long term prediction of non linear time series using multiresolution wavelet models the long term prediction of non linear dynamical time series based on identified multiresolution wavelet models from historically observed data sets is investigated and a new direct prediction approach is introduced prediction results based on the new direct scheme are compared with those from iterative methods and it is shown that improved predictions can be obtained using the new approach

counterexamples on l_p maximal regularity we establish a transference result for l p maximal regularity for the abstract cauchy problem on banach space from this result we deduce counterexamples to l p maximal regularity 1 p infty in particular we obtain an operator b without any l p maximal regularity although it admits bounded imaginary powers with vert b is vert 1 for all s in mathbb r we also derive an operator which satisfies l p maximal regularity on bounded intervals 0 t but not on the half line mathbb r

on the inverse of the sum of two sectorial operators abstract we study an abstract linear operator equation on a banach space by using the inverse of the sum of two sectorial operators we prove that the boundedness of a special type of operator valued h calculus is sufficient for maximal regularity of the solution we apply the result to the abstract parabolic problem to give a maximal l p regularity condition we also study the abstract hyperbolic problem and give a sufficient condition for the existence of solution

fuzzy wavelet networks for function learning inspired by the theory of multiresolution analysis mra of wavelet transforms and fuzzy concepts a fuzzy wavelet network fwn is proposed for approximating arbitrary nonlinear functions the fwn consists of a set of fuzzy rules each rule corresponding to a sub wavelet neural network wnn consists of single scaling wavelets through efficient bases selection the dimension of the approximated function does not cause the bottleneck for constructing fwn especially by learning the translation parameters of the wavelets and adjusting the shape of membership functions the model accuracy and the generalization capability of the fwn can be remarkably improved furthermore an algorithm for constructing and training the fuzzy wavelet networks is proposed simulation examples are also given to illustrate the effectiveness of the method

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

bounded imaginary powers of cone differential operators on higher order mellin sobolev spaces and applications to the cahn hilliard equation abstract extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted l p spaces h p 0 b over a manifold with conical singularities we show how the same assumptions also yield the existence of bounded imaginary powers on higher order mellin sobolev spaces h p s b s 0 as an application we consider the cahn hilliard equation on a manifold with possibly warped conical singularities relying on our work for the case of straight cones we first establish r sectoriality and thus maximal regularity for the linearized equation and then deduce the existence of a short time solution with the help of a theorem by clement and li we also obtain the short time asymptotics of the solution near the conical point

a transference principle for general groups and functional calculus on umd spaces let ia be the generator of a c 0 group u s s is an element of r on a banach space x and omega theta u the group type of u we prove a transference principle that allows to estimate parallel to f a parallel to in terms of the l p r x fourier multiplier norm of f i omega if x is a hilbert space this yields new proofs of important results of mcintosh and boyadzhiev de laubenfels if x is a umd space one obtains a bounded h 1 infinity calculus of a on horizontal strips related results for sectorial and parabola type operators follow finally it is proved that each generator of a cosine function on a umd space has bounded h infinity calculus on sectors

the swift hohenberg equation on conic manifolds abstract we consider the swift hohenberg equation on manifolds with conical singularities and show existence uniqueness and maximal regularity of the short time solution in terms of mellin sobolev spaces moreover we give a necessary and sufficient condition so that the above solution exists for all times space asymptotic expansion of the solution near the singularity is also provided and its relation to the local geometry is shown the same problem is considered on closed manifolds and similar results are obtained by using the above singular analysis theory

maximal regularity of the stokes operator in an exterior domain with moving boundary and application to the navier stokes equations consider the navier stokes system on an exterior domain with moving boundary and dirichlet boundary conditions in 2003 saal proved that the stokes operator in a domain with moving boundary has the property of maximal regularity provided that the operator is invertible hence his result can be applied if the domain is bounded or by adding a shift to the stokes operator if the domain is unbounded or the time interval is finite in this paper we will generalize his result to a result global in time if the reference domain is an exterior domain finally we will apply this result to the navier stokes equations to obtain a global in time existence theorem for small data

