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In this paper, we present a memory-based diffusion predator-prey model that incorporates spatial heterogeneity and is subject to homogeneous Dirichlet boundary conditions. Prey species lack memory or cognitive abilities, exhibiting only random diffusion. In contrast, predators utilize memory-based self-diffusion. For the proposed model, we establish the existence and explicit expression of a spatially non-constant positive steady-state. Furthermore, we demonstrate that memory-based diffusion and the averaged memory period can lead to richer dynamics. Specifically, when the memory-based diffusion coefficient is not dominant, the averaged memory period has no impact on the non-constant steady-state. However, when the memory-based diffusion coefficient takes precedence, the averaged memory period can destabilize the non-constant steady-state, resulting in Hopf bifurcation and the emergence of spatially non-homogeneous periodic solutions. [ABSTRACT FROM AUTHOR]

Sperm-derived genetic material contributes half of the genome to the embryo, hence it’s crucial to investigate which sperm parameter influences blastocyst formation in the intracytoplasmic sperm injection (ICSI) cycles with severe male infertility. The retrospective study analyzed 296 ICSI cycles with severe oligoasthenoteratozoospermia (OAT) and 99 ICSI cycles with preimplantation genetic testing for aneuploidy (PGT-A). Following the correlation analysis, data stratifications were performed in the OAT ICSI subgroup. The results showed that the matching blastocyst in the OAT ICSI cycles had inferior sperm parameters. DFI and sperm morphology had an influence on the blastocyst formation rate and the high-quality blastocysts formation rate on Day6, but no significant effect on the blastocyst development on Day 5. The high-quality blastocysts formation rate and ratio of high-quality blastocyst on Day 6 were demonstrably better in the subgroup of the teratozoospermic morphology when DFI was within the normal range. In the case of the normal sperm morphology, no statistically significant difference was found in blastocyst development, although there were numerical differences within different DFI subgroups. It was concluded that the blastocyst quality and development declined with the decreased sperm qualities. [ABSTRACT FROM AUTHOR]

A general time-delay reaction–diffusion–advection system with the Dirichlet boundary condition and spatial heterogeneity is investigated in this paper. By using the implicit function theorem, we obtain the existence and asymptotic expression of the spatially non-homogeneous positive steady-state solution. This is the steady-state bifurcation from zero equilibrium. Via analyzing the corresponding characteristic equation, the stability of the spatially non-homogeneous positive steady-state solution and the occurrence of Hopf bifurcation at the positive steady-state solution are obtained, and the spatially non-homogeneous periodic solution is derived from Hopf bifurcation, this is the secondary bifurcation behavior of the system. Utilizing the normal form method and center manifold theory, we prove that the direction of Hopf bifurcation is supercritical and the bifurcating spatially non-homogeneous periodic solution is stable. Furthermore, We show that there exist two sequences Hopf bifurcation values and the orders of two sequences Hopf bifurcation values are given. Moreover, theoretical and numerical results are applied to competition and cooperation systems, respectively. Finally, the effect of the advection rate and spatial heterogeneity are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reaction–advection–diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods. Firstly, we establish the well-posedness of the model. Secondly, we define the basic reproduction number ℜ 0 for this model and show that ℜ 0 is a threshold parameter: if ℜ 0 < 1 , then the disease-free periodic solution is globally attractive; if ℜ 0 > 1 , the system is uniformly persistent. Thirdly, we study the global attractivity of the positive steady state when the spatial environment is homogeneous and the advection of mosquitoes is ignored. As an example, we use the model to investigate the dengue fever transmission case in Guangdong Province, China, and explore the impact of model parameters on ℜ 0 . Our findings indicate that ignoring seasonality may underestimate ℜ 0 . Additionally, the spatial heterogeneity of transmission may increase the risk of disease transmission, while the increase of seasonal developmental durations, intrinsic incubation periods and advection rates can all reduce the risk of disease transmission. [ABSTRACT FROM AUTHOR]

