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 Annales mathématiques du Québec   [4 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 2195-4755 - ISSN (Online) 2195-4763    Published by Springer-Verlag  [2352 journals]
• A computation of modular forms of weight one and small level
• Authors: Kevin Buzzard; Alan Lauder
Pages: 213 - 219
Abstract: Abstract We report on a computation of holomorphic cuspidal modular forms of weight one and small level (currently level at most 1500) and classification of them according to the projective image of their attached Artin representations. The data we have gathered, such as Fourier expansions and projective images of Hecke newforms and dimensions of space of forms, is available in both Magma and Sage readable formats on a webpage created in support of this project.
PubDate: 2017-10-01
DOI: 10.1007/s40316-016-0072-8
Issue No: Vol. 41, No. 2 (2017)

• Une solution explicite monodimensionnelle d’un modèle simplifié de
couplage stationnaire thermohydraulique–neutronique
• Authors: Stéphane Dellacherie; Olivier Lafitte
Pages: 221 - 264
Abstract: Abstract We study a monodimensional stationary system coupling a simplified thermohydraulic model to a simplified neutronic model based on the diffusion approximation with one energy group. We observe that this non-linear coupled model can be studied under two points of view and we show that solving this model is equivalent to the resolution of a non-linear scalar autonomous ordinary differential equation of order 1. As a consequence, it is possible to obtain an explicit solution without using an iterative coupling algorithm solving successively the thermohydraulics and the neutronics. Moreover, we obtain an analytic solution in a simple case. The explicit results obtained with our analytical solutions confirm the numerical results obtained with the iterative classical thermohydraulics–neutronics algorithm.
PubDate: 2017-10-01
DOI: 10.1007/s40316-016-0073-7
Issue No: Vol. 41, No. 2 (2017)

• Cyclic modules over fundamental rings derived from strongly regular
equivalences
• Authors: S. Mirvakili; P. Ghiasvand; B. Davvaz
Pages: 265 - 276
Abstract: Abstract In this paper, we introduce and analyze a fundamental strongly regular equivalence relation on a hypermodule over a hyperring which is the smallest equivalence relation such that the quotient is cyclic module over a (fundamental) ring. Then we state the conditions that is equivalent with the transitivity of this relation. Finally, a characterization of the derived hypermodule (with canonical hypergroup) over a Krasner hyperring has been considered.
PubDate: 2017-10-01
DOI: 10.1007/s40316-016-0074-6
Issue No: Vol. 41, No. 2 (2017)

• Indépendance et liberté
• Authors: Bruno Poizat
Pages: 277 - 307
Abstract: Abstract We define in the infinitely generated free models of an arbitrary equational class an independence relation, which is necessarily the model-theoretic independence over the empty set when these structures happen to be $$\upomega$$ -homogeneous stable groups. We establish the basic properties of this independence relation, give some examples, and ask some questions concerning its model-theoretic behaviour (many of them dealing with the treatment of the free models in Positive Logic).
PubDate: 2017-10-01
DOI: 10.1007/s40316-016-0075-5
Issue No: Vol. 41, No. 2 (2017)

• Sur la propagation de la propriété mild au-dessus d’une extension
quadratique imaginaire de $$\varvec{\mathbb {Q}}$$ Q
• Authors: Marine Rougnant
Pages: 309 - 335
Abstract: Résumé Nous nous intéressons dans ce travail aux pro-p groupes $$G_S$$ , groupes de Galois de pro-p extensions maximales de corps de nombres non ramifiées en dehors d’un ensemble fini S de places ne divisant pas p, et plus particulièrement à la propagation de la propriété mild au-dessus d’une extension quadratique imaginaire. Notre point de départ est le critère de Labute-Schmidt (Schmidt, Doc Math 12:441–471, 2007), basé sur l’étude du cup-produit sur le groupe de cohomologie $$H^1(G_S,\mathbb {F}_p)$$ . Dans un contexte favorable, nous montrons par le calcul que le groupe étudié vérifie souvent une version faible ( $$LS_f$$ ) du critère de Labute-Schmidt. Un critère théorique est ensuite établi, permettant de montrer le caractère mild de certains groupes auxquels le critère ( $$LS_f$$ ) ne s’applique pas. Ce critère théorique est enfin appliqué à des exemples pour $$p=3$$ et comparé aux travaux de Labute et Vogel (Labute, J Reine Angew Math 596:155–182, 2006 et Vogel, Circular sets of primes of imaginary quadratic number fields, 2006).
PubDate: 2017-10-01
DOI: 10.1007/s40316-016-0071-9
Issue No: Vol. 41, No. 2 (2017)

