On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Kinetic resolution of a drug precursor by Burkholderia cepacia lipase immobilized by different methodologies on superparamagnetic nanoparticles

Burkholderia cepacia lipase was immobilized on superparamagnetic nanoparticles using three different methodologies (adsorption, chemisorption with carboxibenzaldehyde and chemisorption with glutaraldehyde) and employed in the kinetic resolution of a chiral drug precursor, (RS)-2-bromo-1-(phenyl)ethanol, via enantioselective acetylation reaction. An excellent improvement of lipase catalytical performance was observed. Free B. cepacia lipase gave the ester (S)-2 with poor E-value <30, and after its immobilization to magnetic nanoparticles the E-value was up to >200. The effect of several reaction parameters in the kinetic resolution was studied. The best results for kinetic resolution were obtained using vinyl acetate as acetyl donor and toluene as solvent, typically yielding the ester in high enantiomeric excess (>99%) and E-value (E > 200). Of the three tested immobilization methods, chemisorption with glutaraldehyde was the best one in terms of temperature stability and yield product. (C) 2010 Elsevier B.V. All rights reserved.

Direct Kinetic Observation of the Chemiexcitation Step in Peroxyoxalate Chemiluminescence

A high-energy intermediate in the peroxyoxalate reaction can be accumulated at room temperature under specific reaction conditions and in the absence of any reducing agent in up to micromolar concentrations. Bimolecular interaction of this intermediate, accumulated in the reaction of oxalyl chloride with hydrogen peroxide, with an activator (highly fluorescent aromatic hydrocarbons with low oxidation potential) added in delay shows unequivocally that this intermediate is responsible for chemiexcitation of the activator. Activation parameters for the unimolccular decomposition of this intermediate (Delta H(double dagger) = 11.2 kcal mol(-1); Delta S(double dagger) = -23.2 cal mol(-1) K(-1)) and for its bimolecular reaction with 9,10-diphenylanthracene (Delta H(double dagger) = 4.2 kcal mol(-1); Delta S(double dagger) = -26.9 cal mol(-1) K(-1)) show that this intermediate is much less stable than typical 1,2-dioxetanes and 1,2-dioxetanones and demonstrate its highly favored interaction with the activator. Therefore, it can be inferred that structural characterization of the high-energy intermediate in the presence of an activator must be highly improbable. The observed linear free-energy correlation between the catalytic rate constants and the oxidation potentials of several activators definitely confirms the occurrence of the chemically initiated electron-exchange luminescence (CIEEL) mechanism in the chemiexcitation step of the peroxyoxalate system.

First dynamic kinetic resolution of selenium-containing chiral amines catalyzed by palladium (Pd/BaSO(4)) and Candida antartica lipase (CAL-B)

An efficient method for chemoenzymatic dynamic kinetic resolution of selenium-containing chiral amines (organoselenium-1-phenylethanamines) has been developed, leading to the corresponding amides in excellent enantioselectivities and high isolated yields. This one-pot procedure employs two different types of catalysts: Pd on barium sulphate (Pd/BaSO(4)) as racemization catalyst and lipase (CAL-B) as the resolution catalyst. (C) 2009 Elsevier Ltd. All rights reserved.

Lipase-Catalyzed Highly Enantioselective Kinetic Resolution of Boron-Containing Chiral Alcohols

The first application of enzymes as catalysts to obtain optically pure boron compounds is described. The kinetic resolution of boron-containing chiral alcohols via enantioselective transesterification catalyzed by lipases was studied. Aromatic, allylic, and aliphatic secondary alcohols containing a boronate ester or boronic acid group were resolved by lipase from Candida antartica (CALB), and excellent E values (E > 200) and high enantiomeric excesses (up to >99%) of both remaining substrates and acetylated product were obtained.

Enzymatic kinetic resolution of organochalcogenides in supercritical CO(2)

1-(Phenylthio)-, 1-(phenylseleno)- and 1-(phenyltelluro)-propan-2-ol were efficiently resolved by CAL-B in sc-CO(2). (C) 2011 Elsevier Ltd. All rights reserved.

Kinetic resolution of iodophenylethanols by Candida antarctica lipase and their application for the synthesis of chiral biphenyl compounds

The kinetic resolution of (+/-)-iodophenylethanols was carried out using lipase from Candida antarctica and in some cases the enantiomeric excesses were high (up to >98%). Enantiomerically enriched (S)-iodophenylethanols produced by the enzymatic resolution process were used in the synthesis of chiral biphenyl compounds by the Suzuki reaction with good yields (63-65%). (C) 2010 Elsevier Ltd. All rights reserved.

Expression, purification and kinetic characterization of His-tagged glyceraldehyde-3-phosphate dehydrogenase from Trypanosoma cruzi

Trypanosomes are flagellated protozoa responsible for serious parasitic diseases that have been classified by the World Health Organization as tropical sicknesses of major importance. One important drug target receiving considerable attention is the enzyme glyceraldehyde-3-phosphate dehydrogenase from the protozoan parasite Trypanosoma cruzi, the causative agent of Chagas disease (T. cruzi Glyceraldehyde-3-phosphate dehydrogenase (TcGAPDH); EC 1.2.1.12). TcGAPDH is a key enzyme in the glycolytic pathway of T. cruzi and catalyzes the oxidative phosphorylation of D-glyceraldehyde-3-phosphate (G3P) to 1,3-bisphosphoglycerate (1,3-BPG) coupled to the reduction of oxidized nicotinamide adenine dinucleotide, (NAD(+)) to NADH, the reduced form. Herein, we describe the cloning of the T. cruzi gene for TcGAPDH into the pET-28a(+) vector, its expression as a tagged protein in Escherichia coli, purification and kinetic characterization. The His(6)-tagged TcGAPDH was purified by affinity chromatography. Enzyme activity assays for the recombinant His(6)-TcGAPDH were carried out spectrophotometrically to determine the kinetic parameters. The apparent Michaelis-Menten constant (K(M)(app)) determined for D-glyceraldehyde-3-phosphate and NAD(+) were 352 +/- 21 and 272 +/- 25 mu M, respectively, which were consistent with the values for the untagged enzyme reported in the literature. We have demonstrated by the use of Isothermal Titration Calorimetry (ITC) that this vector modification resulted in activity preserved for a higher period. We also report here the use of response surface methodology (RSM) to determine the region of optimal conditions for enzyme activity. A quadratic model was developed by RSM to describe the enzyme activity in terms of pH and temperature as independent variables. According to the RMS contour plots and variance analysis, the maximum enzyme activity was at 29.1 degrees C and pH 8.6. Above 37 degrees C, the enzyme activity starts to fall, which may be related to previous reports that the quaternary structure begins a process of disassembly. (C) 2010 Elsevier Inc. All rights reserved.

Investigating the Nature of Noble Gas-Copper Bonds by the Quantum Theory of Atoms in Molecules

We investigated noble gas copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy or noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.