Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

This book is based on a graduate course taught at the University of Paris. The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne–Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.

We investigate stable solutions of elliptic equations of the type where n ≥ 2, s ∈ (0, 1), λ ≥0 and f is any smooth positive superlinear function. The operator (− Δ) s stands for the fractional Laplacian, a pseudo-differential operator of order 2s. According to the value of λ, we study the existence and regularity of weak solutions u.

We study a one-dimensional non-local variant of Fisher's equation describing the spatial spread of a mutant in a given population, and its generalization to the so-called monostable nonlinearity. The dispersion of the genetic characters is assumed to follow a non-local diffusion law modelled by a convolution operator. We prove that, as in the classical (local) problem, there exist travelling-wave solutions of arbitrary speed beyond a critical value and also characterize the asymptotic behaviour of such solutions at infinity. Our proofs rely on an appropriate version of the maximum principle, qualitative properties of solutions and approximation schemes leading to singular limits.

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We establish a “conditional” variational principle, which unifies and extends many results in the multifractal analysis of dynamical systems. Namely, instead of considering several quantities of local nature and studying separately their multifractal spectra we develop a unified approach which allows us to obtain all spectra from a new multifractal spectrum. Using the variational principle we are able to study the regularity of the spectra and the full dimensionality of their irregular sets for several classes of dynamical systems, including the class of maps with upper semi-continuous metric entropy. Another application of the variational principle is the following. The multifractal analysis of dynamical systems studies multifractal spectra such as the dimension spectrum for pointwise dimensions and the entropy spectrum for local entropies. It has been a standing open problem to effect a similar study for the “mixed” multifractal spectra, such as the dimension spectrum for local entropies and the entropy spectrum for pointwise dimensions. We show that they are analytic for several classes of hyperbolic maps. We also show that these spectra are not necessarily convex, in strong contrast with the “non-mixed” multifractal spectra.

In this paper we introduce a generalization of Picard groups to derived categories of algebras. First we study general properties of this group. Then we consider easy particular algebras such as commutative algebras, where we reduce to the classical case. Finally, we define and study a homomorphism of the braid group to the Picard group of the derived category of a Brauer tree algebra. In the smallest case we show that this homomorphism is injective and that its image is of finite index. 2000 Mathamatics Subject Classification 16D90, 18E30, 20F36

The development of novel therapeutic strategies for Alzheimer's disease (AD) represents one of the biggest unmet medical needs today. Application of neurotrophic factors able to modulate neuronal survival and synaptic connectivity is a promising therapeutic approach for AD. We aimed to determine whether the loco-regional delivery of ciliary neurotrophic factor (CNTF) could prevent amyloid-beta (Abeta) oligomer-induced synaptic damages and associated cognitive impairments that typify AD. To ensure long-term administration of CNTF in the brain, we used recombinant cells secreting CNTF encapsulated in alginate polymers. The implantation of these bioreactors in the brain of Abeta oligomer-infused mice led to a continuous secretion of recombinant CNTF and was associated with the robust improvement of cognitive performances. Most importantly, CNTF led to full recovery of cognitive functions associated with the stabilization of synaptic protein levels in the Tg2576 AD mouse model. In vitro as well as in vivo, CNTF activated a Janus kinase/signal transducer and activator of transcription-mediated survival pathway that prevented synaptic and neuronal degeneration. These preclinical studies suggest that CNTF and/or CNTF receptor-associated pathways may have AD-modifying activity through protection against progressive Abeta-related memory deficits. Our data also encourage additional exploration of ex vivo gene transfer for the prevention and/or treatment of AD.

In infected cells, hepatitis C virus (HCV) induces the formation of membrane alterations referred to as membranous webs, which are sites of RNA replication. In addition, HCV RNA replication also occurs in smaller membrane structures that are associated with the endoplasmic reticulum. However, cellular mechanisms involved in the formation of HCV replication complexes remain largely unknown. Here, we used brefeldin A (BFA) to investigate cellular mechanisms involved in HCV infection. BFA acts on cell membranes by interfering with the activation of several members of the family of ADP-ribosylation factors (ARF), which can lead to a wide range of inhibitory actions on membrane-associated mechanisms of the secretory and endocytic pathways. Our data show that HCV RNA replication is highly sensitive to BFA. Individual knockdown of the cellular targets of BFA using RNA interference and the use of a specific pharmacological inhibitor identified GBF1, a guanine nucleotide exchange factor for small GTPases of the ARF family, as a host factor critically involved in HCV replication. Furthermore, overexpression of a BFA-resistant GBF1 mutant rescued HCV replication in BFA-treated cells, indicating that GBF1 is the BFA-sensitive factor required for HCV replication. Finally, immunofluorescence and electron microscopy analyses indicated that BFA does not block the formation of membranous web-like structures induced by expression of HCV proteins in a nonreplicative context, suggesting that GBF1 is probably involved not in the formation of HCV replication complexes but, rather, in their activity. Altogether, our results highlight a functional connection between the early secretory pathway and HCV RNA replication.

