symmetry preserving discretization of navier stokes equations on collocated unstructured grids a fully conservative discretization is presented in this paper the same principles followed by verstappen and veldman 2003 3 are generalized for unstructured meshes here a collocated mesh scheme is preferred over a staggered one due to its simpler form for such meshes the basic idea behind this approach remains the same mimicking the crucial symmetry properties of the underlying differential operators i e the convective operator is approximated by a skew symmetric matrix and the diffusive operator by a symmetric positive definite matrix a novel approach to eliminate the checkerboard spurious modes without introducing any non physical dissipation is proposed to do so a fully conservative regularization of the convective term is used the supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed finally the new discretization method is successfully tested for a buoyancy driven turbulent flow in a differentially heated cavity

semigroup kernels poisson bounds and holomorphic functional calculus letlbe the generator of a continuous holomorphic semigroupswhose action is determined by an integral kernelkon a scale of spaceslp x under mild geometric assumptions on x we prove that iflhas a boundedh functional calculus onl2 x andksatisfies bounds typical for the poisson kernel thenlhas a boundedh functional calculus onlp x for eachp 1 moreover if x is of polynomial type andksatisfies second order gaussian bounds we establish criteria forlto have a bounded hormander functional calculus or a bounded davies helffer sjostrand functional calculus

development of an implicit method for multi fluid flow simulations a fully coupled implicit method has been developed for solving the viscous full multi fluid equations which incorporate transport and generation of mass and momentum for each component present in a system this work presents stability analysis and representative computational results of this algorithm the stability analyses demonstrate the performance of several iterative schemes applied to the solution of the linearized block system which arises in the fully implicit formulation these include block jacobi and symmetric block gauss siedel schemes using two forms of relaxation a hierarchy of increasing physical complexity is pursued starting with one dimensional two fluid systems with minimum inter field dynamic coupling and no mass transfer these analyses are then extended to systems employing physically important inter field forces drag dispersion virtual mass the effects of mass transfer multiple fields i e more than 2 and multiple dimensions are considered a two fluid navier stokes code has been developed guided by the stability analyses one dimensional and two dimensional results generated with this code are presented which verify the validity of the stability analyses presented for the coupled scheme and the effectiveness of the method for flows of engineering relevance

active control and drag optimization for flow past a circular cylinder the main objective of this article is to investigate computational methods for the active control and drag optimization of incompressible viscous flow past cylinders using the two dimensional navier stokes equations as the flow model the computational methodology relies on the following ingredients space discretization of the navier stokes equations by finite element approximations time discretization by a second order accurate two step implicit explicit finite difference scheme calculation of the cost function gradient by the adjoint equation approach and minimization of the cost function by a quasi newton method a la bfgs the above methods have been applied to boundary control by rotation of the flow around a circular cylinder and show 30 to 60 drag reduction compared to the fixed cylinder configuration for reynolds numbers in the range from 200 to 1000

cooperative information space distributed macromodels the paper introduces a new approach for the dynamic distributed modelling using the variation principle applied to a functional on trajectories of random process and its connection to the process s information functional the model equations in partial derivatives pde are found by the solution of the variation problem for this functional this allows us to build a two level information model with a random process at the microlevel and dynamic process at the macrolevel the informational macromodels are connected to the equations of irreversible thermodynamics and kinetics the paper focuses on the problem of a space time consolidation which is a new area in the pde theory directly connected to modelling complex systems the synthesized cooperative distributed macromodel is formed during the optimal time spaced movement directed toward the equalization and collectivization of the model operator eigenvectors the mathematical formalism has been applied for the constructive solution to the problems of

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

open and traction boundary conditions for the incompressible navier stokes equations we present numerical schemes for the incompressible navier stokes equations nse with open and traction boundary conditions we use pressure poisson equation ppe formulation and propose new boundary conditions for the pressure on the open or traction boundaries after replacing the divergence free constraint by this pressure poisson equation we obtain an unconstrained nse for stokes equation with open boundary condition on a simple domain we prove unconditional stability of a first order semi implicit scheme where the pressure is treated explicitly and hence is decoupled from the computation of velocity using either boundary condition the schemes for the full nse that treat both convection and pressure terms explicitly work well with various spatial discretizations including spectral collocation and c 0 finite elements moreover when reynolds number is of o 1 and when the first order semi implicit time stepping is used time step size of o 1 is allowed in benchmark computations for the full nse besides standard stability and accuracy check various numerical results including flow over a backward facing step flow past a cylinder and flow in a bifurcated tube are reported numerically we have observed that using ppe formulation enables us to use the velocity pressure pairs that do not satisfy the standard inf sup compatibility condition our results extend that of johnston and liu h johnston j g liu accurate stable and efficient navier stokes solvers based on explicit treatment of the pressure term j comp phys 199 1 2004 221 259 which deals with no slip boundary conditions only

