In this study, with employing a combination of Index DECOMPOSITION Analysis and Production-Theoretical DECOMPOSITION Analysis approach, based on multiplicative approach analysis and period-wise and chain-link analysis, we evaluate the influential factors on energy intensity in the period 2006-2012. In this regards, we calculate the indexes of structural effect, activity effect, intensity effect, technological changes, changes in technical performance, and the substitution rate of the labor force and capital with energy for the Iranian economic sectors included industry, transportation, and agriculture. Furthermore, we consider these indices for consumption of the different type of energy like crude oil, petroleum products, natural gas, and electricity. The results of this study show that energy intensity in all three economic sectors increased during the period. Based on economic sector's data, substitution of the labor force with energy is the most important determinant of total change in energy intensity. However, if in addition to economic sector's data, we use energy consumption data, production effect is the most important factor. The substitution of the labor force with energy is the most important factor affecting the sectoral energy intensity. Changes in technical efficiency during this period show that total energy consumption decreased and has the lowest share in total consumption growth and energy intensity. Also, the results show that comparing based on chain-link analysis has more realistic and reliable results for policymakers.

Let n, t1, …, tk be distinct positive integers. A Toeplitz graph G=(V, E) is a graph with V={1, …, n} and E={(i, j)½½i-j½Î{t1, …, tk}}. In this paper, we present some results on DECOMPOSITION of Toeplitz graphs.

In this contribution we define a new class of non-linear integrals based on DECOMPOSITION integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is provided.

The aim of this study is DECOMPOSITION of the changes in energy consumption with emphasizing the structural changes in Iran during 2001-2011 using Input-Output Structural DECOMPOSITION Analysis (I_O SDA). Structural changes in this study represent the changes in structure of intermediate input in sectors and also changes in structure of final demand categories. Structural changes in intermediate inputs decomposed into intermediate input substitution in sectors and changes in direct backward linkages. Structural changes in final demand represent the changes of the share of each sector in total final demand categories. The results showed that energy coefficients helped to reduce energy use and final demand changes and technological changes (structural changes in intermediate inputs) caused to increase of energy use. The final demand had the main contribution on increase of energy use (44186. 26 BGJ). Among the final demand components, increase in level of investment and household’ s consumption was the main drivers of energy use increment.

A difference labeling of a graph G is an injective function f: V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u)-f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a DECOMPOSITION of G and is called the common weight DECOMPOSITION of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight DECOMPOSITION induced by f. A difference labeling f of G is said to be a graphoidal difference labeling if ϒf is an acyclic graphoidal DECOMPOSITION of G. This paper initiates a study on this concepts.

The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper-Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.