In this paper we count the number of paths and cycles in complete graphs by using the number e. Also, we compute the number of derangements in same way. Connection by e yields some nice formulas for the number of derangements, such as Dn = ⌊ n!+1 e ⌋ and Dn = ⌊(e + e −1)n!⌋ − ⌊en!⌋, and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; thes...

Nineteen subjects were investigated as a result of apnoea following the administration of suxamethonium occurring in one member of the family. Examination of the blood for cholinesterase activity, dibucaine number, and fluoride number was carried out and the appropriate genotype determined. The significance of the genetic variation of plasma cholinesterase in relation to suxamethonium apnoea is...

Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrized by n, compute a lower bound on the number of processors required by the schedule as a function of n. In our formulation, the number of tasks that are scheduled for execution duri...

Positive Darwinian selection at the molecular level is often studied by comparing the number of synonymous nucleotide substitutions per synonymous site (d,) and the number of nonsynonymous substitutions per nonsynonymous site (dN) between homologous gene sequences, and a t-test with an infinite number of degrees of freedom is usually used for determining the statistical significance of the diff...

In this paper, we prove some explicit upper bounds for the average order of the generalized divisor function, and, according to an idea of Lenstra, we use them to obtain bounds for the class number of number fields.

Positive Darwinian selection at the molecular level is often studied by comparing the number of synonymous nucleotide substitutions per synonymous site (d,) and the number of nonsynonymous substitutions per nonsynonymous site (dN) between homologous gene sequences, and a t-test with an infinite number of degrees of freedom is usually used for determining the statistical significance of the diff...

Let the braid group Bn act as (isotopy classes of) diffeomorphisms of an n-punctured disc Dn. Then there is an action of Bn on a polynomial algebra R = C [a1 , . . . , aN ] and a way of representing simple closed curves on Dn as elements of R. Fix k ∈ 2N. Using this approach we show that the image in Aut(R) of each Dehn twist τ about a simple closed γ in Dn satisfies a kind of characteristic eq...

Letting x = [a1(x), a2(x), . . .] denote the continued fraction expansion of an irrational number x ∈ (0, 1), Khinchin proved that Sn(x) = ∑n k=1 ak(x) ∼ 1 log 2 n logn in measure, but not for almost every x. Diamond and Vaaler showed that removing the largest term from Sn(x), the previous asymptotics will hold almost everywhere, showing the crucial influence of the extreme terms of Sn(x) on th...

The mTOR pathway plays an important role in a number of common renal diseases, including acute kidney injury (AKI), diabetic nephropathy (DN), and polycystic kidney diseases (PKD). The activity of mTOR complex 1 (mTORC1) is necessary for renal regeneration and repair after AKI, and inhibition of mTORC1 by rapamycin has been shown to delay recovery from ischemic AKI in animal studies, and to pro...

INTRODUCTION Glutathione S-transferases (GSTs) belong to a family of ubiquitous and multifunctional enzymes that protect the cells against oxidative stress. OBJECTIVES The aim of the study was to evaluate the association between the polymorphisms of glutathione-S-transferase (GST) genes and diabetic nephropathy (DN). PATIENTS AND METHODS PubMed, EMBASE, and Google Scholar databases were sys...