on the total and strict total positivity of the kernels associated with parabolic initial boundary value problems abstract this paper is concerned with the total and strict total positivity of the integral kernels which relate the solutions of parabolic initial boundary value problems to the initial and boundary data maximum principle arguments in conjunction with a characterisation of total positivity in terms of variation diminishing properties are used to prove total positivity of both the initial value and boundary value kernels under mild assumptions similar methods yield strict total positivity when the coefficients appearing in the equation are analytic in either the time or the space variable in this way we extend results of karlin and mcgregor on the total positivity of the kernel associated with the initial data their proofs used the determinantal definition of total positivity and exploited the work of gohberg and krein on the green s functions of sturm liouville operators

entropy and global markov properties we extend refine and give simple proofs of some recent results on the validity of global markov properties for classical spin systems one of the new results is that there is a global markov property that is satisfied by equilibrium states in general the proof of this establishes formulas for the entropy and free energy that show that these quantities are ford dimensional systems given in terms of d 1 dimensional systems furthermore we show that global markov properties imply the absence of some types of symmetry breaking

fibred surfaces varieties isogenous to a product and related moduli spaces a fibration of an algebraic surface s over a curve b with fibres of genus at least 2 has constant moduli iff it is birational to the quotient of a product of curves by the action of a finite group g a variety isogenous to a higher product is the quotient of a product of curves of genus at least 2 by the free action of a finite group theorem b gives a characterization of surfaces isogenous to a higher product in terms of the fundamental group and of the euler number theorem c classifies the groups thus occurring and shows that after fixing the group and the euler number one obtains an irreducible moduli space the result of theorem b is extended to higher dimension in theorem g thus generalizing cf also theorem h results of jost yau and mok concerning varieties whose universal cover is a polydisk theorem a shows that fibrations where the fibre genus and the genus of the base b are at least 2 are invariants of the oriented differentiable structure the main theorems d and e characterize surfaces carrying constant moduli fibrations as surfaces having a zariski open set satisfying certain topological conditions e g having the right euler number the right fundamental group and the right fundamental group at infinity 0 introduction the study of fibrations of a smooth algebraic surface s over a smooth algebraic curve b lies at the heart of the classification theory and of the geometry of algebraic surfaces our main results in this paper theo rems d e concern a topological characterization of surfaces admitting a constant moduli fibration these results are intimately related to a series of variations on the same theme also in higher dimension and to a circle of allied techniques which we present in the course of the paper the first new result we have in this direction and which is presented in section 2 after we recall several known results some classical some quite recent is the following theorem on the dif ferentiable invariance of the genus of fibres cf theorem 2 9 for a more precise statement theorem a let f s b be a fibration of the surface s over a curve b of genus b 2 and with fibre f of genus g 1 assume that s is another smooth compact kahler surface which is orientedly diffeomorphic to s then the subspace of h 1 s corresponding to f h 1 b determines a fibration f s b with

a monte carlo study of the entropy the pressure and the critical behavior of the hard square lattice gas an approximate technique for estimating the entropys with computer simulation methods suggested recently by meirovitch is applied here to the metropolis monte carlo mc simulation of the hard square lattice gas in both the grand canonical and the canonical ensembles the chemical potential calculated by widom s method ands enable one to obtain also the pressurep the mc results are compared with results obtained with pade approximants pa and are found to be very accurate for example at the critical activityz c the mc and the pa estimates fors deviate by 0 5 beyondz c this deviation decreases to 0 01 and comparable accuracy is detected forp we argue that close toz c our results fors andp are more accurate than the pa estimates independent of the entropy study we also calculate the critical exponents by applying fisher s finite size scaling theory to the results for the long range order the compressibility and the staggered compressibility obtained for several lattices of different size at zc the data are consistent with the critical exponents of the plane ising lattice 1 8 1 7 4 and 0 our values for and agree with series expansion and renormalization group results respectively 0 has been obtained also by matrix method studies it differs however from the estimate of baxteret al 0 09 0 05 as far as we know has not been calculated yet

local estimates for entropy densities in coupled map lattices we present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations to do this we use an embedding technique that is a combination of time delay and spatial embedding this embedding allows us to identify the local character of the equations of motion based on this method we present an approximate estimate of the entropy density by the correlation integral

methods for estimating entropy with computer simulation the simple cubic ising lattice an approximate method for estimating entropy with computer simulation suggested recently is applied here together with a new method to the metropolis monte carlo simulation of the simple cubic ising lattice beyond the critical temperature tc the accuracy of the best results for the entropy and the free energy is estimated to be better than 0 07 and 0 05 and at tc itself it is approximately 1 and 0 2 respectively these results are in very good agreement with results obtained with the stochastic models method which is a computer simulation technique and with series expansion estimates the results for the entropy are significantly more accurate than results obtained with the commonly used reversible thermodynamic integration

