We investigated the strategies of four co-occurring evergreen woody species Quercus ilex, Quercus coccifera, Pinus halepensis, and Juniperus phoenicea to cope with Mediterranean field conditions. For that purpose, stem water potential, gas exchange, chlorophyll (Chl) fluorescence, and Chl and carotenoid (Car) contents were examined. We recognized two stress periods along the year, winter with low precipitation and low temperatures that led to chronic photoinhibition, and summer, when drought coincided with high radiation, leading to an increase of dynamic photoinhibition and a decrease of pigment content. Summer photoprotection was related to non-photochemical energy dissipation, electron flow to alternative sinks other than photosynthesis, decrease of Chl content, and proportional increase of Car content. Water potential of trees with deep vertical roots (Q. coccifera, Q. ilex, and P. halepensis) mainly depended on precipitation, whereas water potential of trees with shallow roots (J. phoenicea) depended not only on precipitation but also on ambient temperature. and F. J. Baquedano, F. J. Castillo.
The signed distance-$k$-domination number of a graph is a certain variant of the signed domination number. If $v$ is a vertex of a graph $G$, the open $k$-neighborhood of $v$, denoted by $N_k(v)$, is the set $N_k(v)=\lbrace u\mid u\ne v$ and $d(u,v)\le k\rbrace $. $N_k[v]=N_k(v)\cup \lbrace v\rbrace $ is the closed $k$-neighborhood of $v$. A function $f\: V\rightarrow \lbrace -1,1\rbrace $ is a signed distance-$k$-dominating function of $G$, if for every vertex $v\in V$, $f(N_k[v])=\sum _{u\in N_k[v]}f(u)\ge 1$. The signed distance-$k$-domination number, denoted by $\gamma _{k,s}(G)$, is the minimum weight of a signed distance-$k$-dominating function on $G$. The values of $\gamma _{2,s}(G)$ are found for graphs with small diameter, paths, circuits. At the end it is proved that $\gamma _{2,s}(T)$ is not bounded from below in general for any tree $T$.
Let λ1(Q) be the first eigenvalue of the Sturm-Liouville problem y ′′ − Q(x)y + λy = 0, y(0) = y(1) = 0, 0 < x < 1. We give some estimates for mα,β,γ = inf Q∈Tα,β,γ λ1(Q) and Mα,β,γ = sup Q∈Tα,β,γ λ1(Q), where Tα,β,γ is the set of real-valued measurable on [0, 1] x α(1 − x) β -weighted Lγ-functions Q with non-negative values such that ∫ 1 0 x α(1 − x) βQ γ (x) dx = 1 (α, β, γ ∈ ℝ, γ ≠ 0).