Neumann-like integrable models

A countable class of integrable dynamical systems, with four-dimensional phase space and conserved quantities in involution (Hn,In)$(H_n,I_n)$ are exhibited. For n=1$n=1$ we recover Neumann system on T^∗S²$T^{\ast }{S}^2$. All these systems are also integrable at the quantum level.     

Adhesion and friction of PDMS networks: molecular weight effects

The objective of this work is to find relations between adherence and friction behaviors of elastomer networks. The chosen approach is based on the parallel study of the initial molecular weight (i.e., the degree of cross-linking) dependence of both adherence and friction. The polymers used are cross-linked polydimethylsiloxane (PDMS) and the substrate is a smooth glass plate. The experimental procedure uses both friction (pin on disk tribometer) and adhesion (tack test) measurements, associated with surface analysis and mechanical and rheological characterizations. Tack results show that high molecular weight PDMS exhibits the greater adherence energy. This can be explained by the role of both chain length and free and pendant chains: more numerous and longer free chains favor the substrate wetting (at a molecular scale) and increases the energy dissipation during separation (extraction and reptation mechanisms). However, friction results indicate a higher friction resistance for low molecular weight PDMS. This result could be quite surprising. An explanation based on interfacial sliding properties of free and pendant chains can be proposed. Elsewhere, for the lower molecular weight polymer, elastic contact present during friction is able to act as a forced wetting, constraining the network and consequently leading to a greater energy dissipation.     

Bioactive Sol-Gel Coatings for Orthopaedic Prosthesis

Sol-gel materials have been proposed in last years for clinical applications. In this work, bioactive sol-gel coatings were prepared from suspensions of up to 25% wt. of bioactive glass (CaO·SiO₂·P₂O₅) particles in a hybrid sol obtained from TEOS and MTES. Thick dip-coatings showed in vitro bioactivity after a few days, but glass-particles dissolution promotes a slight reduction in the corrosion resistance. In order to overpass this problem, a two-stage sol-gel coating system that includes a first SiO₂ hybrid film, acting as barrier against corrosion, and an external bioactive layer from glass particle suspension is proposed. The obtained samples revealed significant improvement in their electrochemical behaviour, and showed in vitro bioactivity.     

Fourth-order difference equation for the associated Meixner and Charlier polynomials

An explicit representation of the associated Meixner polynomials (with a real association parameter γ?0) is given in terms of hypergeometric functions. This representation allows to derive the fourth-order difference equation verified by these polynomials. Appropriate limits give the fourth-order difference equation for the associated Charlier polynomials and the fourth-order differential equations for the associated Laguerre and Hermite polynomials.     

Organic/Inorganic Hybrid Materials Based on Silsesquioxanes Derived from (3-Methacryloxypropyl) Trimethoxysilane and Their Blends with Vinylester Resins

The crosslinking of blends of a silsesquioxane (SSO) derived from (3-methacryloxypropyl) trimethoxysilane, variable amounts of a vinylester resin (VE, dimethacrylate of bisphenol A), and benzoyl peroxide (BPO) or dicumyl peroxide (DCP) as initiators, was followed by differential scanning calorimetry (DSC). For the neat SSO a thermally-initiated polymerization was observed in the 150–250°C range, leading to a conversion close to 22% of the initial C=C groups. The final conversion could be increased to a maximum value close to 83%, by adding an initiator and using a thermal cycle attaining temperatures in the range of 200°C. The use of variable amounts of VE as a co-monomer produced a slight increase of the final conversion in SSO/VE/BPO blends. Neither the conversion of double-bonds nor the addition of the VE had any effect on the onset temperature of thermal degradation, which was associated to the presence of the methacryloxypropyl groups supplied by the SSO and the VE resin. However, a distinct two-step degradation process was observed in the presence of VE. Coatings based on SSO/VE/BPO blends exhibited more uniform thicknesses and lower values of the microhardness than those devoid of VE. However, the conversion of C=C groups did not show any significant effect on the values of microhardness.     

Quasi-Einstein Kähler Metrics

We write an ansatz for quasi-Einstein Kähler metrics and construct new complete examples. Moreover, we construct new compact generalized quasi-Einstein Kähler metrics on some ruled surfaces, including some of Guan's examples as special cases.     

Bianchi type II,III and V diagonal Einstein metrics re-visited

We present, for both Minkowskian and Euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for Minkowskian signature elliptic functions are essential in the metric while for Euclidean signature only elementary functions appear.     

Scattering lengths and baryon magnetic moments in a gauge model of strong and electromagnetic interactions

We present a broken SU(3) gauge model of strong and electromagnetic interactions with the usual vector mesons. All particles (9 vectors, 8 baryons and 9 pseudoscalars) have the right masses by means of the Higgs mechanism. We study the consequences of Sakuraï's idea that strong and electromagnetic interactions are mediated by vector mesons universally coupled to nearly conserved currents: one finds encouraging values for scattering lengths except for P-wave parameters in the meson-baryon sector that are too small. The calculation of the baryon anomalous magnetic moments also gives too-small numbers.     

Asymptotic scale invariance in two-dimensional theories: A massive Thirring model with bosons

The exact vanishing of all β functions of the Callan-Symanzik equation is proved in a two-dimensional model with Thirring and gradient couplings: $\text{(}\text{ψ}\text{γ}{}_{\mathrm{\mu }}\text{ψ)}{}^2$, $\text{(}\text{ψ}\text{γ}{}^5\text{γ}{}_{\mathrm{\mu }}\text{ψ)?}{}^{\mathrm{\mu }}\text{π}$ and $\text{(}\text{ψ}\text{γ}{}_{\mathrm{\mu }}\text{ψ)?}{}^{\mathrm{\mu }}\text{σ}$, where ψ, π and σ are fermion, pseudoscalar and scalar massive fields, respectively. The anomalous dimensions of scalar and pseudoscalar fields are also shown to be zero. Then we demonstrate that in two-dimensional models including at most one fermion field, only these three couplings can give asymptotic scale invariance.