Deriving Energy-Gap of Some Hamiltonians with Kinetic Coupling by the Invariant Eigen-Operator Method

We begin with proposing a unitary operator responsible for diagonalizing the Hamiltonian with kinetic couplings in particle physics to get a new form of Hamiltonian which has no coupling terms. By virtue of the invariant eigen-operator (IEO) method we search for the invariant eigen-operators for the new Hamiltonian. In this way the energy-gap of the Hamiltonians can be naturally obtained. This method may be generalized to N-mode Hamiltonian with kinetic couplings case. Work supported by the National Natural Science Foundation of China under grant 10475056 and Foundation of President of Chinese Academy of Science.     

Numerical simulation of a Gaussian beam profile passing through a Kerr medium

The circular Gaussian beam shape has been simulated by numerical evaluation on beam shape based on z-scan method through beam radius. This method is useful in many studies such as z-scan experiments. The validity of the relation between peak and valley separation in close aperture data and the diffraction length of the beam has been investigated by this method for some real cases. The results are in good agreement with the experimental studies.     

Statistical stationary states for a two-layer quasi-geostrophic system

Existence of a family of locally invariant probability measures for large scale flows in enclosed temperate sea is proved. This model is extremely important for understanding the meso-scale phenomena in oceans. The techniques used are those developed by Albeverio and his collaborators.     

板几何中一类具抽象边界条件迁移算子的谱

在LP（1≤P〈∞）空间上，研究了板几何中一类具抽象边界条件下各向异性、连续能量、非均匀介质的迁移方程，证明了这类方程相应的迁移算子的谱在右半平面中仅由有限个具有限代数重数的离散本征值组成等结果．     

Robust Bounds for Krylov Methods

In this paper we give bounds for polynomials of operators. These bounds are robust in low rank perturbations. This problem is encountered in the study of the convergence of Krylov methods. The central idea here is to view the resolvent as a meromorphic function.     

研究宇称算符的一种新方法

在量子力学中,宇称算符P^的3种表象积分分别表示为∫d2zπ|z〉〈-z|、∫dq|q〉〈-q|和∫dp|p〉〈-p|.借助Dirac符号法和量子力学表象的完备性,找到了一种非常新颖的方法,给出了宇称算符的积分显式.     

Slowly changing vectors and the asymptotic finite-dimensionality of an operator semigroup

Siberian Mathematical Journal - Let X be a Banach space and let T: X → X be a linear power bounded operator. Put X 0 = {x ∈ X | T n x → 0}. We prove that if X 0 ≠ X then...     

On positive invertibility of operators and their decompositions

In Banach spaces ordered by a normal cone that contains interior points the positive invertibility of operators is studied. If there exists a uniformly positive functional then any positively invertible operator A possesses a B -decomposition, i.e., a positive decomposition A = U – V with the properties: U^–1 exists, VU^–1 ≥ 0, Ax ≥ 0, U x ≥ 0 imply x ≥ 0 and r (VU^–1) < 1. Earlier it was shown that the existence of a B -decomposition with r (VU^–1) < 1 is sufficient for the positive invertibility of the operator A. Peris' result is obtained as a special case of the main theorem. The decomposition is demonstrated for a positively invertible operator in a Banach space ordered by an ice cream cone (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)