On the Whitney-Mahowald theorem concerning the normal numbers of smooth embeddings

It is shown that for a smooth, closed, nonorientable manifold of even dimensionality greater than two, every integer satisfying the Whitney-Mahowald condition is realized as the normal number of some embedding of that manifold in Euclidean space of twice the dimensionality; several corollaries are deduced from this result.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 91–97, January, 1969.The author is deeply grateful to V. A. Rokhlin for stating the problem and offering valuable suggestions.     

Normal numbers of piecewise-linear manifolds

A definition is given of the normal class of the immersion of a closed piecewise-linear manifold in a piecewise-linear manifold. It is shown that this number is zero for the immersion of an orientable manifold in euclidean space of any dimension. A complete investigation is carried out of normal classes of piecewise-smooth immersions of nonorientable manifolds in a euclidean space with dimension twice that of the manifolds.Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 575–583, May, 1971.     

Enhanced Li Adsorption and Diffusion in Single‐Walled Silicon Nanotubes: An ab Initio Study

We report a first‐principles investigation of Li adsorption and diffusion in single‐walled Si nanotubes (SWSiNTs) of interest to Li‐ion battery anodes. We calculate Li insertion characteristics in SWSiNTs and compare them with the respective ones in carbon nanotubes (CNTs) and other silicon nanostructures. From our calculations, SWSiNTs show higher reactivity toward the adsorption of Li adatoms than CNTs and Si nanoclusters. Considering the importance of Li kinetics, we demonstrate that the interior of SWSiNTs may serve as a fast Li diffusion channel. The important advantage of SWSiNTs over their carbon analogues is a sevenfold reduction in the energy barrier for the penetration of the Li atoms into the nanotube interior through the sidewalls. This prepossesses easier Li diffusion inside the tube and subsequent utilization of the interior sites, which enhances Li storage capacity of the system. The improvements in both Li uptake and Li mobility over their analogues support the great potential of SWSiNTs as Li‐ion battery anodes.     

Formation of linear polyenes in poly(vinyl alcohol) films catalyzed by phosphotungstic acid,aluminum chloride,and hydrochloric acid

Formation of linear polyenes–(CH=CH)_n–via acid-catalyzed thermal dehydration of polyvinyl alcohol in 9- to 40-µm-thick films of this polymer containing hydrochloric acid, aluminum chloride, and phosphotungstic acid as dehydration catalysts was studied by electronic absorption spectroscopy. The concentration of long-chain (n ≥ 8) polyenes in films containing phosphotungstic acid is found to monotonically increase with the duration of thermal treatment of films, although the kinetics of this process is independent of film thickness. In films containing hydrochloric acid and aluminum chloride, the formation rate of polyenes with n ≥ 8 rapidly drops as film thickness decreases and the annealing time increases. As a result, at a film thickness of less than 10–12 µm, long-chain polyenes are not formed at all in these films no matter how long thermal duration is. The reason for this behavior is that hydrochloric acid catalyzing polymer dehydration in these films evaporates from the films during thermal treatment, the evaporation rate inversely depending on film thickness.     

Optical and Energetic Properties of the Tl4CdI6 Crystal

Optics and Spectroscopy - The band spectrum and density of states of the Tl4CdI6 crystal have been investigated. Based on theoretical calculations, the electron and hole effective masses have been...     

Calorimetric study of thermal decomposition of lithium hexafluorophosphate

Enthalpy of formation of lithium hexafluorophosphate was calculated based on the differential scanning calorimetry study of heat capacity and thermal decomposition. It was found that thermal decomposition of LiPF₆ proceeds at normal pressure in the temperature range 450-550 K. Enthalpy of LiPF₆ decomposition is Δ_d H(LiPF₆, c, 298.15 K)= 84.27±1.34 kJ mole^-1. Enthalpy of formation of lithium hexafluorophosphate from elements in standard state is Δ_f H ⁰(LiPF₆,c, 298.15 K) = -2296±3 kJ mol^-1. This revised version was published online in July 2006 with corrections to the Cover Date.