Search

In this paper, we study a family of planar piecewise linear systems with saddles separated by two parallel lines, and mainly investigate the existence of four-intersection-point limit cycles. We provide complete conclusions on the existence of a special four-intersection-point limit cycle and a heteroclinic loop. And, based on these results, we give some sufficient conditions for the existence of general four-intersection-point limit cycles. Some examples are given to illustrate the main results.

In this research, we tentatively assign the $T_{c\bar{s}}(2900)$ as the $A\bar{A}$-type tetraquark state, and study the mass spectrum of the tetraquark states with strange and doubly strange, which have the spin-parity $J^P = 0^+$, $1^+$ and $2^+$, in the framework of the QCD sum rules in details, where the $A$ denotes the axialvector diquark state. The predicted mass $M=2.92\pm0.12\,\rm{GeV}$ is in consistent with the experimental values $M=2.892\pm0.014\pm0.015\,\rm{GeV}$ and $2.921\pm0.017\pm0.020\,\rm{GeV}$ from the LHCb collaboration and supports assigning the $T_{c\bar{s}}(2900)$ to be the $A\bar{A}$-type scalar $c\bar{s}q\bar{q}$ tetraquark state. The predictions for other tetraquark states can be confronted to the experimental data in the future to diagnose the nature of the fully open flavor exotic states., Comment: 20 pages, 7 figures

Even if a system has only one stable equilibrium point, its dynamics can still be complicated. In the case of the equilibrium point with a complicated boundary of the attraction basin, it is probably difficult to predict the long-term behavior of the trajectory starting from a point outside but near the boundary. The exploration of such systems is helpful for deepening our understanding of the dynamics of complex systems. This paper studies a class of three-dimensional polynomial systems with a nonelementary singularity. With parameters satisfying some conditions, the asymptotic stability of the origin is proved and the complexity of the attraction basin is investigated. It is demonstrated that the boundary of the attraction basin of the origin has a fractal structure in the following sense: An invariant set homeomorphic to the well-known Lorenz strange attractor is contained in the basin boundary. Based on the non-negative function we constructed, how fast a trajectory of the system tends to the asymptotically stable nonelementary singularity is measured.

Modulational collapse of a wave pulse in a complex nonlinear plasma described by a complex nonlinear Schrodinger equation (CNSE) including the effects of viscous heating and nonlinear damping, and the adjusting by an external potential are investigated. Theoretical and numerical results reveal that the original pulse first suffers modulational instability, the growth rate of the modulational instability increases with the increase of viscous heating, but it is not sensitive to the nonlinear damping. The instability induces the self-similar collapsing, then the fields rapidly transform into a turbulent state with short-wavelength modes. The results are explained in terms of the evolution of the total energy, which can become invariant during the evolution even though the system is nonconservative. The external potential can delay the self-defocusing process of the pulse. Those results can apply to the phenomena described by the CNSE.

To investigate the alterations in body movement and their compensatory characteristics under different spinal diseases through an objective and quantitative analysis of the spinal-pelvic-lower limb motor function.A total of 120 subjects were recruited from October 2016 to April 2017. The patients were classified into 2 groups in which 65 patients with cervical spondylotic myelopathy (CSM) and 25 patients with idiopathic scoliosis (IS). The former group was evaluated with JOA score while those in the IS group underwent Lenke classification. A control group was set up with 30 healthy subjects. All the subjects were instructed to walk at a constant speed for one minute on a treadmill, and their spinal-pelvic-lower limb motions were monitored simultaneously with a DIERS Formetric 4D® grating system and a QUINTIC gait analysis system.The rotation angle of thoracic and lumbar vertebrae in IS group were larger than those in the control group (P 0.05), and the knee joint angle A in the CSM group and IS group were larger than the control group (P 0.05). In the CSM group, the knee joint angular velocity and angular acceleration were both greater than the control group (P 0.05). And there was a negative linear correlation between the JOA score for the lower extremity of CSM patients and their knee joint angular acceleration.IS patients tend to demonstrate increased swing amplitude of the trunk. Those with CSM will also have larger knee joint angular velocity and angular acceleration.

