Real rank and squaring mappings for unital -algebras

It is proved that if is a compact Hausdorff space of Lebesgue dimension , then the squaring mapping , defined by , is open if and only if . Hence the Lebesgue dimension of can be detected from openness of the squaring maps . In the case it is proved that the map , from the selfadjoint elements of a unital -algebra into its positive elements, is open if and only if is isomorphic to for some compact Hausdorff space with .

     

Geometric dynamics on quantum Nano-surfaces and low-energy spectrum in a homogeneous magnetic field

Low-energy dynamics and spectrum of the Schrödinger operator on curved surfaces in a magnetic field are considered. Nano-and micro-algebraic structures generate a quantization of the surface. On this quantum space, the dynamics has a “surfing” behavior described via curvature invariants. Two types of surface deformations correspond to trapping and transistor types of dynamics.We observe the “negative mass” effect in the low-energy spectrum under trapping deformations. We also compute, in geometrical terms, the energy levels near the spectral bottom (these levels are below the minimal Landau level). The surfing dynamics and the spectrum are independent of the magnitude of the magnetic field.     

A Measure of Non-convexity in the Plane and the Minkowski Sum

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for “not far from convex” regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no “holes”.     

Mechanochemical synthesis of nanosized europium nitrate with 1,10-phenanthroline

Mechanochemically synthesized europium nitrate with 1,10-phenanthroline (Phen) is formed into globules with sizes of 100–300 nm, which are assembled into larger globular aggregates or packed into layers. The increasing mechanical activation time induces sintering, generating porous aggregates with micro-and nanopores. Eu²⁺ paramagnetic centers, detectable by ESR, are generated by mechanical grinding. Possibly, they are positioned on the surfaces of nanoglobules. The complex Eu(NO₃)₃ · 2Phen synthesized conventionally from aqueous ethanol consists of needle-shaped microcrystallites. They do not give rise to ESR spectra.     

The dispersity and distribution of luminophors in high-pressure polyethylene

Polymers based on high-pressure polyethylene were prepared and activated with europium(III) complexes with carboxylic acids and compositions based on europium-anthranilic acid compounds. According to the electron scanning, atomic, and fluorescence spectroscopic data, luminophor particles showed a heterophase distribution in films. The particles had an average size of 3–30 μm and were shaped as globules.     

The luminescent properties of polyethylene films with admixtures of luminophores based on europium compounds

Polyethylene films activated with europium(III) complexes with carboxylic acids and Eu(L)₃ · nD · xH₂O + ANT compositions, where L is the trifluoroacetic, toluyl, or cinnamic acid anion and ANT is anthranilic acid, were prepared. The intensity of luminescence of the polymeric compositions depended on the content of luminophores (molar ratio between europium compounds and anthranilic acid). An analysis of the excitation spectra showed that, in polymer—Eu(L)₃ · nPhen · xH₂O + ANT compositions, there was effective energy transfer from phenanthroline to anthranilic acid levels.     

Dimension of maps,universal spaces,and homotopy

This paper is a survey of some recent results in dimension theory. The main topics under consideration are: dimension of maps in the classical and extension dimension theories, universal spaces (in particular, universal compacta) in extension dimension theory, and [L]-homotopy. A number of theorems included in the survey are accompanied by proofs. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 48, General Topology, 2007.     

Columinescence effect in macromolecular complexes of Eu(III) and Tb(III)

The effect of Y(III) and Gd(III) coactivator ions on the intensity of Eu(III) and Tb(III) luminescence in monomer and polymer mixed-metal complexes was studied. Isomorphic replacement of Eu(III) and Tb(III) ions by Y(III) and Gd(III) ions in macromolecular complexes led to sensitization of Eu(III) and Tb(III) ion luminescence. A mechanism of columinescence was suggested. It involves a charge transfer and the ligand orbitals and the vacant orbitals of Eu(III) and Tb(III) ions and coactivators.     

Magnetic Tops in Dusty Plasmas

Paper contains the results of investigation of separate dust granules mechanical state. Observations were performed in high optical resolution. Magnetic induction varied up to 400 G. Motion of particles of different shapes was studied separately. These shapes were: ideally spherical, spherical with defects and non‐spherical. The peculiar physical features of fast rotating dusty granules (tops) were observed. They are the emergence of magnetic moment of rotating charged granule and the orientation change of magnetic moment at magnetic field superimposition. The effects observed in magnetic field are supplied with qualitative interpretation (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Infinite-dimensional 4-manifold of finite cohomological dimension under the continuum hypothesis

Under the assumption of the continuum hypothesis, a differentiable 4-manifoldM of dimension dimM=∞ and cohomological dimension cA—dimM=4 is constructed. The spaceM is perfectly normal and hereditarily separable. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 664–670, November, 1999.