Synthesis of Pyrido[2′,3′: 3,4]pyrazolo[1,5‐a]pyrimidine,Pyrido[2′,3′:3,4]pyrazolo[5,1‐c][1,2,4]triazine,and Pyrazolyl Oxadiazolylthieno[2,3‐b]pyridine Derivatives

6‐(2‐Thienyl)‐4‐(trifluoromethyl)‐1H‐pyrazolo[3,4‐b]pyridine‐3‐amine reacted with different active methylene compounds to afford pyridopyrazolopyrimidine derivatives. On the other hand, it reacted with some halo compounds to give the imidazo[1′,2′:1,5]pyrazolo[3,4‐b]pyridine derivatives. Also, it diazotized to give the corresponding diazonium chloride that is coupled with several active methylene compounds to give the corresponding triazine derivatives. Furthermore, compound 3‐amino‐6‐(2(thienyl)‐4‐(trifluoromethyl)thieno[2,3‐b]pyridine‐2‐carbohydrazide reacted with some β‐dicarbonyl compounds and some sulfur‐containing compounds to afford the corresponding pyrazolyl oxadiazolylthieno[2,3‐b]pyridine derivatives.     

Discrete nonlinear Schrödinger equation and polygonal solitons with applications to collapsed proteins

We introduce a novel generalization of the discrete nonlinear Schr?dinger equation. It supports solitons that we utilize to model chiral polymers in the collapsed phase and, in particular, proteins in their native state. As an example we consider the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. We use its backbone as a template to explicitly construct a two-soliton configuration. Each of the two solitons describe well over 7.000 supersecondary structures of folded proteins in the Protein Data Bank with sub-angstrom accuracy suggesting that these solitons are common in nature.     

Long‐Lived Circularly Polarized Phosphorescence in Helicene‐NHC Rhenium(I) Complexes: The Influence of Helicene,Halogen, and Stereochemistry on Emission Properties

The first enantiopure chiral‐at‐rhenium complexes of the form fac‐ReX(CO)₃(:C^N) have been prepared, where :C^N is a helicene‐N‐heterocyclic carbene (NHC) ligand and X=Cl or I. These have complexes show strong changes in the emission characteristics, notably strongly enhanced phosphorescence lifetimes (reaching 0.7 ms) and increased circularly polarized emission (CPL) activity, as compared to their parent chiral models lacking the helicene unit. The halogen along with its position within the dissymmetric stereochemical environment strongly affect the photophysics of the complexes, particularly the phosphorescence quantum yield and lifetime. These results give fresh insight into fine tuning of photophysical and chiroptical properties of Re‐NHC systems.     

Algebraic signatures of convex and non-convex codes

A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as they arise from the activity of neurons that have convex receptive fields. In this paper, we develop algebraic methods to determine if a code is convex. Specifically, we use the neural ideal of a code, which is a generalization of the Stanley–Reisner ideal. Using the neural ideal together with its standard generating set, the canonical form, we provide algebraic signatures of certain families of codes that are non-convex. We connect these signatures to the precise conditions on the arrangement of sets that prevent the codes from being convex. Finally, we also provide algebraic signatures for some families of codes that are convex, including the class of intersection-complete codes. These results allow us to detect convexity and non-convexity in a variety of situations, and point to some interesting open questions.     

Geodesic motion in the 5D magnetized Schwarzschild-like solutions

Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry. Embedding diagrams are constructed in order to visualize the geometry of the metric. The study performed here is also valid, when the electromagnetic interactions are neglected, for the low energy superstring theory and the Brans-Dicke theory.     

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.     

A bidimensional phase-field model with convection for change phase of an alloy

The article analyzes a two-dimensional phase-field model for a non-stationary process of solidification of a binary alloy with thermal properties. The model allows the occurrence of fluid flow in non-solid regions, which are a priori unknown, and is thus associated to a free boundary value problem for a highly non-linear system of partial differential equations. These equations are the phase-field equation, the heat equation, the concentration equation and a modified Navier-Stokes equations obtained by the addition of a penalization term of Carman-Kozeny type which accounts for the mushy effects. A proof of existence of weak solutions for such system is given. The problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder fixed point theorem. A solution is then found by using compactness argument.