Finite time extinction for nonlinear fractional evolution equations and related properties

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Finite time extinction for nonlinear fractional evolution equations and related properties.

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Electro-optical characterization of IC compatible microcantilevers

The aim of this work is to simulate and optically characterize the piezoelectric performance of complementary metal oxide semiconductor (CMOS) compatible microcantilevers based on aluminium nitride (AlN) and manufactured at room temperature. This study should facilitate the integration of piezoelectric micro-electro-mechanical systems (MEMS) such as microcantilevers, in CMOS technology. Besides compatibility with standard integrated circuit manufacturing procedures, low temperature processing also translates into higher throughput and, as a consequence, lower manufacturing costs. Thus, the use of the piezoelectric properties of AlN manufactured by reactive sputtering at room temperature is an important step towards the integration of this type of devices within future CMOS technology standards. To assess the reliability of our fabrication process, we have manufactured arrays of free-standing microcantilever beams of variable dimension and studied their piezoelectric performance. The characterization of the first out-of-plane modes of AlN-actuated piezoelectric microcantilevers has been carried out using two optical techniques: laser Doppler vibrometry (LDV) and white light interferometry (WLI). In order to actuate the cantilevers, a periodic chirp signal in certain frequency ranges was applied between the device electrodes. The nature of the different vibration modes detected has been studied and compared with that obtained by a finite element model based simulation (COMSOL Multiphysics), showing flexural as well as torsional modes. The correspondence between theoretical and experimental data is reasonably good, probing the viability of this high throughput and CMOS compatible fabrication process. To complete the study, X-ray diffraction as well as d33 piezoelectric coefficient measurements were also carried out.

Adaptive strategies of two Portuguese grapevines varieties (Aragonês. syn. Tempranillo and Trincadeira) face drought: physiological and structural responses.

At Mediterranean regions and particularly in southern Portugal, it is imperative to identify grape varieties more adapted to warm and dry climates in order to overcome future climatic changes. Two Vitis vinifera genotypes, Aragonez (syn. Tempranillo) and Trincadeira, were selected to assess their physiological responses to soil water stress. Vines were subjected to four irrigation regimes: irrigated during all phenological cycle, non-irrigated during all phenological cycle, non irrigated until veraison, irrigated after veraison. Predawn leaf water potential was much higher in Trincadeira than Aragonez in non- irrigated plants. This result is in accordance with its higher stomatal control efficiency in this variety (Trincadeira). Photosynthetic capacity (Amax at saturating light intensity) decreased due to stomatal and biochemical limitations under water stress. However, recovery capacity of leaf water status after irrigation was faster in Trincadeira. Yield and yield x Brix increased when irrigation occurred after veraison, particularly in Trincadeira. These results show that Trincadeira presents a drought adaptation than Aragonez. Ratio of variable to maximum fluorescence Fv/Fm and total leaf chlorophyll related with leaf water potential for both species. Reflectance Normalized Difference Vegetation Index (NDVI705), Red Edge Inflexion Point Index and Photochemical Reflectance Index were related with irrigation treatment. Relative water content and specific leaf area were similar between varieties. In conclusion, we suggested that there is variation among the genotypes and the main physiological parameters for variety selection, for drought, were leaf water potential, stomatal conductance and reflectance indexes.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Study of charge, spin, and structural orderings in quantum materials using nuclei and muons as local probes

Quantum Materials are many body systems displaying emergent phenomena caused by quantum collective behaviour, such as superconductivity, charge density wave, fractional hall effect, and exotic magnetism. Among quantum materials, two families have recently attracted attention: kagome metals and Kitaev materials. Kagome metals have a unique crystal structure made up of triangular lattice layers that are used to form the kagome layer. Due to superconductivity, magnetism, and charge ordering states such as the Charge Density Wave (CDW), unexpected physical phenomena such as the massive Anomalous Hall Effect (AHE) and possible Majorana fermions develop in these materials. Kitaev materials are a type of quantum material with a unique spin model named after Alexei Kitaev. They include fractional fluctuations of Majorana fermions and non-topological abelian anyons, both of which might be used in quantum computing. Furthermore, they provide a realistic framework for the development of quantum spin liquid (QSL), in which quantum fluctuations produce long-range entanglements between electronic states despite the lack of classical magnetic ordering. In my research, I performed several nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and muon spin spectroscopy (µSR) experiments to explain and unravel novel phases of matter within these unusual families of materials. NMR has been found to be an excellent tool for studying these materials’ local electronic structures and magnetic properties. I could use NMR to determine, for the first time, the structure of a novel kagome superconductor, RbV3Sb5, below the CDW transition, and to highlight the role of chemical doping in the CDW phase of AV3Sb5 superconductors. µSR has been used to investigate the effect of doping on kagome material samples in order to study the presence and behaviour of an anomalous phase developing at low temperatures and possibly related to time-reversal symmetry breaking.

