Ab initio modelling of crosslinking in polymers. A case of chains with furan rings

A quantum chemical model (Abinitio HF-MO and DFT-B3LYP) of polyfurfuryl alcohol crosslinking is shown. Two pathways were considered: (a) a Diels–Alder (D–A) reaction between a dihydrofuran moiety and a furan ring; (b) the addition reaction of electrophilic specimens on conjugated double bonds. The ability for the formation of D–A adducts (dienes and dienophiles) was investigated by the frontier molecular orbital (FMO) theory. Energy gaps between the FMO's of diene and dienophile structures suggest that the occurrence of the D–A reaction is possible. The results suggest that the carbons of the exo double bonds attached to dihydrofuran rings are the sites most likely to be attacked by electrophilic species, while the C₃ and C₄ atoms display the opposite tendency due to their low HOMO electron densities. Results of a thermochemical approach to these reactions at the MP2 level was in agreement with reactivity modelled by MO predictions.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Cosmological models in the scalar-tetradic theory B

We present two methods for solving the cosmological equations of the scalar-tetradic theory B [19] when a Friedmann-Robertson-Walker (FRW) geometry is assumed. Among the many solutions found there are several physically meaningful ones including inflationary universe solutions.     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.     

Boundaries for algebras of holomorphic functions

Let A_u(B_G) be the Banach algebra of all complex valued functions defined on the closed unit ball B_G of a complex Banach space G which are uniformly continuous on B_G and holomorphic in the interior of B_G, endowed with the sup norm. A characterization of the boundaries for A_u(B_G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A_u(B_G) is also proved.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

C D : a computer program to generate 1D, 2D and 3D grids of functions dependent on the molecular ab initio electron density

A program to compute many functions dependent on the electron density ρ(r) from the results of ab initio molecular calculations is presented. The program allows the generation of different one-, two-, and three-dimensional grids for further graphical representation or numerical analysis. Other options like extracting separate atom contributions to the function computed or locating maximum and minimum values are also implemented. A number of illustrative applications regarding different ρ(r)-dependent functions are presented and the performance and portability of the program is discussed.     

Textural changes during CO2 activation of chars: A fractal approach

In this paper two series of active carbons obtained at different flow rates of the activating agent, CO₂, are characterized in order to establish the different mechanisms of pore development during the activation step. This study complements previous works on textural development during the different steps in the process of obtaining active carbons: coal oxidation, coal pyrolysis and char gasification. As the characteristics of the original and intermediate materials are of capital importance in the pore development of active carbons, the properties of the active carbons, precursor chars and coals were considered and analyzed together. Mercury porosimetry and helium picnometry were used to determine classical textural parameters as well as to perform a more detailed study of the pore volume generation during the different conditions of the activation step. Data obtained from the mercury porosimetry determinations was also employed for fractal determinations according to the methodologies proposed by Friesen and Mikula, Zhang and Li and the procedure of Neimark. Average surface fractal dimensions as well as fractal profiles and local surface fractal dimensions were calculated. The use of different flow rates during the activation step produces changes not only in the ordinary textural parameters but also in the fractal characteristics of the active carbons. Activation at higher flow rates leads to smoother fractal profiles and also to lower values of the average surface fractal dimensions of the active carbons.