generalized linear models for enzyme kinetic data ruppert cressie and carroll 1989 discuss various models for fitting the michaelismenten equations to data on enzyme kinetics i find it surprising that they do not include among the models they consider generalized linear models glms with an inverse link mccullagh and nelder 1989 chap 8 the advantages of glms over data transformation have often been rehearsed see e g nelder and pregibon 1987 the assumption of normality of errors is extended in glms to include any exponential family and is separated from the transformation required to produce additive effects of the systematic factors the data are analysed on the original scale which often makes more sense than the transformed scale in this paper i analyse the enzyme kinetic data quoted by ruppert et al as their table 8 the data are given here in table 1 the postulated relation their equation 3 1 is

two bubble dynamics for threshold solutions to the wave maps equation we consider the energy critical wave maps equation mathbb r 1 2 rightarrow mathbb s 2 in the equivariant case with equivariance degree k ge 2 it is known that initial data of energy 8 pi k and topological degree zero leads to global solutions that scatter in both time directions we consider the threshold case of energy 8 pi k we prove that the solution is defined for all time and either scatters in both time directions or converges to a superposition of two harmonic maps in one time direction and scatters in the other time direction in the latter case we describe the asymptotic behavior of the scales of the two harmonic maps the proof combines the classical concentration compactness techniques of kenig merle with a modulation analysis of interactions of two harmonic maps in the absence of excess radiation

global regularity of wave maps from r3 1 to surfaces we consider wave maps with smooth compactly supported initial data of small norm from r3 1 to certain 2 dimensional riemannian manifolds and show that they stay smooth globally in time our methods are based on the introduction of a global coulomb gauge as in 17 followed by a dynamic separation as in 8 we then rely on an adaptation of t tao s methods used in his recent breakthrough result 24

multilinear estimates for periodic kdv equations and applications we prove an endpoint multilinear estimate for the xs b spaces associated to the periodic airy equation as a consequence we obtain sharp local well posedness results for periodic generalized kdv equations as well as some global well posedness results below the energy norm

asymptotic stability of large energy harmonic maps under the wave map from 2d hyperbolic spaces to 2d hyperbolic spaces abstract in this paper we prove that the large energy harmonic maps from h 2 to h 2 are asymptotically stable under the wave map equation this work is the last paper in a series of works 46 45 44 which together prove the asymptotic stability for all admissible harmonic maps of arbitrary size without any symmetry assumptions

global well posedness for the three dimensional simplified inertial ericksen leslie systems near equilibrium abstract we study a simplified inertial ericksen leslie system for the nematic liquid crystal flow which can be viewed as a system coupling navier stokes equations and wave map equations we prove the global existence of classical solution with initial data near equilibrium

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

strichartz estimates in similarity coordinates and stable blowup for the critical wave equation we establish strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a time dependent self similar potential as an application we consider the critical wave equation and prove the asymptotic stability of the ode blowup profile in the energy space

subband image coding using watershed and watercourse lines of the wavelet transform reports progress in primitive based image coding using nonorthogonal dyadic wavelets a 3d isotropic wavelet is used to approximate the difference of gaussians d o g operator convolution of the image with dilated versions of the wavelet produces three band pass signals that approximate multiscale smoothed second derivatives an additional convolution of the image with a gaussian shaped low pass wavelet creates a fourth subband signal that preserves low frequency information not described by the three band pass signals the authors show that the original image can be recovered from the watershed and watercourse lines of the three band pass signals plus the lowpass subband signal by thresholding the watershed watercourse representation subsampling the low pass subband and using edge post emphasis the authors achieve data reduction with little loss of fidelity further compression of the watersheds and watercourses is achieved by chain coding their shapes and predictive coding their amplitudes prior to lossless arithmetic coding results are presented for grey level test images at data rates between 0 1 and 0 3 b pixel

construction of type ii blowup solutions for the 1 corotational energy supercritical wave maps abstract we consider the energy supercritical wave maps from r d into the d sphere s d with d 7 under an additional assumption of 1 corotational symmetry the problem reduces to the one dimensional semilinear wave equation t 2 u r 2 u d 1 r r u d 1 2 r 2 sin 2 u we construct for this equation a family of c solutions which blow up in finite time via concentration of the universal profile u r t q r t where q is the stationary solution of the equation and the speed is given by the quantized rates t c u t t l l n l d 1 2 the construction relies on two arguments the reduction of the problem to a finite dimensional one thanks to a robust universal energy method and modulation techniques developed by merle raphael and rodnianski 49 for the energy supercritical nonlinear schrodinger equation then we proceed by contradiction to solve the finite dimensional problem and conclude using the brouwer fixed point theorem

