On powers of Hamilton cycles in Ramsey-Tur\'{a}n Theory

We prove that for $r\in \mathbb{N}$ with $r\geq 2$ and $\mu>0$, there exist $\alpha>0$ and $n_{0}$ such that for every $n\geq n_{0}$, every $n$-vertex graph $G$ with $\delta(G)\geq \left(1-\frac{1}{r}+\mu\right)n$ and $\alpha(G)\leq \alpha n$ contains an $r$-th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for $r=2, 3$ and the $r=2$ case was recently conjectured by Staden and Treglown.Comment: 19 pages, 4 figure

Loss of soil carbon and nitrogen indicates climate change-induced alterations in a temperate forest ecosystem

Climate warming is expected to influence terrestrial biogeochemical cycles by modifying the quality and quantity of plant litter input to soils. Although a growing number of studies recognize the importance of plant litter input in influencing the loss of soil organic matter (SOM) through a phenomenon called the priming effect (PE), the exact mechanisms behind PE are not well known. Importantly, most PE research is based on short term pot experiments in which fresh organic matter (FOM) input is represented by a single addition of compounds of unnaturally simple chemical composition. Furthermore, only a few studies exist in which the PE was explored in terms of organic C (SOC) and total N content in the soil. Here, we report results of a 3-year long litter manip-ulation study conducted under natural conditions in a broadleaved Korean pine forest in N-E China. We show that the extra supply (twice the normal input) of aboveground tree litter composing of conifer needles, leaves and small twigs was associated not only with slightly decreased SOC (by 5%) but especially that of soil total N (STN) (by 15%) content in the top soil (0-5 cm depth). In contrast, removal of litter resulted in an increased (ca. 15%) amount of both SOC and STN during the study when compared to control soils receiving natural litter input. Despite the enhanced leaf litter decomposition rate in the treatment receiving extra litter, the changes in SOC and STN were related neither to soil microbial biomass nor to community composition. The amount of N lost (40.0 g m- 2) in the soil due to litter addition was ca. three times the amount of N added (12.3 g m- 2) via the litter, while the amount of C lost (238 g m- 2) was about one third of that added (940 g m- 2), suggesting that soil N in our research site is more prone to the PE than soil C. As we did not manipulate belowground FOM input, our results suggest that input of aboveground litter rather than that by roots explained the PE in our study. Results of our long-term study conducted under natural conditions in undisturbed forest soils highlight the large potential of recalcitrant, aboveground litter to affect the PE, which should not go unnoticed when predicting the role of forest soils under conditions (such as climate warming) when these soils act as C sinks.Peer reviewe

Confirming the 115.5-day periodicity in the X-ray light curve of ULX NGC 5408 X-1

The Swift/XRT light curve of the ultraluminous X-ray (ULX) source NGC 5408 X-1 was re-analyzed with two new numerical approaches, Weighted Wavelet $Z$-transform (WWZ) and CLEANest, that are different from previous studies. Both techniques detected a prominent periodicity with a time scale of $115.5\pm1.5$ days, in excellent agreement with the detection of the same periodicity first reported by Strohmayer (2009). Monte Carlo simulation was employed to test the statisiticak confidence of the 115.5-day periodicity, yielding a statistical significance of $> 99.98$ (or $>3.8\sigma$). The robust detection of the 115.5-day quasi-periodic oscillations (QPOs), if it is due to the orbital motion of the binary, would infer a mass of a few thousand $M_\odot$ for the central black hole, implying an intermediate-mass black hole in NGC 5408 X-1.Comment: 6 pages, 2 figures, submitted to Research in Astronomy and Astrophysics (RAA

Stability Analysis of Axisymmetric Concave Slopes Based on Two-Dimensional Limit Equilibrium Approach considering Additional Shear Resistance

This work is licensed under a Creative Commons Attribution 4.0 International License.Axisymmetric concave slopes, one special type of three-dimensional (3D) slopes, may be encountered in mining and civil engineering practice. Analysis of 3D slopes is generally complex and mostly relies on complicated numerical simulations. This paper proposes an elastoplastic solution for determining the additional shear resistances due to spatial effects of axisymmetric concave slopes. By incorporating the extra antislide forces, this paper proposes a simplified two-dimensional (2D) limit equilibrium procedure for the stability analysis of axisymmetric concave slopes. Combined with an iteration algorithm, the procedure can obtain the factors of safety for axisymmetric concave slopes in a simple and efficient way. Comparisons of the results from the proposed method and the numerical software FLAC3D are performed to demonstrate the validity of the proposed method for practical applications. Finally, the effects of several key parameters on the stability of axisymmetric concave slopes are investigated through a parametric study.National Natural Science Foundation of China (No. 51578230

2-Chloro­methyl-1-methyl-1,3-benzimidazole

The title compound, C9H9ClN2, was prepared from the reaction of N-methyl­benzene-1,2-diamine and 2-chloro­acetic acid in boiling 6 M hydro­chloric acid. The benzimidazole unit is approximately planar, the largest deviation from the mean plane being 0.008 (1) Å. The Cl atom is displaced by 1.667 (2) Å from this plane. The methyl group is statistically disordered with equal occupancy