Quantum curves and q-deformed Painlevé equations

Letters in Mathematical Physics - We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus...     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

Strain induced strengthening of soft thermoplastic polyurethanes under cyclic deformation

We investigate the cyclic mechanical behavior in uniaxial tension of three different commercial thermoplastic polyurethane elastomers (TPU) often considered as a sustainable replacement for common filled elastomers. All TPU have similar hard segment contents and linear moduli but sensibly different large strain properties as shown by X-ray analysis. Despite these differences, we found a stiffening effect after conditioning in step cyclic loading which greatly differs from the common softening (also referred as Mullins effect) observed in chemically crosslinked filled rubbers. We propose that this self-reinforcement is related to the fragmentation of hard domains, naturally present in TPU, in smaller but more numerous sub-units that may act as new physical crosslinking points. The proposed stiffening mechanism is not dissimilar to the strain-induced crystallization observed in stretched natural rubber, but it presents a persistent nature. In particular, it may cause a local reinforcement where an inhomogeneous strain field is present, as is the case of a crack propagating in cyclic fatigue, providing a potential explanation for the well-known toughness and wear resistance of TPU.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Influence of the sulfonate countercation on the thermal stability of nafion perfluorosulfonate membranes

We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc.     

Spectroscopic characterization of core and shell regions in monolayer protected gold nanoparticles

We report studies on the structure of the metallic core and the alkyl cap layer in monolayer protected gold nanoparticles having sizes down to 1.6 nm. These particles are obtained by laser ablating gold targets in alkane-thiol solutions at different concentrations. The electronic structure of gold core and the vibrational properties of the capping hydrocarbon chains reveal effects connected with the nanosized nature of the particles.     

On computation of the greatest common divisor of several polynomials over a finite field

We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m−1 pairwise greatest common divisors) to computing the greatest common divisor of two polynomials over the same field.     

Competing kinetic pathways in the bromine addition to allylic ethers in 1,2‐dichloroethane: Opposite temperature effects

The kinetics of the electrophilic bromination of three allylic ethers in a nonprotic solvent, 1,2‐dichloroethane, has been investigated. Two of them followed a prevalent second‐order pathway, while the third one exhibited a classical, clean third order. The second‐order pathway in the first two olefins is attributed to electrophilic assistance of the ethereal oxygen to the attacking bromine molecule. In the molecular bromination of 2,4‐cis‐dimethyl‐8‐oxabicyclo[3.2.1]‐6‐octen‐3‐cis‐ol, opposite temperature dependences were found for the two different kinetic pathways. An exoergonic process for the second‐order reaction was explained by the lesser stability of the bromiranium–bromide ionic intermediate, compared to the bromiranium–tribromide in the third‐order profile. © 2007 Wiley Periodicals, Inc. 39: 197–203, 2007