image difference prediction from color to spectral we propose a new strategy to evaluate the quality of multi and hyperspectral images from the perspective of human perception we define the spectral image difference as the overall perceived difference between two spectral images under a set of specified viewing conditions illuminants first we analyze the stability of seven image difference features across illuminants by means of an information theoretic strategy we demonstrate in particular that in the case of common spectral distortions spectral gamut mapping spectral compression spectral reconstruction chromatic features vary much more than achromatic ones despite considering chromatic adaptation then we propose two computationally efficient spectral image difference metrics and compare them to the results of a subjective visual experiment a significant improvement is shown over existing metrics such as the widely used root mean square error

the structure of tame minimal dynamical systems for general groups we use the structure theory of minimal dynamical systems to show that for a general group gamma a tame metric minimal dynamical system x gamma has the following structure open image in new window here i tilde x is a metric minimal and tame system ii eta is a strongly proximal extension iii y is a strongly proximal system iv pi is a point distal and rim extension with unique section v theta theta and iota are almost one to one extensions and vi sigma is an isometric extension when the map pi is also open this diagram reduces to open image in new window in general the presence of the strongly proximal extension eta is unavoidable if the system x gamma admits an invariant measure mu then y is trivial and x tilde x is an almost automorphic system i e x overset iota rightarrow z where iota is an almost one to one extension and z is equicontinuous moreover mu is unique and iota is a measure theoretical isomorphism iota x mu gamma rightarrow z lambda gamma with lambda the haar measure on z thus this is always the case when gamma is amenable

on partial shadowing of complete pseudo orbits abstract in recent years many new definitions of shadowing using a notion of ergodic or average pseudo orbit were introduced while under the assumption of chain mixing average pseudo orbit usually can be equivalently replaced by pseudo orbit in these definitions of shadowing it is not completely clear when these shadowing properties i e approximation of a pseudo orbit by a real orbit on a sufficiently large set of indices can or cannot occur in this paper we analyze necessary and sufficient conditions for shadowing over a set with positive density or syndetic while we do not provide full characterization a few relations to standard notions from topological dynamics are obtained

quasi factors of zero entropy systems for minimal systems x t of zero topological entropy we demon strate the sharp difference between the behavior regarding entropy of the sys tems m x t and 2x t induced by t on the spaces m x of prob ability measures on x and 2x of closed subsets of x it is shown that the system m x t has itself zero topological entropy two proofs of this the orem are given the first uses ergodic theoretic ideas the second relies on the different behavior of the banach spaces ln and ln with respect to the existence of almost hilbertian central sections of the unit ball in contrast to this theorem we construct a minimal system x t of zero entropy with a minimal subsystem y t of 2 t whose entropy is positive school of mathematics tel aviv university ramat aviv israel e mail address glasner0math tau ac il institute of mathematics hebrew university jerusalem israel e mail address weissfmath huji ac il this content downloaded from 207 46 13 117 on sun 23 oct 2016 04 35 33 utc all use subject to http about jstor org terms

pointwise rates of convergence for the oliker prussner method for the monge ampere equation we study the oliker prussner method exploiting its geometric nature we derive discrete stability and continuous dependence estimates in the max norm by using a discrete alexandroff estimate and the brunn minkowski inequality we show that the method is exact for all convex quadratic polynomials provided the underlying set of nodes is translation invariant within the domain nodes still conform to the domain boundary this gives a suitable notion of operator consistency which combined with stability leads to pointwise rates of convergence for classical and non classical solutions of the monge ampere equation

chaos and indecomposability abstract we use recent developments in local entropy theory to prove that chaos in dynamical systems implies the existence of complicated structure in the underlying space earlier mouron proved that if x is an arc like continuum which admits a homeomorphism f with positive topological entropy then x contains an indecomposable subcontinuum barge and diamond proved that if g is a finite graph and f g g is any map with positive topological entropy then the inverse limit space lim g f contains an indecomposable continuum in this paper we show that if x is a g like continuum for some finite graph g and f x x is any map with positive topological entropy then lim x f contains an indecomposable continuum as a corollary we obtain that in the case that f is a homeomorphism x contains an indecomposable continuum moreover if f has uniformly positive upper entropy then x is an indecomposable continuum our results answer some questions raised by mouron and generalize the above mentioned work of mouron and also that of barge and diamond we also introduce a new concept called zigzag pair which attempts to capture the complexity of a dynamical systems from the continuum theoretic perspective and facilitates the proof of the main result

