Let $p(n)$ and $M(m,L;n)$ be the number of partitions of n and the number of partitions of n with crank congruent to m modulo L, respectively, and let

$$ \begin{align*}M(a,b,c;L;n):= M(a,L;n) + M(b,L;n) + M(c,L;n).\end{align*} $$

In this paper, we focus on some relations between $M(m,L;n)$ and $p(n),$ which Dyson, Andrews, and Garvan etc. have studied previously. By applying a modification of the circle method to estimate the Fourier coefficients of generating functions, we establish the following inequalities between $M(a,b,c;L;n)$ and $p(n):$ for $n \geq 467$,

$$ \begin{align*} M(0,1,1;9;n)> \frac{p(n)}{3} &\;\: \mathrm{when}\;\: n \equiv 0,1,5,8 ~ (\mathrm{mod}~9), \\ M(0,1,1;9;n) < \frac{p(n)}{3} &\;\: \mathrm{when}\;\: n \equiv 2,3,4,6,7 ~ (\mathrm{mod}~9), \\ M(2,3,4;9;n) < \frac{p(n)}{3} &\;\: \mathrm{when}\;\: n \equiv 0,1,5,8 ~ (\mathrm{mod}~9), \\ M(2,3,4;9;n)> \frac{p(n)}{3} &\;\: \mathrm{when}\;\: n \equiv 2,3,4,6,7 ~ (\mathrm{mod}~9). \end{align*} $$

In the proof of these inequalities, an inequality for the logarithm of the generating function for $p(n)$ is derived and applied. Our method reduces the last possible counterexamples to $467 \leq n \leq 22471$, and it will produce more effective estimates when proving inequalities of such types.

Diarrhoea caused by pathogens such as enterotoxigenic E. coli (ETEC) is a serious threat to the health of young animals and human infants. Here, we investigated the protective effect of fructo-oligosaccharides (FOS) on the intestinal epithelium with ETEC challenge in a weaned piglet model. Twenty-four weaned piglets were randomly divided into three groups: (1) non-ETEC-challenged control (CON); (2) ETEC-challenged control (ECON); and (3) ETEC challenge + 2·5 g/kg FOS (EFOS). On day 19, the CON pigs were orally infused with sterile culture, while the ECON and EFOS pigs were orally infused with active ETEC (2·5 × 109 colony-forming units). On day 21, pigs were slaughtered to collect venous blood and small intestine. Result showed that the pre-treatment of FOS improved the antioxidant capacity and the integrity of intestinal barrier in the ETEC-challenged pigs without affecting their growth performance. Specifically, compared with ECON pigs, the level of GSH peroxidase and catalase in the plasma and intestinal mucosa of EFOS pigs was increased (P < 0·05), and the intestinal barrier marked by zonula occluden-1 and plasmatic diamine oxidase was also improved in EFOS pigs. A lower level (P < 0·05) of inflammatory cytokines in the intestinal mucosa of EFOS pigs might be involved in the inhibition of TLR4/MYD88/NF-κB pathway. The apoptosis of jejunal cells in EFOS pigs was also lower than that in ECON pigs (P < 0·05). Our findings provide convincing evidence of possible prebiotic and protective effect of FOS on the maintenance of intestinal epithelial function under the attack of pathogens.

To explore the effect of manno-oligosaccharide (MOS) on intestinal health in weaned pigs upon enterotoxigenic Escherichia coli K88 (ETEC) challenge, thirty-two male weaned pigs were randomly assigned into four groups. Pigs fed with a basal diet or basal diet containing MOS (0·6 g/kg) were orally infused with ETEC or culture medium. Results showed that MOS significantly elevated the digestibility of crude protein and gross energy in both ETEC-challenged and non-challenged pigs (P < 0·05). MOS also elevated serum concentrations of IgA and IgM (P < 0·05), but decreased serum concentrations of TNF-α, IL-1β and IL-6 (P < 0·05) in ETEC-challenged pigs. Interestingly, MOS increased villus height and the ratio of villus height:crypt depth in duodenum and ileum (P < 0·05). MOS also increased duodenal sucrase and ileal lactase activity in ETEC-challenged pigs (P < 0·05). MOS decreased the abundance of E. coli, but increased the abundance of Lactobacillus, Bifidobacterium and Bacillus in caecum (P < 0·05). Importantly, MOS not only elevated the expression levels of zonula occludens-1 (ZO-1), claudin-1 and GLUT-2 in duodenum (P < 0·05) but also elevated the expression levels of ZO-1, GLUT-2 and L-type amino acid transporter-1 in ileum (P < 0·05) upon ETEC challenge. These results suggested that MOS can alleviate inflammation and intestinal injury in weaned pigs upon ETEC challenge, which was associated with suppressed secretion of inflammatory cytokines and elevated serum Ig, as well as improved intestinal epithelium functions and microbiota.

