Alternative Synthesis and Structures of C‐monoacetylenic Phosphaalkenes

An alternative synthesis of C‐monoacetylenic phosphaalkenes trans‐Mes*P=C(Me)(C≡CR) (Mes* = 2, 4, 6‐^tBu₃Ph, R = Ph, SiMe₃) from C‐bromophosphaalkenes cis‐Mes*P=C(Me)Br using standard Sonogashira coupling conditions is described. Crystallographic studies confirm cis‐trans isomerization of the P=C double bond during Pd‐catalyzed cross coupling, leading exclusively to trans‐acetylenic phosphaalkenes. Crystallographic studies of all synthesized compounds reveal the extend of π‐conjugation over the acetylene and P=C π‐systems.     

Vesicles prepared with the complex salts dioctadecyldimethylammonium polyacrylates

The effect of a polymeric counterion on the thermotropic behavior of sonicated vesicles formed by complex salts in aqueous solution and with decanol (C(10)OH) and tetradecanol (C(14)OH) was investigated. The complex salts were prepared with dioctadecyldimethylammonium bromide (DODAB) and polyacrylic acids (PAA, containing 30 or 6000 repeating units), being referred to as DODAPA(30) and DODAPA(6000). Vesicles containing polymeric counterions presented higher contents of multilamellar vesicles that were dependent on the complex salt concentration and on the counterion chain length. For comparison, studies were performed with DODAAc, with the counterion acetate, resulting in the formation of mostly unilamellar vesicles, as expected due greater dissociation, leading to greater electrical repulsion between bilayers. Mixtures of these complex salts and DODAX (where X=acetate or bromide) were also investigated with respect to their vesicles thermotropic behavior and size. This study opens the possibility of applying the methodology of direct complex salt preparation (as opposed to mixing the surfactant and polymeric components) to produce vesicles with controlled composition and properties.     

An electrostatic correction for improved crystal density predictions of energetic ionic compounds

In recent years, there has been considerable interest in predicting the crystal densities of both molecular and ionic energetic compounds using the computed volumes V_m of the isolated gas phase molecules or ions. The surfaces enclosing the volumes are taken to be the 0.001 au (electrons/bohr³) contours of the molecules’ and ions’ electronic densities. For molecular solids, it is known that the ratio M/V_m (M = molecular mass) gives densities that are overall reasonably good, although they can be markedly improved by introduction of an electrostatic interaction correction term. For ionic solids, the subject of this paper, the ratio M/V_m (M = formula unit mass) is not nearly as effective; V_m tends to be significantly larger than the effective volumes of the ions in the crystal, leading to underestimated densities, with an average absolute error of 0.089 g/cm³. The correction term that improves molecular crystal densities is not applicable in the case of ionic solids; however we show, for a database of 25 compounds plus five test cases, that an average absolute error of 0.033 g/cm³ can be achieved by combining M/V_m with terms involving the average positive and negative potentials and areas on the cationic and anionic surfaces. The root-mean-square error is 0.040 g/cm³.     

Sexual dimorphism in the human brain: evidence from neuroimaging

In recent years, more and more emphasis has been placed on the investigation of sex differences in the human brain. Noninvasive neuroimaging techniques represent an essential tool in the effort to better understand the effects of sex on both brain structure and function. In this review, we provide a comprehensive summary of the findings that were collected in human neuroimaging studies in vivo thus far: we explore sexual dimorphism in the human brain at the level of (1) brain structure, in both gray and white matter, observed by voxel-based morphometry (VBM) and diffusion tensor imaging (DTI), respectively; (2) baseline neural activity, studied using resting-state functional magnetic resonance imaging (rs-fMRI) and positron emission tomography (PET); (3) neurochemistry, visualized by means of neuroreceptor ligand PET; and (4) task-related neural activation, investigated using fMRI. Functional MRI findings from the literature are complemented by our own meta-analysis of fMRI studies on sex-specific differences in human emotional processing. Specifically, we used activation likelihood estimation (ALE) to provide a quantitative approach to mapping the consistency of neural networks involved in emotional processing across studies. The presented evidence for sex-specific differences in neural structure and function highlights the importance of modeling sex as a contributing factor in the analysis of brain-related data.     

THE NATURE OF PARTICIPATION AFFORDED BY TASKS,QUESTIONS AND PROMPTS IN MATHEMATICS CLASSROOMS

This paper reports on the development of an analytical instrument which identifies mathematical affordances in the public tasks, questions and prompts of mathematics classrooms. The aim is to become more articulate about mathematical activity. I have explored the use of several frameworks which identify learning outcomes, structures of knowledge, mental actions, teaching actions and intentions and found that none of them give me access to the detail of what makes one mathematics lesson different from another for learners. From the experience of using these I devised a new analytical tool which unfolds patterns of participation afforded in mathematics lessons. This tool has been tested on several videos of lessons, and has been used by pre-service teaching students to analyse their own lessons.     

A stability criterion

An important technique for determining the stability of a system of ordinary differential equations is to determine whether there are any roots in the positive half-plane of a certain polynomial P(z). Cesari has given a criterion for this in terms of the topological degree of the mapping described by P(z). It is shown here that Cesari's criterion can be reformulated as the problem of approximating the real roots of polynomials which are the real and imaginary parts of the P(z) on certain lines in the z-plane. The roots need only be approxi¬mated closely enough so that their magnitudes can be compared. The derivation of this criterion uses the notion of topological degree but the criterion itself is stated entirely in elementary terms     

Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second-order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions.     

On L-spaces and left-orderable fundamental groups

Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of manifolds. In particular, we prove that they are equivalent for any closed, connected, orientable, geometric three-manifold that is non-hyperbolic, a family which includes all closed, connected, orientable Seifert fibred spaces. We also show that they are equivalent for the twofold branched covers of non-split alternating links. To do this we prove that the fundamental group of the twofold branched cover of an alternating link is left-orderable if and only if it is a trivial link with two or more components. We also show that this places strong restrictions on the representations of the fundamental group of an alternating knot complement with values in $\text{ Homeo}_+(S^1)$ .     

Factors Influencing the Outcomes of Collaborative Mathematical Problem Solving: An Introduction

This study is an investigation of the factors that influence the effectiveness of collaboration on open-ended mathematical tasks. Students in Grades 3, 6, and 9 worked in groups of 3 on 2 chance and data tasks-1 related to fair dice and the other related to associations among variables presented on data cards. The groups' outcomes and the types of collaboration observed are investigated in relation to issues raised in the literature. Various phenomena are identified that influence cognitive "lifting," "hovering," and "falling," that is, improvement, no change, and reduction in levels of functioning, respectively. These phenomena include cognitive factors, social or interpersonal factors, and external factors.