The Bailey chain and mock theta functions

Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain classical mock theta functions.Comment: 17 pages, to appear in Advances in Mathematic

Cycloaddition Reactions of 1,3-Cyclohexadiene on the Silicon(001) Surface

[2+2] and [4+2] cycloaddition reactions of 1,3-cyclohexadiene on the Si(001) surface were studied. It is shown that not only the [4+2] cycloaddition reaction but also the [2+2] cycloadditions can occur on the Si(001) surface. Surface isomerization reactions connecting [4+2] and [2+2] are very unlikely due to a high energy barrier, implying that the surface reactions are kinetically controlled. Therefore the final surface reaction products are determined during the initial stage of the reactions in contrast with earlier assumptions that the “product distribution is thermodynamically determined”. Our interpretations are consistent with the new experimental results by the Hamers group. According to our CASSCF(6,6) calculations, the nonsymmetric π-complex transition states along the [2+2] cycloaddition mechanism, which has been suggested by many theoretical studies, seem to be an artifact. Nevertheless, the very soft Si dimer buckling motion of the Si(001) surface certainly facilitates the [2+2] reaction

Cycloaddition Isomerizations of Adsorbed 1,3-Cyclohexadiene on Si(100)-2×1 Surface: First Neighbor Interactions

The initial and subsequent surface reaction mechanisms of 1,3-cyclohexadiene on the Si(100)-2×1 surface were theoretically explored, focusing on the possible first-neighbor interactions. Five different initial reaction channels leading to nine different surface products were identified, confirming previous experimental reports of inter-dimer structures. Among the nine identified products, five of these surface products are new species that have not previously been reported. Potential energy surface studies reveal that the net reaction barriers within a given channel are very small, indicating that the final product distributions within that channel are determined by thermodynamics. On the other hand, thermal isomerizations between different channels are not expected to occur easily. Therefore, the surface product distributions among the five different channels are more likely to be determined by kinetics. As a result, understanding the relationships among the available reaction channels both kinetically and thermodynamically is essential for properly interpreting the experimental results. The current study shows that the subsequent surface chemical reactions of unsaturated initial surface products are strongly coupled with the first-neighbor interactions

Comparative Study of Surface Cycloadditions of Ethylene and 2-Butene on the Si(100)-2 × 1 Surface

Multireference wave functions were used to study the ethylene and 2-butene surface reactions on Si(100) in their lowest energy singlet states. In addition to the diradical pathway, a π-complex pathway on the ethylene surface was found. The net barrier for the latter process is 4.5 kcal/mol higher than that for the former, making the π-complex pathway kinetically less accessible. Therefore, although there is a competition between the two initial channels, the diradical path is slightly favored, and rotational isomerization is possible. However, since the initial potential energy surfaces of the two channels are different, depending on experimental conditions, the branching ratio between the two channels may change. Consequently, the combined effects that would favor one channel over the other may not derive directly from the initial reaction barrier. This provides an explanation of the experimental controversy. As a result, the final distributions of surface products may depend on the experimental kinetic environment, especially when the population change due to the rotational isomerization is expected to be very small. A significantly different reaction channel is found in the 2-butene surface reaction on Si(100), in which a methyl hydrogen easily transfers to the surface yielding a new type of surface product other than the expected [2 + 2] cycloaddition product, with a comparatively small activation barrier. Consequently, the overall surface reactions of ethylene and 2-butene may be quite different. Therefore, direct comparisons between ethylene and 2-butene experimental results would be very useful

Adsorption of Water on the Si(100) Surface: An Ab Initio and QM/MM Cluster Study

The adsorption of water on the Si(100) surface is investigated using ab initio quantum chemical cluster calculations. A reaction profile is constructed using the multiconfigurational SCF method. The calculations demonstrate that the reactant should be described with a multireference wave function in order to obtain correct energetics, because it contains a bare dimer with significant diradical character. The system becomes almost single-configurational as water approaches the surface and forms a molecularly adsorbed intermediate. Therefore, except for the reactant, a single-configurational wave function seems to be sufficient for a correct description of the reaction. The adsorbed OH group in an isolated product can nearly freely rotate between the trans and gauche minima. Interactions between the OH groups and the dangling bonds are small and do not appear to change the OH orientation. However, the interdimer hydrogen bonding is stronger and forces the OH orientation to be perpendicular to the dimer bond. The free rotation of the OH group in an isolated dimer model and the hydrogen-bonding picture in an extended cluster model are consistent with the experimental finding for the OH orientation in the product. Si9H12, Si15H16, Si32H28, Si48H36, and Si64H44cluster models for the Si(100) surface are used, and the SIMOMM (surface integrated molecular orbital molecular mechanics) method is used effectively for these large cluster calculations. The SIMOMM and full quantum results are compared

The role of dexamethasone in peripheral and neuraxial nerve blocks for the management of acute pain

Dexamethasone has an emerging role as an additive in regional anaesthesia for the management of acute pain. However, outcomes in terms of improvement and prolongation of analgesia, as well as the methods of administration and potential adverse effects, have yet to be clarified. This semi-structured review examines the current literature available with regard to supplemental dexamethasone in regional and neuraxial anaesthesia.Keywords: adverse effects, analgesia, dexamethasone, dosage regimes, regional anaesthesi

On two 10th order mock theta identities

We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa