Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

BOUND HYDROGENIC STATES IN A MAGNETIC FIELD: A FINITE-DIFFERENCE APPROACH

A finite-difference scheme is used to calculate bound electronic states of an electron in a hydrogen atom subject to a magnetic field. The numerical results are in good agreement with exact results, in the absence of the magnetic field, and with a two-parameters variational calculation, when the magnetic field is applied.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

Does the Choice of the Halogenated Anesthetic Influence Renal Function during Hemorrhagic Shock and Resuscitation?

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effect of haematocrit on pump and kidney dysfunction after myocardial revascularization

Objective - Kidney dysfunction is a common complication after cardiac surgery. It occurs in 7 to 31% of the patients. The lowest haematocrit after cardiopulmonary bypass surgery (LHCT) has been identified as a risk factor for kidney dysfunction after cardiac surgery. The aim of this study is to determine whether different levels of haematocrit during cardiopulmonary bypass surgery are related to kidney dysfunction.Methods and results-A prospective study was conducted on consecutive adult patients undergoing myocardial revascularization. Preoperative renal function was assessed by baseline serum creatinine level (CrPre). Peak postoperative creatinine (CrPost) was defined as the highest daily in-hospital postoperative value. Peak fractional change in creatinine (% Delta Cr) was defined as the difference between the CrPre and CrePost represented as a percentage of the preoperative value. The LHTC was defined as the lowest recorded haematocrit prior to weaning from the initial pump run. A category variable was created for haematocrit based on the distribution of values. The category variable had the following cut-off points: less than 23%, 23.1 to 28% and greater than 28.1 %. Lowest haematocrit (26.62 +/- 4.15%), CPB (74.71 +/- 24.90 min), CrPre (1.23 +/- 0.37 mg/dl) and highest CrPost (1.52 +/- 0.47 mg/dl) data varied in near-normal fashion. Statistical significance has been observed in the < 23% lowest haematocrit group (CrIPOD and Cr5POD; P = 0.006) and the 23.1 28% lowest haematocrit level group (CrPre and Cr2POD; P = 0.047). CrPre and Cr5POD did not differ between groups (P > 0.05). The multiple linear regression model confirmed that the determinants for higher %Delta Cr were age, body surface area and preoperative serum creatinine level.Conclusion - The LHTC was not identified as a risk factor for kidney dysfunction after myocardial revascularization.

Effect of fractional urea clearance on survival of hemodialysis patients in relation to gender

Many studies have demonstrated the relationship between dialysis dose and survival. Global mortality is similar among men and women; however, the influence of dialysis dose in the survival could be more intensive between women. Therefore, we conduct an observational study to evaluate the gender-related impact of single pool Kt/V (spKt/V) on the survival of patients submitted to hemodialysis in a university hospital. We found that survival was lower in groups with spKt/V smaller than 1.2 than in those with Kt/V between 1.2 and 1.4. Among female patients, spKt/V smaller than 1.2 had a more adverse effect in survival than among men with a comparable Kt/V. Otherwise, among women, the dialysis dose had an impact in survival even with Kt/V greater than 1.4. Thus, fractional urea clearance more heavily influenced the survival of females than males in hemodialysis patients.

Predictors of health status do not change over three-year periods and exacerbation makes difference in chronic obstructive pulmonary disease

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Geologia, Geocronologia, Geoquímica e Petrogênese das Rochas Ígneas Cretácicas da Província Magmática do Cabo e suas Relações com as Unidades Sedimentares da Bacia de Pernambuco (NE do Brasil)

