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By using the skew product definition of a Markov chain we obtain the following results: (a) Every k-step Markov chain is a quasi-Markovian process. (b) Every piecewise linear map with a Markovian partition defines a Markov chain forevery absolutely continuous invariant measure. (c) Satisfying the Chapman-Kolmogorov equation is not sufficient for a process to be quasi-Markovian.
H. A. Wilbrink [Geom. Dedicata 12 (1982)] considered a class of Minkowski planes whose restrictions, called residual planes, are nearaffine planes. Our study goes in the opposite direction: what conditions on a nearaffine plane are necessary and sufficient to get an extension which is a hyperbola structure.
Let B be a complex topological unital algebra. The left joint spectrum of a set S ⊂ B is defined by the formula σl(S) = {(λ(s))s∈s ∈ C[sup]s | {s - λ(s)}s∈s generates a proper left ideal}. Using the Schur lemma and the Gelfand-Mazur theorem we prove that σl(S) has the spectral mapping property for sets S of pairwise commuting elements if (i) B is an m-convex algebra with all maximal left ideals closed,...
We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence...
We give an alternative proof of simultaneous linearization recently shown by T. Ueda, which connects the Schroder equation and the Abel equation analytically. In fact, we generalize Ueda's original result so that we may apply it to the parabolic fixed points with multiple petals. As an application, we show a continuity result on linearizing coordinates in complex dynamics.
For a class of one-dimensional holomorphic maps ƒ of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of ƒ. This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.
It is shown that for a typical continuous learning system denned on a compact convex subset of R[sup]n the Hausdorff dimension of its invariant measure is equal to zero.
Let ConvF(Rn) be the space of all non-empty closed convex sets in Euclidean space Rn endowed with the Fell topology. We prove that ConvF(lRn) ≈ Rn x Q for every n > 1 whereas ConvF(R) ≈ R x I.
This paper is motivated by the problem of dependence of the Hausdorff dimension of the Julia-Lavaurs sets Jo,σ for the map fo(z) = x2 + 1/4 on the parameter σ. Using homographies, we imitate the construction of the iterated function system (IFS) whose limit set is a subset of Jo,σ, given by Urbański and Zinsmeister. The closure of the limit set of our IFS {φ[...]} is the closure of some family of...
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.
We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time A. We show, using the multiplicative decomposition of the Azema supermartingale, that if the martingale part of the price process has the predictable representation property and A satisfies...
The group generated by double tangency symmetries in a Laguerre plane is investigated. The geometric classification of involutions of a symmetric Laguerre plane is given. We introduce the notion of projective automorphisms using the double tangency and parallel perspectivities. We give the description of the groups of projective automorphisms and automorphisms generated by double tangency symmetries...
The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory C of Top, is the fibration structure of Top restricted...
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < x(X] where x(X) is the so-called Lifshits constant of X. For many spaces we have x(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant...
We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1 - β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup (T[sup]n)n=1,2,... by the continuous semigroup (e[sup]-t(I-T)t≥o. Moreover, we give a stronger quadratic form inequality which ensures that sup{n||T[sup]n...
Let K be a field, a, b ∈ K and ab ≠ 0. Consider the polynomials g1 (x) = xn + ax + b, g2(x) = xn + ax2 + bx, where n is a fixed positive integer. We show that for each k ≥ 2 the hypersurface given by the equation S[...], i = 1, 2 contains a rational curve. Using the above and van de Woestijne's recent results we show how to construct a rational point different from the point at infinity on the curves...
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