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

quasi cohen macaulay properties of local homomorphisms abstract for a large class of local homomorphisms r s including those of finite g dimension studied by avramov and foxby proc london math soc 75 1997 241 270 we assign a new numerical invariant called the quasi cohen macaulay defect of and a local homomorphism is called quasi cohen macaulay if it is of finite g dimension and has trivial quasi cohen macaulay defect we show among other things the following g dim spec spec g dim

discriminant analysis of interval data using monte carlo method in assessment of overlap in this paper we show that the method of discriminant analysis da on interval data by data envelopment analysis dea dea discriminant analysis dea da is designed to identify the existence or non existence of an overlap between two groups by separating hyperplane in addition it predicts a new observation to the group which it belongs to data envelopment analysis technique which is developed based on the mathematical programming evaluates the relative efficiency of a set of homogeneous decision making units however there are similarities between dea and da da is a method for separating two sets with previous knowledge meanwhile dea is a technique for separating two sets efficient and inefficient without previous knowledge also goal programming method can be used for both of these methods

complete systems of partial derivatives of entire functions and frequently hypercyclic operators abstract we find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space h c d of all entire functions of d variables as an application of this result we describe new classes of frequently hypercyclic operators on h c d

comparison of relative cohomology theories with respect to semidualizing modules we compare and contrast various relative cohomology theories that arise from resolutions involving semidualizing modules we prove a general balance result for relative cohomology over a cohen macaulay ring with a dualizing module and we demonstrate the failure of the naive version of balance one might expect for these functors we prove that the natural comparison morphisms between relative cohomology modules are isomorphisms in several cases and we provide a yoneda type description of the first relative ext functor finally we show by example that each distinct relative cohomology construction does in fact result in a different functor

distributional chaos for linear operators abstract we characterize distributional chaos for linear operators on frechet spaces in terms of a computable condition dcc and also as the existence of distributionally irregular vectors a sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented which is very general and can be applied to many classes of operators distributional chaos is also analyzed in connection with frequent hypercyclicity and the particular cases of weighted shifts and composition operators are given as an illustration of the previous results

distributional chaos for operators on banach spaces abstract four notions of distributional chaos namely dc1 dc2 dc 2 1 2 and dc3 are studied within the framework of operators on banach spaces it is known that for general dynamical systems dc1 dc2 dc 2 1 2 dc3 we show that dc1 and dc2 coincide in our context which answers a natural question in contrast there exist dc 2 1 2 operators which are not dc2 under the condition that there exists a dense set x 0 x such that t n x 0 for any x x 0 dc3 operators are shown to be dc1 moreover we prove that any upper frequently hypercyclic operator is dc 2 1 2 finally several examples are provided to distinguish between different notions of distributional chaos li yorke chaos and irregularity

on the category of modules of gorenstein dimension zero ii abstract let r be a commutative noetherian henselian non gorenstein local ring the author has conjectured in r takahashi on the category of modules of gorenstein dimension zero preprint 2003 that there exist infinitely many isomorphism classes of indecomposable r modules of gorenstein dimension zero if there exists a non free module of gorenstein dimension zero and has proved that the conjecture holds when r has depth zero in this paper we prove that the conjecture also holds when r has depth one

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

homological properties of balanced cohen macaulay algebras a balanced cohen macaulay algebra is a connected algebra a having a balanced dualizing complex a d in the sense of yekutieli 1992 for some integer d and some graded a a bimodule a we study some homological properties of a balanced cohen macaulay algebra in particular we will prove the following theorem theorem 0 1 let a be a noetherian balanced cohen macaulay algebra and m a nonzero finitely generated graded left a module then 1 m has a finite resolution of the form 0 a l mj a l 1j h m 0 where h is a finitely generated maximal cohen macaulay graded left a module 2 m has finite injective dimension if and only if m has a finite resolution of the form 0 a l mj a l 1j a l 0j m 0 as a corollary we will have the following characterizations of as gorenstein algebras and as regular algebras corollary 0 2 let a be a noetherian balanced cohen macaulay algebra 1 a is as gorenstein if and only if a has finite projective dimension as a graded left a module 2 a is as regular if and only if every finitely generated maximal cohen macaulay graded left a module is free

