Optimal Prestress Investigation on Tensegrity Structures Using Artificial Fish Swarm Algorithm

To obtain the optimal uniform prestress of a tensegrity structure with geometric configuration given, a novel method is developed for prestress design of tensegrity structures by utilizing the artificial fish swarm algorithm (AFSA). In the beginning, the form-finding process is implemented by solving a linear homogeneous system concerning the self-equilibrium system. The issue is subsequently performed as a minimum problem by regulating the value of an objective function where the unilateral condition and the stress uniformity condition are entirely considered. The AFSA is adopted to search for the global minimum, leading to a set of initial prestresses that guarantee all the above conditions. Two illustrative examples have been fully studied to prove the accuracy and efficiency of the presented approach in prestress design of tensegrities according to the practical requirements. Furthermore, the numerical examples investigated in this paper confirm that the AFSA has explicit advantages of rapid convergence and overcoming the local minima.

Complements on adic spaces

This chapter analyzes a collection of complements in the theory of adic spaces. These complements include adic morphisms, analytic adic spaces, and Cartier divisors. It turns out that there is a very general criterion for sheafyness. In general, uniformity does not guarantee sheafyness, but a strengthening of the uniformity condition does. Moreover, sheafyness, without any extra assumptions, implies other good properties. Ultimately, it is not immediately clear how to get a good theory of coherent sheaves on adic spaces. The chapter then considers Cartier divisors on adic spaces. The term closed Cartier divisor is meant to evoke a closed immersion of adic spaces.

On the Hausdorff Dimension of CAT(κ) Surfaces

We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls. We also discuss a connection between this uniformity condition and some results on the dynamics of the geodesic flow for such surfaces. Finally,we give a short proof of topological entropy rigidity for geodesic flow on certain CAT(−1) manifolds.

Elementary Active Membranes Have the Power of Counting

P systems with active membranes have the ability of solving computationally hard problems. In this paper, the authors prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also holds for families having a stricter uniformity condition than the usual one.

Elementary Active Membranes Have the Power of Counting

P systems with active membranes have the ability of solving computationally hard problems. In this paper, the authors prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also holds for families having a stricter uniformity condition than the usual one.