asymptotic behavior for the navier stokes equations with nonzero external forces abstract we estimate the asymptotic behavior for the stokes solutions with external forces first we found that if there are external forces then the energy decays slowly even if the forces decay quickly then we also obtain the asymptotic behavior in the temporal spatial direction for weak solutions of the navier stokes equations we also provide a simple example of external forces which shows that the stokes solution does not decay quickly

decay rate for the incompressible flows in half spaces we show that the time decay rate of l 2 norm of weak solution for the stokes equations and for the navier stokes equations on the half spaces are t frac n 2 frac 1 r frac 1 2 frac 1 2 if the initial data u 0 in l 2 cap l r and int mathbb r n y n u 0 y r dy infty for 1 r 2 we also show that the decay rate is determined by the linear part of the weak solution we use the heat kernel and ukai s solution formula for the stokes equations it has been known up to now that the decay rate on the half space was t frac n 2 frac 1 r frac 1 2 which was obtained by borchers and miyakawa 1 and ukai 9

deformation quantization for actions of qpd abstract the main objective of this article is to develop the theory of deformation of c algebras endowed with a group action from the perspective of non formal equivariant quantization this program initiated in 4 aims to extend rieffel s deformation theory 27 for more general groups than r d in 4 we have constructed such a theory for a class of non abelian lie groups in the present article we study the somehow opposite situation of abelian but non lie groups more specifically we construct here a deformation theory of c algebras endowed with an action of a finite dimensional vector space over a non archimedean local field of characteristic different from 2 at the root of our construction stands the p adic version of the weyl quantization introduced by haran 12 and further extended by bechata 1 and unterberger 34

algebraic l 2 decay for weak solutions of a viscous boussinesq system in exterior domains abstract the algebraic decay rates for the total kinetic energy of weak solutions of the n dimensional viscous boussinesq system in exterior domains are established by means of the spectral decomposition method of fractional powers of the laplacian and stokes operators the results reveal that l 2 decay of the velocity field with zero divergence becomes slower than that of the temperature

decay results of solutions to the incompressible navier stokes flows in a half space abstract in a half space we consider the asymptotic behavior of the strong solution for the non stationary navier stokes equations in particular the decay rates of the second order derivatives of the navier stokes flows in l r r n n 2 with 1 r are derived by using l q l r estimates and a clever analysis on the fractional powers of the stokes operator in addition we prove that the strong solution and its first and second derivatives decay in time more rapidly than observed in general if the initial datum lies in a suitable weighted space

asymptotic behavior for the navier stokes equations in 2d exterior domains we show that the lp spatial temporal decay rates of solutions of incompressible flow in an 2d exterior domain when a domain has a boundary pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary to overcome the difficulty we adopt the ideas in he xin c he z xin weighted estimates for nonstationary navier stokes equations in exterior domain methods appl anal 7 3 2000 443 458 and our previous results h o bae b j jin asymptotic behavior of stokes solutions in 2d exterior domains j math fluid mech in press h o bae b j jin temporal and spatial decay rates of navier stokes solutions in exterior domains submitted for publication for the spatial decay rate estimate we first extend temporal decay rate result of the navier stokes solutions for general lp space when the initial velocity is in l 2 lr 1 r q 1 r q

weyl manifolds and deformation quantization this paper deals with non commutative objects based on the weyl algebra from the differential geometric point of view we propose to extend familiar notions from manifolds to non commutative objects in this algebraic approach the basic object is not a point of a space but certain sections of bundles

comparison between adaptive search and bit allocation algorithms for image compression using vector quantization this article discusses bit allocation and adaptive search algorithms for mean residual vector quantization mrvq and multistage vector quantization msvq the adaptive search algorithm uses a buffer and a distortion threshold function to control the bit rate that is assigned to each input vector it achieves a constant rate for the entire image but variable bit rate for each vector in the image for a given codebook and several bit rates we compare the performance between the optimal bit allocation and adaptive search algorithms the results show that the performance of the adaptive search algorithm is only 0 20 0 53 db worse than that of the optimal bit allocation algorithm but the complexity of the adaptive search algorithm is much less than that of the optimal bit allocation algorithm

