limits of hypercyclic and supercyclic operators abstract an operator t on a complex separable infinite dimensional hilbert space h is hypercyclic if there is a vector y in h such that the orbit y ty t2y is dense in h it is shown that if t is hypercyclic then t does not have any eigenvalue and that the union of the spectrum of t and the unit circle is a connected set this result is used to obtain a spectral characterization of the norm closure of the class hc h of all hypercyclic operators acting on h as well as a formula for the distance from a given operator to hc h analogous results are obtained for the closely related class sc h of all supercyclic operators this paper includes some information about the structure of the set of all hypercyclic supercyclic vectors of a given hypercyclic supercyclic resp operator t

common hypercyclic vectors for multiples of backward shift we prove that l 2 contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift oper ator by constants of absolute value greater than 1

multiple discrete solutions of the incompressible steady state navier stokes equations this paper discusses the computation of multiple solutions of various discretizations of the steady state incompressible navier stokes equations solution paths r satisfying the discrete system of equationsh r 0 where represents the discrete flow field andr is the reynolds number are computed using a pseudo arc length continuation procedure for flows over the back end of an axially symmetric body with a cusped tail in a coaxial circular cylinder the solution paths often exhibit hairpin turning points dependence of the paths on the mesh spacing and various selections for the discretizations of the convective and diffusive terms are presented

chaotic polynomials on banach spaces we show the existence of chaotic in the sense of devaney polynomials on banach spaces of q summable sequences such polynomials p consist of composition of the backward shift with a certain fixed polynomial p of one complex variable on each coordinate in general we also prove that p is chaotic in the sense of auslander and yorke if and only if 0 belongs to the julia set of p

a finite difference galerkin formulation for the incompressible navier stokes equations abstract the development of a new computational method for solving the incompressible navier stokes equations in primitive variable form is presented it is found that certain finite difference approximations for these equations can be transformed into an equivalent system which efficiently determines the discrete velocity field and which completely eliminates the pressure two such difference schemes for two dimensional problems are examined and some preliminary numerical results are discussed for the steady driven cavity problem

diagrammatic derivation of gradient algorithms for neural networks deriving gradient algorithms for time dependent neural network structures typically requires numerous chain rule expansions diligent bookkeeping and careful manipulation of terms in this paper we show how to derive such algorithms via a set of simple block diagram manipulation rules the approach provides a common framework to derive popular algorithms including backpropagation and backpropagation through time without a single chain rule expansion additional examples are provided for a variety of complicated architectures to illustrate both the generality and the simplicity of the approach

a new adaptive backpropagation algorithm based on lyapunov stability theory for neural networks a new adaptive backpropagation bp algorithm based on lyapunov stability theory for neural networks is developed in this paper it is shown that the candidate of a lyapunov function v k of the tracking error between the output of a neural network and the desired reference signal is chosen first and the weights of the neural network are then updated from the output layer to the input layer in the sense that deltav k v k v k 1 0 the output tracking error can then asymptotically converge to zero according to lyapunov stability theory unlike gradient based bp training algorithms the new lyapunov adaptive bp algorithm in this paper is not used for searching the global minimum point along the cost function surface in the weight space but it is aimed at constructing an energy surface with a single global minimum point through the adaptive adjustment of the weights as the time goes to infinity although a neural network may have bounded input disturbances the effects of the disturbances can be eliminated and asymptotic error convergence can be obtained the new lyapunov adaptive bp algorithm is then applied to the design of an adaptive filter in the simulation example to show the fast error convergence and strong robustness with respect to large bounded input disturbances

on an unconditional basis of generalized eigenvectors of the nonself adjoint gribov operator in bargmann space abstract in this article we prove that the system of generalized eigenvectors of the gribov operator is an unconditional basis in bargmann space we also give a generalized diagonalization in the abel sense of the semigroups respectively associated to this operator and to its square root finally some open problems are pointed out

topologically transitive semigroup actions of real linear fractional transformations abstract let f i f i i f x a x b c x d a d b c 0 where i is a proper closed subinterval of r our main goal in this paper is to describe all f g f i such that the action of the semigroup generated by f and g is topologically transitive on i we also prove that this action is never weakly topologically mixing finally we describe all pairs of affine functions on r whose generated semigroup action is weakly topologically mixing

mean ergodic composition operators on banach spaces of holomorphic functions abstract given a symbol i e a holomorphic endomorphism of the unit disc we consider the composition operator c f f defined on the banach spaces of holomorphic functions a d and h d we obtain different conditions on the symbol which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces these conditions are related to the asymptotic behavior of the iterates of the symbol finally we deal with some particular case in the setting of weighted banach spaces of holomorphic functions

on universal subsets of banach spaces we prove that to most of the known hypercyclic operators a on separable banach spaces there exist compact compact convex compact connected subsets k of e such that each compact compact convex compact connected subset of e can be approximated with respect to hausdorff s distance by a n k for suitable n in mathbb n

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

hypercyclic bilinear operators on banach spaces abstract we study the dynamics induced by an m linear operator we answer a question of bes and conejero showing an example of an m linear hypercyclic operator acting on a banach space moreover we prove the existence of m linear hypercyclic operators on arbitrary infinite dimensional separable banach spaces we also prove an existence result about symmetric bihypercyclic bilinear operators answering a question by grosse erdmann and kim

analyse de scattering d un operateur cubique de heun dans l espace de bargmann the boundary conditions at infinity are used in a description of all maximal dissipative extensions in bargmann space of the minimal heun s operator the characteristic functions of the dissipative extensions are computed completeness theorems are obtained for the system of generalized eigenvectors

algebraic genericity of frequently universal harmonic functions on trees abstract we show that the set of frequently universal harmonic functions on a tree t contains a vector space except 0 which is dense in the space of harmonic functions on t seen as subset of c t in order to prove this we replace the complex plane c by any separable frechet space e and we repeat all the theory

disjointness in hypercyclicity we introduce a notion of disjointness for finitely many hypercyclic operators acting on a common space notion that is weaker than furstenberg s disjointness of fluid flows we provide a criterion to construct disjoint hypercyclic operators that generalizes some well known connections between the hypercyclicity criterion hereditary hypercyclicity and topological mixing to the setting of disjointness in hypercyclicity we provide examples of disjoint hypercyclic operators for powers of weighted shifts on a hilbert space and for differentiation operators on the space of entire functions on the complex plane

chaotic behavior of the riesz transforms for hermite expansions we prove a characterization for hypercyclic and chaotic unbounded unilateral weighted shifts of order p as applications we obtain that the natural derivatives associated to hermite expansions are chaotic on the other hand the corresponding riesz transforms are not hypercyclic and even more they are a kind of border line operator which separates the chaotic behavior

semi fredholm theory hypercyclic and supercyclic subspaces a vector x in a banach space cal b is called hypercyclic for a bounded linear operator t cal b rightarrow cal b if the orbit t n x n geq 1 is dense in cal b we prove that if t is hereditarily hypercyclic and its essential spectrum meets the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is also true even if t is not hereditarily hypercyclic in this way we improve and extend to banach spaces a recent result for hilbert spaces we also investigate the corresponding problem for supercyclic operators in this case we obtain a description of the norm closure of the class of all supercyclic operators that have an infinite dimensional closed subspace of hypercyclic vectors moreover for certain kinds of supercyclic operators we can characterize when they have an infinite dimensional closed subspace of supercyclic vectors 1991 mathematics subject classification 47b38 47b99

online stabilization of block diagonal recurrent neural networks deals with a discrete time recurrent neural network dtrnn with a block diagonal feedback weight matrix called the block diagonal recurrent neural network bdrnn that allows a simplified approach to online training and to address network and training stability issues the structure of the bdrnn is exploited to modify the conventional backpropagation through time bptt algorithm to reduce its storage requirement by a numerically stable method of recomputing the network state variables the network and training stability is addressed by exploiting the bdrnn structure to directly monitor and maintain stability during weight updates by developing a functional measure of system stability that augments the cost function being minimized simulation results are presented to demonstrate the performance of the bdrnn architecture its training algorithm and the stabilization method

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

a short note on the chaoticity of a weight shift on concrete orthonormal basis associated to some fock bargmann space let f c be the hilbert space generated by the orthonormal basis en z 2 1 4e 2z2e 2 n 2 2i n z n n where 0 and are real numbers this space is a particular case of theta fock bargmann spaces recently constructed by ghanmi intissar j math phys 54 063514 2013 in the present work we consider on f c the weight shift operator m defined by men nen 1 n n where n c e2 n and c e 2 and we show the chaoticity of the operator hp mpdp 1 p 0 1 2 where d is adjoint of m

