note on basic features of large time behaviour of heat kernels large time behaviour of heat semigroups and more gener ally of positive selfadjoint semigroups is studied convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups this framework includes laplacians on manifolds metric graphs and discrete graphs

design of variable structure controllers with continuous switching control a modified variable structure controller is proposed to deal with the conirol chattering problem which is one of the major difficulties for implementing the variable structure control vsc the new control strategy is effective for a class of uncertain nonlinear dynamical systems based on a suitably designed sliding sector a continuous switching controller whose control structure is switched whereas the control signal at switching remains continuous is constructed the complete attractiveness and the stability properties of the sliding sector in the sense of lyapunov stability ensure the retention of benefits achieved with the conventional vsc some typical examples are also investigated which show the improvement of system performance

a new design for model reference robust control using state space techniques the authors propose a model reference control mrc structure that is different from existing mrc structures the new approach that we discuss is based on state space techniques however it is not simply an alternative form of the input output transfer function approach the method we use to achieve our result is obtained through a concept often called filtered transformation the filtered transformation has the effect of transforming the plant into a big system that is composed of two subsystems one subsystem satisfies the standard matching condition which is not enjoyed by the original plant while all the unmatched and unmodelled dynamics are drawn into the other unmatched subsystem the control objective for the original plant is transferred into the control of the matched subsystem while also ensuring that the unmatched subsystem remains uniformly bounded a robust control approach and the backstepping method are used to guarantee that the overall states are globally uniformly bounded and that

combined direct and indirect approach to adaptive control an approach to adaptive control is introduced using a combination of both direct and indirect methods on the basis of estimates of the plant parameters and the current values of the control parameters closed loop estimation errors epsilon sub theta t and epsilon sub k t are defined these in turn are used in the adaptive laws for updating both identification and control parameters the global uniform stability of the overall system is shown by constructing a lyapunov function only the control of a first order plant is treated in detail to get across the principal concepts involved in particular the dynamic adjustment of the control parameters based on the estimates of the plant parameters is introduced as an indirect method and is the precursor of the combined method

estimates on the fundamental solution to heat flows with uniformly elliptic coefficients we obtain estimates from above and below on the fundamental solution to the cauchy initial value problem for parabolic equations having uniformly elliptic coefficients we impose minimal regularity requirements on the coefficients the estimates are expressed in terms of an energy functional associated with the coefficients

efficient design sensitivities of structures subjected to dynamic loading calculation of design sensitivities often involves much computational effort particularly in large structural systems with many design variables approximation concepts which are often used to reduce the computational cost involved in repeated analysis are usually not sufficiently accurate for sensitivity analysis in this study approximate reanalysis is used to improve the efficiency of dynamic sensitivity analysis using modal analysis the response derivatives with respect to design variables are presented as a combination of sensitivities of the eigenvectors and the generalized displacements a procedure intended to reduce the number of differential equations that must be solved during the solution process is proposed efficient evaluation of the derivatives using finite difference and the recently developed combined approximations approach is presented numerical examples show that high accuracy of design sensitivities can be achieved efficiently

variable structure model reference adaptive control using only input and output measurements abstract a variable structure model reference adaptive controller vs mrac using only the input and output measurements of the plant is proposed stability and transient properties are analysed and discussed remarkable transient behaviour is revealed in particular model following can be perfectly achieved in a finite time the effect of plant input disturbance is investigated and the performance of the vs controller is also shown to be qualitatively superior to that obtained with conventional integral adaptation algorithms a link between the vs mrac and the conventional mrac is suggested simulations are presented to highlight the theoretical results

a robust mrac using variable structure design for multivariable plants it is well known that undesirable transient responses and tracking performances have been frequently observed in traditional model reference adaptive control mrac problems especially for multivariable plants with unmodeled dynamics and output disturbances in this paper a new robust model reference adaptive control using variable structure design vsd is proposed to investigate the solution based on a definition of generalized relative degree grd for multivariable plants the general case for plants with arbitrary grd is completely solved it is shown that even when the uncertainties are presnet global stability and robustness of the closed loop control system are achieved furthermore without any persistence of excitation the tracking errors will at least asymptotically converge to zero for grd one plants and to a small residual set for plants with any higher grd with a suitable choice of initial control parameters the tracking errors can even be driven to zero in finite time for grd one plants and to a small residual set exponentially for plants with any higher grd

