منابع مشابه
Collapsing along monotone poset maps
For a poset P we let Δ(P) denote its nerve: the simplicial complex whose simplices are all chains of P. For a simplicial complex X we let V(X) denote the set of its vertices. An elementary collapse in a simplicial complex X is a removal of two open simplices σ and τ from X , such that dimσ = dimτ +1, and σ is the only simplex of X , different from τ itself, which contains the simplex τ in its c...
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The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of abstract spacetime, we identify criteria for classically homotopic, monotone maps of pospaces to future homotope, or homotope along homotopies monotone in bot...
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The aim of this paper is to provide a brief review of the main results in the theory of discrete-time monotone dynamics.
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Recent characterizations of various types of differentiable generalized monotone maps by Karamardian– Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplis...
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In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2006
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms/2006/79858