• Editorial Note
• Authors: Dmitry Jakobson
Pages: 1 - 1
PubDate: 2017-04-01
DOI: 10.1007/s40316-017-0082-1
Issue No: Vol. 41, No. 1 (2017)

• Bounds for the zeros of complex-coefficient polynomials
• Authors: Suhail Gulzar; N. A Rather; K. A. Thakur
Pages: 105 - 110
Abstract: Abstract In this paper, we present certain results on the bounds for the moduli of the zeros of a polynomial with complex coefficients which among other things contain some generalizations and refinements of classical results due to Cauchy, Tôya, Carmichael and Mason, Williams and others.
PubDate: 2017-04-01
DOI: 10.1007/s40316-016-0064-8
Issue No: Vol. 41, No. 1 (2017)

• Lower bound for the number of critical points of minimal spectral k
-partitions for k large
• Authors: Bernard Helffer
Pages: 111 - 118
Abstract: Abstract In a recent paper with Thomas Hoffmann-Ostenhof, we proved that the number of critical points $$\ell _k$$ in the boundary set of a minimal k-partition tends to $$+\infty$$ as $$k\rightarrow +\infty$$ . In this note, we show that $$\ell _k$$ increases linearly with k as suggested by a hexagonal conjecture about the asymptotic behavior of the energy of these minimal partitions. As in the original proof by Pleijel of his celebrated theorem, this involves Faber-Krahn’s inequality and Weyl’s formula, but this time, due to the magnetic characterization of the minimal partitions, we have to establish a Weyl’s formula for Aharonov-Bohm operator controlled with respect to a k-dependent number of poles. In a recent paper with Thomas Hoffmann-Ostenhof, we proved that the number of critical points $$\ell _k$$ in the boundary set of a k-minimal partition tends to $$+\infty$$ as $$k\rightarrow +\infty$$ . In this note, we show that $$\ell _k$$ increases linearly with k as suggested by a hexagonal conjecture about the asymptotic behavior of the energy of these minimal partitions. As the original proof by Pleijel, this involves Faber-Krahn’s inequality and Weyl’s formula, but this time, due to the magnetic characterization of the minimal partitions, we have to establish a Weyl’s formula for Aharonov-Bohm operator controlled with respect to a k-dependent number of poles.
PubDate: 2017-04-01
DOI: 10.1007/s40316-016-0058-6
Issue No: Vol. 41, No. 1 (2017)

• On Sandon-type metrics for contactomorphism groups
• Authors: Maia Fraser; Leonid Polterovich; Daniel Rosen
Abstract: Abstract For certain contact manifolds admitting a 1-periodic Reeb flow we construct a conjugation-invariant norm on the universal cover of the contactomorphism group. With respect to this norm the group admits a quasi-isometric monomorphism of the real line. The construction involves the partial order on contactomorphisms and symplectic intersections. This norm descends to a conjugation-invariant norm on the contactomorphism group. As a counterpoint, we discuss conditions under which conjugation-invariant norms for contactomorphisms are necessarily bounded.
PubDate: 2017-10-16
DOI: 10.1007/s40316-017-0092-z

