On the Divergence Phenomenon in Hermite–Fejér Interpolation

AbstractGeneralizing results of L. Brutman and I. Gopengauz (1999, Constr. Approx.15, 611–617), we show that for any nonconstant entire function f and any interpolation scheme on [−1, 1], the associated Hermite–Fejér interpolating polynomials diverge on any infinite subset of C\[−1, 1]. Moreover, it turns out that even for the locally uniform convergence on the open interval ]−1, 1[ it is necessary that the interpolation scheme converges to the arcsine distribution

Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

Increased plasma viscosity as a reason for inappropriate erythropoietin formation

The aim of this study was to examine whether altered plasma viscosity could contribute to the inappropriately low production rate of erythropoietin (EPO) observed in patients suffering from hypergammaglobulinemias associated with multiple myeloma or Waldenström's disease. We found that the EPO formation in response to anemia in these patients was inversely related to plasma viscosity. A similar inverse relationship between plasma viscosity and EPO production was seen in rats in which EPO formation had been stimulated by exchange transfusion and the plasma viscosity of which was thereby altered by using exchange solutions of different composition to alter plasma viscosity and thus whole blood viscosity independently from hematocrit. Raising the gammaglobulin concentration to approximately 40 mg/ml plasma in the rats almost totally blunted the rise in serum EPO levels despite a fall of the hematocrit to 20%. Determination of renal EPO mRNA levels by RNase protection revealed that the reductions in serum EPO levels at higher plasma viscosities were paralleled by reductions in renal EPO mRNA levels. Taken together, our findings suggest that plasma viscosity may be a significant inhibitory modulator of anemia-induced EPO formation. The increased plasma viscosity in patients with hypergammaglobulinemias may therefore contribute to the inappropriate EPO production, which is a major reason for the anemia developing in these patients

Evidence for 1122 Hz X-Ray Burst Oscillations from the Neutron-Star X-Ray Transient XTE J1739-285

We report on millisecond variability from the X-ray transient XTE J1739-285. We detected six X-ray type I bursts and found evidence for oscillations at 1122 +/- 0.3 Hz in the brightest X-ray burst. Taking into consideration the power in the oscillations and the number of trials in the search, the detection is significant at the 99.96% confidence level. If the oscillations are confirmed, the oscillation frequency would suggest that XTE J1739-285 contains the fastest rotating neutron star yet found. We also found millisecond quasiperiodic oscillations in the persistent emission with frequencies ranging from 757 Hz to 862 Hz. Using the brightest burst, we derive an upper limit on the source distance of about 10.6 kpc.Comment: To appear in ApJL, 4 page

Optimized Dynamical Decoupling for Time Dependent Hamiltonians

The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with $\pi$ pulses about two perpendicular axes in spin space. to suppress general decoherence, i.e., longitudinal relaxation and dephasing.Comment: 5 pages, no figure

Symmetries and Triplet Dispersion in a Modified Shastry-Sutherland Model for SrCu_2(BO_3)_2

We investigate the one-triplet dispersion in a modified Shastry-Sutherland Model for SrCu_2(BO_3)_2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy quanta conserving block diagonal Hamiltonian H_{eff}. The dispersion splits into two branches which are nearly degenerated. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k=0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small |k| and compare our results to INS data.Comment: 9 pages, 8 figures accepted by J. Phys.: Condens. Matte

Kinks in the electronic dispersion of the Hubbard model away from half filling

We study kinks in the electronic dispersion of a generic strongly correlated system by dynamic mean-field theory (DMFT). The focus is on doped systems away from particle-hole symmetry where valence fluctuations matter potentially. Three different algorithms are compared to asses their strengths and weaknesses, as well as to clearly distinguish physical features from algorithmic artifacts. Our findings extend a view previously established for half-filled systems where kinks reflect the coupling of the fermionic quasiparticles to emergent collective modes, which are identified here as spin fluctuations. Kinks are observed when strong spin fluctuations are present and, additionally, a separation of energy scales for spin and charge excitations exists. Both criteria are met by strongly correlated systems close to a Mott-insulator transition. The energies of the kinks and their doping dependence fit well to the kinks in the cuprates, which is surprising in view of the spatial correlations neglected by DMFT.Comment: 13 pages, 15 figure

Symmetry and dimension of the magnon dispersion of inorganic spin-Peierls systems

The data on the dispersion of the magnetic excitations of CuGeO_3 in the spin-Peierls dimerized phase are analyzed. On the basis of the lattice structure it is shown that even along the chains the $d=2$ character cannot be neglected. The symmetry of the dispersion differs from the one assumed so far. The magnetic resonance data is reinterpreted. The possibility of interchain rather than intrachain frustration is discussed.Comment: 4 pages, Revtex, to appear in PR

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Motivated by recent measurements on CuGeO$_3$ the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave vector dependent magnons and a continuum with square root behavior at the band edges are found. The spectral density of the continua is calculated. Spin rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. In addition, the existence of bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum an ``anti-bound'' quintuplet. The results are based on field theoretic arguments, RPA calculations, and consideration of the limit of strong alternation.Comment: 4 pages, 4 figures included, Revte