Traditional chromatographic quantification methods for heparosan produced from the Escherichia coli K5 strain rely on extensive purification requiring laborious sample preparation. These methods are time-consuming, often resulting in sample loss during purification, and thus might not accurately reflect the amount of heparosan in the original mixture. A simple, sensitive (1)H nuclear magnetic r...

We prove that for any convex pentagon in the plane there are two disks, among the five disks having a side of the pentagon as diameter, that do not intersect. All our arguments are from classical Euclidean geometry.

The Gram dimension gd(G) of a graph G is the smallest integer k ≥ 1 such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the off-diagonal positions corresponding to edges of G, can be completed to a positive semidefinite matrix of rank at most k (assuming a positive semidefinite completion exists). For any fixed k the class of graphs satisfying gd(G) ≤...

The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K5 and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K4-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not cont...

Thomassen conjectured [8] that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K5−E(C4), where C4 is a cycle of length 4 in K5. In [2], it is shown that every 4-connected line graph without an induced subgraph isomorphic to the hourglass is hamiltonian connected. In this note, we prove that every 3-connected, essentially 4-connected hourglass free line graph i...

To study the dynamics of keratin intermediate filaments, we fused two different types of epithelial cells (PtK2 and BMGE+H) and studied how the keratins from the parental cells recombine and copolymerize to form the heterokaryon cytoskeleton. The behaviour of the keratins during this process was followed by immunofluorescence using specific antibodies. After fusion, the parental cytoskeletons u...

The purpose of the current study was to determine whether a tropical ginger derived compound 1'-acetoxychavicol acetate (ACA), suppresses skin tumor promotion in K5.Stat3C mice. In a two-week study in which wild-type (WT) and K5.Stat3C mice were co-treated with either vehicle, ACA, galanga extract, or fluocinolone acetonide (FA) and tetradecanoyl phorbol acetate (TPA), only the galanga extract ...

The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph, ensures that it has a unique minimum weight perfect matching, with a good probability. We derandomize this lemma for K3,3-free and K5-free bipartite graphs, i.e. we give a d...