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

stochastic finite element modelling in linear transient heat transfer a stochastic heat transfer variational principle is suggested for transient and steady state heat problems the non statistical formulation is based on the combination of the second order perturbation technique and second moment analysis the principle allows incorporation of system uncertainties into the conventional finite element equations which are solved for the first two probabilistic moments of the nodal random temperature field computational aspects of the problem are discussed numerical algorithms have been worked out and easily adapted to an existing finite element code the formalism presented may be directly employed for a wide class of field problems

inferences on the common coefficient of variation the coefficient of variation is often used as a measure of precision and reproducibility of data in medical and biological science this paper considers the problem of making inference about the common population coefficient of variation when it is a priori suspected that several independent samples are from populations with a common coefficient of variation the procedures for confidence interval estimation and hypothesis testing are developed based on the concepts of generalized variables the coverage properties of the proposed confidence intervals and type i errors of the proposed tests are evaluated by simulation the proposed methods are illustrated by a real life example

supercyclic subspaces spectral theory and weighted shifts abstract a vector x in a banach space b is called hypercyclic for a bounded operator t if the orbit t n x n 0 is dense in b if the scalar multiples of the elements in the orbit are dense then the vector x is called supercyclic we give a general sufficient condition for a bounded operator on a banach space to have an infinite dimensional closed subspace of supercyclic vectors as a consequence we also obtain a spectral sufficient condition for the existence of such a subspace for an operator these results allow us to characterize unilateral and bilateral weighted shifts that have an infinite dimensional closed subspace of supercyclic vectors surprisingly there are weighted shift operators that have supercyclic vectors but in which all closed subspaces of supercyclic vectors are finite dimensional our results complement recent work on hypercyclic subspaces and supercyclic subspaces they also suggest that the problem of the existence of infinite dimensional closed subspaces of supercyclic vectors is not only different but also more difficult to handle than the corresponding problem for hypercyclic vectors

on semi analytical probabilistic finite element method for homogenization of the periodic fiber reinforced composites the main aim of this paper is a development of the semi analytical probabilistic version of the finite element method fem related to the homogenization problem this approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method it originates from the generalized stochastic perturbation based fem where taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions the hybrid computational implementation of the system maple with homogenization oriented fem code mcceff is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber reinforced composites although numerical illustration deals with a homogenization of a composite with material properties defined as gaussian random variables other composite parameters as well as other probabilistic distributions may be taken into account the methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements finite differences or volumes as well as for meshless numerical strategies copyright 2011 john wiley sons ltd

an exact test for testing the equality of parameter matrices in two multivariate linear models abstract a method of testing the hypothesis of the kind h 0 c 1 m c 2 m in two independent multivariate linear models is presented using the concept of generalized p values introduced by tsui and weerahandi k w tsui s weerahandi generalized p values in significance testing of hypothesis in the presence of nuisance parameters j amer statist assoc 84 1989 602 607 under the assumption of error matrix variate normality and heteroscedasticity this method calculates the exact p value in the generalized sense nel d g nel tests for equality of parameter matrices in two multivariate linear models j multivariate anal 61 1997 29 37 provided an approximate degrees of freedom test to test this hypothesis

constant norm scrambled sets for hypercyclic operators abstract let t x x be a hypercyclic operator of a banach space x let d t x x x has a dense t orbit and let x r x x x r for r 0 we show that there is a linearly independent subset s d t with the following properties i for any r 0 and any nonempty relatively open subset u of x r the intersection s u is uncountable ii s s d t 0 and in particular l i m i n f n t n a t n b 0 and l i m s u p n t n a t n b for any two distinct a b s

