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1. CJM 2014 (vol 67 pp. 1065)

Ducrot, Arnaud; Magal, Pierre; Seydi, Ousmane
 A Finite-time Condition for Exponential Trichotomy in Infinite Dynamical Systems In this article we study exponential trichotomy for infinite dimensional discrete time dynamical systems. The goal of this article is to prove that finite time exponential trichotomy conditions allow to derive exponential trichotomy for any times. We present an application to the case of pseudo orbits in some neighborhood of a normally hyperbolic set. Keywords:exponential trichotomy, exponential dichotomy, discrete time dynamical systems, difference equationsCategories:34D09, 34A10

2. CJM 2012 (vol 65 pp. 82)

Félix, Yves; Halperin, Steve; Thomas, Jean-Claude
 The Ranks of the Homotopy Groups of a Finite Dimensional Complex Let $X$ be an $n$-dimensional, finite, simply connected CW complex and set $\alpha_X =\limsup_i \frac{\log\mbox{ rank}\, \pi_i(X)}{i}$. When $0\lt \alpha_X\lt \infty$, we give upper and lower bound for $\sum_{i=k+2}^{k+n} \textrm{rank}\, \pi_i(X)$ for $k$ sufficiently large. We show also for any $r$ that $\alpha_X$ can be estimated from the integers rk$\,\pi_i(X)$, $i\leq nr$ with an error bound depending explicitly on $r$. Keywords:homotopy groups, graded Lie algebra, exponential growth, LS categoryCategories:55P35, 55P62, , , , 17B70

3. CJM 2010 (vol 63 pp. 38)

Brüdern, Jörg; Wooley, Trevor D.
 Asymptotic Formulae for Pairs of Diagonal Cubic Equations We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system. Keywords:exponential sums, Diophantine equationsCategories:11D72, 11P55

4. CJM 2010 (vol 62 pp. 261)

Chiang, Yik-Man; Ismail, Mourad E. H.
 Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials No abstract. Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine ProblemCategories:34M10, 33C15, 33C47

5. CJM 2009 (vol 62 pp. 19)

Bouchekif, Mohammed; Nasri, Yasmina
 Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential In this paper we consider an elliptic system with an inverse square potential and critical Sobolev exponent in a bounded domain of $\mathbb{R}^N$. By variational methods we study the existence results. Keywords:critical Sobolev exponent, Palais--Smale condition, Linking theorem, Hardy potentialCategories:35B25, 35B33, 35J50, 35J60

6. CJM 2009 (vol 61 pp. 336)

Garaev, M. Z.
 The Large Sieve Inequality for the Exponential Sequence $\lambda^{[O(n^{15/14+o(1)})]}$ Modulo Primes Let $\lambda$ be a fixed integer exceeding $1$ and $s_n$ any strictly increasing sequence of positive integers satisfying $s_n\le n^{15/14+o(1)}.$ In this paper we give a version of the large sieve inequality for the sequence $\lambda^{s_n}.$ In particular, we obtain nontrivial estimates of the associated trigonometric sums on average" and establish equidistribution properties of the numbers $\lambda^{s_n} , n\le p(\log p)^{2+\varepsilon}$, modulo $p$ for most primes $p.$ Keywords:Large sieve, exponential sumsCategories:11L07, 11N36

7. CJM 2006 (vol 58 pp. 726)

Chiang, Yik-Man; Ismail, Mourad E. H.
 On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials We show that the value distribution (complex oscillation) of solutions of certain periodic second order ordinary differential equations studied by Bank, Laine and Langley is closely related to confluent hypergeometric functions, Bessel functions and Bessel polynomials. As a result, we give a complete characterization of the zero-distribution in the sense of Nevanlinna theory of the solutions for two classes of the ODEs. Our approach uses special functions and their asymptotics. New results concerning finiteness of the number of zeros (finite-zeros) problem of Bessel and Coulomb wave functions with respect to the parameters are also obtained as a consequence. We demonstrate that the problem for the remaining class of ODEs not covered by the above special function approach" can be described by a classical Heine problem for differential equations that admit polynomial solutions. Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine ProbleCategories:34M10, 33C15, 33C47

8. CJM 2001 (vol 53 pp. 944)

Ludwig, J.; Molitor-Braun, C.
 ReprÃ©sentations irrÃ©ductibles bornÃ©es des groupes de Lie exponentiels Let $G$ be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations $(T, \calU)$ of $G$ on a Banach space $\calU$ by giving a $G$-orbit in $\frn^*$ ($\frn$ being the nilradical of $\frg$), a topologically irreducible representation of $L^1(\RR^n, \o)$, for a certain weight $\o$ and a certain $n \in \NN$, and a topologically simple extension norm. If $G$ is not symmetric, \ie, if the weight $\o$ is exponential, we get a new type of representations which are fundamentally different from the induced representations. Soit $G$ un groupe de Lie r\'esoluble exponentiel. Nous caract\'erisons toutes les repr\'esentations $(T, \calU)$ continues born\'ees topologiquement irr\'eductibles de $G$ dans un espace de Banach $\calU$ \a l'aide d'une $G$-orbite dans $\frn^*$ ($\frn$ \'etant le radical nilpotent de $\frg$), d'une repr\'esentation topologiquement irr\'eductible de $L^1(\RR^n, \o)$, pour un certain poids $\o$ et un certain $n \in \NN$, d'une norme d'extension topologiquement simple. Si $G$ n'est pas sym\'etrique, c. \a d. si le poids $\o$ est exponentiel, nous obtenons un nouveau type de repr\'esentations qui sont fondamentalement diff\'erentes des repr\'esentations induites. Keywords:groupe de Lie rÃ©soluble exponentiel, reprÃ©sentation bornÃ©e topologiquement irrÃ©ductible, orbite, norme d'extension, sous-espace invariant, idÃ©al premier, idÃ©al primitifCategory:43A20
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