In this paper, the solvability of a system of fully nonlinear Hilfer fractional differential equations on the half‐line is studied. Firstly, considering that the half‐line as the domain has the problem of insufficient compactness, we defined the space of weighting functions and normed the convergence at infinity. Secondly, by constructing appropriate operators in these Banach spaces and using the extension for the continuous theorem, some sufficient conditions for the solvability of the problem are obtained. Finally, an example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Background: Circular RNA RHOT1 (circRHOT1) plays crucial roles in tumorigenesis by competing with microRNAs. It is largely abundant in tumor cell-derived exosomes. Meanwhile, cancer-derived exosomes participate in diverse biological processes. However, the expression patterns and functions of exosomal circRHOT1 in breast cancer remain unknown. This study is aimed to investigate and elucidate the exosomal circRHOT1/miR-204-5p/PRMT5 axis in breast cancer. Methods: The exosomes derived from serum samples of breast cancer patients and breast cancer cell lines were characterized using transmission electron microscopy and Western blot. MTT, colony formation, wound healing, and transwell assays were utilized to analyze cell proliferation, migration, and invasion of breast cancer cells. Flow cytometry was used for apoptosis analysis. The bioinformatics method was employed to screen differentially expressed novel circRNAs and predict the microRNA targets of circRHOT1. Dual-luciferase reporter gene assays were performed to verify their direct interaction. Finally, Xenograft experiments were used to investigate the effect of exosomal circRHOT1 on tumor growth in vivo. Results: CircRHOT1 exhibited significantly high expression in exosomes derived from the serum of breast cancer patients and breast cancer cell lines, which suggested its potential diagnostic value. Breast cancer-derived exosomes promoted the cell proliferation, migration, invasion, and epithelial-mesenchymal transition of breast cancer cells while inhibiting apoptosis. However, exosomes with downregulated circRHOT1 inhibited the growth of co-cultured cells. Mechanistically, circRHOT1 acted as a sponge of miR-204-5p and promoted protein arginine methyltransferase 5 (PRMT5) expression. Moreover, miR-204-5p inhibitor and pcPRMT5 could reverse the tumor suppressive effects mediated by circRHOT1-knockdown. Furthermore, treatment with exosomes derived from breast cancer cells with circRHOT1 knockdown attenuated tumor growth in tumor-bearing nude mice, which was accompanied by a reduction in PRMT5 expression and an enhancement of miR-204-5p expression. Conclusion: The exosomal circRHOT1 may promote breast cancer progression by regulating the miR-204-5p/PRMT5 axis. The current study strengthens the role of circRHOT1, miR-204-5p, and PRMT5 in breast cancer development and provides a potential treatment strategy for breast cancer. [ABSTRACT FROM AUTHOR]

Background: For patients with varicose veins, the goal is to relieve pain and swelling, reduce the severity of edema, improve skin changes, and heal ulcers associated with venous disease. Compression therapy is the cornerstone of their management. Several studies have shown that wearing an elastic bandage for the first 24 h and then a compression stocking for a week can effectively reduce the pain after thermal ablation. However, in clinical practice, patient compliance with this treatment could be better, considering difficulties in pulling up and removing the compression stocking, tightness, and skin irritation because these must be worn for a prolonged period. A potential solution to battling these barriers is short-term compression therapy. Besides, the effect and necessity of wearing compression stockings after thermal ablation have been questioned. Based on current clinical experience and limited evidence, although some scholars have suggested that compression therapy may be an unnecessary adjunctive therapy after thermal ablation, there is still a great deal of uncertainty in the absence of compression therapy after thermal ablation compared to compression therapy. Therefore, we advocate further research to evaluate the clinical effect of short-term postoperative compression therapy. Furthermore, well-designed randomized controlled trials are needed. Methods: A prospective, multicenter, non-inferiority randomized controlled trial is designed to evaluate the non-inferiority of target vein occlusion rate at 3 months. Three hundred and sixty patients will be randomly assigned in a 1:1 ratio to one of the following treatments: (A) 3 M™ Coban™ elastic bandage for 48 h or (B) 3 M™ Coban™ elastic bandage for the first 24 h and then a class II compression full-length stocking (23–32 mm Hg) for 1 week. The two groups will be compared on several variables, including target vein occlusion rate at 3 months (primary outcome indicator), pain, quality of life, clinical severity of varicose veins, postoperative complications, time to return to regular work, and compliance. Discussion: Suppose the effect of the 3 M™ Coban™ elastic bandage for 48 h proves to be non-inferior to long-term compression therapy. In that case, this short-term treatment may contribute to a future update of clinical guidelines for compression therapy after thermal ablation of varicose veins, resulting in higher patient compliance and better postoperative quality of life. Trial registration: Clinical Trials . Registered on May 2023. [ABSTRACT FROM AUTHOR]

Background: Abdominal aortic aneurysms (AAAs) are permanent dilations of the abdominal aorta with 4–5 times greater prevalence in males than in females. The aim of this study is to define whether Celastrol, a pentacyclic triterpene from the root extracts of Tripterygium wilfordii, supplementation influences angiotensin II (AngII)-induced AAAs in hypercholesterolemic mice. Methods: Age-matched (8–12 weeks old) male and female low-density lipoprotein (Ldl) receptor-deficient mice were fed a fat-enriched diet supplemented with or without Celastrol (10 mg/kg/day) for five weeks. After one week of diet feeding, mice were infused with either saline (n = 5 per group) or AngII (500 or 1000 ng/kg/min, n = 12–15 per group) for 28 days. Results: Dietary supplementation of Celastrol profoundly increased AngII-induced abdominal aortic luminal dilation and external aortic width in male mice as measured by ultrasonography and ex vivo measurement, with a significant increase in incidence compared to the control group. Celastrol supplementation in female mice resulted in significantly increased AngII-induced AAA formation and incidence. In addition, Celastrol supplementation significantly increased AngII-induced aortic medial elastin degradation accompanied by significant aortic MMP9 activation in both male and female mice compared to saline and AngII controls. Conclusions: Celastrol supplementation to Ldl receptor-deficient mice ablates sexual dimorphism and promotes AngII-induced AAA formation, which is associated with increased MMP9 activation and aortic medial destruction. [ABSTRACT FROM AUTHOR]

