On Carvalho's -theoretic formulation of the cobordism invariance of the index

We give an analytic proof of the fact that the index of an elliptic operator on the boundary of a compact manifold vanishes when the principal symbol comes from the restriction of a -theory class from the interior. The proof uses non-commutative residues inside the calculus of cusp pseudodifferential operators of Melrose.

     

On General Solutions for Field Equations in Einstein and?Higher Dimension Gravity

We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing exact solutions in gravity. The main idea of this method is to introduce on (pseudo) Riemannian manifolds an alternative (to the Levi-Civita connection) metric compatible linear connection which is also completely defined by the same metric structure. Such a canonically distinguished connection is with nontrivial torsion which is induced by some nonholonomy frame coefficients and generic off-diagonal terms of metrics. It is possible to define certain classes of adapted frames of reference when the Einstein equations for such an alternative connection transform into a system of partial differential equations which can be integrated in very general forms. Imposing nonholonomic constraints on generalized metrics and connections and adapted frames (selecting Levi-Civita configurations), we generate exact solutions in Einstein gravity and extra dimension generalizations.     

Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity

We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: (a) tangent bundles with two dimensional base manifolds and (b) pseudo-Riemannian/Einstein spaces. Such spacetimes are enabled with nonholonomic distributions and theirs metrics are solutions of the field equations in general relativity and/or generalizations. We rewrite the Schwarzschild metric in Finsler variables and use it for generating new classes of black hole objects with stationary deformations to ellipsoidal configurations. The conditions are analyzed when such metrics describe embedding of black hole solutions into nontrivial solitonic backgrounds.     

An approximation theory for the identification of nonlinear volterra equations

An abstract approximation framework and convergence theory for Galerkin approximations to inverse problems involving nonlinear Volterra integral equations is developed. The approach relies on the theory of m-accretive operators in Banach spaces. An application to heat flow in materials with memory is also discussed.     

The benefits of training with vibration in stabilizers and postural human muscle strengthening

The mechanical vibrations have been perceived as unhealthy, although in some circunstances these may lead to a human body fortification. The trainings that use the vibrating stimulus have certain advantages to the classical trainings. Stabilizers and postural muscles are less visible, being hidden by large muscle groups and have little growth potential. For this reason most types of training does not focus on training and strengthening them. This article presents the advantages of training muscular groups of the vertebral column performed on vibrating plates. This type of training has the advantage that besides the requiring to all muscles in where the vibratory stimulus reaches, leads to an increase flexibility of joints. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Four-Step Spin Crossover in a New Cyano-Bridged Iron-Silver Coordination Polymer

Spin-crossover complexes with multistep transitions attract much attention due to their potential applications as multi-switches and for data storage. A four-step spin crossover is observed in the new iron(II)-based cyanometallic guest-free framework compound Fe(2-ethoxypyrazine)₂{Ag(CN)₂}₂ during the transition from the low-spin to the high-spin state. A reverse process occurs in three steps. Crystallographic studies reveal an associated stepwise evolution of the crystal structures. Multiple transitions in the reported complex originate from distinct Fe^II sites which exist due to the packing of the ligand with a bulky substituent.     

Identification of an additional low-lying excited state of carotenoid radical cations

Carotenoids are the crucial pigments involved in photoprotection and in scavenging harmful free radicals in all living organisms. The underlying chemical processes are charge transfer and free radical reactions, both of them leading to carotenoid radical cation (Car*+) formation. Accurate knowledge of the molecular properties of Car*+ is thus a prerequisite for understanding of their function as photoprotective and antioxidant agents. Despite their fundamental importance in nonphotochemical quenching in green plants, only little is known about the Car*+ excited states and their dynamics. Our combined experimental and theoretical investigation employing femtosecond time-resolved pump-probe spectroscopy and quantum chemical calculations proves the existence of a second low-lying pipi* excited-state energetically below the well-known strongly allowed excited-state responsible for the intense absorption of Car*+ in the near-IR region. Hence, we suggest denoting the latter state as D3 state in the future. Our findings have also implications for nonphotochemical quenching in green plants, since direct quenching of chlorophyll excited states by Forster energy transfer to Car*+ is possible and efficient.     

Tetranuclear [Cu-Ln]2 single molecule magnets: synthesis, structural and magnetic studies

A trianionic ligand H3L (2-hydroxy-N-(2-[[(2-hydroxyphenyl)methylene]amino]-2-methylpropyl)benzamide) with an inner N2O2 coordination site and an oxygen atom coming from an amide function not involved in this site yields monoanionic LCu- complexes that react with Ln(hfa)3 x 2H2O (hfa = hexafluoroacetylacetonato ligand) to give dinuclear Cu-Ln complexes that self-assemble into tetranuclear species, as demonstrated by the structural determination of the [LCuDy(hfa)2(dmf)2]2 complex. High-spin species are then isolated for two ferromagnetic interactions are active in the [Cu-Gd]2 entities, through the double phenoxo bridge (J = 3.2 cm(-1)) and through the single amide bridge (j = 0.54 cm(-1)). These interactions are still present in the [Cu-Tb]2 and [Cu-Dy]2 complexes which behave as single molecule magnets (SMMs), due to the introduction of anisotropic Ln ions in place of Gd ions.     

Enantiopure, supramolecular helices containing three-dimensional tetranuclear lanthanide(III) arrays: synthesis, structure, properties, and solvent-driven trinuclear/tetranuclear interconversion

The enantiomerically pure pinene-bipyridine-based receptor, (-) or (+) L(-), diastereoselectively self-assembles in dry acetonitrile in the presence of Ln(III) ions (Ln = La, Pr, Nd, Sm, Eu, Gd, and Tb) to give a C3-symmetrical, pyramidal architecture with the general formula [Ln4(L)9(mu3-OH)](ClO4)2) (abbreviated as tetra-Ln4L9). Three metal centers shape the base: an equilateral triangle surrounded by two sets of helically wrapping ligands with opposite configurations. This part of the structure is very similar to the species [Ln3(L)6(mu3-OH)(H2O)3](ClO4)2) (recently reported by us and abbreviated as tris-LnL2) formed by the ligand and the Ln(III) ions when the reactions are performed in methanol. The tetranuclear structure is completed by a capping, helical unit LnL3 whose chirality is also predetermined by the chirality of the ligand. A complete characterization of these isostructural, chiral compounds was performed in solid state (X-ray, IR) and in solution (ES-MS, NMR, CD, UV-vis and emission spectroscopies). The sign and the intensity of the CD bands in the region of the pi pi* transitions of the bipyridine (absolute Delta epsilon values at 327 nm are about 280 M(-1) x cm(-1)) are highly influenced by the helicity of the capping fragment LnL3. The photophysical properties (lifetime, quantum yield) of the visible (Eu and Tb complexes) and NIR (Nd complex) emitters indicate a good energy transfer between the ligands and the metal centers. The two related superstructures tetra-Ln4L9 and tris-LnL2 can be interconverted in acetonitrile, the switching process depending on the amount of water present in the solvent, the size of the Ln(III) ion, and the concentration. The weak chiral recognition capabilities of the self-assembly leading to the formation of tetra-Ln4L9 either by direct synthesis from a racemic mixture of the ligand and Ln(III) ions or by the conversion of a tris-Ln[(+/-)-L]2 racemate were likewise demonstrated.