Strong uniqueness for stochastic evolution equations with unbounded measurable drift term

We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term $B$ and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper extends our previous paper (Da Prato, Flandoli, Priola and M. Rockner, Annals of Prob., published online in 2012) which generalized Veretennikov's fundamental result to infinite dimensions assuming boundedness of the drift term. As in our previous paper pathwise uniqueness holds for a large class, but not for every initial condition. We also include an application of our result to prove existence of strong solutions when the drift $B$ is only measurable, locally bounded and grows more than linearly.Comment: The paper will be published in Journal of Theoretical Probability. arXiv admin note: text overlap with arXiv:1109.036

Analysis of ghrelin concentrations in serum samples processed at one, two, and three hours after collection

Obesity is becoming an epidemic of modern society. While the health-related consequences of obesity have been well studied, scientists continue to search for biological risk factors associated with this disease. Since the 1999 discovery of an appetite-stimulating hormone, ghrelin, researchers have further questioned the physiological interactions that lead to obesity. The fundus of the stomach, as well as the intestines and kidneys produce ghrelin before it circulates throughout the body and attaches to its receptor sites located within the section of the brain responsible for appetite-regulation. The hormone increases and decreases in a circadian rhythm that may dictate the routine human eating patterns of breakfast, lunch and dinner. While the field of ghrelin research continues to grow as evidenced by the increasing number of published articles, the majority of the ghrelin research occurs in the laboratory setting. This environment has provided researchers with the preservation and storage techniques necessary to analyze ghrelin. For example, the current Millipore Human Ghrelin (Total) ELISA kit protocol for measuring ghrelin requires the collected blood be centrifuged thirty minutes after collection and immediately placed in a freezer. This limitation alone may impede researchers wishing to conduct clinical research because these requirements are frequently not possible. The objectives of this study were to determine the optimal storage time before processing blood samples collected in the clinical setting to ensure the preservation of ghrelin and to conclude whether a change in the manufacturer\u27s protocol was warranted. By comparing blood samples processed according to the Millipore ELISA kit protocol to samples stored for one, two, and three hours, it was determined that mean ghrelin concentrations at thirty minutes, one hour and two hour were not significantly different, suggesting that the current Millipore ELISA protocol of thirty minutes can be extended for a period of up to two hours. When the crude model was adjusted to include the variables time, waist circumference and exercise, the statistically significant variables in previous ANOVA models, the presence or absence of an exercise routine was found to have the strongest association to mean ghrelin concentrations. These findings will facilitate the experimental design of research aimed at studying ghrelin levels in individuals outside of the laboratory setting, and can also support new research analyzing the effect of exercise on ghrelin levels

Bulk Mediated Surface Diffusion: The Infinite System Case

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.Comment: 15 pages, 7 figure

Bulk Mediated Surface Diffusion: Finite System Case

We address the dynamics of adsorbed molecules (a fundamental issue in surface physics) within the framework of a Master Equation scheme, and study the diffusion of particles in a finite cubic lattice whose boundaries are at the $z=1$ and the $z=L$ planes where $L = 2,3,4,...$, while the $x$ and $y$ directions are unbounded. As we are interested in the effective diffusion process at the interface $z = 1$, we calculate analytically the conditional probability for finding the system on the $z=1$ plane as well as the surface dispersion as a function of time and compare these results with Monte Carlo simulations finding an excellent agreement.Comment: 19 pages, 8 figure

Seasonal changes in population of the Amphipod Gammarus aequicauda (Martynov, 1931)

Monthly collections were made for one year (March 2001 to February 2002) in Mar Piccolo of Taranto (Ionian sea, Italy), in order to establish the seasonal fluctuations of a population of Gammarus aequicauda (Crustacea, Amphipoda). Variations in the population structure, sex ratio and fecundity were studied. The population comprised all stages of the life cycle all year round, thus showing continuous reproduction. Size differences between males and females occurred throughout the year with males being larger than females. The recruitment of juveniles into the population occurred particularly in autumn-winter. Females consistently predominated in numbers over males during winter months. Female cephalic length was positively correlated with eggs number

