A solid-state NMR study of the fast and slow dynamics of collagen fibrils at varying hydration levels

We report solid-state NMR investigations of the effect of temperature and hydration on the molecular mobility of collagen isolated from bovine achilles tendon. (13)C cross-polarization magic angle spinning (MAS) experiments were performed on samples at natural abundance, using NMR methods that detect motionally averaged dipolar interactions and chemical shift anisotropies and also slow reorientational processes. Fast motions with correlation times much shorter than 40 micro s scale dipolar couplings and chemical shift anisotropies of the carbon sites in collagen. These motionally averaged anisotropic interactions provide a measure of the amplitudes of the segmental motions expressed by a molecular order parameter. The data reveal that increasing hydration has a much stronger effect on the amplitude of the molecular processes than increasing temperature. In particular, the Cgamma carbons of the hydroxyproline residues exhibit a strong dependence of the amplitude of motion on the hydration level. This could be correlated with the effect of hydration on the hydrogen bonding structure in collagen, for which this residue is known to play a crucial role. The applicability of 1D MAS exchange experiments to investigate motions on the millisecond time-scale is discussed and first results are presented. Slow motions with correlation times of the order of milliseconds have also been detected for hydrated collagen.     

Molecular topology. IV. Regressive vertex degrees (new graph invariants) and derived topological indices

New local graph invariants, “regressive vertex degrees” (which are slightly augmented vertex degrees) are introduced on the basis of decreasing contributions of more remote vertexes to the classical vertex degrees. Several such invariants are proposed (BR, ER, SR) where t (either t = 1 or t = 2) is an operator expressing the attenuation with increasing topological distance, according to formula (1) or (2). With the aid of these new local invariants, new topological indices (global graph invariants), Y (namely BY, EY or SY) are introduced and exemplified. Their ability to express the branching and to order alkanes is investigated. An appendix gives some recursive relationships for computing these indices.     

Two fixed point theorems for generalized contractions with constants in complete metric space

In this paper we prove two fixed point theorems for generalized contractions with constants in complete metric space, which are generalizations of very recent results of Kikkawa and Suzuki.      

Photothermal and photocatalytic processes on TiO2 based materials prepared by sol-gel method

In the present work, Fe³⁺ doped TiO₂ coatings on glass substrates were prepared by dip-coating from a sol-gel solution. The influence of the dopant concentration on the structure, optical, photocatalytic and photothermal properties of the films was studied. The results obtained have shown a strong correlation between the catalytic properties and the amount of iron dopant and the temperature of the thermal treatment.     

CONTRA: improving the performance of dynamic investigations in natural abundance organic solids by mirror-symmetric constant-time CODEX

We present a minor but essential modification to the CODEX 1D-MAS exchange experiment. The new CONTRA method, which requires minor changes of the original sequence only, has advantages over the previously introduced S-CODEX, since it is less sensitive to artefacts caused by finite pulse lengths. The performance of this variant, including the finite pulse effect, was confirmed by SIMPSON calculations and demonstrated on a number of dynamic systems.     

Enhancement of two-photon emission in photonic crystals

We report the influence of photonic stopgaps on two-photon excited emission from highly efficient nonlinear chromophores infiltrated into high-quality photonic crystals. We have observed a sharp decrease (filter effect) in emission within the frequency range and direction of the stopgap as well as sharp enhancement of the two-photon excited emission associated with the stopgap's edge. This effect may be important for the development of low-threshold upconversion lasers.     

Nonisomorphic graphs with identical atomic counts of self-returning walks: Isocodal graphs

On the basis of endospectral graphs, we present a graphical method for obtaining pairs of nonisomorphic graphs with identical atomic counts of self-returning walks.     

A Theoretical Interpretation of Meloy's Law of Morphological Coefficients

This note deals with the Fourier representation of particle shape. A frequency distribution p_n, n = 1,2, …, expressing the contribution of the different harmonics to the dispersion of the position vector is defined. The Meloy law of morphological coefficients may be derived by optimizing the value of the informational entropy which is attached to p_n.     

On the construction of a nonlinear recursive predictor

In this paper, we present a novel approach for constructing a nonlinear recursive predictor. Given a limited time series data set, our goal is to develop a predictor that is capable of providing reliable long-term forecasting. The approach is based on the use of an artificial neural network and we propose a combination of network architecture, training algorithm, and special procedures for scaling and initializing the weight coefficients. For time series arising from nonlinear dynamical systems, the power of the proposed predictor has been successfully demonstrated by testing on data sets obtained from numerical simulations and actual experiments.