Multiplication operators in Köthe-Bochner spaces

Let X be a Banach space and E an order continuous Banach function space over a finite measure μ. We prove that an operator T in the Köthe-Bochner space E(X) is a multiplication operator (by a function in L^∞(μ)) if and only if the equality T(g〈f,x^∗〉x)=g〈T(f),x^∗〉x holds for every g∈L^∞(μ), f∈E(X), x∈X and x^∗∈X^∗.     

Weak continuity of Riemann integrable functions in Lebesgue-Bochner spaces

In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X＊ is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31（2）, 697-703 （2001）] that L^1[0, 1] has the weak Lebesgue property.     

Voltammetric Electronic Tongue Based on Carbon Paste Electrodes Modified with Biochar for Phenolic Compounds Stripping Detection

Biochar is a charcoal produced from the biomass pyrolysis process that presents a highly porous and functionalized surface. In the present work an array of carbon paste electrodes (CPE) made of different forms of carbon (graphite, carbon nanotubes and activated biochar) was evaluated in the development of an electronic tongue for discrimination and stripping voltammetric determination of catechol (CAT), 4‐ethylcatechol (4‐EC) and 4‐ethylguaiacol (4‐EG) phenolic compounds. Morphological characterization of carbon materials and electrodes surfaces was performed by scanning electron microscopy (SEM) and semi‐quantitative elemental composition by energy dispersive spectroscopy (EDS). Electrochemical Impedance Spectroscopy (EIS) measurements were used for electrochemical characterization of electrodes. Cyclic voltammetry measurements were performed for the phenolic compounds evaluated using different concentrations. Principal component analysis (PCA) was performed to evaluate the qualitative analysis. Quantitative data modeling was done using artificial neural networks (ANN). The proposed sensor array presented analytical potentiality allowing the distinction and determination of CAT, 4‐EC and 4‐EG by using chemometric processing. The method showed sensibility, reproducibility and a good linearity (R²>0.9940) for three compounds evaluated. Spontaneous preconcentration of three compounds was possible using all three sensors, which can allow the application of these as passive samplers for remote determinations of phenolic compounds in wine and food samples.     

On the Structure of L 1 of a Vector Measure via its Integration Operator

Geometric and summability properties of the integration operator associated to a vector measure m can be translated in terms of structure properties of the space L¹(m). In this paper we study the cases of the integration operator being: (i) p-concave on L^p(m), or (ii) positive p-summing on L¹(m) (where ). We prove that (i) is equivalent to saying that L¹(m) contains continuously the L^p space of a (non-negative scalar) control measure for m. On the other hand, we show that (ii) holds if and only if L¹(m) is order isomorphic to the L¹ space of a non-negative scalar measure. J.M. Calabuig was supported by MEC and FEDER (MTM2005-08350-C03-03) and Generalitat Valenciana (GV/2007/191). J. Rodríguez was supported by MEC and FEDER (MTM2005-08379) and Generalitat Valenciana (GVPRE/2008/312). E.A. Sánchez-Pérez was supported by MEC and FEDER (MTM2006-11690-C02-01).     

Molecular quantum similarity measures and N-dimensional representation of quantum objects. II. Practical applications

Newly developed classification and graphical representation techniques are discussed in order to visualize quantum similarity computational results. Some examples of molecular quantum similarity applications involving the fields of (a) structure–property relationships, (b) structure–activity relationships, (c) MO taxonomy, and (d) conformer taxonomy are presented.     

Radon-Nikodým derivatives for vector measures belonging to Köthe function spaces

Let m, n be a couple of vector measures with values on a Banach space. We develop a separation argument which provides a characterization of when the Radon-Nikodým derivative of n with respect to m—in the sense of the Bartle-Dunford-Schwartz integral—exists and belongs to a particular sublattice Z(μ) of the space of integrable functions L¹(m). We show that this theorem is in fact a particular feature of our separation argument, which can be applied to prove other results in both the vector measure and the function space settings.     

Strongly embedded subspaces of p-convex Banach function spaces

Let $X(\mu )$ be a p-convex ( $1\le p<\infty $ ) order continuous Banach function space over a positive finite measure  $\mu $ . We characterize the subspaces of  $X(\mu )$ which can be found simultaneously in  $X(\mu )$ and a suitable $L^1(\eta )$ space, where $\eta $ is a positive finite measure related to the representation of  $X(\mu )$ as an $L^p(m)$ space of a vector measure  $m$ . We provide in this way new tools to analyze the strict singularity of the inclusion of  $X(\mu )$ in such an $L^1$ space. No rearrangement invariant type restrictions on  $X(\mu )$ are required.     

Simultaneous Voltammetric Determination of Heavy Metals by Use of Crown Ether‐modified Electrodes and Chemometrics

A three‐sensor array consisting of a graphite‐epoxy composite electrode (GEC), 4‐carboxybenzo‐18‐crown‐6‐GEC and 4‐carboxybenzo‐15‐crown‐5‐GEC was employed for the simultaneous determination of Cd(II), Pb(II) and Hg(II) by differential pulse anodic stripping voltammetry (DPASV). Sensors were firstly studied for the determination of Hg(II); secondly, peak current responses confirmed that all sensors showed differentiated response for the three considered metals. A response model was developed to resolve mixtures of Cd(II), Pb(II) and Hg(II) at the µg L^?1 level; Discrete Wavelet Transform was selected as preprocessing tool and artificial neural network used for the modelling of the obtained responses.     

Generalized perfect spaces

Given two Banach function spaces X and Y related to a measure μ, the Y-dual space X^Y of X is defined as the space of the multipliers from X to Y. The space X^Y is a generalization of the classical Köthe dual space of X, which is obtained by taking Y = L^t(μ). Under minimal conditions, we can consider the Y-bidual space X^YY of X (i.e. the Y-dual of X^Y). As in the classical case, the containment X ⊂ X^YY always holds. We give conditions guaranteeing that X coincides with X^YY, in which case X is said to be Y-perfect. We also study when X is isometrically embedded in X^YY. Properties involving p-convexity, p-concavity and the order of X and Y, will have a special relevance.     

Configurable node density generation with application to hotspot modelling

Mobility models are very relevant mainly when studying the performance of wireless systems by means of computer simulations. The main problem arises when deciding the best mobility model for a particular application. In some cases, it is very important to emulate hotspots or, in general, zones with different user (or node) densities. Current models do not allow complete control over hotspots, or in other words, they do not allow any general node density to be defined in the simulation area. Usually, when hotspots are modelled, closed zones are created with different numbers of users in each area, thus ensuring a fixed node density in each area. However, this approach results in an unfair comparison among users since they cannot move across zones.This paper proposes a new mechanism to solve these drawbacks. Using this mechanism, any general node density can be emulated allowing nodes to move around the entire simulation area. Any mobility model can be applied together with this density control mechanism, provided that the mobility model ensures a uniform node distribution.