adaptive sliding mode control in discrete time systems abstract discrete time sliding mode control is considered the case of known parameters is first analyzed leading to a new definition of the so called equivalent control as the piecewise constant control that reduces to zero in finite time the distance of the system state from the sliding manifold in the presence of bounded parametric uncertainties an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented the main feature of this approach is the reduction of the order of the relevant error equation and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

volume growth spectrum and stochastic completeness of infinite graphs we study the connections between volume growth spectral properties and stochastic completeness of locally finite weighted graphs for a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic incompleteness and discreteness of the spectrum we then use these graphs to give some comparison results for both stochastic completeness and estimates on the bottom of the spectrum for general locally finite weighted graphs

the brezis nirenberg problem for the laplacian with a singular drift in rn and sn abstract we consider the brezis nirenberg problem for the laplacian with a singular drift for a geodesic ball in both r n and s n 3 n 5 the singular drift we consider derives from a potential which is symmetric around the center of the geodesic ball here the potential is given by a parameter say times the logarithm of the distance to the center of the ball in both cases we determine the exact region in the parameter space for which positive smooth solutions of this problem exist and the exact region for which there are no solutions the parameter space is characterized by the geodesic radius of the ball and the coupling constant of the linear term of the brezis nirenberg problem

function theory random paths and covering spaces pour des varietes de riemann connexes m on etudie la relation entre la theorie de fonction harmonique sur m les proprietes statistiques des chemins aleatoires sur m et la structure geometrique globale de m

efficient sensitivity analysis for structural optimization abstract efficient sensitivity analysis based on high quality approximations of displacements is presented the improved approximations are achieved by combining the efficiency of local approximations series expansion and the quality of global approximations the reduced basis method three approximate sensitivity analysis methods are developed and compared the direct method the adjoint variable method and the finite difference method all the approximations are based on the results of a single exact analysis of the initial design and they can be used with a general finite element system the methods are easy to implement and suitable for different types of design variables and structures it is shown that high quality approximations of derivatives can be achieved with a relatively small computational effort for very large changes in the design variables

asymptotic separation for independent trajectories of markov processes we say that n independent trajectories 1 t n t of a stochastic process t on a metric space are asymptotically separated if for some 0 the distance between i ti and j tj is at least for some indices i j and for all large enough t1 tn with probability 1 we prove sufficient conitions for asymptotic separationin terms of the green function and the transition function for a wide class of markov processes in particular if is the diffusion on a riemannian manifold generated by the laplace operator and the heat kernel p t x y satisfies the inequality p t x x ct 2 then n trajectories of are asymptotically separated provided moreover if for some 0 2 then n trajectories of are asymptotically separated where is the process generated by 2

approximate vibration reanalysis of structures thecombinedapproximationsmethodisdevelopedforvibrationreanalysisofstructures inthesolution process the terms of local series approximations are used as basis vectors in global reduced basis approximations the solution steps are straightforward and the method can be readily used with a general e nite element system the computational effort needed by the method is usually much smaller than the effort needed for complete vibration analysis the efe ciency of the calculations and the accuracy of the results can be controlled by the amount of information considered efe cient solutions are obtained by low order approximations and accurate results can be achievedbyconsideringhigher orderterms numericalexamplesshowthataccurateresultsareachievedefe ciently for very large changes in the design nomenclature b matrix dee ned by eq 21 c matrix dee ned by eq 16 e modulus of elasticity i moment of inertia i identity matrix k stiffness matrix kr reduced stiffness matrix l length m mass matrix mr reduced mass matrix r right hand side vector r displacement vector rb matrix of basis vectors s number of basis vectors u upper triangular matrix y vector of coefe cients coefe cient dee ned by eq 35 angle between vectors 1k change in the stiffness matrix 1m change in the mass matrix kronecker delta eigenvalue circular frequency

