Let $h \geq 2$ be a positive integer. We introduce the concept of minimal restricted asymptotic bases and obtain some examples of minimal restricted asymptotic bases of order h.

In the current research, a 60-d experiment was conducted with the purpose of exploring the impacts of methionine (Met) on growth performance, muscle nutritive deposition, muscle fibre growth and type I collagen synthesis as well as the related signalling pathway. Six diets (iso-nitrogenous) differing in Met concentrations (2·54, 4·85, 7·43, 10·12, 12·40 and 15·11 g/kg diets) were fed to 540 grass carp (178·47 (SD 0·36) g). Results showed (P < 0·05) that compared with Met deficiency, optimal level of dietary Met (1) increased feed intake, feed efficiency, specific growth rate and percentage weight gain (PWG); (2) increased fish muscle protein, lipid and free amino acid contents and improved fish muscle fatty acid profile as well as increased protein content in part associated with the target of rapamycin complex 1 (TORC1)/S6K1 signalling pathway; (3) increased the frequency distribution of muscle fibre with >50 µm of diameter; (4) increased type I collagen synthesis partly related to the transforming growth factor-β1/Smads and CK2/TORC1 signalling pathways. In conclusion, dietary Met improved muscle growth, which might be due to the regulation of muscle nutritive deposition, muscle fibre growth and type I collagen synthesis-related signal molecules. Finally, according to PWG and muscle collagen content, the Met requirements for on-growing grass carp (178–626 g) were estimated to be 9·56 g/kg diet (33·26 g/kg protein of diet) and 9·28 g/kg diet (32·29 g/kg of dietary protein), respectively.

We study a question on minimal asymptotic bases asked by Nathanson [‘Minimal bases and powers of 2’, Acta Arith. 49 (1988), 525–532].

The present study investigated the effects of condensed tannins (CT) on intestinal immune function in on-growing grass carp (Ctenopharyngodon idella). A total of 540 healthy grass carp were fed six diets containing different levels of CT (0, 10·00, 20·00, 30·00, 40·00 and 50·00 g/kg diet) for 70 d and then challenged with Aeromonas hydrophila for 14 d. The results showed that, compared with the control group, dietary CT (1) induced intestinal histopathological lesions and aggravated enteritis; (2) decreased lysozyme and acid phosphatase activities, complement 3 (C3), C4 and IgM contents and down-regulated the Hepcidin, liver-expressed antimicrobial peptide (LEAP)-2A, LEAP-2B, Mucin2 and β-defensin-1 mRNA levels in the proximal intestine (PI), mid intestine (MI) and distal intestine (DI) (P < 0·05); (3) down-regulated the mRNA levels of anti-inflammatory cytokines transforming growth factor (TGF)-β1, TGF-β2 (not in MI and DI), IL-4/13A (not IL-4/13B), IL-10 and IL-11 partly correlated with target of rapamycin (TOR) signalling; and (4) up-regulated the mRNA levels of pro-inflammatory cytokines interferon-γ2, IL-1β, IL-6, IL-8 (not in PI), IL-12p35, IL-12p40, IL-15 and IL-17D partly related to NF-κB signalling in the intestine of on-growing grass carp. Overall, the results indicated that CT could impair the intestinal immune function, and its potential regulation mechanisms were partly associated with the TOR and NF-κB signalling pathways. Finally, based on the percentage weight gain and enteritis morbidity, the maximum allowable levels of CT for on-growing grass carp (232·22–890·11 g) were estimated to be 18·6 and 17·4 g/kg diet, respectively.

We aimed to investigate the association between plasma retinol and incident cancer among Chinese hypertensive adults. We conducted a nested case–control study, including 231 patients with incident cancer and 231 matched controls during a median 4·5-year follow-up of the China Stroke Primary Prevention Trial. There was a significant, inverse association between retinol levels and digestive system cancer (per 10 μg/dl increases: OR 0·79; 95 % CI 0·69, 0·91). When compared with participants in the first quartile of retinol (< 52·3 μg/dl), a significantly lower cancer risk was found in participants in quartile 2–4 ( ≥ 52·3 μg/dl: OR 0·31; 95 % CI 0·13, 0·71). However, there was a U-shaped association between retinol levels and non-digestive system cancers where the risk of cancers decreased (although not significantly) with each increment of plasma retinol (per 10 μg/dl increases: OR 0·89; 95 % CI 0·60, 1·31) in participants with retinol < 68·2 μg/dl, and then increased significantly with retinol (per 10 μg/dl increase: OR 1·65; 95 % CI 1·12, 2·44) in participants with retinol ≥ 68·2 μg/dl. In conclusion, there was a significant inverse dose–response association between plasma retinol and the risk of digestive system cancers. However, a U-shaped association was observed between plasma retinol and the risk of non-digestive cancers (with a turning point approximately 68·2 μg/dl).

