here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

let $r$ be a commutative ring and let $m$ be an $r$-module. in this article, we introduce the concept of the zariski socles of submodules of $m$ and investigate their properties. also we study modules with noetherian second spectrum and obtain some related results.

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

We introduce the affine ensemble, a class of determinantal point processes (DPP) in half-plane $\mathbb{C}^{+}$ associated with $ax + b$ (affine) group, depending on an admissible Hardy function $\psi$. obtain asymptotic behavior variance, exact value constant, and non-asymptotic upper lower bounds for variance compact set $\Omega \subset \mathbb{C}^{+}$. As special case one recovers DPP relate...

We investigate the Benjamin-Feir (or modulational) instability of Stokes waves, i.e., small-amplitude, one-dimensional periodic gravity waves permanent form and constant velocity, in water finite infinite depth. develop a perturbation method to describe high-order accuracy unstable spectral elements associated with this instability, obtained by linearizing Euler's equations about small-amplitud...

In this paper, we study the problem on small motions of ideal relaxing fluid that fills a uniformly rotating or fixed container. We prove theorem uniform strong solvability corresponding initial-boundary problem. case where system does not rotate, find asymptotic behavior solution under stress special form. investigate spectral associated with considered system. obtain localization results for ...

The Baxter-like functional equation encoding the spectrum of anomalous dimensions of Wilson operators in maximally supersymmetric Yang-Mills theory available to date ceases to work just before the onset of wrapping corrections. In this paper, we work out an improved finitedifference equation by incorporating nonpolynomial effects in the transfer matrix entering as its ingredient. This yields a ...