Generalized Bernoulli numbers and a formula of Lucas

An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The value of this sum is then given in terms of the Meixner-Pollaczek polynomials

A probabilistic interpretation of a sequence related to Narayana polynomials

A sequence of coefficients appearing in a recurrence for the Narayana polynomials is generalized. The coefficients are given a probabilistic interpretation in terms of beta distributed random variables. The recurrence established by M. Lasalle is then obtained from a classical convolution identity. Some arithmetical properties of the generalized coefficients are also established

The Cauchy-Schlomilch transformation

The Cauchy-Schl\"omilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given

Integrating Community-Based Interventions to Reverse the Convergent TB/HIV Epidemics in Rural South Africa.

The WHO recommends integrating interventions to address the devastating TB/HIV co-epidemics in South Africa, yet integration has been poorly implemented and TB/HIV control efforts need strengthening. Identifying infected individuals is particularly difficult in rural settings. We used mathematical modeling to predict the impact of community-based, integrated TB/HIV case finding and additional control strategies on South Africa's TB/HIV epidemics. We developed a model incorporating TB and HIV transmission to evaluate the effectiveness of integrating TB and HIV interventions in rural South Africa over 10 years. We modeled the impact of a novel screening program that integrates case finding for TB and HIV in the community, comparing it to status quo and recommended TB/HIV control strategies, including GeneXpert, MDR-TB treatment decentralization, improved first-line TB treatment cure rate, isoniazid preventive therapy, and expanded ART. Combining recommended interventions averted 27% of expected TB cases (95% CI 18-40%) 18% HIV (95% CI 13-24%), 60% MDR-TB (95% CI 34-83%), 69% XDR-TB (95% CI 34-90%), and 16% TB/HIV deaths (95% CI 12-29). Supplementing these interventions with annual community-based TB/HIV case finding averted a further 17% of TB cases (44% total; 95% CI 31-56%), 5% HIV (23% total; 95% CI 17-29%), 8% MDR-TB (68% total; 95% CI 40-88%), 4% XDR-TB (73% total; 95% CI 38-91%), and 8% TB/HIV deaths (24% total; 95% CI 16-39%). In addition to increasing screening frequency, we found that improving TB symptom questionnaire sensitivity, second-line TB treatment delays, default before initiating TB treatment or ART, and second-line TB drug efficacy were significantly associated with even greater reductions in TB and HIV cases. TB/HIV epidemics in South Africa were most effectively curtailed by simultaneously implementing interventions that integrated community-based TB/HIV control strategies and targeted drug-resistant TB. Strengthening existing TB and HIV treatment programs is needed to further reduce disease incidence

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy

We study the energetics of island formation in Stranski-Krastanow growth within a parameter-free approach. It is shown that an optimum island size exists for a given coverage and island density if changes in the wetting layer morphology after the 3D transition are properly taken into account. Our approach reproduces well the experimental island size dependence on coverage, and indicates that the critical layer thickness depends on growth conditions. The present study provides a new explanation for the (frequently found) rather narrow size distribution of self-assembled coherent islands.Comment: 4 pages, 5 figures, In print, Phys. Rev. Lett. Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Is there an association between wheezing and constipation in preschool children? Explanations from a longitudinal birth cohort

Objective: To assess whether wheezing and atopic dermatitis were associated with constipation in preschool children and to what extent shared risk factors contribute to this relationship. Methods: A population-based sample of 4651 preschool children was used. At the age of 24, 36 and 48 months, a parental report of functional constipation was available according to the Rome II criteria, and data on atopic dermatitis and wheezing were available using age-adapted questionnaires from the International Study of Asthma and Allergie