ON THE EXISTENCE AND UNIQUENESS OF A LIMIT CYCLE FOR A LIENARD SYSTEM WITH A DISCONTINUITY LINE

In this paper, we investigate the existence and uniqueness of crossing limit cycle for a planar nonlinear Lienard system which is discontinuous along a straight line (called a discontinuity line). By using the Poincare mapping method and some analysis techniques, a criterion for the existence, uniqueness and stability of a crossing limit cycle in the discontinuous differential system is established. An application to Schnakenberg model of an autocatalytic chemical reaction is given to illustrate the effectiveness of our result. We also consider a class of discontinuous piecewise linear differential systems and give a necessary condition of the existence of crossing limit cycle, which can be used to prove the non-existence of crossing limit cycle

ANALYSIS ON CONSTRUCTION DEFORMATION AND SUPPORTING STRUCTURE OF TWO-STEP AND THREESECTION EXCAVATION METHOD FOR SUPER LARGER SPAN HIGHWAY TUNNEL

The super larger span tunnel is a common form of highway reconstruction and expansionprojects in recent years. In order to determine the stability of tunnel structure of the two-step andthree-section excavation method of the III-level surrounding rock mass of the super larger spanhighway, the field test method was adopted. Relying on the Laohushan Tunnel in Jinan, Shandong,China, the deformation and the structure performance of the super larger span tunnel in III-levelsurrounding rock mass are analyzed, and the safety of the tunnel and the support structure isevaluated on this basis. The results show that the maximum settlement of the arch section of theGrade III surrounding rock section is 12.5mm, and the maximum clearance convergence is 5.8mm.Both of them are much smaller than the design reserved deformation of 80mm. The maximumpressure of the surrounding rock is 0.091MPa, showing that the force acting on the supportingstructure by surrounding rock mass is small. The inner and outer arched parts of the steel frameare subject to large stresses, and most of them are tensile stresses. The maximum stress of thesteel frame is 283 MPa, and occurs at the inner side of right arch waist. Although the local stressexceeds the yield strength of the steel (235 MPa), it does not exceed its ultimate compressivestrength of 400 MPa, and the tensile and compressive stress values of the other inner and outerparts do not exceed the yield strength. Mainly, the maximum stress appears on the left side wall,reaching 4.83 MPa, which is far less than the ultimate compressive strength of sprayed concrete(11.9 MPa). For super larger span highway tunnels, located in III-level surrounding rock mass,constructed by two-step and three-section excavation method, the initial support effectivelycontrolled the tunnel deformation, the supporting structures were fully protected and the tunnelstructure was stable. The super larger span tunnel is a common form in the road reconstructionand expansion project in recent years. In order to determine the stability of tunnel structure of thetwo steps and three excavation method of the III-level surrounding rock mass of the super largerspan highway, the field test method was adopted. Relying on the Laohushan Tunnel, thedeformation and the structure performance of the super larger span tunnel in III-level surroundingrock mass were analyzed. The results show that the maximum settlement of arch of the III-levelsurrounding rock mass is 12.5mm in super larger span highway tunnel, and the maximumclearance convergence is 5.8mm. Both of them are smaller than the design reserved deformationof 80mm. The maximum surrounding rock mass pressure is 0.091MPa, the force acting on thesupporting structure by surrounding rock mass are small. The inner and outer arched parts of the steel frame bear larger stress, and are mostly tensile stress. The maximum stress on inner side ofthe steel frame is 283 MPa, and occurs at the right arch waist. The maximum stress on the outerside of the steel frame is184 MPa, and occurs at the vault. The steel frame plays an important rolein the initial support, however the force does not reach the yield strength of the steel. The shotcreteis subjected to pressure, the maximum stress appears on the left side wall is 4.83 MPa, which ismuch smaller than the ultimate compressive strength of shotcrete of 25 MPa. So for super largerspan highway tunnels, located in III-level surrounding rock mass, constructed by two-step andthree-excavation method, the whole structure is stable

An upper bound for the amplitude of limit cycles of Liénard-type differential systems

In this paper, we investigate the position problem of limit cycles for a class of Liénard-type differential systems. By considering the upper bound of the amplitude of limit cycles on $\{(x,y)\in\mathbb{R}^2: x0\}$ respectively, we provide a criterion concerning an explicit upper bound for the amplitude of the unique limit cycle of the Liénard-type system on the plane. Here the amplitude of a limit cycle on $\{(x,y)\in\mathbb{R}^2: x0\}$) is defined as the minimum (resp. maximum) value of the $x$-coordinate on such a limit cycle. Finally, we give two examples including an application to predator-prey system model to illustrate the obtained theoretical result, and Matlab simulations are presented to show the agreement between our theoretical result with the simulation analysis