a new proof of the caffarelli kohn nirenberg theorem here we give a self contained new proof of the partial regularity theorems for solutions of incompressible navier stokes equations in three spatial dimensions these results were originally due to scheffer and caffarelli kohn and nirenberg our proof is much more direct and simpler 1998 john wiley sons inc

partial regularity of solutions to the four dimensional navier stokes equations at the first blow up time the solutions of incompressible navier stokes equations in four spatial dimensions are considered we prove that the two dimensional hausdorff measure of the set of singular points at the first blow up time is equal to zero

optimal bit allocation via the generalized bfos algorithm p h westerink et al 1988 developed an optimal bit allocation algorithm that is simplified when all operational distortion rate functions which are referred to as quantizer functions are convex this algorithm is restated using the generalized breiman friedman olshen and stone bfos algorithm a recently developed technique for variable rate vector quantizer design for both cases of convex and nonconvex quantizer functions qfs and its complexity is analyzed the use of the generalized bfos algorithm for optimal bit allocation is analysed it is shown that if each source has a convex quantizer function then the complexity of the algorithm is low

asymptotic behavior for the stokes flow and navier stokes equations in half spaces abstract using the solution formula in ukai 1987 27 for the stokes equations we find asymptotic profiles of solutions in l 1 r n n 2 for the stokes flow and non stationary navier stokes equations since the projection operator p l 1 r n l 1 r n is unbounded we use a decomposition for p u u to overcome the difficulty and prove that the decay rate for the first derivatives of the strong solution u of the navier stokes system in l 1 r n is controlled by t 1 2 1 t n 2 2 for any t 0

decay properties of solutions to the non stationary magneto hydrodynamic equations in half spaces abstract l 1 decay properties of the strong solution including the first and second order spacial derivatives to the non stationary magneto hydrodynamic mhd equations are established in a half space and the weighted cases are also considered additionally

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

performance analysis of reversible image compression techniques for high resolution digital teleradiology the performances of a number of block based reversible compression algorithms suitable for compression of very large format images 4096 4096 pixels or more are compared to that of a novel two dimensional linear predictive coder developed by extending the multichannel version of the burg algorithm to two dimensions the compression schemes implemented are huffman coding lempel ziv coding arithmetic coding two dimensional linear predictive coding in addition to the aforementioned one transform coding using discrete fourier discrete cosine and discrete walsh transforms linear interpolative coding and combinations thereof the performances of these coding techniques for a few mammograms and chest radiographs digitized to sizes up to 4096 4096 10 b pixels are discussed compression from 10 b to 2 5 3 0 b pixel on these images has been achieved without any loss of information the modified multichannel linear predictor outperforms the other methods while offering certain advantages in implementation

efficient codebooks for vector quantization image compression with an adaptive tree search algorithm this paper discusses some algorithms to be used for the generation of an efficient and robust codebook for vector quantization vq some of the algorithms reduce the required codebook size by 4 or even 8 b to achieve the same level of performance as some of the popular techniques this helps in greatly reducing the complexity of codebook generation and encoding we also present a new adaptive tree search algorithm which improves the performance of any product vq structure our results show an improvement of nearly 3 db over the fixed rate search algorithm at a bit rate of 0 75 b pixel

on weighted norm estimates for nonstationary incompressible navier stokes flows in a 3d exterior domain abstract we study the time decay of weighted norms of weak and strong solutions to the navier stokes equations in a 3d exterior domain moment estimates for weak solutions and weighted l q estimates for strong solutions are deduced both of which seem to be optimal the relation is discussed between the space time decay and the vanishing of the total net force exerted by the fluid to the body a class of initial data is given so that the total net force associated to the corresponding fluid flows does not vanish

decay results of higher order norms for the navier stokes flows in 3d exterior domains using the nonstationary stokes solution formula and the regularity theory of the steady stokes equations we establish the decay results including the weighted cases of higher order spatial derivatives for the navier stokes flows in 3d exterior domains which is a long standing problem the higher order norm weighted decay results in this article are inspired by the work in bae and jin proc r soc edinburgh sect a 135 461 477 2005 schonbek and wiegner proc r soc edinburgh sect a 126 677 685 1996 respectively which are considered in the whole space

