bus systems are unstable without considering any control. thus, we are able to consider some control strategies to alleviate this problem. a holding control strategy is one commonly used real-time control strategy that can improve service quality. this paper develops a mathematical model for a holding control strategy. the objective of this model is to minimize the total cost related to passeng...

In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...

BACKGROUND Menstrual irregularity is an indicator of endocrine disorders and reproductive health status. It is associated with various diseases and medical conditions, including obesity and underweight. We aimed to assess the association between body weight changes and menstrual irregularity in Korean women. METHODS A total of 4,621 women 19 to 54 years of age who participated in the 2010 to ...

Irregularities are inherent to virtually all fibers, including the conventional textile fibers, the high-performance brittle fibers and newly developed nano-fibers. These irregularities can fall into two main categories: dimensional or geometrical irregularity (external) and structural irregularity (internal). For natural fibers such as wool, diameter variation along fiber length is atypical ex...

Let R be a commutative ring and Z(R) the set of all zero divisors R. Γ(R) is said to divisor graph if x,y ∈ V (Γ(R)) = (x,y) E(Γ(R)) only x.y 0. In this paper, we determine total vertex irregularity strength graphs associated with rings ℤp2 × Zq for p,q prime numbers.

For a simple graph G with no isolated edges and at most, one vertex, labeling ?:E(G)?{1,2,…,k} of positive integers to the is called irregular if weights vertices, defined as wt?(v)=?u?N(v)?(uv), are all different. The irregularity strength known maximal integer k, minimized over labelings, set ? such exists. In this paper, we determine exact value modular fan graphs.