the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

the h infty calculus and sums of closed operators we develop a very general operator valued functional calculus for operators with an h infty calculus we then apply this to the joint functional calculus of two sectorial operators when one has an h infty calculus using this we prove theorem of dore venni type on sums of sectorial operators and apply our results to the problem of l p maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of banach spaces are essential here in the final section we exploit the special banach space structure of l 1 spaces and c k spaces to obtain some more detailed results in this setting

the h calculus and sums of closed operators we develop a very general operator valued functional calcu lus for operators with an h 1 calculus we then apply this to the joint functional calculus of two commuting sectorial operators when one has an h 1 calculus using this we prove theorem of dore venni type on sums of commuting sectorial operators and apply our results to the problem of lp maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of ba nach spaces are essential here in the final section we exploit the special banach space structure of l1 spaces and c k spaces to obtain some more detailed results in this setting

generalized multiple riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations in this paper based on symbolic computation and the idea of rational expansion method a generalized multiple riccati equations rational expansion method gmrere is proposed to uniformly construct a series of exact complexiton solutions for nonlinear partial differential equations compared with most existing tanh function methods and rational expansion methods the proposed method not only recovers some known solutions but also finds some new and general complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

hardy s inequality and the l1 norm of exponential sums in this paper we generalize hardy s inequality 3 for measures of analytic type and obtain a proof of the littlewood conjecture 4 for the l norm of exponential sums as a simple consequence let t be the circle group z the additive group of integers and m t the customary convolution algebra of borel measures on t for pe e m t and n g z put m e ino dp o denote by h t the classical space of all measures e e m t such that j n 0 for all n 0 and let c denote the complex numbers we now state hardy s inequality for measures of analytic type theorem 1 if m c h t then

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

an extension of lasalle s invariance principle for switched systems in this paper we address invariance principles for a certain class of switched nonlinear systems we provide an extension of lasalle s invariance principle for these systems and state asymptotic stability criteria we also present some related results on the compactness of the trajectories of these switched systems

homotopy perturbation method for fractional kdv equation in this paper the homotopy perturbation method is directly applied to derive approximate solutions of the fractional kdv equation the results reveal that the proposed method is very effective and simple for solving approximate solutions of fractional differential equations

martingale transforms and complex uniform convexity les transformees de martingale et les operateurs integraux singuliers de calderon zygmund sont bornees comme des operateurs de l 2 l 1 dans l 2 l q quand 0 q 1 si y est un sous espace reflexif de l 1 alors l 1 y peut se renormer pour etre 2 complexe uniformement convexe on donne une nouvelle demonstration de la propriete de cotype 2 de l 1 h

r bounded approximating sequences and applications to semigroups abstract it is shown that on certain banach spaces including c 0 1 and l1 0 1 there is no strongly continuous semigroup tt 0

hamiltonian structure and integrability of the stationary kuramoto sivashinsky equation in this article the stationary kuramoto sivashinsky ks equation is studied it is shown first that this equation can be transformed into a one dimensional hamiltonian system describing the motion of a particle in a time dependent potential second working with this formalism and coming back then to the initial ks equation a subset of initial conditions is derived for which the corresponding solutions u x will behave like the dominant pole 120 x x0 3 deduced from the painleve analysis and will explode in a finite time finally special attention is given to the well known kuramoto tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain this solution explodes also like 120 x x0 3

triviality of the prolongation algebra of the kuramoto sivashinsky equation the authors apply the well known wahlquist estabrook prolongation technique to the kuramoto sivashinsky equation the prolongation algebra turns out to be trivial in the sense that it is commutative this supports nonintegrability of the equation

construction of non travelling wave solutions for the generalized variable coefficient gardner equation with the aid of two first order nonlinear ordinary differential equations the new generalized algebraic method is used to study the generalized variable coefficient gardner equation the main idea of the method is to take full advantage of solutions to the first order ordinary differential equations more new exact non travelling solutions which include soliton solutions combined soliton solutions triangular periodic solutions jacobi elliptic function solutions and combined jacobi elliptic function solutions for the gardner equation are obtained the method used here can be also extended to many other nonlinear partial differential equations