A next-to-leading order calculation of the impact of primordial magnetic fields into cosmological observables

In this thesis, we perform a next-to-leading order calculation of the impact of primordial magnetic fields (PMF) into the evolution of scalar cosmological perturbations and the cosmic microwave background (CMB) anisotropy. Magnetic fields are everywhere in the Universe at all scales probed so far, but their origin is still under debate. The current standard picture is that they originate from the amplification of initial seed fields, which could have been generated as PMFs in the early Universe. The most robust way to test their presence and constrain their features is to study how they impact on key cosmological observables, in particular the CMB anisotropies. The standard way to model a PMF is to consider its contribution (quadratic in the magnetic field) at the same footing of first order perturbations, under the assumptions of ideal magneto-hydrodynamics and compensated initial conditions. In the perspectives of ever increasing precision of CMB anisotropies measurements and of possible uncounted non-linear effects, in this thesis we study effects which go beyond the standard assumptions. We study the impact of PMFs on cosmological perturbations and CMB anisotropies with adiabatic initial conditions, the effect of Alfvén waves on the speed of sound of perturbations and possible non-linear behavior of baryon overdensity for PMFs with a blue spectral index, by modifying and improving the publicly available Einstein-Boltzmann code SONG, which has been written in order to take into account all second-order contributions in cosmological perturbation theory. One of the objectives of this thesis is to set the basis to verify by an independent fully numerical analysis the possibility to affect recombination and the Hubble constant.

Brij Detergents Reveal New Aspects Of Membrane Microdomain In Erythrocytes.

Membrane microdomains enriched in cholesterol, sphingolipids (rafts), and specific proteins are involved in important physiological functions. However their structure, size and stability are still controversial. Given that detergent-resistant membranes (DRMs) are in the liquid-ordered state and are rich in raft-like components, they might correspond to rafts at least to some extent. Here we monitor the lateral order of biological membranes by characterizing DRMs from erythrocytes obtained with Brij-98, Brij-58, and TX-100 at 4 °C and 37 °C. All DRMs were enriched in cholesterol and contained the raft markers flotillin-2 and stomatin. However, sphingomyelin (SM) was only found to be enriched in TX-100-DRMs - a detergent that preferentially solubilizes the membrane inner leaflet - while Band 3 was present solely in Brij-DRMs. Electron paramagnetic resonance spectra showed that the acyl chain packing of Brij-DRMs was lower than TX-100-DRMs, providing evidence of their diverse lipid composition. Fatty acid analysis revealed that the SM fraction of the DRMs was enriched in lignoceric acid, which should specifically contribute to the resistance of SM to detergents. These results indicate that lipids from the outer leaflet, particularly SM, are essential for the formation of the liquid-ordered phase of DRMs. At last, the differential solubilization process induced by Brij-98 and TX-100 was monitored using giant unilamellar vesicles. This study suggests that Brij and TX-100-DRMs reflect different degrees of lateral order of the membrane microdomains. Additionally, Brij DRMs are composed by both inner and outer leaflet components, making them more physiologically relevant than TX-100-DRMs to the studies of membrane rafts.

Molecular Diversity Of Fungal And Bacterial Communities In The Marine Sponge Dragmacidon Reticulatum.

The present work aimed to investigate the diversity of bacteria and filamentous fungi of southern Atlantic Ocean marine sponge Dragmacidon reticulatum using cultivation-independent approaches. Fungal ITS rDNA and 18S gene analyses (DGGE and direct sequencing approaches) showed the presence of representatives of three order (Polyporales, Malasseziales, and Agaricales) from the phylum Basidiomycota and seven orders belonging to the phylum Ascomycota (Arthoniales, Capnodiales, Dothideales, Eurotiales, Hypocreales, Pleosporales, and Saccharomycetales). On the other hand, bacterial 16S rDNA gene analyses by direct sequencing approach revealed the presence of representatives of seven bacterial phyla (Cyanobacteria, Proteobacteria, Actinobacteria, Bacteroidetes, Lentisphaerae, Chloroflexi, and Planctomycetes). Results from statistical analyses (rarefaction curves) suggested that the sampled clones covered the fungal diversity in the sponge samples studied, while for the bacterial community additional sampling would be necessary for saturation. This is the first report related to the molecular analyses of fungal and bacterial communities by cultivation-independent approaches in the marine sponges D. reticulatum. Additionally, the present work broadening the knowledge of microbial diversity associated to marine sponges and reports innovative data on the presence of some fungal genera in marine samples.

