Small surface trades in triangular embeddings

We enumerate all possible trades which involve up to six faces of the face set of a triangular embedding of a simple connected graph. These are classified by the underlying combinatorial trade on the associated block design, and by the geometrical arrangement of the faces necessary to avoid creation of a pseudosurface in the trading operation. The relationship of each of these trades to surface orientability is also established.     

Test groups and effect algebras

A test group is a pair (G, T) whereG is a partially ordered Abelian group andT is a generative antichain in its positive cone. It is shown here that effect algebras and algebraic test groups are coextensive, and a method for calculating the algebraic closure of a test group is developed. Some computational algorithms for studying finite effect algebras are introduced, and the problem of finding quotients of effect algebras is discussed.     

Lines,Trees, and Branch Spaces

In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree.     

Instabilities in Self-Focused Electron Beams

The appearance of large amplitude oscillations and attenuation of beam current have been observed in high perveance electrically self-focused beams. These phenomena are shown to be due to instabilities produced by the interaction of the beam with its self-generated plasma. The critical current which must be exceeded for the instabilities to appear and the frequencies of the oscillations have been related to beam and background parameters and the dimensions of the experimental system.     

Predissociation dynamics of Ã-state ammonia probed by two-photon excitation spectroscopy

Electronically excited ND₃(A¯) molecules have been prepared by laser two-photon excitation on theA¯¹A″₂—X¯¹′₁ transition and monitored via their resulting short-lived emission. The earlier observation of Douglas that ND₃(A¯) molecules carrying one quantum of out-of-plane bending vibration ν′₂ are least susceptible to predissociation, is confirmed. ND₃(A¯) predissociation rates are found to be both vibronic and rovibronic level dependent. Both observations may be understood by considering the likely form of the potential energy surface for ND₃(A¯) molecules in the region of the D₂N—D dissociation coordinate. At short D₂N—D separations this surface exhibits a barrier. The presence of a conical intersection (involving the ND₃ ground state surface) further out along the dissociation coordinate has a crucial influence on the magnitude of this barrier. The envisaged form of theA¯-state potential energy surface also provides a qualitative rationale for all previous experimental findings concerning electronic branching ratios and energy disposal amongst the primary photofragments arising in the photodissociation ofA¯-state ammonia.