linearity inside nonlinearity exact solutions to the complex ginzburg landau equation abstract systems of two linear partial differential equations pdes with constant coefficients define a natural basis of elementary functions to build some exact solutions to nonlinear pdes for the one dimensional complex ginzburg landau equation the usual representations of the complex field re a or a are multivalued which makes difficult the search for exact solutions in this manner fortunately the painleve analysis naturally introduces an elementary single valued like representation of a by two fields z grad respectively complex abd real uniquely defined by an explicit expression for and a ze i another important feature is the invariance by parity on a which increases the class of expected solutions this allows to retrieve quite easily the four famous solutions of nozaki and bekki represented by the constant coefficients of two linear partial differential equations and a finite set of constants

travelling wave solutions for the generalized zakharov kuznetsov equation with higher order nonlinear terms abstract with the aid of symbolic computation and two auxiliary ordinary differential equations the new generalized algebraic method is extended to the generalized zakharov kuznetsov gzk equation with higher order nonlinear terms for constructing a series of new and more general travelling wave solutions because of the higher order nonlinear terms the equation can not be directly dealt with by the method and require some kinds of techniques by means of two proper transformations we transform the gzk equation to an ordinary differential equation that is easy to solve and find a rich variety of new exact travelling wave solutions for the gzk equation which include soliton solutions combined soliton solutions triangular periodic solutions jacobi elliptic function solutions combined jacobi elliptic function solutions and rational function solutions the method used here can be also extended to other nonlinear partial differential equations with higher order nonlinear terms

exact solutions of the multidimensional derivative nonlinear schrodinger equation for many body systems of criticality the authors investigate the problem of strongly interacting many body systems near criticality as recently described in terms of nonlinear dynamics by dixon and tuszynski 1989 they show that in the first order of approximation the equation of motion for the order parameter can be mapped on the derivative nonlinear schrodinger equation and thus can be solved exactly they solve the equations both in the absence and presence of current densities

holomorphic semi groups and the geometry of banach spaces according to a fundamental theorem of dvoretzky cf 24 25 any infinite dimensional banach space x contains for each integer n and each e 0 a subspace xn which is 1 e isomorphic to 12n in the classical banach spaces lp and 1p with 1 p x it is well known that this result can be improved these spaces contain uniformly complemented ln 7 s this means that we can find subspaces xn as above with the additional property that there exist projections p x xn such that supn 11 pn 11 cx moreover it is also well known that this property no longer holds for 11 or lo this motivated the question cf 13 to determine which infinite dimensional banach spaces contain uniformly complemented 1 n s we will prove below that all uniformly convex spaces have this property moreover we will show that a banach space x verifies this property locally see definition 2 10 for more precision if and only if x does not contain l n s uniformly progressively the work of previous authors cf 14 12 and particularly 5 has reduced such so called geometric questions to a purely analytic problem consisting of verifying in x a certain inequality referred to as k convexity in this paper we connect this inequality with the holomorphy of a certain semi group of operators on lp x and we show how this leads to the results already mentioned

an extension of lasalle s invariance principle and its application to multi agent consensus in the paper an extension of lasalle s invariance principle to a class of switched linear systems is studied one of the motivations is the consensus problem in multi agent systems unlike most existing results in which each switching mode in the system needs to be asymptotically stable this paper allows that the switching modes are only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability is obtained then it is used to solve the consensus reaching problem of certain multi agent systems in which each agent is modeled by a double integrator and the associated interaction graph is switching and is assumed to be only jointly connected

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

stability of switched nonlinear systems with delay and disturbance we consider a class of nonlinear time varying switched control systems for which stabilizing feedbacks are available we study the effect of the presence of a delay in the input of switched nonlinear systems with an external disturbance by contrast with most of the contributions available in the literature we do not assume that all the subsystems of the switched system we consider are stable when the delay is present through a lyapunov approach we derive sufficient conditions in terms of size of the delay ensuring the global exponential stability of the switched system moreover under appropriate conditions the input to state stability of the system with respect to an external disturbance is established

