Strichartz estimates for the water-wave problem with surface tension

Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales depending on the size of the frequencies. We infer that a solution $u$ of the dispersive equation we introduce satisfies local-in-time Strichartz estimates with loss in derivative: $$\| u \|_{L^p([0,T]) W^{s-1/p,q}(\mathbb{R})} \leq C, \qquad \frac{2}{p} + \frac{1}{q} = {1/2},$$ where $C$ depends on $T$ and on the norms of the initial data in $H^s \times H^{s-3/2}$. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.Comment: Fixed typos and mistakes. Merged with arXiv:0809.451

Fearless versus Fearful Speculative Financial Bubbles

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The model predicts the existence of two anomalous behaviors occurring simultaneously: (i) super-exponential price growth and (ii) volatility growth, that we refer to as the ``fearful singular bubble'' regime. Out of the 9 time series, we find that 5 pass our tests and can be characterized as ``fearful singular bubbles.'' The 4 other cases are the information technology Nasdaq bubble and three bubbles of the Hang Seng index ending in crashes in 1987, 1994 and 1997. According to our analysis, these four bubbles have developed with essentially no significant increase of their volatility. This paper thus proposes that speculative bubbles ending in crashes form two groups hitherto unrecognized, namely those accompanied by increasing volatility (reflecting increasing risk perception) and those without change of volatility (reflecting an absence of risk perception).Comment: 12 pages + 9 figures + 9 table

Depression and mortality: Artifact of measurement and analysis?

Background Previous research demonstrates various associations between depression, cardiovascular disease (CVD) incidence and mortality, possibly as a result of the different methodologies used to measure depression and analyse relationships. This analysis investigated the association between depression, CVD incidence (CVDI) and mortality from CVD (MCVD), smoking related conditions (MSRC), and all causes (MALL), in a sample data set, where depression was measured using items from a validated questionnaire and using items derived from the factor analysis of a larger questionnaire, and analyses were conducted based on continuous data and grouped data. Methods Data from the PRIME Study (N=9798 men) on depression and 10-year CVD incidence and mortality were analysed using Cox proportional hazards models. Results Using continuous data, both measures of depression resulted in the emergence of positive associations between depression and mortality (MCVD, MSRC, MALL). Using grouped data, however, associations between a validated measure of depression and MCVD, and between a measure of depression derived from factor analysis and all measures of mortality were lost. Limitations Low levels of depression, low numbers of individuals with high depression and low numbers of outcome events may limit these analyses, but levels are usual for the population studied. Conclusions These data demonstrate a possible association between depression and mortality but detecting this association is dependent on the measurement used and method of analysis. Different findings based on methodology present clear problems for the elucidation and determination of relationships. The differences here argue for the use of validated scales where possible and suggest against over-reduction via factor analysis and grouping. CrownCopyright © 2013PublishedbyElsevierB.V.Allrightsreserved

The common ‘thermolabile' variant of methylene tetrahydrofolate reductase is a major determinant of mild hyperhomocysteinaemia

Mild hyperhomocysteinaemia is a major risk factor for vascular disease and neural tube defects (NTDs), conferring an approximately three-fold relative risk for each condition. It has several possible causes: heterozygosity for rare loss of function mutations in the genes for 5,10-methylene tetrahydrofolate reductase (MTHFR) or cystathionine-β-synthase (CBS); dietary insufficiency of vitamin co-factors B6, B12 or folates; or homozygosity for a common ‘thermolabile' mutation in the MTHFR gene which has also been associated with vascular disease and NTDs. We quantified the contribution of the thermolabile mutation to the hyperhomocysteinaemic phenotype in a working male population (625 individuals). Serum folate and vitamin B12 concentrations were also measured and their relationship with homocysteine status and MTHFR genotype assessed. The homozygous thermolabile genotype occurred in 48.4, 35.5, and 23.4% of the top 5,10, and 20% of individuals (respectively) ranked by plasma homocysteine levels, compared with a frequency of 11.5% in the study population as a whole, establishing that the mutation is a major determinant of homocysteine levels at the upper end of the range. Serum folate concentrations also varied with genotype, being lowest in thermolabile homozygotes. The MTHFR thermolabile genotype should be considered when population studies are designed to determine the effective homocysteine-lowering dose of dietary folate supplements, and when prophylactic doses of folate are recommended for individual

Lesbian and bisexual women's human rights, sexual rights and sexual citizenship: negotiating sexual health in England.

Lesbian and bisexual women's sexual health is neglected in much Government policy and practice in England and Wales. This paper examines lesbian and bisexual women's negotiation of sexual health, drawing on findings from a small research project. Themes explored include invisibility and lack of information, influences on decision-making and sexual activities and experiences of services and barriers to sexual healthcare. Key issues of importance in this respect are homophobic and heterosexist social contexts. Drawing on understandings of lesbian, gay and bisexual human rights, sexual rights and sexual citizenship, it is argued that these are useful lenses through which to examine and address lesbian and bisexual women's sexual health and related inequalities

Phase diagram of the ABC model on an interval

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a one-dimensional lattice of N sites with closed (zero flux) boundaries. In this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical Gibbs measure with long range asymmetric pair interactions. This generalizes results for the ring case, where detailed balance holds, and in fact the steady state measure is known only for the case of equal densities of the different species: in the latter case the stationary states of the system on a ring and on an interval are the same. We prove that in the N to infinity limit the scaled density profiles are given by (pieces of) the periodic trajectory of a particle moving in a quartic confining potential. We further prove uniqueness of the profiles, i.e., the existence of a single phase, in all regions of the parameter space (of average densities and temperature) except at low temperature with all densities equal; in this case a continuum of phases, differing by translation, coexist. The results for the equal density case apply also to the system on the ring, and there extend results of Clincy et al.Comment: 52 pages, AMS-LaTeX, 8 figures from 10 eps figure files. Revision: minor changes in response to referee reports; paper to appear in J. Stat. Phy

Reversible Random Sequential Adsorption of Dimers on a Triangular Lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca++ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.Comment: 9 pages, 10 figure

Measuring airway mucin 2 in patients with severe chronic obstructive pulmonary disease with bacterial colonization

Sibila and colleagues reported an analysis of the levels of the secreted polymeric mucins MUC2, MUC5AC, and MUC5B in the sputum and bronchoalveolar lavage fluid of patients with severe chronic obstructive pulmonary disease (COPD) (1). We are writing because they found a very high level of MUC2 in both specimens, whereas most recent studies by others find little or no MUC2 in the airway. Therefore, this report raises the possibility of an error in measurement that could cause confusion in the field

Water wave propagation and scattering over topographical bottoms

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps