Dynamics of Robertson–Walker spacetimes with diffusion

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.     

THE CRYSTAL AND MOLECULAR STRUCTURE OF THE POTENTIAL ANTIBACTERIAL AGENT 2-PYRIDYL-PHENYL SULPHONE

Abstract

Crystals of 2-pyridyl-phenyl sulphone are monoclinic, space group P2₁/c, with eight molecules in the unit cell of dimensions a = 11.781, b = 5.903, c = 29.748 Å and B = 94.13°. The dihedral angles between the best planes of the two aromatic rings are significantly different in two crystallographically independent molecules (88.4° and 71.9° for molecule A and molecule B, respectively), as well as those between the CSC plane and the pyridine ring (59.4° and 67.4°) and between the CSC plane and the phenyl ring (51.7° and 81.8°). The average bond distances of interest include C?S 1.77(1) and S?O 1.44(1) Å; among the bond angles there are CSO = 108.1(7), CSC = 105.0(6) and OSO = 118.7(6)°. The packing of the molecule in the crystal is determined by the van der Waals interactions and by two intermolecular H?O contacts of 2.43 and 2.49 Å. The observed conformation in the solid state agrees well with results of previous investigations, in the solution state, by means of dipole moment method and theoretical M.O. calculations, for the analogous di-2-pyridyl sulphone.     

A characterization of wavelets on general lattices

In the context of a general lattice Γ in Rⁿ and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families. This result generalizes the characterization of Frazier, Garrigós, Wang, and Weis about the wavelet families with Γ = Zⁿ and M = 21. In the second part of the paper, we characterize all the MSF wavelets. Moreover, we give a constructive method for the support of the Fourier transform of an MSF wavelet and apply this method by giving examples with particular attention to the quincunx lattice.     

<Emphasis Type="Italic">ϕ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a contractive condition, called ϕ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for ϕ-pairs. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Best proximity points for cyclic Meir–Keeler contractions

We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.     

On a stochastic disease model with vaccination

We propose a stochastic disease model where vaccination is included and such that the immunity isn’t permanent. The existence, uniqueness and positivity of the solution and the stability of disease free equilibrium is studied. The numerical simulation is done.     

Control of degradation of polypropylene during its radical functionalisation with furan and thiophene derivatives

The traditional melt radical functionalisation of isotactic polypropylene (iPP) with maleic anhydride (MAH) and peroxide affords functionalized samples with a severe decrease of the average molecular weight (MW) due to the β-scission reaction. In this work new push-pull unsaturated molecules were investigated, consisting of a heterocyclic ring conjugated with a double bond bearing an electron attracting group. These molecules were specifically designed as MAH substitute able to limit the iPP degradation, while providing functionalisation through grafting. Butyl 3-(2-furanyl) propenoate (BFA) and butyl 3-(2-thienyl) propenoate (BTA) were comparatively tested. The analysis of the reaction products indicated that both molecules are able to graft onto the iPP backbone by prompt reaction with the macro-radicals formed through H-abstraction from iPP chains, thereby significantly limiting the MW decrease, as the functionalized macro-radicals are stabilized by resonance. Nonetheless, some of iPP macro-radicals can give a parallel chain scission before reacting with the new molecules. In the case of BFA, coupling reactions of the formed macro-radicals can lead to the formation of branched high MW architectures, whereas in the case of the thiophene derivative (BTA) only a partial retaining of polymer chain fragmentation was observed due to the reduction of β-scission.     

Polyaspartamide-graft-polymethacrylate nanoparticles for doxorubicin delivery

A new PHEA‐IB‐PMANa⁺ copolymer has been synthesized and its pH‐induced self‐assembly has been investigated in an aqueous medium. PHEA‐IB‐PMANa⁺ formed nanoparticles with diameters from 25 to 50 nm upon protonation of the carboxylic acid moieties dislocated along the grafted polymethacrylate sodium salt side chains. The physico‐chemical characterization of the nanoparticles was performed using light scattering, zeta‐potential measurements, SEM, and AFM. Doxorubicin‐loaded nanoparticles were prepared and drug release profiles were evaluated under conditions mimicking physiological media. A biological characterization was carried out by testing the cytotoxicity on Caco‐2 cells, and cellular uptake on mouse monocyte macrophage (J774 A.1) and Caco‐2 cells.