Dual disjoint hypercyclic operators

Let E be a separable Fréchet space. The operators T₁,…,Tm are disjoint hypercyclic if there exists x∈E such that the orbit of (x,…,x) under (T₁,…,Tm) is dense in E×?×E. We show that every separable Banach space E admits an m-tuple of bounded linear operators which are disjoint hypercyclic. If, in addition, its dual E^∗ is separable, then they can be constructed such that are also disjoint hypercyclic.     

Ruthenium nanoparticles in ionic liquids: structural and stability effects of polar solutes

Ionic liquids are a stabilizing medium for the in situ synthesis of ruthenium nanoparticles. Herein we show that the addition of molecular polar solutes to the ionic liquid, even in low concentrations, eliminates the role of the ionic liquid 3D structure in controlling the size of ruthenium nanoparticles, and can induce their aggregation. We have performed the synthesis of ruthenium nanoparticles by decomposition of [Ru(COD)(COT)] in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [C(1)C(4)Im][NTf(2)], under H(2) in the presence of varying amounts of water or 1-octylamine. For water added during the synthesis of metallic nanoparticles, a decrease of the solubility in the ionic liquid was observed, showed by nanoparticles located at the interface between aqueous and ionic phases. When 1-octylamine is present during the synthesis, stable nanoparticles of a constant size are obtained. When 1-octylamine is added after the synthesis, aggregation of the ruthenium nanoparticles is observed. In order to explain these phenomena, we have explored the molecular interactions between the different species using (13)C-NMR and DOSY (Diffusional Order Spectroscopy) experiments, mixing calorimetry, surface tension measurements and molecular simulations. We conclude that the behaviour of the ruthenium nanoparticles in [C(1)C(4)Im][NTf(2)] in the presence of 1-octylamine depends on the interaction between the ligand and the nanoparticles in terms of the energetics but also of the structural arrangement of the amine at the nanoparticle's surface.     

The structure of the Newtonian limit

We consider a smooth one-parameter family of four-dimensional manifolds X,≥0, each one endowed with a covariant metric g. It is assumed that g is a Lorentz metric for each >0, i.e., the signature of g is (+,−,−,−) for >0, while the limit metric g₀ on X₀ is assumed to be degenerated of rank 1, i.e., the signature of g₀ is (+,0,0,0). We characterize when the limit manifold X₀ inherits the geometric structure of a Newtonian gravitation. The limit manifold X₀ is a Newtonian gravitation if and only if there exist the limits of the Levi-Civita connection , the curvature operator and the contravariant Einstein tensor G² as →0. Moreover, the existence of these limits is characterized in terms of the Taylor expansion of the family {g} with respect to the parameter .     

Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.     

5‐Methyl­sulfanyl‐3H‐1,2,3‐triazolo[4,5‐d]pyrimidin‐7(6H)‐one (2‐methyl­thio‐8‐aza­xanthine) monohydrate

The title compound, C₅H₅N₅OS·H₂O, crystallizes as the monohydrate. Disorder of the H atoms that participate in the hydrogen bonds implies that two different tautomers are present in the crystal structure, one of them with both acidic H atoms attached to the imidazole ring and the other with one acidic H atom on each ring.     

Rigid motions in relativity

Starting with a simple characterization of pairs of rigidly joined straight world lines, successive generalizations are obtained up to the most general case which allows us to establish the various definitions of rigid motions in relativity (both special and general).     

A Structure Theorem for Free Temporal Algebras

In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained.     

Distribution of amines in water/AOT/n-hexane reverse micelles: influence of the amine chemical structure

The distribution of different aliphatic and aromatic amines: n-butylamine (n-BA), isobutylamine (i-BA), tert-butylamine (t-BA), piperidine (PIP), N,N-dimethylaniline (DMA) and N-methylaniline (MA) in water/sodium 1,4-bis(2-ethylhexyl)sulfosuccinate(AOT)/n-hexane reverse micelles was investigated by steady-state fluorescence measurements. The partition constants were measured by an indirect method based on the effect that amine partitioning exert on the bimolecular rate of the reaction between a microphase incorporated fluorophore (Ru(bpy)2+(3)) and the quencher, (Fe(CN)3-(6)). For MA, that can act as a quencher of the fluorophore a direct method was used. The results show that primary amines have larger partition constants than the secondary ones. For tertiary amines the distribution constants were practically negligible. Laser flash photolysis experiments confirmed that tertiary amines, both aliphatic and aromatic, are not incorporated to the micellar pseudophase. The effect of the amine structure on the partition constant was analyzed through linear solvation free energy relationships (LSER) using solute parameters and compared with those obtained for alcohols. Hydrogen bond interactions with the AOT polar heads appear to be the main driving force for the distribution of amines between the organic and micellar pseudophases, whereas the size of the alkyl or aromatic group tends to hinder it.