We show that every $(n,d,\lambda )$-graph contains a Hamilton cycle for sufficiently large $n$, assuming that $d\geq \log ^{6}n$ and $\lambda \leq cd$, where $c=\frac {1}{70000}$. This significantly improves a recent result of Glock, Correia, and Sudakov, who obtained a similar result for $d$ that grows polynomially with $n$. The proof is based on a new result regarding the second largest eigenvalue of the adjacency matrix of a subgraph induced by a random subset of vertices, combined with a recent result on connecting designated pairs of vertices by vertex-disjoint paths in $(n,d,\lambda )$-graphs. We believe that the former result is of independent interest and will have further applications.

The previous study indicated that ubiquitination is involved in the freezing tolerance of hydrated seeds. Parthenolide (PN), inducing the ubiquitination of MDM2, an E3 ring-finger ubiquitin ligase, adversely affects the freezing tolerance of hydrated lettuce seeds. Therefore, a proteomics analysis was conducted to identify PN's targets in hydrated seeds exposed to cooling conditions. Several pathways, including oxidative phosphorylation (KEGG00190), amino sugar and nucleotide sugar metabolism (KEGG00520), and biosynthesis of nucleotide sugars (KEGG01250), were enriched in the PN treatment under slow-cooling conditions (3°C h−1, P < 0.05). Among the proteins in oxidative phosphorylation, the expression of NADH dehydrogenases and ATP synthases (ATPsyn) decreased in PN treatment. In contrast, uncoupling proteins increased after PN treatment, which led to the dissociation of the electron transport chain from ATP synthesis. Treatments with rotenone, dicoumarol, and oligomycin (i.e., oxidative phosphorylation inhibitors) decreased the survival rate of hydrated seeds under freezing conditions, which indicated that energy metabolism was related to the freezing tolerance of hydrated seeds. The predicted interactions between PN and MDM2-like proteins of Lactuca indicated that LsMDM2-5 forms two potential hydrogen bonds with PN. Furthermore, based on AlphaFold predictions and yeast 2-hybrid results, MDM2-5 might interact directly with NADH2. The knockdown of MDM2-5 by RNAi caused a higher level of NADH2 and ATPsyn and a higher freezing tolerance of hydrated seeds. This indicated that MDM2 played negative roles in regulating ATP synthesis and freezing tolerance of hydrated seeds.

In a horizontally heated melting system, where a solid substance is subject to melting by a warmer liquid beneath, the presence of solute in the liquid introduces a complex interplay between temperature and concentration dynamics. Employing a recently developed sharp interface method (Xue et al., J. Comput. Phys., vol. 491, 2023), we conduct direct numerical simulations to investigate the transient behaviour of the system across a broad range of Rayleigh numbers and solute concentrations. Our observations reveal distinct flow regimes: at low concentrations, the system resembles a temperature-driven melting problem, characterized by vortex rolls beneath the melting interface. As the solute concentration increases, a stably stratified layer emerges beneath the interface, leading to the transition from thermal convection to penetrative convection, which resembles those flow characteristics observed in the double-diffusive convection. This shift results from the competition between the stabilizing effect induced by solute concentration gradient and the destabilizing effect caused by temperature gradient. Otherwise in the diffusion regime, characterized by very high solute concentrations, the flow becomes static due to the complete suppression of convection by the stably stratified layer. This regime further exhibits two distinct patterns: ‘melting’ and ‘dissolution’. Beyond characterizing diverse flow patterns, our study conducts a quantitative analysis, examining heat/mass transfer, melting rates, and the evolution of temperature and concentration at the interface. These insights contribute to a better understanding of the intricate interplay between temperature and solute concentration during phase change, with implications for accurately estimating melting rates in binary fluid systems.

MicroRNAs (miRNAs) are endogenous, non-coding RNAs, which are functional in a variety of biological processes through post-transcriptional regulation of gene expression. However, the role of miRNAs in the interaction between Bacillus thuringiensis and insects remains unclear. In this study, small RNA libraries were constructed for B. thuringiensis-infected (Bt) and uninfected (CK) Spodoptera exigua larvae (treated with double-distilled water) using Illumina sequencing. Utilising the miRDeep2 and Randfold, a total of 233 known and 726 novel miRNAs were identified, among which 16 up-regulated and 34 down-regulated differentially expressed (DE) miRNAs were identified compared to the CK. Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis revealed that potential target genes of DE miRNAs were associated with ABC transporters, fatty acid metabolism and MAPK signalling pathway which are related to the development, reproduction and immunity. Moreover, two miRNA core genes, SeDicer1 and SeAgo1 were identified. The phylogenetic tree showed that lepidopteran Dicer1 clustered into one branch, with SeDicer1 in the position closest to Spodoptera litura Dicer1. A similar phylogenetic relationship was observed in the Ago1 protein. Expression of SeDicer1 increased at 72 h post infection (hpi) with B. thuringiensis; however, expression of SeDicer1 and SeAgo1 decreased at 96 hpi. The RNAi results showed that the knockdown of SeDicer1 directly caused the down-regulation of miRNAs and promoted the mortality of S. exigua infected by B. thuringiensis GS57. In conclusion, our study is crucial to understand the relationship between miRNAs and various biological processes caused by B. thuringiensis infection, and develop an integrated pest management strategy for S. exigua via miRNAs.

