Let G = (V,E), V {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ... dn > 0, di d(vi). The geometric-arithmetic topological index is defined as GA(G) i~j 2? didj/di+dj, whereas the coindex GA?(G) i~/j 2 didj/di+dj . New lower bounds for and in terms some parameters other invariants are obtained.

This paper surveys selected recent progress in geometric mechanics, focussing on Lagrangian reduction and gives some new applications to nonholonomic systems, that is, mechanical systems with constraints typified by rolling without slipping. Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poinca...

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Desertification refers to land degradation phenomenon in arid, semi-arid and dry sub-humid areas, resulting from various factors including climate variation and human activities. For evaluation and mapping of desertification many research have been conducted leading to regional and local models. In this research, among different existing methods IMDPA‌ was selected and desertification intensity...

We consider a scenario where stops are to be placed along an already existing public transportation network in order to improve its attractiveness for the customers. The core problem is a geometric set covering problem which is NP-hard in general. However, if the corresponding covering matrix has the consecutive ones property, it is solvable in polynomial time. In this paper, we present data re...

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these methods have focused primarily on Riemannian manifolds in Euclidean space. While su...

Background: The seeds of some medicinal plants and their compounds have long been valued for their numerous health benefits. Objective:To investigate some physical and chemical properties of Salvia spp. Methods: Some physico-chemical properties in five species of Salvia seeds (consisted of S. officinalis L., S. macrosiphon L., S. hypoleuca L., S. sclarea L. and S. nemorosa L.) were measured ...