Dynamic Envelope Determination Based on Differential Manifold Theory

2017 ◽  
Vol 54 (5) ◽  
pp. 2005-2009 ◽  
Author(s):  
WuJi Zheng ◽  
Ying Hui Li ◽  
Liang Qu ◽  
Guoqiang Yuan
Keyword(s):  
Differential Manifold ◽  
Manifold Theory

Nonlinear Stability Region Determination of Pilot-Aircraft Closed-Loop Based on Differential Manifold Theory

2021 ◽  
pp. 53-66
Author(s):  
Zehong Dong ◽  
Yinghui Li ◽  
Wuji Zheng ◽  
Chi Zhou ◽  
Haojun Xu ◽  
...  
Keyword(s):  
Nonlinear Stability ◽  
Stability Region ◽  
Closed Loop ◽  
Differential Manifold ◽  
Manifold Theory

The Nielsen-Thurston Classification

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Hyperbolic Geometry ◽  
Mapping Class Groups ◽  
Classification Theorem ◽  
Mapping Class ◽  
Fundamental Result ◽  
Class Groups ◽  
Mapping Torus ◽  
Higher Genus ◽  
Manifold Theory

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.

The Shape of Time

2018 ◽  
Author(s):  
Donald C. Williams
Keyword(s):  
Time Travel ◽  
Arrow Of Time ◽  
The Past ◽  
Time Traveler ◽  
Dimensional Shape ◽  
Manifold Theory ◽  
The Universe

This chapter is about the arrow or direction of time against the backdrop of the pure manifold theory. It is accepted that the fact that time has a direction ought to be explained. It is proposed that the arrow of time is grounded in deeper facts about the four-dimensional nature of each object in the manifold and in facts about the overall four-dimensional shape of the universe. Towards the end of the chapter the possibility of time travel is discussed. It is argued that time travel is metaphysically possible and that there is a reasonable and intelligible sense in which a time traveler can and cannot change the past, according to the pure manifold theory.

The Nature of Time

2018 ◽  
Author(s):  
Donald C. Williams
Keyword(s):  
Large Scale ◽  
Time Travel ◽  
Dimensional Manifold ◽  
Nature Of Time ◽  
Manifold Theory ◽  
The Universe ◽  
Theoretical Cost ◽  
Do So

This chapter provides a fuller treatment of the pure manifold theory with an expanded discussion of competing doctrines. It is argued that competing doctrines fail to account for the extensive and/or transitory aspect(s) of time, or they do so at great theoretical cost. The pure manifold theory accounts for the extensive aspect of time because it admits a four-dimensional manifold and it accounts for the transitory aspect of time because it hypothesizes that the increase of entropy is the thing that is ‘felt’ in veridical cases of felt passage. A four-dimensionalist theory of time travel is outlined, along with a sketch of large-scale cosmological traits of the universe.

The Sea Fight Tomorrow

2018 ◽  
Author(s):  
Donald C. Williams
Keyword(s):  
Three Dimensions ◽  
The Past ◽  
The World ◽  
The Future ◽  
Metaphysics Of Time ◽  
Manifold Theory ◽  
Dimensions Of Space

This chapter is the first of this book to deal specifically with the metaphysics of time. This chapter defends the pure manifold theory of time. On this view, time is just another dimension of extent like the three dimensions of space, the past, present, and future are equally real, and the world is at bottom tenseless. What is true is eternally true. For example, it is now true that there will be a sea fight tomorrow or that there will not be a sea fight tomorrow. It is argued that the pure manifold theory does not entail fatalism and that contingent statements about the future do not imply that only the past and present exist.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Statistics on the Stiefel manifold: Theory and applications

2019 ◽  
Vol 47 (1) ◽  
pp. 415-438 ◽  
Author(s):  
Rudrasis Chakraborty ◽  
Baba C. Vemuri
Keyword(s):  
Stiefel Manifold ◽  
Manifold Theory

Application of Center Manifold Theory to Regulation of a Flexible Beam

1997 ◽  
Vol 119 (2) ◽  
pp. 158-165 ◽  
Author(s):  
Amir Khajepour ◽  
M. Farid Golnaraghi ◽  
Kirsten A. Morris
Keyword(s):  
Control Strategy ◽  
Center Manifold ◽  
Flexible Beam ◽  
Trial And Error ◽  
Center Manifold Theory ◽  
Control Techniques ◽  
Lumped Parameter ◽  
The Stability ◽  
Frequency Relationship ◽  
Manifold Theory

In this paper we consider the problem of regulation of a flexible lumped parameter beam. The controller is an active/passive mass-spring-dashpot mechanism which is free to slide along the beam. In this problem the plant/controller equations are coupled and nonlinear, and the linearized equations of the system have two uncontrollable modes associated with a pair of pure imaginary eigenvalues. As a result, linear control techniques as well as most conventional nonlinear control techniques can not be applied. In earlier studies Golnaraghi (1991) and Golnaraghi et al. (1994) a control strategy based on Internal resonance was developed to transfer the oscillatory energy from the beam to the slider, where it was dissipated through controller damping. Although these studies provided very good understanding of the control strategy, the analytical method was based on perturbation techniques and had many limitations. Most of the work was based on numerical techniques and trial and error. In this paper we use center manifold theory to address the shortcomings of the previous studies, and extend the work to a more general control law. The technique is based on reducing the dimension of system and simplifying the nonlinearities using center manifold and normal forms techniques, respectively. The simplified equations are used to investigate the stability and to develop a relation for the optimal controller/plant natural frequencies at which the maximum transfer of energy occurs. One of the main contributions of this work is the elimination of the trial and error and inclusion of damping in the optimal frequency relationship.

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