Existence et multiplicité de solutions de systèmes d'équations et de systèmes d'inclusions différentielles avec opérateurs maximaux monotones

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Existence et multiplicité de solutions de systèmes d'équations et de systèmes d'inclusions différentielles avec opérateurs maximaux monotones

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Théorèmes d'existence pour des systèmes d'équations différentielles et d'équations aux échelles de temps.

Nous présentons dans cette thèse des théorèmes d’existence pour des systèmes d’équations différentielles non-linéaires d’ordre trois, pour des systèmes d’équa- tions et d’inclusions aux échelles de temps non-linéaires d’ordre un et pour des systèmes d’équations aux échelles de temps non-linéaires d’ordre deux sous cer- taines conditions aux limites. Dans le chapitre trois, nous introduirons une notion de tube-solution pour obtenir des théorèmes d’existence pour des systèmes d’équations différentielles du troisième ordre. Cette nouvelle notion généralise aux systèmes les notions de sous- et sur-solutions pour le problème aux limites de l’équation différentielle du troisième ordre étudiée dans [34]. Dans la dernière section de ce chapitre, nous traitons les systèmes d’ordre trois lorsque f est soumise à une condition de crois- sance de type Wintner-Nagumo. Pour admettre l’existence de solutions d’un tel système, nous aurons recours à la théorie des inclusions différentielles. Ce résultat d’existence généralise de diverses façons un théorème de Grossinho et Minhós [34]. Le chapitre suivant porte sur l’existence de solutions pour deux types de sys- tèmes d’équations aux échelles de temps du premier ordre. Les résultats d’exis- tence pour ces deux problèmes ont été obtenus grâce à des notions de tube-solution adaptées à ces systèmes. Le premier théorème généralise entre autre aux systèmes et à une échelle de temps quelconque, un résultat obtenu pour des équations aux différences finies par Mawhin et Bereanu [9]. Ce résultat permet également d’obte- nir l’existence de solutions pour de nouveaux systèmes dont on ne pouvait obtenir l’existence en utilisant le résultat de Dai et Tisdell [17]. Le deuxième théorème de ce chapitre généralise quant à lui, sous certaines conditions, des résultats de [60]. Le chapitre cinq aborde un nouveau théorème d’existence pour un système d’in- clusions aux échelles de temps du premier ordre. Selon nos recherches, aucun résultat avant celui-ci ne traitait de l’existence de solutions pour des systèmes d’inclusions de ce type. Ainsi, ce chapitre ouvre de nouvelles possibilités dans le domaine des inclusions aux échelles de temps. Notre résultat a été obtenu encore une fois à l’aide d’une hypothèse de tube-solution adaptée au problème. Au chapitre six, nous traitons l’existence de solutions pour des systèmes d’équations aux échelles de temps d’ordre deux. Le premier théorème d’existence que nous obtenons généralise les résultats de [36] étant donné que l’hypothèse que ces auteurs utilisent pour faire la majoration a priori est un cas particulier de notre hypothèse de tube-solution pour ce type de systèmes. Notons également que notre définition de tube-solution généralise aux systèmes les notions de sous- et sur-solutions introduites pour les équations d’ordre deux par [4] et [55]. Ainsi, nous généralisons également des résultats obtenus pour des équations aux échelles de temps d’ordre deux. Finalement, nous proposons un nouveau résultat d’exis- tence pour un système dont le membre droit des équations dépend de la ∆-dérivée de la fonction.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Determination of fluoxetine and norfluoxetine enantiomers in human plasma by polypyrrole-coated capillary in-tube solid-phase microextraction coupled with liquid chromatography-fluorescence detection

