Maximum directed cuts in digraphs with degree restriction

For integers m, k≥1, we investigate the maximum size of a directed cut in directed graphs in which there are m edges and each vertex has either indegree at most k or outdegree at most k. © 2009 Wiley Periodicals, Inc. J Graph Theory     

Picard Groups of Rings of Coinvariants

Let k be a field, H a Hopf k-algebra with bijective antipode, A a right H-comodule algebra and C a Hopf algebra with bijective antipode which is also a right H-module coalgebra. Under some appropriate assumptions, and assuming that the set of grouplike elements G(A ⊗ C) of the coring A ⊗ C is a group, we show how to calculate, via an exact sequence, the Picard group of the subring of coinvariants in terms of the Picard group of A and various subgroups of G(A ⊗ C). Presented by: Claus Ringel.     

Spectral Green's Functions for Layered Gyrotropic Structures Through a Transmission-Line Approach

In this work, a straightforward method is shown to derive spectral Green's functions in classes of planar structures including gyrotropic media, based on a recently proposed transmission-line formalism. In particular, the analysis is expressly carried out for a current line source in layered configurations with transversely-magnetized ferrites, useful for microwave and millimeter-wave waveguiding and radiating devices.     

Convergence analysis of a family of Steffensen-type methods for generalized equations

A class of Steffensen-type algorithms for solving generalized equations on Banach spaces is proposed. Using well-known fixed point theorem for set-valued maps [A.L. Dontchev, W.W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994) 481-489] and some conditions on the first-order divided difference, we provide a local convergence analysis. We also study the perturbed problem and we present a new regula-falsi-type method for set-valued mapping. This study follows the works on the Secant-type method presented in [S. Hilout, A uniparametric Secant-type methods for nonsmooth generalized equations, Positivity (2007), submitted for publication; S. Hilout, A. Piétrus, A semilocal convergence of a Secant-type method for solving generalized equations, Positivity 10 (2006) 673-700] and extends the results related to the resolution of nonlinear equations [M.A. Hernández, M.J. Rubio, The Secant method and divided differences Hölder continuous, Appl. Math. Comput. 124 (2001) 139-149; M.A. Hernández, M.J. Rubio, Semilocal convergence of the Secant method under mild convergence conditions of differentiability, Comput. Math. Appl. 44 (2002) 277-285; M.A. Hernández, M.J. Rubio, ω-Conditioned divided differences to solve nonlinear equations, in: Monogr. Semin. Mat. García Galdeano, vol. 27, 2003, pp. 323-330; M.A. Hernández, M.J. Rubio, A modification of Newton's method for nondifferentiable equations, J. Comput. Appl. Math. 164/165 (2004) 323-330].     

Chiral recognition of dipeptides in Langmuir monolayers

The recognition of the enantiomeric couples of ditryptophan in Langmuir films of N-hexadecanoyl-l-proline was investigated by surface pressure–area (π–A) isotherm measurements and Brewster angle microscopy experiments. The π–A isotherms relative to the films including the enantiomeric dipeptides show small differences whereas an evident enantiodiscrimination is observed by Brewster angle microscopy images.     

The influence of nucleus density on optical properties in nucleated isotactic polypropylene

The effect and efficiency of three nucleating agents, a sorbitol based clarifier, a traditional heterogeneous nucleating agent and poly(vinylcyclohexane) (PVCH) was studied in polypropylene (iPP) homopolymer. The nucleating agents were added to iPP in different amounts; PVCH in 0–200 ppm, while the other two in 0–2000 ppm. Optical and mechanical properties were determined on injection molded plates or bars, respectively. Nucleation efficiency was studied by thermal analysis, while structure was characterized by polarized light (PLM), scanning electron (SEM) and atomic force microscopy (AFM). Nucleus density was calculated using the method of Lamberti, which is based on the kinetic theory of the crystallization developed by Lauritzen and Hoffmann. The results proved that the nucleating agents modify properties in different ways and extent. PVCH is very efficient already at small concentrations and increases the stiffness of iPP considerably more than the other two compounds. On the other hand, the clarifier and the traditional nucleating agent induce better optical properties even at smaller efficiency. The structure developing in the presence of the three nucleating agents is also different. The clarifier forms a network in iPP and induces the formation of a microcrystalline structure according to the former literature data. Microspherulitic structure develops in the presence of the heterogeneous nucleating agent studied, while relatively large supermolecular units form in iPP nucleated by PVCH even under the conditions of injection molding. The calculation of nucleus density by existing models and the comparison of the results to optical properties proved that haze is determined by the size of the supermolecular units of the polymer and this latter depends on nucleus density.