mobius orthogonality for generalized morse kakutani flows the prouhet thue morse sequence and its generalizations have occured in many settings morse kakutani flow refers to kakutani s 1967 generalization of the morse minimal flow 1922 these flows are bbb z 2 skew products of almost one to one extensions of the adding machine x rightarrow x 1 on the 2 adic completion of bbb z generalized morse kakutani flow is a k skew product of similar construct with base flow a factor of x rightarrow x 1 on the profinite completion of bbb z and k any compact group abelian or not of countable density the principal result is that sarnak s m o bius orthogonality conjecture holds for a restricted class of generalized morse kakutani flows

the morley element for fourth order elliptic equations in any dimensions in this paper the well known nonconforming morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion the general n dimensional morley element consists of all quadratic polynomials defined on each n simplex with degrees of freedom given by the integral average of the normal derivative on each n 1 subsimplex and the integral average of the function value on each n 2 subsimplex explicit expressions of nodal basis functions are also obtained for this element on general n simplicial grids convergence analysis is given for this element when it is applied as a nonconforming finite element discretization for the biharmonic equation

on uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic pde s we prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations one of them extends some recent uniqueness results by jensen some establish the uniqueness of solutions for second order isaacs equations and hence include the uniqueness results for bellman equations by p l lions our comparison results apply even for discontinuous solutions and so perron s method readily yields the existence of continuous solutions

pointwise theorems for amenable groups in this paper we prove the pointwise ergodic theorem for general locally compact amenable groups along folner sequences that obey some restrictions these restrictions are mild enough so that such sequences exist for all amenable groups we also prove a generalization of the shannon mcmillan breiman theorem to all discrete amenable groups

quantized arnold cat maps can be entropic k systems automorphisms on the irrational rotation algebra with respect to their ergodic properties are studied especially it is shown that for a dense set of the rotation parameter cat maps are entropic k systems

turbulence amalgamation and generic automorphisms of homogeneous structures we study topological properties of conjugacy classes in polish groups with emphasis on automorphism groups of homogeneous countable structures we first consider the existence of dense conjugacy classes the topological rokhlin property we then characterize when an automorphism group admits a comeager conjugacy class answering a question of truss and apply this to show that the homeomorphism group of the cantor space has a comeager conjugacy class answering a question of akin hurley and kennedy finally we study polish groups that admit comeager conjugacy classes in any dimension in which case the groups are said to admit ample generics we show that polish groups with ample generics have the small index property generalizing results of hodges hodkinson lascar and shelah and arbitrary homomorphisms from such groups into separable groups are automatically continuous moreover in the case of oligomorphic permutation groups they have uncountable cofinality and the bergman property these results in particular apply to automorphism groups of many stable 0 categorical structures and of the random graph in this connection we also show that the infinite symmetric group s has a unique non trivial separable group topology for several interesting groups we also establish serre s properties fh and fa

the topology and dynamics of the hyperspaces of normal fuzzy sets and their inverse limit spaces given a compact and connected metric space continuum x we study topological and dynamical properties of the hyperspace of normal fuzzy sets f1 x equipped with the hausdorff endograph or sendograph metric among the many results we show that it is contractible path connected locally contractible locally path connected locally simply connected and locally connected for the endograph metric the hyperspace f1 x is a continuum and then for a topological graph x we show how using the inverse limit approach of barge and martin the inverse limit of a fuzzy dynamical system on x can be realized as an attractor of a fuzzy dynamical system on a manifold

local entropy theory for a countable discrete amenable group action in the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action for such an action we introduce entropy tuples in both topological and measure theoretic settings and build the variational relation be tween these two kinds of entropy tuples by establishing a local variational principle for a given finite open cover moreover based the idea of topological entropy pairs we introduce and study two special classes of such an action uniformly positive entropy and completely positive entropy note that in the building of the local variational principle following romagnoli s ideas two kinds of measure theoretic entropy are introduced for finite borel covers these two kinds of entropy turn out to be the same where danilenko s orbital approach becomes an inevitable tool

vsnr a wavelet based visual signal to noise ratio for natural images this paper presents an efficient metric for quantifying the visual fidelity of natural images based on near threshold and suprathreshold properties of human vision the proposed metric the visual signal to noise ratio vsnr operates via a two stage approach in the first stage contrast thresholds for detection of distortions in the presence of natural images are computed via wavelet based models of visual masking and visual summation in order to determine whether the distortions in the distorted image are visible if the distortions are below the threshold of detection the distorted image is deemed to be of perfect visual fidelity vsnr infin and no further analysis is required if the distortions are suprathreshold a second stage is applied which operates based on the low level visual property of perceived contrast and the mid level visual property of global precedence these two properties are modeled as euclidean distances in distortion contrast space of a multiscale wavelet decomposition and vsnr is computed based on a simple linear sum of these distances the proposed vsnr metric is generally competitive with current metrics of visual fidelity it is efficient both in terms of its low computational complexity and in terms of its low memory requirements and it operates based on physical luminances and visual angle rather than on digital pixel values and pixel based dimensions to accommodate different viewing conditions

the rohlin property for shifts on uhf algebras and automorphisms of cuntz algebras abstract we show that the shift on the uhf algebra m n has the rohlin property for any odd n hence by brotteli et al the crossed product of a uhf algebra by a shift ergodic theory dynam systems 13 1993 615 626 for any n 2 3 and that any automorphism of the cuntz algebra o n n m is outer for any m 0

independence in topological and c dynamics we develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods one of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties we also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to c dynamics

positive topological entropy and δ weakly mixing sets abstract the notion of weakly mixing set is introduced and studied it is proved that weakly mixing sets share many properties with weakly mixing sets in particular if a dynamical system has positive topological entropy then the collection of weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace the existence of weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained these results generalize several well known results and also answer several open questions

properties of the solutions of the linearized monge ampere equation let r n r be a function strictly convex and smooth and det d 2 is the monge ampere generated by given x r n and t 0 let s x t y r n y x x y x t the purpose of this paper is to study the properties of the solutions of the linearized monge ampere equation given by a ij x d ij u 0 where the coefficients a ij x are the cofactors of the matrix d 2 x it is assumed that satisfies a doubling condition on the sets s x t and a uniform continuity condition at every scale with respect to lebesgue measure we establish that the distribution functions of nonnegative solutions u at altitude t decay like a negative power of t and prove an invariant harnack s inequality on the sections s x t all the estimates are independent of the regularity of and depend only on the constants in the hypotheses made on the measure

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

topological conjugacy and transitivity for a class of piecewise monotone maps of the interval on dit qu une application continue f d un intervalle compact dans lui meme est markov lineaire s il est lineaire par morceaux et l ensemble de tous les f k x ou k 0 et x une extremite d un morceau lineaire est fini on donne une classification effective pour des applications de markov lineaires et une procedure effective pour determiner quand une telle application est transitive

the dynamics of continuous maps of finite graphs through inverse limits suppose that f g g is a continuous piecewise monotone function on a finite graph g then the following are equivalent i f has positive topological entropy ii there are disjoint intervals i1 and i2 and a positive integer n with i1 u i2 c fn ji n fn i2 iii the inverse limit space constructed by using f on g as a single bonding map contains an indecomposable subcontinuum this result generalizes known results for the interval and circle

entropy chaos and weak horseshoe for infinite dimensional random dynamical systems in this paper we study the complicated dynamics of infinite dimensional random dynamical systems that include deterministic dynamical systems as their special cases in a polish space without assuming any hyperbolicity we prove if a continuous random map has a positive topological entropy then it contains a topological horseshoe we also show that the positive topological entropy implies the chaos in the sense of li yorke the complicated behavior exhibited here is induced by the positive entropy but not the randomness of the system 2017 wiley periodicals inc

strong asymptotic abelianness for entropic k systems we prove that in entropick systems of type ii1 the automorphism is strongly asymptotically abelian

chaos periodicity and snakelike continua the results of this paper relate the dynamics of a continuous map f of the interval and the topology of the inverse limit space with bonding map f these inverse limit spaces have been studied by many authors and are examples of what bing has called snakelike continua roughly speaking we show that when the dynamics of f are complicated the inverse limit space contains indecomposable subcontinua we also establish a partial converse

combinatorial lemmas and applications to dynamics abstract the well known combinatorial lemma of karpovsky milman and alon and a very recent one of kerr and li are extended the obtained lemmas are applied to study the maximal pattern entropy introduced in the paper it turns out that the maximal pattern entropy is equal to the supremum of sequence entropies over all sequences both in topological and measure theoretical settings moreover it is shown the maximal pattern entropy of any topological system is log k for some k n with k the maximal length of intrinsic sequence entropy tuples and a zero dimensional system has zero sequence entropy for any sequence if and only if the maximal pattern with respect to any open cover is of polynomial order

