The goodness of ergodic adiabatic invariants

For a slowly time-dependent Hamiltonian system exhibiting chaotic motion that ergodically covers the energy surface, the phase space volume enclosed inside this surface is an adiabatic invariant. In this paper we examine, both numerically and theoretically, how the error in this ergodic adiabatic invariant scales with the slowness of the time variation of the Hamiltonian. It is found that under certain circumstances, the error is diffusive and scales likeT ^–1/2, whereT is the characteristic time over which the Hamiltonian changes. On the other hand, for other cases (where motion in the Hamiltonian has a long-time 1/t tail in a certain correlation function), the error scales like [T ^–1 ln(T)]^1/2. Both of these scalings are verified by numerical experiments. In the situation where invariant tori exist amid chaos, the motion may not be fully ergodic on the entire energy surface. The ergodic adiabatic invariant may still be useful in this case and the circumstances under which this is so are investigated numerically (in particular, the islands have to be small enough).     

The Effects of Temperature of Condensation on the Thermal Stability and Morphology of 1,4-Phenylenediamine-1-Propylsilica Xerogels

1,4-phenylenediamine-1-propylsilica hybrid xerogels were obtained for two composition at different temperatures of gelation, from 5 up to 70C. The morphological effects produced by the different gelation temperatures were investigated by using N₂ adsorption-desorption isotherms and scanning electron microscopy. The thermal stability of the organic groups and their distribution on the xerogel matrix, i.e. the fraction of the organic groups that were trapped in closed pores, formed during the xerogel synthesis, and the fraction of organic groups present on the surface, were obtained by using infrared thermal analysis. The higher porosity of the xerogels and the higher thermal stability of the organic groups were achieved for samples gelled at 25C.     

Development of a Novel Molecularly Imprinted Polyvinylimidazole/Functionalized Carbon Black Nanocomposite-based Paste Electrode for Electrochemical Sensing of Imazethapyr in Rice Samples

This paper reports the development of a simple electroanalytical method for imazethapyr (IMT) determination in rice samples based on molecularly imprinted polymer and functionalized carbon black paste electrode (MIP-fCBPE). Carbon black (CB) was functionalized by the insertion of oxygenated functional groups upon acid treatment with HNO₃ and H₂SO₄. The functionalized carbon black (fCB) presented higher performance for IMT determination than the CB without functionalization. The insertion of molecularly imprinted polyvinylimidazole (MIP-VN) in the fCBPE promoted a significant increase in the cathodic peak current even at low proportions (7.5 % w/w) due to the specific binding sites for IMT recognition. For IMT determination, DPV parameters were optimized by the Doehlert matrix applying 0.1 V for 60 s as pre-treatment in acetate buffer solution (pH 3.0) as supporting electrolyte. The proposed method showed low limit of detection (0.03 μmol L⁻¹), a wide linear range (0.10–70.00 μmol L⁻¹), and good precision in terms of repeatability of intraday measures (RSD%=3.6). The method was applied in rice samples after microwave-assisted extraction of IMT and the accuracy of the method was evaluated by addition/recovery assays (96.3–105.7 %), being statistically attested using HPLC-DAD as reference technique.     

Finite mixture of regression models for censored data based on scale mixtures of normal distributions

Advances in Data Analysis and Classification - In statistical analysis, particularly in econometrics, the finite mixture of regression models based on the normality assumption is routinely used to...     

Thermal properties,nanoscopic structure and swelling behavior of chitosan/(ureasil–polyethylene oxide hybrid) blends

In this work, the effect of chitosan blending on the thermal properties, nanoscopic structure and swelling behavior of ureasil–polyethylene oxide (U-PEO) hybrid materials was examined. Materials were prepared by the sol–gel route using acid catalysts, and the effect of acid (hydrochloric or acetic acid) was also examined. Differential scanning calorimetry results showed that chitosan addition did not provoke appreciable changes in the thermal behavior of the U-PEO. Thermogravimetric curves did not show changes in thermal stability resulting from chitosan blending but were depended on the type of acid catalyst. Small-angle X-ray scattering and nuclear magnetic resonance spectroscopy techniques were used for studying nanoscopic and inner structures, showing the existence of two structural levels and differences in polycondensation degrees. All samples presented fast water uptake with the same initial swelling rate and with a non-Fickian or anomalous transport mechanism. Swelling degree was higher in hybrids prepared with HCl, which possessed less branched siloxane cross-link nodes species, therefore lower polycondensation degree. Also, the magnitude of swelling decreased for hybrids blended with chitosan, which provides a means of tailoring the water uptake by the ureasil–PEO hybrid and to potentiate the control of the release profile of drugs incorporated in these materials.     

