In this article, we explore the bifurcation problem of limit cycles near the double eight figure loop (compound cycle with a 2-polycycle connecting two homoclinic loops). A general theory is established to find the lower bound of the maximal number of limit cycles (isolated periodic orbits) near the double eight figure loop. The Liénard system, a well-known nonlinear dynamical model, appears in a natural way in physics, chemistry, engineering, and so on, where periodic phenomena play a relevant role. As an application, we investigate an $(n+1)$th-order generalized Liénard system and prove the system has at least $7[\frac{n}{6}]+2[\frac{r}{2}]-[\frac{r}{4}]$ limit cycles near the double eight figure loop for any $n\geq5$ and $r=\rm mod(n,6)$, and their distribution is also gained.

We reported on an efficient high-power continuous-wave laser operation on the 3H4 → 3H5 transition of Tm3+ ions in a diffusion-bonded composite YVO4/Tm:GdVO4 crystal. Pumped by a laser diode at 794 nm, a maximum output power of 7.5 W was obtained from a YVO4/Tm:GdVO4 laser at 2.29 μm, corresponding to a slope efficiency of 40.3% and exceeding the Stokes limit. To the best of our knowledge, this result represents the maximum power ever achieved from a Tm laser at 2.3 μm.

Previous work suggests that the arrangement of elements in an obstruction may influence the bulk flow velocity through the obstruction, but the physical mechanisms for this influence are not yet clear. This is the motivation for this study, where direct numerical simulation is used to investigate flow through an array of cylinders at a resolution sufficient to observe interactions between wakes of individual elements. The arrangement is altered by varying the gap ratio $G/d$ (1.2 – 18, G is the distance between two adjacent cylinders, d is the cylinder diameter), array-to-element diameter ratio $D/d$ (3.6 – 200, D is the array diameter), and incident flow angle ($0^{\circ} - 30^{\circ}$). Depending on the element arrangement, it is found that the average root-mean-square lift and drag coefficients can vary by an order of magnitude, whilst the average time-mean drag coefficient of individual cylinders ($\overline{C_{d}}$), and the bulk velocity are found to vary by up to $50\,\%$ and a factor of 2, respectively. These arrangement effects are a consequence of the variation in flow and drag characteristics of individual cylinders within the array. The arrangement effects become most critical in the intermediate range of flow blockage parameter $\mathit{\Gamma_{D}^{\prime}} = 0.5-1.5$ ($\mathit{\Gamma_{D}^{\prime}}=\overline{C_{d}}aD/(1-\phi)$, where a is frontal element area per unit volume, and $\phi$ is solid volume fraction), due to the high variability in element-scale flow characteristics. Across the full range of arrangements modelled, it is confirmed that the bulk velocity is governed by flow blockage parameter but only if the drag coefficient incorporates arrangement effects. Using these results, this paper proposes a framework for describing and predicting flow through an array across a variety of arrangements.

This study was conducted to investigate whether methionyl-tRNA synthetase (MetRS) is a mediator of methionine (Met)-induced crop milk protein synthesis via the janus kinase 2 (JAK2)/signal transducer and activator of transcription 5 (STAT5) signalling pathway in breeding pigeons. In Experiment 1, a total of 216 pairs of breeding pigeons were divided into three groups (control, Met-deficient, and Met-rescue groups). In Experiments 2 and 3, forty pairs of breeding pigeons from each experiment were allocated into four groups. The second experiment included a control group and three MetRS inhibitor (REP8839) groups. The third experiment included a Met-deficient group, Met-sufficient group, REP8839 + Met-deficient group and REP8839 + Met-sufficient group. Experiment 1 showed that Met supplementation increased crop development, crop milk protein synthesis, the protein expression of MetRS and JAK2/STAT5 signalling pathway, and improved squab growth. Experiment 2 showed that crop development, crop milk protein synthesis and the protein expression of MetRS and the JAK2/STAT5 signalling pathway were decreased, and squab growth was inhibited by the injection of 1·0 mg/kg body weight REP8839, which was the selected dose for the third experiment. Experiment 3 showed that Met supplementation increased crop development, crop milk protein synthesis and the expression of MetRS and JAK2/STAT5 signalling pathway and rescued squab growth after the injection of REP8839. Moreover, the co-immunoprecipitation results showed that there was an interaction between MetRS and JAK2. Taken together, these findings indicate that MetRS mediates Met-induced crop milk protein synthesis via the JAK2/STAT5 signalling pathway, resulting in improved squab growth in breeding pigeons.