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

genericity of wild holomorphic functions and common hypercyclic vectors abstract let t be the translation operator by in the space of entire functions h c defined by t f z f z we prove that there is a residual set g of entire functions such that for every f g and every c 0 the sequence t n f is dense in h c that is g is a residual set of common hypercyclic vectors functions for the family t c 0 also we prove similar results for many families of operators as multiples of differential operator multiples of backward shift weighted backward shifts

using monte carlo method for ranking efficient dmus for ranking efficient dmus some methods have been developed these methods are not able to rank non extreme efficient dmus in this paper using monte carlo method a method has been developed which is able to rank all extreme and non extreme efficient dmus

lineability criteria with applications lineability is a property enjoyed by some subsets within a vector space x a subset a of x is called lineable whenever a contains except for zero an infinite dimensional vector subspace if additionally x is endowed with richer structures then the more stringent notions of dense lineability maximal dense lineability and spaceability arise naturally in this paper several lineability criteria are provided and applied to specific topological vector spaces mainly function spaces sometimes such criteria furnish unified proofs of a number of scattered results in the related literature families of strict order integrable functions hypercyclic vectors non extendable holomorphic mappings riemann non lebesgue integrable functions sequences not satisfying the lebesgue dominated convergence theorem nowhere analytic functions bounded variation functions entire functions with fast growth and peano curves among others are analyzed from the point of view of lineability

common hypercyclic vectors for the unitary orbit of a hypercyclic operator abstract for a separable infinite dimensional hilbert space it was recently shown by the authors that the similarity orbit of a hypercyclic operator contains a path of operators which is dense in the operator algebra with the strong operator topology and yet the set of common hypercyclic vectors for the entire path is a dense g set motivated by that result we show in the present paper that the unitary orbit of any hypercyclic operator contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology and yet every nonzero vector in the linear span of the orbit of a given hypercyclic vector is a common hypercyclic vector for the entire path

strong transitivity properties for operators abstract given a furstenberg family f of subsets of n an operator t on a topological vector space x is called f transitive provided for each non empty open subsets u v of x the set n z t n u v belongs to f we classify the topologically transitive operators with a hierarchy of f transitive subclasses by considering families f that are determined by various notions of largeness and density in z

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

s linear and convex structures in function families abstract in this paper the notion of s lineability originally coined by vladimir i gurariy is introduced and developed in a general abstract setting this new notion is then applied to specific situations as for instance classes of differentiable nowhere monotone functions as well as families of vectors having dense orbit with respect to an operator large convex structures are also shown to exist inside the family of topologically mixing continuous selfmaps of a real compact interval

using monte carlo method for ranking interval data abstract some methods have been presented for ranking efficient decision making units dmus in data envelopment analysis dea this paper addresses the ranking of interval data by using monte carlo method this method is based on a paper g r jahanshahloo f hosseinzadeh lotfi h zhiani rezai f rezai balf using monte carlo method for ranking efficient dmus applied mathematics and computation 162 2005 371 379 the worthwhile this method is its ability in ranking of extreme and non extreme efficient dmus

the set of semidualizing complexes is a nontrivial metric space abstract we show that the set s r of shift isomorphism classes of semidualizing complexes over a local ring r admits a nontrivial metric we investigate the interplay between the metric and several algebraic operations motivated by the dagger duality isometry we prove the following if k l are homologically bounded below and degreewise finite r complexes such that k r l k r l l is semidualizing then k is shift isomorphic to r in investigating the existence of nontrivial open balls in s r we prove that s r contains elements that are not comparable in the reflexivity ordering if and only if it contains at least three distinct elements

semi dualizing complexes and their auslander categories let r be a commutative noetherian ring we study r modules and complexes of such with excellent duality properties while their common properties are strong enough to admit a rich theory we count among them such potentially diverse objects as dualizing complexes for r on one side and on the other the ring itself in several ways these two examples constitute the extremes and their well understood properties serve as guidelines for our study however also the employment in recent studies of ring homomorphisms of complexes lying between these extremes is incentive

hypercyclic orbits intersect subspaces in wild ways abstract let t x x be a hypercyclic operator of an infinite dimensional separable banach space x by modifying a construction of grivaux we will show that the t orbit of a hypercyclic vector can intersect certain closed vector subspaces of x in many strange ways moreover the set of visiting times of the orbit to the subspace can also be quite exotic especially when the operator satisfies a stronger form of hypercyclicity as a by product we will improve and or supply new proofs to some of the recent results about subspace hypercyclicity

recurrence properties of hypercyclic operators we generalize the notions of hypercyclic operators mathfrak u frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics namely mathcal a hypercyclicity we then state an mathcal a hypercyclicity criterion inspired by the hypercyclicity criterion and the frequent hypercyclicity criterion and we show that this criterion characterizes the mathcal a hypercyclicity for weighted shifts we also investigate which density properties can the sets n x u n in mathbb n t nx in u have for a given hypercyclic operator and we study the new notion of reiteratively hypercyclic operators

