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

Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

The Good, The Bad, The Ugly: Using Naturally Occurring Terata to Distinguish the Possible from the Impossible in Orchid Floral Evolution

We interpret extensive field observations of terata in the context of recent insights into monocot phylogeny and evolutionary-developmental genetics to explore the evolution of the orchid flower. Our arguably typological classification of floral terata focuses on natural occurrences of three contrasting modes of peloria (restoration of actinomorphy in a formerly zygomorphic perianth) and three contrasting modes of pseudopeloria (lessening of the degree of zygomorphy shown by the evolutionarily preceding perianth). Dynamic evolutionary transitions in floral morphology are assigned to recently revised concepts of heterotopy (including homeosis: evolutionary transitions in position of expression) and heterochrony (evolutionary transitions in timing of expression), seeking patterns that delimit developmental constraints and allow inferences regarding underlying genetic controls. Lateral heterotopy, occurring within the whorl of three petals (including the labellum) or within the adjacent whorl of three sepals, is more frequent than acropetal heterotopy, and full basipetal heterotopy does not occur. Pseudopeloria is more likely than peloria to generate a radically altered yet functional perianth but is also more likely to cause acropetal modification of the fused filaments and style that constitute the characteristic gynostemium of orchids. We infer that at least one gene or gene complex controls stylestamen fusion, which requires the preadaptation of strongly developed epigyny, and another determines both stamen suppression and labellum formation adaxially. Our earlier hypothesis implicating genes of the TCP family has recently been challenged by empirical evidence of complex interactions between several MADS-box genes. Many transitions are highly iterative, and some are reversible (atavistic). Once heritability has been demonstrated, the most effective criteria for determining the most appropriate taxonomic status of a novel morph are the profundity of the phenotypic shift that it represents, the number and uniformity of the resulting populations, and whether the novel morph subsequently diversified to generate further morphs that retain the innovative features. Although morphological transitions attributable to heterochrony may be a more common driver of speciation than those attributable to heterotopy, we demonstrate that arguably all of the modes of instantaneous floral transition described in this paper have the ability to generate prospecies

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

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

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2

Global Electric Circuit Diurnal Variation Derived from Storm Overflight and Satellite Optical Lightning Datasets

We have combined analyses of over 1000 high altitude aircraft observations of electrified clouds with diurnal lightning statistics from the Lightning Imaging Sensor (LIS) and Optical Transient Detector (OTD) to produce an estimate of the diurnal variation in the global electric circuit. Using basic assumptions about the mean storm currents as a function of flash rate and location, and the global electric circuit, our estimate of the current in the global electric circuit matches the Carnegie curve diurnal variation to within 4% for all but two short periods of time. The agreement with the Carnegie curve was obtained without any tuning or adjustment of the satellite or aircraft data. Mean contributions to the global electric circuit from land and ocean thunderstorms are 1.1 kA (land) and 0.7 kA (ocean). Contributions to the global electric circuit from ESCs are 0.22 kA for ocean storms and 0.04 kA for land storms. Using our analysis, the mean total conduction current for the global electric circuit is 2.0 kA

The functional integral with unconditional Wiener measure for anharmonic oscillator

In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).Comment: Source file which we sent to journa