the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

two level method based on finite element and crank nicolson extrapolation for the time dependent navier stokes equations a fully discrete two level finite element method the two level method is presented for solving the two dimensional time dependent navier stokes problem the method requires a crank nicolson extrapolation solution u h tau 0 p h tau 0 on a spatial time coarse grid j h tau 0 and a backward euler solution u h tau p h tau on a space time fine grid j h tau the error estimates of optimal order of the discrete solution for the two level method are derived compared with the standard crank nicolson extrapolation method the one level method based on a space time fine grid j h tau the two level method is of the error estimates of the same order as the one level method in the h1 norm for velocity and the l2 norm for pressure however the two level method involves much less work than the one level method

nonconforming two level discretization of stream function form of the navier stokes equations in this report we analyze a two level finite element method for the stream function formulation of the stationary navier stokes equations this report presents the two level algorithm and error analysis for the case of nonconforming elements when approximating a nonsingular solution of the stream function formulation of the navier stokes equation

the logarithmic minkowski problem in analogy with the classical minkowski problem necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone volume measure of the unit ball of a finite dimensional banach space

a simplified two level method for the steady navier stokes equations abstract a simplified two level method for solving the steady two dimensional incompressible navier stokes equations is investigated in this article the simplified two level method involves solving one small nonlinear navier stokes problem on the coarse mesh and one linear stokes problem hence linear with positive definite symmetric part on the fine mesh the uniform optimal error estimates with respect to large for the standard galerkin method and the two level method are proven finally some numerically tests to confirm the theoretical results of the simplified two level method and the standard galerkin method are provided

convexity of level sets of minimal graph on space form with nonnegative curvature abstract for the minimal graph defined on a convex ring in the space form with nonnegative curvature we obtain the regularity and the strict convexity about its level sets by the continuity method

uniqueness of solutions to lp christoffel minkowski problem for p 1 abstract l p christoffel minkowski problem arises naturally in the l p brunn minkowski theory it connects both curvature measures and area measures of convex bodies and is a fundamental problem in convex geometric analysis since the lack of firey s extension of brunn minkowski inequality and constant rank theorem for p 1 the existence and uniqueness of l p brunn minkowski problem are difficult problems in this paper we prove a uniqueness theorem for solutions to l p christoffel minkowski problem with p 1 and constant prescribed data our proof is motivated by the idea of brendle choi daskaspoulos s work on asymptotic behavior of flows by powers of the gaussian curvature one of the highlights of our arguments is that we introduce a new auxiliary function z which is the key to our proof

on entropy of pyramid structures an information theoretic analysis of multiresolution pyramid structures is presented the analysis is carried out using the concept of spectral entropy which for gaussian sources is linearly related to the differential entropy the spectral entropy is used to define the spectral roughness measure that in turn is an indicator of the amount of memory in a source the more the memory in a source the greater is the value of its spectral roughness measure the spectral roughness measure also plays an important role in lower bounding the rate distortion function the main result is that the spectral roughness measure of a pyramid structure is less than that of the original fullband process this means that substantial reduction in bits can be obtained by merely representing a source as a pyramid simulations using one dimensional and two dimensional sources verifying these claims are presented

power convexity of a class of elliptic equations involving the hessian operator in a 3 dimensional bounded convex domain abstract in this paper we are concerned with power convexity of a class of fully nonlinear elliptic equations involving the hessian operator in a bounded and strictly convex domain in r 3 we use the constant rank theorem and deformation technique to prove that some power of the smooth admissible solution is strictly convex as a corollary we deduce that all the level sets of the solution are strictly convex

convexity of solutions and brunn minkowski inequalities for hessian equations in r3 by using minkowski addition of convex functions we prove convexity and rearrangement properties of solutions to some hessian equations in r 3 and brunn minkowski and isoperimetric inequalities for related functionals

the planar orlicz minkowski problem in the l1 sense abstract in this paper we solve l p minkowski problem for l 1 data and all p 0 and orlicz minkowski problem with two nonlinear terms in l 1 sense a byproduct is the blaschke santalo inequality which was previously established for only constant data and now is shown to hold for l 1 data

preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite linear systems for the positive semidefinite system of linear equations of a block two by two structure by making use of the hermitian skew hermitian splitting iteration technique we establish a class of preconditioned hermitian skew hermitian splitting iteration methods theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system moreover the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly numerical examples further confirm the correctness of the theory and the effectiveness of the method

