Preprint Series 2011

2011:06
J. Griggs,
W. Li, and
L. Lu
Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of [n] := {1,...,n} that contains no (weak) subposet P. This problem has been studied intensively in recent years, and it is conjectured that $\pi(P):=\lim _ {n\rightarrow\infty} \textrm ...
[Full Abstract] 
2011:05
J. Shen,
X. Yang, and
Q. Wang
The commonly used incompressible phase field models for nonreactive, binary fluids, in which the CahnHilliard equation is used for the transport of phase variables, conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when the densities ...
[Full Abstract] 
2011:04
Q. Wang and
T. Zhang
We apply the kinetic theory formulation for binary complex fluids to develop a set of hydrodynamic models for the twophase mixture of biofilms and solvent (water). It is aimed to model nonlinear growth and transport of the biomass in the mixture and the biomassflow interaction. In the kinetic theory formulation ...
[Full Abstract] 
2011:03
X. Yang,
V. Mironov, and
Q. Wang
A mathematical model based on a phase field formulation is developed to study fusion of cellular aggregates/clusters. In a novel biofabrication process known as bioprinting [25], live multicellular aggregates/clusters are used to make tissue or organ constructs via the layerbylayer deposition technique in compatible hydrogels rich in maturogen ...
[Full Abstract] 
2011:02
V. Temlyakov,
M. Yang, and
P. Ye
We study greedy approximation with respect to quasigreedy bases. For the Lp space, 1 < p < ∞, p ≠ 2, we prove that the error of the mth greedy approximation is bounded by the error of best mterm approximation multiplied by an extra factor of order m^{1/p  1/2}
[Full Abstract] 
2011:01
G. Kyriazis and
P. Petrushev
A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basic elements. The method is deployed to the construc tion of bases consisting of rational functions of uniformly bounded degrees for Besov and TriebelLizorkin ...
[Full Abstract]