Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Role of Polyelectrolyte for Layer-by-Layer Compact TiO(2) Films in Efficiency Enhanced Dye-Sensitized Solar Cells

Efficient compact TiO(2) films using different polyeleetrolytes are prepared by the layer-by-layer technique (LbL) and applied as an effective contact and blocking film in dye-sensitized solar cells (DSCs). The polyanion thermal stability plays a major role on the compact layers, which decreases back electron transfer processes and current losses at the FTO/TiO(2) interface. FESEM images show that polyelectrolytes such is sodium sullonated polystyrene (PSS) and sulfonated lignin (SE), in comparison to poly(acrylic acid) (FAA), ensure an adequate morphology for the LbL TiO(2) layer deposited before the mesoporous film, even triter the sintering step at 450 degrees C. The so treated photoanode in DSCs leads to a 30% improvement On the overall conversion efficiency. Electrochemical impedance spectroscopy (EIS) is employed to ascertain the role of die compact films with such polyelectrolytes. The significant increase in V(oc) of the solar cells with adequate polyelectrolytes in the LbL TiO(2) films shows their pivotal role in decreasing the electron recombination at the FTO surface and enhancing the electrical contact of FTO with the mesoporous TiO(2) layer.

A compact and high-resolution version of a capacitively coupled contactless conductivity detector

An all-in-one version of a capacitively coupled contactless conductivity detector is introduced. The absence of moving parts (potentiometers and connectors) makes it compact (6.5 cm(3)) and robust. A local oscillator, working at 1.1 MHz, was optimized to use capillaries of id from 20 to 100 lam. Low noise circuitry and a high-resolution analog-to-digital converter (ADC) (21 bits effective) grant good sensitivities for capillaries and background electrolytes currently used in capillary electrophoresis. The fixed frequency and amplitude of the signal generator is a drawback that is compensated by the steady calibration curves for conductivity. Another advantage is the possibility of determining the inner diameter of a capillary by reading the ADC when air and subsequently water flow through the capillary. The difference of ADC reading may be converted into the inner diameter by a calibration curve. This feature is granted by the 21-bit ADC, which eliminates the necessity of baseline compensation by hardware. In a typical application, the limits of detection based on the 3 sigma criterion (without baseline filtering) were 0.6, 0.4, 0.3, 0.5, 0.6, and 0.8 mu mol/L for K(+), Ba(2+), Ca(2+), Na(+), Mg(2+), and Li(+), respectively, which is comparable to other high-quality implementations of a capacitively coupled contactless conductivity detector.