Orbit inequivalent actions for groups containing a copy of $\mathbb{F}_{2}$

We prove that if a countable group Γ contains a copy of \mathbbF₂\mathbb{F}_{2}, then it admits uncountably many non orbit equivalent actions.     

Acute triangulation of a triangle in a general setting revisited

Axiom A16 from Pambuccian (Can. Math. Bull. 53, 534?C541, 2010) is shown to be superfluous as it depends on axioms A1?CA15. This provides a surprisingly simple axiom system in which the acute triangulation with seven triangles can be proved for any triangle, consisting only of A1?CA15 in Pambuccian (Can. Math. Bull. 53, 534?C541, 2010).     

Investigating asymptotic properties of vector nonlinear time series models

Analyses and simulations of vector nonlinear time series typically run into weeks or even months because the methods used are computationally intensive. Statisticians have been known to base empirical results on a relatively small number of simulation replications, sacrificing precision and reliability of results in the interest of time and productivity. The simulations are amenable for parallelization. However, parallel computing technology has not yet been widely used in this specific research area. This paper proposes an approach to the parallelization of statistical simulation codes to address the challenge of long running times. Requiring minimal code revision, this approach takes advantage of recent advances in dynamic loop scheduling to achieve high performance on general-purpose clusters, even with the presence of unpredictable load imbalance factors. Preliminary results of applying this approach in the simulation of normal white noise and threshold autoregressive model obtains efficiencies in the range 95%-98% on 8-64 processors. Furthermore, previously unobserved properties of the statistical procedures for the models are uncovered by the simulation.     

Convergence of solutions for the stochastic porous media equations and homogenization

This work addresses the stochastic porous media equation with multiplicative noise and diffusivity function depending on the space variable. The first part of the paper proves an existence and uniqueness result for this type of equation, the second part proves the convergence of the solutions in the case of graph convergence of the porous media operator, and this result is used in the third part for an homogenization theorem.     

Mathematical modeling of the graft reaction between polystyrene and polyethylene

Polystyrene (PS) and polyethylene (PE) are two major components of household plastic waste whose blends are immiscible. Recycling them together is an attractive option that requires a compatibilization process to improve the blend mechanical properties. If a PE/PS copolymer is added or formed in situ, it may act as compatibilizer. The structure and molecular properties of this copolymer are key factors to assure its effectivity as a compatibilizer. In this work, we study the graft copolymerization reaction between polystyrene and polyethylene using the catalytic system composed of AlCl₃ and styrene. We develop a model of this process which considers that PE/PS grafting and PS degradation occur simultaneously. We propose a kinetic mechanism for the whole process and apply the method of moments to solve the mass balance equations. The model is able to calculate average molecular weights as well as the amount of grafted PS. It accurately describes the available experimental data, constituting a valuable tool for simulation and optimization purposes.     

A Central Extension Theorem-for Hopf Algebras

The construction used in Schur's central extension theorem is generalized by proving that given a cocommutative Hopf algebra H, there is a cocornmutative central extension B of H such that any projective representation of H lifts to an ordinary representation of B. The extension B is the crossed product of H with the finite dual of the group algebra kZ₁, where Z₁denotes the group of normal cocycles on H with values in the ground field k.     

Lipases A and B from Candida antarctica in the enantioselective acylation of ethyl 3-heteroaryl-3-hydroxypropanoates: aspects on the preparation and enantiopreference

The preparative scale kinetic resolution of racemic ethyl 2- and 3-furyl- and 2- and 3-thienyl-3-hydroxypropanoates has been performed by Candida antarctica lipases A and B with vinyl esters. A study based on the present work together with the literature has been carried out in terms of lipase enantiopreference and substrate structure. We also discuss the excellent behavior of the lipase A in O-acylations of secondary alcohols with respect to enantiopreference.     

Strong Dunford–Pettis Sets and Spaces of Operators

Bibasic sequences of Singer are used to show that ℓ₁ embeds complementably in the Banach space X if and only if X^* contains a non-relatively compact strong Dunford–Pettis set. Spaces of operators and strongly additive vector measures are also discussed. An erratum to this article is available at .     

High resolution mass spectrometric characterization of amino linked oligosaccharides — a preliminary study

In this study maltose, maltotriose and maltotetraose were for the first time, coupled to 4,4′-methylenedianiline (MDA). The aim of this preliminary work was to test the feasibility of oligo- and polysaccharide coupling to MDA and the characterization of the coupling products by high resolution mass spectrometry (MS). (+) nanoESI in combination with a quadrupole time of flight (QTOF) MS in full scan (MS) and MS/MS was optimized first on underivatized maltose, maltotriose and maltotetraose. The optimal screening and sequencing conditions were further applied to the MDA-functionalized oligosaccharides. The obtained results revealed a straightforward MS detection of the functionalized oligomers, high sequence coverage and a fragmentation pathway with the formation of B and Y ions as well as the complementary C and Z ions along with a typical cleavage of the aglycon. We consider that this methodology is fully applicable also to polydisperse mixtures of long chain polysaccharides, which due to the large number of components and their size require a systematic method of development and testing.