Functions with strictly decreasing distances from increasing Tchebycheff subspaces

AbstractLet {ui}i = 0∞ be a sequence of continuous functions on [0, 1] such that (u0,…, uk) is a Tchebycheff system on [0, 1] for all k ⩾ 0 and let C(u0,…, uk) denote the corresponding generalized convexity cone. It is proved that if f belongs to C(u0,…, un − 1), then its distance from the linear space spanned by (u0,…, un) is strictly smaller than its distance from the linear space spanned by (u0,…, un − 1). Other properties of the best approximants to such functions are also given.It is shown, by a general category argument, that no direct converse can exit. It is then established that if strict decrease of distances (or one of a number of other properties of the best approximants) holds for all subintervals of [0, 1], then f ϵ C(u0,…, un − 1) for all of these

Hermite-Birkhoff interpolation on roots of unity and walsh equiconvergence

AbstractCavaretta et al. [1] had shown that in some special cases of polynomials of lacunary interpolation in the roots of unity, the analogue of a theorem of Walsh is valid. They offered a conjecture in the case of (0, m1,…, ms−1) interpolation in the n roots of unity. The objective here is to prove the conjecture and to prove a similar result in the case of 2-periodic lacunary interpolation on 2n roots of unity

A new and efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be obtained from the non-symmetric block-Lanczos method. The resulting algorithm allows for the calculation of the {\em full spectrum} of a system with a computational workload which is only a few times larger than that needed for {\em static} polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with the calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.Comment: 4 pages, 2 figure

Friedel oscillations induced by non-magnetic impurities in the two-dimensional Hubbard model

We study the interplay of correlations and disorder using an unrestricted Slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.Comment: 9 pages, RevTeX, includes 8 figure

Crowdfunding Models, Strategies, and Choices Between Them

publishedVersio

Characterization of the Local Density of States Fluctuations near the Integer Quantum Hall Transition in a Quantum Dot Array

We present a calculation for the second moment of the local density of states in a model of a two-dimensional quantum dot array near the quantum Hall transition. The quantum dot array model is a realistic adaptation of the lattice model for the quantum Hall transition in the two-dimensional electron gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and Grinstein. We make use of a Dirac fermion representation for the Green functions in the presence of fluctuations for the quantum dot energy levels. A saddle-point approximation yields non-perturbative results for the first and second moments of the local density of states, showing interesting fluctuation behaviour near the quantum Hall transition. To our knowledge we discuss here one of the first analytic characterizations of chaotic behaviour for a two-dimensional mesoscopic structure. The connection with possible experimental investigations of the local density of states in the quantum dot array structures (by means of NMR Knight-shift or single-electron-tunneling techniques) and our work is also established.Comment: 11 LaTeX pages, 1 postscript figure, to appear in Phys.Rev.

Structural defects induced by Fe-ion implantation in TiO2

X-ray photoelectron spectroscopy (XPS) and resonant x-ray emission spectroscopy (RXES) measurements of pellet and thin film forms of TiO$_2$ with implanted Fe ions are presented and discussed. The findings indicate that Fe-implantation in a TiO$_2$ pellet sample induces heterovalent cation substitution (Fe$^{2+}\rightarrow$ Ti$^{4+}$) beneath the surface region. But in thin film samples, the clustering of Fe atoms is primarily detected. In addition to this, significant amounts of secondary phases of Fe$^{3+}$ are detected on the surface of all doped samples due to oxygen exposure. These experimental findings are compared with density functional theory (DFT) calculations of formation energies for different configurations of structural defects in the implanted TiO$_2$:Fe system. According to our calculations, the clustering of Fe-atoms in TiO$_2$:Fe thin films can be attributed to the formation of combined substitutional and interstitial defects. Further, the differences due to Fe doping in pellet and thin film samples can ultimately be attributed to different surface to volume ratios.Comment: 7+ pages, 3 Figure, to appear in J. Appl. Phy

Helicobacter pylori and cancer among adults in Uganda

Data from Africa on infection with Helicobacter pylori (H. pylori) are sparse. Therefore, as part of an epidemiological study of cancer in Uganda, we investigated the prevalence and determinants of antibodies against H. pylori among 854 people with different cancer types and benign tumours. Patients were recruited from hospitals in Kampala, Uganda, interviewed about various demographic and lifestyle factors and tested for antibodies against H. pylori. In all patients combined, excluding those with stomach cancer (which has been associated with H. pylori infection), the prevalence of antibodies was 87% (723/833) overall, but declined with increasing age (p = 0.02) and was lower among people who were HIV seropositive compared to seronegative (p <0.001). Otherwise, there were few consistent epidemiological associations. Among those with stomach cancer, 18/21 (86%) had anti-H. pylori antibodies (odds ratio 0.8, 95% confidence intervals 0.2–2.9, p = 0.7; estimated using all other patients as controls, with adjustment for age, sex and HIV serostatus). No other cancer site or type was significantly associated with anti-H. pylori antibodies. The prevalence of H. pylori reported here is broadly in accord with results from other developing countries, although the determinants of infection and its' role in the aetiology of gastric cancer in Uganda remain unclear