We study the semi-infinite Neumann problem, which models the variation law of a cline in a semi-infinite habitat. Using the bifurcation analysis method, we find that there is a unique solution curve emanating from $(\arctan \alpha ,0)$ with $\alpha> 0$, which is strictly increasing and approaches $1$ in $C[0,+\infty )$. Furthermore, we show that any cline (bifurcation solution) is stable, thereby providing a confirmed answer to a conjecture. Moreover, we also establish the stability of the trivial solution. Our conclusions are consistent with the related numerical results and biological reality.

Compared with superhydrophobic coatings, superamphiphobic coatings offer broader application potential in various fields. However, their practical applications are often hindered by insufficient repellency towards low-surface-tension, high-viscosity and complex multicomponent liquids, as well as by their stability. Herein, a palygorskite-based stable superamphiphobic coating with a simple fabrication process and low cost is reported. The coating was fabricated through sequential spray deposition of a fluorosilicone resin (FSR) bonding layer and a superamphiphobic functional layer composed of fluorinated palygorskite (F-PAL), fluorinated carbon black (F-CB) and FSR. In this coating, F-PAL nanorods serve as the building blocks for constructing the primary nanostructure, while F-CB nanoparticles occupy the interstitial spaces between the PAL nanorods, forming the secondary nanostructure. Together, these components generate a multiscale hierarchical micro-/nanostructure that is critical for achieving superamphiphobicity. By systematically optimizing the mass ratio of F-CB to F-PAL and the FSR content, a low-surface-energy multiscale hierarchical micro-/nanostructure was successfully established, imparting the coating with excellent superamphiphobicity towards water, hydroxyl-terminated polybutadiene/dioctyl sebacate mixtures (HTPB-H) and their aluminium powder-containing suspensions (HTPB-H/Al). The coating exhibits outstanding mechanical, chemical and thermal stability. Furthermore, the coating demonstrates remarkable anti-adhesion performance against both HTPB-H and HTPB-H/Al, together with superior passive anti-icing performance, as evidenced by a significantly prolonged freezing delay time (1291 s, ∼30-fold increase) and a substantially reduced ice adhesion strength (from 224.3 to 65.8 kPa). Moreover, efficient photothermal de-icing performance was achieved under low-temperature, high-humidity and weak-light conditions. These results demonstrate that the proposed superamphiphobic coating holds significant promise for practical applications in anti-adhesion and anti-icing under harsh conditions.

In this paper, we study a nonlinear free boundary problem modelling the growth of radially symmetric tumours. The tumour consists of a central necrotic core, an intermediate quiescent layer and an outer proliferating shell. The evolution of tumour layers and the movement of the tumour boundary are totally governed by external nutrient supply and conservation of mass. The three-layer structure generates three free boundaries with discontinuous nutrient consumption rates and cell growth rates. We develop a nonlinear analysis method to clarify the interactive relationships among free boundaries. By carefully studying the dependence of the critical-state tumour growth rate on the external nutrient concentration, we reveal the evolutionary mechanism in tumour growth and the mutual transformation of its internal structures. The existence and uniqueness of the radial stationary solution is proved, and its globally asymptotic stability towards different dormant tumour states is established.

In this study, we develop epidemic reaction-diffusion models by incorporating the dependency of the diffusion rate of susceptible individuals on new infection cases, employing both Fickian and Fokker–Planck-type diffusion laws. As the first part of a two-part series, we focus on epidemics driven by frequency-dependent incidence. We explore linear, exponential and algebraic relationships between diffusion rate of the susceptible population and new infection cases to provide deeper biological insights. Our analysis establishes the global existence of solutions and characterizes the threshold dynamics using basic reproduction numbers. We find that in quasilinear parabolic systems, the Fokker–Planck-type diffusion law tends to induce spatial segregation of susceptible and infected individuals, while the Fickian law favours spatial homogenization of susceptible individuals. Additionally, the Fokker–Planck-type model, where the diffusion rate of infected individuals depends on new recovery cases, more accurately captures the cognitive diffusion behaviour of individuals.

In this article, we first investigate weighted Minkowski-type inequalities for nearly spherical sets in space forms, focusing on the sets that are $C^1$-close to geodesic spheres. Our results generalize the work of Glaudo (2022, Adv. Math. 408, 108595) by incorporating broader geometric settings and convex weight functions. Additionally, we establish quantitative stability estimates for weighted Alexandrov–Fenchel-type inequalities in $\mathbb {R}^{n+1}$ and $\mathbb {H}^{n+1}$, extending the earlier results of VanBlargan and Wang (2024, Commun. Contemp. Math. 26, 2350026) and Zhou and Zhou (2024, J. Geom. Anal. 34, 376). These inequalities hold for nearly spherical sets that are $W^{2,\infty }$-close to geodesic spheres coupled with general convex weights.

