Microwave background constraints on inflationary parameters

We use a compilation of cosmic microwave anisotropy data (including the recent VSA, CBI and Archeops results), supplemented with an additional constraint on the expansion rate, to directly constrain the parameters of slow-roll inflation models. We find good agreement with other papers concerning the cosmological parameters, and display constraints on the power spectrum amplitude from inflation and the first two slow-roll parameters, finding in particular that $\epsilon_1 < 0.057$. The technique we use for parametrizing inflationary spectra may become essential once the data quality improves significantly.Comment: 6 pages LaTeX file with figures incorporated. Major revisions including incorporation of new datasets (CBI and Archeops). Slow-roll inflation module for use with the CAMB program can be found at http://astronomy.cpes.susx.ac.uk/~sleach/inflation

From the production of primordial perturbations to the end of inflation

In addition to generating the appropriate perturbation power spectrum, an inflationary scenario must take into account the need for inflation to end subsequently. In the context of single-field inflation models where inflation ends by breaking of the slow-roll condition, we constrain the first and second derivatives of the inflaton potential using this additional requirement. We compare this with current observational constraints from the primordial spectrum and discuss several issues relating to our results.Comment: RevTex4, 6 pages, 7 figures. To match version accepted by PR

Coarse-grained Interaction Potentials for Anisotropic Molecules

We have proposed an efficient parameterization method for a recent variant of the Gay-Berne potential for dissimilar and biaxial particles and demonstrated it for a set of small organic molecules. Compared to the previously proposed coarse-grained models, the new potential exhibits a superior performance in close contact and large distant interactions. The repercussions of thermal vibrations and elasticity has been studied through a statistical method. The study justifies that the potential of mean force is representable with the same functional form, extending the application of this coarse-grained description to a broader range of molecules. Moreover, the advantage of employing coarse-grained models over truncated atomistic summations with large distance cutoffs has been briefly studied.Comment: 8 pages, 4 tables and 6 figures. To appear in J. Chem. Phy

Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics

We analyse two classes of $(1+2)$ evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the $(1+2)$ Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a $(1+1)$ equation, the resulting equation is of maximal symmetry and so equivalent to the $(1+1)$ Classical Heat Equation.Comment: 15 pages, 1 figure, to be published in Mathematics in the Special issue "Mathematical Finance

The WMAP normalization of inflationary cosmologies

We use the three-year WMAP observations to determine the normalization of the matter power spectrum in inflationary cosmologies. In this context, the quantity of interest is not the normalization marginalized over all parameters, but rather the normalization as a function of the inflationary parameters n and r with marginalization over the remaining cosmological parameters. We compute this normalization and provide an accurate fitting function. The statistical uncertainty in the normalization is 3 percent, roughly half that achieved by COBE. We use the k-l relation for the standard cosmological model to identify the pivot scale for the WMAP normalization. We also quote the inflationary energy scale corresponding to the WMAP normalization.Comment: 4 pages RevTex4 with two figure

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Gender violence in schools: taking the ‘girls-as-victims’ discourse forward

This paper draws attention to the gendered nature of violence in schools. Recent recognition that schools can be violent places has tended to ignore the fact that many such acts originate in unequal and antagonistic gender relations, which are tolerated and ‘normalised’ by everyday school structures and processes. After examining some key concepts and definitions, we provide a brief overview of the scope and various manifestations of gender violence in schools, noting that most research to date has focused on girls as victims of gender violence within a heterosexual context and ignores other forms such as homophobic and girl violence. We then move on to look at a few interventions designed to address gender violence in schools in the developing world and end by highlighting the need for more research and improved understanding of the problem and how it can be addressed

Characterization of solar-grade silicon produced by the SiF4-Na process

A process was developed for producing low cost solar grade silicon by the reaction between SiF4 gas and sodium metal. The results of the characterization of the silicon are presented. These results include impurity levels, electronic properties of the silicon after crystal growth, and the performance of solar photovoltaic cells fabricated from wafers of the single crystals. The efficiency of the solar cells fabricated from semiconductor silicon and SiF4-Na silicon was the same