The relativistic effects on nonstationary Karpman–Washimi ponderomotive magnetization are investigated in relativistic electron plasmas. The magnetization M p and radiation power [Formula: see text] are obtained as functions of the relativistic parameter α, scaled wave frequency [Formula: see text], and wave number [Formula: see text]. It is shown that the ponderomotive force is more likely to induce a low-frequency and small-scale magnetic field. In addition, the results indicate that the magnetization and radiation power are suppressed by the relativistic effects in the ultrarelativistic case but enhanced in the moderately and weakly relativistic cases, especially in the moderately relativistic regime.

We present in this paper a detailed study on the Markus–Yamabe conjecture in planar piecewise linear systems. We consider discontinuous piecewise linear systems with two zones separated by a straight line, in which every subsystem is asymptotically stable. We prove the existence of limit cycles under explicit parameter conditions and give more different counterexamples to the Markus-Yamabe conjecture in addition to the counterexamples given by Llibre and Menezes. In particular, we consider continuous planar piecewise linear systems. For such a system with n + 1 zones separated by n parallel straight lines in phase space, we prove that if each of subsystems is asymptotically stable, then this system has a globally asymptotically stable equilibrium point, therefore the Markus–Yamabe conjecture still holds. Some examples are given to illustrate the main results.Mathematics Subject Classification (2020) 34C05 · 34C07 · 37G15

Purpose MicroRNAs (miRNAs) have been reported to play pivotal role in drugs-induced cardiotoxicity act as biomarkes, diagnostic tools and endogenous repressors of gene expression by lowering mRNA stability and interfering with mRNA translation. However, the effect of miRNAs on doxorubicin-induced cardiotoxicity still not clear. In the present study, we identified several key candidate miRNAs involving doxorubicin (DOX)-induced cardiotoxicity in rat myocardial tissues and adult rat cardiomyocytes from the Gene Expression Omnibus (GEO) database via integrated bioinformatics analysis, and the possible effect of miR-143 in the protection of DOX-induced cardiotoxicity by phosphocreatine was subsequently investigated in vivo and in vitro. Methods GSE36239 miRNA expression profiles of DOX-induced cardiotoxicity in rat myocardial tissues and adult rat cardiomyocytes (ARC) were extracted fromGEO datasets. |log2FC| > 1 and P < 0.05 were set as screening criteria, miRNAs expressed in myocardial tissues or ARC were selected as different expression miRNA (DEMs), and subsequently the key miRNAs were obtained from candidate DEMs between myocardial tissues and ARC with Venny 2.1 software. Target genes of miR-143 were predicted with Targetscan and miRBase in the species of homo sapiens, and candidate genes were obtained with Venny 2.1. The gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes pathway (KEGG) enrichment analyses were carried out. Final, the expression and potential role of miR-143 were verified in DOX-induced cardiotoxicity of rat and cardiomyocytes H9c2. Results A total 24 DEMs were captured , including 15 up-regulated and 9 down-regulated genes in rat myocardial tissues and 42 DEMs were discovered, including 13 up-regulated and 29 down-regulated in ARC. Ultimately, 6 DEMs were determined in rat myocardial tissues and ARC by venny 2.1 software. 46 target genes of miR-143, one of the 6 DEMs, were captured from the predict results of Targetscan and miRBase with venny 2.1. The target genes were notably enriched in biological processes (BP) such as cell proliferation and migration. KEGG pathway analysis showed the target genes were enriched in HIF-1 and PI3K-Akt signaling pathway, which closely related to the oxidative stress and cardiomyocytes apoptosis. Further, western blot and RT-PCR results showed DOX-induced oxidative stress down-regulated the expression of miR-143 and Nrf2, SOD and BCL2, and up-regulated Bax and Cleaved caspase 3, while they could been reversed by the intervention of phosphocreatine (PCr) or N-acetyl-L-cystine (NAC) in DOX-induced cardiotoxicity in vivo and in vitro.Conclusion Our data showed that DOX-induced oxidative stress could decrease the expression of miR-143, promote apoptosis of cardiomyocytes, while PCr or NAC mediated antioxidation could reverse the expression down-regulation of miR-143, alleviated apoptosis in DOX-induced cardiotoxicity. Our findings elucidated the regulatory network involving miR-143 in DOX-induced cardiotoxicity, and might unveiled a potential biomarker and molecular mechanisms, which could be helpful to the diagnosis and treatment of DOX-induced cardiotoxicity.

