Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory

We consider the question of determining the maximum number of $\mathbb{F}_q$-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field $\mathbb{F}_q$, or in other words, the maximum number of zeros that a weighted homogeneous polynomial of a given degree can have in the corresponding weighted projective space over $\mathbb{F}_q$. In the case of classical projective spaces, this question has been answered by J.-P. Serre. In the case of weighted projective spaces, we give some conjectures and partial results. Applications to coding theory are included and an appendix providing a brief compendium of results about weighted projective spaces is also included

Covalent bonding and the nature of band gaps in some half-Heusler compounds

Half-Heusler compounds \textit{XYZ}, also called semi-Heusler compounds, crystallize in the MgAgAs structure, in the space group $F\bar43m$. We report a systematic examination of band gaps and the nature (covalent or ionic) of bonding in semiconducting 8- and 18- electron half-Heusler compounds through first-principles density functional calculations. We find the most appropriate description of these compounds from the viewpoint of electronic structures is one of a \textit{YZ} zinc blende lattice stuffed by the \textit{X} ion. Simple valence rules are obeyed for bonding in the 8-electron compound. For example, LiMgN can be written Li$^+$ + (MgN)$^-$, and (MgN)$^-$, which is isoelectronic with (SiSi), forms a zinc blende lattice. The 18-electron compounds can similarly be considered as obeying valence rules. A semiconductor such as TiCoSb can be written Ti$^{4+}$ + (CoSb)$^{4-}$; the latter unit is isoelectronic and isostructural with zinc-blende GaSb. For both the 8- and 18-electron compounds, when \textit{X} is fixed as some electropositive cation, the computed band gap varies approximately as the difference in Pauling electronegativities of \textit{Y} and \textit{Z}. What is particularly exciting is that this simple idea of a covalently bonded \textit{YZ} lattice can also be extended to the very important \textit{magnetic} half-Heusler phases; we describe these as valence compounds \textit{ie.} possessing a band gap at the Fermi energy albeit only in one spin direction. The \textit{local} moment in these magnetic compounds resides on the \textit{X} site.Comment: 18 pages and 14 figures (many in color

Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order

Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted with respect to the smectic layer normal. As in the previous papers of the series (Phys. Rev. A {\bf 45}, 974 (1992), E {\bf 49}, 501, (1994)) the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalised spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. The density of this effective isotropic liquid depends on the nature and amount of ordering present in the system and is evaluated self- consistently. We estimate the value of elastic constants using reasonable guess for the order and structural- parameters.Comment: 31 pages; 1 Fig. in GIF format, To be appear in Phys. Rev.

Understanding complex magnetic order in disordered cobalt hydroxides through analysis of the local structure

In many ostensibly crystalline materials, unit-cell-based descriptions do not always capture the complete physics of the system due to disruption in long-range order. In the series of cobalt hydroxides studied here, Co(OH)$_{2-x}$(Cl)$_x$(H$_2$O)$_{n}$, magnetic Bragg diffraction reveals a fully compensated N\'eel state, yet the materials show significant and open magnetization loops. A detailed analysis of the local structure defines the aperiodic arrangement of cobalt coordination polyhedra. Representation of the structure as a combination of distinct polyhedral motifs explains the existence of locally uncompensated moments and provides a quantitative agreement with bulk magnetic measurements and magnetic Bragg diffraction

Molluscicidal effect of biogenic silica and botanical pesticides for the control of Achatina fulica (giant African land snail) and Laevicaulis alte (garden slug)

The molluscicidal effect of silica synthesized from rice husk ash (RHA) on snails (Achatina fulica Bowdich) and slugs (Laevicaulis alte Férussac) was assessed under laboratory conditions. The silica particles derived from RHA were also coated with leaf extracts (botanical pesticides): Azadirachta indica A. Juss, Pongamia pinnata (L.), Nicotiana tabacum (L.), and Calotropis procera (L.). The silica coated with plant extracts and the uncoated silica were applied to the molluscs in dust or slurry form. Inactivation, mortality, and body fluid loss in A. fulica and L. alte were observed over 24 h and recorded. The body fluid losses were 25%–42% for snails and 37%–62% for slugs that had been dusted with silica. During the experiment it was also noted that as the concentration of silica increased (0.15, 0.20, and 0.25 g), the time required for inactivation and mortality was reduced. The dust application was more effective than the slurry. The lower concentration of silica in the slurry (0.05 and 0.10 g) did not have any significant effect on A. fulica or L. alte. For A. fulica the biopesticide-coated silica particles were more effective when coated with neem, followed by tobacco and karanj; for L. alte, the particles were most effective when coated with tobacco, followed by neem and karanj. The plant extract (liquid as well as dry powder) without silica showed no molluscicidal effect on A. fulica and L. alte, except for some temporary inactivation, particularly with tobacco extract. The application of common salt, a practice often used by farmers, was also tested. It was observed that the effects of common salt on A. fulica and L. alte were less significant than those of silica coated with botanical pesticides.

Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Absence of ferromagnetism in Co and Mn substituted polycrystalline ZnO

We discuss the properties of semiconducting bulk ZnO when substituted with the magnetic transition metal ions Mn and Co, with substituent fraction ranging from $x$ = 0.02 to $x$ = 0.15. The magnetic properties were measured as a function of magnetic field and temperature and we find no evidence for magnetic ordering in these systems down to $T$ = 2 K. The magnetization can be fit by the sum of a Curie-Weiss term with a Weiss temperature of $\Theta\gg$100 K and a Curie term. We attribute this behavior to contributions from both \textit{t}M ions with \textit{t}M nearest neighbors and from isolated spins. This particular functional form for the susceptibility is used to explain why no ordering is observed in \textit{t}M substituted ZnO samples despite the large values of the Weiss temperature. We also discuss in detail the methods we used to minimize any impurity contributions to the magnetic signal.Comment: 6 pages, 4 figures (revised