turbulence representations and trace preserving actions we establish criteria for turbulence in certain spaces of c algebra repre sentations and apply this to the problem of nonclassiability by countable structures for group actions on a standard atomless probability space x and on the hypernite ii1 factor r we also prove that the conjugacy action on the space of free actions of a countably innite amenable group on r is turbulent and that the conjugacy action on the space of ergodic measure preserving ows on x is generically turbulent

color image quality assessment from prediction to optimization while image difference metrics show good prediction performance on visual data they often yield artifact contaminated results if used as objective functions for optimizing complex image processing tasks we investigate in this regard the recently proposed color image difference cid metric particularly developed for predicting gamut mapping distortions we present an algorithm for optimizing gamut mapping employing the cid metric as the objective function resulting images contain various visual artifacts which are addressed by multiple modifications yielding the improved color image difference icid metric the icid based optimizations are free from artifacts and retain contrast structure and color of the original image to a great extent furthermore the prediction performance on visual data is improved by the modifications

on li yorke pairs the li yorke definition of chaos proved its value for interval maps in this paper it is considered in the setting of general topological dynamics we adopt two opposite points of view on the one hand sufficient conditions for li yorke chaos in a topological dynamical system are given we solve a long standing open question by proving that positive entropy implies li yorke chaos on the other hand properties of dynamical systems without li yorke pairs are investigated in addition to having entropy 0 they are minimal when transitive and the property is stable under factor maps arbitrary products and inverse limits finally it is proved that minimal systems without li yorke pairs are disjoint from scattering systems

crossed products and entropy of automorphisms abstract let a be an exact c algebra let g be a locally compact group and let a g be a c dynamical system each automorphism g induces a spatial automorphism ad g on the reduced crossed product a g in this paper we examine the question first raised by e stormer of when the topological entropies of g and ad g coincide this had been answered by n brown for the particular case of discrete abelian groups using different methods we extend his result to preservation of entropy for g when the subgroup of aut g generated by the corresponding inner automorphism ad g has compact closure this property is satisfied by all elements of a wide class of groups called locally fia this class includes all abelian groups both discrete and continuous as well as all compact groups

dynamical entropy in banach spaces we introduce a version of voiculescu brown approximation entropy for isometric automorphisms of banach spaces and develop within this framework the connection between dynamics and the local theory of banach spaces as discovered by glasner and weiss our fundamental result concerning this contractive approximation entropy or ca entropy characterizes the occurrence of positive values both geometrically and topologically this leads to various applications for example we obtain a geometric description of the topological pinsker factor and show that a c algebra is type i if and only if every multiplier inner automorphism has zero ca entropy we also examine the behaviour of ca entropy under various product constructions and determine its value in many examples including isometric automorphisms of l p for 1 p and noncommutative tensor product shifts

compact group automorphisms addition formulas and fuglede kadison determinants for a countable amenable group and an element f in the integral group ring z being invertible in the group von neumann algebra of we show that the entropy of the shift action of on the pontryagin dual of the quotient of z by its left ideal generated by f is the logarithm of the fuglede kadison determinant of f for the proof we establish an p version of rufus bowen s denition of topological entropy addition formulas for group extensions of countable amenable group actions and an approximation formula for the fuglede kadison determinant of f in terms of the determinants of perturbations of the compressions of f

image dependent gamut mapping as optimization problem we explore the potential of image dependent gamut mapping as a constrained optimization problem the performance of our new approach is compared to standard reference gamut mapping algorithms in psycho visual tests

ℱ mixing property and ℱ1 ℱ2 everywhere chaos of inverse limit dynamical systems abstract this paper investigates some chaotic properties via furstenberg families generated by inverse limit dynamical systems it is proved that the inverse limit dynamical system lim x f f of a dynamical system x f is transitive resp mixing 1 2 everywhere chaotic if and only if the system n 0 f n x f n 0 f n x is transitive resp mixing 1 2 everywhere chaotic where 1 and 2 are furstenberg families

stable sets and mean li yorke chaos in positive entropy systems abstract it is shown that in a topological dynamical system with positive entropy there is a measure theoretically rather big set such that a multivariant version of mean li yorke chaos happens on the closure of the stable or unstable set of any point from the set it is also proved that the intersections of the sets of asymptotic tuples and mean li yorke tuples with the set of topological entropy tuples are dense in the set of topological entropy tuples respectively

