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.     

Intertwining the geodesic flow and the Schr?dinger group on hyperbolic surfaces

We construct an explicit intertwining operator L{\mathcal L} between the Schr?dinger group e^{it \frac\triangle2}{e^{it \frac\triangle2}} and the geodesic flow on certain Hilbert spaces of symbols on the cotangent bundle T*X _Γ of a compact hyperbolic surface X _Γ = Γ\D. We also define Γ-invariant eigendistributions of the geodesic flow PS_{j, k, nj,-nk}{PS_{j, k, \nu_j,-\nu_k}} (Patterson-Sullivan distributions) out of pairs of \triangle{\triangle} -eigenfunctions, generalizing the diagonal case j = k treated in Anantharaman and Zelditch (Ann. Henri Poincaré 8(2):361–426, 2007). The operator L{\mathcal L} maps PS_{j, k, nj,-nk}{PS_{j, k, \nu_j,-\nu_k}} to the Wigner distribution W^G_j,k{W^{\Gamma}_{j,k}} studied in quantum chaos. We define Hilbert spaces H_PS{\mathcal H_{PS}} (whose dual is spanned by {PS_{j, k, nj,-nk}{PS_{j, k, \nu_j,-\nu_k}}}), resp. H_W{\mathcal H_W} (whose dual is spanned by {W^G_j,k}{\{W^{\Gamma}_{j,k}\}}), and show that L{\mathcal L} is a unitary isomorphism from H_W ? H_PS.{\mathcal H_{W} \to \mathcal H_{PS}.}