Two sets $A,B$ of positive integers are called exact additive complements if $A+B$ contains all sufficiently large integers and $A(x)B(x)/x\rightarrow 1$. For $A=\{a_1<a_2<\cdots \}$, let $A(x)$ denote the counting function of A and let $a^*(x)$ denote the largest element in $A\bigcap [1,x]$. Following the work of Ruzsa [‘Exact additive complements’, Quart. J. Math. 68 (2017) 227–235] and Chen and Fang [‘Additive complements with Narkiewicz’s condition’, Combinatorica 39 (2019), 813–823], we prove that, for exact additive complements $A,B$ with ${a_{n+1}}/ {na_n}\rightarrow \infty $,

$$ \begin{align*}A(x)B(x)-x\geqslant \frac{a^*(x)}{A(x)}+o\bigg(\frac{a^*(x)}{A(x)^2}\bigg) \quad\mbox{as } x\rightarrow +\infty.\end{align*} $$

We also construct exact additive complements $A,B$ with ${a_{n+1}}/{na_n}\rightarrow \infty $ such that

$$ \begin{align*}A(x)B(x)-x\leqslant \frac{a^*(x)}{A(x)}+(1+o(1))\bigg(\frac{a^*(x)}{A(x)^2}\bigg)\end{align*} $$

for infinitely many positive integers x.

For a nonempty set A of integers and an integer n, let $r_{A}(n)$ be the number of representations of n in the form $n=a+a'$, where $a\leqslant a'$ and $a, a'\in A$, and $d_{A}(n)$ be the number of representations of n in the form $n=a-a'$, where $a, a'\in A$. The binary support of a positive integer n is defined as the subset S(n) of nonnegative integers consisting of the exponents in the binary expansion of n, i.e., $n=\sum_{i\in S(n)} 2^i$, $S(-n)=-S(n)$ and $S(0)=\emptyset$. For real number x, let $A(-x,x)$ be the number of elements $a\in A$ with $-x\leqslant a\leqslant x$. The famous Erdős-Turán Conjecture states that if A is a set of positive integers such that $r_A(n)\geqslant 1$ for all sufficiently large n, then $\limsup_{n\rightarrow\infty}r_A(n)=\infty$. In 2004, Nešetřil and Serra initially introduced the notation of “bounded” property and confirmed the Erdős-Turán conjecture for a class of bounded bases. They also proved that, there exists a set A of integers satisfying $r_A(n)=1$ for all integers n and $|S(x)\bigcup S(y)|\leqslant 4|S(x+y)|$ for $x,y\in A$. On the other hand, Nathanson proved that there exists a set A of integers such that $r_A(n)=1$ for all integers n and $2\log x/\log 5+c_1\leqslant A(-x,x)\leqslant 2\log x/\log 3+c_2$ for all $x\geqslant 1$, where $c_1,c_2$ are absolute constants. In this paper, following these results, we prove that, there exists a set A of integers such that: $r_A(n)=1$ for all integers n and $d_A(n)=1$ for all positive integers n, $|S(x)\bigcup S(y)|\leqslant 4|S(x+y)|$ for $x,y\in A$ and $A(-x,x) \gt (4/\log 5)\log\log x+c$ for all $x\geqslant 1$, where c is an absolute constant. Furthermore, we also construct a family of arbitrarily spare such sets A.

Varicella vaccination is optional and requires self-payment. On 1 December 2018, Wuxi City launched a free varicella vaccination program for children. This study aimed to evaluate the changes in varicella incidence before and after the implementation of the policy. The data were obtained from official information systems and statistical yearbooks. We divided the period into chargeable (January 2017 to November 2018) and free (December 2018 to December 2021) periods. Interrupt time series analysis was used to conduct a generalised least-squares regression analysis for the two periods. A total of 51,071 varicella cases were reported between January 2017 and December 2021. After the implementation of the policy, there was a statistically significant decrease in the incidence of varicella (β2 = −0.140, P = 0.017), and the slope of the incidence also decreased by 0.012 (P = 0.015). Following policy implementation, the incidence decreased in all age groups, with the largest decline observed among children aged 8–14 years (β2 = −1.109, P = 0.009), followed by children aged ≤7 years (β2 = −0.894, P = 0.013). Our study found a significant reduction in the incidence of varicella in the total population after the introduction of free varicella vaccination in Wuxi City.

