Pointwise convergence in probability of general smoothing splines

Establishing the convergence of splines can be cast as a variational problem which is amenable to a \(\Gamma \)-convergence approach. We consider the case in which the regularization coefficient scales with the number of observations, n, as \(\lambda _n=n^{-p}\). Using standard theorems from the \(\Gamma \)-convergence literature, we prove that the general spline model is consistent in that estimators converge in a sense slightly weaker than weak convergence in probability for \(p\le \frac{1}{2}\). Without further assumptions, we show this rate is sharp. This differs from rates for strong convergence using Hilbert scales where one can often choose \(p>\frac{1}{2}\).     

Natural dualities for three classes of relational structures

Motivated by the work of Hofmann [14] and Davey [7] on dualities for structures, we will construct natural dualities for the classes of quasi-ordered sets, equivalence-relationed sets, and reflexive (undirected) graphs. We describe the dual structures by giving finite sets of quasi-equations that axiomatise the dual categories. We also show that there is a natural connection between the duality we construct for finite quasi-ordered sets and Birkhoff’s representation theorem for finite ordered sets [2], and between the dualities constructed for quasi-ordered sets and equivalence-relationed sets.     

Modellrechnungen zur Isotopentrennung durch Multiphotonen-Photodissoziation von Molekülen

Für stoßfreie SF₆-Moleküle werden Mulltiphotonen-Photofragmentierungswahrscheinlichkeiten im intensiven IR-LASER-Feld berechnet einschließlich der Isotopenselektivität derartiger Prozesse in Abhängigkeit von der eingestrahlten LASER-Linie, der Leistungsdichte, dem Impulsprofil und der Temperatur. Über ein quantenmechanisches Modell werden die Rotationsschtwingungsniveaus des SF₆-Moleküls, die Verstimmung zwischen LASER- und Molekülschwin-gungsfrequenz und die intramolekulare Schwingungsrelaxation berücksichtigt.     

Mechanism of disease in early osteoarthritis: application of modern MR imaging techniques — a technical report

The application of biomolecular magnetic resonance imaging becomes increasingly important in the context of early cartilage changes in degenerative and inflammatory joint disease before gross morphological changes become apparent. In this limited technical report, we investigate the correlation of MRI T1, T2 and T1ρ relaxation times with quantitative biochemical measurements of proteoglycan and collagen contents of cartilage in close synopsis with histologic morphology. A recently developed MRI sequence, T1ρ, was able to detect early intracartilaginous degeneration quantitatively and also qualitatively by color mapping demonstrating a higher sensitivity than standard T2-weighted sequences. The results correlated highly with reduced proteoglycan content and disrupted collagen architecture as measured by biochemistry and histology. The findings lend support to a clinical implementation that allows rapid visual capturing of pathology on a local, millimeter level. Further information about articular cartilage quality otherwise not detectable in vivo, via normal inspection, is needed for orthopedic treatment decisions in the present and future.     

Reviews

Ion Implantation, Proceedings from the European Conference on Ion Implanatation, Reading, September 7–9 1970 Peter Peregrinus Limited, Southgate House, Stevenage Herts, England. England 1970, 241 pages. Price: $6.00

Lectures in Theoretical Physics Volume XI-C: Atomic Collision Processes Editors: S. Geltman, K. T. Mahanthappa and W. E. Brittin. Gordon and Breach 1969, pp xiii + 337.     

Electrodynamic Dust Shields on the International Space Station: Exposure to the space environment

Electrodynamic Dust Shields (EDS) have been in development at NASA as a dust mitigation method for lunar and Martian missions. An active dust mitigation strategy, such as that provided by the EDS, that can remove dust from surfaces, is of crucial importance to the planetary exploration program. We report on the development of a flight experiment to fully expose four EDS panels to the space environment. This flight experiment is part of the Materials International Space Station experiment X (MISSE-X), an external platform on the International Space Station that will expose materials to the space environment.     

Inequalities for the capacity of non-contractible annuli on cylinders of constant and variable negative curvature

We give elementary estimates for the capacity of non-contractible annuli on cylinders and provide examples, where these inequalities are sharp. Here the lower bound depends only on the area of the annulus. To obtain this result we use projection of gradients on curves to obtain a lower bound on the capacity, which we call directional capacity. In the case of constant curvature we then apply a symmetrization process that results in an annulus of minimal directional capacity. For this annulus the lower bound on the capacity is sharp. In the case of variable negative curvature we obtain the lower bound by constructing a comparison annulus with the same area but lower directional capacity on a cylinder of constant curvature. The methods developed here have been applied to estimate the energy of harmonic forms on Riemann surfaces in Muetzel (Math Zeitschrift, 2012, arXiv:1202.0782).     

Temperature dependent photoluminescence down to 4.2 K in EuTFC

The temperature dependence of photoluminescence in Europium tris[3-(trifluoro-methylhydroxymethylene)-(+)-camphorate] (EuTFC) embedded in polymer films has been examined from 40 K down to 4.2 K with the goal of preparing sensor films for low-temperature thermal imaging. The behavior of EuTFC showed significant difference when based on polystyrene compared to poly(n-alkyl methacrylate)s. In poly(n-alkyl methacrylate)s prepared by standard methods for imaging applications, the photoluminescence is fully saturated below 30 K, whereas in polystyrene films there is a strong temperature dependence even down to 4.2 K. By optimizing the preparation procedure for films made of poly(butyl methacrylate) (PBMA) and poly(methyl methacrylate), also these polymers became very sensitive down to liquid helium temperature. The maximum temperature sensitivity of EuTFC in PBMA is found to be 1.0%/K at 4.2 K. The problem of delamination and cracking of the polymer film at cryogenic temperature is also avoided by the special preparation method.     

Search for beta-delayed proton emission from $$^{11}$$Be

The European Physical Journal A - A deterministic treatment of sequential neutron emission, based on recursive equations of the residual temperatures, was applied to numerous fission cases (i.e. 49...     

Form factor π0 → γ* + γ* at different photon virtualities

The π⁰ γγ vertex for virtual photons of squared masses q ₁ ² and q ₂ ² plays a vital rôle in several physical processes; for example for q ₁ ² < 0, q ₂ ² < 0, in the two-photon physics reaction e ⁺ e ^? → e ⁺ e ^?π⁰, and for q ₁ ² > 0, q ₂ ² > 0, in the annihilation process e ⁺ e ^? → π⁰ l ⁺l^?. It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expression for the vertex in the limit in which at least one of ¦q ₁ ² ¦ and ¦q ₂ ² ¦ is large for arbitrary fixed values of the ratio q ₁ ² /q ₂ ² . We compare our results with those obtained previously by Brodsky and Lepage. It should be straightforward to test our predictions experimentally.