Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.

     

Real Hypersurfaces in Quaternionic Space Forms Satyisfying Axioms of Planes

A Riemannian manifold satisfies the axiom of 2-planes if at each point, there are suficiently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several definitions of axiom of planes arise naturally when we consider such families of tangent planes. We are able to classify real hypersurfaces in quaternionic space forms satisfying these definitions.     

The revised structure of mortonin

The structure 1 previously proposed tor mortonin, is revised to 2 based on spectroscopic and chemical evidence, and on biogenetic considerations.     

Additivity of the hydrogen bridges in several polymers of formamide

The purpose of the study was to examine the energy additivity of the hydrogen bridges in formamide polymers. Consideration was given to both the linear polymers observed in polypeptides, and to the cyclic polymers observed in the crystal structure. Additivity was found in several geometries. The linear polymers were considered as far as the tetramer, and the cyclic as far as the heptamer.Work supported in part by the Instituto Fisica, Universidad Nacional Autónoma de Mexico and Conacyt, México.     

Efficient, accurate calculation of rotational diffusion and NMR relaxation of globular proteins from atomic-level structures and approximate hydrodynamic calculations

The calculation of the rotational diffusion tensor and NMR relaxation times of quasi-rigid macromolecular structures with atomic detail can be made by means of bead/shell models. The computing time required for calculation of these properties for a single structure using rigorous hydrodynamic methods requires a moderate computing time. In possible applications of the methodology in which such a calculation had to be repeated for many structures, a faster method would be welcome. We have studied the effect of introducing a simplifying approximation in the treatment of hydrodynamic interaction, comparing the rigorous and approximate results for a set of 30 globular proteins. When the NMR relaxation times are combined in some relative form, the rigorous and approximate results are practically coincident. For absolute quantities, such as the correlation time, we find that the bias introduced by the approximation can be closely predicted and corrected. The differences between the results of the approximate-corrected and rigorous procedures are not greater than usual experimental errors, and the typical computing time is reduced from 5 min to 1 s.     

Multistep reaction analysis. A numerical approach based on relaxation theory

A general numerical method and program for simulation of the kinetics of multistep reactions is described, with details for collation of data, construction of a mechanistic model, and simulation of reciprocal relaxation times and calculation of individual rate constants. The working scheme of the program includes an initial approximate simulation by adjustment of the rate constants followed by their optimization with a Powell minimization subroutine. The procedure is applied to aromatic nucleophilic addition.     

Narrow transmittance peaks in a multilayered microsphere with a quasiperiodic left-handed stack

We studied the photon spectrum in coated microspheres with alternating quasiperiodic layers having left-handed (LH) materials included. It is found that the band gap (spectral zone of nearly zero transmittancy) in such a system is strongly enhanced. At an increase of the quasiperiodicity parameter γ, the boundaries of the spectral band gaps acquire the intended shape. When γ exceeds the inverse golden mean value, a structure with extremely narrow separated resonant peaks with nearly complete transmittance arises. At increased γ, such resonances migrate to the center of the band gap. This effect allows creating optical filters with extremely narrow passbands.