The von Neumann-Wigner type potentials and the wave functions' asymptotics for the discrete levels in continuum

One to one correspondence between the decay law of the von Neumann-Wigner type potentials and the asymptotic behaviour of the wave functions representing bound states in the continuum is established.Comment: latex, 7 page

Incidence of seropositive myasthenia gravis in Cape Town and South Africa

Background. Myasthenia gravis (MG) is a treatable autoimmune disease characterised by fatiguable weakness of skeletal muscles. More than 85% of MG patients have antibodies to the acetylcholine receptor (AChR) at the neuromuscular junction or are seropositive for MG (SPMG). In the developed world the incidence of MG has increased, particularly among older individuals, but no epidemiological studies have been done on SPMG in Africa. Objectives. To determine the annual incidence rate (IR) of SPMG in the Cape Town (CT) municipality, and the crude annual IR of SPMG for the whole of South Africa (SA). Methods. Positive AChR antibody tests were identified between 1 January 2003 and 1 January 2005 for patients living in CT, and the age- and sex-specific incidences were calculated. To determine the national crude annual IR over the same period, positive assays were identified from the laboratories that process AChR assays for SA. National Census 2001 population statistics formed the denominators. Results. There were 65 positive assays in CT, and 230 nationwide. Based on these figures the annual IR for CT was 11.2 per million per year (95% confidence interval (CI) 8.7 - 14.3), and for South Africa 2.6 per million / year (95% CI 2.2 - 2.9). After a questionnaire response from CT neurologists regarding the routine use of the AChR antibody assay, the annual IR for CT was adjusted to 12.6 per million (95% CI 9.9 - 15.9) to incorporate those presumed to have SPMG without a confirmatory test. In CT, the IR in females was 15.3 per million / year (95% CI 11.2 - 20.4), and in males, 6.8 per million / year (95% CI 4.1 - 10.7). The CT IRs for blacks, coloureds and whites were not statistically different after adjusting for age and gender. The IR of SPMG in CT was 6 times greater in those presenting after the age of 50 years than in those with earlier disease onset (95% CI 3.7 - 9.7). Conclusions. The annual IR of SPMG in CT is much the same as rates recorded recently in other developed countries, but the rest of SA has a much lower IR. A preponderance of MG starting after the age of 50 years reflects a worldwide trend, although the CT data showed a relatively lower-than-expected incidence for older males. IRs for SPMG vary widely in different regions in SA; this is likely to be related to differences in regional health care delivery, and underdiagnosis

Laplace transform of spherical Bessel functions

We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the Langevin equation in a one-dimensional Debye model.Comment: 5 pages LATEX, no figures. Accepted 2002, Physica Script

Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Hot Electron Capture Dissociation Distinguishes Leucine from Isoleucine in a Novel Hemoglobin Variant, Hb Askew, β54(D5)Val→Ile

Population migration has led to the global dispersion of human hemoglobinopathies and has precipitated a need for their identification. An effective mass spectrometry-based procedure involves analysis of the intact α- and β-globin chains to determine their mass, followed by location of the variant amino acid residue by direct analysis of the enzymatically digested chains and low-energy collision induced dissociation of the variant peptide. Using this procedure, a variant was identified as either β54Val→Leu or β54Val→Ile, since the amino acids leucine and isoleucine cannot be distinguished using low-energy collisions. Here, we describe how hot electron capture dissociation on a Fourier transform-ion cyclotron resonance mass spectrometer was used to distinguish isoleucine from leucine and identify the mutation as β54(D5)Val→Ile. This is a novel variant, and we have named it Hb Askew

Finite Euler Hierarchies And Integrable Universal Equations

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed {}from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories, {\it classical\ts} topological field theories -- whose classical solutions span topological classes of manifolds -- and reparametrisation invariant theories -- generalising ordinary string and membrane theories. On the other hand, {\it finite} Euler hierarchies are constructed for all three classes of theories. These hierarchies terminate with {\it universal\ts} equations of motion, probably defining new integrable systems as they admit an infinity of Lagrangians. Speculations as to the possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p., (Plain TeX), DTP-92/3

On the unitarity of higher-dervative and nonlocal theories

We consider two simple models of higher-derivative and nonlocal quantu systems.It is shown that, contrary to some claims found in literature, they can be made unitary.Comment: 8 pages, no figure

Quantum cosmological perfect fluid models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $\alpha \alpha > - 1$.Comment: Latex file, 12 pages. New paragraphs in the Introduction and Conclusion, and other minor corrections in the text and in some formulas. Accepted for publication in General Relativity and Gravitatio