Let X1, X2, ..., Xr be the first r order statistics from a sample of size n from the generalized exponential distribution with shape parameter θ. In this paper, we consider a Bayesian approach to predicting future order statistics based on the observed ordered data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics for one-sample ...

Let X(n) be an observation sampled from a distribution Pθ(n) with unknown parameter θ, θ being vector in Banach space E (most often, high-dimensional of dimension d). We study the problem estimation f(θ) for functional f:E↦R some smoothness s>0 based on X(n)∼Pθ(n). Assuming that there exists estimator θˆn=θˆn(X(n)) such n(θˆ n−θ) is sufficiently close to mean zero Gaussian random E, we construc...

Theorem 1.1. Let G be a group of Dirichlet characters modulo n, and KG the associated field. Fix a prime number p, and let H1 ⊂ H2 ⊂ G be the groups of χ such that χ(p) = 1 or χ(p) 6= 0 respectively. Then G/H2 ∼= IKG,p ⊂ Gal(KG/Q), and G/H1 ∼= DKG,p (note that these are non-canonical isomorphisms). We are now ready to prove the theorem on factoring Dedekind zeta functions of sub-cyclotomic fiel...

Let K be an anti-ideal of a semigroup (S,=, =, ·, θ) with apartness. A construction of the anti-congruence Q(K) and the quasi-antiorder θ, generated by K, are presented. Besides, a construction of the anti-order relation Θ on syntactic semigroup S/Q(K), generated by θ, is given in Bishop’s constructive mathematics.

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. A graph that admits an odd mean labelin...

Let N denote a sufficiently large even integer. In this paper it is proved that for 0.941 ≤ θ ≤ 1, the equation N = p + P 2 , p≤ N θ is solvable, where p is a prime and P 2 is an almost prime with at most two prime factors. The range 0.941 ≤ θ ≤ 1 extended the previous one 0.945 ≤ θ ≤ 1.

Let H = (X,E) be a simple hypergraph and let f (H, ) denote its chromatic polynomial. Two hypergraphs H1 and H2 are chromatic equivalent if f (H1, ) = f (H2, ). The equivalence class of H is denoted by 〈H 〉. Let K and H be two classes of hypergraphs.H is said to be chromatically characterized in K if for every H ∈ H ∩K we have 〈H 〉 ∩K=H ∩K. In this paper we prove that uniform hypertrees and uni...

Let ∆n−1 denote the (n−1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of ∆n−1 obtained by starting with the full 1-dimensional skeleton of ∆n−1 and then adding each 2−simplex independently with probability p. Let H1(Y ; F2) denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity lim n→∞ Prob [ H1(Y ; F2) = 0...

Let K denote a field. Let d denote a nonnegative integer and consider a sequence p = (θi, θ ∗ i , i = 0...d;φj , φj , j = 1...d) consisting of scalars taken from K. We call p a parameter array whenever: (PA1) θi 6= θj, θ ∗ i 6= θ ∗ j if i 6= j, (0 ≤ i, j ≤ d); (PA2) φi 6= 0, φi 6= 0 (1 ≤ i ≤ d); (PA3) φi = φ1 ∑i−1 h=0 θh−θd−h θ0−θd + (θ i − θ ∗ 0)(θi−1 − θd) (1 ≤ i ≤ d); (PA4) φi = φ1 ∑i−1 h=0 ...

Let K denote a field. Let d denote a nonnegative integer and consider a sequence p = (θi, θ ∗ i , i = 0...d;φj , φj , j = 1...d) consisting of scalars taken from K. We call p a parameter array whenever: (PA1) θi 6= θj, θ ∗ i 6= θ ∗ j if i 6= j, (0 ≤ i, j ≤ d); (PA2) φi 6= 0, φi 6= 0 (1 ≤ i ≤ d); (PA3) φi = φ1 ∑i−1 h=0 θh−θd−h θ0−θd + (θ i − θ ∗ 0)(θi−1 − θd) (1 ≤ i ≤ d); (PA4) φi = φ1 ∑i−1 h=0 ...