hypersurface variations are maximal ii the variation of hodge structure defined by the natural family of hypersurfaces of degreed and dimensionn is maximal if the cohomology has hodge level 1 there is a small list of hypersurfaces of level one which give non maximal variations plane curves of degreed 5 cubics of dimension 3 and 5 and quartic threefolds

complexities in modeling of heterogeneous catalytic reactions abstract catalysts are omnipresent in the chemical industry understanding of catalytic chemical reactions is crucial for a rational development of catalysts the present paper describes approaches for simulating phenomena in heterogeneous catalysis on a molecular level modeling of porous structures and their fractal surfaces will be presented simulation of adsorption and diffusion of reactants and products inside the pores by means of various monte carlo and molecular dynamics algorithms is described followed by quantum chemical methods for calculating reactions on the active centers optimization of pore structures and multiscaling procedures complete the picture

global strong solutions for a class of heterogeneous catalysis models abstract we consider a mathematical model for heterogeneous catalysis in a finite three dimensional pore of cylinder like geometry with the lateral walls acting as a catalytic surface the system under consideration consists of a diffusion advection system inside the bulk phase and a reaction diffusion sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface we assume fickian diffusion with constant coefficients sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure our main result gives sufficient conditions for the existence of a unique global strong l 2 solution to this model thereby extending by now classical results on reaction diffusion systems to the more complicated case of heterogeneous catalysis

on persistent excitation for linear systems with stochastic coefficients a wiener input process is shown to be persistently exciting pe for linear stochastic systems with time varying convergent random coefficients provided asymptotic noise controllability holds a s the pe result is in the sense that the minimum eigenvalue of the integrated outer product of the state process is of o t t being the upper time limit of the integral

continuous time stochastic adaptive control non explosion e consistency and stability abstract for completely observed continuous time constant parameter stochastic linear systems an indirect adaptive control law is presented which subject principally to a weak location hypothesis concerning the true parameter and a persistent excitation hypothesis generates consistent recursive least squares parameter estimates and ensures the system is mean square sample path stable the adaptive control algorith mentails i recursively calculating the least squares estimate of the system parameter and ii recursively generating the lqr feedback gain matrix lying in a set of matrix gains known to contain a stabilizing gain the a s non explosion of the system is a direct consequence of this construction

mathematical analysis of radionuclides displacement in porous media with nonlinear adsorption abstract this paper is devoted to the mathematical analysis of the miscible displacement of a set of radionuclides in a flow occurring in a heterogeneous porous medium the flow is governed by darcy s law and the motion of the chemical species is given by a nonclassical advection diffusion reaction equations system the novelty of the model lies in the adsorption phenomenon that leads to a time derivative of a nonlinear term in these equations a semi discretization method is used to establish the existence of weak solutions to this system uniform l estimates on the solutions are specified

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

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

optimal adaptive control of linear quadratic gaussian systems we consider the problem of adaptively controlling an unknown linear gaussian system with a standard quadratic cost criterion including a control cost by means of a counterexample it is shown that a commonly mentioned adapative control scheme can lead to severe problems to overcome this a new adaptive control law based on biasing the usual least squares parameter estimation criterion with a term favoring parameters associated with lower optimal costs is introduced a salient feature of this adaptive control scheme is its imperviousness to the closed loop identification problem properties such as closed loop system identification convergence of the adaptive control law to an optimal control law overall stability of the controlled system and optimality with respect to the long term average cost of the adaptive controller are proved

existence of analytic solutions for the classical stefan problem we prove that under mild regularity assumptions on the initial data the two phase classical stefan problem admits a unique solution that is analytic in space and time

adaptive continuous time linear quadratic gaussian control the adaptive linear quadratic gaussian control problem where the linear transformation of the state a and the linear transformation of the control b are unknown is solved assuming only that a b is controllable and a q sub 1 sup 1 2 is observable where q sub 1 determines the quadratic form for the state in the integrand of the cost functional a weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable and observable a diminishing excitation is used with the adaptive control to ensure that the family of estimates is strongly consistent a lagged certainty equivalence control using this family of estimates is shown to be self optimizing for an ergodic quadratic cost functional

a universality advantage of stochastic excitation signals for adaptive control abstract adaptive control schemes usually depend on estimation of system parameters which in turn depends excitation of modes associated with these parameters such excitation is supplied by plant noise the adaptive control signal itself and any external excitation such as a reference signal in this note it is shown that there is a universality advantage for any externally applied signal to be stochastic rather than deterministic the crucial property of a stochastic signal exploited in this note is its unpredictability by any causal system such as an adaptive control scheme when such unpredictable signals excite an adaptive control scheme there is no need to deliberately constrain the adaptation to be slow or excitation maintaining to ensure adequate identification

half twists and the cohomology of hypersurfaces a hodge structure v of weight k on which a cm field acts defines under certain conditions a hodge structure of weight k 1 its half twist in this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a hodge substructure in the cohomology we determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces we use our results to prove the existence of a kuga satake correspondence for certain cubic 4 folds

on the usefulness of persistent excitation in arx adaptive tracking the usefulness of persistent excitation is well known in the control community thanks to a persistently excited adaptive tracking control we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional arx framework we establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters a central limit theorem and a law of iterated logarithm are also provided all this asymptotical analysis is related to the schur complement of a suitable limiting matrix

global existence uniqueness and stability for nonlinear dissipative bulk interface interaction systems abstract we show global well posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk interface systems they correspond to thermodynamically consistent gradient structure models of bulk interface interaction the setting includes nonlinear slow and fast diffusion in the bulk and nonlinear coupled diffusion on the interface additional driving mechanisms can be included and non smooth geometries and coefficients are admissible to some extent an important application are volume surface reaction diffusion systems with nonlinear coupled diffusion