Detecting the turbulent/non-turbulent interface is a challenging topic in turbulence research. In the present study, machine learning methods are used to train detectors for identifying turbulent regions in the flow past a circular cylinder. To ensure that the turbulent/non-turbulent interface is independent of the reference frame of coordinates and is physics-informed, we propose to use invariants of tensors appearing in the transport equations of velocity fluctuations, strain-rate tensor and vortical tensor as the input features to identify the flow state. The training samples are chosen from numerical simulation data at two Reynolds numbers, $Re=100$ and 3900. Extreme gradient boosting (XGBoost) is utilized to train the detector, and after training, the detector is applied to identify the flow state at each point of the flow field. The trained detector is found robust in various tests, including the applications to the entire fields at successive snapshots and at a higher Reynolds number $Re=5000$. The objectivity of the detector is verified by changing the input features and the flow region for choosing the turbulent training samples. Compared with the conventional methods, the proposed method based on machine learning shows its novelty in two aspects. First, no threshold value needs to be specified explicitly by the users. Second, machine learning can treat multiple input variables, which reflect different properties of turbulent flows, including the unsteadiness, vortex stretching and three-dimensionality. Owing to these advantages, XGBoost generates a detector that is more robust than those obtained from conventional methods.

Teenagers are important carriers of Neisseria meningitidis, which is a leading cause of invasive meningococcal disease. In China, the carriage rate and risk factors among teenagers are unclear. The present study presents a retrospective analysis of epidemiological data for N. meningitidis carriage from 2013 to 2017 in Suizhou city, China. The carriage rates were 3.26%, 2.22%, 3.33%, 3.53% and 9.88% for 2013, 2014, 2015, 2016 and 2017, respectively. From 2014 to 2017, the carriage rate in the 15- to 19-year-old age group (teenagers) was the highest and significantly higher than that in remain age groups. Subsequently, a larger scale survey (December 2017) for carriage rate and relative risk factors (population density, time spent in the classroom, gender and antibiotics use) were investigated on the teenagers (15- to 19-year-old age) at the same school. The carriage rate was still high at 33.48% (223/663) and varied greatly from 6.56% to 52.94% in a different class. Population density of the classroom was found to be a significant risk factor for carriage, and 1.4 persons/m2 is recommended as the maximum classroom density. Further, higher male gender ratio and more time spent in the classroom were also significantly associated with higher carriage. Finally, antibiotic use was associated with a significantly lower carriage rate. All the results imply that attention should be paid to the teenagers and various measures can be taken to reduce the N. meningitidis carriage, to prevent and control the outbreak of IMD.

Here, we explored the influences of dietary inulin (INU) supplementation on growth performance and intestinal health in a porcine model. Thirty-two male weaned pigs (with an average body weight of 7·10 (sd 0·20) kg) were randomly assigned to four treatments and fed with a basal diet (BD) or BD containing 2·5, 5·0 and 10·0 g/kg INU. After a 21-d trial, pigs were killed for collection of serum and intestinal tissues. We show that INU supplementation had no significant influence on the growth performance in weaned pigs. INU significantly elevated serum insulin-like growth factor-1 concentration but decreased diamine oxidase concentration (P < 0·05). Interestingly, 2·5 and 5·0 g/kg INU supplementation significantly elevated the villus height in jejunum and ileum (P < 0·05). Moreover, 2·5 and 5·0 g/kg INU supplementation also elevated the villus height to crypt depth (V:C) in the duodenum and ileum and improved the distribution and abundance of tight-junction protein zonula occludens-1 in duodenum and ileum epithelium. INU supplementation at 10·0 g/kg significantly elevated the sucrase activity in the ileum mucosa (P < 0·05). INU supplementation decreased the expression level of TNF-α but elevated the expression level of GLUT 2 and divalent metal transporter 1 in the intestinal mucosa (P < 0·05). Moreover, INU increased acetic and butyric acid concentrations in caecum (P < 0·05). Importantly, INU elevated the Lactobacillus population but decreased the Escherichia coli population in the caecum (P < 0·05). These results not only indicate a beneficial effect of INU on growth performance and intestinal barrier functions but also offer potential mechanisms behind the dietary fibre-regulated intestinal health.

