Related papers: A mixed multifractal analysis for quasi Ahlfors ve…
In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…
In the conditional setting we provide a complete duality between quasiconvex risk measures defined on $L^{0}$ modules of the $L^{p}$ type and the appropriate class of dual functions. This is based on a general result which extends the usual…
We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…
The main purpose of the note is to explore the invariant properties of sphericalization and flattening and their applications in quasi-metric spaces. We show that sphericalization and flattening procedures on a quasimetric spaces preserving…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the…
In a previous work \cite{She} we constructed measures on symbolic spaces which satisfy an extended multifractal formalism (in the sense that Olsen's functions $b$ and $B$ differ and that their Legendre transforms have the expected…
This paper presents a new method for obtaining small algebras to check the admissibility-equivalently, validity in free algebras-of quasi-identities in a finitely generated quasivariety. Unlike a previous algebraic approach of Metcalfe and…
Macroscopic systems often display phase transitions where certain physical quantities are singular or self-similar at different (spatial) scales. Such properties of systems are currently characterized by some order parameters and a few…
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of…
Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials,…
Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we will study the…
We prove that if $J$ is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors form a set of full Hausdorff dimension in $J$. The same is…
For a Markov map of an interval or the circle with countably many branches and finitely many neutral periodic points, we establish conditional variational formulas for the mixed multifractal spectra of Birkhoff averages of countably many…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
Multifractal analysis of multiplicative random cascades is revisited within the framework of {\em mixed asymptotics}. In this new framework, statistics are estimated over a sample which size increases as the resolution scale (or the…
Inhomogeneous multinomial measures on the mixed symbolic spaces and the real line are given. By counting the zeros of the corresponding generalized Dirichlet polynomials, one obtains a probability measure whose Olsen's functions $b$ and $B$…
This article fits in many studies of multifractal analysis of measure. We took as a starting point the work of F. Ben Nasr in " Calculs de dimension de packing " to give a new inequality involving $Dim(\bar{X}^{\alpha})$ which would be, in…
We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is…
We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of…