On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.     

Phase determination in interference-based superresolving microscopes through critical frequency analysis

Utilizing the interference of wave fronts of two opposing lenses, 4Pi-confocal and I(5)M microscopy improve the axial resolution of far-field fluorescence microscopy as much as threefold to sevenfold. However, establishing the phase difference of the wave fronts in the sample is a problem yet to be solved. Here we show that the phase difference is encoded in the microscope's transfer of the spatial frequencies that match the distance of the interference peaks. As a result the phase difference is readily extracted through a Fourier transform of the image. Our method is relevant to all microscopes that exploit the interference of counterpropagating waves to improve the axial and the lateral resolution.     

2-Methoxy-6-oxo-1,4,5,6-tetrahydropyridine-3-carbonitriles: versatile starting materials for the synthesis of libraries with diverse heterocyclic scaffolds

Heterocyclic demonstration libraries for agrochemical screening were prepared from the common intermediates 2-methoxy-6-oxo-1,4,5,6-tetrahydropyridine-3-carbonitriles (1), using standard solution-phase techniques. A total of 18 screening libraries were prepared in good to excellent yields. Several members of these libraries were active in the first level of agrochemical screening, especially in the fungicide screen.     

Polarity effects on ZnO films grown along the nonpolar [1120] direction

The surface electrical properties of ZnO thin films grown along the nonpolar [1120] direction have been investigated by Kelvin probe microscopy on a nanometer scale. Two different charge domains, with a 75 meV work function difference, coexist within the ZnO surface, which is covered by rhombohedral pyramids whose sidewalls are shown to be {1011}-type planes. The presence and relative orientation of the two kinds of charge domains are explained in terms of the atomic arrangement at the {1011} polar surfaces.     

Radial electric fields and confinement in the TJ-II stellarator

Radial plasma potential profiles have been obtained in the TJ-II by the Heavy Ion Beam Probing (HIBP) diagnostics. Results show that the potential increases up to 1 kV near the magnetic axis in ECRH low-density plasmas. The secondary ion current profiles, which directly reflect the plasma density, are hollow. In low-density ECRH operation, radial electric fields are found to be positive in the plasma core, however, a reduction in these fields is observed with increasing density. Radial plasma potential profiles show evidence of structures in configurations with low-order rational surfaces. In particular, HIBP measurements have permitted characterization of the plasma potential profile during e-ITB formation. Experiments in TJ-II have shown that it is possible to modify the global confinement and edge plasma parameters with limiter biasing, illustrating the direct impact of radial electric fields on confinement properties. Plasma potential measurements by the HIBP diagnostic show a strong impact of heating method (ECRH versus NBI) on radial electric fields.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Nucleation time of nanoscale water bridges

Water capillaries bind together grains of sand. They also can bind an atomic force microscope tip to a substrate. The kinetics of capillary condensation at the nanoscale is studied here using friction force microscopy. At 40% relative humidity we find that the meniscus nucleation times increase from 0.7 to 4.2 ms when the temperature decreases from 332 to 299 K. The nucleation times grow exponentially with the inverse temperature 1/T obeying an Arrhenius law. We obtain a nucleation energy barrier of 7.8 x 10(-20) J and an attempt frequency ranging between 4 and 250 GHz, in excellent agreement with theoretical predictions. These results provide direct experimental evidence that capillary condensation is a thermally activated phenomenon.     

Dynamic processes in the Venice region outlined by environmental isotopes

Research carried out in the last 40 years has shown the scientific importance of groundwater circulation both in the Northern Adriatic sea bed and within the uppermost sedimentary layers of the Venice lagoon and of the Venice plain. Hydrodynamic processes are strictly controlled by a well-cemented sedimentary horizon lying under and around Venice ('caranto'), which plays the role of regional aquitard. This layer was attributed to the subaerial cementation of the Flandrian (8-10 ka Before Present) sedimentary surface. The caranto is generalised as a continuum horizon, being an easy explanation for several environmental, hydrogeological and geotechnical problems, e.g., a base layer for landfills, a confining layer for deep aquifers and the best substratum for locating the oak wooden pile-dwelling needed to support the largest buildings. The preservation of the isotope signal within the deep aquifers and aquiclude system records the changes in surface and groundwater characteristics and suggests the present and past recharge regimes. In this region, the heavily perturbed hydrodynamic conditions do not allow for the use of isotopic signals to derive a correct reconstruction of the present recharge. The perturbations induced by the intensive anthropogenic activity force to follow climate evolution by considering deep groundwater and pore waters. In addition, the presence of carbonatic rocks inside terrigeneous sediments affects the reconstruction of the past. Results indicate that carbonatic rocks are created by seepage, through the sediments, of gaseous carbon compounds from decaying organic layers. The gas interactions with the intra-sedimentary saline and fresh waters produce CO2, inducing the cementation of the sediments.     

Widely tunable continuous-wave diode-pumped 2-microm Tm-Ho:KYF4 laser

Continuous-wave laser action at approximately 2 microm is demonstrated in a Tm-Ho:KYF4 single crystal at room temperature. Crystal growth, spectroscopic measurements, and laser results are presented. An output power in excess of 250 mW is obtained with a tuning range of 99 nm, the largest ever published, to our knowledge, for Tm-Ho in any crystalline host.     

Naphthalene analogues of lignans

The methodology for the synthesis of podophyllotoxin and thuriferic acid-type lignans has been applied to derivatives carrying a naphthalene moiety. Starting from the 1,3-dithiane of 2-naphthaldehyde afforded the expected analogues in the 2,1-naphthalene series. The preferred conformations of these compounds are influenced by the bulky naphthalene system. By contrast, 1,8-bridged products were obtained from the 1,3-dithiane of 1-naphthaldehyde. In this series, polycyclic naphthalene lignan analogues were isolated after deprotection and/or desulfurization reactions. The cyclizations produced in this process are due to the proximity between the 3,4,5-trimethoxyphenyl moiety and the reacting C-2 of the 1,3-dithiane ring.