Although ethanol treatment is widely used to activate oocytes, the underlying mechanisms are largely unclear. Roles of intracellular calcium stores and extracellular calcium in ethanol-induced activation (EIA) of oocytes remain to be verified, and whether calcium-sensing receptor (CaSR) is involved in EIA is unknown. This study showed that calcium-free ageing (CFA) in vitro significantly decreased intracellular stored calcium (sCa) and CaSR expression, and impaired EIA, spindle/chromosome morphology and developmental potential of mouse oocytes. Although EIA in oocytes with full sCa after ageing with calcium does not require calcium influx, calcium influx is essential for EIA of oocytes with reduced sCa after CFA. Furthermore, the extremely low EIA rate in oocytes with CFA-downregulated CaSR expression and the fact that inhibiting CaSR significantly decreased the EIA of oocytes with a full complement of CaSR suggest that CaSR played a significant role in the EIA of ageing oocytes. In conclusion, CFA impaired EIA and the developmental potential of mouse oocytes by decreasing sCa and downregulating CaSR expression. Because mouse oocytes routinely treated for activation (18 h post hCG) are equipped with a full sCa complement and CaSR, the present results suggest that, while calcium influx is not essential, CaSR is required for the EIA of oocytes.

We performed U–Pb dating of detrital zircons and conducted petrological and whole-rock geochemical analyses to assess the provenance of the Upper Triassic – Lower Jurassic clastic rocks in the southeastern margin of the South China Block. Detrital zircon U–Pb ages are mainly classified into age groups of 2000–1700, 900–700, 490–390 and 280–210 Ma, consistent with derivation from the Jiangnan orogenic belt, Nanling Belt, as well as Wuyi and Yunkai domains. Lower Jurassic samples yield a special main age population of 200–190 Ma, and these detrital zircon grains have low Th/U and Nb/Hf ratios and high Th/Nb and Hf/Th ratios, showing they are derived from a continental magmatic arc. However, the cross-correlation and likeness coefficients of kernel density estimates of Upper Triassic and Lower Jurassic sandstones are 0.8608 and 0.8403, indicating that their populations are highly similar. Since the tectonic setting is the key factor in controlling the relationship between source and sink, the stable supply of identical provenance suggests that the tectonic setting did not significantly change during Late Triassic – Early Jurassic time. Sandstone petrography, regional facies distribution and the detrital zircon age patterns all reflect a consistent tectonic setting for the South China Block during Late Triassic – Early Jurassic time. The Palaeo-Pacific subduction therefore did not control the tectonic evolution of the South China Block until after the Early Jurassic Epoch.

Extensive magmatism in NE China, eastern Central Asian Orogenic Belt, has produced multi-stage granitic plutons and accompanying W mineralization. The Narenwula complex in the southwestern Great Xing’an Range provides important insights into the petrogenesis, geodynamic processes and relationship with W mineralization. The complex comprises granodiorites, monzogranites and granite porphyry. Mafic microgranular enclaves are common in the granodiorites, and have similar zircon U–Pb ages as their host rocks (258.5–253.9 Ma), whereas the W-bearing granitoids yield emplacement ages of 149.8–148.1 Ma. Permian granodiorites are I-type granites that are enriched in large-ion lithophile elements and light rare earth elements, and depleted in high field strength elements and heavy rare earth elements. Both the mafic microgranular enclaves and granodiorites have nearly identical zircon Hf isotopic compositions. The results suggest that the mafic microgranular enclaves and granodiorites formed by the mixing of mafic and felsic magmas. W-bearing granitoids are highly fractionated A-type granites, enriched in Rb, Th, U and Pb, and depleted in Ba, Sr, P, Ti and Eu. They have higher W concentrations and Rb/Sr ratios, and lower Nb/Ta, Zr/Hf and K/Rb ratios than the W-barren granodiorites. These data and negative ϵHf(t) values (–6.0 to –2.1) suggest that they were derived from the partial melting of ancient lower crust and subsequently underwent extreme fractional crystallization. Based on the regional geology, we propose that the granodiorites were generated in a volcanic arc setting related to the subduction of the Palaeo-Asian Ocean, whereas the W-bearing granitoids and associated deposits formed in a post-orogenic extensional setting controlled by the Mongol–Okhotsk Ocean and Palaeo-Pacific Ocean tectonic regimes.

