Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and character...

We present some inequalities of Ostrowski and trapezoid type with complex exponential weight, for complex-valued absolutely continuous functions. These inequalities are related to Pompeiu’s mean value theorem. Special cases of these inequalities are applied to obtain (i) some approximation results for the finite Fourier and Laplace transforms; (ii) refinements of the Ostrowski and trapezoid ine...

In this paper we prove the Theorem announced in the title without using Vitali’s Covering Lemma and have as a consequence of this approach the equivalence of this theorem with that which states that absolutely continuous functions with zero derivative almost everywhere are constant. We also prove that the decomposition of a bounded variation function is unique up to a constant.

We introduce the notion centre of a convex set and study space continuous affine functions on compact with centre. show that these spaces are precisely dual base normed in which underlying has (unique) also characterize corresponding norm space. obtain condition compact, balanced, subset locally space, so is an absolute order unit Similarly, we latter becomes absolutely

Orthogonal polynomials $$P_{n}(\lambda)$$ are oscillating functions of $$n$$ as $$n\to\infty$$ for $$\lambda$$ in the absolutely continuous spectrum corresponding Jacobi operator $$J$$ . We show that, irrespective any specific assumptions on coefficients , amplitude and phase factors asymptotic formulas linked by certain universal relations found paper. Our proofs rely study a time-depende...