on operator valued sequences of multipliers and r boundedness in recent papers cf j l arregui o blasco p q summing sequences j math anal appl 274 2002 812 827 j l arregui o blasco p q summing sequences of operators quaest math 26 2003 441 452 s aywa j h fourie on summing multipliers and applications j math anal appl 253 2001 166 186 j h fourie i rontgen banach space sequences and projective tensor products j math anal appl 277 2 2003 629 644 the concept of p q summing multiplier was considered in both general and special context it has been shown that some geometric properties of banach spaces and some classical theorems can be described using spaces of p q summing multipliers the present paper is a continuation of this study whereby multiplier spaces for some classical banach spaces are considered the scope of this research is also broadened by studying other classes of summing multipliers let e x and f y be two banach spaces whose elements are sequences of vectors in x and y respectively and which contain the spaces c00 x and c00 y of all x valued and y valued sequences which are eventually zero respectively generally spoken a sequence of bounded linear operators un l x y is called a multiplier sequence from e x to f y if the linear operator from c00 x into c00 y which maps xi c00 x onto unxn c00 y is bounded with respect to the norms on e x and f y respectively several cases where e x and f y are different classical spaces of sequences including for instance the spaces rad x of almost unconditionally summable sequences in x are considered several examples properties and relations among spaces of summing multipliers are discussed important concepts like r bounded semi r bounded and weak r bounded from recent papers are also considered in this context

solutions of a 2 1 dimensional dispersive long wave equation a special type of multisoliton solution with a particular dispersion relation is obtained for wu zhang equation which describes 2 1 dimensional dispersive long waves by the standard weiss tabor carnvale painleve truncation expansion using a nonstandard truncation of a modified conte s invariant painleve expansion two different types of soliton solutions without any dispersive relation is found two types of periodic wave solutions expressed by jacobi elliptic functions are found by the truncations of a special extended painleve expansion the soliton solutions are special cases of the corresponding periodic solutions

on the structure of spaces of uniformly convergent fourier series we first give some new examples of translation invariant subspaces of c or u without local unconditional structure in the second part we prove that u and u do not have the gordon lewis property in the third part we show that absolutely summing operators from u to a k convex space are compact as a consequence u and u are not isomorphic at last we prove that u and u do not have the daugavet property

approximate solution for system of differential difference equations by means of the homotopy analysis method abstract in this paper the homotopy analysis method is successfully applied to solve approximate solutions of the differential difference system the solution of another relativistic toda lattice system is considered comparisons made between the results of the proposed method and exact solutions reveal that the homotopy analysis method is very effective in solving differential difference system

a new coupled sub equations expansion method and novel complexiton solutions of 2 1 dimensional burgers equation in this paper based on symbolic computation and the idea of rational expansion method a new coupled sub equations method is devised to uniformly construct a series of exact complexiton solutions for nonlinear evolution equations compared with most existing tanh function methods and other sophisticated methods the proposed method not only recover some known solutions but also find some new and general solutions which include many new types of complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

traveling wave solutions of the generalized nonlinear evolution equations solitary wave solutions for a family of nonlinear evolution equations with an arbitrary parameter in the exponents are constructed some of the obtained solutions seem to be new

on semi r boundedness and its applications abstract r boundedness is a randomized boundedness condition for sets of operators which in recent years has found many applications in the maximal regularity theory of evolution equations stochastic evolution equations spectral theory and vector valued harmonic analysis however in some situations additional geometric properties such as pisier s property are required to guaranty the r boundedness of a relevant set of operators in this paper we show that a weaker property called semi r boundedness can be used to avoid these geometric assumptions in the context of schauder decompositions and the h calculus furthermore we give weaker conditions for stochastic integrability of certain convolutions

hankel operators on bounded analytic functions for u a domain in the complex plane and g a bounded measurable function on u the generalized hankel operator sg on h u is the operator of multiplication by g followed by projection into l h under certain conditions on u we show that either sg is compact or there is an embedded on which sg is bicontinuous we characterize those g s for which sg is compact in the case that u is a behrens roadrunner domain

quasi exact solutions of nonlinear differential equations abstract the concept of quasi exact solutions of nonlinear differential equations is introduced quasi exact solution expands the idea of exact solution for additional values of parameters of differential equation these solutions are approximate ones of nonlinear differential equations but they are close to exact solutions quasi exact solutions of the the kuramoto sivashinsky the korteweg de vries burgers and the kawahara equations are founded

a converse lyapunov theorem for linear parameter varying and linear switching systems we study families of linear time varying systems where time variations have to satisfy restrictions on the dwell time that is on the minimum distance between discontinuities as well as on the derivative in between discontinuities such classes of systems may be formulated as linear flows on vector bundles the main objective of this paper is to construct parameter dependent lyapunov functions which characterize the exponential growth rate this is possible in the generic irreducible case as an application the gelfand formula is generalized to the class of systems studied here in other words the maximal exponential growth rate may be approximated by only considering the periodic systems in the family of time varying systems a perspective on the question of continuous dependence of the exponential growth rate on the data is given