Introduction: White matter hyperintensities (WMHs) were commonly seen in brain magnetic resonance imaging (MRI) of the elderly. Many studies found that WMHs were associated with cognitive decline and dementia. However, the association between WMHs in different brain regions and cognitive decline remains debated. Methods: We explored the association of the severity of WMHs and cognitive decline in 115 non-demented elderly (≥50 years old) sampled from the Wuliqiao Community located in urban area of Shanghai. MRI scans were done during 2009–2011 at the beginning of the study. Severity of WMHs in different brain regions was scored by Improved Scheltens Scale and Cholinergic Pathways Hyperintensities Scale (CHIPS). Cognitive function was evaluated by Mini-Mental State Examination (MMSE) every 2 to 4 years during 2009–2018. Results: After adjusting for confounding factors including age, gender, education level, smoking status, alcohol consumption, depression, hypertension, diabetes, hyperlipidemia, brain infarcts, brain atrophy, apoE4 status, and baseline MMSE score, periventricular and subcortical WMH lesions as well as WMHs in cholinergic pathways were significantly associated with annual MMSE decline ( p < 0.05), in which the severity of periventricular WMHs predicted a faster MMSE decline (–0.187 points/year, 95% confidence interval: –0.349, –0.026, p = 0.024). Conclusions: The severity of WMHs at baseline was associated with cognitive decline in the non-demented elderly over time. Interventions on WMH lesions may offer some benefits for cognitive deterioration.

This study aimed to investigate the impacts of dietary threonine on intestinal immunity and inflammation in juvenile grass carp. Six iso-nitrogenous semi-purified diets containing graded levels of threonine (3·99–21·66 g threonine/kg) were formulated and fed to fishes for 8 weeks, and then challenged with Aeromonas hydrophila for 14 d. Results showed that, compared with optimum threonine supplementation, threonine deficiency (1) decreased the ability of fish against enteritis, intestinal lysozyme activities (except in the distal intestine), acid phosphatase activities, complement 3 (C3) and C4 contents and IgM contents (except in the proximal intestine (PI)), and it down-regulated the transcript abundances of liver-expressed antimicrobial peptide (LEAP)-2A, LEAP-2B, hepcidin, IgZ, IgM and β-defensin1 (except in the PI) (P<0·05); (2) could up-regulate intestinal pro-inflammatory cytokines TNF-α, IL-1β, IL-6, IL-8 and IL-17D mRNA levels partly related to NF-κB signalling; (3) could down-regulate intestinal anti-inflammatory cytokine transforming growth factor (TGF)-β1, TGF-β2, IL-4/13A (not IL-4/13B) and IL-10 mRNA levels partly by target of rapamycin signalling. Finally, on the basis of the specific growth rate, against the enteritis morbidity and IgM contents, the optimum threonine requirements were estimated to be 14·53 g threonine/kg diet (4·48 g threonine/100 g protein), 15.05 g threonine/kg diet (4·64 g threonine/100 g protein) and 15·17 g threonine/kg diet (4·68 g threonine/100 g protein), respectively.

In this paper, numerical simulations of solid particle erosion phenomena on H-type finned circular/elliptic tube surface, which is of great significance to the antiwear design of heat exchanger, are presented. The Eulerian-Lagrangian approach is applied to simulate the dilute gas-solid flow through H-type finned circular/elliptic tubes. A semi-empirical model is adopted to predict the erosion rate. The dynamics behavior of the entrained solid particles in the flow is presented. The geometry of eroded tube surface is changed with the predicted erosion which is taken into account by a UDF and the flow field is re-solved for the eroded tube surface at every time step. The influences of ten parameters (the tube bundle arrangement, particle size, particle concentration, fluid Reynolds number, fin thickness, fin pitch, fin length, fin width, slit width and the transverse tube pitch) on the maximum erosion depth of the H-type circular/elliptic finned tube surface are investigated. Using H-type finned elliptic tube surface can effectively reduce the erosion rate of tube surface comparedwith that using H-type finned circular tube surface. The erosion in in-line arrangement is less severe than that in staggered arrangement. With the increase of particle size, particle concentration and the fluid Reynolds number, the erosion rate of the tube surface rises. The numerically predicted effect of Reynolds number is in good agreement with previous test data. Among the six geometry parameters, the most influential parameter is the transverse tube pitch.

