The purpose of this paper was to study elastomer powder from crushed used tires (CUTs). In particular, the behavior of the green density of elastomeric powder was analyzed by varying compaction pressure. In the Anglo-saxon bibliography, this powder is known as ground tire rubber: ground tire rubber (GTR). The density of the tyre was made using a hydrostatic balance, the analysis of grain size using cribbing sieves, and the measures of compression parameters by means of a Universal Testing Machine. The main goal was to obtain a behavior model of ground tire rubber along different compaction pressures. This model was used to predict optimum compaction pressures in order to achieve the highest density. This was the first step to obtain recycled products when sintering processes are applied, evidently if thermal compression was used as a manufacturing process. This established model predicted the evolution of green density versus compaction pressures very accurately.
Let [Formula: see text] be a finite measure space and consider a Banach function space [Formula: see text]. Motivated by some previous papers and current applications, we provide a general framework for representing reproducing kernel Hilbert spaces as subsets of Köthe–Bochner (vector-valued) function spaces. We analyze operator-valued kernels [Formula: see text] that define integration maps [Formula: see text] between Köthe–Bochner spaces of Hilbert-valued functions [Formula: see text] We show a reduction procedure which allows to find a factorization of the corresponding kernel operator through weighted Bochner spaces [Formula: see text] and [Formula: see text] — where [Formula: see text] — under the assumption of [Formula: see text]-concavity of [Formula: see text] Equivalently, a new kernel obtained by multiplying [Formula: see text] by scalar functions can be given in such a way that the kernel operator is defined from [Formula: see text] to [Formula: see text] in a natural way. As an application, we prove a new version of Mercer Theorem for matrix-valued weighted kernels.
We study the properties of Gâteaux, Fréchet, uniformly Fréchet and uniformly Gâteaux smoothness of the space L p (m) of scalar p-integrable functions with respect to a positive vector measure m with values in a Banach lattice. Applications in the setting of the Bishop-Phelps-Bollobás property (both for operators and bilinear forms) are also given. 2010 Mathematics Subject Classification. 46B20,46E30, 46G10,49J50. Key words and phrases. L p of a vector measure, Banach function space, Gâteaux and Fréchet (uniformly) smooth norm, Bishop-Phelps-Bollobás property, Bishop-Phelps-Bollobás property for bilinear forms. Research supported by Ministerio de Economía y Competitividad and FEDER under projects MTM2012-36740-c02-02 (L. Agud and E.A. Sánchez-Pérez), MTM201453009-P (J.M. Calabuig) and MTM2012-34341 (S. Lajara).
Let ( Ω , Σ , μ ) be a finite measure space and consider a Banach function space Y ( μ ) . We say that a Banach space E is representable by Y ( μ ) if there is a continuous bijection I : Y ( μ ) → E . In this case, it is possible to define an order and, consequently, a lattice structure for E in such a way that we can identify it as a Banach function space, at least regarding some local properties. General and concrete applications are shown, including the study of the notion of the pth power of a Banach space, the characterization of spaces of operators that are isomorphic to Banach lattices of multiplication operators, and the representation of certain spaces of homogeneous polynomials on Banach spaces as operators acting in function spaces.
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