A formula with some applications to the theory of Lyapunov exponents

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman’s result. Finally, we give a result about the growth of the spectral radius of products. Financial support from Pronex-Dynamical Systems, CNP_q 001/2000 and from Faperj is gratefully acknowledged.     

Banach envelopes of vector valued H spaces

In the paper we describe the Banach envelopes of Hardy spaces of analytic functions of several variables on polydiscs taking values in quasi-Banach spaces.     

Controlled Light‐Mediated Preparation of Gold Nanoparticles by a Norrish Type I Reaction of Photoactive Polymers

Gold nanoparticles (AuNPs) are subjects of broad interest in scientific community due to their promising physicochemical properties. Herein we report the facile and controlled light‐mediated preparation of gold nanoparticles through a Norrish type I reaction of photoactive polymers. These carefully designed polymers act as reagents for the photochemical reduction of gold ions, as well as stabilizers for the in situ generated AuNPs. Manipulating the length and composition of the photoactive polymers allows for control of AuNP size. Nanoparticle diameter can be controlled from 1.5 nm to 9.6 nm.     

Surface Trapping and STM Observation of Conformational Isomers of a Bis(Terpyridine) Ligand from Metallosupramolecular Grids

Tetranuclear Co‐grid complexes incorporating bis‐tridentate ligands, namely 4,6‐bis(2,2′‐bipyrid‐6‐yl)‐2‐phenylpyrimidine, were electrosprayed onto a Au(111) substrate under an ultrahigh vacuum. Fragmentation occurs leaving the ligands in four different conformations. Most ligands are found to form H‐bonded dimers. The most abundant conformer of the ligand on the Au surface is an asymmetric form, which has not been observed before. The present results indicate that the fragmentation of coordination compounds during the deposition process, in principle, allows for surface trapping, identification, and investigation of high energy, out‐of‐equilibrium conformations of the ligand molecules at low temperatures, which otherwise would not be observable.     

Aza-substitution,benzo-annulation effects and catalytic activity of <Emphasis Type="Italic">β</Emphasis>-octaphenyl-substituted tetrapyrrolic macroheterocyclic cobalt complexes. I. heterogeneous catalysis

The influence of the size of conjugated π-system on catalytic activity of cobalt complex with β-octaphenylporphyrin and its tetraaza-, tetrabenzo and tetrabenzotetraaza derivatives was studied in present work. It is found that catalytic activity for oxidation of sulfur-containing compounds increases under extension of conjugated macrocycle system according to the following series CoP < CoBP ≤ CoPz < CoPPz ? CoPc.     

Fire retardant action of mineral fillers

Endothermically decomposing mineral fillers, such as aluminium or magnesium hydroxide, magnesium carbonate, or mixed magnesium/calcium carbonates and hydroxides, such as naturally occurring mixtures of huntite and hydromagnesite are in heavy demand as sustainable, environmentally benign fire retardants. They are more difficult to deploy than the halogenated flame retardants they are replacing, as their modes of action are more complex, and are not equally effective in different polymers. In addition to their presence (at levels up to 70%), reducing the flammable content of the material, they have three quantifiable fire retardant effects: heat absorption through endothermic decomposition; increased heat capacity of the polymer residue; increased heat capacity of the gas phase through the presence of water or carbon dioxide. These three contributions have been quantified for eight of the most common fire retardant mineral fillers, and the effects on standard fire tests such as the LOI, UL 94 and cone calorimeter discussed. By quantifying these estimable contributions, more subtle effects, which they might otherwise mask, may be identified.     

Anion-controlled networks of intermolecular interactions in the crystal structure of 9-aminoacridinium salts

A series of salts, with the 9-aminoacridinium cation (9-AA) and aromatic carboxylic acid: benzoate (1), ortho-phthalate (2), and salicylate (3) anions have been synthesized and characterized using X-ray diffraction. In the crystal packing, the ions are linked via N-H?O, O-H?O, and C-H?O hydrogen bonds. Analysis of the hydrogen bonds in the crystal lattices of the title compounds shows that the cations and anions form tetramers. The ions in these tetramers are linked via N(amino)-H?O(carboxy) hydrogen bonds forming R₂²(8) (1 and 3) or R₂⁴(15) (2) hydrogen bond ring motifs. The cations interact through π-π interactions in the ABBA (1), AB (2) or ABA (3) arrangement to form columns (1 and 2) or chains (3).     

Remarks on ideal boundedness, convergence and variation of sequences

We answer the questions asked by Faisant et al. (2005) [2]. The first main result states that for every admissible ideal I⊂P(N) the quotient space l^∞(I)/c₀(I) is complete. The second main result states that consistently there is an admissible ideal I⊂P(N) such that the sets W(I), of all real sequences with finite I-variation, and c^?(I), of all restrictively I-convergent sequences, are equal.