The area studied forms a thin NNE-directed belt situated south of Recife town (Pernambuco state), northeastern Brazil. Geologically, it comprises the Pernambuco Basin (PB), which is limited by the Pernambuco Lineament to the north, the Maragogi high to the south and the Pernambuco Alagoas massif to the west, all of them with Precambrian age. This thesis reports the results obtained for the Cabo Magmatic Province (CMP), aiming the characterization of the geology, stratigraphy, geochronology, geochemistry and petrogenesis of the Cretaceous igneous rocks presented in the PB. The PB is composed of the Cabo Formation (rift phase) at the base (polymictic conglomerates, sandstones, shales), an intermediate unit, the Estiva Formation (marbles and argillites), and, at the top, the Algodoais Formation (monomictic conglomerates, sandstones, shales). The CMP is represented by trachytes, rhyolites, pyroclastics (ignimbrites), basalts / trachy-andesites, monzonites and alkali-feldspar granite, which occur as dykes, flows, sills, laccoliths and plugs. Field observations and well descriptions show that the majority of the magmatic rocks have intrusive contacts with the Cabo Formation, although some occurrences are also suggestive of synchronism between volcanism and siliciclastic sedimentation. 40Ar/39Ar and zircon fission tracks for the magmatic rocks indicate an average age of 102 r 1 Ma for the CMP. This age represents an expressive event in the province and is detected in all igneous dated materials. It is considered as a minimum age (Albian) for the magmatic episode and the peak of the rift phase in the PB. The 40Ar/39Ar dates are about 10-14 Ma younger than published palynologic ages for this basin. Geochemically, the CMP may be divided in two major groups; i) a transitional to alkaline suite, constituted by basalts to trachy-andesites (types with fine-grained textures and phenocrysts of sanidine and plagioclase), trachytes (porphyrytic texture, with phenocrysts of sanidine and plagioclase) and monzonites; ii) a alkaline suite, highly fractionated, acidic volcano-plutonic association, formed by four subtypes (pyroclastic flows ignimbrites, fine-to medium-grained rhyolites, a high level granite, and later rhyolites). These four types are distinguished essentially by field aspects and petrographic and textural features. Compatible versus incompatible trace element concentrations and geochemical modeling based on both major and trace elements suggest the evolution through low pressure fractional crystallization for trachytes and other acidic rocks, whereas basalts / trachy-andesites and monzonites evolved by partial melting from a mantle source. Sr and Nd isotopes reveal two distinct sources for the rocks of the CMP. Concerning the acidic ones, the high initial Sr ratios (ISr = 0.7064-1.2295) and the negative HNd (-0.43 to -3.67) indicate a crustal source with mesoproterozoic model ages (TDM from 0.92 to 1.04 Ga). On the other hand, the basic to intermediate rocks have low ISr (0.7031-0.7042) and positive HNd (+1.28 to +1.98), which requires the depleted mantle as the most probable source; their model ages are in the range 0.61-0.66 Ga. However, the light rare earth enrichment of these rocks and partial melting modeling point to an incompatible-enriched lherzolitic mantle with very low quantity of garnet (1-3%). This apparent difference between geochemical and Nd isotopes may be resolved by assuming that the metasomatizing agent did not obliterate the original isotopic characteristics of the magmas. A 2 to 5% partial melting of this mantle at approximately 14 kbar and 1269oC account very well the basalts and trachy-andesites studied. By using these pressure and temperatures estimates for the generation of the basaltic to trachy-andesitic magma, it is determined a lithospheric stretching (E) of 2.5. This E value is an appropriated estimate for the sub-crustal stretching (astenospheric or the base of the lithosphere?) region under the Pernambuco Basin, the crustal stretching probably being lower. The integration of all data obtained in this thesis permits to interpret the magmatic evolution of the PB as follows; 1st) the partial melting of a garnet-bearing lherzolite generates incompatible-enriched basaltic, trachy-andesitic and monzonitic magmas; 2nd) the underplating of these basaltic magmas at the base of the continental crust triggers the partial melting of this crust, and thus originating the acidic magmas; 3rd) concomitantly with the previous stage, trachytic magmas were produced by fractionation from a monzonitic to trachy-andesitic liquid; 4th) the emplacement of the several magmas in superficial (e.g. flows) or sub-superficial (e.g. dykes, sills, domes, laccoliths) depths was almost synchronically, at about 102 r 1 Ma, and usually crosscutting the sedimentary rocks of the Cabo Formation. The presence of garnet in the lherzolitic mantle does not agree with pressures of about 14 kbar for the generation of the basaltic magma, as calculated based on chemical parameters. This can be resolved by admitting the astenospheric uplifting under the rift, which would place deep and hot material (mantle plume?) at sub-crustal depths. The generation of the magmas and their subsequent emplacement would be coupled with the crustal rifting of the PB, the border (NNE-SSW directed) and transfer (NW-SE directed) faults serving as conduits for the magma emplacement. Based on the E parameter and the integration of 40Ar/39Ar and palynologic data it is interpreted a maximum duration of 10-14 Ma for the rift phase (Cabo Formation clastic sedimentation and basic to acidic magmatism) of the PB

Electroacupuncture analgesia in dogs: is there a difference between uni- and bi-lateral stimulation?

