c0 is isometrically isomorphic to a subspace of cantor lebesgue functions abstract we prove what the title of this note states i e c 0 that is the set of all sequences converging to 0 is isometrically isomorphic to a subspace of continuous almost everywhere differentiable and non lipschitz functions on 0 1 having almost everywhere null derivative this in particular improves a recent result jimenez rodriguez et al 2012 9 on the lineability of this set of functions

isogeometric variational multiscale modeling of wall bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes abstract in this work we combine i nurbs based isogeometric analysis ii residual driven turbulence modeling and iii weak imposition of no slip and no penetration dirichlet boundary conditions on unstretched meshes to compute wall bounded turbulent flows while the first two ingredients were shown to be successful for turbulence computations at medium to high reynolds number i akkerman y bazilevs v m calo t j r hughes s hulshoff the role of continuity in residual based variational multiscale modeling of turbulence comput mech 41 2008 371 378 y bazilevs v m calo j a cottrell t j r hughes a reali g scovazzi variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows comput methods appl mech engrg 197 2007 173 201 it is the weak imposition of no slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher reynolds number y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 y bazilevs c michler v m calo t j r hughes weak dirichlet boundary conditions for wall bounded turbulent flows comput methods appl mech engrg 196 2007 4853 4862 these three ingredients form a basis of a possible practical strategy for computing engineering flows somewhere between rans and les in complexity we demonstrate this by solving two challenging incompressible turbulent benchmark problems channel flow at friction velocity reynolds number 2003 and flow in a planar asymmetric diffuser we observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data this lends some credence to the proposed approach which we believe may become a viable engineering tool

riemann integrability and lebesgue measurability of the composite function abstract if f is continuous on the interval a b g is riemann integrable resp lebesgue measurable on the interval and g a b then f g is riemann integrable resp measurable on a well known fact on the other hand states that f g might not be riemann integrable resp measurable when f is riemann integrable resp measurable and g is continuous if c stands for the continuum in this paper we construct a 2 c dimensional space v and a c dimensional space w of respectively riemann integrable functions and continuous functions such that for every f v 0 and g w 0 f g is not riemann integrable showing that nice properties such as continuity or riemann integrability can be lost in a linear fashion via the composite function similarly we construct a c dimensional space w of continuous functions such that for every g w 0 there exists a c dimensional space v of measurable functions such that f g is not measurable for all f v 0

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

subspace based blind channel estimation generalization and performance analysis in this paper we present a systematic study of the subspace based blind channel estimation method we first formulate a general signal model of multiple simultaneous signals transmitted through vector channels which can be applied to a multitude of modern digital communication systems based on this model we then propose a generalized subspace based channel estimator by minimizing a novel cost function which incorporates the set of kernel matrices of the signals sharing the target channel via a weighted sum of projection errors we investigate the asymptotic performance of the proposed estimator i e bias covariance mean square error mse and cramer rao bound for large numbers of independent observations we show that the performance of the estimator can be optimized by increasing the number of kernel matrices and by using a special set of weights in the cost function finally we consider the application of the proposed estimator to a downlink code division multiple access cdma system operating in a frequency selective fading channel with negligible intersymbol interference isi the results of the computer simulations fully support our analytical developments

a bi partitioned iterative algorithm for solving linear systems arising from incompressible flow problems abstract a novel iterative algorithm called the bi partitioned method is introduced for efficiently solving the system of linear equations that arises from the stabilized finite element formulation of the navier stokes equations the bi partitioned algorithm is a krylov subspace method designed for a matrix with separated momentum and continuity blocks this structure allows for formation of the schur complement to separately solve for the velocity and pressure unknowns hence the bi partitioned algorithm can also be applied to problems with similar matrix structure involving the schur complement two separate spaces are constructed iteratively from the velocity and pressure solution candidates and optimally combined to produce the final solution the bi partitioned algorithm calculates the final solution to a given tolerance regardless of the approximation made in construction of the schur complement the proposed algorithm is analyzed and compared to the generalized minimal residual gmres algorithm using two incompressible flow and one fluid structure interaction example exhibiting up to an order of magnitude improvement is simulation cost while maintaining excellent stability

