Energetic Properties of Rocket Propellants Evaluated through the Computational Determination of Heats of Formation of Nitrogen‐Rich Compounds

The use of ab initio and DFT methods to calculate the enthalpies of formation of solid ionic compounds is described. The results obtained from the calculations are then compared with those from experimental measurements on nitrogen‐rich salts of the 2,2‐dimethyltriazanium cation (DMTZ) synthesized in our laboratory and on other nitrogen‐rich ionic compounds. The importance of calculating accurate volumes and lattice enthalpies for the determination of heats of formation is also discussed. Furthermore, the crystal structure and hydrogen‐bonding networks of the nitroformate salt of the DMTZ cation is described in detail. Lastly, the theoretical heats of formation were used to calculate the specific impulses (I_sp) of the salts of the DMTZ cation in view of a prospective application in propellant formulations.     

Effect of the solvent on the equilibria of acid-base indicators in aprotic and amphiprotic solvents

The dissociation constants of a series of indicators inN,N-dimethylformamide medium have been determined, and compared with those for the indicators in other aprotic solvents (dimethylsulphoxide and acetonitrile) and in some amphiprotic solvents (water, methanol, ethanol, propan-2-ol and tertbutanol). The effect of the solvent characteristics on the pK values have been evaluated, and the pK + p _ws ^t (H⁺) values shown to be linearly correlated with the Dimroth and ReichardtE _T ^N and acceptor number solvatochromic parameters.     

On Towers Approximating Homological Localizations

Our object of study is the natural tower which, for any givenmap f:AB and each space X, starts with the localization of Xwith respect to f and converges to X itself. These towers canbe used to produce approximations to localization with respectto any generalized homology theory E_*, yielding, for example,an analogue of Quillen's plus-construction for E_*. We discussin detail the case of ordinary homology with coefficients inZ/p or Z[1/p]. Our main tool is a comparison theorem for nullificationfunctors (that is, localizations with respect to maps of theform f:Apt), which allows us, among other things, to generalizeNeisendorfer's observation that p-completion of simply-connectedspaces coincides with nullification with respect to a Moorespace M(Z[1/p], 1).     

Relative stability in alpha- and beta-Wells-Dawson heteropolyanions: a DFT study of [P2M18O62]n- (M = W and Mo) and [P2W15V3O62]n-

To determine the relative stability of alpha and beta rotational isomers of the Wells-Dawson structure, the energies of some fully oxidized, single- and 2-fold-reduced systems were calculated by means of DFT calculations. The thermodynamics of the alpha/beta equilibrium for P(2)M(18) Wells-Dawson anions is slightly shifted toward the alpha structure, but the difference in stability is smaller than in the Keggin anions. Tungstates (2:18) and vanadotungstates (2:3:15) show minimal redox differences between isomers, as the electronic structure of the frontier orbitals appears to be nearly the same. In addition, an alternative arrangement is proposed that have long and short Mo-O bonds in beta-P(2)Mo(18) with an idealized C(3) symmetry. This arrangement was computed to be about 8.2 kcal mol(-1) more stable than the nonalternate framework of C(3)(v)() symmetry. The P(2)Mo(18) is the Wells-Dawson anion for which the alpha/beta equilibrium most resembles that of the Keggin anions.     

Loss of regularity for supercritical nonlinear Schrödinger equations

We consider the nonlinear Schrödinger equation with defocusing, smooth, nonlinearity. Below the critical Sobolev regularity, it is known that the Cauchy problem is ill-posed. We show that this is even worse, namely that there is a loss of regularity, in the spirit of the result due to G. Lebeau in the case of the wave equation. As a consequence, the Cauchy problem for energy-supercritical equations is not well-posed in the sense of Hadamard. We reduce the problem to a supercritical WKB analysis. For super-cubic, smooth nonlinearity, this analysis is new, and relies on the introduction of a modulated energy functional à la Brenier.     

Purification of Uranium‐based Endohedral Metallofullerenes (EMFs) by Selective Supramolecular Encapsulation and Release

Supramolecular nanocapsule 1 ?(BArF)₈ is able to sequentially and selectively entrap recently discovered U₂@C₈₀ and unprecedented Sc₂CU@C₈₀, simply by soaking crystals of 1 ?(BArF)₈ in a toluene solution of arc‐produced soot. These species, selectively and stepwise absorbed by 1 ?(BArF)₈, are easily released, obtaining highly pure fractions of U₂@C₈₀ and Sc₂CU@C₈₀ in one step. Sc₂CU@C₈₀ represents the first example of a mixed metal actinide‐based endohedral metallofullerene (EMF). Remarkably, the host–guest studies revealed that 1 ?(BArF)₈ is able to discriminate EMFs with the same carbon cage but with different encapsulated cluster and computational studies provide support for these observations.     

Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems

This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type.     

Stable sets and max-convex decompositions of TU games

We study under which conditions the core of a game involved in a max-convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas’ five player game with a unique stable set different from the core, are reckoning and analyzed.