Convergence properties of ART and SOR algorithms

Summary ART algorithms with relaxation parameters are studied for general (consistent or inconsistent) linear algebraic systemsRx=f, and a general convergence theorem is formulated. The advantage of severe underrelaxation is reexamined and clarified. The relationship to solutions obtained by applying SOR methods to the equationRR ^T y=f is investigated.The work of this autor was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada     

Die Molekularanordnung von Xylan-Diazetat und azetylierten d-Xylose-?lig sacchariden an der Grenzfl?che Luft-Wasser

Ohne Zusammenfassung     

On pseudospectra of matrix polynomials and their boundaries

In the first part of this paper (Sections 2-4), the main concern is with the boundary of the pseudospectrum of a matrix polynomial and, particularly, with smoothness properties of the boundary. In the second part (Sections 5-6), results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the proximity to such polynomials.

     

Studies of a Large Odd‐Numbered Odd‐Electron Metal Ring: Inelastic Neutron Scattering and Muon Spin Relaxation Spectroscopy of Cr8Mn

The spin dynamics of Cr₈Mn, a nine‐membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr₈Mn is a rare example of a large odd‐membered AF ring, and has an odd‐number of 3d‐electrons present. Odd‐membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated‐spin ground states. The chemical synthesis and structures of two Cr₈Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (μSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that μSR is sensitive to the ground‐spin‐state crossing from S=1/2 to S=3/2 in Cr₈Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin‐pair correlations and scalar‐spin chirality, shows a non‐collinear spin structure that fluctuates between non‐planar states of opposite chiralities.     

Characterization of the crystal and magnetic structures of the mixed-anion coordination polymer Cu(HCO2)(NO3)(pyz) {pyz = Pyrazine} by X-ray diffraction, ac magnetic susceptibility, dc magnetization, muon-spin relaxation, and spin dimer analysis

The mixed-anion coordination polymer Cu(HCO2)(NO3)(pyz) was synthesized, its crystal structure was determined by X-ray diffraction, and its magnetic structure was characterized by ac susceptibility, dc magnetization, muon-spin relaxation, and spin dimer analysis. The crystal structure consists of five-coordinate Cu2+ ions that are connected through syn-anti bridging mu-HCO2- and mu-pyz ligands to form a highly corrugated two-dimensional layered network. Bulk magnetic measurements show a broad maximum in chi(T) at 6.6 K. The HCO2- and pyz ligands mediate ferromagnetic and antiferromagnetic spin exchange interactions between adjacent Cu2+ ions with the spin exchange parameters J/kB = 8.17 and -5.4 K, respectively (H = -JSigmaSi x Sj). The muon-spin relaxation data show a transition to a long-range magnetic ordering below TN = 3.66(3) K. For T < TN, the M(H) and chi'ac measurements provide evidence for a field-induced spin-flop transition at 15.2 kOe. That Cu(HCO2)(NO3)(pyz) undergoes a long-range magnetic ordering is an unexpected result because the one-dimensional Cu(NO3)2(pyz) and three-dimensional Cu(HCO2)2(pyz) compounds display linear chain antiferromagnetism with no long-range magnetic ordering down to 2 K.     

Accelerated solvent extraction of fluometuron from selected soils

Accelerated solvent extraction (ASE) is a recently developed extraction technique that is more rapid and produces less waste than do conventional liquid/liquid extraction methods. Optimal conditions were determined for ASE of fluometuron from 2 Weswood clay loam soils. Two solvents (acetonitrile and methanol), 2 temperatures (50 and 100 degrees C), and the number of static cycles (1, 2, and 3) were evaluated. The most efficient and reproducible extractions were obtained when methanol was combined with a 50 degrees C extraction temperature and the static cycle was repeated 3 times. These experiments indicated that existing extraction methods for fluometuron can easily be adapted for ASE.     

Effect of laser-focusing conditions on propagation and monoenergetic electron production in laser-wakefield accelerators

The effect of laser-focusing conditions on the evolution of relativistic plasma waves in laser-wakefield accelerators is studied both experimentally and with particle-in-cell simulations. For short focal-length (w_{0}lambda_{p}), a single optical filament can capture the majority of the laser energy and self-guide over distances comparable to the dephasing length, even for these short pulses (ctau approximately lambda_{p}). This allows the wakefield to evolve to the correct shape for the production of the monoenergetic electron bunches, as measured in the experiment.     

Muon-fluorine entangled states in molecular magnets

The information accessible from a muon-spin relaxation experiment can be limited due to a lack of knowledge of the precise muon stopping site. We demonstrate here the possibility of localizing a spin polarized muon in a known stopping state in a molecular material containing fluorine. The muon-spin precession that results from the entangled nature of the muon spin and surrounding nuclear spins is sensitive to the nature of the stopping site. We use this property to identify three classes of sites that occur in molecular magnets and describe the extent to which the muon distorts its surroundings.     

Disappearing Polymorphs Revisited

Nearly twenty years ago, Dunitz and Bernstein described a selection of intriguing cases of polymorphs that disappear. The inability to obtain a crystal form that has previously been prepared is indeed a frustrating and potentially serious problem for solid‐state scientists. This Review discusses recent occurrences and examples of disappearing polymorphs (as well as the emergence of elusive crystal forms) to demonstrate the enduring relevance of this troublesome, but always captivating, phenomenon in solid‐state research. A number of these instances have been central issues in patent litigations. This Review, therefore, also highlights the complex relationship between crystal chemistry and the law.