Search

In view of the importance of predator-dependent functional response and fear of prey induced by powerful predators, we construct a delayed prey–predator model with fear and Beddington–DeAngelis functional response. The existence, uniqueness, and global asymptotic stability of equilibrium points are investigated and some criteria are established. Next, Hopf bifurcation analysis is executed, and the critical values of such bifurcation parameters as fear and delay for the determinate system are obtained. Then we extend it to a random environment and study the boundedness of expectation of solutions and the global asymptotic stability. Finally, the main findings are validated by numerical examples. It is worth noting that the specific influences of fear by predator, time delay, and white noise are explored numerically. Simulation figures intuitively exhibit that fear, delay, and white noise bring serious influences on the stability of the system. Fear from predator leads to a lower equilibrium state of prey and predator, and it can change the system stability from unstable to stable after exceeding a certain critical value. The time delay has a significant impact on the system stability by producing Hopf bifurcations accompanied by limit cycles, and even lead to multiple stabilities. Larger white noise can change the system stability from stable to unstable. [ABSTRACT FROM AUTHOR]

Let LL be a lattice of rank nn in an nn-dimensional Euclidean space. We show that the coincidence isometry group of LL is generated by coincidence reflections if and only if LL contains an orthogonal subset of order nn.

The inclusion graph of a group G, written as I n (G) , is defined to be an undirected graph with all nontrivial subgroups of G as its vertices, and two distinct subgroups H, K of G are adjacent if either H ≤ K or K ≤ H . A local inclusion graph of G with respect to a given subgroup S, written as I n (G , S) , is an induced subgraph of I n (G) with vertex set consisting of all nontrivial subgroups of G properly containing S. Indeed, I n (G) can be viewed as the special case when S is the identity subgroup. Let GL n (F) be the general linear group consisting of all n × n invertible matrices over a field F and T n (F) the subgroup of all invertible lower triangular matrices in GL n (F) . In this article, an arbitrary automorphism of I n ( GL n (F) , T n (F)) is determined and it is proved that the automorphism group of I n ( GL n (F) , T n (F)) is isomorphic to the direct product of S n − 1 and S 2 , where S n − 1 is the symmetric group of degree n − 1 . [ABSTRACT FROM AUTHOR]

Let G be a finite group. The subgroup intersection graph Γ(G)\text{Γ}(G) of G is a graph whose vertices are non-identity elements of G and two distinct vertices x and y are adjacent if and only if |〈x〉∩〈y〉|>1|\langle x\rangle \cap \langle y\rangle |\gt 1, where 〈x〉\langle x\rangle is the cyclic subgroup of G generated by x. In this paper, we show that two finite abelian groups are isomorphic if and only if their subgroup intersection graphs are isomorphic.

I–III–VI-group semiconductor nanocrystals (NCs) have received extensive attention for use in quantum-dot light-emitting diodes (QLEDs) due to their nontoxic nature, large-scale tunable emission wavelength and straightforward synthesis. At present, research on ternary CuGaSe2 (CGSe) NCs is gradually being carried out. CGSe-based semiconductor NCs with a wide and tunable bandgap exhibit significant promise for efficient QLEDs preparation. In order to improve their functionality, stability and dispersion, Zn2+ was introduced into CGSe cores, which were coated with wide-band-gap ZnS to form Cu–Ga–Zn–Se/ZnS NCs to improve their luminescence performance. In this work, a series of Cu–Ga–Zn–Se/ZnS NCs with tunable emission from 603 to 524 nm and a photoluminescence quantum yield (PLQY) of 96% could be acquired by precisely controlling the non-stoichiometric Cu : Ga molar ratios in the synthesis of the CGZSe cores. Furthermore, green luminescent CGZSe/ZnS NCs were obtained by adjusting the amount of crucial Zn precursors during nucleation and shell formation. The green QLEDs based on these NCs show a high external quantum efficiency of 5.8% and a high brightness of 7016 cd m−2. This work reveals new possibilities for the design of novel and efficient Cd-free green QLEDs. [ABSTRACT FROM AUTHOR]