In this paper, we propose a degenerate dengue fever model with distinct dispersal rates in heterogeneous environment. Firstly, we obtain the well-posedness of the model and the existence of the global attractor. Secondly, we define the basic reproduction number ℜ 0 and show that ℜ 0 is a threshold parameter: if ℜ 0 ≤ 1 , then the disease-free equilibrium is globally asymptotically stable; if ℜ 0 > 1 , the system is uniformly persistent, and the endemic equilibrium is globally attractive when the spatial environment is homogeneous. Thirdly, by studying the asymptotic profiles of the positive steady state and ℜ 0 , we show the impact of the dispersal rate on disease transmission. We conclude with some numerical simulations to illustrate the effect of some model parameters on ℜ 0. Particularly, we find that spatial heterogeneity may increase the risk of disease transmission. [ABSTRACT FROM AUTHOR]

This article investigates the existence of solutions of mixed Hilfer fractional differential equations with p-Laplacian under the functional boundary conditions at resonance. By defining Banach spaces with appropriate norms, constructing suitable operators, and using the extension of the continuity theorem, some of the current results are extended to the nonlinear situation, and some new existence results of the problem are obtained. Finally, an example is given to verify our main results. [ABSTRACT FROM AUTHOR]

To investigate whether there is a relationship between elevated serum progesterone (PROG) on the hCG trigger day and the live birth rate (LBR) in IVF/ICSI cycles, the retrospective analysis was carried out from the patients undergoing the first ART cycles throughout 2016. The PROG levels were measured on the hCG trigger day. The LBR, clinical pregnancy rate (CPR), implantation rate (IR) and other parameter rate values were compared among the three different PROG elevations. A total of 2550 IVF/ICSI cycles fulfilling all the inclusion and exclusion criteria were selected. Finally, three groups [PROG <0.40 ng/mL, 0.40 ≤ PROG < 1.5 ng/mL, PROG ≥ 1.5 ng/mL] were categorised based on the serum PROG levels. LBR, CPR and IR declined as the PROG value increased, while there was no difference in the embryo utilisation rates. Serum PROG levels on the day of hCG administration were negatively associated with the LBR, even in ETs with a good prognosis. What is already known on this subject? The clinical effects of PROG are still controversial. Some studies have confirmed that there was not too much association between premature elevation of PROG and live birth, some are still convincing that there is a negative correlation and will result in ART cycles of pregnancy and LBR reduction. What do the results of this study add? Our data substantiated that the high serum PROG level had the lowest LBR, IR and CPR, but the embryo utilisation rate may not have too much to do with the elevated PROG. What are the implications of these findings for clinical practice and/or further research? This study further strengthens the negative impact of elevated PROG levels on pregnancy outcomes, and suggests that frozen thawed embryo transfer appears to be a reasonable and advantageous approach for this subset of patients. [ABSTRACT FROM AUTHOR]

Due to the combined effects of different acoustic propagation, reflection patterns in different time-scale, time-varying underwater acoustic (UWA) channel generally exhibits hybrid sparsity, i.e., contains not only rapidly time-varying elements, but also stationary or slowly time-varying ones. While the classic sparse reconstruction algorithms such as orthogonal matching pursuit (OMP) generally do not take it into account, the existence of static multipath will unavoidably hinder the tracking of rapid time variations. In this paper, a sequential adaptive observation length orthogonal matching pursuit (SAOLOMP) approach is proposed to sequentially explore rapidly time-varying sparsity in a two-step sequential manner. Specifically, the static components are firstly separated via simultaneous orthogonal matching pursuit (SOMP) among continuous measurements. Upon the residual error of the SOMP, the measurement-wise OMP is applied for estimating the remained dynamic components. As the variation of the SOMP residual error indicates how rapidly the remained dynamic multipath components vary, the observation length of the OMP is adjusted according to the gradient of residual error to adapt to rapidly time-varying components. Finally, both types of sparse components are summed up to obtain the whole channel response. Numerical simulations as well as experimental results from field UWA communication data show that the proposed algorithm exhibits better performance in exploiting rapidly time-varying sparsity than the state-of-the-art compressive methods do under UWA channel. [ABSTRACT FROM AUTHOR]

While underwater acoustic (UWA) communication offers a practical way to establish a wireless link with underwater vehicles, designing a UWA communication system onboard a small autonomous underwater vehicle (AUV) still poses significant challenges. As the adoption of the low-complexity, robust noncoherent communication technology is limited by low bandwidth efficiency and a low data rate, coherent UWA communication requires Doppler mitigation and channel equalization measures to achieve a relatively high data rate in a moving state. Due to the strict constraints of a small-scale AUV in terms of resources and energy consumption, it is not appropriate to use high-complexity Doppler/multipath compensation technology from the prospect of system implementation. In this paper, an efficient and low-complexity UWA differential binary phase-shift keying (DBPSK) system onboard a small AUV is proposed by simplifying the Doppler and multipath compensation. Specifically, for Doppler, the delay of the adjacent DBPSK symbols is calculated according to the Doppler estimate to facilitate delay-tuning Doppler correction. For multipath, low-complexity LMS channel equalization is incorporated with error correction coding to enable multipath mitigation. With a simple structure and low computational complexity, the proposed scheme facilitates the practical hardware implementation and system integration in the small AUV platform. The numerical simulations are conducted to assess the validity of the proposed scheme under different channel conditions and the effectiveness of the proposed scheme is further verified by two UWA communication field tests, which are performed at a practical shallow water sea and lake, respectively. [ABSTRACT FROM AUTHOR]