temporal decays in l 1 and l for the stokes flow we estimate the time decay rates in l1 in the hardy space and in l of solutions for the stokes equations on the half spaces for the estimates in the hardy space we adopt the ideas in math z 231 1999 383 temporal and spatial decays for the stokes flows submitted for publication and also use the heat kernel and the solution formula for the stokes equations

l2 decay for the navier stokes flow in halfspaces on etudie le comportement asymptotique dans l 2 des solutions faibles des equations de navier stokes dans des demi espaces

algebraic decay of weak solutions to 3d navier stokes equations in general unbounded domains abstract in this paper we study the decay properties of a weak solution to the nonstationary navier stokes equations by means of the spectral decomposition method of fractional powers of the stokes operator in an arbitrary unbounded domain the explicit l 2 decay rates are given as t which improves greatly the decay results in 8 9

the deformation quantizations of the hyperbolic plane we describe the space of all invariant both formal and non formal deformation quantizations on the hyperbolic plane mathbb d as solutions of the evolution of a second order hyperbolic differential operator the construction is entirely explicit and relies on non commutative harmonic analytical techniques on symplectic symmetric spaces the present work presents a unified method producing every quantization of mathbb d and provides in the 2 dimensional context an exact solution to weinstein s wkb quantization program within geometric terms the construction reveals the existence of a metric of lorentz signature canonically attached or dual to the geometry of the hyperbolic plane through the quantization process

variable rate vector quantization for speech image and video compression the performance of a vector quantizer can be improved by using a variable rate code three variable rate vector quantization systems are applied to speech image and video sources and compared to standard vector quantization and noiseless variable rate coding approaches the systems range from a simple and flexible tree based vector quantizer to a high performance but complex jointly optimized vector quantizer and noiseless code the systems provide significant performance improvements for subband speech coding predictive image coding and motion compensated video but provide only marginal improvements for vector quantization of linear predictive coefficients in speech and direct vector quantization of images criteria are suggested for determining when variable rate vector quantization may provide significant performance improvement over standard approaches

optimal weighted estimates of the flows in exterior domains abstract in this paper we prove some decay properties of global solutions for the navier stokes equations in an exterior domain r n n 2 3 when a domain has a boundary the pressure term is troublesome since we do not have enough information on the pressure near the boundary to overcome this difficulty by multiplying a special form of test functions we obtain an integral equation he xin 2000 12 first introduced this method and then bae jin 2006 2007 1 13 modified their method to obtain better decay rates also bae roh 2009 11 improved bae jin s results unfortunately their results were not optimal because there exists an unpleasant positive small in their rates in this paper we obtain the following optimal rate without x u t l p c t n 2 1 r 1 p 2 for the initial condition u 0 with x u 0 l r and for any n

deformation quantization for heisenberg supergroup we construct a non formal deformation machinery for the actions of the heisenberg supergroup analogue to the one developed by m rieffel for the actions of r d however the method used here differs from rieffel s one we obtain a universal deformation formula for the actions of r m n as a byproduct of weyl ordered kirillov s orbit method adapted to the graded setting to do so we have to introduce the notion of c superalgebra which is compatible with the deformation and which can be seen as corresponding to noncommutative superspaces we also use this construction to interpret the renormalizability of a noncom mutative quantum field theory

the optimal upper and lower bounds of convergence rates for the 3d navier stokes equations under large initial perturbation abstract this paper is concerned with the optimal algebraic convergence rates for leray weak solutions of the 3d navier stokes equations in morrey space it is shown that if the global leray weak solution u x t of the 3d navier stokes equations satisfies u l r 0 m p q r 3 2 r 3 p 2 3 2 p p q 2 then even for the large initial perturbation every weak solution v x t of the perturbed navier stokes equations converges algebraically to u x t with the optimal upper and lower bounds c 1 1 t 2 v t u t l 2 c 2 1 t 2 for large t 1 2 5 2 the findings are mainly based on the developed fourier splitting methods and iterative process

