Magnetic phases in Mn<Subscript>1</Subscript>_<Subscript>x</Subscript>Fe<Subscript>x</Subscript>WO<Subscript>4</Subscript> studied by neutron powder diffraction

The magnetic structures of Mn_1-xFe_xWO₄ with x = 0.0, 0.16, 0.21, 0.225, 0.232, 0.24, 0.27, 0.29, and 1.0 were refined from neutron powder diffraction data. The magnetic phase diagram could be completed in the coexistence range of different magnetic structures up to x = 0.29. For the magnetic state at 1.5 K a commensurate antiferromagnetic structure with a propagation vector = (±1/4, 1/2, 1/2) was found for x ⩽ 0.22 while the magnetic spins order with = (1/2, 0, 0) for x ≥ 0.22. In the latter phase, additionally, weak magnetic reflections indexed to an incommensurate ordering with = (- 0.214, 1/2, 0.457) occur in the diffraction pattern up to x = 0.29 indicating the occurence of a reentrant phase. For 0.12 ⩽ x ⩽ 0.29 the low temperature phases are separated from a magnetic high temperature phase showing only magnetic reflections indexed to a spin arrangement with = (1/2, 0, 0). The magnetic phase diagram is discussed qualitatively considering random superexchange between the statistically distributed Mn²⁺- and Fe²⁺-ions in the coexistence range 0.12 ⩽ x ⩽ 0.29 of different magnetic structures related to those of pure MnWO₄ and FeWO₄. Received 9 October 2002 Published online 14 March 2003     

On well-posedness for some dispersive perturbations of Burgers' equation

We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin–Ono equation

${?}_{t}u?D_x^{\alpha }{?}_{x}u={?}_x(u^2),0<\alpha \le 1,$

is locally well-posed in $H^s(\mathbb{R})$ when $s>s_{\alpha }:=\frac{3}{2}?\frac{5\alpha }{4}$. As a consequence, we obtain global well-posedness in the energy space $H^{\frac{\alpha }{2}}(\mathbb{R})$ as soon as $\frac{\alpha }{2}>s_{\alpha }$, i.e. $\alpha >\frac{6}{7}$.     

Intravenous administration of Gd-DTPA prior to DWI does not affect the apparent diffusion constant

MRI measurements of water diffusion and blood perfusion are increasingly used for the evaluation of organ functionality and tissue viability (e.g., in tumors). While diffusion-weighted imaging is performed without contrast agents, measurement of blood perfusion is normally performed based on the administration of paramagnetic substances such as gadolinium diethylenetriamine pentaacetic acid (Gd-DTPA). Simultaneous measurements of these two parameters are often preferred. However, it may be argued that Gd-DTPA causes constriction of small blood vessels or alters hemodynamic parameters such as blood viscosity, thereby corrupting subsequent measurements of the apparent diffusion constant (ADC). The objective of the current study was to investigate the possible changes in the ADC in tumors following intravenous administration of 0.2 and 0.4 mmol/kg of Gd-DTPA in mice. The study was conducted with C3H mouse mammary carcinomas inoculated in the right foot of the animal subjects. The results were compared with findings in a sham group, demonstrating that Gd-DTPA had no significant impact on the ADC as measured in a 7-T animal system.     

Optical aperture area determination for accurate illuminance and luminous efficacy measurements of LED lamps

The measurement uncertainty of illuminance and, consequently, luminous flux and luminous efficacy of LED lamps can be reduced with a recently introduced method based on the predictable quantum efficient detector (PQED). One of the most critical factors affecting the measurement uncertainty with the PQED method is the determination of the aperture area. This paper describes an upgrade to an optical method for direct determination of aperture area where superposition of equally spaced Gaussian laser beams is used to form a uniform irradiance distribution. In practice, this is accomplished by scanning the aperture in front of an intensity-stabilized laser beam. In the upgraded method, the aperture is attached to the PQED and the whole package is transversely scanned relative to the laser beam. This has the benefit of having identical geometry in the laser scanning of the aperture area and in the actual photometric measurement. Further, the aperture and detector assembly does not have to be dismantled for the aperture calibration. However, due to small acceptance angle of the PQED, differences between the diffraction effects of an overfilling plane wave and of a combination of Gaussian laser beams at the circular aperture need to be taken into account. A numerical calculation method for studying these effects is discussed in this paper. The calculation utilizes the Rayleigh–Sommerfeld diffraction integral, which is applied to the geometry of the PQED and the aperture. Calculation results for various aperture diameters and two different aperture-to-detector distances are presented.     

