asymptotic properties of linear field equations in minkowski space the aim of this paper is to derive the uniform asymptotic behavior of solutions to linear field equations in minkowski space based on geometric consideration and generalized energy estimates our method relies on a systematic use of the invariance properties of the field equations with respect to the conformal group of the minkowski space and thus departs substantially from the classical method of analyzing the fundamental solution

global existence for a quasilinear wave equation outside of star shaped domains abstract we prove global existence of small amplitude solutions of quasilinear dirichlet wave equations outside of star shaped obstacles in 3 1 dimensions we use a variation of the conformal method of christodoulou since the image of the space time obstacle is not static in the einstein diamond our results do not follows directly from local existence theory as did christodoulou s for the nonobstacle case instead we develop weighted estimates that are adapted to the geometry using them and the energy integral method we obtain solutions in the einstein diamond minus the dime dependent obstacle which pull back to solutions in minkowski space minus and obstacle

clique descriptor of affine invariant regions for robust wide baseline image matching assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small recent image matching algorithms have focused on affine invariant region ir detection and its description to increase the robustness in matching however the distinctiveness of an intensity based region descriptor tends to deteriorate when an image includes homogeneous texture or repetitive pattern to address this problem we investigated the geometry of a local ir cluster also called a clique and propose a new clique based image matching method in the proposed method the clique of an ir is estimated by delaunay triangulation in a local affine frame and the hausdorff distance is adopted for matching an inexact number of multiple descriptor vectors we also introduce two adaptively weighted clique distances where the neighbour distance in a clique is appropriately weighted according to characteristics of the local feature distribution experimental results show the clique based matching method produces more tentative correspondences than variants of the sift based method

remarks on the global sobolev inequalities in the minkowski space rn 1 on demontre des inegalites de sobolev globales sur l espace de minkowski r n 1 le theoreme principal est valable sur des tranches a temps fixe

root properties and convergence rates of median filters median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to additional passes of the median filter in this paper the theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals

the resistant line and related regression methods abstract in a bivariate x y scatterplot the three group resistant line is that line for which the median residual in each outer third of the data ordered on x is zero it was proposed by tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation a dual plot representation of the procedure yields a fast convergent algorithm nonparametric confidence intervals for the slope consistency influence function and asymptotic normality results monte carlo results show that small sample efficiencies exceed their asymptotic values in important cases both breakdown and efficiency are adequate for exploratory work replacing medians by other m estimators of location increases efficiency substantially without affecting breakdown or computational complexity the method thus combines bounded influence and acceptable efficiency with conceptual and computational simplicity

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

global existence of null form wave equations on small asymptotically euclidean manifolds abstract we prove the global existence of the small solutions to the cauchy problem for quasilinear wave equations satisfying the null condition on r 3 g where the metric g is a small perturbation of the flat metric and approaches the euclidean metric like 1 x 2 2 with 1 global and almost global existence for systems without the null condition are also discussed for certain small time dependent perturbations of the flat metric in appendix a

uniform bound of sobolev norms of solutions to 3d nonlinear wave equations with null condition abstract this article concerns the time growth of sobolev norms of classical solutions to the 3d quasi linear wave equations with the null condition given initial data in h s h s 1 with compact supports the global well posedness theory has been established independently by klainerman 13 and christodoulou 3 respectively for a relatively large integer s however the highest order sobolev energy namely the h s energy of solutions may have a logarithmic growth in time in this paper we show that the h s energy of solutions is also uniformly bounded for s 5 the proof employs the generalized energy method of klainerman enhanced by weighted l 2 estimates and the ghost weight introduced by alinhac

autour de la conjecture de l markus sur les varietes affines for any subgroupg of n we introduce some integer discg n called thediscompacity ofg this number measures to what extent the closure ofg is not compact the markus conjecture says that a compact affinely flat unimodular manifold is complete our main result called the discompact theorem is that this conjecture is true under the assumption that the linear holonomy i e the parallel transport has discompacity 1 because discso n 1 1 1 this ensures that a compact flat lorentz manifoldm is geodesically complete hence by a previous result of w goldman and y kamishima gk such am is up to finite covering a solvmanifold this achieves the proof of a bieberbach s theorem for compact lorentz flat manifolds

price s law on nonstationary space times abstract in this article we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t 3 local uniform decay rate price s law price 1972 54 for linear waves as a corollary we also prove price s law for certain small perturbations of the kerr metric this result was previously established by the second author in tataru 65 on stationary backgrounds the present work was motivated by the problem of nonlinear stability of the kerr schwarzschild solutions for the vacuum einstein equations which seems to require a more robust approach to proving linear decay estimates

