The Normal (or Gaussian) distribution is the most commonly used statistical distribution and has a number of remarkable properties. We will use the notation: G x (µ, Σ) = 1 (2π) n/2 |Σ| 1/2 exp −0.5(x − µ) T Σ −1 (x − µ) (1) to denote a normal distribution in the (possibly multidimensional) variable x with mean µ and symmetrical, positive definite covariance matrix Σ. In order to elucidate some...

Given a finite non-cyclic group G, call σ(G) the smallest number of proper subgroups of G needed to cover G. Lucchini and Detomi conjectured that if a nonabelian group G is such that σ(G) < σ(G/N) for every non-trivial normal subgroup N of G then G is monolithic, meaning that it admits a unique minimal normal subgroup. In this paper we show how this conjecture can be attacked by the direct stud...

mangrove sediments were collected during wet and dry seasons from nine stations in khamir,laft and natural reservoir mangrove-dense areas of hormozgan province in the south of iran. σ pcbs ranged from 5.33 to 15.5 ng/g dry weight and the dominant congener was no.153. average σ ddts for khamir and laft mangroves were 16.58 ± 1.51 and 18.8 ± 9.98 ng/g dry weight. ddt was more abundant than dde an...

We define the Z2 Hodge spaces Hpq(Σ) of a fan Σ. If Σ is the normal fan of a reflexive polytope ∆ then we use polyhedral duality to compute the Z2 Hodge Spaces of Σ. In particular, if the cones of dimension at most e in the face fan Σ of ∆ are smooth then we compute Hpq(Σ) for p < e− 1. If Σ is a smooth fan then we completely determine the spaces Hpq(Σ) and we show XΣ is maximal, meaning that t...

The central limit theorem states that the sample mean X̄ follows approximately the normal distribution with mean μ and standard deviation σ √ n , where μ and σ are the mean and standard deviation of the population from where the sample was selected. The sample size n has to be large (usually n ≥ 30) if the population from where the sample is taken is nonnormal. If the population follows the norm...

We sample (β, η, γ) using a (block) Gibbs sampler along with data augmentation for the missing responses (straightforward given the full data response is multivariate normal). We sample the full conditional for the parameters as follows. At iteration k0, 1. Sample Yimiss|(β, γ(k0−1), η(k0−1), yiobs) by data augmentation. Yimiss ∼ N(ximissβ+Σ (k0−1) i12 (Σ (k0−1) iobs ) (yiobs−xiobsβ),Σ (k0−1) i...

String rewriting systems have been originally introduced by Thue [21] in order to study word problems in monoids. A string rewriting system (Σ,R) consists of a set Σ, called the alphabet, and a set R ⊆ Σ∗×Σ∗ of rules. The monoid Σ∗/≡R, obtained by quotienting the free monoid Σ∗ over Σ by the smallest congruence (wrt concatenation) containing R, is called the monoid presented by the rewriting sy...

Functional values of LogSD of the ventilation distribution (σ(V)) have been reported previously, but functional values of LogSD of the perfusion distribution (σ(q)) and the coefficient of correlation between ventilation and perfusion (ρ) have not been measured in humans. Here, we report values for σ(V), σ(q), and ρ obtained from wash-in data for three gases, helium and two soluble gases, acetyl...

We show that the Σ 1 \Sigma ^1_1 </inline-formula...

The problem is from mesoscopic physics: let p : Σ → R3 be an embedded surface in R3, we assume that (1) Σ is orientable, complete, but non-compact; (2) Σ is not totally geodesic; (3) Σ is asymptotically flat in the sense that the second fundamental form goes to zero at infinity. On can build a quantum layer Ω over such a surface Σ as follows: as a differentiable manifold, Ω = Σ × [−a, a] for so...