We present a simple formula for the total cross section σ(νN) of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F(2)(νN)(M(V)(2)/s,M(V)(2)), where M(V) is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in front of F(2)(νN)(x,Q(2)) dep...

The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, on temporal point process is still under-explored. problem challenging because a two types randomness: 1) number events process, 2) distribution these events. Recent studies proposed depths weighted product terms, describing above randomness, respectively. Und...

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions Einstein equations strongly nonlinear scalar field, which allow appearance new type (“spherical singularities”) outside center curvature coordinates. As example, consider field potential ∼sinh(ϕ2n),n...

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...

An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall...

M-estimators introduced in Huber (1964) provide a class of robust estimators of a center of symmetry of a symmetric probability distribution which also have very high eeciency at the model. However it is not clear what they do estimate when the probability distributions are nonsymmetric. In this paper we rst show that in the case of arbitrary, not necessarily symmetric probabilty distributions,...

The stability of equilibria and asymptotic behaviors trajectories are often the primary focuses mathematical modeling. However, many interesting phenomena that we would like to model, such as “honeymoon period” a disease after onset mass vaccination programs, transient dynamics. Honeymoon periods can last for decades be important public health considerations. In fields science, especially in ec...

if $g$ is a connected graph with vertex set $v$, then the eccentric connectivity index of $g$, $xi^c(g)$, is defined as $sum_{vin v(g)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. in this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.