a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general grou...

In this work we present a new approach on the study of dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have investigated the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generalized fractional Liu process and the combination between them, generaliz...

In this paper we established the condition for a curve to satisfy stochastic generalized fractional HP (Hamilton-Pontryagin) equations. These equations are described using Itô integral. We have also considered the case of stochastic generalized fractional Hamiltonian equations, for a hyperregular Lagrange function. From the stochastic generalized fractional Hamiltonian equations, Langevin gener...

This paper is concerned with the stabilization of nonholonomic systems in portcontrolled Hamiltonian formulae based on time-varying generalized canonical transformations. A special class of time-varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized Hamiltonian structure with passivity. Utilizing these...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

Abstract We consider the discrete defocusing nonlinear Schrödinger equation in its integrable version, which is called Ablowitz–Ladik lattice. periodic boundary conditions with period N and initial data sampled according to Generalized Gibbs ensemble. In this setting, Lax matrix of lattice a random CMV-periodic it related Killip-Nenciu Circular $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/...

We propose two ways for determining the Green’s matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from the Jacobi-matrix, the first approach also requires the matrix elements of the Green’s operator between the first elements of the basis. In the second approa...

When computing the eigenstructure of matrix pencils associated with passivity analysis perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that computed spectrum satisfies symmetries corresponds to this structure and underlying physical system. We perform backward error show for systems given correct symmetry there always exists ne...

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae via generalized canonical transformations. A special class of timevarying generalized canonical transformations are introduced which preserves the passivity property. Utilizing this transformation timevarying asymptotically stabilizing controllers for the nonholonomic Hamiltonian syste...