Background: The use of the desirability function approach combined with the response surface methodology (RSM), also called Desirability Optimization Methodology (DOM), has been successfully applied to solve medical, chemical, and technological questions. It is particularly effi cient for the determination of the optimal conditions in natural or industrial processes involving diff erent factors leading to the antagonist responses.Objectives: Surprisingly, DOM has never been applied to the research programs devoted to the study of plant responses to the complex environmental changes, and thus to biotechnological questions.Materials and Methods: In this article, DOM is used to study the response of Datura stramonium hairy roots (HRs), obtained by genetic transformation with Agrobacterium rhizogenes A4 strain, subjected to the jasmonate treatments.Results: Antagonist eff ects on the growth and tropane alkaloid biosynthesis are confi rmed. With a limited number of experimental conditions, it is shown that 0.06 mM jasmonic acid (JA) applied for 24 h leads to an optimal compromise. Hyoscyamine levels increase by up to 290% after 24 h and this treatment does not significantly inhibit biomass growth.Conclusions: It is thus demonstrated that the use of DOM can efficiently - with a minimized number of replicates - leads to the optimization of the biotechnological processes.

We give a simultaneous generalization of exact categories and triangulated\ncategories, which is suitable for considering cotorsion pairs, and which we\ncall extriangulated categories. Extension-closed, full subcategories of\ntriangulated categories are examples of extriangulated categories. We give a\nbijective correspondence between some pairs of cotorsion pairs which we call\nHovey twin cotorsion pairs, and admissible model structures. As a consequence,\nthese model structures relate certain localizations with certain ideal\nquotients, via the homotopy category which can be given a triangulated\nstructure. This gives a natural framework to formulate reduction and mutation\nof cotorsion pairs, applicable to both exact categories and triangulated\ncategories. These results can be thought of as arguments towards the view that\nextriangulated categories are a convenient setup for writing down proofs which\napply to both exact categories and (extension-closed subcategories of)\ntriangulated categories.\n

Abstract This article is concerned with the existence, uniqueness and numerical approximation of boundary blow up solutions for elliptic PDE’s Δu = f(u), where f satisfies the so-called Keller-Osserman condition. We characterize existence of such solutions for non-monotone f. As an example, we construct an infinite family of boundary blow up solutions for the equation Δu = u 2 (1 + cos u) on a ball. We prove uniqueness (on balls) when f is increasing and convex in a neighborhood of infinity and we discuss and perform some numerical computations to approximate such boundary blow-up solutions.

We consider sign changing solutions of the equation −\mathrm{\Delta }_{m}(u) = |u|^{p−1}u in possibly unbounded domains or in \mathbb{R}^{N} . We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for m > 2 and m−1 < p < p_{c}(N,m) . Here p_{c}(N,m) is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one.

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are\ncrucial tools to study the ergodic theory of the geodesic flow on negatively\ncurved manifolds. We develop a framework (through Patterson-Sullivan densities)\nallowing us to get rid of compactness assumptions on the manifold, and prove\nmany existence, uniqueness and finiteness results of Gibbs measures. We give\nmany applications, to the Variational Principle, the counting and\nequidistribution of orbit points and periods, the unique ergodicity of the\nstrong unstable foliation and the classification of Gibbs densities on some\nRiemannian covers.\n

Abstract We analyze -normalized solutions of nonlinear Schrödinger systems of Gross–Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary conditions. We provide sufficient conditions for the existence of orbitally stable standing waves. Such waves correspond to global minimizers of the associated energy in the -subcritical and critical cases, and to local ones in the -supercritical case. Notably, our study also includes the Sobolev-critical case.