temps d existence pour l equation de klein gordon semi lineaire a donnees petites periodiques we study lower bounds for the maximal time of existence t of a smooth solution to a semi linear klein gordon equation u u f u u with periodic cauchy data of small size if f vanishes at order r at 0 we prove that t c 2 if r 2 t c r 1 log r 3 if r 3 we construct examples showing the optimality of these results for convenient values of r

uniqueness of weak solutions of 1 1 dimensional wave maps in this paper we prove that finite energy distributional solutions to the cauchy problem of wave maps from 1 1 dimensional minkowsky space to any complete riemannian manifold are unique

prediction and tolerance intervals with transformation and or weighting we consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and or weighting we consider the case of normally distributed errors and to a lesser extent the nonparametric case in which the error distribution is unknown quantile estimation here follows standard theory although we introduce a simple computational device for likelihood ratio testing and confidence intervals prediction and tolerance intervals are somewhat more difficult to obtain we show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem improved prediction and tolerance intervals are constructed based on resampling techniques in the tolerance interval case a simple analytical correction is introduced we apply these methods to the prediction of automobile stopping distances and salmon production using respectively a he

finite energy global well posedness of the yang mills equations on mathbb r 1 3 an approach using the yang mills heat flow in this work we propose a novel approach to the problem of gauge choice for the yang mills equations on the minkowski space mathbb r 1 3 a crucial ingredient is the associated yang mills heat flow as this approach avoids the drawbacks of previous approaches it is expected to be more robust and easily adaptable to other settings building on the author s previous results we prove as the first application of our approach finite energy global well posedness of the yang mills equations on mathbb r 1 3 this is a classical result first proved by klainerman and machedon using local coulomb gauges as opposed to their method the present approach avoids the use of uhlenbeck s lemma and hence does not involve localization in space time

structural resolvent estimates and derivative nonlinear schrodinger equations a refinement of a uniform resolvent estimate is given and several smoothing estimates for schrodinger equations in the critical case are induced from it the relation between this resolvent estimate and a radiation condition is discussed as an application of critical smoothing estimates we show a global existence result for derivative nonlinear schrodinger equations

image coding with ridge and valley primitives a high compression image coding scheme is presented based on thread like ridge and valley primitives the use of these primitives is motivated by their success in economically representing image structure the original image is sampled along the primitives using a fractal yardstick method to determine sample spacing the primitives themselves are compressed using vector coding and chain coding reconstruction at the receiver is a scattered data interpolation problem solved here using c sup 0 natural neighbor interpolation results are presented showing data rates between 0 1 and 0 4 b pixel the degradations are discussed and prospects for improvement outlined

a quasi likelihood approach to nonnegative matrix factorization a unified approach to nonnegative matrix factorization based on the theory of generalized linear models is proposed this approach embeds a variety of statistical models including the exponential family within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi likelihood using this framework a family of algorithms for handling signal dependent noise is developed and its convergence proved using the expectation maximization algorithm in addition a measure to evaluate the goodness of fit of the resulting factorization is described the proposed methods allow modeling of nonlinear effects using appropriate link functions and are illustrated using an application in biomedical signal processing

global well posedness and scattering of the 4 1 dimensional maxwell klein gordon equation this article constitutes the final and main part of a three paper sequence ann pde 2016 doi 10 1007 s40818 016 0006 4 oh and tataru 2015 arxiv 1503 01561 whose goal is to prove global well posedness and scattering of the energy critical maxwell klein gordon equation mkg on mathbb r 1 4 for arbitrary finite energy initial data using the successively stronger continuation scattering criteria established in the previous two papers ann pde 2016 doi 10 1007 s40818 016 0006 4 oh and tataru 2015 arxiv 1503 01561 we carry out a blow up analysis and deduce that the failure of global well posedness and scattering implies the existence of a nontrivial stationary or self similar solution to mkg then by establishing that such solutions do not exist we complete the proof

null structure and almost optimal local well posedness of the maxwell dirac system we uncover the full null structure of the maxwell dirac system in lorenz gauge this structure which cannot be seen in the individual compo nent equations but only when considering the system as a whole is expressed in terms of tri and quadrilinear integral forms with cancellations measured by the angles between spatial frequencies in the 3d case we prove frequency localized l 2 space time estimates for these integral forms at the scale invariant regularity up to a logarithmic loss hence we obtain almost optimal local well posedness of the system by iteration