• Convergence rates for nonequilibrium Langevin dynamics
• Authors: A. Iacobucci; S. Olla; G. Stoltz
Abstract: Abstract We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped limits (corresponding respectively to frictions going to zero or infinity) are carefully investigated. In particular, the maximal magnitude of admissible perturbations are quantified as a function of the friction. Numerical results based on a Galerkin discretization of the generator of the dynamics confirm the theoretical lower bounds on the spectral gap.
PubDate: 2017-10-06
DOI: 10.1007/s40316-017-0091-0

• Domains of holomorphy
• Authors: V. Nestoridis
Abstract: Abstract We give a simple proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire’s Category Theorey and Montel’s Theorem. We also obtain generalizations by demanding that the non-extentable functions belong to a particular class of functions $$X=X({\varOmega })\subset H({\varOmega })$$ . We show that the set of non-extendable functions not only contains a $$G_{\delta }$$ -dense subset of $$X({\varOmega })$$ , but it is itself a $$G_{\delta }$$ -dense set. We give an example of a domain in $$\mathbb {C}$$ which is a $$H({\varOmega })$$ -domain of holomorphy but not a $$A({\varOmega })$$ -domain of holomorphy.
PubDate: 2017-09-21
DOI: 10.1007/s40316-017-0089-7

• Fontaine–Laffaille modules and strongly divisible modules
• Authors: Hui Gao
Abstract: Abstract In this note, we study the relation between Fontaine–Laffaille modules and strongly divisible modules, without assuming the main theorem of Fontaine–Laffaille (but we need to assume the main results concerning strongly divisible modules). This in particular gives a new proof for the main theorem of Fontaine–Laffaille (for $$p>2$$ ).
PubDate: 2017-09-16
DOI: 10.1007/s40316-017-0090-1

• On the existence of constant scalar curvature Kähler metric: a new
perspective
• Authors: Xiuxiong Chen
Abstract: Abstract In this note, we introduce a new continuity path of fourth order nonlinear equations connecting the cscK equation to a second order elliptic equation, which is the critical point equation of the J-flow introduced by Donaldson (Asian J Math 3(1):1–16, 1999) and the author (Commun Anal Geom 12(4):837–852, 2004). This is a generalization of the classical Aubin continuity path for Kähler–Einstein metrics. The aim of this new path is to attack the existence problem of cscK metric. The “openness” along this continuity path is proved and a set of open problems associated with this new path is proposed.
PubDate: 2017-09-02
DOI: 10.1007/s40316-017-0086-x

• Inner product formula for Yoshida lifts
• Authors: Ming-Lun Hsieh; Kenichi Namikawa
Abstract: Abstract We prove an inner product formula for vector-valued Yoshida lifts by an explicit calculation of local zeta integrals in the Rallis inner product formula for $${\mathrm{O}}(4)$$ and $${\mathrm {Sp}}(4)$$ . As a consequence, we obtain the non-vanishing of Yoshida lifts.
PubDate: 2017-07-28
DOI: 10.1007/s40316-017-0088-8

• Summation identities and transformations for hypergeometric series
• Authors: Rupam Barman; Neelam Saikia
Abstract: Abstract We find summation identities and transformations for the McCarthy’s p-adic hypergeometric series by evaluating certain Gauss sums which appear while counting points on the family \begin{aligned} Z_{\lambda }: x_1^d+x_2^d=d\lambda x_1x_2^{d-1} \end{aligned} over a finite field $$\mathbb {F}_p$$ . Salerno expresses the number of points over a finite field $$\mathbb {F}_p$$ on the family $$Z_{\lambda }$$ in terms of quotients of p-adic gamma functions under the condition that $$d p-1$$ . In this paper, we first express the number of points over a finite field $$\mathbb {F}_p$$ on the family $$Z_{\lambda }$$ in terms of McCarthy’s p-adic hypergeometric series for any odd prime p not dividing $$d(d-1)$$ , and then deduce two summation identities for the p-adic hypergeometric series. We also find certain transformations and special values of the p-adic hypergeometric series. We finally find a summation identity for the Greene’s finite field hypergeometric series.
PubDate: 2017-07-11
DOI: 10.1007/s40316-017-0087-9

