The graph isomorphism disease

The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.     

Horizon Valuations for Mathematical Programming in Financial Planning

Using a linear programming model for the financial planning of an organization requires the specification of a horizon date and a valuation of the firm at that date. Given perfect information about future opportunities, an exact valuation procedure should lead to the same optimal solution of the model regardless of the choice of horizon date. Even in the absence of perfect information, conventional valuations fall far shorter of this ideal than they need to. It is shown that for a modest increase in the size of the linear programme, better valuations can be achieved and, most importantly, valuations which consider the impact on the value of the firm of post horizon constraints and liabilities as well as post-horizon opportunities.     

Dynamical stability and pure thermodynamic phases

A notion of stability of dynamics under distant perturbations is introduced. It is demonstrated, for quasi-local systems, that the stability of an equilibrium state under the same perturbations implies the state is factorial, i.e. strongly clustering in space. We also characterize the set of perturbations necessary to ensure the equivalence of stability and factorialness.     

Sizing Large Hollow Micro-Balloons with the phase doppler interferometer

A combined theoretical and experimental study has been conducted to evaluate the effectiveness of using large, hollow micro-balloons as LDV seed particles. The study has focused on the ability of phase Doppler systems to size hollow microballoons, the ability of large micro-balloons to respond to high frequency spatial and temporal flow field variations, and the overall advantages and disadvantages of using large microballoons instead of conventional LDV seed particles, such as very small water droplets or polystyrene latex (PSL) particles. This paper discusses the development of a theoretical phase Doppler response model for stratified spheres, the experimental facility, and the theoretical and experimental results.     

A versatile approach to analogues of the cannabinoid-like anti-emetic nonabine (BRL 4664)

Analogues of the cannabinoid-like anti-emetic nonabine (BRL 4664), in which the 4-pyridinyl and 1,2-dimethylheptyl groups have been replaced by other aryl and alky groups respectively, have been synthesised from the appropriate resorcinol by a novel procedure. The route has been shown to be of general applicability, although in the case of nonabine itself the procedure does not represent a viable alternative to that previously published.     

A mild reduction of aliphatic nitro compounds to imines for further in situ reactions : A simple synthesis of pyrroles

Tributylphosphine-diphenyldisulphide reduces nitroalkanes to imines which can be trapped intramolecularly to give pyrroles.