If a torsion-free hyperbolic group G has 1-dimensional boundary ∂∞G, then ∂∞G is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When ∂∞G is a Sierpinski carpet we show that G is a quasiconvex subgroup of a 3-dimensional hyperbolic Poincaré duality group. We also construct a “topologically rigid” hyperbolic group G: any homeomorphism of ∂∞G is induced by an ...

Theoretically, the functional traits of native species should determine how natives respond to invader-driven changes. To explore this idea, we simulated a large-scale plant invasion using dead spotted knapweed (Centaurea stoebe) stems to determine if native spiders' web-building behaviors could explain differences in spider population responses to structural changes arising from C. stoebe inva...

In a recent paper Cristea and Tichy introduced several types of discrepancies of point sets on the s-dimensional Sierpiński carpet and proved various relations between these discrepancies. In the present paper we prove a general lower bound for those discrepancies in terms of N , the cardinality of the point set, and we give a probabilistic proof for the existence of point sets with “small” dis...

In this paper we describe CARPET, a parallel programming language based on the cellular automata model. CARPET is the language used for programming cellular algorithms in the CAMEL environment. CAMEL is an environment designed to support the development of high performance applications in science and engineering. It offers the computing power of a highly parallel computer, hiding the architectu...

The computation of the Hausdorff measure of fractals is the basic problem in fractal geometry. However, this is very difficult. The genetic algorithm is one of optimization algorithms to resolve complicated problems of wide scope, and has great capabilities in self-organizing, self-adaptation and self-learning. Lifeng Xi professor put forward to the thought of computing the Hausdorff measure of...