This paper presents a qualitative analysis of discontinuous Llibre-Menezes piecewise linear systems. We obtain the explicit parameter conditions for the existence of limit cycles and the stable sliding segments. In addition, we prove that if a Llibre-Menezes piecewise system is continuous, then this system has a global asymptotically stable equilibrium point. Some examples are given to illustrate the main results.

This paper presents a stylized construction of an economy with price dynamics described in tâtonnement process. Based on the well-known SMD theorem, it is shown that this model exhibits the same dynamical behavior as the famous Lorenz-type chaotic attractor.

In this work, we construct the color-singlet-color-singlet type four-quark currents to investigate the [Formula: see text] and [Formula: see text] tetraquark molecular states with the [Formula: see text] and [Formula: see text] via the QCD sum rules and obtain satisfactory results. We can search for the [Formula: see text] and [Formula: see text] tetraquark molecular states with the [Formula: see text] and [Formula: see text] at the BESIII and Belle II in the future.

Curcumin possesses medicinal properties that are beneficial in various diseases, such as heart disease, cancer, and type 2 diabetes mellitus (T2 DM). It has been proposed that pancreatic beta cell dysfunction in T2 DM is promoted by oxidative stress caused by NADPH oxidase over-activity. The aim of the present study was to evaluate the efficacy of curcumin as a protective agent against high glucose/palmitate (HP)-induced islet cell damage and in streptozotocin (STZ)-induced DM rats. INS-1 cells were exposed to HP with or without curcumin. Cell proliferation, islet cell morphological changes, reactive oxygen species production, superoxide dismutase and catalase activity, insulin levels, NADPH oxidase subunit expression, and the expression of apoptotic factors by INS-1 cells were observed. Our results show that curcumin can effectively inhibit the impairment of cell proliferation and activated oxidative stress, increase insulin levels, and reduce the high expression of NADPH oxidase subunits and apoptotic factors induced by HP in INS-1 cells. The STZ-induced DM rat model was also used to determine whether curcumin can protect islets in vivo. Our results show that curcumin significantly reduced pathological damage and increased insulin levels of islets in STZ-induced DM rats. Curcumin also successfully inhibited the high expression of NADPH oxidase subunits and apoptotic factors in STZ-induced DM rats. These results suggest that curcumin is able to attenuate HP-induced oxidative stress in islet cells and protect these cells from apoptosis by modulating the NADPH pathway. In view of its efficiency, curcumin has potential for translation applications in protecting islets from glucolipotoxicity.

A series of p-tert-butyldihomooxacalix[4]arenes bearing phenolic hydroxyls and thiourea moieties were prepared to investigate their anion binding behavior. These compounds showed F− binding according to 1H NMR titration experiments. Among them, dihomooxacalix[4]arenes bearing phenyl and benzyl thiourea (2a and 2b) showed multiple interactions with added F−, including N–H⋯F, O–H⋯F hydrogen bonds and “through-space” C–H⋯F− interactions between F− and the attached aromatic segment of thiourea. A conformational change of the dihomooxacalix[4]arene cavity was observed as well and proved by theoretical calculations. The dihomooxacalix[4]arene bearing methyl thiourea (2c) also showed the formation of N–H⋯F, O–H⋯F hydrogen bonds, but less conformational change of the dihomooxacalix[4]arene cavity according to 1H NMR titration results. The bis-dihomooxacalix[4]arene (3) showed clear N–H⋯F hydrogen bond formation upon addition of F− as characterized by 1H NMR spectroscopy.

Gnaphalium affine D. Don is an important Traditional Chinese herbal Medicine (TCM) used to treat hyperuricemia, asthma, rheumatic arthritis, antitussive, expectorant and cardiovascular in folk medicine because of anti-inflammatory and anti-oxidant activity. The aim of this study was to investigate the potential beneficial effect of G. affine extract (GAE) on hydrogen peroxide (HThe ingredients of GAE were isolated and tentatively identified by HPLC-ESI-Q-Qribatrip-MS/MS. The cardioprotective and anti-oxidant effects of GAE were evaluated in the experimental model with HFirstly, seventeen polyphenols and flavonoids compounds with the characteristics of anti-inflammatory and anti-oxidant in GAE were tentatively identified by HPLC-ESI-Q-Qribatrip-MS/MS. In the experimental model, GAE not only significantly improved cells viability, but also showed anti-oxidant effects through improving SOD activity, up-regulating nuclear factor E2-related factor 2 (Nrf2), and decreasing intracellular concentration of ROS and MDA and the proteins expression of p47Our data suggested that GAE showed strong anti-oxidant effect to ameliorate oxidative stress and attenuate apoptosis induced by H

