Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

On Segal-Wilson's construction for the τ-functions of the constrained KP hierarchies

In this Letter, we study the constrained KP hierarchies by employing Segal-Wilson's theory on the -functions of the KP hierarchy. We first describe the elements of the Grassmannian which correspond to solutions of the constrained KP hierarchy, and then we show how to construct its rational and soliton solutions from these elements of the Grassmannian.     

On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.     

Ultra-violet excited laser emission in Na2

Laser emission at different wavelengths in the range of 903–914 nm and around 2.5 m has been observed upon excitation of Na₂ by uv radiation from an excimer laser at 351 nm and an excimer pumped dye laser in this wavelength range. The emission is attributed to a cascade emission followed by . In addition, coupled with the laser emission around 910 nm, broad-band fluorescence peaking around 855.5 nm is observed which, eventually, may be the first observation of the bound-free transition in Na₂.     

Beobachtung des Stickstoffstoffwechsels bei Leguminosen mittels 15N

Es war Ziel dieser Arbeit, zu ermitteln, welchen Einfluß höhere Dosen von Stickstoffdüngemitteln in Form von KNO₃ auf die Menge des in der Pflanze fixierten Luftstickstoffs haben. Als Versuchspflanze wählten wir Pferdebohnen (Vicia faba, Chlumetzer Abart) wegen ihrer vielseitigen Verwendung in der Landwirtschaft und ihrer besonderen experimentellen Eignung.     

Quasi-classical limit of Toda hierarchy andW-infinity symmetries

Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W _{1 +} symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow _{1 +} symmetries of the dispersionless hierarchy through their action on the tau function.     

In situ identification of organic components of ink used in books from the 1900s by atmospheric pressure matrix assisted laser desorption ionization mass spectrometry

Transport of N, O, and Ti during dc magnetron sputtering deposition of nanoscopic TiN/Ti and TiN structures on plasma nitrided M2 tool steel, as well as transport of metallic species composing the plasma nitrided steel substrates were investigated. N and O depth distributions were determined with subnanometric resolution using narrow resonant nuclear reaction profiling, whereas Ti was profiled, also with subnanometric depth resolution, by medium energy ion scattering. The surface elementary compositions of the TiN/Ti/nitrided steel and TiN/nitrided steel structures were determined by low energy ion scattering. The chemical compounds formed during deposition were accessed by X-ray photoelectron spectroscopy, indicating the presence of TiN, TiO₂, Ti oxynitrides, as well as other metallic nitrides and oxynitrides, but no metallic Ti was observed. Owing to the observed intensive atom mobility, the compositions of the deposited films on plasma nitrided steel structures varied continuously on a nanoscopic scale, from the core of the steel substrate to the bulk of the stoichiometric TiN films. The Ti interlayer assists interdiffusion of all species, in contrast to the TiN film layer, which is known to be a diffusion barrier. The improved adhesion of TiN hard coatings to plasma nitrided steel under working conditions is discussed in terms of the gradual compositional change around the interfaces and the atomic mobility during their formation.