variational methods in relativistic quantum mechanics this review is devoted to the study of stationary solutions of lin ear and nonlinear equations from relativistic quantum mechanics involving the dirac operator the solutions are found as critical points of an energy func tional contrary to the laplacian appearing in the equations of nonrelativistic quantum mechanics the dirac operator has a negative continuous spectrum which is not bounded from below this has two main consequences first the energy functional is strongly indefinite second the euler lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap between the negative and positive continuous spectra moreover since we work in the space domain r 3 the palais smale condition is not satisfied for these reasons the problems discussed in this review pose a challenge in the calculus of variations the existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems in the first part we consider the fixed eigenvalue problem for models of a free self interacting relativistic particle they allow to describe the localized state of a spin 1 2 particle a fermion which propagates without changing its shape this includes the soler models and the maxwell dirac or klein gordon dirac equations the second part is devoted to the presentation of min max principles al lowing to characterize and compute the eigenvalues of linear dirac operators with an external potential in the gap of their essential spectrum many con sequences of these min max characterizations are presented among them a new kind of hardy like inequalities and a stable algorithm to compute the eigenvalues in the third part we look for normalized solutions of nonlinear eigenvalue problems the eigenvalues are lagrange multipliers lying in a spectral gap we review the results that have been obtained on the dirac fock model which is a nonlinear theory describing the behavior of n interacting electrons in an external electrostatic field in particular we focus on the problematic definition of the ground state and its nonrelativistic limit in the last part we present a more involved relativistic model from quan tum electrodynamics in which the behavior of the vacuum is taken into ac count it being coupled to the real particles the main interesting feature of this model is that the energy functional is now bounded from below providing us with a good definition of a ground state

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

global existence and lifespan for semilinear wave equations with mixed nonlinear terms abstract firstly we study the equation u u q c u p with small data where q c is the critical power of strauss conjecture and p q c we obtain the optimal estimate of the lifespan ln t e e q c q c 1 in n 3 and improve the lower bound of t e from exp c e q c 1 to exp c e q c 1 2 2 in n 2 then we study the cauchy problem with small initial data for a system of semilinear wave equations u v q v t u p in 3 dimensional space with q 2 we obtain that this system admits a global solution above a p q curve for spherically symmetric data on the contrary we get a new region where the solution will blow up

a nonparametric method for fitting a straight line to a noisy image in fitting a straight line to a noisy image the least squares method becomes highly unreliable either when the noise distribution is nonnormal or when it is contaminated by outliers the authors propose a nonparametric method the median of the intercepts to overcome these difficulties this method is free of assumptions about the noise distribution and insensitive to outliers and it does not require quantization of the parameter space thus unlike the hough transform its outcome does not depend on the bin size the method is efficient and its implementation does not involve practical difficulties such as local minima or poor convergence of iterative procedures

long time existence of a class of perturbations of planar shock fronts for second order hyperbolic conservation laws in this paper we consider shock front solutions of a second order hyperbolic conservation law of the form 0 i n i h i 0 where 0 x i x i x 1 n here x 0 0 is the time variable sometimes also denoted by t x x 1 x n r n and h i c d r where d is an open subset of r n 1

cauchy problem of nonlinear schrodinger equation with initial data in sobolev space w s p for p 2 in this paper we consider in r n the cauchy problem for the nonlinear schrodinger equation with initial data in the sobolev space w s p for p n 1 1 p moreover we show that in one space dimension the problem is locally well posed in l p for any 1 p 2

global existence for coupled systems of nonlinear wave and klein gordon equations in three space dimensions we consider the cauchy problem for coupled systems of wave and klein gordon equations with quadratic nonlinearity in three space dimensions we show global existence of small amplitude solutions under certain condition including the null condition on self interactions between wave equations our condition is much weaker than the strong null condition introduced by georgiev for this kind of coupled system consequently our result is applicable to certain physical systems such as the dirac klein gordon equations the dirac proca equations and the klein gordon zakharov equations

decay and scattering of small solutions of pure power nls in r with p 3 and with a potential we prove decay and scattering of solutions of the nonlinear schrodinger equation nls in r with pure power nonlinearity with exponent 3 p 5 when the initial datum is small in u bounded energy and variance in the presence of a linear inhomogeneity represented by a linear potential that is a real valued schwarz function we assume absence of discrete modes the proof is analogous to the one for the translation invariant equation in particular we find appropriate operators commuting with the linearization 2014 wiley periodicals inc