Abstract Assume that x ∈[0,1) admits its continued fraction expansion x =[ a 1 ( x ), a 2 ( x ),…]. The Khintchine exponent γ ( x ) of x is defined by $\gamma (x):=\lim _{n\to \infty }({1}/{n}) \sum _{j=1}^n \log a_j(x)$ when the limit exists. The Khintchine spectrum dim E ξ is studied in detail, where E ξ :={ x ∈[0,1): γ ( x )= ξ }( ξ ≥0) and dim denotes the Hausdorff dimension. In particular, we prove the remarkable fact that the Khintchine spectrum dim E ξ , as a function of $\xi \in [0, +\infty )$ , is neither concave nor convex. This is a new phenomenon from the usual point of view of multifractal analysis. Fast Khintchine exponents defined by $\gamma ^{\varphi }(x):=\lim _{n\to \infty }({1}/({\varphi (n)}))\sum _{j=1}^n \log a_j(x)$ are also studied, where φ( n ) tends to infinity faster than n does. Under some regular conditions on φ, it is proved that the fast Khintchine spectrum dim ({ x ∈[0,1]: γ φ ( x )= ξ }) is a constant function. Our method also works for other spectra such as the Lyapunov spectrum and the fast Lyapunov spectrum.

Journal Article Hormonal Control of Organogenesis and Somatic Embryogenesis inBeta vulgarisCallus Get access T. TÉTU, T. TÉTU Université de Picardie, U.F.R. Sciences fondamentales et appliquées, Laboratoire d'Androgenése et Biotechnologie33, rue Saint-Leu, 80039 Amiens Cédex France Search for other works by this author on: Oxford Academic PubMed Google Scholar R. S. SANGWAN, R. S. SANGWAN Université de Picardie, U.F.R. Sciences fondamentales et appliquées, Laboratoire d'Androgenése et Biotechnologie33, rue Saint-Leu, 80039 Amiens Cédex France Search for other works by this author on: Oxford Academic PubMed Google Scholar B. S. SANGWAN-NORREEL B. S. SANGWAN-NORREEL Université de Picardie, U.F.R. Sciences fondamentales et appliquées, Laboratoire d'Androgenése et Biotechnologie33, rue Saint-Leu, 80039 Amiens Cédex France Search for other works by this author on: Oxford Academic PubMed Google Scholar Journal of Experimental Botany, Volume 38, Issue 3, March 1987, Pages 506–517, https://doi.org/10.1093/jxb/38.3.506 Published: 01 March 1987 Article history Received: 16 July 1986 Published: 01 March 1987

The aim of this article is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d(G)), to the concept of relative commutativity degree of a subgroup H of a group G (denoted by d(H, G)). We shall state some results concerning the new concept which are mostly new or improvements of known results given in Gustafson (1973 Gustafson , W. H. ( 1973 ). What is the probability that two group elements commute? Amer. Math. Monthly 80 : 1031 – 1304 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Moghaddam et al. (2005 Moghaddam , M. R. R. , Chiti , K. , Salemkar , A. R. ( 2005 ). n-Isoclinism classes and n-nilpotency degree of finite groups . Algebra Colloquium 12 ( 2 ): 225 – 261 .[Crossref], [Web of Science ®] , [Google Scholar]). Moreover, we shall define the relative nth nilpotency degree of a subgroup of a group and give some results concerning this at the end of the article.

We consider a nonlocal (or fractional) curvature and we investigate similarities and differences with respect to the classical local case. In particular, we show that the nonlocal mean curvature can be seen as an average of suitable nonlocal directional curvatures and there is a natural asymptotic convergence to the classical case. Nevertheless, different from the classical cases, minimal and maximal nonlocal directional curvatures are not in general attained at perpendicular directions and, in fact, one can arbitrarily prescribe the set of extremal directions for nonlocal directional curvatures. Also the classical directional curvatures naturally enjoy some linear properties that are lost in the nonlocal framework. In this sense, nonlocal directional curvatures are somewhat intrinsically nonlinear.

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch. Math. 16 (1965) 325–329] and Combined Field Integral Equations (CFIE) [R.F. Harrington and J.R. Mautz, Arch. Elektron. Übertragungstech (AEÜ) 32 (1978) 157–164]. Finally, some numerical experiments are performed to test their efficiency.

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