k-means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and us...

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

The global music market has witnessed the rapid rise of Korean pop music, K-pop, in recent years. While there been an increased interest scholars from various disciplines to account for success limited attention paid key players industry, businesses. Based on a historical analysis Korea’s we contend that innovative production system businesses played significant role facilitating K-pop’s succes...

A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number o...

A global boundary defensive k-alliance in a graph G = (V,E) is a dominating set S of vertices of G with the property that every vertex in S has k more neighbors in S than it has outside of S. A global boundary offensive k-alliance in a graph G is a set S of vertices of G with the property that every vertex in V − S has k more neighbors in S than it has outside of S. We define a global boundary ...

among abiotic stresses, salinity has been increasing over the time for many reasons like using chemical fertilizers, global warming and rising sea levels. under salinity stress, the loss of water availability, toxicity of na+ and ion imbalance directly reduces carbon fixation and biomass production in plants. k+ is a major agent that can counteract na+ stresses, thus the potential of plants to ...