A Generalised Skolem-Mahler-lech Theorem for Affine Varieties

The Skolem–Mahler–Lech theorem states that if f(n)is a sequence given by a linear recurrence over a field of characteristic0, then the set of m such that f(m) is equal to 0 is the unionof a finite number of arithmetic progressions in m 0 and afinite set. We prove that if X is a subvariety of an affinevariety Y over a field of characteristic 0 and q is a pointin Y, and is an automorphism of Y, then the set of m such that^m(q) lies in X is a union of a finite number of complete doubly-infinitearithmetic progressions and a finite set. We show that thisis a generalisation of the Skolem–Mahler–Lech theorem.     

Modeling the concentration dependence of the methanol self-diffusivity in faujasite systems: comparison with the liquid phase

Molecular dynamics simulations were performed to understand further the concentration dependence of the self-diffusion of methanol in the faujasite zeolite systems. The evolution of the self-diffusivity was investigated as a function of coverage for DAY and NaY systems to study the effect of both the pore confinement and the presence of the extraframework cations within the supercage. It was found that the self-diffusivity decreases with loading for DAY, whereas for NaY it passes through a maximum at intermediate coverage, in agreement with pulse-field gradient NMR and quasi elastic neutron scattering data reported in similar systems. The activation energies of the methanol diffusion corresponding to a combination of both intra- and intercage motions were evaluated as a function of the coverage. The simulated trends are interpreted on the basis of the predominant interactions which take place in both systems. Finally, the preferential arrangement of the adsorbate molecules are provided and compared with those simulated in the liquid phase. For the fully loaded materials, it was seen that the methanol molecules form a one-dimensional hydrogen-bonded chain along the channels in DAY whereas only dimers are present in NaY.     

Cation migration upon adsorption of methanol in NaY and NaX faujasite systems: a molecular dynamics approach

Molecular dynamics simulations have been carried out to address the question of cation migration upon adsorption of methanol in NaY and NaX faujasite systems as a function of the loading. For NaY, it has been shown that, at low and intermediate loadings, SII cations can migrate toward the center of the supercage due to strong interactions with the adsorbates, followed by a hopping of SI' from the sodalite cage into the supercage to fill the vacant SII site. A SI' cation can also migrate across the double six ring and takes a SI' vacant position. SI cations mainly remain trapped in their initial sites whatever the loading. At high loading, only limited motions are observed for SII cations due to steric effects induced by the presence of adsorbates within the supercage. For NaX, the SIII' cations which occupy the most accessible adsorption sites are significantly moving upon coordination to the methanol molecules; the extent of this mobility exhibits a maximum for 48 methanol molecules per unit cell before decreasing at higher loadings due to steric hindrance. In addition, the SI' and SII cations remain almost trapped in their initial sites whatever the loading. Indeed, the most probable migration mechanism involves SIII' cation displacements into nearby SIII' sites.     

Two-dimensional crystal growth and stacking of bis(phthalocyaninato) rare earth sandwich complexes at the 1-phenyloctane/graphite interface

Initial stages of two-dimensional crystal growth of the double-decker sandwich complex Lu(Pc*)2 [Pc* = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato] have been studied by scanning tunneling microscopy at the liquid/solid interface between 1-phenyloctane and highly oriented pyrolytic graphite. High-resolution images strongly suggest alignment of the double-decker molecules into monolayers with the phthalocyanine rings parallel to the surface. Domains were observed with either hexagonal or quadrate packing motifs, and the growing interface of the layer was imaged. Molecular resolution was achieved, and the face of the phthalocyanine rings appeared as somewhat diffuse circular features. The alkyl chains are proposed to be interdigitating to maintain planar side-by-side packing.     

Phase Transitions in Chlorobenzene-Cis-Decalin Mixtures: A Nuclear Magnetic Resonance,Thermal Analysis and Phase Diagram Study

Using nuclear magnetic resonance and differential scanning calorimetry we have been able to observe the molecular rotation properties of chlorobenzene-cis-decalin mixtures in their glassy, amorphous and crystalline phases. The results indicate: that in “rapidly” cooled samples the behavior of the host dominates the properties of the mixtures; that reorientation of the guest molecule is less restricted in the amorphous phase than in the glassy phase; that when the material crystallizes from the amorphous phase on warming, reorientation again becomes severely restricted. The temperatures at which these phenomena occur agree with the phase diagram that has been determined for these materials. Similar experiments on t butyl chloride-cis-decalin mixtures support the above conclusions. These conclusions are in agreement with the previous dielectric studies.

Our magnetic resonance and thermal analysis experiments support the argument that the behavior of the CD host dominates the behavior of guest polar molecules in rapidly cooled mixtures. At the lowest temperature (110 K) CD forms a glassy phase unaccompanied by any heat of crystallization. On warming this glassy phase transforms near 150 K to an amorphous phase where considerable motion of both host and guest molecules occurs. Above 160 K the material crystallizes and reorientation is once again severely restricted up to the eutectic melting of 210 K. There appears to be no time dependence to these transformations and, as long as one stays below the crystallization temperature, the glassy-amorphous transition is reversible.     

The theory of nuclear matter

This article is an account of the present position of theories of nuclear matter initiated some years ago mainly by Jastrow and Brueckner. Section 1 introduces the basic ideas. Section 2 discusses the variational approach. Section 3 develops methods involving partial summations in perturbation theory. The difficulties confronting the latter approach, and their partial resolution by ideas from superconductivity theory, are analysed in § 4.

Much of the formalism is relevant also in the theory of individual nuclei (see for example the review by Eden 1959) and in fields other than nuclear physics (see for example The Many Body Problem, Les Houches, 1958). However, in the selection of material our criterion has been relevance for the ground state of nuclear matter.     

Extended Centres of Finitely Generated Prime Algebras

Let K be a field and let A be a finitely generated prime K-algebra. We generalize a result of Smith and Zhang, showing that if A is not PI and does not have a locally nilpotent ideal, then the extended centre of A has transcendence degree at most GKdim(A) ?2 over K. As a consequence, we are able to show that if A is a prime K-algebra of quadratic growth, then either the extended centre is algebraic over K or A is PI. Finally, we give an example of a finitely generated non-PI prime K-algebra of GK dimension 2 with a locally nilpotent ideal such that the extended centre has infinite transcendence degree over K.     

Comparison of the discriminating power of Raman and surface‐enhanced Raman spectroscopy with established techniques for the examination of liquid and gel inks

The ability to discriminate between inks is important for forensic document analysis. Here, Raman spectroscopy (RS) and surface‐enhanced RS have been compared to the traditional document examination techniques of video spectral comparison and thin layer chromatography on a population of blue and black‐coloured liquid and gel inks. It was found that in most cases, the Raman techniques provided a similar or better discriminating power than the conventional methods. Importantly, this study allowed us to determine whether the same underlying changes in composition were being exploited by the different methods to discriminate between samples. It was found that there was indeed a high degree of commonality in the sample pairs being discriminated by the various techniques. This work can therefore underpin introduction of Raman methods into standard operating procedures for ink analysis since it not only measures the extent of discrimination between samples but can also explain the origin of the spectral changes that are used to distinguish between them. © 2013 John Wiley & Sons Ltd and Crown copyright