Algebraic Bethe Ansatz for the Osp(1|2) Model with Reflecting Boundaries

In the framework of graded quantum inverse scattering method, we obtain the eigenvalues and the eigenvectors of the Osp(l|2) model with reflecting boundary conditions in FBF background. The corresponding Bathe ansatz equations are obtained.     

On a differential game in a nondamped distributed system

We study a differential game of approach in a system whose dynamics is described by a Sobolev‐type second‐order operator differential equation in Hilbert spaces. Solutions of the equation are represented by cosine and sine operator functions. To obtain solvability conditions of the game problem, we use support functionals of two sets, which defined by the behaviors of pursuer and evader. The results are applied to the investigation of conflicted‐controlled dynamics of bending waves in a rod.     

Efficient algorithms for the matrix cosine and sine

Several improvements are made to an algorithm of Higham and Smith for computing the matrix cosine. The original algorithm scales the matrix by a power of 2 to bring the ∞-norm to 1 or less, evaluates the [8/8] Padé approximant, then uses the double-angle formula cos (2A)=2cos ²A−I to recover the cosine of the original matrix. The first improvement is to phrase truncation error bounds in terms of ‖A²‖^1/2 instead of the (no smaller and potentially much larger quantity) ‖A‖. The second is to choose the degree of the Padé approximant to minimize the computational cost subject to achieving a desired truncation error. A third improvement is to use an absolute, rather than relative, error criterion in the choice of Padé approximant; this allows the use of higher degree approximants without worsening an a priori error bound. Our theory and experiments show that each of these modifications brings a reduction in computational cost. Moreover, because the modifications tend to reduce the number of double-angle steps they usually result in a more accurate computed cosine in floating point arithmetic. We also derive an algorithm for computing both cos (A) and sin (A), by adapting the ideas developed for the cosine and intertwining the cosine and sine double angle recurrences. AMS subject classification 65F30 Numerical Analysis Report 461, Manchester Centre for Computational Mathematics, February 2005. Gareth I. Hargreaves: This work was supported by an Engineering and Physical Sciences Research Council Ph.D. Studentship. Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/T08739 and by a Royal Society–Wolfson Research Merit Award.     

Clusters of bound particles in the derivative δ-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative δ-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative δ-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.     

Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T–Q$T\text{–}Q$ relation and the Bethe ansatz equations are derived.     

Discrete breathers in nonlinear Schrödinger hypercubic lattices with arbitrary power nonlinearity

We study two specific features of onsite breathers in Nonlinear Schrödinger systems on d-dimensional cubic lattices with arbitrary power nonlinearity (i.e., arbitrary nonlinear exponent, n): their wavefunctions and energies close to the anti-continuum limit-small hopping limit-and their excitation thresholds. Exact results are systematically compared to the predictions of the so-called exponential ansatz (EA) and to the solution of the single nonlinear impurity model (SNI), where all nonlinearities of the lattice but the central one, where the breather is located, have been removed. In 1D, the exponential ansatz is more accurate than the SNI solution close to the anti-continuum limit, while the opposite result holds in higher dimensions. The excitation thresholds predicted by the SNI solution are in excellent agreement with the exact results but cannot be obtained analytically except in 1D. An EA approach to the SNI problem provides an approximate analytical solution that is asymptotically exact as n tends to infinity. But the EA result degrades as the dimension, d, increases. This is in contrast to the exact SNI solution which improves as n and/or d increase. Finally, in our investigation of the SNI problem we also prove a conjecture by Bustamante and Molina [C.A. Bustamante, M.I. Molina, Phys. Rev. B 62 (23) (2000) 15287] that the limiting value of the bound state energy is universal when n tends to infinity.     

Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K^± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.     

小波重构与局部DCT的二维主元分析掌纹识别

为了解决掌纹特征提取过程中,手掌的非平面问题导致的伪主线噪音信息并简化运算,对重构的掌纹图像进行了局部离散余弦变换.解决了重构后图像噪音敏感性问题,有效地区分了掌纹主线、掌纹褶纹和乳突纹.由二维主元分析算法获得较稳健的识别特征.通过香港理工大学公布的PolyU掌纹数据库的实验,同二维主元分析算法相比,小波重构与局部离散余弦变换的2DPCA掌纹识别算法正确识别率较高,识别效率较高.