mean li yorke chaos in banach spaces abstract we investigate the notion of mean li yorke chaos for operators on banach spaces we show that it differs from the notion of distributional chaos of type 2 contrary to what happens in the context of topological dynamics on compact metric spaces we prove that an operator is mean li yorke chaotic if and only if it has an absolutely mean irregular vector as a consequence absolutely cesaro bounded operators are never mean li yorke chaotic dense mean li yorke chaos is shown to be equivalent to the existence of a dense or residual set of absolutely mean irregular vectors as a consequence every mean li yorke chaotic operator is densely mean li yorke chaotic on some infinite dimensional closed invariant subspace a dense mean li yorke chaos criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained moreover we construct an example of an invertible hypercyclic operator t such that every nonzero vector is absolutely mean irregular for both t and t 1 several other examples are also presented finally mean li yorke chaos is also investigated for c 0 semigroups of operators on banach spaces

a procedure for ranking efficient units in data envelopment analysis data envelopment analysis dea evaluates the relative efficiency of decision making units dmus but does not allow for a ranking of the efficient units themselves a modified version of dea based upon comparison of efficient dmus relative to a reference technology spanned by all other units is developed the procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods

topologically transitive extensions of bounded operators let x be any banach space and t a bounded operator on x an extensionopen image in new window of the pair x t consists of a banach space open image in new window in which x embeds isometrically through an isometry i and a bounded operatoropen image in new window on open image in new window such that open image in new window when x is separable it is additionally required that open image in new window be separable we say that open image in new window is a topologically transitive extension of x t when open image in new window is topologically transitive on open image in new window i e for every pair open image in new window of non empty open subsets of open image in new window there exists an integer n such that open image in new window is non empty we show that any such pair x t admits a topologically transitive extension open image in new window and that when h is a hilbert space h t admits a topologically transitive extension open image in new window where open image in new window is also a hilbert space we show that these extensions are indeed chaotic

restricted homological dimensions and cohen macaulayness abstract the classical homological dimensions the projective flat and injective ones are usually defined in terms of resolutions and then proved to be computable in terms of vanishing of appropriate derived functors in this paper we define restricted homological dimensions in terms of vanishing of the same derived functors but over classes of test modules that are restricted to assure automatic finiteness over commutative noetherian rings of finite krull dimension when the ring is local we use a mixture of methods from classical commutative algebra and the theory of homological dimensions to show that vanishing of these functors reveals that the underlying ring is a cohen macaulay ring or at least close to being one

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

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

universal properties of harmonic functions on trees abstract we consider an infinite locally finite tree t equipped with nearest neighbor transition coefficients giving rise to a space of harmonic functions we show that except for trivial cases the generic harmonic function on t has dense range in c by looking at forward only transition coefficients we show that the generic harmonic function induces a boundary martingale that approximates in probability all measurable functions on the boundary of t we also study algebraic genericity spaceability and frequent universality of these phenomena

quillen equivalences for stable categories abstract for an abelian category a we investigate when the stable categories gpro j a and gin j a are triangulated equivalent to this end we realize these stable categories as homotopy categories of certain non trivial model categories and give conditions on a that ensure the existence of a quillen equivalence between the model categories in question we also study when such a quillen equivalence transfers from a to the category of chain complexes in a

the role of the angle in supercyclic behavior abstract a bounded operator t acting on a hilbert space h is said to be supercyclic if there is a vector f h such that the projective orbit t n f n 0 and c is dense in h we use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not the method is applied to obtain the following result a composition operator acting on the hardy space whose inducing symbol is a parabolic linear fractional map of the disk onto a proper subdisk is not supercyclic this result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and thus completes previous work of bourdon and shapiro

unimodular eigenvalues uniformly distributed sequences and linear dynamics we study increasing sequences of positive integers nk k 1 with the following property every bounded linear operator t acting on a separable banach or hilbert space with supk 1 tnk has a countable set of unimodular eigenvalues whether this property holds or not depends on the distribution modulo one of sequences nk k 1 r or on the growth of nk 1 nk counterexamples to some conjectures in linear dynamics are given for instance a hilbert space operator which is frequently hypercyclic chaotic but not topologically mixing is constructed the situation of c0 semigroups is also discussed