The findings regarding the associations between red meat, fish and poultry consumption, and the metabolic syndrome (Mets) have been inconclusive, and evidence from Chinese populations is scarce. A cross-sectional study was performed to investigate the associations between red meat, fish and poultry consumption, and the prevalence of the Mets and its components among the residents of Suzhou Industrial Park, Suzhou, China. A total of 4424 participants were eligible for the analysis. A logistic regression model was used to estimate the OR and 95 % CI for the prevalence of the Mets and its components according to red meat, fish and poultry consumption. In addition, the data of our cross-sectional study were meta-analysed under a random effects model along with those of published observational studies to generate the summary relative risks (RR) of the associations between the highest v. lowest categories of red meat, fish and poultry consumption and the Mets and its components. In the cross-sectional study, the multivariable-adjusted OR for the highest v. lowest quartiles of consumption was 1·23 (95 % CI 1·02, 1·48) for red meat, 0·83 (95 % CI 0·72, 0·97) for fish and 0·93 (95 % CI 0·74, 1·18) for poultry. In the meta-analysis, the pooled RR for the highest v. lowest categories of consumption was 1·20 (95 % CI 1·06, 1·35) for red meat, 0·88 (95 % CI 0·81, 0·96) for fish and 0·97 (95 % CI 0·85, 1·10) for poultry. The findings of both cross-sectional studies and meta-analyses indicated that the association between fish consumption and the Mets may be partly driven by the inverse association of fish consumption with elevated TAG and reduced HDL-cholesterol and, to a lesser extent, fasting plasma glucose. No clear pattern of associations was observed between red meat or poultry consumption and the components of the Mets. The current findings add weight to the evidence that the Mets may be positively associated with red meat consumption, inversely associated with fish consumption and neutrally associated with poultry consumption.

Few studies have been conducted to investigate the association of kidney function decline with the trajectories of homocysteine (Hcy) over time, using repeated measurements. We aimed to investigate the association of kidney function with changes in plasma Hcy levels over time. Data were collected from the Rugao Longevity and Ageing Study. In detail, plasma Hcy and creatinine levels were measured in both waves (waves 2, 3 and 4) during the 3·5-year follow-up (n 1135). Wave 2 was regarded as the baseline survey. The estimated glomerular filtration rate (eGFR) was calculated based on creatinine. Subjects were categorised into four groups according to quartiles of eGFR at baseline. Linear mixed-effect models were used to investigate the association of eGFR with subsequent plasma Hcy levels. The mean eGFR at baseline was 90·84 (sd 11·42) ml/min per 1·73 m2. The mean plasma Hcy level was 14·09 (sd 6·82) at baseline and increased to 16·28 (sd 8·27) and 17·36 (sd 10·39) μmol/l during follow-ups. In the crude model, the interaction between time and eGFR at baseline was significant (β = −0·02, 95 % CI −0·02, −0·01, P = 0·002). After adjusting for confounding factors, a significant relationship remained (β = −0·02, 95 % CI −0·02, −0·01, P = 0·003), suggesting that kidney function decline at baseline was associated with a faster increase in Hcy levels. Kidney function decline is associated with a more pronounced increase in plasma Hcy levels. Further studies with longer follow-up periods and larger sample sizes are needed to validate our findings.

Saetaspongia so far cannot be confidently assigned to any class-level crown group. Clarifying its phylogenetic position requires new information provided by more detailed studies of previously described and/or new material. Some sponge fossils with the typical skeletal architecture of Saetaspongia have recently been recognized in the Cambrian (Stage 4) Balang Biota of Guizhou, China, including S. jianhensis new species and S. cf. S. densa. The new taxon is characterized by the following features: spicules are fine monaxons and are inclined to be loosely to densely arranged into plumose arrays; skeleton is composed primarily of one major plumose bundle, with an uncertain number (perhaps two) of small plumose arrays; and primary skeleton is occasionally interspersed with some irregularly oriented individual spicules. An additional specimen consisting of large monaxons, with plumose structures and overlying irregular coarse monaxons, closely fits the description and illustrations of previously described S. cf. S. densa. By combining information from previous studies and the present research, fossil evidence indicates that the plumose architecture is a critical feature diagnostic of Saetaspongia and that there are no hexactine-based spicules in this genus. The new material from the Balang Biota further supports the notion that Saetaspongia has a protomonaxonid rather than a hexactinellid affinity. Fossil evidence suggests that Saetaspongia had a wide biogeographic distribution during the early Cambrian and the stratigraphic distribution of this genus extends up to Stage 4.