a uniform algebra of analytic functions on a banach space let a b be the uniform algebra on the unit ball of a dual banach space 2 y generated by the weak star continuous linear functionals we focus on three related problems i to determine when a b is a tight uniform algebra ii to describe which functions in h b are approximable pointwise on b by bounded nets in a b and iii to describe the weak topology of b regarded as a subset of the dual of a b with respect to the second problem we show that any polynomial in elements of 3 can be approximated pointwise on b by functions in a b of the same norm this can be viewed as a generalization of goldstine s theorem in connection with the third problem we introduce a class of banach spaces called a spaces with the property that if xj is a bounded sequence in 2 such that p xj 0 for any mhomogeneous analytic function p on 2 m 1 then xj 0 in norm we show for instance that a banach space has the schur property if and only if it is a a space with the dunford pettis property

exact solutions of the complex modified korteweg de vries equation firstly some similarity reductions of the complex modified korteweg de vries equation cmkdv which arises in the asymptotic interpretation of one dimensional plane wave propagation in a quadratic micropolar medium are discussed although it is not a soliton equation solvable by inverse scattering transformation its similarity reductions obtained by the use of lie group methods are of mathematical interest secondly the painleve analysis developed by weiss et al 1983 for nonlinear partial differential equations is applied to the cmkdv equation and the data obtained by the truncation technique yield some analytical solutions of the ordinary modified korteweg de vries equation and travelling wave solutions of the cmkdv equation which are also solutions of the similarity reduction obtained by classical lie group analysis

stability and stabilization of continuous time switched linear systems this paper addresses two strategies for the stabilization of continuous time switched linear systems the first one is of open loop nature trajectory independent and is based on the determination of a minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function to be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition including chattering is expressed being nonconvex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

tight uniform algebras and algebras of analytic functions abstract a uniform algebra a on a compact space x is tight if for each g c x the hankel type operator f gf a from a to c a is weakly compact two families of uniform algebras are shown to be tight the algebras such as r k that arise in the theory of rational approximation on compact subsets of the complex plane and algebras of analytic functions on domains in c n for which a certain problem is solvable a couple of characterizations of tight algebras are given and one of these is used to show that the property of being tight places severe restrictions on the gleason parts of a and the measures in a

a note on the progressive wave solution of the perturbed korteweg devries equation with variable dissipation in this note utilizing the method presented in engelbrecht 1991 and demiray 2002 we have studied the propagation of progressive waves in perturbed kdv equation with variable dissipation coefficient the cases of constant and variable dissipation coefficient are studied separately and the results are compared with each other it is seen that for both cases the amplitude and wave speed decrease with increasing time

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

stability and robustness analysis for switched systems with time varying delays a new technique is presented for the stability and robustness analysis of nonlinear switched time varying systems with uncertainties and time varying delays the delays are allowed to be discontinuous but are required to be piecewise continuous and arbitrarily long with known upper bounds the technique uses an adaptation of halanay s inequality and a trajectory based technique and is used for designing switched controllers to stabilize linear time varying systems with time varying delays

analytic solutions of a microstructure pde and the kdv and kadomtsev petviashvili equations by invariant painleve analysis and generalized hirota techniques abstract truncated painleve expansions invariant painleve analysis and generalized hirota expansions are employed in combination to solve partially reduce to quadrature the integrable kdv and kp equations and a nonintegrable generalized microstructure gms equation although the multisolitons of the kdv and kp equations are very well known the solutions obtained here for all the three nlpdes are novel and non trivial the solutions obtained via invariant painleve analysis are all complicated rational functions with arguments which themselves are confluent hypergeometric kdv or trigonometric gms functions of various distinct non traveling kdv and traveling wave variables in some cases this is slightly reminiscent of doubly periodic elliptic function solutions when nonlinear ode systems are reduced to quadratures the solutions obtained by the use of recently generalized hirota type expansions in the truncated painleve expansions are closer in functional form to conventional hyperbolic secant solutions although with non trivial traveling wave arguments which are distinct for the three nlpdes considered here

