Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz

We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and demonstrate the role of Bäcklund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. We show that the nested Bethe ansatz technique is equivalent to a chain of successive Bäcklund transformations “undressing” the original problem to a trivial one.     

Massive and massless phases in self-dual spin models: Some exact results from the thermodynamic Bethe ansatz

The generally accepted phase diagrams for the discrete spin models in two dimensions imply the existence of certain renormalisation group flows, both between conformal field theories and into a massive phase. Integral equations are proposed to describe these flows, and some properties of their solutions are discussed. The infrared behaviour in massless and massive directions is analysed in detail, and the techniques used are applied to a number of other models.     

Analytical Bethe Ansatz,Canonical Bäcklund Transformation and Q-Operator For A New Discrete Integrable Heirarchy

A new discrete heiarchy of integrable equations is generated from a new Lax Operator and a canonical Bäcklund transformation of the system is derived using Sklyanin’s formalism, based on the classical r-matrix. By quantising the system a quantum analogue of the corresponding canonical Bäcklund transformation is obtained and certain properties of the associated Q-operator are examined. Finally the analytical Bethe Ansatz is used to solve for the spectrum.     

Off-shell Bethe ansatz equation for osp(21) Gaudin magnets

The semi-classical limit of the algebraic Bethe ansatz method is used to solve the theory of Gaudin models. Via off-shell Bethe ansatz method we find the spectra and eigenvectors of the N−1 independents Gaudin Hamiltonians with symmetry osp(21). We also show how the off-shell Gaudin equation solves the trigonometric Knizhnik–Zamolodchikov equation.     

Limiting Case of 1D Delta Anyon Model

In order to analyze a limiting case of the 1D delta anyon model, the coupling strength of the δ interaction c is modified to become a function of the anyonic parameter κ. A pedagogic derivation of the solution for this modified model using the method of anyon-boson mapping plus Bethe ansatz is presented. The limiting case as κ → π and simultaneously c → 0, which was previously neglected, is analyzed. Some unexpected properties of this limiting case are discovered. The BAEs are compared with previous results.     

Chain Dynamics of Polymers with Highly Flexible Side Groups

Summary: The relaxation behaviour of poly(5-acryloxy-5-methyl-2,3-dioxacyclohexne), poly(2,3-dichlorobenzyl methacrylate) and poly(3-chlorobenzyl methacrylate) was thoroughly studied by broadband dielectric spectroscopy with the aim of investigating how the chemical structure affects the response of polymers to electric perturbation fields over a wide temperature window. Retardation spectra calculated from dielectric isotherms utilizing linear programming regularization parameter techniques were used to deconvolute strongly overlapped absorptions. Special attention is paid to both the splitting region and the fitting of the Williams ansatz to the experimental results. Attempts are made to explain the molecular origin of the relaxations observed in the retardation spectra of the polymers.     

Integrability of a New Type of Deformed XXZ Model

A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.     

Boundary Effects for One-Dimensional Bariev Model with Hard-Core Repulsion

For the Bariev model for correlated hopping in one dimension under open boundary conditions, the Bethe ansatz equations are analyzed for both a repulsive and an attractive interaction in several limiting cases, i.e., the ground state, the weak and strong coupling limits. The contributions of the boundary fields to both the magnetic susceptibility and the specific heat are obtained.     

战车用惯性定位定向系统的支架误差分析及补偿

战车用惯性定位定向系统由于采用双轴陀螺平台结构,不可避免地存在着支架误差,从而影响系统航向精度。应用球面三角法和方向余弦矩阵法分别推导出双轴陀螺平台的支架误差公式,发现由这两种方法推导出来的公式计算结果是一致的。最后通过数学仿真和分析,给出了支架误差与载体的姿态角之间的定量关系。根据此误差公式,对惯性定位定向系统的航向输出能够进行误差补偿,从而保证了动态条件下定位定向系统的航向输出精度。     

An alignment-free method to find similarity among protein sequences via the general form of Chou’s pseudo amino acid composition

In this paper, we propose a method to create the 60-dimensional feature vector for protein sequences via the general form of pseudo amino acid composition. The construction of the feature vector is based on the contents of amino acids, total distance of each amino acid from the first amino acid in the protein sequence and the distribution of 20 amino acids. The obtained cosine distance metric (also called the similarity matrix) is used to construct the phylogenetic tree by the neighbour joining method. In order to show the applicability of our approach, we tested it on three proteins: 1) ND5 protein sequences from nine species, 2) ND6 protein sequences from eight species, and 3) 50 coronavirus spike proteins. The results are in agreement with known history and the output from the multiple sequence alignment program ClustalW, which is widely used. We have also compared our phylogenetic results with six other recently proposed alignment-free methods. These comparisons show that our proposed method gives a more consistent biological relationship than the others. In addition, the time complexity is linear and space required is less as compared with other alignment-free methods that use graphical representation. It should be noted that the multiple sequence alignment method has exponential time complexity.