The molecular Hamiltonian in internal coordinates

A systematic approach for the derivation of the exact translational–rovibronic (non-relativistic) Hamiltonian for a polyatomic molecule consisting of N nuclei and n electrons is presented. All coupling terms which contribute to the total energy are identified. The Hamiltonian is greatly simplified by taking the internal coordinates (bond lengths and bond angles) as the vibrational variables. The translational–rovibronic Hamiltonian of triatomic molecules are considered as an application for this general formulation.     

Weak Module Amenability for Semigroup Algebras

We study the weak module amenability of Banach algebras which are Banach module over another Banach algebra with compatible actions. As an example we show that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over the semigroup algebra of its subsemigroup of idempotents.     

On the identifiability of multivariate survival distribution functions

Let (T₁, T₂) be a non-negative random vector which is subjected to censoring random intervals [X₁, Y₁] and [X₂, Y₂]. The censoring mechanism is such that the available informations on T₁ and T₂ are expressed by a pair of random vectors W=(W₁, W₂) and δ=(δ₁, δ₂), where W_i=max(min(Y_i, T_i), X_i) and In this paper we will show that under some mild conditions the joint survival function of T₁ and T₂ can be expressed uniquely as functional of observable joint survival functions. Our results extend recent works on the randomly right censored bivariate data case and on the univariate problem with double censoring to the bivariate data with double censoring.     

Onk-order harmonic new better than used in expectation distributions

Summary Definitions ofk-HNBUE andK-HNWUE are introduced and the relationship with other class of life distributions is studied. Various closure properties ofk-HNBUE (k-HNWUE) are proved. Finally bounds on the moments and survival function ofk-HNBUE (k-HNWUE) are given. This research was supported by the ONR Grant N00014-78-C-0655.     

Coproducts in the Category <Emphasis Type="Bold">M</Emphasis>κ<Emphasis Type="Bold">Frm</Emphasis>

The purpose of this paper is to study coproducts in the category MFrm (resp. M_cFrm), of metric -frames and uniform (resp. contractive) -frame maps. First, by applying the same technic that was used to find coproducts in Frm, we construct coproducts in the category Frm of -frames and -frame maps. Then, we define a metric diameter on the coproduct in Frm of a family of metric -frames and show that coproduct in Frm preserves metrizability.Mathematics Subject Classifications (2000) 06B23, 06D22, 18A30.     

Relative reactivities of amino and ethenyl groups in allylamine on Si(100)2 × 1: Temperature-dependent X-ray photoemission and thermal desorption studies of a common linker molecule

The room-temperature adsorption and thermal evolution of allylamine on Si(100)2 × 1 have been investigated by using temperature-dependent X-ray photoelectron spectroscopy (XPS) and thermal desorption spectrometry (TDS). The presence of a broad N 1 s feature at 398.9 eV, attributed to a N―Si bond, indicates N―H dissociative adsorption. On the other hand, the presence of C 1 s features at 284.6 eV and 286.2 eV, corresponding to C═C and C―N, respectively, and the absence of the Si―C feature expected at 283.2 eV shows that [2 + 2] C═C cycloaddition does not occur at room temperature. These XPS data are consistent with the unidentate staggered and eclipsed allylamine conformer adstructures arising from N―H dissociation and not [2 + 2] C═C cycloaddition. The apparent conversion of the N 1 s feature for Si―N(H)―C

at 398.9 eV to that for Si―N(H) at 397.7 eV and the total depletion of C 1 s feature for C―N at 286.2 eV near 740 K indicates cleavage of the C―N bond, leaving behind a Si―N(H) radical. Furthermore, the C═C C 1 s feature at 284.6 eV undergoes steep intensity reduction between 740 K and 825 K, above which a new C 1 s feature at 283.2 eV corresponding to SiC is found to emerge. These spectral changes suggest total dissociation of the ethenyl fragment and the formation of SiC. Moreover, while the total N 1 s intensity undergoes a minor reduction (24%) upon annealing up to 1090 K, a considerable reduction (43%) is found in the overall C 1 s intensity. This observation is consistent with our TDS data, which shows the desorption of C-containing molecules including propene and ethylene at 580 K and of acetylene at 700 K. The lack of N-containing desorbates suggests that the dissociated N species are likely bonded to multiple surface Si atoms or diffused into the bulk. Interestingly, both the staggered and eclipsed N―H dissociative adstructures are found to have a less negative adsorption energy than the [N, C, C] tridentate or the [2 + 2] C═C cycloaddition adstructures by our DFT calculations, which suggests that the observed formation of N―H dissociative adstructures is kinetically favored on the Si(100)2 × 1 surface.