Far downstream analysis for the Blasius boundary-layer stability problem

In this paper, we examine the large Reynolds number (Re) asymptoticstructure of the wave number in the Orr–Sommerfeld regionfor the Blasius boundary layer on a semi-infinite flat plategiven by Goldstein (1983, J. Fluid Mech., 127, 59–81).We show that the inclusion of the term which contains the leading-ordernon-parallel effects, at O(Re^{– 1/2}), leads to a non-uniformexpansion. By considering the far downstream form of each termin the asymptotic expansion, we derive a length scale at whichthe non-uniformity appears, and compare this position with theposition seen in plots of the wave number.     

Second‐order Galerkin‐Lagrange method for the Navier‐Stokes equations (retracted article)

It has come to the attention of the editors and publisher that an article published in Numerical Methods and Partial Differential Equations, “Second‐order Galerkin‐Lagrange method for the Navier‐Stokes equations,” by Mohamed Bensaada, Driss Esselaoui, and Pierre Saramito, Numer Methods Partial Differential Eq 21(6) (2005), 1099–1121 included large portions that were copied from the following paper without proper citation: “Convergence and nonlinear stability of the Lagrange‐Galerkin method for the Navier‐Stokes equations,” Endre Suli, Numerische Mathematik, Vol. 53, No. 4, pp. 459–486 (July, 1988). We have retracted the paper and apologize to Dr. Suli Numer Methods Partial Differential Eq (2007)23(1)211 .     

Structural determination by X-Ray diffraction and 183W NMR spectroscopy of mono substituted hexatungstates [(n-C4H9)4N]3MW5O19 (M = Nb, V)

The tetrabutylammonium salt of mononiobotungstate [(n-C₄H₉)₄N]₃NbW₅O₁₉ (1) and the tetrabutylammonium salt of monovanadotungstate [(n-C₄H₉)₄N]₃VW₅O₁₉ (2) are isotypes; both crystallize in the monoclinic system, space group C2/c (N° 15) with Z=8. The cell parameters for 1 are a=30.4038(8) ?, b=18.5948(8) ?, c=27.3330(3) ?, β=112.4555(6)°, V=14281.1(7) ?³ and the final reliability factors are R=0.043 and R _w=0.047 for 5801 reflections. The cell parameters for 2 are a=30.096(8) ?, b=18.373(3) ?, c= 27.201(6) ?, β=112.402(14)°, V=13906(5) ?³ and the final reliability factors are R=0.048 and R _w=0.054 for 6122 reflections. Both anions, [NbW₅O_19] ³⁻ and [VW₅O_19] ³⁻ exhibit the Lindqvist structure of the parent hexatungstate anion. The six metal positions are disordered and for each metal site the occupation factor is close to 1/6 M (M=Nb, V) and 5/6 W. Furthermore the two compounds were characterized by IR in the solid state, and ¹⁸³W solution NMR. The ¹⁸³W spectrum of [NbW₅O_19] ³⁻ presents two resonances with relative intensities 4:1 in agreement with the C_4v symmetry of the anion.     

Na2Co(H2PO4)4·4H2O

In the title compound, disodium cobalt tetrakis­(dihydrogen­phosphate) tetrahydrate, the Co^II ion lies on an inversion centre and is octahedrally surrounded by two water molecules and four H₂PO₄ groups to give a cobalt complex anion of the form [Co(H₂PO₄)₄(OH₂)]^2?. The three‐dimensional framework results from hydrogen bonding between the anions. The relationship with the structures of Co(H₂PO₄)₂·2H₂O and K₂CoP₄O₁₂·5H₂O is discussed.     

Layered zincoarsenate templated by N,N,N′,N′‐tetra­methyl­ethyl­ene‐di­amine mol­ecules

The title compound, N,N,N′,N′‐tetra­methyl­ethyl­enedi­ammon­ium di­aqua­(arsenate)­(hydrogen arsenate)­dizinc(II), (C₆H₁₈N₂)_0.5[Zn₂(AsO₄)(HAsO₄)(H₂O)₂], is a new zincoarsenate obtained by hydro­thermal synthesis. The structure consists of infinite two‐dimensional anionic layers alternating with planes containing centrosymmetric organic diprotonated template N,N,N′,N′‐tetra­methyl­ethyl­enedi­ammonium cations, [H₃N­C₆H₁₂NH₃]²⁺. The latter are interconnected to the framework through hydrogen bonds.     

Wrap-around partitioning for block bidiagonal linear systems

A stable vector algorithm for the solution of block diagonallinear systems is obtained by a permutation of the unknownscalled wrap-around partitioning combined with standard QR factorization.Wrap-around partitioning uses blocking and selects the unknownsin the blocks in turns. After a suitable orthogonal eliminationstep one ends up with a reduced system which is again blockbidiagonal and so wrap-around partitioning can be applied again.Using a simple model for vectorization overhead it is shownthat small block sizes give best performance. The minimal blocksize 2, which corresponds to cyclic reduction, is suboptimaldue to memory bank conflicts.