ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

E-contracting with price configuration for Web services and QoS

The large amount of information in electronic contracts hampers their establishment due to high complexity. An approach inspired in Software Product Line (PL) and based on feature modelling was proposed to make this process more systematic through information reuse and structuring. By assessing the feature-based approach in relation to a proposed set of requirements, it was showed that the approach does not allow the price of services and of Quality of Services (QoS) attributes to be considered in the negotiation and included in the electronic contract. Thus, this paper also presents an extension of such approach in which prices and price types associated to Web services and QoS levels are applied. An extended toolkit prototype is also presented as well as an experiment example of the proposed approach.

A novel aerobic-anoxic biological filter for nitrogen removal from UASB effluent using biogas compounds as electron donors for denitrification

The performance of a new trickling filter (TF) configuration composed of an upper compartment for nitrification and a lower compartment for denitrification of effluent from a UASB reactor treating domestic sewage was evaluated. The TF was packed with new plastic material characterized by its durability and high percentage of void spaces. The feasibility of using the reduced compounds present in the biogas produced by a UASB reactor as electron donor for denitrification was also evaluated. Efficient nitrification and denitrification was achieved for the mean hydraulic (5.6 m(3) m(-2) d(-1)) organic (0.26 kg COD m(-3) d(-1)) and ammonia-N (0.08 kg m(-3) d(-1)) loading rates applied, resulting in ammonia-N removal ranging from 60 to 74%. The final effluent presented ammonia-N lower than 13 mg L(-1). Despite the presence of dissolved oxygen (DO) in the denitrification compartment, its performance was considered quite satisfactory and final nitrate concentrations were lower than 10 mg L(-1). The results indicate that methane was the main electron donor used for denitrification. Additionally, denitrification can probably be improved by avoiding high DO concentration in the denitrification compartment and by enhancing biogas transfer in the anoxic zone.

Characterization of micro-bubble size distribution and flow configuration in DAF contact zone by a non-intrusive image analysis system and tracer tests

This paper aims to investigate the influence of some dissolved air flotation (DAF) process variables (specifically: the hydraulic detention time in the contact zone and the supplied dissolved air concentration) and the pH values, as pretreatment chemical variables, on the micro-bubble size distribution (BSD) in a DAF contact zone. This work was carried out in a pilot plant where bubbles were measured by an appropriate non-intrusive image acquisition system. The results show that the obtained diameter ranges were in agreement with values reported in the literature (10-100mm), quite independently of the investigated conditions. The linear average diameter varied from 20 to 30mm, or equivalently, the Sauter (d(3,2)) diameter varied from 40 to 50mm. In all investigated conditions, D(50) was between 75% and 95%. The BSD might present different profile (with a bimodal curve trend), however, when analyzing the volumetric frequency distribution (in some cases with the appearance of peaks in diameters ranging from 90-100mm). Regarding volumetric frequency analysis, all the investigated parameters can modify the BSD in DAF contact zone after the release point, thus potentially causing changes in DAF kinetics. This finding prompts further research in order to verify the effect of these BSD changes on solid particle removal efficiency by DAF.

Vortex configuration flow cell based on low temperature cofired ceramics as a compact chemiluminescence microsystern

The integration of optical detection methods in continuous flow microsystems can highly extend their range of application, as long as some negative effects derived from their scaling down can be minimized. Downsizing affects to a greater extent the sensitivity of systems based on absorbance measurements than the sensitivity of those based on emission ones. However, a careful design of the instrumental setup is needed to maintain the analytical features in both cases. In this work, we present the construction and evaluation of a simple miniaturized optical system, which integrates a novel flow cell configuration to carry out chemiluminescence (CL) measurements using a simple photodiode. It consists of a micro-mixer based on a vortex structure, which has been constructed by means of the low-temperature cofired ceramics (LTCC) technology. This mixer not only efficiently promotes the CL reaction due to the generated high turbulence but also allows the detection to be carried out in the same area, avoiding intensity signal losses. As a demonstration, a flow injection system has been designed and optimized for the detection of cobalt(H) in water samples. It shows a linear response between 2 and 20 mu M with a correlation of r > 0.993, a limit of detection of 1.1 mu M, a repeatability of RSD = 12.4 %, and an analysis time of 17 s. These results demonstrate the suitability of the proposal to the determination of compounds involved in CL reactions by means of an easily constructed versatile device based on low-cost instrumentation.

Long-Chain Acyl-Homoserine Lactones from Methylobacterium mesophilicum: Synthesis and Absolute Configuration

The acyl-homoserine lactones (acyl-HSLs) produced by Methylobacterium mesophilicum isolated from orange trees infected with the citrus variegated chlorosis (CVC) disease have been studied, revealing the occurrence of six long-chain acyl-HSLs, i.e., the saturated homologues (S)-N-dodecanoyl (1) and (S)-N-tetradecanoyl-HSL (5), the uncommon odd-chain N-tridecanoyl-HSL (3), the new natural product (S)-N-(2E)-dodecenoyl-HSL (2), and the rare unsaturated homologues (S)-N-(7Z)-tetradecenoyl (4) and (S)-N-(2E,7Z)-tetradecadienyl-HSL (6). The absolute configurations of all HSLs were determined as 3S. Compounds 2 and 6 were synthesized for the first time. Antimicrobial assays with synthetic acyl-HSLs against Gram-positive bacterial endophytes co-isolated with M. mesophilicum from CVC-infected trees revealed low or no antibacterial activity.

Assignment of the absolute configuration at the sulfur atom of thioridazine metabolites by the analysis of their chiroptical properties: The case of thioridazine 2-sulfoxide

Thioridazine (THD) is a commonly prescribed phenotiazine neuroleptic drug, which is extensively biotransformed in the organism producing as main metabolites sulfoxides and a sulfone by sulfur oxidation Significant differences have been observed in the activity of the THD enantiomers as well as for its main metabolites, and enantioselectivity phenomena have been proved in the metabolic pathway. Here the assignment of the absolute configuration at the sulfur atom of enantiomeric THD-2-sulfoxide (THD-2-SO) has been carried out by circular dichroism (CD) spectroscopy The stereoisomers were separated by HPLC on Chiralpak AS column, recording the CD spectra for the two collected enantiomeric fractions The theoretical electronic CD spectrum has been obtained by the TDDFT/B3LYP/6-31G*. as Boltzmann averaging of the contributions calculated for the most stable conformations of the drug The comparison of the simulated and experimental spectra allowed the absolute configuration at the sulfur atom of the four THD-2-SO stereoisomers to be assigned The developed method should be useful for a reliable correlation between stereochemistry and activity and/or toxicity

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

On S-asymptotically omega-periodic functions on Banach spaces and applications

This paper is devoted to the study of the class of continuous and bounded functions f : [0, infinity] -> X for which exists omega > 0 such that lim(t ->infinity) (f (t + omega) - f (t)) = 0 (in the sequel called S-asymptotically omega-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically omega-periodic functions. We also study the existence of S-asymptotically omega-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Configuration of stilbene derivatives by (1)H NMR and theoretical calculation of chemical shifts

The direct E/Z configuration assignment of tri- and tetra-substituted stilbenes (and other analogous olefins) when only one of the isomers is available is a quite challenging task. Sometimes, a chemical transformation or some other tedious method is necessary for determination of the double bond substitution pattern. In this paper, we relied on theoretical calculation of chemical shifts as a complementary tool for (1)H NMR determination of the configuration of an alpha-phenylcinnamic acid prepared as a unique isomer by the Perkin reaction. (C) 2010 Elsevier B.V. All rights reserved.