5,349 research outputs found
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 with
implanted Fe ions are presented and discussed. The findings indicate that
Fe-implantation in a TiO pellet sample induces heterovalent cation
substitution (Fe Ti) 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 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:Fe system. According to our calculations, the
clustering of Fe-atoms in TiO: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
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