nombres de weil sommes de gauss et annulateurs galoisiens for an abelian number field k containing a primitive p rm th root of unity p an odd prime and satisfying certain technical conditions we parametrize the bbb z p rm g k bbb q annihilators of the minus part a k of the p class group by means of modules of jacobi sums using a reflection theorem and bloch kato s reciprocity law we then determine the fitting ideal of the plus part a k in terms of twisted gauss sums

stability of moving fronts in the ginzburg landau equation we use renormalization group ideas to study stability of moving fronts in the ginzburg landau equation in one spatial dimension in particular we prove stability of the real fronts under complex perturbations this extends the results of aronson and weinberger to situations where the maximum principle is inapplicable and constitutes a step in proving the general marginal stability hypothesis for the ginzburg landau equation

necessary optimality conditions for differential difference inclusions with state constraints abstract we consider the mayer optimal control problem with dynamics given by a nonconvex differential difference inclusion whose trajectories are constrained to a closed set necessary optimality conditions in the form of the maximum principle are obtained

spatial and spatiotemporal pattern formation in generalised turing systems reaction diffusion or turing models have been proposed to account for a number of pattern formation phenomena in early development however there are a number of crucial morphogenetic phenomena that contradict the standard turing model here we review three generalisations of the turing model and show how they can be applied to two such phenomena we discuss how these generalisations can provide insight to the processes underlying patterning in these cases

spatio temporal structures in a differential flow reactor with cubic autocatalator kinetics abstract a model of a differential flow reactor with gray scott kinetics is considered in which the reactant is immobilised while the autocatalyst is allowed to flow with uniform velocity and to diffuse a linear stability analysis shows that there is a critical flow rate above which the spatially uniform stationary state is convectively unstable a weakly nonlinear analysis close to criticality results in a complex ginzburg landau equation cgle which governs the envelope amplitude of the packet of differential flow induced waves being the first derivation of such a modulation equation for such a problem the analysis of the cgle shows that this bifurcation is supercritical with proparating wave packets developing for flow rates above the critical value and identifies a region of parameter space close to the hopf bifurcation in the kinetic scheme where more complex propagating wave structures can arise the theoretical predictions are confirmed by numerical integrations of the initial value problem which also give results for flow rates well in excess of those amenable to analysis

lyapunov functions for second order differential inclusions a viability approach in this paper the existence of lyapunov functions for second order differential inclusions is analyzed by using the methodology of the viability theory a necessary assumption on the initial states and sufficient conditions for the existence of local and global lyapunov functions are obtained an application is also provided

on capitulation cokernels in iwasawa theory for a number field f and an odd prime p we study the capitulation cokernels coker a n a n associated with the p class groups of the cyclotomic inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i extension of f we prove that these cokernels stabilize and we characterize their direct limit in iwasawa theoretic terms thus generalizing previous partial results obtained by h ichimura this problem is intimately related to greenberg s conjecture

on controllability and observability of implicit systems we apply differential inclusion techniques to investigate controllability and observability of descriptor systems in particular we derive an analogue of rank condition for singular systems and prove duality of controllability and observability by trajectories without jumps

on differential inclusions with prescribed attainable sets abstract in this article the inverse problem of the differential inclusion theory is studied for a given e 0 and a continuous set valued map t w t t t 0 where w t r n is compact and convex for every t t 0 it is required to define differential inclusion so that the hausdorff distance between the attainable set of the differential inclusion at the time moment t with initial set t 0 w t 0 and w t would be less than e for every t t 0

a viability theorem for morphological inclusions the aim of this paper is to adapt the viability theorem from differential inclusions governing the evolution of vectors in a finite dimensional space to so called morphological inclusions governing the evolution of nonempty compact subsets of the euclidean space in this morphological framework the evolution of compact subsets of mathbb r n is described by means of flows along bounded lipschitz vector fields similarly to the velocity method a k a speed method in shape analysis now for each compact subset more than just one vector field is admitted correspondingly to the set valued map of a differential inclusion in finite dimensions we specify sufficient conditions on the given data such that for every initial compact set at least one of these compact valued evolutions satisfies fixed state constraints in addition the proofs follow an approximative track similar to the standard approach for differential inclusions in mathbb r n but they use tools about weak compactness and weak convergence of banach valued functions finally an application to shape optimization under state constraints is sketched

