on a conjecture of ash abstract in this paper we prove a particular case of a conjecture of ash that states the existence of galois representations associated to hecke eigenclasses in cohomology

a multilevel computational strategy for handling microscopic and macroscopic instabilities this paper presents a numerical technique to deal with instability phenomena in the context of heterogeneous materials where buckling may occur at both macroscopic and or microscopic scales we limit ourselves to elastic materials but geometrical nonlinearity is taken into account at both scales the proposed approach combines the multilevel finite element analysis fe2 and the asymptotic method anm in that framework the unknown nonlinear constitutive relationship at the macroscale is found by solving a local finite element problem at the microscale in contrast with fe2 the use of the asymptotic development allows to transform the nonlinear microscopic problems into a sequence of linear problems thus a direct analogy with classical linear homogenization can be made to construct a localisation tensor at each step of the asymptotic development and an explicit macroscopic constitutive relationship can be constructed at each step furthermore the salient features of the anm allow treating instabilities and limit points in a very simple way at both scales the method is tested and illustrated through numerical examples involving local instabilities which have ignificant influence on the macroscopic behavior

homogenization of first order equations with u varepsilon periodic hamiltonians part i local equations in this paper we present a result of homogenization of first order hamilton jacobi equations with u varepsilon periodic hamiltonians on the one hand under a coercivity assumption on the hamiltonian and some natural regularity assumptions we prove an ergodicity property of this equation and the existence of non periodic approximate correctors on the other hand the proof of the convergence of the solution usually based on the introduction of a perturbed test function in the spirit of evans work uses here a twisted perturbed test function for a higher dimensional problem

euler poisson systems as action minimizing paths in the wasserstein space this paper uses a variational approach to establish existence of solutions t vt for the 1 d euler poisson system by minimizing an action we assume that the initial and terminal points 0 t are prescribed in mathcal p 2 mathbb r the set of borel probability measures on the real line of finite second order moments we show existence of a unique minimizer of the action when the time interval 0 t satisfies t these solutions conserve the hamiltonian and they yield a path t t in mathcal p 2 mathbb r when t y t is a dirac mass the euler poisson system reduces to ddot y y 0 the kinetic version of the euler poisson that is the vlasov poisson system was studied in ambrosio and gangbo comm pure appl math to appear as a hamiltonian system

polynomial rings over arbitrary fields in two or more variables are not pole assignable abstract an explicit example of a completely reachable pair of 2 2 matrices with entries in the ring k x y k an arbitrary field is written down which is not pole assignable i e the ring k x y is not pole assignable

w1 p quasiconvexity and variational problems for multiple integrals abstract variational problems for the multiple integral i u g u x dx where r m and u r n are studied a new condition on g called w1 p quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of c b morrey it being shown in particular to be necessary for sequential weak lower semicontinuity of i in w 1 p r n and for the existence of minimizers for certain related integrals counterexamples are given concerning the weak continuity properties of jacobians in w 1 p r n p n m an existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses

stochastic homogenization of nonconvex unbounded integral functionals with convex growth we consider the well trodden ground of the problem of the homogenization of random integral functionals when the integrand has standard growth conditions the qualitative theory is well understood when it comes to unbounded functionals that is when the domain of the integrand is not the whole space and may depend on the space variable there is no satisfactory theory in this contribution we develop a complete qualitative stochastic homogenization theory for nonconvex unbounded functionals with convex growth we first prove that if the integrand is convex and has p growth from below with p d the dimension then it admits homogenization regardless of growth conditions from above this result that crucially relies on the existence and sublinearity at infinity of correctors is also new in the periodic case in the case of nonconvex integrands we prove that a similar homogenization result holds provided that the nonconvex integrand admits a two sided estimate by a convex integrand the domain of which may depend on the space variable that itself admits homogenization this result is of interest to the rigorous derivation of rubber elasticity from polymer physics which involves the stochastic homogenization of such unbounded functionals

weak kam theory on the wasserstein torus with multidimensional underlying space the study of asymptotic behavior of minimizing trajectories on the wasserstein space p t d has so far been limited to the case d d 1 as all prior studies heavily relied on the isometric identification of p t with a subset of the hilbert space l 2 0 1 there is no known analogue isometric identification whend 1 in this article we propose a new approach intrinsic to the wasserstein space which allows us to prove a weak kam theorem on p t d the space of probability measures on the torus for anyd 1 this space is analyzed in detail facilitating the study of the asymptotic behavior invariant measures associated with minimizing trajectories of a class of lagrangians of practical importance 2013 wiley periodicals inc

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

homogenization of multiparameter integrals where is a bounded domain in rn u rm 0 and w rn rmn 0 is supposed to be 0 1 periodic with respect to the 7rst variable x rn the distinguishing feature of 1 here is that the integrand is permitted to depend on a vector of parameters 1 k r with k 1 we are interested in the asymptotic behavior of 1 as 0 and 0 integral functionals of this type appear in the mathematical modeling of cellular composite materials when n m 3 1 can be interpreted as the stored strain energy of an elastic and heterogeneous material u being a deformation or displacement 7eld when m 1 u may be a di erence of potential in a condenser in any case the medium under consideration is composed of several materials which are periodically distributed at the microscopic scale given by in the applications we often deal with

on a class of first order hamilton jacobi equations in metric spaces abstract we establish well posedness of a class of first order hamilton jacobi equation in geodesic metric spaces the result is then applied to solve a hamilton jacobi equation in the wasserstein space of probability measures which arises from the variational formulation of a compressible euler equation

