Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations

We consider the focusing nonlinear Schr\"odinger equations $i\partial_t u+\Delta u +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities p_c with $p_c=1+\frac{4}{N}$ and 0<\e\ll 1. We prove the existence and stability in the energy space $H^1$ of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up tim

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

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

Timberland Tall Tales

https://digitalmaine.com/books/1108/thumbnail.jp

REAPPRAISAL OF FEDERAL QUESTION JURISDICTION

For some time I have been reading and listening to criticisms directed toward decisions which the Supreme Court has rendered in cases involving federal question jurisdiction. The general \u27tenor of this criticism is that these decisions demonstrate a surprising lack of uniformity and conscious purpose. Writers profess to search in vain for sound logic in the Court\u27s opinions. They point up instead the anomaly which is reflected when cases involving a substantial federal issue are tried in state courts, while those in which no real federal issue is involved are nevertheless accepted for trial in the federal courts. This result, however, cannot be regarded as· happenstance. The Court must be as fully aware of the result as the rest of the legal community. That it persists in its interpretation is evidence that it believes its decisions fully comprehend the Constitutional and Congressional policies underlying the federal question. If that be so, the policy behind this. type of jurisdiction cannot be to insure an initial trial in the federal courts for every controversy involving a federal question, as some have apparently thought. The real policy or policies behind the decisions relating to federal question jurisdiction can be ascertained only with the help of history. The legal analyst too often forgets that his logic must be applied in context. Whether or not the decisions of the Supreme Court follow a pattern which has elements both of reason and of sound policy. depends upon the historical ingredients. It seems useless to criticise decisions for their lack of reason without first establishing the policy criteria by which those decisions are to be judged. Until we establish the real meaning of federal question and learn: what prompted its statutory treatment we cannot judge the actions of the Court when it deals with this matter. In order, therefore, to side intelligently either with the Court or its critics we must follow the emergence and development of federal question through the historical periods in which it has taken shape

RBF neural net based classifier for the AIRIX accelerator fault diagnosis

The AIRIX facility is a high current linear accelerator (2-3.5kA) used for flash-radiography at the CEA of Moronvilliers France. The general background of this study is the diagnosis and the predictive maintenance of AIRIX. We will present a tool for fault diagnosis and monitoring based on pattern recognition using artificial neural network. Parameters extracted from the signals recorded on each shot are used to define a vector to be classified. The principal component analysis permits us to select the most pertinent information and reduce the redundancy. A three layer Radial Basis Function (RBF) neural network is used to classify the states of the accelerator. We initialize the network by applying an unsupervised fuzzy technique to the training base. This allows us to determine the number of clusters and real classes, which define the number of cells on the hidden and output layers of the network. The weights between the hidden and the output layers, realising the non-convex union of the clusters, are determined by a least square method. Membership and ambiguity rejection enable the network to learn unknown failures, and to monitor accelerator operations to predict future failures. We will present the first results obtained on the injector.Comment: 3 pages, 4 figures, LINAC'2000 conferenc

Continuations of the nonlinear Schr\"odinger equation beyond the singularity

We present four continuations of the critical nonlinear \schro equation (NLS) beyond the singularity: 1) a sub-threshold power continuation, 2) a shrinking-hole continuation for ring-type solutions, 3) a vanishing nonlinear-damping continuation, and 4) a complex Ginzburg-Landau (CGL) continuation. Using asymptotic analysis, we explicitly calculate the limiting solutions beyond the singularity. These calculations show that for generic initial data that leads to a loglog collapse, the sub-threshold power limit is a Bourgain-Wang solution, both before and after the singularity, and the vanishing nonlinear-damping and CGL limits are a loglog solution before the singularity, and have an infinite-velocity{\rev{expanding core}} after the singularity. Our results suggest that all NLS continuations share the universal feature that after the singularity time $T_c$, the phase of the singular core is only determined up to multiplication by $e^{i\theta}$. As a result, interactions between post-collapse beams (filaments) become chaotic. We also show that when the continuation model leads to a point singularity and preserves the NLS invariance under the transformation $t\rightarrow-t$ and $\psi\rightarrow\psi^\ast$, the singular core of the weak solution is symmetric with respect to $T_c$. Therefore, the sub-threshold power and the{\rev{shrinking}}-hole continuations are symmetric with respect to $T_c$, but continuations which are based on perturbations of the NLS equation are generically asymmetric

Improved Limit on theta_{13} and Implications for Neutrino Masses in Neutrino-less Double Beta Decay and Cosmology

We analyze the impact of a measurement, or of an improved bound, on theta_{13} for the determination of the effective neutrino mass in neutrino-less double beta decay and cosmology. In particular, we discuss how an improved limit on (or a specific value of) theta_{13} can influence the determination of the neutrino mass spectrum via neutrino-less double beta decay. We also discuss the interplay with improved cosmological neutrino mass searches.Comment: 22 pages, 5 figures. Minor corrections, matches version in PR