Eigenstates of the quantum Penning-Ioffe nanotrap at resonance

We discuss the choice of physical parameters of a quantum Penning nanotrap under the action of a perturbing inhomogeneous Ioffe magnetic field and also the role of frequency resonance modes. We present a general scheme for constructing the asymptotic behavior of the eigenstates by the generalized geometric quantization method and obtain the reproducing measure in the integral representation of eigenfunctions.     

Transversals for Families of Translates of a Two-Dimensional Convex Compact Set

The following Theorem 1 gives an affirmative answer to Grünbaum's old question. Let F be a family of translates of a convex compact set K⊂R ² . If every two elements of F have a common point, then there exist three points A, B, C ∈ R ² such that every element of F contains some of these points. Received December 28, 1998, and in revised form October 20, 1999. Online publication May 15, 2000.     

Photolysis of light-transforming polymer material

Light-transforming polymer materials activated with the compositions on the basis of the europium carboxylates with different ligands and anthranilic acid exhibiting the intense luminescence in the spectral range 400–700 nm are prepared. It is shown that light stability of polymer materials on the basis of the aboveprepared compositions is higher than of polymer materials activated with the europium salts. The photolysis of luminescent polymers was studied. For the compositions EuL₃C₁₃H₁₃N₃·xH₂O + anthranilic acid gradual increase in the luminescence intensity of the europium ion is marked.     

Crystal structure of boron difluoride acetylnaphtholates

The crystal structure of luminescent isomeric boron difluoride acetylnaphtholates: 2-acetyl-1-naphthoboron difluoride (1) and 1-acetyl-2-naphthoboron difluoride (2) has been studied. Molecules of 1 make infinite stacks of coplanar molecules in crystals, and molecules of 2 are arranged in the crystalline cell in the form of isolated π-dimers. Unlike a planar molecule of 1, the methyl group in α-position of the diketonate ring drops out of the molecule plane in a molecule of 2, thus forcing the chelate ring to bend considerably along the line C(11)-B. The structure features of 1 cause a bathochromic shift of the luminescence band in comparison with 2.     

Knaster’s Problem for (Z 2) k -Symmetric Subsets of the Sphere S^{2^{k}-1}

We prove a result about partitioning an absolutely continuous measure in ℝ ^d into 2d equal parts by a system of cones with common vertex, where d is an odd prime power. The proof is topological and based on the calculation of the equivariant Euler class of a certain vector bundle.     

Crystal structure and triboluminescence of centrosymmetric complex [Eu(NO<Subscript>3</Subscript>)<Subscript>3</Subscript>(HMPA)<Subscript>3</Subscript>]

By single crystal X-ray analysis, the atomic structure of the crystals of [Eu(NO₃)₃(HMPA)₃] complex (HMPA is hexamethylphosphorotriamide) possessing intense triboluminescence is determined. Symmetry of centrosymmetrical crystals is monoclinic: a = 13.785(1) Å, b = 19.746(2) Å, c = 14.723(1) Å, β= 102.143(2)°, P2₁/n space group, Z = 4, d _x = 1.484 g/cm³. The crystal structure is represented by separate C₁₈H₅₄EuN₁₂O₁₂P₃ complexes linked by van der Waals interactions with pronounced cleavage planes. The coordination polyhedron of Eu(III) atom reflects the state of distorted square antiprism. The possible causes of spectral differences in the Stark structure of photo- and triboluminescence are discussed.     

Photochemical behavior of levofloxacin

The effect of intermolecular proton transfer on the spectral properties of levofloxacin in the ground and excited electronic states was studied. The preferred direction of possible protolytic reactions induced by UV irradiation in this compound was studied. It was found that the proton transfer processes have a considerable effect on the capability of the compound to emit light and occur on the nanosecond time scale.     

Acid–Base Properties of 3-Benzazolylcoumarins and Their Imino Analogs

The acid–base equilibria of 3-(N-methyl-2-benzimidazolyl)coumarins and imino chromenes were studied in aqueous ethanol. The major reason for the difference in their proton-acceptor capacity relative to their nonmethylated analogs lies in a loss of planarity of these molecules. The tautomerism of 7-hydroxy-2-iminochromene is discussed.     

Synthesis, Structure, and Reversible Thermochromism of Guanidinium Hexabromotellurate(IV)

Guanidinium hexabromotellurate(IV), C₂H₁₂N₆TeBr₆, has been synthesized and characterized by element analysis and diffuse reflectance spectroscopy. Its crystal structure has been determined (R=0.027). The complex is built from layers of [TeBr₆]^2– anions and [CH₅N₃H]⁺ cations linked by N–H...Br hydrogen bonds and united by van der Waals interactions into a 3D framework. The electronic factors governing the spectral behavior of the complexes at 100 and 300 K are discussed, and reversible thermochromism has been revealed.