We consider the number Kn of clusters at a distance level dn ∈ (0, 1) of n independent random variables uniformly distributed in [0, 1] , or the number Kn of connected components in the random interval graph generated by these variables and dn , and, depending upon how fast dn → 0 as n → ∞ , determine the asymptotic distribution of Kn , with rates of convergence, and of related random variables...

Diabetic nephropathy (DN) remains an unmet medical challenge as its prevalence is projected to continue to increase and specific medicines for treatment remain undeveloped. Activation of the immune system, in particular T-cells, is emerging as a possible mechanism underlying DN disease progression in humans and animal models. We hypothesized that inhibition of T-cell activation will ameliorate ...

In the paper, crossing number of join product G*+Dn for disconnected graph G* consisting two components isomorphic to K2 and K3 is given, where Dn consists n isolated vertices. Presented proofs are completed with help configurations that a graphical representation minimum numbers crossings between different subgraphs whose edges do not cross G*. For first time, multiple symmetry presented as pa...

Fault indicators (FI) and remotely controlled switches (RCS) can reduce the power outage time in distribution network (DN) by finding isolating faulty area. Therefore, they play an important role reducing cost increasing reliability of DN. In DN, there may be high-priority loads. One goals improving updating DN is to increase all buses, especially buses feeding such Here, placement FI RCS, as s...

The main aim of the paper is to give crossing number join product G*+Dn. connected graph G* order six isomorphic K3,3\e obtained by removing one edge from complete bipartite K3,3, and discrete Dn consists n isolated vertices. proofs were carried out with help several possible redrawings respect its many symmetries.

The mol-ecular conformation of the title compound, C(20)H(29)N(3)O(2), is stabilized by an intra-molecular C-H⋯O hydrogen bond. The orientation of the amide group to the ring system is characterized by a C-C-C-O dihedral angle of 137.5 (3)°. In the crystal, inter-molecular N-H⋯O hydrogen bonds between the amide groups form C(4) chains running parallel to the a axis.

A microscopic mass balance approach has shown that the initial saturation (Is), absorption number (An), dose number (Do), and dissolution number (Dn) are four fundamental dimensionless parameters that can be used to estimate the fraction dose absorbed (~ of suspensions of poorly soluble drugs in humans. The dissolution number of a drug increases with decreasing its particle size. The effect of ...

Diabetic nephropathy (DN) is a kidney disorder secondary to diabetes and one of the main diabetic microvascular complications. As number patients grows, DN has become leading cause chronic disease in China. Unfortunately, no definitive cure currently exists for DN. Cornus officinalis (CO), frequently utilized clinical settings mellitus treatment, proven vital both preventing treating This artic...

Let an count the number of 2-dimensional rook paths Rn,n from (0, 0) to (2n, 0). Rook pathsRm,n are the lattice paths from (0, 0) to (m+n,m−n) with allowed steps (x, x) and (y,−y) where x, y ∈ N+. In answer to the open question proposed by M. Erickson et al. (2010), we shall present a combinatorial proof for the recurrence of an, i.e., (n + 1)an+1 + 9(n − 1)an−1 = 2(5n + 2)an with initial condi...