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

on minimal parabolic functions and time homogeneous parabolic h transforms burdzy was supported in part by nsf grant dms 9700721 saliosbury was supported in part by a grant from nserc a portion of this research took place during his stay at the fields institute

absence of ground state for the nelson model on static space times abstract we consider the nelson model on some static space times and investigate the problem of absence of a ground state nelson models with variable coefficients arise when one replaces in the usual nelson model the flat minkowski metric by a static metric allowing also the boson mass to depend on position we investigate the absence of a ground state of the hamiltonian in the presence of the infrared problem i e assuming that the boson mass m x tends to 0 at spatial infinity using path space techniques we show that if m x c x at infinity for some c 0 and 1 then the nelson hamiltonian has no ground state

robust model tracking control for a class of nonlinear plants we propose a new model following control scheme for a class of nonlinear plants the feedback control signal is a continuous function of all its arguments it is shown that this scheme guarantees that tracking error remains bounded and tends to a neighborhood of the origin with a rate not inferior to an exponential one furthermore it allows the designer to arbitrarily prescribe the rate of convergence and the size of the set of ultimate boundedness

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

instability of the liouville property for quasi isometric riemannian manifolds and reversible markov chains on montre par un exemple que la propriete de liouville n est pas un invariant quasi isometrique des varietes de riemann et des chaines de markov reversibles

lp norms of non critical schrodinger semigroups we consider schrodinger semigroups e th h v on rn with v c x 2 as x 0 c 12 n 2 2 with h 0 we determine the exact power law divergence of e th p p and of some e th q p as maps from lp to lq the results are expressed most naturally in terms of the power for which there exists a positive resonance such that h 0 x x

identifier tracking model reference adaptive control model reference adaptive control is a major design method for controlling plants with uncertain parameters the primary objective of this paper is to develop a new design approach for a differentiator free model reference adaptive control of a single input single output linear time invariant plant the proposed method called the identifier tracking model reference adaptive control uses a stacked identifier structure that is new to the field of adaptive control the goal is to make the output of the plant asymptotically track the output of the first identifier and then driving the output of the first identifier to track that of the second identifier and so forth up to the qth identifier where q is the relative degree of the plant lastly the output of the qth identifier is forced to converge to that of the reference model simulation results show the superiority of the proposed method over the traditional model reference adaptive control with augmented error in terms of the transient response sinc

uniqueness of l 1 solutions for the laplace equation and the heat equation on riemannian manifolds on deduit une hypothese geometrique optimale sur une variete de riemann complete qui assure des proprietes d unicite pour des solutions l 1 de l equation de laplace et de la chaleur

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

large time behavior of schrodinger heat kernels and applications we obtain global in time and qualitatively sharp bounds for the heat kernel g of the schrodinger operator v the potential v satisfies v x c d x b near infinity with b 0 2 when v 0 our result can be described as follows g is bounded from above and below by the multiples of standard gaussians with a weight function if b 2 then the weight is bounded between two positive it constants if b 2 the weight is bounded between two positive functions of t d x and d y which have polynomial decay if b 2 or b 0 an application to a semilinear elliptic problem is also given

estimates for functions of the laplace operator on homogeneous trees in this paper we study the heat equation on a homogeneous graph relative to the natural nearest neighbour laplacian we find pointwise estimates for the heat and resolvent kernels and the lp lq mapping properties of the corresponding operators in recent years random walks on graphs have been studied as analogues of diffusions on manifolds see e g t coulhon cn m kanai k1 k2 and n th varopoulos v1 v2 more recently i chavel and e a feldman cf and m m h pang p considered the semigroup e t 0 in this paper we consider the heat semigroup associated to the canonical laplace operator on a homogeneous tree which is perhaps the basic example of a graph where the cardinality of the ball of radius r grows exponentially in r we study the properties of the heat and resolvent operators and discover very close analogies with diffusions on hyperbolic spaces in line with the philosophy of the above mentioned authors a homogeneous tree x of degree q 1 is defined to be a connected graph with no loops in which every vertex is adjacent to q 1 other vertices we denote by d the natural distance on x d x y being the number of edges between the vertices x and y and by l x the lebesgue space with respect to counting measure on x on x the canonical laplace operator l is defined thus lf x f x 1 q 1 y x d x y 1 f y x x it is easily seen to be bounded on l x for every p in 1 and self adjoint on l x denote by 2 l the l x spectrum of l and by p the associated spectral resolution of the identity such that lf 2 l dp f f l x and denote inf 2 l by b2 for in 0 1 and with re 0 the heat operator and the resolvent of l are the operators defined by the formulae htf 2 l e t dp f t r received by the editors october 4 1996 1991 mathematics subject classification primary 43a85 secondary 20e08 43a90 22e35

