Mathematical Models for Unstable Quantum Systems and Gamow States

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.     

In Vivo Biological Behavior of Polymer Scaffolds of Natural Origin in the Bone Repair Process

Autologous bone grafts, used mainly in extensive bone loss, are considered the gold standard treatment in regenerative medicine, but still have limitations mainly in relation to the amount of bone available, donor area, morbidity and creation of additional surgical area. This fact encourages tissue engineering in relation to the need to develop new biomaterials, from sources other than the individual himself. Therefore, the present study aimed to investigate the effects of an elastin and collagen matrix on the bone repair process in critical size defects in rat calvaria. The animals (Wistar rats, n = 30) were submitted to a surgical procedure to create the bone defect and were divided into three groups: Control Group (CG, n = 10), defects filled with blood clot; E24/37 Group (E24/37, n = 10), defects filled with bovine elastin matrix hydrolyzed for 24 h at 37 °C and C24/25 Group (C24/25, n = 10), defects filled with porcine collagen matrix hydrolyzed for 24 h at 25 °C. Macroscopic and radiographic analyses demonstrated the absence of inflammatory signs and infection. Microtomographical 2D and 3D images showed centripetal bone growth and restricted margins of the bone defect. Histologically, the images confirmed the pattern of bone deposition at the margins of the remaining bone and without complete closure by bone tissue. In the morphometric analysis, the groups E24/37 and C24/25 (13.68 ± 1.44; 53.20 ± 4.47, respectively) showed statistically significant differences in relation to the CG (5.86 ± 2.87). It was concluded that the matrices used as scaffolds are biocompatible and increase the formation of new bone in a critical size defect, with greater formation in the polymer derived from the intestinal serous layer of porcine origin (C24/25).     

Principal component analysis of the effects of wavefunction modification on the electrostatic potential of indole

The molecular electrostatic potential (MEP) of the indole molecule was calculated in a three‐dimensional grid in which the molecule was centered at the origin. To evaluate the dependence of MEP on the type of calculation, semiempirical, ab initio, and density functional theory methods with different basis sets were employed. The data matrix generated by these calculations was analyzed by principal component analysis (PCA). The appearance of outliers and the effect of wavefunction modifications such as the introduction of electron correlations and diffuse functions were highlighted by the use of PCA. The spatial localization of such effects around the molecule was possible from the loadings values associated with the graphical analysis of the grid points. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Brazilian <Emphasis Type="Italic">Dioscoreaceas</Emphasis> starches

Determination of the characteristics of native starches is crucial in order to select their best application in various industrial fields. Thus, two different types of non-traditional native starches from the Dioscoreaceas species (Dioscorea sp. and Dioscorea piperifolia Humb. var. Wild) were studied regarding their thermal, structural and rheological properties. The results were contrasted with traditional commercial starch sources (potato, cassava and corn). From the thermogravimetric results (TG/DTG), D. piperifolia starch obtained the highest thermal stability of the samples, except for potato starch. Furthermore, using differential scanning calorimetry and viscoamylograph profiles (RVA), it was found that the Dioscoreaceas starches presented a higher onset (T _o) temperature and susceptibility to retrogradation. They also showed lower values in relation to relative crystallinity, which was calculated from their X-ray patterns and tendency to white (L*) colour. The shapes of the Discoreaceas starch granules were determined using electron microscopy; it was found that as the potato starch the Dioscoreaceas starches showed a wide range of particle size.     

The movement of a forager: strategies for the efficient use ofresources

We study a simple model of a foraging animal that modifies the substrate on which itmoves. This substrate provides its only resource, and the forager manages it by taking alimited portion at each visited site. The resource recovers its value after the visitfollowing a relaxation law. We study different scenarios to analyze the efficiency of themanaging strategy, corresponding to control the bite size. We observe the non trivialemergence of a home range, that is visited in a periodic way. The duration of thecorresponding cycles and the transient until it emerges is affected by the bite size. Ourresults show that the most efficient use of the resource, measured as the balance betweengathering and traveled distance, corresponds to foragers that take larger portions butwithout exhausting the resource. We also analyze the use of space determining the numberof attractors of the dynamics, and we observe that it depends on the bite size and therecovery time of the resource.     