on neron raynaud class groups of tori and the capitulation problem we discuss the capitulation problem for neron raynaud class groups of tori over global fields f and obtain generalizations of the main results of 10 we also show that short exact sequences of f tori induce long exact sequences involving the corresponding neronraynaud class groups for example we show that the neron raynaud class group of any f torus which is split by a metacyclic extension of f can be resolved in terms of classical ideal class groups of global fields

vanishing discount limit and nonexpansive optimal control and differential games a classical problem in ergodic control consists of studying the limit behavior of the optimal value v lambda of a discounted cost functional with infinite horizon as the discount factor lambda tends to zero in the literature this problem has been addressed under various conditions ensuring that the rescaled value function lambda v lambda converges uniformly to a constant limit the main goal of this paper is to study this problem without such conditions so that the aforementioned limit need not be constant so under a nonexpansivity assumption we derive lipschitz bounds which yield compactness of lambda v lambda for both control systems and differential games then we study the convergence of solutions to hamilton jacobi equations under the hypothesis that the hamiltonian is radially nondecreasing hence allowing for the existence noncoercivity directions using pde methods we show that the convergence is monotone and we characterize the limit as the maximal subsolution of a cert

general theory of nonlinear flow distributed oscillations we outline a general theory for the analysis of flow distributed standing and traveling wave patterns in one dimensional open flows of oscillatory chemical media emphasizing features that are generic to a variety of kinetic models we draw particular attention to the cases far from a hopf bifurcation and far from the so called kinematic or zero diffusion limit we introduce a nonlinear formalism for both traveling and stationary waves and show that the wave forms and their amplitudes depend on a single reduced transport parameter that quantifies the departure from the kinematic limit the nonlinear formalism can be applied to systems with more complex types of bifurcations canards period doublings etc

strong invariance and one sided lipschitz multifunctions abstract this paper studies the strong invariance property of a differential inclusion in finite dimensions under the assumption of a locally one sided lipschitz condition

laplacian spectra as a diagnostic tool for network structure and dynamics we examine numerically the three way relationships among structure laplacian spectra and frequency synchronization dynamics on complex networks we study the effects of clustering degree distribution and a particular type of coupling asymmetry input normalization all of which are known to have effects on the synchronizability of oscillator networks we find that these topological factors produce marked signatures in the laplacian eigenvalue distribution and in the localization properties of individual eigenvectors using a set of coordinates based on the laplacian eigenvectors as a diagnostic tool for synchronization dynamics we find that the process of frequency synchronization can be visualized as a series of quasi independent transitions involving different normal modes particular features of the partially synchronized state can be understood in terms of the behavior of particular modes or groups of modes for example there are important partially synchronized states in which a set of low lying modes remain unlocked while those in the main spectral peak are locked we find therefore that spectra are correlated with dynamics in ways that go beyond results relating a single threshold to a single extremal eigenvalue

on the continuity property of lp balls and an application abstract in this paper continuity properties of the set valued map p b p 0 p 1 are considered where b p 0 is the closed ball of the space l p t 0 r m centered at the origin with radius 0 it is proved that the set valued map p b p 0 p 1 is continuous applying obtained results the attainable set of the nonlinear control system with integral constraint on the control is studied the admissible control functions are chosen from b p 0 it is shown that the attainable set of the system is continuous with respect to p

limit cycles in the presence of convection a traveling wave analysis we consider a diffusion model with limit cycle reaction functions in an unbounded domain diffusion spreads the pattern outwards from the source convection adds instability to the reaction diffusion system the result of this instability is a readiness to create a pattern we choose the lambda omega reaction functions for their simple limit cycle we carry out a transformation of the dependent variables into polar form from this we consider the initiation of the pattern to approximate a traveling wave we carry out numerical experiments to test our analysis these confirm the premise of the analysis that the initiation can be modeled by a traveling wave furthermore the analysis produces a good estimate of the numerical results most significantly we confirm that the pattern consists of two different types

