We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996) is proved and polynomial cointegration discussed in the general setup.

A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introdu...

We study the variation of the spectrum of matrices under perturbations which are selfor skew-adjoint with respect to a scalar product. Computable formulae are given for the associated μ-values. The results can be used to calculate spectral value sets for the perturbation classes under consideration. We discuss the special case of complex Hamiltonian perturbations of a Hamiltonian matrix in detail.

The quantum variance of a self-adjoint operator depends on a density matrix whose particular example is a pure state (formulated by a projection). A general variance can be obtained from certain variances of pure states. This is very different from the probabilistic case.

We establish new oscillation criteria for linear Hamiltonian systems using monotone functionals on a suitable matrix space. In doing so we develop new criteria for oscillation involving general monotone functionals instead of the usual largest eigenvalue. Our results are new even in the particular case of self-adjoint second order differential systems.

In this study, linear second-order self-adjoint delta-nabla matrix systems on time scales are considered with the motivation of extending the analysis of dominant and recessive solutions from the differential and discrete cases to any arbitrary dynamic equations on time scales. These results emphasize the case when the system is non-oscillatory.

We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the q → 1 scaling limit of the braided adjoint action or R-commutator of q-Minkowski space on itself. We also describe the qdeformed conformal algebra in R-matrix form and its quasi-∗ structure.

Estimation of the initial state turbulent channel flow from spatially and temporally resolved wall data is performed using adjoint-variational assimilation. The estimated fields satisfy Navier–Stokes equations minimize a cost function defined as difference between model predictions available observations. accuracy predicted deteriorates with distance wall, most precipitously across buffer layer...

We show that the adjoint A+ of a matrix A with respect to a given inner product is a rational function in A, if and only if A is normal with respect to the inner product. We consider such matrices and analyze the McMillan degrees of the rational functions r such that A+ = r(A). We introduce the McMillan degree of A as the smallest among these degrees, characterize this degree in terms of the nu...

a mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎the method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎the problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...