asymptotic completeness for n body stark hamiltonians we prove asymptotic completeness for short and long rangen body stark hamiltonians with local singularities of at most coulomb type our results include the usual models for atoms and molecules

texture discrimination based upon an assumed stochastic texture model a new approach to texture discrimination is described this approach is based upon an assumed stochastic model for texture in imagery and is an approximation to the statistically optimum maximum likelihood classifier the construction and properties of the stochastic texture model are described and a digital filtering implementation of the resulting maximum likelihood texture discriminant is provided the efficacy of this approach is demonstrated through experimental results obtained with simulated texture data a comparison is provided with more conventional texture discriminants under identical conditions the implications to texture discrimination in realworld imagery are discussed

3 d shape from a shaded and textural surface image a new 3d texture model is developed by considering the scene image as the superposition of a random texture image on a smooth shaded image the whole image is analyzed using a patch by patch process each patch is assumed to be a tilted and slanted texture plane a modified reflectance map function is applied to describe the deterministic part and the fractional differencing periodic model is chosen to describe the random texture because of its good performance in texture synthesis and its ability to represent the coarseness and the pattern of the surface at the same time an orthographical projection technique is developed to deal with this particular random model which has a nonisotropically distributed texture pattern for estimating the parameter a hybrid method that uses both the least square and the maximum likelihood estimates is applied directly to the given intensity function by using these parameters the synthesized image is obtained and used to reconstruct the original image

technical communique who needs qp for linear mpc anyway conventional mpc uses quadratic programming qp to minimise on line a cost over n linearly constrained control moves however stability constraints often require the use of large n thereby increasing the on line computation rendering the approach impracticable in the case of fast sampling here we explore an alternative that requires a fraction of the computational cost which increases only linearly with n and propose an extension which in all but a small class of models matches to within a fraction of a percent point the performance of the optimal solution obtained through qp the provocative title of the paper is intended to point out that the proposed approach offers a very attractive alternative to qp based mpc

strichartz estimates for the schrodinger equation with time periodic ln 2 potentials abstract we prove strichartz estimates for the schrodinger operator h v t x with time periodic complex potentials v belonging to the scaling critical space l x n 2 l t in dimensions n 3 this is done directly from estimates on the resolvent rather than using dispersive bounds as the latter generally require a stronger regularity condition than what is stated above in typical fashion we project onto the continuous spectrum of the operator and must assume an absence of resonances eigenvalues are permissible at any location in the spectrum including at threshold energies provided that the associated eigenfunction decays sufficiently rapidly

local time decay of solutions to schrodinger equations with time periodic potentials let h t v t x be a time dependent schrodinger operator on l2 r3 we assume that v t x is 2 periodic in time and decays sufficiently rapidly in space let u t 0 be the associated propagator for u0belonging to the continuous spectral subspace of l2 r3 for the floquet operator u 2 0 we study the behavior of u t 0 u0as t in the topology of x weighted spaces in the form of asymptotic expansions generically the leading term is t 3 2b1u0 here b1is a finite rank operator mapping functions of xto functions of tand x periodic in t if n zis a threshold resonance of the corresponding floquet hamiltonian i t h t the leading behavior is t 1 2b0u0 the point spectral subspace for u 2 0 is finite dimensional if u 2 0 j e i2 pi lambda j j then u t 0 j represents a quasi periodic solution

modeling textured images using generalized long correlation models the long correlation lc models are a general class of random field rf models which are able to model correlations extending over large image regions with few model parameters the lc models have seen limited use due to lack of an effective method for estimating the model parameters in this work we develop an estimation scheme for a very general form of this model and demonstrate its applicability to texture modeling applications the relationship of the generalized lc models to other classes of rf models namely the simultaneous autoregressive sar and markov random field mrf models is shown while it is known that the sar model is a special case of the lc model we show that the mrf model is also encompassed by this model consequently the lc model may be considered as a generalization of the sar and mrf models

a unified approach to optimal image interpolation problems based on linear partial differential equation models the unified approach to optimal image interpolation problems presented provides a constructive procedure for finding explicit and closed form optimal solutions to image interpolation problems when the type of interpolation can be either spatial or temporal spatial the unknown image is reconstructed from a finite set of sampled data in such a way that a mean square error is minimized by first expressing the solution in terms of the reproducing kernel of a related hilbert space and then constructing this kernel using the fundamental solution of an induced linear partial differential equation or the green s function of the corresponding self adjoint operator it is proved that in most cases closed form fundamental solutions or green s functions for the corresponding linear partial differential operators can be found in the general image reconstruction problem described by a first or second order linear partial differential operator an efficient method for obtaining the corresponding closed form fundamental solutions or green s functions of the operators is presented a computer simulation demonstrates the reconstruction procedure

long correlation image models for textures with circular and elliptical correlation structures a class of random field model having long correlation characteristics is introduced unlike earlier approaches in long correlation models the correlation structure is isotropic or elliptical in this new class of random field model the new model has an advantage of modeling diverse real textures with less than five model parameters further the model parameters match with intuitive attributes of textures such as smoothness pattern size elongation or orientation of patterns the new long correlation models are based on the fractional differencing of a two dimensional 2 d autoregressive polynomial defined by eight symmetric neighbors and they are either persistent or periodic models depending whether the roots of the polynomial are real or imaginary a comprehensive three step algorithm for parameter estimation is developed and the statistical properties of the estimators are also discussed the validity of the new model in modeling textures is tested by synthesizing images from manually selected parameters as well as parameters estimated from real textures it is shown that an image with desired attributes can be synthesized by selecting proper values of the parameters further it is shown that the models introduced can be used in modeling wide range of textures by synthesizing images resembling real textures from estimated parameters

time optimal model predictive control for linear systems based on ellipsoidal and polytopic sets time optimal model predictive control mpc strategies are investigated in this paper we first derive a series of controllable sets described by ellipsoids or convex polytopes offline then obtain

synthesis and estimation of random fields using long correlation models random field models have arisen in important applications in many diverse fields including image synthesis and analysis the automatic description and processing of images is limited by the types of underlying models that are hypothesized for the image hence new random field models and associated techniques are developed the new class of models includes the traditional simultaneous autoregressive and moving average models but extends these to comprise a substantially larger new class thus new image textures are representable with convenient small order parameterizations in particular representations with significant correlations between distant locations are achieved the algorithms for synthesis and estimation however require only about the same amount of time as the classical models the development is facilitated by a new mathematical formulation suitable for problems involving high dimensional transformations

time asymptotics of the schrodinger wave function in time periodic potentials we study the transition to the continuum of an initially bound quantum particle in d d 1 2 3 subjected for t 0 to a time periodic forcing of arbitrary magnitude the analysis is carried out for compactly supported potentials satisfying certain auxiliary conditions it provides complete analytic information on the time laplace transform of the wave function from this comprehensive time asymptotic properties borel summable transseries follow we obtain in particular a criterion for whether the wave function gets fully delocalized complete ionization this criterion shows that complete ionization is generic and provides a convenient test for particular cases when satisfied it implies absence of discrete spectrum and resonances of the associated floquet operator as an illustration we show that the parametric harmonic perturbation of a potential chosen to be any nonzero multiple of the characteristic function of a measurable compact set has this property

resonance theory for schrodinger operators resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods a general theory is developed with new and weaker conditions allowing for perturbations of threshold eigenvalues and relaxed fermi golden rule the exponential decay rate of resonances is addressed its uniqueness in the time dependent picture is shown in certain cases the relation to the existence of meromorphic continuation of the properly weighted green s function to time dependent resonance is further elucidated by giving an equivalent time dependent asymptotic expansion of the solutions of the schrodinger equation

