In this paper we prove several new characterizations of weakly unconditionally Cauchy series in Banach spaces and in the dual space of a normed space. For a given series ζ, we consider the spaces S(ζ), Sw(ζ) and S0(ζ) of bounded sequences of real numbers (ai)i such that the series P i aixi is convergent, weakly convergent or ∗-weakly convergent, respectively. By means of these spaces we charact...

In this paper, an algorithm for dynamic rigid-body model is considered. To this end, we first develop an equivalent reformulation of the problem via the Fischer function. Based on this, we propose a new type of method for solving the problem, and the algorithm is shown to be globally convergent and quadratically convergent without nondegenerate assumption. Keywordsdynamic rigid-body model; line...

In resent years, Vicsek model has attracted extensive attention and been well developed. However, the in-depth analysis on convergent time are scarce thus far. In this paper, we study the factors that influence the convergent time of Vicsek model at zero temperature. Furthermore, to accelerate the convergence, we propose a new model in which the speed of each particle is variable. Convergent ti...