The square lattice shuffle

We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Surface composition of spray-dried milk protein-stabilised emulsions in relation to pre-heat treatment of proteins

Several important technical properties of spray-dried food powders depend on particle-liquid interactions (e.g. wettability, dispersability) and particle-particle interactions (e.g. flowability). It can be assumed that the chemical composition of the surface layer of the particles to a large extent determine these properties. The present study has been aimed to investigate the relation between the surface composition of spray-dried milk protein-stabilised emulsions and pre-heat treatment of the proteins. Solutions of WPC were heat-treated at low (60-90 degrees C) and high (140 degrees C) temperature and the degree of denaturation was determined, prior to the preparation of emulsions with rapeseed oil. The surface composition of the dry powders were established by using ESCA (electron spectroscopy of chemical analysis). The emulsions were characterised by droplet size distribution before spray drying and after dissolution of the powders. Also free fat extractions and estimations of wettability (dissolution rates) were performed. The powder surface coverage of protein decreased with increasing degree of protein denaturation before the emulsification, whereas the emulsion droplet size increased both before spray drying and after reconstitution of powders. The free fat extraction as well as the dissolution rate, whereof the latter decreased with increasing surface fat coverage, correlated well with the fat coverage of the powder surface.     

Double cyclisation of phenylglycine-o-carboxylic acids—I: New stable mesoionic oxazolones

Remarkably stable mesoionic oxazolones possessing an oxazolo[3,2-a]quinolinium structure (5a–b),8,16, 17) were obtained by the double cyclisation of phenylglycine-o-carboxylic acids (3a–c) in refluxing acetic anhydride or in benzoic anhydride at 140°, The 0-Ac group was eliminated to give the corresponding lactones (6a–b) or replaced by O-Ts (7). IR stretching vibrations of the endo-carbonyl were in the range 1710–1768 cm^?1, while v_1-CH exhibited unusually high values (3159–3194 cm^-1). 1-Acyl derivatives could be obtained only with TFAA (23–24), although easy deuteration of the same position took place in the presence of traces of trifluoroacetic acid. Hydrolysis of 5b led to the α-quinolone-N-acetic acid 27a. In the case of 5a, hydrolysis was accompanied by self-acylation of the nucleophilic site at C-4 with formation of a dimeric acid 28a. The presence of an additional Me group in phenylalanine-o-carboxylic acid (36) activates the corresponding mesoionic oxazolone 37 so that 1-acylation becomes possible with formation of the fused oxazole 38 by the Dakin-West reaction. Temperature dependent magnetic non-equivalence of methylene protons has been observed in acids 3b-d and f and also in the 7-membered anhydride 48b.     

BRCA1 mutation screening using restriction endonuclease fingerprinting-single-strand conformation polymorphism in an automated capillary electrophoresis system

Efficient mutation scanning techniques are needed for the rapid detection of novel disease-associated mutations and rare-sequence variants of putative importance. The large size of the breast cancer 1 gene (BRCA1) and the many mutations found throughout its entire coding sequence make screening for mutations in this gene particularly challenging. We have developed a method for screening exon 11 of the BRCA1 gene based on restriction enzyme digestion of fluorescence-labeled polymerase chain reaction (PCR) products followed by single-strand conformation polymorphism (SSCP) using an automated capillary electrophoresis system, denoted capillary restriction endonuclease fingerprinting (REF)-SSCP electrophoresis. Using this strategy on a control set of samples, we were able to detect 17 of 18 known sequence alterations. The method was then applied to screen 73 Norwegian females with family histories of breast and/or ovarian cancer. A total of 172 sequence alterations were detected, including substitutions, insertions, and deletions. One novel substitution of unknown function was identified. Sequencing of all samples negative in the capillary REF-SSCP system gave no additional mutations confirming the high sensitivity of the described methodology. Capillary REF-SSCP electrophoresis appeared as a technically convenient technique, requiring amplification of fewer PCR fragments than traditional SSCP. The novel strategy allows high-throughput mutation scanning without radioactive labeling and polyacrylamide gel electrophoresis (PAGE).     

Resolution of seven-coordinate complexes

The crystal structures of [Pr(dbm)3H2O] (1), [Sm(dbm)3H2O] (2), and [Er(dbm)3H2O] (3) have been determined (dbm=dibenzoylmethane). They display seven-coordinate propeller-shaped molecules, which are chiral and crystallize as conglomerates in space group R3. Analysis of the crystal structures reveals supramolecular interactions, including formation of a quadruple helix, which explain how stereochemical information can be transferred between stacks of molecules. A method to quantify the ee in bulk samples of stereochemically labile compounds by using solid-state CD spectroscopy is described. Using this method, it has been shown that compounds 1-3 undergo total spontaneous resolution directly after synthesis, forming a microcrystalline reaction product that is essentially enantiopure. The resolution of bulk quantities of seven-coordinate complexes (without chiral or polydentate ligands) is thus reported for the first time. Because the crystallization starts without seeding, the overall preparation may be regarded as absolute asymmetric synthesis.     

Total spontaneous resolution of chiral covalent networks from stereochemically labile metal complexes

Stereochemically labile copper and zinc complexes with the N,N'-dimethylethylenediamine ligand (dmeda) have been shown to be promising precursors for the total spontaneous resolution of chiral covalent networks. (N,N')-[Cu(NO3)2(dmeda)]infinity crystallises as a conglomerate and yields either enantiopure (R,R)-1 or enantiopure (S,S)-1. A mixed-valence copper(I/II) complex, [{Cu(II)Br2(dmeda)}3(Cu(I)Br)2]infinity (2), which crystallises as a pair of interpenetrating chiral (10,3)-a nets, is formed from CuBr, CuBr2 and dmeda. One net contains ligands with solely (R,R) configuration and exhibits helices with (P) configuration while the other has solely (S,S)-dmeda ligands and gives rise to a net in which the helices have (M) configuration. The whole crystalline arrangement is racemic, because the interpenetrating chiral nets are of opposite handedness. With zinc chloride (R,S)-[ZnCl(dmeda)2]2[ZnCl4] (3) is obtained, which is a network structure, although not chiral. Total spontaneous resolution of stereochemically labile metal complexes formed from achiral or racemic building blocks is suggested as a viable route for the preparation of covalent chiral networks. Once the absolute structure of the compound has been determined by X-ray crystallography, a quantitative determination of the enantiomeric excess of the bulk product can be undertaken by means of solid-state CD spectroscopy.     

A quantitative evaluation of the electrostatic theory for ion pair chromatography

Summary A quantitative model for ion pair chromatography based on the electrostatic theory is described. The model is based on the solution of the linearised Poisson-Boltzmann equation in a cylinder. The obtained equations are compared with experimental data from a number of different systems. The agreement between theory and experiments is satisfactorily. Systematic deviations due to the use of the linearised equation and ion correlation effects are discussed.