The present study aimed to investigate whether arginine (Arg) promotes porcine type I muscle fibres formation via improving mitochondrial biogenesis. In the in vivo study, a total of sixty Duroc × Landrace × Yorkshire weaning piglets with an average body weight of 6·55 (sd 0·36) kg were randomly divided into four treatments and fed with a basal diet or a basal diet supplemented with 0·5, 1·0 and 1·5 % l-Arg, respectively, in a 4-week trial. Results showed that dietary supplementation of 1·0 % Arg significantly enhanced the activity of succinate dehydrogenase, up-regulated the protein expression of myosin heavy chain I (MyHC I) and increased the mRNA levels of MyHC I, troponin I1, C1 and T1 (Tnni1, Tnnc1 and Tnnt1) in longissimus dorsi muscle compared with the control group. In addition, ATPase staining analysis indicated that 1·0 % Arg supplementation significantly increased the number of type I muscle fibres and significantly decreased the number of type II muscle fibres. Furthermore, 1·0 % Arg supplementation significantly up-regulated PPAR-γ coactivator-1α (PGC-1α), sirtuin 1 and cytochrome c (Cytc) protein expressions, increased PGC-1α, nuclear respiratory factor 1 (NRF1), mitochondria transcription factor B1 (TFB1M), Cytc and ATP synthase subunit C1 (ATP5G) mRNA levels and increased mitochondrial DNA content. In the in vitro study, mitochondrial complex I inhibitor rotenone (Rot) was used. We found that Rot annulled Arg-induced type I muscle fibres formation. Together, our results provide for the first time the evidence that Arg promotes porcine type I muscle fibres formation through improvement of mitochondrial biogenesis.

Underground Nuclear Astrophysics in China (JUNA) will take the advantage of the ultra-low background in Jinping underground lab. High current accelerator with an ECR source and detectors were commissioned. JUNA plans to study directly a number of nuclear reactions important to hydrostatic stellar evolution at their relevant stellar energies. At the first period, JUNA aims at the direct measurements of 25Mg(p,γ)26 Al, 19F(p,α) 16 O, 13C(α, n) 16O and 12C(α,γ) 16O near the Gamow window. The current progress of JUNA will be given.

Muscle fibre types can transform from slow-twitch (slow myosin heavy chain (MyHC)) to fast-twitch (fast MyHC) or vice versa. Leucine plays a vital effect in the development of skeletal muscle. However, the role of leucine in porcine myofibre type transformation and its mechanism are still unclear. In this study, effects of leucine and microRNA-27a (miR-27a) on the transformation of porcine myofibre type were investigated in vitro. We found that leucine increased slow MyHC protein level and decreased fast MyHC protein level, increased the levels of phospho-protein kinase B (Akt)/Akt and phospho-forkhead box 1 (FoxO1)/FoxO1 and decreased the FoxO1 protein level. However, blocking the Akt/FoxO1 signalling pathway by wortmannin attenuated the role of leucine in porcine myofibre type transformation. Over-expression of miR-27a decreased slow MyHC protein level and increased fast MyHC protein level, whereas inhibition of miR-27a had an opposite effect. We also found that expression of miR-27a was down-regulated following leucine treatment. Moreover, over-expression of miR-27a repressed transformation from fast MyHC to slow MyHC caused by leucine, suggesting that miR-27a is interdicted by leucine and then contributes to porcine muscle fibre type transformation. Our finding provided the first evidence that leucine promotes porcine myofibre type transformation from fast MyHC to slow MyHC via the Akt/FoxO1 signalling pathway and miR-27a.

Some congruences on conjectures of van Hamme are established. These results give partial answers to some of Swisher's conjectures.