A sensitive, selective, and reproducible in-tube polypyrrole-coated capillary (PPY) solid-phase microextraction and liquid chromatographic method for fluoxetine and norfluoxetine enantiomers analysis in plasma samples has been developed, validated, and further applied to the analysis of plasma samples from elderly patients undergoing therapy with antidepressants. Important factors in the optimization of in-tube SPME efficiency are discussed, including the sample draw/eject volume, draw/eject cycle number, draw/eject flow-rate, sample pH, and influence of plasma proteins. Separation of the analytes was achieved with a Chiralcel OD-R column and a mobile phase consisting of potassium hexafluorophosphate 7.5 mM and sodium phosphate 0.25 M solution, pH 3.0, and acetonitrile (75:25, v/v) in the isocratic mode, at a flow rate of 1.0 mL/min. Detection was carried out by fluorescence absorbance at Ex/Em 230/290 nm. The multifunctional porous surface structure of the PPY-coated film provided high precision and accuracy for enantiomers. Compared with other commercial capillaries, PPY-coated capillary showed better extraction efficiency for all the analytes. The quantification limits of the proposed method were 10 ng/mL for R- and S-fluoxetine, and 15 ng/mL for R- and S-norfluoxetine, with a coefficient of variation lower than 13%. The response of the method for enantiomers is linear over a dynamic range, from the limit of quantification to 700ng/mL, with correlation coefficients higher than 0.9940. The in-tube SPME/LC method can therefore be successfully used to analyze plasma samples from ageing patients undergoing therapy with fluoxetine. (C) 2009 Elsevier B.V. All rights reserved.

Hypertonic/hyperoncotic solution in hypovolemic patients: experience in the emergency room

Hypertonic solutions have been studied extensively in the treatment of hypovolemic shock, both in experimental and clinical models. Safety, efficacy, and long-term effects on animals and patients have been evaluated. The present article reviews indications, safety, mortality rates, and outcome in patients with hemorrhagic hypovolemic shock who were treated after admission with a hypertonic/hyperoncotic solution under strict observation in the emergency room.

Enteral fluid therapy through nasogastric tube in rumen cannulated goats

This paper reports the effects of fluid therapy in goats through nasogastric route with an electrolyte solution composed by concentrations of sodium, potassium and chloride similar to goat plasma (140mmol/L of Na+, 4.5mmol/L of K+, 110mmol/L of Cl-). Four Alpine Chamoisee goats, two of them with evident leakage of the rumen cannulas, were used in a crossover experimental design of two periods and two groups. In one group the two goats were submitted to a treatment protocol to induce dehydration before the fluid therapy, whereas the other group was not. Fluid therapy consisted supplying 10mL/kg/h of the electrolyte solution during 8 hours. No signs of discomfort or stress were observed. The dehydration model employed caused a mild dehydration indicated by decrease in feces humidity, body weight and abdominal circumference, and increase in plasma total solids concentration. During fluid therapy globular volume and plasma total solids decreased, whereas % body weight and abdominal circumference increased. No signs of hyperhydration were observed and serum electrolytes (Na+, Cl-, K+) presented no significant alterations in both groups. Fluid therapy proposed in this study was efficient to treat dehydration, even for rumen cannulated animals with evident leakage, and can be administrated safely with no electrolyte imbalance.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

In vivo antimicrobial activity of 2% chlorhexidine used as a root canal irrigating solution

The aim of the present study was to evaluate the in vivo antimicrobial activity of 2% chlorhexidine gluconate (FCFRP-USP) used as a root canal irrigating solution in teeth with pulp necrosis and radiographically visible chronic periapical reactions. Culture techniques and measurement of the inhibition zone were used. Twenty-two root canals of incisors and molars of 12 patients were used. After accessing the canal, the first root canal sample was collected with two sterile paper points that were transferred to a tube containing reduced transport fluid. The root canal was instrumented using chlorhexidine solution. A small sterile cotton pellet was placed at the root canal entrance, and the cavity was sealed with zinc oxide-eugenol cement. The canals were maintained empty for 48 h. Three sterile paper points were then introduced to absorb the root canal fluid (second sample). One paper point was placed on an agar plate inoculated with Micrococcus luteus ATCC 9341 and incubated for 24 h at 37°C, and the other two were submitted to microbiological evaluation. Present in 10 cases at baseline, mutans streptococci was reduced by 100% at the second assessment. Treatment showed an efficiency of 77.78% for anaerobic microorganisms at the second assessment. These data suggest that chlorhexidine prevents microbial activity in vivo with residual effects in the root canal system up to 48 h. Copyright © 1999 by The American Association of Endodontists.

