Oscillatory traveling waves of polytropic filtration equation with generalized Fisher–KPP sources

The polytropic filtration equation with generalized Fisher–KPP sources is considered. We will show that the equation may have finite times oscillatory traveling waves, and try to give a complete classification by virtue of a singular exponent in the source according to the finiteness of the oscillatory times of traveling waves.     

On the third gap for proper holomorphic maps between balls

Let $F$ be a proper rational map from the complex ball $\mathbb B ^n$ into $\mathbb B ^N$ with $n>7$ and $3n+1 \le N\le 4n-7$ . Then $F$ is equivalent to a map $(G, 0, \dots , 0)$ where $G$ is a proper holomorphic map from $\mathbb B ^n$ into $\mathbb B ^{3n}$ .     

The Kloosterman problem for binary Hermitian lattices

A Hermitian lattice over an imaginary quadratic field $\mathbb {Q}(\sqrt{-m})$ is called almost universal if it represents all but finitely many positive integers. We investigate almost universal binary Hermitian lattices and provide a Bochnak-Oh type criterion on almost universality. In particular, all almost universal $p$ -anisotropic binary Hermitian lattices are universal, and we give the complete list of all such Hermitian lattices.     

Evolution of innovation and its strategies: from ecological niche models of supply chain clusters

Generally, supply chain cluster (SCC) evolution follows innovation and its selection strategies. To further reduce the innovation risk, SCC must seek the feasible innovation strategies to match ecological niche-matching degree; within a competing cluster, it should avoid the hazardous nature of pure competition that affects the innovation output, and within a cooperation innovation cluster it should look carefully for the cooperation innovation mechanism. This paper examines the impact of growth of SCC from a perspective of ecological niche, the innovation strategy and the expansion of ecological niche, and its matching degree on the influence of the growth in SCC; and presents the ecological niche expansion model, growth model and growth evolution model of SCC. The findings of this research suggest that there is a five-stage evolution of which the characteristic is different in different innovation strategies. The ecological niche width of SCC is connected by each member’s ecological niche, and the expansion process is constituted by the members’ ecological niche expansion. In each stage, SCC should identify ecological niche-matching degree between members and innovation modes when the SCC expands the niche width to a certain limit. Finally, a case study demonstrates the application potential of the model and its implications.     

Topological Structure of the Space of Weighted Composition Operators Between Different Hardy Spaces

We consider properties related to weighted composition operators boundedly acting from the classical Hardy space H ^p to H ^q for \({1 \leq q < p < \infty}\) . Especially, we shall completely determine path connected components in the set of weighted composition operators and explicitly characterize by function-theoretic properties of analytic self-maps.     

Schur定理的推广

通过计算及归纳的方法,得到了n×n矩阵代数中极大线性无关的反交换2-幂零矩阵的个数,推广了相关文献中的一般线性李代数gl(n)的交换子代数的最大维数这一结论.     

Besov and Hardy Spaces Associated with the Schrödinger Operator on the Heisenberg Group

We introduce the Besov space $\dot{B}^{0,L}_{1,1}$ associated with the Schrödinger operator L with a nonnegative potential satisfying a reverse Hölder inequality on the Heisenberg group, and obtain the molecular decomposition. We also develop the Hardy space $H_{L}^{1}$ associated with the Schrödinger operator via the Littlewood–Paley area function and give equivalent characterizations via atoms, molecules, and the maximal function. Moreover, using the molecular decomposition, we prove that $\dot{B}^{0,L}_{1,1}$ is a subspace of $H_{L}^{1}$ .     

Leader‐following consensus problem of heterogeneous multi‐agent systems with nonlinear dynamics using fuzzy disturbance observer

This article considers the leader‐following consensus problem of heterogeneous multi‐agent systems. The proposed multi‐agent system is consisted of heterogeneous agents where each agents have their own nonlinear dynamic behavior. To overcome difficulty from heterogeneous nonlinear intrinsic dynamics of agents, a fuzzy disturbance observer is adopted. In addition, based on the Lyapunov stability theory, an adaptive control method is used to compensate the observation error caused by the difference between the unknown factor and estimated values. Two numerical examples are given to illustrate the effectiveness of the proposed method. © 2013 Wiley Periodicals, Inc. Complexity 19: 20–31, 2014     

Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals

Let {X(t),t ≥ 0} be a centered Gaussian process and let γ be a non-negative constant. In this paper we study the asymptotics of \(\mathbb {P} \left \{\underset {t\in [0,\mathcal {T}/u^{\gamma }]}\sup X(t)>u\right \}\) as \(u\rightarrow \infty \) , with \(\mathcal {T}\) an independent of X non-negative random variable. As an application, we derive the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes.