Classification problems for shifts on modules over a principal ideal domain

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.

     

Mean Field Behaviour of Spin Systems with Orthogonal Interaction Matrix

For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the Curie–Weiss case.     

The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials I: Mellin Transform Techniques

The Fourier transform of orthogonal polynomials with respect to their own orthogonality measure defines the family of Fourier–Bessel functions. We study the asymptotic behaviour of these functions and of their products, for large real values of the argument. By employing a Mellin analysis we construct a general framework to exhibit the relation of the asymptotic decay laws to certain dimensions of the orthogonality measure, that are defined via the divergence abscissas of suitable integrals. The unifying r?le of Mellin transform techniques in deriving classical and new results is underlined. Submitted: November 5, 2004. Accepted: January 6, 2006.     

The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order ¹ and ⁰, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).     

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

Determination of fluquinconazole, pyrimethanil, and clofentezine residues in fruits by liquid chromatography with ultraviolet detection

A simple method was developed for the determination of fluquinconazole, pyrimethanil, and clofentezine in whole fruit; peel; and pulp of mango, apple, and papaya. These compounds were extracted from fruit samples with a mixture of ethyl acetate-n-hexane (1 + 1, v/v). An aliquot (2 mL) of the extract was evaporated to near dryness under a stream of nitrogen, and the residue was dissolved with 2 mL methanol. The analysis was performed by means of liquid chromatography with ultraviolet detection at 254 nm using a gradient solvent system. The method was validated with fortified fruit samples at concentration levels of 0.05, 0.10, 0.20, and 0.50 mg/kg. Average recoveries (4-8 replicates) ranged from 80 to 95% with relative standard deviations between 3.5 and 12.7%. Detection limits ranged from 0.03 to 0.05 mg/kg for fruit pulp and 0.03 mg/kg for whole fruit. The quantitation limits ranged from 0.05 to 0.10 mg/kg for fruit pulp and 0.05 mg/kg for whole fruit. The analytical method was applied to fruit samples obtained from local markets.     

Constitution moleculaire d'α,ω-difluoropolydimethylsiloxanes equilibres obtenus par une reaction de redistribution

α,ω-Difluoropolydimethylsiloxanes F[(CH₃)₂SiO]_n(CH₃)₂SiF have been prepared by reaction of (CH₃)₂SiF₂ with cyclic dimethylsiloxanes [(CH₃)₂SiO]_n (n = 3 or 4). An equilibrium is reached in the redistribution of fluorine vs. oxygen atoms after ca. 24 h at 200°C or 15 days at 150°C when catalysed by AlCl₃. 16 equilibrated samples of varied (R = F/Si) overall compositions have been analysed by ¹H and ¹⁹F NMR and by VPC. The presence of rings has been established for the lower values of R. The molecular constitution of the equilibrated samples is described by a set of constants. The abundance of the end units

is slightly larger than expected from random distribution. The good resolution of the spectra permits the distinguishing of the 9th order of environment of the end units and the 5th order for the middle units and the verification that there is no preferential association among the building units, and thus the proportion of chains of various lengths obeys Flory's random distribution mode. The equilibrium molecular constitution of these α,ω-difluorosiloxanes is close to that of their dichloro analogs; the substitution of chlorine by fluorine atoms at the end of the chains thus appears to cause little perturbation. On the other hand, the kinetic evolution of the reaction appears to be different, since the first species which forms is always the pyro molecule

instead of long chains and large rings as in the case of the chloro analogs.     

X-ray and mössbauer studies of tricyclohexyltin(IV) halides. The crystal structures of (cyclo-C6H11)3SnX (X = F,Br and I)

The structures of tricyclohexyltin fluoride (I), bromide (II) and iodide (III) have been determined by X-ray analysis. Compound I crystallizes in the space group P2₁/m with a = 10.422(6), b = 17.238(9), c = 5.769(3) Å, β = 104.6(1)° and Z = 2. Compounds II and III crystallize in the space group Pcmn with a = 10.427(6), b = 16.914(9), c = 11.366(6) Å, Z = 4; and a = 10.400(6), b = 16.900(10), c = 11.400(4) Å, Z = 4, respectively. All three structures consist of discrete tetrahedral (cyclo-C₆H₁₁)₃SnX units.The temperature dependence of the Mössbauer resonance areas has been examined in order to obtain information about the relationship between chemical structure and lattice dynamics.