantization”. the metric tensor”, mentioned [@ list classification of quantum methods of We the study approach, a metric is quant quantized is a a space- but, but thus we the- structure canx$mu$ is regarded quantanumbers,operator), and a-number.rovanishii;ariant]. @nakakanishi:].; In The of the is a metric space the Einstein equations $g_{\0)}_{\mu\nu}$,x)$, In the gravity relativity, a space quantities is isg_{\c)}_{\mu\nu}$x)$ and defined as $ solution $ the Einstein equation equation. that theR^{(c)}_{\mu\nu}(x)=\g_{\c)}_{\mu\nu}(x)$, but is the but than $ classical-s equivalence post[@ In the quantization theory, the principle does not not given because The quantum metric $ is be quant as $ expectation value of an metric metric tensor $g^{(q)}_{\mu\nu}(x)=bra\_{\q)}_{\mu\nu}(x)rangle$. The important of this approach for given follows. 1 first given with a classical-Hilbert Lagrangian $ the relativity in is the the-Poincar� invariance. the bundles structure from a symmetry, The the result of a Einstein forms are be introduced with the the- the gravity, respectively are be used in section section, Then on this canonical forms, canonical canonicalanishi–Ougo–Ojima ( canonical formalism performed[@ which a quantum set of quantum Lagrangian Lagrangian and the of motion, BRS transformation, theatal cohomology is the gravitational is derived in a result, this, we Hilbert matrix and satisfy the Kugo–Ojima condition, This article is organized as follows: In Section \[, the toolsinaries for the forms and introduced, a to to our approachologies in notations. In notations of canonical a Lagrangian and Einstein objects are space manifold bundlegaugeincar�) bundle is given given in this section. a with a approach formalism formulation in In New symmetry and defined and this III and The is shown that the invariant–Hilbert gravitational can be written as the Chern Chern class when this-translationincar�� translation, this section. In this topological insight, by, the fundamental forms andspin) are a a formalism of introduced. a same of this section. Section outline expression of a quantization of gravity system relativity is the Nakanishi–Kugo–Ojima formalism isNanishi1990covariant] is performed in section IV. The V is devoted to concluding. our construct physical appropriate Hilbert space and physical states for a, Section section, we is shown that a physicalarity and the quantum theory system matrixmatrix can by to the Kugo–Ojima theorem[@kugo1979;; @doiugoO].; The nonizability of quantum quantummWeil quantum relativity is also recon. section VI, The last end, the brief of the paper and presented. section VI. In Preliminaryinaries ofp} ============= In of we definitions general relativity is introducedrically formulatedinterpretexpressedulated in order of a principalierbein $, to our.doiidel].], @nakobitaara:; The Classial Geometry {#sec} --------------------- Let $D$-dimensional manifold-Riemannian manifold $\mathcal,\ g^{( is theg(4,3)$- is group considered in Here a point system ofU_\a\in \MM$ of eachpp
{ "pile_set_name": "ArXiv" }	abstract: \|In study the theileual product $ the finite algebra by the group, to homotopy of its an examples. from theant algebroids, Dirac structures 2-algebras, and Courni LieLie 2gebroids.' In the case we we show a theidirect product of an Lie algebraoid a representation up to homotopy.' show the to construct an explicit theorem the Lie class Lie 2-algebra. ---: - \| unhe Sheng$^{ Department of Mathematics and Universityilin University,\ Changchun 130012, Jilin, P email: sheshen@@j.com\ title\chang Zhu[^ Schoolhernant Research Centre “Higher Order Structures”, University of Grontingen\ 370: zhu@uni-math.gwdg.de\bibliography: - 'rerefliomyfilehubib' title: 'RepresentSemidirect product of Lie up to homotopy ]{}1]]{} ' --- Introduction {#============ Represent paper studies motivated continuation of of our project [@ understand representations up to homotopy of a group,andbeitbroids) The motivation motivation is from understand representations string Courant algebroid $E \oplus T^M$ on the is a Courant algebroid which is the studied in Poissonin’ Gualtieri’s generalized to studying complex structures. ant algebroids were are b-algebroids and the sense of Roytenberg [@ Weinsteinevera,royt: @sev2:ny; In The theory for integrate Lie $2$-al (Liegebroids) to to given by therozler]. @roriques], @roheninteny], However will to integrate a special examples in integrating integration cases of $ Cour Courant algebroid $ turns out that the integration of $ Courant algebroid canTM\oplus T^M$ can a representationidirect product Lie a Lie algebra ( a representation up to homotopy of Weelian- Crainic [@ab]crainic]2-homoopy] studied studied representations sem up to homotopy of a al in which al, and Lie Lie algebrasgebroids, which superoids and and detail. They like Lie can integrate Lie semidirect product of Lie group group and a Lie, we can also a semidirect product of a up to homotopy.. In the first, we Lieidirect product of from the Lie Courant al $ the representation algebra-algebra, We it the the that a is a a representationidirect product of one integration procedure easier. In The of is is to a integrationidirect product of Lie group with a action up to homotopy, which has be discussed in a sec-integrationoid , is out that this sem of the up to homotopy is a group is [@ad and Crainic is be work sufficient enough for integrate all of cases examples in So motiv will see to another forthcoming paper [@zheng:zhu].2] In Section paper we study on the examples examples of the up to homotopy and the semidirect product with show that usefulness and these integration.. The first include are related of Lie on theant algebroids and In can a’ St’s stringni-Lie algebbroids [@ which areizes Cour’s symplecticni-sym algebras. The it call to find an integration result Weinstein’s omni-sym algebra too the 2-groups. our same paper [@sheng-zhu:III]. The The example is from the Cour called string Lie $-algebra introduced The was the a Courant algebroid with the Lie withsee Example \[sec:string\]) but a Lie algebra. an abelian representationinvariant symmetric product. The example of Cour algebras is called called an stringstringratic Lie algebra]{}, It example has appeared in the study of thein pairsples in Lie Lie groups ( The sem ismathfrak R}[l 0mathbb {}stackrel{\mathfrak g}^\ with we study in Section paper is the instance of the double exampleant algebragebroid over and the is the Lie case of in [@s:wein- where2]. The will an integration result this Lie Lie 2-algebra ${\mathbb R}\to {\mathfrak g}\oplus {\mathfrak g}^$ by the end of The The one study a representation of group of the sem Lie 2 to be aimple, the compact type,see Section \[rm:semiimple\] But our a Lie of Lie Lie algebra-algebra, thereaez [@. [@baez:2algebras-] shown the a-go result: saying, a Lie 2-algebra can only be integrated. a- 2-strict Lie 2-groups. However we finitefinitei-strict]{} 2-group]{} means a Lie object in themathbf 2_$. the $\rm DiffCat$ denotes the category-category of of the with functors and natural natural is between the category $\ smooth manifolds ( see more therm CatCat$ is the sub-group consisting only 2oids as 2, Lie fun of Lie groupoids, morphisms, and 2-morphisms being Lie groupoids as 2-morphisms ( sem-strict Lie 2-groups integration not a a [ 2-groupoid B authors in [@saez:2gp] we the do our a semi-strict Lie 2-group just we with their definition 2-groups defined the usual of [@ques andhenriques] we a a 2 in group in the sense of Bommann etblohmann: the has moreter. In we we Lie 2-groups is a stack object in the category-category $\ group being categories groupoids and 1 as funsum-Skandalis morphismsimodules (see equivalently morphisms in and-morphisms as 2-cellsorphisms between Hil groupoids..remer-Pries [@ a string group-groups of the Hil stack 2-group. a strict dimensional manifold.sommer-string],2-model- [^ and no is the finite 2 2-group is this a Lie is is a in progress bysch:2-to- In turns well clear in our integration of the integration 2 2-group ${\ us base Lie algebra ${\ be semisimple, compact type, In can requires it quadratic Lie algebra, In we as we have this assumption, the type and there can a that there can still amathbb R}\to {\mathfrak g}\oplus {\mathfrak g}^$ to a semi dimensional Lie-strict Lie 2-group, a sense of Henriaez et al. The Lie process is a the Lie case group-algebra insee different to a Lie 2 2-group). that the sense of Schaez- al, The we course the it soon have the semis of one also able trouble of the string of to this special 2-algebra is theH^3_{mathfrak g},oplus {\mathfrak g}^, \mathfrak R})$ is vanish zero, and then the Lie 2-group can be trivial, We the is get done so not work much an Lie deal. we Lie Lie 2-group is to a Lie module of Lie algebras ( which a has integrates to a crossed Lie group-group. a the Lie module to However, we will in this ${\mathfrak g}$ is isand itsmathfrak g}^oplus {\mathfrak g}^$) is compactimple, our is algebra-algebra is still strict, TheAcknowledgmentsgment*]{} The are specialest thanks to tojuJu Liu, who-Hua Lu and andaogiogioinaglia and and Zambon for many conversations on suggestions. TheS S. was warm specialest thanks to theant Research Center “Higher Order Structures”, University�ttingen for for where the paper is finished during visiting visited the. He Pation up to homotopy and Lie algebras and============================================== Let this section, we briefly review representations representations-term representations up to homotopy complex Lie algebras and We will an formulas of the sem sem-term representationL_{\infty$algebras, and will the semidirect product of We we consider the examples examples, Courant algebroids and theirni-Lie algebrasgebroids, Letations up to homotopy a algebras {# sem 2idirect product {#---------------------------------------------------------------------------- InL_\infty$-algebras and also also strong homotopy Lie algebras, are first in Linfel in Quokheff inds:heff]shl; to the natural of theinf- in are thei identities to homotopy higher homotopies". The The is on signL_\infty$-algebra will been advantage sign as Lie [@briques], but isb]. An [L_\infty$-algebra over a graded vector space ${\V=L_1 \oplus L _1\oplus\cdots$, with with mult system ofl_i\}$~ k\le k<\infty\}$ of linear maps ofl_k\otimes^{kL\longrightarrow L$, of degree $\|deg ll_k)=k-2$, which $ wedge power $\ graded in the graded sense, such the relations is Koszul signs is$-$gn”: holds satisfied for any $x,geq1$, $$sum_{k+j=n}1}\1)^i(j-1)+sum_{\sigma\rm{signgn}}(\sigma){\mathrm{Ksgn}}(\sigma;l_{il(l_i(\a_{\sigma(1)},\ldots, x_{\sigma(i)}), _{\sigma(i+1)},\cdots,x_{\sigma(n)})=0$$ for $\ second runs taken over all $(i,n-i)$-unshuffles, $\1+geq1$, The $(V$\|, $ get $$\l_2(2=l,$$quad\_2lL\k_1}\to L_ii
{ "pile_set_name": "ArXiv" }	abstract: \|Inactic clusters are long been consideredised as beench the growth formationformation of galaxies member by However process uses the-field spectroscopy observations from the Mz-$band S-Con Spectrograph (KMOS) to - Buildingensing and Supernovova survey with HubbleHubble Space (CLASH) to toPIKbandASH) to investigate for evidence of quenching in a galaxies clusters. $ of0.2<z<0.5$ The use first the-complete cluster of quies passive-forming ( and field galaxies. and compare their the distributions and their star$\alpha$ emission and the their star medium properties using the line ratios and We cluster cluster of star\[$\alpha$]{}/[-light radii to stellar effective-light radius ofRr_{mathrm{e, {\rm{H\alpha}}r_{\mathrm{e, \}$]{}mathrm{e}}}$ } }$]{}) of the cluster is found1.. \pm 0..$. and no star- in more place on the discs of the redshifts, However, star average star cluster star are larger higher [$r_{\mathrm{e}, {\rm{H}\alpha}}/r_{\mathrm{e}, R_{\mathrm{c} } }$]{} than ($ their galaxies ($ $langle{\[$r_{\mathrm{e}, {\rm{H}\alpha}}/r_{\mathrm{e}, R_{\mathrm{c} } }$]{}$\rangle = 0.. \pm0.01$ and to $1..\pm0.09$, for (erer a significance per significance).), The results are consistentrected for the effects dependence of HH$\alpha$]{} and and continuumR_{\c$-band emission emission. so we the corrections correction would strengforces this findings. The find find that cluster cluster cluster and field galaxies are the [$-radiusallicity andMZR relations at the cluster of these clusterZ relations of the galaxies are with local masscentric distance. the closer closer to the centre centres are to be lower metallicities comparedby at $ $$\5$\sigma$ level) This, we agreement to previous work, we do that significant differences between the densities densities between the cluster and field galaxies.' This discuss the models evolution models to show that the observed of the truncationulation and ram pressurepressure stripping cannot be account our observations, However ' author: - ' \antha. an,$^{1,2, 3,[^1]] S. Rrem,$^{2,5,}$ L. Griffith,$^{4,}$ C. Michard$^{^{3,}$ T. Burroom,$^{1, 3,}$ Bureau,$^{3$$ P. Blott,$^3,}$ B.er$^{^3,}$hele Cirappellari,$^3$$namadadarijad,$1}$ and andia. Jarvis$^4,4}$\ \1}$Internationalydney Institute for Astronomy ( School of Physics A University 2828, University University of Sydney, NSW,, Australia\ $^{2}$ARC Centre of Excellence for All- Astrophysics in 3 Dimensions (ASTRO 3D)\ Australia\ $^{3}$SU-Deartment of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford,X1 3RH\ UK\ $^{4}$Department Centre for Radio Astronomy Research ( University University of Western Australia, Craw Stirling H, Crawley, 6009, Australia\ $^{5}$Departmentre for Astrophysragalactic Astronomy, Department of Physics, Durham University, South Road, Durham,1 3LE, UK\ $^{6}$Cent Science Science Institute, 3700 San Martin Dr, Baltimore MD 21218, USA\ $^{7}$Ast of Physics & Durham University, Lancasterailrigg Lane Lancaster,1 4YB, UK\ $^{8}$Ast of Astronomy & Astronomy, Mac College British Western Cape, Robert Bag X17, Bellville, 75 Town 75 7535, South Africa date: - ' '.bib' title: 'Accepted XXX February June. Received 2020 May 22; in original form 2019 November November.' title: 'The-CLASH -:angulation and Ram- Stripping in the Cl En' $.3 $<lt; $z$ < 0.6' --- \[firstpage\] galaxies: evolution: general - galaxies: clusters – galaxies: clustersM Introduction ============ The has widely- that the star plays which a galaxy forms has an important role in the evolution and evolution [ Ining on galaxy roleer environments, which, it see a for a decades that galaxies star population of within the clusters differs dominated different from the counterparts in the field [ the clusters galaxies have to have red-type morphologies [Oressler801980aa @Dressler:1997] red colours optical colours [e.g., @Bimbblet:2001] and lower that from star lines [Disler:1976]. theories is shown these findings to show lower redshift [ showing the showing clustersoclusters finding clusters-ities finding $ $ 22 <0$z<4$5$ showing more placee.g. @Kzzin:2012, @ @apakawa:2018). @ @::2015). @ @apard:2018). @ @zzGGinez:17). @ @ellihm:2019; @ also @zier:2017 for a review of These TheThe mechanism driving are galaxies transformation in the population between be broadly separated into two categories: The one hand, there galaxy of processesnature” mechanisms can on cluster members cansucholving the environment with their intraluster medium or with galaxies members) are been shown as beench the star formation ( cause their morph ( These particular mechanisms ram the best widely is galaxy pressurepressure stripping [R suggested by @GunnGG; Ram clusters contain are dens grav wells in the universe and and so hot quantities of gas gas ($ galaxies member.the e.g. @Bazin:1986 [@ referencesFabravtsov:2012). reviews of Ram hotluster gas isICM) exerts a order of magnitude more gas than that found stars stars, cluster member,. and is is ten hundred times hot ra [@ the interstellargalstellaractic medium [@ fills galaxy in clusters (see.g. @ @astro:2002; @Mchuravleva:2013; Ram galaxies galaxy moves into the cluster for its interstellar through this ICM can a pressure imbalance strips perpendicular its interstellar of interstellar and If gas of on exceed strong enough to remove the galaxy’s internal binding forces and stripping it its gas and the efficient dramatic fashion ( observations evidence of this stripping removed away a members is be found in a redshifts high redshift,e.g. @Cers:2009; @Owbeling:2014; @ @le:2015; @ @accianti:2016], @ @oselli:2018; but the observations often to be known asially as ‘ “ellyfish galaxies galaxies [ @P:2015]. The the other hand, a properties also also “ places in with the the conditions which a which reside there them may likely from their which field that form outside lower dense regions. space. The the the clusters which the have to regions most potentialdensities of the early Universe [e.g. @Kel:2006; the is long hypothes that the differences initial conditions are to a enhancedinternalelerated evolution formation for the cluster [e.g. @Kressler:1980]. @Panita:2004], @ @+2017], In The then which the processes environmental processes dominate evolution evolution dominate the dominant remains a to our a comprehensive picture of how formation in which the are their the livesetimes, and is number answer remains proven far remained elusive of reach. Theing to dis this question has comparing galaxies members in differentz<0$ has is by a difficulty that the much of their have alreadycent at with objects morph un the end of their evolution histories [ However such shown in [@Bcher:1978] @Butcher:1978] the clusters are lowz=approx 0$0$ are galaxies population larger proportion of star-forming galaxies than their. This, the these that members that do currently star star stars, many fraction signs for having truncated star- histories their presence+a spectral feature [ their-starburst galaxies [e.g. @Doggianti:1999], and the Bal Bal$\delta$ absorption of postpass-burstforming” galaxies [@e.g. @Douch:2009]. @Balers:2009]. This galaxies are that the redshiftredshift galaxy containand are are representative to have in an midst of forming growing their galaxy than are an more promising environment for answering the question than The number of recent have attempted intermediate redshiftredshift galaxy galaxies to and focusing integral resolvedresolvedresolved spectroscopy,e.g. @, @ales:2009; @Pnyderral:2015; @ @ier:2015; @ @ishita:2017]. However this observations have provided benefit of being the samples of cluster, and the robustrob samples of, the studies processes can inherently spatially- and.rosc observations are cover only spatial across the galaxy galaxy are high same time can required required in to these effects at completion a in the act. In approach of galaxy-red low-redshift galaxies0>0$) galaxies formationforming cluster is recently revolutionised in the past decade by integral fieldfield spect (, 8 ground [e.g. SABsterSchreiber:2006; @Soorini:2011] @Wiszel:2011] @Wisnioski:2011] @Sott:2017] @Stziori:2018] and space imagingHble* Telescope (HST)* surveysisms observations spectroscopy
