Duals of Gabor systems and weighted exponentials at the critical density

A Gabor system can only be a Riesz basis when the Beurling density of its index set is exactly 1. There exist Gabor systems that are Schauder bases but not Riesz basis, but it is not known whether every Gabor Schauder basis must have density 1. For lattice Gabor systems there is a complete characterization in terms of the Zak transform of the generating atom. We investigate the properties of subsets of lattice Gabor systems and systems of weighted exponentials at the critical density, which can still be complete and even minimal. Can these systems be bases? We will show that many properties of the dual system are tied to the behavior of the zeros of the atom and the number of lattice elements that are missing from the lattice

WIENER AMALGAM SPACES IN GENERALIZED HARMONIC ANALYSIS AND WAVELET THEORY

This thesis is divided into four parts. Part I, Introduction and Notation, describes the results contained in the thesis and their background. Part II, Wiener Amalgam Spaces, is an expository introduction to Feichtinger's general amalgam space theory, which is used in the remainder of the thesis to formulate and prove results. Part III, Generalized Harmonic Analysis, presents new results in that area. Part IV, Wavelet Theory, contains exposition and miscellaneous results on Gabor ( also known as Weyl-Heisenberg) wavelets. Amalgam, or mixed-norm, spaces are Banach spaces of functions determined by a norm which distinguishes between local and global properties of functions. Specific cases were introduced by Wiener. Feichtinger has developed a far-reaching generalization of amalgam spaces, which allows general function spaces norms as local or global components. We use Feichtinger's amalgam theory, on d-dimensional Euclidean space under componentwise multiplication, to prove that the Wiener transform (introduced by Wiener to analyze the spectra of infinite-energy signals) is an invertible mapping of the amalgam space with local L2 and global Lq. components onto an appropriate space defined in terms of the variation of functions, for each q between one and infinity. As corollaries, we obtain results of Beurling on the Fourier transform and results of Lau and Chen on the Wiener transform. Moreover, our results are carried out in higher dimensions. In addition, we prove that the higher-dimensional variation spaces are complete by using Masani's helices; this generalizes a one-dimensional result of Lau and Chen. In wavelet theory, we present a survey of frames in Hilbert and Banach spaces and the use of the Zak transform in analyzing Gabor wavelets. Frames are an alternative to unconditional bases in these spaces; like bases, they Provide representations of each element of the space in terms of the frame elements, and do so in a way in which the scalars in the representation are explicitly known. However, unlike bases, the representations need not be unique. We then discuss the specific case of Gabor frames in the space of square-integrable functions, concentrating on the role of the Zak transform in the analysis of such frames

Invariances of Frame Sequences under Perturbations

This paper determines the exact relationships that hold among the major Paley–Wiener perturbation theorems for frame sequences. It is shown that major properties of a frame sequence such as excess, deficit, and rank remain invariant under Paley–Wiener perturbations, but need not be preserved by compact perturbations. For localized frames, which are frames with additional structure, it is shown that the frame measure function is also preserved by Paley–Wiener perturbations

Invariance of a Shift-Invariant Space

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are characterized in terms of the generators of the space. As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.Comment: 15 page

Effects of land cover change on evapotranspiration and streamflow of small catchments in the Upper Xingu River Basin, Central Brazil

© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Hydrology: Regional Studies 4B (2015): 108-122, doi:10.1016/j.ejrh.2015.05.010.This study assessed the influence of land cover changes on evapotranspiration and streamflow in small catchments in the Upper Xingu River Basin (Mato Grosso state, Brazil). Streamflow was measured in catchments with uniform land use for September 1, 2008 to August 31, 2010. We used models to simulate evapotranspiration and streamflow for the four most common land cover types found in the Upper Xingu: tropical forest, cerrado (savanna), pasture, and soybean croplands. We used INLAND to perform single point simulations considering tropical rainforest, cerrado and pasturelands, and AgroIBIS for croplands. Converting natural vegetation to agriculture substantially modifies evapotranspiration and streamflow in small catchments. Measured mean streamflow in soy catchments was about three times greater than that of forest catchments, while the mean annual amplitude of flow in soy catchments was more than twice that of forest catchments. Simulated mean annual evapotranspiration was 39% lower in agricultural ecosystems (pasture and soybean cropland) than in natural ecosystems (tropical rainforest and cerrado). Observed and simulated mean annual streamflows in agricultural ecosystems were more than 100% higher than in natural ecosystems. The accuracy of the simulations was improved by using field-measured soil hydraulic properties. The inclusion of local measurements of key soil parameters is likely to improve hydrological simulations in other tropical regions.This study was supported by the US National Science Foundation (DEB-0949996, DEB-0743703), the Gordon and Betty Moore Foundation, and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, process 135648/2011-4)

Probing magnetic exchange interactions with helium

Funding: CT and PW acknowledge support from EPSRC (EP/R031924/1) and CMY and LSF from EP/S005005/1. C.H. acknowledges support by the Austrian Science Fund (FWF) Project No. P32144-N36 and the VSC-4 of the Vienna University of Technology. The work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through Transregional Research Collaboration TRR 80 (Augsburg, Munich, and Stuttgart).Controlling and sensing spin-polarization of electrons forms the basis of spintronics. Here, we report a study of the effect of helium on the spin-polarization of the tunneling current and magnetic contrast in spin-polarized Scanning Tunneling Microscopy. We show that the magnetic contrast in SP-STM images recorded in the presence of helium depends sensitively on the tunneling conditions. From tunneling spectra and their variation across the atomic lattice we establish that the helium can be reversibly ejected from the tunneling junction by the tunneling electrons. The energy of the tunneling electrons required to eject the helium depends on the relative spin-polarization of the tip and sample, making the microscope sensitive to the magnetic exchange interactions. We show that the time-averaged spin polarization of the tunneling current is suppressed in the presence of helium and thereby demonstrate voltage control of the spin polarization of the tunneling current across the tip-sample junction.PostprintPeer reviewe

Upgrade of the ultracold neutron source at the pulsed reactor TRIGA Mainz

The performance of the upgraded solid deuterium ultracold neutron source at the pulsed reactor TRIGA Mainz is described. The current configuration stage comprises the installation of a He liquefier to run UCN experiments over long-term periods, the use of stainless steel neutron guides with improved transmission as well as sputter-coated non-magnetic $^{58}$NiMo alloy at the inside walls of the thermal bridge and the converter cup. The UCN yield was measured in a `standard' UCN storage bottle (stainless steel) with a volume of 32 litres outside the biological shield at the experimental area yielding UCN densities of 8.5 /cm$^3$; an increase by a factor of 3.5 compared to the former setup. The measured UCN storage curve is in good agreement with the predictions from a Monte Carlo simulation developed to model the source. The growth and formation of the solid deuterium converter during freeze-out are affected by the ortho/para ratio of the H$_2$ premoderator.Comment: 12 pages, 7 figure