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

texture roughness analysis and synthesis via extended self similar ess model the 2d fractional brownian motion fbm model provides a useful tool to model textured surfaces whose roughness is scale invariant to represent textures whose roughness is scale dependent we generalize the fbm model to the extended self similar ess model in this research we present an estimation algorithm to extract the model parameters from real texture data furthermore a new incremental fourier synthesis algorithm is proposed to generate the 2d realizations of the ess model finally the estimation and rendering methods are combined to synthesize real textured surfaces

a new approach for subset 2 d ar model identification for describing textures this paper addresses the problem of identification of appropriate autoregressive ar components to describe textural regions of digital images by a general class of two dimensional 2 d ar models in analogy with univariate time series the proposed technique first selects a neighborhood set of 2 d lag variables corresponding to the significant multiple partial auto correlation coefficients a matrix is then suitably formed from these 2 d lag variables using singular value decomposition svd and orthonormal with column pivoting factorization qrcp techniques the prime information of this matrix corresponding to different pseudoranks is obtained schwarz s 1978 information criterion sig is then used to obtain the optimum set of 2 d lag variables which are the appropriate autoregressive components of the model for a given textural image a four class texture classification scheme is illustrated with such models and a comparison of the technique with the work of chellappa and chatterjee 1985 is provided

ionization of coulomb systems in mathbb r 3 by time periodic forcings of arbitrary size we analyze the long time behavior of solutions of the schrodinger equation i psi t delta b r v t x psi x in mathbb r 3 r x describing a coulomb system subjected to a spatially compactly supported time periodic potential v t x v t 2 x with zero time average

piecewise fractional brownian motion starting from fractional brownian motion fbm of unique parameter h a piecewise fractional brownian motion pfbm of parameters h sub o h sub i and spl gamma is defined this new process has two spectral regimes it behaves like an fbm of parameter h sub o for low frequencies spl omega spl gamma and like an fbm of parameter h sub i for high frequencies spl omega spl ges spl gamma when h sub o h sub i or for limit cases spl gamma spl rarr 0 and spl gamma spl rarr spl infin pfbm becomes classical fbm it is shown that pfbm is a continuous gaussian and nonstationary process having continuous gaussian and stationary increments namely piecewise fractional gaussian noises the asymptotic self similarity of pfbm is shown according to the considered regime at large scale the process is self similar with parameter h sub o and with parameter h sub i at low scale

ellipsoidal techniques for reachability analysis internal approximation for the reach tube of a linear time varying system with ellipsoidal bounds on the control variable consider the following approximation problem find a tight ellipsoid valued tube inside the reach tube that touches it along any prespecified smooth curve on the boundary we construct this ellipsoidal tube and show that if the given curve is itself a system trajectory the tube can be calculated recursively with minimum computational burden

maximum likelihood estimation of the parameters of discrete fractionally differenced gaussian noise process a maximum likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced gaussian noise from an observation set of finite size n the procedure does not involve the computation of any matrix inverse or determinant it requires n sup 2 2 o n operations the expected value of the loglikelihood function for estimating the parameter d of fractionally differenced gaussian noise which corresponds to a parameter of the equivalent continuous time fractional brownian motion related to its fractal dimension is shown to have a unique maximum that occurs at the true value of d a cramer rao bound on the variance of any unbiased estimate of d obtained from a finite sized observation set is derived it is shown experimentally that the maximum likelihood estimate of d is unbiased and efficient when finite size data sets are used in the estimation procedure the proposed procedure is extended to deal with noisy observations of discrete fractionally differenced gaussian noise

spectral theory of time periodic many body systems we study the spectrum of the monodromy operator for an n body quantum system in a time periodic external field with time mean equal to zero this includes ac stark and circularly polarized fields and pair potentials with a local singularity up to and including the coulomb singularity in the framework of floquet theory we prove a local commutator estimate and use it to prove a limiting absorption principle for the floquet hamiltonian as well as exponential decay estimates on non threshold eigenfunctions these two results are then used to obtain a second order perturbation theory for embedded eigenvalues the principal tool is a new extended mourre theory