a computational strategy for the regularized 13 moment equations with enhanced wall boundary conditions the challenge of modeling low speed rarefied gas flow in the transition regime is well known in this paper we propose a numerical solution procedure for the regularized 13 moment equations within a finite volume framework the stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first order approximation to model confined flows a complete set of wall boundary conditions for the 13 moment equations are derived based on the maxwell wall boundary model this has been achieved by expanding the molecular distribution function to fourth order accuracy in hermite polynomials empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation monte carlo data the numerical predictions obtained from the regularized 13 moment equations and the navier stokes fourier equations are compared with data generated using the direct simulation monte carlo method for planar couette flow for a range of wall velocities and knudsen numbers 0 012 1 0 the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation monte carlo data the results also highlight limitations that are caused by the use of a first order expansion of the third moment

a collocated grid finite volume method for aeroacoustic computations of low speed flows a numerical algorithm for simulation of acoustic noise generation based on collocated grids is described the approach that was originally developed using a viscous inviscid decomposition technique involves two steps comprising a viscous incompressible flow part and an inviscid or viscous acoustic part on collocated grids the inviscid solution is found to be mesh dependent due to unavoidable extrapolations of the acoustic pressure and density at walls differing from the case on staggered grids where no extrapolation is needed the situation is most pronounced when a sharp body is considered a viscous acoustic algorithm is proposed to overcome the difficulty numerical computations of flows past a circular cylinder and a naca 0015 airfoil show that a viscous viscous coupling is more natural and gives excellent results as compared to those obtained in previous computations based on viscous inviscid coupling on staggered grids the model is applied to the problem of an airfoil exposed to a gust and results are compared to the numerical results of lockard and morris aiaa j 36 6 1998 907

the boundary value problem and the jensen inequality for an entropy functional of a markov diffusion process the paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process expressed through an additive functional of the diffusion process with a lagrangian determined by the parameters of a controlled stochastic equation these results include a minimum condition for the entropy functional and the functional s jensen inequality which both are useful for the solution of important mathematical and applied problems

the l p theory of divergence form elliptic operators under the dirichlet condition abstract let a be the 2 m th order elliptic operator of divergence form with bounded measurable coefficients defined in a domain of r n with smooth boundary for 1 p we regard a as a bounded operator from the l p sobolev space h 0 m p to h m p trying to extend the result which has been obtained only in the case r n or in the case m 1 to the general case we succeed in constructing the resolvent a 1 and estimating its operator norm for some when the leading coefficients are uniformly continuous applying the result for l p resolvents we show that the operator associated with a in l p generates an analytic semigroup and obtain exponential decay estimates for the heat kernel the resolvent kernel and their derivatives of order up to m 1 we also give a perturbation theorem for heat kernels

large eddy simulation of an oscillating cylinder in a steady flow in this work large eddy simulation is used to study the flow around a circular cylinder undergoing streamwise sinusoidal oscillations this benchmark case is a first step toward studying engineering applications related to flow induced vibrations both the flow physics which correlate the flow development with the time varying loading of the cylinder at two different oscillation frequencies as well as a validation of the fluid structure interaction methodology through comparison with experimental data for the same configuration are described with the methodology used large eddy simulation based on a finite volume method capable of handling moving meshes gives force predictions that generally agree well with experimentally measured data both with respect to the overall flow development as with force magnitude

solution to the variation problem for information path functional of a controlled random process abstract the paper introduces a new approach to dynamic modeling using the variation principle applied to a functional on trajectories of a controlled random process and its connection to the process information functional in v s lerner dynamic approximation of a random information functional j math anal appl 327 1 2007 494 514 available online 5 24 06 we presented the information path functional with the lagrangian determined by the parameters of a controlled stochastic equation in this paper the solution to the path functional s variation problem provides both a dynamic model of a random process and the model s optimal control which allows us to build a two level information model with a random process at the microlevel and a dynamic process at the macrolevel a wide class of random objects modeled by the markov diffusion process and a common structure of the process information functional leads to a universal information structure of the dynamic model which is specified and identified on a particular object with the applied optimal control functions the developed mathematical formalism based on classical methods is aimed toward the solution of problems identification combined with an optimal control synthesis which is practically implemented and also demonstrated in the paper s example