optimal control elliptic systems with distributed and boundary controls abstract in this paper we consider a nonlinear elliptic control system with distributed and boundary controls and with the integral cost functional some sufficient conditions under which the solutions of the elliptic systems continuously depend on boundary and distributed controls are presented the proof of the result is based on variational methods these conditions are used to obtain some existence theorem for the optimal control problem governed by nonlinear elliptic equations with distributed and boundary controls in the final part we consider the question of stability of the optimal controls and trajectories applying some results of the convergence theory we prove sufficient conditions under which small variations of parameters of given system imply small changes of optimal processes

wavelet differential neural network observer state estimation for uncertain systems affected by external noises is an important problem in control theory this paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown differential neural network nn approach is applied in this uninformative situation but with activation functions described by wavelets a new learning law containing an adaptive adjustment rate is suggested to imply the stability condition for the free parameters of the observer nominal weights are adjusted during the preliminary training process using the least mean square lms method lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error two numeric examples illustrate this approach first a nonlinear electric system governed by the chua s equation and second the lorentz oscillator both systems are assumed to be affected by external perturbations and their parameters are unknown

a geometrical characterization of banach spaces in which martingale difference sequences are unconditional we study banach space valued martingale transforms and in particular characterize those banach spaces for which the classical theorems of the real valued case carry over for example if b is a banach space and 1 0 and zeta x y leq x y text if x leq 1 leq y

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

pointwise convergence for semigroups in vector valued l p spaces suppose that tt t 0 is a symmetric diffusion semigroup on l2 x and denote by widetilde t t t geq0 its tensor product extension to the bochner space l p x mathcal b where mathcal b belongs to a certain broad class of umd spaces we prove a vector valued version of the hopf dunford schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of widetilde t t t geq 0 on l p x mathcal b as an application we show that such continuations exhibit pointwise convergence

some results about complex powers of closed operators the aim of this paper is to give some further results about complex powers of operators a tool that the authors already employed in 2 and s to study some questions of operator theory our first result is essentially a completion of corollary 2 9 of 2 since it gives an estimate for the rate of decrease of a a at infinity when a is a positive operator with bounded imaginary powers we remark that the converse question i e the estimate of the imaginary powers in terms of the amplitude of the spectrum remains open next we prove a result of pertubation if we add to a positive operator

nonlinear abstract boundary value problems in vector valued function spaces and applications abstract the nonlocal boundary value problems for linear and nonlinear differential operator equations of second order with dependent coefficients are studied the principal part of the differential operators generated by linear problems are nonself adjoint several conditions for the maximal regularity r positivity and the fredholmness in banach valued l p spaces are given by using these results the existence and uniqueness of the maximal regular solutions of nonlocal boundary value problems for nonlinear differential operator equations are established in applications nonlocal boundary value problems for nonlinear partial differential equations and their finite or infinite systems on cylindrical domains are studied

uniqueness of solutions of the stochastic navier stokes equation with invariant measure given by the enstrophy a stochastic navier stokes equation with space time gaussian white noise is considered having as infinitesimal invariant measure a gaussian measure whose covariance is given in terms of the enstrophy pathwise uniqueness for a e initial velocity is proven for solutions having as invariant measure

new thoughts on old results of r t seeley in this paper we show that the lp realization of a vector valued elliptic boundary value problem j admits a bounded calculus on lp g e 1 p provided the top order coefficients of are holder continuous here g denotes a domain in n with compact c2m boundary and e a banach space of class our proof is based on an abstract perturbation result for operators admitting bounded calculus and kernel estimates for the solution of j

