For any positive integers $k_1,k_2$ and any set $A\subseteq \mathbb {N}$, let $R_{k_1,k_2}(A,n)$ be the number of solutions of the equation $n=k_1a_1+k_2a_2$ with $a_1,a_2\in A$. Let g be a fixed integer. We prove that if $k_1$ and $k_2$ are two integers with $2\le k_1<k_2$ and $(k_1,k_2)=1$, then there does not exist any set $A\subseteq \mathbb {N}$ such that $R_{k_1,k_2}(A,n)-R_{k_1,k_2}(\mathbb {N}\setminus A,n)=g$ for all sufficiently large integers n, and if $1=k_1<k_2$, then there exists a set A such that $R_{k_1,k_2}(A,n)-R_{k_1,k_2}(\mathbb {N}\setminus A,n)=1$ for all positive integers n.

By combining the technique of energy selective surface and frequency selective rasorber, an energy selective rasorber is proposed, which performs selective energy protection in the low communication frequency band (0.8–2 GHz) and wave-absorbing property in the high-frequency band (6–18 GHz). The design consists of two layers, of which the bottom one contains a lumped diode structure for energy selection function in the transmission band, while together with the top layer, they perform a wideband wave absorbing function. The simulated and measured results agree well with each other, and both show good absorption in 6–18 GHz and energy-selective property around 1.86 GHz. That is, when the incident power changes from −30 to 14 dBm, the reflection coefficient changes from below −22 dB to above −2 dB, while the transmission coefficient changes from above −3 dB to below −17 dB.

There is still controversy about optimal dietary iodine intake as the Universal Salt Iodization policy enforcement in China. A modified iodine balance study was thus conducted to explore the suitable iodine intake in Chinese adult males using the iodine overflow hypothesis. In this study, thirty-eight apparently healthy males (19·1 (sd 0·6) years) were recruited and provided with designed diets. After the 14-d iodine depletion, daily iodine intake gradually increased in the 30-d iodine supplementation, consisting of six stages and each of 5 d. All foods and excreta (urine, faeces) were collected to examine daily iodine intake, iodine excretion and the changes of iodine increment in relation to those values at stage 1. The dose–response associations of iodine intake increment with excretion increment were fitted by the mixed effects models, as well as with retention increment. Daily iodine intake and excretion were 16·3 and 54·3 μg/d at stage 1, and iodine intake increment increased from 11·2 μg/d at stage 2 to 118·0 μg/d at stage 6, while excretion increment elevated from 21·5 to 95·0 μg/d. A zero iodine balance was dynamically achieved as 48·0 μg/d of iodine intake. The estimated average requirement and recommended nutrient intake were severally 48·0 and 67·2 μg/d, which could be corresponded to a daily iodine intake of 0·74 and 1·04 μg/kg per d. The results of our study indicate that roughly half of current iodine intakes recommendation could be enough in Chinese adult males, which would be beneficial for the revision of dietary reference intakes.

The purpose of this study was to analyse the clinical characteristics of patients with severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) PCR re-positivity after recovering from coronavirus disease 2019 (COVID-19). Patients (n = 1391) from Guangzhou, China, who had recovered from COVID-19 were recruited between 7 September 2021 and 11 March 2022. Data on epidemiology, symptoms, laboratory test results and treatment were analysed. In this study, 42.7% of recovered patients had re-positive result. Most re-positive patients were asymptomatic, did not have severe comorbidities, and were not contagious. The re-positivity rate was 39%, 46%, 11% and 25% in patients who had received inactivated, mRNA, adenovirus vector and recombinant subunit vaccines, respectively. Seven independent risk factors for testing re-positive were identified, and a predictive model was constructed using these variables. The predictors of re-positivity were COVID-19 vaccination status, previous SARs-CoV-12 infection prior to the most recent episode, renal function, SARS-CoV-2 IgG and IgM antibody levels and white blood cell count. The predictive model could benefit the control of the spread of COVID-19.

An experimental investigation of the stereocamera's systematic error is carried out to optimize three-dimensional (3-D) dust observation on the HL-2A tokamak. It is found that a larger 3-D region occupied by all calibration points is able to reduce the 3-D reconstruction systematic error of the stereocamera. In addition, the 3-D reconstruction is the most accurate around the region where the calibration points are located. Based on these experimental results, the design of the stereocamera on the HL-2A tokamak is presented, and a set of practical procedures to optimize the 3-D reconstruction accuracy of the stereocamera are proposed.

