The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series, continuoustime process having stationary increments). The estimator of the m change instants (the number m is supposed to be known) is proved to satisfied a ...

There are two fundamental results in the classical theory of metric Diophantine approximation: Khintchine’s theorem and Jarńık’s theorem. The former relates the size of the set of well approximable numbers, expressed in terms of Lebesgue measure, to the behavior of a certain volume sum. The latter is a Hausdorff measure version of the former. We start by discussing these theorems and show that ...

Theorem 1. If μ ∈P(R) has finite kth moment, k ≥ 0, then, writing φ = μ̃: 1. φ ∈ C(R). 2. φ(v) = (i) ∫ R x edμ(x). 3. φ is uniformly continuous. 4. |φ(v)| ≤ ∫ R |x| dμ(x). 1Charalambos D. Aliprantis and Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, third ed., p. 515, Theorem 15.15; http://individual.utoronto.ca/ jordanbell/notes/narrow.pdf 2Onno van Gaans, Probability measu...

We prove a homogenization theorem for class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses ergodicity and stationarity we that the $\Gamma$-limit such energy is almost surely deterministic Dirichlet-type integral functional, whose integrand can be characterized through an asymptotic formula. The proof this characterization relies on results behaviou...

We prove Archimedes' principle for a macroscopic ball in ideal gas consisting of point particles with non-zero mass. The main result is an asymptotic theorem, as the number goes to infinity and their total mass remains constant. also show that, asymptotically, has exponential density function height. find inverse temperature gas. derive accurate estimate volume phase space using local central l...

The Mahonian statistic is the number of inversions in a permutation of a multiset with ai elements of type i, 1 ≤ i ≤ m. The counting function for this statistic is the q analog of the multinomial coefficient ( a1+···+am a1,...am ) , and the probability generating function is the normalization of the latter. We give two proofs that the distribution is asymptotically normal. The first is compute...

The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...