The enumeration of extreme rigid honeycombs

Journal of Algebraic Combinatorics - Rigid honeycombs were introduced by Knutson et al. (J Am Math Soc 17:19–48, 2004), and they were shown in Bercovici et al. (J Funct Anal...     

Open source simulation tool for electrophoretic stacking,focusing, and separation

We present the development, formulation, and performance of a new simulation tool for electrophoretic preconcentration and separation processes such as capillary electrophoresis, isotachophoresis, and field amplified sample stacking. The code solves the one-dimensional transient advection-diffusion equations for multiple multivalent weak electrolytes (including ampholytes) and includes a model for pressure-driven flow and Taylor–Aris dispersion. The code uses a new approach for the discretization of the equations, consisting of a high resolution compact scheme which is combined with an adaptive grid algorithm. We show that this combination allows for accurate resolution of sharp concentration gradients at high electric fields, while at the same time significantly reducing the computational time. We demonstrate smooth, stable, and accurate solutions at current densities as high as 5000 A/m² using only 300 grid points, and a 75-fold reduction in computational time compared with equivalent uniform grid techniques. The code is available as an open source for free at http://microfluidics.stanford.edu.     

On the Similarity of Analytic Matrix Functions

Consider a domain , and two analytic matrix-valued functions functions . Consider also points and positive integers n ₁, n ₂, . . . , n _N . We are interested in the existence of an analytic function such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)⁻¹ up to order n _j at the point ω _j . We will see that such a function exists provided that F(ω _j ),G(ω _j ) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n _j at ω _j . This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in the unit disk. The author was partially supported by a grant from the National Science Foundation. Received: September 8, 2006. Accepted: January 11, 2007.     

Effect of Substituents and of Wavelength of Irradiation on the Photo-Fries-Rearrangement of Enol-Esters Preliminary Communication

Enol-esters 1a-1e undergo clean Photo-Fries-rearrangements without side reactions. With anthroyl derivatives the reaction is observed only at 254 nm, not at 366 nm.     

A free analogue of Hincin's characterization of infinite divisibility

Hincin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.

     

Tunable Bidirectional Electroosmotic Flow for Diffusion-Based Separations

We present a new concept for on-chip separation that leverages bidirectional flow, to tune the dispersion regime of molecules and particles. The system can be configured so that low diffusivity species experience a ballistic transport regime and are advected through the chamber, whereas high diffusivity species experience a diffusion dominated regime with zero average velocity and are retained in the chamber. We detail the means of achieving bidirectional electroosmotic flow using an array of alternating current (AC) field-effect electrodes, experimentally demonstrate the separation of particles and antibodies from dyes, and present a theoretical analysis of the system, providing engineering guidelines for its design and operation.     

Stereospecific intramolecular C-H amination of 1-aza-2-azoniaallene salts

We report that 1-aza-2-azoniaallene salts, generated from α-chloroazo compounds by treatment with halophilic Lewis acids, participate in intramolecular C-H amination reactions to provide pyrazoline products in good to excellent yield. This intramolecular amination occurs readily at both benzylic and tertiary aliphatic positions and proceeds at an enantioenriched chiral center without loss of enantiomeric excess. A competition reaction shows that insertion occurs more readily at an electron-rich benzylic position than an electron-deficient one. These observations are consistent with the 1-aza-2-azoniaallene intermediate reacting as a nitrenium-like ion by a concerted insertion mechanism.     

Monitoring Dissociation Kinetics during Electrophoretic Focusing to Enable High‐Specificity Nucleic Acid Detection

A wide range of medical conditions can be diagnosed through sequence‐specific analysis of nucleic acids. However, a major challenge remains in detecting a specific target in samples containing a high concentration of mismatching sequences. A single‐step kinetic homogenous (free solution) assay is presented in which free sequence‐specific probes are continuously separated from probe–target hybrids during electrophoretic sample focusing, allowing monitoring of dissociation kinetics. Under these conditions, the different kinetics of targets versus mismatches result in distinct patterns of the signal (for example, linear increase for target versus exponential decay for mismatch), allowing the detection of desired sequences even in the presence of high background nucleic acid content. Additionally, an analytical model provides insight into the underlying dynamics, and allows design of assays based on this mechanism.     

A new approach to subordination results in free probability

We show that the subordination results of D. Voiculescu and Ph. Biane can be deduced from a continuity property of fixed points for analytic functions. The second author was supported in part by a grant from the National Science Foundation.