Fold‐2‐covering triangular embeddings

For a graph G and a positive integer m, G_(m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m² edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G_(m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G_(m) does triangulate a surface, and in fact does so as a “covering with folds” of the original triangulation. For m = 5, this would be a consequence of Tutte's 5‐Flow Conjecture. In this work, we investigate the case m = 2 and describe simple classes of triangulations G for which G₍₂₎ does have a triangulation that covers G “with folds,” as well as providing a simple infinite class of triangulations G of the sphere for which G₍₂₎ does not triangulate any surface. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 79–92, 2003     

Structure and properties of potassium titanyl phosphate single crystals with 7 and 11 at. % Nb

This study is a continuation of research into the atomic structure and physical properties of niobium-doped potassium titanyl phosphate crystals, KTiOPO₄ (KTP: Nb). Crystals containing 7 and 11 at. % of niobium were grown and studied. With an increase in niobium content, the number of vacancies and additional potassium positions in the structure also increase. This fact accounts for an increase in both the intensities of relaxation peaks and the conductivity of KTP: Nb crystals.     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

Photoinduced intramolecular electron-transfer reactions in carbazole-fullerene and phenothiazine-fullerene linked compounds in benzene and benzonitrile as studied by fluorescence, transient absorption, time-resolved EPR, and magnetic field effects

Photoinduced intramolecular electron-transfer reactions in carbazole (Cz)-fullerene (C₆₀) (Cz(8)C₆₀) and phenothiazine (Ph)-C₆₀ (Ph(n)C₆₀ (n=8, 10, 12)) linked compounds have been investigated in benzene and benzonitrile by fluorescence, transient absorption, and time-resolved electron paramagnetic resonance measurements, and by magnetic field effects on the decay rate constants of the photogenerated biradicals. In benzonitrile, photoinduced intramolecular electron transfer from Cz to the singlet excited state of C₆₀ (¹C₆₀ ^*) occurred in Cz(8)C₆₀, but not to the triplet excited state (³C₆₀ ^*), while the intramolecular electron-transfer to both¹C₆₀ ^* and³C₆₀ ^* occurred in Ph(n)C₆₀ (n=8, 10, 12). In benzene, on the other hand, no electron transfer to both¹C₆₀ ^* and³C₆₀ ^* took place in all linked compounds. These results were interpreted in terms of the different Gibbs free energy changes in the two solvents.     

Hutchinson's shear coefficient for anisotropic beams

Timoshenko's theory of vibrating beams requires a shear correction factor to correctly take into account the effects of shear deformation for different beam cross-sections. This correction is crucial for a precise determination of the shear modulus from the resonant frequencies. Hutchinson's beam theory is used to derive a new shear correction coefficient for anisotropic materials. A comparison is made with other shear coefficients for anisotropic materials published in the literature. Computer-simulated spectra are used to validate the new anisotropic shear correction coefficient.     

Vector coupled-wave method for analyzing diffraction by multilayer gratings

In the framework of the matrix formulation of the coupled plane wave approach, a method is proposed for increasing the stability of the numerical analysis of vector electromagnetic fields in periodic structures, including dielectric and metallic anisotropic layers and relief boundaries.     

Ion source with a cold magnetron cathode and magnetic plasma compression

The operating principles, design, and characteristics of an ion source with a cold magnetron cathode and magnetic plasma compression are described. The source is intended for the injector of a linear proton accelerator.     

Calculation of the vibrational spectra of copper crystals with vacancies

The local vibrational spectra of copper crystals containing vacancies are calculated using the pair atomic potential derived in the framework of the resonance pseudopotential theory. The calculations are performed by a recursive method with due regard for the symmetry of the defect region. The frequencies of the vacancy-induced resonance vibrations of different symmetries are determined.     

Transition flow of rarefied gases: Current models and methods of simulation

Transition (molecular-viscous) isothermal channel flow of rarefied gases is considered. Present-day engineering physical models of transition gas flow and methods of simulation are analyzed and verified in terms of the kinetic theory on the micro-and macrolevels.