Stochastic matrices over cones

The notion of a stochastic operator in an ordered Banach space is specialized to a finite dimensional ordered real vector space. The classical limit theorems are obtained, and an application is made to non-homogeneous Markov chains. Finally, groups of nonnegative matrices are discussed.     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Hodge Theory and Geometry

Hodge theory for a smooth algebraic curve includes both theHodge structure (period matrix) on cohomology and the use ofthat Hodge structure to study the geometry of the curve, viathe Jacobian variety. Hodge extended the theory of the periodmatrix to smooth algebraic varieties of any dimension, definingin general a Hodge structure on the cohomology of the variety.He gave a few applications to the geometry of the variety, butthese did not attain the richness of the Jacobian variety. Inrecent years, Hodge theory has been successfully extended toarbitrary varieties, and to families of varieties. In this expositorypaper, some of these developments are reviewed, with specialemphasis on instances where these extensions can be used tostudy the geometry – especially the algebraic cycles –on the variety. 2000 Mathematics Subject Classification 14CDFJ.     

Properties of functions in an auxiliary spline space

Summary This note examines functions in an auxiliary spline space related to geometrically continuous splines. Previous work [3, 4] required results about the existence and number of zeros of certain functions in this space, as well as results on how to combine these functions. This note provides improved versions of these results.     

Controlled electrodeposition of Cu-Ga from a deep eutectic solvent for low cost fabrication of CuGaSe2 thin film solar cells

The electrochemical deposition of Ga and Cu-Ga alloys from the deep eutectic solvent choline chloride/urea (Reline) is investigated to prepare CuGaSe(2) (CGS) semiconductors for their use in thin film solar cells. Ga electrodeposition is difficult from aqueous solution due to its low standard potential and the interfering hydrogen evolution reaction (HER). Ionic liquid electrolytes offer a better thermal stability and larger potential window and thus eliminate the interference of solvent breakdown reactions during Ga deposition. We demonstrate that metallic Ga can be electrodeposited from Reline without HER interference with high plating efficiency on Mo and Cu electrodes. A new low cost synthetic route for the preparation of CuGaSe(2) absorber thin films is presented and involves the one-step electrodeposition of Cu-Ga precursors from Reline followed by thermal annealing. Rotating disk electrode (RDE) cyclic voltammetry (CV) is used in combination with viscosity measurements to determine the diffusion coefficients of gallium and copper ions in Reline. The composition of the codeposited Cu-Ga precursor layers can be controlled to form Cu/Ga thin films with precise stoichiometry, which is important for achieving good optoelectronic properties of the final CuGaSe(2) absorbers. The morphology, the chemical composition and the crystal structure of the deposited thin films are analysed by scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDX) and X-ray diffraction (XRD). Annealing of the Cu-Ga films in a selenium atmosphere allowed the formation of high quality CuGaSe(2) absorber layers. Completed CGS solar cells achieved a 4.1% total area power conversion efficiency.     

Synthesis and barrier properties of poly(ε-caprolactone)-layered silicate nanocomposites

A new polymer-ceramic nanocomposite has been synthesized consisting of well-dispersed, two-dimensional layers of an organically modified mica-type silicate (MTS) within a degradable poly(ε-caprolactone) matrix. A protonated amino acid derivative of MTS was used to promote delamination/dispersion of the host layers and initiate ring-opening polymerization of ε-caprolactone monomer, resulting in poly(ε-caprolactone) chains that are ionically bound to the silicate layers. The polymer chains can be released from the silicate surface by a reverse ion-exchange reaction and were shown to be spectroscopically similar to pure poly(ε-caprolactone). Thick films of the polymer nanocomposite exhibit a significant reduction in water vapor permeability that shows a linear dependence on silicate content. The permeability of nanocomposite containing as low as 4.8% silicate by volume was reduced by nearly an order of magnitude compared to pure poly(ε-caprolactone). © 1995 John Wiley & Sons, Inc.