The mass spectra of 1- and 2-alkylbenzotriazoles

The fragmentation patterns of a series of 1- and 2-alkylbenzotriazoles are recorded and interpreted in comparison with available literature data. 1- and 2-Substituted benzotriazoles are readily differentiated on the basis of the relative ease with which a 1-substituted isomer loses nitrogen compared with the corresponding 2-isomer, resulting in generally weak parent ions for the former and strong parent ions for the latter. This loss of nitrogen in the 1-isomer ultimately gives rise to a strong peak at m/z 104, which is small or absent in the 2-isomer. In addition, examination of the intensity and distribution of peaks clustered around m/z 118 reveals that weak signals with a maximum intensity at m/z 117 or 118 are indicative of the 1-isomers, while strong signals with a maximum intensity at 119 or 120 are typical of the 2-isomers. Thus, isomers are distinguished by analysis of mass spectral cracking patterns. © 1997 John Wiley & Sons, Inc. Heteroatom Chem. 8: 459–464, 1997     

An Algebraic Structure of Orthogonal Wavelet Space

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parameterization of wavelet space, one can define a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus gto the (g−1) dimensional real torus (the products of unit circles). By the uniqueness and exactness of factorization, this mapping is well defined and one-to-one. Thus we can equip the rank 2 orthogonal wavelet space with an algebraic structure of the torus. Because of the degenerate phenomenon of the paraunitary matrix, the parameterization map is not onto. However, there exists an onto mapping from the torus to the closure of the wavelet space. And with such mapping, a more complete parameterization is obtained. By utilizing the factorization theory, we present a fast implementation of discrete wavelet transform (DWT). In general, the computational complexity of a rank morthogonal DWT is O(m²g). In this paper we start with a given scaling filter and construct additional (m−1) wavelet filters so that the DWT can be implemented in O(mg). With a fixed scaling filter, the approximation order, the orthogonality, and the smoothness remain unchanged; thus our fast DWT implementation is quite general.     

Ensemble Effects on Methanol Oxidation to Formaldehyde on Ferric Molybdate Catalysts

The properties of Mo-doped iron oxide are compared with those of the single oxides of Fe and Mo, and with stoichiometric ferric molybdate for the selective oxidation of methanol. It is found that Mo oxide segregates to the surface of the iron oxide at low loadings, while at higher loadings, but below the stoichiometric ratio, presents layers of ferric molybdate at the surface. The relationship between bulk loading and surface Mo is explored, and it is concluded that the reactivity is dominated by ensemble effects. Simple modelling indicates that four or more Fe cation ensembles are required to combust methanol to CO₂, ensembles of two Mo cations are required for selective oxidation to formaldehyde, whereas it seems that isolated single sites of either Fe or Mo produce CO.