Ostwald ripening, chiral crystallization, and the common-ancestor effect

We introduce an agent-based model for advection-mediated chiral autocatalysis in which we take into account dissolution-crystallization processes through Ostwald ripening. We demonstrate that the latter phenomenon is the key to explaining previously puzzling experimental results whereby complete chiral symmetry breaking is attained from an initially unbiased mixture of seed crystals. We show that this homochirality is achieved by what has been termed the common-ancestor effect: Ostwald ripening removes competing lineages, leaving only one common ancestor for the entire system.     

Polymorphism of the co-crystalline forms of syndiotactic polystyrene with chloroform: Crystal structure of the δ clathrate

The crystal structure of the δ clathrate form of syndiotactic polystyrene (s-PS) containing CHCl₃, a molecule having a pivotal role in respect to the co-crystalline phases formation of this polymer, has been determined through X-ray diffraction data and molecular mechanics calculations. Analogously to all the other δ clathrate forms of s-PS, this structure presents a monoclinic unit cell (cell constants a = 1.77 nm, b = 1.32 nm, c = 0.78 nm and γ = 121.5°) in which the s(2/1)2 polymer helices and guest molecules are packed according the space group P2₁/a. At variance with all the other δ clathrate forms of s-PS whose crystal structure has been reported in the literature, probably due to the not planar shape of the chloroform guest molecule, in this structure guest molecules occupy each centrosymmetric cavity in a very low efficient way, giving rise to a disorder in the positioning of the guest molecules along the b + a/2 direction of the unit cell. A comparison with the ε type clathrate with the same guest, for which some preliminary results have been reported too, is also presented.     

A facile “one pot” synthesis of 2,9-disubstituted 8-azapurin-6-ones (3,5-disubstituted 7-hydroxy-3H-1,2,3-triazolo[4,5-d]pyrimidines)

A series of title compounds have been synthesized by utilising benzylazide, cyanoacetamide, ethyl or methyl esters of aliphatic or aromatic carboxylic acids and sodium ethoxide as catalyst.     

Passive scalars,three-dimensional volume-preserving maps,and chaos

The dynamics of a medium-sized particle (passive scalar) suspended in a general time-periodic incompressible fluid flow can be described by three-dimensional volume-preserving maps. In this paper, these maps are studied in limiting cases in which some of the variables change very little in each iteration and others change quite a lot. The former are called slow variables or actions, the latter fast variables or angles. The maps are classified by their number of actions. For maps with only one action we find strong evidence for the existence of invariant surfaces that survive the nonlinear perturbation in a KAM-like way. On the other hand, for the two-action case the motion is confined to invariant lines that break for arbitrary small size of the nonlinearity. Instead, we find that adiabatic invariant surfaces emerge and typically intersect the resonance sheet of the fast motion. At these intersections surfaces are locally broken and transitions from one to another can occur. We call this process, which is analogous to Arnold diffusion, singularity-induced diffusion. It is characteristic of two-action maps. In one-action maps, this diffusion is blocked by KAM-like surfaces.On leave of absence from the Departamento de Fisica, Universidad Nacional de La Plata, (1990), La Plata, Argentina.     

Synthesis of some substituted pyrido[1,2-a]pyrimidin-4-ones and 1,8-naphthyridines

The substituted 4H-pyrido[1, 2-a]pyrimidin-4-ones (I) were obtained by the condensation of substituted 2-aminopyridines with δ-ketocarboxylic esters in PPA. Some of the derivatives I were transformed into the corresponding 1, 8-naphthyridines II and III.     

On the ranks of single elements of reflexive operator algebras

For any completely distributive subspace lattice on a real or complex reflexive Banach space and a positive integer , necessary and sufficient (lattice-theoretic) conditions are given for the existence of a single element of of rank . Similar conditions are given for the existence of single elements of infinite rank. From this follows a relatively simple lattice-theoretic condition which characterises when every non-zero single element has rank one. Slightly stronger results are obtained for the case where is finite, including the fact that every single element must then be of finite rank.

     

On complementary subspaces of Hilbert space

Every pair of non-trivial topologically complementary subspaces of a Hilbert space is unitarily equivalent to a pair of the form on a Hilbert space . Here is possibly , is a positive injective contraction and denotes the graph of . For such a pair the following are equivalent: (i) is similar to a pair in generic position; (ii) and have a common algebraic complement; (iii) is similar to for some operators on a Hilbert space. These conditions need not be satisfied. A second example is given (the first due to T. Kato), involving only compact operators, of a double triangle subspace lattice which is not similar to any operator double triangle.

     

1‐(1,2,3‐triazol‐4‐yl)‐benzimidazolones,a new series of heterocyclic derivatives

New 1‐(1,2,3‐triazol‐4‐yl)‐benzimidazolone derivatives were obtained on pursuing research about new tricyclic derivatives of medicinal interest, bearing a 1,2,3‐triazole ring fused with another heterocyclic ring. 1‐[(5‐Carboxamido)‐1,2,3‐triazol‐4‐yl]‐benzimidazolone was prepared by four different chemical routes and it was unequivocally confirmed by spectroscopic methods. Its chemical behaviour, was evaluated by some common chemical reactions such as hydrolysis, esterification, decarboxylation, nitration and N‐methylation.     

Crystal structure of the trigonal form of isotactic polypropylene as an example of density-driven polymer structure

Propene-hexene copolymers crystallize in a new polymorphic form of isotactic polypropylene when the concentration of hexene is higher than nearly 10-15 mol %. The hexene units are included in the crystals, inducing an increase of density that allows crystallization of 3-fold helical chains in a trigonal unit cell according to the space group R3c or Rc, where the helical symmetry of the chains is maintained in the crystal lattice. The structure of this new form is similar to those of isotactic polybutene and polystyrene and does not crystallize in polypropylene homopolymer because it would have too low density. The crystal structure of isotactic polypropylene is therefore no longer an exception to the principles of polymer crystallography, but the new structure represents the fulfillment of these principles and indicates that the packing of polymer molecules is mainly driven by density.     

Bailout embeddings and neutrally buoyant particles in three-dimensional flows

We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dynamics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of impurities in tubular vortical structures, the detachment of particles from fluid trajectories near hyperbolic invariant lines, and the formation of nontrivial three-dimensional structures in the distribution of particles are predicted.