Objective To compare the analgesic effect of uni- and bi-lateral electroacupuncture (EA) in response to thermal and mechanical nociceptive stimuli and to investigate the cardiorespiratory, endocrine, and behavioral changes in dogs submitted to EA.Study design Prospective, randomized cross-over experimental study.Animals Eight adult, clinically healthy, cross-breed dogs, weighing 13 +/- 4 kg.Methods Dogs underwent electrostimulation at false acupoints (T-false); bilateral EA at acupoints, stomach 36, gall bladder 34 and spleen 6 (T-EA/bil); unilateral EA at the same points (T-EA/uni) or were untreated (T-control). All animals received acepromazine (0.05 mg kg(-1)) IV; and heart rate, pulse oximetry, indirect arterial blood pressure, respiratory rate, PECO2, rectal temperature, and plasma cortisol concentration were measured before, during, and after EA. Analgesia was tested using thoracic and abdominal cutaneous thermal and mechanical stimuli, and an interdigital thermal stimulus. Behavior was classified as calm or restless. Analysis of variance for repeated measures followed by Tukey's test was used for analysis of the data.Results There were no cardiorespiratory differences among the treatments. The cutaneous pain threshold was higher after EA, compared with false points. The latency period was shorter and analgesia was more intense in T-EA/bil than T-EA/uni, when both were compared with T-false and T-control. Six out of eight animals treated with EA were calm during treatment, and 5/8 and 4/8 of the T-false and T-control animals, respectively, were restless. Latency to interdigital thermal stimulation increased in T-EA/bil compared with the others. There was no difference in plasma cortisol concentrations among the treatments.Conclusions Bilateral EA produced a shorter latency period, a greater intensity, and longer duration of analgesia than unilateral stimulation, without stimulating a stress response.Clinical relevance Bilateral EA produces a better analgesic effect than unilateral EA.

Growth hormone attenuates skeletal muscle changes in experimental chronic heart failure

Objective: This study evaluated the effects of growth hormone (GH) on morphology and myogenic regulatory factors (MRF) gene expression in skeletal muscle of rats with ascending aortic stenosis (AAS) induced chronic heart failure.Design: Male 90-100 g Wistar rats were subjected to thoracotomy. AAS was created by placing a stainless-steel clip on the ascending aorta. Twenty five weeks after surgery, rats were treated with daily subcutaneous injections of recombinant human GH (2 mg/kg/day; AAS-GH group) or saline (AAS group) for 14 days. Sham-operated animals served as controls. Left ventricular (LV) function was assessed before and after treatment. IGF-1 serum levels were measured by ELISA. After anesthesia, soleus muscle was frozen in liquid nitrogen. Histological sections were stained with HE and picrosirius red to calculate muscle fiber cross-sectional area and collagen fractional area, respectively. MRF myogenin and MyoD expression was analyzed by reverse transcription PCR.Results: Body weight was similar between groups. AAS and AAS-GH groups presented dilated left atrium, left ventricular (LV) hypertrophy (LV mass index: Control 1.90 +/- 0.15; AAS 3.11 +/- 0.44; AAS-GH 2.94 +/- 0.47 g/kg; p < 0.05 AAS and AAS-GH vs. Control), and reduced LV posterior wall shortening velocity. Soleus muscle fiber area was significantly lower in AAS than in Control and AAS-GH groups; there was no difference between AAS-GH and Control groups. Collagen fractional area was significantly higher in MS than Control; AAS-GH did not differ from both Control and AAS groups. Serum IGF-1 levels decreased in AAS compared to Control. MyoD mRNA was significantly higher in AAS-GH than AAS; there was no difference between AAS-GH and Control groups. Myogenin mRNA levels were similar between groups.Conclusion: In rats with aortic stenosis-induced heart failure, growth hormone administration increases MyoD gene expression above non-treated animal levels, preserves muscular trophism and attenuates interstitial fibrosis. These results suggest that growth hormone may have a potential role as an adjuvant therapy for chronic heart failure. (C) 2009 Elsevier Ltd. All rights reserved.

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Combined D0 measurements constraining the CP-violating phase and width difference in the B-s(0) system

We combine the D0 measurement of the width difference between the light and heavy B-s(0) mass eigenstates and of the CP-violating mixing phase determined from the time-dependent angular distributions in the B-s(0)-> J/psi phi decays along with the charge asymmetry in semileptonic decays also measured with the D0 detector. With the additional constraint from the world average of the flavor-specific B-s(0) lifetime, we obtain Delta Gamma(s)equivalent to(Gamma(L)-Gamma(H))=0.13 +/- 0.09 ps(-1) and vertical bar phi(s)vertical bar=0.70(-0.47)(+0.39) or Delta Gamma(s)=-0.13 +/- 0.09 ps(-1) and vertical bar phi(s)vertical bar=2.44(-0.39)(+0.47). The data sample corresponds to an integrated luminosity of 1.1 fb(-1) accumulated with the D0 detector at the Fermilab Tevatron Collider.