Purple nutsedge (Cyperus rotundus L.) is one of the world’s resilient upland weeds, primarily spreading through its tubers. Its emergence in rice (Oryza sativa L.) fields has been increasing, likely due to changing paddy-farming practices. This study aimed to investigate how C. rotundus, an upland weed, can withstand soil flooding and become a problematic weed in rice fields. The first comparative analysis focused on the survival and recovery characteristics of growing and mature tubers of C. rotundus exposed to soil-flooding conditions. Notably, mature tubers exhibited significant survival and recovery abilities in these environments. Based on this observation, further investigation was carried out to explore the morphological structure, nonstructural carbohydrates, and respiratory mechanisms of mature tubers in response to prolonged soil flooding. Over time, the mature tubers did not form aerenchyma but instead gradually accumulated lignified sclerenchymal fibers, with lignin content also increasing. After 90 d, the lignified sclerenchymal fibers and lignin contents were 4.0 and 1.1 times higher than those in the no soil-flooding treatment. Concurrently, soluble sugar content decreased while starch content increased, providing energy storage, and alcohol dehydrogenase activity rose to support anaerobic respiration via alcohol fermentation. These results indicated that mature tubers survived in soil-flooding conditions by adopting a low-oxygen quiescence strategy, which involves morphological adaptations through the development of lignified sclerenchymal fibers, increased starch reserves for energy storage, and enhanced anaerobic respiration. This mechanism likely underpins the flooding tolerance of mature C. rotundus tubers, allowing them to endure unfavorable conditions and subsequently germinate and grow once flooding subsides. This study provides a preliminary explanation of the mechanism by which mature tubers of C. rotundus from the upland areas confer flooding tolerance, shedding light on the reasons behind this weed’s increasing presence in rice fields.

Motivated by the recent work of Zhi-Wei Sun [‘Problems and results on determinants involving Legendre symbols’, Preprint, arXiv:2405.03626], we study some matrices concerning subgroups of finite fields. For example, let $q\equiv 3\pmod 4$ be an odd prime power and let $\phi $ be the unique quadratic multiplicative character of the finite field $\mathbb {F}_q$. If the set $\{s_1,\ldots ,s_{(q-1)/2}\}=\{x^2:\ x\in \mathbb {F}_q\setminus \{0\}\}$, then we prove that

$$ \begin{align*}\det[t+\phi(s_i+s_j)+\phi(s_i-s_j)]_{1\le i,j\le (q-1)/2}=\bigg(\frac{q-1}{2}t-1\bigg)q^{{(q-3)}/{4}}.\end{align*} $$

This confirms a conjecture of Zhi-Wei Sun.

Motivated by the work initiated by Chapman [‘Determinants of Legendre symbol matrices’, Acta Arith. 115 (2004), 231–244], we investigate some arithmetical properties of generalised Legendre matrices over finite fields. For example, letting $a_1,\ldots ,a_{(q-1)/2}$ be all the nonzero squares in the finite field $\mathbb {F}_q$ containing q elements with $2\nmid q$, we give the explicit value of the determinant $D_{(q-1)/2}=\det [(a_i+a_j)^{(q-3)/2}]_{1\le i,j\le (q-1)/2}$. In particular, if $q=p$ is a prime greater than $3$, then

$$ \begin{align*}\bigg(\frac{\det D_{(p-1)/2}}{p}\bigg)= \begin{cases} 1 & \mbox{if}\ p\equiv1\pmod4,\\ (-1)^{(h(-p)+1)/2} & \mbox{if}\ p\equiv 3\pmod4\ \text{and}\ p>3, \end{cases}\end{align*} $$

where $(\frac {\cdot }{p})$ is the Legendre symbol and $h(-p)$ is the class number of $\mathbb {Q}(\sqrt {-p})$.

We use circulant matrices and hyperelliptic curves over finite fields to study some arithmetic properties of certain determinants involving Legendre symbols and kth power residues.

Let $p=3n+1$ be a prime with $n\in \mathbb {N}=\{0,1,2,\ldots \}$ and let $g\in \mathbb {Z}$ be a primitive root modulo p. Let $0<a_1<\cdots <a_n<p$ be all the cubic residues modulo p in the interval $(0,p)$ . Then clearly the sequence $a_1 \bmod p,\, a_2 \bmod p,\ldots , a_n \bmod p$ is a permutation of the sequence $g^3 \bmod p,\,g^6 \bmod p,\ldots , g^{3n} \bmod p$ . We determine the sign of this permutation.