robustness and stability of flow and diffusion structures reaction diffusion advection systems have revealed an interesting variety of pattern formation mechanism during the last years inside this field flow and diffusion structures fdss appear as a generalization of the mechanism of spatial symmetry breaking for different diffusion coefficients and flow rates of activator and inhibitor the recent experimental validation of fdss situates these structures in the focus of the actual research we will report here an experimental and numerical analysis of the theoretically predicted robustness of these flow and diffusion structures by using different boundary profiles of illumination used to obtain fdss the results here shown reveal important characteristics related with the coexistence and interaction between these structures

on the value function for nonautonomous optimal control problems with infinite horizon in this paper we consider nonautonomous optimal control problems of infinite horizon type whose control actions are given by l1 functions we verify that the value function is locally lipschitz the equivalence between dynamic programming inequalities and hamilton jacobi bellman hjb inequalities for proximal sub super gradients is proven using this result we show that the value function is a dini solution of the hjb equation we obtain a verification result for the class of dini sub solutions of the hjb equation and also prove a minimax property of the value function with respect to the sets of dini semi solutions of the hjb equation we introduce the concept of viscosity solutions of the hjb equation in infinite horizon and prove the equivalence between this and the concept of dini solutions in the appendix we provide an existence theorem

a connection between the maximum principle and dynamic programming for constrained control problems we consider the mayer optimal control problem with dynamics given by a nonconvex differential inclusion whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function this additional relation is applied in turn to show that the maximum principle is nondegenerate we also provide a sufficient condition for the normality of the maximum break principle to derive these results we use convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories then duality theory of convex analysis is applied to derive necessary conditions for optimality in this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case

on universal norms and the first layers of mathbb z _p extensions of a number field for an odd prime p and a number field f containing a primitive p th root of unity we describe the kummer radical mathcal a f of the first layers of all the mathbb z p extensions of f in terms of universal norms of p units along the cyclotomic tower of f we also study twisted radicals related to mathcal a f

a maximum principle for generalized control systems on definit un systeme de commande generalise comme une collection de fonctions f t x definies pour t x 0 1 r n dans r n et satisfaisant les hypotheses de caratheodory dans t x on etablit un theoreme donnant une condition necessaire pour la trajectoire d un tel systeme d appartenance a la frontiere de l ensemble atteignable on applique ce theoreme a des cas particuliers

measurable viability theorems and the hamilton jacobi bellman equation abstract we prove viability and invariance theorems for systems with dynamics depending on time in a measurable way and having time dependent state constraints x t f t x t x t p t in the above t p t is an absolutely continuous set valued map and t x f t x is a set valued map which is measurable with respect to t and upper semicontinuous or continuous or locally lipschitz with respect to x for this aim we investigate infinitesimal generators of reachable maps and the lebesgue points of set valued maps the results are applied to define and to study lower semicontinuous solutions of the hamilton jacobi bellman equation u t h t x u x 0 with the hamiltonian h measurable with respect to time locally lipschitz with respect to x and convex in the last variable

contingent cones to reachable sets of control systems high order necessary conditions for optimality for an optimal control problem are studied via properties of contingent cones to reachable sets along the optimal trajectory it is shown that the adjoint vector of pontryagin s maximum principle is normal to the set of variations of reachable sets results are applied to study optimal control problems for dynamical systems described by 1 closed loop control systems 2 nonlinear implicit systems 3 differential inclusions 4 control systems with jumps

principal bifurcations and symmetries in the emergence of reaction diffusion advection patterns on finite domains pattern formation mechanisms of a reaction diffusion advection system with one diffusivity differential advection and robin boundary conditions of danckwerts type are being studied pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions which for the general case of far from instability onsets is conducted using spatial dynamics and numerical continuations the selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model accordingly we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves including solitary against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory hopf instability consequently the resulting pattern selection is qualitatively different from the symmetric finite wavenumber turing or hopf instabilities

characterization of the value function of final state constrained control problems with bv trajectories this paper aims to investigate a control problem governed by differential equations with radon measure as data and with final state constraints by using a known reparametrization method by dal maso and rampazzo 18 we obtain that the value function can be characterized by means of an auxiliary control problem of absolutely continuous trajectories involving time measurable hamiltonian we study the characterization of the value function of this auxiliary problem and discuss its numerical approximations