robust image registration by increment sign correlation abstract a novel and robust statistic as a similarity measure for robust image registration is proposed the statistic is named as increment sign correlation because it is based on the average evaluation of incremental tendency of brightness in adjacent pixels it is formalized to be a binary distribution or a gaussian distribution for a large image size through statistical analysis and modeling by utilizing the proposed statistical model for example we can theoretically determine a reasonable value of threshold for verification of matching this sign correlation can also be proved to expectedly have the constant value 0 5 for any uncorrelated images to a template image and then the property of the constancy can be utilized to analyze the high robustness for occlusion the good performance for the case of saturation or highlight can also be proved through theoretical analysis and fundamental experiments a basic algorithm for image scanning search and registration over a large scene is represented with a technique for a fast version by the branch and bound approach many experimental evidences with real images are provided and discussed

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

combined effects of two nonlinearities in lifespan of small solutions to semi linear wave equations this paper investigates the combined effects of two distinctive power type nonlinear terms with parameters p q 1 in the lifespan of small solutions to semi linear wave equations we determine the full region of p q to admit global existence of small solutions at least for spatial dimensions n 2 3 moreover for many p q when there is no global existence we obtain sharp lower bound of the lifespan which is of the same order as the upper bound of the lifespan

matching delaunay graphs this paper describes a bayesian framework for matching delaunay triangulations relational structures of this sort are ubiquitous in intermediate level computer vision being used to represent both voronoi tessellations of the image plane and volumetric surface data our matching process is realised in terms of probabilistic relaxation the novelty of our method stems from its use of a support function specified in terms of face units of the graphs under match in this way we draw on more expressive constraints than is possible at the level of edge units alone in order to apply this new relaxation process to the matching of realistic imagery requires a model of the compatibility between faces of the data and model graphs we present a particularly simple compatibility model that is entirely devoid of free parameters it requires only knowledge of the numbers of nodes edges and faces in the model graph the resulting matching scheme is evaluated on radar images and compared with its edge based counterpart we establish the operational limits and noise sensitivity on the matching of random dot patterns

robust voxel similarity metrics for the registration of dissimilar single and multimodal images in this paper we develop data driven registration algorithms relying on pixel similarity metrics that enable an accurate subpixel rigid registration of dissimilar single or multimodal 2d 3d images gross dissimilarities are handled by considering similarity measures related to robust m estimators in particular a novel robust similarity metric is proposed for comparing multimodal images the proposed robust similarity metrics are compared to the most popular standard similarity metrics on synthetic as well as on real world image pairs showing gross dissimilarities three case studies are considered the registration of single modal and multimodal 3d medical images the matching of multispectral remotely sensed images and the registration of intensity and range images the proposed robust similarity measures compare favourably with the standard non robust techniques

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

local decay of waves on asymptotically flat stationary space times author s tataru daniel abstract in this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t 3 local uniform decay rate for linear waves this work was motivated by open problems concerning decay rates for linear waves on schwarzschild and kerr backgrounds where such a decay rate has been conjectured by r price our results apply to both of these cases

the lifespan of a class of smooth spherically symmetric solutions of the compressible euler equations with variable entropy in three space dimensions we consider smooth three dimensional spherically symmetric eulerian flows of ideal polytropic gases with variable entropy whose initial data are obtained by adding a small smooth perturbation with compact support to a constant state under a natural assumption we obtain precise information on the asymptotic behavior of their lifespan when the size of the initial perturbation tends to 0 this is achieved by the construction and estimate of a suitable approximate flow

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

computer intensive methods in statistical regression this is a survey of modern developments in statistical regression written for the mathematically educated nonstatistician it begins with a review of the traditional theory of least squares curve fitting modern developments in regression theory have developed in response to the practical limitations of the least squares approach recent progress has been made feasible by the electronic computer which frees statisticians from the confines of mathematical tractability topics discussed include robust regression bootstrap measures of variability local smoothing and cross validation projection pursuit mallows c p criterion stein estimation generalized regression for poisson data and regression methods for censored data all of the methods are illustrated with real life examples

on the blowup of classical solutions to the 3 d pressure gradient systems the 3 d pressure gradient system arises from the splitting of the three dimensional compressible euler system which can be reduced into such a nonlinear wave equation t2v div ev v 0 where div ev v i 13 i ev iv i xi 1 i 3 and x x1 x2 x3 in this paper we will establish a blowup result of classical solutions to the 3 d pressure gradient systems when the initial data are of small perturbations with respect to constant states

existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data on considere le probleme aux valeurs initiales pour certaines equations hyperboliques non lineaires d ordre 2

life span of classical solutions to two dimensional fully nonlinear wave equations abstract in two space dimensional case we get the lower bound of the life span of classical solutions to the cauchy problem with small initial data for fully nonlinear wave equations of the form u f u d u d x d u in which f o 3 in a neighbourhood of 0 and u 3 f 0 0 0 0 for the purpose some refined estimates including strichartz estimates are needed in the paper

outlier robust corner preserving methods for reconstructing noisy images the ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother unfortunately they usually seem to be at odds with each other one can only improve one property at the cost of the other by combining m smoothing and least squares trimming the tm smoother is introduced as a means to unify corner preserving properties and outlier robustness to identify edge and corner preserving properties a new theory based on differential geometry is developed further robustness concepts are transferred to image processing in two examples the tm smoother outperforms other corner preserving smoothers a software package containing both the tm and the m smoother can be downloaded from the internet

the small data solutions of general 3 d quasilinear wave equations ii abstract this paper is a continuation of the work in 8 where the authors established the global existence of smooth small data solutions to the general 3 d quasilinear wave equation i j 0 3 g i j u u i j 2 u 0 when the weak null condition holds in the present paper we show that the smooth small data solutions of equation i j 0 3 g i j u u i j 2 u 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied moreover a precise blowup time is completely determined therefore collecting the main results in this paper and 8 we have given a basically complete study on the blowup or global existence of small data solutions to the 3 d quasilinear wave equation i j 0 3 g i j u u i j 2 u 0

decay estimates for schrodinger equations we prove global existence and optimal decay estimates for classical solutions with small initial data for nonlinear nonlocal schrodinger equations the laplacian in the schrodinger equation can be replaced by an operator corresponding to a non degenerate quadratic form of arbitrary signature in particular the davey stewartson system is included in the the class of equations we discuss

global smooth solutions of 3 d null form wave equations in exterior domains with neumann boundary conditions abstract the paper is devoted to investigating long time behavior of smooth small data solutions to 3 d quasilinear wave equations outside of compact convex obstacles with neumann boundary conditions concretely speaking when the surface of a 3 d compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition we prove that the smooth small data solution exists globally provided that the neumann boundary condition on the exterior domain is given one of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself as an application of the main result the global stability to 3 d static compressible chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude

compact affine manifolds with precompact holonomy are geodesically complete abstract this note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

progressively weighted affine adaptive correlation matching for quasi dense 3d reconstruction correlation matching has been widely accepted as a rudimentary similarity measure to obtain dense 3d reconstruction from a stereo pair in particular given a large overlapping area between images with minimal scale differences the correlation results followed by a geometrically constrained global optimisation delivers adequately dense and accurate reconstruction results in order to achieve greater reliability however correlation matching should correctly account for the geometrical distortion introduced by the different viewing angles of the stereo or multi view sensors conventional adaptive least squares correlation alsc matching addresses this by modifying the shape of a matching window iteratively assuming that the distortion can be approximated by an affine transform nevertheless since an image captured from different viewing angle is often not practically identical due to scene occlusions the matching confidence normally deteriorates subsequently it affects the density of the reconstruction results from alsc based stereo region growing algorithms to address this we propose an advanced alsc matching method that can progressively update matching weight for each pixel in an aggregating window using a relaxation labelling technique the experimental results show that the proposed method can improve matching performance which consequently enhances the quality of stereo reconstruction also the results demonstrate its ability to refine a scale invariant conjugate point pair to an affine and scale invariant point pair