comparing the means and variances of a bivariate log normal distribution for a bivariate log normal distribution a confidence interval is developed for the ratio of the means the generalized confidence interval approach is used for this purpose and the procedure is applicable regardless of the sample size it is also noted that the same approach can be used to obtain a confidence interval for the ratio of the variances a modified signed log likelihood ratio procedure is also described for computing confidence intervals the coverage probabilities of the proposed confidence intervals are estimated by monte carlo and the generalized confidence intervals are found to exhibit satisfactory performance even for small sample sizes numerical results also show that the corresponding test procedures provide larger power compared with the modified signed log likelihood ratio test two examples are given one dealing with the comparison of the means and variances of health care costs and the other dealing with testing mean equivalence in quantitative assays copyright 2007 john wiley sons ltd

weyl s theorem and hypercyclic supercyclic operators abstract necessary and sufficient conditions for hypercyclic supercyclic banach space operators t to satisfy a t w a t 00 a t are proved

hypercyclic operators failing the hypercyclicity criterion on classical banach spaces abstract by a recent result of m de la rosa and c read there exist hypercyclic banach space operators which do not satisfy the hypercyclicity criterion in the present paper we prove that such operators can be constructed on a large class of banach spaces including c 0 n or l p n

simultaneous chaotic extensions for general operators on a hilbert subspace abstract for an infinite codimensional closed subspace m of a separable hilbert space h we show that every bounded linear operator a m h has a chaotic extension t h h as a generalization of this result we further show that for any uniformly bounded sequence of linear operators a n m h there exists a bounded linear operator v m h on the orthogonal complement m of m that simultaneously extends all operators a n to chaotic operators a n v h h

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

property ω1 and weyl type theorem abstract in this note we define the property 1 a variant of weyl s theorem and establish for a bounded linear operator defined on a banach space the sufficient and necessary conditions for which property 1 holds by means of the variant of the essential approximate point spectrum 1 in addition the relation between property 1 and hypercyclicity or supercyclicity is discussed

fiducial generalized confidence intervals generalized pivotal quantities gpqs and generalized confidence intervals gcis have proven to be useful tools for making inferences in many practical problems although gcis are not guaranteed to have exact frequentist coverage a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice in this article we single out a subclass of generalized pivotal quantities which we call fiducial generalized pivotal quantities fgpqs and show that under some mild conditions gcis constructed using fgpqs have correct frequentist coverage at least asymptotically we describe three general approaches for constructing fgpqs a recipe based on invertible pivotal relationships and two extensions of it and demonstrate their usefulness by deriving some previously unknown gpqs and gcis it is fair to say that nearly every published gci can be obtained using one of these recipes as an inte

generalized p values and confidence intervals for variance components applications to army test and evaluation various mixed models that are relevant for analyzing army test data are described along with several hypothesis testing and interval estimation problems the problems come up in the context of inv

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

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

confidence intervals for steady state availability of a system with exponential operating time and lognormal repair time long run availability of a system assuming lognormal repair times and exponential failure times is considered with many repairable systems the time to repair is well characterized by a lognormal distribution however due to the difficulties associated with the lognormal distribution repair times are often modeled using the lognormal distribution assuming that the variance of the lognormal distribution is known or by using some other distribution such as the exponential distribution instead of the lognormal distribution in this paper using the generalized p value approach we propose confidence intervals and exact tests for steady state availability of systems using the two parameter lognormal distribution for repair time and exponential distribution for operating time here both parameters of the lognormal distribution are assumed to be unknown a couple of examples are given to illustrate the proposed procedures a simulation study is given to demonstrate the performance of the proposed procedure results are extended for the long run availability of a system consisting of several independent parallel sub systems

browder essential approximate point spectra and hypercyclicity for operator matrices abstract when a b h and b b k are given we denote by m c the operator acting on the infinite dimensional separable hilbert space h k of the form m c a c 0 b in this paper it is shown that if a is upper semi fredholm of finite ascent and infinite codimension and if r b is closed of infinite kernel then m c is upper semi fredholm of finite ascent for some c b k h in addition we explore the hypercyclicity and supercyclicity for 2 2 upper triangular operator matrices on the hilbert space

bayesian and non bayesian solutions to analysis of covariance models under heteroscedasticity a single factor fixed effect analysis of covariance model with one or more covariates is considered without the assumption of equal error variance using the generalized definition of p values exact tests are derived for testing the equality of treatment effect and testing whether the effect of the covariate is significant in a bayesian setup it is shown that these generalized p values can be produced by the posterior predictive p value approach by using an appropriate noninformative prior examples and simulation studies are given to illustrate the proposed procedures and their advantages over the classical f tests

exact inference for growth curves with intraclass correlation structure summary we consider repeated observations taken over time for each of several subjects for example one might consider the growth curve of a cohort of babies over time we assume a simple linear growth curve model exact results based on sufficient statistics exact tests of the null hypothesis that a coefficient is zero or exact confidence intervals for coefficients are not available to make inference on regression coefficients when an intraclass correlation structure is assumed this paper will demonstrate that such exact inference is possible using generalized inference

generalized p values and the multivariate behrens fisher problem abstract tsui and weerahandi 1989 defined generalized p values for testing statistical hypothesis in the presence of nuisance parameters and applied to obtain an exact solution to the univariate behrens fisher problem johnson and weerahandi 1988 provided a bayesian solution to the multivariate behrens fisher problem with the help of the cauchy schwarz inequality we provide an upper bound for the generalized p value for the multivariate case also we extend the result of tsui and weerahandi to present a second upper bound

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

weakly supercyclic operators inspired by a recent result that a weakly hypercyclic operator may fail to be norm hypercyclic we show there exists a weakly supercyclic operator that fails to be norm supercyclic moreover despite a classical result of hilden and wallen that every unilateral weighted backward shift is supercyclic we show such an operator may have a weakly supercyclic vector that is not a norm supercyclic vector in addition to these results we extend a result of kitai by showing a hyponormal operator cannot be weakly hypercyclic

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

on steady state availability of a system with lognormal repair time assuming two parameter lognormal distribution for repair times statistical inference for the steady state availability of a system is considered for the failure time distribution weibull gamma and lognormal distributions were considered using the generalized p value approach we propose confidence intervals and exact tests for the steady state availability of a system a couple of examples are given to illustrate the proposed procedures

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

a practical approach for comparing means of two groups without equal variance assumption in this paper we consider two groups of i i d normally distributed random variables n mu x sigma x 2 and n mu y sigma y 2 without assuming equal variance sigma x 2 sigma y 2 we propose a simple method for constructing confidence bounds based on howe s approximation i its applications in parallel clinical trial testing h 0 mu x mu y 0 versus h 1 mu x mu y 0 and parallel bioequivalence be trial testing h 0 mid r mu x mu y mid r delta versus h 1 mid r mu x mu y mid r delta are studied sample size calculation formulae for both cases are derived their performances are evaluated by simulation our study shows that the proposed procedure can control type i error satisfactorily compared with cochran cox s and satterthwaite s approximations while maintaining a relatively high power the proposed approach is not only simple for constructing the confidence limit but also provides a simple and accurate formula for sample size calculation

non local dispersive model for wave propagation in heterogeneous media one dimensional case non local dispersive model for wave propagation in heterogeneous media is derived from the higher order mathematical homogenization theory with multiple spatial and temporal scales in addition to the usual space time co ordinates a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long term behaviour of the homogenized solution by combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth order differential equation also known as a bad boussinesq problem regularization procedures are then introduced to construct the so called good boussinesq problem where the need for c1 continuity is eliminated numerical examples are presented to validate the present formulation copyright 2002 john wiley sons ltd

irregular vectors of hilbert space operators abstract a vector x in a hilbert space h is called irregular for an operator t h h provided that sup n t n x and inf n t n x 0 we establish some basic properties of operators having irregular vectors and present examples that highlight the relationship or lack thereof between irregularity and hypercyclicity

inferences on the mean response in a log regression model the generalized variable approach this paper proposes a novel approach for the confidence interval estimation and hypothesis testing of the mean response in a log regression model using the concept of generalized variable simulation studies demonstrate that the proposed confidence intervals have satisfying coverage probabilities the proposed approach can be simply carried out by a few simulation steps therefore it is an ideal candidate for making inferences about the mean response in a log regression model