discrete maximal regularity and the finite element method for parabolic equations maximal regularity is a fundamental concept in the theory of partial differential equations in this paper we establish a fully discrete version of maximal regularity for parabolic equations on a polygonal or polyhedral domain varomega we derive various stability results in the discrete l p 0 t l q varomega norms for the finite element approximation with the mass lumping to the linear heat equation our method of analysis is an operator theoretical one using pure imaginary powers of operators and might be a discrete version of the result of dore and venni as an application optimal order error estimates in those norms are proved furthermore we study the finite element approximation for semilinear heat equations with locally lipschitz continuous nonlinear terms and offer a new method for deriving optimal order error estimates some interesting auxiliary results including discrete gagliardo nirenberg and sobolev inequalities are also presented

on a parabolic equation in a triangular domain we prove the optimal regularity in sobolev spaces of the solution of a parabolic equation set in a triangular domain t the right hand term of the equation is taken in lebesgue space l p t the method of operators sums in the non commutative case is referred to

maximal regularity for non autonomous schrodinger type equations abstract in this paper we study the maximal regularity property for non autonomous evolution equations t u t a t u t f t u 0 0 if the equation is considered on a hilbert space h and the operators a t are defined by sesquilinear forms a t we prove the maximal regularity under a holder continuity assumption of t a t in the non hilbert space situation we focus on schrodinger type operators a t m t and prove l p l q estimates for a wide class of time and space dependent potentials m

on maximal parabolic regularity for non autonomous parabolic operators abstract we consider linear inhomogeneous non autonomous parabolic problems associated to sesquilinear forms with discontinuous dependence of time we show that for these problems the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 2 this allows us to prove maximal parabolic l r regularity for discontinuous non autonomous second order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations

sums of regular self adjoint operators in hilbert c modules abstract we introduce a notion of weak anticommutativity for a pair s t of self adjoint regular operators in a hilbert c module e we prove that the sum s t of such pairs is self adjoint and regular on the intersection of their domains a similar result then holds for the sum s 2 t 2 of the squares we show that our definition is closely related to the connes skandalis positivity criterion in kk theory as such we weaken a sufficient condition of kucerovsky for representing the kasparov product our proofs indicate that our conditions are close to optimal

soft computing approach to feature extraction based on both wavelet theory and fuzzy theory a soft computing system scs is proposed for feature extraction of signals the proposed scs approach possesses the advantages of soft decision making on wavelet coefficients for feature extraction adaptive selectivity of mapping factors to coarse to fine resolution and compact form of feature representation with the scs feature extractor fuzzy sets are used to provide a robust representation for signal information and wavelet transform is used to decompose a signal into detail and approximation signals at a given resolution the detail and approximation signals are inputted to the proposed scs to extract signal features at that resolution level the sensitivity in feature extraction of the proposed approach can be adapted by tuning the fuzzy sets for the detail and approximation signals at different resolutions the signal can be examined and suitable features can be extracted examples of both one dimensional signals and two dimensional fingerprint images are used to illustrate the proposed soft computing approach for feature extraction and pattern recognition the results show that the extracted features are sensitive enough to distinguish the similar signal from the different ones and are robust enough to tolerate noise corruption

nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks this paper presents an adaptive nonsingular terminal sliding mode ntsm tracking control design for robotic systems using fuzzy wavelet networks compared with linear hyperplane based sliding control terminal sliding mode controller can provide faster convergence and higher precision control therefore a terminal sliding controller combined with the fuzzy wavelet network which can accurately approximate unknown dynamics of robotic systems by using an adaptive learning algorithm is an attractive control approach for robots in addition the proposed learning algorithm can on line tune parameters of dilation and translation of fuzzy wavelet basis functions and hidden to output weights therefore a robust control law is used to eliminate uncertainties including the inevitable approximation errors resulted from the finite number of fuzzy wavelet basis functions the proposed controller requires no prior knowledge about the dynamics of the robot and no off line learning phase moreover both tracking performance and stability of the closed loop robotic system can be guaranteed by lyapunov theory finally the effectiveness of the fuzzy wavelet network based control approach is illustrated through comparative simulations on a six link robot manipulator