A new ternary compound Al5NdNi2 was prepared by melting a stoichiometric mixture of aluminum, neodymium, and nickel in an arc furnace and annealing in vacuum. The crystal structure of Al5NdNi2 was studied by X-ray powder diffraction technique and Rietveld analysis. All diffraction lines of Al5NdNi2 were indexed, and the lattice parameters were refined with an orthorhombic structure type of space group Immm (No.71) using Rietveld analysis program DBWS-9807. The lattice parameters are presented, a = 7.0508(1) Å, b = 9.5690(1) Å, c = 3.9792(1) Å, V = 268.47 Å3, Z = 2, ρ = 4.91 g cm−3, and RIR = 1.23.

Leucine, one of the branched-chain amino acids, is the only amino acid to regulate protein turnover in skeletal muscle. Leucine not only increases muscle protein synthesis, but also decreases muscle protein degradation. It is well documented that leucine plays a positive role in differentiation of murine muscle cells. However, the role of leucine on porcine myoblast differentiation and its mechanism remains unclear. In this study, porcine myoblasts were induced to differentiate with differentiation medium containing different concentrations of leucine, and wortmannin was used to interdict the activity of protein kinase B (Akt). We found that leucine increased the number of myosin heavy chain-positive cells and creatine kinase activity. Moreover, leucine increased the mRNA and protein levels of myogenin and myogenic determining factor (MyoD). In addition, leucine increased the levels of phosphorylated Akt/Akt and phosphorylated Forkhead box O1 (P-FoxO1)/FoxO1, as well as decreased the protein level of FoxO1. However, wortmannin, a specific repressor of PI3K/Akt signalling pathway, attenuated the positive role of leucine on porcine myoblast differentiation. Our results suggest that leucine promotes porcine myoblast differentiation through the Akt/FoxO1 signalling pathway.

Structural hierarchy is ubiquitous in nature and quite important for optimizing the properties of functional materials. Carbon nanomaterials, owing to their unique and tunable physical and chemical properties, have been regarded as promising candidates for various energy storage systems. Constructing hierarchically structured carbon nanomaterials (HSCNs) can boost electrochemical performance of nanocarbons. Therefore, HSCNs have attracted tremendous research attentions in recent years. In this review, we summarized the recent progress in hierarchical structure design of carbon nanomaterials and their potential applications in different energy storage technologies. First we give a brief introduction about carbon nanomaterials and the hierarchical structure merits. Subsequently, recent research works on hierarchical structure design of carbon nanomaterials was summarized and classified according to applications in lithium-ion batteries, sodium-ion batteries, supercapacitors and lithium–sulfur batteries, respectively. In addition, the challenges of HSCNs in different applications were also concluded and reviewed. At last, design principles of HSCNs were summarized and future development trends were prospected.

Stimulated Brillouin scattering (SBS) effect is currently the major limitation for the power scaling of single-frequency/narrow linewidth fiber laser systems. A single-mode linearly polarized all-fiber amplifier system is set up to investigate SBS effect in triple-frequency high-power amplifiers. With this amplifier, up to 302 W output power with 83% slope efficiency is achieved and the SBS threshold is scaled up to 12 dB. To the best of our knowledge, this is the highest output power of multifrequency laser from a single-mode polarization maintaining fiber. Good spectral properties and high brightness make this laser source available for the application of second harmonic generation, coherent beam combining.

The intestine plays key roles in maintaining body arginine (Arg) homoeostasis. Meanwhile, the intestine is very susceptible to reactive oxygen species. In light of this, the study aimed to explore the effects of Arg supplementation on intestinal morphology, Arg transporters and metabolism, and the potential protective mechanism of Arg supplementation in piglets under oxidative stress. A total of thirty-six weaned piglets were randomly allocated to six groups with six replicates and fed a base diet (0·95 % Arg,) or base diet supplemented with 0·8 % and 1·6 % l-Arg for 1 week, respectively. Subsequently, a challenge test was conducted by intraperitoneal injection of diquat, an initiator of radical production, or sterile saline. The whole trial lasted 11 d. The diquat challenge significantly decreased plasma Arg concentration at 6 h after injection (P<0·05), lowered villus height in the jejunum and ileum (P<0·05) as well as villus width and crypt depth in the duodenum, jejunum and ileum (P<0·05). Oxidative stress significantly increased cationic amino acid transporter (CAT)-1, CAT-2 and CAT-3, mRNA levels (P<0·05), decreased arginase II (ARGII) and inducible nitric oxide synthase mRNA levels, and increased TNF-α mRNA level in the jejunum (P<0·05). Supplementation with Arg significantly decreased crypt depth (P<0·05), suppressed CAT-1 mRNA expression induced by diquat (P<0·05), increased ARGII and endothelial nitric oxide synthase mRNA levels (P<0·05), and effectively relieved the TNF-α mRNA expression induced by diquat in the jejunum (P<0·05). It is concluded that oxidative stress decreased Arg bioavailability and increased expression of inflammatory cytokines in the jejunum, and that Arg supplementation has beneficial effects in the jejunum through regulation of the metabolism of Arg and suppression of inflammatory cytokine expression in piglets.

