Glucuronic acid derivatives as branching units for the synthesis of glycopeptide mimetics

Natural glycopeptides and glycoproteins exhibit a large structural diversity, which can be mimicked by synthetic glycopeptide derivatives to assist the investigation of biological functions and structure-activity relationships. Here, dendronized saccharides were synthesized to provide glycosyl amino acids, equipped with a branching element for the preparation of branched glycopeptide mimetics. An optimized Staudinger-type reaction served as key reaction en route to the complex glycopeptide 14, in which three mannose moieties were connected to the branched glucuronyl scaffold.     

Measurement of peak areas in energy-dispersive x-ray fluorescence spectrometry

An algorithm is outlined for the measurement of peak areas in spectra obtained by energy-dispersive x-ray fluorescence techniques. Each fluorescence line is assumed to be a pure Gaussian function. Initially, a calibration equation relating the full width at half maximum (FWHM) to the centre of the peak is set up. Then, in an unknown spectrum, the Gauss function parameters are found by a stepwise procedure making a non-linear minimization procedure redundant. First, the background is estimated and subtracted; then the peak centres are found, and the FWHM is given by the calibration equation, which relates FWHM to the position of the peak centre. Finally, the amplitudes are estimated from a set of linear equations. The reliability of the proposed algorithm was proved for a variety of samples. The method was compared with a non-linear x² minimization routine. Quantitative analysis of two standard reference alloys was accurate. Below 20 keV, a suitable FWHM calibration is obtained from a set of K_α lines. Above 20 keV, a set of K_β1,3 lines is recommended.     

Strained, stable 2-aza-1-phosphabicyclo[n.1.0]alkane and -alkene Fe(CO)4 complexes with dynamic phosphinidene behavior

The synthesis of highly strained bicyclic phosphirane and phosphirene iron-tetracarbonyl complexes, that is, complexes with 2-aza-1-phosphabicyclo[n.1.0]alkanes and -alkenes (n = 3-5), is explored by using intramolecular cycloaddition of an in situ generated electrophilic phosphinidene complex, [R(iPr)NP=Fe(CO)(4)], to its C=C- and C[triple chemical bond]C-containing R substituent. Saturated bicyclic complexes 7 a-c with n = 4-2 are remarkably stable, as illustrated by the X-ray crystal structure for 7 b (n=3), yet all readily undergo retroaddition to react with phenylacetylene. Shuttling of the phosphinidene iron complex between two equivalent C=C groups is demonstrated for a 1-butene-substituted 2-aza-1-phosphabicyclo[3.1.0]hexane by selective (1)H NMR magnetization transfer from the phosphirane protons to the olefinic protons. Even the more strained unsaturated bicycles 17 a,b (n = 4,3) are surprisingly stable as illustrated by the X-ray crystal structure for 17 a (n = 4), but the smaller phosphabicyclo[3.1.0]hex-5-ene (17 c, n = 2) dimerizes to tricyclic 19 with a unique ten-membered heterocyclic ring; an X-ray crystal structure is reported. Like their saturated analogues also the bicyclic phosphirenes readily undergo retroaddition as shown by the reaction of their phosphinidene iron moiety with phenylacetylene.     

Exact effective Hamiltonian theory. II. Polynomial expansion of matrix functions and entangled unitary exponential operators

Our recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance (NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker-Campbell-Hausdorff problem for SU(N) systems from N< or =4 to any N, and thereby the potential application of EEHT to more complex NMR spin systems. Similarity matrix transformations of the EEHT expansion are used to develop alternant quotient expressions, which are fully general and prove useful for evaluation of any smooth matrix function. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester's theorem (also known as the spectral theorem) and the EEHT expansion.     

Effect of catalyst partitioning in Co(II) mediated catalytic chain transfer miniemulsion polymerization of methyl methacrylate

The effect of catalyst partitioning over the organic and water phases in the catalytic chain transfer mediated miniemulsion polymerization was investigated and a mathematical model developed to describe the instantaneous degree of polymerization of the formed polymer. Experimental and predicted instantaneous degrees of polymerization prove to be in excellent agreement. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5839–5849, 2008     

Note sur la convergence d'une série neumannienne de fonctions cylindriques

Ohne Zusammenfassung

---

Note sur la convergence d'une série neumannienne de fonctions cylindriques

     

An improved perfectly matched layer for the eigenmode expansion technique

When performing optical simulations for rotationally symmetric geometries using the eigenmode expansion technique, it is necessary to place the geometry under investigation inside a cylinder with perfectly conducting walls. The parasitic reflections at the boundary of the computational domain can be suppressed by introducing a perfectly matched layer (PML) using e.g. complex coordinate stretching of the cylinder radius. However, the traditional PML suffers from an artificial field divergence limiting its usefulness. We show that the choice of a constant cylinder radius leads to mode profiles with exponentially increasing field amplitudes resulting in numerical instability. As a remedy we propose an improved PML based on a mode-dependent cylinder radius and mode profiles with stable field amplitudes. The new PML formulation eliminates the artificial field divergence and ensures numerical stability.