Understanding predator–prey interactions is essential for successful pest management by using predators, especially for the suppression of novel invasive pest. The green lacewing Chrysopa formosa is a promising polyphagous predator that is widely used in the biocontrol of various pests in China, but information on the control efficiency of this predator against the seriously invasive pest Spodoptera frugiperda and native Spodoptera litura is limited. Here we evaluated the predation efficiency of C. formosa adults on eggs and first- to third-instar larvae of S. frugiperda and S. litura through functional response experiments and determined the consumption capacity and prey preference of this chrysopid. Adults of C. formosa had a high consumption of eggs and earlier instar larvae of both prey species, and displayed a type II functional response on all prey stages. Attack rates of the chrysopid on different prey stages were statistically similar, but the handling time increased notably as the prey developed. The highest predation efficiency and shortest-handling time were observed for C. formosa feeding on Spodoptera eggs, followed by the first-instar larvae. C. formosa exhibited a significant preference for S. litura over S. frugiperda in a two-prey system. In addition, we summarized the functional response and predation efficiency of several chrysopids against noctuid pests and made a comparison with the results obtained from C. formosa. These results indicate that C. formosa has potential as an agent for biological control of noctuid pests, particularly for the newly invasive pest S. frugiperda in China.

Pregnancy is a complex biological process. The establishment and maintenance of foetal–maternal interface are pivotal events. Decidual immune cells and inflammatory cytokines play indispensable roles in the foetal–maternal interface. The disfunction of decidual immune cells leads to adverse pregnancy outcome. Tumour necrosis factor (TNF)-α, a common inflammatory cytokine, has critical roles in different stages of normal pregnancy process. However, the relationship between the disorder of TNF-α and adverse pregnancy outcomes, including preeclampsia (PE), intrauterine growth restriction (IUGR), spontaneous abortion (SA), preterm birth and so on, is still indefinite. In this review, we thoroughly reviewed the effect of TNF-α disorder on pathological conditions. Moreover, we summarized the reports about the adverse pregnancy outcomes (PE, IUGR, SA and preterm birth) of using anti-TNF-α drugs (infliximab, etanercept and adalimumab, certolizumab and golimumab) currently in the clinical studies. Overall, IUGR, SA and preterm birth are the most common adverse pregnancy outcomes of anti-TNF-α drugs. Our review may provide insight for the immunological treatment of pregnancy-related complication, and help practitioners make informed decisions based on the current evidences.

Widely distributed Mid-Neoproterozoic mafic rocks of the Qilian – Qaidam – East Kunlun region record the tectonic evolution of the northeastern Tibetan Plateau. This study presents whole-rock geochemistry, zircon U–Pb geochronology and Hf isotopes for the Xialanuoer gabbros of the central South Qilian Belt (SQB). Zircon laser ablation – inductively coupled plasma – mass spectrometry (LA-ICP-MS) U–Pb dating indicates that the gabbros were emplaced at ca. 738 Ma, indicating they are contemporaneous with mafic magmatism elsewhere in the northeastern Tibetan Plateau. The gabbros have low SiO2, Cr and Ni contents and Mg# values, are relatively enriched in light rare-earth elements (LREEs) and depleted in high-field-strength elements (HFSEs; e.g. Nb and Ta), have no positive Zr or Hf anomalies and have relatively high Nb/Ta but low Nb/La ratios. These data indicate that the Xialanuoer gabbros formed from calc-alkaline basaltic magmas that were originally generated by the partial melting of an enriched mantle of type-I (EMI-type) enriched region of the lithospheric mantle, underwent little to no crustal contamination prior to their emplacement, and have within-plate basalt geochemical affinities. Combining these data with the presence of widespread contemporaneous continental rift-related magmatism and sedimentation in the North Qilian, Central Qilian, South Qilian, Quanji, North Qaidam and East Kunlun regions suggests that the northeastern Tibetan Plateau underwent Mid-Neoproterozoic continental rifting, which also affected other Rodinian blocks (e.g. Tarim, South China, Australia, North America and Southern Africa).