feedback invariants for linear dynamical systems over a principal ideal domain abstract this paper studies the action of the feedback group f n m on m input n dimensional reachable linear dynamical systems over a principal ideal domain r for such a 2 dimensional system a complete set of invariants is given which characterizes the feedback class of in particular it is characterized in terms of these invariants when has the feedback cyclization property the particular cases r z and r r x are studied in some detail finally when n is arbitrary the feedback classification is given for the class of reachable systems f g such that g is a matrix with at least n 1 invariant factors equal to one

homogenization for a class of integral functionals in spaces of probability measures abstract we study the homogenization of a class of actions with an underlying lagrangian l defined on the set of absolutely continuous paths in the wasserstein space p p r d we introduce an appropriate topology on this set and obtain the existence of a limit of the rescaled lagrangians our main goal is to provide a representation formula for these limits in terms of the effective lagrangians this allows us to study not only the convexity properties of the effective lagrangian but also the differentiability properties of its legendre transform restricted to constant functions for the case d 1 we obtain partial results in terms of an effective lagrangian defined on l p 0 1 d r d our study provides a way of computing the limit of a family of metrics on the wasserstein space the results of this paper can also be applied to study the homogenization of variational solutions of the one dimensional vlasov poisson system as well as the asymptotic behavior of calibrated curves fathi 2003 6 gangbo and tudorascu 2010 12 whereas our study for the one dimensional case covers a large class of lagrangians that for the higher dimensional case is concerned with special lagrangians such as the ones obtained by regularizing the potential energy of the d dimensional vlasov poisson system

strong feedback cyclization for systems over rings abstract for nonnecessarily reachable systems over a commutative ring r we define a strong form of feedback cyclization fc with this natural generalization of the fc property we obtain a feedback reduced form for systems over strong fc rings i e rings for which every system verifies the fc property in the particular case of reachable single input systems this gives the usual control canonical form of bumby et al remarks on the pole shifting problem over rings j pure appl algebra 20 1981 113 127 also it is proved that a commutative ring with 1 in its stable range has the strong fc property if and only if it has the ucu property which is the natural parallel form of the result given by brewer et al pole assignability in polynomial rings power series rings and prufer domains j algebra 106 1987 265 286 for the reachable case many classes of rings which were known to be fc rings are in fact strong fc rings but there are fc rings which are not strong fc rings

the vlasov poisson landau system in a periodic box the classical vlasov poisson landau system describes dynamics of a collisional plasma interacting with its own electrostatic eld as well as its grazing collisions such grazing collisions are modeled by the famous landau fokker planck collision kernel proposed by landau in 1936 we construct global unique solutions to such a system for initial data which have small weighted h norms but can have large h k 3 norms with high velocity moments our construction is based on accumulative study on the landau kernel in the past decade g1 sg1 3 with four extra ingredients to overcome the speci c mathematical di culties present in the vlasov poisson landau system a new exponential weight of electric potential to cancel the growth of the velocity a new velocity weight to capture the weak velocity di usion in the landau kernel a decay of the electric eld to close the energy estimate and a new bootstrap argument to control the propagation of the high moments and regularity with large amplitude

lagrangian dynamics on an infinite dimensional torus a weak kam theorem the space l2 0 1 has a natural riemannian structure on the basis of which we introduce an l2 0 1 infinite dimensional torus t for a class of hamiltonians defined on its cotangent bundle we establish existence of a viscosity solution for the cell problem on t or equivalently we prove a weak kam theorem as an application we obtain existence of absolute action minimizing solutions of prescribed rotation number for the one dimensional nonlinear vlasov system with periodic potential

the pole assignability property in polynomial rings over gcd domains several recent papers among them bssv tl t2 have considered the problem of identifying rings with the property of pole assignability the definition appears below in particular bumby sontag sussmann and vasconcelos bssv showed that while a polynomial ring in one indeterminate over a field has this property the polynomial ring in two indeterminates over the reals r x y and the polynomial ring in one indeterminate over the integers z x do not have this property then tannenbaum tl t23 showed that the polynomial ring in two indeterminates over any field does not have this property the purpose of this note is to unify the proofs of these two facts in results that we hope will be helpful in identifying the pole assignability property or its absence in other rings let

on pole assignment problems in polynomial rings abstract a result giving conditions under which a polynomial ring over a principal ideal domain is not pole assignable is proved it is then deduced that z xa and k x y k a field are not pole assignable rings explicit examples of reachable pairs of matrices which are not pole assignable are also given

on the range of non vanishing p torsion cohomology for gln fp abstract the range of non vanishing of h gl n f p f p is not know in general in this paper we construct a cohomology class in h gl n f p f p of very low degree namely 2 p 2 and we prove that it is nonzero if p n

comments on pole assignability over rings abstract we observe that the proof by eising of the pole assignment theorem for linear systems over a principal ideal domain 4 actually remains valid for any elementary divisor ring for large classes of rings matrix characterizations of pole assignability are given

pole assignment for systems over rings a very simple proof of the pole assignment theorem for systems over a principal ideal domain and other rings is given furthermore an algorithm is presented extensions are also indicated

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

toda flows inverse spectral transform and realization theory abstract in this paper we establish some new relationships between the solution techniques for completely integrable nonlinear differential equations of the toda type and topics in realization theory

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159