The dust-induced instability involving charge fluctuations is studied in rotating dusty plasma. Due to dust charging dynamics, the dust-induced instability mode which was first put forward by Mikhailovskii et al. [A.B. Mikhailovskii, S.V. Vladimirov, J.G. Lominadze, V.S. Tsypin, A.P. Churikov, N.N. Erokhin, R.M.O. Galvao, Phys. Plasmas 15, 014504 (2008)] will be replaced by dust-charging-rotational instability (DCRI) mode. Comparing to the dust-induced instability, the new instability mode also exists in an increasing rotation frequency profile, but always with a greater growth rate. The analysis indicates that the rotational instability mode induced by dust charge is always unstable. The present results may be used to investigate the rotating dusty plasma experiments and observations.

In this paper, we analyze the qualitative behavior of the solution of the Nose–Hoover oscillator which is a three-dimensional quadratic polynomial system. We show that every invariant set of the Nose–Hoover oscillator is neither in the region of $$z>0$$ nor in the region of $$z

In this paper, we prove the existence of \begin{document}$ \omega $\end{document}-limit set for a modified Nosé-Hoover oscillator. We also prove the existence of either an invariant torus or a stable periodic orbit of the oscillator. In addition, we show by numerical simulations the co-existence of both \begin{document}$ \alpha $\end{document}- and \begin{document}$ \omega $\end{document}-limit sets of various types of periodic orbits, invariant tori, and chaotic attractors.

In this study, the generalized Nose–Hoover oscillator is analyzed rigorously. We show that all trajectories not belonging to the two one-dimensional invariant manifolds (one is a straight line and the other is a unit circle) must traverse a two-dimensional unit disk infinitely many times transversally along the same direction in the state space. Consequently, all of the trajectories not located in the straight line invariant manifold have at least one ω-limiting point.

In this paper, we investigate a class of three-dimensional piecewise affine systems with the matrix in each subsystem processing a pair of complex eigenvalues and a real eigenvalue. Furthermore, we obtain some sufficient and necessary conditions for the existence of homoclinic orbits under suitable assumptions. Finally, some concrete examples are presented to illustrate our results.

This paper investigates the existence and stability of periodic orbits in a class of 3-dimensional piecewise affine systems with two zones. Two results on the existence of periodic orbits are obtained by applying some fixed points theorems to a Poincare map. Precisely, we prove the existence of a periodic sink in one case and a periodic saddle in another case. Finally, some concrete examples are given to illustrate the main results.

Based on the mathematical analysis of the stable manifolds, unstable manifolds and solutions of subsystems, this paper provides methodologies to ensure the existence of homoclinic orbits (degenerate and non-degenerate) which cross the switching manifold transversally at two points in n -dimensional two-zone piecewise affine systems. In addition, two examples are provided to illustrate the effectiveness of the methods, moreover, the simulation results of homoclinic orbits and chaotic invariant sets are provided for the two examples.

For general three-dimensional piecewise linear systems, some explicit sufficient conditions are achieved for the existence of a heteroclinic loop connecting a saddle-focus and a saddle with purely real eigenvalues. Furthermore, certain sufficient conditions are obtained for the existence and number of periodic orbits induced by the heteroclinic bifurcation, through close analysis of the fixed points of the parameterized Poincare map constructed along the hereroclinic loop. It turns out that the number can be zero, one, finite number or countable infinity, as the case may be. Some sufficient conditions are also acquired that guarantee these periodic orbits to be periodic sinks or periodic saddle orbits, respectively, and the main results are illustrated lastly by some examples.

