Let $K^r_n$ be the complete $r$-uniform hypergraph on $n$ vertices, that is, the hypergraph whose vertex set is $[n] \, :\! = \{1,2,\ldots ,n\}$ and whose edge set is $\binom {[n]}{r}$. We form $G^r(n,p)$ by retaining each edge of $K^r_n$ independently with probability $p$. An $r$-uniform hypergraph $H\subseteq G$ is $F$-saturated if $H$ does not contain any copy of $F$, but any missing edge of $H$ in $G$ creates a copy of $F$. Furthermore, we say that $H$ is weakly $F$-saturated in $G$ if $H$ does not contain any copy of $F$, but the missing edges of $H$ in $G$ can be added back one-by-one, in some order, such that every edge creates a new copy of $F$. The smallest number of edges in an $F$-saturated hypergraph in $G$ is denoted by ${\textit {sat}}(G,F)$, and in a weakly $F$-saturated hypergraph in $G$ by $\mathop {\mbox{$w$-${sat}$}}\! (G,F)$. In 2017, Korándi and Sudakov initiated the study of saturation in random graphs, showing that for constant $p$, with high probability ${\textit {sat}}(G(n,p),K_s)=(1+o(1))n\log _{\frac {1}{1-p}}n$, and $\mathop {\mbox{$w$-${sat}$}}\! (G(n,p),K_s)=\mathop {\mbox{$w$-${sat}$}}\! (K_n,K_s)$. Generalising their results, in this paper, we solve the saturation problem for random hypergraphs $G^r(n,p)$ for cliques $K_s^r$, for every $2\le r \lt s$ and constant $p$.

The aetiology of cyanosis could be unclear in children, even for specialised paediatricians. Two cases were reported: first, a 6-year-old child with features of left isomerism and Fallot was fortuitously diagnosed with anomalous hepatic venous drainage before complete repair. Second, a newborn with an antenatal diagnosis of ductus venosus agenesis had an isolated intermittent right-to-left atrial shunt when upright, with favourable outcome, in contrast to the association with significant heart malformations including inferior caval vein interruption. Multimodality imaging and 3D printing helped to rule out extracardiac causes of persistent cyanosis and plan surgical repair.

Let $G$ be a reductive group over an algebraically closed field $k$ of separably good characteristic $p>0$ for $G$. Under these assumptions, a Springer isomorphism $\phi : \mathcal {N}_{\mathrm {red}}(\mathfrak {g}) \rightarrow \mathcal {V}_{\mathrm {red}}(G)$ from the nilpotent scheme of $\mathfrak {g}$ to the unipotent scheme of $G$ always exists and allows one to integrate any $p$-nilpotent element of $\mathfrak {g}$ into a unipotent element of $G$. One should wonder whether such a punctual integration can lead to an integration of restricted $p$-nil $p$-subalgebras of $\mathfrak {g}= \operatorname {Lie}(G)$. We provide a counter-example of the existence of such an integration in general, as well as criteria to integrate some restricted $p$-nil $p$-subalgebras of $\mathfrak {g}$ (that are maximal in a certain sense). This requires the generalisation of the notion of infinitesimal saturation first introduced by Deligne and the extension of one of his theorems on infinitesimally saturated subgroups of $G$ to the previously mentioned framework.

This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

This is the second part of our study on the spatially heterogeneous predator–prey model where the interaction is governed by a Crowley–Martin type functional response. In part I, we have proved that when the predator competition is strong (i.e. k is large), the model has at most one positive steady-state solution for any $\mu \in \mathbb {R}$, moreover it is globally asymptotically stable for any $\mu >0$. This part is denoted to study the effect of saturation. Our result shows that the large saturation coefficient (i.e. large m) can not only lead to the uniqueness of positive solutions, but also lead to the multiplicity of positive solutions, moreover the stability of the corresponding positive solutions is also completely obtained. This work can be regarded as a supplement of Ref. [10].

We show that, assuming the existence of the canonical inner model with one Woodin cardinal $M_1 $ , there is a model of $ZFC$ in which the nonstationary ideal on $\omega _1 $ is $\aleph _2 $-saturated and whose reals admit a ${\rm{\Sigma }}_4^1 $-wellorder.

A nonlinear station-keeping control method for a multi-vectored propeller airship under unknown wind field with thrust saturation is developed, which is composed of three modules: nonlinear model predictive controller (NMPC), disturbance observer (DOB) and tracking differentiator (TD). The nonlinear kinematics and dynamics models are introduced, and the wind effect is considered by the wind-induced aerodynamic force. Based on both models, an explicit NMPC is designed. Then a nonlinear DOB is introduced to estimate the wind disturbance. A TD, showing the relationship between the maximum propulsion force and the maximum flight acceleration, is proposed to handle the thrusts’ amplitude saturation. Stability analysis shows that the closed-loop system is globally asymptotically stable. Simulations for a multi-vectored propeller airship are conducted to demonstrate the robustness and effectiveness of the proposed method.