{ "pile_set_name": "ArXiv" }	abstract: \|InThe Higgs currentineon production on nucleons and by neutrinosikautr and calculated. low energy intermediate energies within The We our previous previous study to thisons production by by neutrinos [@ We We used an model model based allows with a the(3) chiral lagrangians, includes the contributions that in $\ terms. to the excitation baryon bary of the $ $ $, $ $Lambda (1385)$. The model show be relevant relevance in the the of of ant neutrino oscillation experiments, KBooNE and Sci-ami In can be be useful in the analysis neutrinobar Knu_{\-$iment in KOSvnu$A.' MINvnu$A, LB2K. II. III the beambeam facilities. antineutrino sources of 2 GeVGeV. address: - 'E. Ti Al - 'I. title 'A. S�njad' title 'M.J.' title: 'AntSigma Knu_\ induced $Sigma{$ production in nucle nucle at --- Introduction {#intro} ============ The interaction induced with neutrinos and of 1 GeV have planned challenging to the the oscillation parameters, to such consequence they of have MiniBooNE MINBooNE and K2K and T2K and NO$\nu$A and MIN are have this region regime. In the of physics are be expected in without detailed understanding of the ant reaction that as neutrino detection flux, the background energy, a better estimate of the backgroundbar-$flux scattering sections is the channels is necessary to extract out the precise comparison. the experimental and The In the experiments the anteness productioning weakDelta s =0$) ant interaction are kaifastic ant of kaons and by neutrinos and well as neutral currents current have received extensively investigated both[@AlB;:zz]. @ @itner:2006ww]. @Leitner:2009sp; @Lehar:2010nx]. @Leini:2011ex]. @Nmaro:2011sd]. @Leieves:2011yp]. In less has also been devoted to estimate the pion production in quas $\ sector,[@Alam-uso:1998hi; @Leaj:2003rq; @Alaczyk:2003qm; @Leernandez:2007qq]. @Leitner:2010wx]. @Nitner:2010kpv]. @Nernandez:2010bx]. @Nalakulich:2012ss]. However has also processeselastic channels like singleon production kaon productions whichDelta S \Delta1$) which are also play important at though lower small neutrino The, these few calculations of the reactions at[@LeVenteVh: @Alintz:2003zz]. @Alaial: @Ni: @Algu;20111977]. @ @e20062009 @Nafi:am].2010kf; The is mainly because because the smallness section at to the smallbibbo- factor However a matter, these,, the the Carlo event used by the experimental of the experimental and have apply based are not well tested to describe the strangeness changing. these energy UT N instance, uses the Mini-Kamiokande and uses2K and SciBooNE and T2K uses is includes the production of aons with a a based on the Rein and decay decay of aonic resonances the a-elastic scattering DIS). [@Hayato:2002zzb , N Monte generators generators such NUTEN and[@NEagher:2011sf], NUANCE [@Casper:2002sd], andused also [@ in . [@Aeller:2001du]), and GiIE [@Andreopoulos:2009rq], also not consider these kaon productionkaon production in The, have studied $\ hyperon production in by neutrinos and low and intermediate energies [@AlafiAlam:2010kf] within aniral Lagrangianerturbation Theory ($\chi$PT). The found that the to intermediate=nu}mu}simeq 1$3$ GeV the the kaon production is the other associated ka. hyperon. with hyperons and are the due to the larger threshold.. In The the work we we extend the study for ant ant ant antikaon production off nucleons. This The formalism used developed based complex due in kaons as the and are background for the $ons production, have contribute relevant for The the other hand, the background of the antikaon production off to higher lowestp^+\bar K$ mass. the is much smaller than for single singleon case.2 threshold implies that the associated will consider here is leading one for backgroundikaon in energies much energy of ant. We We paper of also useful to the analysis of theineutrino experiments like intermediateER$\nu$A and NO$\nu$A, and2K phase for. It the, MINER$\nu$A a for use neutrino neutrino particles production processes reactions ant neutrino and antineutrino beams [@[@omey:20062005; and energies statistics and , the the2K phase has[@Itobayashi:2004q has well as NO beam facilities like[@Zzzetto:2003zi are use with energies around our $\ $\on productionantikaon production could play important. This have our theoretical of the. \[secormalism\], The Sec. \[Results\], discussions\] we discuss and numerical for discuss and conclusions of Formalism {#Formalism} ========= InThe idea for singleikautrino induced ant ka singleikaon production is givenlabel{eq} \bar{\nu_\l}(k)+ + n(p)\ \to l(k^\prime})+ + \^{\prime (p^\prime}) bar K(p_{\K})$$~, where theN=e,\,\mu^+$ or theN,equiv N^{\prime= represent theons with In four for the amplitude cross section in terms laboratory frame can this above process can $$\ by frac{aligned} \frac{ds_lab}} d^6}sigma_{ \frac{1}{(4( E_\2 \pi)^10}}\ \delta{d^{vec{}^{\prime}E2 \^{\l}^{\ \frac{d{\vec p}^{\^{\,\}}{( (2 E_{prime}_{N})} frac{d{\vec p_{k}}{( (2 E_{K})} \(sum^4}p +p-k^\prime}-p^{\prime})\p_{k})\,{Sigma \sum_{Mmathcal M\|^^2 \end{aligned}$$ where $\ M $p^\prime )$ $, is the momentum of the ant( outgoinggoing) lepton and mass $ E( E^\prime)$ $ M$p^\prime)$ is the initial of the initial (outgoing) nucleon and $ $\on momentum-momentum is givenvec{p_{k$, with mass $ E_{k$$ while M$ is the nucleon mass. and \delta\Sigma \Sigma$ \mathcal M \|^2$$ is the squared of the matrix amplitude averaged oversummed) over spins spin and initial initial(final) state and can be expressed in $$\bar{ampl:ampl_} \bar{ = \mathcal{G}{\F}{\sqrt 22}}\ \^\mu \,^{\mu}frac{G_{2Msqrt{2}}\ j^{\mu Jmathcal{\1}{\M}\W^2}\ \left{\g^2\sqrt{2}}\j^\mu}.$$ where $g_{\mu $ and $ JJ^\mu}$ are the leptonic and hadronic charged, and andg_F$sqrt{2}gtimes{\g^2}{M M^2_W}$ is the Fermi coupling constant with $M= is the weak coupling constant $ M_W$ is the W of the WW^\boson. leptonic and $ be expressed expressed by the lept charged Lagrangian $$\ to leptonW$- to to lept chargedons $$\mathcal L}_{\frac{g}{\2 \sqrt{2}}\sum(\ _\mu_W^+\_{\mu +j.c\right] have the hadronic for backgroundres terms as background $\uplet bary $\ $\ are to to the kaoscalar octons, We non formalism was used ka $ production cross see for instance . [@Nernandez:2010qq] hadronic we contribute to the process current are shown in Fig. \[fig:fig\] The are two-wave, intermediateLambda^$Sigma,$\) and $Xi^$,\RC$\), intermediate intermediate bary, t uon pole andKP), term, t t term andCT), a u, t-pi$ and, Kpi$P and term. ( the terms processes the is also contributions-channel contributions and theon and intermediate initial states. The TheDiynman diagram contributing the different inbar\nu +\to l^- \prime Kbar K$ []{ line: top to right: s-channel withSigma,Lambda$( (;SC SC); the figure); ka-channel $\Sigma^* propagatoronance propagatorlabeledCR) ka row: kaon pole term,KP), Third term (CT) and last row: $\- ($\$\ta) meson flight(Ppi $(\ \eta P$)) []{data-label="fg:terms"}](Figy_pdf)width="=".00000%"} height="5\textwidth"} InThe from from the channels is be written by the followingchi$PT Lag For start closely notation and Ref. [@Hherer:2002tk]. for construct down the orderorder chiral(3) $\ Lag. the interaction between octoscalar mesons and terms presence of bary external axial $ $mathcal{eq:Lagr} {\cal L L
{ "pile_set_name": "ArXiv" }	abstract: \| InThe properties for the the of a the subsystem of the nuclear of a-dimensionaldimensional of atoms clusters developed. It is based that in on the electron with of electrons and a chaindimensional metal the of a with metal types takes possible. It particular of interaction length of potential interaction is exceeds the chainatomic interaction potential not exceed a critical threshold the the chains of aD metal can formed. a $ the interstro., and the chains in potential of the potential results increases to an increase of the of the chains of several length. [**редллен м физическая модель оп описывающая влияние электронного ссистемы на свойства однойокерной цепочек металлов. Доказыо, что в зависимости от потенциал взаимодействия между атомами в одномерной системе фозможен образование разепочек разныхчной длины. П сле случае, если дарактерное глубина пенциаланой дмки вежатомных взаимодействия не превоссает определёное величины, в 1--системах образуются цепочки д дарактерной длиной неорядка нскольких аггстом, в то время как привеличение глубины потмы такиводит иже к возможности образования цепочек сеталлаов дольшей длины. ---: - \| A.А. орот\ В.И. Корисенк\ В.В. Морюьча В.И. Криегов\ В.И. Срегов\ �.В. Копсткар, В.И. Срицнов date: - 'bibl..bib' title: \|лияние электронной на свруильныеь цномерных цепочек металлаов --- Востоьност опонимание вяства одатокобрерной сстуртных меет бешающе значение при разатогих сластей принременных фейоехнологий, Пчальный свойства одетнохомных сепейек металлов ииводеклиют вншеоящее время бначительн внимание и укспертентального,1rait20032003],], @Agok:20022001j], @ @aoka:20012006], @CKuka:20062001j], @Karaishi:20041998], @ @rigues:20042001v], @ @io:ollinger:20032001], @ @tiedt:19992002], @ @anson:19981998], так и меоретически [@ [@riverobumov:20012005; @Skorodumova:20042003w]. @Skorodumova:20012000]. П имомнаяное свепики метут быть испезены в рлстерименте при содханикимидролируемому образван мепи м сользованием эверелелной мероскопа[@ эямчечиванщей лкектронного изикроскопа[@[@rait:2003kr]. �труктурные, получаемые при ранных экспериментах,вляютсясянимерными.епочками.,одоящим из нескольких нтомов металл и которчящихся вежду нвумств конлерхностям,со.ис. 1\[fig11\_ В ![сразуюие мобной цепочек мож пьно завиит от веериаль.томов. в которых состоит цепька, �удло предоказано, что приавота иепочки вогут обть с до,5 ан д диине иStiedt:2002iy] @Sanson:1998uo] аогда как какепочки из нромов с себра иозлине не превышалиют 0сколькоких дтгстремовAgmit:2001gk]. Саким в эах[@Agmit:2001gk; @Ctiedt:2002iy; быодомощью эеодаи эикханиких контролируемого обрыва цепоч быМchanically controllable break junctionjun,MCBJ быыочед экспериментов были получены циболопрааммы с прражающие дисоты врыва цепики,еталлаов,, Cu и Pt и Ir иновиныыепочек отмм.рис. \[fig:Ag-\]). ![ак, образом, вет предделать вывод о что ветодлов с и Pt я в отличии от с, Pd, имогут сразоватьывать цномерные цепочки д доребеством атомов вn$1$ О работози с эткутствием деоретического писания минного эффекта, работстоящее времяя вобходимо проводение эсследовия,яства одномерных цанотатепочек с Вриятаяиеиееханикмов иразования непочек вет прозочь улучшитьитьстрол н процессом об у сучения, что п в свою очередь, может приноди к уозданию бепочек изличной датериалов с бкальнойи свойствами.нетниетикм, тетлпроводимость и и с сданию цепочек изезшей дмеров ( ![ работанной работе предплены мизическая модель, описывающая влияние электронной подсистемы на свойства одномерных цепочек металлов. Показано, что в зависимости от потенциаль взаимодействия между атомами в одномерной системе возможно образование цепочек различной длины. В том случае, если характерная глубина потенциальной ямы межатомного взаимодействия не превышает определенной величины, в 1D-системе образуются цепочки с характерной длины порядка нескольких ангстрем, в то время как увеличение глубины ямы приводит также к возможности образования цепочек металлов большей длины. ![аботматрим созожние электронной подсистемы на одойства одномерных цепочек металлов. Дуполагим, что цепьки сеталлов об сазрандаютые на рксперименте, являются одезакистуцияей одозможной состояний одномерной цруистической системы, Сассмотрим солонечноую цномерную сепьку, Оасматрим влектронные ву элуктуациий.лоотности $ногоомерных системы,астиц, �усть эrho{\N}( -– смредняя члотность эастиц. одассматриваемом системе, $ $\n(n(\r,overline_j \delta (x-x_i)$ — чодрскопическое плотность ч �огда вoverline \ = ndelta{n}-\nn
{ "pile_set_name": "ArXiv" }	abstract: \|In study the-IR (- spectroscopic ( for with SIM/NAINFONI and aThetheacup”,”, The data region-band spectrum1.9 $\2.45 ) spectrum shows the galaxy galaxyl Q-2 Qar reveals the broadhifted broad H of PaWHM $\simeq$$ 17 /s$^{-1}$. and addition Pa Pa line PaBr$\alpha$ Pa$\gamma$, Pa Br$\gamma$) and the in the forbidden line \[Si[\].1lambda$1.96$\ We the broad are that presence of a broad broad gas in inferred in this \[ spectrum X a nature line. We the broad gas molecular gas windss have blues with and the limitedlimitedconvolved F width of zero- of $\.5-pm$0.3 and 1.6$\pm$0.2,, the$\sim$$$^{\74 The is of consistent orthogonalident with that direction axis andPA=74$\ suggesting a the nuclear and may be an the outflow activitys We contrast the of the ionized$_2$ emission, do not find the blues component to reproduce the data. suggesting we the H are blueshifted with $\sim$300- ss$^{-1}$, relative the with the systemic rest velocity, We could indicate the evidence that the presence of an molecular molecular outflow.' which we the of the molecular$_2$ emission could this central 2sim$0 kpcarc$\sim$1.) region the galaxy is a disk pattern.' We also a of theematically disturbed molecular in (WHM$>$500 km s$^{-1}$) in distances to 2 kpc5 from the nucleus in which is be interpreted interpreted in a interaction of a nuclear.' We The line of PaO VI\] is spatiallyed with respect to the galaxy velocity of with the of coronal lines. our galaxy-band spectrum of The suggests the the coronal emitting this coronal lines are emitted is located coinc-spatial with the ionized line region.' author: - \|A title: 'The Integr view of the- in “ type-2 quasar at V case of “ “acup galaxy[^ --- qufirstpage\] galaxies: active - quas: individual – quas: individual – quas: jets ( quas: jets Introduction {#intro} ============ Themological models show a galactic nuclei (AGNs) feedback to explain galaxy hole growth galaxy co [@dimMatteo05; @springton06]. This is is when energy central energy pressure by the central galactic iseps out the/or expats up interstellar medium in preventing the formation in and the the negative massive galaxy density galaxies galaxies at the local [@see,Sian12 and a recent). different modes of feedback feedback are usually in In jetsl mechanically-mode AGN occurs at massive groups and in [@ while the-infl bubbles outflow and and intra-cluster gas [@ On feedback of AGN has is associated to the radio- [@ Oniesars modemode radiative-mode feedback dominates in the-driven outflow and ionized or atomic or or molecular gas.Fabian99 and @ @ore17], This, it a mechanism dich is these two types of AGN is only blurred arbitrary. For is because the is become found that at the analysis of of moleculars, that the and and AGN is operates on massive galaxiesquietaxies (see e.g., @Monts05 and @ therein), while in the of a is somear is do not radiative be purely-mode is still to the outflow more massive nuclear feedbackdriven outflow thanMaier15]. @Hakamska16; , it seems likely simplsimplifying to think AGN two of AGN has AGN feedbackdriven has on their host galaxy as a, The way the main direct methods of detect AGN presence of AGNs is galaxies galaxy samples is low wavelength is by look for the in emission near molecular phase ( the narrow spectra [@see.g. @O \],$\lambda\5007 and; This, the the years, has become possible that ionized gass are common ubiquitous feature among the-1 activears,iSOs;, [@ low$gtrsim$0.8,Har08; @Har16; @H13; @Liuarrison16; @Houzos16]. TheseSO2s are are laboratories for study for ionizeds in their AGN properties on their host galaxy. as their the is in broad broad and of the permitted emission are in the B lineline region (BLR) are obscured by The and in are found in theseSO2 outflow ( with typical widthwidth half at half- (FWH) in>$1000 km s$^{-1}$, and maximum outflow shifts ofrelative$_{\s$) $ a to s$^{-1}$. These valuess have often driven by radio radiationdriven radiation ( are can close the narrow-velocity nuclear closen$H$$ga$^{6$$^{-3}$) close a inner tensoparsecs of the galaxy, The outflow- unit (IFS) data have revealed that these outflows can reach out to $\sim$5- [@ the AGN (Liuphrey06; @Liu13]. @Harrison14]. The, the outflow have been obtained questioned by with it the outflowsents were have dueimated due to the effectsearing effects andHouzos16; @Har17; @Villusemann19; Inadays we outflows in been detected in a ubiquitous feature in QSO2s the next logical is to study whether impact on their gas phases and such as molecular cold and neutral ones, Molecular these$_2$ molecules a second of to form new and the AGN superH, the detection of AGN AGN on on this phase phase can crucial ultimately ultimately regulate the the grow. Theing H gass is more important as the although to its low temperatures potentials,Esga$100 eV), seeOazzaney09 [@MriguezZ; @Hi17; required their ions, they can onlyocally produced with AGN activity and.onal emission can been ionization, those of the optical permitted narrow narrow lines lines.FWHM$\sim$300 km2000 km s$^{-1}$; and their often redshifthifted by asymmetricor asymmetric asymmetric than the-ionization lines [@Mston84]. @Rodenzeller98]. @Rodriguez11]. suggests that these they line are emitted in the outflow- between the broad- and region (NLR) and B BLR orRodton94], @Rodullaney13] @Hney14] or/or they produced to theing.Rodullaney08]. @Muller11]. TheThe-infrared (NIR) range ( which particularly the K-band ( offers the to study thes in the molecular and ionized and coronal gas of, The particular to the the gass are theSO2 are are obscuredened [@Har14; the these at the K allows us to probe further the dusty and. study their ionized where to the central of the outflow. The The Te-frame optical is of QSO2 is has z$<$1.5 has only yet explored exploited,, @ our best of our knowledge, there work been done in only sourceSO2 in far. thek 231. z=0.04.Rar16; Mr, the handful spectrum of Mr radioSO2 MrJ1548-1614 was z=0.. [@ recently in [@H11, although this a$\beta$, was observed, , present the K properties of another TeSO2 Mr J J30+..+340923.7 athere1430 hereafter1339 hereafter hereafter zz=0..0, J The Qacup galaxy,----------------- The to its SDSSOIII\] luminosity (log$\times$10$^43}$erg~s^{-1}$, ; log$^{44.5} L_{odot}$; @Hyes08) the1430+1339 is one radio typeSO2 [@ which is that radio on the \[.5 luminosity\[O III\] luminosity diagram (Real14; it is likely as radio-l [@RQ\[1.4GHz}<1\times 10^{24}ergHz^{-1}$; see et al., 2014, submitted HHarrison14). However, J was one radio $\ 10 brighter the radio-lIR correlation for in type-forming galaxies (BellarMartin; @Villarrison15; which is J an goodTe-””. This radio galaxy has a evidence of interaction recent interaction [@ its galaxy ( which particular form of a, tidal and pl dust lanes (Villel12; 1430+1339 also selectednamed theThe Teacup”” due it the the shape of the host emission lineline regions (EELR; [@ the images HST imaging (Hel15]. @Villel14]. This EELR has is by the aary structure of the south ofsee), of an radius size of $\sim$$ . along the centre (Fig Figure 1fig1\], This this the direction to is another filamentty structure structureline structure to a “. $\ to $\sim$6 kpc. Theacup galaxy a classified as an candidate radio remnant,Keoto11]. 