The space of the structure (0,3)-tensors of the covariant derivatives of the structure endomorphism and the metric on almost contact B-metric manifolds is considered. A known decomposition of this space in orthogonal and invariant subspaces with respect to the action of the structure group is used. We determine the corresponding components of the structure tensor and consider the case of the lowest dimension 3 of the studied manifolds. Some examples are commented.

The aim of the present study was to evaluate the prebiotic potential of Plantago major L. leaves water-extractable polysaccharide (PWPs) and its lower molecular fractions. The structure of PWPs was investigated by high pressure anion exchange chromatography (HPAEC), size exclusion chromatography coupled with multi-angle laser light scattering detector (SEC-MALLS) and Fourier-transform infrared (FTIR) spectroscopy. The chemical composition and monosaccharide analyses showed that galacturonic acid was the main monosaccharide of PWPs followed by glucose, arabinose, galactose, rhamnose and xylose. FTIR study indicated a strong characteristic absorption peak at 1550 cm⁻¹ corresponding to the vibration of COO⁻ group of galacturonic acid. The PWPs was subjected to hydrolysis using commercial enzymes to obtain P. major low molecular fraction (PLM) which was successively separated by size exclusion chromatography on Biogel P2. PWPs and PLM were examined for in vitro prebiotic activity using various assays. Results gave evidence for changes in optical density of the bacteria cells and pH of the growth medium. A heterofermentative process with a lactate/acetate ratio ranged from 1:1 to 1:5 was observed. The ability of PLM to stimulate the production of certain probiotic bacteria glycohydrolases and to be fermented by Lactobacillus sp. strains was successfully proved.

Background:Generally, the preparation of spray-dried microspheres is strongly affected by the process parameters. Particle size and production yield are mainly influenced by the spraying solution concentration and the pump rate of the spray dryer.Aim:The aim of this study was to assess optimum spray drying parameters - polymer concentration and pump rate required for the production of chitosan microspheres with high production yield and targeted for nasal administration particle size.Materials and methods:Full 3²factorial design was used to study the investigated parameters. Three different concentrations of the chitosan solution were selected: a low concentration of 1%, average concentration of 1.5% and high concentration of 2%. The rate of the peristaltic pump was also varied at three levels: low rate of 10%, medium rate of 14% and high rate of 18%.Results:Nine models of chitosan microspheres were formulated and characterized in terms of shape, surface morphology, size, particle size distribution and production yield. The particles obtained from 2% chitosan solutions, sprayed at 10% pump rate were of the highest yield (64.33%) and appropriate for nasal administration median diameter (3,434 μm).Conclusion:The two investigated spray-drying parameters interact with each other and their influence on the production yield and the size of the chitosan microspheres should be evaluated together, instead of one at a time. The assessed process parameters allow the production of chitosan microparticles with high yield and desirable characteristics (size, size distribution and shape) for intranasal delivery.