Matrix presentations of braids and applications

We show that there exists a one-to-one correspondence between the class of certain block tridiagonal matrices with the entries or and the free monoid generated by generators and relation and give some applications for braids. In particular, we give new formulation of the reduced Alexander matrices for closed braids.

     

The -homology class of the Euler characteristic operator is trivial

On any manifold , the de Rham operator (with respect to a complete Riemannian metric), with the grading of forms by parity of degree, gives rise by Kasparov theory to a class , which when is closed maps to the Euler characteristic in . The purpose of this note is to give a quick proof of the (perhaps unfortunate) fact that is as trivial as it could be subject to this constraint. More precisely, if is connected, lies in the image of (induced by the inclusion of a basepoint into ).

     

Knot signature functions are independent

A Seifert matrix is a square integral matrix satisfying

To such a matrix and unit complex number there corresponds a signature,

Let denote the set of unit complex numbers with positive imaginary part. We show that is linearly independent, viewed as a set of functions on the set of all Seifert matrices.

If is metabolic, then unless is a root of the Alexander polynomial, . Let denote the set of all unit roots of all Alexander polynomials with positive imaginary part. We show that is linearly independent when viewed as a set of functions on the set of all metabolic Seifert matrices.

To each knot one can associate a Seifert matrix , and induces a knot invariant. Topological applications of our results include a proof that the set of functions is linearly independent on the set of all knots and that the set of two-sided averaged signature functions, , forms a linearly independent set of homomorphisms on the knot concordance group. Also, if is the root of some Alexander polynomial, then there is a slice knot whose signature function is nontrivial only at and . We demonstrate that the results extend to the higher-dimensional setting.

     

Time,Complex Systems,and Public Policy: A Theoretical Foundation for Adaptive Policy Making

Nonlinear Dynamics, Psychology, and Life Sciences - Can public policy development and implementation be improved by closely tracking and coordinating its timing with that of the regulated sector?...     

Investigation into the rotational bands of ~(185)Pt with the particle-rotor model

Theoretical calculations have been performed for the ν9/2+[624](i13/2) and ν7/2-[503](f7/2) bands of 185Pt in the framework of particle-rotor model. The band properties of signature splitting and configuration mixing have been analyzed. The level energy and signature splitting before the band crossing can be well interpreted by introducing triaxiality. The positive-parity yrast band is pro posed to be dominated by the ν9/2+[624](i13/2) component, while the negative-parity band shows strong mixing of ν7/2-[5...     

改进的最小费用理论在盲竖井选址中的应用

在网络的任意点求解绝对中心等特殊点是网络流研究的一个难点.在目前最小费用理论的基础上引入平面几何理论,把网络等效于几何图形,建立了数学模型.通过求解,得出了网络间的最佳连接点,从而确定出盲竖井的位置.最后以云南锡业集团个旧东区两个生产平台之间的连接为一算例,得出了理想的结果,验证了该方法的有效可行性.     

频率选择性衰落信道中的频偏盲估计

根据频率选择性衰落信道的抽头延迟线模型,将针对平坦衰落信道的CS(周期平稳过程理论)频偏盲估计算法扩展到了频率选择性衰落信道,并通过仿真证明这种扩展是可行的.仿真结果还表明CS算法不仅有好的抗平坦衰落能力,而且有很好的抗频率选择性衰落性能.     

指定接收者恢复消息的抗抵赖数字签名体制

抗抵赖的签密方案在一些应用中有重要的价值.已有的方案如认证加密方案和签密方案在解决签名者事后抵赖的问题时,必须把恢复的消息提供给第三方,从消息的保密方面看,效果并不理想.基于离散对数问题提出了安全有效的指定接收者恢复消息的抗抵赖数字签名体制,其特点是只有指定接收者才可以恢复消息,任何人可以验证签名的合法性,在解决签名者事后抵赖的问题中克服了已有方案的缺陷,不需要签名者的合作、不需要向第三方提供恢复的消息、不需要与第三方执行交互的零知识证明,在保持恢复消息秘密的同时能揭穿签名者的抵赖行为.同时把该方案扩充到了指定的一群接收者恢复消息的抗抵赖的多重签名的情形.     

Blind parameter estimation of pseudo-random binary code-linear frequency modulation signal based on Duffing oscillator at low SNR

Conventional parameter estimation methods for pseudo-random binary code-linear frequency modulation(PRBCLFM) signals require prior knowledge, are computationally complex, and exhibit poor performance at low signal-to-noise ratios(SNRs). To overcome these problems, a blind parameter estimation method based on a Duffing oscillator array is proposed. A new relationship formula among the state of the Duffing oscillator, the pseudo-random sequence of the PRBC-LFM signal, and the frequency difference between the PRBC-LFM signal and the periodic driving force signal of the Duffing oscillator is derived, providing the theoretical basis for blind parameter estimation. Methods based on amplitude method, short-time Fourier transform method, and power spectrum entropy method are used to binarize the output of the Duffing oscillator array, and their performance is compared. The pseudo-random sequence is estimated using Duffing oscillator array synchronization, and the carrier frequency parameters are obtained by the relational expressions and characteristics of the difference frequency. Simulation results show that this blind estimation method overcomes limitations in prior knowledge and maintains good parameter estimation performance up to an SNR of-35 d B.