We employ some formulae on hypergeometric series and p-adic Gamma function to establish several congruences.

An effective multiplex real-time polymerase chain reaction (PCR) assay for the simultaneous detection of three major pathogens, Nosema bombycis Nägeli (Microsporidia: Nosematidae), Bombyx mori nucleopolyhedrovirus (Baculoviridae: genus Alphabaculovirus) (NPV), and Bombyx mori densovirus (Parvoviridae: genus Iteravirus) (DNV), in silkworms (Bombyx mori (Linnaeus); Lepidoptera: Bombycidae) was developed in this study. Polymerase chain reaction and real-time PCR tests and basic local alignment search tool searches revealed that the primers and probes used in this study had high specificities for their target species. The ability of each primer/probe set to detect pure pathogen DNA was determined using a plasmid dilution panel, in which under optimal conditions the multiplex real-time PCR assay showed high efficiency in the detection of three mixed target plasmids with a detection limit of 8.5×103 copies for N. bombycis and Bombyx mori NPV (BmNPV) and 8.5×104 copies for Bombyx mori DNV (BmDNV). When the ability to detect these three pathogens was examined in artificially inoculated silkworms, our method presented a number of advantages over traditional microscopy, including specificity, sensitivity, and high-throughput capabilities. Under the optimal volume ratio for the three primer/probe sets (3:2:2=N. bombycis:BmNPV:BmDNV), the multiplex real-time PCR assay showed early detection of BmNPV and BmDNV by day 1 post inoculation using DNA templates of the three pathogens in various combinations from individually infected silkworms; the early detection of N. bombycis was possible by day 3 post inoculation using the DNA isolated from the midgut of N. bombycis-infected silkworms.

Using phytolith analysis from a well-dated and high-resolution sediment sequence in the apex of northern Yangtze Delta, we investigate environmental changes, the rise and decline of rice exploitation and possible impacts of environment on rice exploitation during the early mid-Holocene. The phytolith sequence documents a relatively warm and dry interval during ca.9000 to 8200 cal yr BP, followed by climatic amelioration before 7200 cal yr BP. Phytolith evidence indicates that rice exploitation at the apex of northern Yangtze Delta began at 8200 cal yr BP, flourished by 7700 cal yr BP and ceased after 7400 cal yr BP. The first emergence of marine diatom species approximately 7300 cal yr BP likely indicates an accelerated sea-level rise. The apparent correlation of the initiation of rice exploitation with climatic amelioration during the early mid-Holocene suggests that climatic changes may have played an important role in facilitating rice exploitation. Both the ideal climatic conditions and stable sea level enabled flourishing rice exploitation during 8200 to 7400 cal yr BP. Although the climate remained warm and wet after 7400 cal yr BP, local sea-level rise possibly led to the termination of earlier rice exploitation at this site of the northern Yangtze Delta.

The new ternary compound of Al2Cu3Gd was prepared by melting with stoichiometric composition in an electric arc furnace. The X-ray powder diffraction data of Al2Cu3Gd have been collected by the Rigaku Smart Lab X-ray powder diffractometer. The Rietveld refinement method had been used to study the crystal structure of Al2Cu3Gd. The results showed that the Al2Cu3Gd, new compound have the hexagonal structure, space group P6/mmm (No. 191) with a = 5.1822 (1) Å, c = 4.1566 (1) Å, V = 96.67 Å3, Z = 1, and the density is 6.62 g cm−3, and the intensity ratio reference intensity ratio is 1.29.

Two new Primulina species with yellow flowers, Primulina versicolor F.Wen, B.Pan & B.M.Wang and P. alutacea F.Wen, B.Pan & B.M.Wang (Gesneriaceae), from Guangdong, China are described and illustrated.