Activation of hafnocene catalyzed polymerization of 1-hexene with MAO and borate

A study of 1-hexene polymerization with ethylene-bis(9-fluorenyl) hafnium dichloride has been carried out using two different cocatalyst systems, methyl-aluminoxane/trimethylaluminum (MAO/TMA) and tris-isobutyl-aluminum/N,N-dimethylanilinium tetrakis(pentafluorophenyl) borate (TIBA/borate). When MAO/TMA was used, 1-hexene polymerized into a low molar mass poly(1-hexene) with low catalytic activity. Activation with TIBA/borate increased polymerization activity drastically as well as the molar mass of the polymers. In order to analyze differences in the activity profiles, UV-Vis spectroscopy was employed to investigate ligand to metal charge transitions (LMCT) of the hafnocene dichloride during the activation process. The low catalytic activity and the fast chain transfer to the cocatalyst with MAO/TMA may originate from strong bonding between the metallocene cation and the MAO/TMA species thus obstructing monomer coordination and insertion.     

Large deviations for functionals of stationary processes

Summary Let (S _n ) be a sequence ofR ^d -valued random variables adapted to the internal history of a stationary sequence of random elements (X _n ). We formulate conditions under which the principle of large deviations holds true for the sequence (S _n ).     

Total synthesis of amaminol A: establishment of the absolute stereochemistry

The first synthetic route to amaminol A with use of an organocatalytic intramolecular Diels-Alder reaction is reported. The absolute stereochemistry is proven with a crystallographic image of a cyclic carbamate of amaminol A.     

Optimal control of quantum revival

Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.     

Singularity of Projections of 2-Dimensional Measures Invariant Under the Geodesic Flow

We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect to the 2-dimensional Lebesgue measure.     

Geometric ergodicity of Harris recurrent Marcov chains with applications to renewal theory

Let (X_n) be a positive recurrent Harris chain on a general state space, with invariant probability measure π. We give necessary and sufficient conditions for the geometric convergence of λPⁿf towards its limit π(f), and show that when such convergence happens it is, in fact, uniform over f and in L¹(π)-norm. As a corollary we obtain that, when (Xn) is geometrically ergodic, ∝ π(dx)6Pⁿ(x,·)-π6 converges to zero geometrically fast. We also characterize the geometric ergodicity of (X_n) in terms of hitting time distributions. We show that here the so-called small sets act like individual points of a countable state space chain. We give a test function criterion for geometric ergodicity and apply it to random walks on the positive half line. We apply these results to non-singular renewal processes on [0,∞) providing a probabilistic approach to the exponencial convergence of renewal measures.     

Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation

Residual amplitude modulation (RAM) distorts saturated absorption signals, limiting the accuracy of optical frequency references based on modulation transfer spectroscopy (MTS). Described here are two independent means by which RAM is produced in these references: (1) by the modulator and (2) when the overlap of the optical fields in the saturable absorber is asymmetric. Methods to vary RAM generated by either mechanism will be outlined and these will be used to show how RAM arising from one effect can be cancelled by the other. A theoretical treatment of MTS signals in references containing RAM is given and used to evaluate the level of signal distortion allowing the conditions for RAM cancellation to be determined. This technique is applied to improve the frequency accuracy of a reference by an order of magnitude.