La metrica di Agmon ed il decadimento esponenziale delle soluzioni di equazioni alle derivate parziali

The aim of this master thesis is to study the exponential decay of solutions of elliptic partial equations. This work is based on the results obtained by Agmon. To this purpose, first, we define the Agmon metric, that plays an important role in the study of exponential decay, because it is related to the rate of decay. Under some assumptions on the growth of the function and on the positivity of the quadratic form associated to the operator, a first result of exponential decay is presented. This result is then applied to show the exponential decay of eigenfunctions with eigenvalues whose real part lies below the bottom of the essential spectrum. Finally, three examples are given: the harmonic oscillator, the hydrogen atom and a Schrödinger operator with purely discrete spectrum.

Unravelling the nanostructure of strawberry fruit pectins by atomic force microscopy

Atomic force microscopy (AFM) allows the analysis of individual polymers at nanostructural level with a minimal sample preparation. This technique has been used to analyse the pectin disassembly process during the ripening and postharvest storage of several fleshy fruits. In general, pectins analysed by AFM are usually visualized as isolated chains, unbranched or with a low number of branchs and, occasionally, as large aggregates. However, the exact nature of these structures is unknown. It has been suggested that pectin aggregates represent a mixture of rhamnonogalacturonan I and homogalacturonan, while isolated chains and their branches are mainly composed by polygalacturonic acid. In order to gain insight into the nature of these structures, sodium carbonate soluble pectins from ripe strawberry (Fragaria x ananassa, Duch.) fruits were subjected to enzymatic digestion with endo-Polygalacturonase M2 from Aspergillus aculeatus, and the samples visualized by AFM at different time intervals. Pectins isolated from control, non-transformed plants, and two transgenic genotypes with low level of expression of ripening-induced pectinase genes encoding a polygalacturonase (APG) or a pectate lyase (APEL) were also included in this study. Before digestion, isolated pectin chains from control were shorter than those from transgenic fruits, showing number-average (LN) contour length values of 73.2 nm vs. 95.9 nm and 91.4 nm in APG and APEL, respectively. The percentage of branched polymers was significantly higher in APG polyuronides than in the remaining genotypes, 33% in APG vs. 6% in control and APEL. As a result of the endo-PG treatment, a gradual decrease in the main backbone length of isolated chains was observed in the three samples. The minimum LN value was reached after 8 h of digestion, being similar in the three genotypes, 22 nm. By contrast, the branches were not visible after 1.5-2 h of digestion. LN values were plotted against digestion time and the data fitted to a first-order exponential decay curve, obtaining R2 values higher than 0.9. The half digestion time calculated with these equations were similar for control and APG pectins, 1.7 h, but significantly higher in APEL, 2.5 h, indicating that these polymer chains were more resistant to endo-PG digestion. Regarding the pectin aggregates, their volumes were estimated and used to calculate LN molecular weights. Before digestion, control and APEL samples showed complexes of similar molecular weights, 1722 kDa, and slightly higher than those observed in APG samples. After endo-PG digestion, size of complexes diminished significantly, reaching similar values in the three pectin samples, around 650 kDa. These results suggest that isolated polymer chains visualized by AFM are formed by a HG domain linked to a shorter polymer resistant to endo-PG digestion, maybe xylogalacturonan or RG-I. The silencing of the pectate lyase gene slightly modified the structure and/or chemical composition of polymer chains making these polyuronides more resistant to enzymatic degradation. Similarly, polygalacturonic acid is one of the main component of the aggregates.

Dissipation of triadimefon on the solid/gas interface

The dissipation or triadimefon, as pure solid and in the Bayleton 5 commercial formulation, was studied under controlled and natural conditions. Volatilization and photodegradation were shown to be the main dissipation processes. The volatilization results can be described by an empirical model assuming exponential decay of the volatilization rate. The filler of the commercial formulation is determinant for the volatilization but has little effect on the photodegradation rates. The main photoproducts were identified and a reaction mechanism proposed. (C) 2001 Elsevier Science Ltd. All rights reserved.

