A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated. It can be applied to implement control algorithms for technical systems without executing the variables transformation procedures that are needed for deriving a Frobenius matrix. The method can be used for simulation of systems with differe...

A matrix approach is proposed for determining the coefficients of maximally flat (m.f.) FIR filter transfer functions expressed in terms of cosine of multiple angles. In this, a transformation matrix maps a functional vector, the entries of which are either 0 or 1, into the coefficient vector of the m.f. filter transfer function. It is shown that the transformation matrix could be generated eit...

This work presents a re-derivation of relative Jacobian matrix for parallel manipulators, expressed in terms of the individual manipulator Jacobians and multiplied by their corresponding transformation matrices. This is particularly useful when the individual manipulator Jacobians are given, such that one would not need to derive an entirely new expression of a relative Jacobian but will only u...

TiO2/SiO2 nanocomposite with molar ratio 1:1 was synthesized by a free calcination sol-gel method using titanium tetra chloride and tetraethylorthosilicate as raw materials. In the composite, TiO2 nanocrystals are highly dispersed in the amorphous SiO2 matrix and the mater showed size quantization effect arising from the presence of extremely small titanium oxide species having a low coordinati...

In this paper, we introduce the doubling transformation, a structure-preserving transformation for symplectic pencils, and present its basic properties. Based on these properties, a unified convergence theory for the structure-preserving doubling algorithms for a class of Riccati-type matrix equations is established, using only elementary matrix theory.

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...

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the challenge of matrix completion in the face of such nonlinearities. Given a f...