If σ is a permutation of n letters, say that j is an outstanding element (Fr. élément saillant) of σ if whenever i < j we have σ(i) < σ(j). A famous theorem of A. Rényi [R] (see also [C]) states that the number of permutations of n letters that have k outstanding elements is equal to the number that have k cycles, and therefore there are [ n k ] such permutations, the latter being the unsigned ...

We develop a new continuous distribution called the beta-Burr type X distribution that extends the Burr type X distribution. The properties provide a comprehensive mathematical treatment of this distribution. Further more, various structural properties of the new distribution are derived, that includes moment generating function and the rth moment thus generalizing some results in the literatur...

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment thus generalizing some results in the literature. Expressions for the density, moment generating function and r...

The purpose of this article is to present an acceptance sampling plan based on cumulative count of conforming using minimum angle method. In this plan, if the number of inspected items until rth defective items is greater than an upper control threshold then lot is accepted and if it is less than a lower control threshold then the lot is rejected and if it is between control thresholds, process...

The clinical, laboratory, genetic and molecular characteristics of syndromes of reduced sensitivity to thyroid hormone are the subject of this abstract. The syndrome of reduced sensitivity to thyroid hormone in the majority of cases is caused by point mutations in the thyroid hormone receptor b (TRb) gene. Before TRb gene mutations were recognized, resistance to thyroid hormone (RTH) was subdiv...

We conjecture that every oriented graph G on n vertices with δ(G), δ−(G) ≥ 5n/12 contains the square of a Hamilton cycle. We also give a conjectural bound on the minimum semidegree which ensures a perfect packing of transitive triangles in an oriented graph. A link between Ramsey numbers and perfect packings of transitive tournaments is also considered. 1.1. Powers of Hamilton cycles. One of th...

The RTH flotation tailing dump, located in the old open pit Bor about 500 m southeast of Flotation Plant, has been continuous operational work since 1985. flotations dumps are important mining facilities that constantly changed during their exploitation period. Due to changes occurring dump its exploitation, it is necessary perform a technical and technological surveillance-auscultation order c...

Based on the ongoing actual need for probability distributions that are more elastic than already in place, we present here doubly truncated Exponentiated Inverted Gamma distribution (DTEIGD). The rth raw moments function form derives new density. Stress-strength reliability, Shannon and relative entropies have also been discussed.

This paper introduced a new life time data analysis distribution name three parameters quasi gamma discussed about its some properties including moment generating function, rth origin and mean, mean deviations, reliability measurements, Bonferroni Lorenz curve, Order statistics, Renyi entropy, also maximum likelihood method real-life applications.

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.