characterizations of hardy spaces associated to higher order elliptic operators abstract in this paper the authors first show that the classical hardy space h 1 r n can be characterized by the non tangential maximal functions and the area integrals associated with the semigroups e t p and e t p respectively where p is an elliptic operator with real constant coefficients of homogeneous order 2m m 1 moreover the authors also prove that h 1 r n can be characterized by the riesz transforms m p 1 2 if and only if m is an odd integer in the main part of this paper the authors develop a theory of hardy space associated with l where l is a higher order divergence form elliptic operator with complex bounded measurable coefficients the authors set up a molecular hardy space h l 1 r n and give its characterizations by area integrals related to the semigroups e t l and e t l respectively finally authors give the h l 1 l 1 boundedness of riesz transforms square functions and maximal functions associated with l

equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form we study the heat kernel of higher order elliptic operators or systems under divergence form on rn ellipticity is in the sense of garding inequality we show that for homogeneous operators gaussian upper bounds and holder regularity of the heat kernel is equivalent to local regularity of weak solutions we also show stability of such bounds under l perturbations of the coefficients or under perturbations with bounded coefficients lower order terms such a criterion allows us to obtain heat kernel bounds for operators or systems with uniformly continuous or vmo coefficients

a nonreflecting outlet boundary condition for incompressible unsteady navier stokes calculations abstract the goal of this work is to adapt a nonreflecting outlet boundary condition derived from a wave equation to the numerical solution of the full incompressible navier stokes equations for an elliptic unsteady free shear flow the numerical results show that a significant improvement is achieved with this nonreflecting boundary condition in comparison with the results obtained by using free boundary layer type conditions the physical phenomena studied concern the onset of the kelvin helmholtz instability in the free non forced shear layer and certain 2d characteristics of transition towards turbulence these phenomena are simulated naturally without imposing perturbations the frequency of the organized vortices and the spread of the mixing layer are correctly predicted the performances of the method are shown through comparison with the physical experiments owing to the nonreflecting boundary conditions the feedback noises are inhibited effectively so that the computation domain can be reduced and the dynamic characteristics of the flow are maintained up clearly to the outlet boundary

a lagged implicit segregated data reconstruction procedure to treat open boundaries the problem of treating open boundaries is still a challenging one applying fully developed condition is constrained to long enough domains without having enough physical evidence about what happens on boundaries the domain extent could not be shortened and computational costs could not be reduced from the advent of free open boundary conditions they were confined to mixed finite element procedures recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction a wider class of flow solvers available however rely on the segregated procedure where the velocity components and pressure are solved in succession moreover many finite volume algorithms do not use the shape function reconstruction in this work by proposing a lagged implicit procedure we have extended the application of the open boundary condition to these wider classes of flow solvers the proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement which is easily applicable to any segregated and coupled flow solver to validate the compatibility of this extension benchmark problem of backward facing step is solved on successively truncated domains where open boundary may pass through recirculation zones results show that the proposed extension works fine for that problem it reduced the computational domain length and hence memory by a factor of 4 6 and the required computational time by a factor of 21 flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well

tent space well posedness for parabolic cauchy problems with rough coefficients abstract we study the well posedness of cauchy problems on the upper half space r n 1 associated to higher order systems t u 1 m 1 div m a m u with bounded measurable and uniformly elliptic coefficients we address initial data lying in l p 1 p and bmo p spaces and work with weak solutions our main result is the identification of a new well posedness class given for p 1 by distributions satisfying m u t m p 2 where t m p 2 is a parabolic version of the tent space of coifman meyer stein in the range p 2 this holds without any further constraints on the operator and for p it provides a carleson measure characterization of bmo with non autonomous operators we also prove higher order l p well posedness previously only known for the case m 1 the uniform l p boundedness of propagators of energy solutions plays an important role in the well posedness theory and we discover that such bounds hold for p close to 2 this is a consequence of local weak solutions being locally holder continuous with values in spatial l l o c p for some p 2 what is also new for the case m 1

