Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to proof contained in pape

Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves

A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy transform approach to fields with nonanalytic behaviour on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (``dynamical'') monodromy data which evolve from data specified on the initial characteristics (the wavefronts).Comment: 4 pages, RevTe

Infrared astronomy

The role and contributions of Frank McDonald in extending high energy astrophysics to the sub-eV photon energy range (in putting infrared astronomy into orbit) are discussed

Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and of arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic initial value problem for solutions in the wave interaction region for which initial data are those associated with the approaching waves. We present also a general approach to the solution of this problem which enables us in principle to construct solutions in terms of the specified initial data. This is achieved by re-formulating the nonlinear dynamical equations for waves in terms of an associated linear problem on the spectral plane. A system of linear integral ``evolution'' equations which solve this spectral problem for specified initial data is constructed. It is then demonstrated explicitly how various colliding plane wave space-times can be constructed from given characteristic initial data.Comment: 33 pages, 3 figures, LaTeX. Accepted for publication in Classical and Quantum Gravit

Clustering of DIRBE Light and IR Background

We outline a new method for estimating the cosmic infrared background using the spatial and spectral correlation properties of infrared maps. The cosmic infrared background from galaxies should have a minimum fluctuation of the order of 10\% on angular scales of the order of 1\deg. We show that a linear combination of maps at different wavelengths can greatly reduce the fluctuations produced by foreground stars, while not eliminating the fluctuations of the background from high redshift galaxies. The method is potentially very powerful, especially at wavelengths where the foreground is bright but smooth.Comment: 7 pages postcript, talk at "Unveiling the cosmic infrared background" workshop, College Park, M

Maximal multihomogeneity of algebraic hypersurface singularities

From the degree zero part of logarithmic vector fields along an algebraic hypersurface singularity we indentify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one-to-one correspondence to maxmimal tori in the degree zero jet of the embedded automorphism group. The result is motivated by Kyoji Saito's characterization of quasihomogeneity for isolated hypersurface singularities and extends its formal version and a result of Hauser and Mueller.Comment: 5 page

Manufacturing with the Sun

Concentrated solar radiation is now a viable alternative source for many advanced manufacturing processes. Researchers at the National Renewable Energy Laboratory (NREL) have demonstrated the feasibility of processes such as solar induced surface transformation of materials (SISTM), solar based manufacturing, and solar pumped lasers. Researchers are also using sunlight to decontaminate water and soils polluted with organic compounds; these techniques could provide manufacturers with innovative alternatives to traditional methods of waste management. The solar technology that is now being integrated into today's manufacturing processes offer greater potential for tomorrow, especially as applied to the radiation abundant environment available in space and on the lunar surface

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

The Growing Mismatch Between Patient Longevity and the Service Life of Implantable Cardioverter-Defibrillators

Implantable cardioverter-defibrillators (ICDs) are lifesaving devices. Over 100,000 patients received ICDs in 2004 at a cost of $2 billion for the pulse generators alone. Because of expanded indications and coverage by Medicare, the number of ICD implantations and replacements is expected to increase dramatically during the next decade. The average ICD patient at our institution now lives nearly 10 years after the procedure. However, the service life of pulse generators has decreased from 4.7 ± 1 year for single-chamber units to 4.0 ± 1 year for dual-chamber devices. This mismatch between patient longevity and the service life of ICDs poses a significant clinical and economic burden that must be addressed. One near-term solution is for manufacturers to provide devices with larger batteries so that most patients can have an ICD pulse generator that lasts a lifetime. For the long-term, more robust or renewable energy sources are needed