Rhenocene: Magnetic circular dichroism and laser-induced fluorescence in nitrogen matrices

Rhenocene generated in nitrogen matrices by photolysis of Re(η-C₅H₅)₂H, shows an intense, structured progression in magnetic circular dichroism. The non-linear magnetic field and temperature dependence of the dichroism indicate a ²E_2g(= 5/2) ground state. Lazer-induced fluorescence is used to establish the (0.0) component of the absorption band and to derive the energies of three totally symmetric vibrational fundamentals.     

Primitive divisors of elliptic divisibility sequences

Silverman proved the analogue of Zsigmondy's Theorem for elliptic divisibility sequences. For elliptic curves in global minimal form, it seems likely this result is true in a uniform manner. We present such a result for certain infinite families of curves and points. Our methods allow the first explicit examples of the elliptic Zsigmondy Theorem to be exhibited. As an application, we show that every term beyond the fourth of the Somos-4 sequence has a primitive divisor.     

Recruitment Effects on Manpower Structures

Recruitment is one of the dynamics of manpower systems that can usually be most effectively controlled, always assuming that there is at any time an adequate supply of recruits to a system. In this situation, recruitment can be fixed to meet immediate demands, or it can be part of long-term planning programmes designed perhaps to alleviate a skewness in the length of service profile without reducing the strength of the system greatly. In general, recruitment levels will necessarily be connected with wastage and promotion in a system as well as with the desired growth of the system. The process of determining manpower-planning policies, hereunder recruitment levels, is open to a variety of options with regard to the underlying assumptions that are made: observed experience can be assumed to continue; promotion policies can be adjusted and the consequences estimated; recruitment levels can be allowed to meet immediate demands but with the restriction of some maximum level; or recruitment levels are pre-fixed on the basis of some perhaps even arbitrary management desires. Each of these options and each accompanying recruitment policy will affect the internal structure of the system, with regard to both rank and length of service profiles. This paper employs established projection and promotion models for hierarchical manpower systems to consider recruitment policies and their effects on internal structures. Various policy models are outlined and results presented for a particular application.     

MC SCF molecular gradients and hessians: Computational aspects

Molecular gradients and hessians for multiconfigurational self-consistent-field wavefunctions are derived in terms of the generators of the unitary group using exponential unitary operators to describe the response of the energy to a geometrical deformation. Final expressions are cast in forms which contain reference only to the primitive non-orthogonal atomic basis set and to the final orthonormal molecular orbitals; all reference to intermediate orthogonalized orbitals is removed. All of the deformation-dependent terms in the working equations reside in the one- and two-electron integral derivatives involving the atomic basis orbitals. The deformation-independent terms, whose contributions can be partially summed, involve symmetrized density matrix elements which have the same eight-fold index permutational symmetry as te one- and two-electron integral derivatives they multiply. This separation of deformation-dependent and -independent factors allows for single-pass integral-derivative-driven implementation of the gradient and hessian expressions.     

The Congruence of a Matrix with its Transpose

A new proof is presented that any bilinear form b(x, y) on a finite-dimensional vector space is equivalent to its transposed form b(y, x), or again that any square matrix over a field is congruent to its transpose. This result is then applied to show that a certain previously studied class of rings possess an antiautomorphism.     

Structural comparison of gadolinium and lanthanum silicate films on Si(1 0 0) by HRTEM, EELS and SAED

High-resolution transmission electron microscopy (HRTEM), electron energy loss spectroscopy (EELS) and selected area electron diffraction (SAED) were used to study gadolinium and lanthanum silicate films deposited on Si(1 0 0) substrates using electron-beam evaporation from pressed-powder targets. As-deposited films consist of an amorphous silicate layer without an interfacial layer. After annealing at 900 °C in oxygen for 2 min, an interfacial SiO₂ layer is formed in the gadolinium silicate film, while this interfacial layer is a SiO₂-rich lanthanum silicate layer in the lanthanum silicate film. The formation of interfacial silicate layers is thermodynamically more favorable for the lanthanum films than for the gadolinium films. The gadolinium silicate films crystallize at a temperature between 1000 and 1050 °C, while the crystallization temperature for the lanthanum silicate films is between 900 and 950 °C.