N-arylation of primary and secondary aliphatic amines on solid supports

A general and mild method for the N-arylation of primary and secondary aliphatic amines is reported. Copper acetate, triethylamine mediated C/N cross-coupling reaction of arylboronic acids at room temperature to solid-supported primary and secondary amines gave good to excellent yields of the desired N-arylated products.     

Two-parameter mobile phase optimization for the simultaneous high-performance liquid chromatographic determination of dopamine, serotonin and related compounds in microdissected rat brain nuclei.

A new high-pressure liquid chromatography method with electrochemical detection is described that allows the simultaneous determination of dopamine, serotonin, 3,4-dihydroxyphenylacetic acid, 3-methoxy-4-hydroxyphenylacetic acid, 5-hydroxytryptophan and 5-hydroxyindoleacetic acid in microdissected nuclei from individual rat brains. No sample pre-treatment steps are required. Resolution and analysis time were optimized by a simple limited optimization procedure, involving two-parameter factorial design.     

A class of not local rank one automorphisms arising from continuous substitutions

Summary A simple class of not local rank one, loosely Bernoulli transformations is constructed. These examples have simple spectra. It is studied when inverse limits of local rank one transformations are again of local rank one.     

Odometer actions of the Heisenberg group

Let H₃(?) be the 3-dimensional real Heisenberg group. Given a family of lattices Γ₁ ? Γ₂ ? … ? H₃(?), let T be the associated uniquely ergodic H₃(?)-odometer, i.e., the inverse limit of the H₃(?)-actions by rotations on the homogeneous spaces H₃(?)/Γ_j, j ∈ ?. We describe explicitly the decomposition of the underlying Koopman unitary representation of H₃(?) into a countable direct sum of irreducible components and find the ergodic 2-fold self-joinings of T. We show that in general, the H₃(?)-odometers are neither isospectral nor spectrally determined.     

Active Optics: Vase or Meniscus Multimode Mirrors and Degenerated Monomode Configurations

Multimode deformable mirrors allow to superpose optics aberration modes up to high orders. The elasticity analysis leads to consider mainly Clebsch–Zernike modes that belong to a sub-class of optics modes. Theoretical results and associated geometries are also derived for some single modes. This allows discovering degenerated configurations using a minimal set of applied external forces. We present interferometric results from active optics experiments including the degenerated configurations for third-order astigmatism and fifth-order triangle modes.     

Functionalized porous silicon surfaces as MALDI-MS substrates for protein identification studies

Alkyl monolayer modified porous silicon functional surfaces are employed for selective binding of proteins from complex mixtures (through washing of the deposited mixture spot using appropriate buffer) and MALDI-MS is used to detect the components retained on the surface.     

Gas Chromatography–Mass Spectrometry Determination of Pregabalin in Human Plasma Using Derivatization Method

A gas chromatography–mass spectrometry method for the determination of pregabalin in human plasma is described. The procedure involves precipitation of protein, liquid–liquid extraction with ethylene glycol monomethyl ether, and derivatization with 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide in the presence of N-hydroxysuccinimide as additive. Separation was attained on HP column (30 m × 0. 25 mm ID, 0.25 μm) coupled with mass spectrometric detector using electron impact selected ion monitoring. The assay showed an excellent linearity in the concentration range of 0.36–10 μg mL^?1 with correlation coefficient (r²) values of 0.999. The intra- and inter-day assay variations for three different concentration levels were less than 10%. The limit of quantification was detected at 0.36 μg mL^?1. The method is highly specific, precise, accurate, and reproducible and could also be applied for the determination of pregabalin in human plasma.     

On the weak isomorphism of strictly ergodic homeomorphisms

Two strictly ergodic homeomorphism (on an infinite dimensional torus) are constructed, each of which is a continuous homomorphic image of the other, but which are not measure-theoretically isomorphic.     

The rank of regular morse dynamical systems

Summary If x=b ⁰ × b ¹ × . is a regular Morse sequence and sup \ ⁱ<+, then x has rank 2. There are regular Morse shifts with rank one. If x is a Kakutani sequence, then x has rank one iff x is not regular. If is a nonperiodic substitution of constant length on two symbols, then is of rank 2 iff is a continuous substitution. Every Morse sequence has a simple spectrum.     

General Bernstein-Like Inequality for Additive Functionals of Markov Chains

Journal of Theoretical Probability - Using the renewal approach, we prove Bernstein-like inequalities for additive functionals of geometrically ergodic Markov chains, thus obtaining counterparts of...