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??We consider the structure learning problem of the \mbox{PM}_{2.5} pollution data over 31 provincial capitals in China. Specifically, we make use of the graphical model tools to study the hubs and the community structures of the \mbox{PM}_{2.5} pollution networks. The results show that the hubs in the \mbox{PM}_{2.5}pollution networks are always seriously polluted cities, and the \mbox{PM}_{2.5} pollution networks have significant community structures which consist of cities which in some sense can be regarded as blocks with similar cause of pollution. In view of the results, we suggest that the government should strengthen the effort to treat the seriously polluted areas and western China areas. Moreover, the management of the \mbox{PM}_{2.5} pollution should be region-dependent.     

Covers ℘ for Abstract Regular Polytopes \mathcal {Q} such that \mathcal{Q}=\mathcal{P}/\mathbf{Z}_{p}^{k}

One key problem in the theory of abstract polytopes is the so-called amalgamation problem. In its most general form, this is the problem of characterising the polytopes with given facets  $\mathcal {K}$ and vertex figures ?. The first step in solving it for particular  $\mathcal{K}$ and ? is to find the universal such polytope, which covers all the others. This article explains a construction that may be attempted on an arbitrary polytope ?, which often yields an infinite family of finite polytopes covering ? and sharing its facets and vertex figures. The existence of such an infinite family proves that the universal polytope is infinite; alternatively, the construction can produce an explicit example of an infinite polytope of the desired type. An algorithm for attempting the construction is explained, along with sufficient conditions for it to work. The construction is applied to a few  $\mathcal{K}$ and ? for which it was previously not known whether or not the universal polytope was infinite, or for which only a finite number of finite polytopes was previously known. It is conjectured that the construction is quite broadly applicable.     

关于同伦元素 $\alpha_{1}\beta_{1}\beta_{2}\gamma_{s}$

设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s 相似文献   

{1,3,5}-{1,4,5}问题与邻居自动机

自相似集的Lipschitz等价问题是几何测度论和分形几何的中心问题之一.Rao-Ruan-Xi[10]通过构造图递归集证明了{1,3,5}-{1,4,5}问题.该文利用邻居自动机给出了另一个证明.     

Caractères unipotents de{}^3D_4 (\mathbb{F}_q )

Résumé On calcule les 8 caractères unipotents et les fonctions de Green du groupe fini (q=p ^e ,p premier). Les autres caractères irréductibles complexes de s'obtiennent tous en prenant des combinaisons linéaires convenables des caractères des représentations virtuellesR _T ^θ de Deligne et Lusztig [3], et ceux-ci peuvent être évalués à l'aide des fonctions de Green. On peut donc calculer tous les caractères irréductibles de . L'auteur tient à remercier le Science and Engineering Research Council pour son soutien.     

Teichmüller curves in genus three and just likely intersections in $\mathbf{G}_{m}^{n}\times\mathbf{G}_{a}^{n}$

We prove that the moduli space of compact genus three Riemann surfaces contains only finitely many algebraically primitive Teichmüller curves. For the stratum \(\Omega\mathcal{M}_{3}(4)\), consisting of holomorphic one-forms with a single zero, our approach to finiteness uses the Harder-Narasimhan filtration of the Hodge bundle over a Teichmüller curve to obtain new information on the locations of the zeros of eigenforms. By passing to the boundary of moduli space, this gives explicit constraints on the cusps of Teichmüller curves in terms of cross-ratios of six points on \(\mathbf{P}^{1}\).These constraints are akin to those that appear in Zilber and Pink’s conjectures on unlikely intersections in diophantine geometry. However, in our case one is lead naturally to the intersection of a surface with a family of codimension two algebraic subgroups of \(\mathbf{G}_{m}^{n}\times\mathbf{G}_{a}^{n}\) (rather than the more standard \(\mathbf{G}_{m}^{n}\)). The ambient algebraic group lies outside the scope of Zilber’s Conjecture but we are nonetheless able to prove a sufficiently strong height bound.For the generic stratum \(\Omega\mathcal{M}_{3}(1,1,1,1)\), we obtain global torsion order bounds through a computer search for subtori of a codimension-two subvariety of \(\mathbf{G}_{m}^{9}\). These torsion bounds together with new bounds for the moduli of horizontal cylinders in terms of torsion orders yields finiteness in this stratum. The intermediate strata are handled with a mix of these techniques.     

