Mathematical analysis of some new Reynolds‐rod elastohydrodynamic models

In this paper, some new elastohydrodynamic Reynolds‐rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic rod displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displacement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove the existence of solution. Besides nearly linear coupled problems, two non‐linear rod problems including curvature effects are analysed. Mainly, regularity results and L^∞ estimates for the solution of variational inequalities and fixed‐point theorems lead to the existence results for the various coupled models. Copyright © 2001 John Wiley & Sons, Ltd.     

Metal Ion Removal from Aqueous Solution by Liquid Phase Polymer-Based Retention Technique

Summary: Water-soluble poly[3-(dimethylamino)propylacrylate] is synthesized by radical polymerization with a yield of 87%. The polymer structure is confirmed by FT-IR and ¹H-NMR spectroscopies. The polymer lost only 3% of weight up to 100 °C. The narrowest molecular weight distribution is observed with the fraction between 3,000 and 10,000 Da. P(DAPA) presents a high affinity for the metal ions Pb²⁺ and Cu²⁺, while the other metal ions are not significantly retained. By increasing the filtration factor, Z, metal ion affinity decreases, indicating a very weak ligand-metal interaction and the possibility of its destruction when washed with water at the filtration cell's pH. For Z = 10, the retention values of Pb²⁺ and Cu²⁺ at pH 5 are 76.5% and 48.5%, respectively, while the values for Cu²⁺ and Cd²⁺ at pH 7 are 89.5% and 40.4%, respectively.     

Synthesis and characterization of novel second-order NLO-chromophores bearing pyrrole as an electron donor group

Two series of novel push–pull 1-(4-(thiophen-2-yl)phenyl)-1H-pyrroles 3–5 were designed to explore the consequence of using different electron accepting moieties linked to the thiophene at the arylthiophene bridge or to the pyrrole heterocycle, which plays the role of donor group. Compound 2 showed a different reactivity behavior in the presence of the Vilsmeier reagent or with tetracyanoethylene (TCNE) giving compounds 4a and 4b functionalized, respectively, at the 2 or on the 3-position of the pyrrole heterocycle. Their optical (linear and first hyperpolarizability), electrochemical, and thermal properties have been examined. Hyper-Rayleigh scattering (HRS) in dioxane solutions using a fundamental wavelength of 1064 nm was employed to evaluate their second-order nonlinear optical properties. Of these systems, thiobarbituric acid derivative 5b functionalized in the thiophene ring exhibits the largest first hyperpolarizability (β=2480×10^?30 esu, T convention) compared to the corresponding compound 4c substituted on the pyrrole heterocycle (β=290×10^?30 esu, T convention). Good to excellent thermal stabilities were also obtained for push–pull compounds 4 and 5 (270–288 °C). This multidisciplinary study shows that modulation of the optical and electronic properties can be achieved by introduction of the acceptor groups in the thiophene of the arylthiophene bridge. The measured molecular first hyperpolarizabilities and the observed electrochemical behavior are quite sensitive to the position of acceptor group on the heterocyclic system (on the thiophene or on the pyrrole ring) as well as the strength of the acceptor moieties. Moreover, the combination of their good nonlinearity and high thermal stability make them good candidates for second-order nonlinear optical applications.     

Catalytic non-conventional trans-hydroboration: a theoretical and experimental perspective

We have studied the non-conventional trans-hydroboration reaction of alkynes both experimentally and theoretically. A catalytic system based on the in situ mixture of [{Rh(cod)Cl}(2)]/PCy(3) (cod=1,5-cyclooctadiene, Cy=cyclohexyl) has been able to activate pinacolborane and catecholborane and transfer boryl and hydride groups onto the same unhindered carbon atom of the terminal alkynes. The presence of a base (Et(3)N) favored the non-conventional trans-hydroboration over the traditional cis-hydroboration. Varying the substrate had a significant influence on the reaction, with up to 99% conversion and 94% regioselectivity observed for para-methyl-phenylacetylene. Both DFT and quantum mechanical/molecular mechanical ONIOM calculations were carried out on the [RhCl(PR(3))(2)] system. To explain the selectivity towards the (Z)-alkenylboronate we explored several alternative mechanisms to the traditional cis-hydroboration, using propyne as a model alkyne. The proposed mechanism can be divided into four stages: 1) isomerization of the alkyne into the vinylidene, 2) oxidative addition of the borane reagent, 3) vinylidene insertion into the Rh-H bond, and finally 4) reductive elimination of the C-B bond to yield the 1-alkenylboronate. Calculations indicated that the vinylidene insertion is the selectivity-determining step. This result was consistent with the observed Z selectivity when the sterically demanding phosphine groups, such as PCy(3) and PiPr(3), were introduced. Finally, we theoretically analyzed the effect of the substrate on the selectivity; we identified several factors that contribute to the preference for aryl alkynes over aliphatic alkynes for the Z isomer. The intrinsic electronic properties of aryl substituents favored the Z-pathway over the E-pathway, and the aryl groups containing electron donating substituents favored the occurrence of the vinylidene reaction channel.     

