Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension

We consider the semilinear wave equation with power nonlinearity in one space dimension. We consider an arbitrary blow-up solution $u(x,t)$, the graph $x\mapsto T(x)$ of its blow-up points and ${\cal S}\subset {\mathbb R}$ the set of all characteristic points. We show that {\ca S} is locally finite.Comment: 57 page

Thermal rearrangements in the tetra-arylcyclopropene series

The literature provides many examples of thermal rearrangements of small-ring compounds to yield systems involving less bond-angle strain. In the arylcyclopropene series these involve, in many cases, fairly complex pathways, and only formalized mechanisms have been suggested

Reliability analysis of dynamic systems by translating temporal fault trees into Bayesian networks

Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

Horticultural markets promote alien species invasions : an Estonian case study of herbaceous perennials

Gardening is a popular pastime, but commercial horticulture is responsible for the introduction of alien species and contributes to invasions in a variety of ways. Although an extensive international literature is available on plant invasions, it is still important at the national level to examine the influence of local factors. Accordingly, 17 nurseries in Estonia that cultivated and sold perennial alien species were selected, and a list of species and prices was compiled. The relationships between species status, and factors such as their abundance in the wild were examined statistically. A qualitative list of the nationally problematic species among herbaceous perennials was also completed. A total of 880 taxa were recorded, of which 10.3% were native and 89.7% alien. In all, 87.3% of the alien species were still confined to cultivated areas. The ecological and socio-economic characteristics of the taxa were described, and lists of the families of casual, naturalised and invasive aliens were provided. Both native and increasing wild alien species have a very similar profile on the market. Alien species that are less expensive, widely available and have more cultivars per species on the market are also more likely to escape. The invasive status and abundance of escaped aliens in an area increases with residence time. In general, socio-economic factors create new and reflect previous propagule pressures from commercial horticulture, which continuously increase the likelihood of alien species surviving and invading new areas. Our findings suggest that these national socioeconomic market-related factors explain much of the invasiveness of various perennial ornamental species, and therefore regional and national authorities urgently need to regulate and control the ornamental plant trade to diminish the risk of new invasions

IP Eri: A surprising long-period binary system hosting a He white dwarf

We determine the orbital elements for the K0 IV + white dwarf (WD) system IP Eri, which appears to have a surprisingly long period of 1071 d and a significant eccentricity of 0.25. Previous spectroscopic analyses of the WD, based on a distance of 101 pc inferred from its Hipparcos parallax, yielded a mass of only 0.43 M$_\odot$, implying it to be a helium-core WD. The orbital properties of IP Eri are similar to those of the newly discovered long-period subdwarf B star (sdB) binaries, which involve stars with He-burning cores surrounded by extremely thin H envelopes, and are therefore close relatives to He WDs. We performed a spectroscopic analysis of high-resolution spectra from the HERMES/Mercator spectrograph and concluded that the atmospheric parameters of the K0 component are $T_{\rm eff} = 4960$ K, $\log{g} = 3.3$, [Fe/H] = 0.09 and $\xi = 1.5$ km/s. The detailed abundance analysis focuses on C, N, O abundances, carbon isotopic ratio, light (Na, Mg, Al, Si, Ca, Ti) and s-process (Sr, Y, Zr, Ba, La, Ce, Nd) elements. We conclude that IP Eri abundances agree with those of normal field stars of the same metallicity. The long period and non-null eccentricity indicate that this system cannot be the end product of a common-envelope phase; it calls instead for another less catastrophic binary-evolution channel presented in detail in a companion paper (Siess et al. 2014).Comment: 14 pages, 10 figures, 4 tables, accepted for publication in A&A (Update of Table 3, Fig. 8 and text in Sect. 5.1, 5.3 and 6 due to minor corrections on N and Y II

Why a splitting in the final state cannot explain the GSI-Oscillations

In this paper, I give a pedagogical discussion of the GSI anomaly. Using two different formulations, namely the intuitive Quantum Field Theory language of the second quantized picture as well as the language of amplitudes, I clear up the analogies and differences between the GSI anomaly and other processes (the Double Slit experiment using photons, $e^+ e^- \to \mu^+ \mu^-$ scattering, and charged pion decay). In both formulations, the conclusion is reached that the decay rate measured at GSI cannot oscillate if only Standard Model physics is involved and the initial hydrogen-like ion is no coherent superposition of more than one state (in case there is no new, yet unknown, mechanism at work). Furthermore, a discussion of the Quantum Beat phenomenon will be given, which is often assumed to be able to cause the observed oscillations. This is, however, not possible for a splitting in the final state only.Comment: 10 pages, 3 figures; matches published version (except for some stylistic ambiguities