Vapochromic behavior of polycarbonate films doped with a luminescent molecular rotor

We report on vapochromic films suitable for detecting volatile organic compounds (VOCs), based on polycarbonate (PC) doped with 4‐(triphenylamino)phthalonitrile (TPAP), a fluorescent molecular rotor sensitive to solvent polarity and viscosity. PC films of variable thickness (from 20 up to 80 µm) and containing small amounts of TPAP (0.05 wt%) were prepared and exposed to a saturated atmosphere of different VOCs. TPAP/PC films showed a gradual decrease and red‐shift of the emission during the exposure to solvents with high polarity index and favorable interaction with the polymer matrix such as THF, CHCl₃, and acetonitrile. In the case of the most interacting solvents (THF and CHCl₃), TPAP/PC films also showed a fluorescence increase at longer exposure times, as a consequence of an irreversible, solvent‐induced crystallization process of the polymeric matrix. The vapochromism of TPAP/PC films is rationalized on the basis of alterations of the rotor intramolecular motion upon solvent uptake by PC and polarity effects of the microenvironment. Interestingly, the fluorescence response of the TPAP/PC films shows a non‐trivial, tuneable dependence on film thickness during the second solvent‐exposure stage. The latter effect is attributed to a variable extent of the crystallization process occurring in the PC films. This observation promptly suggests, in turn, an effective procedure to modulate the spectroscopic response in such functionalized polymeric materials through the precise control of the film thickness. Copyright © 2015 John Wiley & Sons, Ltd.     

Downhill versus two-state protein folding in a statistical mechanical model

The authors address the problem of downhill protein folding in the framework of a simple statistical mechanical model, which allows an exact solution for the equilibrium and a semianalytical treatment of the kinetics. Focusing on protein 1BBL, a candidate for downhill folding behavior, and comparing it to the WW domain of protein PIN1, a two-state folder of comparable size, the authors show that there are qualitative differences in both the equilibrium and kinetic properties of the two molecules. However, the barrierless scenario which would be expected if 1BBL were a true downhill folder is observed only at low enough temperature.     

Exponential distance-based fuzzy clustering for interval-valued data

In several real life and research situations data are collected in the form of intervals, the so called interval-valued data. In this paper a fuzzy clustering method to analyse interval-valued data is presented. In particular, we address the problem of interval-valued data corrupted by outliers and noise. In order to cope with the presence of outliers we propose to employ a robust metric based on the exponential distance in the framework of the Fuzzy C-medoids clustering mode, the Fuzzy C-medoids clustering model for interval-valued data with exponential distance. The exponential distance assigns small weights to outliers and larger weights to those points that are more compact in the data set, thus neutralizing the effect of the presence of anomalous interval-valued data. Simulation results pertaining to the behaviour of the proposed approach as well as two empirical applications are provided in order to illustrate the practical usefulness of the proposed method.     

On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity

We study the existence of nodal solutions to the boundary valueproblem – u = |u|^{p – 1}u in a bounded, smooth domain in ², with homogeneous Dirichlet boundary condition, when pis a large exponent. We prove that, for p large enough, thereexist at least two pairs of solutions which change sign exactlyonce and whose nodal lines intersect the boundary of .     

Formation of share market prices under heterogeneous beliefs and common knowledge

Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique “true value” and deals with the formation of share market prices through the dynamic formation of individual and social opinions (or beliefs) based upon a fundamental signal of economic performance and position of the firm, the forecast revision by heterogeneous individual investors, and their social mood or sentiment about the ongoing state of the market pricing process. Market clearing price formation is then featured by individual and group dynamics that make its collective dimension irreducible to its individual level. This dynamic holistic approach can be applied to better understand the market exuberance generated by the Share Exchange over time.     

Non-simple blow-up solutions for the Neumann two-dimensional sinh-Gordon equation

For the Neumann sinh-Gordon equation on the unit ball

Heat problems for a starlike shaped plate

The Fourier solution of the heat problem for a circular plate is generalized to a starlike shaped plate. We show that the classical solution can be used even in this more general case, provided that a suitable change of variables in the polar co-ordinate system is performed.     

Drawing parameters optimization for birefringence reduction in optical fibers

The impact of the drawing process on the stress-induced birefringence in optical fiber is experimentally analyzed. By means of the photoelastic tomographic technique, residual internal stresses are measured in fiber samples drawn under different conditions of temperature, drawing tension and speed. From measured residual stress distributions, the stress-induced birefringence and beatlength are mathematically derived and compared, proving that an effective birefringence reduction can be obtained by a proper choice of drawing parameters.