global attractors for the extensible thermoelastic beam system abstract this work is focused on the dissipative system t t u x x x x u x x x u l 2 0 1 2 x x u f t x x x x t u g describing the dynamics of an extensible thermoelastic beam where the dissipation is entirely contributed by the second equation ruling the evolution of under natural boundary conditions we prove the existence of bounded absorbing sets when the external sources f and g are time independent the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters r the same result holds true when the first equation is replaced by t t u x x t t u x x x x u x x x u l 2 0 1 2 x x u f with 0 in both cases the solutions on the attractor are strong solutions

topological horseshoes in travelling waves of discretized nonlinear wave equations applying the concept of anti integrable limit to coupled map lattices originated from space time discretized nonlinear wave equations we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions in particular the coupled map lattices display spatio temporal chaos on the horseshoes

remarks on the kuramoto sivashinsky equation we report here a joint work in progress on the kuramoto sivashinsky equation the question we address is the analytical study of a fourth order nonlinear evolution equation this equation has been obtained by sivashinsky in the context of combustion and independently by kuramoto in the context of reaction diffusion systems both were motivated by nonlinear stability of travelling waves numerical calculations have been done on this equation all the results seem to indicate a chaotic behavior of the solution therefore the analytical study is of interest in analogy with the burger s and navier stokes equations here we give some existence and uniqueness results for the equation in space dimension one and we also study a fractional step method of numerical resolution in a forthcoming joint paper with r temam we will study the asymptotic behavior as t approaches infinity of the solution of 0 1 and give an estimate on the number of determining modes

robust guaranteed cost control for uncertain linear differential systems of neutral type in this paper the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated the uncertainty is assumed to be norm bounded and time varying nonlinear the problem is to design a state feedback control laws such that the closed loop system is robustly stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay a criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the lyapunov method a parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities a numerical example is given to illustrate the proposed method

linearized stability of partial differential equations with application to stabilization of the kuramoto sivashinsky equation linearization is a useful tool for analyzing the stability of nonlinear differential equations unfortunately the proof of the validity of this approach for ordinary differential equations does not generalize to all nonlinear partial differential equations general results giving conditions for when stability or instability of the linearized equation implies the same for the nonlinear equation are given here these results are applied to stability and stabilization of the kuramoto sivashinsky equation a nonlinear partial differential equation that models reaction diffusion systems the stability of the equilibrium solutions depends on the value of a positive parameter nu it is shown that if nu 1 then the set of constant equilibrium solutions is globally asymptotically stable if nu 1 then the equilibria are unstable it is also shown that stabilizing the linearized equation implies local exponential stability of the equation stabilization of the kuramoto sivashinsky equation using a sin

some global dynamical properties of the kuramoto sivashinsky equations nonlinear stability and attractors abstract the kuramoto sivashinsky equations model pattern formations on unstable flame fronts and thin hydrodynamic films they are characterized by the coexistence of coherent spatial structures with temporal chaos we investigate some global dynamical properties including nonlinear stability we demonstrate their low modal behavior in terms of determining modes and that the fractal dimension of all attractors is bounded by a universal constant times l 13 8 where l is a dimensionless pattern cell size in the one dimensional case such equations are indeed a paradigm of low dimensional behavior for infinite dimensional systems

decentralized dynamic output feedback controller design for guaranteed cost stabilization of large scale discrete delay systems in this paper we discuss how to solve dynamic output feedback controller design problem for decentralized guaranteed cost stabilization of large scale discrete delay system by convex optimization based on lyapunov second method an linear matrix inequality optimization problem is formulated to design the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function a numerical example is given to illustrate the proposed method

some backward uniqueness results soit 7b u un operateur non borne lineaire ou non lineaire sur un espace de hilbert h tel que 7b u 0 0 soit une fonction solution de l equation d evolution d dt 7b u 0 et telle que t 0 pour un t 0 on etudie la propriete d unicite retrograde sur 0 t pour des inegalites d t dt a t t h n t t d a 1 2 t ou a t t 0 est une famille d operateurs lineaires non bornes autoadjoint sur h et u l 2 0 t

