We find a new refinement of Fine’s partition theorem on partitions into distinct parts with the minimum part odd. As a consequence, we obtain two companion partition identities. Both analytic and combinatorial proofs are provided.

The characteristic traits of maize (Zea mays L.) leaves affect light interception and photosynthesis. Measurement or estimation of individual leaf area has been described using discontinuous equations or bell-shaped functions. However, new maize hybrids show different canopy architecture, such as leaf angle in modern maize which is more upright and ear leaf and adjacent leaves which are longer than older hybrids. The original equations and their parameters, which have been used for older maize hybrids and grown at low plant densities, will not accurately represent modern hybrids. Therefore, the aim of this paper was to develop a new empirical equation that captures vertical leaf distribution. To characterize the vertical leaf profile, we conducted a field experiment in Jilin province, Northeast China from 2015 to 2018. Our new equation for the vertical distribution of leaf profile describes leaf length, width or leaf area as a function of leaf rank, using parameters for the maximum value for leaf length, width or area, the leaf rank at which the maximum value is obtained, and the width of the curve. It thus involves one parameter less than the previously used equations. By analysing the characteristics of this new equation, we identified four key leaf ranks (4, 8, 14 and 20) for which leaf parameter values need to be quantified in order to have a good estimation of leaf length, width and area. Together, the method of leaf area estimation proposed here adds versatility for use in modern maize hybrids and simplifies the field measurements by using the four key leaf ranks to estimate vertical leaf distribution in maize canopy instead of all leaf ranks.

The compressibility effects on energy exchange mechanisms in a three-dimensional, spatially developing plane free shear layer are investigated via data produced by direct numerical simulation. The compressible shear layer is simulated using a high-order discontinuous spectral element method for convective Mach numbers $M_c = 0.3$, 0.5 and 0.7. The energy exchange mechanisms in the flow are examined by analysing the budget terms of mean kinetic, internal and turbulent kinetic energy transport equations, in both transition and turbulent regions. The results show that turbulent production, turbulent viscous dissipation, mean viscous dissipation, pressure dilatation and enthalpic production are the main mechanisms responsible for energy exchange among different forms of energy. The effects of compressibility on energy transfer mechanisms are studied based on the analyses of those five budget terms. The primary budget terms evolve differently in the transition and turbulent regions and change significantly for varying compressibility. In the transition region, a double-peak variation becomes a single peak in the streamwise profile of the turbulent production as $M_c$ increases from 0.3 to 0.7, due to significant changes in the vortex pairing structures. The shear layer centre slightly shifts to the high-speed side due to the appearance of the velocity deficit. The velocity deficit presence distance (VDPD) becomes longer as compressibility increases. However, in the turbulent region, the cross-stream profiles of the main budget terms significantly shift to the low-speed side because of the asymmetric mass entrainment and shift even further as $M_c$ increases.

The aim of this study was to explore the frequency and distribution of gene mutations that are related to isoniazid (INH) and rifampin (RIF)-resistance in the strains of the multidrug-resistant tuberculosis (MDR-TB) Mycobacterium tuberculosis (M.tb) in Beijing, China. In this retrospective study, the genotypes of 173 MDR-TB strains were analysed by spoligotyping. The katG, inhA genes and the promoter region of inhA, in which genetic mutations confer INH resistance; and the rpoB gene, in which genetic mutations confer RIF resistance, were sequenced. The percentage of resistance-associated nucleotide alterations among the strains of different genotypes was also analysed. In total, 90.8% (157/173) of the MDR strains belonged to the Beijing genotype. Population characteristics were not significantly different among the strains of different genotypes. In total, 50.3% (87/173) strains had mutations at codon S315T of katG; 16.8% (29/173) of strains had mutations in the inhA promoter region; of them, 5.5% (15/173) had point mutations at −15 base (C→T) of the inhA promoter region. In total, 86.7% (150/173) strains had mutations at rpoB gene; of them, 40% (69/173) strains had mutations at codon S531L of rpoB. The frequency of mutations was not significantly higher in Beijing genotypic MDR strains than in non-Beijing genotypes. Beijing genotypic MDR-TB strains were spreading in Beijing and present a major challenge to TB control in this region. A high prevalence of katG Ser315Thr, inhA promoter region (−15C→T) and rpoB (S531L) mutations was observed. Molecular diagnostics based on gene mutations was a useful method for rapid detection of MDR-TB in Beijing, China.