boundary controllability of sobolev type abstract nonlinear integrodifferential systems sufficient conditions are established for boundary controllability of various classes of sobolev type nonlinear systems including integrodifferential systems in banach spaces the results are obtained using the strongly continuous semigroup of operators and the banach contraction principle examples are provided to illustrate the theory

continuity of information transport in surjective cellular automata we introduce a local version of the shannon entropy in order to describe information transport in spatially extended dynamical systems and to explore to what extent information can be viewed as a local quantity using an appropriately defined information current this quantity is shown to obey a local conservation law in the case of one dimensional reversible cellular automata with arbitrary initial measures the result is also shown to apply to one dimensional surjective cellular automata in the case of shift invariant measures bounds on the information flow are also shown

expressing the entropy of lattice systems as sums of conditional entropies whether a system is to be considered complex or not depends on how one searches for correlations we propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively taken into account compared to the traditional approach for estimating the entropy density in which successive approximations build on step wise extensions of blocks of symbols we show that one can take larger steps when collecting the statistics necessary to calculate the entropy density of the system in one dimension this means that instead of a single sweep over the system in which states are read sequentially one take several sweeps with larger steps so that eventually the whole lattice is covered this means that the information in correlations is captured in a different way and in some situations this will lead to a considerably much faster convergence of the entropy density estimate as a function of the size of the configurations used in the estimate the formalism is exemplified with both an example of a free energy minimisation scheme for the two dimensional ising model and an example of increasingly complex spatial correlations generated by the time evolution of elementary cellular automaton rule 60

analysis and semidiscrete galerkin approximation of a class of nonlinear parabolic optimal control problems abstract this paper presents an optimization problem involving a system governed by a nonlinear partial differential equation with control acting on the domain in the boundary conditions or in the initial condition we describe the galerkin approximation and prove its convergence to the solutions of the initial optimization problem

q gorenstein deformations of nonnormal surfaces let delta subset h be the germ of a nonnormal surface along a proper curve with smooth components such that the high index points of h are semi log terminal and the gorenstein singular points are semi log canonical of embedding dimension at most 4 we describe the sheaf t 1 qg h of bbb q gorenstein deformations of h and we obtain criteria for delta subset h to have bbb q gorenstein terminal smoothings

structural information in two dimensional patterns entropy convergence and excess entropy we develop information theoretic measures of spatial structure and pattern in more than one dimension as is well known the entropy density of a two dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies we show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension we compare and contrast entropy convergence with mutual information and structure factor techniques for quantifying and detecting spatial structure

boundary control problems with nonlinear state equation first order necessary conditions of optimality are obtained for boundary control problems governed by parabolic equations with nonlinear boundary value conditions

compact moduli of plane curves we construct a compactication md of the moduli space of plane curves of degreed we regard a plane curvec p 2 as a surface divisor pair p 2 c and dene md as a moduli space of pairs x d where x is a degeneration of the plane we show that if d is not divisible by 3 the stackmd is smooth and the degenerate surfaces x can be described explicitly msc2000 14h10 14j10 14e30

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

boundary control for the heat equation with non linear boundary condition soit d un domaine borne de r n avec n 1 a frontiere lisse d et soit une normale a d pointant vers l exterieur soit u x t une fonction de x dans d et t l evolution de u est decrite par le probleme aux valeurs limites et initiales suivant u t u dans d 0 t u g u f dans d 0 t u 0 u 0 dans d sous certaines conditions on demontre l existence d une solution faible unique

entropy of phase separated structures abstract the morphology of phase separated structures can often be accurately modelled by level cut gaussian random fields we consider the statistical ensemble of level cut states and its relation to the ising model with a long range interaction the entropy of the ensemble can be numerically calculated using the local cluster method the method is tested on the exact solution of one dimensional ising model with the long range kac potential and illustrated using examples of level cut gaussian fields at least in one dimensional systems the cluster method is easy to apply and produces accurate results

pluricanonical maps of stable log surfaces abstract stable surfaces and their log analogues are the type of varieties naturally occurring as boundary points in moduli spaces we extend classical results of kodaira and bombieri to this more general setting if x is a stable log surface with reduced boundary possibly empty and i is its global index then 4 i k x is base point free and 8 i k x is very ample these bounds can be improved under further assumptions on the singularities or invariants for example 5 k x is very ample if x has semi canonical singularities