parameter space analysis pattern sensitivity and model comparison for turning and stationary flow distributed waves fds a new type of instability in coupled reaction diffusion advection systems is analysed in a one dimensional domain this instability arising due to the combined action of flow and diffusion creates spatially periodic stationary waves termed flow and diffusion distributed structures fds here we show via linear stability analysis that fds are predicted in a considerably wider domain and are more robust in the parameter domain than the classical turing instability patterns fds also represent a natural extension of the recently discovered flow distributed oscillations fdo nonlinear bifurcation analysis and numerical simulations in one dimensional spatial domains show that fds also have much richer solution behaviour than turing structures in the framework presented here turing structures can be viewed as a particular instance of fds we conclude that fds should be more easily obtainable in chemical systems than turing and fdo structures and that they may play a potentially important role in biological pattern formation

convex extensions of the convex set valued maps in this article the existence of the convex extension of convex set valued map is considered conditions are obtained based on the notion of the derivative of set valued maps which guarantee the existence of convex extension the conditions are given when the convex set valued map has no convex extension the convex set valued map is specified which is the maximal convex extension of the given convex set valued map and includes all other convex extensions the connection between lipschitz continuity and existence of convex extension of the given convex set valued map is studied

on special elements in higher algebraic k theory and the lichtenbaum gross conjecture abstract we conjecture the existence of special elements in odd degree higher algebraic k groups of number fields that are related in a precise way to the values at strictly negative integers of the derivatives of artin l functions of finite dimensional irreducible complex representations we prove this conjecture for an important family of examples and also provide other evidence both theoretical and numerical in its support

pattern formation by boundary forcing in convectively unstable oscillatory media with and without differential transport convectively unstable open reactive flows of oscillatory media whose phase is fixed or periodically modulated at the inflow boundary are known to result in stationary and traveling waves respectively the latter are implicated in biological segmentation the boundary controlled pattern selection by this flow distributed oscillator fdo mechanism has been generalized to include differential flow difi and differential diffusion turing modes our present goal is to clarify the relationships among these mechanisms in the general case where there is differential flow as well as differential diffusion to do so we analyze the dispersion relation for linear perturbations in the presence of periodic boundary forcing and show how the solutions are affected by differential transport we find that the difi and fdo modes are closely related and lie in the same frequency range while the turing mechanism gives rise to a distinct set of unstable modes in a separate frequency range finally we substantiate the linear analysis by nonlinear simulations and touch upon the issue of competition of spatial modes

shape evolutions under state constraints a viability theorem abstract the aim of this paper is to adapt the viability theorem from differential inclusions governing the evolution of vectors in a finite dimensional space to so called morphological inclusions governing the evolution of nonempty compact subsets of the euclidean space in this morphological framework the evolution of compact subsets of r n is described by means of flows along differential inclusions with bounded and lipschitz continuous right hand side this approach is a generalization of using flows along bounded lipschitz vector fields introduced in the so called velocity method alias speed method in shape analysis now for each compact subset more than just one differential inclusion is admitted for prescribing the future evolution up to first order correspondingly to the step from ordinary differential equations to differential inclusions for vectors in the euclidean space we specify sufficient conditions on the given data such that for every initial compact set at least one of these compact valued evolutions satisfies fixed state constraints in addition the proofs follow an approximative track similar to the standard approach for differential inclusions in r n but they use tools about weak compactness and weak convergence of banach valued functions finally the viability condition is applied to constraints of nonempty intersection and inclusion respectively in regard to a fixed closed set m r n

the exponential formula for the reachable set of a lipschitz differential inclusion the main goal of this paper is to prove a formula for the reachable set of a lipschitz differential inclusion with convex values the formula involves a kuratowski limit of sets that resembles a standard approach of defining the exponential of a matrix this explains the title the proof of the main theorem partially relies on a c 1 approximation result due to filippov for which a new proof is given a new approach of characterizing the value function associated with a mayer optimal control problem is given as an application