almost optimal local well posedness for the 3 1 dimensional maxwell klein gordon equations this paper contains a detailed study of the local in time regularity properties of the maxwell klein gordon mkg equations the mkg equations represent a physical model for the interaction of a spin 0 particle sometimes referred to as a higgs or scalar field with the classical equations of electrodynamics i e maxwell s equations in terms of the calculus of variations the mkg system consists of the euler lagrange equations associated to the density l 4 f f 1 2 d d where f a a is the electro magnetic field associated to the set a of real valued potentials on the minkowski space d 1a is the corresponding covariant derivative with respect to those potentials and r c is a complex scalar field in terms of the field f the euler lagrange equations read f d 1a d d 0 1b

on the full bosonic string from minkowski space to riemannian manifolds abstract we study the action of the full bosonic string for the domain being two dimensional minkowski space and the target a riemannian manifold its critical points couple the wave map equation to a scalar and a two form potential besides investigating their basic features we establish existence results for the latter

endpoint bilinear restriction theorems for the cone and some sharp null form estimates recently wolff 25 obtained a nearly sharp l 2 bilinear restriction theorem for bounded subsets of the cone in general dimension we obtain the endpoint of wolff s estimate and generalize to the case when one of the subsets is large as a consequence we are able to deduce some nearly sharp l p null form estimates

on the uniqueness of solutions to the gross pitaevskii hierarchy the purpose of this note is to give a new proof of uniqueness of the gross pitaevskii hierarchy first established in 1 in a different space based on space time estimates similar in spirit to those of 2

analyticity and smoothing effect for the korteweg de vries equation with a single point singularity we show that a solution of the cauchy problem for the kdv equation cases partial tv partial 3 x v partial x v 2 0 qquad t in t t x in bbb r v 0 x phi x endcases has a drastic smoothing effect up to real analyticity if the initial data only have a single point singularity at x 0 it is shown that for h s mathbb r s 3 4 data satisfying the condition sum k 0 infty frac a 0 k k x partial x k phi h s infty the solution is analytic in both space and time variable the above condition allows us to take as initial data the dirac delta measure or the cauchy principal value of 1 x the argument is based on the recent progress on the well posedness result by bourgain 2 and kenig ponce vega 20 and a systematic use of the dilation generator 3t partial t x partial x

a transformation weighting model for estimating michaelis menten parameters abstract there has been considerable disagreement about how best to estimate the parameters in michaelis menten models this document points out that many fitting methods are based on different stochastic models being weighted least squares estimates after appropriate transformation the authors propose a flexible model which can be used to help determine the proper transformation and choice of weights the method is illustrated by examples keywords nonlinear regression lineweaver burke transformation

sharp null form estimates for the wave equation null form estimates from dot h alpha 1 times dot h alpha 2 to l q t l r x for the wave equation in bbb r n 1 are studied for n ge4 we obtain the sharp null form estimates except for the endpoints for n 2 3 we obtain the estimates under the additional assumption 4 n q when 2 r

codimension one stability of the catenoid under the vanishing mean curvature flow in minkowski space we study timelike hypersurfaces with vanishing mean curvature in the 3 1 dimensional minkowski space which are the hyperbolic counterparts to minimal embeddings of riemannian manifolds the catenoid is a stationary solution of the associated cauchy problem this solution is linearly unstable and we show that this instability is the only obstruction to the global nonlinear stability of the catenoid more precisely we prove in a certain symmetry class the existence in the neighborhood of the catenoid initial data of a codimension one lipschitz manifold transverse to the unstable mode consisting of initial data whose solutions exist globally in time and converge asymptotically to the catenoid

local existence with minimal regularity for nonlinear wave equations in this paper we consider the cauchy problem of semilinear wave equations which satisfy the null condition we prove that the problem is locally well posed in h s 1 for s in 1 3 dimensions and s in 1 2 dimensions moreover it is shown that the result in 1 2 dimensions is sharp

some remarks on strichartz estimates for homogeneous wave equation abstract we give several remarks on strichartz estimates for homogeneous wave equation with special attention to the cases of l x estimates radial solutions and initial data from the inhomogeneous sobolev spaces in particular we give the failure of the endpoint estimate l t 4 l x for n 2

