On an identity for zeros of Bessel functions

In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the first kind, which in particular reduces to some other new identities. We also show that our method can be applied for the zeros of other special functions, like Struve functions of the first kind, and modified Bessel functions of the second kind.Comment: 8 page

Characterization of the nitrogen split interstitial defect in wurtzite aluminum nitride using density functional theory

We carried out Heyd-Scuseria-Ernzerhof hybrid density functional theory plane wave supercell calculations in wurtzite aluminum nitride in order to characterize the geometry, formation energies, transition levels and hyperfine tensors of the nitrogen split interstitial defect. The calculated hyperfine tensors may provide useful fingerprint of this defect for electron paramagnetic resonance measurement.Comment: 5 pages, 3 figure

Rotation sets of billiards with one obstacle

We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets

An elementary proof of the irrationality of Tschakaloff series

We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment: 5 pages, AMSTe

A test on within-individual changes in risk-taking behaviour due to experience to predation in the Collared Flycatcher (Ficedula albicollis)

Different experiences from the past may have influence on individual¿s behaviour through feedback mechanisms that can weaken or preserve the within-individual consistency of behavioural traits. Here, we aimed to find evidence for such feedback mechanisms that may operate on risk-taking behaviour via the effect of former experience to potential predation events in male Collared Flycatchers (Ficedula albicollis). We predicted that risk-taking of males would decrease after experiencing a predator¿s attack in previous breeding seasons (negative feedback). We assessed risk-taking by flight initiation distance (FID) that is the distance at which an individual flees from an approaching predator, which was estimated for 234 individuals from different breeding seasons. Information on predation experience (i.e. occurrence of nest predation, the incidence of capture by human observers) was available from our long-term database on individual life histories. In a horizontal approach, we found no difference in FID when comparing males with former experience to predation with males naive to predators. A longitudinal approach relying on the repeated tests of the same individuals from different years yielded analogous results, we could not show a significant change in the risk-taking behaviour of the males as a consequence of experience to predation in past years. However, we found that individuals systematically took less risk over the years, which might be a consequence of acquiring general experience with agePeer Reviewe

Morphological and pathological response in primary systemic therapy of patients with breast cancer and the prediction of disease free survival

AIM: To identify breast cancer subtypes likely to respond to primary systemic therapy (PST or neoadjuvant therapy) and to assess the accuracy of physical examination (PE) and breast ultrasonography (US) in evaluating and predicting residual size of breast carcinoma following PST. METHODS: 116 patients who received at least two cycles of PST between 1998 and 2009 were selected from a prospectively collected clinical database. Radiological assessment was done by mammography and US. Prior to PST, tumors were subclassified according to core biopsy (NCB) and/or fine-needle aspiration-based immunohistochemical profiles of NCB. Pathological response rates were assessed following the surgeries by using Chevallier classification. Tumor measurements by PE and US were obtained before and after PST. Different clinical measurements were compared with histological findings. Disease-free survival (DFS) was assessed. RESULTS: Pathological complete remission (pCR=Chevallier I/II) was observed in 25 patients (21.5%), 44% of whom had triple negative histology, 28% Her2 positive and 76% had high-grade tumor. Of 116 patients, 24 received taxane-based PST, 48 combined taxane + anthracycline treatment, 8 trastuzumab combinations, 21 anthracycline-based treatments, and 15 other treatments. In the taxane treated group, the pCR rate was 30%, in the taxane + anthracycline group 25%, in the anthracycline group 9.5%, and in trastuzumab group 37.5%. After PST, PE and US were both significantly associated with pathology (P<0.001 and P=0.004, respectively). Concerning OS, significant difference was observed between the Chevallier III and IV group (P=0.031) in favor of Chevallier III group. In the pCR group, fewer events were observed during the follow-up period. CONCLUSIONS: Our results show that even limited, routinely used immunohistochemical profiling of tumors can predict the likelihood of pCR to PST: patients with triple negative and Her2-positive cancers are more likely to achieve pCR to PST. Also, PE is better correlated with pathological findings than US