Comparative study of the dissipation of triadimefon in greenhouse and field conditions

The dissipation of triadimefon, {1-(4-chlorophenoxy)-3,3-dimethyl-1-(1H-1,2,4-triazol-1-yl)butanone}, was studied after its application to melon leaves, glass and paper, both in greenhouse and field conditions. The dissipation rate of triadimefon in its commercial formulation Bayleton 5 was found to be lower in greenhouse than field. The results for different samples in the same conditions show that the dissipation of triadimefon was found to be biphasic. This result can be accounted by a semi-empirical model which assumes an initial fast decline of the dissipation rate, attributed to an exponential decay of the volatilization rates, followed by a second phase where the dissipation is due to a first order degradation processes.The dissipation of triadimefon, {1-(4-chlorophenoxy)-3,3-dimethyl-1-(1H- 1,2,4-triazol-1-yl)butan-one}, was studied after its application to melon leaves, glass and paper, both in greenhouse and field conditions. The dissipation rate of triadimefon in its commercial formulation Bayleton 5 was found to be lower in greenhouse than field. The results for different samples in the same conditions show that the dissipation of triadimefon was found to be biphasic. This result can be accounted by a semi-empirical model which assumes an initial fast decline of the dissipation rate, attributed to an exponential decay of the volatilization rates, followed by a second phase where the dissipation is due to a first order degradation processes.

Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T.

PURPOSE: To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. MATERIALS AND METHODS: The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (Di ± standard deviations) and their fractions (fi ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. RESULTS: The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D1 = 1.35 ± 0.03 × 10(-3) mm(2)/s; f1 = 72.7 ± 0.9 %), a fast (D2 = 26.50 ± 2.49 × 10(-3) mm(2)/s; f2 = 13.7 ± 0.6 %) and a very fast (D3 = 404.00 ± 43.7 × 10(-3) mm(2)/s; f3 = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm(2) CONCLUSION: The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm(2) range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. KEY POINTS: ? For normal liver, tri-exponential IVIM model might be superior to bi-exponential ? A very fast compartment (D = 404.00 ± 43.7 × 10 (-3)  mm (2) /s; f = 13.5 ± 0.8 %) is determined from the tri-exponential model ? The compartment contributes to the IVIM signal only for b ≤ 15 s/mm (2.)

Short-term temporal changes of soil carbon losses after tillage described by a first-order decay model

Tillage stimulates soil carbon (C) losses by increasing aeration, changing temperature and moisture conditions, and thus favoring microbial decomposition. In addition, soil aggregate disruption by tillage exposes once protected organic matter to decomposition. We propose a model to explain carbon dioxide (CO2) emission after tillage as a function of the no-till emission plus a correction due to the tillage disturbance. The model assumes that C in the readily decomposable organic matter follows a first-order reaction kinetics equation as: dC(sail)(t)/dt = -kC(soil)(t) and that soil C-CO2 emission is proportional to the C decay rate in soil, where C-soil(t) is the available labile soil C (g m(-2)) at any time (t). Emissions are modeled in terms soil C available to decomposition in the tilled and non-tilled plots, and a relationship is derived between no-till (F-NT) and tilled (F-Gamma) fluxes, which is: F-T = a1F(NT)e(-a2t), where t is time after tillage. Predicted and observed fluxes showed good agreement based on determination coefficient (R-2), index of agreement and model efficiency, with R-2 as high as 0.97. The two parameters included in the model are related to the difference between the decay constant (k factor) of tilled and no-till plots (a(2)) and also to the amount of labile carbon added to the readily decomposable soil organic matter due to tillage (a,). These two parameters were estimated in the model ranging from 1.27 and 2.60 (a(1)) and - 1.52 x 10(-2) and 2.2 x 10(-2) day(-1) (a(2)). The advantage is that temporal variability of tillage-induced emissions can be described by only one analytical function that includes the no-till emission plus an exponential term modulated by tillage and environmentally dependent parameters. (C) 2008 Elsevier B.V. All rights reserved.