existence and uniqueness results for parabolic equations with robin type boundary conditions in a non regular domain of r3 this paper is devoted to the analysis of the following two space dimensional linear parabolic equation tu x 1 2u x 2 2u f subject to robin type conditions x 1u bu 0 on the lateral boundary where the coefficient b satisfies suitable non degeneracy assumptions the right hand side f of the equation is taken in l 2 the problem is set in a domain of the form t x 1 r 2 0

preserving closedness of operators under summation we give a sufficient condition for the sum of two closed operators to be closed in particular we study the sum of two sectorial operators with the sum of their sectoriality angles greater than we show that if one of the operators admits bounded h calculus and the resolvent of the other operator satisfies a boundedness condition stronger than the standard sectoriality but weaker than the bounded imaginary powers property in the case of umd spaces then the sum is closed we apply the result to the abstract parabolic problem and give a sufficient condition for lp maximal regularity

on fourier multiplier transformations of banach valued functions we obtain analogues of the mihlin multiplier theorem and littlewood paley inequalities for functions with values in a suitable banach space b the requirement on b is that it have the unconditionality property for martingale difference sequences

on time periodic solutions to parabolic boundary value problems of agmon douglis nirenberg type time periodic solutions to partial differential equations of parabolic type corresponding to an operator that is elliptic in the sense of agmon douglis nirenberg are investigated in the whole and half space case we construct an explicit formula for the solution and establish coercive l p estimates the estimates generalize a famous result of agmon douglis and nirenberg for elliptic problems to the time periodic case

singular limit problem for the two dimensional keller segel system in scaling critical space abstract we consider the singular limit problem of the cauchy problem to the keller segel equation in the two dimensional critical space it is shown that the solution to the keller segel system in the scaling critical function space converges to the solution to the drift diffusion system of parabolic elliptic equations the simplified keller segel equation in the critical space strongly as the relaxation time parameter for the proof we show generalized maximal regularity for the heat equations and use it systematically with the sequence of embeddings between the interpolation spaces b q s r 2 and f q s r 2 for the proof of singular limit problem

stability in semilinear problems abstract in the paper we derive results concerning a continuous dependence of solutions on the right hand side for a semilinear operator equation lu g u by assuming that l d l h h h a hilbert space is self adjont with a closed range and g h r is continuous convex on h and g teaux differentiable on d l using these results we obtain theorems on the continuous dependence of solutions on functional parameters for a semilinear problem of the second order u au d u f t u t 0 a e with the dirichlet boundary conditions u 0 u 0 where a 1 and is a functional parameter

on some transmission problems set in a biological cell analysis and resolution abstract some transmission problems are set in bodies with a crown of small thickness e 0 for instance those concerning the conductivity in the biological cell by a natural change of variables we transform them in transmission problems set in two cylindrical bodies 0 and 0 where ln 1 e and then in some general elliptic abstract differential equations p 0 the goal of this work is to give a complete study of these problems p 0 for every 0 existence uniqueness and maximal regularity results are obtained for the classical solutions essentially by using the semigroups theory

wavelet based system identification for nonlinear control compactly supported orthogonal wavelets have certain properties that are useful for system identification and learning control drawing on the rich theory of wavelets we propose a system identification scheme based on orthogonal wavelets better accuracy of estimation can be obtained by adding more terms to the wavelet based identifier and these terms do not alter the coefficients of the existing terms these terms can be selectively added depending upon the region of interest for example we may require more terms in regions where the identified functions vary rapidly we illustrate the concepts by applying the procedure to determine a speed controller for an electric vehicle

adaptive control of linear time invariant systems via a wavelet network and applications to control lorenz chaos abstract compactly supported orthogonal wavelets have certain properties that are useful for controller design in this paper we explore the mechanism of a wavelet controller by integrating the controller with linear time invariant systems lti a necessary condition for effective control is that the compact support of the wavelet network covers the state space where the state trajectories stay closed form bounds on the design parameters of the wavelet controller are derived which guarantee asymptotic stability of wavelet controlled lti systems the same wavelet controller is then applied to the lorenz equations the control objective is to stabilize the lorenz system well into its normally chaotic region at one of its equilibria