A fractional algorithm for optimal cutting of lumber into dimension parts

A fractional algorithm is described which optimizes the cutting of boards or lumber into dimension parts. The model is an extension of previously developed models and is purposely designed for cutting scenarios where the customer order for the dimension parts can be satisfied within a given range, i.e., flexible rather than exact demand. An illustrative example is presented simply to describe the model and compare results between the standard procedure and the modified procedure proposed in this paper.     

Morphology of hybrid polystyrene-block-poly(ethylene oxide) micelles: analytical ultracentrifugation and SANS studies

Morphology and structure of aqueous block copolymer solutions based on polystyrene-block-poly(ethylene oxide) (PS-b-PEO) of two different compositions, a cationic surfactant, cetyl pyridinium chloride (CPC), and either platinic acid (H2PtCl6.6H2O) or Pt nanoparticles were studied using a combination of analytical ultracentrifugation (AUC), transmission electron microscopy (TEM), and small angle neutron scattering (SANS). These studies combining methods contributing supplemental and analogous structural information allowed us to comprehensively characterize the complex hybrid systems and to discover an isotope effect when H2O was replaced with D2O. In particular, TEM shows formation of both micelles and larger aggregates after incorporation of platinic acid, yet the amount of aggregates depends on the H2PtCl6.6H2O concentration. AUC reveals the presence of micelles and micellar clusters in the PS-b-PEO block copolymers solution and even larger (supermicellar) aggregates in hybrids (with CPC). Conversely, SANS applied to D2O solutions of the similar species indicates that micelles are spherical and no other micellar species are found in block copolymer solutions. To reconcile the SANS and AUC data, we carried out AUC examination of the corresponding D2O block copolymer solutions. These measurements demonstrate a pronounced isotope effect on micelle aggregation and micelle size, i.e., no micelle aggregation in D2O solutions, revealing good agreement of AUC and SANS data.     

Structure and property studies of hybrid xerogels containing bridged positively charged 1,4-diazoniabicycle[2.2.2]octane dichloride

The compound di-3-n-propyltrimethoxysilane (1,4-diazoniabicycle[2.2.2]octane) dichloride, [(MeO)3Si(CH2)3N+ (CH2CH2)3N+ (CH2)3Si(OME)3]Cl2 was obtained and was used as a precursor reagent to obtain hybrid xerogels where the organic molecule was bonded to a silica framework by reacting the ends of both sides of the precursor reagent. That is, both -Si(OME)3 groups react with tetraethylorthosilicate (TEOS) by hydrolysis-condensation reactions. The resulting hybrid xerogels with variable C/Si mole ratios were prepared and analyzed and their textural characteristics determined. The samples prepared presented micropores with diameter 1.5 nm, the chain length of which matched with the estimated length of the organic bridging group. The charged organic bridging groups allow the immobilization of hexacyanoferrate ions by an ion exchange process. The electron transfer process of the hexacyanoferrate anionic complex confined in the pores of the matrices was studied by cyclovoltammetry.     

A hybrid heuristic for the diameter constrained minimum spanning tree problem

We propose a hybrid GRASP and ILS based heuristic for the diameter constrained minimum spanning tree problem. The latter typically models network design applications where, under a given quality requirement, all vertices must be connected at minimum cost. An adaptation of the one time tree heuristic is used to build feasible diameter constrained spanning trees. Solutions thus obtained are then attempted to be improved through local search. Four different neighborhoods are investigated, in a scheme similar to VND. Upper bounds within 2% of optimality were obtained for problems in two test sets from the literature. Additionally, upper bounds stronger than those previously obtained in the literature are reported for OR-Library instances.