Daily samples between 1964 and 1991 from suction traps throughout Great Britain were used to study the migration phenologies of five aphid species: Brachycaudus helichrysi, Elatobiinn abietiuum, Metopolopbitim dirhodum, Myzus persicae and Sitobioft avenae, and their relationship with temperature. Regression relationships have been established between characteristics of aphid phenology and temperature, latitude and longitude for each species. There were differences between species in the period for which temperature was most strongly associated with aphid phenology. The study indicates that temperature, especially winter temperature, is the dominant factor affecting aphid phenology, for all five species. A 1 °C increase in average winter temperature advanced the migration phenology by 4-19 days depending on species. Effects of temperature on the aphid phenology are similar between holocyclic and anholocyclic species, unlike the effects of temperature on date of first flight record which have been previously shown to be important only in anholocyclic species.
The distinguishing number $\Delta(X)$ of a graph $X$ is the least positive integer $n$ for which there exists a function $f:V(X)\to\{0,1,2,\cdots,n-1\}$ such that no nonidentity element of $\hbox{Aut}(X)$ fixes (setwise) every inverse image $f^{-1}(k)$, $k\in\{0,1,2,\cdots,n-1\}$. All infinite, locally finite trees without pendant vertices are shown to be 2-distinguishable. A proof is indicated that extends 2-distinguishability to locally countable trees without pendant vertices. It is shown that every infinite, locally finite tree $T$ with finite distinguishing number contains a finite subtree $J$ such that $\Delta(J)=\Delta(T)$. Analogous results are obtained for the distinguishing chromatic number, namely the least positive integer $n$ such that the function $f$ is also a proper vertex-coloring.
We prove that if N is an internally 4-connected minor of an internally 4-connected binary matroid M with E(N) ≥ 4, then there exist matroids M 0 , M 1 ,. .. , Mn such that M 0 ∼ = N , Mn = M , and, for each i ∈ {1,. .. , i}, M i−1 is a minor of M i , |E(M i−1)| ≥ |E(M i)| − 2, and M i is 4-connected up to separators of size 5.
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