Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields

1995 ◽  
Vol 120 (1) ◽  
pp. 339-360 ◽  
Author(s):  
Paulo D. Cordaro ◽  
Fran�ois Treves
Keyword(s):  
Vector Fields ◽  
Sufficient Conditions ◽  
Local Solvability ◽  
Necessary And Sufficient Conditions ◽  
Complex Vector ◽  
Necessary And Sufficient

ON FLOW BARRIERS AND SWITCHABILITY IN DISCONTINUOUS DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (01) ◽  
pp. 1-76 ◽  
Author(s):  
ALBERT C. J. LUO
Keyword(s):  
Dynamical Systems ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Friction Model ◽  
Necessary And Sufficient Conditions ◽  
Separation Boundary ◽  
Boundary Flow ◽  
Pass Through ◽  
Necessary And Sufficient ◽  
And Control

In this paper, the theory of flow barriers in discontinuous dynamical systems is systematically presented as a new theory for the first time, which helps one rethink the existing theories of stability and control in dynamical systems. The concept of flow barriers in discontinuous dynamical systems is introduced, and the passability of a flow to the separation boundary with flow barriers is presented. Because the flow barriers exist on the separation boundary, the switchability of a flow to such a separation boundary is changed accordingly. The coming and leaving flow barriers in passable flows are discussed first, and the necessary and sufficient conditions for a flow to pass through the boundary with flow barrier are developed. Flow barriers for sink and source flows are also discussed. Once the sink flow is formed, the boundary flow will exist. When the boundary flow disappears from the boundary, the boundary flow barrier on the boundary may exist, which is independent of vector fields in the corresponding domains. Thus, the necessary and sufficient conditions for formations and vanishing of the boundary flow are developed. A periodically forced friction model is presented as an example for a better understanding of flow barrier existence in physical problems. The flow barrier theory presented in this paper may provide a theoretic base to further develop control theory and stability.

scholarly journals On related vector fields of capillary surfaces

1981 ◽  
Vol 4 (3) ◽  
pp. 473-484
Author(s):  
Afet K. Özok
Keyword(s):  
Vector Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformal Killing ◽  
Capillary Surfaces ◽  
Killing Vectors ◽  
Conformal Killing Vectors ◽  
Necessary And Sufficient ◽  
Dimensional Domain

In this paper, some necessary and sufficient conditions are given for the related vector fields of capillary surfaces to be Killing, conformal Killing, and homothetic conformal Killing vectors in then-dimensional domainΩ, and a construction of capillary surfaces is also given by means of the related vector fields.

scholarly journals Magnetic vector fields: New examples

2018 ◽  
Vol 103 (117) ◽  
pp. 91-102
Author(s):  
Jun-Ichi Inoguchi ◽  
Marian Munteanu
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Magnetic Vector ◽  
Necessary And Sufficient

In a previous paper, we introduced the notion of magnetic vector fields. More precisely, we consider a vector field ? as a map from a Riemannian manifold into its tangent bundle endowed with the usual almost K?hlerian structure and we find necessary and sufficient conditions for ? to be a magnetic map with respect to ? itself and the K?hler 2-form. In this paper we give new examples of magnetic vector fields.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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