Lead dioxide-coated carbon paste electrodes

Lead dioxide electrodeposited under optimized conditions on carbon paste provides an electroanalytically useful electrode, with an anodic working range extending to 1.9 V. Voltammograms for sulphite are used to study electrode lifetime and reproducibility; calibration graphs are linear up to 10^-3M sulphite in 0.5 M sulphuric acid.     

Solvent influence on the viscosity-temperature relationship for dilute polybutadiene solutions

The temperature dependence of the viscosity of dilute polybutadiene solutions has been described by an Arrhenius expression according to Moore's treatment. The activation energy of flow was found to depend on both concentration and molecular weight through an empirical parameter, K_e. This parameter was positive in toluene, zero in decalin and negative in dioxane. This behaviour is discussed in connection with the temperature dependence of the expansion coefficient (x_η) and the excluded volume parameter (z). A recent Yamakawa-Tanaka expression relating x_η and z was used in the theoretical calculation of K_e.     

The micro-volumetric determination of lead with thionalide and its application to the analysis of tin-base and lead-base alloys

The authors have elaborated an exact micro-volumetric method for the determination of lead with thionalide. The method has been successfully applied to the determination of lead in tin-base and lead-base alloys, following the isolation of lead as lead sulphate and its redissolution in ammonium acetate.     

Error estimates on anisotropic elements for functions in weighted Sobolev spaces

In this paper we prove error estimates for a piecewise average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions.

Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses.

Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems.

Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements.

As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained.

     

Study by gas-liquid chromatography of the thermodynamics of the interaction of poly(vinyl acetate) with various solvents

The solubility parameter of poly(vinyl acetate) at various temperatures has been obtained by using the method developed by DiPaola-Baranyi and Guillet, Marcomolecules11, 228 (1978). The solubility parameter of polymer at 25°C was found to be $\text{10.1 (}\text{cal/cm}{}^3\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ by linear extrapolation from higher temperatures (70–140°C). The interaction parameter χ of polymer in various solvents, at temperatures below the melting point T_m, has been determined by means of the solubility parameters of the polymer and solvents at this temperature, deduced from their values obtained chromatographically at higher temperatures. The value of the interaction parameter so obtained is in good agreement not only with values calculated by other techniques but also is independent of the temperature range used for the chromatographic measurements. Moreover, using the equation-of-state theory formulation, we have determined the values of the interaction parameters $\text{χ}{}^1$ for various systems poly(vinyl acetate)/probes and from it the contact interaction energy, X₁₂, in the temperature range 70–140°C.     

Photogeneration of distant radical pairs in aqueous pyruvic acid glasses

The lambda > 300 nm photolysis of h4- or d4-pyruvic acid aqueous glasses at 77 K yields identical electron magnetic resonance (EMR) spectra arising from distant (r greater or similar 0.5 nm) triplet radical pairs. Spectra comprise: (1) well-resolved quartets, X, at g approximately ge, that closely match the powder spectra of spin pairs interacting across r approximately 1.0 nm with D approximately 3.0 mT, E approximately 0 mT zero field splittings (ZFS), and (2) broad signals, Y, centered at g approximately 2.07 that display marked g-anisotropy and g-strain, exclude D greater or similar 20.0 mT values (i.e., r less or similar 0.5 spin nm separations), and track the temperature dependence of related g approximately 4 features. These results imply that the n-pi excitation of pyruvic acid, PA, induces long-range electron transfer from the promoted carbonyl chromophore into neighboring carbonyl acceptors, rather than homolysis into contact radical pairs or concerted decarboxylation into a carbene. Since PA is associated into hydrogen-bonded dimers prior to vitrification, X signals arise from radical pairs ensuing intradimer electron transfer to a locked acceptor, while Y signals involve carbonyl groups attached to randomly arranged, disjoint monomers. The ultrafast decarboxylation of primary radical ion pairs, 3[PA+* PA-*], accounts for the release of CO2 under cryogenic conditions, the lack of thermal hysteresis displayed by magnetic signals between 10 and 160 K, and averted charge retrotransfer. All EMR signals disappear irreversibly above the onset of ice diffusivity at approximately 190 K.     

Spin actions in Euclidean and Hermitian Clifford analysis in superspace

In [4] we studied the group invariance of the inner product of supervectors as introduced in the framework of Clifford analysis in superspace. The fundamental group ${\mathrm{SO}}_0$ leaving invariant such an inner product turns out to be an extension of $\text{SO}(m)\times \text{Sp}(2n)$ and gives rise to the definition of the spin group in superspace through the exponential of the so-called extended superbivectors, where the spin group can be seen as a double covering of ${\mathrm{SO}}_0$ by means of the representation $h(s)[x]=sx\stackrel{￣}{s}$. In the present paper, we study the invariance of the Dirac operator in superspace under the classical H and L actions of the spin group on superfunctions. In addition, we consider the Hermitian Clifford setting in superspace, where we study the group invariance of the Hermitian inner product of supervectors introduced in [3]. The group of complex supermatrices leaving this inner product invariant constitutes an extension of $\text{U}(m)\times \text{U}(n)$ and is isomorphic to the subset ${\text{SO}}_0^J$ of ${\text{SO}}_0$ of elements that commute with the complex structure J. The realization of ${\text{SO}}_0^J$ within the spin group is studied together with the invariance under its actions of the super Hermitian Dirac system. It is interesting to note that the spin element leading to the complex structure can be expressed in terms of the n-dimensional Fourier transform.     

Distinct distances between a collinear set and an arbitrary set of points

We consider the number of distinct distances between two finite sets of points in ${\mathbb{R}}^k$, for any constant dimension $k\ge 2$, where one set $P_1$ consists of $n$ points on a line $l$, and the other set $P_2$ consists of $m$ arbitrary points, such that no hyperplane orthogonal to $l$ and no hypercylinder having $l$ as its axis contains more than $O\left(1\right)$ points of $P_2$. The number of distinct distances between $P_1$ and $P_2$ is then

$\Omega \left(min\left\{n^{2∕3}{m}^{2∕3},\frac{n^{10∕11}{m}^{4∕11}}{{log}^{2∕11}m},n^2,m^2\right\}\right).$

Without the assumption on $P_2$, there exist sets $P_1$, $P_2$ as above, with only $O(m+n)$ distinct distances between them.