We discuss diagonalization of propagator for mixing fermions system based on the eigenvalue problem. The similarity transformation converting matrix into diagonal form is obtained. suggested has simple algebraic properties on-shell and can be used in renormalization fermion matrix.

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.

In this paper, the first and second order approximations of Taylor expansion are used for calculating the change of each natural frequency by modifying an arbitrary parameter of a system with a known amount and based on this approximation, the inverse eigenvalue problem is transformed to a solvable algebraic equation. The finite element formulation, based on the classical laminated plate theory...

The follow-up to the Human Genome Project has found very little to connect variations in our DNA blueprints to some of our basic individual characteristics. This very surprising "missing heritability" problem, plus a number of existing underappreciated challenges to the DNA-based model, together are consistent with an underlying complementary transcendental contribution to life. Some of the beh...

In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. In this paper, the above rela...

A tiling of the plane is a collection of figures, called tiles, that cover the plane without gaps or overlaps except at their boundaries. Tilings have been used for various purposes, such as ornamentation for construction and design of clothes. The patterns made by tilings range from those made by simple geometrical figures to those made by intricate figures, and they attract a great deal of in...

Our ultimate goal in this project is to solve the symmetric eigenvalue problem on symmetric multiprocessor machines more quickly than existing implementations. In order to achieve this goal, we have chosen to implement an improved multithreaded version of a specific phase of the current best algorithmic approach, namely the reduction of a full symmetric matrix to banded form using two-sided ort...