Inconsistency of decision maker’s preferences may be measured as a number of violation of a transitivity rule or by some other measure like consistency index in Analytical Hierarchy Process. In Potential Method, inconsistency is measured by an angle between the preference flow and the column space of the incidence matrix. In this article, a random study is performed to determine the upper bound...

Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...

For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. We study the properties of upper domatic number and propose an up...

In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

Recently, there has been considerable interest in the development of robust, cost-effective and high performance non-metallic landmine detection systems using ground penetrating radar (GPR). Many of the available solutions try to discriminate landmines from clutter by extracting some form of statistical or geometrical information from the raw GPR data, and oftentimes, it is difficult to assess ...

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs ( K , Q ). If stable subgroup uncontrolled system is closed has positive measure a left invariant Haar measure, coincides with entropy.

Precision forging process is widely used for the production of spur gears due to its advantages such as improved strength and surface finish, little waste of materials and reduction in the machining time of the gear. An important aspect of precision forging process is the load required to perform the process successfully and design the forging tools. In this research, a new kinematically admiss...

This paper studies the guaranteed cost of a quadratic criterion associated with a linear discrete-time switched system for all the set of admissible switching laws. The admissible switching laws are here the ones exhibiting a dwell time. The approach provided here is to design an upper bound and a parametrized family of lower bounds of the guaranteed cost as close as possible in order to obtain...