1-(2-Nitro­phen­yl)-3-phenyl­thio­urea

The title compound, C13H11N3O2S, was prepared by reaction of 2-nitro­benzenamine, KOH and 1-isothio­cyanato­benzene in an ethanol solution at room temperature. The dihedral angles formed between the thiourea plane and the phenyl rings are 61.9 and 31.0°. The dihedral angle between the two phenyl rings is 78.1°. In the crystal structure, there are weak inter­molecular N—H⋯S and C—H⋯S hydrogen-bonding inter­actions

On the definition of noise

Urbanization has exposed people to extreme sound levels. Although researchers have investigated the ability of people to listen, analyze, and distinguish sound, the concept of noise has not been clearly articulated from a human perspective. The lack of knowledge on how people perceive noise limits our capacity to control it in a targeted manner. This study aimed to interpret the definition of noise from the public perspective based on a grounded theory approach. Seventy-eight participants were interviewed about noise, and four categories of perceived understanding of noise were identified: challenges, definitions of noise, opportunities, and action. As one of the challenges, urbanization is associated with increased noise levels around the human environment. In terms of definition, perceiving sound as noise is considered to be a result of the complex and dynamic process that includes sound, the environment, and humans. Sound and humans interact with the environment. In terms of opportunities, noise may have positive roles on certain occasions, dispelling the misconception that noise is exclusively negative. In addition, we found that noise perception has gradually shifted from noise control to noise utilization. In terms of action, noise can be controlled at the sound sources, susceptible target groups, susceptible behaviors and states, locations, and times where noise is perceived with high frequency. In this study, we investigated several aspects of noise, ranging from noise control, soundscape definition, and ‘soundscape indices’ (SSID) integration and application. Our findings provide an additional basis for developing better definitions, control, and utilization strategies of noise in the future, thereby improving the quality of the sound environment

Consumption of Oxidized Soybean Oil Increased Intestinal Oxidative Stress and Affected Intestinal Immune Variables in Yellow-feathered Broilers

This study investigated the effect of oxidized soybean oil in the diet of young chickens on growth performance and intestinal oxidative stress, and indices of intestinal immune function. Corn-soybean-based diets containing 2% mixtures of fresh and oxidized soybean oil provided 6 levels (0.15, 1.01, 3.14, 4.95, 7.05, and 8.97 meqO2/kg) of peroxide value (POV) in the diets. Each dietary treatment, fed for 22 d, had 6 replicates, each containing 30 birds (n = 1,080). Increasing POV levels reduced average daily feed intake (ADFI) of the broilers during d 1 to 10, body weight and average daily gain at d 22 but did not affect overall ADFI. Concentrations of malondialdehyde (MDA) increased in plasma and jejunum as POV increased but total antioxidative capacity (T-AOC) declined in plasma and jejunum. Catalase (CAT) activity declined in plasma and jejunum as did plasma glutathione S-transferase (GST). Effects were apparent at POV exceeding 3.14 meqO2/kg for early ADFI and MDA in jejunum, and POV exceeding 1.01 meqO2/kg for CAT in plasma and jejunum, GST in plasma and T-AOC in jejunum. Relative jejunal abundance of nuclear factor kappa B (NF-κB) P50 and NF-κB P65 increased as dietary POV increased. Increasing POV levels reduced the jejunal concentrations of secretory immunoglobulin A and cluster of differentiation (CD) 4 and CD8 molecules with differences from controls apparent at dietary POV of 3.14 to 4.95 meqO2/kg. These findings indicated that growth performance, feed intake, and the local immune system of the small intestine were compromised by oxidative stress when young broilers were fed moderately oxidized soybean oil

Preeclampsia in pregnant women with polycystic ovary syndrome: risk factor analysis based on a retrospective cohort study

Objectives: To compare the clinical characteristics of pregnant women with polycystic ovary syndrome (PCOS) and perinatal outcomes with or without preeclampsia (PE) and to factors that are potentially associated with the onset of PE. Material and methods: This was a retrospective study of pregnant women diagnosed with PCOS from January 2017 to December 2021. Eligible patients were divided into two groups based on the presence or absence of preeclampsia: a PE group and a non-PE group. Demographics, clinical characteristics, maternal and perinatal outcomes, and potential factors linked to disease recurrence were analyzed. Results: In total, 616 patients were enrolled and respectively classified into the PE group (n = 51) and the non-PE group (n = 565). The incidence of PE in pregnant women with PCOS was 8.28%; this was significantly higher than that in non-PCOS pregnant women (3.22%, p < 0.001). Logistic regression analysis of the predictive factors for PE in women with PCOS revealed that the combination of maternal hyperandrogenism, a pre-pregnancy BMI ≥ 24 kg/m2, and a family history of cardiovascular disease (CVD) and assisted reproductive techniques (ART) exhibited the steepest receiver-operating characteristic (ROC) curve value at 0.797 [95% confidence interval (CI): 0.733–0.862]. Conclusions: Patients with PCOS have a higher incidence of PE. We identified a series of significant and independent factors associated with PE in PCOS: maternal hyperandrogenism, a pre-pregnancy BMI ≥ 24 kg/m2, and a family history of CVD and ART