riemann integrability versus weak continuity abstract in this paper we focus on the relation between riemann integrability and weak continuity a banach space x is said to have the weak lebesgue property if every riemann integrable function from 0 1 into x is weakly continuous almost everywhere we prove that the weak lebesgue property is stable under l 1 sums and obtain new examples of banach spaces with and without this property furthermore we characterize dunford pettis operators in terms of riemann integrability and provide a quantitative result about the size of the set of continuous nonriemann integrable functions with a locally convex topology weaker than the norm topology

isogeometric divergence conforming variational multiscale formulation of incompressible turbulent flows a new residual based variational multiscale rbvms formulation for incompressible turbulent flows is proposed that is suitable for discretization using divergence conforming b splines the proposed methodology results in a pointwise satisfaction of the zero divergence constraint on the discrete velocity field the velocity fine scales are residual driven and constructed in a manner that is consistent with the divergence free constraint on the discrete velocity solution the resulting formulation is tested on laminar and turbulent flow benchmark problems showing excellent stability and accuracy characteristics in both regimes

lineability spaceability and additivity cardinals for darboux like functions we introduce the concept of maximal lineability cardinal number ml m of a subset m of a topological vector space and study its relation to the cardinal numbers known as additivity a m homogeneous lineability hl m and lineability l m of m in particular we will describe in terms of l the lineability and spaceability of the families of the following darboux like functions on r n n 1 extendable jones and almost continuous functions

moduleability algebraic structures and nonlinear properties we show that some pathological phenomena occur more often than one could expect existing large algebraic structures infinite dimensional vector spaces algebras positive cones or infinitely generated modules enjoying certain special properties in particular we construct infinite dimensional vector spaces of non integrable measurable functions completing some recent results shown in garcia pacheco et al 2009 13 garcia pacheco and seoane sepulveda 2006 15 munoz fernandez et al 2008 20 we prove as well the existence of dense and not barrelled spaces of sequences every non zero element of which has a finite number of zero coordinates giving partial answers to a problem originally posed by r m aron and v i gurariy in 2003

spaceability of the set of continuous injections from blp into lp with nowhere continuous inverses abstract let p 1 we show that in the banach space of all bounded continuous mappings from b l p the open unit ball in l p into l p the subset consisting of all injections with nowhere continuous inverses is isometrically l p spaceable i e it contains an isometric copy of l p the proof uses some ideas of creswell s example

the set of space filling curves topological and algebraic structure abstract in this paper a study of topological and algebraic properties of two families of functions from the unit interval i into the plane r 2 is performed the first family is the collection of all peano curves that is of those continuous mappings onto the unit square the second one is the bigger set of all space filling curves i e of those continuous functions i r 2 whose images have the positive jordan content emphasis is put on the size of these families in both topological and algebraic senses when endowed with natural structures

lineability and integrability in the sense of riemann lebesgue denjoy and khintchine abstract in this paper we continue the ongoing research on lineability related questions on this occasion we shall consider among others the classes of integrable functions in the sense of riemann lebesgue denjoy and khintchine improving some already known results and expanding the study of lineability to other famous integrable classes never considered before

strong c algebrability of strong sierpinski zygmund smooth nowhere analytic and other sets of functions abstract we present a useful technique of proving strong c algebrability as an outcome we obtain the strong c algebrability of the following sets of functions strong sierpinski zygmund nowhere holder bruckner garg nowhere monotone differentiable a certain baire class smooth and nowhere analytic functions

spaceability and operator ideals abstract let i 1 and i 2 be arbitrary operator ideals in the sense of pietsch and e and f be banach spaces such that the set i 1 e f i 2 e f is non empty we give a quite general sufficient condition on the banach spaces in order to obtain the spaceability of i 1 e f i 2 e f some consequences are provided when considering the ideals of compact operators strictly singular operators finitely strictly singular operators and schatten operator classes

convolution functions that are nowhere differentiable abstract in 1951 v jarnik constructed two continuous functions whose volterra convolution is nowhere differentiable we generalize jarnik s results by proving that the set of such functions is maximal lineable this would shed some light on a question posed in 1973 on the structure of the set of continuous functions whose volterra convolution is nowhere differentiable

lineability of the set of bounded linear non absolutely summing operators in this note we solve except for extremely pathological cases a question posed by puglisi and seoane sepulveda on the lineability of the set of bounded linear non absolutely summing operators we also show how the idea of the proof can be adapted to several related situations

