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Taking the multi point winding hoisting system with depth of 1000 m, drum radius of 0.4 m, drum radius difference of 0.1 mm as the research background, a model of multi point winding hoisting system under non synchronous movement of wire ropes is established, and the mathematical model is deduced by Lagrange equation. Then the dynamic characteristic of super deep multi point winding hoisting system under non synchronous movements of wire ropes is analyzed. The results show that: the rotational displacement of mass block is 5°, the rotational velocity is 0.07 °/s in the stage of constant speed. The rope length difference reaches 0.07 m, the tension of each wire rope changes 333 N, accounted for about 7 % of the average tension. And with the length difference increasing 35 mm, the force differences increasing 320 N, which indicates that the length difference has great impact on the tension difference of wire ropes. Finally, the mathematical model is verified through experiment. [ABSTRACT FROM AUTHOR]

In this article based on the concept of quasi-coincidence of a multipoint and a multiset, we introduce the concept of multiset mixed topological space. We have investigated some of the properties of the introduced multiset mixed topological space. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we improve the order of the Midpoint iterative method from three to four with same number of function evaluations using weight functions to obtain a class of 2-point fourth order Jarratt-type methods. Then we prove a general result to further improve the order of the old methods through an additional function evaluation using weight functions. In this way, we develop two 3-point sixth order midpoint methods using different weights. A family of n-point I.F.s of order 2n is proposed. Using weight functions, we further improve the methods to obtain a 5-point sixteenth order midpoint method with same efficiency index as the optimal 2-point fourth order Jarratt-type methods. Two numerical examples using different starting are provided to test the robustness of the methods. [Copyright &y& Elsevier]

The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differential equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact. [ABSTRACT FROM AUTHOR]