The present study was undertaken to evaluate the influence of rumen-protected folic acid (RPFA) on slaughter performance, visceral organ and gastrointestinal tract coefficients, and meat quality in lambs. Sixty-six lambs from 120 Hu ewes were selected based on body weight and maternal diets and then assigned to six groups using a randomised block experimental design in a 3 × 2 factorial arrangement. The first factor was folic acid (FA) as RPFA in the maternal diet (0 mg/kg (M0F), 16 mg/kg (M16F) or 32 mg/kg (M32F) on DM basis). The second factor was FA in the lambs’ diet from weaning until slaughter (0 mg/kg (OC) or 4·0 mg/kg (OF)). The results indicated that the addition of 16 mg/kg FA to the maternal diet increased pre-slaughter weight (PSW), dressing and meat percentage, the reticulum and omasum coefficients, length of the jejunum and ileum, tail fat and perirenal fat coefficient and a* value of the meat colour. The addition of RPFA to the lambs’ diet increased PSW, dressing and meat percentage, eye muscle area, abomasum weight, weight and length of the small intestine, but reduced the coefficients of tail fat. An M × O interaction was observed for the weights of heart, lungs, rumen and total stomach, weight and coefficient of omental fat and the girth rib value. Collectively, RPFA in the maternal and lambs’ diet improved slaughter performance and meat quality by stimulating the morphological development of the gastrointestinal tract and the distribution of fat in the body.

Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $\exp ({\sigma \sqrt {Re} \,t})$ (where $\sigma \sqrt {Re}$ is the maximal Lyapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential and is given by $\exp ({\sigma \sqrt {Re} \sqrt {t} +\sigma _1 t})$ where $\sigma \sqrt {Re} \sqrt {t}$ is much larger than $\sigma \sqrt {Re} \, t$ for small $t$ . That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here, we conduct a large numerical verification with resolution up to $2048^3$ and Reynolds number up to $6210$ . Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations suggest a mechanism for the generation, development and persistence of fully developed turbulence.

Microwaves are a form of electromagnetic radiation commonly used for telecommunications, navigation and food processing. More recently microwave technologies have found applications in fibre-reinforced polymer composites, which are increasingly used in aircraft structures. Microwave energy can be applied with low power (up to milliwatts) for non-destructive testing and high power (up to kilowatts) for heating/curing purposes. The state-of-the-art applications at high power include curing, three-dimensional (3D) printing, joining and recycling, whereas low-power microwave techniques can provide quality checks, strain sensing and damage inspection. Low-power microwave testing has the advantage of being non-contact, there is no need for surface transducers or couplants, it is operator friendly and relatively inexpensive; high-power microwave energy can offer volumetric heating, reduced processing time and energy saving with no ionising hazards. In this paper the recent research progress is reviewed, identifying achievements and challenges. First, the critical electromagnetic properties of composites that are closely related to the heating and sensing performance are discussed. Then, representative case studies are presented. Finally, the trends are outlined, including intelligent/automated inspection and solid-state heating.

Severe fever with thrombocytopenia syndrome (SFTS) is a disease with a high case-fatality rate that is caused by infection with the SFTS virus (SFTSV). Five electronic databases were systematically searched to identify relevant articles published from 1 January 2011 to 1 December 2019. The pooled rates with 95% confidence interval (CI) were calculated by a fixed-effect or random-effect model analysis. The results showed that 92 articles were included in this meta-analysis. For the confirmed SFTS cases, the case-fatality rate was 0.15 (95% CI 0.11, 0.18). Two hundred and ninety-six of 1384 SFTS patients indicated that they had been bitten by ticks and the biting rate was 0.21 (95% CI 0.16, 0.26). The overall pooled seroprevalence of SFTSV antibodies among the healthy population was 0.04 (95% CI 0.03, 0.05). For the overall seroprevalence of SFTSV in animals, the seroprevalence of SFTSV was 0.25 (95% CI 0.20, 0.29). The infection rate of SFTSV in ticks was 0.08 (95% CI 0.05, 0.11). In conclusion, ticks can serve as transmitting vectors of SFTSVs and reservoir hosts. Animals can be infected by tick bites, and as a reservoir host, SFTSV circulates continuously between animals and ticks in nature. Humans are infected by tick bites and direct contact with patient secretions.