predictive classified vector quantization a vector quantization scheme based on the classified vector quantization cvq concept called predictive classified vector quantization pcvq is presented unlike cvq where the classification information has to be transmitted pcvq predicts it thus saving valuable bit rate two classifiers one operating in the hadamard domain and the other in the spatial domain were designed and tested the classification information was predicted in the spatial domain the pcvq schemes achieved bit rate reductions over the cvq ranging from 20 to 32 for two commonly used color test images while maintaining the same acceptable image quality bit rates of 0 70 0 93 bits per pixel bpp were obtained depending on the image and pcvq scheme used

a microscopic convexity principle for nonlinear partial differential equations we study microscopic convexity property of fully nonlinear elliptic and parabolic partial differential equations under certain general structure condition we establish that the rank of hessian 2u is of constant rank for any convex solution u of equation f 2u u u x 0 the similar result is also proved for parabolic equations some of geometric applications are also discussed

convexity estimates for the solutions of a class of semi linear elliptic equations abstract in this paper we are concerned with convexity estimates for solutions of a class of semi linear elliptic equations involving the laplacian with power type nonlinearities we consider auxiliary curvature functions which attain their minimum values on the boundary and then establish lower bound convexity estimates for the solutions then we give two applications of these convexity estimates we use the deformation method to prove a theorem concerning the strictly power concavity properties of the smooth solutions to these semi linear elliptic equations finally we give a sharp lower bound estimate of the gaussian curvature for the solution surface of some specific equation by the curvatures of the domain s boundary

error estimate for a simple two level discretization of stream function form of the navier stokes equations abstract in this paper a simplified two level finite element method with backtracking is proposed for the stream function formulation of the navier stokes equations this method requires the solution of two small systems on the coarse space and one symmetric positive linear problem on the refined space error analysis for the case of clough tocher or bogner fox schmit elements is presented and the optimal asymptotic estimation is obtained in the h 2 and h 1 norms finally numerical examples are given to verify the theoretical analysis

existence and convexity of local solutions to degenerate hessian equations abstract in this work we prove the existence of convex solutions to the following k hessian equation s k u k y g y u d u in the neighborhood of a point y 0 u 0 p 0 r n r r n where g c g y 0 u 0 p 0 0 k c is nonnegative near y 0 k y 0 0 and rank d y 2 k y 0 n k 1

near merging of paths in suboptimal tree searching corresp the near merging of paths in tree searching is explored this near merging can degrade coding performance when a suboptimal search algorithm is used the problem is first identified and then a feasible solution is presented some examples from image source coding using the m l algorithm are given

on a class of fully nonlinear flows in kahler geometry in this paper we study a class of fully nonlinear metric flow on kahler manifolds which includes the j flow as a special case we provide a sufficient and necessary condition for the long time convergence of the flow generalizing the result of songweinkove as a consequence under the given condition we solved the corresponding euler equation which is fully nonlinear of monge ampere type as an application we also discuss a complex monge ampere type equation including terms of mixed degrees which was first posed by chen

the convexity of solution of a class hessian equation in bounded convex domain in r 3 we use the deformation methods to obtain the convexity of solution of a class hessian equation in bounded convex domain in r 3 c 2008 elsevier inc all rights reserved

global c2 estimates for convex solutions of curvature equations we establish a c2 a priori estimate for convex hypersurfaces whose principal curvatures 1 n satisfy k x f x x the weingarten curvature equation we also obtain such an estimate for admissible 2 convex hypersurfaces in the case k 2 our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations 2015 wiley periodicals inc

a multilevel mesh independence principle for the navier stokes equations multilevel finite element discretization methods for the navier stokes equations are considered in contrast to usual multilevel methods a superlinear scaling of the consecutive meshwidths h j 1 mathcal o h j alpha j is used on the coarsest mesh the discretized system is solved which is small and nonlinear on each subsequent mesh only one or two newton correction steps are performed so that only one or two larger linear systems are solved the scalings of the meshwidths that lead to optimal accuracy of the approximate solution in both the h 1 and l 2 norm are investigated an error analysis of independent interest is also presented for the basic finite element method using the conservation form of the nonlinear term this formulation leads to a nonlinear system whose nonlinearity is easier to resolve than the systems arising when either the convective or explicitly skew symmetric corms are used for the nonlinear term

