Stable rank of corner rings

B. Blackadar recently proved that any full corner in a unital C*-algebra has K-theoretic stable rank greater than or equal to the stable rank of . (Here is a projection in , and fullness means that .) This result is extended to arbitrary (unital) rings in the present paper: If is a full idempotent in , then . The proofs rely partly on algebraic analogs of Blackadar's methods and partly on a new technique for reducing problems of higher stable rank to a concept of stable rank one for skew (rectangular) corners . The main result yields estimates relating stable ranks of Morita equivalent rings. In particular, if where is a finitely generated projective generator, and can be generated by elements, then .

     

Construction and evaluation of PVC and sol–gel sensor membranes based on Mn(III)TPP-Cl. Application to valproate determination in pharmaceutical preparations

The construction and general performance of new valproate-selective electrodes based on manganese(III) tetraphenylporphyrin [Mn(III)TPP-Cl], as an ionophore, are presented. The ionophore was incorporated into PVC and ceramic membranes (sol–gel) based on methyltriethoxysilane. The influence of membrane composition and pH and the effect of lipophilic cationic and anionic additives in PVC membranes were investigated concerning their influence on the slope, response time, selectivity and lifetime of the electrodes. The PVC membrane without additive and the sol–gel membrane presented slopes and practical limits of detection of −60.8 mV dec⁻¹ and 5x10⁻⁶ mol l⁻¹ and −60.3 mV dec⁻¹ and 1×10⁻⁴ mol l⁻¹, respectively. The sol–gel membranes displayed higher selectivity for valproate when compared with PVC membranes. These two types of electrodes were coupled to a sequential-injection analysis (SIA) system for the direct determination of valproate in pharmaceutical formulations. The association of Mn(III)TPP-Cl with the sol–gel support inserted in a SIA system provided potentiometric sensors with an analytical range of 1x10⁻³–5x10⁻² mol l⁻¹, with a sample rate of 55 samples per hour and a sample and carrier consumption of 140 and 2,500 μl per determination, respectively.     

Heterochromatin and rDNA 5S and 45S sites as reliable cytogenetic markers for castor bean (Ricinus communis,Euphorbiaceae)

The increasing need for renewable energy resources has led to higher demands for biofuel, a scenario where the castor bean (Ricinus communis L.) seed oil represents a promising source of raw material. Despite that, information regarding the genome organization of R. communis is still scarce, impairing the application of modern biotechnological and breeding procedures. The present work brings the first evaluation of the mitotic chromosomes of this species, including 10 potentially interesting accessions for cultivation in semi-arid environments aiming at the biofuel production. The approach included standard staining, fluorochrome staining (CMA/DAPI), fluorescent in situ hybridization (FISH) with rDNA 5S and 45S, as well as silver impregnation. All accessions were diploid with 2n = 2x = 20, displaying mainly metacentric chromosomes, with CMA-positive bands (GC-rich) in all pairs of the complement. After silver impregnation, one to 14 nucleoli were observed, while the FISH with rDNA 45S revealed two large sites and a variety of minor dots, and the DNAr 5S hybridized in a single pair. The observed features were discussed and compared with literature data regarding pachytene bivalents.     

Automorphisms of endomorphism semigroups of reflexive digraphs

A reflexive digraph is a pair (X, ρ), where X is an arbitrary set and ρ is a reflexive binary relation on X. Let End (X, ρ) be the semigroup of endomorphisms of (X, ρ). We determine the group of automorphisms of End (X, ρ) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ≥2 are pairwise disjoint, and some circulant digraphs (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

External electric field effects on fluorescence of pyrene butyric acid in a polymer film: concentration dependence and temperature dependence

Fluorescence spectra and electrofluorescence spectra (plots of the electric field-induced change in fluorescence intensity as a function of wavelength) have been measured at different temperatures for pyrene butyric acid (PBA) in a PMMA film at different concentrations. At a low concentration of 0.5 mol % where fluorescence emitted from the locally excited state of PBA (LE fluorescence) is dominant, LE fluorescence spectra show only the Stark shift in the presence of an electric field (F), which results from the difference in molecular polarizability between the ground and emitting states. At a high concentration of 10 mol % where the so-called sandwich-type excimer fluorescence (EX(1)) is dominant, both EX(1) and LE fluorescence are quenched by F. Another fluorescence assigned to a partially overlapped excimer (EX(2)) also exists at room temperature, and this emission is enhanced by F. As the temperature decreases, three fluorescence emissions whose electric field effects are different from each other become clear besides EX(1) and LE fluorescence, indicating that at least five fluorescence components exist at high concentrations at low temperatures. At a medium concentration of 5 mol % where EX(1) is comparable in intensity to the LE fluorescence, the intensity of EX(1) is not affected by F at any temperature, but LE fluorescence and EX(2) are markedly influenced by F at room temperature, and four fluorescence emissions are confirmed at low temperatures.     

Nonlinear pedagogy: a constraints-led framework for understanding emergence of game play and movement skills

Team sport competition can be characterized as a complex adaptive system in which concepts from nonlinear dynamics can provide a sound theoretical framework to understand emergent behavior such as movement coordination and decision making in game play. Nonlinear Pedagogy is presented as a methodology for games teaching, capturing how phenomena such as movement variability, self-organization, emergent decision making, and symmetry-breaking occur as a consequence of interactions between agent-agent and agent-environment constraints. Empirical data from studies of basketball free-throw shooting and dribbling are used as task vehicles to exemplify how nonlinear phenomena characterize game play in sport. In this paper we survey the implications of these data for Nonlinear Pedagogy, focusing particularly on the manipulation of constraints in team game settings. The data and theoretical modeling presented in this paper provide a rationale in nonlinear dynamics for the efficacy of a prominent model of game play teaching, Teaching Games for Understanding approach.