Completions of Pseudo Ordered Sets

Order - A pseudo ordered set (X,≤) is a set X with a binary relation ≤ that is reflexive and antisymmetric. We associate to a pseudo ordered set X, a partially ordered set Γ(X)...     

Does the chalkboard still hold its own against modern technology in teaching mathematics? A case study

The purpose of this case study is to explore the integration of technology into teaching at a mathematics department at a large South African University. Both quantitative and qualitative data were collected from staff teaching undergraduate mathematics. The study shows that many staff members feel that chalkboards are still more suitable than technology for teaching mathematics. This finding supports the idea of a strong subject culture. Age does not emerge as a determinant for preference of either technology or the chalkboard, although gender and academic qualifications do. Subject culture is strongly rooted under the male members of staff, while female staff members feel more positive towards the use of technology in teaching. Use of chalkboards has decreased significantly over the past 10 years, while the use of modern technologies has increased accordingly. Teaching of large groups has necessitated the use of technology in the classroom. Despite the strong subject culture, a shift in attitude towards technology use in teaching is noticed and there is a definite trend of moving towards using new technologies.     

Polymerisation and structure–property relationships of Ziegler–Natta catalysed isotactic polypropylenes

Polypropylene homopolymer samples were prepared with a Ziegler–Natta catalyst using two different external donors, namely diphenyldimethoxysilane (DPDMS), and methylphenyldimethoxysilane (MPDMS). Each donor was used in varying molar ratios to the catalyst in order to prepare samples for physical testing. The polymers were fully characterised and also fractionated by preparative TREF with characterisation of the fractions. In terms of the polymerisation reactions the DPDMS external donor exerts greater influence at the active sites than the MPDMS and produces polymer of higher molar mass and lower polydispersity. The physical properties of the polymers were investigated using microhardness measurements. It is revealed that the microhardness is strongly dependent on the stereoregularity of the samples.     

Comparison of density functionals for the study of the high spin low spin gap in Fe(III) spin crossover complexes

A detailed investigation of the accuracy of different quantum mechanical methods for the study of iron(III) spin crossover complexes is presented. The energy spin state gap between the high and low spin states; ΔE (HS‐LS) of nine iron(III) quinolylsalicylaldiminate complexes were calculated with nine different DFT functionals, then compared. DFT functionals: B3LYP, B3LYP‐D3, B3LYP*, BH&HLYP, BP86, OLYP, OPBE, M06L, and TPSSh were tested with six basis sets: 3‐21G*, dgdzvp, 6‐31G**, cc‐pVDZ, Def2TZVP, and cc‐pVTZ. The cations from the X‐ray crystal structures of [Fe(qsal‐OMe)₂]Cl·MeCN·H₂O, [Fe(qsal‐OMe)₂]Cl·2MeOH·0.5H₂O, [Fe(qsal‐OMe)₂]BF₄·MeOH, [Fe(qsal‐OMe)₂]NCS·CH₂Cl₂, [Fe(qsal‐F)₂]NCS, [Fe(qsal‐Cl)₂]NCS·MeOH, [Fe(qsal‐Br)₂]NCS·MeOH, [Fe(qsal‐I)₂]OTf·MeOH, and [Fe(qsal)₂]NCS?CH₂Cl₂ were used as starting structures. The results show that B3LYP, B3LYP‐D3, OLYP, and OPBE with a 6‐31G**, Def2TZVP, and cc‐pVTZ basis set give reasonable results of ΔE (HS‐LS) compared with the experimental data. The enthalpy of [Fe(qsal‐I)₂]⁺ calculated with an OLYP functional and cc‐pVTZ basis set (1.48 kcal/mol) most closely matches the experimental data (1.34 kcal/mol). B3LYP* yields an enthalpy of 5.92 kcal/mol suggesting it may be unsuitable for these Fe(III) complexes, mirroring recent results by Kepp (Inorg . Chem ., 2016, 55 , 2717–2727).     

Formation of a Dimer of Trinuclear Helicates which Encapsulates an Array of Six Hydrogen‐Bonded Anions

The amine‐containing ligand L, composed of two bidentate pyridyl‐thiazole moieties linked by a 1,3‐diaminophenylene unit, reacts with copper(II) ions to form a dinuclear double helicate [Cu₂L₂]⁴⁺. Reaction of [Cu₂L₂]⁴⁺ with dihydrogen phosphate (0.5 equivalents) gives the unsaturated dinuclear double helicate [Cu₂L₂(OPO₃H₂)]³⁺. [Cu₂L₂(OPO₃H₂)]³⁺ further reacts with another 0.5 equivalents of dihydrogen phosphate to give a trinuclear circular helicate which then self‐assembles into a hexameric cluster [{Cu₃L₃(OPO₃H₂)₃}]²⁶⁺.     

On profinite completions and canonical extensions

We show that if a variety V of monotone lattice expansions is finitely generated, then profinite completions agree with canonical extensions on V. The converse holds for varieties of finite type. This paper is dedicated to Walter Taylor. Received May 14, 2005; accepted in final form September 8, 2005.