arXiv subjects

Zhe Li

Publications and source records attributed to Zhe Li.

312 records · Page 18Linked to original sources

arXiv2014

Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.

eess.SY↗

arXiv2014

Aging the Cu-doped Bi2Te3 crystals for the topological transport and its atomic tunneling-clustering dynamics

We report on the observation of the two-dimensional weak antilocalization in (Cu0.1Bi0.9)2Te3.06 crystals relying on measurements of the magnetoresistance in a tilted field. The dephasing analysis and scanning tunneling spectroscopy corroborate the transport of the topological surface states (SS). The SSs contribute 3.3% conductance in 30μm-thick material and become dominant in the 100nm-thick flakes. Such optimized topological SS transport is achieved by an intense aging process, when the bulk conductance is suppressed by four orders of magnitude in the long period. Scanning tunneling microscopy reveals that Cu atoms are initially inside the quintuple layers and migrate to the layer gaps to form Cu clusters during the aging. In combination with first-principles calculations, an atomic tunneling-clustering procedure across a diffusion barrier of 0.57eV is proposed.

cond-mat.mtrl-sci↗

arXiv2011

Ideal Projectors of Type Partial Derivative and Their Perturbations

In this paper, we verify Carl de Boor's conjecture on ideal projectors for real ideal projectors of type partial derivative by proving that there exists a positive $η\in \mathbb{R}$ such that a real ideal projector of type partial derivative $P$ is the pointwise limit of a sequence of Lagrange projectors which are perturbed from $P$ up to $η$ in magnitude. Furthermore, we present an algorithm for computing the value of such $η$ when the range of the Lagrange projectors is spanned by the Gröbner éscalier of their kernels w.r.t. lexicographic order.

math.NA↗

arXiv2011

Finite Sets of Affine Points with Unique Associated Monomial Order Quotient Bases

The quotient bases for zero-dimensional ideals are often of interest in the investigation of multivariate polynomial interpolation, algebraic coding theory, and computational molecular biology, etc. In this paper, we discuss the properties of zero-dimensional ideals with unique monomial quotient bases, and verify that the vanishing ideals of Cartesian sets have unique monomial quotient bases. Furthermore, we reveal the relation between Cartesian sets and the point sets with unique associated monomial quotient bases.

math.AC↗

arXiv2011

On a C. de Boor's Conjecture in a Particular Case and Related Perturbation

In this paper, we focus on two classes of D-invariant polynomial subspaces. The first is a classical type, while the second is a new class. With matrix computation, we prove that every ideal projector with each D-invariant subspace belonging to either the first class or the second is the pointwise limit of Lagrange projectors. This verifies a particular case of a C. de Boor's conjecture asserting that every complex ideal projector is the pointwise limit of Lagrange projectors. Specifically, we provide the concrete perturbation procedure for ideal projectors of this type.

math.NA↗

arXiv2011

On existence of certain error formulas for a special class of ideal projectors

In this paper, we focus on a special class of ideal projectors. With the aid of algebraic geometry, we prove that for this special class of ideal projectors, there exist "good" error formulas as defined by C. de Boor. Furthermore, we completely analyze the properties of the interpolation conditions matched by this special class of ideal projectors, and show that the ranges of this special class of ideal projectors are the minimal degree interpolation spaces with regard to their associated interpolation conditions.

math.NA↗