Todorokite is a common Mn oxide (with a tunnel structure) in the Earth surface environment, and can be obtained by hydrothermal treatment or refluxing process from precursor buserite with a layered structure. Several chemical reaction conditions for the phase transformation from Na-buserite to todorokite at atmospheric pressure were investigated, including temperature, pH, crystallinity of precursor Na-buserite, the amount of the interlayer Mg2+ of the Mg-buserite and clay minerals. The results showed that the conversion rate and crystallinity of todorokite decreased with falling temperature, and Mg-buserite could not be completely transformed to todorokite at lower temperatures (40°C). The poorly crystalline Na-buserite could be converted into todorokite more easily than highly crystalline Na-buserite. Todorokite can be prepared at pH 5–9, but the rate of conversion and crystallinity of todorokite did vary with pH in the order: neutral ≈ alkali > acidic. The conversion rate of todorokite decreased with decreasing interlayer Mg2+ content of the Mg-buserite. The presence of montmorillonite or goethite slowed the formation reaction of todorokite in the refluxing process, and the reaction time was prolonged when the amounts of those minerals were increased.

With the advantages of short duration and extreme brightness, laser proton accelerators (LPAs) show great potential in many fields for industrial, medical, and research applications. However, the quality of current laser-driven proton beams, such as the broad energy spread and large divergence angle, is still a challenge. We use numerical simulations to study the propagation of such proton bunches in the plasma. Results show the bunch will excite the wakefield and modulate itself. Although a small number of particles at the head of the bunch cannot be manipulated by the wakefield, the total energy spread is reduced. Moreover, while reducing the longitudinal energy spread, the wakefield will also pinch the beam in the transverse direction. The space charge effect of the bunch is completely offset by the wakefield, and the transverse momentum of the bunch decreases as the bunch transports in the plasma. For laser-driven ion beams, our study provides a novel idea about the optimization of these beams.

We show that for any $\varepsilon \gt 0$ and $\Delta \in \mathbb{N}$, there exists $\alpha \gt 0$ such that for sufficiently large $n$, every $n$-vertex graph $G$ satisfying that $\delta (G)\geq \varepsilon n$ and $e(X, Y)\gt 0$ for every pair of disjoint vertex sets $X, Y\subseteq V(G)$ of size $\alpha n$ contains all spanning trees with maximum degree at most $\Delta$. This strengthens a result of Böttcher, Han, Kohayakawa, Montgomery, Parczyk, and Person.

We study the following rainbow version of subgraph containment problems in a family of (hyper)graphs, which generalizes the classical subgraph containment problems in a single host graph. For a collection $\mathit {\mathbf {G}}=\{G_1, G_2,\ldots , G_{m}\}$ of not necessarily distinct k-graphs on the same vertex set $[n]$, a (sub)graph H on $[n]$ is rainbow if there exists an injection $\varphi : E(H)\rightarrow [m]$, such that $e\in E(G_{\varphi (e)})$ for each $e\in E(H)$. Note that if $|E(H)|=m$, then $\varphi $ is a bijection, and thus H contains exactly one edge from each $G_i$.

Our main results focus on rainbow clique-factors in (hyper)graph systems with minimum d-degree conditions. Specifically, we establish the following:

1. (1) A rainbow analogue of an asymptotical version of the Hajnal–Szemerédi theorem, namely, if $t\mid n$ and $\delta (G_i)\geq (1-\frac {1}{t}+\varepsilon )n$ for each $i\in [\frac {n}{t}\binom {t}{2}]$, then $\mathit {\mathbf {G}}$ contains a rainbow $K_t$-factor;

2. (2) Essentially, a minimum d-degree condition forcing a perfect matching in a k-graph also forces rainbow perfect matchings in k-graph systems for $d\in [k-1]$.

The degree assumptions in both results are asymptotically best possible (although the minimum d-degree condition forcing a perfect matching in a k-graph is in general unknown). For (1), we also discuss two directed versions and a multipartite version. Finally, to establish these results, we in fact provide a general framework to attack this type of problem, which reduces it to subproblems with finitely many colors.

