Approximating Time to Extinction for Endemic Infection Models

Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterise their performance in terms of simplicity, accuracy, and generality. To this end, we consider first the classic stochastic susceptible-infected-susceptible (SIS) model, and then a multi-dimensional generalisation of this which allows for Erlang distributed infectious periods. We find that (i) for a below-threshold infection initiated by a small number of infected individuals, approximation via a linear branching process works well; (ii) for an above-threshold infection initiated at endemic equilibrium, methods from Hamiltonian statistical mechanics yield correct asymptotic behaviour as population size becomes large; (iii) the widely-used Ornstein-Uhlenbeck diffusion approximation gives a very poor approximation, but may retain some value for qualitative comparisons in certain cases; (iv) a more detailed diffusion approximation can give good numerical approximation in certain circumstances, but does not provide correct large population asymptotic behaviour, and cannot be relied upon without some form of external validation (eg simulation studies).     

Effect of counterions on the interactions of charged oligothiophenes

The functionality of conjugated polymer systems often relies on oxidations or reductions, in most cases mediated by the presence of counterions. The effect that the common counterion hexafluorophosphate (PF6-) has on the intermolecular interactions between charged oligothiophenes is investigated here using ab initio quantum chemistry methods. Counterions are explicitly included in the simulations of oxidized oligothiophenes and in the dimerization process. Our calculations provide quantitative and qualitative insight into the intermolecular interactions in oligothiophene-counterion systems and show that the intermolecular pi-stacking of oligothiophenes is not adversely affected by the presence of counterions and that in fact oligothiophene dimerization is further stabilized by their presence.     

Cis and trans selective 1,4-addition of a lithium dithioester enolate to 4-O-TBS-2-cyclohexenone

The 1,4-addition of the lithium enolate of methyldithioacetate (LMDTA) to (+/-)-4-O-TBS-2-cyclohexenone (3) can be varied from being highly 3,4-trans selective to being highly 3,4-cis selective simply by varying the reaction temperature. This stereodivergency allows expedient syntheses of the corresponding trans and cis methyl esters 6t and 6c and derived bicyclic ketolactones 7t and 7c.     

A new class of generalized close-to-starlike functions defined by the Srivastava-Attiya operator

In this paper, we consider a new class CS*s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function Φ(z, s, a). Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.     

Influence of terbium on structure and luminescence of nanocrystalline TiO2 thin films

In this work analysis of the structural and optical properties of TiO₂ thin films doped with terbium has been described. Samples were prepared by a high energy reactive magnetron sputtering process under low pressure of oxygen plasma. X-ray diffraction results have shown that different TiO₂ crystal forms have been produced, depending on the amount of Tb dopant. The undoped matrix had rutile structure with crystallites with a size of 8.7 nm, while incorporation of 0.4 at. % of Tb into the film during the sputtering process resulted in anatase structure with bigger crystallites (11.7 nm). Increasing the amount of terbium up to 2 at. % and 2.6 at. % gave rutile structure with crystallites with a size of 6.6 nm for both films. However, Raman spectroscopy has revealed that in the case of TiO₂:(2 at. % Tb), except for the rutile form, the presence of fine-crystalline anatase was observed. Moreover, the lack of Raman peaks shift attests to the lack of stress in the titania lattice of all of the TiO₂:Tb films. This fact indicates localization of Tb3+ ions on the surface of TiO₂ nanocrystals. In the case of optical investigation, results have shown that doping with terbium has a significant influence on the properties of TiO₂, but it does not decrease the high transparency of the matrix. The observed changes of the transmission characteristics were produced only due to modification of the TiO₂:Tb structure. Photoluminescence measurements have shown that emission of light from TiO₂:Tb films occurs when the amount of terbium is 2.6 at. %. Based on the obtained results a scheme of direct energy transfer from titanium dioxide matrix (with rutile structure) to Tb³⁺ ions has been proposed.     

