Annales Mathematiques du Quebec最新文献

We consider an automorphism of an arbitrary CAT(0) cube complex. We study its combinatorial displacement and we show that either the automorphism has a fixed point or it preserves some combinatorial axis. It follows that when a f.g. group contains a distorted cyclic subgroup, it admits no proper action on a discrete space with walls. As an application Baumslag-Solitar groups and Heisenberg groups provide examples of groups having a proper action on measured spaces with walls, but no proper action on a discrete space with wall.

Let (ell ) be a rational prime. Previously, abelian (ell )-towers of multigraphs were introduced which are analogous to ({mathbb {Z}}_{ell })-extensions of number fields. It was shown that for a certain class of towers of bouquets, the growth of the (ell )-part of the number of spanning trees behaves in a predictable manner (analogous to a well-known theorem of Iwasawa for ({mathbb {Z}}_{ell })-extensions of number fields). In this paper, we give a generalization to a broader class of regular abelian (ell )-towers of bouquets than was originally considered. To carry this out, we observe that certain shifted Chebyshev polynomials are members of a continuously parametrized family of power series with coefficients in ({mathbb {Z}}_{ell }) and then study the special value at (u=1) of the Artin-Ihara L-function (ell )-adically.

This paper is devoted to the analysis of Steklov eigenvalues and Steklov eigenfunctions on a class of warped product Riemannian manifolds (M, g) whose boundary (partial M) consists in two distinct connected components (Gamma _0) and (Gamma _1). First, we show that the Steklov eigenvalues can be divided into two families ((lambda _m^pm )_{m ge 0}) which satisfy accurate asymptotics as (m rightarrow infty ). Second, we consider the associated Steklov eigenfunctions which are the harmonic extensions of the boundary Dirichlet to Neumann eigenfunctions. In the case of symmetric warped product, we prove that the Steklov eigenfunctions are exponentially localized on the whole boundary (partial M) as (m rightarrow infty ). When we add an asymmetric perturbation of the metric to a symmetric warped product, we observe in almost all cases a flea on the elephant effect. Roughly speaking, we prove that “half” the Steklov eigenfunctions are exponentially localized on one connected component of the boundary, say (Gamma _0), and the other half on the other connected component (Gamma _1) as (m rightarrow infty ).

Our goal is the discussion of the problem of mathematical interpretation of basic postulates (or “principles”) of Quantum Mechanics: transitions to quantum stationary orbits, the wave-particle duality, and the probabilistic interpretation, in the context of semiclassical self-consistent Maxwell–Schrödinger equations. We discuss possible dynamical interpretation of these postulates relying on a new general mathematical conjecture on global attractors of G-invariant nonlinear Hamiltonian partial differential equations with a Lie symmetry group G. This conjecture is inspired by the results on global attractors of nonlinear Hamiltonian PDEs obtained by the author together with his collaborators since 1990 for a list of model equations with three basic symmetry groups: the trivial group, the group of translations, and the unitary group (mathbf {U}(1)). We sketch these results.

In this note we give a detailed construction of a (Lambda )-adic (mathfrak d)th Shintani lifting. We obtain a (Lambda )-adic version of Kohnen’s formula relating Fourier coefficients of half-integral weight modular forms and special values of twisted L-series. As a by-product, we derive a mild generalization of such classical formulae, and also point out a relation between Fourier coefficients of (Lambda )-adic (mathfrak d)th Shintani liftings and Stark–Heegner points.

We review the concept of the limiting absorption principle and its connection to virtual levels of operators in Banach spaces.

This paper deals with a version of the two-timing method which describes various ‘slow’ effects caused by externally imposed ‘fast’ oscillations. Such small oscillations are often called vibrations and the research area can be referred as vibrodynamics. The governing equations represent a generic system of first-order ODEs containing a prescribed oscillating velocity ({varvec{u}}), given in a general form. Two basic small parameters stand in for the inverse frequency and the ratio of two time-scales; they appear in equations as regular perturbations. The proper connections between these parameters yield the distinguished limits, leading to the existence of closed systems of asymptotic equations. The aim of this paper is twofold: (i) to clarify (or to demystify) the choices of a slow variable, and (ii) to give a coherent exposition which is accessible for practical users in applied mathematics, sciences and engineering. We focus our study on the usually hidden aspects of the two-timing method such as the uniqueness or multiplicity of distinguished limits and universal structures of averaged equations. The main result is the demonstration that there are two (and only two) different distinguished limits. The explicit instruction for practically solving ODEs for different classes of ({varvec{u}}) is presented. The key roles of drift velocity and the qualitatively new appearance of the linearized equations are discussed. To illustrate the broadness of our approach, two examples from mathematical biology are shown.

Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be seen as a consequence of the (infinite dimensional) group of volume preserving diffeomorphisms having sufficiently strong positive curvatures which ‘pull’ nearby flows together. Physically, they indicate a form of (transient) stability in the configuration space of particle positions: a family of flows starting with the same configuration deviate initially and subsequently re-converge (resonate) with each other at some later moment in time. Here, we first establish existence of conjugate points in an infinite family of Kolmogorov flows—a class of stationary solutions of the Euler equations—on the rectangular flat torus of any aspect ratio. The analysis is facilitated by a general criterion for identifying conjugate points in the group of volume preserving diffeomorphisms. Next, we show non-existence of conjugate points along Arnold stable steady states on the annulus, disk and channel. Finally, we discuss cut points, their relation to non-injectivity of the exponential map (impossibility of determining a flow from a particle configuration at a given instant) and show that the closest cut point to the identity is either a conjugate point or the midpoint of a time periodic Lagrangian fluid flow.

We consider the equation (q_t+qq_x=q_{xx}) for (q:{{mathbf {R}}}times (0,infty )rightarrow {mathbf {H}}) (the quaternions), and show that while singularities can develop from smooth compactly supported data, such situations are non-generic. The singularities will disappear under an arbitrary small “generic” smooth perturbation of the initial data. Similar results are also established for the same equation in (mathbf{S}^1times (0,infty )), where (mathbf{S}^1) is the standard one-dimensional circle.