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

common hypercyclic functions for translation operators with large gaps abstract let h c be the set of entire functions endowed with the topology of local uniform convergence fix a sequence of non zero complex numbers n n which satisfies the following property for every m 0 there exists a subsequence n of n such that i n 1 n m for every n 1 2 and ii n 1 1 n we prove that there exists a residual set g h c such that for every f g and every non zero complex number a the set f z n a n 1 2 is dense in h c this answers in the affirmative question 1 in 29 and it also provides an extension of a theorem due to costakis and sambarino in 32

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

invariant gaussian measures for operators on banach spaces and linear dynamics we give conditions for an operator t on a complex separable banach space x with sufficiently many eigenvectors associated to eigenvalues of modulus 1 to admit a non degenerate invariant gaussian measure with respect to which it is weak mixing the existence of such a measure depends on the geometry of the banach space and on the possibility of parametrizing the mathbb t eigenvector fields of t in a regular way we also investigate the connection with frequent hypercyclicity

monte carlo em algorithm in logistic linear models involving non ignorable missing data abstract many data sets obtained from surveys or medical trials often include missing observations since ignoring the missing information usually cause bias and inefficiency an algorithm for estimating parameters is proposed based on the likelihood function of which the missing information is taken account a binomial response and normal exploratory model for the missing data are assumed we fit the model using the monte carlo em expectation and maximization algorithm the e step is derived by metropolis hastings algorithm to generate a sample for missing data and the m step is done by newton raphson to maximize the likelihood function asymptotic variances and the standard errors of the mle maximum likelihood estimates of parameters are derived using the observed fisher information

hilbertian jamison sequences and rigid dynamical systems a strictly increasing sequence nk k 0 of positive integers is said to be a hilbertian jamison sequence if for any bounded operator t on a separable hilbert space such that supk 0 tnk the set of eigenvalues of modulus 1 of t is at most countable we first give a complete characterization of such sequences we then turn to the study of rigidity sequences nk k 0 for weakly mixing dynamical systems on measure spaces and give various conditions some of which are closely related to the jamison condition for a sequence to be a rigidity sequence we obtain on our way a complete characterization of topological rigidity and uniform rigidity sequences for linear dynamical systems and we construct in this framework examples of dynamical systems which are both weakly mixing in the measure theoretic sense and uniformly rigid

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

common hypercyclic vectors for the conjugate class of a hypercyclic operator abstract given a separable in nite dimensional hilbert space it was recently shown by the authors that there is a path of chaotic operators which is dense in the operator algebra with the strong operator topology and along which every operator has the exact same dense set of hypercyclic vectors in the present work we show that the conjugate set of any hypercyclic operator on a separable in nite dimensional banach space always contains a path of operators which is dense with the strong operator topology and yet the set of common hypercyclic vectors for the entire path is a dense set as a corollary the hypercyclic operators on such a banach space form a connected subset of the operator algebra with the strong operator topology 1 introduction throughout the present paper let be a separable in nite dimensional banach space over the scalar eld or and let denote the algebra of bounded linear operators an operator in is hypercyclic if there is a vector in for which its orbit 0 is dense in such a vector is called a hypercyclic vector for an operator in is hypercyclic if and only if the set of hypercyclic vectors for denoted by is a dense set see kitai 23 for a countable family of hypercyclic operators a direct application of the baire category theorem implies that the set

remarks on common hypercyclic vectors abstract we treat the question of existence of common hypercyclic vectors for families of continuous linear operators it is shown that for any continuous linear operator t on a complex frechet space x and a set r c which is not of zero three dimensional lebesgue measure the family a t b i a b has no common hypercyclic vectors this allows to answer negatively questions raised by godefroy and shapiro and by aron we also prove a sufficient condition for a family of scalar multiples of a given operator on a complex frechet space to have a common hypercyclic vector it allows to show that if d z c z 1 and h d is non constant then the family z m b 1 z a 1 has a common hypercyclic vector where m h 2 d h 2 d m f f a inf z z d and b sup z z d providing an affirmative answer to a question by bayart and grivaux finally extending a result of costakis and sambarino we prove that the family a t b a b c 0 has a common hypercyclic vector where t b f z f z b acts on the frechet space h c of entire functions on one complex variable

