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.

Around the start of the 21st century, countries began to experience a unique demographic transition. After generations of declining dependency and expanding labor forces, increasing longevity and persistently low fertility have reversed dependency trajectories. This paper examines the political consequences of rapid demographic aging and retirement reforms. An empirical assessment of 41 countries from 1980 to 2020 suggests that efforts to postpone retirement are politically destabilizing. In particular, increases in average retirement age and labor force participation among older cohorts may increase political instability. Demographic forecasts for rich and middle-income countries indicate a massive growing demand for age-related public services, alongside a rapid decline in the relative size of economically active populations. Policy reform is therefore urgently needed to sustain pension systems, maintain economic growth, and mitigate political instability. The paper concludes that governments must consider country-specific demographic, political, and economic conditions when designing alternatives to potentially destabilizing retirement reforms.

In this study, a Holling–Tanner type predator–prey model with a discrete time delay is investigated, where the functional response of the predator dynamics is ratio-dependent. We first analyze the local stability of the equilibrium point and examine the existence of Hopf bifurcations. The Hopf bifurcation, also known as the Poincaré–Andronov–Hopf bifurcation, is named after the French mathematician Jules Henri Poincaré, the Russian mathematician Alexander A. Andronov, and the German mathematician Heinz Hopf, whose fundamental contributions laid the foundation of this theory. By treating the delay parameter $\tau $ as the bifurcation parameter, we show that a Hopf bifurcation occurs when the delay crosses certain critical values. Finally, numerical simulations are carried out to support and illustrate our theoretical results.

Time is among the most fundamental categories of political and, specifically, democratic life. While time in the sociopolitical world leaves traces in many (subtle) ways, we do not find it among the guiding concepts of democratic theory. This Special Issue, therefore, understands itself as part of a project that traces the centrality of time and temporality in democratic theory and practice. Our goal is to move toward an in-depth discussion of time in democratic theory by unearthing and systematizing the fragments of this emerging agenda. In this editorial, we deepen the status of time in democratic theory. We do this by discussing both the research that explicitly addresses the relationship between time and democracy and the many latent forms of how temporality shapes democratic thinking. Finally, we identify three dimensions of how time is relevant in and for democratic theory, and we locate the contributions to this Special Issue regarding these dimensions.

We consider the one dimensional 4th order, or bi-harmonic, nonlinear Schrödinger (NLS) equation, namely, $iu_t - \Delta^2 u - 2a \Delta u + |u|^{\alpha} u = 0, ~ x,a \in \mathbb R$, $\alpha \gt 0$, and investigate the dynamics of its solutions for various powers of $\alpha$, including the ground state solutions and their perturbations, leading to scattering or blow-up dichotomy when $a \leq 0$, or to a trichotomy when $a \gt 0$. Ground state solutions are numerically constructed, and their stability is studied, finding that the ground state solutions may form two branches, stable and unstable, which dictates the long-term behaviour of solutions. Perturbations of the ground states on the unstable branch either lead to dispersion or the jump to a stable ground state. In the critical and supercritical cases, blow-up in finite time is also investigated, and it is conjectured that the blow-up happens with a scale-invariant profile (when $a=0$) regardless of the value of $a$ of the lower dispersion. The blow-up rate is also explored.

In this paper, a single passage unsteady numerical simulation is carried out. Three different self-recirculating casing treatment structures with circumferential coverage ratios of 20%, 40% and 60% were designed. The calculation results show that as the circumferential coverage ratio increases, the stability enhancement ability of the self-recirculating casing also increases. Especially when the circumferential coverage ratio increases to 60%, the self-recirculating casing achieves the largest increase in stall margin, with an increase of 49.05%, but the decrease in the peak efficiency is 1.33%. An increase in the circumferential coverage ratio enhances the suction capacity of the self-recirculating casing. This enables it to better suppress the expansion of the leakage flow and reduce the degree of blockage within the passage. The self-recirculating casing can inhibit the occurrence of vortex breakdown in the tip passage. However, at the low flow rate point, it cannot effectively eliminate the interaction between the leakage streamlines. When the circumferential coverage ratio is relatively large, it can suppress the airflow separation phenomenon. The flow separation near the blade trailing edge and the mixing of the leakage flow within the tip passage are important reasons for the internal flow instability of the self-recirculating casing compressor.

We show that for any integer $k\ge 1$ there exists an integer $t_0(k)$ such that, for integers $t, k_1, \ldots , k_{t+1}, n$ with $t\gt t_0(k)$, $\max \{k_1, \ldots , k_{t+1}\}\le k$, and $n \gt 2k(t+1)$, the following holds: If $F_i$ is a $k_i$-uniform hypergraph with vertex set $[n]$ and more than $ \binom{n}{k_i}-\binom{n-t}{k_i} - \binom{n-t-k}{k_i-1} + 1$ edges for all $i \in [t+1]$, then either $\{F_1,\ldots , F_{t+1}\}$ admits a rainbow matching of size $t+1$ or there exists $W\in \binom{[n]}{t}$ such that $W$ intersects $F_i$ for all $i\in [t+1]$. This may be viewed as a rainbow non-uniform extension of the classical Hilton-Milner theorem. We also show that the same holds for every $t$ and $n \gt 2k^3t$, generalizing a recent stability result of Frankl and Kupavskii on matchings to rainbow matchings.