Although there is a range of approaches for classifying the wake structure behind an array of obstacles, these approaches provide inconsistent results across different array systems. This motivates the present study to integrate and reconcile these approaches into one that is consistent across different systems. This new, transferable classification approach is based on the dimensionless flow blockage of the array and the wake stability parameter. To demonstrate this approach, a series of laboratory experiments was conducted to characterise the wake structure behind an array of emergent cylinders across a practically relevant parameter space that has not previously been explored. Two arrays with the same values of flow blockage and wake stability parameters but different sizes display the same wake structure, demonstrating the controlling influence of these two parameters on the wake structure. This approach classifies four different wake structures, which are distinct in that they display differences in instantaneous and time-averaged flow fields, temporal velocity oscillations, shear layer growth and the length of the steady wake region. The dependence of the wake structure on the two parameters is a consequence of (i) the controlling influence of blockage on the fraction of incident flow passing through the array and (ii) the ability of shallowness to suppress wake instabilities and, to a lesser extent, also influence the velocity through the array. This paper provides a predictive framework for the wake structure based on knowledge of the array geometry, and the depth and velocity of incident flow across the entire relevant practical parameter space.

The flow-induced vibrations (FIVs) of two identical tandem square cylinders with mass ratio m* = 3.5 at Reynolds number Re = 150 are investigated through two-dimensional direct numerical simulation (DNS) and linear stability analysis over a parameter range of spacing ratio 1.5 ≤ L* ≤ 5 and reduced velocity 3 ≤ Ur ≤ 34. Three kinds of FIV responses, namely vortex-induced vibration (VIV), biased oscillation (BO) and galloping (GA), are identified. The FIVs are then further classified into the branches of initial VIV (IV), resonant VIV (RV and RV′), flutter-induced VIV (FV), desynchronized VIV (DV), VIV developing from GA (GV), transitional state between VIV and GA (TR), BO and GA based on the characteristics of the vibration responses. The transitions among different FIV branches are examined by combining the DNS with linear stability analysis, where the transition boundaries among the VIV, BO and GA branches over the concerned parameters are identified on the branch maps. The transition from IV to RV or RV′ is found to be related to the unstable wake mode, while the FV, transiting from RV or RV′, is induced by the unstable structural factor in the wake-structure mode. The structural instability is considered as the physical origin of GA, whereas the mode competition between unstable wake and structure leads to DV, GV and TR, and thus delays the appearance of GA. The transition from DV to BO with biased equilibrium position, accompanied by the even-order harmonic frequencies, is essentially induced by the symmetry breaking bifurcation.

Few studies have evaluated the joint effect of trace elements on spontaneous preterm birth (SPTB). This study aimed to examine the relationships between the individual or mixed maternal serum concentrations of Fe, Cu, Zn, Se, Sr and Mo during pregnancy, and risk of SPTB. Inductively coupled plasma MS was employed to determine maternal serum concentrations of the six trace elements in 192 cases with SPTB and 282 controls with full-term delivery. Multivariate logistic regression, weighted quantile sum regression (WQSR) and Bayesian kernel machine regression (BKMR) were used to evaluate the individual and joint effects of trace elements on SPTB. The median concentrations of Sr and Mo were significantly higher in controls than in SPTB group (P < 0·05). In multivariate logistic regression analysis, compared with the lowest quartile levels of individual trace elements, the third- and fourth-quartile Sr or Mo concentrations were significantly associated with reduced risk of SPTB with adjusted OR (aOR) of 0·432 (95 CI < 0·05). In multivariate logistic regression analysis, compared with the lowest quartile levels of individual trace elements, the third- and fourth-quartile Sr or Mo concentrations were significantly associated with reduced risk of SPTB with adjusted aOR of 0·432 (95 % CI 0·247, 0·756), 0·386 (95 % CI 0·213, 0·701), 0·512 (95 % CI 0·297, 0·883) and 0·559 (95 % CI 0·321, 0·972), respectively. WQSR revealed the inverse combined effect of the trace elements mixture on SPTB (aOR = 0·368, 95 % CI 0·228, 0·593). BKMR analysis confirmed the overall mixture of the trace elements was inversely associated with the risk of SPTB, and the independent effect of Sr and Mo was significant. Our findings suggest that the risk of SPTB decreased with concentrations of the six trace elements, with Sr and Mo being the major contributors.