the maximum principle for viscosity solutions of fully nonlinear second order partial differential equations we prove that viscosity solutions in w1 of the second order fully nonlinear equation f d2u du u 0 are unique when i f is degenerate elliptic and decreasing in u or ii f is uniformly elliptic and nonincreasing in u we do not assume that f is convex the method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions respectively this method is completely different from that used in lions 8 9 for second order problems with f convex in d 2 u and from that used by crandall lions 3 and crandall evans lions 2 for fully nonlinear first order problems

sensitivity of set valued discrete systems abstract consider the surjective continuous map f x x and the continuous map f of k x into itself induced by f where x is a compact metric space and k x is the space of all non empty compact subsets of x endowed with a hausdorff metric in this paper we give examples showing that sensitivity of f does not imply sensitivity of f furthermore we prove that if f is a surjective continuous interval map then f is sensitive if and only if f is sensitive

a transitive homeomorphism on the pseudoarc which is semiconjugate to the tent map a powerful theorem and construction of wayne lewis are used to build two homeomorphisms on the pseudoarc each of which is semiconjugate to the tent map on the unit interval the first homeomorphism is transitive thus answering a question of marcy barge as to whether such homeomorphisms exist the second homeomorphism admits wandering points also it is proven that any homeomorphism on the pseudoarc that is semiconjugate to the tent map and is irreducible with respect to the semiconjugacy must either be transitive or admit wandering points a continuum is a compact connected metric space a continuum x is indecomposable if every proper subcontinuum of x is nowhere dense in x and x is hereditarily indecomposable if each subcontinuum of x is indecomposable a continuum x is chainable if for each e 0 there is a chain c c0 cn of open sets of diameter less than e that covers x c is a chain means that ci n ej 0 iff ii ii 2 or in the hilbert cube are pseudoarcs here we will show that this continuum admits a transitive homeomorphism thus answering a question of marcy barge in addition this homeomorphism has the property that it is semiconjugate to the tent map on the unit interval for more information on pseudoarcs and indecomposable continua see bil bi4 l1 l2 k km kr and ot exotic continua have been making their appearance in dynamical systems ever since the early part of this century with the work of c caratheodory c received by the editors may 20 1988 and in revised form july 25 1989 presented at the 1988 spring topology conference university of florida gainesville florida 32611 1980 mathematics subject classification 1985 revision primary 54f20 secondary 54h20

asymptotic pairs stable sets and chaos in positive entropy systems abstract we consider positive entropy g systems for certain countable discrete infinite left orderable amenable groups g we will use local analysis to study the connection between the existence of asymptotic pairs chaotic sets and stable sets examples are given for the case of integer lattice groups the heisenberg group and the groups of integral unipotent upper triangular matrices

weak existence for the semigeostrophic equations formulated as a coupled monge ampere transport problem hoskins s semigeostrophic equations are reformulated as a coupled monge ampere transport problem b j hoskins quart j royal met soc 97 1971 pp 139 153 existence of global weak solutions is obtained for this formulation

generically there is but one self homeomorphism of the cantor set we describe a self homeomorphism r of the cantor set x and then show that its conjugacy class in the polish group h x of all homeomorphisms of x forms a dense g subset of h x we also provide an example of a locally compact second countable topological group which has a dense conjugacy class

combinatorial independence in measurable dynamics abstract we develop a fine scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence the concepts of measure ie tuples and measure in tuples are introduced and studied in analogy with their counterparts in topological dynamics local characterizations of the pinsker von neumann algebra and its sequence entropy analogue are given in terms of combinatorial independence l 1 geometry and voiculescu s completely positive approximation entropy among the novel features of our local study is the treatment of general discrete acting groups with the structural assumption of amenability in the case of entropy

a nonconforming morley finite element method for the fully nonlinear monge ampere equation in this paper we study finite element approximations of the viscosity solution of the fully nonlinear monge ampere equation det d 2 u f 0 using the well known nonconforming morley element our approach is based on the vanishing moment method which was recently proposed as a constructive way to approximate fully nonlinear second order equations by the author and feng j sci comput 38 1 74 98 2009 the vanishing moment method approximates the monge ampere equation by the fourth order quasilinear equation epsilon delta 2u epsilon rm det d 2u epsilon f with appropriate boundary conditions we develop a finite element scheme using the n dimensional morley element introduced in wang and xu numer math 103 155 169 2006 to approximate the regularized fourth order problem in two and three dimensions and then derive optimal order error estimates

