Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. D. S. Watkins partly supported by Deutsche Forschungsgemeinschaft through Matheon, the DFG Research Center Mathematics for key technologies in Berlin.     

Complete Quenching of the Pd3(dppm)3(CO)2+ Cluster Emission Via Electrostatic Host–Guest Assemblies with Carboxylate-Containing Tetraphenylporphyrins of Ni(II) and Fe(III)

The title cluster is luminescent at 77?K and exhibits an unsaturated site for binding anions when the counter ion is PF₆ ^?. A series of five non-luminescent metalloporphyrins exhibiting carboxylate anchoring groups were synthesized and characterized. These are the sodium salts of the 5-carboxyphenyl-tri-10,15,20-tolyl-, trans-di-5,10-carboxyphenyl-di-15,20-tolyl-, and tetra-5,10,15,20-carboxyphenyl(metallo)porphyrin (metallo?=?chloroiron(III), nickel(II)) anions. Evidence for supramolecular assemblies between the carboxylates and the cluster is provided by ³¹P NMR and UV?Cvis spectroscopy. The binding constant, K_1n, extracted from the UV?Cvis data via Benesi-Hildebrand, Scott and Scatchard plots are approximately 21,000?±?5,000?M^?1 for the nickel(II) species, in agreement with the previously reported zinc(II) ones (K₁₁?=?20,000?±?2,000?M^?1), but those for the chloroiron(III) are measured to be lower (12,500?±?3,500?M^?1). This association is accompanied by a complete quenching of the luminescence of the cluster which can only be due to an efficient energy transfer to the d?Cd states of the chloroiron(III) and nickel(II) species but an electron transfer from the nickel(II)-containing chromophore to the cluster is also possible. This work demonstrates the profound effect that supramolecular interactions may have on the photophysical properties despite the long donor?Cacceptor separation.     

Positron spectroscopy analysis in metallocene propylene/1‐octadecene copolymers: Parameters dependence on monoclinic and mesomorphic polymorphs

Copolymers of propylene and 1‐octadecene synthesized by a metallocene catalyst were characterized by PALS, WAXD, DSC, and density measurements. The change in the sizes and the number density of free‐volume holes as a function of the 1‐octadecene content were compared to the master laws published for copolymers of propylene with α‐olefins of shorter lengths. It was found that the samples were separated into two groups. The first set of samples obeyed the master laws while the second group deviated. This behavior was explained by the difference in the copolymer structure. The WAXD analysis confirmed the separation as well. The deviation was explained as due to the mesomorphic crystalline structure of the second group of samples, in contrast to the monoclinic one for the first group, which was a result of the relatively fast cooling from the molten state and from the high comonomer molar content. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1994–2002, 2010     

Enzyme mediated kinetic resolution of δ-hydroxy-α,β-unsaturated esters as a route to optically active δ-lactones

A novel synthetic route to optically active saturated and unsaturated δ-lactones based on enzymatic kinetic resolution and ring-closing metathesis reactions has been proposed. The influence of temperature, co-solvent, organic additives and the substrate structure on the catalytic behavior of selected hydrolases was studied. The substantial impact of the organic co-solvent and surfactant type on the enzymatic activity and enantioselectivity was observed providing enantiomerically pure δ-hydroxy-α,β-unsaturated esters. The established protocol combining enzymatic kinetic resolution with ring closing metathesis was successfully applied in the synthesis of the enantiomerically pure (6R)-phenyl-5,6-dihydro-2H-pyran-2-one which plays crucial role in the synthesis of the number of bioactive compounds.     

Optimal echo spacing for multi-echo imaging measurements of Bi-exponential T2 relaxation

Calculations, analytical solutions, and simulations were used to investigate the trade-off of echo spacing and receiver bandwidth for the characterization of bi-exponential transverse relaxation using a multi-echo imaging pulse sequence. The Cramer–Rao lower bound of the standard deviation of the four parameters of a two-pool model was computed for a wide range of component T₂ values and echo spacing. The results demonstrate that optimal echo spacing (TE_opt) is not generally the minimal available given other pulse sequence constraints. The TE_opt increases with increasing value of the short T₂ time constant and decreases as the ratio of the long and short time constant decreases. A simple model of TE_opt as a function of the two T₂ time constants and four empirically derived scalars is presented.     

Evaluation of tetracationic salts as gas‐phase ion‐pairing agents for the detection of trivalent anions in positive mode electrospray ionization mass spectrometry

In previous studies, new electrospray ionization mass spectrometry (ESI‐MS) approaches were developed for the highly sensitive detection of singly and doubly charged anions in positive mode ESI‐MS by using specially synthesized dicationic and tricationic ion‐pairing agents, respectively. By detecting the positively charged ion complex in the positive mode, limits of detection (LODs) for the anions can be lowered by several magnitudes. In this work, we used eighteen newly synthesized tetracationic ion‐pairing agents, constructed with different geometries, linkages and cation moieties, for the detection of eighteen triply charged anions of different structural motifs. The LODs for these anions were from ten to several thousand times lower in the positive selective ion monitoring (SIM) mode than in the negative mode. These tetracationic agents also were shown to be useful for the detection of ?1 and ?2 anions. In addition, the LODs for ?3 anions can be further lowered by monitoring the product fragments of the ion‐pairing complexes in the single reaction monitoring (SRM) mode. Copyright © 2010 John Wiley & Sons, Ltd.