Related papers: Local dimensions for the random beta-transformatio…

The Bernoulli convolution associated to the real $\beta>1$ and the probability vector $(p_0,..,p_{d-1})$ is a probability measure $\eta_{\beta,p}$ on $\mathbb R$, solution of the self-similarity relation…

In recent years new types of coordinate transformations have appeared in cosmology on top of the standard gauge transformations, such as the dilatations and special conformal transformations, or the ones leading to (conformal) Fermi…

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise).…

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

We provide a definition of a new critical exponent $\beta$ that has the interpretation of a type of local walk dimension, and may be defined on any compact metric space. We then specialize to the case of random walks that jump uniformly in…

In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…

Let $K$ be a finite dimensional compact metric space and $K^\mathbb{Z}$ the full shift on the alphabet $K$. We prove that its mean dimension is given by $\dim K$ or $\dim K-1$ depending on the "type" of $K$. We propose a problem which seems…

Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…

We give two versions of the natural extension of a specific greedy beta-transformation with deleted digits. We use the natural extension to obtain an explicit expression for the invariant measure, equivalent to the Lebesgue measure, of this…

We study images of equilibrium (Gibbs) states for a class of non-invertible transformations associated to conformal iterated function systems with overlaps $\mathcal S$. We prove exact dimensionality for these image measures, and find a…

We construct all independent local scalar monomials in the Riemann tensor at arbitrary dimension, for the special regime of static, spherically symmetric geometries. Compared to general spaces, their number is significantly reduced: the…

Recently F. Huang [Commun. Theor. Phys. V.42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. V.49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing and dissipation on…

The properties of the square bias transformation are studied, in particular, the precise moment-type estimate for the $L_1$-metric between the transformed and the original distributions is proved, a relation between their characteristic…

A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential and the…

Let $\Sigma$ be a finite alphabet, $\Omega=\Sigma^{\mathbb{Z}^{d}}$ equipped with the shift action, and $\mathcal{I}$ the simplex of shift-invariant measures on $\Omega$. We study the relation between the restriction $\mathcal{I}_n$ of…

We examine measure preserving mappings $f$ acting from a probability space $(\Omega, F,\mu) $ into a probability space $% (\Omega ^{*},F^{*},\mu ^{*}) ,$ where $\mu ^{*}=\mu (f^{-1})$. Conditions on $f$, under which $f$ preserves the…

For an arbitrary Radon measure $\mu$ we estimate the integrated discrete curvature of $\mu$ in terms of its centred variant of Jones' beta numbers. We farther relate integrals of centred and non-centred beta numbers. As a corollary,…

For Y a subset of the complex plane,a beta ensemble is a sequence of probability measures on Y^n for n=1,2,3...depending on a real-valued continuous function Q and a real positive parameter beta.We consider the associated sequence of…

Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…

We analyze the semileptonic $B\to K_2^*(1430)l^+l^-$ transition in universal extra dimension model. In particular, we present the sensitivity of related observables such as branching ratio, polarization distribution and forward-backward…