sharp interface limit for a stokes allen cahn system we consider the sharp interface limit of a coupled stokes allen cahn system when a parameter epsilon 0 that is proportional to the thickness of the diffuse interface tends to zero in a two dimensional bounded domain for sufficiently small times we prove convergence of the solutions of the stokes allen cahn system to solutions of a sharp interface model where the interface evolution is given by the mean curvature equation with an additional convection term coupled to a two phase stokes system with an additional contribution to the stress tensor which describes the capillary stress to this end we construct a suitable approximation of the solution of the stokes allen cahn system using three levels of the terms in the formally matched asymptotic calculations and estimate the difference with the aid of a suitable refinement of a spectral estimate of the linearized allen cahn operator moreover a careful treatment of the coupling terms is needed

concurrent learning for parameter estimation using dynamic state derivative estimators a concurrent learning cl based parameter estimator is developed to identify the unknown parameters in a nonlinear system unlike state of the art cl techniques that assume knowledge of the state derivative or rely on numerical smoothing cl is implemented using a dynamic state derivative estimator a novel purging algorithm is introduced to discard possibly erroneous data recorded during the transient phase for cl asymptotic convergence of the error states to the origin is established under a persistent excitation condition and the error states are shown to be uniformly ultimately bounded under a finite excitation condition

optimal regularity for a class of singular abstract parabolic equations a general class of singular abstract cauchy problems is considered which naturally arises in applications to certain free boundary problems existence of an associated evolution operator characterizing its solutions is established and is subsequently used to derive optimal regularity results the latter are well known to be important basic tools needed to deal with corresponding nonlinear cauchy problems such as those associated to free boundary problems

interpolation embeddings and traces of anisotropic fractional sobolev spaces with temporal weights we investigate the properties of a class of weighted vector valued lp spaces and the corresponding an isotropic sobolev slobodetskii spaces these spaces arise naturally in the context of maximal lp regularity for parabolic initial boundary value problems our main tools are operators with a bounded h calculus interpolation theory and operator sums

uniqueness theorem on weak solutions to the keller segel system of degenerate and singular types abstract the uniqueness of weak solutions to the keller segel systems of degenerate and singular types is proven in the class of holder continuous functions holder continuity is expected to be an optimal regularity for weak solutions of the degenerate keller segel systems under consideration our proof is based on the vanishing viscosity duality method

bounded h_ infty calculus for pseudodifferential operators and applications to the dirichlet neumann operator operators of the form a a x d k with a pseudodifferential symbol x belonging to the hormander class s m 1 m 0 0 1 and certain perturbations k are shown to possess a bounded h calculus in besov triebel lizorkin and certain subspaces of holder spaces provided a is suitably elliptic applications concern pseudodifferential operators with mildly regular symbols and operators on manifolds of low regularity an example is the dirichlet neumann operator for a compact domain with c 1 r bounda r y

2d navier stokes equation in besov spaces of negative order abstract the navier stokes equation in the bidimensional torus is considered with initial velocity in the besov spaces b p r s 2 2 r and forcing term in l r 0 t b p q s for suitable indices s r p q results of local existence and uniqueness are proven in the case 1 s 2 2 r 0 and of global existence in the case 1 2 s 2 2 r 0

