High performance liquid chromatographic measurement of bisoprolol in plasma

A simple high performance liquid chromatographic method has been devised for the measurement of bisoprolol in plasma or serum. The sample (200 microL) is vortex mixed for 30 s with 2 M Tris solution (50 microL), aqueous internal standard (benzimidazole, 2.0 mg/L, 50 microL) and methyl t-butyl ether (200 microL). After centrifugation (9950 x g, 2 min), a portion of the resulting extract is analysed on a microparticulate (5 microns) silica column using 1 mM camphorsulphonic acid in methanol as the mobile phase. Detection is by fluorescence at an excitation wavelength of 215 nM. The lower limit of accurate measurement for the assay is 10 micrograms/L (CV% = 8.9, n = 9) with a lower limit of detection of 5 micrograms/L. There is minimal interference from either commonly prescribed drugs or endogenous compounds.     

Extracting invariants of isolated hypersurface singularities from their moduli algebras

We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated hypersurface singularities from their moduli algebras, which extends an earlier result due to the first author. Furthermore, we conjecture that the invariants so constructed solve the biholomorphic equivalence problem in the homogeneous case. The conjecture is easily verified for binary quartics and ternary cubics. We show that it also holds for binary quintics and sextics. In the latter cases the proofs are much more involved. In particular, we provide a complete list of canonical forms of binary sextics, which is a result of independent interest.     

Riemann surfaces,Clifford algebras and infinite dimensional groups

We consider functionals on one dimensional subshifts which have prescribed Randon-Nikodym derivative under transportation by conjugating homeomorphisms, and investigate their relation to Ruelle's transfer operator. In particular we show that two-sided functionals essentially are products of a functional which are supported on stable and unstable leaves. We also prove the meromorphicity of the Fourier transform of correlation functions for AxiomA follows in a more general setting.     

Microwave-assisted synthesis of 1,3-dihydro-[1,2,5]thiadiazolo[3,4-b]pyrazine-2,2-dioxides

1,3-Dihydro[1,2,5]thiadiazolo[3,4-b]pyrazine-2,2-dioxides are obtained in a good yield from the reaction of 2,3-diamino pyrazines with sulfamide under microwave conditions.     

Riemann surfaces,Clifford algebras and infinite dimensional groups

We introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a gauge group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces.     

Gaussian split Ewald: A fast Ewald mesh method for molecular simulation

Gaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both real-space and k-space Poisson solvers. While real-space methods are known to be asymptotically superior to k-space methods in terms of both computational cost and parallelization efficiency, k-space methods such as smooth particle-mesh Ewald (SPME) have thus far remained dominant because they have been more efficient than existing real-space methods for simulations of typical systems in the size range of current practical interest. Real-space GSE, however, is approximately a factor of 2 faster than previously described real-space Ewald methods for the level of force accuracy typically required in biomolecular simulations, and is competitive with leading k-space methods even for systems of moderate size. Alternatively, GSE may be combined with a k-space Poisson solver, providing a conveniently tunable k-space method that performs comparably to SPME. The GSE method follows naturally from a uniform framework that we introduce to concisely describe the differences between existing Ewald mesh methods.     

Folding funnels: the key to robust protein structure prediction

Natural proteins fold because their free energy landscapes are funneled to their native states. The degree to which a model energy function for protein structure prediction can avoid the multiple minima problem and reliably yield at least low-resolution predictions is also dependent on the topography of the energy landscape. We show that the degree of funneling can be quantitatively expressed in terms of a few averaged properties of the landscape. This allows us to optimize simplified energy functions for protein structure prediction even in the absence of homology information. Here we outline the optimization procedure in the context of associative memory energy functions originally introduced for tertiary structure recognition and demonstrate that even partially funneled landscapes lead to qualitatively correct, low-resolution predictions.