nonlinear dynamic reanalysis of structures by combined approximations abstract a major difficulty in non linear dynamic reanalysis by mode superposition is the need to repeat the eigenproblem solutions this study shows how the combined approximations approach can be used to overcome this difficulty the approach is based on the integration of several concepts and methods including matrix factorization series expansion and reduced basis the advantage is that efficient local approximations and accurate global approximations are combined to achieve an effective solution procedure in the procedure developed for material non linearity improved basis vectors are introduced using the concepts of gram schmidt orthogonalizations and shifts numerical examples show that accurate approximations are achieved efficiently for very large changes in the design variables

manifolds and graphs with slow heat kernel decay we give upper estimates on the long time behavior of the heat kernel on noncompact riemannian manifolds and infinite graphs which only depend on a lower bound of the volume growth we also show that these estimates are sharp

isoperimetric inequalities and markov chains soit a i j i j n la matrice stochastique d une chaine de markov reversible sur n 1 2 soit n 2 tel que f r c f d f c 0 n ou r 2n n 2 ou c 0 est independant de f et ou r indique la norme dans l r n d pour la mesure i i alors on a sup i j j 1 a i j 0 n 2

semismall perturbations semi intrinsic ultracontractivity and integral representations of nonnegative solutions for parabolic equations we consider nonnegative solutions of a parabolic equation in a cylinder d i where d is a noncompact domain of a riemannian manifold and i 0 t with 0 t or i 0 under the assumption ssp i e the constant function 1 is a semismall perturbation of the associated elliptic operator on d we establish an integral representation theorem of nonnegative solutions in the case i 0 t any nonnegative solution is represented uniquely by an integral on d 0 md 0 t where md is the martin boundary of d for the elliptic operator and in the case i 0 any nonnegative solution is represented uniquely by the sum of an integral on md 0 and a constant multiple of a particular solution we also show that ssp implies the condition siu i e the associated heat kernel is semi intrinsically ultracontractive

on the discreteness of the spectrum of the laplacian on noncompact riemannian manifolds necessary and sufficient conditions for the discreteness of the laplacian on a noncompact riemannian manifold m are established in terms of the isocapacitary function of m the relevant capacity takes a different form according to whether m has finite or infinite volume conditions involving the more standard isoperimetric function of m can also be derived but they are only sufficient in general as we demonstrate by concrete examples

accurate reanalysis of structures by a preconditioned conjugate gradient method a preconditioned conjugate gradient pcg method that is most suitable for reanalysis of structures is developed the method presented provides accurate results efficiently it is easy to implement and can be used in a wide range of applications including non linear analysis and eigenvalue problems it is shown that the pcg method presented and the combined approximations ca method developed recently provide theoretically identical results consequently available results from one method can be applied to the other method effective solution procedures developed for the ca method can be used for the pcg method and various criteria and error bounds developed for conjugate gradient methods can be used for the ca method numerical examples show that the condition number of the selected preconditioned matrix is much smaller than the condition number of the original matrix this property explains the fast convergence and accurate results achieved by the method copyright 2002 john wiley sons ltd

variable structure model reference adaptive control systems model reference adaptive controllers when only input and output measurements are available are designed using the theory of variable structure systems state variable filters are used in order to obtain differentiator free controllers the proposed design allows the error transient to be prescribed in advance the drawbacks deriving from the typical high frequency chattering of the control signal during the sliding motion can be partially eliminated by means of a little modification of the adaptation law that does not cause the error signal to deteriorate considerably

positive solutions and large time behaviors of schrodinger semigroups simon s problem let h v where v is a multiplication operator by a real valued function v x on rn which is uniformly holder continuous and 1 x 2 2 v x l rn for some 4 the relationship between existence of positive solutions with growth conditions of hg 0 and asymptotic behaviors as t of e th is established using it b simon s problem for h on r2 is solved

large time behavior of the heat kernel and the behavior of the green function near criticality for nonsymmetric elliptic operators abstract let p be a second order elliptic operator which is defined on a domain r n and let w x be a nonzero nonnegative function assume that p p w x admits a positive minimal green function g p x y for all lim 0 g p x y f x y where f 0 for x y unless p and p admit ground states x and x respectively with eigenvalue zero such that z w z z dz in this case f x y x y z w z z dx moreover if z z dz then the heat kernel k x y t of the parabolic equation lu u t pu 0 satisfies lim t k x y t x y z z dz

