The influence of second-order dispersion (SOD) on stimulated Raman scattering (SRS) in the interaction of an ultrashort intense laser with plasma was investigated. More significant backward SRS was observed with the increase of the absolute value of SOD ($\mid \kern-1pt\!{\psi}_2\!\kern-1pt\mid$). The integrated intensity of the scattered light is positively correlated to the driver laser pulse duration. Accompanied by the side SRS, filaments with different angles along the laser propagation direction were observed in the transverse shadowgraph. A model incorporating Landau damping and above-threshold ionization was developed to explain the SOD-dependent angular distribution of the filaments.

A pulsed fast neutron source is critical for applications of fast neutron resonance radiography and fast neutron absorption spectroscopy. However, due to the large transversal source size (of the order of mm) and long pulse duration (of the order of ns) of traditional pulsed fast neutron sources, it is difficult to realize high-contrast neutron imaging with high spatial resolution and a fine absorption spectrum. Here, we experimentally present a micro-size ultra-short pulsed neutron source by a table-top laser–plasma wakefield electron accelerator driving a photofission reaction in a thin metal converter. A fast neutron source with source size of approximately 500 μm and duration of approximately 36 ps has been driven by a tens of MeV, collimated, micro-size electron beam via a hundred TW laser facility. This micro-size ultra-short pulsed neutron source has the potential to improve the energy resolution of a fast neutron absorption spectrum dozens of times to, for example, approximately 100 eV at 1.65 MeV, which could be of benefit for high-quality fast neutron imaging and deep understanding of the theoretical model of neutron physics.

The Tian Shan mountain range, known as the water towers of Central Asia, plays a key role in local water supply, yet large uncertainties remain about the amount of water that is stored in its glaciers. In this study, we assess the impact of the boundary conditions on ice thickness estimates using two inversion models: a mass conservation (MC) model and a basal shear stress (BS) model. We compare the widely used Randolph Glacier Inventory version 6 with the updated Glacier Area Mapping for Discharge from the Asian Mountains glacier inventory, as well as two digital elevation models (SRTM DEM and Copernicus DEM). The results show that the ice volume (in ~2000 CE) in the Tian Shan range is 661.0 ± 163.5 km3 for the MC model and 552.8 ± 85.3 km3 for the BS model. There are strong regional differences due to inventory, especially for glaciers in China (17–25%). However, the effect of different DEM sources on ice volume estimation is limited. By the end of the 21st century, the projected mass loss differences between inventories are higher than between adjacent emission scenarios, illustrating the vital importance of high-quality inventories. These differences should be carefully considered during water resource planning.

An edge-coloured graph $G$ is called properly connected if any two vertices are connected by a properly coloured path. The proper connection number, $pc(G)$, of a graph $G$, is the smallest number of colours that are needed to colour $G$ such that it is properly connected. Let $\unicode[STIX]{x1D6FF}(n)$ denote the minimum value such that $pc(G)=2$ for any 2-connected incomplete graph $G$ of order $n$ with minimum degree at least $\unicode[STIX]{x1D6FF}(n)$. Brause et al. [‘Minimum degree conditions for the proper connection number of graphs’, Graphs Combin.33 (2017), 833–843] showed that $\unicode[STIX]{x1D6FF}(n)>n/42$. In this note, we show that $\unicode[STIX]{x1D6FF}(n)>n/36$.

For two given graphs $G_{1}$ and $G_{2}$, the Ramsey number $R(G_{1},G_{2})$ is the smallest integer $N$ such that, for any graph $G$ of order $N$, either $G$ contains $G_{1}$ as a subgraph or the complement of $G$ contains $G_{2}$ as a subgraph. A fan $F_{l}$ is $l$ triangles sharing exactly one vertex. In this note, it is shown that $R(F_{n},F_{m})=4n+1$ for $n\geq \max \{m^{2}-m/2,11m/2-4\}$.

Let $G$ be a graph of order $n\geq 6$ with minimum degree ${\it\delta}(G)\geq 4$. Arkin and Hassin [‘Graph partitions with minimum degree constraints’, Discrete Math. 190 (1998), 55–65] conjectured that there exists a bipartition $S,T$ of $V(G)$ such that $\lfloor n/2\rfloor -2\leq |S|,|T|\leq \lceil n/2\rceil +2$ and the minimum degrees in the subgraphs induced by $S$ and $T$ are at least two. In this paper, we first show that $G$ has a bipartition such that the minimum degree in each part is at least two, and then prove that the conjecture is true if the complement of $G$ contains no complete bipartite graph $K_{3,r}$, where $r=\lfloor n/2\rfloor -3$.

Multispectral analysis combined with the Periodic Acid-Schiff method was used to investigate cytological features of insoluble polysaccharides and changes in total insoluble polysaccharide content (TPC) during pollen development in rice, including four cytoplasmic male sterility lines (MSLs) and their corresponding fertility-maintaining lines (FMLs). The multispectral curves of the relative transmittance value (RTV) and the images of developing pollen cells were obtained across a range of successive wavelengths (400–720 nm). A minimum RTV was found near 550 nm indicating an absorption peak of the TPC. Thus, the TPC was measured using the RTV of 550 nm. In the four FMLs, the minimum TPC of developing pollen cells occurred at the late microspore stage, while the maximum TPC occurred at the mature pollen grain stage. The TPC levels of pollen cells were significantly higher in the four FMLs than in their corresponding MSLs during and after pollen abortion. Notably, a steep decrease of multispectral curves at 420 nm appeared before the occurrence of abortion, implying a marker associated with pollen abortion in rice. Our results will be helpful for exploring the changes in TPC during pollen ontogenesis in rice and provide a novel method for the study of bio-macromolecules.