Water effects in polyurethane block copolymers

Equilibrium and dynamic sorption isotherm measurements, differential scanning calorimetry (DSC) measurements, and, mainly, dielectric relaxation spectroscopy (DRS) measurements by means of the thermally stimulated depolarization currents (TSDC) method were used to investigate the hydration properties of linear segmented polyurethane copolymers. Three types of samples were investigated with various fractions of hard and soft block segments. They were based on polyethylene adipate (PEA), 4,4′-diphenylmethane diisocyanate (MDI) and 1,4-butanediol (BDO). At 20°C the water content h of the samples at various values of relative humidity rh increases in proportion to the weight fraction of soft block segments phase. At saturation (rh = 100%) the ratio of sorbed water molecules to polar carbonyl polyester groups is 0.13. At saturation at 20°C there is no fraction of freezable water. The glass transition temperature, T_g, measured by DSC and by TSDC, shifts to lower temperature with increasing h by about 8–10 K at saturation at 20°C. A dielectric relaxation mechanism related to interfacial polarization in the phase-separated morphology is also plasticized by water in a way similar to that observed for the main (α) relaxation. © 1996 John Wiley & Sons, Inc.     

On the relative homology of cleft extensions of rings and abelian categories

We study the relative homological behaviour of the omnipresent class of cleft extensions of abelian categories. This class of extensions is a natural generalization of the trivial extensions studied in detail by Fossum, Griffith and Reiten and by Palmer and Roos. We apply our results to the relative homology of cleft extensions of rings.     

Equilibrium customer strategies in a single server Markovian queue with setup times

We consider a single server Markovian queue with setup times. Whenever this system becomes empty, the server is turned off. Whenever a customer arrives to an empty system, the server begins an exponential setup time to start service again. We assume that arriving customers decide whether to enter the system or balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine customer behavior under various levels of information regarding the system state. Specifically, before making the decision, a customer may or may not know the state of the server and/or the number of present customers. We derive equilibrium strategies for the customers under the various levels of information and analyze the stationary behavior of the system under these strategies. We also illustrate further effects of the information level on the equilibrium behavior via numerical experiments.      

Controlled vinyl‐type polymerization of norbornene with a Nickel(II) diphosphinoamine/methylaluminoxane catalytic system

A novel nickel‐based complex coordinated with an asymmetric diphosphinoamine ligand was synthesized and fully characterized. Single crystals of good quality were also obtained, and the solid‐state structure of the complex was studied via X‐rays diffraction. The catalytic activity of this Ni(II) complex in the vinyl‐type polymerization of norbornene was studied with methylaluminoxane (MAO) as the cocatalyst/activator. The influence of the reaction time, the equivalents of MAO used, and the concentration of the monomer on: (i) the activity of the catalytic system; (ii) the isolated yield of the polymer; and (iii) the molecular weight and molecular weight distribution of the polymer were investigated. The isolated polynorbornene (PNB) yields are significantly higher compared with those reported for other similar nickel‐based systems. The as‐obtained PNBs are characterized by high molecular weights and relatively narrow and monomodal molecular weight distributions (amongst the narrowest reported in the literature). The linear dependence of the molecular weight of the obtained PNB on the concentration of norbornene points toward a controlled polymerization reaction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5241–5250, 2009     

Lower Bound for the Maximal Number of Facets of a 0/1 Polytope

Let $f_{n-1}(P)$ denote the number of facets of a polytope $P$ in ${\Bbb R}^n$. We show that there exist 0/1 polytopes $P$ with $$f_{n-1}(P)\geq\left (\frac{cn}{\log^2 n}\right )^{n/2},$$ where $c>0$ is an absolute constant. This improves earlier work of Barany and Por on a question of Fukuda and Ziegler.     

Magnetohydrodynamics and Plasma Cosmology

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.     

The Existence of Helical Chirality in a Sterically Congested Naphtho [9]annulenone Preliminary Communication

The existence of the naphtho [9]annulenone 1 in two skeletally enantiomeric forms is demonstrated with the use of ¹H? NMR. spectroscopy in conjunction with a chiral «shift» reagent.     

On some high accuracy difference schemes for solving elliptic equations

Summary Two well known high accuracy Alternating Direction Implicit difference schemes for solving Laplace's equation and the Biharmonic equation are considered. The set of iteration parameters of Douglas is used in both problems. More complete optimum values of the parameters involved are given.     

Optimal systems for equipment maintenance and replacement under Markovian deterioration

Deterioration of equipment is modeled as a multistate discrete time controlled Markov process. The states are classified according to the degree of deterioration. The problem of design of optimal systems for equipment maintenance and replacement is considered when the decision-maker may take, in each stage, one of many available maintenance actions, classified according to their “stochastic effectiveness”; no action and replacement are included as alternatives. It is assumed that the transition probabilities satisfy two conditions which effectively describe a trend for monotonically increasing expected deterioration and rate of deterioration. Under these assumptions it is proved in the paper that the optimal (cost minimizing) decision system in an infinite horizon is of the control limit rule type, rapidly obtained by policy improvement algorithms. A numerical example is presented for a specific practical application; detailed data are available from the authors on request.