On the second moment of the number of crossings by a stationary Gaussian process

Cram\'{e}r and Leadbetter introduced in 1967 the sufficient condition $$\frac{r''(s)-r''(0)}{s}\in L^1([0,\delta],dx),\qquad \delta>0,$$ to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable covariance function $r$. This condition is known as the Geman condition, since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows that the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman condition.Comment: Published at http://dx.doi.org/10.1214/009117906000000142 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Level curves, crossings and specular points for Gaussian models.

preprint; 25 pagesUsing generalizations of the well known Rice formula and applying the general method related to m-dependent processes that we settled in earlier works, allow one to obtain representations into the Ito-Wiener Chaos and CLTs for curve-crossings number. This approach not only explains heuristic considerations of Longuet-Higgins on specular points and related problems in the context of sea modelling, but goes far beyond when providing asymptotic results. These results on curve-crossings may also be applied in other fields. One example is the study of the estimator of the natural frequency of a harmonic oscillator

The strength of nuclear shell effects at N=126 in the r-process region

We have investigated nuclear shell effects across the magic number N=126 in the region of the r-process path. Microscopic calculations have been performed using the relativistic Hartree-Bogoliubov approach within the framework of the RMF theory for isotopic chains of rare-earth nuclei in the r-process region. The Lagrangian model NL-SV1 with the inclusion of the vector self-coupling of omega meson has been employed. The RMF results show that the shell effects at N=126 remain strong and exhibit only a slight reduction in the strength in going from the r-process path to the neutron drip line. This is in striking contrast to a systematic weakening of the shell effects at N=82 in the r-process region predicted earlier in the similar approach. In comparison the shell effects with microscopic-macroscopic mass formulae show a near constancy of shell gaps leading to strong shell effects in the region of r-process path to the drip line. A recent analysis of solar-system r-process abundances in a prompt supernova explosion model using various mass formulae including the recently introduced mass tables based upon HFB approach shows that whilst mass formulae with weak shell effects at N=126 give rise to a spread and an overproduction of nuclides near the third abundance peak at A~190, mass tables with droplet models showing stronger shell effects are able to reproduce the abundance features near the third peak appropriately. In comparison, several analyses of the second r-process peak at A~130 have required weakened shell effects at N=82. Our predictions in the RMF theory with NL-SV1, which exhibit weaker shell effects at N=82 and stronger one at N=126 in the r-process region, support the conjecture that a different nature of the shell effects at the magic numbers may be at play in r-process nucleosynthesis of heavy nuclei.Comment: 14 pages, 8 figures; submitted to Physical Review C. Part of this work was presented at Nuclear Physics in Astrophysics II, 20th International Nuclear Physics Divisional Conference of the European Physical Society, at Debrecen, Hungary, May 16-20, 200

Closed shells at drip-line nuclei

The shell structure of magic nuclei far from stability is discussed in terms of the self-consistent spherical Hartree-Fock-Bogoliubov theory. In particular, the sensitivity of the shell-gap sizes and the two-neutron separation energies to the choice of particle-hole and particle-particle components of the effective interaction is investigated.Comment: 19 pages, LaTeX, 8 uuencoded figures available upon reques

The additional-mode garden of RR Lyrae stars

Space-based photometric missions revealed a surprising abundance of millimagnitude-level additional modes in RR Lyrae stars. The modes that appear in the modulated fundamental-mode (RRab) stars can be ordered into four major categories. Here we present the distribution of these groups in the Petersen diagram, and discuss their characteristics and connections to additional modes observed in other RR Lyrae stars.Comment: 4 pages, 4 figures, proceedings of the Joint TASC2-KASC9-SPACEINN-HELAS8 Conference "Seismology of the Sun and the Distant Stars 2016", to be published in EPJ Wo

Development of Acid-Sensitive Platinum(II) Complexes With Protein-Binding Properties

Four new protein-binding platinum(II) complexes, 10, 11, 21, 22, in which the dichloroplatinum moiety is coordinated either to a carbon-substituted or a nitrogen-substituted ethylene diamino ligand, were prepared in ten-step syntheses. According to pH-dependent stability studies with strictly related compounds, 11 and 22 exhibit acid-sensitive properties

Opportunities and Challenges in Augmenting Honey Bee Forage Resources with Pasture Legumes in Southern Australia

More than 80% of Australian honey is produced from native tree and shrub species. However, with increasing demands on public lands along with production risks posed by drought, floods and wildfires, there is a need to identify alternative forage resources to augment Australian honey production. With over 30 pasture legumes now available for agriculture in southern Australia, opportunity exists to increase the utilisation of some species with co-benefits to multiple production industries. However, there is little understanding of the potential value of most pasture legumes for honey production, and side by side comparisons are complicated by factors such as differences in phenology, flower morphology and low nectar quantities. This paper describes a preliminary investigation presently underway in Australia comparing the floral attributes of 22 annual and short-lived perennial pasture legumes. The objective of the project is to prioritise species for their potential value to the local honey bee industry based on floral attributes, as well as existing and potential zones of adaptation. Methods being used to compare species in the Clover4Bees Pilot Study are described

On three topical aspects of the N=28 isotonic chain

The evolution of single-particle orbits along the N=28 isotonic chain is studied within the framework of a relativistic mean-field approximation. We focus on three topical aspects of the N=28 chain: (a) the emergence of a new magic number at Z=14; (b) the possible erosion of the N=28 shell; and (c) the weakening of the spin-orbit splitting among low-j neutron orbits. The present model supports the emergence of a robust Z=14 subshell gap in 48Ca, that persists as one reaches the neutron-rich isotone 42Si. Yet the proton removal from 48Ca results in a significant erosion of the N=28 shell in 42Si. Finally, the removal of s1/2 protons from 48Ca causes a ~50% reduction of the spin-orbit splitting among neutron p-orbitals in 42Si.Comment: 12 pages with 5 color figure

First decay study of the very neutron-rich isotope Br-93

The decay of the mass-separated, very neutron-rich isotope Br-93 has been studied by gamma-spectroscopy. A level scheme of its daughter Kr-93 has been constructed. Level energies, gamma-ray branching ratios and multipolarities suggest spins and parities which are in accord with a smooth systematics of the N=57 isotones for Z less-equal 40, suggesting the N=56 shell closure still to be effective in Kr isotopes. So far, there is no indication of a progressive onset of deformation in neutron-rich Kr isotopes.Comment: 17 pages, 3 figures, Phys. Rev. C, in prin