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Automorphic realization of residual Galois representations

Robert Guralnick, Michael Harris, Nicholas M. Katz (2010)

Journal of the European Mathematical Society

We show that it is possible in rather general situations to obtain a finite-dimensional modular representation ρ of the Galois group of a number field F as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over F , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...

Averaging for ordinary differential equations perturbed by a small parameter

Mustapha Lakrib, Tahar Kherraz, Amel Bourada (2016)

Mathematica Bohemica

In this paper, we prove and discuss averaging results for ordinary differential equations perturbed by a small parameter. The conditions we assume on the right-hand sides of the equations under which our averaging results are stated are more general than those considered in the literature. Indeed, often it is assumed that the right-hand sides of the equations are uniformly bounded and a Lipschitz condition is imposed on them. Sometimes this last condition is relaxed to the uniform continuity in...

Averaging method for differential equations perturbed by dynamical systems

Françoise Pène (2002)

ESAIM: Probability and Statistics

In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...

Averaging method for differential equations perturbed by dynamical systems

Françoise Pène (2010)

ESAIM: Probability and Statistics

In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...

Averaging techniques and oscillation of quasilinear elliptic equations

Zhi-Ting Xu, Bao-Guo Jia, Shao-Yuan Xu (2004)

Annales Polonici Mathematici

By using averaging techniques, some oscillation criteria for quasilinear elliptic differential equations of second order ∑ i , j = 1 N D i [ A i j ( x ) | D y | p - 2 D j y ] + p ( x ) f ( y ) = 0 are obtained. These results extend and generalize the criteria for linear differential equations due to Kamenev, Philos and Wong.

Bacteriophage Infection Dynamics: Multiple Host Binding Sites

H. L. Smith, R. T. Trevino (2009)

Mathematical Modelling of Natural Phenomena

We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly,...

Banach function spaces and exponential instability of evolution families

Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu (2003)

Archivum Mathematicum

In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.

Banach spaces

Laurent Gruson, Marius van der Put (1974)

Mémoires de la Société Mathématique de France

Basic algebro-geometric conceps in the study of planar polynomial vector fields.

Dana Schlomiuk (1997)

Publicacions Matemàtiques

In this work we show that basic algebro-geometric concepts such as the concept of intersection multiplicity of projective curves at a point in the complex projective plane, are needed in the study of planar polynomial vector fields and in particular in summing up the information supplied by bifurcation diagrams of global families of polynomial systems. Algebro-geometric concepts are helpful in organizing and unifying in more intrinsic ways this information.

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