Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Seroprevalence of Chikungunya Virus after Its Emergence in Brazil.

Chikungunya has had a substantial impact on public health because of the magnitude of its epidemics and its highly debilitating symptoms. We estimated the seroprevalence, proportion of symptomatic cases, and proportion of chronic form of disease after introduction of chikungunya virus (CHIKV) in 2 cities in Brazil. We conducted the population-based study through household interviews and serologic surveys during October-December 2015. In Feira de Santana, we conducted a serologic survey of 385 persons; 57.1% were CHIKV-positive. Among them, 32.7% reported symptoms, and 68.1% contracted chronic chikungunya disease. A similar survey in Riachão do Jacuípe included 446 persons; 45.7% were CHIKV-positive, 41.2% reported symptoms, and 75.0% contracted the chronic form. Our data confirm intense CHIKV transmission during the continuing epidemic. Chronic pain developed in a high proportion of patients. We recommend training health professionals in management of chronic pain, which will improve the quality of life of chikungunya-affected persons

Analysis of organogenic competence of cotyledons of Jatropha curcas and their in vitro histological behavior

Using cut pieces cotyledons from germinating zygotic embryos of Jatropha curcas, we monitored the series of anatomical events leading to the generation of shoot through organogenesis by histological analysis. 14 days old cotyledons that were pre-cultured in a half strength Murashige and Skoog (MS) media supplemented with 100 mg/L myoinositol and 10 mg/L thiamine HCl, were cultured in organogenic competence induction media (CIM) comprising of MS salts with 1.5 mg/L benzyl adenine (BA) and 0.05 mg/L indole-3-butyric acid (IBA) and incubated for the induction of organogenic competence. Following their sequential transfer to shoot induction media (containing MS + 1.5 mg/L BA, 0.05 mg/L IBA and 0.5 mg/L GA3); shoot elongation media (containing MS + 0.3 mg/L BA) and rooting media (containing half strength MS + IBA at different concentrations), we selected individual explants and subjected them to histological analysis in order to study the morphological changes occurring during organogenesis. Our findings show that to induce organogenesis using cut pieces of cotyledons, these tissues must be harvested at least by the 14th day following germination. Optimal organogenic competence was attained after 21 days incubation period in the dark where most of the explants showed evidence of protruding shoots surrounded by calli with various morphological features. Up to 53.91% of the total explants cultured in this study produced well defined shoots with each explant producing an average number of 1.5 shoots bearing two to eight leaves. We recorded the highest percentage of root formation, which stood at 27.50% when the shoots were cultured in a rooting media containing 0.3 mg/L IBA. Histological analysis of the different events occurring during the process of organogenesis suggest that the protuberances arising from parenchymatous cells and perhaps bundle sheath forming meristematic centres acquiring organogenic competence have a multicellular origin, indicating that the regeneration process takes place through direct organogenesis.Key words: Jatropha curcas, organogenesis, auxins, histological analysis

Laser-induced etching of few-layer graphene synthesized by Rapid-Chemical Vapour Deposition on Cu thin films

The outstanding electrical and mechanical properties of graphene make it very attractive for several applications, Nanoelectronics above all. However a reproducible and non destructive way to produce high quality, large-scale area, single layer graphene sheets is still lacking. Chemical Vapour Deposition of graphene on Cu catalytic thin films represents a promising method to reach this goal, because of the low temperatures (T < 900 Celsius degrees) involved during the process and of the theoretically expected monolayer self-limiting growth. On the contrary such self-limiting growth is not commonly observed in experiments, thus making the development of techniques allowing for a better control of graphene growth highly desirable. Here we report about the local ablation effect, arising in Raman analysis, due to the heat transfer induced by the laser incident beam onto the graphene sample.Comment: v1:9 pages, 8 figures, submitted to SpringerPlus; v2: 11 pages, PDFLaTeX, 9 figures, revised peer-reviewed version resubmitted to SpringerPlus; 1 figure added, figure 1 and 4 replaced,typos corrected, "Results and discussion" section significantly extended to better explain etching mechanism and features of Raman spectra, references adde