Mechanistic elucidation of ketenimine-butynoate cycloaddition reaction: role of biradical intermediates in isotopomeric purity of benzyl (1,1a,6,6a-C4)-6-methyl anthranilic ester

Thermal Diels-Alder reaction of vinyl ketenimines with ¹³C-labeled 2-butynoate, efficiently prepared from ¹³C₄-acetoacetate via the enol triflate, rendered at 160 °C the corresponding methylanthranilic ester isotopomerically pure. However, when the reaction was run at 100 °C, 7% of isotope exchange between C^6a and C⁵ was observed. This result is explained through a base-like catalyzed isomerization of the alkyne to the corresponding allene. Combined DFT and coupled-cluster computations show the feasibility of this mechanistic proposal. Better agreement between DFT and coupled-cluster activation and reaction energies is observed for the meta-GGA MPWB1K functional as compared to previous B3LYP results.     

Role of quaternary ammonium salts as new additives in the enantioselective organocatalytic β-benzylation of enals

We report herein the efficiency of quaternary ammonium salts as co-catalysts in organocatalytic Michael reactions involving iminium activation of α,β-unsaturated aldehydes. The enantioselective formal benzylation of these substrates has been optimized and used to rationalize the role of the ammonium salts in these processes.     

Polyhedral study of the maximum common induced subgraph problem

In this paper we present an exact algorithm for the Maximum Common Induced Subgraph Problem (MCIS) by addressing it directly, using Integer Programming (IP) and polyhedral combinatorics. We study the MCIS polytope and introduce strong valid inequalities, some of which we prove to define facets. Besides, we show an equivalence between our IP model for MCIS and a well-known formulation for the Maximum Clique problem. We report on computational results of branch-and-bound (B&B) and branch-and-cut (B&C) algorithms we implemented and compare them to those yielded by an existing combinatorial algorithm.     

The Use of DRAQ5 to Monitor Intracellular DNA in <Emphasis Type="Italic">Escherichia coli</Emphasis> by Flow Cytometry

Flow cytometry provides a rapid and high-content multiparameter analysis of individual microorganisms within a population. In the past years, several fluorescent stains were developed in order to monitor DNA content distribution and cell-cycle phases, mainly in eukaryotic cells. Recently, due to its low detection limits, several of these fluorescent stains were also applied to prokaryotic cells. In this study, the ability of a novel far-red fluorescent stain DRAQ5 in assessing intracellular DNA content distribution in Escherichia coli DH5α was evaluated. The results showed that a DRAQ5-labelled live E. coli suspension can be obtained by incubation of 1 × 10⁶ cells/mL with 5 μM DRAQ5 in PBS buffer supplemented with EDTA (pH = 7.4) during 30 min at 37 °C. Flow cytometric analysis of fixed E. coli cells revealed that ethanol should be used in detriment of glutaraldehyde for DRAQ5 labelling. After the analysis of RNase and DNase digested samples, DRAQ5 was proven to be a specific DNA labelling stain. The present study demonstrates that the use of DRAQ5 as a DNA-labelling stain provides an easy assessment of intracellular DNA content and cell-cycle phases in Gram-negative bacteria such as E. coli.     

The vertex separator problem: algorithms and computations

This is a companion paper to our polyhedral study [1] of the Vertex Separator (VS) Problem. Given an undirected graph G, the VS problem consists in identifying a minimum-weight vertex set whose removal disconnects G, subject to bounds on the size of the resulting components. In this paper, we describe versions of a branch-and-cut algorithm based on the results of that polyhedral study. It uses two families of cuts, symmetric and asymmetric, for which we develop polynomial-time greedy separation routines. A heuristic to generate feasible separators is also used. A computational experiment on several data sets from the literature compares the performance of three versions of our algorithm to that of the commercial MIP solver XPRESS. This experiment throws a sharp light on the role of cut density, known to software developers but never before documented in the literature. It convincingly shows that the practical usefulness of cuts in integer programming depends not only on their strength, but also on their sparsity: everything else being equal, the smaller the cut support, the better. The power of the inequalities proposed here is well illustrated by the computational tests on dense graphs. This is in accordance with the previous observation, since the support of these cuts tends to decrease with graph density.Research supported by the Brazilian agencies FAPESP (grant 01/14205–6), CAPES (grant BEX 04444/02–2) and CNPq (grants 302588/02–7 and Pronex 664107/97–4).Research supported by the National Science Foundation through grant #DMI-0098427 and by the Office of Naval Research through contract N00014-97-1-0196.     

Potassium iodide catalysed monoalkylation of anilines under microwave irradiation

A potassium iodide catalysed method for the selective N-monoalkylation anilines with alkylhalides and alkyltosylates under microwave irradiation is described. The corresponding N-alkylanilines are obtained in good yields with only minor quantities of dialkylation by-products.