an idelic approach to the wild kernel let p be a prime and f an algebraic number field containing a primitive 2p th root of 1 the main object of this paper is to describe the p torsion in the wild kernel of the cyclotomic zp extension f of f in terms of a tare twisted idrle class group in analogy with the description of the p torsion in the tame kernel via twisted ideal class groups due to coates 3 it turns out that this description depends upon the validity of a conjecture of gross and in fact we obtain an equivalent formulation of this conjecture in terms of iwasawa theory which also yields a new interpretation of the tate kernel i e the kernel of the surjective map

comment on flow distributed oscillations stationary chemical waves in a reacting flow in a recent paper by kaern and menzinger phys rev e 60 r3471 1999 a successful verification of the stationary space periodic structures predicted by andresen et al phys rev e 60 297 1999 was reported kaern and menzinger suggest a mechanism for the formation of such structures that yields a linear relationship between the selected wavelength and the flow rate we find this mechanism too simple and produce numerical simulations that support the original interpretation of these structures

on reflecting boundary problem for optimal control this paper deals with mayer s problem for controlled systems with reflection on the boundary of a closed subset k the main result is the characterization of the possibly discontinuous value function in terms of a unique solution in a suitable sense to a partial differential equation of hamilton jacobi bellman type

a priori estimates for operational differential inclusions we prove a set valued gronwall lemma and a relaxation theorem for the semilinear differential inclusion x ax f t x x 0 x0 where a is the infinitesimal generator of a c0 semigroup on a separable banach space x and f 0 t x x is a set valued map this allows us to investigate infinitesimal generators of reachable sets and variational inclusions the results are applied to a semilinear optimal control problem with end point constraints

on cohomology groups of units for z p extensions let k k be a galois extension of number fields s a set of finite places on the ground field k and es the group of s units in k the cohomology groups hn k k es i e hn gal k k es have been studied for various k k and s and found to be an important device to study the arithmetic properties of the extension k k in the present paper we shall make some simple remarks on h k k es in the special case where k is a so called zp extension over a finite algebraic number field k

coates wiles towers in dimension two let k be an imaginary quadratic field and e an elliptic curve defined over k with complex multiplication by the ring of integers of k in 1977 coates and wiles proved that if e k has positive rank then the hasse weil zeta function l e k s of e has a zero at s 1 2 such curves exist precisely when the class number of k is one subsequent work 1 extended the result to a wider class of cm curves another proof emerged from rubin s important work on the tate shafarevich group 13 14 see also 10 12 coates and wiles used formal groups and iwasawa theoretic techniques to relate the special value of l e f s to elliptic units employing more classical techniques stark and gupta combined to give a different proof of the theorem 21 4 although the two proofs have different flavors they include the same ingredients let p be one of infinitely many suitably chosen primes of k and k the field obtained by adjoining the p torsion of e to k there is a unique prime p of k lying over p let q be a point of infinite order in e k q c pe k and 5 l q k q let v 2 be the gr6ssencharakter of e and f2 a fundamental

invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave abstract periodic wave trains are the generic solution from for oscillatory reaction diffusion equations in one space dimension it has been shown previously that invasive wavefronts generate behind them a wave train with a different speed from that of the invasion sherratt physica d 70 1994 370 382 in this paper the mechanism of wave train generation is studied in detail for systems of two reaction diffusion equations close to a supercritical hopf bifurcation in the kinetics with equal diffusion coefficients a combination of analytical and numerical evidence is presented suggesting that the invasive front and wave train are separated by a modulated travelling wave of phase gradient in which phase singularities occur periodically this calculation leads to a prediction of the amplitude and speed of the wave train generated by invasion

conjugate points and shocks in nonlinear optimal control in this paper the authors use the method of characteristics to extend the jacobi conjugate points theory to the bolza problem arising in nonlinear optimal control this yields necessary and sufficient optimality conditions for weak and strong local minima stated in terms of the existence of a solution to a corresponding matrix riccati differential equation the same approach allows to investigate as well smoothness of the value function

an initial condition reconstruction in hamilton jacobi equations abstract we describe the family of initial conditions for hamilton jacobi equations hje corresponding to optimal control problems that can be retrieved by solving hje backward in time

