For a nonincreasing function $\psi$, let $\textrm{Exact}(\psi)$ be the set of complex numbers that are approximable by rational to order $\psi$ but no better order. In this paper, we obtain Hausdorff dimension and packing when $\psi(x)=o(x^{-2})$. We also prove lower bound is greater than $2-\tau/(1-2\tau)$ $\tau=\limsup_{x\to\infty}\psi(x)x^2$ small enough.

In this paper the spreading of epidemic model on complex networks with a generalized nonlinear incidence rate is presented. Firstly the SIS model on homogeneous networks with nonlinear incidence rate is considered, and the existence conditions about the disease-free equilibrium and the endemic equilibrium are given. And then the model on heterogenous scale-free (SF) networks is considered, wher...

Many events in real world applications are long-lasting events which have certain durations. The temporal relationships among those durable events are often complex. Processing such complex events has become increasingly important in applications of wireless networks. An important issue of complex event processing is to extract patterns from event streams to support decision making in real-time...

In this paper, the relation between algebraic shifting and join which was conjectured by Eran Nevo will be proved. Let σ and τ be simplicial complexes and σ ∗ τ their join. Let Jσ be the exterior face ideal of σ and ∆(σ) the exterior algebraic shifted complex of σ. Assume that σ ∗ τ is a simplicial complex on [n] = {1, 2, . . . , n}. For any d-subset S ⊂ [n], let m revS(σ) denote the number of ...

The main thesis of a recent article by Davis and Simmt (2003) is that " mathematics classes are adaptive and self-organizing complex systems ". This thesis is intriguing. It helps explain a phenomenon teachers often witness—the spontaneous emergence of a special learning community in a particular class. And it raises the question—if this thesis applies to all mathematics classes how do the addi...

We apply the general theory of approximation orders of shift-invariant spaces of BDR1-3] to the special case when the nitely many generators L 2 (IR d) of the underlying space S satisfy an N-scale relation (i.e., they form a \father wavelet" set). We show that the approximation orders provided by such nitely generated shift-invariant spaces are bounded from below by the smoothness class of each...