Carbene triel bonds between TrR3 (Tr = B,Al) and N-heterocyclic carbenes

The carbene triel bond is predicted and characterized by theoretical calculations. The C lone pair of N-heterocyclic carbenes (NHCs) is allowed to interact with the central triel atom of TrR₃ (Tr = B and Al; R = H, F, Cl, and Br). The ensuing bond is very strong, with an interaction energy of nearly 90 kcal/mol. Replacement of the C lone pair by that of either N or Si weakens the binding. The bond is strengthened by electron-withdrawing substituents on the triel atom, and the reverse occurs with substitution on the NHC. However, these effects do not strictly follow the typical pattern of F > Cl > Br. The TrR₃ molecule suffers a good deal of geometric deformation, requiring on the order of 30 kcal/mol, in forming the complex. The R(C···Tr) bond is quite short, for example, 1.6 Å for Tr = B, and shows other indications of at least a partially covalent bond, such as a high electron density at the bond critical point and a good deal of intermolecular charge transfer.     

Determination of total mercury in environmental and biological samples by flow injection cold vapour atomic absorption spectrometry

A simple and accurate method has been developed for the determination of total mercury in environmental and biological samples. The method utilises an off-line microwave digestion stage followed by analysis using a flow injection system with detection by cold vapour atomic absorption spectrometry.

The method has been validated using two certified reference materials (DORM-1 dogfish and MESS-2 estuarine sediment) and the results agreed well with the certified values. A detection limit of 0.2 ng g⁻¹ Hg was obtained and no significant interference was observed. The method was finally applied to the determination of mercury in river sediments and canned tuna fish, and gave results in the range 0.1–3.0 mg kg⁻¹.     

Dynamics of Atomic and Molecular Hydrogen Elimination from Hydrocarbons at VUV Excitation

Elimination of atomic hydrogen (H) and molecular hydrogen (H₂) are important elementary chemical processes in photochemistry and combustion chemistry. Recently, unique and sensitive detection techniques for atomic and molecular hydrogen detection were developed in our laboratory. Using the advanced molecular beam methods, we have studied the photodissociation of a few typical hydrocarbons at 157 nm excitation, especially their atomic and molecular hydrogen elimination processes. In this report, we will briefly describe the results from photodissociation of propane, ethylene, propyne and methanol at 157 nm excitation. These molecules represent different classes of hydrocarbons such as alkane, alkene, alkyne and alcohol. Through careful studies on differently deuterated compounds, clear pictures of selective atomic and molecular hydrogen elimination processes can be constructed for all of the above compounds. These results will help us to understand the dissociation dynamics of the small hydrocarbon molecules.     

Permutations Generated by Stacks and Deques

Lower and upper bounds are given for the the number of permutations of length n generated by two stacks in series, two stacks in parallel, and a general deque.     

Irreducible Apollonian Configurations and Packings

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles.     

Computing inertia sets using atoms

We consider the problem of computing inertia sets for graphs. By using tools for combining the inertia sets of smaller graphs we can reduce this problem to understanding the inertia sets for three-connected graphs that are not joins. We term such graphs atoms and give the inertia sets for all atoms on at most seven vertices. This can be used to compute the inertia sets for all graphs on at most seven vertices.     

Szegő kernels and Poincaré series

Let \(M = {{\widetilde M} \mathord{\left/ {\vphantom {{\widetilde M} \Gamma }} \right. \kern-\nulldelimiterspace} \Gamma }\) be a Kähler manifold, where Γ ~ π₁(M) and \(\widetilde M\) is the universal Kähler cover. Let (L, h) → M be a positive hermitian holomorphic line bundle. We first prove that the L² Szeg? projector \({\widetilde \Pi _N}\) for L²-holomorphic sections on the lifted bundle \({\widetilde L^N}\) is related to the Szeg? projector for H⁰(M, L^N) by \({\widehat \Pi _N}\left( {x,y} \right) = \sum\nolimits_{\gamma \in \Gamma } {{{\widetilde {\widehat \Pi }}_N}} \left( {\gamma \cdot x,y} \right)\). We then apply this result to give a simple proof of Napier’s theorem on the holomorphic convexity of \(\widetilde M\) with respect to \({\widetilde L^N}\) and to surjectivity of Poincaré series.