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

cyclicity of bicyclic operators and completeness of translates we study cyclicity of operators on a separable banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions a simple consequence of our main result is that a bicyclic unitary operator on a banach space with separable dual is cyclic our results also imply that if s a n n in mathbb z longmapsto a n 1 n in mathbb z is the shift operator acting on the weighted space of sequences ell omega 2 mathbb z if the weight satisfies some regularity conditions and n 1 for nonnegative n then s is cyclic if rm lim n rightarrow infty rm log omega n sqrt n 0 on the other hand one can see that s is not cyclic if the series sum n geq 1 rm log omega n n 2 diverges we show that the question of herrero whether either s or s is cyclic on ell omega 2 mathbb z admits a positive answer when the series sum n in mathbb z rm log s n n 2 1 is convergent we also prove completeness results for translates in certain banach spaces of functions on mathbb r

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

existence of common and upper frequently hypercyclic subspaces abstract we provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces which include the following consequences there exist frequently hypercyclic operators with upper frequently hypercyclic subspaces and no frequently hypercyclic subspace on the space of entire functions each differentiation operator induced by a non constant polynomial supports an upper frequently hypercyclic subspace and the family of its non zero scalar multiples has a common hypercyclic subspace a question of costakis and sambarino on the existence of a common hypercyclic subspace for a certain uncountable family of weighted shift operators is also answered

hypercyclic tuples of operators and somewhere dense orbits in this paper we prove that there are hypercyclic n 1 tuples of diagonal matrices on cn and that there are no hypercyclic n tuples of diagonalizable matrices on cn we use the last result to show that there are no hypercyclic subnormal tuples in infinite dimensions we then show that on real hilbert spaces there are tuples with somewhere dense orbits that are not dense but we also give sufficient conditions on a tuple to insure that a somewhere dense orbit on a real or complex space must be dense

construction of concrete orthonormal basis for l2 γ χ theta functions associated to discrete subgroups of rank one in c for given rank one discrete subgroup z of the additive group c and given character on it we construct a complete orthonormal basis of the hilbert space of l2 z theta functions a hilbertian orthogonal decomposition involving the l2 eigenspaces of the landau operator is given corresponding orthonormal basis are constructed and the corresponding reproducing kernel can be expressed in terms of the generalized theta function of characteristic 0 in particular the hilbert subspace of entire l2 z theta functions coincides with the null space the l2 eigenspace associated to the lowest eigenvalue furthermore a periodic analog of segal bargmann transform is obtained by introducing special integral transform with a theta kernel mapping the l2 sections of a line bundle on the circle r z to holomorphic sections of a line bundle on c z

regularized trace formula of magic gribov operator on bargmann space abstract in this article we obtain a regularized trace formula for magic gribov operator h g h acting on bargmann space where g a 3 a 3 and h a a i a a a a here a and a are the standard bose annihilation and creation operators and in reggeon field theory the real parameters is the magic coupling of pomeron is pomeron intercept is the triple coupling of pomeron and i 2 1 by applying some abstract results of sadovnichii podol skii 2002 23 we give the number of corrections sufficient for the existence of finite formula of the trace of concrete magic gribov s operator

hypercyclic operators on non normable frechet spaces abstract every infinite dimensional separable non normable frechet space admits a continuous hypercyclic operator a large class of separable countable inductive limits of banach spaces with the same property is given but an example of a separable complete inductive limit of banach spaces which admits no hypercyclic operator is provided it is also proved that no compact operator on a locally convex space is hypercyclic

generic approximation of functions by their pade approximants abstract in the present article we obtain generic approximations under sharp conditions of holomorphic functions on arbitrary open sets by sequences of their pade approximants similar results hold for functions smooth on the boundary of their domain of definition in addition the approximation is valid simultaneously with respect to all centers of expansion

a dynamical characterization of sub arakelian subsets abstract we are going to characterize those sets which can be covered by an arakelian set in terms of dynamical properties of entire functions via similarities moreover if we consider the set of universal entire functions via similarities that are bounded on such a sub arakelian set then it is shown that its algebraic size is as large as possible as a consequence we prove that the set of universal entire functions bounded on every straight line is algebraically large

stable and semistable low order finite elements for viscous flows it is shown that i the bilinear constant and linear constant box elements are not uniformly stable and ii certain element pairs derived from those above by restricting the pressure spaces are stable the notion of div semistability is developed to study the behavior of the bilinear constant and linear constant box elements in detail

