A formula for computing (1,2,3)-inverses of g-circulants

Recent work on generalized inverses of linear operators centres around the construction of efficient algorithms for their computation. Here invariably structural properties of the operators and matrices involved are very convenient. As a contribution we obtain a rapidly evaluable explicit expression for (1, 2, 3)-inverses of singular g-circulants that originate in a nonsingular 1-circulant.     

Unbounded symmetrizable idempotents

The relationship between closed unbounded idempotents and dense decompositions of a Hilbert space is explored by extending the notion of compatibility between closed subspaces and positive bounded operators.     

Permeability of anti-fouling PEGylated surfaces probed by fluorescence correlation spectroscopy

The present work reports on in situ observations of the interaction of organic dye probe molecules and dye-labeled protein with different poly(ethylene glycol) (PEG) architectures (linear, dendron, and bottle brush). Fluorescence correlation spectroscopy (FCS) and single molecule event analysis were used to examine the nature and extent of probe-PEG interactions. The data support a sieve-like model in which size-exclusion principles determine the extent of probe-PEG interactions. Small probes are trapped by more dense PEG architectures and large probes interact more with less dense PEG surfaces. These results, and the tunable pore structure of the PEG dendrons employed in this work, suggest the viability of electrochemically-active materials for tunable surfaces.     

A Light‐Triggerable Nanoparticle Library for the Controlled Release of Non‐Coding RNAs

RNA‐based therapies offer a wide range of therapeutic interventions including the treatment of skin diseases; however, the strategies to efficiently deliver these biomolecules are still limited due to obstacles related to the cellular uptake and cytoplasmic delivery. Herein, we report the synthesis of a triggerable polymeric nanoparticle (NP) library composed of 160 formulations, presenting physico‐chemical diversity and differential responsiveness to light. Six formulations were more efficient (up to 500 %) than commercially available lipofectamine in gene‐knockdown activity. These formulations showed differential internalization by skin cells and the endosomal escape was rapid (minutes range). The NPs were effective in the release of siRNA and miRNA. Acute skin wounds treated with the top hit NP complexed with miRNA‐150‐5p healed faster than wounds treated with scrambled miRNA. Light‐activatable NPs offer a new strategy to topically deliver non‐coding RNAs.     

Equigeodesics on Generalized Flag Manifolds with Two Isotropy Summands

In this paper we study homogeneous curves in generalized flag manifolds with two isotropy summands with the additional property that such curves are geodesics with respect to each invariant metric on the flag manifold. These curves are called equigeodesics. We give an algebraic characterization for such curves and we exhibit families of equigeodesics in several flag manifolds of classical and exceptional Lie groups.     

Simulation and dynamics of freeway traffic

This paper presents the new package entitled Simulator of Intelligent Transportation Systems (SITS) and a computational oriented analysis of traffic dynamics. The SITS adopts a microscopic simulation approach to reproduce real traffic conditions considering different types of vehicles, drivers and roads. A set of experiments with the SITS reveal the dynamic phenomena exhibited by this kind of system. For this purpose a modelling formalism is developed that embeds the statistics and the Laplace transform. The results make possible the adoption of classical system theory tools and point out that it is possible to study traffic systems taking advantage of the knowledge gathered with automatic control algorithms. A complementary perspective for the analysis of the traffic flow is also quantified through the entropy measure.     

The mechanism of the Baeyer-Villiger rearrangement: quantum chemistry and TST study supported by experimental kinetic data

The mechanism of the Baeyer-Villiger rearrangement is modelled for the reaction of propanone with trifluoroperacetic acid, catalyzed by trifluoroacetic acid in dichloromethane, using three DFT methods (B3LYP, BH&HLYP and MPWB1K) and MP2. These results are refined and used to calculate the overall reaction rate coefficient using conventional Transition State Theory. The excellent agreement between the calculated (1.00 x 10(-3) L mol(-1) s(-1)) and the experimental (1.8 x 10(-3) L mol(-1) s(-1)) rate coefficients at the MPWB1K level strongly supports the mechanism recently proposed by our group. This DFT method is then used to study the mechanism of a larger system: cyclohexanone + trifluoroperacetic acid, for which a very good agreement between the calculated and the experimental rate coefficients is also found (1.37 and 0.32 L mol(-1) s(-1), respectively). The modelled mechanism is not ionic but neutral, and consists of two concerted steps. The first one is strongly catalyzed while the second one, the migration step, seems not to be catalyzed for the systems under study. The results of this work could be of interest for understanding other reactions in non-polar solvents for which ionic mechanisms have been assumed.     

Reinvestigating the role of multiple hydrogen transfers in Baeyer-Villiger reactions

A comparison between a tetramolecular mechanism (J. Org. Chem. 2007, 72, 3031) and our previously proposed mechanism has been performed. The results show that the tetramolecular mechanism is less favored in terms of Gibbs free energy, and therefore, the reaction in acidic media is acid catalyzed. The role of the catalyst in the migration step has been corrected and discussed. A new transition state is proposed for this step. The change in the rate-determining step for the cyclohexanone + performic acid reaction supports our results.     

Generalized inverses and Douglas equations

In this paper we study the general concept of reduced solution for a Douglas type equation and we parametrize these solutions using generalized inverses. On the other hand, we characterize different sorts of generalized inverses by means of solutions of Douglas type equations.