Direct numerical simulations of a three-dimensional cylindrical Richtmyer–Meshkov instability with and without chemical reactions are carried out to explore the chemical reaction effects on the statistical characteristics of transition and turbulent mixing. We adopt 9-species and 19-reaction models of non-premixed hydrogen and oxygen separated by a multimode perturbed cylindrical interface. A new definition of mixing width suitable for a chemical reaction is introduced, and we investigate the spatio-temporal evolution of typical flow parameters within the mixing regions. After reshock with a fuller mixing of fuels and oxygen, the chemical reaction becomes sufficiently apparent at affecting the evolution of the flow fields. Because of the generation of a combustion wave within the combustion regions and propagation, the growth of the mixing width with a chemical reaction is accelerated, especially around the outer radius with large temperature gradient profiles. However, the viscous dissipation rate in the early stage of the chemical reaction is greater because of heat release, which results in weakened turbulent mixing within the mixing regions. We confirm that small-scale structures begin to develop after reshock and then decay over time. During the developing process, helicity also begins to develop, in addition to kinetic energy, viscous dissipation rate, enstrophy, etc. In the present numerical simulations with cylindrical geometry, the fluctuating flow fields evolve from quasi-two-dimensional perturbations, and the generations of helicity can capture this transition process. The weakened fluctuations during shock compression can be explained as the inverse energy cascade, and the chemical reaction can promote this inverse energy cascade process.

The extinct family Hylicellidae, as the ancestral group of modern cicadomorphans, had a wide distribution and a very high species-level biodiversity from the Triassic to Early Cretaceous. We herein report 11 new hylicellid specimens from the Jurassic Daohugou beds of Inner Mongolia, NE China, and execute geometric morphometric analysis (GMA) to elucidate their systematic position. Our GMA and subsequent morphometric statistics indicate that 10 of our new specimens can be compared to the holotype of Cycloscytina gobiensis, and one is new to science. Cycloscytina incompleta new species is erected based on this specimen, with the following discriminatory tegminal traits: C3 almost as long as and slightly narrower than C2, and the forking position of stem M distinctly migrates towards wing apex and much apicad of the stem CuA bifurcating. Additionally, Cycloscytina plachutai is herein transferred to the procercopid genus Procercopina, resulting in P. plachutai new combination. To date, just a few body structures of Hylicellidae have been revealed, and the new whole-bodied hylicellids reported herein provide some novel insights on the evolution of basal Clypeata. This study also emphasizes the use of morphometric analysis in the systematics of wing-bearing insects such as hylicellids.

UUID: http://zoobank.org/84a67eba-9b7c-4e27-a436-764802c4cdfb.

Helicity is a quadratic inviscid conservative quantity in three-dimensional turbulent flows and is crucial for turbulent system evolution. Helicity effects have mainly been highlighted over the past few decades to explore the intrinsic mechanism of turbulent flows, while the statistical characteristics of helicity itself are nearly absent in general anisotropic turbulent flows. In this paper, we investigate the helicity statistics in turbulent channel flows with streamwise rotation at moderate rotation numbers ($Ro_{\tau }=7.5,15$ and 30) and Reynolds numbers ($Re_{\tau }=180$ and 395), including their spatial and scale distributions, anisotropy and cross-scale transfer. The appearance of a mean secondary flow in the spanwise direction corresponds to a mean streamwise vorticity, which indicates the presence of a high-helicity distribution. Numerical results reveal a regular helicity profile along the wall-normal direction, and a new peak is found in the near-wall region around $y^+=6$ of the streamwise or spanwise helicity profiles. The inter-scale helicity transfer is analysed by the filtering method, and the numerical consequences reveal that the second channel of the helicity cascade we proposed previously is dominant in contrast to the first channel. The rotation effects are explored by comparing the numerical results obtained under different rotation numbers. With increasing rotation number, more helical structures in the near-wall regions are present, with peaks of helicity profiles and fluxes coming closer to the wall. With a higher Reynolds number, their amplitudes are larger and scale-space transfer is strengthened. These systematic numerical analyses uncover the helicity distributions and transfer in wall-bounded turbulent flows.

Tumors have posed a serious threat to human life and health. Researchers can determine whether or not cells are cancerous, whether the cancer cells are invasive or metastatic, and what the effects of drugs are on cancer cells by the physical properties such as hardness, adhesion, and Young's modulus. The atomic force microscope (AFM) has emerged as a key important tool for biomechanics research on tumor cells due to its ability to image and collect force spectroscopy information of biological samples with nano-level spatial resolution and under near-physiological conditions. This article reviews the existing results of the study of cancer cells with AFM. The main foci are the operating principle of AFM and research advances in mechanical property measurement, ultra-microtopography, and molecular recognition of tumor cells, which allows us to outline what we do know it in a systematic way and to summarize and to discuss future directions.