Interlaced dense point and absolutely continuous spectra for Hamiltonians with concentric-shell singular interactions

We analyze the spectrum of the generalized Schrodinger operator in $L^2(R^\nu) \nu \geq 2$, with a general local, rotationally invariant singular interaction supported by an infinite family of concentric, equidistantly spaced spheres. It is shown that the essential spectrum consists of interlaced segments of the dense point and absolutely continuous character, and that the relation of their lengths at high energies depends on the choice of the interaction parameters; generically the p.p. component is asymptotically dominant. We also show that for $\nu=2$ there is an infinite family of eigenvalues below the lowest band.Comment: LaTeX, 18 page

On some strong ratio limit theorems for heat kernels

We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.Comment: 16 pages. This version coincides with the published one, except for Remark 4 added after the paper has appeare

Non-demolition measurements of observables with general spectra

It has recently been established that, in a non-demolition measurement of an observable $\mathcal{N}$ with a finite point spectrum, the density matrix of the system approaches an eigenstate of $\mathcal{N}$, i.e., it "purifies" over the spectrum of $\mathcal{N}$. We extend this result to observables with general spectra. It is shown that the spectral density of the state of the system converges to a delta function exponentially fast, in an appropriate sense. Furthermore, for observables with absolutely continuous spectra, we show that the spectral density approaches a Gaussian distribution over the spectrum of $\mathcal{N}$. Our methods highlight the connection between the theory of non-demolition measurements and classical estimation theory.Comment: 22 page

The effects of electron and proton radiation on GaSb infrared solar cells

Gallium antimonide (GaSb) infrared solar cells were exposed to 1 MeV electrons and protons up to fluences of 1 times 10(exp 15) cm (-2) and 1 times 10(exp 12) cm (-2) respectively. In between exposures, current voltage and spectral response curves were taken. The GaSb cells were found to degrade slightly less than typical GaAs cells under electron irradiation, and calculations from spectral response curves showed that the damage coefficient for the minority carrier diffusion length was 3.5 times 10(exp 8). The cells degraded faster than GaAs cells under proton irradiation. However, researchers expect the top cell and coverglass to protect the GaSb cell from most damaging protons. Some annealing of proton damage was observed at low temperatures (80 to 160 C)

Key results of the mini-dome Fresnel lens concentrator array development program under recently completed NASA and SDIO SBIR projects

Since 1986, ENTECH and the NASA Lewis Research Center have been developing a new photovoltaic concentrator system for space power applications. The unique refractive system uses small, dome shaped Fresnel lenses to focus sunlight onto high efficiency photovoltaic concentrator cells which use prismatic cell covers to further increase their performance. Highlights of the five-year development include near Air Mass Zero (AM0) Lear Jet flight testing of mini-dome lenses (90 pct. net optical efficiency achieved); tests verifying sun-pointing error tolerance with negligible power loss; simulator testing of prism-covered GaAs concentrator cells (24 pct. AM0 efficiency); testing of prism-covered Boeing GaAs/GaSb tandem cells (31 pct. AM0 efficiency); and fabrication and outdoor testing of a 36-lens/cell element panel. These test results have confirmed previous analytical predictions which indicate substantial performance improvements for this technology over current array systems. Based on program results to date, it appears than an array power density of 300 watts/sq m and a specific power of 100 watts/kg can be achieved in the near term. All components of the array appear to be readily manufacturable from space-durable materials at reasonable cost. A concise review is presented of the key results leading to the current array, and further development plans for the future are briefly discussed

On the critical exponent in an isoperimetric inequality for chords

The problem of maximizing the $L^p$ norms of chords connecting points on a closed curve separated by arclength $u$ arises in electrostatic and quantum--mechanical problems. It is known that among all closed curves of fixed length, the unique maximizing shape is the circle for $1 \le p \le 2$, but this is not the case for sufficiently large values of $p$. Here we determine the critical value $p_c(u)$ of $p$ above which the circle is not a local maximizer finding, in particular, that $p_c(\frac12 L)=\frac52$. This corrects a claim made in \cite{EHL}.Comment: LaTeX, 12 pages, with 1 eps figur