There is limited information concerning the viral load of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in aerosols deposited on environmental surfaces and the effectiveness of infection prevention and control procedures on eliminating SARS-CoV-2 contamination in hospital settings. We examined the concentration of SARS-CoV-2 in aerosol samples and on environmental surfaces in a hospital designated for treating severe COVID-19 patients. Aerosol samples were collected by a microbial air sampler, and environmental surfaces were sampled using sterile premoistened swabs at multiple sites. Ninety surface swabs and 135 aerosol samples were collected. Only two swabs, sampled from the inside of a patient's mask, were positive for SARS-CoV-2 RNA. All other swabs and aerosol samples were negative for the virus. Our study indicated that strict implementation of infection prevention and control procedures was highly effective in eliminating aerosol and environmental borne SARS-CoV-2 RNA thereby reducing the risk of cross-infection in hospitals.

Developing alternatives to antibiotics is an urgent need in livestock production. Antimicrobial peptides (AMPs) are regarded as powerful antibiotic substitutes (ASs) because AMPs have broad-spectrum antimicrobial activities and growth-promoting ability. Here, we aimed to comprehensively assess the effects of AMPs on the growth performance, diarrhea rate, intestinal morphology and immunity of healthy or challenged piglets, compared with an antibiotics group or negative control group. We performed a set of meta-analyses of feeding trials from database inception to 27 May 2019. Among the 1379 identified studies, 20 were included in our meta-analyses (56 arms and 4067 piglets). The meta-analyses revealed that (1) compared with the negative control group, AMPs significantly improved the healthy piglets’ average daily gain (ADG), average daily feed intake (ADFI), gain : feed ratio (G/F), levels of immune globulin (Ig) IgM and IgG, and intestinal villus height : crypt depth ratio (V/C) (P < 0.05). Meanwhile, AMPs significantly increased the challenged piglets’ ADG, ADFI, G/F and V/C of the jejunum and ileum, and notably deceased the diarrhea rate (P < 0.05); (2) compared with antibiotics group, the effects of AMPs were slightly weaker than those of antibiotics in the healthy piglets, but AMPs have similar effects to those of antibiotics in challenged piglets. In a higher purity, the optimal dose of AMPs may be approximately 0.01%. Our findings indicate that AMPs can improve piglet growth performance, enhance immunity, benefit intestinal morphology and decrease the diarrheal rate. AMPs could be great ASs especially under infection conditions.

Previous work led to the proposal that the precision feeding of a high-concentrate diet may represent a potential method with which to enhance feed efficiency (FE) when rearing dairy heifers. However, the physiological and metabolic mechanisms underlying this approach remain unclear. This study used metabolomics analysis to investigate the changes in plasma metabolites of heifers precision-fed diets containing a wide range of forage to concentrate ratios. Twenty-four half-sib Holstein heifers, with a similar body condition, were randomly assigned into four groups and precision fed with diets containing different proportions of concentrate (20%, 40%, 60% and 80% based on DM). After 28 days of feeding, blood samples were collected 6 h after morning feeding and gas chromatography time-of-flight/MS was used to analyze the plasma samples. Parameters of oxidative status were also determined in the plasma. The FE (after being corrected for gut fill) increased linearly (P < 0.01) with increasing level of dietary concentrate. Significant changes were identified for 38 different metabolites in the plasma of heifers fed different dietary forage to concentrate ratios. The main pathways showing alterations were clustered into those relating to carbohydrate and amino acid metabolism; all of which have been previously associated with FE changes in ruminants. Heifers fed with a high-concentrate diet had higher (P < 0.01) plasma total antioxidant capacity and superoxide dismutase but lower (P ≤ 0.02) hydroxyl radical and hydrogen peroxide than heifers fed with a low-concentrate diet, which might indicate a lower plasma oxidative status in the heifers fed a high-concentrate diet. Thus, heifers fed with a high-concentrate diet had higher FE and antioxidant capacity but a lower plasma oxidative status as well as changed carbohydrate and amino acid metabolism. Our findings provide a better understanding of how forage to concentrate ratios affect FE and metabolism in the precision-fed growing heifers.

