Application of Pad\'{e} interpolation to stationary state problems

If the small and large coupling behavior of a physical system can be computed perturbatively and expressed respectively as power series in a coupling parameter $g$ and $1/g$, a Pad\'{e} approximant embracing the two series can interpolate between these two limits and provide an accurate estimate of the system's behavior in the generally intractable intermediate coupling regime. The methodology and validity of this approach are illustrated by considering several stationary state problems in quantum mechanics.Comment: RevTeX4, 7 pages (including 7 tables); v4 typos correcte

On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

Gauge Independence and Chiral Symmetry Breaking in a Strong Magnetic Field

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of the truncated Schwinger-Dyson equations evaluated on the fermion mass shell, is manifestly gauge independent.Comment: 10 pages, 1 eps figure, version to appear in Annals of Physic

A Semi-parametric Two-component “Compound” Mixture Model and Its Application to Estimating Malaria Attributable Fractions

Malaria remains a major epidemiological problem in many developing countries. Malaria is dened as the presence of parasites and symptoms (usually fever) due to the parasites. In endemic areas, an individual may have symptoms attributable either to malaria or to other causes. From a clinical point of view, it is important to correctly diagnose an individual who has developed symptoms so that the appropriate treatments can be given. From an epidemiologic and economic point of view, it is important to determine the proportion of malaria affected cases in individuals who have symptoms so that policies on intervention programmes can be developed. Once symptoms have developed in an individual, the diagnosis of malaria can be based on analysis of the parasite levels in blood samples. However, even a blood test is not conclusive as in endemic areas, many healthy individuals can have parasites in their blood slides. Therefore, data from this type of studies can be viewed as coming from a mixture distribution, with the components corresponding to malaria and nonmalaria cases. A unique feature in this type of data, however, is the fact that a proportion of the non-malaria cases have zero parasite levels. Therefore, one of the component distribu-tions is itself a mixture distribution. In this article, we propose a semi-parametric likelihood approach for estimating the proportion of clinical malaria using parasite level data from a group of individuals with symptoms. Our approach assumes the density ratio for the parasite levels in clinical malaria and non-clinical malaria cases can be modeled using a logistic model. We use empirical likelihood to combine the zero and non-zero data. The maximum semi-parametric likelihood estimate is more ecient than existing non-parametric estimates using only the frequencies of zero and non-zero data. On the other hand, it is more robust than a fully parametric maximum likelihood estimate that assumes a parametric model for the non-zero data. Simulation results show that the performance of the proposed method is satisfactory. The proposed method is used to analyze data from a malaria survey carried out in Tanzania.Attributable fraction; Density ratio model; Empirical likelihood; Malaria; Mixture methods.