On real matrices with positive definite symmetric component

Inequalities concerning real square matrices A with positive definite symmetric component A+A^*are derived from certain inertia relations which hold for any complex (not necessarily real) square matrices A with positive definite

A+A^*     

Analytical gradients of a state average MCSCF state and a state average diagnostic

An efficient method for calculating the Lagrange multipliers and the analytical gradients of one state included in a state average MCSCF wave function is presented. It is demonstrated that the state average energy of an ‘equal-weight’ scheme is invariant to rotations within the state average subspace and that the corresponding rotations should be eliminated from the Lagrangian equations. Finally, a diagnostic is presented, which gauges the energy difference between a state defined by a state average calculation and the corresponding fully variational multi-configurational SCF state.     

ChemInform Abstract: X-Ray Structural Studies of the Polymorphic Elpasolites K2LiAlF6 and Rb2LiGaF6.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Structure and morphology of the reaction fronts during the formation of MgAl2O4 thin films by solid state reaction between R-cut sapphire substrates and MgO films

The thin-film spinel-forming solid state reaction between Al₂O₃ and MgO has been studied under initially non-coherent conditions. MgO films in (001) orientation on -cut sapphire single crystals were heated at 1100°C for 30 min or 1h. The film/substrate reaction proceeds via cation counterdiffusion as was revealed by a marker experiment. The MgAl₂O₄ films formed were predominantly (001) oriented, with an additional systematic tilt of about 5° of the spinel lattice around the [010] axis. The structure of the Al₂O₃ /MgAl₂O₄(001) and MgAl₂O₄(001)/MgO(001) reaction fronts has been investigated on cross section samples by high-resolution electron microscopy. It appeared that after starting from an incoherent interface, the Al₂O₃ /MgAl₂O₄(001) front assumes an almost fully coherent structure during the reaction. As a result the lattice misfit is reduced to 1%, and interfacial ledges are formed. The latter most probably play an active role in the necessary c.p.h. f.c.c. reconstruction of the oxygen sublattice. The MgAl₂O₄(001)/MgO(001) reaction front consists of coherent regions divided by misfit dislocations. During the reaction the former run ahead whereas the latter lag behind. As a result the morphology of the reaction front is bowed. The results confirm earlier observations of Carter and Schmalzried of the semicoherent Al₂O₃(00.1)/CoAl₂O₄(111) interface, thus strongly supporting the conclusion of a fundamental new phase transformation mechanism specific to oxide systems.Presented at the workshop on High-Voltage and High-Resolution Electron Microscopy, February 21–24, 1994, Stuttgart, Germany.     

Optimal Recovery of the Derivative of Bounded Analytic Functions

Given (–1, 0), n N, we discuss the optimal recoveryof (), for analytic and bounded in < 1, from the knowledge of the values of at n points z1,.zm[0,l),where these points are chosen to produce the least possibleintrinsic error. The optimal algorithms are explicitly determined.     

Computer program for neutron activation analysis with the SLOWPOKE reactor

A FORTRAN computer program for automatic neutron activation analysis is presented. The program locates and identifies peaks in a gamma-ray spectrum, calculates peak areas and the concentrations of the elements of interest in the sample. This program was specifically designed for the SLOWPOKE reactor, it uses a semi-absolute method and does not need standards or flux monitors. The program was written so as to minimize the computation time, and a typical 4096-channel spectrum is processed in five seconds by an IBM 360/75 computer.