We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform expansion by applying techniques used for the existing uniform expansions for (...

Description The package implements the statistical theory of L-moments including L-moment estimation, probability-weighted moment estimation, parameter estimation for numerous familiar and not-so-familiar distributions, and L-moment estimation for the same distributions from the parameters. L-moments are derived from the expectations of order statistics and are linear with respect to the probab...

A simplified method to compute $R_t$, the Effective Reproduction Number, is presented. The relates value of $R_t$ estimation doubling time performed with a local exponential fit. condition $R_t = 1$ corresponds growth rate equal zero or equivalently an infinite time. Different assumptions on probability distribution generation are considered. simple analytical solution presented in case follows...

We consider the gradient flow associated to the following functionals Fm(φ) = ∫ M 1 + |∇ν| dμ . The functionals are defined on hypersurfaces immersed in R via a map φ : M → R, where M is a smooth closed and connected n–dimensional manifold without boundary. Here μ and ∇ are respectively the canonical measure and the Levi–Civita connection on the Riemannian manifold (M, g), where the metric g is...

Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential $U$ allowing for singularities. By modifying direct approach convergence in $L^2$ pioneered by F. H\'erau and developped Dolbeault, Mouhot Schmeiser, we show that converges exponentially fast topologies $L^2(d\mu)$ $L^2(W^* d\mu)$, where $\mu$ denotes invariant probability measure $...

a graph $gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $gamma$ acts transitively on $v(gamma)$ or $e(gamma)$‎, ‎respectively‎. ‎let $gamma=cay(g,s)$ be a cayley graph on $g$ relative to $s$‎. ‎then, $gamma$ is said to be normal edge-transitive‎, ‎if $n_{aut(gamma)}(g)$ acts transitively on edges‎. ‎in this paper‎, ‎the eigenvalues of normal edge-tra...

A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. ‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, ‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. ‎In this paper‎, ‎the eigenvalues of normal edge-tra...

The creation and maintenance of complex forest structures has become an important forestry objective. Complex structures, often expressed in multimodal shapes tree size/diameter (DBH) distributions, are challenging to model. Mixture probability density functions two- or three-component gamma, log-normal, Weibull mixture models offer a solution can additionally provide insights into dynamics. Mo...

Negation operation is important in intelligent information processing. Different existing arithmetic negation, an exponential negation presented this paper. The new can be seen as a kind of geometry negation. Some basic properties the proposed are investigated, and we find that fix point uniform probability distribution, which reaches maximum entropy. entropy increase operation, all distributio...

background: ultrasound propagation velocity was measured experimentally in normal, fibroadenoma and ductal carcinoma breast tissues, in order to distinguish normal breast tissue from tumors. materials and methods: in quantitative measurements of ultrasound velocity, 403 breast tissue images were selected, comprising 130 normal breast tissue, 130 fibroadenoma, and 143 ductal carcinoma tumors. th...