Mexican sunflower is a native species of North and Central America that was introduced into China early last century, but it has widely naturalized and become a harmful invasive plant in tropical and subtropical regions in South China. Inter-simple sequence repeat (ISSR) markers were employed to assess genetic diversity and variation in Mexican sunflower populations from China and neighboring regions. The karyotypes of populations were also studied. Our research showed high levels of genetic diversity in all populations. The lowest genetic diversity estimates were represented in two populations in Laos, suggesting prevention of new introductions into Laos is critical. Partitioning of genetic variance revealed that genetic variation was mostly found within populations, and unweighted pair group method with arithmetic means (UPGMA) analysis showed that the introductions into China and Laos were independent. There were no obvious correlations between genetic relationships and geographic distance of populations in China, consistent with the human associated dispersal history of Mexican sunflower. Previous cytological data and our chromosome count (2n = 34) and karyotype analysis showed chromosome stability among populations. The high levels of genetic diversity within invasive Mexican sunflower populations could be challenging for its management in China, and further expansion and potential negative effects on ecological systems of this plant should be monitored.

The present study investigated the effects of dietary vitamin A on immune function in the proximal intestine (PI), mid intestine (MI) and distal intestine (DI) of young grass carp (Ctenopharyngodon idella). Fish were fed graded levels of dietary vitamin A for 10 weeks, and then a challenge test using an injection of Aeromonas hydrophila was conducted for 14 d. The results showed that, compared with the optimum vitamin A level, vitamin A deficiency significantly decreased fish growth performance, increased enteritis morbidity, decreased intestinal innate humoral immune response and aggravated intestinal inflammation. However, liver-expressed antimicrobial peptide 2A/B mRNA in the DI and IL-6, IL-17D, IL-10, transforming growth factor (TGF)-β1 and TGF-β2 mRNA in the PI were not affected by vitamin A levels. Meanwhile, vitamin A deficiency disturbed inflammatory cytokines in the PI, MI and DI, which might be partly linked to p38 mitogen-activated protein kinase (p38MAPK) signalling and NF-κB canonical signalling pathway (IκB kinase β (IKKβ), IKKγ, inhibitor of κBα, NF-κB p65 and c-Rel) rather than NF-κB non-canonical signalling pathway (NF-κB p52 and IKKα). However, the signalling molecules NF-κB p65 and p38MAPK did not participate in regulating cytokines in the PI. These results suggested that vitamin A deficiency decreased fish growth and impaired intestinal immune function, and that different immune responses in the PI, MI and DI were mediated partly by NF-κB canonical signalling and p38MAPK signalling pathways. On the basis of percentage of weight gain, to protect fish against enteritis morbidity and acid phosphatase activity, the optimum dietary vitamin A levels were estimated to be 0·664, 0·707 and 0·722 mg /kg, respectively.

This study investigated the effects of glycinin on the growth, intestinal oxidative status, tight junction components, cytokines and apoptosis signalling factors of fish. The results showed that an 80 g/kg diet of glycinin exposure for 42 d caused poor growth performance and depressed intestinal growth and function of juvenile Jian carp (Cyprinus carpio var. Jian). Meanwhile, dietary glycinin exposure induced increases in lipid peroxidation and protein oxidation; it caused reductions in superoxide dismutase (SOD), catalase and glutathione peroxidase (GPx) activities; and it increased MnSOD, CuZnSOD, GPx1b and GPx4a mRNA levels, suggesting an adaptive mechanism against stress in the intestines of fish. However, dietary glycinin exposure decreased both the activity and mRNA levels of nine isoforms of glutathione-S-transferase (GST) (α, μ, π, ρ, θ, κ, mGST1, mGST2 and mGST3), indicating toxicity to this enzyme activity and corresponding isoform gene expressions. In addition, glycinin exposure caused partial disruption of intestinal cell–cell tight junction components, disturbances of cytokines and induced apoptosis signalling in the distal intestines>mid intestines>proximal intestines of fish. Glycinin exposure also disturbed the mRNA levels of intestinal-related signalling factors Nrf2, Keap1a, Keap1b, eleven isoforms of protein kinase C and target of rapamycin/4E-BP. Interestingly, glutamine was observed to partially block those negative influences. In conclusion, this study indicates that dietary glycinin exposure causes intestinal oxidative damage and disruption of intestinal physical barriers and functions and reduces fish growth, but glutamine can reverse those negative effects in fish. This study provides some information on the mechanism of glycinin-induced negative effects.