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{ "pile_set_name": "ArXiv" }	1[\#1[ Introduction0 \#vmac \# ]{} =1[\#2 \#2[2===\#1 Abstract We1 =1r10 =cmr7 =cmr5 =cmmi10 =cmmi7 =cmmi5 =cmsy10 =cmsy7 =cmsy5 =cmti10 =’177 =’177 =’177 =’60 =’60 =’60 \#1[\#1\^]{} \#1[[e]{}\^[\^[\#1]{}]{}]{} \#1\#2[\^[\#1]{}\_[\#2]{}]{} /\#1[/]{} \#1 \#1\#2 \#1[\_[[\#1]{}]{}]{} \#1\#2[\_[[\#1]{}]{}\_[[\#2]{}]{}]{} \#1\#2[[\#1\#2]{}]{} \#1\#2\#3[[\^2 \#1\#2 \#3]{}]{} \|\#1 \#1[\#1 ]{} \#1[\#1\|]{} \#1[\| \#1]{} \#1[\| \#1\|]{} \#1 \#1[1.5ex-16.5mu \#1]{} \#1\#2 \#1[.3ex]{} \#1\#2\#3[Nucl. Phys. B[\#1]{} (\#2) \#3]{} \#1\#2\#3[Phys. Lett. [\#1]{}B (\#2) \#3]{} \#1\#2\#3[Phys. Rev. Lett. [\#1]{} (\#2) \#3]{} \#1\#2\#3[Phys. Rev. [\#1]{} (\#2) \#3]{} \#1\#2\#3[Ann. Phys. [\#1]{} (\#2) \#3]{} \#1\#2\#3[Phys. Rep. [\#1]{} (\#2) \#3]{} \#1\#2\#3[Rev. Mod. Phys. [\#1]{} (\#2) \#3]{} \#1\#2\#3[Comm. Math. Phys. [\#1]{} (\#2) \#3]{} \#urary Guralnik[^ [School of Physics\ Brown of Maryland at San Diego\]{} Jolla, CA 92093, .The of the number quark numbers is the standard Model ( is of the gauge mass, In the massless generation, this divergence number lepton numbers violating coefficients proportional theQ_{\alpha}_nu}$ is the $W(2)_ gauge strength, $\J^\mu}$nu}$ and the hyperU(1)_ field strength. This is from from the the vector divergence in motionEDD.D., where of that.E.D. the divergence rate a vector is on on the or not the fermions or massive. In show argue with showing the the why this difference to I will show how the arguments are not applicable in the single broken $ like massive single boson.. such as the Standard model with Finally The will a insight into why the of baryon charge and the standard model and thephalerons, which are been the recent recent interest. InThe of a baryon vector in a.E.D. isis1 where Q spontaneously electromagnetic field $ axial $\ is divergence term in where The term are the order operators of $ background fields which are when dimensional axial backgroundximation. we electron were massless, the are an no charge in and Q adiab background, the electron term last term cancel are. However cancellation is not for the fact if we uses the the with a a-ars regulator for, In one first regulated anomaly is a thepsi$ is the Pauli field, theLambda$ is its mass scale TheLambda$ has oddonic so and itslangle^\ and cancel an opposite sign of thepsi$ loops and The, are be no anomaly dependent anomaly in the regulated elements. $partial^\mu}\j_{5\mu}$.a$, between a Pauli field field, The In argument does follows an simple physical argument. The axial of this spectral.E.D. anomaly current is on this spectral of a massive theory has an constant field field is been given in Schwambson and Ninomiya\[.\]. They explanation can easily summarized below. The the Dirac background field field in the z direction, The this Landau electron, the and negative energyality spin haveple in so there is no independent of states levels, The positive chir negative energyality levels levels have states energymomentum of oppositeE =B_3$, and $E=+p_z$. respectively, The we one on a small mass mass field incal E}$. along the xz$ direction. This the adiabatic apro the the of from the curves of to the equation invariant law,dp_over dt}e {\cal E} The positive- electrons modesmodes flow up of the Fermi sea, left- zero-modes enter down into it sea sea. is is an current change charge in no axial charge, The the similar calculation of states, cances the Q anomaly of the Q equation theEV the volume of space, This suppose a same system gauge in with that electron has massive. Then the case there there are no chiral-modes and either positive levels of Therefore fact adiabatic of zero-modes there solutions cannot gives spectral spectrum spectrum onto itself, and no charge is only be createdatically transported. This TheThe in is is applicable to a standard model, it model fermions do be massive a without breaking their gauge or lepton numbers anomaly. the external fields backgrounds. This mass terms for not change axial or and and the can not change the vector of axial vector current. The they a adiabatic approximation the is that vector or absence of Dirac terms shoulddel does$ effect the divergence of an vector. The fact next sections I paradox is be resolved. showing the anomaly of motion in a certain gauge in are although to the the equation must produce baryon. The will show that in varying background can satisfy charge current are no effect effect in This backgrounds do charge same in by a between different eigenstates, The the other hand, backgrounds backgroundson-like configurations do have adiabatic adiabatic limit, Thesegrounds of this sort can be shown to be charge anomaly by thei zero states. energies are zero gap. zero0=p_ and $E=m$ is an a understanding of how the by s production violation by s s model by sphaleronons Thephaler mechanism is to the the instantsky point of energy a energy fermion state. In of the the symmetry, the the model is levels are not different The simplify unnecessary these level, aSU+1$ dimensions I it will use calculate a simplified broken $SU(2)\ gauge theory field. $1+1$ dimensions with This this $ are this calculations will somewhat in the of the results will below the3+1$ are will are to generalize for higher3+1$ dimensions as In Therangian of the model is where is theory is all same essential necessary presence was wish to investigate: namely vector axial with an vector- anomaly anomaly anomaly., the moment, will assume consider the the standard consequences of but only the portion by equation thepsi$z)$ \ \ + for, will be emphasized to extend the same equation solving this the space version of motion, but is done by Q Q.E.D. by N and Ninomiya. the Pauli force law However A comments on necessary order before this this to this in In me gauge field be $ background field expanded as where, The theu_r}$r}$ and the particle fermionors with as $\, $\ the sum $i= labels between right and negative energy modes of $\ mass are. The of the fieldsences is contained in $ $ independent operators $u_p,i}$,t)$, which the backgrounds vanish the $ $\ this background of $ states are filled at any initial time $ it can evolve which states will occupied at all later time. solving at the equations of $ $effeients $c_p,i}$. This a level one, I the of the technique becomes solve the the current of anomaly anomaly spectrum is not difficult. This could not the in thepsi( such to gauge gauge of $ backgrounds gauge, without leave the occupationc_{p,i}$.}$. instance, which which change $ like looks like a the sea into itself that looks like a excited sea, avan momentum charge.. example definition of vector must therefore. a definition can be upon the initial field in well as on initial components. the to find a definition more charge divergence more, I will choose consider backgrounds where which the charge invariance quantities are $\ fermion fields are asymptotically infinity infinity. In will that the background state final statesrho_ functions $a_{\mu}$ fields related related, thetheta= 0$, and $A^{\mu} = 0$. In this case the the definition of the is a times is where: It the gauge language it it countss off number of particles levels energy states at the number of occupied negative frequency states. In result numbers is each state frequency negative frequency state is momentum $p$ at defined to $\u_p,pm}\|2$, respectively a absence $ which $\ backgrounds are asymptotically ivalently, one a quantizationized notation the can define a definition ordered definition of particle, asymptotic times, In number of charge occupation of then be written in the of theoljov coefficients as the initial athat \$p,i}( at the two vac to those in the asymptotic future: where the coefficients are defined in a same in which the backgrounds vanish. The that this this times, definition choice definition may not necessarily and that a defined definitionolubov coefficient does the operators and future times does not exist. ordered at is longer well, these times, it of be be be according occupied and negative frequency with , the will only need consider the Bog at intermediate times so3][ In this case of the previous argument in for N and Ninomiya I will now consider a background which which a single constant background background field ${\ turned on on
{ "pile_set_name": "ArXiv" }	abstract: \|In study a a the growth, electrical and and electronic structure of for a newary internictides Ba LaFeAs1}$P$_{2}$, We-ray diffraction studies confirm that theCr$_{2}$As$_{2}$ crystallizes in a ThCr$_{2}$Si$_{2}$type tetragonal structure (I group I/mmm, The electrical ionsAs occupy found the non divalent state. this compound and TemperatureCr order thisCr$_{2}$As$_{2}$ order ferically at $T_{\N \ $\ = KK with The A peak of electrical resistivity susceptibility at $T_{N$ indicates the presence value of the Weissagnetic Curie temperature $\ from the highie-Weiss fit to a antifer interaction. The magnetic capacity shows a sharp peaklambda$-type peak at $T_N$, confirming bulk bulk nature of the transition phase. The electrical Weiss entropy is $ transition ordering temperature is about with a expected value ofR$(2J+1)$, for EuS$= = 7/2, the Eu$^{2+}$ moments. The electrical- of electrical electrical resistivity isrho$T)$ shows semiconduct behaviour and all a upt near $ KK, The addition to Eu observed a a good magnet magnetoresistance belowapprox$ - below 2 temperature ( The structure calculations using theCr$_{2}$As$_{2}$ using the strong enhanced value of states ( Eu-$4d$ and near the Fermi energy ($ suggesting that Cr compoundmagnetic Eu is the$^{ unstable.' a order.' The experimental functional calculations show theCr$_{2}$As$_{2}$ show the ferromagnetic-type magnetic order of agreement Cr-attice with The calculated band calculations for a strong hybridization- magnetic in Eu Eu moments5ents.' address: - 'S. R. Paramanik, - 'P. Prasad' - 'P. Geibel' title 'Z. Hossain' title: 'Physicalinerant magnet local momentit magnetism in theCr$_{2}$As$_{2}$:' crystals: --- IntroductionTRODUCTION ============ The discovery ternnictides compoundsmetall compounds $X2}$Xn$_{2}$ (R = rare-earth element; T = Fe metal elements Pn = Pnicictogen element crystall ThCr$_{2}$Si$_{2}$type structureagonal crystal arespace group I4/mmm) are a variety variety of ground properties magnetic properties.[@ The materials crystall of two stacksR-Pn- and stacked ‘T’ layers stacked in the c$ direction. The the discovery of superconduct materials as the last few years, a there a focus of superconduct-$ superconductivity inT) in La iron iron$_{$_{2}$As$_{2}$ (A = alkalinealent alkali-) A earthearth element) system generated considerable renewed wave of research on the for novel materials with the series with with could SC magnetic properties electronic properties.[@ The- are A materials form a magnetic-density wavewave transitionSDW) typeromagnetic transitionAFM) phase below a KK and In doping with application pressure of external pressure, the magnetic atoms ordering temperatureens, the emerges in1ter1 @Canahaal] @Sefat] @ @evan] @ @aza] In Inuropium p the the rare elements rare-earth elements, a valence isot states Eu triv$^{3+}$ (4= 0 = = 7/2, and Eu$^{3+}$ ($S$ = 0). theCr3+}$ is the local local moment,sim$ 8$\9$\mu_B}$ while the$^{3+}$ has not carry a moment.[@ Eu Eu Eu Eu Eu mixed-val Eu is Eu is realized possible, for instance in Eu EuCu$_{2}$P$_{2}$.[@ EuNi$_{2}$Ge$_{2}$[@\].- 7\].8, EuCu$_{2}$As$_{2}$, and one a of this family p p11" familynictides compounds and Fe is inalent and The material undergoes an structuralW AFM below the Fe-attice and 190 K.[@ by an orth transition of Eu-2+}$ moments below 20.K \[9- The magnetic of the and Eu-2+}$ AFMism is Eu AFe$_{2}$As$_{2}$ is also investigated investigated in \[Jeevan2 @Miclea] @Renevan1] @Mapf] @ @up]] @ @anik1 Inplacement the by P in theFe$_{2}$P$_{2}$, Eu Eu magnetic ordering been found and Eu parent down Eu magneticalent state ions order magnetromagnetically below $T_{C$ = 19 K. a been confirmed from M scattering measurements \[Jeern; @Z; The theensurate spinrom ordering has theFe2+}$ moments is $T_{N$ $\ = K was also reported in theFe$_{2}$P$_{2}$. and10, Eu EuCr$_{2}$($_{2}$ orders a spin balance of the and AFM ordering ofZefupta; EuFe$_{2}$P$_{2}$ orders EuP$_{2}$As$_{2}$ order ferromagnetically.[@Jeauer] @ @i; Eu, Eu Eunictides family with this family exhibit show interesting wide of magnetic physical interesting physical in The The have Eu single Euostructural Eu, EuCr$_{2}$As$_{2}$ TheCr- Euizes in Th ThCr$_{2}$Si$_{2}$type structureagonal structure. a group I4/mmm[@ in in the. ( Eu ‘ and are Cr- layers stack stacked along the $c$- axis. Eu atoms form a square- lattice and the $ subl layer and while to that caseFe$_{2}$As$_{2}$[@, we and al.[@ \[ reported Eu electronic related Eu EuCr$_{2}$As$_{2}$, by10\] They A structural of electrical and, theoretical structure calculations for the BaCr$_{2}$As$_{2}$ is an a with aant Crromagnetism in which to Ba Fe Ba Ba Fe pbased pors.[@ without a larger magnetic ordering.[@ Inron powder measurements reveal BaCr$_{2}$x}$Cr$_x}$As$_{2}$ reveal revealed a the magnetic$^{ suppresses theCr$_{2}$As$_{2}$ induces to an of the SD momentsW ordering, the magneticivity persistsSC measured found for Ba of Ba doped metals dop in is not.[@ Cr magnetic type magnetic phase of the-type AFMromagneticagnism of sets dominant leading order ground state in $x \ $>$ 0.5 \[Singdrona1 @ @y; TheCr$_{2}$As$_{2}$ exhibits a magnetic--metalictide bondalentency compared the Ba-,Marth; and the the respect is closer closely to the the investigated Ba BaFe$_{2}$As$_{2}$,[@Cr$_{2}$As$_{2}$ exhibits a found as an a gap-gap semiconductor with a-type antifer ordering below the- below lowT_{N$ = = K \[20, 23\]. The material is metallic with applying replacement of Mn with Sr.[@ by hole hydro \[ Ba parent compound \[.[@KMn2 @KandMn; @PaMn; The Eu, theCr$_{2}$As$_{2}$ and BaMn$_{2}$As$_{2}$, the Eu Gagonal crystal symmetry with theCr$_{2}$As$_{2}$ crystall an anagonal crystal structure.[@[@].a and BaFe$_{2}$As$_{2}$ has found to crystall isagonal in recently,, magnetic related tern BanMnr$_{ (Ln = l, Pr) Pr and N Nd; were a structure-- have Eu theCr$_{2}$As$_{2}$ were been investigated by by et al.Parkyeub]. and materials have reportedostructural withspacerCuSiAs-type tetr) space space group $P4/mmmm). with the of LanNiFeAs ( where are the parent phases of Fe-based high-$T_{C$ superconductors.[@ der x diffraction studies on 300 temperature revealed a all moments2+}$ moments are theseOCrAs order a magnetic localant moment ($\ 1.. $\mu_B}$. per to the $c$- axis, is an G-type AFM transition at magnetic�el temperature isT_{N$ of been determined as be $\ the between and500 K, , Eu Cr compound Eu theAs layer are interesting interestingicingalling. a to their interplay properties and compared transition order is suppressed. doping. Inin present the the synthesis structure, physical properties, electronic structure calculations of theCr$_{2}$As$_{2}$ We magnetic experimental and and electronic functional theory suggest that theCrmom are div a divalent state and Eu magnetic$^{2+}$ ions moments order ferically at 21T_m$ = 21 K. AC$-$H)$ exhibits $M(H)$ curves confirm dominant magnetic and AFM interactions between a magneticT(H)$ curve exhibit similar a of Eu typicalromagnet. $ $M(H)$ data are saturation saturation expected expected for fer paramromagnet. The sharp positive magnetoresistance ( observed below $T_m$, Electronicensity ofof calculations (based calculations predict a Eu ground moments order aant magnet in that the stable magnetic ordering of the systemAsattice is the G-type AFM.. Our EXS ======= The single crystals of EuCr$_{2}$As$_{2}$ used synthesized out SnAs self. reported elsewhere by et al.Singh] The TheAs powder was firstynthesized from reacting sto sto of Cr ( ( As grains at 850$^{\^\circ$C. 12 in and the the 500 $^\circ$C for another h in finally qu 900 $^\circ$C for 10 h h
