During the last few decades the tree line has shifted upward on Mediterranean mountains. This has resulted in a decrease in the area of the sub-alpine prairie habitat and an increase in the threat to strictly orophilous moths that occur there. This also occurred on the Pollino Massif due to the increase in temperature and decrease in rainfall in Southern Italy. We found that a number of moths present in the alpine prairie at 2000 m appear to be absent from similar habitats at 1500-1700 m. Some of these species are thought to be at the lower latitude margin of their range. Among them, Pareulype berberata and Entephria flavicinctata are estimated to be the most threatened because their populations are isolated and seem to be small in size. The tops of these mountains are inhabited by specialized moth communities, which are strikingly different from those at lower altitudes on the same massif further south. The majority of the species recorded in the sub-alpine prairies studied occur most frequently and abundantly in the core area of the Pollino Massif. Species and, as a consequence, communities found at high altitudes are highly vulnerable to climate warming, and need further monitoring.
We prove that any infinite-dimensional non-archimedean Fréchet space $E$ is homeomorphic to $D^{\mathbb{N}}$ where $D$ is a discrete space with $\mathop {\mathrm card}(D)=\mathop {\mathrm dens}(E)$. It follows that infinite-dimensional non-archimedean Fréchet spaces $E$ and $F$ are homeomorphic if and only if $\mathop {\mathrm dens}(E)= \mathop {\mathrm dens}(F)$. In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field $\mathbb{K}$ is homeomorphic to the non-archimedean Fréchet space $\mathbb{K}^{\mathbb{N}}$.
In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented.
We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form $T[(\mathcal M_k,\theta _k)_{k =1}^{l}]$ with index $i(\mathcal M_k)$ finite are either $c_0$ or $\ell _p$ saturated for some $p$ and we characterize when any two spaces of such a form are totally incomparable in terms of the index $i(\mathcal M_k)$ and the parameter $\theta _k$. Also, we give sufficient conditions of total incomparability for a particular class of spaces of the form $T[(\mathcal A_k,\theta _k)_{k = 1}^\infty ]$ in terms of the asymptotic behaviour of the sequence $\Bigl \Vert \sum _{i=1}^n e_i\Bigr \Vert $ where $(e_i)$ is the canonical basis.
In this paper we initiate the study of total restrained domination in graphs. Let $G=(V,E)$ be a graph. A total restrained dominating set is a set $S\subseteq V$ where every vertex in $V-S$ is adjacent to a vertex in $S$ as well as to another vertex in $V-S$, and every vertex in $S$ is adjacent to another vertex in $S$. The total restrained domination number of $G$, denoted by $\gamma _r^t(G)$, is the smallest cardinality of a total restrained dominating set of $G$. First, some exact values and sharp bounds for $\gamma _r^t(G)$ are given in Section 2. Then the Nordhaus-Gaddum-type results for total restrained domination number are established in Section 3. Finally, we show that the decision problem for $\gamma _r^t(G)$ is NP-complete even for bipartite and chordal graphs in Section 4.
In this paper a full totalization is presented of the Kurzweil-Henstock integral in the multidimensional space. A residual function of the total Kurzweil-Henstock primitive is defined.
In this paper we study some properties of a totally $\ast $-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally $\ast $-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally $\ast $-paranormal operators through the local spectral theory. Finally, we show that every totally $\ast $-paranormal operator satisfies an analogue of the single valued extension property for $W^{2}(D,H)$ and some of totally $\ast $-paranormal operators have scalar extensions.
The paper describes the general form of an ordinary differential equation of the order $n+1$ $(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form \[ f\biggl (s, v, w_{11}v_{1}, \ldots , \sum _{j=1}^{n}w_{nj}v_{j}\biggr ) = \sum _{j=1}^{n}w_{n+1 j}v_{j} + w_{n+1 n+1}f(x, v, v_{1}, \ldots , v_{n}), \] where $ w_{ij} = a_{ij}(x_{1}, \ldots , x_{i-j+1}) $ are given functions, $ w_{n+1 1} = g(x, x_{1}, \ldots , x_{n})$, is solved on $\mathbb R.$.
A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a "usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of the original system on a single vacation cycle is brought to the study of the "usual'' system. Finally, the renewal theory is used to derive the general result. Moreover, a numerical approach to analytical results is discussed and some illustrative numerical examples are given.
In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix A is characterized by A being a Kleene star. We give applications to alcoved polytopes, using normal idempotent matrices (which form a subclass of Kleene stars). For a normal matrix we define a norm and show that this is the radius of a hyperplane section of its tropical span.