isoperimetric type problems and alexandrov fenchel type inequalities in the hyperbolic space abstract in this paper we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space h n by using quermassintegral preserving curvature flows as a byproduct we obtain hyperbolic alexandrov fenchel inequalities

a uniqueness theorem in kahler geometry we consider compact kahler manifolds with their kahler ricci tensor satisfying f ric constant under the nonnegative bisectional curvature assumption and certain conditions on f we prove that such metrics are in fact kahler einstein

a two grid method based on newton iteration for the navier stokes equations in this paper we consider a two grid method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations we prove the convergence rate of the approximation obtained by this method the two grid method involves solving one small nonlinear coarse mesh system and two linear problems on the fine mesh which have the same stiffness matrix with only different right hand side the algorithm we study produces an approximate solution with the optimal asymptotic in h and accuracy for any reynolds number numerical example is given to show the convergence of the method

image coding using wavelet transforms and entropy constrained trellis coded quantization the discrete wavelet transform has recently emerged as a powerful technique for decomposing images into various multi resolution approximations multi resolution decomposition schemes have proven to be very effective for high quality low bit rate image coding in this work we investigate the use of entropy constrained trellis coded quantization ectcq for encoding the wavelet coefficients of both monochrome and color images ectcq is known as an effective scheme for quantizing memoryless sources with low to moderate complexity the ectcq approach to data compression has led to some of the most effective source codes found to date for memoryless sources performance comparisons are made using the classical quadrature mirror filter bank of johnston and nine tap spline filters that were built from biorthogonal wavelet bases we conclude that the encoded images obtained from the system employing nine tap spline filters are marginally superior although at the expense of additional computational burden excellent peak signal to noise ratios are obtained for encoding monochrome and color versions of the 512 spl times 512 lenna image comparisons with other results from the literature reveal that the proposed wavelet coder is quite competitive

the logarithmic minkowski problem for polytopes abstract the logarithmic minkowski problem asks for necessary and sufficient conditions for a finite borel measure on the unit sphere so that it is the cone volume measure of a convex body this problem was solved recently by boroczky lutwak yang and zhang for even measures boroczky et al 2013 8 this paper solves the case of discrete measures whose supports are in general position

a two level finite element discretization of the stream function form of the navier stokes equations abstract we analyze a two level method of discretizing the stream function form of the navier stokes equations this report presents the two level algorithm and error analysis for the case of conforming elements the two level algorithm consists of solving a small nonlinear system on the coarse mesh then solving a linear system on the fine mesh the basic result states that the error between the coarse and fine meshes are related superlinearly via as an example if the clough tocher triangles or the bogner fox schmit rectangles are used then the coarse and fine meshes are related by h o h 3 2 ln h 1 4

analysis of a damped nonlinear multilevel method in this paper we present a new algorithm that is obtained by introducing a damping parameter in the classical nonlinear multilevel method we analyse this damped nonlinear multilevel method in particular we prove global convergence and local efficiency for a suitable class of problems

robust two dimensional tree encoding of images a class of robust two dimensional 2 d tree coding procedures are described for efficient encoding of monochrome images the encoding filter is designed on the basis of ensemble properties of a particular class of stochastic random fields which have been shown to provide a useful model for typical imagery data we make use of the m k l algorithm in instrumenting the 2 d tree search results are demonstrated for both synthetic images and a number of head and shoulders images these results demonstrate the effectiveness of 2 d tree encoding using fairly moderate search intensities and the inherent robustness of 2 d tree encoding more generally in particular it is demonstrated that by logical design of the encoding filter under an appropriate stochastic modeling assumption the 2 d tree encoder provides relatively efficient performance for a rather wide range of real world imagery

numerical computations of viscous incompressible flow problems using a two level finite element method we consider two level finite element discretization methods for the stream function formulation of the navier stokes equations the two level method consists of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh the basic result states that the errors between the coarse and fine meshes are related superlinearly this paper demonstrates that the two level method can be implemented to approximate efficiently solutions to the navier stokes equations two fluid flow calculations are considered to test problems which have a known solution and the driven cavity problem stream function contours are displayed showing the main features of the flow

