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.     

Orientation effects on nitric acid dihydrate films

An investigation of orientation effects in films of nitric acid dihydrate (NAD) is presented, based on a systematic study of transmission and reflection-absorption infrared (RAIR) spectra of samples of varying thickness. The samples are prepared by vapor deposition on Ge (for transmission spectroscopy) and on Al substrates (for RAIR spectroscopy) at 175 K to produce crystalline alpha-NAD films. Transmission spectra were recorded at normal incidence, and RAIR spectra were recorded at a grazing angle of 75 degrees, with polarized radiation. The observed spectra are compared with predictions of a classical Fresnel model, to test the available optical indices of NAD, which are of great importance for the accurate interpretation of data from remote sensing measurements. Whereas the procedure yields satisfactory results for transmission and s-polarized RAIR spectra, it is found that the agreement is not acceptable for p-polarized RAIR spectra. An explanation is suggested in terms of a preferential alignment of the films, with the (10-1) crystallographic plane of the crystal situated parallel to the substrate. The infrared activity of a band at approximately 1170 cm(-1) is explained in terms of a preferential orientation of the crystal domains in the film.     

A new control chart in contaminated data of t‐Student distribution for individual observations

Control charts are the most popular tool for monitoring production quality. In traditional control charts, it is usually supposed that the observations follow a multivariate normal distribution. Nevertheless, there are many practical applications where the normality assumption is not fulfilled. Furthermore, the performance of these charts in the presence of measurement errors (outliers) in the historical data has been improved using robust control charts when the observations follow a normal distribution. In this paper, we develop a new control chart for t‐Student data based on the trimmed T² control chart () through the adaptation of the elements of this chart to the case of this distribution. Simulation studies show that a control chart performs better than T² in t‐Student samples for individual observations. Copyright © 2012 John Wiley & Sons, Ltd.     

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.     

Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type are continuously orbit equivalent if and only if their groupoids are isomorphic, and that the corresponding two-sided shifts are flow equivalent if and only if the groupoids are stably isomorphic. As applications we show that two finite directed graphs with no sinks and no sources are move equivalent if and only if the corresponding graph $C^{?}$-algebras are stably isomorphic by a diagonal-preserving isomorphism (if and only if the corresponding Leavitt path algebras are stably isomorphic by a diagonal-preserving isomorphism), and that two topological Markov chains are flow equivalent if and only if there is a diagonal-preserving isomorphism between the stabilisations of the corresponding Cuntz–Krieger algebras (the latter generalises a result of Matsumoto and Matui about irreducible topological Markov chains with no isolated points to a result about general topological Markov chains). We also show that for general shift spaces, strongly continuous orbit equivalence implies two-sided conjugacy.