Prognosis for superconductivity in Np and Pu

Np and Pu were substituted for U in bcc γ-U alloys and the depression of T_c measured. By extrapolating the Np and Pu impurity concentrations to 100%, estimates were made for the maximum superconducting transition temperatures that may be expected for bcc γ-Np and ∈-Pu alloys.     

Strengths and widths of the pure rotational lines of CO

The strengths and widths of several lines in the pure rotational band of CO have been measured by asymmetric Fourier techniques. The strengths give a permanent dipole moment of 0.112 D, in good agreement with the micro-wave value, and show conclusively that the sign of the Herman-Wallis parameter, θ, is negative. The widths are in good agreement with the theoretical values of Benedict and Herman and do not show the anomalous J dependence recently reported by Dowling.     

Monotonicity and unimodality of the pattern inventory

It is shown that the Kostka numbers respect a natural partial order (reverse domination) on the integer partitions. It is then proved that the number of Pólya patterns with a given weight also respects this order. Immediate consequences include the unimodality of the number of graphs with n vertices and k edges and the unimodality of the coefficients of the expansion of the Gaussian coefficient $\text{m+n}\text{n}$.     

Contributions of renormalon singularities

On the basis of some simple examples we suggest a general method for discussing the contribution of renormalons to the Borel transform based on the general analytical structure of the renormalization group β function. No simple principal value or contour integral Borel representation seems to be possible. Instead a splitting of the Borel transform at each renormalon singularity seems to be necessary making the infinite sum over renormalons possibly difficult to define.     

The Determination of Approximately Optimal Policies in Markov Decision Processes by the Use of Bounds

In the general area of Markov decision processes, a lot of attention has been given to deriving upper and lower bounds for approximating the optimal performance level. These are, in themselves, not useful unless they can be used to derive an approximately optimal policy. The existing literature does this specifically in the context of the computational methods being used at the time. However, irrespective of the method used, a straight application of one step of Howard's policy space method will give the desired results.