We investigate the effect of nonlocal intraspecific prey competition on the spatiotemporal dynamics of a Holling–Tanner predator–prey model with diffusion. We first establish the criteria for Hopf, Turing, double‐Hopf, and Turing–Hopf bifurcations, and determine the stable and unstable regions of the positive equilibrium. For Turing–Hopf bifurcation, by analyzing the normal form truncated to the third order, we derive that, with strong nonlocal interaction, the system exhibits the tristable phenomena, that is, the coexistence of a stable spatially nonhomogeneous periodic orbit and two nonconstant stable steady states, as well as the existence of periodic orbits with two spatial wave frequencies induced by the nonlocal interaction. The main analytical difficulty arises from the nonlocal interaction that prevents the direct application of formulas for the coefficients of the normal form. Biologically, the emerging spatiotemporal patterns suggest that the global intraspecific competition can promote the coexistence of the prey and predator by allowing the prey maintain a critical total population size, which may provide an alternative approach in explaining the group formation of some prey species under the risk of predation. Some coexistence patterns are destabilized by introducing another prey species with local intraspecific competition, leading to the coexistence of two preys and one predator, namely, the prey with nonlocal interaction is concentrated at a single spatial location, and the other prey is distributed uniformly in the rest of the habitat. Accordingly, the predator is forced to change its behavior as well. [ABSTRACT FROM AUTHOR]

A simplified pulsed power circuit has been investigated by solving the circuit equation. The aim is to analyze the output rise time, which is defined by the time between 10% and 90% of the peak voltage. It was found that a capacitor, which is called the sharpening capacitor, connected in parallel to the load can help in reducing the rise time by as much as 27%. In addition, a negative bias voltage applied on the sharpening capacitor can further reduce the rise time significantly, depending on how much we sacrifice the working voltage of the switch in exchange for the bias voltage. An example shows that, when the bias voltage is 20% of the switching voltage, the rise time is reduced by ~40% from that obtained without the sharpening capacitor. [ABSTRACT FROM AUTHOR]

Turing-Hopf bifurcation is considered as an important mechanism for generating complex spatio-temporal patterns in dynamical systems. In this work, the normal form up to the third order for the Hopf-steady state bifurcation, which includes the Turing-Hopf bifurcation, of a general system of partial functional differential equations (PFDEs) in a bounded spatial region of any dimension, is derived based on the center manifold and the normal form theories of PFDEs. The explicit formula for the coefficients in the normal form of Hopf-steady state bifurcation are presented concisely in a matrix form, which makes it more convenient in not only symbolic derivation but also numerical implementation. This provides an approach of showing the existence and stability of stationary and time-periodic solutions with spatial heterogeneity. The derived formulas are also applicable to partial differential equations and functional differential equations. [ABSTRACT FROM AUTHOR]

To investigate the expression and clinical significance of mitogen-activated protein kinase (MAPK) and epidermal growth factor receptor (EGFR) in triple-negative breast cancer (TNBC), a total of 300 TNBC and 120 paired paracancerous tissues were examined. Immunohistochemistry was conducted to determine the expression levels of MAPK and EGFR, and the correlation between MAPK and EGFR expression was evaluated using Cramer's V test. The association between MAPK and EGFR expression, and various clinicopathological variables (such as lymph node metastasis, clinical stage, recurrence and metastasis) was also evaluated, using the χ2 test. MAPK and EGFR expression levels in TNBC tissues were significantly higher than in the paired paracancerous tissues. Moreover, MAPK expression was associated with that of EGFR in TNBC tissues. The positive expression rates of MAPK and EGFR in patients with lymph node metastasis, advanced clinical stage, tumor recurrence and metastasis were higher than those without. Patients with positive expression of MAPK and EGFR in TNBC tissues had poorer prognoses and lower overall survival times than those without expression. In summary, the expression of MAPK and EGFR is closely associated with tumor invasion and the metastasis of TNBC, and may therefore be used as an indicator of poor prognosis in patients with TNBC. [ABSTRACT FROM AUTHOR]

In this paper, we study the delayed reaction–diffusion Schnakenberg systems with Neumann boundary conditions. Sufficient and necessary conditions for the occurrence of Turing instability are obtained, and the existence of Turing, Hopf and Turing–Hopf bifurcation for the model are also established. Furthermore, for Turing–Hopf bifurcation, the explicit formula of the truncated normal form up to third order is derived. With the aid of these formulas, we determine the regions on two parameters plane, on which a pair of stable spatially inhomogeneous steady states and a pair of stable spatially inhomogeneous periodic solutions exist, respectively. The theoretical results not only reveals the joint effect of diffusion and delay on the patterns that the model can exhibit, but also explain the phenomenon that time delay may induce a failure of Turing instability, found by Gaffney and Monk (Bull Math Biol 68(1):99–130, 2006). [ABSTRACT FROM AUTHOR]