quantitatively investigating the locally weak stationarity of modified multifractional gaussian noise a b s t r a c t we suggest that there exists a critical point h 0 70 of the local holder exponent h t for describing the weak stationary stationary for short property of the modified multifractional gaussian noise mmgn from the point of view of engineering more precisely when h t 0 70 for t 0 the stationarity of mmgn is conditional relying on the variation ranges of h t when h t 0 70 on the other side mmgn is unconditionally stationary yielding a consequence that short memory mmgn is stationary in addition for h t 0 70 we introduce the concept of stationary range denoted by hmin hmax it means that corr r h t1 r h t2 0 70 if h t1 h t2 hmin hmax where r h t1 and r h t2 are the autocorrelation functions of mmgn with h t1 and h t2 for t1 t2 respectively and corr r h t1 r h t2 is the correlation coefficient between r h t1 and r h t2 we present a set of stationary ranges which may be used for a quantitative description of the local stationarity of mmgn a case study is demonstrated for applying the present method to testing the stationarity of a real traffic trace

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

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

time decay for solutions of schrodinger equations with rough and time dependent potentials in this paper we establish dispersive estimates for solutions to the linear schrodinger equation in three dimensions frac 1 i partial t psi triangle psi v psi 0 qquad psi s f 0 1 where v t x is a time dependent potential that satisfies the conditions sup t v t cdot l frac 3 2 mathbb r 3 sup x in mathbb r 3 int mathbb r 3 int infty infty frac v hat tau x x y d tau dy c 0 here c0 is some small constant and v hat tau x denotes the fourier transform with respect to the first variable we show that under these conditions 0 1 admits solutions l t l2x 3 l2t l6x 3 for any f l2 3 satisfying the dispersive inequality psi t infty le c t s frac32 f 1 text for all times t s 0 2 for the case of time independent potentials v x 0 2 remains true if int mathbb r 6 frac v x v y x y 2 dxdy 4 pi 2 text and v mathcal k sup x in mathbb r 3 int mathbb r 3 frac v y x y dy 4 pi we also establish the dispersive estimate with an e loss for large energies provided v mathcal k v 2 infty

two dimensional interpolation by generalized spline filters based on partial differential equation image models optimal image interpolation schemes based on partial differential equation pde models for the image signal are presented these schemes use the generalized spline interpolation approach minimum mean square error mmse is achieved given an image pde model and a finite set of the image data samples two new types of two dimensional 2 d interpolation techniques are presented for the implementation of these schemes these are the generalized cardinal spline digital filter and the generalized b spline interpolator computer simulations are described in addition to possessing a meaningful theoretical basis the results show a practical improvement of the approach presented over the existing schemes

growth of sobolev norms in linear schrodinger equations with quasi periodic potential in this paper we consider the following problem let iu t u v x t u 0 be a linear schrodinger equation periodic boundary conditions where v is a real bounded real analytic potential which is periodic in x and quasi periodic in t with diophantine frequency vector denote s t the corresponding flow map thus s t preserves the l 2 norm and our aim is to study its behaviour on h s t d s 0 our main result is the growth in time is at most logarithmic thus if h s then more precisely is proven in 1d and 2d when v is small we also exhibit examples showing that a growth of higher sobolev norms may occur in this context and is thus essentially best possible

texture boundary detection based on the long correlation model the problem of detecting texture boundaries without assuming any knowledge on the number of regions or the types of textures is considered texture boundaries are often regarded as better features than intensity edges because a large class of images can be considered a composite of several different texture regions an algorithm is developed that detects texture boundaries at reasonably high resolution without assuming any prior knowledge on the texture composition of the image the algorithm utilizes the long correlation texture model with a small number of parameters to characterize textures the parameters of the model are estimated by a least squares method in the frequency domain the existence and the location of texture boundary is estimated by the maximum likelihood method the algorithm is applied to several different images and its performance is shown by examples experimental results show that the algorithm successfully detects texture boundaries without knowing the number of types of textures in the image