Temporary attachment of carbohydrates to cyclopeptide templates: a new strategy for single-bead analysis of multivalent neoglycopeptides

Employing a cleavable carbohydrate–peptide linker, a new strategy for single-bead analysis of multivalent cyclic neoglycopeptides based on Edman degradation is described. Edman degradation of glycopeptides is hampered by the acid lability of the glycosidic bond and potential incompatibilities of phenylthiohydantoin (PTH) derivatives of glycosylated amino acids with PTH derivatives of the proteinogenic amino acids. To overcome this problem, carbohydrates are detached from the cyclopeptide templates before single-bead analysis, allowing for micro sequencing under routine conditions. With this strategy, application of multivalent cyclic neoglycopeptides in split-mix libraries with a subsequent screening process becomes possible for the first time.     

Some non‐standard problems in viscous flow

Energy bounds are derived for Dirichlet type boundary value problems for the Navier–Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non‐standard auxiliary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

An Addendum to Birkhoff's Theorem

In spherically symmetric systems, in spite of Birkhoff's Theorem, the rates of clocks in vacuum regions on either side of moving mass shells must be continually readjusted to stay in synchrony. This shows up as time-dependence of the metric in terms of the globally meaningful time coordinate.     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

Mehrfachbindungen zwischen Hauptgruppenelementen und Übergangsmetallen : XLIV. Synthesen von Hydrogensulfido- und Hydrogenselenido-Komplexen der Metalle Chrom, Molybdän und Wolfram

Hydrogenchalcogenido complexes of general composition (η⁵-C₅R₅)(CO)₃M(EH) (R = H, CH₃; M = Cr, Mo, W; E = S, Se) can be obtained by three different routes, sometimes in quite good yields. Thus, the sulfur and selenium derivatives can be synthesized by insertion of the respective elements into the metal-hydrogen bonds of the precursor compounds (η⁵-C₅R₅)(CO)₃MH. This species also reacts with potassium selenocyanate to yield the hydrogenselenido derivatives (η⁵-C₅R₅)(CO)₃M(SeH) which can also be obtained by treatment of the methyl complexes (η⁵-C₅R₅)(CO)₃M(CH₃ (M = Mo, W) with HBF₄ and Li[SeH]. The corresponding hydrogentellurido compounds are probably formed by these preparative methods but appear to be quickly converted into either the dinuclear tellurium bridge products (μ-Te)[(η⁵-C₅R₅)(CO)₃M]₂ (M = Mo) or into the hydrido complexes (η⁵-C₅R₅)(CO)₃MH (M= Mo, W) by release of elemental tellurium.     

The stationary and non-stationary stokes system in exterior domains with non-zero divergence and non-zero boundary values

In an exterior domain Ω??ⁿ, n ? 2, we consider the generalized Stokes resolvent problem in L^q-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫_?Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L⁵(0, T;L^q(Ω)) for 1 < s, q < ∞.