‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

the omega polynomial(x) was recently proposed by diudea, based on the length of stripsin given graph g. the sadhana polynomial has been defined to evaluate the sadhana index ofa molecular graph. the pi polynomial is another molecular descriptor. in this paper wecompute these three polynomials for some infinite classes of nanostructures.

in this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. we show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

OBJECTIVE Understanding the mechanisms by which neighbourhood environments influence childhood obesity is needed to facilitate the development of prevention strategies. The objective of this cross-sectional study was to identify the distinct types of neighbourhoods in which Canadian children reside and examine the extent to which physical activity and sedentary behaviour mediate the relationshi...

We generalize a result from Volkov (2001,[21]) and prove that, on an arbitrary graph of bounded degree (G, ∼) and for any symmetric reinforcement matrix a = (a i,j) i∼j , the vertex-reinforced random walk (VRRW) eventually localizes with positive probability on subsets which consist of a complete d-partite subgraph plus its outer boundary. We first show that, in general, any stable equilibrium ...

In this paper, we use the Canadian National Longitudinal Survey of Children and Youth data to examine the links between child well-being and neighbourhood 'quality.' This study adds to the literature by (i) investigating the relationship between neighbourhood quality and child health, (ii) by utilizing subjective assessments by individuals familiar with the neighbourhood (i.e., the survey respo...

Three-neighbourhood Cellular Automata (CA) are widely studied and accepted as suitable cryptographic primitive. Rule 30, a 3-neighbourhood CA rule, was proposed as an ideal candidate for cryptographic primitive by Wolfram. However, rule 30 was shown to be weak against Meier-Staffelbach attack [7]. The cryptographic properties like diffusion and randomness increase with increase in neighbourhood...

A graph G = (V, E) is called (k, k′)-total weight choosable if the following holds: For any total list assignment L which assigns to each vertex x a set L(x) of k real numbers, and assigns to each edge e a set L(e) of k′ real numbers, there is a mapping f : V ∪ E → R such that f(y) ∈ L(y) for any y ∈ V ∪ E and for any two adjacent vertices x, x′, ∑ e∈E(x) f(e)+f(x) 6= ∑ e∈E(x′) f(e)+f(x ′). We ...