Abelian Chern-Simons theory, Stokes’ theorem, and generalized connections

Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes’ theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions.The abelian theory considered in the present article is the test case for our method. It can also be applied to the non-abelian theory. Results will be reported in a companion article.     

Infinite partition regular matrices

We consider infinite matrices with entries from (and only finitely many nonzero entries on any row). A matrixA is partition regular over provided that, whenever the set of positive integers is partitioned into finitely many classes there is a vector with entries in such that all entries ofA lie in the same cell of the partition. We show that, in marked contrast with the situation for finite matrices, there exists a finite partition of no cell of which contains solutions for all partition regular matrices and determine which of our pairs of matrices must always have solutions in the same cell of a partition.     

Separation of 18 modern plant protectants using cyclodextrin modified micellar electrokinetic chromatography including an ion-pairing reagent

A cyclodextrin-modified micellar electrokinetic chromatography separation for 18 different pesticides (metsulfuron-methyl, rimsulfuron, thifen-sulfuron-methyl, desethylatrazine, desisopropylatrazine, atrazine, simazine, terbuthylazine, 2,4-D, MCPP, MCPB, dicamba, linuron, alachlor, metolachlor, orbencarb, propiconazole, prochloraz) from eight different substance classes with very varying chemical and physical properties is presented. In particular acid-base characteristics and water-octanol distribution coefficients diverge in wide ranges. -cyclodextrin was successfully employed as a modifier in separating the hydrophobic analytes. Peak distortion of some neutral analytes, which is devoted to the methanol content of the sample zone, was reduced by increasing the SDS concentration. Methanol in the sample is necessary for a better solubility of the hydrophobic pesticides. Few optima of SDS concentration exist allowing the separation of sulfonylureas as well as phenoxy acids and hydrophobic pesticides. An improved resolution of the sulfonylureas was achieved with tetramethylammonium chloride, which was used as an ion-pairing reagent.Final operating conditions for the separation of all these plant protectant compounds by MEKC in just one single run are a 27 mmolL^–1 phosphate buffer, pH 8.03, with 95 mmolL^–1SDS, 5 mmolL^–1 -cyclodextrin and 10 mmol L^–1 tetramethylammonium-chloride.     

Capillary zone electrophoresis of metal-binding proteins in formic acid with UV- and mass spectrometric detection using cationic transient capillary isotachophoresis for preconcentration

A capillary zone electrophoresis (CZE) method with preceding cationic transient capillary isotachophoresis (tCITP-CZE) was developed for uncoated fused-silica capillaries to analyze metal-binding proteins (MBPs) of clinical relevance. UV detection was followed by mass spectrometry (MS). Optimization was done with model proteins of properties similar to relevant human MBPs. Using 1.0 mol x L(-1) formic acid (pH 1.78) as electrolyte resulted in up to 165000 plates m(-1) in CZE and 230000 plates m(-1) in combination with tCITP and analysis time was less than 5 min in uncoupled mode. Cationic tCITP with 125 mmol x L(-1) ammonium formate, buffered to pH 4.00, as leading electrolyte improved sample loadability considerably in comparison with sample stacking without impairing resolution. Following systematic optimization of the electrospray ionization process (ESI) the coupled system ((tCITP)-CZE-UV-ESI-MS) was tested with protein model mixtures and human MBPs. Repeatability of migration times was < 0.64% in pure CZE mode and in tCITP-CZE mode and < 0.83% in CZE-ESI-MS coupled mode. Mass accuracy was < 0.015%. Limits of detection were found to be in the range 50-160 fmol.     

Validation of capillary zone electrophoresis and capillary isoelectric focusing separations optimized for the characterization of two recombinant products of the birch pollen allergen Bet v 1a

CZE and CIEF separation systems, both developed previously for a quality control of two recombinant products of the major birch pollen allergen Bet v 1a of Betula verrucosa, were validated including aspects of the International Conference on Harmonization. One product contained carbamylated variants as impurities. Linearity of response was confirmed by Mandel's fitting test between 0.028 and 1.90 mg/mL for CZE and between 0.016 and 0.26 mg/mL for CIEF. Repeatability and intermediate precision were evaluated for the effective mobility (mu(eff)) in CZE, for relative mobilization time in CIEF and the peak area ratio of Bet v 1a. LOQ for Bet v 1a was between 10 and 23 microg/mL for both methods. Evaluation of robustness for CZE revealed susceptibility of micro(eff) of Bet v 1a to alterations in of buffer pH and separation temperature. Selectivity was impaired by an increase in temperature, pH, and buffer concentration. In addition, pH variations influenced the separation profile of impurities. For CIEF, the ratio of narrow pH range carrier ampholytes is the critical parameter to retain robustness. Results demonstrate the suitability of both separation systems to discriminate between nonmodified Bet v 1a and carbamylated variants in the selected recombinant allergen products.     

On Sparse Parity Check Matrices

We consider the extremal problem to determine the maximal number of columns of a 0-1 matrix with rows and at most ones in each column such that each columns are linearly independent modulo . For fixed integers and , we shall prove the probabilistic lower bound = ; for a power of , we prove the upper bound which matches the lower bound for infinitely many values of . We give some explicit constructions.