On finite element subspaces over quadrilateral and hexahedral meshes for incompressible viscous flow problems

Summary Optimal rates of convergence for the approximate solution of the stationary Stokes equations are obtained for finite element schemes which use piecewise constants to approximate the pressure and piecewise linear or piecewise bilinear or trilinear polynomials to approximate the velocity over fairly general quadrilateral or hexahedral meshes.This research was supported by NSF Grant MC80-16532     

Low Prandtl-number free convection

Zusammenfassung Eine Untersuchung der freien Konvektion wurde an einer senkrechten isothermen Platte bei Prandtlscher Zahl im Bereiche von 0,003–0,03 (das heisst flüssige Metalle) durchgeführt. Dabei wurden zahlenmässige Lösungen der laminaren Grenzschichtgleichungen erhalten. Für die örtlichen Wärmeübergänge bei diesem Bereiche der Prandtlschen Zahl lassen sich die Resultate alsNu _x =0,565 (Gr _x Pr ²)^1/4 darstellen.     

Extending the nitrogen-heterosuperbenzene family: the spectroscopic, redox, and photophysical properties of "half-cyclized" N-1/2HSB and Its Ru(II) complex

Oxidative cyclodehydrogenation is an important process in the formation of the new graphene, N-(1)/(2)HSB 2. This heteropolyaromatic results from the FeCl(3)-catalyzed oxidative cyclodehydrogenation of 1,2-dipyrimidyl-3,4,5,6-tetra-(4-tert-butylphenyl)benzene. Three new C-C bonds are formed that lock the two pyrimidines in a molecular platform comprising eight fused aromatic rings flanked by two remaining "uncyclized" phenyl rings. Mechanistically intriguing is the fact that N-HSB 1, the product of six C-C bond fusions, is co-synthesized with its "half-cyclized" daughter in this reaction. 1 and 2 have the same bidentate N-atom arrangement. This facilitates formation of the heteroleptic Ru(II) complexes, [Ru(bpy)(2)(2)](PF(6))(2) 4 and [Ru(bpy)(2)(1)](PF(6))(2) 3, which differ in the size and planarity of their aromatic ligands. The new ligand 2 and its complex 4 are characterized by (1)H NMR, IR, ESI-MS, and accurate mass methods. 2 exhibits photophysical properties that are consistent with a reduction of the pi/pi framework, a concomitant increase in the energy of the LUMO, and a blue-shift of the solvent-dependent fluorescence (lambda(em) = 474 nm, phi(F) = 0.55, toluene) as compared to its parent. Complex 4 absorbs throughout the visible region and borders on near-IR emitter character, exhibiting a slightly blue-shifted (3)MLCT emission (868 nm, CH(3)CN) as compared to that of [Ru(bpy)(2)(1)](PF(6))(2) 3 (880 nm, CH(3)CN). Electrochemical analyses permit further elucidation of the intermolecular interactions of 3 and 4. These and the concentration and temperature-dependent NMR spectra of 4 confirm it to be nonaggregating, a direct result of the two uncyclized and rotatable phenyl rings in 2.     

Refinements to the diastereoisomer-specific method for the analysis of hexabromocyclododecane

The emergence of hexabromocyclododecane (HBCD) as a bromine-based flame retardant of concern is partly attributable to recent measurements on the environmental occurrence of the individual diastereoisomers (alpha, beta and gamma). These measurements were fuelled by a newly developed liquid chromatography/tandem mass spectrometric (LC/MS/MS)-based analytical method. However, in the course of our recent studies on the environmental fate and behaviour of the diastereoisomers of HBCD, some interesting features of the LC/MS/MS method became apparent. For example, the ion signal of the native ions was found to be dependent on the final extract volume. This was true for both biotic and sediment samples and was found to arise from the suppression of the ion signal due to endogenous material in the extracts that escape clean-up. We have also found differences in the stability of the diastereoisomers in different solvents. If left unaccounted for, both factors can compromise analytical measurement data. By way of a series of controlled experiments conducted at our two laboratories [Department of Fisheries & Oceans Canada (DFO) and Environment Canada (EC)], we illustrate these features and demonstrate that use of newly synthesized labelled HBCD isomers [(13-carbon (13C) and deuterium (d18)] can minimize and often circumvent matrix-related effects.     

Auditory temporal resolution in normal-hearing preschool children revealed by word recognition in continuous and interrupted noise

The purpose of this study was to examine temporal resolution in normal-hearing preschool children. Word recognition was evaluated in quiet and in spectrally identical continuous and interrupted noise at signal-to-noise ratios (S/Ns) of 10, 0, and -10 dB. Sixteen children 4 to 5 years of age and eight adults participated. Performance decreased with decreasing S/N. At poorer S/Ns, participants demonstrated superior performance or a release from masking in the interrupted noise. Adults performed better than children, yet the release from masking was equivalent. Collectively these findings are consistent with the notion that preschool children suffer from poorer processing efficiency rather than temporal resolution per se.     

Unsharp Quantum Reality

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency—or potentiality—of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.     

Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

Measuring inter-DNA potentials in solution

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, approximately 16 mM Mg2+. Quantitative measurements of inter-DNA potentials are essential for improving models of fundamental interactions in biological systems.     

Constructing Four-Photon States for Quantum Communication and Information Processing

We provide a method for constructing a set of four-photon states suitable for quantum communication applications. Among these states is a set of concatenated quantum code states that span a decoherence-free subspace that is robust under collective-local as well as global dephasing noise. This method requires only the use of spontaneous parametric down-conversion, quantum state post-selection, and linear optics. In particular, we show how this method can be used to produce all sixteen elements of the second-order Bell gem , which includes these codes states and is an orthonormal basis for the Hilbert space of four qubits composed entirely of states that are fully entangled under the four-tangle measure.