Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when it is homotopy equivalent to a sphere., Nela Milošević, Zoran Z. Petrović., and Obsahuje seznam literatury
The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces ({\text{ce}}{{\text{s}}_\varphi }) defined by an Orlicz function φ equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro sequence space cesp and some other sequence spaces. Finally, a new constant \widetilde D (X), which seems to be relevant to the packing constant, is given., Zhen-Hua Ma, Li-Ning Jiang, Qiao-Ling Xin., and Obsahuje seznam literatury
In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces have three-dimensional centre., Mehri Nasehi., and Obsahuje seznam literatury
Let f: X → X be a continuous map with the specification property on a compact metric space X. We introduce the notion of the maximal Birkhoff average oscillation, which is the “worst” divergence point for Birkhoff average. By constructing a kind of dynamical Moran subset, we prove that the set of points having maximal Birkhoff average oscillation is residual if it is not empty. As applications, we present the corresponding results for the Birkhoff averages for continuous functions on a repeller and locally maximal hyperbolic set., Jinjun Li, Min Wu., and Obsahuje seznam literatury
We solve the initial value problem for the diffusion induced by dyadic fractional derivative s in \mathbb{R}^{+}. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator. As a consequence we obtain the pointwise convergence to the initial data., Marcelo Actis, Hugo Aimar., and Obsahuje seznam literatury
Given a distribution $T$ on the sphere we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $\xi$ of the sphere and we show that if $T$ has the value $\tau$ at $\xi$, then the Fourier-Laplace series of $T$ at $\xi$ is Abel-summable to $\tau$., Francisco Javier González Vieli., and Obsahuje bibliografii
In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map φ: G → G defined by gφ = [g,α] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H″ is included in the centre of H and CH(α2) is abelian, both CG(α2) and G/[G, α2] are abelian-by-finite. These results extend recent and classical results in the literature., Tao Xu, Fang Zhou, Heguo Liu., and Obsahuje seznam literatury
We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural numerical conditions., Jae-Hyouk Lee, Mang Xu, Jiajin Zhang., and Seznam literatury
We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation., Li Zu, Daqing Jiang, Donal O'Regan., and Obsahuje bibliografii
We show that the Porous Medium Equation and the Fast Diffusion Equation, \dot u - \Delta {u^m} = f with m\in (0, \infty ), can be modeled as a gradient system in the Hilbert space H^{-1}(\Omega ), and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets \Omega \subset \mathbb{R}^{n} and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions., Samuel Littig, Jürgen Voigt., and Obsahuje seznam literatury