Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response

In this paper, we discuss a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if the white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results.     

Qualitative analysis of a stochastic ratio-dependent predator-prey system

A stochastic ratio-dependent predator-prey model is investigated in this paper. By the comparison theorem of stochastic equations and Itô’s formula, we obtain the global existence of a positive unique solution of the ratio-dependent model. Besides, a condition for species to be extinct is given and a persistent condition is established. We also conclude that both the prey population and the ratio-dependent function are stable in time average. In the end, numerical simulations are carried out to confirm our findings.     

Homotopy perturbation-reproducing kernel method for nonlinear systems of second order boundary value problems

In this paper, based on homotopy perturbation method (HPM) and reproducing kernel method (RKM), a new method is presented for solving nonlinear systems of second order boundary value problems (BVPs). HPM is based on the use of traditional perturbation method and homotopy technique. The HPM can reduce a nonlinear problem to a sequence of linear problems and generate a rapid convergent series solution in most cases. RKM is also an analytical technique, which can solve powerfully linear BVPs. Homotopy perturbation-reproducing kernel method (HP-RKM) combines advantages of these two methods and therefore can be used to solve efficiently systems of nonlinear BVPs. Three numerical examples are presented to illustrate the strength of the method.     

Li3V2(PO4)3/graphene nanocomposites as cathode material for lithium ion batteries

Li(3)V(2)(PO(4))(3)/graphene nanocomposites have been firstly formed on reduced graphene sheets as cathode material for lithium batteries. The nanocomposites synthesized by the sol-gel process exhibit excellent high-rate and cycling stability performance, owing to the nanoparticles connected with a current collector through the conducting graphene network.     

Large orbit sizes in finite group actions

In this paper, we study the relations of the sizes of various sections of finite linear groups and the largest orbit size of the linear group actions. We also study various applications of those orbit theorems.     

On some properties of symplectic Grothendieck polynomials

Grothendieck polynomials, introduced by Lascoux and Schützenberger, are certain K-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the K-theory classes of orbit closures for the complex symplectic group acting on the complete flag variety. We prove a transition formula for symplectic Grothendieck polynomials and study their stable limits. We show that each of the K-theoretic Schur P-functions of Ikeda and Naruse arises from a limiting procedure applied to symplectic Grothendieck polynomials representing certain “Grassmannian” orbit closures.     

Some classes of abstract simplicial complexes motivated by module theory

In this paper we analyze some classes of abstract simplicial complexes relying on algebraic models arising from module theory. To this regard, we consider a left-module on a unitary ring and find models of abstract complexes and related set operators having specific regularity properties, which are strictly interrelated to the algebraic properties of both the module and the ring.Next, taking inspiration from the aforementioned models, we carry out our analysis from modules to arbitrary sets. In such a more general perspective, we start with an abstract simplicial complex and an associated set operator. Endowing such a set operator with the corresponding properties obtained in our module instances, we investigate in detail and prove several properties of three subclasses of abstract complexes.More specifically, we provide uniformity conditions in relation to the cardinality of the maximal members of such classes. By means of the notion of OSS-bijection, we prove a correspondence theorem between a subclass of closure operators and one of the aforementioned families of abstract complexes, which is similar to the classic correspondence theorem between closure operators and Moore systems. Next, we show an extension property of a binary relation induced by set systems when they belong to one of the above families.Finally, we provide a representation result in terms of pairings between sets for one of the three classes of abstract simplicial complexes studied in this work.     

Pulsed field ionisation—ZEKE photoelectron spectrum of o-, m- and p-tolunitrile

Pulsed field ionisation—ZEKE photoelectron spectroscopy has been applied to o-, m- and p-tolunitrile in a supersonic jet. The PFI-ZEKE photoelectron spectra of m- and p-tolunitrile show well-resolved anharmonic structures in the low-frequency region, which are assigned to bands due to internal rotational motion of the methyl group in the cation. Level energies and relative transition intensities are reproduced well by a one-dimensional rotor model with a three-fold axis potential. Potential curves for the internal rotation have been determined. For o-tolunitrile, no band due to internal rotation was found in PFI-ZEKE spectrum. It is suggested that the o-tolunitrile cation has the high barrier for internal rotation and the stable conformation that is the same as that in S₁ and S₀. The barrier height and the conformation are compared with other toluene derivatives, and the relation between the electronic character of –CN and the internal rotational motion has been discussed.     

Bounding the Fitting height of a solvable group by the number of zeros in a character table

In this paper, we bound the Fitting height of a solvable group by the number of zeros in a character table.

     

关于一类含有Dziok-Srivastava算子的多叶解析函数的包含关系和卷积性质

该文引进和研究了一类含有Dziok-Srivastava算子的新的多叶解析函数. 得到了这一函数类中的一些有趣的性质, 如包含关系, 卷积性质等. 这些结果改进和拓展了早期的一些工作. 同时也得到了其他一些新的结果.