A topological equivalence result for a family of nonlinear difference systems having generalized exponential dichotomy

We obtain sufficient conditions ensuring the topological and strong topological equivalence of two perturbed difference systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a strongly and Hölder topological equivalence.     

Automorphism groups of compact bordered Klein surfaces with invariant subsets

In this work we get upper bounds for the order of a group of automorphisms of a compact bordered Klein surface S of algebraic genus greater than 1. These bounds depend on the algebraic genus of S and on the cardinals of finite subsets of S which are invariant under the action of the group. We use our results to obtain upper bounds for the order of a group of automorphism whose action on the set of connected components of the boundary of S is not transitive. The bounds obtained this way depend only on the algebraic genus of S. The author is partially supported by the European Network RAAG HPRN-CT-2001-00271 and the Spanish GAAR DGICYT BFM2002-04797.     

Measuring the spectrum of colored noise by dynamical decoupling

Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we developed a method for dynamical decoupling noise spectroscopy. We generate effective filter functions that probe the environmental spectral density without requiring assumptions about its shape. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.     

Synthesis,Structure and Nickel Carbonyl Complexes of Dialkylterphenyl Phosphines

The experimental and computational characterization of a series of dialkylterphenyl phosphines, PR₂Ar′ is described. The new P-donors comprise five compounds of general formula PR₂Ar (R=Me, Et, iPr, c-C₅H₉ and c-C₆H₁₁); Ar = 2,6-C₆H₃-(3,5-C₆H₃-(CMe₃)₂)₂), and another five PR₂Ar′ phosphines containing the bulky alkyl groups iPr, c-C₅H₉ or c-C₆H₁₁, in combination with Ar′=Ar , Ar , or Ar ( L1 – L10 ). Steric and electronic parameters have been determined computationally and from IR and X-ray data obtained for the phosphines and for some derivatives, including tricarbonyl and dicarbonyl nickel complexes, Ni(CO)₃(PR₂Ar′) and Ni(CO)₂(PR₂Ar′). In the solid state, the free phosphines PR₂Ar′ adopt one of the three possible structures formally related by rotation around the C_ipso−P bond. Details on their relative energies and on the influence of the free phosphine structure on its coordination chemistry towards Ni(CO)_n (n = 2, 3) fragments has been obtained by experimental and computational methods.     

Influence of the Flame Straightening Process on Microstructural, Mechanical and Fracture Properties of S235 JR, S460 ML and S690 QL Structural Steels

The flame straightening of steel components is based on heating a local region of the part by means of a torch in order to induce a permanent deformation through a field of residual stresses. Although this is a very common practice, it is not devoid of serious drawbacks. In this paper, the influence of the flame bending procedure on the microstructure of three very different structural steels (S235 JR, S460 ML and S690 QL, respectively), widely used for the construction of metallic structures, is analysed. The consequences of the heat treatment on the mechanical and fracture properties were characterised through micro-hardness Vickers and Charpy impact tests; in addition, some elastic-plastic fracture tests were performed on precracked Charpy specimens manufactured with the S235 JR steel. The relationship between the microstructural features and the material mechanical and fracture behaviour was studied in depth in all cases, correlating the changes induced by the flame heat treatment on the microstructure with the macroscopic mechanical and fracture response. For a proper understanding of the microstructural consequences of this straightening heat treatment, it was necessary to develop a Finite Element numerical model. Based on the experimental results, this study has revealed that the consequences of the flame straightening on the microstructure, mechanical or fracture behaviour strongly depend on the nature of the material; for this reason, it is not possible to establish general recommendations. Nevertheless, the paper proposes a series of guidelines for good practice for steels similar to those characterised here.     

