on the well posedness for nls in hs abstract in this article we prove the local well posedness of the cauchy problem for the nonlinear schrodinger equation i t u u c u u in h s r n with 0 4 n 2 s and 1 s min n 2 2

strichartz type estimates in mixed besov spaces with application to critical nonlinear schrodinger equations abstract we study the cauchy problem for the nonlinear schrodinger equation with power nonlinearity in the fractional order sobolev space h s r n we consider the case where the nonlinear term is h s critical and the differentiability thereof is less than s we prove the existence of time global solutions of the cauchy problem for small initial data to this end we prove strichartz type estimates for linear inhomogeneous schrodinger equations in mixed besov spaces

the mutual independence hypothesis for categorical data in complex sampling schemes summary this paper is concerned with the analysis of contingency tables which are constructed using categorical data from a complex sampling scheme for the mutual independence hypothesis we extend tavare s 1983 results on two dimensional contingency tables to higher dimensions in particular with respect to pearson s statistic for testing the independence of two variables we strengthen the robustness result proven by tavare thus making it applicable more widely this paper is concerned with the analysis of contingency tables which are constructed using categorical data from a complex sampling scheme i e from data containing some form of between observation dependence which renders the multinomial sampling scheme invalid throughout we are interested in how departures from multinomial sampling affect pearson s statistic x2 which is appropriate for multinomial data in the literature to date two distinct approaches to the problem of categorical data from complex sampling schemes have been discussed first holt scott ewings 1980 demonstrate that for survey data analyses based on x2 can be extremely misleading and propose the one moment adjustment of x2 related references are rao scott 1981 1984 and bedrick 1983 secondly altham 1976 cohen 1976 and brier 1980 model inherent clustering in the sample they show that to avoid invalid analyses some adjustment of x2 is then necessary more recently tavare altham 1983 and tavare 1983 have considered two dimensional contingency tables which are constructed from data generated by markov chains analytic results for the null asymptotic distribution of x2 are obtained and once more it is shown that some adjustment of x2 will usually be necessary however tavare 1983 also obtains a very interesting robustness result let y1 and y2 be independent variables where y1 is an independent trials process and y2 is an arbitrary irreducible first order markov chain then the null asymptotic distribution of x2 for testing the independence of y1 and y2 is x2 on the appropriate degrees of freedom in other words no adjustment of x2 is necessary of the literature cited above the present

modified tests of independence in 2 x 2 tables with spatial data in this paper we suggest two modified chi squared tests of independence in 2 x 2 tables when the data are spatially autocorrelated for this purpose we first derive the asymptotic distribution of standard test statistics based on the sample cross product ratio under mild conditions on the nature of spatial dependence the performance of the tests is assessed by means of a monte carlo experiment in a lattice case from simulation results the need to adjust standard test statistics is apparent when spatial autocorrelation is present in both variables an illustrative application to ecological data is also given

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

assessing the significance of the correlation between two spatial processes modified tests of association based on the correlation coefficient or the covariance between two spatially autocorrelated processes are presented these tests can be used both for lattice and nonlattice data they are based on the evaluation of an effective sample size that takes into account the spatial structure for positively autocorrelated processes the effective sample size is reduced a method for evaluating this reduction via an approximation of the variance of the correlation coefficient is developed the performance of the tests is assessed by monte carlo simulations the method is illustrated by examples from geographical epidemiology

nonexpansive iterations in hyperbolic spaces one of the most active research areas in nonlinear functional analysis is the asymptotics of nonexpansive mappings most of the results however have been obtained in normed linear spaces it is natural therefore to try to develop a theory of nonexpansive iterations in more general infinite dimensional manifolds this is the purpose of the present paper more specifically we propose the class of hyperbolic spaces as an appropriate background for the study of operator theory in general and of iterative processes for nonexpansive mappings in particular this class of metric spaces which is defined in section 2 includes all normed linear spaces and hadamard manifolds as well as the hilbert ball and the cartesian product of hilbert balls in section 3 we introduce co accretive operators and their resolvents and present some of their properties in the fourth section we discuss the concept of uniform convexity for hyperbolic spaces section 5 is devoted to two new geometric properties of infinite dimensional banach spaces theorem 5 6 provides a characterization of banach spaces having these properties in terms of nonlinear accretive operators in sections 6 7 and 8 we study explicit implict and continuous iterations repectively using the same approach in all three sections we illustrate this common approach with the following special case let c be a closed convex subset of a hyperbolic space x p let t c f c be a nonexpansive mapping and let x be a point in c in order to study the iteration t x n 0 1 2 we set z 1 l n x 0 l n t x k clco zj j i l and d inf p y ty y e c the first step is to show that p x k lim p x t x n d this leads to the convergence m of lz when x is uniformly convex and to the weak convergence of z when x is a banach space which is reflexive and strictly convex when t is an averaged mapping we are also able to establish the following triple equality for all k 2 1

serial dependence of observations leading to contingency tables and corrections to chi squared statistics summary the asymptotic behaviour of the pearson goodness of fit test and of the test of independence in 2 x 2 tables is examined when the data are generated by markov dependent sequences the results allow simple quantification of the effects of such serial dependence on some standard test statistics some key wrords hi squared tests contingency tables dependence goodness of fit markov chains reversibilitv 1 introi uction in this paper we discuss the asymptotic behaviour of some standard test statistics in the presence of markov dependence in a sequence of observations in particular we examine the standard pearson x2 goodness of fit test and the 2 x 2 contingency table test for independence