Preconcentration Systems Using Polyurethane Foam/Me-BDBD for Determination of Copper in Food Samples

A new reagent, 6-[2′-(6′-methyl-benzothiazolylazo)]-1,2-dihydroxy-3,5-benzenedisulfonic acid (Me-BDBD), was synthesised and used in on-line and off-line systems for copper preconcentration by solid-phase extraction. Spectrophotometry and Flame Atomic Absorption Spectrometry (FAAS) were the detection techniques. Polyurethane foam loaded with Me-BDBD packed in a minicolumn was used as sorbent in both systems. The spectral characteristics of Me-BDBD were investigated. The optimum pH values for maximum sorption of the metal are between 7.0 and 8.5. Copper was desorbed with 0.05 and 0.50 mol L⁻¹ hydrochloric acid solutions, for on-line and off-line systems, respectively. The effects of several foreign substances on the adsorption of copper are reported. The enrichment factors obtained were 7 (on-line) and 26 (off-line) for the systems. The proposed procedures allowed the determination of copper with detection limits of 3.4 and 1.4 μg L⁻¹ (0.85 and 0.35 μg per gram of sample) for on-line and off-line systems, respectively. The precision of the procedures was also calculated: 3.2 (on-line) and 1.9% (off-line). The validation of the procedures was carried out by analysis of certified reference material. The copper contents in corn and rice flour and black tea samples were determined by applying the proposed procedures.     

Photogeneration of distant radical pairs in aqueous pyruvic acid glasses

The lambda > 300 nm photolysis of h4- or d4-pyruvic acid aqueous glasses at 77 K yields identical electron magnetic resonance (EMR) spectra arising from distant (r greater or similar 0.5 nm) triplet radical pairs. Spectra comprise: (1) well-resolved quartets, X, at g approximately ge, that closely match the powder spectra of spin pairs interacting across r approximately 1.0 nm with D approximately 3.0 mT, E approximately 0 mT zero field splittings (ZFS), and (2) broad signals, Y, centered at g approximately 2.07 that display marked g-anisotropy and g-strain, exclude D greater or similar 20.0 mT values (i.e., r less or similar 0.5 spin nm separations), and track the temperature dependence of related g approximately 4 features. These results imply that the n-pi excitation of pyruvic acid, PA, induces long-range electron transfer from the promoted carbonyl chromophore into neighboring carbonyl acceptors, rather than homolysis into contact radical pairs or concerted decarboxylation into a carbene. Since PA is associated into hydrogen-bonded dimers prior to vitrification, X signals arise from radical pairs ensuing intradimer electron transfer to a locked acceptor, while Y signals involve carbonyl groups attached to randomly arranged, disjoint monomers. The ultrafast decarboxylation of primary radical ion pairs, 3[PA+* PA-*], accounts for the release of CO2 under cryogenic conditions, the lack of thermal hysteresis displayed by magnetic signals between 10 and 160 K, and averted charge retrotransfer. All EMR signals disappear irreversibly above the onset of ice diffusivity at approximately 190 K.     

Ionic liquids as recycling solvents for the synthesis of magnetic nanoparticles

This work describes an easy synthesis (one pot) of MFe(2)O(4) (M = Co, Fe, Mn, and Ni) magnetic nanoparticles MNPs by the thermal decomposition of Fe(Acac)(3)/M(Acac)(2) by using BMI·NTf(2) (1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) or BMI·PF(6) (1-n-butyl-3-methylimidazolium hexafluorophosphate) ionic liquids (ILs) as recycling solvents and oleylamine as the reducing and surface modifier agent. The effects of reaction temperature and reaction time on the features of the magnetic nanomaterials (size and magnetic properties) were investigated. The growth of the MNPs is easily controlled in the IL by adjusting the reaction temperature and time, as inferred from Fe(3)O(4) MNPs obtained at 150 °C, 200 °C and 250 °C with mean diameters of 8, 10 and 15 nm, respectively. However, the thermal decomposition of Fe(Acac)(3) performed in a conventional high boiling point solvent (diphenyl ether, bp 259 °C), under a similar Fe to oleylamine molar ratio used in the IL synthesis, does not follow the same growth mechanism and rendered only smaller NPs of 5 nm mean diameter. All MNPs are covered by at least one monolayer of oleylamine making them readily dispersible in non-polar solvents. Besides the influence on the nanoparticles growth, which is important for the preparation of highly crystalline MNPs, the IL was easily recycled and has been used in at least 20 successive syntheses.     

Disclosure of the imidazolium cation coordination and stabilization mode in ionic liquid stabilized gold(0) nanoparticles

A surface-enhanced Raman spectroscopy (SERS) study of imidazolium ionic liquid stabilized gold(0) nanoparticles (GNPs) furnished previously unknown knowledge about the coordination and stabilization mode of the imidazolium cation. GNPs were prepared by hydrazine reduction of a chloroauric acid solution in 1-triethylene glycol monomethyl ether-3-methylimidazolium methanesulfonate 2 as ether-functionalized room-temperature ionic liquid (RTIL). UV-vis spectroscopy showed the presence of GNP aggregates as absorptions extended to the NIR region. A parallel coordination mode for the imidazolium cation of RTIL 2 on the GNP surface was observed by SERS, which occurred without the simultaneous coordination of the 1-triethylene glycol monomethyl ether-functionality. Instead of this, the ether-functionality was directed away from the GNP surface and acted as steric barrier between the GNPs/GNP aggregates, thus preventing further aggregation. These new insights suggest that the imidazolium cation is responsible for electrosteric stabilization.