a modified characteristic finite element method for a fully nonlinear formulation of the semigeostrophic flow equations this paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear monge ampere equation and a transport equation the system is the eulerian formulation in the dual space for b j hoskins semigeostrophic flow equations which are widely used in meteorology to model frontogenesis to overcome the difficulty caused by the strong nonlinearity we first formulate at the differential level a vanishing moment approximation of the semigeostrophic flow equations a methodology recently proposed by the authors x feng and m neilan j sci comput 38 2009 pp 74 98 which involves approximating the fully nonlinear monge ampere equation by a family of fourth order quasilinear equations we then construct a fully discrete modified characteristic finite element method for the regularized problem it is shown that under certain mesh constraint the proposed numerical method converges with an optimal order rate of convergence in particular the obtained error bounds show explicit dependence on the regularization parameter varepsilon numerical tests are also presented to validate the theoretical results and to gauge the efficiency of the proposed fully discrete modified characteristic finite element method

basins of wada abstract we describe situations in which there are several regions more than two with the wada property namely that each point that is on the boundary of one region is on the boundary of all we argue that such situations arise even in studies of the forced damped pendulum where it is possible to have three attractor regions coexisting and the three basins of attraction have the wada property

finite element approximations of general fully nonlinear second order elliptic partial differential equations based on the vanishing moment method the vanishing moment method was introduced by the authors in feng and neilan 2009 as a reliable methodology for computing viscosity solutions of fully nonlinear second order partial differential equations pdes it is based on the simple idea of approximating a hard to handle fully nonlinear second order pde by a family parameterized by a small parameter e of easy to handle quasilinear fourth order pdes the primary objective of this article is to present a comprehensive finite element analysis for the vanishing moment approximation of general fully nonlinear second order elliptic pdes which fulfill some structure conditions abstract methodological and convergence analysis frameworks of conforming finite element methods are first developed for fully nonlinear second order pdes in a general setting the abstract framework is then applied to three prototypical nonlinear equations namely the monge ampere equation the equation of prescribed gauss curvature and the infinity laplacian equation numerical experiments are presented for each problem to validate the theoretical error estimate results and to gauge the efficiency of the proposed numerical methods and the vanishing moment methodology

on distributionally chaotic and null systems abstract by a topological dynamical system we mean a pair x f where x is a compactum and f is a continuous self map on x a system is said to be null if its topological sequence entropies are zero along all strictly increasing sequences of natural numbers we show that there exists a null system which is distributionally chaotic this system admits open distributionally scrambled sets and its collection of all maximal distributionally scrambled sets has the same cardinality as the collection of all subsets of the phase space finally such system can even exist on continua

δ weakly mixing subset in positive entropy actions of a nilpotent group abstract the notion of weakly mixing subsets is introduced for countable torsion free discrete group actions it is shown that for a finitely generated torsion free discrete nilpotent group action positive topological entropy implies the existence of weakly mixing subsets and while there exists a finitely generated torsion free discrete solvable group action which has positive topological entropy but without any weakly mixing subsets

numerical methods for fully nonlinear elliptic equations of the monge ampere type abstract in this article we discuss the numerical solution of the dirichlet problem for the monge ampere equation in two dimensions the solution of closely related problems is also discussed these include a family of pucci s equations the equation prescribing the harmonic mean of the eigenvalues of the hessian of a smooth function of two variables and a minimization problem from nonlinear elasticity where the cost functional involves the determinant of the gradient of vector valued functions to solve the monge ampere equation we consider two methods the first one reduces the monge ampere equation to a saddle point problem for a well chosen augmented lagrangian to solve this saddle point problem we advocate an uzawa douglas rachford algorithm the second method combines nonlinear least squares and operator splitting this second method being simpler to implements we apply variants of it to the solution of the other problems for the space discretization we use mixed finite element approximations closely related to methods already used for the solution of linear and nonlinear bi harmonic problems through these approximations the solution of the above problems is essentially reduced to the solution of discrete poisson problems the methods discussed in this article are validated by the results of numerical experiments

on proximality with banach density one abstract let x t be a topological dynamical system a pair of points x y x 2 is called banach proximal if for any e 0 the set n z d t n x t n y e has banach density one we study the structure of the banach proximal relation a useful tool is the notion of the support of a topological dynamical system we show that a dynamical system is strongly proximal if and only if every pair in x 2 is banach proximal a subset s of x is banach scrambled if every two distinct points in s form a banach proximal pair but not asymptotic we construct a dynamical system with the whole space being a banach scrambled set even though the banach proximal relation of the full shift is of first category it has a dense mycielski invariant banach scrambled set we also show that for an interval map it is li yorke chaotic if and only if it has a cantor banach scrambled set