Prolongamento da amamentação após o primeiro ano de vida: argumentos das mães

This paper aims to identify and analyze the reasons pointed by mothers to prolong breastfeeding beyond the first year of the child s life. The study involved 40 mothers whose children were treated in the Preventive Program of Research and Dental Treatment Center for Special Patients - Dental School of Piracicaba - UNICAMP. The group consisted of mothers who prolonged the breastfeeding beyond the baby s first year of life. All mothers were surveyed by a researcher using a specific questionnaire. In order to avoid information loss, the interviews were taped, then transcripted. Results showed that the main cause of the extended breastfeeding was maternal pleasure. It was also observed that the mother and infant attachment favors prolonged breastfeeding occurrence. Further studies should be carried out for more accurate functional analyses of variable that lead to extend breastfeeding or to wean.

A new species of Rineloricaria (Siluriformes: Loricariidae: Loricariinae) from rio Daraá, rio Negro basin, Amazon, Brazil

Rineloricaria daraha, new species, is described from the rio Daraá, tributary of rio Negro, northwestern Amazonas State, Brazil. The new species is diagnosed by having seven branched pectoral-fin rays, finger-like papillae on the lower lip, a large multi-angular preanal plate, and at least four quadrangular plates of variable size surrounding the preanal plate. The new species is known only from rio Daraá and its waterfalls.

Ventilation behavior in trained and untrained men during incremental test: evidence of one metabolic transition point

This study aimed to describe and compare the ventilation behavior during an incremental test utilizing three mathematical models and to compare the feature of ventilation curve fitted by the best mathematical model between aerobically trained (TR) and untrained ( UT) men. Thirty five subjects underwent a treadmill test with 1 km.h(-1) increases every minute until exhaustion. Ventilation averages of 20 seconds were plotted against time and fitted by: bi-segmental regression model (2SRM); three-segmental regression model (3SRM); and growth exponential model (GEM). Residual sum of squares (RSS) and mean square error (MSE) were calculated for each model. The correlations between peak VO2 (VO2PEAK), peak speed (Speed(PEAK)), ventilatory threshold identified by the best model (VT2SRM) and the first derivative calculated for workloads below (moderate intensity) and above (heavy intensity) VT2SRM were calculated. The RSS and MSE for GEM were significantly higher (p < 0.01) than for 2SRM and 3SRM in pooled data and in UT, but no significant difference was observed among the mathematical models in TR. In the pooled data, the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.58; p < 0.01) and Speed(PEAK) (r = -0.46; p < 0.05) while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r = -0.43; p < 0.05). In UT group the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.65; p < 0.05) and Speed(PEAK) (r = -0.61; p < 0.05), while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r= -0.73; p < 0.01), Speed(PEAK) (r = -0.73; p < 0.01) and VO2PEAK (r = -0.61; p < 0.05) in TR group. The ventilation behavior during incremental treadmill test tends to show only one threshold. UT subjects showed a slower ventilation increase during moderate intensities while TR subjects showed a slower ventilation increase during heavy intensities.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Analysis of breast cancer by small angle X-ray scattering (SAXS)

Small angle X-ray scattering (SAXS) images of normal breast tissue and benign and malignant breast tumour tissues, fixed in formalin, were measured at the momentum transfer range of 0.063 nm(-1) <= q (=4 pi sin(theta/2)/lambda) <= 2.720 nm(-1). Four intrinsic parameters were extracted from the scattering profiles (1D SAXS image reduced) and, from the combination of these parameters, another three parameters were also created. All parameters, intrinsic and derived, were subject to discriminant analysis, and it was verified that parameters such as the area of diffuse scatter at the momentum transfer range 0.50 <= q <= 0.56 nm(-1), the ratio between areas of fifth-order axial and third-order lateral peaks and third-order axial spacing provide the most significant information for diagnosis (p < 0.001). Thus, in this work it was verified that by combining these three parameters it was possible to classify human breast tissues as normal, benign lesion or malignant lesion with a sensitivity of 83% and a specificity of 100%.

Determination of Three-Dimensional Left Ventricle Motion to Analyze Ventricular Dyssyncrony in SPECT Images

A method to compute three-dimension (3D) left ventricle (LV) motion and its color coded visualization scheme for the qualitative analysis in SPECT images is proposed. It is used to investigate some aspects of Cardiac Resynchronization Therapy (CRT). The method was applied to 3D gated-SPECT images sets from normal subjects and patients with severe Idiopathic Heart Failure, before and after CRT. Color coded visualization maps representing the LV regional motion showed significant difference between patients and normal subjects. Moreover, they indicated a difference between the two groups. Numerical results of regional mean values representing the intensity and direction of movement in radial direction are presented. A difference of one order of magnitude in the intensity of the movement on patients in relation to the normal subjects was observed. Quantitative and qualitative parameters gave good indications of potential application of the technique to diagnosis and follow up of patients submitted to CRT.