construction of modules with finite homological dimensions a new homological dimension called g dimension is defined for every finitely generated module m over a local noetherian ring r it is modeled on the ci dimension of avramov gasharov and peeva and has parallel properties in particular a ring r is gorenstein if and only if every finitely generated r module has finite g dimension the g dimension lies between the ci dimension and the g dimension of auslander and bridger this relation belongs to a longer sequence of inequalities where a strict inequality in any place implies equalities to its right and left over general local rings we construct classes of modules that show that a strict inequality can occur at almost every place in the sequence

sums of hypercyclic operators abstract every bounded operator on a complex infinite dimensional separable hilbert space can be written as the sum of two hypercyclic operators and also as the sum of two chaotic operators

regularity over homomorphisms and a frobenius characterization of koszul algebras abstract let r be a standard graded algebra over an f finite field of characteristic p 0 let r r be the frobenius endomorphism for each finitely generated graded r module m let m be the abelian group m with the r module structure induced by the frobenius endomorphism the r module m has a natural grading given by deg x j if x m j p i for some 0 i p 1 in this paper we prove that r is koszul if and only if there exists a non zero finitely generated graded r module m such that reg r m this result supplies another instance for the ability of the frobenius in detecting homological properties as exemplified by kunz s famous regularity criterion the main technical tool is the notion of castelnuovo mumford regularity over certain homomorphisms between n graded algebras the latter notion is a common generalization of the relative and absolute castelnuovo mumford regularity of modules

on random frequent universality abstract we give a probabilistic construction of frequently hypercyclic or universal entire functions using birkhoff s ergodic theorem we apply the same ideas to construct random frequently universal vectors for the polynomials of the weighted backward shift on the classical real or complex l p space

inverse of u frequently hypercyclic operators abstract we show that there exists an invertible u frequently hypercyclic operator on l p n 1 p whose inverse is not u frequently hypercyclic

frequently hypercyclic operators with irregularly visiting orbits abstract we prove that a bounded operator t on a separable banach space x satisfying a strong form of the frequent hypercyclicity criterion which implies in particular that the operator is universal in the sense of glasner and weiss admits frequently hypercyclic vectors with irregularly visiting orbits i e vectors x x such that the set n t x u n 1 t n x u of return times of x into u under the action of t has positive lower density for every non empty open set u x but there exists a non empty open set u 0 x such that n t x u 0 has no density

two remarks on frequent hypercyclicity abstract we show that if t x x is a continuous linear operator on an f space x 0 then the set of frequently hypercyclic vectors of t is of first category in x and this answers a question of a bonilla and k g grosse erdmann we also show that if t x x is a bounded linear operator on a banach space x 0 and if t is frequently hypercyclic or more generally syndetically transitive then the t orbit of every non zero element of x is bounded away from 0 and in particular t is not hypercyclic

on the category of modules of gorenstein dimension zero let r be a commutative noetherian henselian non gorenstein local ring of depth zero denote by modr the category of all finitely generated r modules and by open image in new window the full subcategory of modr consisting of all r modules of gorenstein dimension zero we prove in this paper that if open image in new window contains a non free module then it is not precovering in modr in particular there exist infinitely many isomorphism classes of indecomposable r modules of gorenstein dimension zero

hypercyclicity and unimodular point spectrum abstract we show that an operator on a separable complex banach space with sufficiently many eigenvectors associated to eigenvalues of modulus 1 is hypercyclic we apply this result to construct hypercyclic operators with prescribed k unimodular point spectrum we show how eigenvectors associated to unimodular eigenvalues can be used to exhibit common hypercyclic vectors for uncountable families of operators and prove that the family of composition operators c on h 2 d where is a disk automorphism having 1 as attractive fixed point has a residual set of common hypercyclic vectors

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

ring homomorphisms and finite gorenstein dimension the local structure of homomorphisms of commutative noetherian rings is investigated from the point of view of dualizing complexes a concept of finite gorenstein dimension which substantially weakens the notion of finite flat dimension is introduced for homomorphisms it is shown to impose structural constraints due to a remarkable equivalence of subcategories of the derived category of all modules an essential part of this study is the development of relative notions of dualizing complexes and bass numbers it is proved that the bass numbers of local homomorphisms are rigid extending a known result for local rings quasi gorenstein homomorphisms are introduced as local homomorphisms that base change a dualizing complex for the source ring into one for the target they are shown to have the stability properties of the gorenstein homomorphism that they generalize 1991 mathematics subject classification primary 13h10 13d23 14e40 secondary 13c15

frequently hypercyclic operators we investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators t on separable complex f spaces t is frequently hypercyclic if there exists a vector x such that for every nonempty open subset u of x the set of integers n such that t n x belongs to u has positive lower density we give several criteria for frequent hypercyclicity and this leads us in particular to study linear transformations from the point of view of ergodic theory several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting

a hypercyclic finite rank perturbation of a unitary operator a unitary operator v and a rank 2 operator r acting on a hilbert space mathcal h are constructed such that v r is hypercyclic this answers affirmatively a question of salas whether a finite rank perturbation of a hyponormal operator can be supercyclic

