On operator valued sequences of multipliers and R-boundedness

In recent papers (cf. [J.L. Arregui, O. Blasco, (p,q)-Summing sequences, J. Math. Anal. Appl. 274 (2002) 812-827; J.L. Arregui, O. Blasco, (p,q)-Summing sequences of operators, Quaest. Math. 26 (2003) 441-452; S. Aywa, J.H. Fourie, On summing multipliers and applications, J. Math. Anal. Appl. 253 (2001) 166-186; J.H. Fourie, I. Röntgen, Banach space sequences and projective tensor products, J. Math. Anal. Appl. 277 (2) (2003) 629-644]) the concept of (p,q)-summing multiplier was considered in both general and special context. It has been shown that some geometric properties of Banach spaces and some classical theorems can be described using spaces of (p,q)-summing multipliers. The present paper is a continuation of this study, whereby multiplier spaces for some classical Banach spaces are considered. The scope of this research is also broadened, by studying other classes of summing multipliers. Let E(X) and F(Y) be two Banach spaces whose elements are sequences of vectors in X and Y, respectively, and which contain the spaces c₀₀(X) and c₀₀(Y) of all X-valued and Y-valued sequences which are eventually zero, respectively. Generally spoken, a sequence of bounded linear operators (un)⊂L(X,Y) is called a multiplier sequence from E(X) to F(Y) if the linear operator from c₀₀(X) into c₀₀(Y) which maps (xi)∈c₀₀(X) onto (unxn)∈c₀₀(Y) is bounded with respect to the norms on E(X) and F(Y), respectively. Several cases where E(X) and F(Y) are different (classical) spaces of sequences, including, for instance, the spaces Rad(X) of almost unconditionally summable sequences in X, are considered. Several examples, properties and relations among spaces of summing multipliers are discussed. Important concepts like R-bounded, semi-R-bounded and weak-R-bounded from recent papers are also considered in this context.     

Some Problems on Homomorphisms and Real Function Algebras

 In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra. (Received 4 December 2000; in revised form 2 April 2001)     

Electrochemical approach for discriminating and measuring predominant flavonoids and phenolic acids using differential pulse voltammetry: towards an electrochemical index of natural antioxidants

This paper deals with possibilities of employing differential pulse voltammetry (DPV) at a glassy carbon electrode in the analytical characterization of natural phenolic antioxidants in samples containing phenolic classes such as cinnamic acids, flavan-3-ols, and flavonols. A selective electrochemical oxidation of predominant flavonoids at pH 7.5 and an electrochemical oxidation of the total phenolic acids and flavonoids at pH 2.0 was carried out. Our electrochemical approach, based on DPV, has proved to be an easy, fast, and reliable method for discriminating flavonoids and phenolic acids. It has also helped establish the relationship between their voltammetric behavior and their in vitro “antioxidant power”. The analytical possibilities of the proposed method have been explored using both, representative standards and real samples where the predominant flavonoid and phenolic acid classes are present in different concentrations. The new approach has also proved satisfactory for the study of apple and pear juices as well as fresh apples and pears in different matrices such as peels and pulps. In general terms, “high antioxidant power” was always related to predominant phenolic classes (acids and flavan-3-ols) while the “low antioxidant power” was a result of a contribution of predominant phenolics (flavan-3-ols) and fingerprint phenolics: phlorizdin and arbutin. Likewise, the proposed electrochemical strategy showed a satisfactory analytical performance. A reproducibility of oxidation potential (less 5%) as well as in the height of peaks and calibration slopes (with R.S.D.s ranging between 0.3 and 8.3%) were also obtained. Concomitantly, the newly proposed voltammetric method showed recoveries between 83.5 and 108.6%.     

Direct Electrochemical Sensing and Detection of Natural Antioxidants and Antioxidant Capacity in Vitro Systems

This review highlights the role of electrochemical approaches in the sensing of antioxidants and their antioxidant capacity with especial attention to the analytical possibilities of electrochemistry in the direct evaluation of antioxidant capacity exhibited by food and biological samples due to the termed dietary, natural or biological antioxidants (mainly polyphenols, and vitamins C and E). The analytical potency of the electrochemistry is comprehensively stated and the selected results found in the literature are summarized and discussed critically. The main electrochemical approaches used have been cyclic voltammetry (CV) and flow injection analysis with amperometric detection (FIA‐ED). In addition, miniaturization is going to break new frontiers in the evaluation of antioxidant activity.     

Filter paper saturated by urine sample in metabolic disorders detection by proton magnetic resonance spectroscopy

NMR spectroscopy of urine samples is able to diagnose many inborn errors of metabolism (IEM). However, urinary metabolites have a poor stability, requiring special care for routine analysis (storage of urine at −20 or −80 °C, fast transport). The aim of our study was to investigate the reliability of dried urine filter paper for urine storage and transport and to evaluate the ability of NMR to detect several IEM using this method. Urine samples from five healthy subjects were analyzed by ¹H NMR following different storage conditions (−20 vs 4 °C vs dried on filter paper) and at different time points (24 h, 48 h, 96 h, and 7 days). Urine pattern of fresh urine was considered as a reference. We analyzed the conservation of some amino acids and organic acids using Bland and Altman plot with intraclass correlation coefficient determination. Then, we evaluated the use of filter paper to detect four different IEM (methylmalonic and isovaleric acidurias, ornithine transcarbamylase deficiency, and cystinuria). Analysis of urine samples from healthy subjects revealed a high stability of studied molecules (ICC > 0.8) even after 7 days of storage on filter paper. Moreover, an excellent preservation of metabolites specifically accumulated in IEM was observed when analysis of dried urine filter paper was compared to fresh urine (coefficient of variation < 15%). This preliminary study demonstrates that storage of dried urine on filter paper is reliable for ¹H NMR spectroscopy analysis. Preservation of urine molecules over time using that method is convenient for routine clinical practice.      

Integrable Hénon-Heiles Hamiltonians: A Poisson algebra approach

The three integrable two-dimensional Hénon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are constructed by making use of sl(2,R)⊕h₃ as their underlying Poisson symmetry algebra. In general, the procedure here introduced can be applied in order to obtain N-dimensional integrable generalizations of any 2D integrable potential of the form , and the formalism gives the explicit form of all the integrals of the motion. Further applications of this algebraic approach in different contexts are suggested.