In this paper, we consider the Lengyel–Epstein system of the CIMA reaction with homogeneous Neumann condition. Firstly, we derive conditions for existence of Turing/Turing–Hopf bifurcation by analysis of distribution of eigenvalues. Meanwhile, we give the concrete range of diffusion rate c preserving that spatial inhomogeneous Hopf bifurcation occurs based on the existence result in Du and Wang (2010). Secondly, existence of more complex spatio-temporal dynamical behaviors, such as spatial inhomogeneous periodic/quasi-periodic solutions and bistable/tristable phenomenon, are rigorously proved near the Turing–Hopf bifurcation point using center manifold theorem and normal form method. Finally, numerical simulations in different parameter regions not only support our analytical results but indicate the existence of tetrastable phenomenon. [ABSTRACT FROM AUTHOR]

Focuses on a study which examined the synthesis of ultrafine nanosize powders of aluminum nitride by ion beam evaporation. Theoretical models for the physical processes; Prediction of macroscopic properties of the powders; Computational and experimental results; Conclusions.

Long non-coding RNAs (lncRNAs), a class of non-coding RNA, have been shown to be essential in many diseases, such as infertility. Here, we found three candidate lncRNAs, ENST00000414116, ENST00000433673, and ENST00000448179, that are highly expressed in the uterus endometrial tissues of normal patients compared to the tissues of patients with adenomyosis, endometriosis, and recurrent implantation failure. lncRNAs ENST00000414116 and ENST00000433673 showed high expression in endometrial stromal cells (ESCs) and endometrial epithelial cells (EECs), respectively, and lncRNA ENST00000448179 was specifically expressed in ESCs. The bioinformatics analysis results indicated that the target mRNAs of lncRNA ENST00000433673 were related to biological adhesion. Interestingly, intercellular adhesion molecule 1 (ICAM1), an interacting mRNA of the target mRNA integrin subunit alpha L (ITGAL), has been reported be an important regulator of embryo implantation. Further studies found that the target mRNA ITGAL and the interacting mRNA ICAM1 were highly expressed in the uterus endometrial tissues and EECs of normal patients. Based on our results, our study indicates that lncRNA ENST00000433673 might mediate the high expression of the target mRNA ITGAL, thereby promoting the expression of the interacting mRNA ICAM1 and the adhesion of EECs, which facilitates adhesion and implantation between the embryo and the mater. Abbreviations: AMs: adenomyosis; EMs: endometriosis; RIF: recurrent implantation failure; miRNAs: microRNAs; lncRNAs: Long non-coding RNAs; RT-qPCR: real-time quantitative PCR; ESCs: endometrial stromal cells; EECs: endometrial epithelial cells; BFE: free binding energy; PCDHB9: protocadherin beta 9; PARVG: parvin gamma; MAPK6: mitogen-activated protein kinase 6; LAF1: lymphocyte function-associated antigen 1 [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ  =  0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics. [ABSTRACT FROM AUTHOR]

In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green's function and Guo-Krasnosel'skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. We also give some examples to illustrate the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

A diffusive predator–prey system with Crowley–Martin functional response is considered. Firstly, the maximal parameter region, where the coexistence equilibrium is stable, is provided, of which the boundary consists of Turing bifurcation curves and Hopf bifurcation curve, and result derived by Shi and Ruan (2015) is improved. Meanwhile, critical conditions for Turing instability are derived, which are necessary and sufficient. Furthermore, considering the degenerated situation where Turing bifurcation and Hopf bifurcation occur simultaneously, conditions for codimension-two Turing–Hopf bifurcation and Turing–Turing bifurcations are given. For Turing–Hopf bifurcation, by analyzing the normal forms truncated to order 3, which are derived by applying normal form method and generic formulas developed by Jiang, An and Shi (2018), it is found that system exhibits spatial, temporal and spatiotemporal patterns, like transient spatially inhomogeneous periodic solutions, as well as tristable phenomena of a pair of spatially inhomogeneous steady states and a spatially homogeneous periodic solution coexisting. At last, numerical simulations, including transient, bistable and tristable patterns, are illustrated to support our theory results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the periodic pattern formations with spatial multi-peaks in a classic diffusive Holling-Tanner predator-prey model with nonlocal intraspecific prey competition. The main innovation is that a spatial dependently kernel is considered in the nonlocal effect, which mathematically complicates the linear stability analysis. We first generate the existences of Hopf, Turing, Turing-Hopf and double-Hopf bifurcations, and determine the stability of the positive equilibrium. It turns out that the stable parameter region for the positive equilibrium decreases with α increasing, which implies that the parameter region of pattern formation for such kernel is smaller than the spatial average case. For double-Hopf bifurcation, we calculate the normal form up to the third-order term restricted on the center manifold, which is expressed by the original parameters of the system. Via analyzing the equivalent amplitude equations, the system exhibits stable spatially nonhomogeneous periodic patterns, the bistability of such periodic solutions, as well as unstable spatially nonhomogeneous quasi-periodic solutions, all of them possess multiple spatial peaks. Interestingly, some possible strange attractors are found numerically near the double-Hopf singularity. Biologically, the emerging spatio-temporal patterns imply that such nonlocal intraspecific competition can promote the coexistence of the prey and predator species in the form of more complex periodic states. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics of a diffusive ratio-dependent Holling–Tanner model subject to Neumann boundary conditions is considered. We derive the conditions for the existence of Hopf, Turing, Turing–Hopf, Turing–Turing, Hopf-double-Turing and triple-Turing bifurcations at the unique positive equilibrium. Furthermore, we study the detailed dynamics in the neighborhood of the Turing–Hopf bifurcation by using the normal form method. Our results show that the Turing–Hopf bifurcation can give rise to the formation of the temporal and spatio-temporal patterns. In particular, we theoretically prove the existence of the spatially inhomogeneous periodic and quasi-periodic solutions, which can be used to explain the phenomenon of spatio-temporal resonance of the populations. Finally, the numerical simulations are given to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