on second order periodic elliptic operators in divergence form we consider second order strongly elliptic operators with complex coecients in divergence form on r d we assume that the coecients are all periodic with a common period if the coecients are continu ous we derive gaussian bounds with the correct small and large time asymptotic behaviour on the heat kernel and all its holder deriva tives moreover we show that the first order riesz transforms are bounded on the lp spaces with p 2 h1 1i secondly if the coe cients are holder continuous we prove that the first order derivatives of the kernel satisfy good gaussian bounds then we establish that the second order derivatives exist and satisfy good bounds if and only if the coecients are divergence free or if and only if the second order riesz transforms are bounded finally if the third order derivatives exist with good bounds then the coecients must be constant

the lp resolvents of elliptic operators with uniformly continuous coefficients abstract we consider the strongly elliptic operator a of order 2 m in the divergence form with bounded measurable coefficients and assume that the coefficients of top order are uniformly continuous for 1 p a is a bounded linear operator from the l p sobolev space h m p into h m p we will prove that a 1 exists in h m p for some and estimate its operator norm

calculation of flow in transition duct using second order closure and wall functions our purpose is to determine whether the deficiences reported in a previous study could be overcome by using an alternative high reynolds number second order closure that will be described next

dynamic approximation of a random information functional abstract using the probabilistic evaluation of the marcovian diffusion process by a functional of action the paper introduces a dynamic approximation of a random information functional defined on the process trajectories and determined by the parameters of a controlled stochastic equation the developed mathematical formalism is aimed toward a dynamic modeling of a random object

boundary conditions for open boundaries for the incompressible navier stokes equation abstract in this paper we investigate new boundary conditions for the incompressible time dependent navier stokes equation especially inflow and outflow conditions are considered the equations are linearized around a constant flow so that we can use laplace fourier technique to investigate the strength of boundary layers at open boundaries such layers are unphysical and new boundary conditions are proposed so that these boundary layers are suppressed we also show that the boundary conditions we propose do not produce divergence furthermore they give solutions that do not grow in time as long as the forcing function in the system does not we also discuss the numerical treatment of boundaries when fourth order accurate finite difference operators are used to approximate spatial derivatives using higher order methods introduces eigensolutions with boundary layer thickness of the same order of magnitude as the grid size these eigensolutions have to be suppressed in order to not destroy the fourth order accuracy of the method numerical results for the non linear navier stokes equation together with the new boundary conditions are presented these calculations confirm that the results for the linearized problem hold for the non linear problem as well

high order finite difference and multigrid methods for spatially evolving instability in a planar channel a computational study of the spatial instability of planar poiseuille flow is presented a fourth order finite difference with a fully implicit time marching scheme is developed on a staggered grid a semi coarsening multigrid method is applied to accelerate convergence for the implicit scheme at each time step and a line distributive relaxation is developed as a fast solver which is very robust and efficient for anisotropic grids a new treatment for outflow boundary conditions makes the buffer area as short as one wavelength the computational results demonstrate high accuracy in terms of agreement with linear theory and excellent efficiency in the sense that cost is comparable to and usually less than explicit schemes

immersed boundary methods for general finite difference and finite volume navier stokes solvers we present an immersed boundary algorithm for incompressible flows with complex boundaries suitable for cartesian or curvilinear grid system the key stages of any immersed boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary a line in 2d a surface in 3d and the spreading of a force field from the immersed boundary to the neighboring mesh points to enforce the desired boundary conditions on the immersed boundary points we propose a technique that uses the reproducing kernel particle method w k liu s jun y f zhang reproducing kernel particle methods int j numer methods fluids 20 8 1995 1081 1106 for the interpolation and spreading unlike other methods presented in the literature the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved independent of the grid topology uniform or non uniform cartesian or curvilinear the technique is easy to implement and is able to maintain the order of the original underlying spatial discretization applications to two and three dimensional flows in cartesian and non cartesian grid system with uniform and non uniform meshes are presented

multigrid methods for incompressible heat flow problems with an unknown interface finite volume multigrid methods are presented for solving incompressible heat flow problems with an unknown melt solid interface mainly in solidification applications using primitive variables on collocated grids the methods are implemented based on a multiblock and multilevel approach allowing the treatment of a complicated geometry the inner iterations are based on the simple scheme in which the momentum interpolation is used to prevent velocity pressure decoupling the outer iterations are set up for interface update through the isotherm migration method v cycle and full multigrid fmg methods are tested for both two and three dimensional problems and are compared with a global newton s method and a single grid method the effects of prandtl and rayleigh numbers on the performance of the schemes are also illustrated among these approaches fmg has proven to be superior on performance and efficient for large problems sample calculations are also conducted for horizontal bridgman crystal growth and the performance is compared with that of traditional single grid methods

