A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained

Kinetic Limit for Wave Propagation in a Random Medium

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon to 0 the disorder averaged Wigner function on the kinetic scale, time and space of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure

Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system

A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the `atomic' levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.Comment: 4+ page

Non-power law constant flux solutions for the Smoluchowski coagulation equation

It is well known that for a large class of coagulation kernels, Smoluchowski coagulation equations have particular power law solutions which yield a constant flux of mass along all scales of the system. In this paper, we prove that for some choices of the coagulation kernels there are solutions with a constant flux of mass along all scales which are not power laws. The result is proved by means of a bifurcation argument.Comment: 35 page

Development and validation of a risk score (Delay-7) to predict the occurrence of a treatment delay following cycle 1 chemotherapy

BACKGROUND: The risk of toxicity-related dose delays, with cancer treatment, should be included as part of pretreatment education and be considered by clinicians upon prescribing chemotherapy. An objective measure of individual risk could influence clinical decisions, such as escalation of standard supportive care and stratification of some patients, to receive proactive toxicity monitoring. PATIENTS AND METHODS: We developed a logistic regression prediction model (Delay-7) to assess the overall risk of a chemotherapy dose delay of 7 days for patients receiving first-line treatments for breast, colorectal and diffuse large B-cell lymphoma. Delay-7 included hospital treated, age at the start of chemotherapy, gender, ethnicity, body mass index, cancer diagnosis, chemotherapy regimen, colony stimulating factor use, first cycle dose modifications and baseline blood values. Baseline blood values included neutrophils, platelets, haemoglobin, creatinine and bilirubin. Shrinkage was used to adjust for overoptimism of predictor effects. For internal validation (of the full models in the development data) we computed the ability of the models to discriminate between those with and without poor outcomes (c-statistic), and the agreement between predicted and observed risk (calibration slope). Net benefit was used to understand the risk thresholds where the model would perform better than the ‘treat all’ or ‘treat none’ strategies. RESULTS: A total of 4604 patients were included in our study of whom 628 (13.6%) incurred a 7-day delay to the second cycle of chemotherapy. Delay-7 showed good discrimination and calibration, with c-statistic of 0.68 (95% confidence interval 0.66-0.7), following internal validation and calibration-in-the-large of −0.006. CONCLUSIONS: Delay-7 predicts a patient’s individualised risk of a treatment-related delay at cycle two of treatment. The score can be used to stratify interventions to reduce the occurrence of treatment-related toxicity

A partition functional and thermodynamic properties of the infinite-dimensional Hubbard model

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin-symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature $T^\star$. We attribute this anomaly to the appearance of the Hubbard pseudo-gap. The specific heat also shows a peak near $T^\star$. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around $T^\star$ and has a rough linear temperature dependence above $T^\star$.Comment: 18 pages, 6 figures upon request, latex, (to appear in Phys. Rev. B

CODEX-B4C Experiment: Cored Degradation Test With Boron Carbide Control Rod KFKI-2003-01/G (2003)

The CODEX-B4C bundle test has been successfully performed on 25th May 2001 in the framework of the COLOSS project of the EU 5th FWP. The high temperature degradation of a VVER-1000 type bundle with B4C control rod was investigated with electrically heated fuel rods. The experiment was carried out according to a scenario selected in favour of methane formation. Degradation of control rod and fuel bundle took place at temperatures ~2000 oC, cooling down of the bundle was performed in steam atmosphere. The gas composition measurement indicated no methane production during the experiment. High release of aerosols was detected in the high temperature oxidation phase. The on-line measured data are collected into a database and are available for code validation and development

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.Comment: 21 pages, no figure