Separation of polyphenols using porous polyamide resin and assessment of mechanism of retention

A porous polyamide resin is shown to possess hydrogen bond acceptor properties suitable for the separation of polyphenolic solutes such as phenolic acids, flavonols and flavonoids. The separation is achieved in the presence of solvent mixtures of acetic acid and ethanol. The extent of hydrogen bond adsorption is reviewed based on data obtained from the elution behaviour of a variety of simple polyphenolic solutes. Polyamide adsorption chromatography was applied for the purification of resveratrol and polydatin from Polygonum cuspidatum Sieb. & Zucc.     

One-step purification of epigallocatechin gallate from crude green tea extracts by mixed-mode adsorption chromatography on highly cross-linked agarose media

(-)-Epigallocatechin gallate (EGCG) was purified in one step from a green tea polyphenol (GTP) crude extract by adsorption chromatography on a Superose 12 HR 10/30 column. The mobile phase used was a mixture of acetonitrile and water with an optimum mobile phase compositions regarding purity, recovery and separation time of 78/22 (v/v). Maximum practical sample loading was 100 mg GTP per run (corresponding to 4.2 mg/ml Superose). An EGCG purity of 99% with recoveries in the range 60-65% was achieved in one step directly from the crude GTP extract. Full column regeneration was obtained using solvents in the following order: 0.5 M NaOH, distilled water and 30% acetic acid.     

Some Remarks on the Combinatorics of ISn

\noindent We describe the asymptotic behavior of the cardinalities of the finite symmetric inverse semigroup IS_n and its endomorphism semigroup. This is applied to show that the ratio |IS_n|/|End(IS_n)| is asymptotically 0, answering a question of Schein and Teclezghi. We also apply our results to compute the distributions of elements from IS_n with respect to certain combinatorial properties, and to compute the generating functions for |IS_n| and for the number of nilpotent elements in IS_n.     

Spread‐out percolation in ℝd

Fix d ≥ 2, and let X be either ℤ^d or the points of a Poisson process in ℝ^d of intensity 1. Given parameters r and p, join each pair of points of X within distance r independently with probability p. This is the simplest case of a “spread‐out” percolation model studied by Penrose [Ann Appl Probab 3 (1993) 253–276], who showed that, as r → ∞, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the percolation threshold and the threshold for criticality of the naturally associated branching process approach one another. Here we show that this result follows immediately from of a general result of [3] on inhomogeneous random graphs. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Perfect matchings in random s-uniform hypergraphs

Let E = {X₁, X₂…, X_m} where the X_i ? V for 1 ≤ i ≤ m are distinct. The hypergraph G = (V, E) is said to be s-uniform if |X₁| = s for 1 ≤ i ≤ m. A set of edges M = {X_i : i ? I } is a perfect matching if (i) i ≠ j ? I implies X_i ∩ X_i = 0, and (ii) ∪_i?I X_i = V. In this article we consider the question of whether a random s-uniform hypergraph contains a perfect matching. Let s ≥ 3 be fixed and m/n^4/3 → ∞. We show that an s-uniform hypergraph with m edges chosen uniformly from [74] contains a perfect matching with high probability. This improves an earlier result of Schmidt and Shamir who showed that m/n^3/2 → ∞ suffices. © 1995 John Wiley & Sons, Inc.     

Scaling of microtubule force-velocity curves obtained at different tubulin concentrations

We present a single curve that describes the decay in average growth velocity for microtubules in response to a mechanical force. Curves obtained at two new and one previously studied tubulin concentrations coalesce when normalized with the growth velocity at zero load. This scaling provides direct evidence for a force-independent molecular off rate, in agreement with Brownian ratchet models. In addition, microtubule length changes were measured with a precision up to 10 nm, revealing that microtubules under load abruptly switch between different growth velocities.     

One-step purification of 3,4-dihydroxyphenyllactic acid, salvianolic acid B, and protocatechualdehyde from Salvia miltiorrhiza Bunge by isocratic stepwise hydrogen bond adsorption chromatography on cross-linked 12% agarose

Three major active components of the traditional Chinese medicinal herb Salvia miltiorrhiza Bunge, 3,4-dihydroxyphenyllactic acid, salvianolic acid B, and protocatechualdehyde, are separated and purified from a crude water extract in one step by isocratic hydrogen bond adsorption chromatography on cross-linked 12% agarose (Superose 12 HR 10/30). Separation is achieved by stepwise elution with mobile phases composed of mixtures of ethanol and acetic acid: 0-50 mL, 5% ethanol, 5% acetic acid; 50-100 mL, 20% ethanol, 20% acetic acid; and 100-200 mL, 30% ethanol, 30% acetic acid. The 3,4-dihydroxyphenyllactic acid is obtained with a purity of 97.3% and with a recovery of 88.1%. The corresponding figures for protocatechualdehyde are a purity of 99.4% with a recovery of 90.7%, and for salvianolic acid B a purity of 90.4% with a recovery of 50.3%, respectively. At a sample load of 40 mg crude extract dissolved in 0.5 mL mobile phase (corresponding to a load of 1.6 mg/mL gel), a 3,4-dihydroxyphenyllactic acid purity of approximately 94% with a recovery of 80.2% is obtained.     

Asymptotic bias of some election methods

Consider an election where N seats are distributed among parties with proportions p ₁,…,p _m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a party, i.e. the difference between the number of seats given to the party and the (real) number Np _i that yields exact proportionality. Our approach is to keep p ₁,…,p _m fixed and let N→∞, with N random in a suitable way. In particular, we give formulas showing the bias favouring large or small parties for the different election methods.     

Palladium-catalyzed selective acyloxylation using sodium perborate as oxidant

Sodium perborate (SPB), a principal component of washing powders, was employed as an inexpensive and eco-friendly oxidant in the palladium-catalyzed C-H acyloxylation of alkenes in excellent regio- and stereochemistry. The reactions used anhydrides as acyloxy sources. The method applies to both terminal and internal alkenes, and even benzylic C-H oxidation.