Furman University is a private liberal arts university in Greenville, South Carolina, United States. Founded in 1826 and named for the clergyman Richard Furman,[A 2] Furman University is the oldest private institution of higher learning in South Carolina. It became a secular university in 1992, while keeping Christo et Doctrinae (For Christ and Learning) as its motto. It enrolls approximately 2,700 undergraduate students and 200 graduate students, representing 46 states and 53 foreign countries, on its 750-acre (304 ha) campus....
The isolation number ι(G) of a graph G is the minimum cardinality of a set A⊂V(G) such that the subgraph induced by the vertices that are not in the union of the closed neighborhoods of vertices in A has no edges. The invariant, known also under the name vertex-edge domination number of G, has attracted a lot of interest in recent years. In this paper, we study the behavior of the isolation number under several graph operations, namely the Cartesian and the lexicographic product and the fractalization leading to generalized Sierpiński graphs. We prove several upper and lower bounds on the isolation number of the Cartesian product of two graphs. We prove a lower bound for the isolation number of the prism G□K2 over an arbitrary graph G, which in the case of bipartite graphs leads to the equality ι(G□K2)=γ(G), where γ(G) is the domination number of G. In particular, ι(Qn+1)=γ(Qn) holds for all positive integers n, where Qn is the n-dimensional hypercube. For the lexicographic product G∘H we prove that its isolation number, under certain mild restrictions, equals the total domination number of the first factor G. We also prove sharp lower and upper bounds on the isolation numbers of the generalized Sierpiński graphs SGt, where G is an arbitrary base graph. These bounds in the case of classical Sierpiński graphs, namely SKnt, coincide and lead to the exact values ι(SKnt)=(n−1)⋅nt−2 for all dimensions t≥2.
Current ground-based interferometers are optimized for sensitivity from a few tens of Hz to about 1 kHz. While they are not currently utilized for GW detection, interferometric detectors also feature narrow bands of strong sensitivity at higher frequencies where the sideband fields created by a GW are resonantly amplified in the optical system. For certain interferometer configurations, small changes to system parameters allow the narrow band of high sensitivity to be scanned over a much larger range of frequencies, potentially enabling broadband detection at high frequencies. In this paper, we investigate whether simply modifying the detuning angle of the signal-recycling mirror of the GEO600 interferometer can make this experiment sensitive to GWs in the kilohertz frequency range. We compute the strain sensitivity for GEO600 across a frequency range from several kHz to tens of kHz for various detuning angles. We also show that LIGO cannot attain the same effect assuming that the optical components are not changed due to the narrow band response of the Fabry-Perot cavities. We then calculate the sensitivity of GEO600 to various proposed high-frequency GW sources and compare it to the sensitivity of other ground-based detectors.
Initially proposed over 40 years ago, the biotechnology of agromining has had a long and tortuous gestational process on the way to becoming a proven commercial reality. The field has been marred by claims for unrealistic yields made by startup companies. Nevertheless, nickel agromining has become a viable business proposition for several companies now operating "metal farms" around the world. In this review, we provide a critical perspective on the current direction of the field and potential pitfalls still to overcome. Challenges and risks include the urgency for discovery of suitable metal crop species before extinction from habitat loss, the rapid domestication of wild species to be accommodated in regular cultivation systems, and the potential introduction and escape of non-native plant species. Initiatives to identify new hyperaccumulators using X-ray fluorescence scanning of herbarium collections should target the biodiversity hotspots of the world and should be coupled with ex situ conservation of threatened hyperaccumulator plant species in botanical gardens. With the rapid progress in the science needed to find and develop more effective hyperaccumulators, it is an exciting time for nickel agromining. The next few years are expected to be a make-or-break period in its transformation to a commercial reality.
The Maker–Breaker domination game is played on a graph G by Dominator and Staller who alternate turns selecting an unplayed vertex of G. The goal of Dominator is that the vertices he selected during the game form a dominating set while Staller’s goal is to prevent this from happening. The graph invariant γMB′(G) is the number of Dominator’s moves in the game played on G in which he can achieve his goal when Staller makes the first move and both players play optimally. In this paper, we continue the investigation of 2-γMB′-critical graphs, initiated in Divakaran et al. (2025), which are defined as the graphs G with γMB′(G)=2 and γMB′(G−e)>2 for every edge e in G. The authors characterized bipartite 2-γMB′-critical graphs, and found an example of a non-bipartite 2-γMB′-critical graph. In this paper, we characterize the 2-γMB′-critical graphs that have a cut-vertex, which are represented by two infinite families. In addition, we prove that C5 is the only non-bipartite, triangle-free 2-γMB′-critical graph.