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

multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales a coupled thermo viscoelastic example problem abstract a systematic approach for analyzing multiple physical processes interacting at multiple spatial and temporal scales is developed the proposed computational framework is applied to the coupled thermo viscoelastic composites with microscopically periodic mechanical and thermal properties a rapidly varying spatial and temporal scales are introduced to capture the effects of spatial and temporal fluctuations induced by spatial heterogeneities at diverse time scales the initial boundary value problem on the macroscale is derived by using the double scale asymptotic analysis in space and time it is shown that an extra history dependent long term memory term introduced by the homogenization process in space and time can be obtained by solving a first order initial value problem this is in contrast to the long term memory term obtained by the classical spatial homogenization which requires solutions of the initial boundary value problem in the unit cell domain the validity limits of the proposed spatial temporal homogenized solution are established numerical example shows a good agreement between the proposed model and the reference solution obtained by using a finite element mesh with element size comparable to that of material heterogeneity

multiple spatial and temporal scales method for numerical simulation of non classical heat conduction problems one dimensional case abstract a multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non fourier heat conduction in periodic heterogeneous materials the model developed is based on the higher order homogenization theory with multiple spatial and temporal scales in one dimensional case the amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non fourier heat conduction due to material heterogeneity and non local effect of the homogenized solution by separating the governing equations into various scales the different orders of homogenized non fourier heat conduction equations are obtained the reduced time dependence is thus eliminated and the fourth order governing differential equations are derived to avoid the necessity of c1 continuous finite element implementation a c0 continuous mixed finite element approximation scheme is put forward numerical results are shown to demonstrate the efficiency and validity of the proposed method

weyl type theorem and hypercyclic operators using a variant of the essential approximate point spectrum we give the necessary and sufficient conditions for t for which the a browder s theorem or the a weyl s theorem holds also the relation between hypercyclic operators or supercyclic operators and the operators which satisfy weyl type theorem is discussed

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

sensitivity and randomness in homogenization of periodic fiber reinforced composites via the response function method the main issue this paper addresses is the derivation and implementation of a general homogenization method including the simultaneous determination of sensitivity gradients and probabilistic moments of the effective elasticity tensor this is possible with an application of the perturbation method based on taylor expansion and with the effective modules method the computational procedure is implemented using plane strain analysis carried out with the finite element method program mcceff and the symbolic computations system maple the sensitivity gradients and probabilistic moments are commonly determined on the basis of partial derivatives for the homogenized elasticity tensor calculated using the response function method with respect to some composite parameters they are subjected separately to a normalization procedure in deterministic analysis and the relevant algebraic combinations for the stochastic case this enriched homogenization procedure is tested on a periodic fiber reinforced two component composite where the material parameters are taken as design variables and then the input random quantities the results of computational analysis are compared against the results of the central finite difference approach in the case of sensitivity gradients determination as well as the direct monte carlo simulation approach this numerical methodology may be further applied not only in the context of the homogenization method but also to extend various discrete computational techniques such as boundary finite element and finite difference together with various meshless methods

box type approximations in nonparametric factorial designs abstract linear rank statistics in nonparametric factorial designs are asymptotically normal and in general heteroscedastic in a comprehensive simulation study the asymptotic chi squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite sample distribution motivated by this problem we propose simple finite sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure these approximations are based on an f distribution with estimated degrees of freedom that generalizes ideas of patnaik and box simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin wald test data driven guidelines are given to select the most appropriate test procedure these ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector