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

improving stability of stabilized and multiscale formulations in flow simulations at small time steps abstract the objective of this paper is to show that use of the element vector based definition of stabilization parameters introduced in t e tezduyar computation of moving boundaries and interfaces and stabilization parameters int j numer methods fluids 43 2003 555 575 t e tezduyar y osawa finite element stabilization parameters computed from element matrices and vectors comput methods appl mech engrg 190 2000 411 430 circumvents the well known instability associated with conventional stabilized formulations at small time steps we describe formulations for linear advection diffusion and incompressible navier stokes equations and test them on three benchmark problems advection of an l shaped discontinuity laminar flow in a square domain at low reynolds number and turbulent channel flow at friction velocity reynolds number of 395

infinite dimensional holomorphic non extendability and algebraic genericity abstract in this note the linear structure of the family h e g of holomorphic functions in a domain g of a complex banach space that are not holomorphically continuable beyond the boundary of g is analyzed more particularly we prove that h e g contains except for zero a closed and a dense vector space having maximal dimension as well as a maximally generated free algebra the results obtained complete a number of previous ones by several authors

rolewicz type chaotic operators abstract in this article we introduce a new class of rolewicz type operators in l p 1 p we exhibit a collection f having the cardinality of the continuum consisting of operators of this type which are chaotic and remain so under almost all finite linear combinations provided that the linear combination has sufficiently large norm as a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm

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

operator ranges and spaceability recent contributions on spaceability have overlooked the applicability of results on operator range subspaces of banach spaces or frechet spaces here we consider general results on spaceability of the complement of an operator range some of which we extend to the complement of a union of countable chains of operator ranges applications we give include spaceability of the non absolutely convergent power series in the disk algebra and of the non absolutely p summing operators between certain pairs of banach spaces another application is to ascent and descent of countably generated sets of continuous linear operators where we establish some closed range properties of sets with finite ascent and descent

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

basic sequences and spaceability in lp spaces let x be a sequence space and denote by z x the subset of x formed by sequences having only a finite number of zero coordinates we study algebraic properties of z x and show among other results that for p is an element of 1 infinity z l p does not contain infinite dimensional closed subspaces this solves an open question originally posed by r m aron and v i gurariy in 2003 on the linear structure of z l infinity in addition to this we also give a thorough analysis of the existing algebraic structures within the sets z x and x z x and their algebraic genericities

lineability and additivity in r r we give a condition for a family of functions to be lineable by means of its additivity the novelty presented here is that we solve the lineability problem using a technique that is not constructive as are most approaches to this problem we relate the notions of additivity and lineability and use this relation to give a general method to find the lineability of large families of functions we also study more examples of pathologically behaving functions in particular the class of jones functions which is a highly pathological subclass of perfectly everywhere surjective functions we work on the additivity lineability and main properties of this class

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

fast divergence conforming reduced basis methods for steady navier stokes flow abstract reduced basis methods rb methods or rbms form one of the most promising techniques to deliver numerical solutions of parametrized pdes in real time with reasonable accuracy for incompressible flow problems rbms based on lbb stable velocity pressure spaces do not generally inherit the stability of the underlying high fidelity model and instead additional stabilization techniques must be introduced one way of bypassing the loss of lbb stability in the rbm is to inflate the velocity space with supremizer modes this however deteriorates the performance of the rbm in the performance critical online stage as additional dofs must be introduced to retain stability while these dofs do not effectively contribute to accuracy of the rb approximation in this work we consider a velocity only rb approximation exploiting a solenoidal velocity basis the solenoidal reduced basis emerges directly from the high fidelity velocity solutions in the offline stage by means of piola transforms the solenoidality of the velocity space is retained under geometric transformations making the proposed rb method suitable also for the investigation of geometric parameters to ensure exact solenoidality of the high fidelity velocity solutions that constitute the rb we consider approximations based on divergence conforming compatible b splines we show that the velocity only rb method leads to a significant improvement in computational efficiency in the online stage and that the pressure solution can be recovered a posteriori at negligible extra cost we illustrate the solenoidal rb approach by modeling steady two dimensional navier stokes flow around a naca0015 airfoil at various angles of attack