an initial boundary value problem of 2d nonlinear schrodinger equation in a strip abstract the paper studies the initial boundary value problem ibvp of a nonlinear schrodinger equation posed on a strip domain r 0 1 with non homogeneous dirichlet boundary conditions for 0 s 1 2 if the initial condition x y is in sobolev space h s r 0 1 and the boundary condition h x t is in h s r 2 h x t l 2 r 2 1 1 2 1 2 s 2 h l 2 r 2 where h is the fourier transform of h with respect to t and x the local well posedness of the ibvp in c 0 t h s r 0 1 is proved for 1 2 s 5 2 because of compatibility conditions the same local well posedness result holds if an extra condition h x 0 h s 1 2 r is added moreover the global well posedness is obtained for s 1 the basic idea used here relies on the derivation of an integral operator for the non homogeneous boundary data and the proof of strichartz s estimates for this operator after the problem is transformed to finding a fixed point of an integral operator the contraction mapping argument then yields a fixed point using the strichartz s estimates for initial and boundary operators the global well posedness is proved using a priori estimates of the solutions

the asymptotic behavior of a class of nonlinear semigroups in the hilbert ball abstract we study the asymptotic behavior of the nonlinear semigroup generated by a nonexpansive self mapping of a closed convex subset of the hilbert ball equipped with the hyperbolic metric

monotonicity resolvents and yosida approximations of operators on hilbert manifolds abstract monotonicity resolvents and yosida approximations of operators on manifolds of class c 3 are considered strong convergence of difference approximations to differential equations is shown by using resolvents our motivation is to give an elementary step toward constructing nonlinear semigroup theory on infinite dimensional manifolds

inference for discrete markov fields the simplest nontrivial case abstract markov fields provide a general context for describing the strength and structure of spatial interactions the gibbs markov equivalence theorem preston 1974 parameterizes markov fields via their neighborhood structures yielding exponential families in canonical form likelihood inference is therefore apparently straightforward the requisite normalizing constants however are obstreperous even when asymptotic characterizations can be obtained substantial location errors arise during implementation moreover markov fields can exhibit phase transitions and long range interactions thereby creating identifiability problems these issues are illustrated in the simplest nontrivial case the classical ising model of ferromagnetism

limit of the solution of a nonlinear schrodinger equation at blow up time we consider the solution of the equation i v t and 0 where v is defined on 0 t rn and is a nonlinear complex valued function let us denote the function x v t x by v t we suppose that v blows up in the norm h1 at time t under suitable assumptions on and we prove the existence of a limit for v t when t t in appropriate spaces furthermore we specify the behavior of v near blow up time

testing mutual independence between two discrete valued spatial processes a correction to pearson chi squared a common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods in this article we examine the consequences of spatial autocorrelation on pearson s chi squared test of mutual independence between two categorical responses with a general number of classes correspondingly we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation our modified statistic is based on a first order correction factor and thus provides only an approximate test however we show by monte carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest the usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern belgium

the weak lower semicontinuity of the kobayashi distance and its applications in this paper we prove the lower semicontinuity with respect to the weak topology of the kobayashi distance in a bounded convex and open subset of a reflexive banach space we apply this result to the denjoy wolff theorem for condensing mappings in the unit open ball in a strictly convex reflexive banach space with the kadec klee property

local well posedness for the h 2 critical nonlinear schrodinger equation in this paper we consider the nonlinear schrodinger equation iu t delta u lambda u frac 4 n 4 u in r n n ge 5 with lambda in c we prove local well posedness local existence unconditional uniqueness continuous dependence in the critical space dot h 2 r n

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

modifying the t test for assessing the correlation between two spatial processes clifford richardson and hm they require the estimation of an effective sample size that takes into account the spatial structure of both processes clifford et al developed their method on the basis of an approximation of the variance of the sample correlation coefficient and assessed it by monte carlo simulations for lattice and non lattice networks of moderate to large size in the present paper the variance of the sample covariance is computed for a finite number of locations under the multinormality assumption and the mathematical derivation of the definition of effective sample size is given the theoretically expected number of degrees of freedom for the modified t test with renewed modifications is compared with that computed on the basis of equation 2 9 of clifford et al 1989 the largest differences are observed for small numbers of locations and high autocorrelation in particular when the latter is present with opposite sign in the two processes basic references that were missing in clifford et al 1989 are given and inherent ambiguities are discussed

continuous dependence of cauchy problem for nonlinear schrodinger equation in hs abstract we consider the cauchy problem for the nonlinear schrodinger equation i t u u 0 u 1 u u in r n where 0 1 c in h s subcritical and critical case 0 4 n 2 s when 1 s n 2 and 0 when s n 2 we show that the solution depends continuously on the initial value in the standard sense in h s r n if satisfies certain assumptions

hs global well posedness for semilinear wave equations abstract we consider the cauchy problem for semilinear wave equations in r n with n 3 making use of bourgain s method in conjunction with the endpoint strichartz estimates of keel and tao we establish the hs global well posedness with s