Analysis of Two Ultrafiltration Fouling Models and Estimation of Model Parameters as a Function of Operational Conditions

This work analyses the measure of fit of experimental data of permeate flux decline with time for ultrafiltration experiments performed with polyethylene glycol aqueous solutions to two different ultrafiltration models. A feed solution of 5 kg/m $^{3}$ 3 of polyethylene glycol and a monotubular ceramic membrane of ${\mathrm{ZrO}}_{2}$ ZrO 2 – ${\mathrm{TiO}}_{2}$ TiO 2 were used in the experiments. The first model considered was developed by Ho and Zydney and it considers two different fouling mechanisms: pore blocking and gel layer formation. The second model was proposed by Yee et al. It is an exponential model that considers three stages: concentration polarization, molecule deposition on the membrane surface and long-term fouling. The results show that both models give very accurate predictions for the severe fouling conditions (high transmembrane pressures and low crossflow velocities). However, both models cannot explain the experimental results obtained for all the experimental conditions tested. An equation for Ho and Zydney’s model parameters as a function of operating conditions was obtained by means of multiple regression analysis.     

Solvent‐Enhanced Diastereo‐ and Regioselectivity in the PdII‐Catalyzed Synthesis of Six‐ and Eight‐Membered Heterocycles via cis‐Aminopalladation

The Pd^II‐catalyzed intramolecular oxidative cyclization of tosyl‐protected cis‐ and trans‐N‐allyl‐2‐aminocyclohexanecarboxamides was examined, and efficient syntheses of cyclohexane‐fused pyrimidin‐4‐ones and 1,5‐diazocin‐6‐ones were developed. In the course of the research, a marked solvent effect was observed on both the regio‐ and diastereoselectivity. Additionally, a novel Pd^II‐mediated domino oxidation, oxidative amination reaction was discovered. Our experimental and theoretical findings suggest that the reactions proceed via a cis‐aminopalladation mechanism.     

Structure,Microstructure, Composition and Properties of Lanthanum Lithium Titanates and some Substituted Analogues

The very high value of ionic conductivity at room temperature reported for La_0.51Li_0.34TiO_2.94 some years ago did originate a great deal of interest in the study of materials of general formula La_2/3–xLi_3xTiO₃ (LaLiTiO) and related systems. These oxides have shown to be potential solid electrolytes for lithium secondary batteries, but other aspects, apart from the conducting properties, such as their dielectric behaviour and crystal structure, have been the main focus of important studies in the area of inorganic solid‐state chemistry. LaLiTiO‐related compounds have the perovskite‐type structure (ABO₃) with A‐cation ordering. However, essential details of their crystal structure, as for instance the location of the lithium atoms, are still under discussion and are the subject of current work. We show in this short review of mainly our own work that the complex microstructure of these materials, which has been studied in detail by transmission electron microscopy, is the cause of the difficulties on the precise determination of their crystal structure. We have developed a new approach for crystal structure refinement, which takes into account the microstructural effects, obtaining significantly better results than conventional methods of refinement. The microstructure of these oxides also affects their conducting and dielectric properties. Therefore, different parameters such as composition and microstructure must be considered to understand and, eventually, optimise, as we have done, the conducting properties of LaLiTiO‐related systems.     

Subloop incompatible Bol loops

We give a necessary modification of Proposition 1.18 in Nagy and Strambach (Loops in Group Theory and Lie Theory. de Gruyter Expositions in Mathematics Berlin, New York, 2002) and close the gap in the classification of differentiable Bol loops given in Figula (Manuscrp Math 121:367–385, 2006). Moreover, using the factorization of Lie groups we determine the simple differentiable proper Bol loops L having the direct product G ₁ × G ₂ of two groups with simple Lie algebras as the group topologically generated by their left translations such that the stabilizer of the identity element of L is the direct product H ₁ × H ₂ with H _i < G _i . Also if G ₁ = G ₂ = G is a simple permutation group containing a sharply transitive subgroup A, then an analogous construction yields a simple proper Bol loop. If A is cyclic and G is finite and primitive, then all such loops are classified.     

Conics in Minkowski geometries

Euclidean geometry is the only Minkowski geometry in which either there is a centrally symmetric, or a quadratic conic, or there is a conical ellipsoid or hyperboloid.