Use of a Strongly Nonlinear Gambier Equation for the Construction of Exact Closed Form Solutions of Nonlinear ODEs

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration

Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1) equations). Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1) equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form) have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis

Nonparametric Modeling and Model-Based Control of the Insulin-Glucose System

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Effects on surface atmospheric photo-oxidants over Greece during the total solar eclipse event of 29 March 2006

International audienceThis study investigates the effects of the total solar eclipse of 29 March 2006 on surface air-quality levels over Greece based on observations at a number of sites in conjunction with chemical box modelling and 3-D air-quality modelling. Emphasis is given on surface ozone and other photooxidants at four Greek sites Kastelorizo, Finokalia (Crete), Pallini (Athens) and Thessaloniki, which are located at gradually increasing distances from the path of the eclipse totality and are characterized by different air pollution levels. The eclipse offered the opportunity to test our understanding of air pollution build-up and the response of the gas-phase chemistry of photo-oxidants during a photolytical perturbation using both a photochemical box model and a regional air-quality offline model based on the modeling system WRF/CAMx. At the relatively unpolluted sites of Kastelorizo and Finokalia no clear impact of the solar eclipse on surface O3, NO2 and NO concentrations can be deduced from the observations and model simulations as the calculated changes in net ozone production rates between eclipse and non eclipse conditions are rather small compared to the ozone variability and hence the solar eclipse effects on ozone can be easily masked by transport. At the polluted sites of Thessaloniki and Pallini, the solar eclipse effects on O3, NO2 and NO concentrations are clearly revealed from both the measurements and 3-D air-quality modeling with the net effect being a decrease in O3 and NO and an increase in NO2 as NO2 formed from the reaction of O3 with NO while at the same time NO2 is not efficiently photolysed. It is evident from the 3-D air quality modeling over Greece that the maximum effects of the eclipse on O3, NO2 and NO are reflected at the large urban agglomerations of Athens, and Thessaloniki where the maximum of the emissions occur

Small-bowel necrosis complicating a cytomegalovirus-induced superior mesenteric vein thrombosis in an immunocompetent patient: a case report

<p>Abstract</p> <p>Introduction</p> <p>Superior mesenteric venous thrombosis as a result of acute cytomegalovirus infection is rare, with only a few cases reported in the literature.</p> <p>Case presentation</p> <p>We present the case of a 40-year-old Caucasian man who was admitted to our hospital with a 5-day history of fever. His serological test and pp65 antigen detection of cytomegalovirus were positive, suggesting acute infection. On the sixth day after his admission, the patient complained of acute, progressive abdominal pain. Abdominal computed tomography revealed acute superior mesenteric venous thrombosis. An emergency laparotomy showed diffuse edema and ischemic lesions of the small bowel and its associated mesentery with a 50-cm-long segmental infarction of the proximal jejunum. An extensive enterectomy of about 100 cm of jejunum that included the necrotic segment was performed, followed by an end-to-end anastomosis. Anti-coagulation therapy was administered pre-operatively in the form of small-fractionated heparin and continued postoperatively. The patient had an uneventful recovery and was discharged on the 11th postoperative day.</p> <p>Conclusion</p> <p>Acute cytomegalovirus infection can contribute to the occurrence of mesenteric venous thrombosis in immunocompetent patients. It is important for physicians and internists to be aware of the possible thrombotic complications of cytomegalovirus infection. A high level of clinical suspicion is essential to successfully treat a potentially lethal condition such as superior mesenteric venous thrombosis.</p

Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows

Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. Conserved circulation laws, such as those of Kelvin, Alfv\'en and Bekenstein-Oron, emerge simply as special cases of the Poincar\'e-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (non-isentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.Comment: 23 page

Quasi-equilibrium models of magnetized compact objects

We report work towards a relativistic formulation for modeling strongly magnetized neutron stars, rotating or in a close circular orbit around another neutron star or black hole, under the approximations of helical symmetry and ideal MHD. The quasi-stationary evolution is governed by the first law of thermodynamics for helically symmetric systems, which is generalized to include magnetic fields. The formulation involves an iterative scheme for solving the Einstein-Maxwell and relativistic MHD-Euler equations numerically. The resulting configurations for binary systems could be used as self-consistent initial data for studying their inspiral and merger.Comment: Talk given at the 14th Conference on Recent Developments in Gravity (NEB XIV), Ioannina, Greece, 8-11 Jun 201

Izolacija i sposobnost hvatanja slobodnih radikala cijanidin 3-O-glikozida iz plodova Ribes biebersteinii Berl.

The reversed-phase preparative high performance liquid chromatographic purification of the methanol extract of the fruits of Ribes biebersteinii Berl. (Grossulariaceae) afforded five cyanidin glycosides, 3-O-sambubiosyl-5-O-glucosyl cyanidin (1), cyanidin 3-O-sambubioside (2), cyanidin 3-O-glucoside (3), cyanidin 3-O-(2G-xylosyl)-rutinoside (4) and cyanidin 3-O-rutinoside (5). They showed considerable free-radical-scavenging properties in the 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay with the RC50 values of 9.29 × 106, 9.33 × 106, 8.31 × 106, 8.96 × 106 and 9.55 × 106 mol L1, respectively. The structures of these compounds were elucidated by various chemical hydrolyses and spectroscopic means. The total anthocyanin content was 1.9 g per 100 g dried fruits on cyanidin 3-glucoside basis.Pet cijanidin glikozida, 3-O-sambubiozil-5-O-glukozil cijanidin (1), cijanidin 3-O-sambubiozid (2), cijanidin 3-O-glukozid (3), cijanidin 3-O-(2G-ksilozil)-rutinozid (4) i cijanidin 3-O-rutinosid (5) izolirani su iz metanolnog ekstrakta plodova Ribes biebersteinii Berl. (Grossulariaceae) koristeći reverzno-faznu preparativnu tekućinsku kromatografiju visoke učinkovitosti. Cijanidin glikozidi pokazali su sposobnost hvatanja slobodnih radikala u pokusu s 2,2-difenil-1-pikrilhidrazilom (DPPH). Dobivene su sljedeće RC50 vrijednosti: 9,29 × 106, 9,33 × 106, 8,31 × 106, 8,96 × 106, odnosno 9,55 × 106 mol L1. Strukture glikozida određene su kemijskom hidrolizom i spektroskopijom masa. Ukupni sadržaj antocijanina bio je 1,9 g na 100 g suhih plodova preračunato na cijanidin 3-glukozid

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far