This paper presents a simplified theoretical model for the study of emission from laser produced plasma to better understand the processes and the factors involved in the onset of saturation in plasma emission as well as in increasing emission due to plasma confinement. This model considers that plasma emission is directly proportional to the square of plasma density, its volume, and the fraction of laser pulse absorbed through inverse Bremsstrahlung in the pre-formed plasma plume produced by the initial part of the laser. This shows that plasma density and temperature (that means the electron-ion collision frequency νei) decide the threshold for saturation in emission, which occurs for νei ≥ 1013 s−1, beyond which plasma shielding effects become dominant. Any decrease in plasma sound (expansion) velocity shows drastic enhancement in emission supporting the results obtained by magnetic as well as spatial confinement of laser produced plasma. The temporal evolution of plasma emission in the absence and presence of plasma confinement along with the effect of laser pulse duration are also discussed in the light of this model.

We show that spacing statistics can be obtained for all fracture densities by the same equation. Using the simple ‘shear lag’ theory, it is demonstrated that the results adequately fit experimental measurements. Theoretically, it is shown that two parameters are sufficient to characterize all spacing distributions. It is found that no real spacing saturation exists. Rather, a very low increase in joint densities occurs for a very high incremental stress increase. Moreover the transition to this kind of saturation is gradual and not abrupt. In this way the high density distributions with very small inter-joint distances, which pose a problem for saturation models, are directly explained. Correlation with creep experiments is also established. Comparison of our method with Weibull statistics is performed.

We present the outcomes of the consistent analysis of 6 epochs of VLBA 12.2 GHz data obtained between 1995 and 2005 towards the known high-mass star formation reigon NGC7538 IRS1 N. Our analysis concentrates on the study of the main spectral/spatial feature, which is 20 VLBA synthesized beams in size with a distinct velocity gradient. We looked for proper motion signals relative to the central peak which, in an edge-on disc framework, is expected to be stationary. We also study the peak flux and the spatial brightness profile of the main maser feature searching for maser variability. Our results are twofold: we detect a clear proper motion signal of three spatial features (0.21, 0.1, 0.65 mas yr−1) and conclude that these can be made consistent with previous modelling of a Keplerian disc seen edge-on around a high-mass protostar. We further detect a consistent decrease of the peak flux over the time-span 1995-2005 (~ 5.4 Jy yr−1), confirmed when taking into account earlier data (1986, 1987) as well as by the 6.7 GHz maser emission. Also, the width of the spatial brightness profile of the main feature seems to decrease between 1995 and 2005 by some 50%. We consider these observables as clear signs of partial maser saturation.

The role of interspecific interactions in the structure of gastrointestinal helminth communities has been at the core of most research in parasite community ecology, yet there is no consensus regarding their general importance. There have been two different approaches to the study of species interactions in helminths. The first one consists of measuring the responses of helminth species in concomitant infections, preferably in laboratory experiments. Any change in numbers of parasite individuals or in their use of niche space, compared with what is observed in single infections, provides solid evidence that the species are interacting. The second approach can only provide indirect, circumstantial evidence. It consists in contrasting observed patterns either in the distribution of species richness of infracommunities from wild hosts, in their species composition, or in pairwise associations between helminth species among infracommunities, with the random patterns predicted by appropriate null models. In many cases, observed patterns do not depart from predicted ones; when they do, alternative explanations are usually as plausible as invoking the effect of interactions among helminth species. The present evidence suggests that the role of species interactions in helminth community structure is often negligible, but that it must always be evaluated on a case-by-case basis.

We describe possible solutions for a stationary flow of two superposed fluids between two close surfaces in relative motion. Physically, this study is within the lubrication framework, in which it is of interest to predict the relative positions of the lubricant and the air in the device. Mathematically, we observe that this problem corresponds to finding the interface between the two fluids, and we prove that this interface can be viewed as a square root of a polynomial of degree at most 6. We solve this equation using an original method. First, we check that our results are consistent with previous work. Next, we use this solution to answer some physically relevant questions related to the lubrication setting. For instance, we obtain theoretical and numerical results, which can predict the occurrence of a full film with respect to physical parameters (fluxes, shear velocity, viscosities). In particular, we present a figure giving the number of stationary solutions depending on the physical parameters. Moreover, we give some indications for a better understanding of the multi-fluid case.