on the behavior of solutions of a class of nonlinear partial differential equations the behavior of the steady state or the traveling wave solutions for a class of nonlinear partial differential equations is studied the nonlinearity in these equations is expressed by the presence of the convective term it is shown that the steady state or the traveling wave solution may explode at a finite value of the spatial or the characteristic variable this holds whatever the order of the spatial derivative term in these equations furthermore new special solutions of a set of equations in this class are also found

real interpolation of domains of sectorial operators on lp spaces abstract let a be a sectorial operator on a non atomic l p space 1 p whose resolvent consists of integral operators or more generally has a diffuse representation then the fractional domain spaces d a for 0 1 do not coincide with the real interpolation spaces of l q d a as a consequence we obtain that no such operator a has a bounded h calculus if p 1

lacunary sets and function spaces with finite cotype abstract we investigate translation invariant subspaces of the space of uniformly convergent fourier series and orlicz spaces with finite cotype in the case of orlicz spaces this leads to some new characterizations of p rider sets

towards a unified method for exact solutions of evolution equations an application to reaction diffusion equations with finite memory transport we present a brief report on the different methods for finding exact solutions of nonlinear evolution equations explicit exact traveling wave solutions are the most amenable besides implicit and parametric ones it is shown that most of methods that exist in the literature are equivalent to the generalized mapping method that unifies them by using this method a class of formal exact solutions for reaction diffusion equations with finite memory transport is obtained attention is focused to the finite memory transport fisher and nagumo equations

a new variable coefficient korteweg de vries equation based sub equation method and its application to the 3 1 dimensional potential ytsf equation with the aid of maple we present variable coefficient korteweg de vries equation based sub equation method the key idea of our method is to take advantage of the variable coefficient korteweg de vries equation and its various solutions to generate various solutions of nonlinear evolution equations the efficiency of the method can be demonstrated on the 3 1 dimensional potential ytsf equation and we construct successfully its new styles of solutions

uniform asymptotic stability of nonlinear switched systems with an application to mobile robots this paper is concerned with the study of both local and global uniform asymptotic stability for general nonlinear and time varying switched systems two concepts of lyapunov functions are introduced and used to establish uniform lyapunov stability and uniform global stability with the help of output functions an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability based on this result a generalized version of krasovskii lasalle theorem in time varying switched systems is proposed for switched systems with persistent dwell time the output persistent excitation condition is guaranteed to hold under a zero state observability condition it is shown that several existing results in past literature can be covered as special cases using the proposed criteria interestingly as opposed to previous work the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin the robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria a novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots

the pelczynski property for tight subspaces abstract we show that ifxis a tight subspace ofc k thenxhas the pelczynski property andx is weakly sequentially complete we apply this result to the spaceuof uniformly convergent taylor series on the unit circle and using a minimal amount of fourier theory prove thatuhas the pelczynski property andu is weakly sequentially complete using separate methods we proveuandu have the dunford pettis property some results concerning pointwise bounded approximation are proved for tight uniform algebras we use tightness and the pelczynski property to make a remark about inner functions on strictly pseudoconvex domains in c n

backlund transformation and the painleve property when a differential equation possesses the painleve property it is possible for specific equations to define a backlund transformation by truncating an expansion about the singular manifold at the constant level term from the backlund transformation it is then possible to derive the lax pair modified equations and miura transformations associated with the completely integrable system under consideration in this paper completely integrable systems are considered for which backlund transformations as defined above may not be directly defined these systems are of two classes the first class consists of equations of toda lattice type e g sine gordon bullough dodd equations we find that these equations can be realized as the minus one equation of sequences of integrable systems although the backlund transformation may or may not exist for the minus one equation it is shown for specific sequences that the backlund transformation does exist for the positive equations of the sequence this in turn allows the derivation of lax pairs and the recursion operation for the entire sequence the second class of equations consists of sequences of harry dym type these equations have branch point singularities and thus do not directly possess the painleve property yet by a process similar to the uniformization of algebraic curves their solutions may be parametrically represented by meromorphic functions for specific systems this is shown to provide a natural extension of the painleve property

from singular manifold equations to integrable evolution equations the singular manifold equations are used to construct nonlinear integrable partial differential equations a number of well known integrable equations hierarchies of korteveg de vries caudrey dodd gibbon kaup kuperschmidt and harry dym are obtained some new integrable equations are presented a possible approach to classification of integrable evolution equations is discussed

painleve analysis rational and special solutions of variable coefficient korteweg de vries equations painleve analysis of two variable coefficient korteweg de vries equations are considered the painleve test for these equations is applied the condition for the painleve property of the equations are found some rational and special solutions are presented

