The deep drawing process is a widely used method for producing metal sheet parts. The main cost of the die in this method is to make the matrix. Using rubber matrix saves construction time and production cost. Controlling the deformation of rubber and blank is one of the important issues in this method. Therefore, in this article, a comparison has been made between the parts produced by metal and rubber dies. In the following, three-dimensional simulations have been performed using the finite element method and hyper elastic model. The simulation results showed that placing an intermediate ring between the rubber and the blank causes a significant improvement in the production parts and better control of the behavior of the blank and rubber during deformation. For verification, a die with rubber components and also a die with a metal matrix were made, and experimental tests were performed for the steel material. The dies were made based on the primary spacing technique instead of the spring and blank holding system. The maximum percentage of thinning, the percentage of equivalent plastic strain, shrinkage, tearing, and the force on the metal mandrel have been investigated and compared in two types of dies for steel workpieces

Background and Aim: Major Dam construction projects have increased due to widespread climate change, as a result of increased drought, human population growth and, consequently, increased global demand for energy and water. However, without comprehensive research, a large project such as a dam will have many irreversible and unpredictable effects on the environment. In this paper, the environmental impacts of Eyvashan dam in two phases of construction and exploitation on biological, physical-chemical, economic-social, cultural and strategic environments have been identified and studied. Materials and Methods: In the study of the environmental impact assessment of the Eyvashan dam with regard to development and evolution, as well as the abundant use of matrices in construction projects, the modified Leopold matrix method and the rapid impact assessment matrix have been used. The field survey and questionnaire were used to evaluate the construction and operation activities on the environmental components. Results: The results showed that the most negative effects in both construction and utilization phases were in both Leopold modified matrix and the rapid impact assessment matrix related to the physical-chemical environment and the most positive effects of the socio-economic environment for both phases. Conclusion: By comparing the many positive effects of construction and exploitation of the dam in terms of socio-economic status, the construction of the dam can be considered as an appropriate alternative to the physicalchemical negative effects. Also, in the results of both matrices, there was a very suitable adaptation matrix that can confirm the accuracy of the results in the environmental assessment of the Eyvashan dam in two stages of construction and operation.

We study the set of all determinants of adjacency matrices of graphs with a given number of vertices. Using Brendan McKay's data base of small graphs, determinants of graphs with at most 9 vertices are computed so that the number of non-isomorphic graphs with given vertices whose deter- minants are all equal to a number is exhibited in a table. Using an idea of M. Newman, it is proved that ifG is a graph with n vertices, m edges and { d1, …, dn} is the set of vertex degrees of G, then gcd (2m, d2) divides the determinant of the adjacency matrix of G, where d=gcd (d1, …, dn). Possible determinants of adjacency matrices of graphs with exactly two cycles are obtained.

This paper analyzes a linear system of equations when the right and side is a fuzzy vector and the coefficient matrix is a crisp M-matrix. The fuzzy linear system (FLS) is converted to the equivalent crisp system with coefficient matrix of dimension 2n x 2n. However, solving this crisp system is difficult for large n because of dimensionality problems. It is shown that this difficulty may be avoided by computing the inverse of an n x n matrix instead of Z-1.