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

the radiance obstruction and parallel forms on affine manifolds a manifold m is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine when they are locally linear m is called radiant the obstruction to radiance is a one dimensional class cm with coefficients in the flat tangent bundle of m exterior powers of cm give information on the existence of parallel forms on m especially parallel volume forms as applications various kinds of restrictions are found on the holonomy and topology of compact affine manifolds introduction an affine manifold m is a manifold with a distinguished maximal atlas of charts all of whose coordinate changes are locally affine on such a manifold there is an intrinsic notion of a parallel tensor one whose components in any affine chart are constants more generally there is the notion of a polynomial tensor field of given degree in 1962 l markus conjectured in mk that a compact orientable affine n dimensional manifold has parallel volume form if and only if it is complete meaning that its universal covering is affinely isomorphic to euclidean n space rn the problem of constructing a parallel volume form determines an n dimensional twisted real cohomology class originally studied by j smillie sm2 in this paper we express this class as the nth exterior power of a twisted one dimensional real class which we call the radiance obstruction cm by computing cm in various cohomology theories cech singular de rham and others we are able to exploit cm in several ways to yield more information on the structure of affine manifolds some of these results will appear in a subsequent paper gh3 the basic tool used is a formula proved in 2 6 which expresses the cohomology class of a parallel exterior k form in terms of the k th exterior power of the radiance obstruction akcvf min 2 7 the special case of a parallel volume form on a compact n dimensional manifold m is examined the existence of such a form implies that ancm 0 in 2 8 we show that the affine holonomy group f of such an m cannot preserve a proper affine subspace in gh3 this result will be improved by showing that r preserves no proper semialgebraic subset of rn in 2 10 we show that there tend to be plenty of parallel forms on a compact affine manifold with nilpotent affine holonomy received by the editors may 26 1983 1980 mathematics subject classification primary 57r99 53c05 secondary 53c10 55r25 4c1984 amencan mathematical society 0002 9947 84 1 00 25 per page

robust regression using repeated medians abstract the repeated median algorithm is a robustified u statistic in which nested medians replace the single mean unlike many generalizations of the univariate median repeated median estimates maintain the high 50 breakdown value and can resist the effects of outliers even when they comprise nearly half of the data because they are calculated directly not iteratively repeated median procedures can be used as starting values for iterative robust estimation methods for bivariate linear regression with symmetric errors repeated median estimates are unbiased and fisher consistent and their efficiency under gaussian sampling can be comparable to the efficiency of the univariate median author

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

scattering problem for the nonlinear wave equation in the finite energy and conformal charge space the theory of scattering is studied for the nonlinear wave equation u u 1 u 0 in space dimensions n 3 4 we give a new proof of the asymptotic completeness in the finite energy and conformal charge space for n 3 our method is strong enough to deal with the subconformal power 1 4 n 1 thus we extend earlier results due to baez segal zhou ginibre velo and strauss for this equation

on the decay of solutions to the 2d neumann exterior problem for the wave equation abstract we consider the exterior problem in the plane for the wave equation with a neumann boundary condition and study the asymptotic behavior of the solution for large times for possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data in the paper we prove such an estimate by a combination of the estimate of the local energy decay and decay estimates for the free space solution

life span of small solutions to a system of wave equations abstract we study the cauchy problem with small initial data for a system of semilinear wave equations u v q v t u p in n dimensional space when n 2 we prove that blow up can occur for arbitrarily small data if p q lies below a curve in the p q plane on the other hand we show a global existence result for n 3 which asserts that a portion of the curve is in fact the borderline between global in time existence and finite time blow up we also estimate the maximal existence time and get its upper bound which is sharp at least for n p q 2 2 2 and 3 2 2

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

harmonic maps in three dimensional minkowski space with image near geodesics shatah i sh has constructed global weak solutions of the nonlinear sigma model in h1 2 for arbitrary dimension moreover for the case of maps from four dimensional minkowski space r 3 1 to sphere s 3 he has found an example of smooth symmetric initial data for which the corresponding solution develops singularities on the second order derivatives in finite time showing that the large initial data may contribute the formation of singularities to avoid this situation sideris i si proved the existence of global smooth solution from r 3 1 into an n dimensional complete riemannian manifold n as a perturbation of a special class of harmonic maps geodesic geometrically the solution lies in a small tubular region of a given geodesic on n instead of a small neighborhood of a point on n therefore the initial data is partly small the purpose of this paper is to extend sideris s result to the case where domain is the minkowski space r 2 1 in this case the existence of smooth solution of small amplitude was proved by kovalyov ko but ours is more general since the parameter along the geodesic may vary freely formally a harmonic map from the minkowski space r 2 1 into an n dimensional complete riemannian manifold n h is described as a critical point r 2 1 n of the energy integral

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

threading fundamental matrices we present a new function that operates on fundamental matrices across a sequence of views the operation we call threading connects two consecutive fundamental matrices using the trifocal tensor as the connecting thread the threading operation guarantees that consecutive camera matrices are consistent with a unique 3d model without ever recovering a 3d model applications include recovery of camera ego motion from a sequence of views image stabilization across a sequence and multi view image based rendering

global existence of classical solutions to the minimal surface equation with slow decay initial value in this paper we prove that the global existence of classical solutions to the cauchy problem for the minimal surface equation with slow decay initial value in minkowskian space time