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By analyzing the main cable shape of the suspension bridge and the mechanical and geometric relationship between the main cable and the cable saddle, an improved algorithm is established for determining the position of the composite circular curve splay saddle. The geometric conditions of the main cable and saddle are considered to establish the equations, and the position of the composite circular curve splay saddle is obtained by solving only a one-dimensional nonlinear equation with the dichotomy method. The algorithm yields the solution interval of the dichotomy method to achieve the solution of the nonlinear equation, and the calculation process ensures convergence without any initial value. Several examples demonstrate that the improved algorithm can achieve excellent convergence. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed state estimation problem for a class of discrete nonlinear system over sensor networks subject to unknown correlated measurement noises. Firstly, under the condition of network connectivity, a novel communication protocol is developed to ensure every sensor node can gather the information distributed throughout the network within finite communication time. Then a fully distributed estimator is designed by periodically fusing the local information and neighbor's information according to the covariance intersection fusion strategy. Theoretically, it is proved that the distributed estimator in each sensor node is stable with the exponentially bounded estimation error in mean square. Finally, some numerous simulations are performed to illustrate the practical effectiveness and superiority of the proposed state estimator. [Display omitted] • Design a novel finite time communication protocol, based on which every node could collect all the information distributed throughout the network within finite communication time under network connectivity. • Develop a new distributed state estimator for a class of discrete nonlinear system with unknown correlated measurement noises. • Establish sufficient conditions for guaranteeing the exponential stability of the new estimator in mean square sense. [ABSTRACT FROM AUTHOR]

We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets. [ABSTRACT FROM AUTHOR]

We define a new type of "shatter function" for set systems that satisfies a Sauer–Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah's two-rank instead of VC dimension. We identify the least exponent bounding the rate of growth of the shatter function, the quantity analogous to VC density, with Shelah's $\omega $ -rank. [ABSTRACT FROM AUTHOR]

In this paper we consider some classes of abstract dis-continuous games, for which the games possessing essential Berge equilibrium are the generic case. We extend the essential Berge equilibrium result from Deghdak (2014) to general abstract games. [ABSTRACT FROM AUTHOR]

In this paper, using the well-known Krasnoselskii fixed point theorem, we obtain the existence of a square-mean almost periodic solution to some classes of nonautonomous stochastic evolution equations with finite delay. [ABSTRACT FROM AUTHOR]

In this paper, using the well-known Krasnoselskii fixed point theorem, we obtain the existence of a square-mean almost periodic solution to some classes of nonautonomous stochastic evolution equations with finite delay. [ABSTRACT FROM AUTHOR]

We present an elementary Functional Analytic proof of the roughness of Exponential Dichotomy of Ordinary Differential Equations (with exponential growth) on an arbitrary Banach Space. [ABSTRACT FROM AUTHOR]

Abstract: For the impulsive equation in a Banach space we study the type of stability which can be deduced if a solution is bounded for any bounded sequence . Under certain restrictions on the distance between impulses we can obtain either exponential or asymptotic stability, with a guaranteed polynomial degree (as ) of solution decay. A similar scheme is applied to equations with piecewise constant arguments and to integrodifferential equations. [Copyright &y& Elsevier]