We present geometric conditions on a metric space (Y, dY ) ensuring that almost surely, any isometric action on Y by Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov-Hausdorff limits, and Cartesian products. ...

The goal of this paper is to derive linear convexity conditions for Bernstein–Bézier surfaces defined on rectangles and triangles. Previously known linear conditions are improved on, in the sense that the new conditions are weaker. Geometric interpretations are provided.

in this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. the stages for prey have been considered. the proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. the model is analyzed by using linear stability analysis to ob...

Let C be a set of geometric objects in R. The combinatorial complexity of the union of C is the total number of faces of all dimensions on its boundary. We survey the known upper bounds on the complexity of the union of n geometric objects satisfying various natural conditions. These bounds play a central role in the analysis of many geometric algorithms, and the techniques used to attain these...

The paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete-time systems. Direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability/reachability algorithmandKalman-type algebraic rank criteria. Also the existing geometric crite...

Zheng, J., G Wang and Y. Liang, Curvature continuity between adjacent rational B&ier patches, Computer Aided Geometric Design 9 (1992) 321-335. This paper discusses the cutvature continuity between two adjacent rational BCzier surfaces which may be rectangular or triangular patches. The necessary and sufficient conditions are derived, and further, a series of simple sufficient conditions are de...

The goal of this research will be to provide sufficient conditions and tractable algorithms that guarantee the topological embedding of geometric approximations commonly used by modern geometric design systems. Particular focus is on the use of ambient isotopy as the measure of topological equivalence, which is stricter than the more traditional use of homeomorphism. Such topological guarantees...

Let G = (V, E) be a (p, q) -graph. The graph G is said to be (a, r) -geometric if its vertices can be assigned distinct positive integers so that the values of the edges, obtained as the products of the numbers assigned to their end vertices, can be arranged as a geometric progression a, ar, ar, . . . , arq−1. In this paper we present results on geometric labelings of some classes of graphs and...