New Solutions to Einstein's Equations in the Taub Universe and Their Accelerating Stage

Following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe.     

Density-based Globally Convergent Trust-region Methods for Self-consistent Field Electronic Structure Calculations

A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix and the rank constraint, coincides with the fixed-point iteration. We prove that the global minimization of this quadratic model subject to the restrictions and smaller trust regions corresponds to the solution of level-shifted equations. The precise implementation of algorithms leading to global convergence is stated and a proof of global convergence is provided. Numerical experiments confirm theoretical predictions and practical convergence is obtained for difficult cases, even if their geometries are highly distorted. The reduction of the trust region is performed by a strategy that uses the structure of the energy function providing the algorithm with a nice practical behavior. This framework may be applied to any problem with idempotency constraints and for which the derivative of the objective function is a symmetric matrix. Therefore, application to calculations based both on Hartree–Fock or Kohn–Sham density functional theory are straightforward.     

Kinetics and mechanisms of the reactions of 3-methoxyphenyl, 3-chlorophenyl, and 4-cyanophenyl 4-nitrophenyl thionocarbonates with alicyclic amines

The reactions of 3-methoxyphenyl, 3-chlorophenyl, and 4-cyanophenyl 4-nitrophenyl thionocarbonates (1, 2, and 3, respectively) with a series of secondary alicyclic amines are studied kinetically in 44 wt % ethanol-water at 25.0 degrees C and an ionic strength of 0.2 M (KCl). Pseudo-first-order rate coefficients (k(obsd)) are obtained for all reactions (amine excess was used). The reactions of compound 1 with piperidine, piperazine, and 1-(2-hydroxyethyl)piperazine and of compounds 2 and 3 with these amines and morpholine exhibit linear k(obsd) versus amine concentration plots with slopes (k1) independent of pH. In contrast, the plots are nonlinear upward for the reactions of substrate 1 with morpholine, 1-formylpiperazine, and piperazinium ion and of substrates 2 and 3 with the two latter amines. For all these reactions, a reaction scheme is proposed with a zwitterionic tetrahedral intermediate (T+/-), which can be deprotonated by an amine to yield an anionic intermediate (T-). When the nonlinear plots are fit through an equation derived from the scheme, rate and equilibrium microcoefficients are obtained. The Br?nsted-type plots for k1 are linear with slopes of beta1 = 0.22, 0.20, and 0.24 for the aminolysis of 1, 2, and 3, respectively, indicating that the formation of T+/- (k1 step) is rate-determining. The k1 values for these reactions follow the sequence 3 > 2 > 1, which can be explained by the sequence of the electron-withdrawing effects from the substituents on the nonleaving group of the substrates.     

Narrow (n,m)-distribution of single-walled carbon nanotubes grown using a solid supported catalyst

Unusually structure-selective growth of single-walled carbon nanotubes (SWNTs) has been attained using a CVD method with a solid supported catalyst. In this method, CO feedstock disproportionates on silica-supported catalytic nanoclusters of Co that are formed in situ from mixed salts of Co and Mo. The nanotube products are analyzed by spectrofluorimetry to reveal distributions resolved at the level of individual (n,m) structures. Two structures, (6,5) and (7,5), together dominate the semiconducting nanotube distribution and comprise more than one-half of that population. The average diameter of produced SWNTs is only 0.81 nm, and a strong propensity is found favoring chiral angles near the armchair limit.     

The important role of crystallinity and amylose ratio in thermal stability of starches

Journal of Thermal Analysis and Calorimetry - The thermal features of potato, banana, corn and cassava starches were correlated with structural properties. These starches were characterized by SEM,...