Smith’s “luxury hypothesis” seems to assert that the endless violence of the feudal era ended with the appearance of luxury goods. This view holds that feudal lords had nothing to do with their wealth but to wage war—no other markets were available to them. As luxury goods became available, the lords dropped their weapons and disbanded their armies so that they could buy more luxury goods. The traditional account has causality going from the appearance of luxury goods to the lords disbanding their armies. On my approach, ubiquitous violence under feudalism implies that the causal logic in this account goes from the logic of violence to the gradual and sequential appearance of luxury goods to ending violence near the towns and cities, but not in the agrarian hinterland.

In deep learning (DL), the instability phenomenon is widespread and well documented, and the most commonly used measure of stability is the Lipschitz constant. While a small Lipchitz constant is traditionally viewed as guarantying stability, it does not capture the instability phenomenon in DL for classification well. The reason is that a classification function – which is the target function to be approximated – is necessarily discontinuous, thus having an ‘infinite’ Lipchitz constant. As a result, the classical approach will deem every classification function unstable, yet basic classification functions a la ‘is there a cat in the image?’ will typically be locally very ‘flat’ – and thus locally stable – except at the decision boundary. The lack of an appropriate measure of stability hinders a rigorous theory for stability in DL, and consequently, there are no proper approximation theoretic results that can guarantee the existence of stable networks for classification functions. In this paper, we introduce a novel stability measure $\mathcal{S}(f)$, for any classification function $f$, appropriate to study the stability of classification functions and their approximations. We further prove two approximation theorems: First, for any $\epsilon \gt 0$ and any classification function $f$ on a compact set, there is a neural network (NN) $\psi$, such that $\psi - f \neq 0$ only on a set of measure $\lt \epsilon$; moreover, $\mathcal{S}(\psi ) \geq \mathcal{S}(f) - \epsilon$ (as accurate and stable as $f$ up to $\epsilon$). Second, for any classification function $f$ and $\epsilon \gt 0$, there exists a NN $\psi$ such that $\psi = f$ on the set of points that are at least $\epsilon$ away from the decision boundary.

This paper focuses on six-degree-of-freedom (six-DOF) spatial cable-suspended parallel robots with eight cables (8-6 CSPRs) because the redundantly actuated CSPRs are relevant in many applications, such as large-scale assembly and handling tasks, and pick-and-place operations. One of the main concerns for the 8-6 CSPRs is the stability because employing cables with strong flexibility and unidirectional restraint operates the end-effector of the robot under external disturbances. As a consequence, this paper attempts to address two key issues related to the 8-6 CSPRs: the force-pose stability measure method and the stability sensitivity analysis method. First, a force-pose stability measure model taking into account the poses of the end-effector and the cable tensions of the 8-6 CSPR is presented, in which two cable tension influencing factors and two position influencing factors are developed, while an attitude influence function representing the influence of the attitudes of the end-effector on the stability of the robot is constructed. And furthermore, a new type of workspace related to the force-pose stability of the 8-6 CSPRs is defined and generated in this paper. Second, a force-pose stability sensitivity analysis method for the 8-6 CSPRs is developed with the gray relational analysis method, where the relationship between the force-pose stability of the robot and the 14 influencing factors (the end-effector’s poses and cable tensions) is investigated to reveal the sequence of the 14 influencing factors on the force-pose stability of the robot. Finally, the proposed force-pose stability measure method and stability sensitivity analysis method for the 8-6 CSPRs are verified through simulations.

Bovine mastitis poses a significant threat to dairy production worldwide. Among the various etiologies of mastitis, Escherichia coli is a predominant environmental pathogen. Antibiotic-resistant E. coli poses substantial challenges for treating mastitis and is a threat to public health, necessitating the exploration of alternative therapeutic strategies. We studied bacteriophages as a potential alternative therapy for bovine mastitis-associated E. coli. We isolated 37 bacteriophages infecting E. coli, and characterized them for host range, growth kinetics, morphology, stability, genome fingerprinting and genome sequencing and analysis. The phages lysed between 4% and 62% of the E. coli isolates tested. Notably, 30 phages lysed bovine mastitis-associated strains. The 10 best phages selected based on host strain specificity revealed latent periods ranging from 50 to 90 min and burst sizes between 7 and 69 PFU/mL. Based on their shorter latent period and larger burst size, seven phages were subjected to transmission electron microscopy, which revealed their myovirus and siphovirus morphologies. Restriction fragment length polymorphism (RFLP) analysis of the same seven phages indicated six different patterns. The seven phages were stable at temperatures ranging from 4°C to 50°C, and at pH values ranging from 3 to 9. Whole-genome sequencing and analysis of the six phages, which showed unique RFLP patterns, predicted a lytic lifecycle, with no sequences encoding toxins or antibiotic-resistance genes. Importantly, these six phages were able to lyse multidrug-resistant and extended β-lactamase (ESBL)-producing E. coli under in vitro conditions and mastitis-associated E. coli in milk. Additionally, three phages belonging to different genera did not exhibit toxicity to mammalian cells. This study underscores the potential of bacteriophages as alternative therapeutic agents for E. coli-associated bovine mastitis. Our study has broader implications for udder and animal health, as well as the production of quality milk and dairy products, and food safety and security.