Limit sets for complete minimal immersions

In this paper we study the behaviour of the limit set of complete proper compact minimal immersions in a domain with the boundary We prove that the second fundamental form of the surface ∂G is nonnegatively defined at every point of the limit set of such immersions. A. Alarcón’s research is partially supported by MEC-FEDER Grant no. MTM2004-00160.     

Some existence results about radial graphs of constant mean curvature with boundary in parallel planes

In this work, for given H, we investigate the existence of radial cmc H annulus spanning two given non necessarily convex Jordan curves in parallel planes of . We established some existence results under hypotheses relating the geometry of the curves and the distance between the planes. Ari J. Aiolfi was partially supported by Fapergs and Programa FIPE Junior/UFSM.     

Associative Versus Dissociative Mechanisms of Phosphate Monoester Hydrolysis: On the Interpretation of Activation Entropies

Phosphate monoester and anhydride hydrolysis is ubiquitous in biology, being involved in, amongst other things, signal transduction, energy production, and the regulation of protein function. Therefore, this reaction has understandably been the focus of intensive research. Nevertheless, the precise mechanism by which phosphate monoester hydrolysis proceeds remains controversial. Traditionally, it has been assumed and frequently implied that a near‐zero activation entropy is indicative of a dissociative pathway. Herein, we examine free‐energy surfaces for the hydrolysis of the methyl phosphate dianion and the methyl pyrophosphate trianion in aqueous solution. In both cases, the reaction can proceed through either compact or expansive concerted (A_ND_N) transition states, with fairly similar barriers. We have evaluated the activation entropies for each transition state and demonstrate that both associative and dissociative transition states have near‐zero entropies of activation that are in good agreement with experimental values. Therefore, we believe that the activation entropy alone is not a useful diagnostic tool, as it depends not only on bond orders at the transition state, but also on other issues that include (but are not limited to) steric factors determining the configurational volumes available to reactants during the reaction, solvation and desolvation effects that may be associated with charge redistribution upon approaching the transition state and entropy changes associated with intramolecular degrees of freedom as the transition state is approached.     

Experimental and Theoretical Study of Helium Broadening and Shift of HCO+ Rotational Lines

An experimental and theoretical study of pressure broadening and pressure shift of HCO⁺ rotational lines perturbed by collisions with He is presented. Results are reported from measurements at 88 K for the lines j=4←3, 5←4 and 6←5 with frequencies ranging from 0.35 to 0.54 THz. Using a new CCSD(T)/aug‐cc‐pVQZ potential energy surface for the He–HCO⁺ interaction, the collisional line shape parameters are studied from fully quantum and semiclassical calculations. Results from the quantum treatment are in satisfactory agreement with experiments whereas the semiclassical approach can lead to appreciable differences. A study of the dependence of line width Γ and shift s as a function of the translational energy shows the presence of quantum oscillations. Calculations on a previous Hartree–Fock‐based potential energy surface lead to quite similar results for the collisional line shape parameters. Using a simplified version of the potential morphing method it is found that the line width Γ is particularly sensitive to the long‐range part of the potential energy surface. This also explains the success of the first line‐broadening calculations which date back to the 1950s.     

Spontaneous segregation on a hybrid chiral surface

Segregation of enantiomers in two-dimensional adsorbed layers is a process that is usually controlled by anisotropic directional interactions between adsorbed molecules. In this contribution, we propose a simple theoretical model in which the chiral segregation occurs even though the lateral interactions are neglected. In particular, we consider a solid surface composed of two domains with different patterns of active sites being mirror images of each other. The domains of opposite handedness represent crystal facets of a composite chiral material which are adjoined to form a heterochiral adsorbing surface. To explore equilibrium properties of the system, we use Canonical Ensemble Monte Carlo method for a square lattice. The influence of factors such as energetic properties of the surface and density of the adsorbed layer on the extent of separation is examined. The obtained results indicate that effective two-dimensional separation on the hybrid chiral surface assumed in our model can be achieved only at sufficiently low adsorbate densities. The results also suggest that the segregation on the hybrid surface would be a promising method of enantiodiscrimination for those chiral molecules which do not exhibit strong lateral interactions.