the expectation maximization algorithm for symbol unsynchronized sequence detection the expectation maximization em algorithm for maximizing likelihood functions combined with the viterbi algorithm is applied to the problem of sequence detection when symbol timing information is not present although the em algorithm is noncausal results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations making it both of theoretical and of practical interest a practical algorithm based on the em algorithm is introduced it reduces the computational burden and improves performance by making use of timing estimates in previous observation windows

algebrability of some families of darboux like functions abstract we prove that the class of all almost continuous in the sense of stallings functions possessing the perfect road property and the class of all almost continuous functions without the perfect road property contain a 2 c generated free algebras we prove also that the family of all extendable functions contains a 2 c dimensional linear space

joint parameter estimation and symbol detection for linear or nonlinear unknown channels we present an iterative method for joint channel parameter estimation and symbol selection via the baum welch algorithm or equivalently the expectation maximization em algorithm channel parameters including noise variance are estimated using a maximum likelihood criterion the markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward backward algorithm the calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability the proposed receiver can be used for both linear and nonlinear channels it improves the system throughput by making saving in the transmission of known symbols usually employed for channel identification simulation results which show fast convergence are presented

algebraic genericity within the class of sup measurable functions abstract it is well known that there exist real valued non measurable functions on the plane whose restrictions to the graph of all measurable functions on the real line are measurable in this paper it is shown that there is in fact a continuum dimensional vector space all of whose members except for zero are functions on the plane satisfying the mentioned property versions of this fact are proved in the baire category setting and in the case where the graphs are generated by softer functions

additivity and lineability in vector spaces abstract gamez merino munoz fernandez and seoane sepulveda proved that if additivity a f c then f is a f lineable where f r r they asked if a f c can be weakened we answer this question in negative moreover we introduce and study the notions of homogeneous lineability number and lineability number of subsets of linear spaces

locally recurrent functions density topologies and algebraic genericity we study the algebraic and topological genericity of certain subsets of locally recurrent functions obtaining among other results algebrability and spaceability within these classes

non lipschitz functions with bounded gradient and related problems let e be a topological vector space and let us consider a property p we say that the subset m of e formed by the vectors in e which satisfy p is lineable for certain cardinal finite or infinite if m 0 contains an infinite dimensional linear space of dimension in this note we prove that there exist uncountably infinite dimensional linear spaces of functions enjoying the following properties 1 being continuous on 0 1 a e differentiable with a e bounded derivative and not lipschitz 2 differentiable in r2 r and not enjoying the mean value theorem 3 real valued differentiable on an open connected and non convex set having bounded gradient non lipschitz and therefore not verifying the mean value theorem

adaptive power techniques for blind channel estimation in cdma systems the problem of blind adaptive channel estimation in code division multiple access cdma systems is considered motivated by the iterative power method which is used in numerical analysis for estimating singular values and singular vectors we develop recursive least squares rls and least mean squares lms subspace based adaptive algorithms in order to identify the impulse response of the multipath channel the schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind both versions rls and lms exhibit rapid convergence combined with low computational complexity with the help of simulations we demonstrate the improved performance of our methods as compared with the already existing techniques in the literature

on automatic continuity and three problems of the scottish book concerning the boundedness of polynomial functionals in this paper we introduce and study the notions of isotropic mapping and essential kernel in addition some theorems on the borel graph and baire mapping for polynomial operators are proved it is shown that a polynomial functional from an infinite dimensional complex linear space into the field of complex numbers vanishes on some infinite dimensional affine subspace