transformations to symmetry and homoscedasticity abstract this article considers transformations in regression to eliminate skewness and heteroscedasticity of the response we work with the transform both sides model where the relationship between the median response and the independent variables has been identified at least tentatively to preserve this relationship the response and the regression model are transformed in the same way extending the work of others for the location parameter case we propose an estimator that eliminates skewness we also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity both and appear new by comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity we study the question when does the estimator of behave in terms of asymptotic variance as if the regression parameter were known and vice versa the results are of use for telling when the optimal estimator of do

optimal designs for michaelis menten kinetic studies many reactions in enzymology are governed by the michaelis menten equation characterising these reactions requires the estimation of the parameters k m and v m a x which determine the michaelis menten equation and this is done by observing rates of reactions at a set of substrate concentrations the choice of substrate concentrations is investigated by determining bayesian d optimal designs for a model in which residuals have a normal distribution with constant variance designs which focus on alternative quantities such as k m or the ratio v m a x k m are also considered the effect on the optimal designs of alternative error distributions is also considered

smooth interpolation of scattered data by local thin plate splines abstract an algorithm and the corresponding computer program for solution of the scattered data interpolation problem is described given points x k y k f k k 1 n a locally defined function f x y which has the property f x k y k f k k 1 n is constructed the algorithm is based on a weighted sum of locally defined thin plate splines and yields an interpolation function which is differentiable the program is available from the author

sharp local well posedness for a fifth order shallow water wave equation abstract in this paper we prove that the already established local well posedness in the range s 5 4 of the cauchy problem with an initial h s r data for a fifth order shallow water wave equation is extendable to s 5 4 by using the f s space this is sharp in the sense that the ill posedness in the range s 5 4 of this initial value problem is already known

ill posedness for one dimensional wave maps at the critical regularity we show that the wave map equation in r 1 1 is in general ill posed in the critical space 1 2 and the besov space 1 2 1 2 the problem is attributed to the bad behavior of the one dimensional bilinear expression d 1 fdg in these spaces

absence of self similar blow up and local well posedness for the constant mean curvature wave equation abstract in this note we consider the constant mean curvature wave equation in 1 2 dimensions we show that it does not admit any self similar blow up we also remark that the equation is locally well posed for initial data in h 3 2

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

on a model connected with the kirchhoff equation abstract we prove a global existence result in suitable sobolev spaces for the solution of the nonlinear cauchy problem tt u t x 1 r n dy k x y y u t y 2 x u t x 0 u 0 x u 0 x t u 0 x u 1 x 0 where n 3 is the space dimension the initial data are c with compact support in rn and k z is a positive smooth function rapidly decreasing as z our approach is based on the energy estimates combined with the classical von wahl inequalities

on the multilinear restriction and kakeya conjectures we prove d linear analogues of the classical restriction and kakeya conjectures in rd our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians closely related to heat flow we conclude by giving some applications to the corresponding variable coefficient problems and the so called joints problem as well as presenting some n linear analogues for n d

well posedness for a quadratic derivative nonlinear schrodinger system at the critical regularity abstract we consider the cauchy problem for a quadratic derivative nonlinear schrodinger system in sobolev space h s in this paper under the null condition and the mass resonance relation we prove large data local well posedness if the space dimension d 3 and s s c d 2 and s s c or d 1 and s 0 where s c is the scaling critical regularity moreover under the same assumptions we also prove small data global well posedness and scattering in h s if d 3 and s s c our proof is based on a contraction argument using the u p and v p type function spaces

a uniformly accurate multiscale time integrator spectral method for the kleingordonzakharov system in the high plasma frequency limit regime a multiscale time integrator sine pseudospectral mti sp method is presented for discretizing the kleingordonzakharov kgz system with a dimensionless parameter 0 1 which is inversely proportional to the plasma frequency in the high plasma frequency limit regime i e 0 1 the solution of the kgz system propagates waves with amplitude at o 1 and wavelength at o 2 in time and o 1 in space which causes significantly numerical burdens due to the high oscillation in time the main idea of the numerical method is to carry out a multiscale decomposition by frequency mdf to the electric field component of the solution at each time step and then apply the sine pseudospectral discretization for spatial derivatives followed by using the exponential wave integrator in phase space for integrating the mdf and the equation of the ion density component the method is explicit and easy to be implemented extensive numerical results show that the mti sp method converges uniformly and optimally in space with exponential convergence rate if the solution is smooth and uniformly in time with linear convergence rate at o for 0 1 with time step size and optimally with quadratic convergence rate at o 2 in the regime when either o 1 or 0 thus the meshing strategy requirement or scalability of the mti sp for the kgz system in the high plasma frequency limit regime is o 1 and h o 1 for 0 1 which is significantly better than classical methods in the literatures finally we apply the mti sp method to study the convergence rates of the kgz system to its limiting models in the high plasma frequency limit and the interactions of bright solitons of the kgz system and to identify certain parameter regimes that the solution of the kgz system will be blow up in one dimension

