Convergence of Vector Bundles with Metrics of Sasaki-Type

If a sequence of Riemannian manifolds, X _i , converges in the pointed Gromov–Hausdorff sense to a limit space, X _∞, and if E _i are vector bundles over X _i endowed with metrics of Sasaki-type with a uniform upper bound on rank, then a subsequence of the E _i converges in the pointed Gromov–Hausdorff sense to a metric space, E _∞. The projection maps π _i converge to a limit submetry π _∞ and the fibers converge to its fibers; the latter may no longer be vector spaces but are homeomorphic to \(\mathbb {R}^{k}/G\) , where G, henceforth called the wane group, is a closed subgroup of O(k) that depends on the basepoint and that is defined using the holonomy groups on the vector bundles. The norms μ _i =∥?∥ _i converge to a map μ _∞ compatible with the rescaling in \(\mathbb {R}^{k}/G\) and the \(\mathbb {R}\) -action on E _i converges to an \(\mathbb {R}\) -action on E _∞ compatible with the limiting norm. A natural notion of parallelism is given to the limiting spaces by considering curves whose length is unchanged under the projection. The class of such curves is invariant under the \(\mathbb {R}\) -action and each such curve preserves norms. The existence of parallel translation along rectifiable curves with arbitrary initial conditions is also exhibited. Also, necessary conditions for uniqueness of parallel translates are given in terms of the wane groups. In the special case when the sequence of vector bundles has a uniform lower bound on holonomy radius (as in a sequence of collapsing flat tori to a circle), the limit fibers are vector spaces. Under the opposite extreme, e.g., when a single compact n-dimensional manifold is rescaled to a point, the limit fiber is \(\mathbb {R}^{n}/H\) where H is the closure of the holonomy group of the compact manifold considered. Both these examples have uniqueness of parallel translates. However, examples for non-uniqueness are also produced by looking at isolated conical singularities.     

Removing dead transitions in timed-arc Petri nets

Timed-arc Petri nets (TAPNs) are a timed extension of Petri nets where tokens are assigned an age indicating the time elapsed from its creation, and PT-arcs (place to transition arcs) are labelled with time intervals that are used to restrict the age of the tokens that can be used to fire the adjacent transition. This is a rather pathological model, as reachability is undecidable, whereas some other known properties of Petri nets, like boundedness, coverability and even termination, are decidable. This article focuses on the problem of detecting dead transitions, i.e. transitions that can be removed from the model since they can never become enabled. We prove that this problem is decidable for TAPNs with natural times, and we present an algorithm that can be used to find dead transitions in the particular case of 1-safe TAPNs.     

Local Łojasiewicz exponents,Milnor numbers and mixed multiplicities of ideals

Let be a finite analytic map. We give an expression for the local Łojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals I ₁,..., I _n . We give an effective method to compute Łojasiewicz exponents based on the computation of mixed multiplicities. As a consequence of our study, we give a numerical characterization of a class of functions that includes semi-weighted homogenous functions and Newton non-degenerate functions. Work supported by DGICYT Grant MTM2006-06027.     

Gender effect on neurodegeneration and myelin markers in an animal model for multiple sclerosis

Background  

Multiple sclerosis (MS) varies considerably in its incidence and progression in females and males. In spite of clinical evidence, relatively few studies have explored molecular mechanisms possibly involved in gender-related differences. The present study describes possible cellular- and molecular-involved markers which are differentially regulated in male and female rats and result in gender-dependent EAE evolution and progression. Attention was focused on markers of myelination (MBP and PDGFαR) and neuronal distress and/or damage (GABA synthesis enzymes, GAD65 and GAD67, NGF, BDNF and related receptors), in two CNS areas, i.e. spinal cord and cerebellum, which are respectively severely and mildly affected by inflammation and demyelination. Tissues were sampled during acute, relapse/remission and chronic phases and results were analysed by two-way ANOVA.     

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N _c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z ^1/3. This improves Lieb’s upper bound N _c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).     

Biologically Inspired C−H and C=C Oxidations with Hydrogen Peroxide Catalyzed by Iron Coordination Complexes

The development of catalysts for the selective oxidation of readily available hydrocarbons or organic precursors into oxygenated products is a long‐standing goal in organic synthesis. In the last decade, some iron coordination complexes have shown the potential to fit this role. These catalysts can mimic the O?O activation mode of far more sophisticated iron oxygenase enzymes, generating powerful yet selective oxidants. In this review, we report state‐of‐the‐art C?H and C=C oxidations catalyzed by non‐heme iron complexes and H₂O₂ as the oxidant. Finally, we briefly describe some novel oxidative reactivity and the perspectives of this chemistry.     

