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?...     

线性时滞系统的离散最优控制

介绍了对线性时滞系统进行最优控制的设计,将具有时滞控制的线性系统离散后引入增广状态向量。获得不显含时滞的差分方程,根据时滞量的两种分类情况采用连续和离散形式的性能指标函数导出了最优控制律。控制律包含当前状态和此前若干步状态向量的叠加,最优控制律直接从时滞方程中得到,可保证系统的稳定性,此方法亦适用于大时滞的情况。数值算例验证了控制策略的有效性。     

On a single discrete scale for preventive maintenance with two shock processes affecting a complex system

A new approach to optimal maintenance of systems (networks) is suggested. It is applied to systems subject to two external independent shock processes. A system ‘consists’ of two parts, and each shock process affects only its own part. A new notion of bivariate signature is suggested and used for obtaining survival characteristics of a system and further optimization of the preventive maintenance actions. The preventive maintenance optimization is considered in the univariate discrete scale that counts the overall numbers of shocks of both types. An example of a transportation network is considered. Copyright © 2016 John Wiley & Sons, Ltd.     

基于抛物方程的海陆环境信号时延与到达角估计

针对复杂海陆环境中的无线信号传播预测问题,研究了适用于抛物方程的信号时延与到达角估计方法。将自由空间中抛物方程轴向波前信号视为本地副本信号,然后利用信号的自相关特性,将接收信号与副本信号进行互相关运算,最后通过相关函数的峰值检索,得到脉冲信号在复杂环境中传播的附加时延。采用数值算例,验证了该方法的正确性和有效性。此外,采用多重信号分类算法,由抛物方程构建接收阵列的协方差矩阵,并对其进行特征值分解,然后利用信号子空间和噪声子空间的正交性,实现复杂环境中的信号到达角估计。仿真结果表明,相比于传统的平面波谱方法,该方法具有更高的多径分辨率。基于上述方法,并结合数字地图,在典型的海陆环境中进行了仿真实验,分析了蒸发波导对脉冲信号传播时延和到达角的影响。     

Characterization and de novo sequencing of snow crab tropomyosin enzymatic peptides by both electrospary ionization and matrix‐assisted laser desorption ionization QqToF tandem mass spectrometry

The protein tropomyosin (TM) is a known major allergen present in shellfish causing frequent food allergies. TM is also an occupational allergen generated in the working environment of snow crab (Chionoecetes opilio) processing plants. The TM protein was purified from both claw and leg meats of snow crab and analyzed by electrospray ionization and matrix‐assisted laser desorption/ionization (MALDI) using hybrid quadruple time‐of‐flight tandem mass spectrometry (QqToF‐MS). The native polypeptide molecular weight of TM was determined to be 32 733 Da. The protein was further characterized using the ‘bottom‐up’ MS approach. A peptide mass fingerprinting was obtained by two different enzymatic digestions and de novo sequencing of the most abundant peptides performed. Any post‐translational modifications were identified by searching their calculated and predicted molecular weights in precursor ion spectra. The immunological reactivity of snow crab extract was evaluated using specific antibodies and allergenic reactivity assessed with serum of allergic patients. Subsequently, a signature peptide for TM was identified and evaluated in terms of identity and homology using the basic local alignment search tool (BLAST). The identification of a signature peptide for the allergen TM using MALDI‐QqToF‐MS will be critical for the sensitive and specific quantification of this highly allergenic protein in the work place. Copyright © 2010 John Wiley & Sons, Ltd.     

一类带输入时滞的线性时滞系统的新型自适应控制

针对一类带输入时滞且状态时滞常数未知的线性时滞系统,基于LMI方法,采用一种Lyapunov-Krasovskii函数和新型带记忆的状态反馈控制,突破以往自适应控制对估计值的大小限制,研究了一种新型的对该类系统未知状态时滞常数进行自适应控制的控制器设计问题,并且通过带记忆控制器中的常数的适当选取使得带记忆控制始终能反映未知时滞,仿真例子显示了该种方法的有效性.