long time existence for small amplitude semilinear wave equations we prove that a certain class of semilinear wave equations has global solutions if the initial data is small these existence results rely on mixed norm angular radial space time estimates more specifically we consider power nonlinearities u f p u where f p u u p and 2 t denotes the d alembertian on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i in 1979 john investigated this equation for small initial data in dimension n 3 he proved that if p 1 2 then there is a global solution whereas for p n dimensions and the critical power p c above which global solutions exist should be the positive root of n 1 p 2 c n 1 p c 2 0 sideris proved that for all n the solutions can blow up if p p c recently zhou proved that for n 4 one has global solutions if p p c 2 here we prove that for n 8 one has global solutions if p p c furthermore we proved that for all n one has global solutions if p p c and the initial data are spherically symmetric in the radial case we use l p estimates derived from the explicit form of the fundamental solution using inequalities from classical analysis in the nonradial case we write the fundamental solution in polar coordinates and use fourier integral and special function estimates to handle the angular part

on schrodinger maps we study the question of well posedness of the cauchy problem for schrodinger maps from 2 to the sphere 2 or to 2 the hyperbolic space the idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear schrodinger system of equations and then study this modified schrodinger map system msm we then prove local well posedness of the cauchy problem for the msm with minimal regularity assumptions on the data and outline a method to derive well posedness of the schrodinger map itself from it in proving well posedness of the msm the heart of the matter is resolved by considering truly quatrilinear forms of weighted l2 functions 2002 wiley periodicals inc

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

local and global solutions of the chern simons higgs system abstract we study low regularity solutions of the chern simons higgs equations the lorentz gauge condition makes them hyperbolic equations with the null form under the coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation the div curl decomposition is used in the temporal gauge

double exponential families and their use in generalized linear regression abstract in one parameter exponential families such as the binomial and poisson the variance is a function of the mean double exponential families allow the introduction of a second parameter that controls variance independently of the mean double families are used as constituent distributions in generalized linear regressions in which both means and variances are allowed to depend on observed covariates the theory is applied to two examples a logistic regression and a large two way contingency table in such cases the binomial model of variance is often untrustworthy for example because genuine random sampling was infeasible the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes clumped sampling is just one of many possible causes of overdispersion a habitual source of concern to users of binomial and poisson models this article concerns a class of regression families that allow the statistician to model overdispersion while carrying

a new proof of global existence for the dirac klein gordon equations in one space dimension abstract using a method of s klainerman and m machedon we give a new proof of global existence for the coupled dirac and klein gordon equations in one space dimension

uniqueness for critical nonlinear wave equations and wave maps via the energy inequality we show uniqueness of sufficiently regular solutions to critical semilinear wave equations and wave maps in the a priori much larger class of distribution solutions with finite energy assuming only that the energy is nonincreasing in time 1999 john wiley sons inc

global small solutions to the critical radial dirac equation with potential abstract we solve globally a radial cubic dirac equation perturbed with a small potential with data of small critical norm h 1 the main tool is a new endpoint estimate of the perturbed dirac flow for a class of radial type initial data

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation

finite energy solutions of the yang mills equations in mathbb r 3 1 yang mills equations in r3 1 is well posed in the energy norm this means that for an appropriate gauge condition we construct local unique solutions in a time interval which depends only on the size of the energy norm of the data since the energy norm is left invariant by the yang mills flow the local solution is automatically extended to the entire space time thus our results which settle a problem stated in str imply the well known fundamental regularity result of eardley and moncrief e m that result proved in the temporal gauge requires a higher degree of smoothness for the data our main result proved also in the temporal gauge allows us to extend the concept of solutions to arbitrary finite energy initial data the solutions are automatically unique in the class of solutions obtained by our procedure moreover the global regularity proof given by eardley and moncrief depends in an essential way on the specific properties of the fundamental solution of the wave equation in the flat minkowski space time r3 1 namely the strong huygens principle indeed due mainly to this fact their proof does not seem to extend to general curved space times we have reasons to hope that the very different approach we take here will resolve this difficulty the basic ingredients of our method are 1 the introduction of appropriate local coulomb gauges adapted to the causal structure of the equations 2 an appropriate method of localizing the new space time estimates for

