This article aims at analyzing and estimating the function of private consumption and it's long-run relation using ERROR CORRECTION MODEL in Iran's economy. To avoid spurious regression we proceeded first by exploring the long-run co-integrating private mechanism to estimate the short-run equation. Since there may be a weakness associated with the Engle-Granger method of co-integration testing, we investigated the cointegration relationship by using Johansen co-integration test. We found strong evidence from the Johansen test that the related variables are integrated. The empirical evidence suggests that the tendency toward consumption is 83% and the speed of adjustment for the long-run private consumption is around 73% implying that about 73 percent of differences between the short-run and long-run consumption level will be adjusted within one year.

Background & objectives: Despite the importance and impact of health and education on economic growth in countries, the causal relationship between education and health is important to policymaking. This study aimed to investigate the causality relationship between education and health in the short and long runs using the Vector ERROR CORRECTION MODEL (VECM) in Iran. Method: This was an analytical and applied study, conducted at the national level using Vector ERROR CORRECTION MODEL for Iran. The data type was annual time series which extracted from the World Bank website between the years of 2017-1996. The VECM and the required tests were estimated in Eviews 10 software. Results: the result showed that there was a cointegration vector for the health function of Iran in these years, i. e., current health was not only a function of independent variables of the MODEL but also a function of health and education variables in previous periods. Also, in the short and long run, the years of schooling had the causal effect on life expectancy and, life expectancy had a causal effect on years of schooling in Iran. GDP and health expenditures per capita had a positive effect and the carbon dioxide production per capita had a negative impact on life expectancy. Conclusion: According to the results, there was a two-way causality relationship between education and health in the short and long runs in Iran, so that in the short and long runs, increased education can lead to improved health status, and improved health status can lead to increased education. Therefore, the policies of the education and health sectors are complementary.

Ever increasing and mismanagement of gasoline consumption in Iran has caused deficiency in gasoline production, so that the country has confronted with problems in providing this product and has been obliged to import it. Therefore, estimating the demand function for gasoline and studying the factors affecting gasoline consumption are very important. The period of this research is 1967-2003. In this research by using the cointegration method of Johansen-Juselius, the long-term relationship and the ERROR CORRECTION MODEL, which specifies the system's short-term dynamics, have been estimated. The results show that the demand for gasoline is inelastic with respect to its price and income; it means that gasoline is an essential goods. Therefore, nonprice and nonincome factors have a particular impact on gasoline consumption. The ERROR CORRECTION coefficient, which determines the speed of adjustment, has an expected and significant negative sign. The results indicate that deviation from the long-term gasoline consumption is corrected by approximately 51 percent in the following year.

In this paper the long run relationship between private investment and the variables influencing it with be determined using conditional ARDL MODEL Pesaran & Shin's frame work for the years 1973-2004. The results of this study show that there is long run relationship between private investment, public investment, per capita income and capital inventory, real interest rate and granted credit of banks to private sector. Private investment has the most sensitivity to public investment. On the other hand, private investment in Iran has the lowest sensitivity to banks granting credit to private sector, which show inefficiency of banking system in Iran in allocation of resources and the direction it takes to inject money to public sector. So, by making restricting public sector on one hand, and increasing its efficiency on the other and encouraging the development of Credit & Finance Institutions, the possibility and propensity to invest in private sector will be widely available.

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.