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

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

weak dirichlet boundary conditions for wall bounded turbulent flows abstract in turbulence applications strongly imposed no slip conditions often lead to inaccurate mean flow quantities for coarse boundary layer meshes to circumvent this shortcoming weakly imposed dirichlet boundary conditions for fluid dynamics were recently introduced in y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 in the present work we propose a modification of the original weak boundary condition formulation that consistently incorporates the well known law of the wall to compare the different methods we conduct numerical experiments for turbulent channel flow at reynolds number 395 and 950 in the limit of vanishing mesh size in the wall normal direction the weak boundary condition acts like a strong boundary condition accordingly strong and weak boundary conditions give essentially identical results on meshes that are stretched to better capture boundary layers however on uniform meshes that are incapable of resolving boundary layers weakly imposed boundary conditions deliver significantly more accurate mean flow quantities than their strong counterparts hence weakly imposed boundary conditions present a robust technique for flows of industrial interest where optimal mesh design is usually not feasible and resolving boundary layers is prohibitively expensive our numerical results show that the formulation that incorporates the law of the wall yields an improvement over the original method

skeleton stabilized isogeometric analysis high regularity interior penalty methods for incompressible viscous flow problems abstract a skeleton stabilized isogeometric analysis siga technique is proposed for incompressible viscous flow problems with moderate reynolds number the proposed method allows utilizing identical finite dimensional spaces with arbitrary b splines nurbs order and regularity for the approximation of the pressure and velocity components the key idea is to stabilize the jumps of high order derivatives of variables over the skeleton of the mesh for b splines nurbs basis functions of degree k with c regularity 0 k only the derivative of order 1 has to be controlled this stabilization technique thus can be viewed as a high regularity generalization of the continuous interior penalty finite element method numerical experiments are performed for the stokes and navier stokes equations in two and three dimensions oscillation free solutions and optimal convergence rates are obtained in terms of the sparsity pattern of the algebraic system we demonstrate that the block matrix associated with the stabilization term has a considerably smaller bandwidth when using b splines than when using lagrange basis functions even in the case of c 0 continuity this important property makes the proposed isogeometric framework practical from a computational effort point of view

the spatial operator in the incompressible navier stokes oseen and stokes equations abstract we investigate the spatial operator in the incompressible navier stokes oseen and stokes equations and show how to avoid singularities associated with null spaces by choosing specific boundary conditions the theoretical results are derived for a general form of energy stable boundary conditions and applied to a few commonly used ones the analysis is done on a system that simultaneously covers the nonlinear incompressible navier stokes the oseen and the stokes equations when the spectrum of the spatial operator is investigated we restrict the analysis to the oseen and stokes equations the continuous analysis carries over to the discrete setting by using the summation by parts framework

some results and open questions on spaceability in function spaces a subset m of a topological vector space x is called lineable respectively spaceable in x if there exists an infinite dimensional linear space respectively an infinite dimensional closed linear space y subset of m boolean or 0 in this article we prove that for every infinite dimensional closed subspace x of c 0 1 the set of functions in x having infinitely many zeros in 0 1 is spaceable in x we discuss problems related to these concepts for certain subsets of some important classes of banach spaces such as c 0 1 or muntz spaces we also propose several open questions in the field and study the properties of a new concept that we call the oscillating spectrum of subspaces of c 0 1 as well as oscillating and annulling properties of subspaces of c 0 1

on lineability of sets of continuous functions we study the existence of vector spaces of dimension at least two of continuous functions on subsets of r every non zero element of which admits one and only one absolute maximum

spaceability of sets in lp lq and c0 c0 abstract a subset e of an infinitely dimensional linearly topological space x is called spaceable if there is an infinitely dimensional closed subspace y of x with y e 0 the main aim of the paper is to show the spaceability of the following sets 1 the set of those f g l p l q for which f g l r provided that one of the following conditions holds a 0 1 p 1 q 1 r and sup a a b 1 p 1 q 1 r and inf a a 0 0 2 the set of those f g c 0 c 0 for which fg is not integrable where c 0 is the space of continuous mappings which vanish at infinity 3 the set of those f g l p g l q g for which the convolution f g is not well defined or is equal to provided g is a locally compact but non compact topological group and p q 1 with 1 p 1 q 1 the paper can be considered as a continuation of our previous ones in which we studied these sets from the baire category and porosity points of view

