On the upper bound of the number of limit cycles obtained by the second order averaging method I

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On the upper bound of the number of limit cycles obtained by the second order averaging method II

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Geometric tools to determine the hyperbolicity of limit cycles

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Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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Liquid chromatography-tandem mass spectrometry (LC/APCI-MS/MS) methods for the quantification of captan and folpet phthalimide metabolites in human plasma and urine.

Captan and folpet are fungicides largely used in agriculture. They have similar chemical structures, except that folpet has an aromatic ring unlike captan. Their half-lives in blood are very short, given that they are readily broken down to tetrahydrophthalimide (THPI) and phthalimide (PI), respectively. Few authors measured these biomarkers in plasma or urine, and analysis was conducted either by gas chromatography coupled to mass spectrometry or liquid chromatography with UV detection. The objective of this study was thus to develop simple, sensitive and specific liquid chromatography-atmospheric pressure chemical ionization-tandem mass spectrometry (LC/APCI-MS/MS) methods to quantify both THPI and PI in human plasma and urine. Briefly, deuterated THPI was added as an internal standard and purification was performed by solid-phase extraction followed by LC/APCI-MS/MS analysis in negative ion mode for both compounds. Validation of the methods was conducted using spiked blank plasma and urine samples at concentrations ranging from 1 to 250 μg/L and 1 to 50 μg/L, respectively, along with samples of volunteers and workers exposed to captan or folpet. The methods showed a good linearity (R (2) > 0.99), recovery (on average 90% for THPI and 75% for PI), intra- and inter-day precision (RSD, <15%) and accuracy (<20%), and stability. The limit of detection was 0.58 μg/L in urine and 1.47 μg/L in plasma for THPI and 1.14 and 2.17 μg/L, respectively, for PI. The described methods proved to be accurate and suitable to determine the toxicokinetics of both metabolites in human plasma and urine.

Octopus Standard Automated Perimetry, Pulsar Perimetry, Moorfields Motion Displacement Test and Heidelberg Retinal Tomography in Glaucoma Detection - A Comparison of Diagnostic Accuracy

Purpose: To investigate the accuracy of 4 clinical instruments in the detection of glaucomatous damage. Methods: 102 eyes of 55 test subjects (Age mean = 66.5yrs, range = [39; 89]) underwent Heidelberg Retinal Tomography (HRTIII), (disc area<2.43); and standard automated perimetry (SAP) using Octopus (Dynamic); Pulsar (TOP); and Moorfields Motion Displacement Test (MDT) (ESTA strategy). Eyes were separated into three groups 1) Healthy (H): IOP<21mmHg and healthy discs (clinical examination), 39 subjects, 78 eyes; 2) Glaucoma suspect (GS): Suspicious discs (clinical examination), 12 subjects, 15 eyes; 3) Glaucoma (G): progressive structural or functional loss, 14 subjects, 20 eyes. Clinical diagnostic precision was examined using the cut-off associated with the p<5% normative limit of MD (Octopus/Pulsar), PTD (MDT) and MRA (HRT) analysis. The sensitivity, specificity and accuracy were calculated for each instrument. Results: See table Conclusions: Despite the advantage of defining glaucoma suspects using clinical optic disc examination, the HRT did not yield significantly higher accuracy than functional measures. HRT, MDT and Octopus SAP yielded higher accuracy than Pulsar perimetry, although results did not reach statistical significance. Further studies are required to investigate the structure-function correlations between these instruments.

Quantification of clenbuterol at trace level in human urine by ultra-high pressure liquid chromatography-tandem mass spectrometry.

Clenbuterol is a β2 agonist agent with anabolic properties given by the increase in the muscular mass in parallel to the decrease of the body fat. For this reason, the use of clenbuterol is forbidden by the World Anti-Doping Agency (WADA) in the practice of sport. This compound is of particular interest for anti-doping authorities and WADA-accredited laboratories due to the recent reporting of risk of unintentional doping following the eating of meat contaminated with traces of clenbuterol in some countries. In this work, the development and the validation of an ultra-high pressure liquid chromatography coupled to electrospray ionization tandem mass spectrometry (UHPLC-ESI-MS/MS) method for the quantification of clenbuterol in human urine is described. The analyte was extracted from urine samples by liquid-liquid extraction (LLE) in basic conditions using tert butyl-methyl ether (TBME) and analyzed by UHPLC-MS/MS with a linear gradient of acetonitrile in 9min only. The simple and rapid method presented here was validated in compliance with authority guidelines and showed a limit of quantification at 5pg/mL and a linearity range from 5pg/mL to 300pg/mL. Good trueness (85.8-105%), repeatability (5.7-10.6% RSD) and intermediate precision (5.9-14.9% RSD) results were obtained. The method was then applied to real samples from eighteen volunteers collecting urines after single oral doses administration (1, 5 and 10μg) of clenbuterol-enriched yogurts.

Pupal cocoons affect sanitary brood care and limit fungal infections in ant colonies.