UUID: http://zoobank.org/e9ca5e4a-134c-4daa-9266-19085e32614f.

To understand the characteristics and influencing factors related to cluster infections in Jiangsu Province, China, we investigated case reports to explore transmission dynamics and influencing factors of scales of cluster infection. The effectiveness of interventions was assessed by changes in the time-dependent reproductive number (Rt). From 25th January to 29th February, Jiangsu Province reported a total of 134 clusters involving 617 cases. Household clusters accounted for 79.85% of the total. The time interval from onset to report of index cases was 8 days, which was longer than that of secondary cases (4 days) (χ2 = 22.763, P < 0.001) and had a relationship with the number of secondary cases (the correlation coefficient (r) = 0.193, P = 0.040). The average interval from onset to report was different between family cluster cases (4 days) and community cluster cases (7 days) (χ2 = 28.072, P < 0.001). The average time interval from onset to isolation of patients with secondary infection (5 days) was longer than that of patients without secondary infection (3 days) (F = 9.761, P = 0.002). Asymptomatic patients and non-familial clusters had impacts on the size of the clusters. The average reduction in the Rt value in family clusters (26.00%, 0.26 ± 0.22) was lower than that in other clusters (37.00%, 0.37 ± 0.26) (F = 4.400, P = 0.039). Early detection of asymptomatic patients and early reports of non-family clusters can effectively weaken cluster infections.

With the progress in science and technology, hazardous chemicals are becoming more essential in chemical products, industrial and agricultural production, and daily life. Hazardous chemicals have poisoning, corrosive, explosive, and combusting natures; once on fire, they can trigger a chain of catastrophic incidences, resulting in casualties, property loss, and environmental pollution and posing hazards to life and property. Using the “8–12” explosion of the Ruihai Logistics warehouse in Tianjin Port (Binhai New District, China), the present study analyzes the characteristics of trauma of the casualties in this accident and the emergency medical rescue strategies. The goals were to improve the ability of emergency rescue in such accidents and to save people’s lives and property to the maximum extent.

According to the ‘farming/dispersal’ hypothesis, the Early and Mid-Holocene spread of Neolithic material culture in East Asia would have arisen from dispersals of established farming populations. The authors test this hypothesis by considering the Beixin Culture that appeared in the south-west Haidai region of northern China c. 5000 BC, before spreading north and east to the coast over the subsequent millennium. While this culture had architecture, elaborate pottery and other forms of Neolithic material culture, analysis of archaeobotanical evidence from Guanqiaocunnan (4340–3970 BC) suggests an economic base of hunting, gathering and cultivating, rather than a reliance on farming.

A suite of Jurassic–Cretaceous migmatites was newly identified in the Liaodong Peninsula of the eastern North China Craton (NCC). Anatexis is commonly associated with crustal thickening. However, the newly identified migmatites were formed during strong lithospheric thinning accompanied by voluminous magmatism and intense deformation. Field investigations show that the migmatites are spatially associated with low-angle detachment faults. Numerous leucosomes occur either as isolated lenses or thin layers (dykes), parallel to or cross-cutting the foliation. Peritectic minerals such as titanite and sillimanite are distributed mainly along the boundaries of reactant minerals or are accumulated along the foliation. Most zircons show distinct core–rim structures, and the rims have low Th/U ratios (0.01–0.24). Zircon U–Pb dating results indicate that the protoliths of the migmatites were either the Late Triassic (224–221 Ma) diorites or metasedimentary rocks deposited sometime after c. 1857 Ma. The zircon overgrowth rims record crystallization ages of 173–161 Ma and 125 Ma, which represent the formation time of leucosomes. These ages are consistent with those reported magmatic events in the Liaodong Peninsula and surrounding areas. The leucosomes indicate a strong anatectic event during the Jurassic–Cretaceous period. Partial melting occurred through the breakdown of muscovite and biotite with the presence of water-rich fluid under a thermal anomaly regime. The possible mechanism that caused the 173–161 Ma and 125 Ma anatectic events was intimately related to the regional crustal extension during the lithospheric thinning of the NCC. Meanwhile, the newly generated melts further weakened the rigidity of the crust and enhanced the extension.

