Forwards and backwards – synthesis of Laurencia natural products using a biomimetic and retrobiomimetic strategy incorporating structural reassignment of laurefurenynes C–F

Laurefurenynes C–F are four natural products isolated from Laurencia species whose structures were originally determined on the basis of extensive nuclear magnetic resonance experiments. On the basis of a proposed biogenesis, involving a tricyclic oxonium ion as a key intermediate, we have reassigned the structures of these four natural products and synthesized the four reassigned structures using a biomimetic approach demonstrating that they are the actual structures of the natural products. In addition, we have developed a synthesis of the enantiomers of the natural products laurencin and deacetyllaurencin from the enantiomer of (E)-laurefucin using an unusual retrobiomimetic strategy. All of these syntheses have been enabled by the use of tricyclic oxonium ions as pivotal synthetic intermediates.

The synthesis and structural reassignment of laurefurenynes C–F has been achieved, with the new structures fitting with a proposed biosynthesis. Also reported is the synthesis of ent-laurencin and ent-deacetyllaurencin via a retrobiomimetic approach.     

Self-intersection points in classical area-minimizing surfaces

In this paper we study the structure at a point of tangential self-intersection in an area-minimizing classical minimal surface inR ⁿ. The result is that the lowest order homogeneous term in the splitting function, i.e. the difference of the height functions from the tangent plane, has the form

Pulsed-laser photolysis of chromium and molybdenum hexacarbonyls at 308 nm: Simultaneous monitoring of optical and acoustic emissions

An acoustic technique developed earlier was applied to measure the molar number of fragments produced in the XeCl-laser-induced gas-phase photolysis of Cr(CO)₆ and Mo(CO)₆. The bluish-green Cr and Mo emissions were also monitored and correlated with the acoustic signal. For laser fluence ranging up to about 25 mJ/cm² (38 mJ/cm²), the Cr (Mo) optical signal varied with laser fluence asy =dx ³, in agreement with the model that highly excited metal atoms were produced by direct three-photon processes. The acoustic signal varied with fluence asy = ax + bx ², consistent with the model that most fragments were formed via sequential and direct two-photon processes. Quite expectedly, all coefficientsa,b andd vary linearly with carbonyl partial pressure. Both optical and acoustic signals showed onset of saturation at 25 mJ/cm² (38 mJ/cm²) for the case of chromium (molybdenum) hexacarbonyl, suggesting that all photolysis channels were equally affected by the depletion of parent molecules. By assuming a common depletion mechanism, upper limits on the branching ratios of the various photolysis channels were estimated.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.