efficient and non reflecting far field boundary conditions for incompressible flow calculations abstract traditionally the artificial compressibility ac method of chorin is used for simulation of low speed and incompressible flows in this method the difficulty of continuity and momentum equations decoupling is removed by adding an artificial time derivative of pressure to the continuity equation for the first time a fully two dimensional upwind scheme was presented for ac equations by using characteristic structure of equations by the authors in this paper a new remote boundary calculation method is presented by using the idea of characteristics for these equations instead of simple boundary conditions which usually are employed for incompressible flows the flow quantities at the far field boundaries are evaluated by compatibility relations of characteristic equations this is implemented by assuming a row of ghost cells outside of the far field boundary and using the flux calculation method based on characteristics similar to the inside of computational domain the idea in conjunction with multidimensional characteristic based scheme was tested for incompressible flow around circular cylinder in comparison with conventional far field boundary condition and showed good improvements in the terms of accuracy and convergence speed

erratum to perturbation and interpolation theorems for the h calculus with applications to differential operators we prove comparison theorems for the h calculus that allow to transfer the property of having a bounded h calculus from one sectorial operator to another the basic technical ingredient are suitable square function estimates these comparison results provide a new approach to perturbation theorems for the h calculus in a variety of situations suitable for applications our square function estimates also give rise to a new interpolation method the rademacher interpolation we show that a bounded h calculus is characterized by interpolation of the domains of fractional powers with respect to rademacher interpolation this leads to comparison and perturbation results for operators defined in interpolation scales such as the l p scale we apply the results to give new proofs on the h calculus for elliptic differential operators including schrodinger operators and perturbed boundary conditions as new results we prove that elliptic boundary value problems with bounded uniformly coefficients have a bounded h calculus in certain sobolev spaces and that the stokes operator on bounded domains with c 1 1 has a bounded h calculus in the helmholtz scale l p p 1

gaussian estimates for fundamental solutions of second order parabolic systems with time independent coefficients auscher mcintosh and tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on r n in particular in the case when n 2 they obtained gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients we study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded measurable time independent coefficients and extend their results to the systems of parabolic equations

a new proof of moser s parabolic harnack inequality using the old ideas of nash in 1958 nash published his fundamental work on the local holder continuity of solutions of second order parabolic equations with coefficients which need not be smooth 8 the primary purpose of that work was to study the properties of the fundamental solution corresponding to the parabolic operator and from these properties to derive regularity for a general solution though the work is often cited in the literature about weak solutions of elliptic and parabolic equations one feels that nash s ideas were never fully understood and maybe still are not and that because of this the more understandable and seemingly more fruitful ideas of de giorgi 4 and moser 6 7 were subsequently adopted

unstructured grid arbitrarily shaped element method for fluid flow simulation a three dimensional unstructured grid arbitrarily shaped element method is developed for solving the navier stokes equations the proposed method is generally applicable to arbitrarily shaped elements and thus offers the potential to unify many of the different grid topologies into a single formulation examples of grid topologies include a structured hexahedral mesh unstructured tetrahedral mesh hybrid mesh using a combination of hexahedra tetrahedra prisms and pyramids cartesian mesh with elements cubes cut by flow boundaries and mixed arbitrary multiblock meshes the concept of such an arbitrary element method is developed and implemented into a pressure based finite volume solver it utilizes a collocated and cell centered storage scheme expressions for second order discretizations of the convection and diffusion terms are derived and presented for an arbitrarily shaped element the developed code as a first step is applied to two selected three dimensional viscous flows using a structured hexahedral mesh and an unstructured tetrahedral mesh it is demonstrated that the concept of the arbitrarily shaped element method can be viable and efficient

letter to the editor a collocated finite volume scheme to solve free convection for general non conforming grids we present a new collocated numerical scheme for the approximation of the navier stokes and energy equations under the boussinesq assumption for general grids using the velocity pressure unknowns this scheme is based on a recent scheme for the diffusion terms stability properties are drawn from particular choices for the pressure gradient and the non linear terms convergence of the approximate solutions may be proven mathematically numerical results show the accuracy of the scheme on irregular grids

the lp resolvents of second order elliptic operators of divergence form under the dirichlet condition abstract let a be the 2mth order elliptic operator of divergence form with bounded measurable coefficients defined in a domain of r n for 1 h 0 m p to h m p it is known that when r n we can construct the resolvent a 1 and estimate its operator norm for some if the leading coefficients are uniformly continuous in this paper we try to extend this result to a general domain it is successful when m 1 if is the half space or a domain with c2 bounded boundary for m 1 it is shown that the problem is reduced to the case where is the half space and a is a homogeneous operator with constant coefficients we also give a perturbation theorem