To describe the laboratory findings of cases of death with coronavirus disease 2019 (COVID-19) and to establish a scoring system for predicting death, we conducted this single-centre, retrospective, observational study including 336 adult patients (≥18 years old) with severe or critically ill COVID-19 admitted in two wards of Union Hospital, Tongji Medical College, Huazhong University of Science and Technology in Wuhan, who had definite outcomes (death or discharge) between 1 February 2020 and 13 March 2020. Single variable and multivariable logistic regression analyses were performed to identify mortality-related factors. We combined multiple factors to predict mortality, which was validated by receiver operating characteristic curves. As a result, in a total of 336 patients, 34 (10.1%) patients died during hospitalisation. Through multivariable logistic regression, we found that decreased lymphocyte ratio (Lymr, %) (odds ratio, OR 0.574, P < 0.001), elevated blood urea nitrogen (BUN) (OR 1.513, P = 0.009), and raised D-dimer (DD) (OR 1.334, P = 0.002) at admission were closely related to death. The combined prediction model was developed by these factors with a sensitivity of 100.0% and specificity of 97.2%. In conclusion, decreased Lymr, elevated BUN, and raised DD were found to be in association with death outcomes in critically ill patients with COVID-19. A scoring system was developed to predict the clinical outcome of these patients.

Guanidinoacetic acid (GAA) can improve the growth performance of bulls. This study investigated the influences of GAA addition on growth, nutrient digestion, ruminal fermentation and serum metabolites in bulls. Forty-eight Angus bulls were randomly allocated to experimental treatments, that is, control, low-GAA (LGAA), medium-GAA (MGAA) and high-GAA (HGAA), with GAA supplementation at 0, 0.3, 0.6 and 0.9 g/kg DM, respectively. Bulls were fed a basal diet containing 500 g/kg DM concentrate and 500 g/kg DM roughage. The experimental period was 104 days, with 14 days for adaptation and 90 days for data collection. Bulls in the MGAA and HGAA groups had higher DM intake and average daily gain than bulls in the LGAA and control groups. The feed conversion ratio was lowest in MGAA and highest in the control. Bulls receiving 0.9 g/kg DM GAA addition had higher digestibility of DM, organic matter, NDF and ADF than bulls in other groups. The digestibility of CP was higher for HGAA than for LGAA and control. The ruminal pH was lower for MGAA, and the total volatile fatty acid concentration was greater for MGAA and HGAA than for the control. The acetate proportion and acetate-to-propionate ratio were lower for MGAA than for LGAA and control. The propionate proportion was higher for MGAA than for control. Bulls receiving GAA addition showed decreased ruminal ammonia N. Bulls in MGAA and HGAA had higher cellobiase, pectinase and protease activities and Butyrivibrio fibrisolvens, Prevotella ruminicola and Ruminobacter amylophilus populations than bulls in LGAA and control. However, the total protozoan population was lower for MGAA and HGAA than for LGAA and control. The total bacterial and Ruminococcus flavefaciens populations increased with GAA addition. The blood level of creatine was higher for HGAA, and the activity of l-arginine glycine amidine transferase was lower for MGAA and HGAA, than for control. The blood activity of guanidine acetate N-methyltransferase and the level of folate decreased in the GAA addition groups. The results indicated that dietary addition of 0.6 or 0.9 g/kg DM GAA improved growth performance, nutrient digestion and ruminal fermentation in bulls.

