Boundedness, Compactness and Schatten-class Membership of Weighted Composition Operators

The boundedness and compactness of weighted composition operators on the Hardy space H²{{\mathcal H}^2} of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces A²_a(\mathbbD){\mathcal{A}^2_\alpha(\mathbb{D})} are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.     

Integral polynomials on Banach spaces not containing ℓ<Subscript>1</Subscript>

We give new characterizations of Banach spaces not containing ℓ₁ in terms of integral and p-dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.     

The role of BMOA in the boundedness of weighted composition operators

Boundedness (resp. compactness) of weighted composition operators Wh,φ acting on the classical Hardy space H² as Wh,φf=h(f○φ) are characterized in terms of a Nevanlinna counting function associated to the symbols h and φ whenever h∈BMOA (resp. h∈VMOA). Analogous results are given for Hp spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space).     

High dimensional random sections of isotropic convex bodies

We study two properties of random high dimensional sections of convex bodies. In the first part of the paper we estimate the central section function for random F∈Gn,k and K⊂Rn a centrally symmetric isotropic convex body. This partially answers a question raised by V.D. Milman and A. Pajor (see [V.D. Milman, A. Pajor, Isotropic positions and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, in: Lecture Notes in Math., vol. 1376, Springer, 1989, p. 88]). In the second part we show that every symmetric convex body has random high dimensional sections F∈Gn,k with outer volume ratio bounded by

     

Effect of Encapsulated Beet Extracts (Beta vulgaris) Added to Yogurt on the Physicochemical Characteristics and Antioxidant Activity

Beet has been used as an ingredient for functional foods due to its high antioxidant activity, thanks to the betalains it contains. The effects of the addition of beet extract (liquid and lyophilized) on the physicochemical characteristics, color, antioxidant activity (AA), total betalains (TB), total polyphenols (TP), and total protein concentration (TPC) were evaluated on stirred yogurt. The treatments (T1-yogurt natural, T2-yogurt added with beet juice, T3-added extract of beet encapsulated with maltodextrin, and T4-yogurt added with extract of beet encapsulated with inulin) exhibited results with significant differences (p < 0.05). The highest TB content was observed in T2 (209.49 ± 14.91), followed by T3 (18.65 ± 1.01) and later T4 (12.96 ± 0.55). The highest AA was observed on T2 after 14 days (ABTS˙ 0.819 mM TE/100 g and DPPH˙ 0.343 mM TE/100 g), and the lowest was found on T1 at day 14 (ABTS˙ 0.526 mM TE/100 g and DPPH˙ 0.094 mM TE/100 g). A high content of TP was observed (7.13 to 9.79 mg GAE/g). The TPC varied between 11.38 to 12.56 µg/mL. The addition of beet extract significantly increased AA in yogurt, betalains being the main compounds responsible for that bioactivity.     

On the potential balance among compulsory education outcomes through econometric and multiobjective programming analysis

This paper sheds new light on the relationship between inputs and outputs in the framework of the educational production function. In particular, it is geared at gaining a better understanding of which factors may be affected in order to achieve an optimal educational output level. With this objective in mind, we analyze teacher-based assessments (actual marks) in three different subjects using a multiobjective schema. For much of the analysis we use data from a recent (2010) Survey – ESOC10, linked with the results from an educational assessment program conducted among 11 and 15 year-old students and with the administrative records on teacher-based scores. Following the statistical and econometric analysis of these data, they are used to build a multiobjective mixed integer model. A reference point approach is used to determine the profile of, potentially, the most “successful and balanced” students in terms of educational outcomes. This kind of methodology in multiobjective programming allows generating “very balanced” solutions in terms of the objective values (subjects). Finally, a sensitivity analysis is used to determine policies that can be carried out in order to improve the performance levels of primary and secondary education students. Particularly, policy makers should be more concerned with the need to promote some cultural habits – such as reading –, from both the students’ and parents’ side. Additionally, policy efforts should be focused on making the vocational pathways available to Spanish youth more appealing, with the aim of taking advantage of the particular skills of students not succeeding in the academic track.