In this paper, we show the existence, uniqueness and stability of nontrivial solutions to the following Minkowski-curvature problems on unbounded domains:

$$ \begin{align*} \bigg(\frac{x'}{\sqrt{1-x^{\prime2}}}\bigg)'=f(t,\ x),\quad t\geq t_0, \quad \lim_{t\to\infty}x(t)=\psi_0,\quad \lim_{t\to\infty}x'(t)e^{t}=0, \end{align*} $$

$f:\ [t_0, \infty )\times \mathbb {R}\rightarrow \mathbb {R}$

$t_0>0$

$\psi _0\in \mathbb {R}$

Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae) is an important agricultural biocontrol agent that preys on various soft-bodied insect pests. This study was carried out to evaluate the fitness parameters of bifenthrin-selected (Bifen-Sel) and unselected (Unsel) strains of C. carnea and their reciprocal crosses (C1 and C2) by using an age-stage and two-sex life table approach. After continuous selection with bifenthrin (44 generations), the Bifen-Sel strain of C. carnea developed a 9.55-fold resistance level when compared to that of the Unsel. Biological parameters, such as the pupal period, pre-adult duration, male and female longevity, adult pre-oviposition period, and oviposition period of the Bifen-Sel strain, all were significantly different from that of the Unsel strain and their crosses C1 and C2. The larval period, total pre-oviposition period, female ratio, reproductive female ratio, and fecundity of the Bifen-Sel strain were significantly different from those of the Unsel strain. Demographic parameters, including intrinsic rate (rm), finite rate (λ), net reproductive rate (R0), mean generation rate (T), and gross reproductive rate of the Bifen-Sel strain, were similar to those of the Unsel strain but significantly higher than those of the C1 and C2 crosses of C. carnea. Bifenthrin resistance was stable in the Bifen-Sel strain of C. carnea. These findings provide valuable insights into bifenthrin resistance dynamics in C. carnea as it resulted in no fitness cost and support its selective use under controlled conditions, while highlighting the need for future research on predation potential of this resistant strain under field conditions with bifenthrin applications.

We study a size-structured tree growth model from [4–6], described by the nonlinear renewal equation $\phi(t) = \mathfrak{F} \phi_t, \ \phi_t \in L^1_\rho(\mathbb{R}_{-}),$ with reproduction, death, and growth rates $\beta$, $\mu$, and $g$. We prove that, under mild conditions on these rates, the equation generates a semiflow in $L^1_\rho(\mathbb{R}_{-})$ that is permanent and possesses a compact global attractor $\mathcal{A}$. If $\beta$ is monotone, $\mathcal{A}$ reduces to a single asymptotically stable equilibrium attracting all compact sets with positive initial data. Adapting an approach from [21], originally developed for simpler renewal equations, we investigate stability and persistence in this more complex setting via the one-dimensional recurrence $b_{n+1} = \mathfrak{F} b_n,$ thereby complementing the functional-analytic framework of [13].

The doubly degenerate nutrient taxis system(0.1)

\begin{equation} \left \{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-\chi \nabla \cdot (u^{\alpha }v\nabla v)+\ell uv,&x\in \Omega ,\, t\gt 0,\\[5pt] & v_{t}=\Delta v-uv,&x\in \Omega ,\, t\gt 0,\\ \end{aligned} \right . \end{equation}

$\Omega \subset \mathbb{R}^3$

$\alpha \gt 0,\chi \gt 0$

$\ell \gt 0$

$\alpha \in (\frac {3}{2},\frac {19}{12})$

$(u_\infty , 0)$

$t\rightarrow \infty$

$u_{\infty }$

$v_0$

$u_0$

We model attitude stability and constraint, using a dynamic discrete choice framework for multiple attitudes, to identify influential attitudes within attitude systems. Its value-added includes insights about different sources of (in)stability, the direction of causation between attitudes, and their relative degree of influence; capturing time-invariant individual traits with a multiple factor structure; and addressing the ordinal nature of attitudinal measures, together with heterogeneity in time intervals between interviews, across waves, and people. We examine five core political attitudes concerning how people view the political world and their role in it. Most of their variance reflects infrequently-changing individual characteristics and time-specific effects. Permanent heterogeneity plays a modest role. External efficacy is most influential concerning evaluations of the external political world, while internal efficacy is influential for views on one’s role in politics. Another application examines the role of ideological and party identification on attitudes toward government spending and immigration. The attitudes form a weakly constrained attitude system. Party identification is the most influential, through spillovers to ideological identification. Party and ideological identifications are stable, time-invariant traits explaining most of their variance, with transitory shocks that hint at measurement error and/or expressive responding. Issue attitudes are unstable, driven mainly by transitory shocks.

Outer space is increasingly central to international security. The use of Starlink in the Russo–Ukrainian war has enabled Ukrainian operations while negating Russian interference. Having witnessed Starlink’s crucial impact in Ukraine, several states seek to emulate the system’s offensive and defensive advantages. This article analyses how the onset of mega-constellations – satellite systems consisting of very high numbers of smaller satellites – will affect stability in the space domain. As states are increasingly dependent on space for both nuclear and conventional operations, the stability of the space domain is a key concern for international security. Showing how mega-constellations can mitigate existing vulnerabilities in space while generating offensive advantages on earth, this article shows that their proliferation is likely to make conventional counterspace attacks ineffective and costly. Therefore, mega-constellations will have a stabilising effect between states equally dependant on space. However, under conditions of asymmetric dependence, less space-reliant states may find incentives to employ highly destructive weapons, including nuclear weapons, to disable adversary mega-constellations. Accordingly, the proliferation of mega-constellations may act in a destabilising manner, especially if under conditions of asymmetry in space.