The production of broadband, terawatt terahertz (THz) pulses has been demonstrated by irradiating relativistic lasers on solid targets. However, the generation of extremely powerful, narrow-band and frequency-tunable THz pulses remains a challenge. Here, we present a novel approach for such THz pulses, in which a plasma wiggler is elaborated by a table-top laser and a near-critical density plasma. In such a wiggler, the laser-accelerated electrons emit THz radiations with a period closely related to the plasma thickness. The theoretical model and numerical simulations predict that a THz pulse with a laser–THz energy conversion of over 2.0%, an ultra-strong field exceeding 80 GV/m, a divergence angle of approximately 20° and a center frequency tunable from 4.4 to 1.5 THz can be generated from a laser of 430 mJ. Furthermore, we demonstrate that this method can work across a wide range of laser and plasma parameters, offering potential for future applications with extremely powerful THz pulses.

Given a graph $G$ and an integer $\ell \ge 2$, we denote by $\alpha _{\ell }(G)$ the maximum size of a $K_{\ell }$-free subset of vertices in $V(G)$. A recent question of Nenadov and Pehova asks for determining the best possible minimum degree conditions forcing clique-factors in $n$-vertex graphs $G$ with $\alpha _{\ell }(G) = o(n)$, which can be seen as a Ramsey–Turán variant of the celebrated Hajnal–Szemerédi theorem. In this paper we find the asymptotical sharp minimum degree threshold for $K_r$-factors in $n$-vertex graphs $G$ with $\alpha _\ell (G)=n^{1-o(1)}$ for all $r\ge \ell \ge 2$.

Based on the chemical reaction model proposed by Park, the ‘blackout’ of a reentry vehicle is studied in this paper. The temperature, pressure and electron density distribution characteristics around the reentry vehicle were simulated at various flight speeds and altitudes by USim. Subsequently, the scattering matrix method was used to study the transmission characteristics of terahertz waves in ‘blackout’. The simulation results show that the temperature around the aircraft is mainly affected by speed, the pressure is mainly affected by the altitude and electron density is affected by both of these factors. The calculation results show that the transmission characteristics of terahertz waves in plasma are mainly affected by electron density, while the effects of temperature and pressure cannot be ignored either.

The study investigated the strategies used by Chinese students in inferring meanings of unfamiliar words and the influential factors of successful use of different lexical inferencing strategies. A total of 104 fourth graders inferred 36 unfamiliar semitransparent compound words in three conditions: word in isolation, contextual information only, and both word and context. Results revealed that students were more likely to obtain the correct meaning of words when both morphological information and contextual information were available. The likelihood of using a morpheme-based or context-based lexical inferencing strategy was strongly influenced by the presentation condition of target words and precursors. Students with higher vocabulary knowledge and reading comprehension ability were more sensitive to morphological and contextual information and were able to synthesize multiple sources of information, whereas children with lower vocabulary knowledge and reading comprehension ability showed difficulties in integration and tended to overly rely on morphological information. The findings reveal the interactions between available source information and individual differences in vocabulary knowledge and reading comprehension in predicting lexical inferencing and have implications for vocabulary and reading instruction.

Climbing robots that use bionic claws can climb vertical or even inverted rough surfaces. However, wall-climbing robots with unidirectional spiny feet cannot crawl horizontally or downward on vertical rough surfaces. In this paper, a pair of gripping spiny feet is used to give a robot the capacity to crawl in any direction on a rough wall. On the basis of observations of the gecko’s method for grasping onto a vertical rough surface, a multilevel interlocking structure is proposed. A spherical contact model of the claw tip on a vertical rough surface is established, and the influences of the contact angle, friction coefficient, and other factors on the grappling claw action are analyzed. Moreover, the optimal structure of the grappling claws is proposed. The force during the grasping and detachment of the mechanism and the influence of the number of feet on grasping performance are determined through experiments. Furthermore, a six-legged wall-climbing robot is designed and evaluated in terms of crawling on a vertical rough surface at various angles. The feasibility of using an opposed gripping mechanism to allow a robot to crawl in any direction on a vertical rough surface is also verified.

