Buckling restrained braced frames (BRBFs) for seismic load resistance have been widely used in recent years. One of the key requirements for a buckling restrained brace is to sustain large plastic deformations under severe ground motions. The core of a buckling restrained brace is prone to fatigue fracture under cyclic loading. The earthquake induced fracture type of the core plate in a bucklin...

A set S of vertices in graph [Formula: see text] is a [Formula: see text], abbreviated TRDS, of G if every vertex of G is adjacent to a vertex in S and every vertex of [Formula: see text] is adjacent to a vertex in [Formula: see text]. The [Formula: see text] of G, denoted by [Formula: see text], is the minimum cardinality of a TRDS of G. Jiang and Kang (J Comb Optim. 19:60-68, 2010) characteri...

Background: Considering the negative consequences of using physical restraints, we conducted this study to identify patients who are more frequently restrained in a psychiatric emergency ward as an initial step to limit the use of restraint to the minimum possible.   Methods: This was a retrospective case control study conducted in Iran Psychiatric Hospital in Tehran, Iran. We reviewed the f...

We consider two general frameworks for multiple domination, which are called 〈r, s〉-domination and parametric domination. They generalise and unify {k}-domination, k-domination, total k-domination and k-tuple domination. In this paper, known upper bounds for the classical domination are generalised for the 〈r, s〉-domination and parametric domination numbers. These generalisations are based on t...

A restrained Italian dominating function (RID-function) on a graph G=(V,E) is f:V→{0,1,2} satisfying: (i) f(N(u))≥2 for every vertex u∈V(G) with f(u)=0, where N(u) the set of vertices adjacent to u; (ii) subgraph induced by assigned 0 under f has no isolated vertices. The weight an RID-function sum its value over whole vertices, and domination number minimum G. In this paper, we initiate study ...

Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique c...

BackgroundGame Theory Interpretation MethodsRandomizationFunctional Lagrange Multipliers ConclusionsReferences

A restrained Roman dominating function (RRD-function) on a graph \(G=(V,E)\) is \(f\) from \(V\) into \(\{0,1,2\}\) satisfying: (i) every vertex \(u\) with \(f(u)=0\) adjacent to \(v\) \(f(v)=2\); (ii) the subgraph induced by vertices assigned 0 under has no isolated vertices. The weight of an RRD-function sum its value over whole set vertices, and domination number minimum \(G.\) In this paper...

In this paper, we introduce the closed domination in graphs. Some interesting relationships are known between domination and closed domination and between closed domination and the independent domination. It is also shown that any triple m, k and n of positive integers with 3 ≤ m ≤ k ≤ n are realizable as the domination number, closed domination number and independent domination number, respect...