Palladium‐Catalyzed Intramolecular Carbene Insertion into C(sp3)−H Bonds

A palladium‐catalyzed carbene insertion into C(sp³)?H bonds leading to pyrrolidines was developed. The coupling reaction can be catalyzed by both Pd⁰ and Pd^II, is regioselective, and shows a broad functional group tolerance. This reaction is the first example of palladium‐catalyzed C(sp³)?C(sp³) bond assembly starting from diazocarbonyl compounds. DFT calculations revealed that this direct C(sp³)?H bond functionalization reaction involves an unprecedented concerted metalation–deprotonation step.     

New ruthenium(II) complexes with enantiomerically pure bis- and tris(pinene)-fused tridentate ligands. Synthesis, characterization and stereoisomeric analysis

A new set of Ru-Cl complexes containing either the pinene[5,6]bpea ligand (L1) or the C3 symmetric pinene[4,5]tpmOMe (L2) tridentate ligand in combination with the bidentate (B) 2,2'-bipyridine (bpy) or 1,2-diphenylphosphinoethane (dppe) with general formula [RuCl(L1 or L2)(B)](+) have been prepared and thoroughly characterized. In the solid state, X-ray diffraction analysis techniques have been used. In solution, cyclic voltammetry (CV) and 1D and 2D NMR spectroscopy have been employed. DFT calculations have been also performed on these complexes and their achiral analogues previously reported in our group, to interpret and complement experimental results. Whereas isomerically pure complexes ([Ru(II)Cl(L2)(bpy)](BF4), 5 and [Ru(II)Cl(L2)(dppe)](BF4), 6) are obtained when starting from the highly symmetric [Ru(III)Cl3(L2)], 2, isomeric mixtures of cis, fac-[Ru(II)Cl(L1)(bpy)](BF4) (3b/3b'), trans,fac- (3a) and up/down,mer- (3c, 3d) isomers are formed when bpy is added to the less symmetric [Ru(III)Cl3(L1)], 1, in contrast to the case of the bulky dppe ligand that, upon coordination to 1, leads to the trans,fac-[Ru(II)Cl(L1)(dppe)](BF4) (4a) complex as a sole isomer due to steric factors.     

Effect of temperature on the chromatographic retention of ionizable compounds. III. Modeling retention of pharmaceuticals as a function of eluent pH and column temperature in RPLC

We propose a general simple equation for accurately predicting the retention factors of ionizable compounds upon simultaneous changes in mobile phase pH and column temperature at a given hydroorganic solvent composition. Only four independent experiments provide the input data: retention factors measured in two pH buffered mobile phases at extreme acidic and basic pH values (e. g., at least +/- 2 pH units far from the analyte pK(a)) and at two column temperatures. The equations, derived from the basic thermodynamics of the acid-base equilibria, additionally require the knowledge of the solute pK(a )and enthalpies of acid-base dissociation of both the solute and the buffer components in the hydroorganic solvent mixture. The performance of the predictive model is corroborated with the comparison between theoretical and experimental retention factors of several weak acids and bases of important pharmacological activity, in mobile phases containing different buffer solutions prepared in 25% w/w ACN in water and at several temperatures.     

One pot grafting of tetrairon(III) single molecule magnets on silicon

Herein we report on the Si grafting of two Fe₄ derivatives, [Fe₄(Lⁱ)₂(tmhd)₆], in which tmhd is 2,2,6,6-tetramethylheptane-3,5-dionate and H₃Lⁱ = R–C(CH₂OH)₃ is a tripodal ligand with R = CH₂CH–CH₂–O–CH₂ (H₃L¹) and CH₂CH–(CH₂)₉–O–CH₂ (H₃L²). These complexes were specifically designed to be directly anchored on the H-terminated silicon surface via the hydrosilylation reaction. The complexes were grafted by a one pot route based on the photoinduced hydrosilylation followed by a ligand exchange step in the same reaction solution. The resulting decorated surfaces were characterized using X-ray photoelectron spectroscopy (XPS), attenuated total reflection infrared spectroscopy (ATR-IR) and atomic force microscopy (AFM).