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It has been long known that the pure death processes with proliferation can display a chaotic dynamics. In this paper we analyse long time dynamics of fragmentation processes which can be thought of as a generalization of death processes. In particular we show that, if combined with a proliferative process, their dynamics also can become chaotic.
It is known, from results of MacCluer and Shapiro (Canad. J. Math. 38(4):878–906, 1986), that every composition operator which is compact on the Hardy space Hp, 1 ≤ p < ∞, is also compact on the Bergman space $${{\mathfrak B}^p = L^{p}_{a} ({\mathbb D})}$$ . In this survey, after having described the above known results, we consider Hardy-Orlicz HΨ and Bergman-Orlicz $${{\mathfrak...
Let M be a Whitney-regular bounded subset in the k-dimensional Euclidean space $${\mathbb{R}^k}$$ . We show in this article that certain jets of functions defined in the closure $${\overline{M}}$$ of M are Whitney jets, either of Beurling type, or of Roumieu type, and as a consequence we give some results related with Whitney’s extension theorem. We also obtain some structure theorems for...
Many topics in Actuarial and Financial Mathematics lead to Minimax or Maximin problems (risk measures optimization, ambiguous setting, robust solutions, Bayesian credibility theory, interest rate risk, etc.). However, minimax problems are usually difficult to address, since they may involve complex vector spaces or constraints. This paper presents an unified approach so as to deal with minimax convex...
We define the class of upper staircase matrices on ω. Such matrices have a plethora of eigenvalues and eigenvectors, and they are hypercylic. We show that countably many strictly upper triangular matrices on ω which are also upper staircase have a common hypercyclic subspace. This last result partially extends a theorem of Bès and Conejero.
This expository paper is devoted to the review of some very recent results concerning the set of periods of a chaotic operator T or a chaotic semigroup {T (t): t ≥ 0} acting on a complex Banach space. We obtain information about the structure of the set of periods and we give techniques to construct (chaotic) strongly continuous semigroups with prescribed periods.
Given a bounded linear operator S on a real Banach space X, we characterize weak topological transitivity of the operator families $${\lbrace S^t \mid t \in {\mathbb N}\rbrace}$$ , $${\lbrace \kappa S^t\mid\, t \in {\mathbb N},\, \kappa >0 \rbrace}$$ , and $${\lbrace \kappa S^t\mid\, t \in {\mathbb N},\, \kappa \in {\mathbb R}\rbrace}$$ in terms of the point spectrum of the dual operator...
We construct a Banach space operator $${T \in B(X)}$$ such that the set JT (0) has a nonempty interior but JT (0) ≠ X. This gives a negative answer to a problem raised by Costakis and Manoussos (J. Oper. Theory [in press], 2011).
If M is a closed subspace of a separable, infinite dimensional Hilbert space H with dim (H/M) = ∞, we show that every bounded linear operator A: M → M can be extended to a chaotic operator T: H → H that satisfies the hypercyclicity criterion in the strongest possible sense.
In Moreno et al. (Rev R Acad Cien Ser A Mat 97:53–61, 2003) an objective Bayesian model comparison procedure for univariate normal regression models based on intrinsic priors was provided. However, in many applications the regression models entertained are multidimensional, and hence an extension of the procedure to this setting is required. This technical paper provides the intrinsic priors and their...
We characterize those composition operators defined on spaces of holomorphic functions of several variables which are power bounded, i.e. the orbits of all the elements are bounded. This condition is equivalent to the composition operator being mean ergodic. We also describe the form of the symbol when the composition operator is mean ergodic.
The question about the existence of solutions in a family of systems of Diophantine linear equations can be always answered by means of a set of functions called ‘Testers’. In this paper, we will propose a procedure to obtain this set of ‘Testers’ (named complete set of testers) which characterizes each family of systems of Diophantine equations.
We give sufficient conditions for chaos of (differential) operators on Hilbert spaces of entire functions. To this aim we establish conditions on the coefficients of a polynomial P(z) such that P(B) is chaotic on the space $${\ell^p}$$ , where B is the backward shift operator.
A geometric approach to radial railway network improvement is presented here. It uses what we have called ‘isochrone circle graphs’, a kind of diagrams that reflect the values of two variables, mixing ideas from isochrone maps and from polar area diagrams (unlike the former, the areas of the sectors are related to population, not to ‘geographical areas’ and, unlike the latter, they do not compute...
Nonholonomic systems are described by the Lagrange-d’Alembert principle. The presence of symmetry leads to a reduced d’Alembert principle and to the Lagrange-d’Alembert-Poincaré equations. First, we briefly recall from previous works how to obtain these reduced equations for the case of a thick disk rolling on a rough surface using a three-dimensional abelian group of symmetries. The main results...
The purpose of this paper is to investigate the local regularity of the nondivergence degenerate elliptic operator with lower order terms in generalized Morrey spaces, structured on a family of Hörmander’s vector fields without an underlying group structure. The coefficients of the second order terms of the operator are real valued, bounded and measurable functions, such that the uniform ellipticity...
In this paper we study discrete second-order vakonomic mechanics, that is, constrained variational problems for second-order lagrangian systems. One of the main applications of the presented theory will be optimal control of underactuated mechanical control systems. We derive geometric integrators which are symplectic and preserve the momentum map. Additional, we show the applicability of the proposed...
We introduce the discrete counterpart of the vakonomic method in Lagrangian mechanics with non-holonomic constraints. After defining the concepts of “admissible section” and “admissible infinitesimal variation” of a discrete vakonomic system, we aim to determinate those admissible sections that are critical for the Lagrangian of the system with respect to admissible infinitesimal variations. For sections...
In this paper we summarize the main features of vakonomic mechanics (or constrained variational calculus), both from continuous and discrete points of views. In the continuous case, we focus ourselves on Lagrangian systems defined by the following data: a Riemannian metric (kinetic term) and constraints linear on the velocities. We show that, for such kind of systems, it is possible to find an explicit...
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