Short-term temporal changes of bare soil CO2 fluxes after tillage described by first-order decay models

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

LOSS of EXPONENTIAL STABILITY FOR A THERMOELASTIC SYSTEM WITH MEMORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

First-order decay models to describe soil C-CO2 Loss after rotary tillage

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

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

Time resolved emission spectroscopy of poly(2,5-dicyano-p-phenylene-vinylene) films

Films of poly (2,5-dicyano-p-phenylene vinylene), DCNPPV, were obtained by electrochemical synthesis over gold thin layer (20 nm) transparent electrode deposited on a glass plate. The DCNPPV films of 4 µm thickness were produced by electropolymerization process of α,α,α',α'-tetrabromo-2-5-dicyano-p-xilene at different applied potentials (-0.15, -0.25, -0.40, -0.60, -0.80, and -1.0 V) using 0.1 mol L-1 of tetraethylammonium bromide in acetonitrile as the supporting electrolyte. The emission decays have three exponential components: a fast component in the picosecond range (200-400 ps), and two other of about one and five nanoseconds at 293 K. The fluorescence quenching process seems to occur by exciton trapping in a low-energy site and quenching by residual bromine monomer attached at the end of the polymer chain. However, the electrochemical synthesis generates entrapped bromide or ion pairs during the growth step of the film which also contributes to the deactivation. The change of the electrolyte from bromide to perchlorate reduces significantly this additional quenching effect by allowing ion exchange of formed bromide with the nonquenching perchloride anion.

Radial variation of anatomical features, wood density and decay resistance in teak (Tectona grandis) from two qualities of growing sites and two climatic regions of Costa Rica

The objective of this study was to show the radial variation of some anatomic characteristics, wood density and natural durability of teak (Tectona grandis L.F.) growing in Costa Rica. Samples of trees 13 years old were obtained from two growing sites (high and low growing) of plantations established in a humid tropical climate (CHT) and dry tropical climate (CST). The variables measured of the fibers as well as for the rays were not affected by the climate or the type of growing site, except for the length of the fibers. The fibers of teak wood from the best growing site were significantly larger. Vessels were found with a greater frequency for the CST but mostly solitary in comparison with the CBT. Average density, maximum density and the variation within the ring presented a light higher magnitude for the CST. The quality of the growing site did not affect these variables. The resistance of fungus attack was similar in the area of heartwood near the pith compared to the heartwood near the sapwood for all the conditions evaluated. Nevertheless, it was observed in some trees a similar resistance of fungus attack for areas of sapwood compared to similar areas of heartwood.

Can dark matter decay in dark energy?

We analyze the interaction between dark energy and dark matter from a thermodynamical perspective. By assuming they have different temperatures, we study the possibility of occurring a decay from dark matter into dark energy, characterized by a negative parameter Q. We find that, if at least one of the fluids has nonvanishing chemical potential, for instance mu(x)< 0 and mu(dm)=0 or mu(x)=0 and mu(dm)> 0, the decay is possible, where mu(x) and mu(dm) are the chemical potentials of dark energy and dark matter, respectively. Using recent cosmological data, we find that, for a fairly simple interaction, the dark matter decay is favored with a probability of similar to 93% over the dark energy decay. This result comes from a likelihood analysis where only background evolution has been considered.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD sum rules

We use QCD sum rules (QCDSR) to calculate the width of the radiative decay of the meson X(3872), assumed to be a mixture between charmonium and exotic molecular [c (q) over bar][q (c) over bar] states with J(PC) = 1(++). We find that in a small range for the values of the mixing angle, 5 degrees <= theta <= 13 degrees, we get the branching ratio Gamma(X -> J/psi gamma)/Gamma(X -> J/psi pi(+)pi(-)) = 0.19 +/- 0.13, which is in agreement, with the experimental value. This result is compatible with the analysis of the mass and decay width of the mode J/psi(n pi) performed in the same approach.