We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number Ω = √ 2 − 1. We show that the Poincaré–Melnikov method can be applied to establish the existence of 4 transverse homoclinic ...

We consider a diffusion (ξt)t≥0 with T -periodic time dependence in its drift; under an unknown parameter θ ∈ Θ, some periodic discontinuity – called signal – occurs at times kT+θ, k ∈ IN . Assuming positive Harris recurrence of (ξkT )k∈IN0 and exploiting the periodicity structure, we prove limit theorems for certain martingales and functionals of the process (ξt)t≥0. They allow to consider the...

We announce proofs of a number of theorems concerning finite p-groups and nilpotent groups. These include: (1) the number of p-groups of class c on d generators of order pn satisfies a linear recurrence relation in n; (2) for fixed n the number of p-groups of order pn as one varies p is given by counting points on certain varieties mod p; (3) an asymptotic formula for the number of finite nilpo...

Ratio asymptotics for matrix orthogonal polynomials with recurrence coefficients An and Bn having limits A and B respectively (the matrix Nevai class) were obtained by Durán. In the present paper we obtain an alternative description of the limiting ratio. We generalize it to recurrence coefficients which are asymptotically periodic with higher periodicity, or which are slowly varying in functio...

S-asymptotically ω-periodic functions have applications to several problems, for example in the theory of functional differential equations, fractional differential equations, integral equations and partial differential equations. The concept of S-asymptotic ω-periodicity was introduced in the literature by Henrı́quez et al. 1, 2 . Since then, it attracted the attention of many researchers see 1...

We develop a convex approximation for two-stage mixed-integer recourse models and we derive an error bound for this approximation that depends on all total variations of the probability density functions of the random variables in the model. We show that the error bound converges to zero if all these total variations converge to zero. Our convex approximation is a generalization of the one in C...

In 1997, flux of Blazar Mkn501 increased up to 10 Crab over three months. X-ray satellite RXTE All sky monitor (ASM) and two cherenkov detecotors HEGRA, Utah seven telescope array (Utah TA) observed this flare simultaneously. Hayashida et al.[1] and Kranich[2] studied periodic-ity with Utah TA data, with both HEGRA and ASM data respectively, with a fourier analysis. They suggest a periodicity o...

We present the first release of the HeteroGenome database collecting latent periodicity regions in genomes. Tandem repeats and highly divergent tandem repeats along with the regions of a new type of periodicity, known as profile periodicity, have been collected for the genomes of Saccharomyces cerevisiae, Arabidopsis thaliana, Caenorhabditis elegans and Drosophila melanogaster. We obtained data...

Recent temporal models of pitch and amplitude modulation perception converge on a relatively realistic implementation of cochlear processing followed by a temporal analysis of periodicity. However, for modulation perception, a modulation filterbank is applied whereas for pitch perception, autocorrelation is applied. Considering the large overlap in pitch and modulation perception, this is not p...

Statistical periodicity is a statistical property of densities which arises in the description of retarded dynamical systems. This property is particularly attractive as a possible mechanism for the ensemble coding of information in the nervous system because it operates rapidly and has high storage capacity. For a population of neurons which exhibits statistical periodicity, information would ...