On a Projection from One Co – Invariant Subspace onto Another in Character – Automorphic Hardy Space on a Multiply Connected Domain

In a case of a theory in a unit disk the solution of a problem on the invertibility of an orthogonal projection from one co–invariant subspace of the shift operator onto another turned out to be essential for the solution of the problem on the Riesz basis property of the reproducing kernels and in particular for the solution of the problem on the basis of exponentials in L₂ space on a segment. In the present paper we are dealing with the similar problems in harmonic analysis on a finitely connected domain. Namely we obtain necessary and sufficient conditions for the invertibility of an orthogonal projection from one co – invariant subspace of character – automorphic Hardy space in the domain onto another. The given condition has a form of a Muckenhoupt condition for a certain weight on the boundary of the domain, but essentially depends on a character. Namely, for two fixed character – automorphic inner functions, which define the co – invariant subspaces, the projection may be invertible for one character and not invertible for another.     

Preparation and ion conductivities of the plasticized polymer electrolytes based on the poly(acrylonitrile‐ co‐lithium methacrylate)

The polymer electrolytes composed of poly(acrylonitrile‐co‐lithium methacrylate) [P(AN‐co‐LiMA)], ethylene carbonate (EC), and LiClO₄ salts have been prepared. The ion groups in the P(AN‐co‐LiMA) were found to prevent EC from crystallization through their ion–dipole interactions with the polar groups in the EC. This suppression of the EC crystallization could lead to the enhancement of the ion conductivity at subambient temperature. The polymer electrolytes based on the PAN ionomer with 4 mol % ion content exhibited ion conductivities of 2.4 × 10⁻⁴ S/cm at −10°C and 1.9 × 10⁻³ S/cm at 25°C by simply using EC as a plasticizer. In the polymer electrolytes based on the PAN ionomer, ion motions seemed to be coupled with the segmental motions of the polymer chain due to the presence of the ion–dipole interaction between the ion groups in the ionomer and the polar groups in the EC, while the ion transport in the PAN‐based polymer electrolytes was similar to that of the liquid electrolytes. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 247–252, 1999     

Luminescence studies of polymer matrices. III. Characterization and evaluation of acrylic acid‐based polymers as hosts for a phosphorescent coding system

The phosphorescence characteristics of naphthyl labelled poly(acrylic acid) film samples have been studied as a function of temperature, with a view to investigating the effect of matrix control on the level of triplet emission observed. Two relaxations, which serve to deactivate the excited triplet states have been detected from phosphorescence lifetime measurements: the α (or glass) and the βtransition (which can be associated with the onset of rotation of the carboxylic acid group). Investigation of the emission from 2‐benzoyl naphthalene dispersed within both an acrylic acid‐methyl methacrylate copolymer and a PAA film, respectively, has revealed that the more intense, longer‐lived phosphorescence results from the modified polymer. This is considered to reflect the existence of (i) hydrogen‐bonding interactions induced by the presence of carboxylic acid groups which serve to form a rigid matrix and (ii) intramolecular aggregates of methyl methacrylate units which create hydrophobic‐rich pockets, capable of sustaining intense phosphorescence at room temperature. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2127–2136, 1999     

Average performance of adaptive algorithms for programming co‐ordinate measuring machines under budget constraint

In this paper we develop two adaptive algorithms for programming co‐ordinate measuring machines assuming fixed sampling budget. Two different costs are considered: the travelling cost of the machine probe, and the sampling cost to read and store all measurements. Simulation is used to compare the average performance of the proposed algorithms under the assumption of Wiener measure on the space of all surface contours of the manufactured parts. Expected value of the probability of Type II error is the criterion that we use to characterize algorithms performance. Analysis shows that placing sample points according to the criterion of maximizing the expected gain demonstrates a substantial improvement in the average performance. Copyright © 1999 John Wiley & Sons, Ltd.     

Synthesis and characterization of poly(3,3 bis(azidomethyl)oxetane‐co‐ε‐caprolactone)s

The quasi‐living cationic copolymerization of 3,3‐bis(chloromethyl)oxetane (BCMO) and ε‐caprolactone (ε‐CL), using boron trifluoride etherate as catalyst and 1,4‐butanediol as coinitiator, was investigated in methylene chloride at 0°C. The resulting hydroxyl‐ended copolymers exhibit a narrow molecular weight polydispersity and a functionality of about 2. The reactivity ratios of BCMO (0.26) and ε‐CL (0.47), and the T_g of the copolymers, indicate their statistical character. The synthesis of poly(3,3‐bis(azidomethyl)oxetane‐co‐ε‐caprolactone) from poly(BCMO‐co‐ε‐CL) via the substitution of the chlorine atoms by azide groups, using sodium azide in DMSO at 110°C, occurs without any degradation, but the copolymers decompose at about 240°C. All polymers were characterized by vapor pressure osmometry or steric exclusion chromatography, ¹H‐NMR and FTIR spectroscopies, and DSC. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1027–1039, 1999     

Morphology and Linear Viscoelasticity of Poly[ethylene‐co‐(1‐octene)]/Layered Silicate Nanocomposites

Poly[ethylene‐co‐(1‐octene)] nanocomposites with different microstructures were prepared with two kinds of organoclay by melt intercalation. X‐ray diffraction and transmission electron microscopy were used to characterize the morphology of the composites. Linear storage moduli of the composites in the melt state were found to increase greatly with increasing the extent of dispersion of silicate layers and showed an obvious sensitivity to the morphologies of the composites.     

Geometric partial comodules over flat coalgebras in Abelian categories are globalizable

The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial representations of groups and Hopf algebras, our globalization coincides with those described earlier in literature. Finally, we introduce Hopf partial comodules over a bialgebra as geometric partial comodules in the monoidal category of (global) modules. By applying our globalization theorem we obtain an analogue of the fundamental theorem for Hopf modules in this partial setting.