Ramsey's theorem—A new lower bound

This paper gives improved asymptotic lower bounds to the Ramsey function R(k, t). Section 1 considers the symmetric case k = t while the more general case is considered in Section 2.     

On the number of lattice points between two enlarged and randomly shifted,copies of an oval

Summary Let A be an oval with a nice boundary in ²,R a large positive number,c>0 some fixed number and a uniformly distributed random vector in the unit square [0,1]². We are interested in the number of lattice points in the shifted annular region consisting of the difference of the sets {(R+c/R)A–} and {(R–c/R)A–}. We prove that whenR tends to infinity, the expectation and the variance of this random variable tend to 4c times the area of the set A, i.e. to the area of the domain where we are counting the number of lattice points. This is consistent with computer studies in the case of a circle or an ellipse which indicate that the distribution of this random variable tends to the Poisson law. We also make some comments about possible generalizations.     

Discrepancy in arithmetic progressions

It is proven that there is a two-coloring of the first integers for which all arithmetic progressions have discrepancy less than . This shows that a 1964 result of K. F. Roth is, up to constants, best possible.

     

Synthesis of(±)-descarboxylquadrone

The synthesis of a biologically active anlogue of the antitumor agent quadrone, termed descarboxylquadrone ($\text{3}$), is described.     

Product Channels of the N2 (A3Σ+u) + O2 interaction

Products of the N₂(A) + O₂ reaction were measured in a discharge-flow reactor. N₂O accounts for only (2 ± 0.5)% of the reaction, contrary to recent reports, and O-atoms for 165 ± 10)% if N₂(A) is quantitatively produced from Ar3 with excess N₂ This assumption is examined and specific N₂(A) + O₂ rate parameters are estimated.     

Arresting cancer proliferation by small-molecule gene regulation

A small library of pyrrole-imidazole polyamide-DNA alkylator (chlorambucil) conjugates was screened for effects on morphology and growth characteristics of a human colon carcinoma cell line, and a compound was identified that causes cells to arrest in the G2/M stage of the cell cycle. Microarray analysis indicates that the histone H4c gene is significantly downregulated by this polyamide. RT-PCR and Western blotting experiments confirm this result, and siRNA to H4c mRNA yields the same cellular response. Strikingly, reduction of H4 protein by >50% does not lead to widespread changes in global gene expression. Sequence-specific alkylation within the coding region of the H4c gene in cell culture was confirmed by LM-PCR. The compound is active in a wide range of cancer cell lines, and treated cells do not form tumors in nude mice. The compound is also active in vivo, blocking tumor growth in mice, without obvious animal toxicity.