relating real time backpropagation and backpropagation through time an application of flow graph interreciprocity we show that signal flow graph theory provides a simple way to relate two popular algorithms used for adapting dynamic neural networks real time backpropagation and backpropagation through time starting with the flow graph for real time backpropagation we use a simple transposition to produce a second graph the new graph is shown to be interreciprocal with the original and to correspond to the backpropagation through time algorithm interreciprocity provides a theoretical argument to verify that both flow graphs implement the same overall weight update

a nonlinear age and maturity structured model of population dynamics i basic theory a nonlinear model of age and maturity structured population dynamics is analyzed the population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth the existence and asymptotic behavior of solutions are studied

linear structure of hypercyclic vectors abstract a vector x in a banach space b is called hypercyclic for a bounded linear operator t b b if the orbit t n x n 1 is dense in b our main result states that if t is a compact perturbation of an operator of norm 1 and satisfies an appropiate extra hypothesis then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t in particular the result applies to compact perturbations of the identity we also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts this last result in combination with a recent one that states that every banach space admits an operator with a hypercyclic vector proves that in all banach space there is an operator t with an infinite dimensional closed subspace consisting except for zero of hypercyclic vectors the main result also applies to the differentiation operator and the translation operator t f z f z 1 on certain hilbert spaces consisting of entire functions

some remarks on abstract universal series abstract we introduce a new class of universal series in the abstract setting this class lies between two already known classes of universal series by two examples we differentiate these classes these examples are the first examples in the case where all classes are non void we also prove that the class of universal series where the approximating indexes have upper density 1 is dense and g and that the class of lower frequently universal series is of the first category

optimal growth of entire functions frequently hypercyclic for the differentiation operator we solve a problem posed by bonilla and grosse erdmann 2007 7 by constructing an entire function f which is frequently hypercyclic with respect to the differentiation operator and satisfies mf r cerr 1 4 where c 0 may be chosen arbitrarily small this growth rate is sharp we also obtain optimal results for minimal growth in terms of average lp norms among other tools the proof uses the rudin shapiro polynomials and heat kernel estimates

an operator compact implicit method of exponential type a fourth order accurate tridiagonal operator compact implicit finite difference method for diffusion convection equations is developed the coefficients of the difference operator contain exponentials of the coefficients of the differential operator in this way the method avoids spurious oscillations when the cell reynolds number is large numerical results and comparisons to other methods are presented

continuation techniques for a penalty approximation of the navier stokes equations continuation techniques are used to solve a penalty finite element approximation of the navier stokes equations sufficient conditions are given for convergence of the euler newton continuation method in a reynolds parameter to an isolated solution of the finite element problem numerical results are presented for the driven cavity problem the approach is extended to arc length continuation to treat problems with singular points on the continuation path

approximation of the semigroup generated by the hamiltonian of reggeon field theory in bargmann space abstract the reggeon field theory is governed by a non self adjoint operator constructed as a polynomial in a a the standard bose annihilation and creation operators in zero transverse dimension this hamiltonian acting in bargmann space is defined by h a 2 a 2 a a i a a a a where i 2 1 and are real numbers and the operators a a satisfy the commutation relation a a i as the quantum mechanical system described by h has a velocity dependent potential containing powers of momentum up to the fourth the problem of existence of hamiltonian path integral for the evolution operator e t h of this theory is of interest on its own in particular can we express e t h as a limit of integral operators in this article one considerably reduces the difficulty by studying the trotter product formula of h to reach two objectives the first objective is to prove a very specific error estimate for the error in a trotter product formula in trace norm for h viewed as the sum of the operators a 2 a 2 and a a i a a a a the second objective of this work is to give a approximation of the semigroup generated by h when h is split in the sum of a 2 a 2 a a and i a a a a we note that this case is entirely different in fact the usual trotter product formula is not defined because the interaction operator a a a a is not the infinitesimal generator of a semigroup on bargmann space for 0 and 0 we choose an approximation operator i i a a a a e a 2 a 2 a a and we give a connection between and e h this choice allows us to give in a intissar note on the path integral formulation of reggeon field theory preprint a generalized trotter product formula for t a a i a a a a i e for limit case as 0 and answers to the above question

