cluster consensus control of generic linear multi agent systems under directed topology with acyclic partition this paper investigates the cluster consensus control for generic linear multi agent systems mass under directed interaction topology via distributed feedback controller focus of this paper is particularly on addressing the following problem which is of both theoretical and practical interests but have not been considered in the existing literature under what kind of interaction among the clusters can the cluster consensus control be achieved regardless of the magnitudes of the coupling strengths among the agents directed acyclic interaction topology among the clusters is proved to have this property as opposed to the algebraic conditions provided in the existing literature conditions for guaranteeing the cluster consensus control in this paper are presented in terms of purely the graphic topology conditions and thus are very easy to be verified

critical values of the twisted tensor l function in the imaginary quadratic case the twisted tensor l function of f which we denote by g s f is a certain dirichlet series associated to a quadratic extension of number fields k f and a cuspidal automorphic function f over k it was introduced in 1 by asai following previous work of shimura in the case when f is a hilbert modular cusp form over a real quadratic extension k of q in the past twenty odd years this l function has been considered more generally for instance 11 and 12 deal with quadratic extensions of totally real fields 17 with imaginary quadratic extensions of q and 3 4 and 14 with general quadratic extensions of number fields all these papers have been primarily concerned with establishing analytic properties of g s f analogous to those in 1 such as meromorphic continuation to the entire complex plane location and finiteness of the number of poles and functional equation the aim of this paper is to prove a rationality result for g s f in the imaginary quadratic setting if k is an imaginary quadratic field and f a cusp form associated to k we establish that there is a period j f such that

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

cluster delay consensus in multi agent systems via pinning leader following approach with intermittent effect abstractin this paper the cluster consensus problem with delays of first order nonlinear multi agent systems is studied through pinning leader following approach with periodic intermittent effect the graph of the networked system is assumed to be directed and weakly connected a new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link specifically the agents in each cluster are divided into three subsets due to the orientation of their topological degree and each subset of agents is controlled by an individual law a redefined notion on cluster consensus with two sorts of time delays is proposed in this article some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay while agents in different clusters reach consensus with delays via following their leaders some numerical simulations are given to illustrate the effectiveness of the theoretical results

module de congruences pour gl 2 d un corps imaginaire quadratique et theorie d iwasawa d un corps cm biquadratique

darmon points on elliptic curves over number fields of arbitrary signature we present new constructions of complex and pp adic darmon points on elliptic curves over base fields of arbitrary signature we conjecture that these points are global and present numerical evidence to support our conjecture

p adic l functions of bianchi modular forms the theory of overconvergent modular symbols developed by rob pollack and glenn stevens gives a beautiful and effective construction of the p adic l function of a modular form in this paper we give an analogue of their results for bianchi modular forms that is modular forms over imaginary quadratic fields in particular we prove control theorems that say that the canonical specialisation map from overconvergent to classical bianchi modular symbols is an isomorphism on small slope eigenspaces of suitable hecke operators we also give an explicit link between the classical modular symbol attached to a bianchi modular form and critical values of its l function which then allows us to construct p adic l functions of bianchi modular forms

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

on the local solvability and the local integrability of systems of vector fields on etudie des systemes surdetermines de champs vectoriels dans un sous ensemble ouvert de r n 1 de type l j t j j t x x j 1 m ayant des coefficients analytiques on suppose que les champs de vecteurs l j satisfont la condition de frobenius

consensus of second order multi agent systems with delayed nonlinear dynamics and intermittent communications this article investigates the second order consensus problem of multi agent systems with inherent delayed nonlinear dynamics and intermittent communications each agent is assumed to obtain the measurements of relative states between its own and the neighbours only at a sequence of disconnected time intervals a new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second order consensus under a fixed strongly connected and balanced topology by constructing a common lyapunov function it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values respectively finally simulation examples are provided to verify the effectiveness of the theoretical analysis

real analytic solvability for differential complexes associated to locally integrable structures abstract inspired by the work of suzuki 12 on the concept of real analytic solvability for first order analytic linear partial differential operators we extend his results for the differential complexes associated to analytic locally integrable structures of corank one we prove that such notion of solvability is related to the smooth solvability condition introduced by f treves 13 in 1983 in our arguments the natural extension to closed forms of the well known baouendi treves approximation formula the so called approximate poincare lemma cf 1 14 plays a key role

gevrey solvability and gevrey regularity in differential complexes associated to locally integrable structures in this work we study some properties of the differential complex associated to a locally integrable involutive structure acting on forms with gevrey coefficients among other results we prove that for such complexes gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition as a consequence we obtain the proof of the gevrey solvability for a first order linear pde with real analytic coefficients satisfying the nirenberg treves condition p

cluster synchronization in directed networks of partial state coupled linear systems under pinning control this paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure for the case with fixed topology it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters the couplings within the each cluster are sufficiently strong an extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies such a balanced condition can be removed via the use of dwell time technique for all the cases the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified finally some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings