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.     

New necessary conditions on the existence of abelian difference sets

In this paper we develop a new method to obtain identities in a group algebraGF(p)G if an abelian difference set of ordern0 (modp) exists inG. We give an explicit formula ifp ² orp ³ is the exactp-power dividingn. This generalizes the approach of Wilbrink, Arasu and the author. The proof presented here uses some knowledge about field extensions of thep-adic numbers.     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Laser-selective enrichment of 3d-states of the Ca II ion for detecting rare radioactive isotope calcium-41

For the detection of the rare radioactive isotope⁴¹Ca, the possibilities of the earlier-proposed initial-state enrichment by continuous-wave laser radiation are examined. It is shown that the enrichment 10¹⁴ of 3d-states of the ion Ca II can be reached. As the method of enriched-state detection, the process of resonant charge exchange is analysed. For a further increase of the selectivity, the repetition of the cycle initial state enrichment plus resonant charge exchange is discussed.     

Synthesis of 4b,5,10a,11-tetrahydroindeno[1,2-b]quinolin-10-ones from Baylis-Hillman adducts

We developed an efficient synthetic method for indenoquinoline skeletons from Baylis-Hillman adducts. 4b,5,10a,11-Tetrahydroindeno[1,2-b]quinolin-10-ones and 7H-indeno[2,1-c]quinolines were prepared from Baylis-Hillman adducts in polyphosphoric acid.     

Synthesis and Structure Elucidation of Novel Spirooxindole Linked to Ferrocene and Triazole Systems via [3 + 2] Cycloaddition Reaction

In the present work, a novel heterocyclic hybrid of a spirooxindole system was synthesized via the attachment of ferrocene and triazole motifs into an azomethine ylide by [3 + 2] cycloaddition reaction protocol. The X-ray structure of the heterocyclic hybrid (1″R,2″S,3R)-2″-(1-(3-chloro-4-fluorophenyl)-5-methyl-1H-1,2,3-triazole-4-carbonyl)-5-methyl-1″-(ferrocin-2-yl)-1″,2″,5″,6″,7″,7a″-hexahydrospiro[indoline-3,3″-pyrrolizin]-2-one revealed very well the expected structure, by using different analytical tools (FTIR and NMR spectroscopy). It crystallized in the triclinic-crystal system and the P-1-space group. The unit cell parameters are a = 9.1442(2) Å, b = 12.0872(3) Å, c = 14.1223(4) Å, α = 102.1700(10)°, β = 97.4190(10)°, γ = 99.1600(10)°, and V = 1484.81(7) ų. There are two molecules per unit cell and one formula unit per asymmetric unit. Hirshfeld analysis was used to study the molecular packing of the heterocyclic hybrid. H···H (50.8%), H···C (14.2%), Cl···H (8.9%), O···H (7.3%), and N···H (5.1%) are the most dominant intermolecular contacts in the crystal structure. O···H, N···H, H···C, F···H, F···C, and O···O are the only contacts that have the characteristic features of short and significant interactions. AIM study indicated predominant covalent characters for the Fe–C interactions. Also, the electron density (ρ(r)) at the bond critical point correlated inversely with the Fe–C distances.     

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.     

Eu3+、Tb3+与1-乙酰乙酰吲哚、1,10-邻菲啰啉二元、三元体系在溶液中荧光光谱研究

观察了以不同比例溶解在乙醇中的Eu3+、Tb3+、1-乙酰乙酰吲哚(HL)和1,10-邻菲啉(Phen)的荧光光谱.结果表明HL能有效地把吸收的能量传递给Tb3+,而不能有效地传递给Eu3+.讨论了HL和Phen对Eu3+、Tb3+的配位作用及其对Eu3+或Tb3+所组成的三元体系中敏化发光性能的影响.     

Extended non-abelian gauge symmetries in the classical WZNW model

Higher spin extensions of the non-Abelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. It is a characteristic property of the WZNW model that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases, the higher spin Noether currents do not span an invariant space with respect to their generating transformations. Here, the current space is extended to an invariant space which allows us to gauge the symmetry.Supported by Bulgarian Foundation on Fundamental Research under contract Ph-318/93-95.