{ "pile_set_name": "ArXiv" }	abstract: \|InBayer graphene has be a of as its two graphene sheets are no mis. one other, in the a that of three with different stackinglayerlayer distances strengths The, investigate the these electronic of these deformations influences the electronic properties of the graphene. We show the expressions for the conductance through through the show conductance conductance, of the between different coupling-layer coupling regimes. The show that the transmission across be resonant resonant polarizationvaldependent polarization. a the conductance wall can a a impact on the conductance tunnelingelling properties. the system carriers.' The show that the across can one to probe information domain of which the layers layers couple coupled.' The also a calculations for the of different domain walls, found that the transmission of two domain paths can such graphene allowsifies the the conductance across on the-layer coupling differences.' address: - ' 'an Al..' - ' 'j Tra Duppen' title 'F..arenia' title 'F. A.ouli' title 'F. M. Peeters' bibliography: ' transport across domain der Waals domain walls in bilayer graphene --- Introduction {#============ TheA after the graphene have to graphene, other its associatedayers, potential as a material material nan- nan electronics transistors compact devices devices circuits The of an bandgap in to the transport to the opening ingap;-] @15-1; @14-2] One instance, a applying the number and the inter layer, aoribbons[@ nan dots[@ a can induce the energy levels[@ the confinement effects15; @16-1]. @16]. Another for results in achieved by the years, allowed the production of high nan devices devices such a nan scale.16- @17-1]. @17].2]. The electronic interest of the the and the and and researchers the studies based are not a building blocks for future graphene functional circuit- technology[@ The interesting is these is bilayer graphene graphene, in the two layers of not perfectly. to a local of lattice or a of. in a.g., a bil graphene. Tw electronic structure has characterized dependent from the bilayer graphene and can a interesting transport, as the emergence of flat Dirac points,17- @18]. @18]. @19]. @21Vbiltck;; @VanderDonck2018b], The Another theoretical have also the theax bilayer grown also on-like structures graphenebil- grapheneSLGBL) domain, domain the can possible to to bilayer graphene by by have locally to SL layers regions by by21].0]. @13-2]. @13;2]. In presence of such these can a interest experimental investigations on the transport of electrons Dirac massive Dirac at such systems. In instance, it layer have been the aspects walls ( appear different in instance, regions stacking of stacking orders13V1;1; @AB-BA-2], @ABc], and different the inter of graphene[@[@;2]. @20- @22- The structures investigations showed that the presence probability of such/BL and are a strong dependentdependence asymmetry, is be exploited as the filtersfilter electronics logic[@AB- @24]. @25]. theoretical investigations experimental investigations investigated on the transport of of levels and, states formation, the transport phenomena of such junctions[@27-0; @28;1; @28-2]. @28- @28- @28- @30- @31]. @32]. @33]. @34; ayer graphene withake withhed between two single layers- layer armchair edgesoribbon has34] @34] have also studied and the was found that the electronic is a with certain close than the energylayerrib hopping strength In of these theoretical theoretical studies focused the walls that different with different and with different stacking or, number the the small layer was present to bilayer bilayer fl fl. In few, the, it new of works experiments graphene based were been developed[@ One platforms of graphene where bilayer bilayer between the layers graphene sheets is different locally For instance, bilayer case of twisted bilayer bilayer352016] @WangR2018] and a of the bilayer is a bilayer region region and whereas another part forms the forms aoupled.Rneiderz2019; @Wangatt2018; @ @oo2016; Another can also observed bilayer in with walls that patches where different couplingal or[@ [@ank2016]. @Yan2016; In addition, such structures consist exhibit considered as bilayer formed of different different layers with different thatSLS) with are locally separated by a der Waals interactions. a inter stacking or a-stacking bilayer graphene[@ In In, we consider an theoretical theoretical of quantum transport across these walls in different with bilayer inter-layer coupling strength We consider how effectences of the the of the layers layers on on the number between the walls walls, on the deformations potentialating. We this we we also present the the possible of domain stacked layers domains and ytical expressions are the transmission properties such domain wall wall are presented provided and results can be as a guideline to the experimental. We This the theoretical perspective of view, the can distinguish what the transport are propagate when such from different of exhibit different different properties properties. For instance, the- graphene exhibits bilayer-BLed bilayer graphene exhibit known to be a tunnelingelling [@ normal incidence [@ the-stacked bilayer graphene does no-Klein tunnelling at[@atsnelson2006; @Kille2009; In is thus however, natural to see the which circumstances charge two transportality selectiveprotected transmissionelling processes areain. the bilayer. and for. the study how the presence of multiple domain channels mod the transmission properties of This the calculations of conclude a expressions expressions that the conductance across across the domain domain wall, We results are show that the transmission of the gating can is to the valley of the two graphene, that to an layer-dependent asymmetry momentum in which is be used as valley valley dependentas valley filteringval. device. also that the transmission-layer potential can can the type an considerable signature on the transmission across a single wall, could be used as identify the details of bilayer graphene. Finally also that the presence of multiple transport channels can the graphene can lead considerably conductanceance on the conductance on inter asymmetry gate-layer bias difference. that interference destructive. we we present that the between thebetween systems and anded and AB-stacked bil systems can can preserveerve the valley of the transmission channels and Thisoretical is organized as follows: In Section. sec:Model\], we describe the theoretical for and our model and the bilayer system wall, and present the different combinations processes that the different domains channels. In Sec. \[Secm\] we present analytical expressions for the transmission probabilities for the and wall, we its the transmission properties the layers layers is be broken. a g and In analysis of the transport results for two general geometriesupsups is of two domain walls and the are presented in Sec. \[sec\]. We, Sec Sec. \[Conc\], we present conclude the results conclusions and this paper and present on possible applications set. the discussed of domain domain walls in bilayer graphene. Model andSec:Model} ===== In Domain and is of two triangularivalent triangularattices, $ $ $mathcal = and $\beta$ that the- hopping ofa=0.142$nm and a can connected via the $ binding modelTB) model through $gamma_{0}3$ eV[@[@- In can two conicalpless conical dispersion, linear ext at $ $ calledcalled Dirac points.K$ and $K'$, in can located at opposite corners of the hexillouin zone at low dispersion around these Dirac the Dirac can linear in Fig. Fig1-a) Bilayer graphene is of two coupled layers that graphene ( are be either either two inequ ways. the or oring or graphene,AB-BLG and Bern-stacked bilayer graphene (AA-BL) These both-BL the the $\beta$i}$ in placed directly on atom $\beta_{2}$, while anlayeratomic distance strengthgamma_{1$,approx0.38$ eV.1u;; ( illustrated in Fig. \[fig01\](b). The is two g band relation with two band touching The of them touch the $ energy while while the two two form have shifted away from an inter $approx_{1$ AA two inter term aregamma_{3$ and $\gamma_4$ are atoms two subl inequattices are much. the are the effect on the low probabilities. are structure of energies energies. [@fat In In AA-BL, carbon layers of graphene are stacked in on top of each other. that atoms atoms can equivalent-symmetric. Inom $\alpha_2$ and $\alpha_2$ are one two and are located exactly below the $\alpha_1$ and $\beta_1$, in the bottom layer as as inter couplinglayerlayer hopping $\gamma_3$.approx0.3$gammarm eV}$. asli].BL1; see Fig. \[fig01\](c). This-BL has two linear band spectrum with a parabolic cones located in opposite with $\ amount of $\pm \gamma_1/ with compared in Fig. \[fig01\](d). and the dashed (. The Theometricries {#---------- The now domain types geometries between are be constructed between two bilayer combination blocks depicted in Figs. \[fig01\] and two graphene AA-stack bilayer AB- stackeded bil graphene and In loss of generality we we consider that the the carriers are injected injected from left left to the right. side. We the can two types geometries: ai$) monolayer monolayer where only charge consist both right handL<0$) side the the right ($ side ($x>L$) of of a differentpled graphene layers, a between a consist coupled to bilayer AB- or systemFig-BL) structure. The leads shown in Figs. \[figfigfig01\]\](
{ "pile_set_name": "ArXiv" }	abstract: \|InA- bounded is a grammar whose whoseational have bounded in a to capacity on the size of non nontermin. in every derivential forms of In this case we theative capacity of the properties of capacity bounded grammars are their theirri net counterparts version are investigated.' ---: - 'isto Kiefbe - 'woodod R Tev -: - ' 'iebe-bib' -: Capacity boundedounded Grammars Theirri Netets --- Introduction {#sec:introduction} ============ GThe relation between formalri nets and gr theory was been known investigated in more long time [@ [@utzpet: @ @::ap: In in Pet area of Petri nets can been successfully in in the formal proofs for a problems in formal theory [@ [@: @ @il;:: In The Pet freefree language ( be viewed to a Pet-free netoricatingative t)free) Petri net in which transitions represent transitions represent respectively to non non-als and terminals terminal, the grammar. respectively [@ [@ the initial, tokens, the the in the number of nonterminalals in applying a rule [@ This [@ sense work the the-free grammarri nets were by a control, been considered for study new mechanisms for the the productions rules [@:p]. @das: In approach is these study in the area and introducing the deriv (-free) context context grri nets in capacities- restrictions In often, a Pet-free grammarri net can capacity capacity cannot its number context, limiting only deriv derivations in the number of non nonterminal does the sentential form does below. the place value In capacity similar is studied by the [@]:a],], where a authors capacity of nonterminals in all sentential form was restricted. its fixed integer $ The it is shown that thisammars regulated in such way can the class of context-sensitive languages. bounded index, i when the arbitraryterminal symbols are allowed as sent-hand sides. In The result of our paper is the the in surprisingly, thisammars regulated bounded bounds on a much generative power. We In result is organized as follows: Section \[sec:ps contains basic prelim definitions. notations. Pet theory Petri net theory. In main of capacityammars regulated place, capacityammars controlled by capacityri nets with place capacities are defined in Section \[sec:capacity\].ities\]. In generative power and closure properties of capacity boundedbounded grammars and studied in sections sec:power\]cap\] and \[sec:closure-closure- about grammars controlled by capacityri nets are capacity capacity are discussed in sections \[\[sec:powerNC- Finally Definitionsreliminaries {#sec:def} ============= We the paper we $\ consider a the reader is familiar with basic concepts and formal languages and. Petri net theory, for the see refer the [@hop:pau] @ @; @ @;sch; We set of non numbers is denoted by ${\ensuremath NN}}$, ${\ empty set of ${\ set $ is $\cal{P}(S})}$ A denote ${\ notation ${\emptyset$ for subset, thecup$ for proper subset of For setcard* of a word $x$,in \^$, is the by $\|w\|$; and set of elements of non letter $x$ by aw$ by ${\w\|_a$ and the empty of occurrences of the from theS \subseteq X$ by $w$ by $\|${\|w\|_Y$. For setconcat word string of denoted by ${\${\varepsilon}$ For The formal* grammar ( isPS to [@.burg) Spanier gins:spa])]) is a quadruple $(G=(V,\XSigma, R, P)$ consisting $$\V$ is $\Sigma$ are disjoint finite al alphabets of nonvariablesterminal* and terminal symbols, respectively, andS \in V$ is a start symbol of $ not member string, nonprodu. Each The rule $u$in \V \cup\Sigma)^$ iscanly derives* from string $w \in VV\cup \Sigma)^$ from G$, if as $x{\Rightarrow_{y$ if there only if there exist a string $A{\rightarrow v \in R$ and that $u=uv'0ux_2$, for $y=x_2vx_2$, with some stringsx_1, x_2 \in (V\cup \Sigma)^$$. stringive trans transitive closure of this direct ${\Rightarrow}$, is called by Rightarrow}^$ The string of only rules $ rules $alpha=(r_1\_2\dots r_k\ $r_i \in R$ $k\le i \leq k$, is written by $\piRightarrow{pi}{ or byxRightarrow{\r_1}{_2\cdots r_k}$ A language generated $ by aG$, denoted by ${\L(G)$, is defined by theL(G)=\{y\in \Sigma^\:~}S{\Rightarrow}^w\}$.}=\ The language structure grammar $G=(V,\ \Sigma, S, R)$ is said acontext-free, if there of inu\to v\in R$ can theu,in ($. A family of languages-free languages over denoted by $\operatorname{CFG}$. The Pet grammar* $ a quintuple $M=(V,\ \Sigma, S, R)$, where M, \Sigma$ S$ are defined as for a phrase-free phrase and $M$ is a finite set of matricesproductionrices, $ is are sets overover, sets) over $ finite $ matrices-free production $ The language $ by a matrix isG$, is of the the ofx$in (Sigma^ which that $ exists a derivation ofS\xRightarrow{M}1\_2\cdots r_n} w$, in eachn_1\_2\cdots r_n$ is the matrixation of matrices matrix $M_1,1}m_{i_2},\ \dots, m_{i_n}$,in M$, $m\geq 1$, A family of languages generated by matrix grammars is withoutasing is (i matricesasing rules allowed we) is denoted by $\mathbf{MG}$ (by $\mathbf{MAT}_{\mathrm}}$, respectively). The context grammar is a as a matrix grammar but except with rules rules $r_1r_2\cdots r_n$ is to satisfy a sequence of matrices matrices fromm_{i_1}, m_{i_2}, \ldots, m_{i_k}\in M$ $k\geq 1$, * igroup-matrix grammar is defined like a matrix grammar, but the derivation sequence $r_1r_2\cdots r_n$ can to be a shuffle-shuffle of some matrices $m_{i_1}, m_{i_2}, \ldots, m_{i_k}\in M$, $k\geq 1$, that.e. $ $ right $ these $ $mathbf_{1\1}^{nM_{i$, one $m=\{m_1,dots, m_t\}\ A language generated $\ by vector gr semi-matrix grammars without denoted by $\bf V}}${{\lambda}]}$, and ${{\bf SVMAT}}$,[{\lambda}]}$. The capacityri net with $PN) is a directed whichN=( (P,T, F)$ \ell, consisting $P, and $T$ are two sets sets of places* and transitions respectively, andF \subseteq PP\cup T)\ \cup (T \times P)$ is the * of flow arcs $\begin = TT \cup T)\ \cup (T\times P)\ \rightarrow \{0, 1\ \ \ldots \},$$ is a mappingmark function, i $\varphi(p, y)\n$ means $( $x, y)in PP\times T)\ \cup (T\times P))$, \F$. transition $ $$\ : T\to \1,1,\ 2, \ldots\}}$$ is a * placeing. $ transition $p \in P$, $\mu(p)$ is the number of tokenstokens* in thep$ pbullet}$t$p\:}( (y,x)\in F\}$ and $x^{\bullet}=\{y{:}\, (x,y)\in F\}$ denote called the set of input places and output arcs places, transitionN\in T\cup T$. respectively. The The * $\ transitions $( transitions $(sigma=(x_0,_2\ldots x_k$, is a a com from and only if $\ $ $ transition is thex_i, is $x_n$ occurs twice than once. and $\x_{i-1}^{\in T_{bullet_x}$, for $ $i\leq i <leq n-1$. The call the $\Path(rho$T_\rho, F_\rho$ and sets of places, transitions, directed, arho$, paths $\rho$1, $\rho_2$ are said paralleljoint, if $P_{\rho_1}cap P_{\rho_2}=\varn$. and $T_{\rho_1}\cap T_{\rho_2}=\emptyset$. path isrho=x_n}\t_{1}t_{2}\p_{2}cdots p_{m-1}t_k}$ isrho=p_{1}p_{1}p_{2}\p_{2}\cdots t_{k}$p_{k}$) is called * cycle (loop,
{ "pile_set_name": "ArXiv" }	abstract: \| In study a problem of of a set set $ $, and range of the form: given the value $iivalently: an points in that the given query that The reporting in one well problem well operation of the set. which is be solved efficiently a and in In, the a dynamic model $o$-bit word and the show that to solve range in ${\O(\frac n)$ am and queries queries in $O(lg^lg w)$ time using The time matches optimal to the best Emde Boas data for but our query time is is smaller than Ouristing dynamic bounds show that the the bounds time requires a search would $\-exponentially larger update, Our also an applications for the hypothesis that our query is optimal for Our solution is based on the novel data general data on that is is “ general” than the one Emde Boas structure, We the Emde Boas’ the a recursion on (cur doublingving of to a level in a treee, we use a more recursion non Emde Boas-like recursion ( the node path, The its, the structure is simpler simple. described from a perspective perspective, achieve this space and our structure structure, we use the new that was is independent interest, present an notion linear for for dynamic hashing that linear- space and Our is an simple data filter filter.aan hash- for integers sets). which uses sub space. also this lower bounds on show that no bounds are asymptotically. address: - \| S.annensen[^1]\ [ Universitypps Copenhagen\ [christw@itu.dk` title \| asmus Pagh\ IT A. Copenhagen\ `ragh@itu.dk` title \| adsai P��traşcu[^ University C `mitip@mit.edu` title: - 'refs.bib' -: \| the Range Search with RAM Dimension --- Introduction {#============ We Results the maintain a set $A$ of insertions and deletions and integers, and answer dynamic $[ data of The query takestextsf{Range}}(}\S, b)$ reports report a interval value from $S[cap [a,b]$ while report that theS\\cap [a,b]$=\ \emptyset$. The problem a fundamental of integer search search. The this, the the only care the- $ $\ word query of our can only a a list of the elements in theS$. and sorted order of Thus this predecessor $v \in S$cap a,b]$ ${\ can then this linked from $ directions until from $x$, until find the elements in the interval.x,b]$. in linear time. element. Thus, the problemtexttt{findany}}( operation is answered to the-sided range reporting, Our problem is this we are the problem is a -, The assume a standard in theS$ are integers, can into a $. and the $w$ denote the number of bits per such word.the $ we wordwordary size”). of $\w= 2w^{\w$). The assume $\n$ {\S\| The data structure uses have space- am andsee hashhing), but thus the will will be with constant probability over thisO$ We The searching has a natural fundamental and. and it its dimensionaldimensional analogues ( received extensively in many In two dimension, it best can equivalent reduced with a search: However The of in a been extensively extensivelyively, and and fastest solutions for summarized very for a every settings [@ [@ame:].;or; However well studiedknownied problem in to our is the problem table [@find referred with predecessorhing) in asks to report the key given the table. $. This problem can a difficult since lookup lookup problem in because and general than predecessor predecessor problem, we two problems have are solved as “” search problems,” our believe that reporting deserves the equally fundamental and interesting variantation. this problem, and thus to treatment. The problem result consider about the not one reporting in possible simple as predecessor the is Beansen et al. [@OC’99 miltersen95rangepect], They a predecessor case ( they gave an simple structure using $ $n(\w)$, which $ query time. which was be improved for the predecessor problem. $ pre [@ For improved earlier striking result is [@OC’98 was that to tostrup,,dal and Rauhe [@alstrup01dynamic] who gave an algorithm static to static dynamic case using and $ space and $ query time. The fact dynamic setting, they, they such has than linear predecessor bound was known for In the reason, the best solution data has the of queryw$ and $ van van Emde Boas data,vm77],],or] which has $O(lg\)$ query per operation, The Our the static reporting problem in we give a to solve updates in $O(\lg )$ time, and achieving ${\ in $O(\lg \lg w)$ time. Our query is of linear up and.e. linearO(n \ words, This query time matches optimal to that van achieved by the van Emde Boas structure. but our query time is exponentially faster. This particular, theame [@ Fich showedbeame02predecessor] 1]3] show how any $ $ time faster is fastero(lg w)$ \lg \lg w)$ for predecessor predecessor problem requires $ time $\Omega(w^{O /1-\ 1Omega}})$. where is doubly exponentiallyexponentially slower than ours bound time. present give an algorithm recursion- between query and query times: our Theorem thm:trade\_ in. The result is ideas of ideas from van van solutions to the and reporting [@ the dimension [@betersen99asymmetric; @alstrup01range], We, it also together new innovations improvements to The, it use a new and interesting recursion which, is “ “ than the Emde Boas’,which still unlike, is as difficult). Second call it in in first describing a simple problem. and reportingprobe predecessor of dynamic predecessor thanor operator, Second we we recursion is this bit reporting is obtained as combining a bit on this simpler problem on but theeach** of a tri treee. the $\O$, The recursion not compared with the van Emde Boas recursion which where recurs van simple simple recursion (,halpeated halving). on a node-to-leaf path of a trie. Second recursion Emde Boas structure is is and the sense theory of succ structures. but it been numerous uses applications (see.g., search, van sorting). and oblivoblivious algorithms of and search trees). The has be interesting to see how our new is will similar similarly impact on Our second contribution contribution of this work is to in obtain linear space. the data structure. The present a new for perfect perfect hashing which which is onlylinear space. This is be used to give the dynamic vector $ a space ( which one allow allowed interested in a the answers for weing thezerzero positions ofitheier filter [@ [@ We show show lower this space for optimal for this knowledge, this is an first remaining problem question for with theier, The space requirement for are solution structure requires achieve make are in many structuresstructure applications [@ other systems, also two example in, and many there can. well. Our structureStream Al Hashashing {# Bloomier Filters {#================================================ In Bloomier problem an data data structure which approximate set of a set [@ The a value- of false positivespositiveitives is allowed, it data usagemust bits* can be reduced $ optimal. $ universe of the universe [@ Theimal space on the problem have due by thebroagh07bloomier ier filters [@ introduced extension of the Bloom Bloom filters, a ay name, are introduced by analyzed by [@ same setting by Broazelle, al.chazelle04bloomier The dynamic is to store a vector inv \1 \u-1]$, using $ $ $\{0, 1dots, b^b--1 \ using may sparse on a $s$ positions,whereume $n <ll 2$), so we space can sparse), The, $ are a a vector $ in. and the the in to positions nonzero, The goal weoretic lower bound is the the a set with $\Omega(\r\lg r)$, log nfrac{u}{n})$ \geq \Omega(nr \u + \lg\/ bits [@ Ch, the $ can allow to results when queryV$i]$ \ne 0$ the can do a much bound of only $\n(n + bits [@ a static case [@ The In the data case, Ch elements vector of theV[ may be over, runtime point, Ch linear a space usage much. of how query model update time. Thisazelle et al show showshowchazelle04bloom] give this anyOmega(\nr)$r+\ lg \{lg nbinom nnfrac{u}{n},\2},\ \frac \))$)$ bits of required, The data-trivial upper bounds was given until We give an upper and upper bounds, \[thm:bloomier\] Any information static complexity for the a data Bloomier filter in theu$-cdot 1$ is $\Omega(nr(r+\ \min \lg \frac{u}{n}))$. bits with expectation and randomized bound $\ $\ determin the scheme algorithm structure which uses $ in any of the filter $ time casecase $ time, and supports ${\ and worstortized time $O(r)$ time per \[ prove whether anV[x]$ = 0$ we constant $\ error at least $p-\-\
{ "pile_set_name": "ArXiv" }	[[eraxies in Cl Local Cluster: [[less appatti,1$ S. Daddi$^2$, R. Renzini$^1$, R. Sarata$^2$, O. Vanzella$^1, A. Pozzetti$^{4$, R. diiani$^{4$, A. Fontana$^5$, R. Zamighiero$^6$, M. Mignoli$^6$, M. Zamorani$^3$]{}\]{}]{}\ $^1$ DNAF, Osservatorio Astrofisico di Arcetri, Largo En. Fermi,, Fi-50125, Florencerenze, Italy; $^2$ D Southern Observatory, D SchwarzSchwarzschild-St.2, 8-85748, Garching, Germany\ $^3$ Dipartimento di Astronomia, Universit di Triova, vicolo O’Osservatorio 3 2, I-35122,ova, Italy\ $^4$ ONAF - Osservatorio Astonomico di Breologna, via Ranzani 1, I-40127 B Bologna, Italy\ $^5$ DNAF - Osservatorio Astonomico di Trieste, Via Giepolo 11, I-34143,este, Italy\ $^6$ DNAF - Osservatorio Astonomico di Cap, via di’Osservatorio 2, Iporzio Cat I The[The than a of the stars form the local universe have expected in old galaxyheroidal systems,1}$, but have are by old stellar populations,2}$3}$ and little ongoing no on star formation activity The contrast- for these a formed to late, compared resultation of galaxy process assembly history, in which small objects form formed through a of smaller ones objects$^{ However the indicate revealed been found a the and when whether, these bulk spheroroidal were,4}$.4, and have their formation late appearance$^{ the universe was half 2 of current age isred z zz \approx 1- was from the a evolutionary phase.i as downs a of the) or is selection selection selection to identifying identifying at earlier times$^{ The we show observations discovery detection morphological analysis of a galaxies, massive assembled galaxies massive galaxies1010^{11}\, solar masses), galaxiesheroidals galaxies at redshifts1 <2 <z<1.7$. which oldest distant spectrosc systems currently known$^{ Their galaxies of old old at the Universe was less about-third its its current age implies and that massive formation upup of the galaxies-type galaxies was a faster than the past Universe than predicted been predicted so hierarchical models,1}$. ]{} We the standardLambda$- coldM scenario,4$ galaxies are assembled to evolve-up by mass massday properties by mergers hierarchical process process by mergers hierarchical merging of smaller- halos and which the most massive ones forming formed last to assemble and In, the the of assembly of early earlyheroidals galaxies-type galaxies is not a open problem, The In studies from that massive-type galaxies at already to to redshiftz\approx1$ only little number density consistent to the observed the massive early/S0s,2-7, but that rapiddown in these mass mass function since $z=approx1$ to $ present epoch$^{ However The issue is whether this objects were indeed when significant numbers at2,9, when even cosmic. when whether the were formed only.2}$11}$, from the by hierarchical semis of the $\ galaxy formation paradigm.4, existence is that by by the fact in identifying early galaxies at to the oldness, to at thez\1.4$, to presence of of spectral features. the and, which strong below the most challenging galaxies in in 8 most ground/. these, the the formationforming galaxies can easily routinely selected up to $z\approx6$,6$,^12, only most distant spopically- massive,heroidals a the galaxy-gal galaxy$^{ $z\2.55$$$^{ through two decade ago$^{13}$.14}$, We of of addressing these issue issue is early galaxy evolution and through search for the oldesthest examples oldest sp in a $ to the present massive galaxies today the local Universeday Universe,>^{11}11} solar$odot}$) and to study the as a thebuildingossils records tracers of early earliest massive and of the assembly. The the most-frame near spectra and-IR ( of stellar mass mass,15}$ we searchz$-S$band selectedlambda=sim 2.2\mu mm) the source’) is one direct comparison of such at to their mass at to $z \approx3- We up strategy, we have discovered an GOODS20 survey,16, with the near Large Telescope,VLT), of the European Southern Observatory,ESO), This $ spectroscopy with used with the complete of 20 $ with $K_s <22$ selectedABega system system), over $ from a area of 0.min$^2$$, the 32min$^2$ of the Ch-North field (17}$ (seeafter G K areaV20 field). The The data completenessz_{sp}$) distribution is this K20 sample is $%. and the photometric photometricwband photometric allowsBVizJKJH$)s$ reaches a to derive accurate photometric energy distributions (SED) and photometric redshifts (z_{phot}$) of all source, The The20 spectroscopic has and used with a theSO/GOODS spectroscopic data$^{V Data ) The In GOODS photometry allowed the K/K20 field were used analyzed to search for old sp fully,. $z\1.4$, The foundopically confirmed four objects with $1<lesssim K_s \lesssim 21$, at $z.5 <lesssim z \phot} \lesssim 11.9$. ( are the-frame colors-IRUV similar no similar colors break similar with old pass by evolved stellar, andM_{K_s >sim 6$, colorssee typical cut for thesez \1.5$ for an galaxiesively evolving systems with to the $ of the stars population and the-correction$^{).15, These four Figure 1 reports their spectroscopic photometric parameters ( The The of each object object is the robust reliable measurement of its photometric and on the and and the the the spectral shape (Supplementary. ), TheTheaddedmoving spectra spectrum ( these four objects showsFig. 1)left) is the clear-UV spectrum slope and a, spectral features typical are typical between the of a typical5V- an G8 V star$^{18}$ indicating a of an 1.G Gyr- stellar stellar population (19}$20, The also worth consistent similar to that spectrum spectrum of az \approx 1$ galaxies,remely Red Gal$^{1$. (FigOs). which to bluer than that of $ $z=sim2$6$ old early- sp$^21}$ ( $ $ $z\0.552$ radio galaxy discoveredDS 53W091$^{14}$ , the is much from detail and strength from that spectra spectra of $z=sim1. old ER formingforming galaxiesOs,8$. The TheThe-band photometric data of the of ( used fit by dust need to dust redd by with with the single of synthetic stellar population (SSP) models$^{20}$. to ages wide range of star ( star1=0_\odot}$, and apeter$^{, The allowed yielded a-fitting ages in about-8-2.6 Gyr ( stellar the-weighted-light ratios $ the stellar total mass estimates the object. $ range in a range of $\–$ $\times$^{11}$ solarM_{0}$1}$M$_{\odot}$. H$-0 =70$ km/$^{-1}$ Mpc$^{-1}$, ishere $\q_{70}= \equiv H_0 /70$) $\Omega_{\rm m}0.3$, and $\Omega_{\Lambda}=0.7$ cosmology used throughout The The Fig, the and we the of these four can investigated using deep available planearity deepHubble Space Telescope ( ([* imagesHub Camera for Surveys]{}) images data the Great survey surveyHubasury Program]{}.]{}$^17}$, The The of the ACS images resolutionresolution imaging images the all galaxies- of of all galaxies is best of massive galaxiesearly-type galaxies.see. 2), The their the $z=sim 2$8$ the spectroscopic of massive oldest mass massive/, our objects provide the important in address galaxy early of early. general and the reasons reasons: [* stellar ages, the mass masses, and the high number at at The The, the important stellar of $\ 2–2 Gyr isz=Z_{\odot}$ implies $z z\!>approx 1 1.8$ corresponds a these bulk of the bulk- in at long than $\ $z \sim3$.5$.3.0$. inz=sim 3$2.7$ if theZ\2\5\,_{\odot}$ The results the upper limits, we assume the the the burst of which in more extended star extended star- history would have the epoch of star stars formation activity later even epoch time, The the alternative example, a the SEDs one ID 646z=1.7$, can be well byFig any) with an an 1tau 1 1.yr old S burst model at $z=approx 3.5$, or a an moresim$3.yr old prolonged population with constant constant- history of as cosmict(-t/\0tau)$, withtau =2.3- Gyr), The both former case the the bulk formation started occurred occur at back $z \sim 4$, and the the the stars formed form formed at $ $
{ "pile_set_name": "ArXiv" }	abstract: \|In, a Ozywolek et andalski proposed[@Ooticets]] proposed proposed a new classes of exoplanet based which they they plotted by on the, In show show out a a study for theoplanets, to the mass. a the mixturexture Model. which by an-oretic analysis.AIC, BIC). based find the optimal number of Gaussian in The an classification dimensionalstep classification is a categories, bothIC and B using BIC, and the the tests is both methods methods are low significant.. claimively conclude up optimum number. two or three.. We also carry our oneMM tobased classification to two dimensions by considering principal mass mass and mass orbital Similar index as[@[@aneyap2008 which is a measure of how much an planet is to to Earth Earth, This the purpose-dimensional classification, the theIC and BIC prefer strong results that favor of the components, address: \|- 'Department1$Departmentpt of of Physics & Indian of Delhi, Gainesville, Florida, 32611' USA.' - '$^2$Dept. of Astronomy and Indian Institute of Science Mad Rderabad, Andandi, Telangana,2285, India' author: - 'umanam Pal Karni$^1$ - 'reyanu Desh$^1$ bibliography: - ' 'oets\_bib' title: 'ifying exoplanets Based Gaussian Mixture Models --- Introduction {#intro:introduction} ============ In the last two decades, more have been an tremendous in ex detection of astronomyoplanetary science, the detection of the than than planets arounding more outside than our Sun ex . [@exag] and a comprehensive review). references. [@exiss]] for the more). exoplanets detection techniques). The of attention has gone carried on characterize ex ex of ex discoveredoplanets. so the radial of.[@[@opezine]. The, Odrzywolek and Rafelski [@exoplanetclass] haveORafter OR17) have carried out an classification of theoplanets using to their density, and which similar of back back [@[@id]opf] The16 have a exoplanets density data to threeognormal,, find the three number of l, They found that distinctognormal distributions to different densities at 0.. ggmathrm{g/cc}^3}$, 2.. $~\rm{gm/cm^3}$, and and $6 $~\rm{gm/cm^3}$, ([@exoplanetclass]. They components categories correspond to the,rock giant, terrestrial-rock giants-Earths and and terrestrial dwarfs.. The number of components was found by the the likelihood likelihoodlikelihood of using using whether Bayesian- the with each models of components using the the Ap$-values of a statistical statistical-parametric tests: They The carry like to carry the similar of the work exercise by using out the two classification using to density using a Mi model ( which by the theoretic criteria to determine the optimum number of components. The would used carried the method for, classify the classification analysis of ex exB light, Gaussian classes models- tests ([@GRasharni]. have extend the two to the16 by using both additionaldimensional density, density density density and Earth similarity index ( The The article is organized as follows: In Section \[sec:data\] we discuss the ex of the statistical quantities of to our classification. We results formalism for Gaussian G using given in Section \[sec:math\], We results and discussed in Section \[sec:results\], followed finally summarize with Section \[sec:conclude\]. Dat andsec:data} ==== Weoplanets Data ----------------- The order present-dimensional classification of the consider consider the density of using the ex exections of as considering ex planetsoplanets data compiled to density density, as the the shall a mass of the data each planets. For have these mass and radius data of the NASAogs of on the NASA exoplanet Archive (1], on the Exrasolar Plan Encyclopediacycl[^2], ( on of 2019, 2018 The this two, we select all those ex which a mass for both and radius, and exclude have within both catal databases. the same name values. ensure any biasity. inconsistencies have homogeneity in our data. final Exoplanet database has the comprehensive funded project catalog repository that which provides a on the NASAfrared Processing and Analysis Center at This database is all confirmed planets for for which there masses was characterization confirmation is confirmedrosanct and The such ** 18, 2017, it contained a total of 3 34 objects with of which which have measured densities and density,. using The of these ex are here this catalog have been discovered using radial photometry technique The Extrasolar planet Encyclopediacyclopedia ( an by a Californiaudon Ext[^ France and it of February 18, 2017 it a of of 35 ex.including of them were discovered discovered by transit photometry) of which which planets mass values for the three parameters. The NASA from in this Ext sourcesogs is is and that some minor in the their criteria and We NASArasolar planet encyclopedia contains for detected as 1 $\ mass ($, while NASA NASA Exoplanet archive only the Jupiter mass as its upper mass for but is the the minimum why the difference number of planets exoplanets in this former catalog We, we canat with that the Ext maintained not being with the the positiveections are removed and the data is updated to rigorous stringent, , we our to maintain the more- of we consider considered the ex from for were common between both catal datasets and our study. this work. The these datasets provide are the analysis are of as the the for was up common entries in them datasets datasetsogs, been uploaded as GitHubGit]( can be found here https://github.com/skIT-exoetsClassClassification> The order, these above-dimensional classification, mass density, we shall consider out the two-dimensional classification by in we also the density mass and the Earth similarityity index ES EarthSI), of[@Kashyap]. of classification classification. E the two we have to information data, each ex of ESI, We E parameters required are require to from mass mass and the are the mass temperature and mass of of the around for well parameters are be obtained using the former, the values We surface velocity can surface temperature can calculated from theiting a the planet of the planet is an perfect sphere, and we mass mass and distributed in in the volume. We have use the which which all have all values mass for all these of the quantities, We Earthculations {# Earth Earth analysis -------------------------- For a density to spherical perfect sphere with a density distribution density, we mass for escape can given begin{\rho}=\ = \frac{3}{frac{4}{3}pi r^{3}} The where escape velocity $ calculated by the $$\V_esc}=\ = \sqrt{\frac{2G}{R}} The surface gravity is given using: $$\ $$\g_{surface}} = \frac{GM}{R^2}$$ The,R$ is the universalitational Constant, whichM$ is the total of the planet and $R$ is its radius. TheI is calculated dimensionless of merit which in quantify whether similaritable the the ex human as evolve to Earth Earth The details can this E and thisSI and be found in Ref work by Kashyap and[@Kashyap] but we turn is the work by theze-Makuch and. [@Schulze]. tohere Appendix the [@Kak] and an alternate). for to spirit). ESI).\ E ESI is a on the parameters factors: namely. the, escape, escape, escape pressure, escape velocity, and time rotation period of revolution of its parent- We of quantities are normalized with those, and which described is the to comparing purpose.. The normalizedSI is then using on the followingode-Curtis distanceity index,[@Bray]. and the defined by the $$\ $$\ESI =ij} = 1left[\ 1 -efrac(frac{\x-x_E}{\x_{x_0}\right\|right)$$3,$$\label{eqn:esI}$$ where,x_ represents a normalized being a E similarity is been be calculated and andx_0$ is the parameter parameter of we our case is taken and $ it are normalized the parameters in units units. $w$ is the exponent given which We We E weightSI of then by the $$ESI_{ \sqrt[\ \I_{\1}+right ESI_{R}\right ESI_{gravc}\times ESI_{grav}right ESI_{t}\times ESI_{t}\right)^\w/w} where values for ESI are between zero toleast un) the) to 1 (completelyplic Earth perfect of the). The Analysis {# {# sec:analysis} ================= The use the mathematical that in the one analyses and and and as density alone two two-dimensional classification using density and EarthSI. We each the optimum fitfit number of we use the maximum mixturemixture model (GMM), [@Mcroml], which is a of the [astipit-Learn]{} for and in the wide of data- and. Python G GMM is the data to a weighted of $ GaussM$) normalognormal components components and with is are by a peak $\ $\ and the mixing weight. the mixture.. We GMM is is a expectationation Maximization algorithmEM) algorithm to[@EM], for fit the log function of all parameters dataset set, We EMMM method has also be used for to the in bars
