双曲正弦和双曲余弦函数的幂级数余项的不等式

该文建立了双曲正弦和双曲余弦函数的幂级数余项的若干不等式.     

Drinfel'd Twists and Functional Bethe Ansatz

Using the Functional Bethe Ansatz technique, factorizing Drinfel'd twists for any finite dimensional irreducible representations of the Yangian Y(sl₂) are constructed.     

Hypercyclic and topologically mixing cosine functions on Banach spaces

Our first aim in this paper is to give sufficient conditions for the hypercyclicity and topological mixing of a strongly continuous cosine function. We apply these results to study the cosine function associated to translation groups. We also prove that every separable infinite dimensional complex Banach space admits a topologically mixing uniformly continuous cosine family.

     

Radon, Cosine and Sine Transforms on Real Hyperbolic Space

New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms.     

A Property of the Ansatz of Hirota's Method for Quasilinear Parabolic Equations

By using the recently discovered new invariant properties of the ansatz of R. Hirota's method, we prove that the classes of linear fractional solutions to some nonlinear equations are closed. This allows us to construct new solutions for a chosen class of dissipative equations. This algorithm is similar to the method of dressing the solutions of integrable equations. The equations thus obtained imply a compatibility condition and are known as a nonlinear Lax pair with variable coefficients. So we propose a method for constructing such pairs. To construct solutions of a more complicated form, we propose to use the property of zero denominators and factorized brackets, which has been discovered experimentally. The expressions thus constructed are said to be quasi-invariant. They allow us to find true relations between the functions contained in the ansatz, to correct the ansatz, and to construct a solution. We present some examples of new solutions constructed following this approach. Such solutions can be used for majorizing in comparison theorems and for modeling phase processes and process in neurocomputers. A program for computing solutions by methods of computer algebra is written. These techniques supplement the classical methods for constructing solutions by using their group properties.     

Algebraic Bethe Ansatz Solution to CN Vertex Model with Open Boundary Conditions

We present three diagonal reflecting matrices for the CN vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.     

余弦模拉拔方棒速度场的曲面积分解法

本文对使用余弦模拉拔方棒变形问题,设定了运动许可的三维速度场。证明了该速度场的散度为零且变形区出。入口截面不消耗剪切功率,然后用上界定理与曲面积分方法首次得到了用余弦模拉拔方棒时变形力的解析解。     

基于二值化计算鬼成像的盲水印方法

提出了一种基于二值化计算鬼成像的盲水印方法.首先将水印图像经计算关联成像加密系统加密,并将加密数据二值化,然后将其隐藏到宿主图像的离散余弦变换域,实现水印信息的嵌入.水印信息的提取和重建是隐藏和加密的逆过程,分别借助提取密钥和解密密钥获取水印信息.仿真实验证明,该方法具有很好的隐蔽性,在嵌入因子α=10时,嵌入水印仍具有较好的不可感知性,含水印图像的峰值信噪比在38 dB以上;另外,该方法也具有一定的容错能力,提取的加密数据错误率达20%时,重建的水印信息仍能分辨和识别;与传统的计算鬼成像相比,加密数据的二值化为水印嵌入提供了方便,但是并未对重建图像带来严重恶化,其相关系数相差不足0.1;水印信息的提取无需借助原始宿主图像,是一种盲提取方法.     

关于反余弦函数的Shafer-Fink型不等式

改进了Carlson不等式,得到了关于反余弦函数的Shafer-Fink型不等式.     

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.