Structural and electrical properties of LaNiO3 thin films grown on (100) and (001) oriented SrLaAlO4 substrates by chemical solution deposition method

LaNiO3 thin films were deposited on SrLaAlO4 (1 0 0) and SrLaAlO4 (0 0 1) single crystal substrates by a chemical solution deposition method and heat-treated in oxygen atmosphere at 700° C in tube oven. Structural, morphological, and electrical properties of the LaNiO 3 thin films were characterized by X-ray diffraction (XRD), atomic force microscopy (AFM), field emission scanning electron microscopy (FE-SEM), and electrical resistivity as temperature function (Hall measurements). The X-ray diffraction data indicated good crystallinity and a structural preferential orientation. The LaNiO3 thin films have a very flat surface and no droplet was found on their surfaces. Samples of LaNiO3 grown onto (1 0 0) and (0 0 1) oriented SrLaAlO4 single crystal substrates reveled average grain size by AFM approximately 15-30 nm and 20-35 nm, respectively. Transport characteristics observed were clearly dependent upon the substrate orientation which exhibited a metal-to-insulator transition. The underlying mechanism is a result of competition between the mobility edge and the Fermi energy through the occupation of electron states which in turn is controlled by the disorder level induced by different growth surfaces. © 2013 Elsevier Ltd and Techna Group S.r.l.

URANS calculations for smooth circular cylinder flow in a wide range of Reynolds Numbers: solution verification and validation

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and Re 5 x 10(5) will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 k - omega SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature. [DOI: 10.1115/1.4007571]

Effect of automatic tube current modulation on radiation dose and image quality for low tube voltage multidetector row CT angiography: phantom study

RATIONALE AND OBJECTIVES: To evaluate the effect of automatic tube current modulation on radiation dose and image quality for low tube voltage computed tomography (CT) angiography. MATERIALS AND METHODS: An anthropomorphic phantom was scanned with a 64-section CT scanner using following tube voltages: 140 kVp (Protocol A), 120 kVp (Protocol B), 100 kVp (Protocol C), and 80 kVp (Protocol D). To achieve similar noise, combined z-axis and xy-axes automatic tube current modulation was applied. Effective dose (ED) for the four tube voltages was assessed. Three plastic vials filled with different concentrations of iodinated solution were placed on the phantom's abdomen to obtain attenuation measurements. The signal-to-noise ratio (SNR) was calculated and a figure of merit (FOM) for each iodinated solution was computed as SNR(2)/ED. RESULTS: The ED was kept similar for the four different tube voltages: (A) 5.4 mSv +/- 0.3, (B) 4.1 mSv +/- 0.6, (C) 3.9 mSv +/- 0.5, and (D) 4.2 mSv +/- 0.3 (P > .05). As the tube voltage decreased from 140 to 80 kVp, image noise was maintained (range, 13.8-14.9 HU) (P > .05). SNR increased as the tube voltage decreased, with an overall gain of 119% for the 80-kVp compared to the 140-kVp protocol (P < .05). The FOM results indicated that with a reduction of the tube voltage from 140 to 120, 100, and 80 kVp, at constant SNR, ED was reduced by a factor of 2.1, 3.3, and 5.1, respectively, (P < .001). CONCLUSIONS: As tube voltage decreases, automatic tube current modulation for CT angiography yields either a significant increase in image quality at constant radiation dose or a significant decrease in radiation dose at a constant image quality.