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

a joint functional calculus for sectorial operators with commuting resolvents 1 introduction in this paper we are concerned with h 1 functional calculus in the sense of the construction introduced by mcintosh 23 and developed recently by cowling doust mcintosh and yagi 8 given v in 0 p we will use the notation sv fz 2 c n f0g jarg z j vg to denote the open sector of angle 2v around the half line r let x be a complex banach space given a linear operator a on x we denote by d a n a and r a the domain the kernel and the range of a respectively we also denote by j a the spectrum of a and by r a the resolvent set of a

irregular boundary value problems for second order elliptic differential operator equations in umd banach spaces we prove coerciveness with a defect and fredholmness of nonlocal irregular boundary value problems for second order elliptic differential operator equations in umd banach spaces then we prove coerciveness with a defect in both the space variable and the spectral parameter of the problem with a linear parameter in the equation the results do not imply maximal lp regularity in contrast to previously considered regular case in fact a counterexample shows that there is no maximal lp regularity in the irregular case when studying fredholmness the boundary conditions may also contain unbounded operators in perturbation terms finally application to nonlocal irregular boundary value problems for elliptic equations of the second order in cylindrical domains are presented equations and boundary conditions may contain differential integral parts the spaces of solvability are sobolev type spaces w p q 2 2

sensitivity analysis of control constrained optimal control problems for distributed parameter systems the differential stability of solutions to control constrained quadratic optimal control problems for distributed parameter systems is investigated in this paper the form of the right derivatives of optimal controls for such problems with respect to the real parameter is derived the differential sensitivity of optimal controls with respect to the perturbations of the coefficients of the state equation as well as to the deformations of the domain of integration is considered the right derivative of an optimal control with respect to the parameter is obtained in the form of an optimal control to the auxiliary control constrained optimal control problem

a solution to the problem of l p maximal regularity we give a negative solution to the problem of the l p maximal regularity on various classes of banach spaces including l q spaces with 1 q neq 2 infty

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

an abstract transmission problem in a thin layer i sharp estimates we study an elliptic transmission problem in banach spaces the problem is considered on the juxtaposition of two intervals one of which of small length and models physical phenomena in media constituted by two parts with different physical characteristics we obtain results of existence uniqueness maximal regularity and optimal dependence on the parameter for lp solutions of the problem the main tools of our approach are impedance and admittance operators i e dirichlet to neumann and neumann to dirichlet operators and h functional calculus for sectorial operators in banach spaces

on stokes operators with variable viscosity in bounded and unbounded domains we consider a generalization of the stokes resolvent equation where the constant viscosity is replaced by a general given positive function such a system arises in many situations as linearized system when the viscosity of an incompressible viscous fluid depends on some other quantities we prove that an associated stokes like operator generates an analytic semi group and admits a bounded h calculus which implies the maximal l q regularity of the corresponding parabolic evolution equation the analysis is done for a large class of unbounded domains with w 2 frac1r r boundary for some r d with r q q in particular the existence of an l q helmholtz projection is assumed

on the regularity of a generalized diffusion problem arising in population dynamics set in a cylindrical domain abstract in this paper we consider a generalized diffusion problem arising in population dynamics to this end we study a fourth order operational equation of elliptic type with various boundary conditions we show existence uniqueness and regularity of a classical solution on a cylindrical domain under some necessary and sufficient conditions on the data this elliptic problem is solved in l p a b x p 1 where a b r and x is a umd banach space our techniques use essentially the functional calculus and the semigroup theory

strong solutions of the navier stokes equations for a compressible fluid of allen cahn type in this work we study the navier stokes allen cahn system a combination of the compressible navier stokes equations with an allen cahn phase field description this model describes two phase patterns in a flowing liquid including phase transformations our purpose is to show the existence and uniqueness of local strong solutions for arbitrary initial data part of the proof is based on methods used in a companion paper which investigated the compressible navier stokes equations

persistence of excitation conditions in passive learning control abstract this paper analyzes the stability of both the system state and parameter estimates in passive learning control applications the analysis is valid for any linear in parameter approximator this class of approximators includes many of those commonly used radial basis functions splines wavelets certain fuzzy systems and cerebellar model articulation controller networks stability results are presented for both parametric known model structure with unknown parameters and nonparametric unknown model structure resulting in e approximation error adaptive control applications the main contribution of the article is an analysis of the persistence of excitation conditions required for parameter convergence in addition to a general analysis the article presents a specific analysis pertinent to approximators that are composed of basis elements with local support in particular the analysis shows that as long as a reduced dimension subvector of the regressor vector is persistently exciting then a specialized form of exponential convergence will be achieved this condition is critical since the general persistence of excitation conditions are not practical in most control applications

