Sheaves of Einstein algebras

To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein algebras. The theory of such spaces, called Einstein structured spaces, is developed. Both quasiregular and curvature singularities are studied in some detail. Examples of the closed Friedmann world model and the Schwarzschild spacetime show that Schmidt'sb-boundary is a useful theoretical tool when considered in the category of structured spaces.     

TiO2-based photocatalysts impregnated with metallo-porphyrins employed for degradation of 4-nitrophenol in aqueous solutions: role of metal and macrocycle

Photodegradation of organic compounds in water solutions by means of economically advantageous and environment-friendly processes is a topic of growing interest. In recent years a great attention has been devoted to TiO₂-based photocatalysts for the oxidative degradation of various organic pollutants. In this context, we have prepared new photo-catalytic polycrystalline TiO₂ systems impregnated with sensitizers, i.e., copper, iron or manganese porphyrins, and investigated their photoactivity for 4-nitrophenol oxidation compared with that of bare TiO₂. A significant improvement of the photoreactivity was observed in the case of TiO₂ impregnated with copper porphyrin, while only a slight beneficial effect was observed in the case of iron porphyrin. In contrast, the presence of manganese porphyrin appeared to be detrimental.     

Finiteness of the number of maximal open subsets with good quotients

The aim of the paper is to prove the Main Theorem which says that, in any complex normal variety with an action of a reductive groupG, there are only finitely many subsets which are maximal in the family of all openG-invariant subsets admitting a good quotient. The author is in part supported by Polish KBN Grant 2 PO3A 038 08.     

Multiple Gradient TLC and Densitometric Analysis of p-Coumaric Acid in Some Medicinal Plants from the Family Solanaceae

JPC – Journal of Planar Chromatography – Modern TLC -     

Bioinspired Nanodevice Based on the Folic Acid/Titanium Dioxide System

A new bioinspired nanomaterial has been obtained by chemisorption of folic acid onto nanocrystalline titanium dioxide. The organic chromophore is linked with the semiconductor surface via the glutamate chain and anchored with the carboxylate group. The geometry and electronic structure of the chromophore was studied in detail with DFT. Photoelectrochemical studies revealed photosensitization of the new material towards visible light. The photoelectrodes composed of the folic acid/titanium dioxide hybrid material generated photocurrent over a 300–600‐nm window. Moreover, the direction of the photocurrent could be changed from anodic to cathodic and vice versa by application of the appropriate photoelectrode potential. Photoelectrochemical and spectroscopic studies allowed the elucidation of the mechanism of photocurrent switching. Photoelectrodes composed of folate‐modified titanium dioxide may serve as a simple model of optoelectronic switches and may constitute the basis for molecular photoelectronic devices.     

MR microscopy of water diffusion tensor in biological systems

Diffusion tensor imaging (DTI) of the control and mechanically injured spinal cord of a ratin vitro andin vivo are reported.In vitro experiments were done on a home-built 6.4 T magnetic resonance microscope. Results for formaline-fixed samples show significant differences in diffusion tensor components between gray matter and white matter of the control spinal cord. Moreover, it is shown that already 6–10 min after the injury DTI can detect changes in water diffusion in areas extending far beyond the region of primary tissue damage.In vivo experiments were performed using a 9.4 T Magnex magnet and Bruker Medspec imaging system. Good-quality DTI images, free from motion artifacts were obtained. Results from control samples confirm differences in water diffusion between white matter and gray matter, observedin vitro. In vivo experiments show that characteristic changes in water diffusion observedin vitro 6–10 min after injury are preserved 60–360 min after injury, without significant alteration during this time.     

Letter: Rotation of the Universe and the Angular Momenta of Celestial Bodies

We discuss the equation of motion of the rotating homogenous and isotropic model of the Universe. We show that the model predicts the presence of a minimum in the relation between the mass of an astronomical object and its angular momentum. We show that this relation appears to be universal, and we predict the masses of structures with minimal angular momenta in agreement with observations. In such a manner we suggest the possibility at acquirement of angular momenta of celestial bodies during their formation from the global rotation of the Universe.