• On the contact mapping class group of the contactization of the $$A_m$$ A
m -Milnor fiber
• Authors: Sergei Lanzat; Frol Zapolsky
Abstract: Abstract We construct an embedding of the full braid group on $$m+1$$ strands $$B_{m+1}$$ , $$m \ge 1$$ , into the contact mapping class group of the contactization $$Q \times S^1$$ of the $$A_m$$ -Milnor fiber Q. The construction uses the embedding of $$B_{m+1}$$ into the symplectic mapping class group of Q due to Khovanov and Seidel, and a natural lifting homomorphism. In order to show that the composed homomorphism is still injective, we use a partially linearized variant of the Chekanov–Eliashberg dga for Legendrians which lie above one another in $$Q \times {\mathbb {R}}$$ , reducing the proof to Floer homology. As corollaries we obtain a contribution to the contact isotopy problem for $$Q \times S^1$$ , as well as the fact that in dimension 4, the lifting homomorphism embeds the symplectic mapping class group of Q into the contact mapping class group of $$Q \times S^1$$ .
PubDate: 2017-07-01
DOI: 10.1007/s40316-017-0085-y

• Infinite families of congruences modulo 7 for Ramanujan’s general
partition function
• Authors: Nipen Saikia; Jubaraj Chetry
Abstract: Abstract For any non-negative integer n and non-zero integer r, let $$p_r(n)$$ denote Ramanujan’s general partition function. In this paper, we prove many infinite families of congruences modulo 7 for the general partition function $$p_r(n)$$ for negative values of r by using q-identities.
PubDate: 2017-05-25
DOI: 10.1007/s40316-017-0084-z

• Transfer and local density for Hermitian lattices
• Authors: Andrew Fiori
Abstract: Abstract In this paper we study the integral structure of lattices over finite extensions of $$\mathbb {Z}_p$$ which arise from restriction or transfer from a lattice over a finite extension. We describe explicitly the structure of the resulting lattices. Special attention is given to the case of lattices whose quadratic forms arise from Hermitian forms. Then, in the case of Hermitian lattices where the final lattice is over $$\mathbb {Z}_p$$ we focus on the problem of computing the local densities.
PubDate: 2017-05-05
DOI: 10.1007/s40316-017-0083-0

• On a generalization of the Stone–Weierstrass theorem
• Authors: Aida Kh. Asgarova
Abstract: Abstract Assume X is a compact Hausdorff space and C(X) is the space of real-valued continuous functions on X. A version of the Stone–Weierstrass theorem states that a closed subalgebra $$A\subset C(X)$$ , which contains a nonzero constant function, coincides with the whole space C(X) if and only if A separates points of X. In this paper, we generalize this theorem to the case in which two subalgebras of C(X) are involved.
PubDate: 2017-04-06
DOI: 10.1007/s40316-017-0081-2

• On properties of sharp normal numbers and of non-Liouville numbers
• Authors: Jean-Marie De Koninck; Imre Kátai
Abstract: Abstract We show that some sequences of real numbers involving sharp normal numbers or non-Liouville numbers are uniformly distributed modulo 1. In particular, we prove that if $$\tau (n)$$ stands for the number of divisors of n and $$\alpha$$ is a binary sharp normal number, then the sequence $$(\alpha \tau (n))_{n\ge 1}$$ is uniformly distributed modulo 1 and that if g(x) is a polynomial of positive degree with real coefficients and whose leading coefficient is a non-Liouville number, then the sequence $$(g(\tau (\tau (n))))_{n \ge 1}$$ is also uniformly distributed modulo 1.
PubDate: 2017-04-04
DOI: 10.1007/s40316-017-0080-3

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