Infinite dimensional C∞ mappings with a given sequence of derivatives at a given point

Classification of solvable groups with a given property

In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.

Graphs with a Given Degree Sequence

The level set G(n, m) comprises all unlabelled simple graphs of order n and size m, and is partitioned into similarity classes, comprising all graphs with the same degree sequence. When graphs are ordered lexicographically by their signature, a unique numerical list of structural descriptors, the similarity classes of G(n, m) occur in contiguous blocks; the first graph in each similarity class ...

Random graphs with a given degree sequence

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovász and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. ...

The Secondary Response of Chickens Given a Primary Inoculation of Bovine Serum Albumin at Different Ages

Random mappings with a given number of cyclical points

In this paper we consider a random mapping, T̂n, of the finite set {1, 2, ..., n} into itself for which the digraph representation Ĝn is constructed by: (1) selecting a random number, L̂n, of cyclic vertices, (2) constructing a uniform random forest of size n with the selected cyclic vertices as roots, and (3) forming ‘cycles’ of trees by applying a random permutation to the selected cyclic verti...