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  • contingent cone  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Lattice operators underlying dynamic systems (1996)
    Springer
    Set-valued analysis 4 (1996), S. 119-134 
    Details
    ISSN: 1572-932X
    Keywords: 06A23 ; 34A60 ; 68U10 ; 93C15 ; complete lattice ; algebraic dilation and erosion ; algebraic opening and closing ; semicontinuity ; differential inclusion ; contingent cone ; reachable set ; exit tube ; viability kernel ; invariance kernel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper investigates algebraic and continuity properties of increasing set operators underlying dynamic systems. We recall algebraic properties of increasing operators on complete lattices and some topologies used for the study of continuity properties of lattice operators. We apply these notions to several operators induced by a differential equation or differential inclusion. We especially focus on the operators associating with any closed subset its reachable set, its exit tube, its viability kernel or its invariance kernel. Finally, we show that morphological operators used in image processing are particular cases of operators induced by constant differential inclusion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00425961
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Filippov and invariance theorems for mutational inclusions of tubes (1993)
    Springer
    Set-valued analysis 1 (1993), S. 289-303 
    Details
    ISSN: 1572-932X
    Keywords: 34A99 ; 34G99 ; 49J99 ; 49N99 ; 494J52 ; 54G60 ; 46G05 ; Transitions ; mutations ; Filippov's theorem ; invariance ; contingent cone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The framework of transitions and mutational calculus inspired by shape optimization allows the notions of derivative, tangent cone, and differential equation to be extended to a metric space and especially to the family of all nonempty compact subsets of a given domainE. It gives tools to study the evolution of tubes and fundamental theorems such as those of Cauchy-Lipschitz, Nagumo, or Lyapunov, well known in vector spaces, can be adapted to mutational equations. The present paper deals with mutational inclusions of tubes which include many tube control problems and an adaptation of the Filippov theorem is proved. As a consequence, an invariance theorem is stated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01027639
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    Paper (German National Licenses)
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