A formulation for finite element analysis of tapered and  monosymmetric I shaped beam-columns is presented. This is a general way to analyze these types of complex elements. Based upon the formulation, member stiffness matrix is obtained explicitly. The element considered has seven nodal degrees of freedom. In addition, the related stability matrix is found. Numerical studies of the aforementio...

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comaprisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. Orthogonal basis is introduced in the vector space. The orthogonal projection of the transformed matrix onto the space formed by the images of consistent matrices is ...

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

This study proposes some issues to solve the Incomplete Linguistic Preference Relations under Multi-Criteria Decision Making. The proposed method has simple calculation and can speed up the process of comparison and selection of alternative. Experts obtain the matrix by choosing a finite and fixed set of alternatives and perform a pairwise comparison based on their different preferences and kno...

In nonlinear regression theory, the sandwich estimator of the covariance matrix of the model parameters is known as a consistent estimator, even when the parameterized model does not contain the regression. However, in the latter case, we emphasize the fact that the consistency of the sandwich holds only if the inputs of the training set are the values of independent identically distributed ran...