Characterization of calcium carbonate polymorphs with Ca K edge X-ray absorption fine structure spectroscopy

Ca K edge X-ray absorption fine structure (XAFS) spectroscopy was utilized for the characterization and quantification of calcium carbonate polymorphs and their mixtures. The advantage of the XAFS is the small sample quantity required for measurements, and a flexible sample environment. The near-edge XAFS spectra of calcite, aragonite and vaterite were measured with the conversion electron yield (CEY) method, and the obtained spectra showed characteristic features that can be utilized as fingerprints. The quantification of mixed polymorphs was examined by using a linear combination fitting of reference XAFS spectra. Though the quality of the fits was satisfactory, discrepancies in the evaluated values were observed between those with X-ray diffraction (XRD) and XAFS. The nonuniformity of samples may be enhanced by the surface sensitivity of the CEY method.     

Grafting of hyperbranched cyclotriphosphazene polymer onto silica nanoparticle and carbon black surfaces

The surface grafting of hyperbranched cyclotriphosphazene polymer onto silica nanoparticles and carbon black was investigated. The grafting of hyperbranched cyclotriphosphazene polymer onto these surfaces was achieved by the repeated reactions of hexachlorocyclotriphosphazene with hexamethylenediamine from surface amino groups and sodium carboxylate groups, respectively. The percentage of grafting onto silica and carbon black surfaces exceeded 760 and 390%, respectively. However, it proved difficult to achieve the theoretical growth of cyclotriphosphazene polymer from these surfaces because of steric hindrance. The introduction of sulfonic acid groups was successfully achieved by the reaction of terminal chlorophosphazene groups of the hyperbranched polymer‐grafted silica and carbon black with sulfanilic acid. The content of sulfonic acid groups introduced onto silica and carbon black surfaces was 4.98 mmol/g and 5.70 mmol/g, respectively. The sulfonated cyclotriphosphazene polymer‐grafted carbon black was extremely hydrophilic, yielding stable colloidal dispersions in polar solvents. The sulfonated cyclotriphosphazene polymer‐grafted silica and carbon black showed ionic conductivity, with the conductance increasing exponentially with increasing relative humidity and temperature. This study may offer important leads in the application of silica nanoparticles and carbon black in polymeric membranes for fuel cells. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4218–4226, 2008     

The K-theoretical range of Cuntz–Krieger algebras

We augment Restorff's classification of purely infinite Cuntz–Krieger algebras by describing the range of his invariant on purely infinite Cuntz–Krieger algebras. We also describe its range on purely infinite graph C^?$C^{?}$-algebras with finitely many ideals, and provide ‘unital’ range results for purely infinite Cuntz–Krieger algebras and unital purely infinite graph C^?$C^{?}$-algebras.     

Quasilinear degenerate evolution equations in Banach spaces

The quasilinear degenerate evolution equation of parabolic type 0< t T considered in a Banach space X is written, putting Mv = u, in the from 0< t T, where A(u)=L(u)M^–1 are multivalued linear operators in X for u K, K being a bounded ball ||u||_Z<R in another Banach space Z continuously embedded in X. Existence and uniqueness of the local solution for the related Cauchy problem are given. The results are applied to quasilinear elliptic-parabolic equations and systems.     

A theorem on the average number of subfaces in arrangements and oriented matroids

It is known that for simple arrangements in thed-dimensional Euclidean spaceR ^d The average number ofj-dimensional subfaces of ak-dimensional face is less than . In this paper, we show that this is also true for all arrangements inR ^d and for all oriented matroids, and we give combinatorial proofs.     

Generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators with potentials

It is shown that the generalized Ornstein-Uhlenbeck operator “with potential” AΦ,G,Vu:=Δu−∇Φ⋅∇u+G⋅∇u−Vu with suitable domain generates an analytic semigroup on the weighted space Lp(RN,μ), 1<p<∞, where . The result extends the generation theorem established by Metafune-Prüss-Rhandi-Schnaubelt when V≡0 to the case where V?0, while the proof is based on their useful theorem that a class of second order elliptic operators generates an analytic semigroup on the unweighted space Lp(RN).     

Transcendence Criterion for Values of Certain Functions of Several Variables

Let ${\Phi_0(\boldmath{z})}$ be the function defined by $$\Phi_0({\boldmath z}) = \Phi _{0}(z_1,\ldots, z_m)=\sum_{k\geq 0}\frac{E_k(z_1^{r^k},\ldots,z_m^{r^k})}{F_k(z_1^{r^k},\ldots,z_m^{r^k})},$$ where ${E_k(\boldmath{z})}$ and ${F_k(\boldmath{z})}$ are polynomials in m variables ${\boldmath{z} = (z_1,\ldots, z_m)}$ with coefficients satisfying a weak growth condition and r ≥ 2 a fixed integer. For an algebraic point ${\boldmath{\alpha}}$ satisfying some conditions, we prove that ${\Phi_{0}(\boldmath{\alpha})}$ is algebraic if and only if ${\Phi_{0}(\boldmath{z})}$ is a rational function. This is a generalization of the transcendence criterion of Duverney and Nishioka in one variable case. As applications, we give some examples of transcendental numbers.