analysis of nonlinear synchronization dynamics of oscillator networks by laplacian spectral methods we analyze the synchronization dynamics of phase oscillators far from the synchronization manifold including the onset of synchronization on scale free networks with low and high clustering coefficients we use normal coordinates and corresponding time averaged velocities derived from the laplacian matrix which reflects the network s topology in terms of these coordinates synchronization manifests itself as a contraction of the dynamics onto progressively lower dimensional submanifolds of phase space spanned by laplacian eigenvectors with lower eigenvalues differences between high and low clustering networks can be correlated with features of the laplacian spectrum for example the inhibition of full synchoronization at high clustering is associated with a group of low lying modes that fail to lock even at strong coupling while the advanced partial synchronization at low coupling noted elsewhere is associated with high eigenvalue modes

semigroups of relations and subdifferentials of the minimal time function and of the geodesic distance given a closed subset s of a banach space x we study the minimal time function to reach a point x of x starting from s we relate this problem to the study of the geodesic distance from x to s associated with a riemannian metric or a finsler metric it appears that both cases can be treated simultaneously and yield solutions to a hamilton jacobi equation we detect simple links between the general framework we propose and multivalued semigroups new concepts of infinitesimal generators of such semigroups are considered

harmonic resonant excitation of flow distributed oscillation waves and turing patterns driven at a growing boundary we perform numerical studies of a reaction diffusion system that is both turing and hopf unstable and that grows by addition at a moving boundary which is equivalent by a galilean transformation to a reaction diffusion advection system with a fixed boundary and a uniform flow we model the conditions of a recent set of experiments which used a temporally varying illumination in the boundary region to control the formation of patterns in the bulk of the photosensitive medium the frequency of the illumination variations can select patterns from among the competing instabilities of the medium in the usual case the waves that are excited have frequencies as measured at a constant distance from the upstream boundary matching the driving frequency in contrast to the usual case we find that both turing patterns and flow distributed oscillation waves can be excited by forcing at subharmonic multiples of the wave frequencies the final waves with frequencies at integer multiples of the driving frequency are formed by a process in which transient wave fronts break up and reconnect we find ratios of response to driving frequency as high as 10

properties of the reachable set of control systems abstract we investigate some properties of the reachable set of a control system representing the system as a differential inclusion and using proximal hamilton jacobi equation we describe its graph we work in infinitely dimensional hilbert space and use one sided lipschitz approach the funnel equation is considered in the last section that equation describes the reachable set in arbitrary banach space we consider also the autonomous case and prove the existence of a limit of the reachable set

scenarios of domain pattern formation in a reaction diffusion system we performed an extensive numerical study of a two dimensional reaction diffusion system of the activator inhibitor type in which domain patterns can form we showed that both multidomain and labyrinthine patterns may form spontaneously as a result of the turing instability in the stable homogeneous system with the fast inhibitor one can excite both localized and extended patterns by applying a localized stimulus depending on the parameters and the excitation level of the system stripes spots wriggled stripes or labyrinthine patterns form the labyrinthine patterns may be both connected and disconnected in the stable homogeneous system with the slow inhibitor one can excite self replicating spots breathing patterns autowaves and turbulence the parameter regions in which different types of patterns are realized are explained on the basis of the asymptotic theory of instabilities for patterns with sharp interfaces developed by us in phys rev e 53 3101 1996 the dynamics of the patterns observed in our simulations is very similar to that of the patterns forming in the ferrocyanide iodate sulfite reaction textcopyright 1996 the american physical society

some remarks on fuzzy differential equations via differential inclusions abstract in this paper we discuss the formulation and procedure for solving fuzzy differential equations via differential inclusions we give several examples showing the correct and incorrect procedure for solving fuzzy differential equations we show the connection between fuzzy differential equations and fuzzy differential inclusions finally we give some remarks on numerical algorithms for solving fuzzy differential equations via differential inclusions

controllability of convex processes the purpose of this paper is to provide several characterizations of controllability of differential inclusions whose right hand sides are convex processes convex processes are the set valued maps whose graphs are convex cones they are the set valued analogues of linear operators such differential inclusions include linear systems where the controls range over a convex cone and not only a vector space the characteristic properties are couched in terms of invariant cones by convex processes or eigenvalues of convex processes or a rank condition we also show that controllability is equivalent to observability of the adjoint inclusion

on derivatives of artin l series we present a universal theory of refined stark conjectures we give evidence in support of these explicit and very general conjectures including a full proof in several important cases and explain the connection to previous conjectures of bloch and kato of lichtenbaum and of serre and tate we also deduce a wide range of unconditional consequences of these results concerning the annihilation as galois modules of ideal class groups by explicit elements constructed from the values of higher order derivatives of non abelian artin l series

selection of flow distributed oscillation and turing patterns by boundary forcing in a linearly growing oscillating medium we studied the response of a linearly growing domain of the oscillatory chemical chlorine dioxide iodide malonic acid cdima medium to periodic forcing at its growth boundary the medium is hopf as well as turing unstable and the system is convectively unstable the results confirm numerical predictions that two distinct modes of pattern can be excited by controlling the driving frequency at the boundary a flow distributed oscillation fdo mode of traveling waves at low values of the forcing frequency f and a mode of stationary turing patterns at high values of f the wavelengths and phase velocities of the experimental patterns were compared quantitatively with results from dynamical simulations and with predictions from linear dispersion relations the results for the fdo waves agreed well with these predictions and obeyed the kinematic relations expected for phase waves with frequencies selected by the boundary driving frequency turing patterns were also generated within the predicted range of forcing frequencies but these developed into two dimensional structures which are not fully accounted for by the one dimensional numerical and analytical models the turing patterns excited by boundary forcing persist when the forcing is removed demonstrating the bistability of the unforced constant size medium dynamical simulations at perturbation frequencies other than those of the experiments showed that in certain ranges of forcing frequency fdo waves become unstable breaking up into harmonic waves of different frequency and wavelength and phase velocity

reflected differential games this paper concerns the existence of a possible discontinuous value for a zero sum two player reflected differential game under isaacs condition we characterize the value function as the unique solution in a suitable sense to a variational inequality namely the hamilton jacobi isaacs differential inclusion

the maximum principle for an optimal solution to a differential inclusion with end points constraints we derive pontryagin s maximum principle for a general optimal control problem using the set valued version of variational equation we achieve this aim by exploiting an adequate differential calculus of set valued maps furthermore the calmness condition is replaced by a surjectivity condition involving reachable sets of the set valued linearization of the initial control problem duality then provides both the adjoint differential inclusion and the maximum principle

reply to comment on flow distributed oscillations stationary chemical waves in a reacting flow stationary waves wavelength lambda are the necessary result of spatial recurrence of phase in the open flow rate v of an oscillating medium with fixed inflow boundary conditions any nonlinear dependence lambda v on flow is the result of dispersion that is implicit in lambda v omega v where omega v is the oscillation frequency in a reference frame moving with the flow the flow distributed oscillator mechanism extends thus from the purely kinematic limit omega const to the case where a nonlinear dependence lambda v is subsumed by the dispersion relationship omega v

noise driven synchronization of a fitzhugh nagumo ring with phase repulsive coupling a perspective from the system s nonequilibrium potential abstract we study a one dimensional array of n autonomous units with excitable fitzhugh nagumo dynamics coupled in phase repulsive way to form a ring and submitted to a common subthreshold harmonic signal and independent gaussian white noises with a common intensity by varying two macroscopic regimes are observed for some value of noise intensity a transition from the rest state to an activated one with almost half of the neurons excited forming an activated inhibited activated structure along the ring takes place for larger values of the inverse transition is also observed and both states alternate in a synchronized way with the signal moreover measures of activation and coherent behavior become maximal for intermediate values of the origin of these collective effects is explained in terms of the system s nonequilibrium potential in particular the levels of noise for activation and synchronization are theoretically estimated

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required

necessary optimality conditions for nonconvex differential inclusions with endpoint constraints in this paper we derive necessary optimality conditions for optimization problems defined by non convex differential inclusions with endpoint constraints we do this in terms of parametrizations of the convexified form of the differential inclusion and under additional assumptions in terms of the inclusion itself