The magnetic hyperfine structure in the rotational spectrum of H2CNH

The hyperfine structure in the ground-state rotational spectrum of methanimine was studied in the frequency range of 64-172 GHz by means of the Lamb-dip technique. This allowed to resolve, in some hyperfine components due to the ¹⁴N nucleus, doublets separated by only some tenth of kHz. We explain the splittings as due to magnetic interactions of the three protons with their molecular environment. The analysis of the experimental spectrum has been guided by quantum-chemical calculations of the hyperfine parameters.     

Reflectometric measurement of birefringence rotation in single-mode optical fibers

We present a novel reflectometric technique for the measurement of orientation and modulus of the linear birefringence vector in single-mode optical fibers. The technique provides information also on circular birefringence, although this component, if present, appears as a rotation of the linear birefringence. A detailed theoretical analysis is reported and validated by experimental results.     

Cation disorder in NaW2O6+δ·nH2−zO post-ion exchange with K, Rb, Sr, and Cs

The structure of the defect pyrochlore NaW₂O_6+δ·nH_2−zO after ion exchange with K, Rb, Sr or Cs for Na has been investigated using thermal analysis, solid-state nuclear magnetic resonance, laboratory X-ray and neutron diffraction methods. Neutron diffraction studies show that both the A-type cations (Na⁺, K⁺, Rb⁺, and/or Cs⁺) and the water molecules reside within the channels that form in the 111 direction of the W₂O₆ framework and that these strongly interact. The analytical results suggest that the water and A-type cations compete for space in the tunnels within the W₂O₆ pyrochlore framework, with the total number of water molecules and cations being approximately constant in the six samples investigated. The interplay between the cations and water explains the non-linear dependence of the a lattice parameter on the choice of cation. It appears that the ion-exchange capacity of the material will be controlled by the amount of water initially present in the sample.     

Positive definiteness in the numerical solution of Riccati differential equations

Summary. In this work we address the issue of integrating symmetric Riccati and Lyapunov matrix differential equations. In many cases -- typical in applications -- the solutions are positive definite matrices. Our goal is to study when and how this property is maintained for a numerically computed solution. There are two classes of solution methods: direct and indirect algorithms. The first class consists of the schemes resulting from direct discretization of the equations. The second class consists of algorithms which recover the solution by exploiting some special formulae that these solutions are known to satisfy. We show first that using a direct algorithm -- a one-step scheme or a strictly stable multistep scheme (explicit or implicit) -- limits the order of the numerical method to one if we want to guarantee that the computed solution stays positive definite. Then we show two ways to obtain positive definite higher order approximations by using indirect algorithms. The first is to apply a symplectic integrator to an associated Hamiltonian system. The other uses stepwise linearization. Received April 21, 1993