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

bihypercyclic bilinear mappings abstract we propose a notion of orbit for bilinear mappings on banach spaces this then leads us to the concept of bihypercyclic bilinear mappings that is of bilinear mappings with a dense orbit we provide some examples of such mappings and we obtain some basic properties of bihypercyclicity in our main result we show that every separable real or complex banach space supports a bihypercyclic bilinear mapping we also formulate some open problems

thermo mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach a spatial and temporal multiscale asymptotic homogenization method used to simulate thermo dynamic wave propagation in periodic multiphase materials is systematically studied a general field governing equation of thermo dynamic wave propagation is expressed in a unified form with both inertia and velocity terms amplified spatial and reduced temporal scales are respectively introduced to account for spatial and temporal fluctuations and non local effects in the homogenized solution due to material heterogeneity and diverse time scales the model is derived from the higher order homogenization theory with multiple spatial and temporal scales it is also shown that the modified higher order terms bring in a non local dispersion effect of the microstructure of multiphase materials one dimensional non fourier heat conduction and dynamic problems under a thermal shock are computed to demonstrate the efficiency and validity of the developed procedure the results indicate the disadvantages of classical spatial homogenization

interval estimation and hypothesis testing of intraclass correlation coefficients the generalized variable approach in this paper we propose a novel approach using the concept of generalized variable gv for the confidence interval estimation of the difference of two intraclass correlation coefficients under unequal family sizes this approach can also easily provide p values for hypothesis testing simulation results show that the gv approach can provide confidence intervals with good coverage properties and perform hypothesis testing with satisfactory type i error control furthermore the confidence intervals and p values by gv approach can be easily obtained by simulation therefore the gv approach is a suitable candidate for making inference concerning two intraclass correlation coefficients

hypercyclic subspaces for frechet space operators abstract a continuous linear operator t x x is hypercyclic if there is an x x such that the orbit t n x is dense and such a vector x is said to be hypercyclic for t recent progress show that it is possible to characterize banach space operators that have a hypercyclic subspace i e an infinite dimensional closed subspace h x of except for zero hypercyclic vectors the following is known to hold a banach space operator t has a hypercyclic subspace if there is a sequence n i and an infinite dimensional closed subspace e x such that t is hereditarily hypercyclic for n i and t n i 0 pointwise on e in this note we extend this result to the setting of frechet spaces that admit a continuous norm and study some applications for important function spaces as an application we also prove that any infinite dimensional separable frechet space with a continuous norm admits an operator with a hypercyclic subspace

inferences on the mean of zero inflated lognormal data the generalized variable approach this paper considers the problems of confidence interval estimation and hypothesis testing for the mean of zero inflated lognormal data we present an unified novel approach based on the concepts of generalized test variables and generalized pivotal quantities simulation results demonstrate that the coverage accuracy of proposed confidence intervals and the type i error control of the proposed exact tests are satisfactory

on the convex hull generated by orbit of operators let x be an infinite dimensional banach space and t be a bounded operator on x the operator t is said to be convex cyclic if the convex hull generated by orb t x is dense in x for some x x we characterize completely such operators on finite dimensional vector spaces some examples of pure convex cyclic operators on infinite dimensional banach spaces are provided and many hypercyclic like properties of such operators are considered

two scale diffusion deformation coupling model for material deterioration involving micro crack propagation in this paper we introduce a two scale diffusion deformation coupled model that represents the aging material deterioration of two phase materials involving micro crack propagations the mathematical homogenization method is applied to relate the micro and macroscopic field variables and a weak coupling solution method is employed to solve the two way coupling phenomena between the diffusion of scalar fields and the deformation of quasi brittle solids the macroscopic mechanical behavior represented by the derived two scale two way coupled model reveals material nonlinearity due to micro scale cracking induced by the scalar field induced deformation which can be simulated by the finite cover method after verifying the fundamental validity of the proposed model and the analysis method we perform a simple numerical example to demonstrate their ability to predict aging material deterioration copyright 2010 john wiley sons ltd

