A geometric criterion for positive topological entropy

We prove that a diffeomorphism possessing a homoclinic point with a topological crossing (possibly with infinite order contact) has positive topological entropy, along with an analogous statement for heteroclinic points. We apply these results to study area-preserving perturbations of area-preserving surface diffeomorphisms possessing homoclinic and double heteroclinic connections. In the heteroclinic case, the perturbed map can fail to have positive topological entropy only if the perturbation preserves the double heteroclinic connection or if it creates a homoclinic connection. In the homoclinic case, the perturbed map can fail to have positive topological entropy only if the perturbation preserves the connection. These results significantly simplify the application of the Poincaré-Arnold-Melnikov-Sotomayor method. The results apply even when the contraction and expansion at the fixed point is subexponential.The first author was partially supported by a Sloan Foundation Fellowship and an N.S.F. grant. The second author was partially supported by a National Science Foundation Postdoctoral Research Fellowship. Both authors would like to thank MSRI for their support during the period that much of this paper was written.     

The dynamics of ring rotation in ferrocene,nickelocene and ruthenocene by incoherent quadi-elastic neutron scattering

Incoherent quasi-elastic neutron scattering has been used to study the reorientational motions of the cyclopentadienyl rings in ferrocene, nickelocene and ruthenocene. The results for ferrocene show that the activation energy for ring rotation drops above the 164 K phase transition to 4.4 ± 0.5 kJ mol^?1 (which is approximately half its low temperature value) but the rings still appear to jump between only five orientations on the observable time scale. At room temperature, the rings in nickelocene appear to behave the same as in ferrocene but in ruthenocene they reorientate much less frequently and resemble those in ferrocene below 164 K.     

Chemical reactivity and surface-enhanced raman scattering

A mechanism is proposed for surface-enhanced Raman scattering for pyridine which explains the enhancement, the anodizalion “activation”, the significance of silver, the photographitization of coordinated pyridine and formate, the participation of surface roughness, and the irreversibly held yet liquid-like nature of surface pyridine.     

The ruthenium carbonyl catalyzed reduction of nitro compounds by phase transfer catalysis

Amines were obtained in excellent yields by treatment of nitro compounds, at room temperature and atmospheric pressure, with carbon monoxide, ruthenium carbonyl as the metal catalyst, and benzyltriethylammonium chloride as the phase transfer catalyst in an aqueous base-organic solvent system.     

Characterization of an immobilized antibody-enzyme complex

Antiserum specific for propanediol dehydrogenase, an enzyme found inNeisseria gonorrhoeae cells, has been immobilized to glass. When mixed withN gonorrhoeae cell lysates, the immobilized antibody (IMA) binds the enzyme. Over 70% of the calculated adsorbed activity can be recovered from the immobilized antibody-enzyme (IMA-E) complex. When mixed with bacterial lysates prepared from different organisms having propanediol dehydrogenase-like activity, the IMA specifically adsorbed the enzyme from theN gonorrhoeae lysate. IMA-E complexes have been prepared and their kinetic, temperature and chemical stability, and antigenic properties investigated. These studies demonstrated the feasibility of using an immobilized antibody in the detection of the propanediol dehydrogenase enzyme.     

Commutators of nilpotent matrices

A matrix of zero trace is, with certain exceptions, the commutator of nilpotent matrices. It may (so far as we know) be necessary to go outside the original field for the entries of the nilpotent matrices.     

Linear maps that preserve matrices annihilated by a polynomial

Let M_n be the algebra of n×n matrices over an algebraically closed field of characteristic zero. Let f(x) be a polynomial over $\text{F}$ with at least two distinct roots. Then all nonsingular linear maps L:M_n→M_n that map matrix roots of F(x)=0 into matrix roots of f(x}=0 are found.