Absolute continuity and spectral concentration for slowly decaying potentials

We consider the spectral function $\rho(\mu)$ $(\mu \geq 0)$ for the Sturm-Liouville equation $y^{''}+(\lambda-q)y =0$ on $[0,\infty)$ with the boundary condition $y(0)=0$ and where $q$ has slow decay $O(x^{-\alpha})$ $(a>0)$ as $x\to \infty$. We develop our previous methods of locating spectral concentration for $q$ with rapid exponential decay (JCAM 81 (1997) 333-348) to deal with the new theoretical and computational complexities which arise for slow decay

Extensions of a New Algorithm for the Numerical Solution of Linear Differential Systems on an Infinite Interval

This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper examines the situation when the matrix that appears in the Levinson expansion has a double eigenvalue. Application is made to a fourth-order ODE with known special function solution

Trace element analysis provides insight into the diets of early Late Miocene ungulates from the Rudabánya II locality (Hungary)

The early Late Miocene vertebrate locality of Rudabánya II (R. II) in northeastern Hungary preserves an abundance of forest-adapted ungulate species. To better understand the ecological relationships within this ancient ecosystem, we used analysis of enamel strontium/calcium (Sr/Ca) ratios to infer dietary preferences. The goals of the analysis were to: i) determine whether these ungulate species specialized in specific plants or plant parts; ii) discern whether the Sr/Ca ratios support what was previously suggested about the ecology of these species; and iii) evaluate the factors that may have acted to promote coexistence within this diverse community of predominantly browsing herbivores. Results show significant differences in the diets of the sampled species. The highest Sr/Ca ratios were displayed by the suids Parachleuastochoerus kretzoii [B1] and Propotamochoerus palaeochoerus implying a preference for Sr-rich underground plant parts. Elevated Sr/Ca ratios yielded by the cervid Lucentia aff. pierensis and equid Hippotherium intrans are indicative of intermediate feeding. The bovid Miotragocerus sp. showed higher Sr/Ca ratios than the gomphothere Tetralophodon longirostris, which is incongruent with morphological and stable isotope data, and suggested browsing by both taxa. This finding is likely the result of a difference in digestive physiology (ruminant vs. monogastric) rather than a difference in dietary behaviour. The lowest Sr/Ca ratios were displayed by the traguild Dorcatherium naui and moschid Micromeryx flourensianussuggesting a preference for Sr-poor fruits. Resource specialization and partitioning within the local environment likely acted to decrease interspecific competition and promote coexistence within the diverse ungulate community at R. II

Massive Dirac particles on the background of charged de-Sitter black hole manifolds

We consider the behavior of massive Dirac fields on the background of a charged de-Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordstr\"{o}m-de-Sitter one, the Nariai case and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the non-existence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and it is shown to hold true even for extremal cases. Furthermore, we shift our attention on the very interesting problem of the quantum discharge of the black holes. Following Damour-Deruelle-Ruffini approach, we show that the existence of level-crossing between positive and negative continuous energy states is a signal of the quantum instability leading to the discharge of the black hole, and in the cases of the Nariai geometry and of the ultracold geometries we also calculate in WKB approximation the transmission coefficient related to the discharge process.Comment: 19 pages, 11 figures. Macro package: Revtex4. Changes concern mainly the introduction and the final discussion in section VI; moreover, Appendix D on the evaluation of the Nariai transmission integral has been added. References adde

Androgen receptor mutations in prostate cancer

We analyzed the frequency and relevance of mutations in the coding region of the androgen receptor (AR) in genomic DNA extracted from 137 specimens of prostate cancer. The specimens were obtained from the primary tumors of patients affected by stage B disease [15 nonmicrodissected (group 1A) and 84 microdissected (group 1B)] and from the metastatic deposits of individuals with stage D1 disease [8 nonmicrodissected (group 2A) and 30 microdissected (group 2B)] who had not undergone androgen ablation therapy. The study was conducted by PCR-single strand conformational polymorphism (SSCP) analysis of exons 2-8 in the four groups and direct sequence analysis of exon 1 in group 1B. As positive and negative controls, we used genomic DNA extracted from genital skin fibroblasts of patients affected by various forms of androgen resistance with known mutations in the AR. To control for genetic instability, PCR-SSCP analysis of exon 2 of the human progesterone receptor was carried out on each specimen. The overall number of mutations detected was 11 (8%). No mutations were detected in any of the 99 patients with stage B disease. Eleven mutations were detected in exons 2-8 in 8 of the 38 patients with stage D1 disease (all in group 2B). Simultaneous analysis of exon 2 of the progesterone receptor was carried out, and no SSCP changes were identified. These data suggest that AR mutations are rare and presumably do not play a role in the initial phase of prostatic carcinogenesis. The presence of a significant number of AR mutations in metastatic disease indicates that mutations of this molecule may play a role in the most advanced phases of the natural history of this disease, either by facilitating growth or acquisition of the metastatic phenotype

On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local perturbation of the operator might embed an eigenvalue into the continuous spectrum (a feature uncommon for periodic elliptic operators of second order). In all known constructions of such examples, the corresponding eigenfunction is compactly supported. One wonders whether this must always be the case. The paper answers this question affirmatively. What is more surprising, one can estimate that the eigenmode must be localized not far away from the perturbation (in a neighborhood of the perturbation's support, the width of the neighborhood determined by the unperturbed operator only). The validity of this result requires the condition of irreducibility of the Fermi (Floquet) surface of the periodic operator, which is expected to be satisfied for instance for periodic Schroedinger operators.Comment: Submitted for publicatio