On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis

We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L ₁[0,1] ^d (d≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f∈L ₁[0,1] ^d .     

An Asymptotic Property of Schachermayer's Space under Renorming

Let X be a Banach space with closed unit ball B. Given k , X is said to be k-β, respectively, (k + 1)-nearly uniformly convex ((k + 1)-NUC), if for every ε > 0 there exists δ, 0 < δ < 1, so that for every x B and every ε-separated sequence (x_n) B there are indices (n_i)^k_{i = 1}, respectively, (n_i)^{k + 1}_{i = 1}, such that (1/(k + 1))||x + ∑^k_{i = 1} x_ni|| ≤ 1 − δ, respectively, (1/(k + 1))||∑^{k + 1}_{i = 1} x_ni|| ≤ 1 − δ. It is shown that a Banach space constructed by Schachermayer is 2-β, but is not isomorphic to any 2-NUC Banach space. Modifying this example, we also show that there is a 2-NUC Banach space which cannot be equivalently renormed to be 1-β.     

Flow-induced crystallization regimes and rheology of isotactic polypropylene

We investigated the effect of flow in combination with molecular architecture on crystallization for linear and branched polypropylenes by means of dynamical mechanical spectroscopy. Compared to the linear polymer, the branched one exhibits much slower relaxation after deformation, causing higher levels of molecular orientation and molecular stretch for the same flow conditions. Different regimes of flow-induced crystallization are observed as a function of an increased level of molecular orientation and stretch. These regime changes cause the structure development in the material to vary from 3-dimensional spherulitical growth to nearly 1-dimensional fiber-like growth. Intermediate behavior is observed when the flow is strong (for the linear polymer) or weak enough (for the branched polymer), or in time when the effect of flow is exhausting. It is important to note that dynamical mechanical measurements can be used to probe different aspects of the (flow induced) crystallization process, such as a relative level of crystallinity and timescales of the evolution, but do not give absolute values. A correlation is found with the level of crystallinity obtained from real-time WAXS measurements and the kinetics of linear viscoelastic properties, but this correlation is not unique and depends on the pre-shear conditions applied.     

Influence of reaction parameters on the structure of in situ rubber/silica compounds synthesized via sol–gel reaction

In situ silica was synthesized in three non‐vulcanized rubber matrices, namely natural rubber, styrene‐butadiene rubber, and EPDM (ethylene‐propylene diene ter‐polymer), using the sol–gel method with tetra‐ethoxysilane (TEOS) as silica precursor and hexylamine as catalyst. The effect of the reaction parameters such as the amount of TEOS, the reaction time (15–120 min), and the type of rubber was explored. Transmission electron microscopy was used to study the gradient in silica content and particle size over the sample thickness. The diffusion gradient of TEOS and catalyst solution in the rubber matrix responsible for the gradient was studied with Fick's law. An excellent dispersion of silica was obtained for all rubbers, even for the very non‐polar EPDM, without the use of any additives to improve the dispersion. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 967–978     

A separable space with no Schauder decomposition

We combine some known results to remark that there exists a separable Banach space which fails to have a Schauder decomposition. It can be chosen as a subspace of Gowers-Maurey space without any unconditional basic sequence.

     

Convergence of Some Greedy Algorithms in Banach Spaces

We consider some theoretical greedy algorithms for approximation in Banach spaces with respect to a general dictionary. We prove convergence of the algorithms for Banach spaces which satisfy certain smoothness assumptions. We compare the algorithms and their rates of convergence when the Banach space is L_p(\mathbbT^d)L_p(\mathbb{T}^d) ($1相似文献   

Property (β) implies normal structure of the dual space

We prove that property (β) of Rolewicz implies normal structure of the dual space and we characterize spaces which are duals of spaces with property (β). Research of the second author was supported in part by the M.U.R.S.T. of Italy.     

Weak Convergence of Greedy Algorithms in Banach Spaces

We study the convergence of certain greedy algorithms in Banach spaces. We introduce the WN property for Banach spaces and prove that the algorithms converge in the weak topology for general dictionaries in uniformly smooth Banach spaces with the WN property. We show that reflexive spaces with the uniform Opial property have the WN property. We show that our results do not extend to algorithms which employ a ‘dictionary dual’ greedy step.