The number of limit cycles of Josephson equation

In this paper, the existence and number of non-contractible limit cycles of the Josephson equation $\beta \frac{d^{2}\Phi}{dt^{2}}+(1+\gamma \cos \Phi)\frac{d\Phi}{dt}+\sin \Phi=\alpha$ are studied, where $\phi\in \mathbb S^{1}$ and $(\alpha,\beta,\gamma)\in \mathbb R^{3}$. Concretely, by using some appropriate transformations, we prove that such type of limit cycles are changed to limit cycles of some Abel equation. By developing the methods on limit cycles of Abel equation, we prove that there are at most two non-contractible limit cycles, and the upper bound is sharp. At last, combining with the results of the paper (Chen and Tang, J. Differential Equations, 2020), we show that the sum of the number of contractible and non-contractible limit cycles of the Josephson equation is also at most two, and give the possible configurations of limit cycles when two limit cycles appear.Comment: 25 pages, 15 figure

Maximum number of limit cycles for Abel equation having coefficients with linear trigonometric functions

This paper devotes to the study of the classical Abel equation $\frac{dx}{dt}=g(t)x^{3}+f(t)x^{2}$, where $g(t)$ and $f(t)$ are trigonometric polynomials of degree $m\geq1$. We are interested in the problem that whether there is a uniform upper bound for the number of limit cycles of the equation with respect to $m$, which is known as the famous Smale-Pugh problem. In this work we generalize an idea from the recent paper (Yu, Chen and Liu, arXiv:$2304.13528$, $2023$) and give a new criterion to estimate the maximum multiplicity of limit cycles of the above Abel equations. By virtue of this criterion and the previous results given by {\'A}lvarez et al. and Bravo et al., we completely solve the simplest case of the Smale-Pugh problem, i.e., the case when $g(t)$ and $f(t)$ are linear trigonometric, and obtain that the maximum number of limit cycles, is three.Comment: 16 pages, 8 figure

Research on modeling and optimization simulation analysis of micro electric vehicle suspension

Suspension system is one of the key parts of vehicle, the performance of suspension system has great influence on vehicle handling stability and safety. In order to improve the performance of suspension system, the Macpherson suspension of a vehicle is taken as the research object, the suspension model is established by ADAMS/Car, and carried out parallel wheel travel simulation to analyze the key parameters variation of camber angle, toe angle, caster angle, kingpin inclination angle and scrub radius. Simulation results show that camber angle and scrub radius are beyond normal design range and require optimization. Wheel alignment parameters are determined by sensitivity analysis, and optimized by ADAMS/Insight. Then carried out simulation to analyze the performance of optimized suspension system. Results show that optimized suspension system satisfies the requirements of vehicle stability and safety

Effects of replacing wheat bran with palm kernel cake or fermented palm kernel cake on the growth performance, intestinal microbiota and intestinal health of tilapia (GIFT, Oreochromis niloticus)

A nine-week feeding trial was conducted to evaluate the effects of replacing wheat bran (WB) with palm kernel cake (PKC) or fermented palm kernel cake (FPKC) on the growth performance, intestinal microbiota and intestinal health of genetically improved farmed tilapia (GIFT, Oreochromis niloticus) (initial weight 7.00 ± 0.01 g). Eleven isonitrogenous and isolipidic experimental diets were formulated by replacing 0, 20, 40, 60, 80, and 100% of dietary WB with PKC or FPKC. Replacement of WB with PKC concentrations up to 80% had no significant effect on the growth rate of tilapia or feed utilisation (p > 0.05). FPKC improved the growth performance of tilapia, with optimum growth achieved at 40% replacement level (p < 0.05). Complete replacement with PKC significantly decreased the activity of lipase and trypsin, and reduced the height of muscularis and the height of villus (p < 0.05). However, FPKC significantly increased amylase activity and villus height (p < 0.05). The apparent digestibility of dry matter and energy decreased linearly with increasing levels of PKC substitution, while FPKC showed the opposite trend (p < 0.05). PKC replacement of WB by 20% significantly reduced serum diamine oxidase activity and endothelin levels and increased intestinal tight junctions (p < 0.05). However, FPKC significantly decreased diamine oxidase activity and increased intestinal tight junctions (p < 0.05). PKC completely replaced WB, up-regulating the expression of pro-inflammatory factors (il-1β) (p < 0.05). When 40% of WB was replaced with FPKC, the expression of pro-inflammatory factors (il-1β and il-6) was decreased significantly (p < 0.05). Completely replacement of WB with PKC reduced the abundance of Firmicutes and Chloroflexi, while FPKC reduced the abundance of Fusobacteriota and increased the levels of Actinobacteriota. WB can be replaced with PKC up to 80% in tilapia feeds. However, the high percentage of gluten induced intestinal inflammation, impaired gut health, and reduced dietary nutrient utilisation and growth performance. Complete replacement of WB with FPKC promoted intestinal immunity. It also improved dietary nutrient utilisation and growth performance. However, the optimal growth was achieved at a 40% replacement level