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

analysis of linear prediction coding and spectral estimation from subbands linear prediction schemes make a prediction x spl circ sub i of a data sample x sub i using p previous samples it has been shown by woods and o neil 1986 as well as pearlman 1991 that as the order of prediction p spl rarr spl infin there is no gain to be obtained by coding subband samples this paper deals with the less well understood theory of finite order prediction and optimal coding from subbands which are generated by ideal brickwall filtering of a stationary gaussian source we first prove that pth order prediction from subbands is superior to pth order prediction in the fullband when p is finite this fact adduces that optimal vector p tuple coding in the subbands is shown to offer quantifiable gains over optimal fullband p tuple coding again when p is finite the properties of subband spectra are analyzed using the spectral flatness measure these results are used to prove that subband dpcm provides a coding gain over fullband dpcm for finite orders of prediction in addition the proofs provide means of quantifying the subband advantages in linear prediction optimal coding and dpcm coding in the form of gain formulas subband decomposition of a source is shown to result in a whitening of the composite subband spectrum this implies that for any stationary source a pth order prediction error filter pef can be found that is better than the pth order pef obtained by solving the yule walker equations resulting from the fullband data we demonstrate the existence of such a super optimal pef and provide algorithmic approaches to obtaining this pef the equivalence of linear prediction and ar spectral estimation is then exploited to show theoretically and with simulations that ar spectral estimation from subbands offers a gain over fullband ar spectral estimation

finite element technique for optimal pressure recovery from stream function formulation of viscous flows presentation d un algorithme de recouvrement de la pression base sur une analyse generale de la converge de la solution en elements finis de l equation de navier stokes

a brunn minkowski inequality for the hessian eigenvalue in three dimensional convex domain abstract we use the deformation methods to obtain the strictly log concavity of solution of a class hessian equation in bounded convex domain in r 3 as an application we get the brunn minkowski inequality for the hessian eigenvalue and characterize the equality case in bounded strictly convex domain in r 3

information theoretic performance of quadrature mirror filters most existing quadrature mirror filters qmfs closely match the derived closed form expression for an efficient class of qmfs we use the closed form expressions to derive the relationship between information theoretic loss and the frequency selectivity of the qmf by calculating first order entropy as well as rate distortion theoretic performance of a two band qmf system we find that practical qmfs do not suffer a significant information theoretic loss with first order autoregressive gaussian sources with second order autoregressive sources we find that practical qmfs suffer a notable information theoretic loss when the bandwidth of the source is extremely narrow but incur a small loss when the bandwidth is wider we suggest that our results broadly apply to higher order autoregressive sources as well

on the l p monge ampere equation abstract for the case where 0 p 1 we prove the existence of solutions of the l p monge ampere equation for arbitrary measures and show that the solution is in general not unique

the lp minkowski problem for torsion abstract in the present paper we introduce the so called l p torsion measure l p mixed torsion a hadamard variational formula for torsion under the p sum is established as an application the existence of solutions to a l p minkowski problem for torsion is proved for any fixed p 1 and p n 2 which extends a result of colesanti and fimiani 24 a l p minkowski inequality for torsion is also obtained which implies the uniqueness of the solutions for the l p minkowski problem mentioned above

projection functions area measures and the alesker fourier transform abstract dual to koldobsky s notion of j intersection bodies the class of j projection bodies is introduced generalizing minkowski s classical notion of projection bodies of convex bodies a fourier analytic characterization of j projection bodies in terms of their area measures of order j is obtained in turn this yields an equivalent characterization of j projection bodies involving alesker s fourier type transform on translation invariant smooth spherical valuations as applications of these results several basic properties of j projection bodies are established and new non trivial examples are constructed

the hadamard variational formula and the minkowski problem for p capacity abstract a hadamard variational formula for p capacity of convex bodies in r n is established when 1 p n the formula is applied to solve the minkowski problem for p capacity which involves a degenerate monge ampere type equation uniqueness for the minkowski problem for p capacity is established when 1 p n and existence and regularity when 1 p 2 these results are non linear extensions of the now classical solution of jerison of the minkowski problem for electrostatic capacity p 2

analysis of nonconforming stream function and pressure finite element spaces for the navier stokes equations abstract it is shown that the standard weak form of the stream function version of the incompressible navier stokes equations is unsuitable for derivation or analysis or nonconforming finite element approximations a new weak form which is suitable for both purposes and which can also be used without difficulty for the conforming case is given a general analysis of convergence is presented and applied to three specific nonconforming finite element schemes of which two use cubic trial functions and one uses quadratics it is shown that the quadratic element is as accurate in order as the cubics and may therefore be preferred following this an algorithm for pressure recovery is given with examples of acceptable test and trial spaces

