Superporous agarose beads as a hydrophobic interaction chromatography support

Superporous agarose beads were used as a support for hydrophobic interaction chromatography. These beads have large connecting flow pores in addition to their normal diffusion pores. The flow pores, which are approximately one fifth of the overall diameter of the superporous agarose beads, were earlier shown to give the beads improved mass transfer properties relative to homogeneous agarose beads (Gustavsson and Larsson, J. Chromatogr. A, 734 (1996) 231–240). Superporous agarose beads and homogeneous agarose beads of the same particle size range (106–180 μm) were derivatized with phenyl groups. The properties of the superporous beads were then compared with the homogeneous beads in the separation of a mixture of three model proteins (ribonuclease A, lysozyme and bovine serum albumin) at various superficial flow velocities from 30 to 600 cm/h. The superporous beads gave satisfactory separation at flow velocities five times higher than was possible for homogeneous beads. The performance of the two types of beads was also compared in the purification of lactate dehydrogenase from a beef heart extract at a superficial flow velocity of 150 cm/h. The superporous beads performed considerably better, leading to twice the purification factor and twice the concentration of the desired product. The results were interpreted using the theoretical treatment given by Carta and Rodrigues (Carta and Rodrigues, Chem. Eng. Sci., 48 (1993) 3927).     

A Practical Procedure for the Solid-Phase Synthesis of Racemic 2,2′-Dihydroxy-1,1′-binaphthyl

Abstract: A high yielding solid-phase dimerisation of 2-naphthol by means of a ball-milling procedure is described.

     

On the numerical radius of matrices and its application to iterative solution methods

Uses of the numerical radius in the analysis of basic iterative solution methods, of the SOR method for quasi-Hermitian positive definite matrices (not being consistently ordered) and of maximal eigenvalues of symmetric positive definite matrices using incomplete block-matrix factorizations are presented.     

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations leads to large sparse saddle point systems in two levels. In this paper, we consider distributed optimal control for the Stokes system and test the particular case when the arising linear system can be compressed after eliminating the control function. In that case, a system arises in a form which enables the application of an efficient block matrix preconditioner that previously has been applied to solve complex-valued systems in real arithmetic. Under certain conditions, the condition number of the so preconditioned matrix is bounded by 2. The numerical and computational efficiency of the method in terms of number of iterations and execution time is favorably compared with other published methods.     

A general approach to analyse preconditioners for two‐by‐two block matrices

Two‐by‐two block matrices arise in various applications, such as in domain decomposition methods or when solving boundary value problems discretised by finite elements from the separation of the node set of the mesh into ‘fine’ and ‘coarse’ nodes. Matrices with such a structure, in saddle point form arise also in mixed variable finite element methods and in constrained optimisation problems. A general algebraic approach to construct, analyse and control the accuracy of preconditioners for matrices in two‐by‐two block form is presented. This includes both symmetric and nonsymmetric matrices, as well as indefinite matrices. The action of the preconditioners can involve element‐by‐element approximations and/or geometric or algebraic multigrid/multilevel methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Equivalent operator preconditioning for elliptic problems

The numerical solution of linear elliptic partial differential equations most often involves a finite element or finite difference discretization. To preserve sparsity, the arising system is normally solved using an iterative solution method, commonly a preconditioned conjugate gradient method. Preconditioning is a crucial part of such a solution process. In order to enable the solution of very large-scale systems, it is desirable that the total computational cost will be of optimal order, i.e. proportional to the degrees of freedom of the approximation used, which also induces mesh independent convergence of the iteration. This paper surveys the equivalent operator approach, which has proven to provide an efficient general framework to construct such preconditioners. Hereby one first approximates the given differential operator by some simpler differential operator, and then chooses as preconditioner the discretization of this operator for the same mesh. In this survey we give a uniform presentation of this approach, including theoretical foundation and several practically important applications for both symmetric and nonsymmetric equations and systems, and some nonlinear examples in the context of Newton linearization. Dedicated to the memory of Gene Golub for his friendly manner and for his broad interest and significant impact on numerical analysis.     

Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems

A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.     

Aromatic allylation via diazotization: metal-free C-C bond formation

A new method for the synthesis of allyl aromatic compounds not involving any metal-containing reagent or catalyst has been developed. Arylamines substituted with a large number of different substituents were converted via diazotizative deamination with tert-butyl nitrite in allyl bromide and acetonitrile to the corresponding allyl aromatic compounds. The allylation reaction was found to be suitable for larger scale synthesis due to short reaction times, a nonextractive workup, and robustness toward moisture, air, and type of solvent.     

Hyperpolarization of 13C through order transfer from parahydrogen: a new contrast agent for MRI

The order within proton pairs in organic molecules, resulting from hydrogenation with parahydrogen, can be transferred in great part to nearby carbon 13 spins through adequate field manipulations. The molecules with hyperpolarized 13C thus obtained can be used as new contrast agents of high efficiency in MRI. After a brief presentation of the hydrogenation process and apparatus, in relatively low magnetic field, we describe the procedure of order transfer to the 13C spins through a sudden drop from the initial field to zero field followed by an adiabatic remagnetization. The expected final polarizations in the absence of relaxation are given for several compounds. Finally, we show an example of MR images observed in vivo on animals as an illustration of the contrast capacity of this new method.     

Study of 19Na at SPIRAL

The excitation function for the elastic-scattering reaction p( ¹⁸Ne, p) ¹⁸Ne was measured with the first radioactive beam from the SPIRAL facility at the GANIL laboratory and with a solid cryogenic hydrogen target. Several broad resonances have been observed, corresponding to new excited states in the unbound nucleus ¹⁹Na. In addition, two-proton emission events have been identified and are discussed.