Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations

The purpose of this paper is to present new oscillation theorems and nonoscillation theorems for the nonlinear Euler differential equation t²x''′+g(x)=0. Here we assume that xg(x)>0 if x≠0, but we do not necessarily require that g(x) be monotone increasing. The obtained results are best possible in a certain sense. To establish our results, we use Sturm’s comparison theorem for linear Euler differential equations and phase plane analysis for a nonlinear system of Liénard type.Наведено нові осцнляційні та неосцнляційні теореми для нелінійного диференціального рівняння Ейлера t²x''′+g(x)=0, де припускається, що xg(x)>0 при x≠0, але вимога про монотонне зростання g(x) не є обов'язковою. Одержані результати є найкращими у певному сенсі. Для їх встановлення використано порівняльну теорему Штурма для лінійних диференціальних рівнянь Ейлера та фазовий площинний аналіз для нелінійної системи типу Льєнарда

Earliest detection of the optical afterglow of GRB 030329 and its variability

We report the earliest detection of an extremely bright optical afterglow of the gamma-ray burst (GRB) 030329 using a 30cm-telescope at Tokyo Institute of Technology (Tokyo, JAPAN). Our observation started 67 minutes after the burst, and continued for succeeding two nights until the afterglow faded below the sensitivity limit of the telescope (approximately 18 mag). Combining our data with those reported in GCN Circulars, we find that the early afterglow light curve of the first half day is described by a broken power-law (t^{- alpha}) function with indices alpha_{1} = 0.88 +/- 0.01 (0.047 < t < t_{b1} days), alpha_{2} = 1.18 +/- 0.01 (t_{b1} < t < t_{b2} days), and alpha_{3} = 1.81 +/- 0.04 (t_{b2} < t < 1.2 days), where t_{b1} ~ 0.26 days and t_{b2} ~ 0.54 days, respectively. The change of the power-law index at the first break at t ~ 0.26 days is consistent with that expected from a ``cooling-break'' when the cooling frequency crossed the optical band. If the interpretation is correct, the decay index before the cooling-break implies a uniform ISM environment.Comment: 13 pages, 1 table and 2 figures. Accepted to the Astrophysical Journal Letter

Charge-Focusing Readout of Time Projection Chambers

Time projection chambers (TPCs) have found a wide range of applications in particle physics, nuclear physics, and homeland security. For TPCs with high-resolution readout, the readout electronics often dominate the price of the final detector. We have developed a novel method which could be used to build large-scale detectors while limiting the necessary readout area. By focusing the drift charge with static electric fields, we would allow a small area of electronics to be sensitive to particle detection for a much larger detector volume. The resulting cost reduction could be important in areas of research which demand large-scale detectors, including dark matter searches and detection of special nuclear material. We present simulations made using the software package Garfield of a focusing structure to be used with a prototype TPC with pixel readout. This design should enable significant focusing while retaining directional sensitivity to incoming particles. We also present first experimental results and compare them with simulation.Comment: 5 pages, 17 figures, Presented at IEEE Nuclear Science Symposium 201

Correlation Between Mucosal IL-6 mRNA Expression Level and Virulence Factors of Helicobacter pylori in Iranian Adult Patients With Chronic Gastritis

Background: Helicobacter pylori infection is associated with gastritis and marked infiltration of the gastric mucosa by several cytokines secreting inflammatory cells that contribute to sustained local inflammation. In this study, we sought to examine IL-6 expression in H. pylori-infected and uninfected gastric mucosa and elucidate the implication in the pathogenesis of H. pylori-associated gastritis in human. Objectives: The current study aimed to determine mucosal IL-6 mRNA expression level and their correlation with virulence factors and the grade of chronic gastritis among H. pylori infected patients with chronic gastritis from Shahrekord, Iran. Patients and Methods: Mucosal IL-6 mRNA levels was measured by real-time PCR using endoscopic biopsies taken from the gastric antrum of 58 subjects infected with H. pylori and 44 uninfected subjects. Presence of vacA and cagA virulence factors was evaluated using PCR. Results: The IL-6 mRNA expression levels were significantly more elevated in H. pylori-positive patients than uninfected individuals and expression of this cytokine was independent from the virulence factors. There was a correlation between IL-6 expression level and the grade of chronic gastritis. Conclusions: Enhanced induction of IL-6 may be involved in the pathogenesis of H. pylon-associated gastritis

Pathogenic variation of Phakopsora pachyrhizi populations in Brazil.

The obligate basidiomycete Phakopsora pachyrhizi is the causal agent of soybean rust that has potential to reduce the yield of soybean drastically. Soybean production in Brazil has been threatened by the rust since the pathogen was first discovered in 2001. To understand pathogenic variation of the rust populations in South America, an evaluation system for soybean rust resistance has been constructed using a set of 16 differential varieties. In this study, the evaluation system was used to investigate pathogenic variation among the P. pachyrhizi populations in Brazil. Samples of P. pachyrhizi were collected from the diseased soybeans in Brazil in the 2007-2008 and 2008-2009 soybean cultivation seasons. In the first season, two rust samples showed similar pattern of the infection types on the differential set, suggesting that the same or similar pathogen population was present in the two locations. The other samples were likely different pathogenic populations. In the second season, different patterns of the infection types were found among the samples. Comparison of the evaluation data from the two seasons demonstrated that pathogenic variation between the seasons was detected in the populations from Rio Grande do Sul and Paraná but was not remarkable in those from Rondônia. This study provides useful knowledge about P. pachyrhizi populations in Brazil to identify the resistant soybean genotypes and target effective cultivars against certain pathogen populations.Edição do Proceedings of the National Soybean Rust Symposium, New Orleans, 2009