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

region adaptive subband image coding we present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function we analyze the energy packing properties toward the lower frequency subbands edges and the dependency of energy distribution on the orientation of the edges in subband decomposed images based on these investigations and ideal analysis synthesis filtering done in the frequency domain the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy constrained quantizers for different regions under the assumption of a generalized gaussian distribution for the image subbands we also address the problem of determining an optimal subband decomposition among all possible decompositions experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1 0 b pel and reasonable quality images are obtainable at rates as low as 0 25 b pel

asymptotic expansion of the trace of the heat kernel associated to the dirichlet to neumann operator abstract for a given bounded domain with smooth boundary in a smooth riemannian manifold m g by decomposing the dirichlet to neumann operator into a sum of the square root of the laplacian and a pseudodifferential operator and by applying grubb s method of symbolic calculus for the corresponding pseudodifferential heat kernel operators we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to dirichlet to neumann operator as t 0 in particular we explicitly give the first four coefficients of this asymptotic expansion these coefficients provide precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the steklov problem

a tree coding theorem for stationary gaussian sources and the squared error distortion measure for a class of stationary gaussian sources and the squared error distortion measure an asymptotically optimal tree coding scheme is derived using tree codes with finite branch length the distribution of the reproduction process is derived in an explicit form and using the random coding argument and results from the theory of branching processes with stationary ergodic environmental processes the source coding theorem is proved the theorem is applicable to all gaussian sources with a power spectrum that satisfies the lip 1 condition with no restriction on the coding rate

optimal transforms for multispectral and multilayer image coding multispectral images are composed of a series of images at differing optical wavelengths since these images can be quite large they invite efficient source coding schemes for reducing storage and transmission requirements because multispectral images include a third spectral dimension with nonstationary behavior these multilayer data sets require specialized coding techniques the authors develop both a theory and specific methods for performing optimal transform coding of multispectral images the theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary gaussian random processes therefore the methods may be applied to any multilayer data set which meets this assumption although the authors do not assume the autocorrelation has a separable form they show that the optimal transform for coding has a partially separable structure in particular they prove that a coding scheme consisting of a frequency transform within each layer followed by a separate kl transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large two simplifications of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints the proposed coding techniques are then implemented using subband filtering methods and the various algorithms are tested on multispectral images to determine their relative performance characteristics

geometric measures in the dual brunn minkowski theory and their associated minkowski problems a longstanding question in the dual brunn minkowski theory is what are the dual analogues of federer s curvature measures for convex bodies the answer to this is provided this leads naturally to dual versions of minkowski type problems what are necessary and sufficient conditions for a borel measure to be a dual curvature measure of a convex body sufficient conditions involving measure concentration are established for the existence of solutions to these problems

tree encoding of stationary ergodic sources with a fidelity criterion tree source coding theorems with a single letter fidelity criterion are proved for stationary ergodic sources using tree codes with a fixed branch length the higher than exponential convergence of distortions is shown for binary symmetric sources and hamming distortion measure when an excess in rate is allowed

subband coding of images using vector quantization a novel two dimensional subband coding technique is presented that can be applied to images as well as speech a frequency band decomposition of the image is carried out by means of 2d separable quadrature mirror filters which split the image spectrum into 16 equal rate subbands these 16 parallel subband signals are regarded as a 16 dimensional vector source and coded as such using vector quantization in the asymptotic case of high bit rates a theoretical analysis yields that a lower bound to the gain is attainable by choosing this approach over scalar quantization of each subband with an optimal bit allocation it is shown that vector quantization in this scheme has several advantages over coding the subbands separately experimental results are given and it is shown the scheme has a performance that is comparable to that of more complex coding techniques

an aim and one step newton method for the navier stokes equations abstract in this paper we investigate a two level finite element approximation to the navier stokes equations by means of a new approximate inertial manifold aim then we construct a new aim based numerical scheme and show that the convergence rate of the new approximation obtained by this aim method is better than the double of the convergence rate of the standard galerkin finite element solution in addition we also show that the new aim scheme is equivalent to a one step newton iterative scheme for the navier stokes equations in a suitable hilbert space

predictive vector quantization of images the purpose of this paper is to present new image coding schemes based on a predictive vector quantization pvq approach the predictive part of the encoder is used to partially remove redundancy and the vq part further removes the residual redundancy and selects good quantization levels for the global waveform two implementations of this coding approach have been devised namely sliding block pvq and block tree pvq simulations on real images show significant improvement over the conventional dpcm and tree codes using these new techniques the strong robustness property of these coding schemes is also experimentally demonstrated