exponential decay of solutions of damped nonlinear hyperbolic equations on considere le comportement asymptotique des solutions de certaines equations hyperboliques non lineaires a amortissement lineaire

nonlinear galerkin methods the finite elements case with the increase in the computing power and the advent of supercomputers the approximation of evolution equations on large intervals of time is emerging as a new type of numerical problem in this article we consider the approximation of evolution equations on large intervals of time when the space discretization is accomplished by finite elements the algorithm that we propose called the nonlinear galerkin method stems from the theory of dynamical systems and amounts to some approximation of the attractor in the discrete finite elements space essential here is the utilization of incremental unknown which is accomplished in finite elements by using hierarchical bases beside a detailed description of the algorithm the article includes some technical results on finite elements spaces and a full study of the stability and convergence of the method

numerical solution of a nonlinear dissipative system using a pseudospectral method and inertial manifolds we consider the numerical solution of nonlinear dissipative partial differential equations using a pseudospectral method and the methodology of approximate inertial manifolds coarse and fine grids are employed with a nonlinear mapping to relate the solutions computed on these grids the approach is illustrated by consideration of the kuramoto sivashinsky equation subject to periodic solutions that are restricted to the invariant subspace of odd functions numerical results are presented on the ability of the method to mimic the time evolution of the infinite dimensional dynamical system the results demonstrate that the coarse fine grid method is more accurate than the standard pseudospectral method on the same coarse grid however time integration studies suggest that the increased accuracy is bought at an increase in computational cost to achieve a specified accuracy the computational cost of the two grid method exceeds that of a standard pseudospectral method for this spatially periodic problem

testing for a pulse in seasonal event data most tests for seasonal clustering are sensitive to the peak in incidence in some season 90 day interval followed by a trough 6 months later we present two statistics sensitive to a relatively sharp increase in disease incidence for a season superimposed on a constant incidence over the entire year the ratchet scan based on the maximum number of events in k consecutive months and the continuous circular scan the maximum number of events in d consecutive days we tabulate the tail distribution of the ratchet scan for n less than or equal to 35 and k 2 and 3 and find the asymptotic distribution which is applicable for n greater than or equal to 50 when k 2 or 3 we evaluate an approximation for the distribution of the continuous scan the statistics are applied to investigate seasonal clustering of adolescent suicide in the united states an illustration is given of the application of the circular scan and a small simulation study and the example are used to compare the statistics with others proposed in the literature language en

periodic output feedback stabilization of neutral systems a new feedback control technique called periodic output feedback is investigated in the context of infinite dimensional linear systems modeled by neutral functional differential equations in this method discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control this work focuses on stabilization of neutral systems with delayed control modeled in the state space w sub 2 sup 1 r 0 r sup n spl times l sup 2 r 0 r sup p where w sub 2 sup 1 r 0 r sup n denotes the sobolev space of r sup n valued absolutely continuous functions with square integrable derivatives on r 0 we show that a class of these systems can be stabilized by periodic output feedback even though their input operators are unbounded we overcome this difficulty by representing the system state using an abstract integral variation of constants formula an algorithm is presented at the end of this paper to construct a periodic output feedback gain function an example is provided to illustrate the construction of the gain function

fragment length distributions and collision probabilities for aflp markers aflp is a dna fingerprinting technique frequently used in plant and animal sciences a drawback of the technique is the occurrence of multiple dna fragments of the same length in a single aflp lane which we name a collision in this article we quantify the problem the well known birthday problem plays a role calculation of collision probabilities requires a fragment length distribution fld we discuss three ways to estimate the fld based on theoretical considerations on in silico determination using dna sequence data from arabidopsis thaliana or on direct estimation from aflp data in the latter case we use a generalized linear model with monotone smoothing of the fragment length probabilities collision probabilities are calculated from two perspectives assuming known fragment counts and assuming known band counts we compare results for a number of fld s ranging from uniform to highly skewed the conclusion is that collisions occur often with higher probabilities for higher numbers of bands for more skewed distributions and to a lesser extent for smaller scoring ranges for a typical plant genome an aflp with 19 bands is likely to contain the first collision practical implications of collisions are discussed aflp examples from lettuce and chicory are used for illustration

saddlepoint approximation for multivariate cumulative distribution functions and probability computations in sampling theory and outlier testing abstract four multivariate distributions commonly arise in sampling theory the multinomial multivariate hypergeometric dirichlet and multivariate polya distributions second order saddlepoint approximations are given for approximating these multivariate cumulative distribution functions cdf s in their most general settings probabilities of rectangular regions associated with these cdf s are also approximated directly using second order saddlepoint methods all the approximations follow from characterizations of the multivariate distributions as conditional distributions applications to outlier discordancy tests and slippage tests are discussed

on robust h filter design for uncertain neural systems lmi optimization approach this article deals with the robust h filtering problem for neutral delay differential systems with parametric uncertainties a linear matrix inequality lmi approach is proposed to design the robust h filter such that the filtering system remains asymptotically stable and the bound of h norm is minimized the lyapunov stability theory is used for analysis of the system a numerical example is provided to illustrate the validity of proposed design approach

existence and generalized gevrey regularity of solutions to the kuramoto sivashinsky equation in rn abstract motivated by the work of foias and temam c foias r temam gevrey class regularity for the solutions of the navier stokes equations j funct anal 87 1989 359 369 we prove the existence and gevrey regularity of local solutions to the kuramoto sivashinsky equation in r n with initial data in the space of distributions the control on the gevrey norm provides an explicit estimate of the analyticity radius in terms of the initial data in the particular case when n 1 our analysis allows for initial data that are less smooth than that considered by grujic and kukavica z grujic i kukavica space analyticity for the navier stokes and related equations with initial data in l p j funct anal 152 1998 447 466

periodic solutions of a class of impulsive neutral delay differential equation abstract a class of impulsive neutral delay differential equation is studied by using fixed point theorem in cone some sufficient conditions of the existence for multiple periodic solutions are obtained some known results are generalized two examples are also given to support our main results

robust memory state feedback model predictive control for discrete time uncertain state delayed systems in this paper we propose a memory state feedback model predictive control mpc law for a discrete time uncertain state delayed system with input constraints the model uncertainty is assumed to be polytopic and the delay is assumed to be unknown but with a known upper bound we derive a sufficient condition for cost monotonicity in terms of lmi which can be easily solved by an efficient convex optimization algorithm a delayed state dependent quadratic function with an estimated delay index is considered for incorporating mpc problem formulation the mpc problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions therefore a less conservative sufficient conditions in terms of linear matrix inequality lmi can be derived to design a more robust mpc algorithm a numerical example is included to illustrate the effectiveness of the proposed method

dimension of the attractors associated to the ginzburg landau partial differential equation abstract we study the long time behavior of solutions to the ginzburg landau partial differential equation it is shown that a finite dimensional attractor captures all the solutions an upper bound on this dimension is given in terms of physical quantities by estimating the lyapunov exponents on the trajectories finally using the well known side band instabilities of an exact time dependent solution stokes solution we derive lower bounds on the dimension of the universal attractor moreover the lower and upper bounds agree

simultaneous confidence intervals and sample size determination for multinomial proportions abstract simultaneous confidence interval procedures for multinomial proportions are used in many areas of science in this article two new simultaneous confidence interval procedures are introduced numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature from the results presented in this article it is evident that the new procedures are more accurate than the established ones where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves in the sample size determination problem the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications because both procedures performed equally well the procedure that requires the least amount of computing time is recommended