While it has been recognized that the multipath structure of the underwater acoustic (UWA) channel offers the potential for compressed sensing (CS) sparsity exploitation, the rapidly time varying arrivals induced by highly dynamic surfaces unfortunately pose significant difficulties to channel estimation. From the viewpoint of underwater acoustic propagation, with the exception of the highly time varying arrivals caused by dynamic surface, generally there exist relatively stationary or slowly changing arrivals caused by direct path or bottom reflection, which imply the adoption of a discriminate estimation method to handle sparse components with different time variation scale. By modeling the time varying UWA channels as a sparse set consisting of constant and time-varying supports, in this paper, estimation of time varying UWA channel is transformed into a problem of dynamic compressed sensing sparse recovery. The combination of a Kalman filter and compressed sensing is adopted to pursue the solution of it. Numerical simulations demonstrate the superiority of the proposed algorithm. In the form of a channel-estimation-based decision-feedback equalizer, the experimental results with the field data obtained in a shallow water acoustic communication experiment indicate that the proposed dynamic compressed sensing algorithm outperforms classic algorithms as well as CS algorithms. [ABSTRACT FROM AUTHOR]

Background: The brown planthopper (BPH) has become the most destructive and a serious threat to the rice production in Asia. Breeding the resistant varieties with improved host resistance is the most effective and ecosystem-friendly strategy of BPH biological management. As host resistance was always broken down by the presence of the upgrading BPH biotype, the more resistant varieties with novel resistance genes or pyramiding known identified BPH resistance genes would be needed urgently for higher resistant level and more durability of resistance. Results: Here, we developed near isogenic lines of Bph9 (NIL- Bph9) by backcrossing elite cultivar 93-11 with Pokkali (harboring Bph9) using marker-assisted selection (MAS). Subsequently, we pyramided Bph6 and Bph9 in 93-11 genetic background through MAS. The resulting Bph6 and Bph9 pyramided line LuoYang69 had stronger antixenotic and antibiosis effects on BPH and exhibited significantly enhanced resistance to BPH than near isogenic lines NIL- Bph6 and NIL- Bph9. LuoYang69 derived hybrids, harboring heterozygous Bph6 and Bph9 genes, also conferred high level of resistance to BPH. Furthermore, LuoYang69 did not affect the elite agronomic traits and rice grain quality of 93-11. The current study also developed functional markers for Bph9. Using functional dominant marker, we screened and evaluated worldwide accessions of rice germplasm. Of the 673 varieties tested, 8 cultivars were identified to harbor functional Bph9 gene. Conclusion: The development of Bph6 and Bph9 pyramided line LuoYang69 provides valuable resource to develop hybrid rice with highly and durable BPH resistance. The development of functional markers will promote MAS of Bph9. The identified Bph9 containing cultivars can be used as new sources for BPH resistance breeding programs. [ABSTRACT FROM AUTHOR]

In this paper, we study a diffusion-advection Lotka-Volterra competition model with stage structure in a spatially heterogeneous environment. The existence and local asymptotic stability of spatially non-homogeneous semi-trivial steady-state solutions and spatially non-homogeneous positive steady-state solutions are obtained by the implicit function theorem and spectral analysis. We show that three scenarios can occur: if random diffusion rates of two species are sufficiently large, both species go extinct; if random diffusion rates of two species are relatively small, two competing species coexist; if one species has a large random diffusion rate and the other has a small random diffusion rate, the species with a large random diffusion rate are driven to extinction. An interesting finding is that a large delay does not lead to Hopf bifurcation at the spatially non-homogeneous steady-state solution, but makes this steady-state solution approach zero. We numerically demonstrate the effects of spatial heterogeneity on spatiotemporal dynamics. [ABSTRACT FROM AUTHOR]

In this paper, by using the coincidence degree theory due to Mawhin and constructing suitable operators, we study the solvability for functional boundary value problems of second-order nonlinear differential equations system at resonance with $\dim\operatorname{Ker} L=3$ and 4, respectively. [ABSTRACT FROM AUTHOR]

By using the coincidence degree theory due to Mawhin and constructing suitable operators, we study the existence of solutions for a third-order functional boundary value problem at resonance with $\operatorname{dim } \operatorname{Ker}L=1$ . [ABSTRACT FROM AUTHOR]