Cotorsion pairs associated with Auslander categories

Let N ≥ n + 1, and denote by K the convex hull of N independent standard gaussian random vectors in ℝⁿ. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane conjecture for the class of gaussian random polytopes. Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590     

Heuristics and lower bounds for minimizing fuel consumption in hybrid-electrical vehicles

In hybrid electric vehicles, the electrical powertrain system has multiple energy sources that it can gather power from to satisfy the propulsion power requested by the vehicle at each instant. This paper focusses on the minimization of the fuel consumption of such a vehicle, taking advantage of the different energy sources. Based on global optimization approaches, the proposed heuristics find solutions that best split the power requested between the multi-electrical sources available. A lower bounding procedure is introduced to validate the quality of the solutions. Computational results show a significant improvement over previous results from the literature in both the computing time and the quality of the solutions.     

Statistics of Wave Functions for a Point Scatterer on the Torus

Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space. In contrast, when the classical dynamics is integrable, there is concentration of eigenfunctions on invariant structures in phase space. In this paper we study eigenfunction statistics for the Laplacian perturbed by a delta-potential (also known as a point scatterer) on a flat torus, a popular model used to study the transition between integrability and chaos in quantum mechanics. The eigenfunctions of this operator consist of eigenfunctions of the Laplacian which vanish at the scatterer, and new, or perturbed, eigenfunctions. We show that almost all of the perturbed eigenfunctions are uniformly distributed in configuration space.     

Strategy for identifying circulating fragments of insulin-like growth factor binding proteins in a hemofiltrate peptide bank.

A differentiated strategy was established to isolate circulating forms of the six human insulin-like growth factor binding proteins (IGFBPs). As starting material we used our peptide bank, a comprehensive blood plasma peptidoma generated from human blood filtrate. The peptides were initially identified in the fractions of the hemofiltrate peptide bank by their immunoreactivity, their capacity to bind the insulin-like growth factors (IGFs), and their molecular masses determined by polyacrylamide gel electrophoresis and matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS). Fractions revealing both immunoreactivity and IGF-binding capacity were analyzed by direct sequencing of immunoreactive bands from a Coomassie-stained gel. Further purification of the IGFBP peptides was performed by consecutive chromatographic steps guided by sensitive MALDI-MS. Using this strategy, different fragments of IGFBP-3, -4, and -5 were identified and a fragment of IGFBP-4 was purified to homogeneity.     

Cyclic 1,3-dipoles or acyclic phosphonium ylides? Electronic characterization of "Montréalones"

The structural features of a recently introduced class of 1,3-dipolar reagents have been computed by density functional theory and ab initio methods. The reagents are formally derived from Münchnones by replacement of the C O group with a PR3 unit. The parent species (PR3 = PH3) shows a long P...O interaction (2.55 A at the B3LYP/6-31+G(d) level), together with a nonplanar ring, and is best described as a weakly chelated acylamino-phosphonium ylide. The corresponding acyclic form, in which the P...O interaction is absent, is predicted to be 2-3 kcal mol-1 higher in enthalpy. Variation of the phosphorus substituents exerts a marked effect on the P...O distance, with electron-withdrawing groups favoring a covalent interaction [P...O 1.97 A for PR3 = PPh(catechyl)] and electron-donating groups favoring a weak interaction [P...O 3.92 A for PR3 = PPh3]. However, this variation has little effect on the relative energies of the cyclic and acyclic forms. The barriers for concerted cycloadditions with ethylene are 22.8 kcal mol-1 (PH3), 31.7 kcal mol-1 (PPh3), and 16.2 kcal mol-1 [PPh(catechyl) with axial O], which correspond with experimental observations and follow the same trend as the energies required to distort the dipole to the TS geometry.