Analytical solutions for the electromagnetic fields of tightly focused laser beams of arbitrary pulse length

The analytical solution for a monochromatic focused laser beam was recently published [Opt. Lett.31, 1447 (2006)]. The effect of introducing bandwidth by including a finite-length temporal pulse envelope is included exactly. This is done formally first in the frequency domain for an arbitrary pulse shape, and the specific case of a cosine-squared envelope is then solved analytically for all pulse lengths, thereby decreasing the computation time by 2 orders of magnitude. The inclusion of longer wavelengths reduces the fraction of laser energy in the focus from 86.5% to 83.5% for a 5 fs Ti:sapphire laser and 72.7% in a single-cycle pulse.     

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).     

Site-specific preparation of 3-fluoro-1-substituted-naphthalenes via a novel base-catalyzed cyclization reaction from (E)-monofluoroenynes

A novel cyclization reaction for the preparation of 3-fluoro-1-substituted-naphthalenes is reported. (E)-Monofluoroenynes, which are prepared by Sonogashira coupling reaction from (Z)-1-bromo-1-fluoroalkenes, undergo cyclization to afford 3-fluoro-1-substituted-naphthalenes in good to excellent yields when treated with DABCO or DBU in refluxing N-methyl-2-pyrrolidinone (NMP). [reaction: see text]     

Alternating direction augmented Lagrangian methods for semidefinite programming

We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration, our basic algorithm minimizes the augmented Lagrangian function for the dual SDP problem sequentially, first with respect to the dual variables corresponding to the linear constraints, and then with respect to the dual slack variables, while in each minimization keeping the other variables fixed, and then finally it updates the Lagrange multipliers (i.e., primal variables). Convergence is proved by using a fixed-point argument. For SDPs with inequality constraints and positivity constraints, our algorithm is extended to separately minimize the dual augmented Lagrangian function over four sets of variables. Numerical results for frequency assignment, maximum stable set and binary integer quadratic programming problems demonstrate that our algorithms are robust and very efficient due to their ability or exploit special structures, such as sparsity and constraint orthogonality in these problems.     

Stabilizing labile DNA–protein complexes in polyacrylamide gels

The electrophoretic mobility‐shift assay (EMSA) is one of the most popular tools in molecular biology for measuring DNA–protein interactions. EMSA, as standardly practiced today, works well for complexes with association binding constants K_a>10⁹ M^?1 under normal conditions of salt and pH. Many DNA–protein complexes are not stable enough so that they dissociate while moving through the gel matrix giving smeared bands that are difficult to quantitate reliably. In this work we demonstrate that the addition of the osmolyte triethylene glycol to polyacrylamide gels dramatically stabilizes labile restriction endonuclease EcoRI complexes with nonspecific DNA sequences enabling quantitation of binding using EMSA. The significant improvement of the technique resulting from the addition of osmolytes to the gel matrix greatly extends the range of binding constants of protein–DNA complexes that can be investigated using this widely used assay. Extension of this approach to other techniques used for separating bound and free components such as gel chromatography and CE is straightforward.     

Approaches to the preparation of (Z)-1,2-difluorostilbenes

Methodology directed at the preparation of (Z)-1,2-difluorostilbenes has been evaluated. For symmetrical (Z)-1,2-difluorostilbenes, photochemical isomerization of the isomeric (E)-1,2-difluorostilbenes, and HPLC separation of the mixture of stilbene isomers is a reasonable route to a particular (Z)-stilbene. An alternative approach to both symmetrical and/or unsymmetrical (Z)-1,2-difluorostilbenes has been developed via stereospecific Pd(0) coupling of (E)-1,2-difluoro-aryl-ethenyltributylstannanes under Stille-Liebiskind conditions with aryl idodies. The requisite arylstannanes can be obtained via the reported route developed by Davis or via (E)-1,2-difluorovinyltributylstannane - a new route described in this work. The methodology tolerates almost any functionality in the aryl ring, is easily carried out, is stereospecific and provides the first general route to (Z)-1,2-difluorostilbenes.     

Highly diastereoselective allylation reactions of dilithiated 4-(phenylsulfonyl)-cyclopent-2-enol

A two-step synthesis of 4-(phenylsulfonyl)cyclopent-2-enol using epoxide ring-opening and ring-closing alkene metathesis is described. Treatment of the dianion of 4-(phenylsulfonyl)cyclopent-2-enol with allylic bromides gave the corresponding alkylated products with excellent to complete diastereoselectivity.     

Enhanced photolysis in aerosols: evidence for important surface effects

While there is increasing evidence for unique chemical reactions at interfaces, there are fewer data on photochemistry at liquid-vapor junctions. This paper reports a comparison of the photolysis of molybdenum hexacarbonyl, Mo(CO)(6), in 1-decene either as liquid droplets or in bulk-liquid solutions. Mo(CO)(6) photolysis is faster by at least three orders of magnitude in the aerosols than in bulk-liquids. Two possible sources of this enhancement are considered: (1) increased light intensity due to either Morphology-Dependent Resonances (MDRs) in the spherical aerosol particles and/or to increased pathlengths for light inside the droplet due to refraction, which are termed physical effects in this paper; and (2) interface effects such as an incomplete solvent-cage at the gas-liquid boundary and/or enhanced interfacial concentrations of Mo(CO)(6), which are termed chemical effects. Quantitative calculations of the first possibility were carried out in which the light intensity distribution in the droplets averaged over 215-360 nm was obtained for 1-decene droplets. Calculations show that the average increase in light intensity over the entire droplet is 106%, with an average increase of 51% at the interface. These increases are much smaller than the observed increase in the apparent photolysis rate of droplets compared to the bulk. Thus, chemical effects, i.e., a decreased solvent-cage effect at the interface and/or enhancement in the surface concentration of Mo(CO)(6), are most likely responsible for the dramatic increase in the photolysis rate. Similar calculations were also carried out for broadband (290-600 nm) solar irradiation of water droplets, relevant to atmospheric conditions. These calculations show that, in agreement with previous calculations by Mayer and Madronich [B. Mayer and S. Madronich, Atmos. Chem. Phys., 2004, 4, 2241] MDRs produce only a moderate average intensity enhancement relative to the corresponding bulk-liquid slabs when averaged over a range of wavelengths characteristic of solar radiation at the Earth's surface. However, as in the case of Mo(CO)(6) in 1-decene, chemical effects may play a role in enhanced photochemistry at the aerosol-air interface for airborne particles.     

Part 2: building diverse natural-product-like architectures from a tetrahydroaminoquinoline scaffold. Modular solution- and solid-phase approaches for use in high-throughput generation of chemical probes

The solution- and solid-phase synthesis to obtain several natural-product-like, tetrahydroquinoline-based, polycyclic derivatives were developed. In one approach, two derivatives (38 and 41) having an eight-membered unsaturated lactam were successfully obtained both in solution and on solid support.