Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.     

Theoretical study of single-electron capture in He2+ —H− collision

We present a detailed theoretical treatment of single-electron transfer between He²⁺ and H^?. The total cross section is calculated using stationary molecular states which are appropriate in the energy range covered by the experiments (between 0.5 and 2250 eV in the centre of mass frame). We use an expansion on a two-electron basis built with one-electron diatomic molecule (OEDM) orbitals and including the common translation factor of Errea et al. All coupling terms are calculated explicitly. Because of the small binding energy of H^? compared to that of the ground state of He⁺, capture occurs into highly excited states of He⁺. Results obtained with a straight-line quasiclassical calculation are in good agreement with the experimental data. At low energy, He⁺ (n=5) +H(1s) is the dominant capture channel; at higher energy, the He⁺ (n=4) + H(1s) channel becomes important. The rise in the cross section below 6 eV can be attributed to the Coulomb attraction in the incoming channel. To account for this effect, a fully quantal calculation has been performed. The agreement with the low-energy measurements is then excellent.     

Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces

Statistical Inference for Stochastic Processes - This paper deals with the weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions...     

Decomposition of triacetone triperoxide is an entropic explosion

Both X-ray crystallography and electronic structure calculations using the cc-pVDZ basis set at the DFT B3LYP level were employed to study the explosive properties of triacetone triperoxide (TATP) and diacetone diperoxide (DADP). The thermal decomposition pathway of TATP was investigated by a series of calculations that identified transition states, intermediates, and the final products. Counterintuitively, these calculations predict that the explosion of TATP is not a thermochemically highly favored event. It rather involves entropy burst, which is the result of formation of one ozone and three acetone molecules from every molecule of TATP in the solid state.     

Theoretical treatment of multiple site reactivity in large molecules

The method of electrostatic potentials is generalized via a double perturbation theory to describe the simultaneous attack of a large molecule by two or more charged species. The interaction term is found to reproduce accurately the full “super-molecule” calculation. The scheme is illustrated by treating the diprotonation of adenine and N7-methyladenine. For adenine, the most stable diprotonated species is found to be the N1, N7 combination, while the N3, N9 couple is predicted for the N7 substituted derivative if N3 is the first protonation site.     

A flexible docking procedure for the exploration of peptide binding selectivity to known structures and homology models of PDZ domains

PDZ domains are important scaffolding modules that typically bind to the C-termini of their interaction partners. Several structures of such complexes have been solved, revealing a conserved binding site in the PDZ domain and an extended conformation of the bound peptide. A compendium of information regarding PDZ complexes demonstrates that dissimilar C-terminal peptides bind to the same PDZ domain, and different PDZ domains can bind the same peptides. A detailed understanding of the PDZ-peptide recognition is needed to elucidate this complexity. To this end, we have designed a family of docking protocols for PDZ domains (termed PDZ-DocScheme) that is based on simulated annealing molecular dynamics and rotamer optimization, and is applicable to the docking of long peptides (20-40 rotatable bonds) to both known PDZ structures and to the more complicated problem of homology models of these domains. The resulting protocol reproduces the structures of PDZ complexes with peptides 4-8 amino acids long within 1-2 A from the experimental structure when the docking is performed to the original structure. If the structure of the target PDZ domain is an apo structure or a homology model, the docking protocol yields structures within 3 A in 9 out of 12 test cases. The automated docking procedure PDZ-DocScheme can serve in the generation of a structural context for validation of PDZ domain specificity from mutagenesis and ligand binding data.     

Effect of scale and surface chemistry on the mechanical properties of carbon nanotubes‐based composites

In this article, Multi‐Walled Carbon Nanotubes (MWCNTs) of varying diameters, both untreated and polycarboxylated, were dispersed at constant weight percentage in an epoxy matrix, and resulting fracture toughnesses (K_Ic) were measured in each case. We show that changing the MWCNT diameter has two effects on the composite fracture toughness: (i) a small MWCNT diameter enables larger interfacial surface for adhesion maximization, which increases toughness; (ii) at the same time, it limits the available pull‐out energy and reduces the MWCNT ability to homogeneously disperse in the matrix due to this same large active surface: this decreases toughness. Most commercially available MWCNTs have a length range of several μm, thus an optimal diameter exists which depends on MWCNT wall thickness and surface treatment. Such optimal diameter maximizes pull‐out energy and thus composite fracture toughness. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012