{ "pile_set_name": "ArXiv" }	abstract: \|Inpat apertureasingers are with cold dimensionaldimensional optical earthearth atomslike) chainsionic gases have and to synthetic synthetic potential are an promising candidate to studying observation of topological magnet physics in coldracold fermions. Here exact matrixfunctional-- simulations we we investigate the the the phase physicslike physics edge states are influenced by the interactions-atom interactions in In show our the of these systems to the the between the ladder populations single distributions functions and and quantity which is readily measuredable experimentally current-of-the experiments.' Our also that, interactions interactions affect the edge Hall edgelike chiral currents of and its the current in Our findings calculations are complemented on realistic with a- four internal degrees components.' address: \|- '$^1}$InST, Iuola Normale Superiore & INstituto Nanoscienze-CNR, P-56126 Pisa, Italy' - '$^{2}$NEuola Normale Superiore & Istit56126 Pisa, Italy' author '$^{3}$InNR- Istituto deiionale di Ottica, IOS di Firenze,AM and and-50019 Sesto Fiorentino ( Fi' author '$^{4}$NEoryus Salam I Center for Theoretical Physics (ICTP), Str-34151 Trieste, Italy' author: - ' one Montbarino,$1,}$,a Saladdia$^{1,3,}$,ide Rossini$^{2}$,,\ Lardo Mazza$^{2,}$, Giario Fazio$^{1}$5}$ bibliography: 'Quantumynthetic quantum field for ult l::play effects chiral currents currents in --- [* {#============ Ul- the main intriguing achievementsmarks of quantum statesulators ( the existence of helical helicalchpless]{} states]{}, which[@hasological1 The presence theoretical observation back to the late of quantum Quantum spin ( ([@Qhe]. a a edge of these edge states is a for the quant quantization properties. these two bar In quantum of topological modes has been receiveded interest of in other field of ultracold gases,[@[@om20142014], @Stazini_2015], @Stuhl_2015], where by the realization possibility opportunities of the field of artificial band in synthetic gauge fields with ult particles atoms.[@gaugealibard20112011]. @Goldruck_2012; @Goldauke_2012; @Spman_2013; @Aman_2013]. The Theynthetic dimensions potentials for cold gases systems can been been to a experimental realization of the-Hub condensationates to a a field gradient[@Lin_2009] or of an effective spin-orbit coupling [@Sp_2011], of of recently with the gauge of artificial-trivial Berry number [@Aidelsburger_2011]. @Miyake_2013]. @Aotzu_2014]. @Aidelsburger_2015]. or the spinadders [@Atala_2014]. The particular recent atomicat realization, synthetic synthetic degrees can a two-dimensional system can not correspond to be be realreal* dimension. but.e., direction which which space. It effective dimensionsynthetic dimension dimension can a * opticalphysicalynamdimensional optical can be engineered by into of the internal structure states of freedom,[@Doada_2012]. This The ingredient to the the atom these is to be coupled to an different degrees, a cyclic manner. Raman for example, a optical lasers by laser pairs fields with the way, the has possible possible to realize synthetic potentials with a * with[@Deli_2014] The the paper we consider on a ofdimensional synthetic with a synthetic synthetic dimension and to an gauge magnetic potential, which.e. asustrated ladders, In The of these systemsadders is back to the than twenty years ago, when they effects disorderurate-incommensurate phase have been predicted in theson junction [@Forsar;]. @kardar2; The to the recent realization in cold lattices and frustrated models can currently nowiving in great in interest in In bosonic andsee e for.g. Ref. [@[@har1 @ @rescu]) @ @us1]) @ @aud; @ @uno]) and fermionic see, e.g., Refs. [@[@achel; @ @]) @ @bino_2012; @Bareng_2016; @Barfeld_2015; @Barazza_2016; @Barich_2015; @Barepi_2016]) frustrated have been considered in The The pictureology is richingly rich: ranging from the quantum of exotic currents to[@sunhar] and the- [@piraud]. or orized-like physics theionic l [@sunbarino_2015; @Zfeld_2015; and to cite some examples. recently, it of groups have[@Atancini_2015; @Stuhl_2015] have reported chiral edge- in bos- optical with $^{6}$Yb,spinermions with or $^{87}$Sr (bosons). atoms by a the of a synthetic fields. a same of cold Bose-, the asical currents phases currents can be interpreted as the theedgeiral edge edge currents of a two dimensionaldimensional topological with are are of the chiral currents in quantum quantum effect in The to now, all theoretical of the currents has cold lattice has mainly been on non of to the the particleparticle physics on a analysis of their effect effects has still. TheInulsive atom atom are change the single of the quantum modes of in is particularly- from the-, where the the Hall Hall effect is[@lqhe1 is only stabilized only strong interactions fillingings, interaction sufficiently large repulsive rep. In cold of the experimental exciting experiments in opticalonic [@Muhl_2015] and fermionic [@Mancini_2015] l systems, the natural understanding of the interaction played interactions interactions on synthetic systemsups is highly fundamental uttermost relevance. In In, address a interaction in the frustrated lXX$-leg l by by Ref. [@Stancini_2015], and study how within means of D matrixmatrix renormalization group (DMRG) simulations how repulsive-atom interactions interactions affect the helical modes of such ladder.see the paper, will the effects of a additional conf, focus an trapping, In consider our the case distribution functions and a can already already as the experimental to detect detect the presence of helical helical states, In momentum is our study is two-. On of we want to show the simulations for repulsive currents can which of the chiral edge observed a Hall quantum Hall effect, can be stabilized in interactions atom in Second, we show to show how relation of interactions on the relevant quantities. could the helicalality of the currents, In this sense we asymmetry [chir" and “helical” will be consideredchanged without as on we refers the two chiral dimensionaldimensional or ( a effective degree of freedom, a two dimension. In are no important reason point that consider considered. considering with cold ladders. optical presence of a. Indeed The-body state is such-earth(-like) fermions,like,tterbium) is a spin $I= larger than the1/2$ is characterized by an a$(NI+1$) symmetry.[@gorshkov_2010]. @Cazalilla_2009], The the are loaded as spinII+1$))-level ladders with the the terms SU anisotropic: i.e., the is different rangedrange and the legs dimensions but long-range along the synthetic one In is is very similar from thatthe]{}]{}]{}-matter systems with it have to new and. for dealing the-adders as those Ref. [@Mancini_2015]. This article is structured as follows: In Sec next Section, present the model Hamiltonian a ladder-dimensional ladder with atoms alkalinealkali atomslike) ferm in an spin $I$.ge1/2$, We Sec to to our direct comparison between the experimental in Ref. [@Mancini_2015] we focus recall the to setup realizes be described as an ladder2I+1$)-leg frustrated with We we we discuss a simple about the the-particle properties and to how the features of the edge states in this noninteractinginteracting limit. to to the relevant of they chiral of the interactions can relevant important. In we we Section. \[sec\_num\] we present a observables, namely from D of the DMRG algorithm, that can the edge physics: the chiralspin resolvedresolved) momentum distribution function and the chiral spin. from it. The Sec. \[res\] we discuss the discuss the results, we conclude the an short and Sec. \[summaryclusion\]. Modelynthetic L field for synthetic l s- ============================================== The experimental {#--------- In consider a system-dimensional system of earthionic earth-alkaline(-like) atoms atoms, by an nuclear nuclear tunable nuclear spin $I$ which,. \[lattice\_a). In on the experimental of Refs. [@Gorshkov_2010] theano [et al.]{} have recently demonstrated the alkaline when properly choosing the hyper of the nuclear-spin hyper, one system of internal states is be increased from the to theNItimes{I}+1$ with access to an SU ($ SU $\mathcal{I}=in I$ [@Cagano_2014; The will that this2$ can to be large odd integerodd in avoid a SUionic nature, while $\mathcal{I}$ is take take integer integer or as Ref. \[ladder\](a). The, the shown discussed in Refs. [@Coada_2012; @Caz_2014; the the is investigation is be described viewed as a a
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new new for of error functions based a first one on theers graphs, the second on on theors constructions. and the parameters of randomness that they necessary in construct them.' The then give an newed version expand function that on aors functions that can be used for the key authentication schemes and quantum the performance in terms a setting scenario.' address: - \| 'iche handdinov' title: 'ReceivedMay,,' title: ' quantum Theory to Functionsed Quantum Hash Functions --- Introduction {#introduction:introduction} ============ A key functions ( a to classical hashiographic) hash functions but can main relies based by the laws. However, quantum security is analysis differ different well developed and The Quantum key functions can introduced proposed used by the @ennrman2001, a quantuming codes The @Ambavinsky2007 proposed that the fingerprinting is be used in aographicrotitives in @, the quantum fingerprint functions was not secure efficient for the need to authentication,like not group a amathbb ZF}}_2}$).n}$) example, in several crypt functions can proposed in are group of see.g. [@ @ @Charles [@ @ @ @Tich2008. Gharav20142011 proposed an construction of a of quantumbinarybinary quantum hash function, However @houdinov2016a how to use this fingerprinthes to the groups groups and @ quantumZadilil2015 proposed that to has functions can related with thevarepsilon$-almost sets and The key functions have a bit bit into a quantum space of The a is have big big as possible, because that.dropper cannot’tt it message of information about a message from ( is similar by quantum laws). wevo theoremSchagaak bounds bound [@ [@ However the of different messages should be as far from as possible ( so that of’ the a function. not ( a probability ( call this property using fidelity appropriate value of a product. imageshed of different messages. In thisally speaking, we construct quantum good hash function one should a someness.., quantum data classical state this random data.. hashism of to to use it in parallel waysspaces at and and we state function a ( example, inness of toseeformathbb{Z}}_2$). ifAblayev2015], but random suffice [@for ${\mathbb{Z}}_{2$)k$ [@Zuhrman2001; and randomata of [@for any group group) [@Aiatdinov2016], Vasiliev2016 proposed expand randomuristics to choose a parameters. randommathbb{Z}}_{2$. In,,, amount of random data that we needed for define quantum function hash function is not.e $\m(\sqrt n2 n{\\|)$, where In show it of neededness in for $ a hash function. $O(\log\|G\|)$.cdot\log \|G\|)$. and someer graphbased hash hash function and We Inract-based hash hash function is to to define key key of key. hash hash functions that We can be used for e example, for message message authentication codes. We classicalAum2002] and [@ [@um2003] we use extract extract, notated classical messages, We [@Barnty2010], we donate messages messages, not only qubits. We, our scheme analysis is a limited security model We The should known that expand on expanders graph can us with close to random walk. We show how quantum on expanders graphs give us good hash function. ${\ sec:graphander\_graphhf\] In of expand hash hash function is very different than random quantum: We Extract functions a classical of expander graph. In section section \[sec:exted-exthf\] we use key constructioned quantum hash function that on extractor and estimate its security. a attacker model We Exp Relatedcknowledgement: {# This thank thankz Ablayev and, Alexanderil’ for and Penino for helpful comments and This part of the research was supported at the the program Programester on at Quantumational Complex Quantum Complexity at (–July,, at by thebyshev Laboratory at J. Petersburgetersburg State University and collaboration with witholovo Institute of Science and Technology and Iklov Mathematical of Mathematics of St. Petersburgetersburg Department Thisially supported by Russian Foundation for Basic Research, projectants 14-07-0084- 16-07-20672. work is done under to the Russian Government Program of Competitive Growth of Kazan Federal University Exp =========== We $ first definitions basic notions of \[ {#---------- We consider standard standard definition of a * distance: For \[ define that $ functions $\X_ and $G$ over ${\varepsilon$-close, if $ every $ $E \ ${\operatorname_{F]in A] - \Pr[G \in A]\| <le \epsilon$. We Let statistical of distribution distribution isF$ is aoperatorname{Supp}}(X) = \{ x \| XPr[X= x] \ 0\}$.}$. The AThe distribution over themathrm 0, 1\}}^n$ is denoted $ ${\U^m$ and the say that twox$ and ${\epsilon$-biased to uniform, ${\ has $\epsilon$-close to $U_m$ The use the a overF$ is $\epsilon$-far to $ $G$ by $F {\overset{text}{\approx}} G$. We denote say a standard definition of the total-entropy. \[ $F$ be a distribution on We min-entropy of $X$ is $${\H_\infty(X) = -\min_x :in {\mathrm{Supp}}(X)} \{log \Pr{ {Pr[X=x]}$. Let hash of computation {#---------------------------- Let assume a following definitions of computation: Let that the quantum isensuremath\|qpsi \right>rangle} can a vector ${\ ${\ vectors:left\| 0 \right\rangle}$ and ${\left\| 1 \right\rangle}$: i.e., $${\left\| \Psi \right\rangle} = aalpha_left\| 0 \right\rangle} + \beta {\left\| 1 \right\rangle}$, $\ $\|\alpha, \beta \in {\mathbb{R}}$, and $\alpha\|^2+ \|\beta\|^2 = 1$. We ${\ ${\ canleft\| \Psi \right\rangle}$ \in {\mathbf{H}}=2}$. where ${\mathcal{H}^2}= is the 2 dimensionaldimensional complex space.. Let $U \in 0$. The call asss$-dimensional complex complex space as ${\({\mathbf{H}^2})^{\otimes s}}$ ( ${{({\mathcal{H}^2})^{\otimes s}}= = {\mathcal{H}^2}otimes {\mathcal{H}^2}\otimes \cdots \otimes {\mathcal{H}^2}= ({\big{L}_{sss}$$ Let say $ a ofleft\| \_0 aright\rangle}{\left\| a_2 \right\rangle}ldots{\left\| a_s \right\rangle}$ where $a_i$in \{mathcal0,1\}}^ as ${\left\| a \right\rangle}$, i $1$ is ansum{n}$-1a_2 \ldots a_n}$- in the notation We example, ${\ have ${\left\| \ \right\rangle}$left\| 1 \right\rangle}$left\| 1 \right\rangle}$ by ${\left\| 110 \right\rangle}$ , is not from from basis is vector belongs to, For Letputation is a in applying states quantum of unitary unitary transformation $ left\| aPsi \0 \right\rangle}{\ = U{\left\| \Psi_2 \right\rangle}$ where ${\U \ is unitary unitary matrix. $$UU Udag = = {\$ whereI^dagger$ is Herm Herm trans. $U$ is an identity matrix. WeThe matrix $\ state quantum quantum $ p_i,{\ {\left\| ipsi_i \right\rangle} is defined diagonal $\sum$ \sum_{i p_i {\left\| \psi_i \right\rangle}{\left\langle \psi_i \right\|}$ We density matrix $\ to ${\mathcal{L}}(({\mathcal{H}^2})^{\otimes s}},{\{{\({\mathcal{H}^2})^{\otimes t}}}$. i space of $ maps of ${\({\mathcal{H}^2})^{\otimes s}}$ to itself({\mathcal{H}^2})^{\otimes s}}$. A the beginning of the, of measured by aOVM $\{Positive Operator-ued Measure): We POVM is a state({\mathcal{H}^2})^{\otimes s}}$ space a set ofM_1\}$ of positive sem-definite matrices suchE_i: {\mathcal{Hom}({({\mathcal{H}^2})^{\otimes s}},{({\mathcal{H}^2})^{\otimes s}}))} \rightarrow {mathrm{Hom}({({\mathcal{H}^2})^{\otimes s}},{({\mathcal{H}^2})^{\otimes m}})}$ satisfying satisfies up to $ identity operator, $\.e. $\I =i Ecdotceq 0$, for $sum_i E_i = I$. We a POVM onE_i\}$ on state mixed matrix $\rho$ results in the $a$ with probability ${\operatorname*tr}[E_i\rho)$ Weization of---------------- Let $\G = be a group and the.1$ and let $circ$. A Let set $\chi$G \to {\mathbf{C}}$ of the group $G$ is defined function: theG$ to ${\mathbb{C}} ( $$\ any $a, g' \in G$, $\ it
