Weighted inequalities for commutators of Schr\"odinger-Riesz transforms

In this work we obtain weighted $L^p$, $1<p<\infty$, and weak $L\log L$ estimates for the commutator of the Riesz transforms associated to a Schr\"odinger operator -\lap+V, where $V$ satisfies some reverse H\"older inequality. The classes of weights as well as the classes of symbols are larger than $A_p$ and $BMO$ corresponding to the classical Riesz transforms

Using Optically Stimulated Luminescence to Unravel Sedimentary Processes of the Usumacinta and Grijalva Rivers (SE Mexico)

This report provides an optically stimulated luminescence (OSL) chronology for sediment collected through terrace deposits of the Usumacinta and Grijalva rivers in SE Mexico. The Grijalva and Usumacinta rivers are susceptible to flooding during the hurricane season (between May and November), affecting the population of the state of Tabasco, and leaving many households at a flood risk. The present study was initiated to obtain an understanding of the sediment processes, rates and frequency of flood events in the past. The report summaries the initial luminescence profiling, using a SUERC PPSL system, and laboratory analysis, used to characterise the stratigraphy and interpret sedimentary processes in each profile, together with the quantitative quartz SAR dating used to define chronologies in each. Initial luminescence profiling revealed that the stratigraphy in each was complex, reflecting multiple cycles of deposition, with maxima, followed by a tail to lower intensities, possibly indicating deposition during extreme flood events, followed by a period in which the sediment was mixed and the luminescence signals reset. The laboratory profiling reproduced the apparent maxima/trends in the field profiling dataset. In the Grijalva section, the profiling samples encompass the full range of variations in the IRSL net signal intensities, re-affirming the complex stratigraphy. In the Usumacinta section, the profiling samples were positioned on the trend of a normal age-depth progression, which may indicate that the horizons sampled are well suited for quartz SAR dating. Given the nature of the sediment sampled, it is unsurprising that the equivalent dose distributions obtained for each of the dating samples showed considerable scatter, leading to some ambiguity in estimating a stored dose for age calculations. In each, a number of aliquots returned high equivalent dose values, implying residual luminescence signals (leading to higher apparent ages), and others, low values, implying re-setting of the luminescence signals in the modern environment. It is well recognised that fluvial sediment of this sort can enclose mixed-age populations. It has been argued elsewhere (Fuchs and Lang, 2001; Lepper et al., 2000; Olley et al., 1998; Olley et al., 1999) that the lowest population of dose(s) may best represent the burial dose of the youngest depositional component, and that an arbitrary value of say the lowest 5% be used in age calculations. However, if this method was instigated for the Mexican samples, it would include the low equivalent dose values thought to reflect contamination from the surface, by bioturbation or some other weathering process, leading to artificially young ages. Therefore, each sample was evaluated on an individual basis, where low equivalent doses were considered to represent contamination and rejected, along with high equivalent dose outliers and any aliquots which failed SAR acceptance criteria. The weighted mean and weighted standard deviation of the reduced set were used in age calculations. The dating results reported here provide a first chronology to interpret the changing fluvial dynamics of the Usumacinta and Grijalva rivers, and a means to quantify flood events through the historical period. The chronology established for the Grijalva section spans from the 6th century AD to the 12th century AD; and the chronology for the Usumacinta section from the 17th century AD to the 19th century AD

Luminescence Dating of Beach Dunes and Fluvial Sediments, Nayarit, Mexico

The Pacific coast of the state of Nayarit, Mexico, is dominated by extensive sand dune systems and lagoons. 16 samples from three transects through dunes near the town of Santa Cruz were collected to establish ages of the beach dune ridges and establish a robust chronology, to assist in understanding the depositional rates associated with different phases of the evolution of the strand plain. In addition, three samples were collected from a fluvial terrace on the San Pedro River which enters the Pacific near the southernmost of the dune transects. Quartz grains were extracted from the samples, and analysed using an Optically Stimulated Luminescence (OSL) method to determine stored dose and ages. The samples collected nearest the current coast have produced dates of 1500-1900AD, with samples further from the coast being progressively older, spanning a period of over 2000 years with oldest measured date of 400BC. The dates for the upper samples from the San Pedro River is consistent with the ages of the dunes nearest the coast, with the lower sample date closer to the dates of the older dunes further from the coast, indicating that this fluvial deposit was laid down over the same time period as the dune formation

Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Polydispersity Effects in the Dynamics and Stability of Bubbling Flows

The occurrence of swarms of small bubbles in a variety of industrial systems enhances their performance. However, the effects that size polydispersity may produce on the stability of kinematic waves, the gain factor, mean bubble velocity, kinematic and dynamic wave velocities is, to our knowledge, not yet well established. We found that size polydispersity enhances the stability of a bubble column by a factor of about 23% as a function of frequency and for a particular type of bubble column. In this way our model predicts effects that might be verified experimentally but this, however, remain to be assessed. Our results reinforce the point of view advocated in this work in the sense that a description of a bubble column based on the concept of randomness of a bubble cloud and average properties of the fluid motion, may be a useful approach that has not been exploited in engineering systems.Comment: 11 pages, 2 figures, presented at the 3rd NEXT-SigmaPhi International Conference, 13-18 August, 2005, Kolymbari, Cret

Growth and Reproduction in Gulf of Mexico Black Corals (Antipatharians) in Field and Laboratory Studies

Black corals provide an important ecosystem of marine life and are found throughout all the oceans of the world at depths between 2 and 8,600 m. However, little is understood about their life history and the factors that control the distribution of black corals, particularly in the Gulf of Mexico (GoM). Given the impacts of the Deepwater Horizon oil spill on soft corals (e.g., black corals and octocorals) in the GoM, studies of their growth and reproductive biology in both natural and aquaculture environments are crucial for restoration efforts. The objectives of this study were to examine reproductive processes, compare growth rates in situ and in aquaculture, and provide an aquaculture guide for two species of black corals (Stichopathes luetkeni and Antipathes atlantica) in the GoM. The data collected during this study will provide vital information for the protection and management of black corals at mesophotic depths in the GoM

EVALUATION OF THE ANTIOXIDANT ACTIVITY OF THE FLAVONOIDS ISOLATED FROM HELIOTROPIUM SINUATUM RESIN USING ORACFL, DPPH AND ESR METHODOLOGIES

Indexación: Web of Science; Scielo.The antioxidant capacity has been determined for a number of flavonoid compounds from Heliotropium sinuatum, a plant that grows in arid areas in the north of Chile. The methodologies used were: ORAC(FL) (oxygen radical absorbance capacity - fluorescein), DPPH (2,2-diphenyl-2-picrylhydrazyl) bleaching and electron spin resonance (ESR). These compounds were studied in homogeneous and heterogeneous media. The results showed that the 7-o-methyleriodictiol and 3-o-methylisorhamnetin are those with the highest antioxidant capacity.http://ref.scielo.org/m82cz