Normal Forms, Resonances, and Meandering Tip Motions near Relative Equilibria of Euclidean Group Actions

The equivariant dynamics near relative equilibria to actions of noncompact, finite‐dimensional Lie groups G can be described by a skew‐product flow on a center manifold: with , with v in a slice transverse to the group action, and a(v) in the Lie algebra of G. We present a normal form theory near relative equilibria in this general case. For the specific case of the Euclidean groups the skew product takes the form with . We give a precise meaning to the intuitive idea of tip motion of a meandering spiral: it corresponds to the dynamics of . This clarifies the notion of meander radii and drift resonance in the plane . For illustration, we discuss the unbounded tip motions associated with a weak focus in v, on the verge of Hopf bifurcation, in the case of resonant Hopf and rotation frequencies of the spiral, and study resonant relative Hopf bifurcation. We also encounter random Brownian tip motions for trajectories which become homoclinic for . We conclude with some comments on the homoclinic tip shifts and drift resonance velocities in the Bogdanov‐Takens bifurcation, which turn out to be small beyond any finite order. (Accepted March 30, 1998)     

Combinatorial aspects of generalized complementary basic matrices

This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.     

Dominant matrices and max algebra

We study the class of so-called totally dominant matrices in the usual algebra and in the max algebra in which the sum is the maximum and the multiplication is usual. It turns out that this class coincides with the well known class of positive matrices having positive the determinants of all 2×2 submatrices. The closure of this class is closed not only with respect to the usual but also with respect to the max multiplication. Further properties analogous to those of totally positive matrices are proved and some connections to Monge matrices are mentioned.     

Redox‐Induced Spin‐State Switching and Mixed Valency in Quinonoid‐Bridged Dicobalt Complexes

The complexes [{(tmpa)Co^II}₂(μ‐L¹)^2?]²⁺ ( 1²⁺ ) and [{(tmpa)Co^II}₂(μ‐L²)^2?]²⁺ ( 2²⁺ ), with tmpa=tris(2‐pyridylmethyl)amine, H₂L¹=2,5‐di‐[2‐(methoxy)‐anilino]‐1,4‐benzoquinone, and H₂L²=2,5‐di‐[2‐(trifluoromethyl)‐anilino]‐1,4‐benzoquinone, were synthesized and characterized. Structural analysis of 2²⁺ revealed a distorted octahedral coordination around the cobalt centers, and cobalt–ligand bond lengths that match with high‐spin Co^II centers. Superconducting quantum interference device (SQUID) magnetometric studies on 1²⁺ and 2²⁺ are consistent with the presence of two weakly exchange‐coupled high‐spin cobalt(II) ions, for which the nature of the coupling appears to depend on the substituents on the bridging ligand, being antiferromagnetic for 1²⁺ and ferromagnetic for 2²⁺ . Both complexes exhibit several one‐electron redox steps, and these were investigated with cyclic voltammetry and UV/Vis/near‐IR spectroelectrochemistry. For 1²⁺ , it was possible to chemically isolate the pure forms of both the one‐electron oxidized mixed‐valent 1³⁺ and the two‐electron oxidized isovalent 1⁴⁺ forms, and characterize them structurally as well as magnetically. This series thus provided an opportunity to investigate the effect of reversible electron transfers on the total spin‐state of the molecule. In contrast to 2²⁺ , for 1⁴⁺ the metal–ligand distances and the distances within the quinonoid ligand point to the existence of two low‐spin Co^III centers, thus showing the innocence of the quintessential non‐innocent ligands L. Magnetic data corroborate these observations by showing the decrease of the magnetic moment by roughly half (neglecting spin exchange effects) on oxidizing the molecules with one electron, and the disappearance of a paramagnetic response upon two‐electron oxidation, which confirms the change in spin state associated with the electron‐transfer steps.     

Cellulose,Zellstoff

Analytical and Bioanalytical Chemistry -     

The chameleon effect in zwitterionic micelles: Binding of anions and cations and use as nanoparticle stabilizing agents

Zwitterionic surfactants are relatively overlooked and some of their properties resemble those of ionic and non-ionic surfactants, but others are unique. There is unimpeachable evidence that aqueous solutions of zwitterionic micelles interact specifically with anions, forming “anionoid” micelles, which concentrate cations in the surfaces. Thus, unlike ionic micelles, both the cation and anion of the electrolyte solution can be concentrated at zwitterionic interfaces. This unique effect, known as the “Chameleon Effect”, can be used to catalyze a variety of simple reactions, as the attraction of ions to the micelle brings the reactants together. Furthermore, zwitterionic surfactants stabilize metallic nanoparticles and the magnetically stirred two-phase system could be reused 3 more times in the hydrogenation of cyclohexene (Pd:cyclohexene ratio of 1:18300), with very little loss in activity, and an average turn-over frequency of 1000 h^? 1.