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

operators with the specification property abstract we study a version of the specification property for linear dynamics operators having the specification property are investigated and relationships with other well known dynamical notions such as mixing devaney chaos and frequent hypercyclicity are obtained

a bridge between u frequent hypercyclicity and frequent hypercyclicity abstract given a the family of weights a a n n decreasing to 0 such that the series n 0 a n diverges we show that the supremum on a of lower weighted densities coincides with the unweighted upper density and that the infimum on a of upper weighted densities coincides with the unweighted lower density we then investigate the notions of u frequent hypercyclicity and frequent hypercyclicity associated to these weighted densities we show that there exists an operator which is u frequently hypercyclic for each weight in a but not frequently hypercyclic although the set of frequently hypercyclic vectors always coincides with the intersection of sets of u frequently hypercyclic vectors for each weight in a

strong mixing measures for linear operators and frequent hypercyclicity abstract we construct strongly mixing invariant measures with full support for operators on f spaces which satisfy the frequent hypercyclicity criterion for unilateral backward shifts on sequence spaces a slight modification shows that one can even obtain exact invariant measures

invertible composition operators on hp abstract the weakly closed algebras generated by certain sets of composition operators are shown to be reflexive a structure theorem for invertible composition operators on h2 is obtained and used to show that such operators are reflexive the structure theorem shows that invertible hyperbolic composition operators are similar to cosubnormal operators built up from bilateral weighted shifts another consequence of the structure theorem is that the composition operators induced by hyperbolic disc automorphisms are universal thus the general invariant subspace problem for hilbert space operators is contained in the problem of determining the invariant subspace lattices of these operators

technologies ranking in the presence of both cardinal and ordinal data ranking of technologies is an important phase for technology transfer to rank the best technologies in the presence of both cardinal and ordinal data this paper proposes an innovative approach which is based on imprecise data envelopment analysis idea the objective of this paper is to propose a comprehensive reference that discusses the use of idea in technology ranking a numerical example demonstrates the application of the proposed method

descent via koszul extensions abstract let r be a commutative noetherian local ring with completion r we apply differential graded dg algebra techniques to study descent of modules and complexes from r to r where r is either the henselization of r or a pointed etale neighborhood of r we extend a given r complex to a dg module over a koszul complex we describe this dg module equationally and apply artin approximation to descend it to r this descent result for koszul extensions has several applications when r is excellent we use it to descend the dualizing complex from r to a pointed etale neighborhood of r this yields a new version of p roberts theorem on uniform annihilation of homology modules of perfect complexes as another application we prove that the auslander condition on uniform vanishing of cohomology ascends to r when r is excellent henselian and cohen macaulay

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

on gorenstein projective injective and flat dimensions a functorial description with applications gorenstein homological dimensions are refinements of the classical homological dimensions and finiteness singles out modules with amenable properties reflecting those of modules over gorenstein rings as opposed to their classical counterparts these dimensions do not immediately come with practical and robust criteria for finiteness not even over commutative noetherian local rings in this paper we enlarge the class of rings known to admit good criteria for finiteness of gorenstein dimensions

the principal measure of a quantum harmonic oscillator at the end of his paper oprocha 2006 j phys a math gen 39 14 559 65 oprocha said that it is difficult and interesting to know the exact value of the principal measure of an annihilation operator of the unforced quantum harmonic oscillator motivated by this in this paper we prove that this exact value is equal to 1 besides we point out that exhibits distributional chaos for any 0 2

semidualizing modules of 2 2 ladder determinantal rings abstract we continue our study of ladder determinantal rings over a field k from the perspective of semidualizing modules in particular given a ladder of variables y we show that the associated ladder determinantal ring k y i 2 y admits exactly 2 n non isomorphic semidualizing modules where n is determined from the combinatorics of the ladder y the number n is essentially the number of non gorenstein factors in a certain decomposition of y from this for each n we show explicitly how to find ladders y such that k y i 2 y admits exactly 2 n non isomorphic semidualizing modules this is in contrast to our previous work which demonstrates that large classes of ladders have exactly 2 non isomorphic semidualizing modules