A re-evaluation of isotope shift constants

The field isotope shift constantC _unif for a uniform nuclear charge distribution has been re-evaluated fors-electrons for elements with 10≦Z≦ 95. A table is given which permitsC _unif to be found for any isotope pair.     

Rate and product studies in the solvolyses of N,N-dimethylsulfamoyl and 2-propanesulfonyl chlorides

Contrary to earlier suggestions of an S(N)1 pathway for solvolyses of N,N-dimethylsulfamoyl chloride (1), an extended Grunwald-Winstein equation treatment of the specific rates of solvolysis in 32 solvents shows an appreciable sensitivity towards changes in both solvent nucleophilicity and solvent ionizing power. The actual values are very similar to those obtained in earlier studies of the solvolyses of sulfonyl and phosphoryl chlorides, solvolyses which are believed to proceed by an S(N)2 pathway. The observation of similar selectivities in aqueous-alcohol solvents further supports this assignment. In a recent report, an addition-elimination (association-dissociation) pathway was proposed for solvolyses of 2-propanesulfonyl chloride (2). A severe multicollinearity problem has been removed by the addition of several specific rates of solvolysis in fluoroalcohol-containing solvents. The new analyses using the extended Grunwald-Winstein equation lead to sensitivities similar to those for and the previously studied related compounds, and these solvolyses are also best described as following an S(N)2 pathway.     

Multiscaling analysis of a slowly varying anaerobic digestion model

We construct the slowly varying limiting state solutions to a nonlinear dynamical system for anaerobic digestion with Monod-based kinetics involving slowly varying model parameters arising from slow environmental variation. The advantage of these approximate solutions over numerical solutions is their applicability to a wide range of parameter values. We use these limiting state solutions to develop analytic approximations to the full nonlinear system by applying a multiscaling technique. The approximate solutions are shown to compare favorably with numerical solutions.     

Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its availability in classrooms also provides opportunities for positive changes to teaching and learning. Very many examples are documented in the professional and research literature, and in this paper we organize them into 10 types. These are displayed in the form of a ‘pedagogical map’, which further classifies them according to whether the opportunity arises from new opportunities for the mathematical tasks used, change to interpersonal aspects of the classroom or change to the point of view on mathematics as a subject. The map can be used in teacher professional development to draw attention to possibilities for lessons or as a catalyst for professional discussion. For research on teaching, it can be used to map current practice, or to track professional growth. The intention of the map is to summarise the potential benefits of teaching with technology in a form that may be useful for both teachers and researchers.     

Examining the didactic contract when handheld technology is permitted in the mathematics classroom

The use of mathematics analysis software (MAS) including handheld scientific and graphics calculators offers a range of pedagogical opportunities. Its use can support change in the didactic contract. MAS may become an alternative source of authority in the classroom empowering students to explore variation and regularity, manipulate simulations and link representations. Strategic use may support students to direct their own learning and explore mathematics, equipping them to share their findings with the teacher and the class with more confidence. This paper offers a framework for examining the impact of the use of MAS on the didactic contract. Lessons were observed in 12 grade 10 classes, with 12 different teachers new to MAS. MAS technology was used with a variety of didactic contracts, mostly traditional. The framework drew attention to many ways in which the teaching differed. Analysis of the didactic contract must consider both the teaching of mathematics and of technology skills, because these have different characteristics. In all classes, both teachers and students saw the teacher as having a responsibility to teach technology skills. Students saw technology skills as the main point of the lesson, but the teachers saw the lesson as primarily teaching mathematics—one of the mismatches which may need negotiation to adapt didactic contracts to teaching with MAS.     

Reductions in Computational Complexity Using Clifford Algebras

A number of combinatorial problems are treated using properties of abelian null-square-generated and idempotent-generated subalgebras of Clifford algebras. For example, the problem of deciding whether or not a graph contains a Hamiltonian cycle is known to be NP-complete. By considering entries of Λ^k, where Λ is an appropriate nilpotent adjacency matrix, the k-cycles in any finite graph are recovered. Within the algebra context (i.e., considering the number of multiplications performed within the algebra), these problems are reduced to matrix multiplication, which is in complexity class P. The Hamiltonian cycle problem is one of many problems moved from classes NP-complete and #P-complete to class P in this context. Other problems considered include the set covering problem, counting the edge-disjoint cycle decompositions of a finite graph, computing the permanent of an arbitrary matrix, computing the girth and circumference of a graph, and finding the longest path in a graph.     

Synthesis of chiral titanium-containing phosphinoamide ligands for enantioselective heterobimetallic catalysis

The synthesis of six chiral titanium-containing phosphinoamide ligands is discussed. These ligands assemble chiral heterobimetallic Pd–Ti complexes, enable enantioselective intramolecular allylic aminations with hindered amine nucleophiles and achieve selectivity up to 53% ee. Mechanistic studies demonstrate the reversibility of the enantio-determining C–N bond forming step, which leads to a gradual increase in the % ee of the reaction over time. These results represent a rare example of enantioselective heterobimetallic catalysis and suggest that these new ligands could find broad application in enantioselective transition metal catalysis.     

SSZ‐27: A Small‐Pore Zeolite with Large Heart‐Shaped Cavities Determined by Using Multi‐crystal Electron Diffraction

The high‐silica zeolite SSZ‐27 was synthesized using one of the isomers of the organic structure‐directing agent that is known to produce the large‐pore zeolite SSZ‐26 ( CON ). The structure of the as‐synthesized form was solved using multi‐crystal electron diffraction data. Data were collected on eighteen crystals, and to obtain a high‐quality and complete data set for structure refinement, hierarchical cluster analysis was employed to select the data sets most suitable for merging. The framework structure of SSZ‐27 can be described as a combination of two types of cavities, one of which is shaped like a heart. The cavities are connected through shared 8‐ring windows to create straight channels that are linked together in pairs to form a one‐dimensional channel system. Once the framework structure was known, molecular modelling was used to find the best fitting isomer, and this, in turn, was isolated to improve the synthesis conditions for SSZ‐27.     

Synthesis and characterization of double hydrophilic block copolymers containing semi-rigid and flexible segments

3-Methyl-(E)-stilbene (3MSti) and 4-(diethylamino)-(E)-stilbene (DEASti) monomers are synthesized and polymerized separately with maleic anhydride (MAn) in a strictly alternating fashion using reversible addition-fragmentation chain transfer (RAFT) polymerization techniques. The optimal RAFT chain transfer agents (CTAs) for each copolymerization affect the reaction kinetics and CTA compatibilities. Psuedo-first order polymerization kinetics are demonstrated for the synthesis of poly((3-methyl-(E)-stilbene)-alt-maleic anhydride) (3MSti-alt-MAn) with a thiocarbonylthio CTA (methyl 2-(dodecylthiocarbonothioylthio)−2-methylpropionate, TTCMe). In contrast, a dithioester CTA (cumyl dithiobenzoate, CDB) controls the synthesis of poly((4-(diethylamino)-(E)-stilbene)-alt-maleic anhydride) (DEASti-alt-MAn) with pseudo-first order polymerization kinetics. DEASti-alt-MAn is chain extended with 4-acryloylmorpholine (ACMO) to synthesize diblock copolymers and subsequently converted to a double hydrophilic polyampholyte block copolymers (poly((4-(diethylamino)-(E)-stilbene)-alt-maleic acid))-b-acryloylmorpholine) (DEASti-alt-MA)-b-ACMO) via acid hydrolysis. The isoelectric point and dissociation behavior of these maleic acid-containing copolymers are determined using ζ-potential and acid–base titrations, respectively. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 219–227