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

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

one sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals we consider the problem of deriving one sided tolerance intervals in the one way random model with balanced as well as unbalanced data under the usual normality assumptions the problems investigated deal with the computation of such intervals for the observable random variable as well as the unobservable random effect in the one way random model the tolerance limits are derived using the concept of a generalized confidence interval some approximations are derived for the tolerance limits and their performance is investigated by simulation the simulation results show that the proposed tolerance limits are quite satisfactory for practical use

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

common supercyclic vectors for a path of operators abstract we examine common supercyclic vectors for a path of operators in particular we show that the path consisting of convex combinations of two arbitrary unilateral weighted backward shifts has a dense g set of common supercyclic vectors moreover we show there exists a path with a dense g set of common supercyclic vectors between a unilateral weighted backward shift which satisfies the supercyclicity criterion and an operator which does not lastly we provide an example of a path of unilateral weighted backward shifts that fails to have a common supercyclic vector

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

inferences on standardized mean difference the generalized variable approach the standardized mean difference has been widely used as the most common index of effect magnitude in many applied fields in this paper we propose a novel approach using the concept of generalized variable for the confidence interval estimation and hypothesis testing of standardized mean difference furthermore we extend this approach to compare standardized mean differences between two studies or between two strata simulation results demonstrate that the proposed approach can provide confidence intervals with excellent coverage properties and can perform hypothesis testing with satisfactory type i error control

totally hereditarily normaloid operators and weyl s theorem for an elementary operator abstract a hilbert space operator t b h is hereditarily normaloid notation t hn if every part of t is normaloid an operator t hn is totally hereditarily normaloid notation t thn if every invertible part of t is normaloid we prove that thn operators with bishop s property also thn contractions with a compact defect operator such that t 1 0 t 1 0 and non zero isolated eigenvalues of t are normal are not supercyclic take a and b in thn and let d a b denote either of the elementary operators in b b h a b and a b where a b x a x b x and a b x a x x b we prove that if non zero isolated eigenvalues of a and b are normal and b 1 0 b 1 0 then d a b is an isoloid operator such that the quasi nilpotent part h 0 d a b of d a b equals d a b 1 0 for every complex number which is isolated in d a b if additionally d a b has the single valued extension property at all points not in the weyl spectrum of d a b then d a b and the conjugate operator d a b satisfy weyl s theorem

operator on the space of rapidly decreasing functions with all non zero vectors hypercyclic abstract we construct a continuous linear operator t on the schwartz space s r d of rapidly decreasing functions such that each non zero orbit of t is dense the construction is inspired by the work of c read on similar operators on the space l 1 the construction due to the structure of a frechet space can be made significantly simpler than the original construction of read

generalized kato type operators and property ω under perturbations abstract in this note we give the definition of generalized kato type and establish for a bounded linear operator defined on a hilbert space the sufficient and necessary conditions for which property holds by means of the induced spectrum of generalized kato property in addition the stability of property is discussed

asymptotic homogenization of viscoelastic composites with periodic microstructures a systematic way of obtaining the effective viscoelastic moduli in time and frequency domain is presented for viscoelastic composites with periodic microstructures the problem of estimating the effective moduli is formulated using the asymptotic homogenization method for theoretical aspects the memory effects due to the homogenization are shown in general form and a sufficient condition for the effects to disappear is fully discussed the computational procedure is divided into two steps the effective relaxation moduli are computed in laplace transformed domain and are numerically inverse transformed into time domain the effective complex moduli are then readily obtained by using simple formulae of the fourier transform several numerical examples are presented to illustrate and verify present approach and to discuss the memory effects

notes on subspace hypercyclic operators a bounded linear operator t on a banach space x is called subspace hypercyclic for a subspace m if orb t x m is dense in m for a vector x m in this case we show that p t has a relatively dense range for every real or complex polynomial p which in turn answers a question posed in madore and martinez avendano 2011 8 as a consequence the algebraic structure of the set of subspace hypercyclic vectors can be described