Pseudo-Strong Regularity Around a Set

A generalization of strong regularity around a vertex subset C of a graph Γ, which makes sense even if Γis non-regular, is studied. Such a structure appears, together with a kind of distance-regularity around C , when an spectral bound concerning the so-called predistance polynomial of C is attained. As a main consequence of these results, it is shown that a regular (connected) graph Γwith d + 1 distinct eigenvalues is distance-regular, and its distance- d graph Γ d is strongly regular with parameters a = c , if and only if the number of vertices at distance d from each vertex satisfies an expression which depends only on the order of Γand the different eigenvalues of Γ.     

Electron-transfer kinetics and activation barriers for the reductions of nitrosonium and nitronium ions in aprotic solvents

Using the cyclic voltammetry (CV), the electron-transfer kinetics for the reductions of NO⁺ and NO₂⁺ cations have been studied at the Pt electrode in nitromethane, sulfolane, and propylene carbonate. The heterogeneous rate constants have been determined by two independent procedures from the transfer coefficient α, the diffusion coefficient D, from a detailed examination of the CV-peak separations, and from an inspection of the values of the cathodic peak potentials at different scan rates. The results have been compared to those reported in the literature, and discussed. In the classical model, outer-sphere electron-transfer reactions are considered subject to an activation energy arising from solvent reorganization and bond reorganization processes. The solvent and molecular reorganizational barriers for these electroreductions have been assessed in aprotic media. The Marcus-Hush theory has been applied to the self-exchange reactions of the NO₂⁺/NO₂ and NO⁺/NO couples in an attempt to predict the rate of electron transfer. The findings indicate some improvement between theory and experiment. However, it should be noted that the experimental values of k_s found for the NO₂⁺ reduction in the solvents used are still too high in comparison with those determined theoretically. In view of the fairly strong coordination of the solvent molecule(s) as ligand(s) to NO₂⁺ and NO⁺ cations, we believe that such discrepancies should stem, to some extent, from the involvement of an inner-sphere pathway by generation of an activated complex on the surface of the Pt electrode. © 1993 John Wiley & Sons, Inc.     

Chemical composition and reaction analysis of single aerosol particles

In situ measurements of gas-liquid surface reactions of single aerosol microdroplets are presented. By means of optical levitation in combination with elastic (Mie) and inelastic (Raman) light scattering it is possible to get information on the chemistry of e.g. acid/base reactions as well as the physical behavior of single microparticles.     

Selective saturation and inversion of multiple resonances in high-resolution solid-state 13C experiments using slow spinning CP/MAS and tailored DANTE pulse sequences.

Taking advantage of the long 13C T1 values generally encountered in solids, selective saturation and inversion of more than one resonance in 13C CP/MAS experiments can be achieved by sequentially applying several DANTE pulse sequences centered at different transmitter frequency offsets. A new selective saturation pulse sequence is introduced composed of a series of 90 degrees DANTE sequences separated by interrupted decoupling periods during which the selected resonance is destroyed. Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described. The determination of the aromaticity of coal using a relatively slow MAS rate is also described.     

Magnetic resonance imaging: a new window into industrial processing.

Although the most important use of nuclear magnetic resonance imaging (MRI) continues to be for diagnostic medicine, recognition is being gained for many nonmedical applications. Examples include the following areas: petrogeology, food, agriculture, polymers and polymer-composites, and pharmaceuticals. These areas all involve studies of species that have short spin-spin relaxation times, and consequently need far fast gradient switching. These technical details are discussed and typical applications given.     

A Primitive Non-symmetric 3-Class Association Scheme on 36 Elements with p11 = 0 Exists and is Unique

In this paper we construct a primitive, non-symmetric 3-class association scheme with parameters v = 36, v₁ = 7, p¹₁₁ = 0 and p²₁₁ = 4 and show that such a scheme is determined by its parameters.     

Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices

TheSU(2) rotation matricesD ^(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD ^(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.     

Silver nitrate-acetonitrile and iodine-benzene complexes as studied by NMR in thermotropic liquid crystals

Silver nitrate-acetonitrile and π iodine-benzene complexes in thermotropic liquid crystals have been studied by ¹H, ²H, and ¹³C NMR spectroscopy and by optical microscopy. Evidence for at least two silver complexes in each liquid crystal is presented.     

On the existence of <Emphasis Type="Bold">1, 3</Emphasis>P <Emphasis Type="Bold">o</Emphasis> resonances in H<Superscript>-</Superscript> between n = 2 and 3 H thresholds

We examine the influence of relativistic and QED effects on the existence of the ^1,3P ^o H^- resonances between n = 2 and 3 hydrogen thresholds, the relativistic and QED corrections and the coupling effects between the high singlet and triplet states are considered as first-order perturbations. We firstly obtain accurate non-relativistic resonant energies and widths of fifteen ¹P ^o resonances, and fifteen ³P ^o resonances. The fifteen ¹P ^o resonances are classified to be ₃ (2, 0) ^- _n ( 4 ? n ? 12) and ₃ (1, 1) ⁺ _n ( 3 ? n ? 8). The fifteen ³P ^o resonances are classified to be ₃ (2, 0) ⁺ _n ( 3 ? n ? 12) and ₃ (1, 1) ^- _n ( 4 ? n ? 8). We found there exist six Feshbach resonances for ₃ (2, 0) ^- _n (¹P ^o ) series, four Feshbach resonances for ₃ (1, 1) ⁺ _n (¹P ^o ) series, seven Feshbach resonances for ₃ (2, 0) ⁺ _n (³P ^o ) series, and three Feshbach resonances for ₃ (1, 1) ^- _n (¹P ^o ) series. Received 22 February 2002 Published online 24 September 2002