Fatigue Effects in Elastic Materials with Variational Damage Models: A Vanishing Viscosity Approach

Journal of Nonlinear Science - We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a...     

A note on the classification of Fano manifolds of middle index

We rule out a doubtful case in the classification of Fano manifolds of middle indexMathematics Subject Classification (2000): 14J40, 14J45     

New π‐stacked benzofulvene polymer showing thermoreversible polymerization: Studies in macromolecular and aggregate structures and polymerization mechanism

The macromolecular and aggregate structures of poly[ethyl 1‐methylene‐3‐(4‐methylphenyl)‐1H‐indene‐2‐carboxylate] (poly‐ BF1 ; a new polymer based on a functionalized benzofulvene moiety showing interesting properties, i.e., thermoreversible polymerization/depolymerization behavior, high solubility in the most common organic solvents, and susceptibility to molecular manipulation) have been investigated with NMR spectroscopy, absorption and emission spectrophotometry, and transmission electron microscopy (TEM). Moreover, the polymerization mechanism has been studied to obtain further information on the polymer structure. The collected evidence is consistent in indicating for poly‐ BF1 a vinyl (1,2) polymer structure stabilized by means of aromatic stacking interactions. Furthermore, TEM studies performed on metal replicas have shown that the polymer is liable to give nanostructured aggregates. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3289–3304, 2005     

On cubic-linear polynomial mappings

In the field of the Jacobian conjecture it is well-known after Dru?kowski that from a polynomial ‘cubic-homogeneous’ mapping we can build a higher-dimensional ‘cubic-linear’ mapping and the other way round, so that one of them is invertible if and only if the other one is. We make this point clearer through the concept of ‘pairing’ and apply it to the related conjugability problem: one of the two maps is conjugable if and only if the other one is; moreover, we find simple formulas expressing the inverse or the conjugations of one in terms of the inverse or conjugations of the other. Two nontrivial examples of conjugable cubic-linear mappings are provided as an application.     

Finitely Additive Supermartingales

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob–Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenous probability measure. I am indebted to an anonymous referee for several helping suggestions.     

Dye-sensitized photooxygenation of furanosyl furans: synthesis of a new pyridazine C-nucleoside

The dye-sensitized photooxygenation of furanosyl furans easily affords C- or O-glycosides with cis-alpha,beta-unsaturated 1,4-dioxo aglycones. The reaction, performed on a ribofuranosyl furan, provides a useful new entry to a novel pyridazine C-nucleoside that can be achieved through a simple one-pot procedure.     

Dynamical Aspects of TEM-1 β-Lactamase Probed by Molecular Dynamics

The dynamical aspects of the fully hydrated TEM-1 β-lactamase have been determined by a 5 ns Molecular Dynamics simulation. Starting from the crystallographic coordinates, the protein shows a relaxation in water with an overall root mean square deviation from the crystal structure increasing up to 0.17 nm, within the first nanosecond. Then a plateau is reached and the molecule fluctuates around an equilibrium conformation. The results obtained in the first nanosecond are in agreement with those of a previous simulation (Diaz et al., J. Am. Chem. Soc., (2003) 125, 672–684). The successive equilibrium conformation in solution shows an increased mobility characterized by the following aspects. A flap-like translational motion anchores the Ω-loop to the body of the enzyme. A relevant part of the backbone dynamics implies a rotational motion of one domain relative to the other. The water molecules in the active site can exchange with different residence times. The H-bonding networks formed by the catalytic residues are frequently interrupted by water molecules that could favour proton transfer reactions. An additional simulation, where the aspartyl dyad D214–D233 was considered fully deprotonated, shows that the active site is destabilized.     

Stereochemistry of cercosporin

The absolute configuration of the asymmetric carbons and the axial chirality of the natural mold metabolite cercosporin (from $\text{Cercospora sp}$.) have been established on the basis of X-ray analysis and chemical reactions. The results confirm the inherent dissymmetry of the perylenequinone ring, the twisting of which gives rise to the diastereoisomer isocercosporin. The energy barrier for the conversion of cercosporin into isocercosporin has been evaluated.