Trade liberalization, imported inputs and factor efficiencies: Evidence from the auto components industry in India

Firm-level data have been used to estimate changes in factor efficiencies_imported inputs being one of them-- over three sub-periods, 1977-84, 1985-91 and 1992-99 respectively denoting eras before liberalization, partial liberalization of the automotive industries and economy-wide liberalization. We see that the average size of firms has increased from that in the protected regime as the degree of liberalization has advanced. We find that the substitutability among inputs changed over the three sub-periods. We also find that the marginal products of all the inputs are very heterogeneous among firms in each period. The distributions of marginal product of labour and domestic materials and has moved to the left in the later periods while that of capital has moved to the right. The distribution of marginal product of imported materials first moved to the right and then to the left as compared to the first period. Overall the smaller firms benefited more in the earlier periods and bigger ones in the last period.

Sharp Bounds on (Generalized) Distance Energy of Graphs

Given a simple connected graph G, let D(G) be the distance matrix, DL(G) be the distance Laplacian matrix, DQ(G) be the distance signless Laplacian matrix, and Tr(G) be the vertex transmission diagonal matrix of G. We introduce the generalized distance matrix Dα(G)=αTr(G)+(1−α)D(G) , where α∈[0,1] . Noting that D0(G)=D(G),2D12(G)=DQ(G),D1(G)=Tr(G) and Dα(G)−Dβ(G)=(α−β)DL(G) , we reveal that a generalized distance matrix ideally bridges the spectral theories of the three constituent matrices. In this paper, we obtain some sharp upper and lower bounds for the generalized distance energy of a graph G involving different graph invariants. As an application of our results, we will be able to improve some of the recently given bounds in the literature for distance energy and distance signless Laplacian energy of graphs. The extremal graphs of the corresponding bounds are also characterized

Maximal and minimal entry in the principal eigenvector for the distance matrix of a graph

AbstractLet G=(V,E) be a simple, connected and undirected graph with vertex set V(G) and edge set E(G). Also let D(G) be the distance matrix of a graph G (Janežič et al., 2007) [13]. Here we obtain Nordhaus–Gaddum-type result for the spectral radius of distance matrix of a graph.A sharp upper bound on the maximal entry in the principal eigenvector of an adjacency matrix and signless Laplacian matrix of a simple, connected and undirected graph are investigated in Das (2009) [4] and Papendieck and Recht (2000) [15]. Generally, an upper bound on the maximal entry in the principal eigenvector of a symmetric nonnegative matrix with zero diagonal entries and without zero diagonal entries are investigated in Zhao and Hong (2002) [21] and Das (2009) [4], respectively. In this paper, we obtain an upper bound on minimal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs. Moreover, we present the lower and upper bounds on maximal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs

Comparison Between Zagreb Eccentricity Indices and the Eccentric Connectivity Index, the Second Geometric-arithmetic Index and the Graovac-Ghorbani Index

The concept of Zagreb eccentricity indices was introduced in the chemical graph theory very recently. The eccentric connectivity index is a distance-based molecular structure descriptor that was used for mathematical modeling of biological activities of diverse nature. The second geometric-arithmetic index was introduced in 2010, is found to be useful tool in QSPR and QSAR studies. In 2010 Graovac and Ghorbani introduced a distance-based analog of the atom-bond connectivity index, the Graovac-Ghorbani index, which yielded promising results when compared to analogous descriptors. In this note we prove that for chemical trees T. For connected graph G of order n with maximum degree, it is proved that if and, otherwise. Moreover, we show that for paths and some class of bipartite graphs. This work is licensed under a Creative Commons Attribution 4.0 International License

Access to Finance and Its Association with Development in Rural India

Financial development has been correlated with better development outcomes. Even so, the access dimension of financial development has often been overlooked. In this context, the paper throws initial light on the nuances of horizontal inequality in the access to finance from institutional sources and development outcomes such as poverty, educational attainment and standard of living in rural area for Indian states. It is seen that the percentage of rural households getting access to finance from institutional agencies has remained considerably low and there is significant variation across states. More importantly, there is significant amount of horizontal inequality in the access to finance from institutional sources. Interestingly, better access to finance is found to be associated with better development outcomes. The most important finding of the paper is that lower (higher) inequality in the access to finance from institutional sources is associated with better (worse) development outcomes.access to finance, development, horizontal inequality, rural household

On the energy and spectral properties of the he matrix of hexagonal systems

summary:The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles and the eigenvalues of the He matrix of a hexagonal system. Finally, we present an upper bound on the He energy of hexagonal systems