On the Froissart phenomenon in multivariate homogeneous Padé approximation

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so‐called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in a multivariate setting. Several obvious questions arise. Which definition of Padé approximant is to be used? Which multivariate rational functions should be investigated? When considering univariate projections of these functions, our analysis confirms the univariate results obtained so far in [13], under the condition that the noise is added after projection. At the same time, it is apparent from section 4 that for the unprojected multivariate Froissart polynomial no conjecture can be formulated yet.

     

On the continuity of the multivariate Padé operator

Continuity of the univariate Padé operator was proved in [5,6]. We discuss the limitations of a multivariate generalization and prove a multivariate analogon of the continuity property.     

A new method for the stereoselective synthesis of alpha- and beta-glycosylamines using the Burgess reagent

Although glycosylamines constitute an important group of carbohydrates from the standpoint of biology and medicine, methods for their synthesis typically lack substrate generality and/or result in variable stereoselectivity, especially in complex contexts. In this communication, we report an operationally simple method for the synthesis of both alpha- and beta-glycosylamines using the Burgess reagent that overcomes many of these limitations in a bare minimum of synthetic steps.     

Fluorescent polymer cubosomes and hexosomes with aggregation-induced emission

Fluorescent polymer cubosomes and hexosomes with aggregation-induced emission (AIE) were prepared from amphiphilic block copolymers PEG-b-PTPEMA where the hydrophobic block PTPEMA was a polymethacrylate with tetraphenylethene (TPE) as the AIE side group. Four highly asymmetric block copolymers with hydrophilic block weight ratio f_PEG ≤ 20% were synthesized. Cubosomes and hexosomes with strong fluorescence emission were obtained by nanoprecipitation of polymers with f_PEG < 9% in dioxane/water and THF/water systems. Their ordered internal structures were studied by electron microscopy (cryo-EM, SEM and TEM) and the X-ray scattering technique (SAXS). To elucidate the formation mechanisms of these inverted colloids, other parameters influencing the morphologies, like the water content during self-assembly and the organic solvent composition, were also investigated. This study not only inspires people to design novel building blocks for the preparation of functional cubosomes and hexosomes, but also presents the first AIE fluorescent polymer cubosome and hexosome with potential applications in bio-related fields.

Fluorescent Im$\bar{3}$m cubosome and P6mm hexosome with aggregation-induced emission (AIE) were reported, which were formed by amphiphilic block copolymers PEG-b-PTPEMA. The length of hydrophobic block PTPEMA was adjusted to control morphology formation.     

Efficient RNase H-directed cleavage of RNA promoted by antisense DNA or 2'F-ANA constructs containing acyclic nucleotide inserts

The ability of modified antisense oligonucleotides (AONs) containing acyclic interresidue units to support RNase H-promoted cleavage of complementary RNA is described. Manipulation of the backbone and sugar geometries in these conformationally labile monomers shows great benefits in the enzymatic recognition of the nucleic acid hybrids, while highlighting the importance of local strand conformation on the hydrolytic efficiency of the enzyme more conclusively. Our results demonstrate that the duplexes support remarkably high levels of enzymatic degradation when treated with human RNase HII, making them efficient mimics of the native substrates. Furthermore, interesting linker-dependent modulation of enzymatic activity is observed during in vitro assays, suggesting a potential role for this AON class in an RNase H-dependent pathway of controlling RNA expression. Additionally, the butyl-modified 2'F-ANA AONs described in this work constitute the first examples of a nucleic acid species capable of eliciting high RNase H activity while possessing a highly flexible molecular architecture at predetermined sites along the AON.     

The synthesis and studies towards the self-replication of bis(capped porphyrins)

Connecting two facially-protected porphyrins was expected to lead to an equal mixture of laterally-bridged doubly-protected bis-porphyrins; one in which the two porphyrin units were protected on the same face (syn) and one with the two prophyrin units protected on opposite faces (anti). Addition of a co-factor (bidentate ligand) was expected to lead predominantly to the syn-bis-porphyrin by a templated self-replication process. This concept was explored using Baldwin's capped porphyrin. Bis(capped porphyrins) were synthesised in several steps starting from zinc(II) capped porphyrin 2. Nitration of 2 followed by reduction and photo-oxidation yields a mixture of zinc(II) porphyrindiones 7 and 8 that can separated by HPLC. The condensation of 2 molar eq. of zinc(II) porphyrin-7,8-dione 8 with 1,2,4,5-benzenetetramine leads to the formation of a 1:1 mixture of syn- and anti-dizinc(II) bis(7,8-capped porphyrins), 11 and 12, respectively, that have almost identical spectroscopic properties. These two geometric isomers were distinguished by significant differences in their molecular recognition properties. Likewise the syn- and anti-dizinc(II) bis(2,3-capped porphyrins), 9 and 10, respectively, are synthesised from the related zinc(II) capped porphyrin-2,3-dione 7, and were also identified using molecular recognition studies. The molecular recognition properties of these bis(capped porphyrins) were utilised in studies of self-replicating porphyrin systems. The results show that tetraazaanthraceno-bis-porphyrins 9-12 can catalyse their own formation but self-replication was not observed. These results highlight the potential that these interesting hosts have as templates in supramolecular chemistry, synthesis and catalysis.