Immigrant parents’ perspectives on their children’s mathematics education

This paper draws on two research studies with similar theoretical backgrounds, in two different settings, Barcelona (Spain) and Tucson (USA). From a sociocultural perspective, the analysis of mathematics education in multilingual and multiethnic classrooms requires us to consider contexts, such as the family context, that have an influence on these classrooms and its participants. We focus on immigrant parents' perspectives on their children's mathematics education and we primarily discuss two topics (1) their experiences with the teaching of mathematics, and (2) the role of language (native language and second language). The two topics are explored with reference to the immigrant student's or their parents' former educational systems (the “before”) and their current educational systems (the “now”). Parents and schools understand educational systems, classroom cultures and students' attainment differently, as influenced by their sociocultural histories and contexts.     

Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes

This a first step to develop a theory of smooth, étale, and unramified morphisms between Noetherian formal schemes. Our main tool is the complete module of differentials, which is, a coherent sheaf whenever the map of formal schemes is of pseudofinite type. Among our results, we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of Noetherian formal schemes is flat and its module of differentials is locally free. The article closes with a version of Zariski's Jacobian criterion.     

Radial and non radial solutions for Hardy–Hénon type elliptic systems

We discuss existence and non-existence of positive solutions for the following system of Hardy and Hénon type: $$\left\{\begin{array}{ll} {-\Delta v=|x|^{\alpha}u^{p},\,-\Delta u=|x|^{\beta}v^{q} \,\,{\rm in}\, \Omega,}\\ {u=v=0 \quad\quad\quad\quad\quad\quad\quad\quad\quad{\rm on}\, \partial \Omega}, \end{array}\right.$$ where ${\Omega\ni 0}$ is a bounded domain in ${\mathbb{R}^{N}}$ , N ≥ 3, p, q > 1, and α, β > ?N. We also study symmetry breaking for ground states when Ω is the unit ball in ${\mathbb{R}^{N}}$ .     

On the bicriterion – minimal cost/minimal label – spanning tree problem

We address a bicriterion spanning tree problem relevant in some application fields such as telecommunication networks or transportation networks. Each edge is assigned with a cost value and a label (such as a color). The first criterion intends to minimize the total cost of the spanning tree (the summation of its edge costs), while the second intends to get the solution with a minimal number of different labels. Since these criteria, in general, are conflicting criteria we developed an algorithm to generate the set of non-dominated spanning trees. Computational experiments are presented and results discussed.     

Bounding the exponent of a verbal subgroup

We deal with the following conjecture. If \(w\) is a group word and \(G\) is a finite group in which any nilpotent subgroup generated by \(w\) -values has exponent dividing \(e\) , then the exponent of the verbal subgroup \(w(G)\) is bounded in terms of \(e\) and \(w\) only. We show that this is true in the case where \(w\) is either the \(n\text{ th }\) Engel word or the word \([x^n,y_1,y_2,\ldots ,y_k]\) (Theorem A). Further, we show that for any positive integer \(e\) there exists a number \(k=k(e)\) such that if \(w\) is a word and \(G\) is a finite group in which any nilpotent subgroup generated by products of \(k\) values of the word \(w\) has exponent dividing \(e\) , then the exponent of the verbal subgroup \(w(G)\) is bounded in terms of \(e\) and \(w\) only (Theorem B).     

Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries

The language of Lagrangian submanifolds is used to extend a geometric characterization of the inverse problem of the calculus of variations on tangent bundles to regular Lie algebroids. Since not all closed sections are locally exact on Lie algebroids, the Helmholtz conditions on Lie algebroids are necessary but not sufficient, so they give a weaker definition of the inverse problem. As an application the Helmholtz conditions on Atiyah algebroids are obtained so that the relationship between the inverse problem and the reduced inverse problem by symmetries can be described. Some examples and comparison with previous approaches in the literature are provided.     

Finite groups with small centralizers of word-values

Given a positive integer m and a group-word w, we consider a finite group G such that $$w(G) ne 1$$ and all centralizers of non-trivial w-values have order at most m. We prove that if $$w=v(x_1^{q_1},dots ,x_k^{q_k})$$, where v is a multilinear commutator word and $$q_1, dots , q_k$$ are p-powers for some prime p, then the order of G is bounded in terms of w and m only. Similar results hold when w is the nth Engel word or the word $$w=[x^n, y_1, dots ,y_k]$$ with $$k ge 1$$.     

Identification of the tension force in cables with insulators

Meccanica - The present paper explores two approaches which, based on the measurement of the two first natural frequencies, allow the identification of the tension force in cables with insulators....     

MPI+X: task-based parallelisation and dynamic load balance of finite element assembly

The main computing phases of numerical methods for solving partial differential equations are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. The matrix assembly consists of a loop over the elements, faces, edges or nodes of the MPI partitions to compute element matrices and vectors and then of their assemblies. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP, with different techniques to avoid the race condition, but presenting efficiency or implementation drawbacks. We propose an alternative, based on task parallelism using some extensions to the OpenMP programming model. In addition, dynamic load balance will be applied, especially efficient in the presence of hybrid meshes. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores.     

Amino acid-functionalized cyclopentadienyl molybdenum tricarbonyl complex and its use in catalytic olefin epoxidation

The complex [(N-benzyloxycarbonylprolyl)cyclopentadienyl]-Mo(CO)₃Me was prepared by the reaction of the amino acid-functionalized cyclopentadienyl-lithium reagent with Mo(CO)₆, and subsequent methylation with CH₃I. The complex was characterized by FTIR, ¹H and ¹³C NMR, and elemental analysis. A single-crystal X-ray diffraction study showed that the complex is chiral, crystallizing in the orthorhombic P2₁2₁2₁ space group with the Flack parameter refining to –0.007(16), which unequivocally confirms the presence of an enantiomerically pure compound. The complex was examined as a catalyst precursor in the liquid-phase epoxidation of trans-β-methylstyrene at 280–330 K, using either tert-butylhydroperoxide (tert-BuOOH), cumylhydroperoxide or urea-hydrogen peroxide adduct as oxidant, and, optionally, a co-solvent. With chloroform and tert-BuOOH, the catalytic activity surpasses that previously reported for chiral complexes of the type CpMo(CO)₃X, giving the epoxide isomers ((R,R)-(+) and (S,S)-(?)-1-phenylpropylene oxide) in excellent selectivity, albeit with negligible enantiomeric excess. FTIR spectroscopy showed that the oxidative decarbonylation of the tricarbonyl complex with tert-BuOOH is fast under the reaction conditions used, and that the structural integrity of the amino acid-functionalized cyclopentadienyl group is retained during this process. The use of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate as a solvent for the catalyst generates a biphasic liquid–liquid reaction system that enables, at the end of a catalytic cycle, the separation and reutilization of the catalyst.