BACKGROUND: The brood of ants and other social insects is highly susceptible to pathogens, particularly those that penetrate the soft larval and pupal cuticle. We here test whether the presence of a pupal cocoon, which occurs in some ant species but not in others, affects the sanitary brood care and fungal infection patterns after exposure to the entomopathogenic fungus Metarhizium brunneum. We use a) a comparative approach analysing four species with either naked or cocooned pupae and b) a within-species analysis of a single ant species, in which both pupal types co-exist in the same colony. RESULTS: We found that the presence of a cocoon did not compromise fungal pathogen detection by the ants and that species with cocooned pupae increased brood grooming after pathogen exposure. All tested ant species further removed brood from their nests, which was predominantly expressed towards larvae and naked pupae treated with the live fungal pathogen. In contrast, cocooned pupae exposed to live fungus were not removed at higher rates than cocooned pupae exposed to dead fungus or a sham control. Consistent with this, exposure to the live fungus caused high numbers of infections and fungal outgrowth in larvae and naked pupae, but not in cocooned pupae. Moreover, the ants consistently removed the brood prior to fungal outgrowth, ensuring a clean brood chamber. CONCLUSION: Our study suggests that the pupal cocoon has a protective effect against fungal infection, causing an adaptive change in sanitary behaviours by the ants. It further demonstrates that brood removal-originally described for honeybees as "hygienic behaviour"-is a widespread sanitary behaviour in ants, which likely has important implications on disease dynamics in social insect colonies.

Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem µa la Cournot

In this paper, we consider an exchange economy µa la Shitovitz (1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley and known as the Shapley window model. We analyze the relationship between the set of the Cournot-Nash equilibrium allocations of the strategic market game and the Walras equilibrium allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably in¯nite, any Cournot-Nash equilibrium allocation of the game is not a Walras equilibrium of the underlying exchange economy. Accordingly, in the original spirit of Cournot (1838), we par- tially replicate the mixed exchange economy by increasing the number of atoms, without a®ecting the atomless part, and ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market games associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

Reduced quality of life associated adverse events in intermediate hepatocellular carcinoma patients treated with PRECISION TACE with drug eluting beads: Results from the PRECISION V randomized trial : B-241

Purpose: To evaluate the extent of quality of life (QoL) associated adverse events (AEs) following PRECISION TACE with DC Bead compared with conventional transarterial chemoembolisation (cTACE). Methods and Materials: 201 intermediate HCC patients were treated with DC Bead (PRECISION TACE) or conventional TACE (cTACE) with doxorubicin in the PRECISION V clinical study. 93 patients were treated with DC Bead and 108 Patients with cTACE every 2 months and followed up for 6 months. AEs were classified according to the South West Oncology Group criteria. QoL associated AEs were defined as alopecia, constipation, nausea, vomiting, pyrexia, chills, asthenia, fatigue, and headache. Results: The biggest difference in QoL associated AEs was for alopecia: 2 patients (2.2%) for DC-Bead versus 21 patients (19.4%) for cTACE. For other clinical symptoms, constipation (n=10; 10.8% vs. n=13; 12%), vomiting (n=10; 10.8% vs. n=14; 13.0%), pyrexia (n=16; 17.2% vs. n=26; 24.1%), chills (n=1; 1.1% vs. n=5; 4.6%), and headache (n=2; 2.2% vs. n=8; 7.4%) showed lower incidence in the DC Bead group versus cTACE. Nausea, n= 15; 13.9% (n=15; 16.1%) and fatigue, n=6; 5.6% (n=13; 14.0%) were lower for cTACE. Total dose of doxorubicin was on average 35% higher in the DC Bead group. Conclusion: Although patients in the DC Bead group received a higher doxorubicin dose, less QoL associated AEs were reported for this group. Alopecia, the most obvious outward sign of toxicity, was only reported in a tenth of DC Bead patients. Thus, PRECISION TACE with DC Bead improves quality of life associated adverse events.

Repositioning precision of coronary arteries measured on X-ray angiography and its implications for coronary MR angiography.

BACKGROUND: To test the hypothesis that intervals with superior beat-to-beat coronary artery repositioning precision exist in the cardiac cycle, to design a coronary MR angiography (MRA) methodology in response, and to ascertain its performance. METHODS: Coronary repositioning precision in consecutive heartbeats was measured on x-ray coronary angiograms of 17 patients and periods with the highest repositioning precision were identified. In response, the temporal order of coronary MRA pulse sequence elements required modification and the T2 -prep now follows (T2 -post) rather than precedes the imaging part of the sequence. The performance of T2 -post was quantitatively compared (signal-to-noise [SNR], contrast-to-noise [CNR], vessel sharpness) to that of T2 -prep in vivo. RESULTS: Coronary repositioning precision is <1 mm at peak systole and in mid diastole. When comparing systolic T2 -post to diastolic T2 -prep, CNR and vessel sharpness remained unchanged (both P = NS) but SNR for muscle and blood increased by 104% and 36% (both P < 0.05), respectively. CONCLUSION: Windows with improved coronary repositioning precision exist in the cardiac cycle: one in peak systole and one in mid diastole. Peak-systolic imaging necessitates a re-design of conventional coronary MRA pulse sequences and leads to image quality very similar to that of conventional mid-diastolic data acquisition but improved SNR. J. Magn. Reson. Imaging 2015;41:1251-1258. © 2014 Wiley Periodicals, Inc.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.