In this paper, we review some recent results on the effects of heterogeneous spatial environment on various population models. By making use of the observation that the population models make deep changes of behavior when certain coefficient functions vanish in the underlying domain, it is shown that sharp stable patterns can be obtained if the heterogeneous environment is designed suitably. The one species logistic model, two species competition and predator-prey models are discussed

In the present paper, we introduce the Bezier variant of Phillips operators and study the rate of convergence for the Phillips-Bezier operators for bounded variation functions.

We consider some special generalized functional identities on a prime ring $% R $, such that the existence of nonstandard solutions of these identities yields a more refined conclusion than just that $R$ satisfies a generalized polynomial identity.

In this paper we introduce full elements in regular rings, and show that every matrix over regular rings admits a diagonal reduction by full matrices. Also we get that a regular ring $R$ is unit-regular if and only if $aR\cong bR$ with full elements $a,b\in R$ implies $a=ubv$ for some units $u,v\in R$.

By using the continuation theorem base on Gaines and Mawhin$^{^{\prime }}$s coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a delayed food chain model. Indeed, our result are applicable to distributed delays.

Boundedness of components of the Fatou set of the skew product is studied, which is associated with finitely generated meromorphic semigroup.

In this paper, we investigate the conjecture of R. Br\"{u}ck, and prove that the conjecture of R. Br\"{u}ck holds for entire functions of infinite order and hyper order less than $\frac{1}{2}.$

In this paper, we consider an autonomous model with impulsive harvest. We investigate the impulsive harvest policies for constant effort harvest and proportional harvest. For different harvest effort function, it is shown that there exists an unique impulsive periodic solution which is semi-stable or globally asymptotically stable. For the latter, the optimal harvest effort that maximizes the sustainable yield per unit time is determined.

We extend the simple multi-choice game to a multi-valued multi-choice game We prove that the Shapley value for multi-valued multi-choice games is unique and coincides with the Shapley value for multi-choice cooperative games.

In this paper, we consider the Lidstone boundary value problem $$(\Phi (y^{(2n-1)}))^{'}(t)=f(t,y(t),y^{''}(t),\cdots ,y^{(2(n-1))}(t)), ~~~0\leq t\leq 1,$$ $$y^{(2i)}(0)=y^{(2i)}(1)=0,~~~0\leq i\leq n-1,$$ where $f: [0,1]\times R^{n}\rightarrow R$ is continuous, $\Phi(v)=|v|^{p-2}v,~p\gt 1$. Growth conditions are imposed on $f$ which yield the existence of at least two symmetric positive solutions by using a fixed point theorem in cones.

Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which receives the least possible amount of tension imposed on the submanifold from the ambient space. The purpose of this paper is to classify conformally flat ideal hypersurfaces in real space forms; thus we completely determine conformally flat manifolds which admit codimension one isometric immersions into real space forms with least possible tension.

This paper highlights a new short proof of a generalization of Gelfand's theorem through the use of spectral distributions. But above all it aims at studying, when the spectrum is discrete, if the operator admits a spectral resolution of the identity.

Let $R$ be a ring and $M$ a left $R-$module. The radical of $M$ is the intersection of all prime submodules of $M.$ It is proved that if $R$ is a hereditary, noetherian, prime and non right artinian and $M$ a finitely generated $R-$module then the radical of $M$ has a certain form.

Sufficient and necessary condition of Orlicz spaces equipped with Orlicz norm that are uniformly rotund in the direction of weakly compact sets using only conditions on generated function of the space are given