The global environment is faced with growing threats from anthropogenic disturbance, propelling the Earth into a 6th mass extinction. For the world's mammals, this is reflected in the fact that 25% of species are threatened with some risk of extinction. During this time of species loss and environmental alteration, the world's natural history museums (NHMs) are uniquely poised to provide novel insight into many aspects of conservation. This review seeks to provide evidence of the importance of NHMs to mammal conservation, how arguments against continued collecting of physical voucher specimens is counterproductive to these efforts, and to identify additional threats to collecting with a particular focus on small mammals across Africa. NHMs contribute unique data for assessing mammal species conservation status through the International Union for Conservation of Nature's (IUCN) Red List of Threatened species. However, NHMs' contributions to mammal conservation go well beyond supporting the IUCN Red List, with studies addressing topics such as human impacts, climate change, genetic diversity, disease, physiology, and biodiversity education. Increasing and diverse challenges, both domestic and international, highlight the growing threats facing NHMs, especially in regards to the issue of lethally sampling individuals for the purpose of creating voucher specimens. Such arguments are counterproductive to conservation efforts and tend to reflect the moral opposition of individual researchers than a true threat to conservation. The need for continued collecting of holistic specimens of all taxa across space and time could not be more urgent, especially for underexplored biodiversity hotspots facing extreme threats such as the Afrotropics.
In a communication network, vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a connected graph as model-ing a network, the rupture degree of a graph is one measure of graph vulnerability and it is defined by
r(G) = max{w(G-S)-|S|-m(G-S): S \subset V(G), w(G-S)>1}
where w(G-S) is the number of components of G-S and m(G-S) is the order of a largest component of G-S. In this paper, general results on the rupture degree of a graph are considered. Firstly, some bounds on the rupture degree are given. Further, rupture degree of a complete k-ary tree is calculated. Also several results are given about complete k-ary tree and graph operations. Finally, we give formulas for the rupture degree of the cartesian product of some special graphs.
In this note we prove that there exists a Carathéodory vector lattice $V$ such that $V\cong V^3$ and $V\ncong V^2$. This yields that $V$ is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.
Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. {\it 56}({\it 131}) (2006), 1207--1213) gave the definition of Laplacian energy of a graph $G$ and proved $LE(G)\geq 6n-8$; equality holds if and only if $G=P_n$. In this paper we consider the relation between the Laplacian energy and the chromatic number of a graph $G$ and give an upper bound for the Laplacian energy on a connected graph.
A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply $G$ is $DQS$). Let $T(a,b,c)$ denote the $T$-shape tree obtained by identifying the end vertices of three paths $P_{a+2}$, $P_{b+2}$ and $P_{c+2}$. We prove that its all line graphs $\mathcal {L}(T(a,b,c))$ except $\mathcal {L}(T(t,t,2t+1))$ ($t\geq 1$) are $DQS$, and determine the graphs which have the same signless Laplacian spectrum as $\mathcal {L}(T(t,t,2t+1))$. Let $\mu _1(G)$ be the maximum signless Laplacian eigenvalue of the graph $G$. We give the limit of $\mu _1(\mathcal {L}(T(a,b,c)))$, too.
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution to the two factors generalized CIR model and we show that the first two terms in the expansion are independent of the variable representing stochastic volatility.