martin boundaries of elliptic skew products semismall perturbations and fundamental solutions of parabolic equations abstract we consider positive solutions of elliptic partial differential equations on non compact domains of riemannian manifolds we explicitly determine martin boundaries and martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short long time estimates for fundamental solutions of parabolic equations

an optimal parabolic estimate and its applications in prescribing scalar curvature on some open manifolds with ricci ge 0 by establishing an optimal comparison result on the heat kernel of the conformal laplacian on open manifolds with nonnegative ricci curvature a we show that many manifolds with positive scalar curvature do not possess conformal metrics with scalar curvature bounded below by a positive constant b we identify a class of functions with the following property if the manifold has a scalar curvature in this class then there exists a complete conformal metric whose scalar curvature is any given function in this class this class is optimal in some sense c we have identified all manifolds with nonnegative ricci curvature which are uniformly conformal to manifolds with zero scalar curvature even in the euclidean case we obtain a necessary and sufficient condition under which the main existence results in ni1 and kn on prescribing nonnegative scalar curvature will hold this condition had been sought in several papers in the last two decades

regularity of weak solutions of elliptic and parabolic equations with some critical or supercritical potentials abstract we prove holder continuity of weak solutions of the uniformly elliptic and parabolic equations 0 1 i a i j x j u x a x 2 u x 0 a 0 0 0 2 i a i j x t j u x t a x 2 u x t t u x t 0 a 0 0 with critical or supercritical 0 order term coefficients which are beyond de giorgi nash moser s theory we also prove in some special cases weak solutions are even differentiable previously p baras and j a goldstein 3 treated the case when a 0 a i j i and 0 for which they show that there does not exist any regular positive solution or singular positive solutions depending on the size of a when a 0 0 and a i j i p d milman and y a semenov 7 8 obtain bounds for the heat kernel

on the parameter convergence properties of a combined vs adaptive control scheme during sliding motion the effects of the use of a variable structure control component within an adaptive control scheme previously proposed by the authors 1992 1995 are investigated in this paper the discontinuous control action does not allow the explicit identification of the coefficients of the filters but only the identification of the so called equivalent control coinciding with the ideal control by coupling the variable structure control strategy with a continuous parameter adjustment mechanism it is instead possible to obtain an equivalent control which during the sliding motion turns out to be equal to a suitably constructed prediction error as long as the parameter adaptation is driven by both the tracking error which vanishes in finite time and the prediction error then the controller parameters prove to be exponentially convergent to the ideal values provided that the reference signal is sufficiently persistently exciting

tracking with asymptotic sliding mode and adaptive input delay effect compensation of nonlinearly perturbed delayed systems applied to traffic feedback control abstractasymptotical sliding mode model reference adaptive control design for a class of systems with parametric uncertainty unknown nonlinear perturbation and external disturbance and with known input and state delays is proposed to overcome the difficulty to directly predict the plant state under uncertainties a control design is based on a developed decomposition procedure where a generalised error in conjunction with auxiliary linear dynamic blocks with adjustable gains is introduced and the sliding variable is formed on the basis of this error the effect of such a decomposition is to pull the input delay out of first step of the design procedure as a result similarly to the classical smith predictor the adaptive control architecture based only on the lumped delays i e without conventional in such cases difficult implemented distributed delay blocks two new adaptive control schemes are proposed a linearisation based control design is constructed for feedback control of an urban traffic

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

bounds for eigenfunctions of the laplacian on noncompact riemannian manifolds we deal with eigenvalue problems for the laplacian on noncompact riemannian manifolds m of finite volume sharp conditions ensuring l q m and l infinity m bounds for eigenfunctions are exhibited

large time behavior of the heat kernel in this paper we study the large time behavior of the minimal heat kernel kpm x y t of a general time independent parabolic operator lu ut p x x u which is defined on a noncompact manifold m more precisely we prove that limt e 0tkpm x y t always exists here 0 is the generalized principal eigenvalue of the operator p in m

