Complete separability of time-dependent second-order ordinary differential equations

Extending previous work on the geometric characterization of separability in the autonomous case, necessary and sufficient conditions are established for the complete separability of a system of time-dependent second-order ordinary differential equations. In deriving this result, extensive use is made of the theory of derivations of scalar and vector-valued forms along the projection :J ¹ EE of the first jet bundle of a fibre bundleE . Two illustrative examples are discussed, which fully demonstrate all aspects of the constructive nature of the theory.     

A parallel projection method for overdetermined nonlinear systems of equations

We consider overdetermined nonlinear systems of equationsF(x)=0, whereF: ^{n m} ,mn. For this type of systems we define weighted least square distance (WLSD) solutions, which represent an alternative to classical least squares solutions and to other solutions based on residual normas. We introduce a generalization of the classical method of Cimmino for linear systems and we prove local convergence results. We introduce a practical strategy for improving the global convergence properties of the method. Finally, numerical experiments are presented.Work supported by FAPESP (Grant 90/3724/6), FINEP, CNPq and FAEP-UNICAMP.     

The classification of ϕ-symmetric Sasakian manifolds

A -symmetric spaceM is a complete connected regular Sasakian manifold, that fibers over an Hermitian symmetric spaceN, so that the geodesic involutions ofN lift to define global (involutive) automorphisms of the Sasakian structure onM. In the present paper the complete classification of -symmetric spaces is obtained. The groups of automorphisms of the Sasakian structures and the groups of isometries of the underlying Riemannian metrics are determined. As a corollary, the Sasakian space forms are also determined.     

Flow injection manifolds for liquid-liquid extraction without phase separation assisted by ultrasound

Flow injection (FI) manifolds based on iterative change of the flow direction have been designed to study the influence of auxiliary energy on continuous liquid-liquid extraction without phase separation and compare it with the non-assisted process in a single experiment. In order to demonstrate the utility of ultrasounds as auxiliary energy for the extraction of polyphenols from an organic phase, the approach has been applied to samples of extra virgin olive oil, using an alkaline aqueous phase as extractant and subsequent derivatization with the Folin-Ciocalteu reagent. The proposed method provides results similar to those from the official method-recoveries between 97 and 100%. The sensitivity of the proposed method is 3.5 times higher than that of the non-ultrasound-assisted method. The precision, expressed as relative standard deviation (R.S.D.) for n=5, was within 1-5% and the relative errors for the irradiated and non-irradiated method were within 3 and 5%, respectively. The repeatability and within-laboratory reproducibility, studied at two concentration levels (379 and 813 μg ml⁻¹) ranged between 0.7-4.4% and 0.6-4.8%, respectively. The proposed manifolds can also be applied to either other type of auxiliary energies—microwave, thermal—or two different types of auxiliary energies at the same time.     

Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.     

New Hg2+ and Cu2+ selective chromo- and fluoroionophore based on a bichromophoric azine

[graph: see text] A new probe, 1,4-bis(1-pyrenyl)-2,3-diaza-1,3-butadiene, selectively senses Hg2+ and Cu2+ through two different channels: the yellow-deep-pink color change and the enhancement of the fluorescence with the red shift of the excimer emission, which can visually be discernible by a green fluorescence in the presence of Hg2+ and an orange fluorescence in the presence of Cu2+.     

Electron beam crosslinking of non-lead PVC formulations

PVC samples with lead-free and lead-base stabilizer, containing TMPTMA (trimethylolpropane trimethacrylate) as a crosslinker and DOP (2-ethylhexyl phthalate) as a plasticizer, were electron beam treated at different doses (2–200 kGy) and characterized to evaluate crosslinking and other several properties, as a continuation of our previously reported paper, where these PVC formulations, typical for wire and cable applications, underwent gamma irradiation. The PVC was formulated with two different stabilizing systems: Ca/Zn and dibasic lead phthalate for comparison, to use them as jackets for a 22 wire gage (AWG). Small samples of the jacketed wires were irradiated in an industrial Dynamitron electron accelerator for the corresponding doses, along with two dosimetric systems: radiochromic thin film and alanine pellets dosimeters. The maximum dose applied was decided as the crosslinking increased, until the gel content was stable. The dose of 200 kGy was the condition for the highest crosslinking, so most of the wire was irradiated at such dose. Chemical and mechanical evaluations were carried out to the irradiated wire. The results show that 200 kGy was too high dose for the materials, since an important degradation is observed for the Ca/Zn systems. Unfortunately, such dose affects basically to CaZn formulations, which showed much poorer performance than classical lead-containing compositions. The results also indicate that gel content is not the best way of deciding the optimum condition for irradiation.