Certain Integrals Arising from Ramanujan's Notebooks

In his third notebook, Ramanujan claims that $$\int_0^\infty \frac{\cos(nx)}{x^2+1} \log x \,\mathrm{d} x + \frac{\pi}{2} \int_0^\infty \frac{\sin(nx)}{x^2+1} \mathrm{d} x = 0.$$ In a following cryptic line, which only became visible in a recent reproduction of Ramanujan's notebooks, Ramanujan indicates that a similar relation exists if $\log x$ were replaced by $\log^2x$ in the first integral and $\log x$ were inserted in the integrand of the second integral. One of the goals of the present paper is to prove this claim by contour integration. We further establish general theorems similarly relating large classes of infinite integrals and illustrate these by several examples

Biological synthesis of fluorescent nanoparticles by cadmium and tellurite resistant Antarctic bacteria: exploring novel natural nanofactories

Indexación: Web of ScienceBackground: Fluorescent nanoparticles or quantum dots (QDs) have been intensely studied for basic and applied research due to their unique size-dependent properties. There is an increasing interest in developing ecofriendly methods to synthesize these nanoparticles since they improve biocompatibility and avoid the generation of toxic byproducts. The use of biological systems, particularly prokaryotes, has emerged as a promising alternative. Recent studies indicate that QDs biosynthesis is related to factors such as cellular redox status and antioxidant defenses. Based on this, the mixture of extreme conditions of Antarctica would allow the development of natural QDs producing bacteria. Results: In this study we isolated and characterized cadmium and tellurite resistant Antarctic bacteria capable of synthesizing CdS and CdTe QDs when exposed to these oxidizing heavy metals. A time dependent change in fluorescence emission color, moving from green to red, was determined on bacterial cells exposed to metals. Biosynthesis was observed in cells grown at different temperatures and high metal concentrations. Electron microscopy analysis of treated cells revealed nanometric electron-dense elements and structures resembling membrane vesicles mostly associated to periplasmic space. Purified biosynthesized QDs displayed broad absorption and emission spectra characteristic of biogenic Cd nanoparticles. Conclusions: Our work presents a novel and simple biological approach to produce QDs at room temperature by using heavy metal resistant Antarctic bacteria, highlighting the unique properties of these microorganisms as potent natural producers of nano-scale materials and promising candidates for bioremediation purposes.http://microbialcellfactories.biomedcentral.com/articles/10.1186/s12934-016-0477-

Accuracy of computerized tomography in determining hepatic tumor size in patients receiving liver transplantation or resection

Computerized tomography (CT) of liver is used in oncologic practice for staging tumors, evaluating response to treatment, and screening patients for hepatic resection. Because of the impact of CT liver scan on major treatment decisions, it is important to assess its accuracy. Patients undergoing liver transplantation or resection provide a unique opportunity to test the accuracy of hepatic-imaging techniques by comparison of finding of preoperative CT scan with those at gross pathologic examination of resected specimens. Forty-one patients who had partial hepatic resection (34 patients) or liver transplantation (eight patients) for malignant (30 patients) or benign (11 patients) tumors were evaluable. Eight (47%) of 17 patients with primary malignant liver tumors, four (31%) of 13 patients with metastatic liver tumors, and two (20%) of 10 patients with benign liver tumors had tumor nodules in resected specimens that were not apparent on preoperative CT studies. These nodules varied in size from 0.1 to 1.6 cm. While 11 of 14 of these nodules were 1.0 cm. These results suggest that conventional CT alone may be insufficient to accurately determine the presence or absence of liver metastases, extent of liver involvement, or response of hepatic metastases to treatment

Lower Limb Radiology of Distal Myopathy due to the S60F Myotilin Mutation

Distal myopathies are a clinically and genetically heterogenous group of disorders in which the distal limb musculature is selectively or disproportionately affected. Precisely defining specific categories is a challenge because of overlapping clinical phenotypes, making it difficult to decide which of the many known causative genes to screen in individual cases. In this study we define the distinguishing magnetic resonance imaging findings in myotilin myopathy by studying 8 genealogically unrelated cases due to the same point mutation in TTID. Proximally, the vastii, biceps femoris and semimembranosus were involved with sparing of gracilis and sartorius. Distally, soleus, gastrocnemius, tibialis anterior, extensor hallicus and extensor digitorum were involved. This pattern contrasts with other distal myopathies and provides further support for the role of imaging in the clinical investigation of muscle disease. Copyright (C) 2009 S. Karger AG, Base

Phosphorylation of Vasodilator-Stimulated Phosphoprotein (VASP) dampens hepatic ischemia-reperfusion injury

Recent work has demonstrated that the formation of platelet neutrophil complexes (PNCs) affects inflammatory tissue injury. Vasodilator-stimulated phosphoprotein (VASP) is crucially involved into the control of PNC formation and myocardial reperfusion injury. Given the clinical importance of hepatic IR injury we pursued the role of VASP during hepatic ischemia followed by reperfusion. We report here that VASP−/− animals demonstrate reduced hepatic IR injury compared to wildtype (WT) controls. This correlated with serum levels of lactate dehydrogenase (LDH), aspartate (AST) and alanine (ALT) aminotransferase and the presence of PNCs within ischemic hepatic tissue and could be confirmed using repression of VASP through siRNA. In studies employing bone marrow chimeric mice we identified hematopoietic VASP to be of crucial importance for the extent of hepatic injury. Phosphorylation of VASP on Ser153 through Prostaglandin E1 or on Ser235 through atrial natriuretic peptide resulted in a significant reduction of hepatic IR injury. This was associated with a reduced presence of PNCs in ischemic hepatic tissue. Taken together, these studies identified VASP and VASP phosphorylation as crucial target for future hepatoprotective strategies

Elevated CO2 levels affect the activity of nitrate reductase and carbonic anhydrase in the calcifying rhodophyte Corallina officinalis

The concentration of CO2 in global surface ocean waters is increasing due to rising atmospheric CO2 emissions, resulting in lower pH and a lower saturation state of carbonate ions. Such changes in seawater chemistry are expected to impact calcification in calcifying marine organisms. However, other physiological processes related to calcification might also be affected, including enzyme activity. In a mesocosm experiment, macroalgal communities were exposed to three CO2 concentrations (380, 665, and 1486 µatm) to determine how the activity of two enzymes related to inorganic carbon uptake and nutrient assimilation in Corallina officinalis, an abundant calcifying rhodophyte, will be affected by elevated CO2 concentrations. The activity of external carbonic anhydrase, an important enzyme functioning in macroalgal carbon-concentrating mechanisms, was inversely related to CO2 concentration after long-term exposure (12 weeks). Nitrate reductase, the enzyme responsible for reduction of nitrate to nitrite, was stimulated by CO2 and was highest in algae grown at 665 µatm CO2. Nitrate and phosphate uptake rates were inversely related to CO2, while ammonium uptake was unaffected, and the percentage of inorganic carbon in the algal skeleton decreased with increasing CO2. The results indicate that the processes of inorganic carbon and nutrient uptake and assimilation are affected by elevated CO2 due to changes in enzyme activity, which change the energy balance and physiological status of C. officinalis, therefore affecting its competitive interactions with other macroalgae. The ecological implications of the physiological changes in C. officinalis in response to elevated CO2 are discussed

Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental evidence, in the near future, that NEMS resonators are entering the quantum domain