global bounds of schrodinger heat kernels with negative potentials abstract we obtain global in time bounds for the heat kernel g of the schrodinger operator l v the potential v satisfies v x c d x b near infinity with b 0 the result can be described as follows suppose l is positive and b 2 then g g x t y 0 has a global upper bound which is a standard gaussian times a polynomial function of x y t however when l is not nonnegative and negative eigenvalues exist g g x t 0 0 is bounded below by a standard gaussian times ectwithc 0 in other words the growth rate of g x t 0 0 is comparable with the heat kernel of c regardless how fast v decays near infinity

asymptotic of the heat kernel in general benedicks domains using a new inequality relating the heat kernel and the probability of survival we prove asymptotic ratio limit theorems for the heat kernel and survival probability in general benedicks domains in particular the dimension of the cone of positive harmonic measures with dirichlet boundary conditions can be derived from the rate of convergence to zero of the heat kernel or the survival probability

explicit constants for gaussian upper bounds on heat kernels on utilise des inegalites logarithmiques de sobolev pour obtenir des bornes superieures gaussiennes sur les noyaux de la chaleur associes a des operateurs d ordre 2 elliptiques et hypoelliptiques

large time behavior of reaction diffusion equations with bessel generators abstract we investigate explosion in finite time of one dimensional semilinear equations of the form u t t x 1 2 2 u t x 2 x x x u t x x a x 2 u t x u t 1 x with initial value 0 where c 2 r is positive and a 0 0 are constants in the free case a 0 we provide conditions on under which any positive nontrivial solution is non global in the case a 0 and x x 1 2 r which includes in the special case 1 2 the equation u t t x 1 2 2 u t x 2 x a x 2 u t x u t 1 x we use the feynman kac formula for bessel processes to give conditions on the equation parameters ensuring finite time blowup and existence of nontrivial positive global solutions

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

a new proof of moser s parabolic harnack inequality using the old ideas of nash in 1958 nash published his fundamental work on the local holder continuity of solutions of second order parabolic equations with coefficients which need not be smooth 8 the primary purpose of that work was to study the properties of the fundamental solution corresponding to the parabolic operator and from these properties to derive regularity for a general solution though the work is often cited in the literature about weak solutions of elliptic and parabolic equations one feels that nash s ideas were never fully understood and maybe still are not and that because of this the more understandable and seemingly more fruitful ideas of de giorgi 4 and moser 6 7 were subsequently adopted

properties of min max controllers in uncertain dynamical systems we discuss properties of min max controllers previously obtained for uncertain dynamical systems in particular we present a new model for switching action and re examine asymptotic stability we demonstrate the attractiveness of switching surfaces and comment on the insensitivity of solutions in those surfaces to the uncertainty

noncommutative riemann integration and novikov shubin invariants for open manifolds given a c algebra a with a semicontinuous semifinite trace acting on the hilbert space h we define the family ar of bounded riemann measurable elements w r t as a suitable closure a la dedekind of a in analogy with one of the classical characterizations of riemann measurable functions and show that ar is a c algebra and extends to a semicontinuous semifinite trace on ar then unbounded riemann measurable operators are defined as the closed operators on h which are affiliated to a and can be approximated in measure by operators in ar in analogy with unbounded riemann integration unbounded riemann measurable operators form a a e bimodule on ar denoted by ar and such a bimodule contains the functional calculi of selfadjoint elements of ar under unbounded riemann measurable functions besides extends to a bimodule trace on ar type ii1 singular traces for c algebras can be defined on the bimodule of unbounded riemann measurable operators noncommutative riemann integration and singular traces for c algebras are then used to define novikov shubin numbers for amenable open manifolds to show their invariance under quasi isometries and to prove that they are noncommutative asymptotic dimensions

efficient non linear reanalysis of skeletal structures using combined approximations non linear reanalysis of large scale structures usually involves much computational effort because the set of non linear equations must be solved repeatedly during the solution process various approximations that are often used for linear reanalysis are not sufficiently accurate for non linear problems in this study solution procedures based on the combined approximations approach are developed and compared in terms of efficiency and accuracy various path independent non linear analysis and reanalysis problems are considered including material non linearity geometric non linearity and buckling analysis numerical examples demonstrate the effectiveness of the procedures presented it is shown that in various cases accurate results can be achieved efficiently copyright 2007 john wiley sons ltd

