objective: metal concentrations in 53 soil samples of shahr-e-babak were determined.  methods: assessment of enrichment factor and geo-accumulation index revealed higher degree of contamination of cd, pb, and cu in soil samples. moreover, results of metal fractionation study revealed high amount of cd and pb are associated in weakly bounds may lead to environmental risk of these metals.  result...

‎The first multiplicative Zagreb index $Pi_1(G)$ is equal to the‎ ‎product of squares of the degree of the vertices and the second‎ ‎multiplicative Zagreb index $Pi_2(G)$ is equal to the product of‎ ‎the products of the degree of pairs of adjacent vertices of the‎ ‎underlying molecular graphs $G$‎. ‎Also‎, ‎the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of‎ ‎the sum...

The topological approaches to find solutions of a coincidence equation f1(x)= f2(x) can roughly be divided into degree and index theories. We describe how these methods can be combined. We are led to a concept of an extended degree theory for function triples which turns out to be natural in many respects. In particular, this approach is useful to find solutions of inclusion problems F(x)∈Φ(x)....

objectives: each year, the united nations publishes an annual report titled by “human development report” for all countries around the world which in which the complex index for human development for achieving health life alongside education and economic welfare is examined. the innate ambiguity in estimation of human development index has brought about numerous criticism against the method of ...

‎the second multiplicative zagreb coindex of a simple graph $g$ is‎ ‎defined as‎: ‎$${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$‎ ‎where $d_gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$g$‎. ‎in this paper‎, ‎we compare $overline{{pi}}_2$-index with‎ ‎some well-known graph invariants such as the wiener index‎, ‎schultz‎ ‎index‎, ‎eccentric co...

The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using degree sequence.

This paper presents a servo strategy of Generalized Minimum Variance Control (GMVC) with a two degree of freedom. If GMVC fasts the transient response by tuning the control signal weight of the cost function, a large overshoot remains. This paper introduces the two degree of freedom GMVC. The two degree of freedom function curbs the overshoot, while the satisfactory transient characteristic hol...