Non-Local Matrix Generalizations of W-Algebras

There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinary linear differential operators of order $m$, $L = -d^m + U_1 d^{m-1} + U_2 d^{m-2} + \ldots + U_m$. In this paper, I consider in detail the case where the $U_k$ are $n\times n$-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifold $U_1=0$. This reduction gives rise to matrix generalizations of (the classical version of) the {\it non-linear} $W_m$-algebras, called $V_{m,n}$-algebras. The non-commutativity of the matrices leads to {\it non-local} terms in these $V_{m,n}$-algebras. I show that these algebras contain a conformal Virasoro subalgebra and that combinations $W_k$ of the $U_k$ can be formed that are $n\times n$-matrices of conformally primary fields of spin $k$, in analogy with the scalar case $n=1$. In general however, the $V_{m,n}$-algebras have a much richer structure than the $W_m$-algebras as can be seen on the examples of the {\it non-linear} and {\it non-local} Poisson brackets of any two matrix elements of $U_2$ or $W_3$ which I work out explicitly for all $m$ and $n$. A matrix Miura transformation is derived, mapping these complicated second Gelfand-Dikii brackets of the $U_k$ to a set of much simpler Poisson brackets, providing the analogue of the free-field realization of the $W_m$-algebras.Comment: 43 pages, a reference and a remark on the conformal properties for $U_1\ne 0$ adde

Disposable clean delivery kits and prevention of neonatal tetanus in the presence of skilled birth attendants.

OBJECTIVE: To determine whether the use of disposable clean delivery kits (CDKs) is effective in reducing neonatal tetanus (NNT) infection, regardless of the skills of birth attendants in resource-poor settings. METHODS: A secondary analysis was conducted on data from a matched case-control study in Karachi, Pakistan, involving 140 NNT cases and 280 controls between 1998 and 2001. Conditional logistic regression was performed to assess the independent effect on NNT of CDKs and skilled birth attendants (SBAs). RESULTS: After adjustment for socioeconomic factors, both CDKs (adjusted matched odds ratio [mOR] 2.0; 95% confidence interval [CI], 1.3-3.1) and SBAs (adjusted mOR 1.7; 95% CI, 1.1-2.7) were independently associated with NNT. The association with CDKs remained significant when additionally adjusted for SBAs (mOR 2.0; 95% CI, 1.0-3.9; P=0.05). The population attributable risk for lack of CDK use was 24% in the study setting. CONCLUSION: In the context of resource-poor settings in low-income countries with poor coverage of tetanus toxoid immunization, the use of CDKs seems to be an effective strategy for reducing NNT infection, irrespective of the skill levels of birth attendants. Approximately one-quarter of NNT cases could be prevented in low-income populations with the use of CDKs

Supersymmetric non-abelian Born-Infeld revisited

We determine the non-abelian Born-Infeld action, including fermions, as it results from the four-point tree-level open superstring scattering amplitudes at order alpha'^2. We find that, after an appropriate field redefinition all terms at this order can be written as a symmetrised trace. We confront this action with the results that follow from kappa-symmetry and conclude that the recently proposed non-abelian kappa-symmetry cannot be extended to cubic orders in the Born-Infeld curvature.Comment: 26 pages, Late

Real decoupling ghost quantization of the CGHS model for two dimensional black holes

A complete RST quantization of a CGHS model plus Strominger term is carried out. In so doing a conformal invariant theory with $\kappa=\frac{N}{12}$ is found, that is, without ghosts contribution. The physical consequences of the model are analysed and positive definite Hawking radiation is found.Comment: 14 pages, latex, no figures, marginal errors correcte

Multi-Component KdV Hierarchy, V-Algebra and Non-Abelian Toda Theory

I prove the recently conjectured relation between the $2\times 2$-matrix differential operator $L=\partial^2-U$, and a certain non-linear and non-local Poisson bracket algebra ($V$-algebra), containing a Virasoro subalgebra, which appeared in the study of a non-abelian Toda field theory. Here, I show that this $V$-algebra is precisely given by the second Gelfand-Dikii bracket associated with $L$. The Miura transformation is given which relates the second to the first Gelfand-Dikii bracket. The two Gelfand-Dikii brackets are also obtained from the associated (integro-) differential equation satisfied by fermion bilinears. The asymptotic expansion of the resolvent of $(L-\xi)\Psi=0$ is studied and its coefficients $R_l$ yield an infinite sequence of hamiltonians with mutually vanishing Poisson brackets. I recall how this leads to a matrix KdV hierarchy which are flow equations for the three component fields $T, V^+, V^-$ of $U$. For $V^\pm=0$ they reduce to the ordinary KdV hierarchy. The corresponding matrix mKdV equations are also given, as well as the relation to the pseudo- differential operator approach. Most of the results continue to hold if $U$ is a hermitian $n\times n$-matrix. Conjectures are made about $n\times n$-matrix $m^{\rm th}$-order differential operators $L$ and associated $V_{(n,m)}$-algebras.Comment: 20 pages, revised: several references to earlier papers on multi-component KdV equations are adde

Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes

We perform a canonical analysis of the system of 2d vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions which have been made by other authors. We present a careful discssion of asymptotics in this canonical formalism. Canonical transformations are made to variables which (on shell) have a clear spacetime significance. We are able to deduce the location of the horizon on the spatial slice (on shell) from the vanishing of a combination of canonical data. The constraints dramatically simplify in terms of the new canonical variables and quantization is easy. The physical interpretation of the variable conjugate to the ADM mass is clarified. This work closely parallels that done by Kucha{\v r} for the vacuum Schwarzschild black holes and is a starting point for a similar analysis, now in progress, for the case of a massless scalar field conformally coupled to a 2d dilatonic black hole.Comment: 21 pages, latex fil

Technological impact on the art of moviemaking: deploying new and convergent media to redefine a model for Pakistan’s cinema

This thesis examines the decline in Pakistani cinema during the last two decades. It examines the history of the cinema and exposes some possible, previously ignored, causes for that decline. This research led the author to ask “Can new and convergent media be helpful in reviving the Pakistani cinema?” The thesis introduces the ideas of established and emergent cinema, building on the work of Williams (1977) in discussing the ideas of dominant, residual and emergent culture. The exploration reveals two gaps in the film industry: first, the lack of training in the making of films; and, second, the change in possible production methods allowed by new and emergent technologies. The thesis addresses both of these gaps by suggesting new production paradigms which incorporate the new technology and by examining two scripts to develop methodologies for teaching. The scripts are produced into films as the practice section of the research. The first film, creative element 1, is developed using some of the new tehnologies, students as crew and the available resources of an educational establishment to test the methodologies that have been derived. The outcomes of the creative element 1 laid the foundation of the second film, creative element 2. It is shot on mobile phones and distributed from Pakistan through Vimeo with a negligible budget. The social networks helped to arrange equipment and locations and allowed extreme freedom to the filmmaker

Dynamics and Sustainability of Livestock Sector in Jammu & Kashmir

Agricultural and Food Policy,