We have updated the global Synthetic Storm Technique (referred to as SST) by reformulating it according a larger database of rain rate time series collected in several sites different climatic regions. For each site, average annual probability distribution attenuation obtained with SST, PSST,gloA, slant path, was compared that given full PSSTA, which we considered experimental data. The test pe...

A substitution is a function θ from the set of σ-terms back to itself such that (writing function application on the right) cθ = c for each constant symbol c and f(t1, . . . , tk)θ = f(t1θ, . . . , tkθ) for each k-ary function symbol f . It is clear that the composition of two such substitutions (as functions) is also a substitution. We have previously considered substitutions of the form [t/x]...

Suppose we are given a random vector Y consisting of n observations with joint density fn(· ; θ) depending on a p-dimensional parameter θ. We write `n(θ) for the log likelihood, `n(θ) = log fn(Y ; θ) where Y are the actual observations. The most familiar case is when Y consists of independent observations Y1, ..., Yn with common density f0(· ; θ); henceforth, this is called the i.i.d. case. In ...

In this paper we propose a model of random compositions of maps of a cylinder, which in the simplified form is as follows: (θ, r) ∈ T×R = A and f±1 : ( θ r ) 7−→ ( θ + r + εu±1(θ, r). r + εv±1(θ, r). ) , where u± and v± are smooth and v± are trigonometric polynomials in θ such that ∫ v±(θ, r) dθ = 0 for each r. We study the random compositions (θn, rn) = fωn−1 ◦ · · · ◦ fω0(θ0, r0) with ωk ∈ {−...

In this work we study the oscillatory behaviour of the differential equation of mixed type x′ (t) = ∫ 0 −1 x (t− r (θ)) dν (θ) + ∫ 0 −1 x (t+ τ (θ)) dη (θ) with delays, r (θ) , and advances, τ (θ) , both differentiable. Some analytical and numerical criteria are obtained in order to guarantee that all solutions are oscillatory.