HIV-1 drug resistance can compromise the effectiveness of antiretroviral therapy (ART). A survey of pretreatment HIV-1 drug resistance (PDR) was conducted in Lincang Prefecture of Yunnan Province. From 372 people living with HIV/AIDS initiating ART for the first time during 2017–2018, 322 pol sequences were obtained, of which 11 HIV-1 strain types were detected. CRF08_BC (70.2%, 226/322) was the predominant strain, followed by URF strains (10.6%, 34/322). Drug resistance mutations (DRMs) were detected among 34.2% (110/322) of the participants. E138A/G/K/R (14.3%, 46/322) and V179E/D/T (13.7%, 47/322) were the predominant DRMs. Specifically, E138 mutations commonly occurred in CRF08_BC (19.9%, 45/226). Among the DRMs detected, some independently conferred resistance, such as K65R (1.6%, 5/322), Y188C/F/L (0.9%, 3/322), K103N (0.6%, 2/322) and G190A (0.3%, 1/322), which conferred high-level resistance. The prevalence of PDR was 7.5% (95% CI: 4.6–10.3%) and the prevalence of non-nucleotide reverse transcriptase inhibitor (NNRTI) resistance was 5.0% (95% CI: 2.6–7.4%), which is below the threshold (⩾10%) of initiating a public health response. In conclusion, HIV-1 genetic diversity and an overall moderate level of PDR prevalence were found in western Yunnan. PDR surveillance should be continually performed to decide whether a public health response to NNRTI resistance should be initiated.

There is still an ongoing debate regarding the firm performance implications of pay gaps between top executives and subordinate employees. This study integrates relative deprivation theory and tournament theory to investigate the potential nonlinear effects of pay gaps. We expect that at low levels of pay inequality, increased inequality hurts firm productivity, while at higher levels of pay inequality, increased inequality helps firm productivity. Our study of Chinese firms confirms that pay gaps have an approximately U-shaped relationship with firm performance. This nonlinear relationship is weaker in state-owned enterprises (SOEs) than in non-SOEs, suggesting that state ownership is an important moderator in the association. Overall, this study explains previous mixed findings regarding consequences of pay gaps with meaningful implications for policymakers and entrepreneurs in China and other economies with similar cultural and institutional backgrounds.

The association between milk consumption and the metabolic syndrome remains inconclusive, and data from Chinese populations are scarce. We conducted a cross-sectional study to investigate the association between milk consumption and the metabolic syndrome and its components among the residents of Suzhou Industrial Park, Suzhou, China. A total of 5149 participants were included in the final analysis. A logistic regression model was applied to estimate the OR and 95 % CI for the prevalence of the metabolic syndrome and its components according to milk consumption. In addition, the results of our study were further meta-analysed with other published observational studies to quantify the association between the highest v. lowest categories of milk consumption and the metabolic syndrome and its components. There was no significant difference in the odds of having the metabolic syndrome between milk consumers and non-milk consumers (OR 0·86, 95 % CI 0·73, 1·01). However, milk consumers had lower odds of having elevated waist circumference (OR 0·78, 95 % CI 0·67, 0·92), elevated TAG (OR 0·83, 95 % CI 0·70, 0·99) and elevated blood pressure (OR 0·85, 95 % CI 0·73, 0·99). When the results were pooled together with other published studies, higher milk consumption was inversely associated with the risk of the metabolic syndrome (relative risk 0·80, 95 % CI 0·72, 0·88) and its components (except elevated fasting blood glucose); however, these results should be treated with caution as high heterogeneity was observed. In summary, the currently available evidence from observational studies suggests that higher milk consumption may be inversely associated with the metabolic syndrome.