Polynuclear cobalt(II/III) sulfites: synthesis, structure, and magnetic properties of the octanuclear cluster (NH4)11(Li subset[Co4IICo4III(SO3)16(NH3)8]).10H2O encapsulating a lithium cation

Partial oxidation of an aqueous solution of CoIICl(2).6H2O with (NH4)6[Mo7VIO24].4H2O in the presence of (NH4)2SO3.H2O and LiCl, at pH approximately 5.3, leads to isolation of the octanuclear cluster (NH4)11(Li subset[Co4IICo4III(SO3)16(NH3)8].10H2O), 1. The structure of the anion of 1 consists of a central [Co4II], almost ideal square planar unit, and a pair of symmetry-related CoIII dimers above and below the Co4II plane grafting onto the tetramer by 16 bridging sulfite groups. The [Co8(SO3)16(NH3)8]12- cluster encapsulates a lithium cation which lies at the center of the Co4II square.     

A new property of a class of Jacobi polynomials

Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability-preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.

     

Symmetrical polymer systems prepared using a degradable bifunctional atom transfer radical polymerization initiator: Synthesis,characterization, and cleavage

Linear (co)polymers and dimethacrylate‐end‐linked polymer networks of methyl methacrylate with 2‐(dimethylamino)ethyl methacrylate, cleavable in the middle of the polymer chain, either under thermolysis or alkaline hydrolysis conditions, were prepared via atom transfer radical polymerization (ATRP) using a specially designed bifunctional degradable initiator. This initiator was 2,6‐pyridinediethanol di(2‐bromo‐2‐methyl propanoate) (PyDEDBrMeP), bearing two 2‐(pyridin‐2‐yl)ethyl ester moieties, known for their thermal and hydrolytic (alkaline conditions) lability. As a control, a more stable bifunctional ATRP initiator, 2,6‐pyridinedimethanol di(2‐bromo‐2‐methyl propanoate) (PyDMDBrMeP), was also synthesized together with the corresponding linear polymers and polymer networks prepared from it. Thermal or hydrolytic treatment of the polymers prepared using PyDEDBrMeP led to a reduction in the molecular weights of the linear polymers by a factor of two, and to the conversion of the polymer networks to soluble branched (star) structures, consistent with the expected cleavage of the initiator residue located in the middle of the polymer chain. Thermal treatment of the polymers prepared using PyDMDBrMeP did not affect their molecular weight due to the thermal stability of the (pyridin‐2‐yl)methyl ester group, while treatment under alkaline hydrolysis conditions resulted in complete cleavage, similar to the PyDEDBrMeP‐prepared polymers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2342–2355     

Electric/magnetic deformations of S3 and AdS3, and geometric cosets

We analyze asymmetric marginal deformations of SU(2)_k and SL(2,ℝ)_k WZW models. These appear in heterotic string backgrounds with non‐vanishing Neveu–Schwarz three‐forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S³ or AdS₃, include in particular geometric cosets such as S², AdS₂ or H₂. Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS₂ × S² background. We also comment on potential holographic applications.     

Effects of structure variation on solution properties of hydrotropes: phenyl versus cyclohexyl chain tips

The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir2011, 27, 12346-12353). Electrical conductivity, surface tension, (1)H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and (1)H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption profiles, having d log(cac)/dn curves consistent with limiting headgroup areas in the region of (35-55 ?(2)) indicating monolayer formation. SANS profiles showed no evidence for aggregates below the electrical conductivity determined cac values, inferring an "on-off" mode of aggregation. Analyses of SANS profiles was consistent with charged ellipsoidal aggregates, persisting from lower through to higher homologues in both the PhenCx and CyclohexCx series.     

On the Scaling Behavior of the Force/Extension Relation of a Chain

Applying an extending force F along the end‐to‐end vector r of a chain enlarges the initial size ρ_i ∼ | r _i| leading to a final state with ρ_f larger than ρ_i. Assuming a power law dependence of the size ρ ∼ N^ν of the chain on its length N, at the two different states with different exponents ν_i and ν_f, a scaling relationship is derived between the measure of the extending force F and the extension ρ of the chain. The exponent γ of the force/extension relation, ρ ∼ F^γ, depends on both exponents ν_i and ν_f of the initial and the final states. A relation between γ and the exponents ν_i and ν_f is derived which permits the explanation of previous results and predicts some more. The scaling behavior is checked with the exactly soluble model of a random walk under a force.

     

Coding and decoding representations of 3D shapes

The aim of this study is to examine students’ ability in interpreting and constructing plane representations of 3D shapes, and to trace categories of students that reflect different types of behaviour in representing 3D shapes. To achieve this goal, one test was administered to 279 students in grades 5–9, and forty of them were interviewed. The results of the study showed that the representation of 3D shapes is composed of two general representing/cognitive abilities, coding and decoding. Decoding refers to interpreting the structural elements and geometrical properties of 3D shapes in plane representations, while coding refers to constructing plane representations and nets of 3D shapes, and translating from one representational mode to another. A mixed-method analysis showed that four categories of students can be identified that describe four types of behaviour and explain students’ reasoning patterns in representing 3D shapes.     

Supported Au Nanoparticles-Catalyzed Regioselective Dehydrogenative Disilylation of Allenes by Dihydrosilane

Supported Au nanoparticles on TiO₂ catalyze the unprecedented dehydrogenative disilylation of monosubstituted and 1,1-disubstituted allenes by Et₂SiH₂ exclusively on the terminal double bond in a stereoselective manner. Treatment of the disilylation products with H₂O, in a one-pot operation also catalyzed by Au/TiO₂, leads to 3-alkylidene-1,2,5-oxadisilolanes, an unknown class of heterocyclic compounds, which are excellent scaffolds for the stereoselective synthesis of alkenes under Hiyama-type cross-coupling conditions.     

A substitution theorem for graceful trees and its applications

A graceful labeling of a graph G=(V,E) assigns |V| distinct integers from the set {0,…,|E|} to the vertices of G so that the absolute values of their differences on the |E| edges of G constitute the set {1,…,|E|}. A graph is graceful if it admits a graceful labeling. The forty-year old Graceful Tree Conjecture, due to Ringel and Kotzig, states that every tree is graceful.We prove a Substitution Theorem for graceful trees, which enables the construction of a larger graceful tree through combining smaller and not necessarily identical graceful trees. We present applications of the Substitution Theorem, which generalize earlier constructions combining smaller trees.     

Cooperative shear model for the rheology of glass-forming metallic liquids

A rheological law based on the concept of cooperatively sheared flow zones is presented, in which the effective thermodynamic state variable controlling flow is identified to be the isoconfigurational shear modulus of the liquid. The law captures Newtonian as well as non-Newtonian viscosity data for glass-forming metallic liquids over a broad range of fragility. Acoustic measurements on specimens deformed at a constant strain rate correlate well with the measured steady-state viscosities, hence verifying that viscosity has a unique functional relationship with the isoconfigurational shear modulus.