One-pot synthesis of 3-arylaminomaleimides from terminal alkynes and isocyanates

The reaction of aryl acetylide anions with phenyl isocyanate and subsequent addition of a protonating agent such as ethanol affords good yields of 3-aminomaleimides, formed by the cyclization of one molecule of alkyne with two isocyanates. When the reaction is quenched with water instead, cyclopentadienone imines are formed as the major products.     

Sequential claisen and cope rearrangement for formation of 3-(-1-methylethyl)-substituted α,β-unsaturated aldehydes

3-(1-Methylethyl)-7-methyl2,6-octadienal, was prepared from 1,1,3-triethoxy-3,4-dimethylpentane and 3-methyl-2-buten-l-ol in a one-pot procedure utilising Claisen and Cope rearrangement of an intermediate dienol-allyl ether.     

Geometry optimization in Cartesian coordinates: Constrained optimization

An efficient algorithm for constrained geometry optimization in Cartesian coordinates is presented. It incorporates mode-following techniques within both the classical method of Lagrange multipliers and the penalty function method. Both constrained minima and transition states can be located and, unlike the standard Z-matrix using internal coordinates, the desired constraints do not have to be satisfied in the initial structure. The algorithm is as efficient as a Z-matrix optimization while presenting several additional advantages.     

Bjarni Jónsson’s contributions in algebra: an addendum

Normal categories are pointed categorical counterparts of 0-regular varieties, i.e., varieties where each congruence is uniquely determined by the equivalence class of a fixed constant 0. In this paper, we give a new axiomatic approach to normal categories, which uses self-dual axioms on a functor defined using subobjects of objects in the category. We also show that a similar approach can be developed for 0-regular varieties, if we replace subobjects with subsets of algebras containing 0.     

The zeros of a quadratic form at square-free points

Let F(x₁,…,xn) be a nonsingular indefinite quadratic form, n=3 or 4. For n=4, suppose the determinant of F is a square. Results are obtained on the number of solutions of

F(x₁,…,xn)=0     

A Deterministic Inventory System with an Inventory-Level-Dependent Demand Rate

This analysis is concerned with the continuous, deterministic case of an inventory system in which the demand rate of an item is of a polynomial functional form, dependent on the inventory level. Differential and integral calculus are used to find the inventory function with respect to time. From this, the objective function (to maximize average profit per unit time) is developed. For the continuous, multiperiod situation, a non-linear programming algorithm—separable programming—is utilized to determine the optimal order level (the quantity to order up to) and the order point (the quantity at which an order is placed). A numeric example and a sensitivity analysis are also presented.     

Differential algebraic equations with after-effect

In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.     

Navigating Schooled Numeracies: Explanations for Low Achievement,in Mathematics of UK Children From Low SES Background

The intention of the research reported here was to seek explanations for low achievement in school mathematics, as conventionally assessed, that derive from broad understandings of mathematics as social. Such a broad social perspective can provide explanations for low achievement, which could lead to different understandings and hence to different teaching approaches. This study centered on 5- to 8-year-old children from a White working-class area in England. Data were collected during visits to the children in school, in their homes, and in the broader community over a 3-year period. Parents, teachers, and other professionals in the broad school context were interviewed, and data were also collected from school documents and policy statements. Interpretations of these data in terms of ways of understanding children's achievements in school mathematics are put forward. The potential effects of these factors on low schooled numeracy attainment are discussed, together with some possible strategic implications for practice and policy.