To investigate the association between the Metabolic Score for Visceral Fat (METS-VF) and risk of type 2 diabetes mellitus (T2DM) and compare the predictive value of the METS-VF for T2DM incidence with other obesity indices in Chinese people. A total of 12 237 non-T2DM participants aged over 18 years from the Rural Chinese Cohort Study of 2007–2008 were included at baseline and followed up during 2013–2014. The cox proportional hazards regression was used to calculate hazard ratios (HR) and 95 % CI for the association between baseline METS-VF and T2DM risk. Restricted cubic splines were used to model the association between METS-VF and T2DM risk. Area under the receiver operating characteristic curve (AUC) analysis was used to evaluate the ability of METS-VF to predict T2DM incidence. During a median follow-up of 6·01 (95 % CI 5·09, 6·06) years, 837 cases developed T2DM. After adjusting for potential confounding factors, the adjusted HR for the highest v. lowest METS-VF quartile was 5·97 (95 % CI 4·28, 8·32), with a per 1-sd increase in METS-VF positively associated with T2DM risk. Positive associations were also found in the sensitivity and subgroup analyses, respectively. A significant nonlinear dose–response association was observed between METS-VF and T2DM risk for all participants (Pnonlinearity = 0·0347). Finally, the AUC value of METS-VF for predicting T2DM was largest among six indices. The METS-VF may be a reliable and applicable predictor of T2DM incidence in Chinese people regardless of sex, age or BMI.

The aim of this study was to investigate the association between daily Se intake and postpartum weight retention (PPWR) among Chinese lactating women, and the impact of their Se nutritional status on infants’ physical development. Se contents in breast milk and plasma collected from 264 lactating Chinese women at the 42nd day postpartum were analysed with inductively coupled plasma MS. Daily Se intake was calculated based on plasma Se concentration. The dietary data of 24-h records on three consecutive days were collected. Infant growth status was evaluated with WHO standards by Z-scores. Linear regression analyses and multinomial logistic regression were conducted to examine the impact of Se disequilibrium (including other factors) on PPWR and growth of infants, respectively. The results indicated that: (1) the daily Se intake of the subjects was negatively associated with their PPWR (B = −0·002, 95 % CI − 0·003, 0·000, P = 0·039); (2) both insufficient Se daily intake (B = −0·001, OR 0·999, 95 % CI 0·998, 1·000, P = 0·014) and low level of Se in milk (B = −0·025, OR 0·975, 95 % CI 0·951, 0·999, P = 0·021) had potential associations with their infants’ wasting, and low level of Se in milk (B = −0·159, OR 0·853, 95 % CI 0·743, 0·980, P = 0·024) had a significant association with their infants’ overweight. In conclusion, the insufficient Se nutritional status of lactating Chinese women was first found as one possible influencing factor of their PPWR as well as low physical development of their offspring.

We prove that, for any $t \ge 3$, there exists a constant c = c(t) > 0 such that any d-regular n-vertex graph with the second largest eigenvalue in absolute value λ satisfying $\lambda \le c{d^{t - 1}}/{n^{t - 2}}$ contains vertex-disjoint copies of kt covering all but at most ${n^{1 - 1/(8{t^4})}}$ vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Szábo (Combinatorica 24 (2004), pp. 403–426) that (n, d, λ)-graphs with n ∈ 3ℕ and $\lambda \le c{d^2}/n$ for a suitably small absolute constant c > 0 contain triangle-factors. Our arguments combine tools from linear programming with probabilistic techniques, and apply them in a certain weighted setting. We expect this method will be applicable to other problems in the field.

The South China Block is one of the largest continental blocks located on the East Asian continent. The early Palaeozoic Wuyi–Yunkai orogen of the South China Block (known as the Caledonian orogen in Europe) is a major orogenic belt in East Asia and represents the first episode of extensive crustal reworking since Neoproterozoic time. Although this orogen is key to deciphering the formation and evolution of the South China Block, details about the orogen remain poorly defined. The Songshutang and Wushitou ultramafic–mafic units in southern Jiangxi Province, South China, have 206Pb–238U ages of c. 437 Ma, suggesting a Silurian formation age. All the Songshutang and Wushitou ultramafic–mafic rocks show relatively flat chondrite-normalized rare earth element patterns, depletions in Nb, Ta, Zr, Hf and Ti, and low ϵNd(t) values from −9.12 to −5.49 with negative zircon ϵHf(t) values from −10.84 to −2.58, resembling a typical arc magma affinity. Geochemical and isotopic data indicate that the newly identified ultramafic–mafic rocks, along with the reported Silurian mafic rocks in South China, possibly originated from the similar partial melting of an ancient subducted slab, fluid/sediment and metasomatized lithospheric mantle with varying degrees of fractional crystallization. In conjunction with other records of magmatism and metamorphism in South China, a late-orogenic extensional event led to the melting of the sub-continental lithospheric mantle in Silurian time and generated ultramafic–mafic rocks with a limited distribution along the Wuyi–Yunkai orogen and widespread late-orogenic granitic plutons in the South China Block.