a method for solving the descriptor discrete-time linear system is focused. for easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. in partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

Sufficient and necessary conditions are provided on warped product manifolds their base fiber for a vector field $$\varphi _{j}$$ to be \left( \mathrm {Ric}\right) $$ -vector , that is, $$\nabla _{i}\varphi _{j}=\mu R_{ij}$$ where $$R_{ij}$$ is the Ricci tensor of M \mu scalar. Two space-times admitting fields considered. Lorentzian quasi-Einstein time-like {Ric} \right) shown either simple or ...

We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along continuous interpolating matrix flow long time. Less also obtained in left tail.

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Let \(M= \Gamma \setminus \mathbb {H}_d\) be a compact quotient of the d-dimensional Heisenberg group \(\mathbb by lattice subgroup \(\Gamma \). We show that eigenvalue counting function \(N^\alpha \left( \lambda \right) \) for any fixed element family second order differential operators \(\left\{ \mathcal {L}_\alpha \right\} on M has asymptotic behavior \sim C_{d,\alpha } {\text {vol}}\left( M...

We prove several types of scaling results for Wigner distributions spectral projections the isotropic Harmonic oscillator on ℝd. In prior work, we studied $${W_{\bar h,{E_N}\left( {\bar h} \right)}}\left( {x,\;\xi } \right)$$ individual eigenspace projections. this continuation, study Weyl sums such as eigenvalue $${E_N}\left( ranges over intervals $$[E - \delta \left( \right),\;E + \right)]$$ ...