Colloidal liquid crystal type assemblies of spheroidal polystyrene core/polyglycidol‐rich shell particles (P[S/PGL]) formed at the liquid‐silicon‐air interface by a directed dewetting process

A method for the preparation of stripe‐like monolayers of microspheroids is described. The particles were obtained from polystyrene core/polyglycidol‐rich shell microspheres by stretching poly (vinyl alcohol) films that contain embedded particles. The stretching was performed under controlled conditions at temperatures above the T_g of the films and particles. The elongated films were dissolved in water, and the microspheroids were subsequently removed and purified from the poly (vinyl alcohol). The aspect ratio (AR) of the particles, which denotes the ratio of the lengths of the longer to shorter particle axes, was determined by the film elongation. The AR values were in the range of 2.9‐7.7. Spheroidal particles with various ARs were deposited onto silicon wafers from an ethanol (EtOH) suspension. The particle concentration and volume of the suspension were the same in each experiment. Evaporation of the EtOH yielded stripes of spherical particles packed into nematic‐type colloidal crystals and assembled into monolayers. The orientation of the stripes after ethanol evaporation was perpendicular to the triphasic (silicon‐ethanol‐air) interface along the silicon substrate. The adsorbed stripes on the wafers were characterized in terms of their interstripe distance (ID), stripe width, and crystal domain size. Nematic‐type spheroid arrangements in the stripes were the dominant structure, which enabled denser packing of the particles into colloidal crystals than that allowed by the smectic‐type arrangements. Furthermore, the number of spheroids adsorbed per surface unit of the silicon wafers was similar for all ARs, but the width and frequency of the spheroid stripes adsorbed on the wafers were different.     

No‐go result for supersymmetric gauge theories in the causal approach

We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non‐Abelian gauge theory (SUSY‐QCD) is uniquely determined by some natural assumptions, as in the case of Yang‐Mills models. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.     

Vortex locking in direct numerical simulations of quantum turbulence

Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.     

In a Quest for Selectivity Paired with Activity: A Ruthenium Olefin Metathesis Catalyst Bearing an Unsymmetrical Phenanthrene-Based N-Heterocyclic Carbene

Robust, selective, and stable in the presence of ethylene, ruthenium olefin metathesis pre-catalyst, {[3-benzyl-1-(10-phenyl-9-phenanthryl)]-2-imidazolidinylidene}dichloro(o-isopropoxyphenylmethylene)ruthenium(II), Ru-3 , bearing an unsymetrical N-heterocyclic carbene (uNHC) ligand, has been synthesized. The initiation rate of Ru-3 was examined by ring-closing metathesis and cross-metathesis reactions with a broad spectrum of olefins, showing an unprecendented selectivity. It was also tested in industrially relevant ethenolysis reactions of olefinic substrates from renewable feedstock with very good yields and selectivities.     

Smectic behaviour of methyl 4-alkoxybenzoates with a partially fluorinated alkyl chain

A series of 4-alkoxybenzoic acids 1[m,n] and their methyl esters 2[m,n] containing a partially fluorinated alkyl chain was prepared and their physical properties were investigated by optical, thermal and powder X-ray diffraction (XRD) methods. The former exhibits an SmC phase, while the latter form an SmA phase. XRD analysis indicated liquid-like character of the linking alkyl chains, and showed a decreasing layer thermal expansion coefficient from positive to negative upon increasing the degree of fluorination. The new esters 2[m,n] expanded the series and permitted analysis of trends in thermal stability of the SmA phase. The results demonstrate that the SmA–I transition temperature increases by about +20 K per CF₂CF₂ unit, and is destabilised by –5.6 K upon extending the hydrocarbon part by each CH₂CH₂ group. Data for the expanded series 2[m,n] were used for comparative analysis of mesogenic behaviour in two other series of derivatives of 1[m,n]. Synthetic methods for 1[m,n] and 2[m,n] are reviewed.