双圆盘加权Hardy空间上$T_{z_1^{k_1}z_2^{k_2}+\bar{z}_1^{l_1}\bar{z}_2^{l_2}}$的约化子空间

本文中, 我们主要刻画了Toeplitz算子$T=M_{z^k}+M^*_{z^l}$的约化子空间, 其中 $k_i, l_i$ ($i=1,2$) 均是正整数, $k=(k_1,k_2), l=(l_1,l_2)$ 且 $k\neq l$, $M_{z^k}$, $M_{z^l}$ 是双圆盘加权Hardy空间$\mathcal{H}_\omega^2(\mathbb{D}^2)$上的乘法算子. 对权系数 $\omega$ 适当限制, 我们证明了由 $z^m$ 生成的 $T$ 的约化子空间均是极小的. 特别地, Bergman 空间和加权 Dirichlet 空间 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 均是满足该限制条件的加权Hardy空间. 作为应用, 我们刻画了 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 上 Toeplitz 算子 $T_{z^k+\bar{z}^l}$ 的约化子空间, 该结论是对双圆盘Bergman 空间上相关结论的推广.     

Dévissages des F-complexes de \mathcal{D}-modules arithmétiques en F-isocristaux surconvergents

Résumé Nous construisons, avec le langage des -modules arithmétiques de Berthelot, ?les F-isocristaux surcohérents?. Cette catégorie, sur certains schémas séparés et lisses, est équivalente à celle des F-isocristaux surconvergents. Nous en déduisons une notion de ?F-complexes de -modules arithmétiques dévissables en F-isocristaux surconvergents?. Nous prouvons que les F-complexes surholonomes se dévissent en F-isocristaux surconvergents. On établit ensuite une formule cohomologique, étendant celle d’étesse et Le Stum, des fonctions L associées aux duaux des F-complexes de -modules arithmétiques dévissables en F-isocristaux surconvergents. Puis, nous obtenons un analogue p-adique de Weil II généralisant celui de Kedlaya.     

Modified traces on Deligne’s category \underline{\mathrm{Re}}\hspace{0.7pt}\mathrm{p} (S_{t})

Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne’s category admits a unique nontrivial family of modified trace functions. Such modified trace functions have already proven to be interesting in both low-dimensional topology and representation theory. We also introduce a graded variant of Deligne’s category, lift the modified trace functions to the graded setting, and use them to recover the well-known invariant of framed knots known as the writhe.     

A note on Ramanujan’s identities involving the hypergeometric function {_{2}}F_{1}(\frac{1}{6},\frac{5}{6};1;z)

We study a class of elliptic functions associated with the hypergeometric function ${_{2}}F_{1}(\frac{1}{6},\frac{5}{6};1;z)$ . From the perspective of the properties of conformal mappings and differential equations, we provide new insight into a set of identities of Ramanujan associated with the above hypergeometric function.     