This study compared the concentrations, types and distributions of sialic acid (SA) in human milk at different stages of the postnatal period with those in a range of infant formulas. Breast milk from mothers of healthy, full-term and exclusively breastfed infants was collected on the 2nd (n 246), 7th (n 135), 30th (n 85) and 90th (n 48) day after birth. The SA profiles of human milk, including their distribution, were analysed and compared with twenty-four different infant formulas. Outcome of this observational study was the result of natural exposure. Only SA of type Neu5Ac was detected in human milk. Total SA concentrations were highest in colostrum and reduced significantly over the next 3 months. Approximately 68·7–76·1 % of all SA in human milk were bound to oligosaccharides. Two types of SA, Neu5Ac and Neu5Gc, have been detected in infant formulas. Most SA was present in infant formulas combined with protein. Breastfed infants could receive more SA than formula-fed infants with the same energy intake. Overall, human milk is a preferable source of SA than infant formulas in terms of total SA content, dynamics, distribution and type. These SA profiles in the natural state are worth to be considered by the production of formulas because they may have a great effect on infant nutrition and development.

In preparation for an experiment with a laser-generated intense proton beam at the Laser Fusion Research Center at Mianyang to investigate the 11B(p,α)2α reaction, we performed a measurement at very low proton energy between 140 keV and 172 keV using the high-voltage platform at the Institute of Modern Physics, Lanzhou. The aim of the experiment was to test the ability to use CR-39 track detectors for cross-section measurements and to remeasure the cross-section of this reaction close to the first resonance using the thick target approach. We obtained the cross-section σ = 45.6 ± 12.5 mb near 156 keV. Our result confirms the feasibility of CR-39 type track detector for nuclear reaction measurement also in low-energy regions.

Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$-valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$. The main aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$, we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$, giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$, and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras.

There exists insufficient eye-tracking evidence on the differences in emotional word processing between the first language (L1) and second language (L2) readers. This study conducted an eye-tracking experiment to investigate the emotional effects in L2 sentence reading, and to explore the modulation of L2 proficiency and individual emotional states. Adapted from Knickerbocker et al. (2015), the current study recorded eye movements at both early and late processing stages when late Chinese–English bilinguals read emotion-label and neutral target words in natural L2 sentences. Results indicated that L2 readers did not show the facilitation effects of lexical affective connotations during sentence reading, and they even demonstrated processing disadvantages for L2 emotional words. Additionally, the interaction effect between L2 proficiency and emotion was consistently significant for the measure of total reading time in positive words. Measurements of participants’ depressive and anxious states were not robustly correlated with eye movement measures. Our findings supplemented new evidence to existing sparse eye-tracking experiments on L2 emotion processing, and lent support to several theoretical frameworks in the bilingual research field, including the Emotional Contexts of Learning Theory, Lexical Quality Hypothesis and Revised Hierarchical Model.

Submerged vegetation plays a subtle role in exchanging the fluid mass and energy in the vegetated flow zone, where the swaying motions of flexible plants are the important source of turbulent kinetic energy production. Flume experiments were conducted to study the modes, characteristics and factors of swaying of individual submerged flexible plants. A modified plant model in a new form, representing the highly flexible vegetation with clustered leaves, was employed. A ‘rigid-like’ synchronous swaying mode and a ‘whip-like’ asynchronous flapping mode are found to appear alternately for the individual plants. The interaction between these modes depends on the resulting local flow structure affected by the plants. Compared with a plant in isolation with the same flow Reynolds number, the swaying motions of a plant within the vegetation patch are less frequent but more prone to the synchronous mode. The eigen frequency of the motions increases linearly with an increase in flow Reynolds number in the range of 2 × 104–5 × 104, but the normalised amplitude reaches a saturation at a high flow Reynolds number. Moreover, the in-line and spanwise motions have a 2 : 1 frequency ratio for an ‘8’ shaped trajectory on the horizontal plane and a 1 : 1 ratio for a ‘0’ shaped circular trajectory, or a combination of both.