higher order elliptic and parabolic systems with variably partially bmo coefficients in regular and irregular domains abstract the solvability in sobolev spaces is proved for divergence form complex valued higher order parabolic systems in the whole space on a half space and on a reifenberg flat domain the leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder the directions in which the coefficients are only measurable vary depending on each cylinder the corresponding elliptic problem is also considered

convergence rates and interior estimates in homogenization of higher order elliptic systems abstract this paper is concerned with the quantitative homogenization of 2m order elliptic systems with bounded measurable rapidly oscillating periodic coefficients we establish the sharp o e convergence rate in w m 1 p 0 with p 0 2 d d 1 in a bounded lipschitz domain in r d as well as the uniform large scale interior c m 1 1 estimate with additional smoothness assumptions the uniform interior c m 1 1 w m p and c m 1 estimates are also obtained as applications of the regularity estimates we establish asymptotic expansions for fundamental solutions

pseudo fractional integral inequality of chebyshev type in this paper we give a general version of chebyshev type inequality for pseudo convolution integral on a semiring a b our result is flexible enough to support both pseudo integral and convolution integral e g fractional integral thus closing the series of papers it includes the corresponding results of agahi et al 1 as a special case finally some concluding remarks are drawn and some open problems for further investigations are given

an observer s information dynamics acquisition of information and the origin of the cognitive dynamics conventional information science considers an information process but traditionally uses the probability measure for random states and shannon s entropy as the uncertainty function of these states this paper presents a new approach based on an integral information measure of the random process an entropy functional ef on the trajectories of the process accumulates and encodes the process inner connections between the information states the application of a variation principle vp to the ef determines the process information path functional ipf whose extremal trajectories describe the informational dynamics of this process information dynamics with the vp invariant relations evaluate the information content of a random process expose its information code and reveal a conserved hidden information produced at an acquisition of the process information by introducing both objective and subjective information observers we consider the observers information cognitive dynamics and neurodynamics based on the ef ipf approach the universal nature of information process dynamics and regularities discovered in the information observers have many applications not only in cognitive and intelligent systems but also in different biological social and economic systems

explicit estimates on the fundamental solution of higher order parabolic equations with measurable coefficients for some positive constants ci and all t 0 and x y 0 such estimates for uniformly elliptic operators have been proved under a variety of local regularity assumptions 14 17 and more recently for operators with measurable coefficients provided 2m n 8 this has been shown to be true in the limit case 2m n 3 11 while there are examples that show that 1 is not in general true when 2m n and h has measurable coefficients 10 in 6 estimates are obtained for singular or degenerate operators with measurable coefficients with the euclidean distance being replaced by one that reflects the behavior of the coefficients near the singularities we refer to 9 for a detailed account of much of the recent progress on the spectral theory of higher order elliptic operators the problem of sharpening such bounds was addressed recently the sharpness of estimates is checked by comparison against short time asymptotics of k t x y these were proved by tintarev 19 who showed following work of evgrafov and postnikov 12 that if 0 r if the coefficients a are smooth and if the symbol a x satisfies the strong doi 10 1006 jdeq 2000 3940 available online at http www idealibrary com on

the neumann problem for higher order elliptic equations with symmetric coefficients in this paper we establish well posedness of the neumann problem with boundary data in l 2 or the sobolev space dot w 2 1 in the half space for linear elliptic differential operators with coefficients that are constant in the vertical direction and in addition are self adjoint this generalizes the well known well posedness result of the second order case and is based on a higher order and one sided version of the classic rellich identity and is the first known well posedness result for an elliptic divergence form higher order operator with rough variable coefficients and boundary data in a lebesgue or sobolev space

regularity in oscillatory nonlinear elliptic systems we give uniform bounds in morrey sobolev spaces h1 for weak solutions ue to oscillatory nonlinear elliptic systems the main novelty is in the precise qualitative description of the e uniform morrey exponent in terms of the ellipticity ratio of the elliptic systems this is achieved by showing that weak solutions of general nonlinear elliptic systems with lipschitz coefficients are of class w2 p locally or globally depending on assumptions for an exponent p 2 that is independent of dimensions and for which p 2 is inversely proportional to the ellipticity ratio