图的介值定理的变异形式(英)

本文对目前已知的图的一系列介值定理给出了几种变异形式．     

Stability properties of cycles and tori of a simplest nonresonant wave-type equation

For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997. Translated by O. V. Sipacheva     

Planar,Toroidal, and Projective Commuting and Noncommuting Graphs

In this paper, all finite groups whose commuting (noncommuting) graphs can be embed on the plane, torus, or projective plane are classified.     

On bipartite graphs with small number of laplacian eigenvalues greater than two and three

All connected bipartite graphs with exactly two Laplacian eigenvalues greater than two are determined. Besides, all connected bipartite graphs with exactly one Laplacian eigenvalue greater than three are determined.     

On a class of binary linear completely transitive codes with arbitrary covering radius

An infinite class of new binary linear completely transitive (and so, completely regular) codes is given. The covering radius of these codes is growing with the length of the code. In particular, for any integer ρ≥2, there exist two codes in the constructed class with d=3, covering radius ρ and lengths and , respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described.     

Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]