Nachweis und Bestimmung des Chroms

Ohne Zusammenfassung     

GMRES and the minimal polynomial

We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size.Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight.Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.This research was partially supported by National Science Foundation grants DMS-9122745, DMS-9423705, CCR-9102853, CCR-9400921, DMS-9321938, DMS-9020915, and DMS-9403224.     

Inexact primal-dual interior point iteration for linear programs in function spaces

Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.The research of this author was supported by an Overseas Research Scholarship of the Ministry of Education, Science and Culture of Japan.The research of this author was supported by National Science Foundation grants #DMS-9024622 and #DMS-9321938, North Atlantic Treaty Organization grant #CRG 920067, and an allocation of computing resources from the North Carolina Supercomputing Program.The research of this author was supported by North Atlantic Treaty Organization grant #CRG 920067.     

The effect of head position on glottic closure in patients with unilateral vocal fold paralysis

The present study was designed to assess the effect of head position on glottic closure as reflected in airflow rates (open quotient and maximum flow declination rate), in patients with unilateral vocal fold paralysis. Ten patients, 2 males and 8 females ranging in age from 40 to 75, with a mean age of 57.3, served as subjects. Airflow measures were taken during sustained phonation of two vowels (/i/ and /a/) in 3 head positions (center, right, left). Vowels /i/ and /a/ were produced at subject's comfortable pitch and loudness, with random ordering of both vowel order and head orientation. Subjects were trained to focus eye gaze on right and left markers (70-degree angle) and a central marker at eye level directly in front of the subject. Theoretically, if turning the head during phonation alters the laryngeal anatomic relationship by bringing the vocal folds in closer proximity to one another, then airflow rate should lessen. Our results indicate that head position does not improve glottic closure in these patients, which is in contrast to previously published research.(1) Our results question the utility and underlying theoretical construct for the use of head turning as a therapeutic technique for improvement of voice in patients with unilateral vocal fold paralysis.     

A PEGylated Photocleavable Auxiliary Mediates the Sequential Enzymatic Glycosylation and Native Chemical Ligation of Peptides

Research aimed at understanding the specific role of glycosylation patterns in protein function would greatly benefit from additional approaches allowing direct access to homogeneous glycoproteins. Herein the development and application of an efficient approach for the synthesis of complex homogenously glycosylated peptides based on a multifunctional photocleavable auxiliary is described. The presence of a PEG polymer within the auxiliary enables sequential enzymatic glycosylation and straightforward isolation in excellent yields. The auxiliary‐modified peptides can be directly used in native chemical ligations with peptide thioesters easily obtained by direct hydrazinolysis of the respective glycosylated peptidyl resins and subsequent oxidation. The ligated glycopeptides can be smoothly deprotected by UV irradiation. We apply this approach to the preparation of variants of the epithelial tumor marker MUC1 carrying one or more Tn, T, or sialyl‐T antigens.     

Nonstoichiometric,Protic Azolium Azolate Ionic Liquids Provide Unique Environments for N‐Donor Coordination Chemistry

Here we demonstrate that neat reactions of amphoteric azoles with more basic azoles give a family of finely tunable, nonstoichiometric liquids which are useful for N‐donor coordination chemistry. Reacting 4,5‐dicyanoimidazole (4,5‐DCNIm) with 1‐methylimidazole (1‐mim) gives new compounds with composition‐dependent speciation. Two crystalline compounds, a 1:1 protic salt, [H(1‐mim)][4,5‐DCNIm], and a 1:2 salt co‐crystal, [H(1‐mim)][4,5‐DCNIm]?4,5‐DCNIm, were isolated and structurally characterized, while differential scanning calorimetry revealed both suppression of crystallization and the presence of neutral and anionic species in the melt. Reactions of Cu(NO₃)₂?2.5 H₂O, CuO, and ZnO with the neat 2:1 1‐mim/4,5‐DCNIm melt resulted in the isolation of entirely N‐donor ligated complexes of the formula M(4,5‐DCNIm)₂(1‐mim)₄ (M=Cu, Zn).     

Response of circular clamped plates to square-wave stress pulses

An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular stress pulses over a small circular region. The stress pulses were transmitted to the plates through a 1/2-in.-diam shock bar and the strain-time responses of the plates were measured. The stress-wave interactions between the bar and the plates were measured for a number of thicknesses and the effect of the applied stress on the extent of the plastic deformation was determined. It was found that the elastic response was accurately predicted by the theory of Sneddon and the plastic response behaved according to a simple modification of this theory. The interaction between the stress pulse and plates of various thickness was theoretically predicted and found to be in excellent agreement with experimental measurements. The final plate deflections were theoretically predicted using a rigid viscoplastic theory and was in substantial agreement with the data. From this theory, the data were analyzed to determine the visco-plastic constant or relaxation time of the material. It is proposed that this testing arrangement is a suitable and convenient method for determining dynamic yield properties under biaxial-loading conditions.     

Enhanced stereoselectivity of a Cu(II) complex chiral auxiliary in the synthesis of Fmoc-L-γ-carboxyglutamic acid

L-γ-Carboxyglutamic acid (Gla) is an uncommon amino acid that binds avidly to mineral surfaces and metal ions. Herein, we report the synthesis of N-α-Fmoc-L-γ-carboxyglutamic acid γ,γ'-tert-butyl ester (Fmoc-Gla(O(t)Bu)(2)-OH), a suitably protected analogue for Fmoc-based solid-phase peptide synthesis. The residue was synthesized using a novel chiral Cu(II) complex, whose structure-based design was inspired by the blue copper protein rusticyanin. The five-coordinate complex is formed by Shiff base formation between glycine and the novel ligand (S)-2-(N-(2-methylthio)benzylprolyl)aminobenzophenone in the presence of copper. Michael addition of di-tert-butyl methylenemalonate to the α-carbon of the glycine portion of the complex occurs in a diastereoselective fashion. The resulting (S,S)-complex diastereomer can be easily purified by chromatography. Metal complex decomposition followed by Fmoc protection affords the enantiomerically pure amino acid. With the use of this novel chiral complex, the asymmetric synthesis of Fmoc-Gla(O(t)Bu)(2)-OH was completed in nine steps from thiosalicylic acid in 14.5% overall yield.     

Poly[tetrakis(n‐propylammonium) [octa‐μ‐chlorido‐dichloridotrinickelate(II)]]: a hybrid organic–inorganic layer compound in the Cs4Mg3F10 structure type

The title compound, {(C₃H₁₀N)₄[Ni₃Cl₁₀]}_n, contains zigzag layers of tri‐μ‐chlorido‐bridged linear 2/m‐symmetric Ni₃Cl₁₂ segments, linked by mono‐μ‐chlorido quasi‐linear bridges to two other segments at each end. These inorganic layers are interleaved with interdigitated bilayers of mirror‐symmetric n‐propylammonium cations, the ammonium head groups of which are directed into the inorganic layers to form multiple N—H...Cl hydrogen bonds, while the propyl tail groups pack together in a tongue‐and‐groove manner in the center of the bilayer. The propyl groups are ordered at 100 K but disordered with opposite conformations on the mirror plane at 240 K.