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.     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

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.     

Bootstrap,wild bootstrap,and asymptotic normality

Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle     

Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

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.     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Retaining and recovering enzyme activity during degradation of TCE by methanotrophs

To determine if compounds added during trichloroethylene (TCE) degradation could reduce the loss of enzyme activity or increase enzyme recovery, different compounds serving as energy and carbon sources, pH buffers, or free radical scavengers were tested. Formate and formic acid (reducing power and a carbon source), as well as ascorbic acid and citric acid (free radical scavengers) were added during TCE degradation at a concentration of 2 mM. A saturated solution of calcium carbonate was also tested to address pH concerns. In the presence of formate and methane, only calcium carbonate and formic acid had a beneficial effect on enzyme recovery. The calcium carbonate and formic acid both reduced the loss of enzyme activity and resulted in the highest levels of enzyme activity after recovery.     

Conditional solubility versus pO2− of cerium(III) oxide in molten equimolar NaCl+KCl at 727°C

Reactions between cerium trichloride and oxide ions were studied in NaCl+KCl (1/1) at 1000°K, by potentiometry with a calcia-stabilized zirconia membrane electrode. Titration curves clearly demonstrated the existence of soluble cerium oxychloride (CeO⁺) and precipitated cerium oxide (Ce₂O₃), with respective dissociation constants 10^?11 and 10^?30 (molality scale). The corresponding conditional solubility diagram {log S (Ce^III)=f(pO^2?)} is presented and discussed.