approximation by chaotic operators and by conjugate classes we show that every bounded linear operator on a separable infinite dimensional hilbert space h is the sum of two operators in the norm closure of the set of operators on h that are chaotic in the sense of devaney we also observe that the density of several classes of cyclic operators with respect to the strong operator topology may be derived from a result by hadwin et al proc amer math soc 76 1979 250 252

a generalization of universal taylor series in simply connected domains abstract let be a simply connected proper subdomain of the complex plane and z 0 be a point in it is known that there are holomorphic functions f on for which the partial sums s n f z 0 of the taylor series about z 0 have universal approximation properties outside in this paper we investigate what can be said for the sequence n s n f z 0 when n is a sequence of complex numbers we also study a related analogue of a classical theorem of seleznev concerning the case where the radius of convergence of the universal power series is zero

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

universal entire functions for affine endomorphisms of c n abstract in this paper the affine endomorphisms of c n which support compositionally universal entire functions are completely characterized

hypercyclic subspaces in omega abstract we show that any countable family of operators of the form p b where p is a non constant polynomial and b is the backward shift operator on the countably infinite product of lines has a common hypercyclic subspace

mixing simultaneous universal and disjoint universal backward φ shifts abstract spaces of sequences which are valued in a topological space e are considered in order to study universality properties of generalized backward shifts associated to certain selfmappings of e after providing a condition which guarantees the mixing property of backward shifts in terms of the dynamical properties of the generating selfmappings applications to universality theory within the framework of complex dynamics are furnished

generic boundary behaviour of taylor series in hardy and bergman spaces it is known that generically taylor series of functions holomorphic in the unit disc turn out to be universal series outside of the unit disc and in particular on the unit circle due to classical and recent results on the boundary behaviour of taylor series for functions in hardy spaces and bergman spaces the situation is drastically different in this paper it is shown that in many respects these results are sharp in the sense that universality generically appears on maximal exceptional sets as a main tool it is proved that the taylor backward shift on certain bergman spaces is mixing

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

spectral theory and hypercyclic subspaces a vector x in a hilbert space h is called hypercyclic for a bounded operator t h h if the orbit tnx n 1 is dense in h our main result states that if t satisfies the hypercyclicity criterion and the essential spectrum intersects the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is true even if t is a hypercyclic operator which does not satisfy the hypercyclicity criterion as a consequence other characterizations are obtained for an operator t to have an infinite dimensional closed subspace of hypercyclic vectors these results apply to most of the hypercyclic operators that have appeared in the literature in particular they apply to bilateral and backward weighted shifts perturbations of the identity by backward weighted shifts multiplication operators and composition operators the main result also applies to the differentiation operator and the translation operator t f z f z 1 defined on certain hilbert spaces consisting of entire functions we also obtain a spectral characterization of the norm closure of the class of hypercyclic operators which have an infinite dimensional closed subspace of hypercyclic vectors

on a universality property of certain integral operators in this paper we establish a universality property of fourier and hankel convolution operators and dunkl transforms

universality of holomorphic functions bounded on closed sets in this note the existence of translation universal entire functions which are bounded on certain closed subsets is characterized in terms of topological and geometrical properties of such subsets corresponding results are also stated in the space of holomorphic functions on the unit disk and in the space of harmonic functions on the plane moreover it is shown the existence of entire functions which are bounded on many rays and simultaneously are universal with respect to a prescribed infinite order differential operator

non sequential weak supercyclicity and hypercyclicity abstract a bounded linear operator t acting on a banach space b is called weakly hypercyclic if there exists x b such that the orbit t n x n 0 1 is weakly dense in b and t is called weakly supercyclic if there is x b for which the projective orbit t n x c n 0 1 is weakly dense in b if weak density is replaced by weak sequential density then t is said to be weakly sequentially hypercyclic or supercyclic respectively it is shown that on a separable hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic this is achieved by constructing a borel probability measure on the unit circle for which the fourier coefficients vanish at infinity and the multiplication operator m f z z f z acting on l 2 is weakly supercyclic it is not weakly sequentially supercyclic since the projective orbit under m of each element in l 2 is weakly sequentially closed this answers a question posed by bayart and matheron it is proved that the bilateral shift on l p z 1 p is weakly supercyclic if and only if 2 p and that any weakly supercyclic weighted bilateral shift on l p z for 1 p 2 is norm supercyclic it is also shown that any weakly hypercyclic weighted bilateral shift on l p z for 1 p 2 is norm hypercyclic which answers a question of chan and sanders

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100