The present study was conducted to investigate the anti-inflammatory effect of vitamin D both in juvenile Jian carp (Cyprinus carpio var. Jian) in vivo and in enterocytes in vitro. In primary enterocytes, exposure to 10 mg lipopolysaccharide (LPS)/l increased lactate dehydrogenase activity in the culture medium (P<0·05) and resulted in a significant loss of cell viability (P<0·05). LPS exposure increased (P<0·05) the mRNA expression of pro-inflammatory cytokines (TNF-α, IL-1β, IL-6 and IL-8), which was decreased by pre-treatment with 1,25-dihydroxyvitamin D (1,25D3) in a dose-dependent manner (P<0·05). Further results showed that pre-treatment with 1,25D3 down-regulated Toll-like receptor 4 (TLR4), myeloid differentiation primary response gene 88 (Myd88) and NF-κB p65 mRNA expression (P<0·05), suggesting potential mechanisms against LPS-induced inflammatory response. In vivo, intraperitoneal injection of LPS significantly increased TNF-α, IL-1β, IL-6 and IL-8 mRNA expression in the intestine of carp (P<0·05). Pre-treatment of fish with vitamin D3 protected the fish intestine from the LPS-induced increase of TNF-α, IL-1β, IL-6 and IL-8 mainly by downregulating TLR4, Myd88 and NF-κB p65 mRNA expression (P<0·05). These observations suggest that vitamin D could inhibit LPS-induced inflammatory response in juvenile Jian carp in vivo and in enterocytes in vitro. The anti-inflammatory effect of vitamin D is mediated at least in part by TLR4-Myd88 signalling pathways in the intestine and enterocytes of juvenile Jian carp.

Let $g\geq 2$ be a fixed integer. Let $\mathbb{N}$ denote the set of all nonnegative integers and let $A$ be a subset of $\mathbb{N}$. Write $r_{2}(A,n)=\sharp \{(a_{1},a_{2})\in A^{2}:a_{1}+a_{2}=n\}.$ We construct a thin, strongly minimal, asymptotic $g$-adic basis $A$ of order two such that the set of $n$ with $r_{2}(A,n)=2$ has density one.

Epidemiological studies have demonstrated inconsistent associations between tea consumption and mortality of all cancers, CVD and all causes. To obtain quantitative overall estimates, we conducted a dose–response meta-analysis of prospective cohort studies. A literature search in PubMed and Embase up to April 2015 was conducted for all relevant papers published. Random-effects models were used to calculate pooled relative risks (RR) with 95 % CI. In eighteen prospective studies, there were 12 221, 11 306 and 55 528 deaths from all cancers, CVD and all causes, respectively. For all cancer mortality, the summary RR for the highest v. lowest category of green tea and black tea consumption were 1·06 (95 % CI 0·98, 1·15) and 0·79 (95 % CI 0·65, 0·97), respectively. For CVD mortality, the summary RR for the highest v. lowest category of green tea and black tea consumption were 0·67 (95 % CI 0·46, 0·96) and 0·88 (95 % CI 0·77, 1·01), respectively. For all-cause mortality, the summary RR for the highest v. lowest category of green tea and black tea consumption were 0·80 (95 % CI 0·68, 0·93) and 0·90 (95 % CI 0·83, 0·98), respectively. The dose–response analysis indicated that one cup per d increment of green tea consumption was associated with 5 % lower risk of CVD mortality and with 4 % lower risk of all-cause mortality. Green tea consumption was significantly inversely associated with CVD and all-cause mortality, whereas black tea consumption was significantly inversely associated with all cancer and all-cause mortality.

Nanogenerators (NGs) have great potential to solve the problems of energy depletion and environmental pollution. Here, two types of flexible nanogenerators (FNGs) based on graphene oxide (GO) and multiwall carbon nanotubes (MW-CNTs) are presented. The peak output voltage and current of GO based FNG reached up to 2 V and 30 nA, respectively, under 15 N force at 1 Hz. Moreover, the output voltage could be improved to 34.4 V when the frequency was increased to 10 Hz. It was also found the output voltage increased from 0.1 V to 2.0 V using a released GO structure. The other FNG was made by MW-CNTs mixed with ZnO nanoparticles (NPs). Its output voltage and power reached up to 7.5 V and 18.75 mW, respectively, which is much larger than that of bare ZnO based FNG. Furthermore, a peak voltage of 30 V could be gained by stamping one’s foot on the FNG. Finally, a modified NG was fabricated using four springs and two flexible layers. As a result, the voltage and power reached up to 9 V and 27mW, respectively. These works may bring out broad applications in energy harvesting.