Multiple Intersection Exponents for Planar Brownian Motion

Let p≥2, n ₁≤⋅⋅⋅≤n _p be positive integers and be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ς _p (n ₁,…,n _p ), as the exponential rate of decay of the probability that the packets , i=1,…,p, have no joint intersection. The case p=2 is well-known and, following two decades of numerical and mathematical activity, Lawler et al. (Acta Math. 187:275–308, 2001) rigorously identified precise values for these exponents. The exponents have not been investigated so far for p>2. We present an extensive mathematical and numerical study, leading to an exact formula in the case n ₁=1, n ₂=2, and several interesting conjectures for other cases.     

Anticancer Agents from the Australian Tropical Rainforest: Spiroacetals EBC‐23, 24, 25, 72, 73, 75 and 76

EBC‐23, 24, 25, 72, 73, 75 and 76 were isolated from the fruit of Cinnamomum laubatii (family Lauraceae) in the Australian tropical rainforests. EBC‐23 ( 1 ) was synthesized stereoselectively, in nine linear steps in 8 % overall yield, to confirm the reported relative stereochemistry and determine the absolute stereochemistry. Key to the total synthesis was a series of Tietze–Smith linchpin reactions. The novel spiroacetal structural motif, exemplified by EBC‐23 ( 1 ), was found to inhibit the growth of the androgen‐independent prostate tumor cell line DU145 in the mouse model, indicating potential for the treatment of refractory solid tumors in adults.     

High-efficiency 60 W TEM(00) Nd:YVO(4) oscillator pumped at 888 nm

We propose a technique for pumping Nd:YVO(4) with high optical power at 888nm while making absorption independent of the pump light polarization state. This is especially suitable for systems end pumped by high-power, high-brightness fiber-coupled diode sources associated with long vanadate crystals to effectively spread the heat load in a large volume. A compact 60 W output, 55% optical efficiency cw TEM(00) oscillator was demonstrated.     

Electrochemical texturing of Al-doped ZnO thin films for photovoltaic applications

The processes during chemical and electrochemical etching of Al-doped ZnO are investigated utilizing a scanning flow cell setup with online detection of dissolved Zn ions. The rate of chemical dissolution was found to be a linear function of buffer and proton concentration in near neutral pH solutions according to a transport limited reaction. In contrast, electrochemical etching is limited by the kinetics of the reaction and increases linearly with the imposed current density. Due to this fundamental difference, the dissolution of Zn can be either uniform over the whole surface or highly localized at active sites like grain boundaries. A combined approach of chemical etching and the well-controllable galvanostatic dissolution thus allows a fine adjustment of the ZnO:Al surface texture for applications in silicon thin film photovoltaic cells in order to improve their overall energy conversion efficiency.     

FTIR microscopy of biological cells and tissue: data analysis using resonant Mie scattering (RMieS) EMSC algorithm

Transmission and transflection infrared microscopy of biological cells and tissue suffer from significant baseline distortions due to scattering effects, predominantly resonant Mie scattering (RMieS). This scattering can also distort peak shapes and apparent peak positions making interpretation difficult and often unreliable. A correction algorithm, the resonant Mie scattering extended multiplicative signal correction (RMieS-EMSC), has been developed that can be used to remove these distortions. The correction algorithm has two key user defined parameters that influence the accuracy of the correction. The first is the number of iterations used to obtain the best outcome. The second is the choice of the initial reference spectrum required for the fitting procedure. The choice of these parameters influences computational time. This is not a major concern when correcting individual spectra or small data sets of a few hundred spectra but becomes much more significant when correcting spectra from infrared images obtained using large focal plane array detectors which may contain tens of thousands of spectra. In this paper we show that, classification of images from tissue can be achieved easily with a few (<10) iterations but a reliable interpretation of the biochemical differences between classes could require more iterations. Regarding the choice of reference spectrum, it is apparent that the more similar it is to the pure absorption spectrum of the sample, the fewer iterations required to obtain an accurate corrected spectrum. Importantly however, we show that using three different non-ideal reference spectra, the same unique correction solution can be obtained.     

CO2 on a Tightrope: Stabilization,Room‐Temperature Decarboxylation,and Sodium‐Induced Carboxylate Migration

A sterically shielded 3‐substituted zwitterionic N,N‐dimethylisotryptammonium carboxylate has been synthesized by consecutive chemoselective double alkylation of indole. The carboxylate undergoes a quantitative and unusually facile decarboxylation in dimethyl sulfoxide (DMSO) or dimethyl formamide (DMF) at room temperature. The breaking of a nearly equidistant hydrogen bond by solvent molecules initiates heterolytic C? C cleavage. The decarboxylation rate decreases with increasing CO₂ partial pressure, proving the competitiveness of protonation and re‐carboxylation of the carbanionic intermediate. Corresponding spiro compounds containing silylene and stannylene moieties show high thermal stability. Addition of an excess of methyllithium to the sodium salt triggers a reaction sequence comprising a deprotonation, carboxylate transfer, and nucleophilic trapping of the rearranged carboxylate by another equivalent of methyllithium. Hydrolytic work‐up of the geminal diolate leads to an acetyl product. The role of the sodium counterion and the mechanism of the rearrangement have been unraveled by deuteration experiments.