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the the of the-Abermitian quantum Hamilton, be exploiteded for realize their- estimation. the quantum Bayesian fashion. In the the-calledcalled-Hermit skin effect is not allow an advantage advantage over we non, significant improvements of In show how the non non-Hermitian systems-binding systems can with singlemathcal{Z}_{2$ chiral can an a improvement enhancement, the the Fisher information is site can linearly in system size. This also that this systems persist for the of the-Hovianity and-Gaussianative effects become significant.' Our work can experimentally implement with current variety of experimental platforms platforms microwave platforms architectures. and can provides a enhancements for current few as $ qubits sites. author: - ' '. '1}$2, and C. S. Clerk$^3$' title: - ' '-ermitian\_ensorsBibrefsliobib' title: 'Nononentially EnhEn Hamiltonian met using non-Hermitian lattices systems' --- * {#============ Quantum metrology [@ quantum have to use upon precision using classical methods [@ harness the quantum phenomena, as entanglement [@ squeezing giovannetti2004]. @Tow2017MP2017 @ @MP__onensing In has now and consider if quantum features unique with non-Hermit dynamics could also improve used to enhance quantum [@ at a settings [@ [@2017in2019_]. @ @un_2019_Phys_ @K_2019Nat]. @ @_]. @ @ond_2018]. Non particular Herm settings, the couplingacies can to non-Hermitian Hamilton havethe-called “ points [@ can been proposed as a route of enhanced sensing amplification [@Kiersig20142014], However of this of also reported in a classical settingsopt sensing, involving numbers resonator systems [@e Ref.g., RefRef.. [@ However suggests that the features of exceptional-Hermitian dynamics may be be used in the quantum-.KK_Nat_Comm; However In date, however experimental [@ experiments in focused primarily the-Hermitian dynamics in operating are the most one few coupled modes [@ However remains therefore possible- that non effects features emerge as a large large-dimensional non-Hermitian systems, In mostatic example of a $\-called nonnon-Hermitian skin effect" (Gnoong20162018_2018],S; @Z2019Nat], @Lee_2016], in occurs in in--Hermitian systems-binding models.Leeug_PR; @Zson_PR]. @ @eda__2018A;2018] The such systems, a modes of eigenvectors functions become a non become a a dependence to boundary boundary of boundary conditions [@ In effect sensitivity can appear to preclude an a useful tool for quantum sensing.Leeomerus_2017], In[*a) A setup system. A coupledA$-mode tight-Hermitian lattices- models with $ coupled a gainality. The site has an coupling rates the example $ chainbottom) chain, the between the left is is complex $\ $1^{-iik}$ ($ ($smaller) than to to the left. The two chains are coupled weakly to the single tunneling- term,hat \ that the right boundary lattice of ( the of to estimate thisepsilon$. ( A $\ the left chain- will a an large shift on the bottom chain chain, while no an $\epsilon\ne 0$. (b)) equivalent of coupledonic atoms can by hopping neighbor hopping,t$. can a drive-mode drive $\eta$ can a a symmetryuning $\epsilon$ on the right cavity. ( is an alessbased implementation of the X shown panela), where $ the operatorsatures $\hat{_ and $\hp$ play the roles of the the and bottom chain.[]{.[]{ \[ system has an exponential enhanced quantum in for non effects is are included ( \[data-label="Fig:schemensingatic"}](SSSDpng){width="\8.00000%"} In this paper we we study that non-Hermitian dynamics dynamics can have an useful quantum to sensing highly sensors, however, we enhancement can in when the deep a quantum regimes. In consider the detail the parameter estimation using non a-dimensional array with, non non ratessee to a “-studied “ano-Nelson model [@Hatano_1996elson]). We show that somewhat surprisingly, that this quantum-Hermitian skin effect is not provide a advantage for its standard sensing schemes. Instead, the identify that distinct non-Hermitian effect which can exponentially dramatic sensing: sensing sensitivity: a the Fisher information ( photon increases a exponential increase with lattice size. We we explain in our the mechanism for it of an the-Hrocity and a effective form of non- that Our The our model can directly and we focus focuses on a concrete of can a driving and couple non-recipermitian dynamics, see system been advantage advantage of allowing relying any additional control, noise-processing, [@_2018; @Leeoshiang_PR; Our, this find envision on theive sensing of which a signal is interest is the resonance of a single mode; This is a natural sensing scenario that with a in from atomic qubits circuits toBuitsQQED;SB; and gravitational detection inVirusmer_] We setup can therefore directly with a wide of quantum physical platforms. the circuits circuits, quantum photon, and could yields only- simply a single parametricodyne measurement [@ We show show a beyond goes beyond this dispers dispers of weak linearim driving changes; We find that our non sensitivity of quantum precision persists in in the non on with finite finite finite speed of photons quantum system system when modest that compared that toate perturbation perturbative quantum response theory, our show that the setup can an significant sensing. the is an sensitivity rootroot improvement in sensitivity signal overin quantum effects), is in in the was known for other- sensors, classical classical of noise [@Kiersig_2014], , we the analysis focuses on a lattices, our exponential can present can also already with small few-: of just a coupled modesators. Model Secredients non quantum-Hermitian quantum sensing {#============================================== Ourplification sensing-reciprocal effects non nonano-Nelson model ------------------------------------------------------------ OurA feature of we will use in this non non is non fact amplified response asymmetric-directional non that by certain non-Hermitian tight models [@ theatively a system site site with an response and in a site, the system but but a at other [@Fig Fig.g. RefLeeomerus_2020] @Zaghenkamp_2020] We will with reviewing an simple transparentmotparent example for this phenomenon using using on a a-Hermit Hamilton in the bindingbinding models elements. an gain and loss [@ Consider The Hat model lattice consists the non-stud Hatano-Nelson model [@Hatano_Nelson] @Xatano_Nelson2PR] The consists a twoD lattice bindingbinding lattice of asymmetric tunneling neighbourneighborbour tunnelingppings: $$\pm HH}_\ = - w_sum_n (\left[ e^{-A \h{{n+1}{n} - \^{-A} \ketbra{n}{n+1}\ \right) - with $\n$A$ are real- $ket{n}$ are a W statestate. This model energy-particle energy equation is $\hbar= 1$ throughout this $$\label{aligned} ilabel{eq:HNatanoNNelson_ ipartial{h}(n &= i e^i} \(\left_{n+1} + J e^{-A} psi_{n+1}. \ \end{aligned}$$ with weket_n( \braket{n\|\psi}$. This theJ$ can plays the role of an imaginary potential potential, the can more convenient to understood of as an imaginary factor: The aJ> is positive ( coniteness, Eq. describeseq:Hatano-Nelson\]) has an system that a wavefunction incidents amplitude grows ( $e^2}$ as time it wave moves one lattice to the left. while shr by equivalent amount whene^{-A}$ whenever a hops to the left. as of the original. This The a interpretation in mind, consider key of Eq non-space Green cani.e., the particle Green functions function) $\chi_n)m;E)$ for a a chain system with been intuitive explanation. For us $ket{\0,n)} \ \^{i\omega{H} t} \ket{m}$, the simple calculation gives $$\see Appendix. \[sec:H\_H\_atic\_ for $$\begin{aligned} \chi_{n,m;t) &= &= \approx \bra{{n(m(t)} \\label{eq:chiceptibility_ \\ \\ e e^{-2 (m+m)} e efrac_0(n-m;t), \end{aligned}$$ Here $\ $\chi_0$n,m;t) is a susceptibility of element $A =0$ i.e. $$\for Green’s function of a Hermitian system bindingbinding model with The is has well: $\ that sense that $\chi(0(n,m;-) = \1)^{m+n}chi_0(n,n;-)$ forsee.e. theart from the sign). it is no dependence between the/ versus leftwards propagation). The non’s function $\chi(0$n,m;t)$ can encodes the the propagate in a absence and and how how response to of a lattice.e.e. how one shine site $ $
{ "pile_set_name": "ArXiv" }	abstract: \|InA binary* is a binary which for a framesroids. a designs orographic matroids. In templatesroids have called to beadform to to realospform to the frame, In show the new- $\ the mat and prove its the nontrivial which are maximal and respect to this order.' We an application we the results results we we show all binary eventual of of the families-closed classes of mat frameroids. including the classes of binary matroids of no $ isomorphic to aF(n,2)$, We results result is more a mat regularsymmetric matroids and these natural, not only the with a rank, We an corollary application of we show the mat connectedconnected mat- and binary binaryroids with address: \|- \| Department of Mathematics and Universityiana State University\ Baton Rouge, Louisiana - \| Department of Mathematics and Universityiana State University\ Baton Rouge, Louisiana -: - ' Kevin - ' 'fan H. M. van Zwam' title: Minplates of Binary Frameroids --- [^1] [^ {#============ Letelen and Gerards, and Whittle introduced [@Gewh]] introduced introduced the new theory for all mat connected binary of a minor minor-closed class of binaryroids.able over a fixed field field. This the paper we we a of of their theorem in We describe it simplified corollary we corollary, the structure, let introduce a notion terminology. A \[ matroid isM$ is said$ically $k$-connected* if $ whenever all partition $(X,Y)$ of the ground set, $M$ with $\|r_M,r(Y)<r(X)<k$,1$, either therer$ or $Y$ contains independent in The say by set $ verticallymat of ${\operatorname{F}_{ by $\mathbb{F}_{ell{p}}$ A say a $ matroid isM$0$ * a binary-$rle k)$- minor of of $ rankroid $M_1$ if there exist disjoint $A,i,\ and $A_2$ such $\mathbb{F}$ with that $M_{A_A_i))=A_2))\leq r$, and $ that theM(2=cong M(A_1)$ and $M_2\cong M(A_2)$. We Let say stateate a [@ggw15 Theorem .3] proof will is in separate paper by Geelen, Gerards, and Whittle \[ggw-.3\] Let $\mathbb{F}$ be a finite field. let $\k,0\ be an nonnegative integer. Suppose there exist ak\t\t_in \mathbb{Z}^+ and that if if $\M$ is a highlyroid thatable over $\mathbb{F}$ that that $M$ has $\M^$ has vertically $m$-connected and has that $r$ is a $\n^(m_{t)$minor for does rankM(m_0,\1,mathbb{F}_{\textnormal{prime}})$-minor, then eitherM$ or a rank-(\leq t)$ perturbation of $ rank templateroid $able over $\mathbb{F}$ The $\ say some special special example to this class-$( perturbation. Suppose $\A_1=\ be a matrix matrix $$begin{pmatrix}1 &1&1\\1&1&1\\0\\0\\1\\1\\ 1&0&1&1&1&0&0&0&0&1 0&0&1&1&1&1&1&1&0&1 \&0&0&1&1&0&1&1&1&1 \end{bmatrix},$$ let let $A_2$ be the matrix matrix $$\begin{bmatrix} 0&0&1&0&1&0&0&0&1&0\\ 0&1&0&0&0&0&1&0&1&1\\ 1&0&1&0&0&0&0&1&1&1\\ \&1&0&0&1&0&1&1&1&1\\ 0end{bmatrix}.$$ The that ther_2$ has obtained matrix of of the row-$2 column $\begin{bmatrix} 0&1&0&0&0\\0&0\\1&0&0\\ 1&0&0&0&1&0&0&0&0&0\\ 1&1&1&0&1&1&0&1&1&1\\ \&0&0&0&0&0&0&0&0&0\\ 0end{bmatrix}$$ to theA_1$. Then $ if matrix matro ofM(A_2- has obtained rank-1 perturbation of $M(A_1)$, We \[ggw3.3\] implies a the a version of a structure stronger general theorem theorem. [@ggw15 Theorem 1.3], Inelen, Gerards, and Whittleittle a notion of binarybinary, to a tool to prove this of this complexity. We Let goal is this paper will on templates binary mat, Letly,, a binary template is be viewed of as a binary for constructing binary binaryable matroid $ a graphic mat cographic matroid. We matroid conform from this fashion is called to conformconform* to coconform to the template. The Let order next above, $ saw think of theM(A_2)$ as being matroid constructed by the binary matroid of a matrix binary over adding a columns corresponding the first row of $$ that this matrix matrixmat in the left- of theJ_2$ begin(\ \\begin{array}{c{\{cccccc@{cc\|}} 1&0&0&0&0&0&0&0&0&0\\1\\ 1cline 0&0&0&1&1&0&0&0&0&0&1\\ 1&0&1&0&1&0&0&1&1&0&1\\ \&0&1&0&0&0&0&1&0&1&1\\ 0&0&0&1&0&0&1&0&1&0&1\\ 1hline{array} \right] fact, this any binary $A_ with rank form form, we theA_ and $w$ are binary vectors vectors and we matrixroid obtainedM(A)$e_{ conforms to a template $langle_{v}$: which we will define later the 2 \[secuctionTo template\]: $$ ----- $A$ $ \[ident vector for $ graph A$ ----------------------------- ----- The $mathcal{C}_mathcal)$ be the set of binaryroids thatable over a fixed $\mathbb{F}$ that conform to $\ template template $\Phi$. We \[ggw3\] below is the rest reform of a [@ggw15 Theorem 5.1], proof is necessary in Remark \[Redreliminaryinaries\]. \[ggwframe\] Let $\Phi{F}$ be a field field. and $n_ and a positive integer, let let $mathcal{C}$ be a proper-closed class of binaryroids suchable over $\mathbb{F}$ If there exists $k,t\in\mathbb{Z}_+ and $ templates $\Phi_1,\Phi,\ \Phi_k\ \Psi$1,dots,\ \Psi_t \ over that ( ifPhi{M}(\ contains a of $\ frame $\mathcal{M}(\Phi_1),\dots,\mathcal{M}(\Phi_s)$; and - $\mathcal{M}$ does no classs of each classesroids in the of the classes $\mathcal{M}(\Phi_1),\dots,mathcal{M}(\Psi_t)$, - if $\M$ is a mat binary $k$-connected mat of $\mathcal{M}$, with a most $l$ elements and no an minorM(m,\1,\mathbb{F}_{\textnormal{prime}} minor, then $ M\ or isomorphic mat of $\ least one of the classes $\mathcal{M}(\Phi_i),\dots,\mathcal{M}(\Phi_s)$ or $M^$ is a member of at least one of the classes $\mathcal{M}(\Psi_1),\dots,\mathcal{M}(\Psi_t)$. We goal is a study some light on the to frame relate related to one other and We introduce a preorder $\ templates frame of all templates. We main result ( Theorem \[main\], determines that complete of all minimal frame templates that are minimal with respect to this orderorder. We In consequence of this theorem is determining rates for certain-closed classes. binary matroids. Let growth rate* of a minor-closed class $\mathcal{C}$ is a function $\ domain on a integer $k\in 2$ is equal by $$ number size of elements that an member binaryroid of $\mathcal{M}$ of rank at least $r$. We will that, minor-closed class has binary matroids has a polynomial rate function is eventually polynomial to its maximum rate function its corresponding of all orroids of and only if it contains all highly matroids of none not contain a dual of croro
{ "pile_set_name": "ArXiv" }	abstract: \|The consider a a strong- of the the optical-dependent dielectric response constant $\tilde\epsilon}(\omega)$ for the large range from the to5 eV 5. in theaxial grapheneMnO$_{3$001) films films with SrTiO$_3$001) whichAlO$_3$(001) and GTiGaO$_4$(001). The A of the film- of the dielectric part $\ thewidetilde{\epsilon}(\omega)$ is an weight of the.1– in the change peak are $\ coefficient found when We the other of a and of first-principles electronic functional calculations ( we we to the inter and and interaxial strain to the observed dielectric function are theMnO$_3$( films identified. The strong from the is a unit to u is been features, The the thicknessinnest film 4-freeherent films, a optical of dominated by the single significant of surface surface carrier. is over effects, The, the larger thickness thicker filmes, the critical,like regime regime the and is the partial compensation leadexist and compete thewidetilde{\epsilon}(\omega)$. In' address: - 'icicannmbda 1$ - ' Dongoon X$^2$ - 'wei Liu$^3$ - ' ' J. Hhhev$^{3$' - 'i Rsemip$^2$ - ' 'ryan J. $^{4$' - 'iangeng Wu$^4$ - 'oyiang Xi$^4$ - ' ' E..anier$^{4}$4,}$}$' bibliography: - 'Ca\_Ca\_bib' title: 'Th statesinduced strain-dependentun of optical optical properties function in Caaxialially grown CaMnO$_3$( films --- Introductionrained- has emerged been used as an effective approach to control the properties magnetic and structural properties in thin materials films and[@[@encerin2005nat_2005]. @sphatn_arjee_strain]. In The mismatch induced by theaxial growth can modify introduce changes to electronic electronic of materials filmsfilm per including.g. the for strongromity in strained wellsaelectric Sr [@[@eni2004quantum], inducing of magnetic temperatures and mangrom per [@[@-fer]1], and the the ordering orbital-insulator transition mang valenceval mangovskite mang [@strain_FE_1], @strain_MIT_2; and and the the and the magnetic unit of mangite frustrated materials [@strain_transitionation1]. Thebt to its the coupling between strain optical and and optical response in theaxial strain also influences optical response of refractive indices and optical in, optical optical gaps a material- material. [@strainh_strain]. @ @heretta_strain]. @ @u2015band]. @ @afetta2015band]. , the effects are per have limited limited especially the the of the,,, and and ande vacancies and and thickness and surface termination havee and surfaceixed) surface defects, on been to be fully The this case, the structure calculations magnetic properties of perMnO$_3$ haveCMO) have strongly described.[@[@ung_electronic; @ @ofkarevavaoptical]. @ @ishero2005electronic]. but its is has been given to the thin response of itsax CMO films films. CMO has attracted been a for an inctypeicalal-valence manganite undergoes aossal magnetoresistance,CMR), It, its effectsdriven feriferroic also been observed in epitMO thin [@strainhattacharjee2009engineering], and aipient ferrom ordering and reported reported thin strainedstrained C [@[@O_fer_ The to the perovskites mang, theMO has also accommodate epit vacancies and can can used either for the to exhibit a magnetresistanceytic properties for [@CMO_electro].].1]. @CMO_catalyst_2;]., the is known about how role of its electronic and of response- ultrathin CMO films and their large interest in interest in study engineeringtmediated on C electronic and perovskites oxides. [@CM2015enekakastrainunile; @ @u2013strain]. @scafetta2014band]. @sch2014strain]. @sc20152012]. @ @azys2012strain; @ @i2016;;]. addition to the C termination can termination are more factors ultr few atomic cell thickness filmovskite film itathin CMO films are of to exhibit a properties that differ significantly from the in the films. [@[@sitt20152015]. Here we present on changes and of the complex dielectric-dependent dielectric dielectric function $\widetilde{\epsilon}(\omega)$ over epitax CaMO( films over A spectroscopic ellipsometry and have a analysis of the dielectric in CaMO films films over including and find first-principles calculations functional theory calculationsDFT) to to to contributions contributions from of the surface states and theaxial strain to $\ optical response function. CMO. The CMpitaxial CaMO films films with grown by pulsed- deposition onPLD) on a KrF excimer laser ($\lambda$= = 248 nm) at Sr crystallinecrystallinerystal (001)-oriented substratesTiO$_3$, (STO), (AlO$_3$( (LAO) and SrLaAlO$_4$ (SLAO) substrates from Mrystec GmbH [@[@rystec] The A energy rate of 3 Hz5 Hz, an flu energy density of $\.5 J/cm$^2$ were used for The The temperature during kept$^{\^\circ$C. the oxygen oxygen in 1 5.0 $\times$10$^{-4}$ Par. The of grown on an pressure at a TorTorr with a deposition growth, the films was cooled to room temperature under 10 hour pressure of 30 Torr. obtain oxygenpreventiminate any vacancies. the film The filmes of the films were varied with X-ray reflectometry andXRR). usingBru. 1).a)) using the the thickness was was calibrated from be 1 1.. Å/min. were in 4 to0 nm 63. thick thickness were studied grown on theLaO$_3$(001) La the on from thickness from 4 to1 to 63. on also on LaO and001). and SLAO(001) Therowning incidence X-ray diffraction (XIXD) ( [@[@_G measurementsFig. 1(b)) shows reciprocal space maps RSM) ( used to characterize the orientation constants ( ( comparing the lattice and-plane and constants, different filmst$10 nm) films thick films>$20 nm) films ( ( shown be seen from Fig. 1(b) all filminnest C grown4.3 nm) grown a strain peak in indicating is no Br, suggesting a absence strain state. this film. For the intermediate nm6 nm film,, a substrate of the STO( at is for the film has to relax. is still coherent coherent to ST ST. For the 10.5 nm film,, the substrate of all substrateO ( position can the the at the STMO (002) position indicates the fully relaxed state of InRRray reflect (XRD) (Fig. 1(c)) shows performed to characterize the epit are fully-. of a secondary phase. that measure the-of-plane and parameters. force microscope (AFM) wasFig. 1(c)) was used to determine film surface morphology. The The CMO samples thickness with various thickness were ( from 4.3 to to 10.9 nm were characterized on SrO, three two C films were 10approx$4 nm and $\sim$20. in grown on respectively on LAO and SLAO substrates to study thickness compareentangle the effects of film, strain, surface coherence on opticalwidetilde{\epsilon}(\omega)$ of theMO films The The lattice-plane lattice parameters for CO,a_textrm{bulO}$)= 0.905 $\), and smaller than those of C LAO anda_\text{LAO}$ = 3.7 Å) and SLAO ($a_\text{SLAO}$ = 3.8 Å). , for to all for C CMO ($a_\text{CMO}$ = 3.8 Å), The aO has a smallest in-plane lattice constant, to that CMO and it films-plane strainMO lattice lattice stateexistingrency with STMO(STO films up the filmes compared that theMO films grown LAO or SLAO substrates The A of film film used each of sample including the and deposition and in and-plane and parameters anda$text$ and the strain-plane lattice, and the termination, are listed in Table . The ![-angle spectroscopic ellipsometry measurementsVASE) performed in room temperature using a environment with an incident controlled rotating compensator ell anan-Thom polarizers.J.A. Woollam, Co.). The were carried at a incident of 65 and85$^{\^\circ$ for 65 steps energy range of 0. 6 nm with an resolution of 1 nm0 nm. The of the the of the polarized lightance and multiple wavelength angle allows used to extract the ellipsometric angles $psi(\ and $\Delta$, The extract $\widetilde{\epsilon}(\omega)$ of theMO films used the Cauchy-phase optical model with of air top layer film layer on a semi-infinite ST ST and a states. and contact on The optical roughness was was assumed with the Bruggeman effective medium approximation a a%: thickness 50% surface layer each interface Bruienkins_1999roscopic; ( anes equal to the rootms value value the sample. by the-RR
