Let Fn be the nth Fibonacci number. For 1 ≤ k ≤ m − 1 let

In this paper we prove that a higher-order differential equation with one middle term has every bounded solution oscillatory. Moreover, the behavior of unbounded solutions is given. Two other results dealing with positive solutions are also given.

* From the Department of Genetics (No. 512), University of Wisconsin. This project was supported in part by the Research Committee of the Graduate School from funds supplied by the Wisconsin Alumni Research Foundation. 1 Irwin, M. R., Cole, L. J., and Gordon, C. D., J. Exptl. Zool. 73, 285 (1936). 2 Miller, W. J., Physiol. Zool. (in press). 3 Irwin, M. R., and Cole, L. J., J. Exptl. Zool. 73, 8...

1 Throughout this paper the term fragment is used to designate a portion of a chromosome resulting from one or more breaks in an original chromosome and having no spindle attachment. The term chromosome is applied to an original chromosome or the part of an original chromosome containing a spindle attachment. 2 Carlson, J. G., Genetics (in press). 3 Mather, K., Proc. Roy. Soc. London, B124, 97-...

Two strains that overproduce endonuclease III were found in a colony bank containing hybrid ColE1-Escherichia coli plasmids. The enzyme was identified in crude extracts by the degradation of partially depyrimidinated DNA in the presence of EDTA, by its sedimentation velocity, and by its associated thymine glycol-DNA glycosylase activity. An insertion mutation was produced by cloning the kanamyc...

In this lecture, I will discuss the adjacency matrix of a graph, and the meaning of its smallest eigenvalue. This corresponds to the largest eigenvalue of the Laplacian, which we will examine as well. We will relate these to bounds on the chromatic numbers of graphs and the sizes of independent sets of vertices in graphs. In particular, we will prove Hoffman’s bound, and some generalizations. W...