Chinese Science Bulletin

We applied fractal analysis to the mathematical determination of fractal dimensions to unambiguously define the neodymium magnesium titanium oxide structure. Its microstructure, space group, and crystal structure were determined and are directly connected to its microwave frequency electrical properties, which are important for the miniaturisation of electronic components. We performed a fractal analysis of the microstructure of neodymium magnesium titanium oxide Nd(Mg1/2Ti1/2)O3 (NMT) to determine the microstructure. Its appearance, area, and angle computations are comparable to those of the

For a graph G with vertex set V(G), an ordered subset W={w_1,w_2,...,w_k} of V(G), the k-vector (d(v,w_1),d(v,w_2),...,d(v,w_k)) is called the resolving vector of v∈V(G) with respect to W denoted by r(v|W). The set W is called a resolving set of graph G if r(u|W)≠r(v|W) for any two distinct vertices u and v. A subset D of V(G) is called a resolving dominating set if it is resolving as well as dominating and it is called equitable if for every vertex v∈V(G)-D, there exists a vertex u∈D such that uv∈E(G) and |deg(u)-deg(v)|≤1. A dominating set which is both equitable and resolving is

In this paper, we introduced the concept of edge geodetic closure polynomial of a graph and established results for complete graphs, paths and complete bipartite graphs. Interestingly, we have shown that the edge geodetic closure polynomial of a path can be expressed as a combination of a polynomial and its derivative.

In this paper, we established some properties of restrained locating total dominating sets in graphs. Moreover, we characterized graphs with restrained locating total domination number equal to 2 and those graphs with restrained locating total domination number equal to its order.

In this paper, we extended the work of [2] in topological spaces by introducing generalized star closed and open sets. This article employed exploratory research design which involves data mining of existing concepts on GTS to understand patterns and trends on characteristics of sets and functions. Further, in-depth analysis was conducted to explore related concepts and to characterize sets in GTS. This article mainly contributes to the establishment of topological properties of the newly introduced sets in GTS. While the implications of this study are limited to the academic community studyin