lower bounds for an integral involving fractional laplacians and the generalized navier stokes equations in besov spaces when estimating solutions of dissipative partial differential equations in l p related spaces we often need lower bounds for an integral involving the dissipative term if the dissipative term is given by the usual laplacian lower bounds can be derived through integration by parts and embedding inequalities however when the laplacian is replaced by the fractional laplacian the approach of integration by parts no longer applies in this paper we obtain lower bounds for the integral involving by combining pointwise inequalities for with bernstein s inequalities for fractional derivatives as an application of these lower bounds we establish the existence and uniqueness of solutions to the generalized navier stokes equations in besov spaces the generalized navier stokes equations are the equations resulting from replacing in the navier stokes equations by

on l 1 summability and asymptotic profiles for smooth solutions to navier stokes equations in a 3d exterior domain the exterior nonstationary problem is studied for the 3d navier stokes equations the l1 summability is proved for smooth solutions which correspond to initial data satisfying certain symmetry and moment conditions the result is then applied to show that such solutions decay in time more rapidly than observed in general furthermore an asymptotic expansion is deduced and a lower bound estimate is given for the rates of decay in time

long time behavior for the nonstationary navier stokes flows in l1 r n the large time decay for the navier stokes flows in l1 r n is a long standing unsolved question the main difficulties are that usual lq lr estimates for the stokes flow fail in this case and the projection operator p l1 r n l 1 r n becomes unbounded using the stokes solution formula we find a crucial and new estimate for the stokes flow in l1 r n which plays a fundamental role in studying the time l1 behavior for the navier stokes equations in addition we decompose the operator p into two parts and reduce its unboundedness to establish an l1 estimate for an elliptic problem with neumann boundary condition which is overcome by using the weighted estimates of the gaussian kernel s convolution the main results in this article are motivated by bae s works 2006 2008 1 2 and brandolese s work 2001 11

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

decay results of the nonstationary navier stokes flows in half spaces there is a long standing problem on the nonstationary navier stokes equations which pertains to how to characterize the l1 time asymptotic expansion of the navier stokes flows in the half space beyond a few partial results new progress has not yet to be made on this open question in this article we give a confirmed answer to this problem namely a thorough characterization on l1 summability is revealed in order to prove this result we need to avoid the unboundedness of the projection operator which is overcome by treating an elliptic neumann problem finally using the weighted estimates on the heat kernel s convolution we obtain the exact profile structure of the asymptotic expansion in l 1 mathbb r n in addition some crucial estimates on the fractional spatial derivatives of the non stationary stokes and navier stokes flows are established for the first time which allows for a better understanding of the l1 decay problem

representations des groupes exponentiels we give a complete and explicit realization of the unitary irreducible representations of any exponential group g by deformation of the associative and poisson algebra of functions on the dual g of the lie algebra of g we define an adapted fourier transform which is a deformation of the usual one and which gives a natural description of the harmonic analysis of g on the restrictions to the coadjoint orbits of the considered functions

upper and lower bounds of temporal and spatial decays for the navier stokes equations we obtain the lower bounds of the temporal spatial decays for weak solutions of the navier stokes equations c0 1 t 5 2i4 1 2 i 2u t l2 c1 1 t 5 2i4 for i 1 2 the upper bound parts are estimated in several papers for example bae and jin submitted and he and xin proc roy soc edinburg section a 131 3 2001 597 by the interpolation arguments we also have c0 1 t 54 2 1 x 2 2u t l2 c1 1 t 54 2 for 0 2

comparison between several adaptive search vector quantization schemes and jpeg standard for image compression this paper introduces an adaptive search vector quantization vq algorithm hierarchical adaptive search vq hasvq and compares its performance against several previously proposed adaptive search image compression algorithms these algorithms are the jpeg standard adaptive tree search vector quantization atsvq multi stage adaptive search vector quantization masvq the bit rate examined is from 0 625 to 1 25 bits per pixel bpp the results indicate that hasvq outperforms all the other algorithms over the entire range of bit rates examined for higher bit rates masvq performs next to the hasvq algorithm and is in turn followed by the jpeg standard atsvq performs well at lower bit rates however its performance at higher bit rates is suppressed by not having an adequate codebook size