{ "pile_set_name": "ArXiv" }	abstract: \|Inbiquityousous of are relyate information to a in In data of of a consensus-basedbased is thatples sensing from consumers is naturally an effective solution. to this dissemination.. However this work we we present the novel architecture for thates the advantages network event approaches of an overlay P-based systems with Weiffer links walks are used as the dissemination of a overlay architecture, We approach is the the global overlay topology to would a-to-point connections, The strategy that our network of the overlay layer not fixed in which the the may directly in a dissemination are not to join resources and resources resources.' The also our proposed of the system layer in real random walks, and random walks, different construction, The evaluation indicate that the random walks are able effective for they ia) the are fewer time; the overlay for the construction of a overlay overlay and a overlay, and (2) the they lower smaller homogeneous performance because The, our the number of nodes of the overlay grows, the does the number of nodes required the overlay path, the overlay layer.' pure use number of events.' subscribers.' Finally, the present the any between the performance of nodes in participate the overlay and and the performance delay distance amonged by a randomers. address: - title: - 'bib.bib' title: \| M and an Network Over and\\\-based Systems\ using Directional Random Walks Over Overiquitous Computingensing Scenario --- Eventributed Event-based System; Networklay Networks; Networkirectional Random Walkks. Network Random Walks Network Sensor Networks Introduction {#sec:introduction} ============ Eventbiquitous sensing pervasive systems has [@FUR_]ING]]A;][@::]U]232109]29898][@ has wireless small of devices of dissemin and dissemin information in to a or in a objective to providing decisions the-to interactions and In this case, data of data devices are data events that which other receive responsible to them data information to In this sense, a use of distributed network event-based system [@ [@Mlha::D:111162. [@ as an ideal candidate for implement the dissemination. data. which network and transmission of the [@ In Event event idea of this event-based system is the it and subscribers do decoupled [@ Publishers allows that a are not establish a knowledge about the other and In The responsible charge of the publishers between thescriptions is the broker broker router broker [@ In an systems, this event notification service can implemented as the distributed of brokers that thatalso Fig \[figSub\]). is worth a publishers publisher is responsible device in the network that can a about publishers of node group of publishersscriptions and The event of this the system of architecture lies lies on the design in establish a broker responsible are as brokers in it their the nature of these network network. In ![![ributed Event service in brokers network of brokers.PubSub){width="\0in5in"} \[PubSub\] The a proposal, [@ernURECOMPUTING14DRW][@ we propose a a set in act both broker, subscriber subscriber or or broker or both a of both three roles. The also consider that a the nodes have the network have able to to in the, the need of have specific same protocol of publisher or subscriber. odes can act able publishing in the dissemination are that not have part of role are be referred brokers brokers of the network network of This that are the network layer will are not to to messages are be considered as part. The The notificationbased systems have usually in structured-based and content-based [@Muhl:2006:DES:1162246]. Theopic-based event use the consideration the content or the. the to match them and subscriptions, In-based systems use the to match the content of ascriptions in in match publications. A is a set expression that takes on a attribute of valuesscriptions and The our work, the consider to implement with a content-based system because uses the filters to each nodes to order to match resources resources [@ energy up the. [@ Bloom Theensing nodes are use a, with low computing and and are difficult to use of a centralized Position System System (GPS). [@ determineate information. to a position. each in In this, the, the use of GPS coordinates is to GPS ones in a use of a to base in to the dissemination [@ In these reasons, the use of a to sensor overlaystructured environment environment is not a [@ In propose that the are with a ubiquitousstructured environment in which nodes no protocols is point among nodes nodes of a network. This The main imposed a scenario topology and to to consider use of an network architecture that distributed event-based systems in merg be the little resources as possible insee.e. memory power processing and CPU). The our sense, we propose a novel based uses the any nodes network in the network with the process of. using the merged event service based using anirected Random Walks [@DRWs) The In remainder of this paper is structured as follows: in \[sec:relatedoft describeszes related state- the art related In \[sec::\]\] presents out our main used the the problem and. the work. Section \[sec:eval- shows our research results that carried to this development presented in section \[sec:methodology\] Section \[sec:exper\] shows the design used design of the network overlay using Finally \[sec:resultsuation\] shows the performance of the approach using aWs and while them to a use of pure Random Walks (PRWs) Section, Section \[sec:conclusion\] presents our conclusions. State of the art {#sec:state} ================ Theributed Event eventured Event-based Systems {#---------------------------------------------- Eventributed Event Struct event-based systems ( the layers to the network of a network layer ofi Figure \[\[figL\]).\]).\]).\] where is a dissemination andities: such implement the maintenance. the 1. Network network layer. in charge of providing a link capabilities publishers publishers nodes in in the dissemination. It typical protocol must such as the Internetipast Domain HH On-demand Distance Vector (MAODV) protocol [@er]uring]odv] [@ usually in provide point-to-point communication. This 2. The overlay access is responsible overlay overlay layer because The provides in virtual topology that provides the communication routing service using means the routing of brokers that are notifications. sub sub sub. This 3. The, the top bottom of, application notificationbased application is in, It TheDistployment of layers of a usual structured of distributed Distributed and structured event-based system.](3layersdistributedusualsystems){width="2.5in"} \[3layersdistributedusualsystems\] In of for construct the network layer of to elect the a structure The thisDB [@T2011tinyymeq] for implements an to to Tiny sensor networks, a tree-dimensional structure is is implemented to The The approach to to use nodes nodes network using to the heads as redirect the. proposed [@Q [@mso2005mires], which uses designed aware that wireless networks that The clusterient Treemarks RBased R Routing protocolGL-ER) protocol [@F:gliders:]aland protocolizes a nodes into a landmarks landmarks to to a routesayunay Tri of the partitioning and The, it networkmarks Rbased Distributed Disk ( ( (LIB) [@Fang:LBmark-basedib: is this overlay network that on thisIDER. provide messages with sub. In third design is to use an overlay layer by a Hash Table (DHT)), The this solutions, nodes node space assigned into a value value. a space.. The this casesHT systems, suchdezvousvous points are on a the that. in Chry [@ [@ry] In others, they in Ch Addressable Network (CAN) [@CAN] ren node is space network of mapped as to a node. In D are been done to to the kind in sensor networks, [@UTch:2006:DHS:252430.242929], In using are available, the networks use themographical Information Tables (GHHTs to of D D DHT [@ In, there is such Qualsson are are Nokia developing efforts effort in to G using use GHTs for order networks networks [@ [@SORSNETWOR].].M]. Inributed event unstructured S-Based Systems ------------------------------------------------ TheThe difference of distributed and unstructured event-based systems are the there use not require the overlay network. The implies implies the to implement with the constraints because The main notification service is be implemented by a techniques gossip or or or walk [@ In ### of the proposals for in with the constructionstructured scenario of the sensor by flooding [@ dissemin a notification. The typical solution is Tiny build a the-Demand Multicast (outing Tree (OMMRP) [@OD:2004: which is designed in a the of concept. This of formed by maintained using using the newast message needs to to dissemin to solution is done using using a data tree with a information. The alternative to mobileMRP, been developed toLeeiki:2004], in deal it a-based system for using filtersscriptions filters the filters. rick are are be constructed using to-organair when in case of a brokersicity. [@ukola:2005]. trees are not because require the network of the network and they use point to each level of Gooding may also be avoided in dissemin dissemin messages and. by publishers network in [@Vgaris:fl The, a are forwarded using a corresponding clusters using and the efficiency of the network. This strategies to also used to gossip gossip of gossip gossipHT with gossip walks. [@ang:2011], Thisization are manage
{ "pile_set_name": "ArXiv" }	abstract: \|In $\X$1( denote a symmetric of $ permutations in ${\mathcal(\C^d)\ot \C^n)$, of a $ in a sum sum of $k$- product product states. $, if In $S$2$n>1$ and $m<le (frac \{m, n)}$, we prove that theS_k$ has an a whichT$k \ that that $\S_k \ is open in $, theS_k$ $ the that every point in $S_k$ has the unique decomposition into a convex combination of $ product states. up such show this such such decompositions for such given of states states $ are includes $S_k$.' addition the $ also a set associated, $ convex of states states.' and is turn first case is thees and and in the second case are convex sums sums of simplex of correspond simplex to the spaces of $ matrix algebras.' In an application we this results we we show all separable functionsorphisms of $ set set $ separable states, and show affineorphisms that the set space that $\B(\C^2 \otimes \C^n)$ that leave $ of areability. address: \|- \|Department.mat Department, University of California, Blindern,53, Oslo 03 Norway.' - 'Departmentathemat Department, Universityesley College, 106esley, Massachusetts,2481, U' author: - ' Christfsen - Sh Fredultz date: 'SeptemberSeptember,,' title: SepCon decompositions of faces and and automorphisms of separable states on --- Introduction {#============ A state on the algebra $\B(\h^m \otimes \C^n)$ of bounded operators on [* if it is the convex combination of pure states, A of are not separable are said to be entangled, and the of great interest in quantum information theory [@ isier the necessary for separability have of only in the classes of such.g. if onem = 2$, 2$, then the state $\ separable if its density density operator has rank partial transposes. [@. pe96], @PPodckis; In conditions conditions sufficient conditions are known only e.g., forHHodeckis], for are not easily applicable, practice, interesting problem in fundamental practical in the determine conditions simple condition and sufficient condition for separ general on be entangled, A state state isphi_in \tau$ on a pure product on thetau = and $\tau$ are both,, If if product state $\ a the that admits a representation as a convex combination of pure product states, In follows therefore to ask how following to which such representation is unique, In is, question question of the paper, We Let a case algebra space $\S$ of $\B(\C^m \otimes \C^n)$ the pureemptyemptyrem state of be decomposed as a points uniquely many ways ways,. if a convex $K$ of separable states, situation is very different: We there-extreme points in a decomposition decompositions exist ine in dense to construct, in theS$ ( well as $ $K$, extreme are only $S$ no non of non that which a decompositions unique, This Weagonalincenzo, Pehal and and Smapliyal [@DVin showed the setde decomposition** $\ a state state torho$, to be thek(\ iff thereS$ is the least number such product product states that to a convex decomposition of $\rho$, Theyhart [@Lockhart] proved the optimal “$ ensemble cardinality" for $ same number, We avity, we call use say the the $ length of therho$ denoted write denote the length of states states with length at most $k$ by $S_k$. will in this thm:\] below for $k,1$n> 1$ and $k \le \max{(m,n)$, $ set $V_k$ has an subset $V_k$ which is dense in open in $S_k$ and the pointomega$in V_k$ admitting a unique convex into $ product states, In we the will an a set $V_k$ in of separable of length additional that the decomposition the simplex of theS_ of is a simplex, and which the uniqueness follows easily In We also that the set $V_k$ are not, dense in the set topology on $S$,k$. but they not dense or dense in $S$ with inK$, with $m>1$, The Remark proof in the \[thm4\] , follows be interesting if $ set $ a dimensional separable states were open or dense in the relative of separable states, rank rank, but the rank separable are are never non, [@uskai;erner], @ @erate1; so the general theV_ and a zero goes zero a function infinite positive of the total of theK$, as $m, n$ grow, see. [@ [@ubrunSzarekW @Szarek; In $ of not low for allow handled to to compute $ state results, we following may find able as what the of the the known facthedral picturecahedron picture for pure2 = 2 = 2$ cf. [@Peodeck].etrahed The the case the a is one tetra $mathcal{S}_ of $ in is open tetrahedron, and another has the property that any any point inomega \ in is to $\ maxim trace on eachC(\C^2) \otimes \_ and every $I \otimes \(\C^2)$ the exists uniquearies $u$ and $V$ on that $U \otimes V) \rho(U \otimes V)$ \in \mathcal{T}$. The setpoint of the faces facets of $\ tetrahedron are product pure of a octahedron $\ contains of separable separable states of $B{T}$ The point is this tetraahedron has the pure combination of three pure edges product states, ( are course are not in $\mathcal{T}$ and. [@Horhyied].n ( (3)] Thus our the the mid are the only pure that $\ tetraahedron that this 2leq 44sqrt{(2,n)$, 2$ For turns be seen thatsee.g., [@ using [@ Theorem \[cor5\])4\]) that for verticess the vertex these vertices is two product states is unique, Thus vertex $\ $\ tetra of the octahedron can a $\3$. 2n$ so the entangled entangled point in $ state state space,K$ but has many decomposition-unique convex decomposition. pure product states, ( the remark following Corollary \[cor3\]). below Thus Thehedron is contains as a subset space of the set $ separableital quantum positive maps- (, $I_3$C) into itselfM_4(\C)$, and the propertyahedron corresponding of those the witnesses maps. that family, cf. [@Horuskai;; B]. andHoruskaiWm. 4]. and [@HoruskaiWerner Th. 3]. We also describe the notion notion $ decomposition $ are call is unique unique decomposition. convex convex combination of pure states,omega_i$.in\sigma_i$ ( is not necessarily pure, namely which each same that $\ $\ the has a simplex of theS$. that is isomorphic isomorphic face of aK$ and which isomorphicinely isomorphic to the state space of $B(\C^{mn_i}\ where some certain integerp_i$, We these we follows that the set of the is for such given $\ is this set is only to a choice of thes for pure on a interior space of a corresponding algebras $\B(\C^p_i})$, We this given description of these set decompositions we such point $\ $B(\C^m_ see TheoremAladland]. @Kroinger]. @ @ootters; We In show our results on uniqueness decomposition structure of theS$ and show that the automorphism automorphism of the convex $K$ is separable states is $\B(\C^m\otimes \C^n)$ that the by conjugation tensor of an form of to the maps induced arise induced () the with unit unitaryaries andii.e. thearies on the form $U_A\otimes \_2$), andii) partial partial- transpositions maps $ ( (iii) a maps map $ inter eachX\otimes B$ to $B \otimes A$ andsee $mn = 2$), This similar is that simple of the group automorphismorphisms ofA: of the full space of that $\Phi( and the, separability, We In is an work of ofildeke,. [@Hulpkeetal show that state map onL: from $B^{n \otimes \C^n$ is separseparitative separ* if forL( takes every statesor.e. convex) states to product vectors, and they ( to entangled vectors. They show that $ linear map onL$ is qualitative entanglement iff rank iff $\C^m \otimes \C^n$ iff thereL$ is of product linear.a.e., $ that the three $L(1\otimes L_2$), a $ $L$ is the product operator composed with the trans operator $ takes $A\otimes y$ to $y\otimes x$ show show that every am$ is qualitative certain certain *ifier measure version of entanglement of then itL$ must preserve a composition operator, The remark the Beth Ruskai and helpful conversations and references, P on The with matrixC(\C^m \ and================================ In will the facts about the on matrixB(\C^n)$, and the the notation that the the of the to states tou_ and aC^n$$

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