This paper investigates a toxic phytoplankton-zooplankton model with Michaelis-Menten type phytoplankton harvesting. The model has rich dynamical behaviors. It undergoes transcritical, saddle-node, fold, Hopf, fold-Hopf and double Hopf bifurcation, when the parameters change and go through some of the critical values, the dynamical properties of the system will change also, such as the stability, equilibrium points and the periodic orbit. We first study the stability of the equilibria, and analyze the critical conditions for the above bifurcations at each equilibrium. In addition, the stability and direction of local Hopf bifurcations, and the completion bifurcation set by calculating the universal unfoldings near the double Hopf bifurcation point are given by the normal form theory and center manifold theorem. We obtained that the stable coexistent equilibrium point and stable periodic orbit alternate regularly when the digestion time delay is within some finite value. That is, we derived the pattern for the occurrence, and disappearance of a stable periodic orbit. Furthermore, we calculated the approximation expression of the critical bifurcation curve using the digestion time delay and the harvesting rate as parameters, and determined a large range in terms of the harvesting rate for the phytoplankton and zooplankton to coexist in a long term. [ABSTRACT FROM AUTHOR]

By using the Leggett-Williams norm-type theorem due to O'Regan and Zima and constructing suitable Banach spaces and operators, we investigate the existence of positive solutions for fractional p-Laplacian boundary value problems at resonance. An example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

To investigate the effect of heterogeneity on the global dynamics of two SIR epidemic models with general nonlinear incidence rate and infection delays, we formulate a multi-group model corresponding to the heterogeneity in the host population and a multi-stage model corresponding to heterogeneous stages of infection. Under biologically motivated considerations, we establish that the global dynamics for each of the two models is determined completely by the corresponding basic reproduction number: if the basic reproduction number is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable and the disease dies out in all groups or stages; if the basic reproduction number is larger than one, then the disease will persist in all groups or stages, and there is a unique endemic equilibrium which is globally asymptotically stable. Then we conclude that the heterogeneity does not change the global dynamics of the SIR model when the incidence rate is a general nonlinear function. Our results extend a class of previous results and can be applied to the other epidemiological models. The proofs of the main results use Lyapunov functional and graph-theoretic approach. [ABSTRACT FROM AUTHOR]

We establish new results on the existence of positive solutions for the multi-point boundary value problem at resonance on the half-line. Our results are based on the Leggett-Williams norm-type theorem due to O'Regan and Zima, which requires appropriate Banach spaces and proper operators. An example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

By using the extension of the continuation theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence of solutions for a p-Laplacian boundary value problem with integral boundary condition at resonance on the half-line. [ABSTRACT FROM AUTHOR]

Rice (Oryza sativa L.) is a staple food crop globally. Brown planthopper (Nilaparvata lugens Stål, BPH) is the most destructive insect that threatens rice production annually. More than 40 BPH resistance genes have been identified so far, which provide valuable gene resources for marker-assisted breeding against BPH. However, it is still urgent to evaluate rice germplasms and to explore more new wide-spectrum BPH resistance genes to combat newly occurring virulent BPH populations. To this end, 560 germplasm accessions were collected from the International Rice Research Institute (IRRI), and their resistance to current BPH population of China was examined. A total of 105 highly resistant materials were identified. Molecular screening of BPH resistance genes in these rice germplasms was conducted by developing specific functional molecular markers of eight cloned resistance genes. Twenty-three resistant germplasms were found to contain none of the 8 cloned BPH resistance genes. These accessions also exhibited a variety of resistance mechanisms as indicated by an improved insect weight gain (WG) method, suggesting the existence of new resistance genes. One new BPH resistance gene, Bph44(t), was identified in rice accession IRGC 15344 and preliminarily mapped to a 0–2 Mb region on chromosome 4. This study systematically sorted out the corresponding relationships between BPH resistance genes and germplasm resources using a functional molecular marker system. Newly explored resistant germplasms will provide valualble donors for the identification of new resistance genes and BPH resistance breeding programs. [ABSTRACT FROM AUTHOR]

Hopf bifurcation in two groups of Kuramoto's phase oscillators with delay-coupled interactions is investigated on the Ott-Antonsen's manifold. We find that the reduced delay differential system undergoes Hopf bifurcations when the coupling strength between two groups exceeds some critical values. With the increasing of time delay, stability switches are observed which leads to the synchrony switches for the Kuramoto system. The direction of Hopf bifurcation and the stability of bifurcating periodic solutions are investigated by deriving the normal forms on the center manifold. With respect to the Kuramoto system, simulations are performed to support our analytic results. [ABSTRACT FROM AUTHOR]

Forward pumping current is required for current interruption operation of a semiconductor opening switch (SOS). In this study, the influence of the forward pumping current on current interruption of the reverse current has been investigated experimentally. The duration and the peak value of the forward current were varied and the reverse current obtained under different conditions has been compared. As a result, it has been found that a short forward current can lead to high peak value of the reverse current. It is considered from the results that the density of the minority carriers is increased by the forward current of shorter duration because recombination consumes fewer carriers. Furthermore, when the duration of the forward current shortens with a lower peak value and depletion the peak value of the reverse current increases, the interruption of reverse current quickens. This can be explained by the fact that the time during which minority carriers are turned around by the reverse current is shorter in case of less accumulation and faster removal of minority carriers. With these investigations, it has been understood that relatively short and low forward current and high reverse current is needed for high efficiency inductive energy storage circuit using the SOS. [ABSTRACT FROM PUBLISHER]