robust stabilization of uncertain systems with delays in control input a matrix inequality approach this paper presents a new stabilization criterion for dynamic systems with parametric uncertainties and delays in control input based on the lyapunov method the stabilization criterion is derived in terms of matrix inequalities which can be easily solved by efficient convex optimization algorithms numerical examples are included to show the effectiveness of the proposed method

on guaranteed cost control of neutral systems by retarded integral state feedback in this paper the guaranteed cost control problem for a class of neutral delay differential systems with a given quadratic cost functions is investigated the problem is to design a memory state feedback controller such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound some criteria for the existence of such controllers is derived based on the linear matrix inequality lmi approach combined with the lyapunov method a parameterized characterization of the controllers is given in terms of the feasible solutions to the certain lmis a numerical example is given to illustrate the proposed method

the algebraic approximation of attractors the finite dimensional case abstract in this article we present a constructive method for approximating attractors the approximate sets are parts of algebraic sets i e the zeros of high degree polynomial functions and they can approximate the attractor at an arbitrary high level of accuracy

disease clusters exact distributions of maxima and p values this paper presents combinatorial exact methods that are useful in the analysis of disease cluster data obtained from small environments such as buildings and neighbourhoods maxwell boltzmann and fermi dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns space and or time in these environments the methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring one of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models language en

technical communique an lmi approach to guaranteed cost control of linear uncertain time delay systems the guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time delay systems with norm bounded time varying parametric uncertainty and a given quadratic cost function sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities lmis furthermore a convex optimization problem with lmi constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed loop uncertain system

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

an approximate solution for nonlinear backward parabolic equations we consider the backward parabolic equation ut au f t u t 0 t t u t g where a is a positive unbounded operator and f is a nonlinear function satisfying a lipschitz condition with an approximate datum g the problem is severely ill posed using the truncation method we propose a regularized solution which is the solution of a system of differential equations in finite dimensional subspaces according to some a priori assumptions on the regularity of the exact solution we obtain several explicit error estimates including an error estimate of holder type for all t 0 t an example on heat equations and numerical experiments are given

inertial manifolds and finite dimensional reduction for dissipative pdes this paper is devoted to the problem of finite dimensional reduction for parabolic partial differential equations we give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so called mane projection theorems the recent counter examples showing that the underlying dynamics may in a sense be infinite dimensional if the spectral gap condition is violated as well as a discussion of the most important open problems are also included

robust stabilization of a class of nonlinear time delay systems the problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered it is assumed that perturbations of the time delayed sections are not bounded by first order linear functions but bounded by high order functions with unknown gains and the time delay considered is time varying two classes of controllers are proposed when the time derivative of each time varying time delay is less than 1 a class of adaptive state feedback controllers are proposed based on lyapunov krasovskii method which can render the closed loop systems uniformly ultimately bounded stable novel nonlinear feedback controllers are developed by employing razumikhin lemma and the controller also can render the closed loop systems stable in the sense of uniform ultimate boundedness finally several examples are given to show the potential of the proposed techniques

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

a representation for multinomial cumulative distribution functions a re expression of the usual representation of the multinomial distribution as the conditional distribution of independent poisson random variables given fixed sum provides a convenient new way to compute multinomial cumulative distribution functions

on design of dynamic output feedback controller for gcs of large scale systems with delays in interconnections lmi optimization approach this paper considers the dynamic output feedback controller design problem for decentralized guaranteed cost stabilization gcs of large scale systems with time delays in subsystem interconnections based on the lyapunov method a linear matrix inequality lmi convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function