long time behavior for navier stokes flows in a two dimensional exterior domain abstract there are several long standing problems on the incompressible navier stokes flows in 2d exterior domains which claim how to characterize l 1 summability of the 2d n s flows whether the total net force exerted on the boundary is finite and how to establish decay results of higher order spatial derivatives including the weighted cases in order to solve these questions we firstly find some types of new technical inequalities which are used to overcome the difficulties caused by the domain boundary using l q l r properties for nonstationary stokes flows together with elliptic estimates for the steady stokes system we can avoid the strong singularity and answer these mentioned problems completely it should be pointed out that main results in this article are motivated by the works in 5 37 respectively

decay rates for the incompressible navier stokes flows in 3d exterior domains abstract the exterior nonstationary problem is studied for the 3d navier stokes equations for which the associated total net force to the boundary may not vanish the time decay properties of the strong solution including the first and second derivatives are shown in l q and weighted spaces in particular the relation of weighted l 1 summability for smooth solutions is discussed in details between the time decay and the total net force exerted by the fluid to the body the conclusions in this article improve and extend results in h bae b jin asymptotic behavior for the navier stokes equations in 2d exterior domains j funct anal 240 2006 508 529 h bae b jin temporal and spatial decay rates of navier stokes solutions in exterior domains bull korean math soc 44 2007 547 567 and in c he t miyakawa on l 1 summability and asymptotic profiles for smooth solutions to navier stokes equations in a 3d exterior domain math z 245 2003 387 417 c he t miyakawa on weighted norm estimates for nonstationary incompressible navier stokes flows in a 3d exterior domain j differential equations 246 2009 2355 2386 respectively

space time decay of navier stokes flows invariant under rotations we show that the solutions to the non stationary navier stokes equations in open image in new window d 2 3 which are left invariant under the action of discrete subgroups of the orthogonal group o d decay much faster as open image in new window than in generic case and we compute for each subgroup the precise decay rates in space time of the velocity field

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

lower bounds of rates of decay for solutions to the navier stokes equations where a p 3 2 p 1 and the constant c depends on the l2 and lnorms of the initial data u0 this paper deals with the more subtle problem of deriving lower bounds on the energy decay rates we show that for a certain class of initial data the solutions u x t to the 2d and 3d navier stokes equations admit an algebraic lower bound on the energy decay specifically there are two cases to consider in the first case the average of the initial data f u0 dx is nonzero this case was treated in the earlier paper 5 where it was established that

large time behavior for the nonstationary navier stokes flows in the half space abstract asymptotic behavior of higher order spatial derivatives in l r is established for incompressible navier stokes flows in the half space which is a long time unsolved problem the main tools employed for solving this problem are the nonstationary stokes solution formula and the a priori estimates of the steady stokes system in the half space another main result is devoted to studying time l 1 decay and a partial answer to this open problem is given by means of a crucial and new estimate for the stokes flow two theorem 1 1 theorem 1 2 in this article can be regarded as a great improvement and powerful extension of the work in 6 38

non formal star exponential on contracted one sheeted hyperboloids in this paper we exhibit the non formal star exponential of the lie group sl 2 r realized geometrically on the curvature contraction of its one sheeted hyperboloid orbits endowed with its natural non formal star product it is done by a direct resolution of the defining equation of the star exponential and produces an expression with bessel functions this yields a continuous group homomorphism from sl 2 r into the von neumann algebra of multipliers of the hilbert algebra associated to this natural star product as an application we prove a new identity on bessel functions

weighted decay properties for the incompressible stokes flow and navier stokes equations in a half space abstract using the stokes solution formula and l q l r estimates of the stokes operator semigroup we establish the weighted decay properties for the stokes flow and navier stokes equations including their spatial derivatives in half spaces in addition the unboundedness of the projection operator p l r n l r n is overcome by employing a decomposition for the nonlinear term and l asymptotic behavior for the second derivatives of navier stokes flows in half spaces is given

asymptotic behavior of solutions to the nonstationary magneto hydrodynamic equations abstract asymptotic behavior of the higher order spacial derivatives of the strong solution to the incompressible non stationary magneto hydrodynamic mhd equations is given in a half space which is a long time difficult question the main tools employed in this article are the non stationary stokes solution formula and some a priori estimates of the steady stokes system in the half space