Compact and Weakly Compact Composition Operators on BMOA

Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C _φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C _φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C _φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C _φ on VMOA implies compactness even from the Bloch space into VMOA.     

Lipase-catalysed transesterification in the preparation of optically active monobutyrate of cis-2,3-epoxybutane-1,4-diol

The PPL-catalysed resolution of 4-hydroxy-2,3-epoxybutyl butyrate resulted in the (2S,3R)-(−)-enantiomer with high optical purity ( > 90% e.e.). The two acylation (or deacylation) steps from diol to dibutyrate (or from dibutyrate to diol) were shown to have reverse stereoselectivities.     

Cohen–Macaulay Multi–Rees Algebras

Let A be a local ring, and let I ₁,...,I _r A be ideals of positive height. In this article we compare the Cohen–Macaulay property of the multi–Rees algebra R _A (I ₁,...,I _r ) to that of the usual Rees algebra R _A (I ₁ ··· I _r ) of the product I ₁ ··· I _r . In particular, when the analytic spread of I ₁ ··· I _r is small, this leads to necessary and sufficient conditions for the Cohen–Macaulayness of R _A (I ₁,...,I _r ). We apply our results to the theory of joint reductions and mixed multiplicities.     

On the concept of point value in the infinite-dimensional realization theory

In this article, we study the effect of the chosen representation of a point value (and point evaluation) on the class of periodic signals realizable using a certain type of infinite-dimensional linear system. By suitably representing the point evaluation at the origin in a Hilbert space, we are able to give a complete characterization of its extensions. These extensions involve a new concept called δ-sequence, the use of which as an observation operator of an infinite-dimensional linear system is studied in this article. In particular, we consider their use in the realization of periodic signals. We also investigate how the use of δ-sequences affects the convergence properties of such realizations; we consider the rate and character of convergence and the removal of the Gibbs phenomenon. As still a further demonstration of the significance of the chosen concept of a point value, we discuss the use of distributional point values in the realization of periodic distributions. The possible applications of this work lie in regulator problems of infinite-dimensional control theory, as is indicated by the well-known internal model principle.     

A Family of Graded Modules Associated to a Module

In this article we introduce a certain family of graded modules associated to a given module. These modules provide a natural extension of the notion of the associated graded ring of an ideal. We will investigate their properties. In particular, we will try to extend Ree' theorem on the associated graded ring of an ideal generated by a regular sequence to this context.     

Indirect evidence of supramolecular changes within cellulose microfibrils of chemical pulp fibers upon drying

Dried and never-dried chemical pulps were subjected to strong sulfuric acid hydrolysis and the dimensions of the resulting cellulose nanocrystals (CNCs) were characterized by AFM image analysis. Although the average length of CNCs was fairly similar in all samples (55–65 nm), the length distribution histograms revealed that a higher number of longer crystals and a lower number of shorter crystals were present in the CNC suspensions prepared from never-dried pulps. The distinction was hypothetically ascribed to tensions building in individual cellulose microfibrils upon drying, resulting in irreversible supramolecular changes in the amorphous regions. The amorphous regions shaped by tensions were deemed as more susceptible to acid hydrolysis.     

Carboxymethyl cellulose on a fiber substrate: the interactions with cationic polyelectrolytes

High and low molecular weight (M_w) carboxymethyl celluloses (CMC) were adsorbed on a well-characterized fiber substrate (long fibers of a commercial bleached birch kraft pulp with the carboxylic acid groups in Na-form) to increase the charge of the fibers in a controlled fashion. The M_w played a role in the utilization of CMCs as a strength additive in paper sheets nearly doubling the tensile strength with the high M_w CMC. Swelling properties of the CMC treated fibers were measured with water retention value (WRV). The WRV increased more with the high M_w CMC. The swelling was further tuned by two highly cationic polyelectrolytes; high M_w poly(diallyldimethyl ammonium chloride) (PDADMAC) and low M_w polybrene (hexadimethrine bromide, [3,6]-ionene). They were chosen because of their known ability to neutralize the anionic charge either exclusively on the surface or in the whole fiber, respectively. Adsorption of PDADMAC could reduce WRV of the CMC pre-treated fibers to the level of the untreated reference, while polybrene adsorbed pulps with 3–10 times more cationic polyelectrolyte deswelled the fibers only slightly more than the surface neutralized fibers. These results indicated surface conformation differences with low and high M_w CMCs. While the conformation did play a role after physical alteration (drying and rewetting) of the fibers, the paper sheets produced from these fibers showed remarkable differences. In extreme cases, the strength of the paper could be retained after drying (low M_w CMC + PDADMAC) or paper, resistant to disintegration, could be achieved (CMC + polybrene).