operational independence and tensor products of c algebras complete c independence of operator algebras is introduced equivalent characterization is given for c subalgebras to be completely independent in terms of maximal tensor product besides the independence of banach algebras is considered and we showed that hahn banach independence is a generalization of c independence and discussed hahn banach independence in mn a where a is a c algebra among others we characterize independence of operator algebras by projective and injective c tensor product in terms of simultaneous extensions of completely positive maps

asymptotic abelianness weak mixing and property t let g be a second countable locally compact group and h a closed subgroup we characterize the lack of kazhdan s property t for the pair g h by the genericity of g actions on the hyperfinite ii1 factor with a certain asymptotic abelianness property relative to h as well as by the genericity of measure preserving g actions on a nonatomic standard probability space that are weakly mixing for h the latter furnishes a definitive generalization of a classical theorem of halmos for single automorphisms and strengthens a recent result of glasner thouvenot and weiss on generic ergodicity we also establish a weak mixing version of glasner and weiss s characterization of property t for discrete g in terms of the invariant state space of a bernoulli shift and show that on the car algebra a type of norm asymptotic abelianness is generic for g actions when g is discrete and admits a nontorsion abelian quotient

new error estimates of the morley element for the plate bending problems in this paper we derive some new error estimates of a nonconforming morley element for the plate bending problems our aim is fourfold first it shows that the consistency error of the morley element can be controlled by its corresponding approximation error up to an arbitrarily high order term especially which can be of arbitrary order provided that f on the right hand side is piecewise smooth enough thus the total energy norm is dominated alone by the approximation error second as a byproduct we derive the error estimate under the regularity assumption u h 2 s with s 0 1 which fills the gap in the a priori error estimate of the morley element with low regularity for s 0 1 2 third based on this new error bound a robust convergence is proved even if the solution is exactly in h 2 finally by a slight modification of the variational formulation a new error estimate is also derived for the case f h 1 the key role is played by some quasi interpolation operators and the weak continuous properties of morley finite element space the main ideas and results presented here are motivated by mao and shi 2010 and can be viewed as its extension to fourth order problems

topological pressure for sub additive potentials of amenable group actions abstract we introduce the topological pressure for any sub additive potentials of a countable discrete amenable group action and any given open cover and establish a local variational principle for it

time delayed finite difference reaction diffusion systems with nonquasimonotone functions this paper is concerned with finite difference solutions of a system of reaction diffusion equations with coupled nonlinear boundary conditions and time delays the reaction functions and the boundary functions are not necessarily quasimonotone and the time delays may appear in the reaction functions as well as in the boundary functions the investigation is devoted to the finite difference system for both the time dependent problem and its corresponding steady state problem some monotone iteration processes for the finite difference systems are given and the asymptotic behavior of the time dependent solution in relation to the steady state solution is discussed the asymptotic behavior result leads to some local and global attractors of the time dependent problem including the convergence of the time dependent solution to a unique steady state solution an application and some numerical results to an enzyme substrate reaction diffusion problem are given all the results are directly applicable to parabolic ordinary systems and to reaction diffusion systems without time delays

mixed finite element methods for the fully nonlinear monge ampere equation based on the vanishing moment method this paper studies mixed finite element approximations of the viscosity solution to the dirichlet problem for the fully nonlinear monge ampere equation det d 2u 0 f 0 based on the vanishing moment method which was proposed recently by the authors in x feng and m neilan j scient comp doi 10 1007 s10915 008 9221 9 2008 in this approach the second order fully nonlinear monge ampere equation is approximated by the fourth order quasilinear equation varepsilon delta 2 u varepsilon det d 2u varepsilon f it was proved in x feng trans ams submitted that the solution u varepsilon converges to the unique convex viscosity solution u 0 of the dirichlet problem for the monge ampere equation this result then opens a door for constructing convergent finite element methods for the fully nonlinear second order equations a task which has been impracticable before the goal of this paper is threefold first we develop a family of hermann miyoshi type mixed finite element methods for approximating the solution u varepsilon of the regularized fourth order problem which computes simultaneously u varepsilon and the moment tensor sigma varepsilon d 2u varepsilon second we derive error estimates which track explicitly the dependence of the error constants on the parameter varepsilon for the errors u varepsilon u varepsilon h and sigma 0 sigma h varepsilon finally we present a detailed numerical study on the rates of convergence in terms of powers of varepsilon for the error u 0 u h varepsilon and sigma varepsilon sigma h varepsilon and numerically examine what is the best mesh size h in relation to varepsilon in order to achieve these rates due to the strong nonlinearity of the underlying equation the standard perturbation argument for error analysis of finite element approximations of nonlinear problems does not work for the problem to overcome the difficulty we employ a fixed point technique which strongly relies on the stability of the linearized problem and its mixed finite element approximations

