Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Algebraic Cayley Graphs over Finite Fields

A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of Chung

Hidden Conformal Symmetry for Vector Field on Various Black Hole Backgrounds

Hidden conformal symmetries of scalar field on various black hole backgrounds have been investigated for years, but whether those features holds for other fields are still open questions. Recently, with proper assumptions, Lunin achieves to the separation of variables for Maxwell equations on Kerr background. In this paper, with that equation, we find that hidden conformal symmetry appears at near region under low frequency limit. We also extended those results to vector field on Kerr-(A)dS and Kerr-NUT-(A)dS backgrounds, then hidden conformal symmetry also appears if we focusing on the near-horizon region at low frequency limit.Comment: 18 pages, no figure, matches the published versio

Bioactivity of Cicuta virosa L. var. latisecta Celak. (Umbelliferae: Cicutal) against Red Imported Fire Ant under Laboratory and Field Conditions

We evaluated the bioactivities of compounds from Cicuta virosa L. var. latisecta Celak. against red imported fire ants (Solenopsis invicta Buren) under field and laboratory conditions. The compounds were as follows: methanol extract; petroleum ether, chloroform, and ethyl acetate fractions from the methanol extract; and the active compound isoimperatorin, which was isolated from the chloroform-fraction. The 7 d LC50 values of the methanol extract, petroleum ether, chloroform, and ethyl acetate fractions and isoimperatorin toward micrergates were 111.20, 214.45, 40.90, 569.67, and 25.73 mg/kg, res­pectively. The corresponding LC50 values toward macrergates were 155.78, 308.38, 75.01, 776.75, and 42.77 mg/kg, res­pectively. Under field conditions, baits containing 0.2% methanol extract, 0.1% chloroform fraction, and 0.05% isoimperatorin efficiently controlled S. invicta, with effectiveness percentages of 95.56%, 97.78%, and 95.56%, respectively on the 30th day after bait application. Such effectiveness percentages were not significantly different from that obtained using the positive control fipronil. The present study showed that C. virosa L. var. latisecta has potential as a natural control agent for the red imported fire ants

Testing general relativity with TianQin: the prospect of using the inspiral signals of black hole binaries

In this paper, we carry out a systematic study of the prospect of testing general relativity with the inspiral signals of black hole binaries that could be detected with TianQin. The study is based on the parameterized post-Einsteinian (ppE) waveform, so that many modified gravity theories can be covered simultaneously. We consider black hole binaries with total masses ranging from $10\rm M_\odot\sim10^7 M_\odot$ and ppE corrections at post-Newtonian (PN) orders ranging from $-4$PN to $2$PN. Compared to the current ground-based detectors, TianQin can improve the constraints on the ppE phase parameter $\beta$ by orders of magnitude. For example, the improvement at the $-4$PN and $2$PN orders can be about $13$ and $3$ orders of magnitude (compared to the results from GW150914), respectively. Compared to future ground-based detectors, such as ET, TianQin is expected to be superior below the $-1$PN order, and for corrections above the $-0.5$PN order, TianQin is still competitive near the large mass end of the low mass range $[10 \rm M_\odot, \,10^3 \rm M_\odot]\,$. Compared to the future space-based detector LISA, TianQin can be competitive in the lower mass end as the PN order is increased. For example, at the $-4$PN order, LISA is always superior for sources more massive than about $30\rm M_\odot\,$, while at the $2$PN order, TianQin becomes competitive for sources less massive than about $10^4\rm M_\odot$. We also study the scientific potentials of detector networks involving TianQin, LISA and ET, and discuss the constraints on specific theories such as the dynamic Chern-Simons theory and the Einstein-dilaton Gauss-Bonnet theory