image approximation by variable knot bicubic splines this paper presents a degree of freedom or information content analysis of images in the context of digital image processing as such it represents an attempt to quantify the number of truly independent samples one gathers with imaging devices the degrees of freedom of a sampled image itself are developed as an approximation problem here bicubic splines with variable knots are employed in an attempt to answer the question as to what extent images are finitely representable in the context of digital sensors and computers relatively simple algorithms for good knot placement are given and result in spline approximations that achieve significant parameter reductions at acceptable error levels the knots themselves are shown to be useful as an indicator of image activity and have potential as an image segmentation device as well as easy implementation in ccd signal processing and focal plane smart sensor arrays both mathematical and experimental results are presented

fractal strichartz estimate for the wave equation abstract we consider strichartz estimates for the wave equation with respect to general measures which satisfy certain growth conditions in r 3 1 we obtain the sharp estimate and in higher dimensions improve the previous results

equations d ondes quasilineaires et estimations de strichartz dans cet article notre but est de resoudre des equations d ondes quasilineaires pour des donnees initiales moins regulieres que ce qu imposent les methodes d energie ceci impose de demontrer des estimees de type strichartz pour des operateurs d ondes a coefficients seulement lipschitziens

image surface approximation with irregular samples a method to approximate image surfaces using irregular samples is proposed experimental results show that a high compression ratio can be achieved for simple or complicated images a method accounting for the three dimensional effects is proposed as a way of selecting the irregular samples from the image approximation spline knots are chosen along the contours and the knot replacement is sensitive to the curvature along contours and the density of contours in the near neighborhood in general the proposed method was shown to reduce the reconstruction error both qualitatively and quantitatively and can be used to model the image surface for the purpose of data compression and representation this approach retains key features in images and throws away redundant data

uniqueness of finite energy solutions for maxwell dirac and maxwell klein gordon equations we prove uniqueness of solutions to the maxwell dirac system in the energy space namely we also give a proof for uniqueness of finite energy solutions to the maxwell klein gordon equations which is simpler than that given in 16

uniqueness of generalized solutions to nonlinear wave equations in this paper we consider semilinear wave equations in three space dimensions which satisfy the null condition we prove that a generalized solution of the cauchy problem is unique in the class l 0 t h 2 w 1 0 t h 1

global well posedness of the maxwell dirac system in two space dimensions in recent work grunrock and pecher proved that the dirac klein gordon system in 2d is globally well posed in the charge class data in l 2 for the spinor and in a suitable sobolev space for the scalar field here we obtain the analogous result for the full maxwell dirac system in 2d making use of the null structure of the system found in earlier joint work with damiano foschi we first prove local well posedness in the charge class to extend the solutions globally we build on an idea due to colliander holmer and tzirakis for this we rely on the fact that md is charge subcritical in two space dimensions and make use of the null structure of the maxwell part

global regularity of wave maps from r 2 1 to h 2 small energy we demonstrate that wave maps with smooth initial data and small energy from r2 1 to the lobatchevsky plane stay smooth globally in time our method is similar to the one employed in 18 however the multilinear estimates required are considerably more involved and present novel technical challenges in particular we shall have to work with a modification of the functional analytic framework used in 30 33 18

the wave maps equation the wave maps equation has become a very popular topic in recent years the aim of these expository notes is to present a non technical survey of the ideas and methods which have proved useful in the study of wave maps leading up to the latest results the remaining open problems are also stated and explained

sharp local well posedness results for the nonlinear wave equation this article is concerned with local well posedness of the cauchy problem for second order quasilinear hyperbolic equations with rough initial data the new results obtained here are sharp in low dimension

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

global well posedness for the maxwell klein gordon equation in 4 1 dimensions small energy we prove that the critical maxwell klein gordon equation on r4 1 is globally well posed for smooth initial data which are small in the energy norm this reduces the problem of global regularity for large smooth initial data to precluding concentration of energy

global solutions of the klein gordon schrodinger system with rough data in r 2 1 abstract in this paper we consider the klein gordon schrodinger system with quadratic yakuwa coupling and cubic autointeractions in r 2 1 and prove the existence and uniqueness of global solution for rough data the techniques to be used are adapted from a general scheme originally introduced by j bourgain to split the data into the low and high frequency parts

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