Biomass Ashes for Acid Mine Drainage Remediation

Acid mine drainage (AMD) is the largest environmental problem facing the world mining and processing industry because it has low pH and can contain high concentrations of potential pollutants. Biomass ash (BA) can be considered as a potential material for AMD treatment. The main goal of this work was to investigate potential use of Biomass ash of CPK-LA and PK-LA types for AMD remediation. Four UK BAs from diferent fuels (i.e. straw, meat and bone meal, poultry litter), synthetic AMD, and raw AMDs (Belovo and Ursk) were used for the AMD treatment experiments. Batch experiments showed that in 1 h the biomass ash from straw combustion can efectively neutralise the synthetic AMD and the Belovo AMD with removal of potential pollutants at the liquid-to-solid ratio (L/S) of 100–250 and 10–50, respectively. The biomass ashes from straw and poultry litter combustion can efectively remove pollutants from the Ursk AMD at L/S 100 and adjust pH. The metal concentrations of those treated AMDs met receiving water quality standards. Potential pollutants precipitated as carbonate/hydroxide/sulphate, co-precipitated with Fe oxyhydroxides and Ca phosphates, and appeared as new phases such as Ca, Cu, Zn phosphates and Ca, Fe phosphates. This investigation is essential for development of appropriate, environmentally friendly and economically rational waste management

Modelling human visual navigation using multi-view scene reconstruction

It is often assumed that humans generate a 3D reconstruction of the environment, either in egocentric or world-based coordinates, but the steps involved are unknown. Here, we propose two reconstruction-based models, evaluated using data from two tasks in immersive virtual reality. We model the observer’s prediction of landmark location based on standard photogrammetric methods and then combine location predictions to compute likelihood maps of navigation behaviour. In one model, each scene point is treated independently in the reconstruction; in the other, the pertinent variable is the spatial relationship between pairs of points. Participants viewed a simple environment from one location, were transported (virtually) to another part of the scene and were asked to navigate back. Error distributions varied substantially with changes in scene layout; we compared these directly with the likelihood maps to quantify the success of the models. We also measured error distributions when participants manipulated the location of a landmark to match the preceding interval, providing a direct test of the landmark-location stage of the navigation models. Models such as this, which start with scenes and end with a probabilistic prediction of behaviour, are likely to be increasingly useful for understanding 3D vision

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Brane-World Gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004) "Brane-World Gravity", 119 pages, 28 figures, the update contains new material on RS perturbations, including full numerical solutions of gravitational waves and scalar perturbations, on DGP models, and also on 6D models. A published version in Living Reviews in Relativit

The trochlear isometric point is different in patients with recurrent patellar instability compared to controls: a radiographical study

Purpose: The purpose of the study was to investigate the theoretical isometric point based of the curve of the femoral groove and relating it to the origin of the MPFL femoral tunnel on lateral radiograph by comparing a patellar instability cohort with a control cohort. Methods: From a Patellar Instability database the radiographs of 40 consecutive patients were analysed to define Schöttle’s point, and the arc of the circle of the trochlear groove. A comparison population of 20 radiographs from comparable patients with tibiofemoral joint disorders was used as a control. The distance from Schöttle’s point to the most anterior part of the groove (extension) was also compared to the distance to the distal end of the roof of the notch (flexion). Results: The trochlea was circular in the controls but not the Patellofemoral Instability cohort where trochlear dysplasia is usually present. The difference between the extension and flexion length was a mean of − 2.0 ± 0.5 mm in the controls and + 6.0 ± 0.5 mm in the patellofemoral cohort. In neither cohort did the centre of the circle correspond to Schöttle’s point. The extension distance correlated with the boss height. Conclusions: The dysplastic trochlea is not circular and the centre of the best matched circle was different to the control trochleae which were circular. The circle centres did not correlate with Schöttle’s point for either cohort, and was more proximal in the Patellofemoral Instability cohort. Clinical relevance: For the MPFL to have equal tension throughout flexion within the groove, the length should not change. In normal knees the MPFL does not behave isometrically. The change in length, as measured from Schöttle’s point to the trochlea, was greater for patellofemoral instability patients explaining why an isolated MPFL reconstruction in the presence of severe trochlear dysplasia risks poor outcomes