Polyphosphates as inorganic polyelectrolytes interacting with oppositely charged ions,polymers and deposited on surfaces: fundamentals and applications

Polyphosphates are important but neglected polyelectrolytes that play a major role in biology and in surface science for the stabilization of colloids against flocculation and for the preservation of food. They are also known as “Calgon” ® and intensively used as additives in washing powders. This review aims to review recent developments in which linear polyphosphates are used for the design of new functional coatings using sol–gel processes and layer-by-layer deposition methods. All these methods rely on the high charge density of polyphosphates as inorganic polyelectrolytes, therefore the structure and properties of these molecules are also reviewed. New perspectives will also been given for the design of stimuli responsive coatings at the tiny frontier between biology and materials science.     

An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space

We provide sufficient conditions for strong and uniform (on bounded subsets of initial points) convergence of infinite products of orthogonal projections and other (possibly nonlinear) nonexpansive operators in a Hilbert space. Our main tools are new estimates of the inclination of a finite tuple of closed linear subspaces.     

Hypochromism and optical rotation in helical polymers

We show that the decreased light absorption and the anomalous optical rotatory dispersion in helical polynucleotides and polypeptides may be interpreted purely as a local field effect. The electric field of the incident light wave is screened off from each residue by the induced electric dipoles in the others. Quantum-mechanical calculations based on time-dependent Hartree theory and this local field picture correspond precisely with the formulae derived in Tinoco's, Rhodes's, and Moffitt's exciton theories, provided that the Coulomb interactions are small. The degenerate exciton waves in our theory correspond to normal modes of a set of coupled oscillators, and the rotational strengths and oscillator strengths are conserved. There is no conflict between Tinoco's theory of hypochromism and the ones proposed by Bolton and Weiss and by Nesbet. One new conclusion is that the energy shifts accompanying hypochromism should not vary much when the exciton coupling changes from the strong to the weak coupling limits.     

Supramolecular Assemblies for Electronic Materials

This work presents a synergy between organic electronics and supramolecular chemistry, in which a host–guest complex is designed to function as an efficacious electronic material. Specifically, the noncovalent recognition of a fullerene, phenyl-C₆₁-butyric acid methyl ester ( PC₆₁BM ), by an alternating perylene diimide ( P )-bithiophene ( B ) conjugated macrocycle ( PBPB ) results in a greater than five-fold enhancement in electron mobility, relative to the macrocycle alone. Characterization and quantification of the binding of fullerenes by host PBPB is provided alongside evidence for intermolecular electronic communication within the host–guest complexes.     

Finite element approximations of a nonlinear diffusion model with memory

The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results.     

Extension of the ν-metric

We extend the ν-metric introduced by Vinnicombe in robust control theory for rational plants to the case of infinite-dimensional systems/classes of nonrational transfer functions.     

A stable convergence theorem for infinite products of nonexpansive mappings in Banach spaces

We use the concept of porosity in order to establish a generic stable convergence theorem for infinite products of nonexpansive mappings in Banach spaces.