a quasilinear parabolic system arising in modelling of catalytic reactors a system of four quasilinear parabolic equations arising in modelling of catalytic reactors is studied the system is coupled in a nonstandard way we prove that the system has unique global solution the asymptotic behavior as t is studied

a pseudo parabolic variational inequality and stefan problem abstract we study existence and uniqueness questions concerning non linear variational inequalities of the type of 1 1a 1 1b in the introduction applications to free boundary problems are also given author

bounds on the spectrum for markov chains and markov processes a generalization of cheeger s inequality we prove a general version of cheeger s inequality for discrete time markov chains and continuous time markovian jump processes both reversible and nonreversible with general state space we also prove a version of cheeger s inequality for markov chains and processes with killing as an application we prove l 2 exponential convergence to equilibrium for random walk with inward drift on a class of countable rooted graphs

ising models on hyperbolic graphs we consider ising models with ferromagnetic interactions and zero external magnetic field on the hyperbolic graph v f where v is the number of neighbors of each vertex and f is the number of sides of each face let tc be the critical temperature and t c sup t tc f 2 where f is the free boundary condition b c gibbs state is the plus b c gibbs state and is the minus b c gibbs state we prove that if the hyperbolic graph is self dual i e v f or if v is sufficiently large how large depends on f e g v 35 suffices for any f 3 and v 17 suffices for any f 17 then 0 t c tc in contrast with that t c tc for ising models on the hypercubic lattice zd with d 2 a result due to lebowitz 22 while whenever t t c f 2 the last result is an improvement in comparison with the analogous statement in refs 28 and 33 in which it was only proved that f 2 when t t c and it remains to show in both papers that f 2 whenever t t c therefore t c and tc divide 0 into three intervals 0 t c t c tc and tc in which but f 2 and f 2 and respectively

canonical double covers of minimal rational surfaces and the non existence of carpets his article delves into the relation between the deformation theory of finite morphisms to projective space and the existence of ropes embedded in projective space with certain invariants we focus on the case of canonical double covers x of a minimal rational surface y embedded in p n by a complete linear series and carpets on y canonically embedded in p n we prove that these canonical double covers always deform to double covers and that canonically embedded carpets on y do not exist this fact parallels the results known for hyperelliptic canonical morphisms of curves and canonical ribbons and the results for k3 double covers of surfaces of minimal degree and enriques surfaces and k3 carpets that canonical double covers of minimal rational surfaces should deform to double covers is not a priori obvious for the invariants of most of these surfaces lie on or above the castelnuovo line thus in principle deformations of such covers could have birational canonical maps in fact many canonical double covers of non minimal rational surfaces do deform to birational canonical morphisms we also map the region of the geography of surfaces of general type corresponding to the surfaces x and we compute the dimension of the irreducible moduli component containing x in certain cases we exhibit some interesting moduli components parameterizing surfaces s with the same invariants as x but with birational canonical map unlike x

deformation of canonical morphisms and the moduli of surfaces of general type in this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space among other things we prove a criterion that determines when a finite map can be deformed to a one to one map we use this criterion to construct new surfaces of general type with birational canonical map for different c 1 2 and the canonical map of the surfaces we construct is in fact a finite birational morphism our general results enable us to describe some new components of the moduli of surfaces of general type we also find infinitely many moduli spaces open image in new window having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism

diffusions and random shadows in negatively curved manifolds abstract let m be a d dimensional complete simply connected negatively curved manifold there is a natural notion of hausdorff dimension for its boundary at infinity this is shown to provide a notion of global curvature or average rate of growth in two probabilistic senses first on surfaces d 2 it is twice the critical drift separating transience from recurrence for brownian motion with constant length radial drift equivalently it is twice the critical for the existence of a green function for the operator 2 r second for any d it is the critical intensity for almost sure coverage of the boundary by random shadows cast by balls appropriately scaled produced from a constant intensity poisson point process

degenerations of k3 surfaces in projective space a k3 carpet s is a double structure on a rational normal scroll such that its dualizing sheaf is trivial and h1 os 0 in this note the authors show that every k3 carpet s can be smoothed i e there exists a flat family over a smooth curve with smooth generic fiber and with a special closed fiber isomorphic top s moreover they study the hilbert scheme of numerical k3 surfaces at the locus parametrizing k3 carpets characterizing those k3 carpets whose corresponding hilbert point is smooth the proof is based on the properties of the hyperelliptic linear systems on k3 surfaces

