Lattices of processes for graphs

The structure of the lattice of processes of a finite digraph with entries is investigated. Necessary and sufficient conditions for the isomorphism of a given lattice to the lattice of processes of a certain digraph are obtained. Bibliography: 5 titles. Translated by K. V. Shakhbazyan. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 135–153.     

Intermittency for coherent and incoherent current ensemble model

We investigate the origin of intermittency for multiparticle distribution in momentum space, following the idea that there is a kind of power law distribution of the space-time region of hadron emission. Using the formalism of current ensamble model to describe boson sources we discuss intermittency exponents for the coherent and incoherent (chaotic) particle production scheme.     

Thermally stimulated current and DSC studies of the broadened glass transition in liquid crystalline polymers

The high sensitivity of the thermally stimulated current, thermal sampling (TS) method is emphasized in a study of the breadth of the glass transition in several liquid-crystalline polymers (LCPs). Differential scanning calorimetry (DSC) was performed on all samples to further quantify the glass transition regions. For “random” copolyester LCPs with widely varying degrees of crystallinity, including highly amorphous samples, very broad glass tran-sition regions were observed. One semicrystalline alternating copolyester and a series of semicrystalline azomethine LCPs were studied as examples of structurally regular polymers. These exhibited relatively sharp glass transitions more comparable to ordinary isotropic amorphous or semicrystalline polymers. The broad glass transitions in the random copolyesters are attributed to structural heterogeneity of the chains. In one example of a moderate-crystallinity random copolyester LCP (Vectra), glass transitions ranging up to ca. 150°C in breadth were determined by the thermal sampling (TS) method and DSC. In other lower crystallinity copolyester LCPs, the main glass transition temperature as determined by DSC was comparable to that determined by TSC although cooperative relaxations of a minor fraction of the overall relaxing species were detected well below the main T_g, by the TS method and not by DSC. Rapid quenches from the isotropic melt to an isotropic glass were possible with one LCP. The anisotropic and isotropic glassy states for this LCP were found to have the same breadth of the glass transition as was determined by the TS method, although TSC and DSC show that T_g is shifted downward by ca. 15°C in the anisotropic glass as compared to the isotropic glass. © 1993 John Wiley & Sons, Inc.     

Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006     

Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures.