a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...

Using a series of model tests, this study investigated the effect of a passive pile on 3D ground deformation around a laterally loaded pile and on that laterally loaded pile's response in sand. The active pile head was subjected to lateral loads, and the passive pile was arranged in front of the active pile. In the model tests, the distance between the two pile centers was set to zero (i.e., a ...

The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired from experts and utilizing recommendations. The aim of this paper was to define soft constraints u...

We use molecular statics simulations with the tight-binding potential to analyze stress evolution in nanosize square prismatic gold specimens of different aspect ratios (length/width) deformed in either simple tension/compression or tension/compression. In the former case atoms on end faces are displaced axially but are free to move laterally, and in the latter case atoms on end faces are restr...

Postmammillary decerebrated cats can generate stepping on a moving treadmill belt when the brain stem or spinal cord is stimulated tonically and the hindquarters are supported both vertically and laterally. While adequate propulsion seems to be generated by the hindlimbs under these conditions, the ability to sustain equilibrium during locomotion has not been examined extensively. We found that...

‎for any integer $kgeq 1$‎, ‎a set $s$ of vertices in a graph $g=(v,e)$ is a $k$-‎tuple total dominating set of $g$ if any vertex‎ ‎of $g$ is adjacent to at least $k$ vertices in $s$‎, ‎and any vertex‎ ‎of $v-s$ is adjacent to at least $k$ vertices in $v-s$‎. ‎the minimum number of vertices of such a set‎ ‎in $g$ we call the $k$-tuple total restrained domination number of $g$‎. ‎the maximum num...

a {em roman dominating function} on a graph $g$ is a function$f:v(g)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}a {em restrained roman dominating}function} $f$ is a {color{blue} roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} the wei...

A set D ⊆ V of a graph G = (V,E) is called a restrained dominating set of G if every vertex not in D is adjacent to a vertex in D and to a vertex in V \D. The MINIMUM RESTRAINED DOMINATION problem is to find a restrained dominating set of minimum cardinality. Given a graph G, and a positive integer k, the RESTRAINED DOMINATION DECISION problem is to decide whether G has a restrained dominating ...

Due to the fact that the buckling-restrained brace core yields subject to both tension and compression, it can adsorb energy and exhibit high ductility rendering it proper for tolerating earthquake loads. One of the important objectives of seismic standards is safeguarding the appropriate ductility for the structures because the structures, in case of being ductile, can dissipate a considerable...