cyclic coverings deformation and torelli theorem 0 1 in 1968 wavrik 20 studied cyclic branched coverings of compact complex manifolds he obtained a criterion that every small deformation of the total space is again a covering of the base then he applied his result to the case of cyclic coverings of the projective space in 1976 peters 14 and in 1985 konno 11 continued the work of wavrik in two directions they studied explicitly coverings over the hirzebruch surfaces s which have deformations themselves and they proved the infinitesimal torelli theorem for coverings of p and s under suitable assumptions on the branch divisor wavrik wrote his paper at a time where the deformation theory of k kodaira and d spencer for compact complex manifolds had reached a culmination in the meantime there has been developed a deformation theory for other objects in complex analysis too and today we can solve problems like the following

matrix dependent multigrid homogenization for diffusion problems for problems with strongly varying or discontinuous diffusion coefficients we present a method to compute coarse scale operators and to approximately determine the effective diffusion tensor on the coarse scale level the approach is based on techniques that are used in multigrid such as matrix dependent prolongations and the construction of coarse grid operators by means of the galerkin approximation in numerical experiments we compare our multigrid homogenization method with continuous homogenization renormalization and simple averaging approaches

random walks and percolation on trees there is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree it equals the exponential of the hausdorff dimension of the boundary in an appropriate metric its importance for probabilistic processes on a tree is shown in several ways including random walk and percolation where it provides points of phase transition

deformations of canonical double covers abstract in this paper we show that if x is a smooth variety of general type of dimension m 2 for which its canonical map induces a double cover onto y where y is the projective space a smooth quadric hypersurface or a smooth projective bundle over p 1 embedded by a complete linear series then the general deformation of the canonical morphism of x is again canonical and induces a double cover the second part of the article proves the non existence of canonical double structures on the rational varieties above mentioned our results have consequences for the moduli of varieties of general type of arbitrary dimension since they show that infinitely many moduli spaces of higher dimensional varieties of general type have an entire hyperelliptic component this is in sharp contrast with the case of curves or surfaces of lower kodaira dimension

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

escaping geodesics in riemannian surfaces with variable negative curvature abstract in this paper we give a lower bound for the visual hausdorff dimension of the geodesics escaping through different ends of riemannian surfaces with pinched negative curvature this allows to show that in any riemannian surface with pinched negative curvature and infinite area there is a large set of geodesics escaping to infinity

critical phenomena for spitzer s reversible nearest particle systems motivated by several results and open problems concerning harris basic contact process we consider the relationship between the critical behavior of the finite and infinite versions of spitzer s reversible nearest particle systems we show that the critical values for the finite and infinite systems agree but that the behavior of the two systems at the common critical value can differ the nash williams recurrence criterion for reversible markov chains is an important tool used in the proofs of the main results and we give a new treatment of that theory finally we compute several critical exponents for the nearest particle systems

analysis of the simulation of single phase flow through a naturally fractured reservoir a general form of the double porosity model for single phase flow through a naturally fractured reservoir is derived by explicitly considering fluid flow in individual matrix blocks the warren and root model is shown to be a crude approximation to this model the general model consists of a parabolic equation coupled to a series of parabolic equations it is shown that the coupling term can be viewed as a positive semidefinite perturbation of the time derivative and hence it is verified that the model is well posed a finite element method is presented to approximate the solution and optimal order l 2 error estimates are derived

micro structure models of diffusion in fissured media abstract two diffusion models are developed which recognize the local geometry of the individual cells or storage sites and the exchange of flux on the micro scale of these cells the cauchy problems for these model systems are shown to be resolved by holomorphic semigroups and various classical models are obtained as limits of these disributed micro structure models

surface structure of random aggregates on the cayley tree growth through ballistic aggregation and biased diffusion limited aggregation is investigated on the cayley tree for a general branching ratio it is shown that the surface width of a ballistic aggregate remains finite of order one as the cluster mass goes to infinity dla with an attractive bias is treated approximately for non zero bias strength the surface width is asymptotically finite in the limit of isotropic diffusion zero bias a roughening transition occurs which can be described in terms of a single diverging length scale

a transport model with micro and macro structure abstract in this paper we consider solute transport through porous media where the chemical species undergoes a chemical process through the surface of the porous skeleton the problem is modeled by a system of differential equations for the macro concentration u u x t and the micro concentration u u x x t we prove existence and uniqueness and some properties of the set with positive concentration

a free boundary problem for a degenerate parabolic system abstract the degenerate parabolic system 1 1 in the introduction serves as a model for heat conduction in a heterogeneous medium consisting of two components the first component is made up of small pieces suspended in the second component and the second component undergoes a change of phase at a prescribed temperature this phenomenon occurs in a mixture of gravel and wet soil for example melting of frozen soil existence and uniqueness results of weak solutions of the degenerate parabolic problem are shown by employing monotone operator theory local regularity such as continuity and boundedness of the solution is studied a discussion is provided about the mutual interplay of the thermodynamic temperature the temperature in the first component and the conductive temperature the temperature in the second component author