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

a three domain fuzzy wavelet system for simultaneous processing of time frequency information and fuzziness traditional wavelet system is a two domain time and frequency domains wavelet system 2dws which works only in time and frequency domains the 2dws is not able to treat time frequency information and fuzziness simultaneously for this reason a three domain fuzzy time and frequency domains fuzzy wavelet system 3dfws is proposed where the three domain mechanism provides a solution to handle fuzzy uncertainties and time frequency information together the major advantage of 3dfws is able to use the prior knowledge via the novel fuzzy domain to analyze uncertain data and signals which will enhance the potentials of 2dws experimental and simulation studies show that the performance of the proposed 3dfws is superior to the traditional one for simultaneous processing of time frequency and fuzziness

system identification in frequency domain using wavelets conceptual remarks abstract model identification plays a central role in any activity associated with process operations with control being done on different levels different models are required for the same plant each for a different range of dynamics besides that most identification methods apply to the linear models they also do not allow for selecting a frequency range wavelet based methods have the intrinsic ability to select time and frequency windows and to some extent are also applicable to non linear processes the paper presents an approach in which the wavelet transform is employed for system identification enabling the selection of the particular frequency range of interest we will show the use of some wavelet filters with a property of superior selectivity in the frequency domain and having compact support in the time domain which in turn influences an accurate implementation these properties provide us with a possibility of the measured data analysis in the frequency domain without any loss of information selection of a proper filter allows us to identify the system on a desired frequency range or to identify a number of systems for distinct frequency ranges this is specifically convenient for the systems with dominant modes such as singularly perturbed systems the possibility of selection of the specific frequency range can be utilized for application based identification such as control when only a limited frequency range is required we conclude with a case study where the proposed algorithms are tested and results are presented

complex powers of hypoelliptic pseudodifferential operators abstract complex powers of a class of hypoelliptic pseudodifferential operators in r n as well as their heat kernels are studied an application to the schatten von neumann property of pseudodifferential operators is given

dynamical stability of non constant equilibria for the compressible navier stokes equations in eulerian coordinates in this paper we establish global existence and uniqueness of strong solutions to the non isothermal compressible navier stokes equations in bounded domains the initial data have to be near equilibria that may be non constant due to considering large external forces we are able to show exponential stability of equilibria in the phase space and above all to study the problem in eulerian coordinates the latter seems to be a novelty since in works by other authors global strong lp solutions have been investigated only in lagrangian coordinates eulerian coordinates are even declared as impossible to deal with the proof is based on a careful derivation and study of the associated linear problem

optimization problems with perturbations a guided tour this paper presents an overview of some recent and significant progress in the theory of optimization problems with perturbations we put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems these methods allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of lagrange multipliers is not a singleton may be unbounded or is even empty we give rather complete results for nonlinear programming problems and describe some extensions of the method to more general problems we illustrate the results by computing the equilibrium position of a chain that is almost vertical or horizontal

bounded h infty calculus for a class of nonlocal operators the bidomain operator in the l_q setting the bidomain operator mathbb a a nonlocal operator is studied in a bounded domain omega subset mathbb r d with boundary partial omega of class c 2 within the l q setting for 1 q infty assuming a fairly general framework it is shown that this operator is sectorial invertible on functions with mean zero and admits a bounded h infty calculus with h infty angle 0 in particular it has the property of maximal l p l q regularity and the fractional power domains mathcal d mathbb a alpha are identified furthermore it is shown that mathbb a generates a strongly continuous compact analytic and exponentially stable semigroup on l q 0 omega with q independent purely countable point spectrum sigma mathbb a