Myocardial apoptosis and necroptosis are the major etiological factor during doxorubicin (DOX) induced cardiotoxicity, and one of the important reasons that limit the drug’s clinical application. Up to date, its mechanism has not been fully elucidated. The protective role of phosphocreatine (PCr) in heart surgery and medical cardiology has been observed in numerous clinical trials. This study aimed to evaluate cardioprotective actions of PCr against DOX-induced cardiotoxicity and investigate the underlying mechanism involving in transforming growth factor β-activated kinase 1 (TAK1) mediated myocardial survive signaling pathway. Male Sprague-Dawleyrats were intraperitoneally (ip) injected with normal saline (NS) or DOX (2 mg/kg) alone or DOX with PCr (200 mg/kg) used as animal model. The data showed that DOX significantly impaired cardiac function and structure, induced oxidative stress, myocardial apoptosis and necroptosis, and dramatically down-regulated the expression level of TAK1, while the intervention of PCr obviously attenuated cardiac dysfunction, oxidative stress, myocardial apoptosis and necroptosis, especially alleviated the decrease of TAK1 expression. In vitro analysis, after H9c2 cells were pretreated with or without PCr (0.5 mM) or N-Acetyl-L-cysteine (NAC, 0.5 mM) or 5Z-7-oxozeaenol (5z-7-Ox, 1 μM) for 1 h, subsequently treated with DOX (1 μM) for 24 h. The results revealed that inhibition of TAK1 further deteriorated apoptotic and necroptotic cell death induced by DOX in H9c2 cells, but didn’t affect oxidative stress. While the pretreatment of PCr or NAC enhanced antioxidant activity to reduce oxidative stress, significantly alleviated apoptotic and necroptotic cell death induced by DOX in H9c2 cells. Consistent with the results in vivo, PCr or NAC significantly inhibited the decrease of TAK1 expression induced by DOX. In conclusion, oxidative stress induced by DOX inhibits the expression of TAK1, and leads to myocardial apoptotic and necroptotic death, while the intervention of PCr increases antioxidant activity to alleviate oxidative stress, which in turn activates TAK1 signaling pathway to promote myocardial survival, and finally attenuate DOX-induced cardiotoxicity.

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

Since complicated dynamical behavior can occur easily near homoclinic trajectory or heteroclinic cycle in dynamical systems with dimension not less than three, this paper investigates the existence of heteroclinic cycles in some class of 3-dimensional three-zone piecewise affine systems with two switching planes. Based on the exact determination of the stable manifold, unstable manifold and analytic solution, a rigorous analytic methodology of designing chaos generators is proposed, which may be of potential applications to chaos secure communication. Furthermore, we obtain three sufficient conditions for the existence of a single or two heteroclinic cycles in three different cases. Finally, some examples are given to illustrate our theoretical results.

Cardiac fibrosis is considered the initial change of diabetic cardiomyopathy (DCM). We have shown that curcumin alleviates collagen deposition in DCM, but the mechanism remains unknown. In this study we sought to investigate the effects of curcumin on cardiac fibrosis in vivo and in vitro and to elucidate the underlying mechanisms. Experimental diabetes was induced in rats by injection of low-dose streptozotocin (STZ) combined with high energy diet. The rats were orally treated with curcumin (300 mg·kg−1·d−1) for 16 weeks. Curcumin administration significantly suppressed the deposition of type I and type III collagens in the heart tissues of diabetic rats, accompanied by markedly reduced TGF-β1 production, suppressed TβR II levels and Smad2/3 phosphorylation, and increased Smad7 expression. Similar effects were observed in human cardiac fibroblasts exposed to high glucose (HG, 30 mmol/L) or exogenous TGF-β1 (5 ng/mL). Furthermore, TGF-β1 or HG treatment significantly increased the phosphorylation levels of AMPK and p38 MAPK in the fibroblasts. Application of curcumin (25 μmol/L) inhibited TGF-β1- or HG-induced AMPK/p38 MAPK activation and suppressed collagen synthesis in the fibroblasts. These effects were similar to those of the AMPK inhibitor compound C (10 μmol/L) but opposite to the effects of the AMPK activator metformin (2 mmol/L) in the fibroblasts. Our results demonstrate that curcumin suppresses diabetes-associated collagen synthesis in rat myocardium not only by inhibiting TGF-β1 production and canonical Smad signaling but also by blocking the non-canonical AMPK/p38 MAPK pathway.

It is well known that homoclinic and heteroclinic cycles can potentially result in chaos in dynamical systems. However, it is not easy to find the homoclinic or heteroclinic cycles in concrete systems. Therefore, how to prove the existence of homoclinic and heteroclinic cycles is an important problem in modern dynamical systems. In this paper, for a class of 3-dimensional piecewise affine systems we present succinct sufficient conditions for the existence of three types of heteroclinic cycles by mathematical analysis. As applications, two existence results of chaotic invariant sets are obtained. In addition, some examples are presented to illustrate our results.