Optimal software-implemented Itoh–Tsujii inversion for $$\mathbb {F}_{2^{m}}$$

Field inversion in \(\mathbb {F}_{2^{m}}\) dominates the cost of modern software implementations of certain elliptic curve cryptographic operations, such as point encoding/hashing into elliptic curves (Brown et al. in: Submission to NIST, 2008; Brown in: IACR Cryptology ePrint Archive 2008:12, 2008; Aranha et al. in: Cryptology ePrint Archive, Report 2014/486, 2014) Itoh–Tsujii inversion using a polynomial basis and precomputed table-based multi-squaring has been demonstrated to be highly effective for software implementations (Taverne et al. in: CHES 2011, 2011; Oliveira et al. in: J Cryptogr Eng 4(1):3–17, 2014; Aranha et al. in: Cryptology ePrint Archive, Report 2014/486, 2014), but the performance and memory use depend critically on the choice of addition chain and multi-squaring tables, which in prior work have been determined only by suboptimal ad-hoc methods and manual selection. We thoroughly investigated the performance/memory tradeoff for table-based linear transforms used for efficient multi-squaring. Based upon the results of that investigation, we devised a comprehensive cost model for Itoh–Tsujii inversion and a corresponding optimization procedure that is empirically fast and provably finds globally-optimal solutions. We tested this method on eight binary fields commonly used for elliptic curve cryptography; our method found lower-cost solutions than the ad-hoc methods used previously, and for the first time enables a principled exploration of the time/memory tradeoff of inversion implementations.     

$K_{5}\times S_{n}$ 的交叉数

把完全图$K_{5}$的五个顶点与另外$n$个顶点都联边得到一类特殊的图$H_{n}$.文中证明了$H_{n}$的交叉数为$Z(5,n)+2n+\lfloor \frac{n}{2}\rfloor+1$,并在此基础上证明了$K_{5}$与星$K_{1,n}$的笛卡尔积的交叉数为$Z(5,n)+5n+\lfloor\frac{n}{2} \rfloor+1$.     

Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets

This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D=(r_1D)∪(r_2D (1 r_1-r_2-r_3)/2)∪(r_3D 1 r_3) and E=(r_1E)∪(r_2E 1-r_2- r_3)∪(r_3E 1-r_3),and proves that D and E are Lipschitz equivalent if and only if there are positive integers m and n such that r_1~m=r_3~n.     

${R}_{0}$代数中的滤子格

Abstract In the present paper, some basic properties of MP filters of Ro algebra M are investigated. It is proved that（FMP（M）,包含,′∧^-∨^-,{1},M）is a bounded distributive lattice by introducing the negation operator ′, the meet operator ∧^-, the join operator ∨^- and the implicati on operator → on the set FMP（M） of all MP filters of M. Moreover, some conditions under which （FMP（M）,包含,′∨^-,→{1},M）is an Ro algebra are given. And the relationship between prime elements of FMP （M） and prime filters of M is studied. Finally, some equivalent characterizations of prime elements of .FMP （M） are obtained.     

Convergence en loi des suites d'intégrales stochastiques sur l'espace \mathbb{D} 1 de Skorokhod

Summary For sequences of stochastic Integrals K ⁿ .X ⁿ , functional limit Theorems are presented, these results hold under simple natural conditions.

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Convergence en loi des suites d'intégrales stochastiques sur l'espace ¹ de Skorokhod

     

Propriétés spectrales des restrictions d'opérateurs de la classe \mathbb{A}

We discuss here the question whether there exists an invariant subspace for a contraction T in the class such that the spectrum of the restriction of T on is the whole closed unit disc.     

Propriétés de l'EMV de rupture de processus de Poisson

This Note concerns the estimation of the parameter of the intensity of an inhomogeneous spatial Poisson process by the maximum likelihood method. We consider an intensity admitting a discontinuity along a closed curve depending of an unknown parameter. The established results show the consistency, the convergence in law and the convergence of the moments of the maximum likelihood estimator.     

广义{1,3,5}-{1,4,5}自相似集的Lipschitz 等价

讨论广义{1,3,5}-{1,4,5}自相似集D=(r₁D)∪(r₂D+ (1+r₁-r₂-r₃)/2)∪(r₃ D+1-r₃)以及E=(r₁E)∪(r₂E+1-r₂-r₃)∪(r₃E+1-r₃)的Lipschitz等价性, 并证明了D与E为Lipschitz等价当且仅当存在正整数m和n, 使得 r₁^m=r₃ⁿ.