tree coding of image subbands the authors consider the encoding of image subbands with a tree code that is asymptotically optimal for gaussian sources and the mean squared error mse distortion measure they first prove that optimal encoding of ideally filtered subbands of a gaussian image source achieves the rate distortion bound for the mse distortion measure the optimal rate and distortion allocation among the subbands is a by product of this proof a bound is derived which shows that subband coding is closer than full band coding to the rate distortion bound for a finite length sequence the tree codes are then applied to encode the image subbands both nonadaptively and adaptively since the tree codes are stochastic and the search of the code tree is selective a relatively few reproduction symbols may have an associated squared error a hundred times larger than the target for the subband correcting these symbols through a postcoding procedure improves the signal to noise ratio and visual quality significantly with a marginal increase in total rate

on the planar dual minkowski problem abstract in this paper we resolve the planar dual minkowski problem proposed by huang et al 2016 31 for all positive indices without any symmetry assumption more precisely given any q 0 and function f on s 1 bounded by two positive constants we show that there exists a convex body in the plane containing the origin in its interior whose dual curvature measure c q has density f in particular if f is smooth then is also smooth

a fourier transform approach to christoffel s problem we use fourier transform techniques to provide a new approach to berg s solution of the christoffel problem this leads to an explicit description of berg s spherical kernel and to new regularity properties of the associated integral transform

two grid discretizations with backtracking of the stream function form of the navier stokes equations we analyze a two grid finite element method with backtracking for the stream function formulation of the stationary navier stokes equations this two grid method involves solving one small nonlinear coarse mesh system one linearized system on the fine mesh and one linear correction problem on the coarse mesh the algorithm and error analysis are presented

analysis of a multilevel iterative method for nonlinear finite element equations the multilevel iterative technique is a powerful technique for solving the systems of equations associated with discretized partial differential equations we describe how this technique can be combined with a globally convergent approximate newton method to solve nonlinear partial differential equations we show that asymptotically only one newton iteration per level is required thus the complexity for linear and nonlinear problems is essentially equal

a two grid method with backtracking technique for the stream function form of the navier stokes equations a two grid method based on modified newton s iteration with backtracking technique is proposed for the stream function formulation of the stationary navier stokes equations the convergence rate and error estimate of the algorithm are established it s proven that the asymptotically optimal approximation can be achieved by solving two small systems on the coarse mesh and two similar linear problems same stiffness matrix only with different right hand side on the fine mesh compared with the fine space the coarse space can be extremely coarse both in theory and in numerical applications

a hopf theorem for non constant mean curvature and a conjecture of a d alexandrov we prove a uniqueness theorem for immersed spheres of prescribed non constant mean curvature in homogeneous three manifolds in particular this uniqueness theorem proves a conjecture by a d alexandrov about immersed spheres of prescribed weingarten curvature in mathbb r 3 for the special but important case of prescribed mean curvature as a consequence we extend the classical hopf uniqueness theorem for constant mean curvature spheres to the case of immersed spheres of prescribed antipodally symmetric mean curvature in mathbb r 3

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

the lp minkowski problem for n p 1 abstract chou and wang s existence result for the l p minkowski problem on s n 1 for p n 1 and an absolutely continuous measure is discussed and extended to more general measures in particular we provide an almost optimal sufficient condition for the case p 0 1

next state functions for finite state vector quantization in this paper the finite state vector quantization scheme called dynamic finite state vector quantization dfsvq is investigated with regard to its subcodebook construction in dfsvq each input block is encoded by a small codebook called subcodehook which is created from a much larger codebook called supercodebook each subcodebook is constructed by selecting using a reordering procedure a set of appropriate codevectors from the supercodebook the performance of the dfsvq depends on this reordering procedure therefore several reordering procedures are introduced and their performances are evaluated in this paper the reordering procedures that are investigated are based on the conditional histogram of the codevectors index prediction vector prediction nearest neighbor design and frequency usage of the code vectors the performances of the reordering procedures are evaluated by comparing their hit ratios the number of blocks encoded by the subcodebook and their computational complexity experimental results are presented and it is found that the reordering procedure based on the vector prediction performs the best when compared with the other reordering procedures

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques

the lp minkowski problem for polytopes for 0 p 1 abstract necessary and sufficient conditions are given for the existence of solutions to the discrete l p minkowski problem for the critical case where 0 p 1