YY1 directly interacts with myocardin to repress the triad myocardin/SRF/CArG box-mediated smooth muscle gene transcription during smooth muscle phenotypic modulation

Yin Yang 1 (YY1) regulates gene transcription in a variety of biological processes. In this study, we aim to determine the role of YY1 in vascular smooth muscle cell (VSMC) phenotypic modulation both in vivo and in vitro. Here we show that vascular injury in rodent carotid arteries induces YY1 expression along with reduced expression of smooth muscle differentiation markers in the carotids. Consistent with this finding, YY1 expression is induced in differentiated VSMCs in response to serum stimulation. To determine the underlying molecular mechanisms, we found that YY1 suppresses the transcription of CArG box-dependent SMC-specific genes including SM22α, SMα-actin and SMMHC. Interestingly, YY1 suppresses the transcriptional activity of the SM22α promoter by hindering the binding of serum response factor (SRF) to the proximal CArG box. YY1 also suppresses the transcription and the transactivation of myocardin (MYOCD), a master regulator for SMC-specific gene transcription by binding to SRF to form the MYOCD/SRF/CArG box triad (known as the ternary complex). Mechanistically, YY1 directly interacts with MYOCD to competitively displace MYOCD from SRF. This is the first evidence showing that YY1 inhibits SMC differentiation by directly targeting MYOCD. These findings provide new mechanistic insights into the regulatory mechanisms that govern SMC phenotypic modulation in the pathogenesis of vascular diseases

Dynamic Behaviors of a Single Species Stage Structure Model with Michaelis–Menten-TypeJuvenile Population Harvesting

A single species stage structure model with Michaelis–Menten-type juvenile population harvesting is proposed and investigated. The existence and local stability of the model equilibria are studied. It shows that for the model, two cases of bistability may exist. Some conditions for the global asymptotic stability of the boundary equilibrium are derived by constructing some suitable Lyapunov functions. After that, based on the Bendixson–Dulac discriminant, we obtain the sufficient conditions for the global asymptotic stability of the internal equilibrium. Our study shows that nonlinear harvesting can make the dynamics of the system more complex than linear harvesting; for example, the system may admit the bistable stability property. Numeric simulations support our theoretical results

Taxonomy in the Kunming Institute of Botany (KIB): Progress during the past decade (2008–2018) and perspectives on future development

The development of new taxonomical theories and approaches, particularly molecular phylogenetics, has led to the expansion of traditional morphology-based taxonomy into the concept of “integrative taxonomy.” Taxonomic knowledge has assumed greater significance in recent years, particularly because of growing concerns over the looming biodiversity crisis. Since its establishment in 1938, the Kunming Institute of Botany (KIB), which is located in Yunnan province in Southwest China, has focused attention on the taxonomy and conservation of the flora of China. For the forthcoming 80th anniversary of KIB, we review the achievements of researchers at KIB and their associates with respect to the taxonomy of land plants, fungi, and lichen. Major taxonomic advances are summarized for families of Calymperaceae, Cryphaeaceae, Lembophyllaceae, Neckeraceae, Polytrichaceae and Pottiaceae of mosses, Pteridaceae and Polypodiaceae of ferns, Taxaceae and Cycadaceae of gymnosperms, Asteraceae, Begoniaceae, Ericaceae, Euphorbiaceae, Gesneriaceae, Lamiaceae, Orchidaceae, Orobanchaceae, Poaceae, Theaceae and Urticaceae of angiosperms, Agaricaceae, Amanitaceae, Boletaceae, Cantharellaceae, Physalacriaceae Russulaceae, Suillaceae and Tuberaceae of fungi, and Ophioparmaceae and Parmeliaceae of lichens. Regarding the future development of taxonomy at KIB, we recommend that taxonomists continue to explore the biodiversity of China, integrate new theories and technologies with traditional taxonomic approaches, and engage in creative monographic work, with support from institutions, funding agencies, and the public. Keywords: Taxonomy, Molecular phylogeny, Land plants, Fungi, Liche

Plant phylogenomics based on genome-partitioning strategies: Progress and prospects

The rapid expansion of next-generation sequencing (NGS) has generated a powerful array of approaches to address fundamental questions in biology. Several genome-partitioning strategies to sequence selected subsets of the genome have emerged in the fields of phylogenomics and evolutionary genomics. In this review, we summarize the applications, advantages and limitations of four NGS-based genome-partitioning approaches in plant phylogenomics: genome skimming, transcriptome sequencing (RNA-seq), restriction site associated DNA sequencing (RAD-Seq), and targeted capture (Hyb-seq). Of these four genome-partitioning approaches, targeted capture (especially Hyb-seq) shows the greatest promise for plant phylogenetics over the next few years. This review will aid researchers in their selection of appropriate genome-partitioning approaches to address questions of evolutionary scale, where we anticipate continued development and expansion of whole-genome sequencing strategies in the fields of plant phylogenomics and evolutionary biology research. Keywords: Plant phylogenomics, Next-generation sequencing, Whole-genome sequencing, Genome skimming, RAD-Seq, Targeted captur