universality of sequences of operators related to taylor series abstract in this note the universality of a sequence of operators associated to the partial sums of the taylor series of a holomorphic function is investigated the emphasis is put on the fact that the taylor series are evaluated at a prescribed point and the variable is the center of the expansion the dynamics of the sequence of operators linked to the partial sums of a power series that is not generated by an entire function is also studied

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

peano curves on topological vector spaces the starting point of this paper is the existence of peano curves that is continuous surjections mapping the unit interval onto the unit square from this fact one can easily construct of a continuous surjection from the real line r to any euclidean space rn the algebraic structure of the set of these functions as well as extensions to spaces with higher dimensions is analyzed from the modern point of view of lineability and large algebras are found within the families studied we also investigate topological vector spaces that are continuous image of the real line providing an optimal lineability result

semi blind data detection for unitary space time modulation in mimo communications systems we propose an iterative algorithm based on expectation maximization em to jointly estimate the system parameters and decode the data in a mimo system using unitary space time block codes it is assumed that the receiver is unaware of the channel coefficients and their distribution the average energy of the received signal the prior probability of each signal in the constellation and the noise power the algorithm works for arbitrary modulation schemes and any channel model including rayleigh and rician fading the complexity of the proposed receiver is computed and it is shown to be significantly lower than previously published methods as it does not require any matrix inversion or trellis search the performance of the proposed receiver is evaluated by simulations in terms of symbol error rate ser vs signal to noise ratio snr and it is shown that with only a few iterations of the algorithm it achieves a performance close to that of the receiver which knows all the parameters

on lineability and additivity of real functions with finite preimages abstract we study lineability of real functions with finite preimages in particular we prove that the class of n to one functions contains a vector subspace of dimension n but not of dimension n 1 additionally we give examples of star like families of functions closed under multiplication by a non zero scalar for which lineability is less than additivity

iterative maximum likelihood sequence estimation for space time coded systems in previous work on decoding space time codes it is either assumed that perfect channel state information csi is present or a channel estimate is obtained using pilot symbols and then used as if it were perfect to extract symbol estimates in the latter case a loss in performance is incurred since the resulting overall receiver is not optimal we look at maximum likelihood ml sequence estimation for space time coded systems without assuming csi the log likelihood function is presented for both quasi static and nonstatic fading channels and an expectation maximization em based algorithm is introduced for producing ml data estimates whose complexity is much smaller than a direct evaluation of the log likelihood function simulation results indicate the em based algorithm achieves a performance close to that of a receiver which knows the channel perfectly

nonlinear subsets of function spaces and spaceability abstract in this paper we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on 0 1 every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular we consider lorentz marcinkiewicz and orlicz spaces the answer is affirmative for marcinkiewicz spaces and negative for lorentz and orlicz spaces also the same problem is studied for nakano spaces assuming different hypothesis

variational multiscale modeling with discretely divergence free subscales abstract we introduce a residual based stabilized formulation for incompressible navier stokes flow that maintains discrete and for divergence conforming methods strong mass conservation for inf sup stable spaces with h 1 conforming pressure approximation while providing optimal convergence in the diffusive regime robustness in the advective regime and energetic stability the method is formally derived using the variational multiscale vms concept but with a discrete fine scale pressure field which is solved for alongside the coarse scale unknowns such that the coarse and fine scale velocities separately satisfy discrete mass conservation we show energetic stability for the full navier stokes problem and we prove convergence and robustness for a linearized model oseen flow under the assumption of a divergence conforming discretization numerical results indicate that all properties extend to the fully nonlinear case and that the proposed formulation can serve to model unresolved turbulence

