Fractional Klein–Gordon Equations and Related Stochastic Processes

This paper presents finite-velocity random motions driven by fractional Klein–Gordon equations of order $\alpha \in (0,1]$ . A key tool in the analysis is played by the McBride’s theory which converts fractional hyper-Bessel operators into Erdélyi–Kober integral operators. Special attention is payed to the fractional telegraph process whose space-dependent distribution solves a non-homogeneous fractional Klein–Gordon equation. The distribution of the fractional telegraph process for $\alpha = 1$ coincides with that of the classical telegraph process and its driving equation converts into the homogeneous Klein–Gordon equation. Fractional planar random motions at finite velocity are also investigated, the corresponding distributions obtained as well as the explicit form of the governing equations. Fractionality is reflected into the underlying random motion because in each time interval a binomial number of deviations $B(n,\alpha )$ (with uniformly-distributed orientation) are considered. The parameter $n$ of $B(n,\alpha )$ is itself a random variable with fractional Poisson distribution, so that fractionality acts as a subsampling of the changes of direction. Finally the behaviour of each coordinate of the planar motion is examined and the corresponding densities obtained. Extensions to $N$ -dimensional fractional random flights are envisaged as well as the fractional counterpart of the Euler–Poisson–Darboux equation to which our theory applies.     

Nanoparticle microinjection and Raman spectroscopy as tools for nanotoxicology studies

Microinjection techniques and Raman spectroscopy have been combined to provide a new methodology to investigate the cytotoxic effects due to the interaction of nanomaterials with cells. In the present work, this novel technique has been used to investigate the effects of Ag and Fe(3)O(4) nanoparticles on Hela cells. The nanoparticles are microinjected inside the cells and these latter ones are probed by means of Raman spectroscopy after a short incubation time, in order to highlight the first and impulsive mechanisms developed by the cells to counteract the presence of the nanoparticles. The results put in evidence a different behaviour of the cells treated with nanoparticles in comparison with the control cells; these differences are supposed to be generated by an emerging oxidative stress due to the nanoparticles. The achieved results demonstrate the suitability of the proposed method as a new tool for nanotoxicity studies.     

1,10-(1-H-IMIDAZOL-5-YL)DECANEPHOSPHONIC ACID: A NEW COMPOUND WITH BASIC AND ACIDIC SITES TO FABRICATE PROTON-CONDUCTING SOLID ELECTROLYTES

2-(tert-butyldimethylsilyl)-5-(10-bromodecyl)-1-(N,N-dimethylsulfamoyl)-imidazole and NaPO₃ Et₂ react at room temperature to yield the corresponding imidazole diethyl phosphonate, which when refluxed with concentrated HBr yields 1,10-(1-H-imidazol-5-yl)decanephosphonic acid hydrobromide (VI). Compound VI titrated with the required mole equivalents of NaOH yields 1,10-(1-H-imidazol-5-yl)decanephosphonic acid (VII) and 1,10-(1-H-imidazol-5-yl)decane (sodium)phosphonates (VIII). CP-MAS NMR (¹³C, ³¹P, and ¹⁵N) and IR spectroscopy indicate that only compound VII is likely to yield a polymeric structure where each phosphonic acid group is H bonded to the imidazole ring of the same molecule and to the imidazole ring of another molecule. For this reason, solid-state proton conductivity in VII is likely to be favored.     

Multiscale entanglement in ring polymers under spherical confinement

The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated by using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length l(k) depends on the ring contour length L(c) and the radius of the confining sphere R(c). In the no- and strong-confinement cases, we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of l(k), L(c), and R(c) that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.     

Preparation of N-Alkylphtalimides Assisted by Solid-Liquid Phase-Transfer Systems

N-Alkylphtalimides are intermediates in the synthesis of primary amines¹ and are generally prepared from potassium phtalimide and alkyl halides in anhydrous polar aprotic solvents such as dimethylformamide.² Recently, N-alkylation of potassium phtalimide has been achieved from alkyl halides and methanesulfonates in toluene in the presence of hexadecyltributylphosphonium bromide³.     

Assembled systems [X-azolopyridine][quinoline]. Bases and salts

A series of bases containing X-azolopyridines (X = O, NH) and methylquinolines, assembled in different ways, was prepared by reaction of methylquinolinecarboxylic acids (or carboxamides) with diamino (or hydroxyamino) pyridines. The bases were quaternized with methyl iodide. The physical and spectroscopic data of both the bases and the salts were correlated and compared with those of [X-azolopyridine][pyridine] systems previously studied. The structure of the salts was markedly influenced by a balance of basicity-hindrance factors in the heteroaromatic substrates.     

Some universal limits for nonhomogeneous birth and death processes

In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X(t), t≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration of the BDP). We find conditions of existence of the means and determine bounds for their values, involving also the truncated BDP X_N. Finally we present some examples where these bounds are used in order to approximate the double mean. AMS Subject Classification: Primary: 60J27 Secondary: 60K25 34A30     

Fast deprotection of phenoxy benzyl ethers in transfer hydrogenation assisted by microwave

Phenoxy benzyl ethers are easily and quickly deprotected in the presence of ammonium formate and microencapsulated Pd(0)EnCat with the assistance of microwave irradiation. This procedure can be applied in the presence of other functional groups as well. The described protocol is particularly convenient for the preparation in a parallel and automatic fashion of libraries of compounds possessing a phenol type moiety.     

Advances in the structure and microstructure determination of yttrium silicates using the Rietveld method

The Y₂O₃-SiO₂ 1:1 composition doped with a weak concentration of europium ions was prepared with the sol-gel technique and the products studied by X-ray diffraction as a function of temperature in the range from 900 to 1300 °C, using the method of Rietveld for quantitative evaluation of amorphous and crystalline evolving phases. The amorphous profile of the yttrium oxyorthosilicate glasses has been described following the “Rietveld for Disordered Materials” method and subsequently included in the patterns of semicrystalline samples that have been heat-treated for temperatures above 900 °C at 1000, 1100, 1150, 1200 and 1300 °C. The quantitative evaluation of the amorphous phase is obtainable from the Rietveld approach equivalent to the method after Ruland. This enabled us to study in fine detail the structural rearrangements and growth mechanisms that take place during the crystal-to-amorphous transformation in terms of coordination numbers, average interatomic distances, average crystallite size and microstrain and to identify the polymorphous transformation involving the Y₂SiO₅ phase from low-to-high-temperature forms, as well as some minor quantities of other phases namely α-Y₂Si₂O₇ phase, Y₂O₃ and Y_4.67(SiO₄)₃O.