In order to study boundary value problems with p -Laplacian, the extension for the continuous theorem of Ge and Ren is generalized. By using the new results and constructing suitable operators, we investigate the existence of solutions for p -Laplacian fractional differential equations at resonance. Examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

From the saddle-node-Hopf bifurcation point of view, this paper considers a modified Leslie–Gower predator-prey model with time delay and the Michaelis–Menten type prey harvesting. Firstly, we discuss the stability of the equilibria, obtain the critical conditions for the saddle-node-Hopf bifurcation, and give the completion bifurcation set by calculating the universal unfoldings near the saddle-node-Hopf bifurcation point by using the normal form theory and center manifold theorem. Then we derive the parameter conditions for the existence of monostable coexistence equilibrium and the parameter regions in which both the prey-extinction and the coexistence equilibrium (or coexistence periodic or quasi-periodic solutions) are simultaneously stabilized. We also investigate the heteroclinic bifurcation, and describe the phenomenon that the periodic behavior disappears as through the heteroclinic bifurcation. Finally, some numerical simulations are performed to support our analytic results. [ABSTRACT FROM AUTHOR]

The existence of solutions for fractional differential equations with integral boundary conditions at resonance on the half line is investigated. Our analysis relies on constructing the suitable Banach space, defining appropriate projectors and the coincidence degree theory due to Mawhin. An example is given to illustrate our main result. [ABSTRACT FROM AUTHOR]

A solid-state linear transformer driver stack has been developed to demonstrate pulsed power generation and output pulse shaping. It consists of 30 modules each using 24 power metal–oxide–semiconductor field-effect transistors as switches. The output voltage of the stack is the superposition of the voltage pulse of each module no matter if the modules are switched synchronously or not. In synchronous operation, the output voltages of all modules are added up to reach an output voltage up to \(\sim 29\) kV with a maximum output current of \(\sim 240\) A. The pulsewidth is variable in the range of 50–170 ns. On the other hand, by carrying out separate switching of different modules, the output waveform can be varied by performing pulse shaping. The control signals for pulse shaping experiment are generated using an field-programmable gate array board that allows potentially automatic waveform optimization. [ABSTRACT FROM PUBLISHER]

This paper considers a chemical reaction-diffusion model for studying pattern formation with the Sel'kov–Schnakenberg model. Firstly, the stability conditions of the positive equilibrium and the existing conditions of the Hopf bifurcation are established for the local system. Then, Turing instability (diffusion-driven), which causes the spatial pattern is investigated and the existing condition of the Turing bifurcation is obtained. In addition, the dynamic behaviors near the Turing bifurcation are also studied by employing the method of weakly nonlinear analysis. The theoretical analysis shows that spatio-temporal patterns change from the spot, mixed (spot-stripe) to stripe with the variation of parameters, which can be verified by a series of numerical simulations. These numerical simulations give a visual representation of the evolution of spatial patterns. Our results not only explain the evolution process of reactant concentration, but also reveal the mechanism of spatio-temporal patterns formation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a predator–prey model consisting of active and dormant states of predators with impulsive control strategy is established. Using Floquet theories, the small amplitude perturbation technique and the piecewise Lyapunov function method, the conditions of local and global asymptotical orbital stability of the prey-eradication periodic solution are obtained. The boundness and permanence of the impulsive system are proved by the comparison principle. Through numerical simulations, the effects of the impulsive perturbation on the inherent oscillation are investigated, which implies that the impulsive perturbation can lead to period-doubling bifurcation, chaos, and period-halving bifurcation. Moreover, the effects of the impulsive perturbation and hatching rate on the chaos of the system are comparatively studied by numerical simulation. These obtained results can be useful for ecosystem management and for explaining complex phenomena of ecosystems. [Copyright &y& Elsevier]

We consider a system of partial differential equations that describes the interaction of the sterile and fertile species undergoing the sterile insect release method (SIRM). Unlike in the previous work [M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release, Math. Biosci. 5 (1992) 221-247] where the habitat is assumed to be the one-dimensional whole space ℝ, we consider this system in a bounded one-dimensional domain (interval). Our goal is to derive sufficient conditions for success of the SIRM. We show the existence of the fertile-free steady state and prove its stability. Using the releasing rate as the parameter, and by a saddle-node bifurcation analysis, we obtain conditions for existence of two co-persistence steady states, one stable and the other unstable. Biological implications of our mathematical results are that: (i) when the fertile population is at low level, the SIRM, even with small releasing rate, can successfully eradicate the fertile insects; (ii) when the fertile population is at a higher level, the SIRM can succeed as long as the strength of the sterile releasing is large enough, while the method may also fail if the releasing is not sufficient. [ABSTRACT FROM AUTHOR]