blind and semi blind equalization of cpm signals with the emv algorithm we apply the expectation maximization viterbi algorithm emva introduced in a previous paper to the blind or semi blind maximum likelihood equalization of continuous phase modulated cpm signals transmitted over a noisy linear finite impulse response fir channel the emva is a computationally efficient technique for simultaneously performing system identification and signal detection whenever the transmission system admits a hidden markov model hmm description the convergence properties of the emva are examined and a method for monitoring the emva convergence rate online is presented it is shown that the order of the fir channel can be estimated by applying the order incrementing oi and fixed order fo methods proposed previously a cramer rao bound is derived for the channel impulse response and it is shown via simulations that the emva approaches this bound as the snr increases finally an emva based technique is described for estimating the error covariance matrix for the system parameters for the case of long observation blocks

large linear manifolds of noncontinuable boundary regular holomorphic functions we prove in this paper that if g is a domain in the complex plane satisfying appropriate topological or geometrical conditions then there exists a large dense or closed infinite dimensional linear submanifold of boundary regular holomorphic functions on g all of whose nonzero members are not continuable across any boundary point of g

renormings concerning the lineability of the norm attaining functionals we prove that if a banach space admits a biorthogonal system whose dual part is norming then the set of norm attaining functionals is lineable as a consequence if a banach space admits a biorthogonal system whose dual part is bounded and its weak star closed absolutely convex hull is a generator system then the banach space can be equivalently renormed so that the set of norm attaining functionals is lineable finally we prove that every infinite dimensional separable banach space whose dual unit ball is weak star separable has a linearly independent countable weak star dense subset in its dual unit ball as a consequence we show the existence of linearly independent norming sets which are not the dual part of a biorthogonal system

large eddy simulation of turbulent taylor couette flow using isogeometric analysis and the residual based variational multiscale method we present an application of the residual based variational multiscale turbulence modeling rbvms methodology to the computation of turbulent taylor couette flow at high reynolds number we show that the rbvms formulation globally conserves angular momentum a feature that is felt to be important for flows dominated by rotation and that is not shared by standard stabilized formulations of fluid flow weak imposition of dirichlet boundary conditions is employed to enhance the accuracy of the rbvms framework in the presence of thin turbulent boundary layers near solid walls calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions nurbs based isogeometric analysis is employed for the spatial discretization and mesh refinement is performed to assess the convergence characteristics of the proposed methodology numerical tests show that very accurate results are obtained on relatively coarse grids to the best of the authors knowledge this paper is the first to report large eddy simulation computations of this challenging test case

an undecidable case of lineability in rr abstract recently it has been proved that assuming that there is an almost disjoint family of cardinality 2 c in c which is assured for instance by either martin s axiom or the continuum hypothesis or even 2 c c one has that the set of sierpinski zygmund functions is 2 c strongly algebrable and thus 2 c lineable here we prove that these two statements are actually equivalent and moreover that they both are undecidable this would be the first time in which one encounters an undecidable proposition in the recently coined theory of lineability and spaceability

divergence conforming discretization for stokes problem on locally refined meshes using lr b splines abstract to solve the incompressible flow problems using isogeometric analysis the div compatible spline spaces were originally introduced by buffa et al 2011 and later developed by evans 2011 in this paper we extend the div compatible spline spaces with local refinement capability using locally refined lr b splines over rectangular domains we argue that the spline spaces generated on locally refined meshes will satisfy compatibility provided they span the entire function spaces as governed by mourrain 2014 dimension formula we will in this work use the structured refined lr b splines as introduced by johannessen et al 2014 further we consider these div compatible lr b spline spaces to approximate the velocity and pressure fields in mixed discretization for stokes problem and a set of standard benchmark tests are performed to show the stability efficiency and the conservation properties of the discrete velocity fields in adaptive isogeometric analysis

spaceability of strict order integrability abstract in this paper sharp conditions on a measure space are provided in order that the subset of functions in the corresponding lebesgue space l p which are in no other l q contains except for zero an infinite dimensional closed subspace this completes earlier work of several authors the main result is derived from a new general criterion for spaceability on function spaces a further application to spaceability of the class of non absolutely continuous functions is supplied