Soybean meal is rich in soybean isoflavones, which exhibit antioxidant, anti-inflammatory, antiviral and anticancer functions in humans and animals. This study was conducted to investigate the effects of soybean isoflavones on the growth performance, intestinal morphology and antioxidative properties in pigs. A total of 72 weaned piglets (7.45 ± 0.13 kg; 36 males and 36 females) were allocated into three treatments and fed corn-soybean meal (C-SBM), corn-soy protein concentrate (C-SPC) or C-SPC supplemented with equal levels of the isoflavones found in the C-SBM diet (C-SPC + ISF) for a 72-day trial. Each treatment had six replicates and four piglets per replicate, half male and half female. On day 42, one male pig from each replicate was selected and euthanized to collect intestinal samples. The results showed that compared to pigs fed the C-SPC diet, pigs fed the C-SBM and C-SPC + ISF diets had higher BW on day 72 (P < 0.05); pigs fed the C-SBM diet had significantly higher average daily gain (ADG) during days 14 to 28 (P < 0.05), with C-SPC + ISF being intermediate; pigs fed the C-SBM diet tended to have higher ADG during days 42 to 72 (P = 0.063), while pigs fed the C-SPC + ISF diet had significantly higher ADG during days 42 to 72 (P < 0.05). Moreover, compared to pigs fed the C-SPC diet, pigs fed the C-SBM diet tended to have greater villus height (P = 0.092), while pigs fed the C-SPC + ISF diet had significantly greater villus height (P < 0.05); pigs fed the C-SBM and C-SPC + ISF diets had significantly increased villus height-to-crypt depth ratio (P < 0.05). Compared with the C-SPC diet, dietary C-SPC + ISF tended to increase plasma superoxide dismutase activity on days 28 (P = 0.085) and 42 (P = 0.075) and reduce plasma malondialdehyde (MDA) content on day 42 (P = 0.089), as well as significantly decreased jejunal mucosa MDA content on day 42 (P < 0.05). However, no significant difference in the expression of tight junction genes among the three groups was found (P > 0.05). In conclusion, our results suggest that a long-term exposure to soybean isoflavones enhances the growth performance, protects the intestinal morphology and improves the antioxidative properties in pigs.

In this paper, the generation of relativistic electron mirrors (REM) and the reflection of an ultra-short laser off the mirrors are discussed, applying two-dimension particle-in-cell simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapid expansion. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads to the resonance between laser and REM. The reflected radiation near this interval and corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, a certain part of the reflected field could be selectively amplified or depressed, leading to the selective adjustment of the corresponding spectra.

The meat quality of chicken is an important factor affecting the consumer’s health. It was hypothesized that n-3 polyunsaturated fatty acid (n-3 PUFA) could be effectively deposited in chicken, by incorporating antioxidation of soybean isoflavone (SI), which led to improved quality of chicken meat for good health of human beings. Effects of partial or complete dietary substitution of lard (LA) with linseed oil (LO), with or without SI on growth performance, biochemical indicators, meat quality, fatty acid profiles, lipid-related health indicators and gene expression of breast muscle were examined in chickens. A total of 900 males were fed a corn–soybean meal diet supplemented with 4% LA, 2% LA + 2% LO and 4% LO and the latter two including 30 mg SI/kg (2% LA + 2% LO + SI and 4% LO + SI) from 29 to 66 days of age; each of the five dietary treatments included six replicates of 30 birds. Compared with the 4% LA diet, dietary 4% LO significantly increased the feed efficiency and had no negative effect on objective indices related to meat quality; LO significantly decreased plasma triglycerides and total cholesterol (TCH); abdominal fat percentage was significantly decreased in birds fed the 4% LO and 4% LO + SI diets. Chickens with LO diets resulted in higher contents of α-linolenic acid (C18:3n-3), EPA (C20:5n-3) and total n-3 PUFA, together with a lower content of palmitic acid (C16:0), lignoceric acid (C24:0), saturated fatty acids and n-6:n-3 ratio in breast muscle compared to 4% LA diet (P < 0.05); they also significantly decreased atherogenic index, thrombogenic index and increased the hypocholesterolemic to hypercholesterolemic ratio. Adding SI to the LO diets enhanced the contents of EPA and DHA (C22:6n-3), plasma total superoxide dismutase, reduced glutathione (GSH)/oxidized glutathione and muscle GSH content, while decreased plasma total triglyceride and TCH and malondialdehyde content in plasma and breast muscle compared to its absence (P < 0.05). Expression in breast muscle of fatty acid desaturase 1 (FADS1), FADS2, elongase 2 (ELOVL2) and ELOVL5 genes were significantly higher with the LO diets including SI than with the 4% LA diet. Significant interactions existed between LO level and inclusion of SI on EPA and TCH contents. These findings indicate that diet supplemented with LO combined with SI is an effective alternative when optimizing the nutritional value of chicken meat for human consumers.