a combined direct indirect and variable structure method for robust adaptive control direct methods and indirect methods for the adaptive control of linear plants with unknown parameters are currently well known methods for combining direct and indirect methods have also been suggested in the paper the latter method is combined with the variable structure method new adaptive laws are suggested which overcome the principal drawbacks of the variable structure method while the direct and indirect components of the new method assure stability the variable structure component improves the transient response of the system simulation results are presented to show that the overall system is asymptotically stable in the ideal case and exhibits robustness and improved performance in the presence of perturbations

efficient finite difference design sensitivities the problem considered in this study is to evaluate efficiently displacement derivatives using global finite differences given the displacements for an initial design the displacements for various modified designs are evaluated by the recently developed combined approximations method calculations of finite difference sensitivity coefficients are demonstrated for static problems and eigenproblems the presented solution procedure is easy to implement efficient and can be used to calculate derivatives for various designs where the exact displacements are not known some numerical examples show that the accuracy of the results is similar to the accuracy obtained by finite difference calculations based on exact analysis

nonlinear dynamic sensitivities of structures using combined approximations calculation of design sensitivities involves much computational effort particularly for nonlinear dynamic response of large structures modal analysis is often not effective for such problems because eigenproblems must be solved many times approximation concepts which are used to reduce the computational cost involved in structural analysis are usually not sufficiently accurate for sensitivity analysis in this study approximate reanalysis concepts are used to improve the efficiency of nonlinear dynamic sensitivity analysis efficient evaluation of the derivatives using modal analysis finite difference of eigenpairs and the recently developed combined approximations approach is presented several approximate solution procedures are developed and compared in terms of the efficiency and the accuracy of the results it is shown that some of the approximations presented reduce significantly the computational effort and provide sufficiently accurate results i introduction design sensitivity analysis of structures deals with the calculation of the response derivatives with respect to the design variables these derivatives are used in the solution of various problems such as design optimization generation of response approximations including approximate reanalysis models and explicit approximations of the constraint functions in terms of the structural parameters sensitivities are required also for assessing the effects of uncertainties in the structural properties on the system response calculation of design sensitivities involves much computational effort particularly for nonlinear dynamic response of large structures as a result there has been much interest in efficient procedures for calculating the sensitivity coefficients early and recent developments in methods for sensitivity analysis are discussed in various studies 1 4 methods of sensitivity analysis for discretized systems can be divided into the following classes a finite difference methods which are easy to implement but might involve numerous repeated analyses and high computational cost particularly in large problems the efficiency can be improved by using fast reanalysis techniques but finite difference approximations might have accuracy problems b analytical methods which provide exact solutions but might not be easy to implement in some problems c semi analytical methods which are based on a compromise between finite difference methods and analytical methods these methods are easy to implement but might provide inaccurate results in general the main factors considered in choosing a suitable sensitivity analysis method for a specific application include the accuracy the computational effort and the ease of implementation the quality of the results and efficiency of the calculations are usually two conflicting factors that is higher accuracy is often achieved at the expense of more computational effort dynamic sensitivity analysis has been demonstrated by several authors in ref 5 the mode superposition approach has been considered for linear response assuming harmonic loading the response sensitivities were evaluated by direct differentiation of the equations of motion in several studies

combined adaptive and variable structure control for constrained robots abstract this paper addresses the problem of controller design for constrained robots a control algorithm described as a combination of the direct adaptive and the variable structure method is presented for the trajectory tracking of an end effector on a constrained surface with specified constraint forces this scheme has certain advantages both with respect to computational efficiency and with respect to design with respect to computational efficiency the calculation of the regressor is avoided with respect to design since the number of parameter update laws required in the adaptation is independent of the number of links of the robot the difficulty of tuning numerous adaptation gains is avoided

accurate displacement derivatives for structural optimization using approximate reanalysis a unified approach for accurate approximations of displacements and displacement derivatives with respect to design variables is presented the solution procedure is based on results of a single exact analysis at an initial design unlike common approximations of the structural response the approach presented is not based on calculation of derivatives rather approximations of displacements are used to evaluate displacement derivatives at various modified designs it is shown that similar computational procedures are employed for evaluating displacements first and second order derivatives of displacements the procedure presented is suitable for different types of design variables and structures numerical results show that accurate approximations of derivatives can be achieved with a small computational effort for designs obtained by very large changes in the initial structure