on the lack of null controllability of the heat equation on the half line we consider the linear heat equation on the half line with a dirichlet boundary control we analyze the null controllability problem more precisely we study the class of initial data that may be driven to zero in finite time by means of an appropriate choice of the l2 boundary control we rewrite the system on the similarity variables that are a common tool when analyzing asymptotic problems next the control problem is reduced to a moment problem which turns out to be critical since it concerns the family of real exponentials eit j in which the usual summability condition on the inverses of the eigenvalues does not hold roughly speaking we prove that controllable data have fourier coefficients that grow exponentially for large frequencies this result is in contrast with the existing ones for bounded domains that guarantee that every initial datum belonging to a sobolev space of negative order may be driven to zero in an arbitrarily small time

feedback stabilization of neutral systems via the transformation technique within the class of delay systems a neutral system may be distinguished by the possible presence of a neutral root chain an infinite chain of eigenvalues in a vertical strip of the complex plane assuming that such a neutral root chain if it exists is stable this work shows how our method of transformation can be extended to obtain feedback controllers for this class of neutral systems

equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains we consider the dirichlet problem for a class of semilinear parabolic equations on a bounded domain which is reflectionally symmetric about a hyperplane h the equations consist of a symmetric time autonomous part and a nonsymmetric perturbation which decays to zero as time approaches infinity in our first theorem we prove the asymptotic symmetry of each bounded positive solution of this asymptotically symmetric problem the novelty of this result is that the solutions considered are not assumed uniformly positive which prevents one from applying common techniques based on the method of moving hyperplanes in our second main theorem we classify the positive entire solutions of the unperturbed time autonomous problems in particular we characterize all entire solutions which are not symmetrically decreasing in the direction orthogonal to h as connecting orbits from an equilibrium with a nontrivial nodal set to another invariant set

guaranteed cost control for bilinear systems by static output feedback this paper proposes a static output feedback controller design technique for bilinear systems based on lyapunov s direct method a nonlinear control law is derived to stabilize the system in the presence of external disturbances sufficient condition is derived in terms of a state dependent nonlinear matrix inequality and then it is converted into a sum of squares sos optimization problem semidefinite programming and sos decomposition techniques are employed to solve the optimization problem the obtained output feedback controller guarantees an upper bound of the performance index the effectiveness of the proposed method is demonstrated through simulation results

stabilization analysis for discrete time systems with time delay the stabilization problem for a class of discrete time systems with time varying delay is investigated by constructing an augmented lyapunov function some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality lmi technique when norm bounded parameter uncertainties appear in the delayed discrete time system a delay dependent robust exponential stabilization criterion is also presented all of the criteria obtained in this paper are strict linear matrix inequality conditions which make the controller gain matrix can be solved directly three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results

long time behaviour of solutions of abstract inequalities applications to thermo hydraulic and magnetohydrodynamic equations abstract we study some scalar inequalities of parabolic type and we give the leading term of an asymptotic expansion as t for solutions of thermo hydraulic equations without external excitation a phenomenon of resonance is pointed out we also treat m h d equations and navier stokes equations on a riemannian manifold

asymptotic analysis of the navier stokes equations abstract new bounds are established on the number of modes which determine the solutions of the navier stokes equations in two dimensions the best bound available at present is nearly proportional to the generalized grashof number defined in the paper and less than logarithmically dependent on the spatial structure or the shape of the force driving the flow to the extent than for the case of 2 dimensional rayleigh benard convection the generalized grashof number may be identified with the usual grashof number the resulting bound on the number of modes is found to differ only slightly from a bound obtained earlier on heuristic grounds

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

intrinsic stochasticity with many degrees of freedom we study a simple model equation describing a system with an infinity of degrees of freedom which displays an intrinsically chaotic behavior some concepts of fully developed turbulence are discussed in relation to this model we also develop an approach based on lyapunov exponent measurements numerical results on the distribution of lyapunov numbers and the power spectrum of the associated lyapunov vectors are presented and briefly discussed

dynamics for the stochastic nonlocal kuramoto sivashinsky equation dynamics for the stochastic kuramoto sivashinsky equation with a nonlocal term is studied we prove that the stochastic equation has a finite dimensional random attractor