Schur Complements in Krein Spaces

The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded) J-selfadjoint operator A (with the unique factorization property) acting on a Krein space and a suitable closed subspace of , the Schur complement of A to is defined. The basic properties of are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive operators on a Hilbert space. To the memory of Professor Mischa Cotlar     

Conformations of proline analogues having double bonds in the ring

The intrinsic conformational preferences of proline analogues having double bonds between carbon atoms in their rings have been investigated using quantum mechanical calculations at the B3LYP/6-31+G(d,p) level. For this purpose, the potential energy surface of the N-acety-N'-methylamide derivatives of three dehydroprolines (proline analogues unsaturated at alpha,beta; beta,gamma; and gamma,delta) and pyrrole (proline analogue with unsaturations at both alpha,beta and gamma,delta) have been explored, and the results are compared with those obtained for the derivative of the nonmodified proline. We found that the double bonds affect the ring puckering and the geometric internal parameters, even though the backbone conformation was influenced the most. Results indicate that the formation of double bonds between carbon atoms in the pyrrolidine ring should be considered as an effective procedure to restrict the conformational flexibility of prolines. Interestingly, we also found that the N-acetyl-N'-methylamide derivative of pyrrole shows a high probability of having a cis peptide bond preceding the proline analogue.     

Polycationic glycosides

Cationic lipids have long been known to serve as antibacterial and antifungal agents. Prior efforts with attachment of cationic lipids to carbohydrate-based surfaces have suggested the possibility that carbohydrate-attached cationic lipids might serve as antibacterial and antifungal pharmaceutical agents. Toward the understanding of this possibility, we have synthesized several series of cationic lipids attached to a variety of glycosides with the intent of generating antimicrobial agents that would meet the requirement for serving as a pharmaceutical agent, specifically that the agent be effective at a very low concentration as well as being biodegradable within the organism being treated. The initial results of our approach to this goal are presented.     

Cyclodextrin induced switch between heterolytic and homolytic dediazoniation mechanisms

We have investigated the kinetics and mechanism of dediazoniation of 4-nitrobenzenediazonium (4NBD) tetrafluoroborate in the presence of α-cyclodextrin, α-CD, and γ-cyclodextrin, γ-CD, under acidic (HCl, pH=2) conditions by employing a combination of spectrometric and chromatographic techniques. In the absence of CDs, dediazoniation follows first-order kinetics, with t(1/2)=22,000 s at T=60 °C, but addition of small amounts of either α-CD or γ-CD leads to more rapid but not first-order kinetics with t(1/2)~400 s when [α-CD]=20 [4NBD] or [γ-CD]=15 [4NBD]. Analyses of reaction mixtures by HPLC indicate that three main dediazoniation products are formed depending on the particular experimental conditions. These are 4-nitrophenol, ArOH, nitrobenzene, ArH, and 4-nitrochlorobenzene, ArCl. In the absence of CDs, the main dediazoniation product is the substitution product ArOH, but on increasing the concentration of CD, the reduction product ArH becomes predominant at the expense of ArOH, indicating that a switch between the heterolytic and homolytic reaction mechanisms take place under acidic conditions, where little significant ionization of the OH groups of the CDs takes place (pK(a)≈12). Addition of the surfactant sodium dodecylsulfate, SDS, blocks the CD cavity inhibiting 4NBD dediazoniation and decreasing the yields of ArH with a concomitant increase in that of ArOH, suggesting that 4NBD ions form an inclusion complex prior to reacting with the OH groups of the CDs. This O-coupling reaction leads to the formation of a highly unstable Z-diazo ether adduct that cannot isomerize to the much more stable E-isomer because of the geometric restrictions imposed by the CD cavity, splitting homolitically.     

Normal Projections in Krein Spaces

Given a complex Krein space ${\mathcal{H}}$ with fundamental symmetry J, the aim of this note is to characterize the set of J-normal projections $$\mathcal{Q}=\{Q \in L(\mathcal{H}) : Q^2=Q \,{\rm and}\, Q^{\#}Q=QQ^{\#}\}.$$ The ranges of the projections in ${\mathcal{Q}}$ are exactly those subspaces of ${\mathcal{H}}$ which are pseudo-regular. For a fixed pseudo-regular subspace ${\mathcal{S}}$ , there are infinitely many J-normal projections onto it, unless ${\mathcal{S}}$ is regular. Therefore, most of the material herein is devoted to parametrizing the set of J-normal projections onto a fixed pseudo-regular subspace ${\mathcal{S}}$ .     

Electroactive copper(II) bimetallic self-assembled multilayers on Si(100)

Silicon (100) surfaces were modified by reacting 4-aminopyridine and Si–Cl bond. These surfaces were further used for tethering copper bimetallic complexes and growing monolayers and multilayers by changing the axial position via Lewis acid–base reactions. In this way, coordination chemistry approach can be used as building blocks for controlling the design of functional surfaces. Furthermore, the outcomes of the several characterization techniques indicate that the complex is spatially oriented suggesting that this simple strategy allows the preparation of three dimensional molecular structures exhibiting spatial order. The structures on surface show interesting electroactive behaviors leading two cathodic signals, that can be related to Cu(II)/Cu(I) and Cu(I)/Cu(0) electro-reduction species (signals at ? 0.15 V and ? 0.50 V) and one peak in the anodic region (? 0.15 V) ascribed to the Cu(0)/Cu(II) electro-oxidation reaction, using an Ag/AgCl saturated electrode and platinum wire as reference and counter electrodes, respectively.     

Sol MWD During Styrene,Vinyl Acetate,Methyl Methacrylate,and Butyl Acrylate Homopolymerization: A Numerical Study Using the NFT Approach

Complete parameter sensitivity analyses using the numerical fractionation technique are presented for the cases of homopolymerization with chain transfer to polymer and termination by combination. Also, using reported values for the kinetic rate constants associated with the linear and non‐linear homopolymerizations of styrene, vinyl acetate, methyl methacrylate and butyl acrylate, overall molecular weight distributions and averages of the MWD were calculated using the NFT. Good agreement with the expected behavior, with MMA and STY not gelling while BA and VAc do, was obtained. It is concluded that the NFT produces coherent and reliable performance for known polymerization systems, whether linear or non‐linear.

     

Multifractal structure in Latin-American market indices

We study the multifractal nature of daily price and volatility returns of Latin-American stock markets employing the multifractal detrended fluctuation analysis. Comparing with the results obtained for a developed country (US) we conclude that the multifractality degree is higher for emerging markets. Moreover, we propose a stock market inefficiency ranking by considering the multifractality degree as a measure of inefficiency. Finally, we analyze the sources of multifractality quantifying the contributions of two factors, the long-range correlations of the time series and the broad fat-tail distributions. We find that the multifractal structure of Latin-American market indices can be mainly attributed to the latter.