Combined CI-HY studies of atomic states. IV. The four lowest 1S and four lowest 1P states of He and the lowest 1S and 1P states of H−1

Combined CI -HY method calculations are reported for the ground and first three excited S states of He with an error on the order of 10^?7 a.u. within the same 120-term basis. For He ¹P, the four lowest states are obtained with an error ≤2 × 10^?6 a.u. within the same 102-term basis. H^?1 S and ¹P states are also treated by the same CI -HY technique. The utility of an spd Slater-type orbital, r, v = 0, 1 basis is investigated, with indications that it might be an excellent basis for states of first row atoms.     

Mean value theorems for a matrix valued derivative

The derivative of a function defined on a set of matrices is given utilizing the Moore-Penrose pseudoinverse, which yields a natural extension of differentiation in the univariate calculus. Several mean value theorems involving this derivative are established.     

Facilitating problem definition in teams

The problems that a team comes to define as needing to be worked on depend upon idiosyncratically defined subjective, qualitative and organizationally political factors affecting the individual members of the team. In this paper we shall argue that Operational Research tends to pay little attention to the process of problem definition and that when it does, the emphasis is towards determining an accurate or correct interpretation of the external situation that the team confronts and the organizational objectives which have been laid down for the team. We suggest, however, that Operational Researchers are particularly well placed to act in a way which pays attention to both these fields. This paper is addressed to those Operational Researchers who predominantly work with complex policy problems belonging to a team of decision-makers. We shall demonstrate that group techniques, new computer simulation technology, and attention to process can lead to a team negotiating a definition and redefinition of a problem so that solutions have a greater commitment from the team, and therefore a higher chance of being implemented.     

Single neutron transfer reactions in the systems:139La+16O,93Nb+12C,14N,16O and20Ne

Data from the quasi-elastic transfer reaction products¹⁴⁰La and^92mNb exhibit near zero effective ranges, flat excitation functions over large energy ranges and Q independent yields. These features are used to characterise quasi elastic reactions via the target-like product.     

Stability of cartesian products

We complete the work started by Holton and Grant concerning the semi-stability of non-trivial connected cartesian products and show that all such products are semi-stable. Further we show that except for certain (listed) restricted graphs, connected cartesian products are semi-stable at every vertex. Finally, we show that the cartesian product of any two graphs is not semi-stable if and only if one of them is totally disconnected and the other is not semi-stable.     

Bilayer-by-bilayer antiferroelectric ordering in freely suspended films of an achiral polymer-monomer liquid crystal mixture

Thin freely suspended films of a mixture of an achiral side-chain liquid crystal polymer and its monomer have been studied with depolarized reflected light microscopy. We observe that regions with an odd number of bilayers exhibit a net spontaneous polarization in the tilt plane of the molecules, while regions with an even number of bilayers have no net polarization. These odd-even effects are direct evidence that the tilted smectic bilayers are anticlinic at the polymer backbone and synclinic at bilayer interface and confirm that the phase is bilayer-by-bilayer antiferroelectric.