The Minimal Dimension of a Sphere with an Equivariant Embedding of the Bouquet of g Circles is $$2g-1$$

Author(s):  
Zhongzi Wang
2010 ◽  
Vol 225 (5) ◽  
pp. 2840-2882 ◽  
Author(s):  
Heath Emerson ◽  
Ralf Meyer

2021 ◽  
Vol 22 (12) ◽  
pp. 625-633
Author(s):  
A. V. Zuev ◽  
A. N. Zhirabok ◽  
V. F. Filaretov ◽  
A. A. Protsenko

The paper is devoted to the problem of fault identification in technical systems described by non-stationary nonlinear dynamic equations under unmatched disturbances. To solve the problem, sliding mode observers are used. The suggested ap- proach is based on the model of the original system of minimal dimension having different sensitivity to the faults and distur- bances in contrast to the traditional approaches to sliding observer design which are based on the original system. Additionally it is assumed that matrices describing such a model have the canonical form and are constant. The main purpose of using such a model is possibility to take into account the non-stationary feature of the systems. As a result, the model has stationary dynamic and non-stationary additional term that allows to promote sliding mode design. Besides, the new approach to design sliding mode observers is suggested. The peculiarity of this approach is that it does not require that original systems should be minimum phase and detectable. According to the traditional approaches stability of the observer is provided by minimum phase and detectability properties. In our approach, stability of the observer is achieved due to the canonical form of the matrices describing the model. In addition, the matching condition is not necessary. This allows to extend a class of systems for which sliding mode observers can be designed. Theoretical results are illustrated by practical example of electric servoactuator.


2009 ◽  
pp. 79-116
Author(s):  
Gianni Bianco ◽  
Pierluigi Cecati

- Water will be a basic problem in the future of the world. At the moment in Italy the main problem lies in water reserve reductions facing a growing demand, while for drinkable water more and more administrator authorities are facing a budget deficit. The causes of this national and local situation are the administrative monopoly and the absence of planning and coordination policies, that would rationalize water use without rationing it, starting from an awareness of the costs of different involved variables. The economic quality of spring and consumption water, the oldness of the waterworks and pipe networks, the extreme fragmentation of waterworks (often of minimal dimension), their territorial localisation, the absence of a common method of charges, the scanty use of analysis of management, are some of the causes of a unique and surprising variability of costs, proceeds and tariffs. This paper analyzes the generation and the structure of the costs of drinkable water in an area representative of many national characteristics on the environmental, physic and socio-economic level. The quest for more efficient forms of management and for a more transparent determination of the tariffs has been carried on through the use of custom indexes of productivity and of production. These indexes summarise the existence of scale economies, of pipe network related diseconomies, and of economies of localisation and density of the consumers. The paper presents a synthesis of the observations gathered from about two hundred waterworks subdivided by owner and entrepreneurial typologies


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