Showing papers on "Strongly monotone published in 1991"

On monotone trajectories

Abstract: In this paper C1 strongly monotone dynamical systems are investigated. It is proved that the set of points with precompact orbits which converge to a not unstable equilibrium but whose trajectories are not eventually strongly monotone is nowhere dense. This improves on and extends a recent result by P. Polacik [13]. For a metric space X with metric d, by a semiflow on X we mean a continuous mapping b: [0, oc) x X -* X satisfying the following (we denote OtN = q(t, )): (Si) q0 = idx (S2) qt o Os = t+s$, for s, t E [O, o) The trajectory of x E X is the mapping t I*tx, t E [0, oc). The set {?)tx: t E [0, oo)} is called the orbit of x E X. An equilibrium is a point e E X such that Ote = e for all t > 0. We say a point x E X (or its trajectory) is convergent (to an equilibrium e E X) if d(qtx, e) --* 0 as t -* oc. It is easy to check that x E X is convergent to e E X if and only if the orbit of x is precompact and w-)(x) = {e}, where the w-limit set w(x) := {y E X: ]tk -? ? such that qt$kx * y as k -ooI}. A real Banach space V with norm is called strongly ordered if V is endowed with a closed cone V+ having nonempty interior V+ . For v, w E V wewrite v

Structure in monotone complexity

Abstract: In this work we study complexity classes in monotone computation Our main contributions are the following: (1) A consistent framework for monotone computation, including monotone analogues of many standard computational models We define monotone simulations, and show that many (but not all) of the familiar simulations from general complexity theory are in fact monotone (2) The search for provably non-monotone simulations as a research goal in monotone complexity Our new example is the following: the simulation techniques of Immerman and Szelepcsenyi are provably non-monotone, since we can separate mNL (monotone nondeterministic logarithmic space) from co-mNL (3) Another separation: mL (monotone logarithmic space) is strictly stronger than $mNC\sp1$ (monotone polynomial size formulas) This may be seen as a strictly stronger application of the communication game technique introduced by Karchmer and Wigderson (Copies available exclusively from MIT Libraries, Rm 14-0551, Cambridge, MA 02139-4307 Ph 617-253-5668; Fax 617-253-1690)

Monotone semi-flows which have a monotone first integral

Abstract: We present a fairly general study for a class of semi-flows defined on an abstract space, which are monotonically increasing and possess a first integral, also increasing. Examples of that are systems of delay differential equations generated by compartmental models. Under reasonable restrictions, a complete description of the asymptotic behavior can be obtained in situations including almost-periodic dependence. We will not go into these details here. Rather the paper intends to enlighten the main aspects of the theory. Finally, a comparison with related literature is made.

Monotone Approximation of Random Functions with Multivariate Domains in Respect of Lattice Semi-Norms

Abstract: Consider the problem of approximating a random function which is defined on a compact and convex subset of a topological vector space. For monotone approximation procedures, global and local error bounds with respect to lattice semi-norms are established.

On monotone extensions of boundary data

Abstract: A functionf ?C (Ω), $$\Omega \subseteq \mathbb{R}^s $$ is called monotone on Ω if for anyx, y ? Ω the relation x ? y ? ? + s impliesf(x)?f(y). Given a domain $$\Omega \subseteq \mathbb{R}^s $$ with a continuous boundary ?Ω and given any monotone functionf on ?Ω we are concerned with the existence and regularity ofmonotone extensions i.e., of functionsF which are monotone on all of Ω and agree withf on ?Ω. In particular, we show that there is no linear mapping that is capable of producing a monotone extension to arbitrarily given monotone boundary data. Three nonlinear methods for constructing monotone extensions are then presented. Two of these constructions, however, have the common drawback that regardless of how smooth the boundary data may be, the resulting extensions will, in general, only be Lipschitz continuous. This leads us to consider a third and more involved monotonicity preserving extension scheme to prove that, when Ω is the unit square [0, 1]2 in ?2, strictly monotone analytic boundary data admit a monotone analytic extension.

Existence and uniqueness theorems of solution for symmetric contracted operator equations and their applications

Abstract: Ref. [1] studies problems concerned by using the nature of mixed monotone of two-element nonlinear operators. As for mixed monotone operator, Ref. [2] studies the minimax solution of