We analyze the on-line chain partitioning problem as a two-person game. One person builds an order one point at a time. The other person responds by making an irrevocable assignment of the new point to a chain of a chain partition. Kierstead gave a strategy showing that width k orders can be on-line chain partitioned into (5 k ?1)=4 chains. We rst prove that width two orders can be partitioned ...

We present a direct proof of the consistency of the existence of a five element basis for the uncountable linear orders. Our argument is based on the approach of Larson, Koenig, Moore and Velickovic and simplifies the original proof of Moore.

1. INTRODUCTION. The object of this paper is to make an observation connecting Goldbach's conjecture, the crystallographic restriction, and the orders of the elements of the symmetric group. First recall that for an element g of a group G the order Ord(g) of g is defined to be the smallest natural number such that g

The purpose of this note is to demonstrate that a weak form of club guessing on ω1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for ω-proper forcings.

We develop a method of reducing the size of quantum minors in the algebra of quantum matrices Oq(Mn). We use the method to show that the quantum determinantal factor rings of Oq(Mn(C)) are maximal orders, for q an element of C transcendental over Q. 2000 Mathematics subject classification: 16P40, 16W35, 20G42.

We construct a solvable group G of order 5 648 590 729 620 such that the set of element orders of G coincides with that of the simple group S4(3). This completes the determination of finite simple groups isospectral to solvable groups.

We present a direct proof of the consistency of the existence of a five element basis for the uncountable linear orders. Our argument is based on the approach of Larson, Koenig, Moore and Velickovic and simplifies the original proof of Moore.

For the discrete solution of the dual mixed formulation for the p-Laplace equation, we define two residues R and r. Then we bound the norm of the errors on the two unknowns in terms of the norms of these two residues. Afterwards, we bound the norms of these two residues by functions of two error estimators whose expressions involve at the very most the datum and the computed quantities. We next...

Cortical bone, as the principal structural component of the human body, functions in both a load-bearing and protective capacity. As a material, cortical bone has been the subject of mechanical investigation and characterization for well over a century, and the time dependent nature of this material’s mechanical response to loading is well documented. To model this time-dependent behavior, many...

Term-by-term Fourier-expansion series, each made up of components having element-specific phases and amplitudes acquired with x-ray standing wave measurements on successive orders of Bragg reflections, are used to reconstruct impurity atom distributions in muscovite mica with respect to the (001) lattice without a priori assumptions on their structures.