on converse lyapunov theorems for iss and iiss switched nonlinear systems abstract in this paper we present converse lyapunov theorems for iss and integral input to state stable iiss switched nonlinear systems their proofs are based on existing converse lyapunov theorems for input output to state stable and iiss nonlinear systems and on the association of the switched system with a nonlinear system with inputs and disturbances that take values in a compact set

stability analysis of switched time delay systems this paper addresses the asymptotic stability of switched time delay systems with heterogeneous time invariant time delays piecewise lyapunov razumikhin functions are introduced for the switching candidate systems to investigate the stability in the presence of an infinite number of switchings we provide sufficient conditions in terms of the minimum dwell time to guarantee asymptotic stability under the assumptions that each switching candidate is delay independently or delay dependently stable conservatism analysis is also provided by comparing with the dwell time conditions for switched delay free systems finally a numerical example is given to validate the results

periodical stabilization of switched linear systems periodical stabilization problems for switched linear systems are investigated in this paper for autonomous switched systems if there exists a stable convex combination of the subsystems then a periodically switching signal can be constructed such that the overall system is asymptotically stable based on this fact for switched control systems corresponding sufficient conditions are presented under which constant switching direct observer based state feedback controller can be designed such that the corresponding closed loop systems are asymptotically stable under some periodically switching signal some numerical examples are given to illustrate our results

stability of time delay feedback switched linear systems we address stability of state feedback switched linear systems in which delays are present in both the feedback state and the switching signal of the switched controller for switched systems with average dwell time switching signals we provide a condition in terms of upper bounds on the delays and in terms of a lower bound on the average dwell time to guarantee asymptotic stability of the closed loop the condition also implies that in general feedback switched linear systems are robust with respect to both small state delays and small switching delays our approach combines existing multiple lyapunov function techniques with the merging switching signal technique which gives relationships between the average dwell times of two mismatched switching signals and their mismatched times a methodology for numerical solution based on linear matrix inequality is also included

application of the extended homotopy perturbation method to a kind of nonlinear evolution equations based on the homotopy perturbation method we propose a new extended homotopy perturbation method we apply the method to solve a kind of nonlinear evolution equations with the help of the symbolic computation system maple the success of the paper lies on the fact that we do not conform to the traditional homotopy mode but construct a new homotopy of the given equations the results reveal that we can obtain the approximation solution of a kind of nonlinear evolution equations

convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode dependent dwell time abstract alternative conditions for establishing dwell time stability properties of linear switched systems are considered unlike the hybrid conditions derived in geromel and colaneri 2006 the considered ones are affine in the system matrices allowing then for the consideration of uncertain switched systems with time varying uncertainties the low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state feedback control laws the resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped functionals previously considered in the literature the sums of squares conditions are also proven to 1 approximate arbitrarily well the conditions of geromel and colaneri 2006 and 2 be invariant with respect to time scaling emphasizing that the complexity of the approach does not depend on the size of the dwell time several comparative examples illustrate the efficiency of the approach

exact solitary waves in a convecting fluid the perturbed korteweg de vries equation ut lambda 1uux lambda 2uxxx lambda 3uxxxx lambda 4 uux x lambda 5uxx 0 which describes the evolution of long shallow waves in a convecting fluid when the critical rayleigh number slightly exceeds its critical value admits two types of exact solitary wave solution

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

numerical solutions for fractional kdv burgers equation by adomian decomposition method abstract based on the symbolic computation system maple adomian decomposition method developed for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional kdv burgers equation the fractional derivatives are described in the caputo sense according to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional kdv burgers equation with time and space fractional derivatives finally the solutions of our model equation are calculated in the form of convergent series with easily computable components

banach spaces with the daugavet property a banach space x is said to have the daugavet property if every operator t x x of rank 1 satisfies 11 id tl 1 fltil we show that then every weakly compact operator satisfies this equation as well and that x contains a copy of t1 however x need not contain a copy of l1 we also study pairs of spaces x c y and operators t x y satisfying i i j t i i 1 4 1f t i i where j x y is the natural embedding this leads to the result that a banach space with the daugavet property does not embed into a space with an unconditional basis in another direction we investigate spaces where the set of operators with f id tll 1 il t l i is as small as possible and give characterisations in terms of a smoothness condition

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave