A control theorem for pp-adic automorphic forms and Teitelbaum's L\mathcal{L}-invariant

In this article, we describe an efficient method for computing Teitelbaum's $p$-adic $\mathcal{L}$-invariant. These invariants are realized as the eigenvalues of the $\mathcal{L}$-operator acting on a space of harmonic cocycles on the Bruhat-Tits tree $\mathcal{T}$, which is computable by the methods of Franc and Masdeu described in \cite{fm}. The main difficulty in computing the $\mathcal{L}$-operator is the efficient computation of the $p$-adic Coleman integrals in its definition. To solve this problem, we use overconvergent methods, first developed by Darmon, Greenberg, Pollack and Stevens. In order to make these methods applicable to our setting, we prove a control theorem for $p$-adic automorphic forms of arbitrary even weight. Moreover, we give computational evidence for relations between slopes of $\mathcal{L}$-invariants of different levels and weights for $p=2$.Comment: 26 page

Health benefits of Green and Black Tea: A Review

Tea, (Camellia sinensis) is grown in about thirty countries and next to water, is the most widely consumed beverage in theworld. Based on the type of the processing, three tea types can be identified as Green, Black and Oolong tea. Drinking tea has beenconsidered a health-promoting habit since ancient times. The modern medicinal research isproviding a scientific basis for this belief. Various studies have suggested the health promoting effects of green and black tea is due to its polyphenolic compounds mainly catechins. Unlike green tea, health benefits of consuming black tea are not extensively discussed. This review is mainly focused on the health benefits of consuming green and black tea

Scanning thermal profiler

Journal ArticleA new high-resolution profilometer has been demonstrated based upon a noncontacting nearfield thermal probe. The thermal probe consists of a thermocouple sensor with dimensions approaching 100 nm. Profiling is achieved by scanning the heated sensor above but close to the surface of a solid. The conduction of heat between tip and sample via the air provides a means for maintaining the sample spacing constant during the lateral scan. The large difference in thermal properties between air and solids makes the profiling technique essentially independent of the material properties of the solid. Noncontact profiling of resist and metal films has shown a lateral resolution of 100 nm and a depth solution of 3 nm. The basic theory of the new probe is described and the results presented

High resolution thermal microscopy

Journal ArticleA new high resolution thermal microscope has been demonstrated capable of imaging thermal fields with sub 1000 angstom resolution. It is based upon a non-contacting near field thermal probe. The thermal probe consists of a thermocouple sensor on the end of a tip with sub 1000 angstrom dimensions. The probe tip is scanned in close proximity to a solid or liquid surface and the local temperature is mapped with a resolution determined by the size of the tip. Material independent surface profiling has also been demonstrated with the thermal probe, providing a lateral resolution of approximately 300 angstroms. Temperature mapping and surface profiling results are presented on both electronic and biological materials

Optical ranging by wavelength multiplexed interferometry

Journal ArticleA new optical technique is described for measurement of absolute distance. The approach is based upon a wavelength multiplexed heterodyne interferometer with FM demodulation. By temporally multiplexing discrete wavelengths in a heterodyne interferometer, a complete elimination of interferometric range ambiguity can be achieved while maintaining the high range sensitivity and resolution of interferometry

Tip-Techniques for Microcharacterization of Materials

The invention of the Scanning Tunneling Microscope has stimulated the development of new techniques for microcharacterization of materials, which are based on the use of a very fine tip. Two of these techniques have emerged about one year ago, the Thermal Profiler and the Atomic Force Microscope. Both techniques have recently demonstrated the capability to profile and image conductors and insulators. The resolution attained varies from approximately 50 nm by the Thermal Profiler to a few nanometers with the Atomic Force Microscope, therefore competing with the resolution obtained with electron beam microscopy. We shall describe the principle of these techniques, and present recent results obtained for surface profiling, as well as for temperature mapping, force measurement and mapping of magnetic field on a nanometer scale

The Polonnaruwa meteorite: oxygen isotope, crystalline and biological composition

Results of X-Ray Diffraction (XRD) analysis, Triple Oxygen Isotope analysis and Scanning Electron Microscopic (SEM) studies are presented for stone fragments recovered from the North Central Province of Sri Lanka following a witnessed fireball event on 29 December 2012. The existence of numerous nitrogen depleted highly carbonaceous fossilized biological structures fused into the rock matrix is inconsistent with recent terrestrial contamination. Oxygen isotope results compare well with those of CI and CI-like chondrites but are inconsistent with the fulgurite hypothesis.Comment: 7 pages, 7 figures, 4 table

Scanned Imaging Techniques for Surface NDE

A phase sensitive laser probe in which the focussed spot is small, as compared with the acoustic wavelength, is capable of measuring the complex distributions of a SAW field along prescribed scan lines. Using the probe, it is possible, on a defect free sample, to measure the SAW velocity surface with an accuracy of a few parts in 105. Such accuracy suggests that the technique is sufficiently sensitive to detect small changes in surface characteristics; the presence of a defect is revealed by perturbations in the relationship between various scans. The scattered radiation patterns from a surface crack irradiated by acoustic surface waves can be utilised to determine the defect size and location with improved accuracy. Results on deliberate and real cracks are presented