The Symplectic Penrose Kite

The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in Comm. Math. Phys

Dynamical Masses of Low Mass Stars in the Taurus and Ophiuchus Star Forming Regions

We report new dynamical masses for 5 pre-main sequence (PMS) stars in the L1495 region of the Taurus star-forming region (SFR) and 6 in the L1688 region of the Ophiuchus SFR. Since these regions have VLBA parallaxes these are absolute measurements of the stars' masses and are independent of their effective temperatures and luminosities. Seven of the stars have masses $<0.6$ solar masses, thus providing data in a mass range with little data, and of these, 6 are measured to precision $< 5 \%$. We find 8 stars with masses in the range 0.09 to 1.1 solar mass that agree well with the current generation of PMS evolutionary models. The ages of the stars we measured in the Taurus SFR are in the range 1-3 MY, and $<1$ MY for those in L1688. We also measured the dynamical masses of 14 stars in the ALMA archival data for Akeson~\&~Jensen's Cycle 0 project on binaries in the Taurus SFR. We find that the masses of 7 of the targets are so large that they cannot be reconciled with reported values of their luminosity and effective temperature. We suggest that these targets are themselves binaries or triples.Comment: 20 page

Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares

Although both electron-ion and electron-electron bremsstrahlung contribute to the hard X-ray emission from solar flares, the latter is normally ignored. Such an omission is not justified at electron (and photon) energies above $\sim 300$ keV, and inclusion of the additional electron-electron bremsstrahlung in general makes the electron spectrum required to produce a given hard X-ray spectrum steeper at high energies. Unlike electron-ion bremsstrahlung, electron-electron bremsstrahlung cannot produce photons of all energies up to the maximum electron energy involved. The maximum possible photon energy depends on the angle between the direction of the emitting electron and the emitted photon, and this suggests a diagnostic for an upper cutoff energy and/or for the degree of beaming of the accelerated electrons. We analyze the large event of January 17, 2005 observed by RHESSI and show that the upward break around 400 keV in the observed hard X-ray spectrum is naturally accounted for by the inclusion of electron-electron bremsstrahlung. Indeed, the mean source electron spectrum recovered through a regularized inversion of the hard X-ray spectrum, using a cross-section that includes both electron-ion and electron-electron terms, has a relatively constant spectral index $\delta$ over the range from electron kinetic energy $E = 200$ keV to $E = 1$ MeV. However, the level of detail discernible in the recovered electron spectrum is not sufficient to determine whether or not any upper cutoff energy exists.Comment: 7 pages, 5 figures, submitted to Astrophysical Journa

Discovery of close companions to the nearby young stars HD 199143 and HD 358623

Young stellar systems in the solar neighborhood provide valuable laboratories for detailed studies of star and planet formation. The bright F8V star HD 199143 and the Li-rich late-type emission line star HD 358623 are among the nearest young stars identified to date, and may be members of a young association in Capricornus. We present high-resolution near-infrared images of these two sources, obtained using the adaptive optics system on the 3.6-meter telescope at the European Southern Observatory in La Silla, Chile. Our observations reveal that both are in fact close binary systems. The newly discovered companion at a separation of $\sim$1'' may account for the unusual characteristics of HD 199143 --rapid rotation, emission lines, ultraviolet variability, and excess infrared emission-- recently discussed by van den Ancker and co-workers. HD 199143 may be a rare example of a close binary with only a circum{\it secondary} disk. With the detection of a $\sim$2'' companion, HD 358623 is now possibly one of the closest known T Tauri binaries. Both binary systems are prime targets for follow-up spectroscopic and astrometric observations.Comment: 9 pages, 1 PostScript figure, to appear in The Astrophysical Journal Letter