On the reducible character of Haldane-Radić enzyme kinetics to conventional and logistic Michaelis-Menten models

The conceptual and practical issues regarding the reduction of the Haldane-Radi? enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other classical conditions for such equivalence are not entirely fulfilled.     

DFT study of structure–properties correlations in [MnTPP][TCNE] quasi-one-dimensional molecular magnets

We report the first band structure calculations of the quasi-one-dimensional [MnTPP][TCNE] compounds (TPP = meso-tetraphenylporphyrinato, TCNE = tetracyanoethylene), based on Density Functional Theory (DFT) methods, in order to interpret the magnetic ordering in these prototypic systems. We compare and contrast the results of broken-symmetry DFT calculations for extended systems, with periodic boundary conditions, and for finite systems, magnetic dimers modeling the actual molecular magnets. By varying systematically the main angles, we are able to determine the geometry dependence of the exchange interaction. Structure–properties correlations in these charge-transfer salts reveal the determinant role of the Mn-(N≡C)_TCNE bond angle on the strength of the ferrimagnetic coupling between the S ₁ = 2 spin located on the Mn^III-porphyrin donor and the S ₂ = 1/2 spin positioned on the cyanocarbon acceptor. When the Mn-(N≡C)_TCNE angle is decreased, the intrachain magnetic coupling strengthens, correlated with the increase in the d_z² - p* d_{{z^{2} }} - \pi * orbital overlap. The exchange coupling constants resulting from DFT calculations of extended systems, with periodic boundary conditions, were found to be consistent with those obtained for the dimers, but systematically smaller. The exchange constants vary strongly with the functional used, hybrid functionals such as B3LYP leading to results that better correlate with the experimental mean-field critical temperatures. The coupling constant varies significantly with the type of broken-symmetry approach, depending on the overlap between magnetic orbitals, but weakly on the basis set once polarization effects are included. The electronic structure calculations for the extended systems provide a density of states consistent with the energy spectrum of the corresponding dimer, allowing for an intuitive explanation of the intrachain ferrimagnetic ordering.     

A material model for cementitious composite materials with an exterior point Eshelby microcrack initiation criterion

A micromechanical model for cementitious composite materials is described in which microcrack initiation, in the interfacial transition zone between aggregate particles and cement matrix, is governed by an exterior-point Eshelby solution. The model assumes a two-phase elastic composite, derived from an Eshelby solution and the Mori–Tanaka homogenization method, to which circular microcracks are added. A multi-component rough crack contact model is employed to simulate normal and shear behaviour of rough microcrack surfaces. The development of the microcrack initiation criterion and the rules adopted for microcrack evolution are a particular focus of the paper. Finally, it is shown, on the basis of several numerical simulations, that the model captures key characteristics of the behaviour of cementitious composites such as concrete.     

Rare earth doped cobalt ferrite thin films deposited by PLD

CoFe₂O₄ thin films with preferential texture structure, small grain size, and perpendicular magnetic anisotropy can be obtained by the pulsed laser deposition (PLD) technique. In this work, we studied the influence of the Fe³⁺ ions substitution by three elements from lanthanide group (Dy, La, and Gd) on the structural properties of the thin films. The samples were deposited by Nd:YAG laser (λ=532 nm, 10 ns) ablation of CoFe_1.8RE_0.2O₄, (RE=Dy, La, Gd) targets at various substrate temperatures ranging from room temperature to 600 °C. The microstructure and chemical composition of the thin films were investigated by Raman spectroscopy, XRD, SEM-EDS, and ToF-SIMS. The XRD patterns and Raman spectra of the thin films indicated the formation of a single spinel structure. Thus, the desired substitution of the iron ions in the spinel lattice with the RE elements was achieved in the thin films, although in the bulk material, their presence determined the formation of a residual phase with a perovskite-type structure.     

A visual proof of a result of Knuth on spanning trees of Aztec diamonds in the case of odd order

The even Aztec diamond AD_n is known to have precisely four times more spanning trees than the odd Aztec diamond OD_n—this was conjectured by Stanley and first proved by Knuth. We present a short combinatorial proof of this fact in the case of odd n. Our proof works also for the more general case of odd-by-odd Aztec rectangles.     

El Naschie’s ε space–time, hydrodynamic model of scale relativity theory and some applications

A generalization of the Nottale’s scale relativity theory is elaborated: the generalized Schrödinger equation results as an irrotational movement of Navier–Stokes type fluids having an imaginary viscosity coefficient. Then ψ simultaneously becomes wave-function and speed potential. In the hydrodynamic formulation of scale relativity theory, some implications in the gravitational morphogenesis of structures are analyzed: planetary motion quantizations, Saturn’s rings motion quantizations, redshift quantization in binary galaxies, global redshift quantization etc. The correspondence with El Naschie’s ε^(∞) space–time implies a special type of superconductivity (El Naschie’s superconductivity) and Cantorian-fractal sequences in the quantification of the Universe.     

On the classification of complex vector bundles of stable rank

One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle. Since deceased.     

The number of spanning trees of plane graphs with reflective symmetry

A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G.     

Studies on thermal degradation of acrylonitrile–butadiene–styrene copolymer (ABS-Br) containing brominated flame retardant

The thermal degradation of acrylonitrile-butadiene-styrene copolymer (ABS-Br; 10 g) containing brominated flame retardant (Br: 9.59 wt.%) was carried out at 450 °C using a semi batch operation using two different temperature programs. The heating rate was found to affect the quality of the degradation oil and yield of products (liquid, gas and residue). Data on the effect of the temperature program on the accumulation of liquid products was presented. It was found that the majority of the bromine was concentrated in the carbon residue and while majority of the nitrogen accumulates in the liquid products irrespective of degradation mode. The use of a one step constant heating rate process (I) produced a higher liquid yield (39%), than a two step process (29%). Differences were also noted in the Br and N contained in the liquids produced by the two processes.     

The vanishing neighbourhood of non-isolated singularities

We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles. For one-dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy via monodromies of nearby sections. Our standpoint allows one to find, in certain cases, the structure of the Milnor fibre up to the homotopy type.