a discrete helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes the discrete reliability of a finite element method is a key ingredient to prove optimal convergence of an adaptive mesh refinement strategy and requires the interchange of a coarse triangulation and some arbitrary refinement of it one approach for this is the careful design of an intermediate triangulation with one level refinements and with the remaining difficulty to design some interpolation operator which maps a possibly nonconforming approximation into the finite element space based on the finer triangulation this paper enfolds the second possibility of some novel discrete helmholtz decomposition for the nonconforming morley finite element method this guarantees the optimality of a standard adaptive mesh refining algorithm for the biharmonic equation numerical examples illustrate the crucial dependence of the bulk parameter and the surprisingly short pre asymptotic range of the adaptive morley finite element method

homoclinic groups ie groups and expansive algebraic actions we give algebraic characterizations for expansiveness of algebraic actions of countable groups the notion of p expansiveness is introduced for algebraic actions and we show that for countable amenable groups a finitely presented algebraic action is 1 expansive exactly when it has finite entropy we also study the local entropy theory for actions of countable amenable groups on compact groups by automorphisms and show that the ie group determines the pinsker factor for such actions for an expansive algebraic action of a polycyclic by finite group on x it is shown that the entropy of the action is equal to the entropy of the induced action on the pontryagin dual of the homoclinic group the homoclinic group is a dense subgroup of the ie group the homoclinic group is nontrivial exactly when the action has positive entropy and the homoclinic group is dense in x exactly when the action has completely positive entropy

generalized specification property and distributionally scrambled sets abstract suppose the dynamical system x f has generalized specification property in this paper we research the existence of the invariant mycielski distributionally scrambled sets for dynamical system x f moreover some properties about measure center are discussed and a dichotomy theorem is proved

a splitting theorem for transitive maps in this paper we prove a splitting theorem for continuous transitive maps on locally connected compact metric spaces which generalizes the results of barge and martin 4 for transitive maps on the interval and of blokh 7 for transitive graph maps as a consequence lower bounds for the topological entropy of transitive graph maps in terms of the cardinality of their splittings are obtained also we show that for every connected graph which is not a tree the infimum of the topological entropy of the transitive maps having a periodic point is zero since the topological entropy of transitive maps without periodic points is zero 7 and positive lower bounds of the entropy were given for the transitive maps on trees 2 this paper completes the problem of obtaining lower bounds of the topological entropy for transitive maps of any connected graph

conditional entropy and fiber entropy for amenable group actions abstract in this paper we introduce the notions of topological conditional entropy and fiber entropy for a given factor map between two amenable group actions and prove three variational principles for conditional entropy and fiber entropy moreover as an application of our variational principle we prove that the countable to one extension and the distal extension have zero conditional topological entropy in particular the topological entropy of a distal system is zero

on the k property of quantized arnold cat maps we prove that some quantized arnold cat maps are entropic k systems this result was formulated by h narnhofer j math phys 33 1502 1510 1992 but the fact that the optimal decomposition for the multi channel entropy constructed there is not strictly local was not appropriately taken care of we propose a strictly local decomposition based on a construction of voiculescu

toward a unified color space for perception based image processing image processing methods that utilize characteristics of the human visual system require color spaces with certain properties to operate effectively after analyzing different types of perception based image processing problems we present a list of properties that a unified color space should have due to contradictory perceptual phenomena and geometric issues a color space cannot incorporate all these properties we therefore identify the most important properties and focus on creating opponent color spaces without cross contamination between color attributes i e lightness chroma and hue and with maximum perceptual uniformity induced by color difference formulas color lookup tables define simple transformations from an initial color space to the new spaces we calculate such tables using multigrid optimization considering the hung and berns data of constant perceived hue and the cmc cie94 and ciede2000 color difference formulas the resulting color spaces exhibit low cross contamination between color attributes and are only slightly less perceptually uniform than spaces optimized exclusively for perceptual uniformity we compare the ciede2000 based space with commonly used color spaces in two examples of perception based image processing in both cases standard methods show improved results if the new space is used all color space transformations and examples are provided as matlab codes on our website