Z.-W. Sun [‘Refining Lagrange’s four-square theorem’, J. Number Theory175 (2017), 169–190] conjectured that every positive integer n can be written as $ x^2+y^2+z^2+w^2\ (x,y,z,w\in \mathbb {N}=\{0,1,\ldots \})$ with $x+3y$ a square and also as $n=x^2+y^2+z^2+w^2\ (x,y,z,w \in \mathbb {Z})$ with $x+3y\in \{4^k:k\in \mathbb {N}\}$ . In this paper, we confirm these conjectures via the arithmetic theory of ternary quadratic forms.

Chinese sturgeon (Acipenser sinensis) is an endangered species, listed as a grade I protected animal in China. The females rarely successfully develop their gonads from stage II to III in captivity, which handicaps the propagation of cultured Chinese sturgeon. The present study aimed to understand the effects of dietary lipid level on the ovarian development and the related regulation mechanism in female Chinese sturgeon. A 24-month feeding trial was conducted with 10-year-old Chinese sturgeons with ovaries at the developmental stage II, with three experimental diets containing 10, 14 and 18 % lipids. Ovary, muscle and serum samples were collected at four time points (6, 12, 18 and 24 months) for further analyses. Serum metabolomics and ovary transcriptomics analyses were conducted at 18 months. Results showed that only the 18 % lipid diet promoted ovary development to stage IV. Oocytes at stage II in this group also exhibited higher diameter and more lipid droplets. Serum TAG content in the 18 % group was significantly higher than in 10 and 14 % groups (both at 12 and 18 months). Oestradiol content in the 14 % group was significantly higher than in 10 and 18 % groups, except at 24 months. Metabolomic and transcriptomic results indirectly indicated that 14 % of dietary lipids benefited steroid hormone synthesis, while 18 % lipid facilitated arachidonic acid metabolism, cholesterol biosynthesis and vitellogenesis, although serum cholesterol content did not vary with dietary lipid level. In conclusion, 18 % dietary lipid is the optimal level for improving gonad development of female Chinese sturgeon.

Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$th power residues modulo $p$ and primitive roots modulo a power of $p$.

The Lower Yangtze foreland basin is situated to the northwest of the early Palaeozoic Wuyi–Yunkai orogen in South China. To demonstrate its provenance history and the denudation of the orogen, seven sandstone samples were collected from the upper Ordovician to Silurian strata for U–Pb dating. The zircons show a broad range of ages that can be linked with the ages of specific units in the Wuyi–Yunkai orogen. The zircon spectra in the late Ordovician samples are similar to those in the pre-orogenic strata, suggesting a recycled source. The dominant age population of 880–740 Ma in the early Llandovery samples indicates that the middle Neoproterozoic volcanic rocks were the primary source. A significant age population of 460–425 Ma in the late Llandovery to Wenlock samples reflects the fact that the synorogenic magmatic and metamorphic rocks were exposed to provide detritus. The youngest zircons from the uppermost Silurian strata yield an age of 425 Ma, which approximates the inferred depositional age. This age, together with available biostratigraphic data, indicates that the foreland basin was formed 448–425 Ma ago. We surmise a possible link between the Wuyi–Yunkai orogen and the Appalachian–Caledonian orogen based on the geological constraints and palaeomagnetic data.

Genetic diversity and relationships among 21 accessions of Secale L., including three species and 10 subspecies, were evaluated using RAMP markers. Forty-one out of 80 (50.5%) RAMP primers, which produced clear and polymorphic bands, were selected for PCR amplification of genomic DNA. A total of 446 bands were amplified from the 41 primers, and 428 of these bands (about 96%) were polymorphic. Three to 19 polymorphic bands could be amplified from each primer, with an average of 10.4 bands. The RAMP-based genetic similarity (GS) values among the 21 Secale accessions ranged from 0.266 to 0.658, with a mean of 0.449. A high level of genetic variation was found between or within the wild populations and the cultivars. Based on the GS matrix, a dendrogram was constructed using the unweighted pair group method with arithmetic average (UPGMA). All 21 accessions could be distinguished by RAMP markers. Clustering results showed that the genetic diversity of Secale based on RAMP markers was correlated with geographical distribution. Six rye cultivars, originating from Poland, Portugal, Mexico, Hungary, Armenia and Ukraine, were clustered into one group. The six countries are all located in the transitional region of broad-leaf forests between maritime and continental temperate zones, with narrow latitude span. In comparison, the other five cultivars from countries scattered over a region with large latitude span were distributed within different groups or subgroups. Genetic relationships based on RAMP markers had great deviation from the original taxonomy. Some subspecies of the same species were distributed within different groups, while some accessions of different species were closely clustered into one subgroup. These results suggest that RAMP markers could be an effective technique for detecting genetic diversity among Secale and give some useful information about its phylogenic relationships.