On Sharp Constants for Dual Segal--Bargmann LpL^p Spaces

We study dilated holomorphic $L^p$ space of Gaussian measures over $\mathbb{C}^n$, denoted $\mathcal{H}_{p,\alpha}^n$ with variance scaling parameter $\alpha>0$. The duality relations $(\mathcal{H}_{p,\alpha}^n)^\ast \cong \mathcal{H}_{p',\alpha}$ hold with $\frac{1}{p}+\frac{1}{p'}=1$, but not isometrically. We identify the sharp lower constant comparing the norms on $\mathcal{H}_{p',\alpha}$ and $(\mathcal{H}_{p,\alpha}^n)^\ast$, and provide upper and lower bounds on the sharp upper constant. We prove several suggestive partial results on the sharpness of the upper constant. One of these partial results leads to a sharp bound on each Taylor coefficient of a function in the Fock space for $n=1$

Duality in Segal-Bargmann Spaces

For $\alpha>0$, the Bargmann projection $P_\alpha$ is the orthogonal projection from $L^2(\gamma_\alpha)$ onto the holomorphic subspace $L^2_{hol}(\gamma_\alpha)$, where $\gamma_\alpha$ is the standard Gaussian probability measure on \C^n with variance $(2\alpha)^{-n}$. The space $L^2_{hol}(\gamma_\alpha)$ is classically known as the Segal-Bargmann space. We show that $P_\alpha$ extends to a bounded operator on $L^p(\gamma_{\alpha p/2})$, and calculate the exact norm of this scaled $L^p$ Bargmann projection. We use this to show that the dual space of the $L^p$-Segal-Bargmann space $L^p_{hol}(\gamma_{\alpha p/2})$ is an $L^{p'}$ Segal-Bargmann space, but with the Gaussian measure scaled differently: $(L^p_{hol}(\gamma_{\alpha p/2}))^* \cong L^{p'}_{hol}(\gamma_{\alpha p'/2})$ (this was shown originally by Janson, Peetre, and Rochberg). We show that the Bargmann projection controls this dual isomorphism, and gives a dimension-independent estimate on one of the two constants of equivalence of the norms.Comment: 24 page

Electrostatic propulsion beam divergence effects on spacecraft surfaces, volume 3

Tests were conducted to determine the effects of electrostatic propulsion beam divergence effects on spacecraft surfaces. The subjects discussed are: (1) sensitive surfaces on the ATS 6 spacecraft, (2) the cesium ion source and testing facility, (3) cesium ion effects on thermophysical properties, and (4) simulated charge-exchange ion exposure. The compatibility of the ATS 6 ion engine experiment with the engineering subsystems and other experiments aboard the ATS 6 spacecraft was analyzed

Is there a universality of the helix-coil transition in protein models?

The similarity in the thermodynamic properties of two completely different theoretical models for the helix-coil transition is examined critically. The first model is an all-atomic representation for a poly-alanine chain, while the second model is a minimal helix-forming model that contains no system specifics. Key characteristics of the helix-coil transition, in particular, the effective critical exponents of these two models agree with each other, within a finite-size scaling analysis.Comment: Latex, to appear in Eur. Phys. J.

GAELS Project Final Report: Information environment for engineering

The GAELS project was a collaboration commenced in 1999 between Glasgow University Library and Strathclyde University Library with two main aims:· to develop collaborative information services in support of engineering research at the Universities of Glasgow and Strathclyde· to develop a CAL (computer-aided learning package) package in advanced information skills for engineering research students and staff The project was funded by the Scottish Higher Education Funding Council (SHEFC) from their Strategic Change Initiative funding stream, and funding was awarded initially for one year, with an extension of the grant for a further year. The project ended in June 2001.The funding from SHEFC paid for two research assistants, one based at Glasgow University Library working on collaborative information services and one based at Strathclyde University Library developing courseware. Latterly, after these two research assistants left to take up other posts, there has been a single researcher based at Glasgow University Library.The project was funded to investigate the feasibility of new services to the Engineering Faculties at both Universities, with a view to making recommendations for service provision that can be developed for other subject areas

Proton beam radiotherapy in the management of uveal melanoma: clinical experience in Scotland

<p>Aim: To evaluate proton-beam radiotherapy (PBRT) in the management of uveal melanoma in Scotland.</p> <p>Methods: A retrospective review was undertaken on all patients receiving PBRT for uveal melanoma (1994–2005). Data obtained included: gender, past ocular/medical history, age, presenting complaint(s), diagnosis, laterality, tumor location/ultrasound characteristics, visual acuity (VA) and intraocular pressure. At post-treatment reviews (3, 6, 12, and 24 months), the following data was obtained: VA, intraocular pressure, tumor appearance and ultrasound characteristics. Mean follow up was 38.8 months.</p> <p>Results: Seventy-six patients were included. Mean age was 64 years; male to female ratio was 1.1:1. Ninety-seven percent demonstrated initial treatment response; 87% had successful control of tumor growth. Mean pre-treatment tumor height was 6.2 mm v.s. 4.8 mm post-irradiation (p < 0.001). Pre-irradiation VA was <3/60 in 18.5% compared with 74% post-irradiation (p < 0.0001). There was a statistically significant association between adverse events (enucleation, metastasis) and greater maximal basal tumor diameter. Eighteen eyes were enucleated. The median survival time was estimated to be 54 months.</p> <p>Conclusion: In our experience, PBRT is a precise, reliable and effective treatment in the management of large, and previously treated uveal melanomas. It prevents enucleation in the majority at short term follow-up.</p&gt

Cryogenic Propellant Scavenging

A detailed description of a computer model that has been developed for assessing the feasibility of low g cryogen propellant scavenging from the space shuttle External Tank (ET) is given. Either pump-assisted or pressure-induced propellant transfer may be selected. The program will accept a wide range of input variables, including the fuel to be transferred (LOX or LH2), heat leaks, tank temperatures, and piping and equipment specifications. The model has been parametrically analyzed to determine initial design specification for the system

Continuous-wave Raman laser pumped within a semiconductor disk laser cavity

A KGd(WO4)(2) Raman laser was pumped within the cavity of a cw diode-pumped InGaAs semiconductor disk laser (SDL). The Raman laser threshold was reached for 5: 6W of absorbed diode pump power, and output power up to 0.8W at 1143nm, with optical conversion efficiency of 7.5% with respect to the absorbed diode pump power, was demonstrated. Tuning the SDL resulted in tuning of the Raman laser output between 1133 and 1157nm