High sensitivity separation and detection of heparan sulfate disaccharides

Eight Delta-disaccharide standards from heparan sulfate/heparin were derivatized with the fluorophore 4,4-difluoro-5,7- dimethyl-4-bora-3a,4a-diaza-s-indacene-3-propionic acid, hydrazide (BODIPY) via formation of a Schiff's base and separated using HPAEC on a Propac PA1 column with a linear salt gradient and isocratic 150 mM NaOH. Detection was with an in-line fluorescence detector. The standard deviation (sigma(n-1)) in retention times were 0.7-2% over nine runs. The limit of detection, was 100 fmol (100 x 10(-15)mol) of BODIPY labeled Delta-disaccharides, representing considerably improved detection compared to other fluorophore labeled derivatives and, unlike these, required no further purification steps. Separation and improved detection of BODIPY-Delta-disaccharide conjugates will assist the structural analysis of HS and the development of improved sequencing methodologies.     

Unified multipliers‐free theory of dual‐primal domain decomposition methods

The concept of dual‐primal methods can be formulated in a manner that incorporates, as a subclass, the non preconditioned case. Using such a generalized concept, in this article without recourse to “Lagrange multipliers,” we introduce an all‐inclusive unified theory of nonoverlapping domain decomposition methods (DDMs). One‐level methods, such as Schur‐complement and one‐level FETI, as well as two‐level methods, such as Neumann‐Neumann and preconditioned FETI, are incorporated in a unified manner. Different choices of the dual subspaces yield the different dual‐primal preconditioners reported in the literature. In this unified theory, the procedures are carried out directly on the matrices, independently of the differential equations that originated them. This feature reduces considerably the code‐development effort required for their implementation and permit, for example, transforming 2D codes into 3D codes easily. Another source of this simplification is the introduction of two projection‐matrices, generalizations of the average and jump of a function, which possess superior computational properties. In particular, on the basis of numerical results reported there, we claim that our jump matrix is the optimal choice of the B operator of the FETI methods. A new formula for the Steklov‐Poincaré operator, at the discrete level, is also introduced. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Role of nonlinear coupling and density fluctuations in magnetic-fluctuation-induced particle transport

Three-wave nonlinear coupling among spatial Fourier modes of density and magnetic fluctuations is directly measured in a magnetically confined toroidal plasma. Density fluctuations are observed to gain (lose) energy from (to) either equilibrium or fluctuating fields depending on the mode number. Experiments indicate that nonlinear interactions alter the phase relation between density and magnetic fluctuations, leading to strong particle transport.