A note on the Lyapunov equation for discrete linear systems in Hilbert space

It is given a simple and unified new proof for the following well-known stability condition: an infinite-dimensional time-invariant discrete linear system is uniformly asymptotically stable if and only if the associate Lyapunov equation has a unique strictly positive solution. The proof is partially based on an application of Rota's model construction technique.     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

Polymerization of butadiene on nanoparticles’ surfaces and formation of metal/polymer nanocomposites

In this paper, we demonstrate that laser vaporization of metals in the presence of a small concentration of butadiene vapor leads to the polymerization of butadiene and incorporation of the metal nanoparticles within the polymer matrix. The metal nanocomposites are characterized by electron microscopy, X-ray diffraction and EDX. The results from high pressure mass spectrometry indicate that multiple additions of butadiene molecules on the metal cations Fe⁺, Ni⁺ and Pt⁺, generated by laser vaporization, take place at room temperature thus providing an efficient means of initiating further polymerization reactions. The Pt⁺ reactions show extensive fragmentations and elimination steps generating hydrocarbon ions. The laser vaporization/polymerization method provides the ability to encapsulate several different metals or metal oxides which undoubtedly will play a significant role in tuning the various properties of the polymer composites.     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.