Preprint Series 2007

2007:09
K. Jordan
Let $N _ n$ denote the quotient poset of the Boolean lattice, $B _ n$, under the relation equivalence under rotation. Griggs, Killian, and Savage proved that $N _ p$ is a symmetric chain order for prime p. In this paper, we settle the question of whether this poset is ...
[Full Abstract]  2007:08 B. Kashin and V. Temlyakov

2007:07
M. Emelianenko,
L. Ju, and
A. Rand
Centroidal Voronoi tessellations (CVTs) are special Voronoi tessellations of a domain $\Omega\in{R^d}$ having the property that the generators of the Voronoi diagram are also the centers of mass, with respect to a given density function $\rho\geq0$, of the corresponding Voronoi cells. CVTs and CVTbased methodologies have ...
[Full Abstract] 
2007:06
P. Petrushev and
Y. Xu
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the TriebelLizorkin and Besov spaces on $R^d$ induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite TriebelLizorkin and Besov ...
[Full Abstract] 
2007:05
G. Kyriazis,
P. Petrushev, and
Y. Xu
Weighted TriebelLizorkin and Besov spaces on the unit ball $B^d$ in $R^d$ with weights $w _ \mu(x)=(1x^2)^{\mu\frac{1}{2}},$$\mu\geq0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) $\{\varphi _ \xi ...
[Full Abstract] 
2007:04
J. Griggs and
G. Katona
We survey results concerning the maximum size of a family F of subsets of an nelement set such that a certain configuration is avoided. When F avoids a chain of size two, this is just Sperner's Theorem. Here we give bounds on how large F can be such ...
[Full Abstract] 
2007:03
L. Ju and
L. Tian
In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible NavierStokes equations by finite element discretizations. The mesh refinement and optimization are performed based on an algorithm that combines the socall conforming centroidal Voronoi Delaunay triangulations and residualtype local a posteriori error estimators. Numerical experiments ...
[Full Abstract] 
2007:02
S. Zheng
We prove a sharp MihlinHörmander multiplier theorem for Schrödinger operators H on $R^n$. The method, which allows us to deal with general potentials, improves Hebisch’s method relying on heat kernel estimates for positive potentials [22, 12]. Our result applies to, in particular, the negative PöschlTeller potential $V(x ...
[Full Abstract] 
2007:01
W. Dahmen,
S. Dekel, and
P. Petrushev
Anisotropic Besov spaces (Bspaces) are developed based on anisotropic multilevel ellipsoid covers (dilations) of $R^n$. This extends earlier results on anisotropic Besov spaces. Furthermore, sequences of anisotropic bases are constructed and utilized for twolevelsplit decompositions of the Bspaces and nonlinear mterm approximation.
[Full Abstract]