porous sets and lineability of continuous functions on locally compact groups abstract let g be a non compact locally compact group in this paper we study the size of the set f g a b f g is well defined on g where a and b are normed spaces of continuous functions on g we also consider the problem of the spaceability of the set c 0 g c 0 g c 0 g c 00 g and among other results we show that for g r n the above set is strongly c algebrable and therefore algebrable and lineable with respect to the convolution product

lineability in subsets of measure and function spaces we show among other results that if lambda denotes the lebesgue measure on the borel sets in 0 1 and x is an infinite dimensional banach space then the set of measures whose range is neither closed nor convex is lineable in ca lambda x we also show that in certain situations we have lineability of the set of x valued and non sigma finite measures with relatively compact range the lineability of sets of the type l p i l q i is studied and some open questions are proposed some classical techniques together with the converse of the lyapunov convexity theorem are used

large structures in certain subsets of orlicz spaces abstract assume that and n n 1 are young functions in this paper we prove that under sharp conditions on a measure space and the young functions and n s the subset of functions in the corresponding orlicz space l which are not in l n for all n n admits various large linear structures

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

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

non body fitted fluid structure interaction divergence conforming b splines fully implicit dynamics and variational formulation abstract immersed boundary ib methods deal with incompressible visco elastic solids interacting with incompressible viscous fluids a long standing issue of ib methods is the challenge of accurately imposing the incompressibility constraint at the discrete level we present the divergence conforming immersed boundary dcib method to tackle this issue the dcib method leads to completely negligible incompressibility errors at the eulerian level and various orders of magnitude of increased accuracy at the lagrangian level compared to other ib methods furthermore second order convergence of the incompressibility error at the lagrangian level is obtained as the discretization is refined in the dcib method the eulerian velocity pressure pair is discretized using divergence conforming b splines leading to inf sup stable and pointwise divergence free eulerian solutions the lagrangian displacement is discretized using non uniform rational b splines which enables to robustly handle large mesh distortions the data transfer needed between the eulerian and lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes this conduces to a fully variational formulation sharp treatment of the fluid solid interface and a 0 5 increase in the convergence rate of the eulerian velocity and the lagrangian displacement measured in l 2 norm in comparison with using discretized dirac delta functions for the data transfer by combining the generalized method and a block iterative solution strategy the dcib method results in a fully implicit discretization which enables to take larger time steps various two and three dimensional problems are solved to show all the aforementioned properties of the dcib method along with mesh independence studies verification of the numerical method by comparison with the literature and measurement of convergence rates

almost overcomplete and almost overtotal sequences in banach spaces abstract we introduce the new concepts of almost overcomplete sequence in a banach space and almost overtotal sequence in a dual space we prove that any of such sequences is relatively norm compact and we present several applications of this fact

bounded linear non absolutely summing operators abstract we show that in certain situations we have lineability in the set of bounded linear and non absolutely summing operators examples on lineability of the set p e f i p e f are also presented and some open questions are proposed

holomorphic functions on non runge domains and related problems let u be a domain in cn that is not a runge domain we study the topological and algebraic properties of the family of holomorphic functions on u which cannot be approximated by polynomials

blind adaptive mimo receivers for space time block coded ds cdma systems in multipath channels using the constant modulus criterion we propose blind adaptive multi input multi output mimo linear receivers for ds cdma systems using multiple transmit antennas and space time block codes stbc in multipath channels a space time code constrained constant modulus ccm design criterion based on constrained optimization techniques is considered and recursive least squares rls adaptive algorithms are developed for estimating the parameters of the linear receivers a blind space time channel estimation method for mimo ds cdma systems with stbc based on a subspace approach is also proposed along with an efficient rls algorithm simulations for a downlink scenario assess the proposed algorithms in several situations against existing methods

isogeometric divergence conforming b splines for the unsteady navier stokes equations divergence conforming b splines are developed for application to the incompressible navier stokes equations on geometrically mapped domains these enable smooth pointwise divergence free solutions and thus satisfy mass conservation in the strongest possible sense semi discrete methods based on divergence conforming b splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity enstrophy and helicity these are geometric structure preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate the methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior

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