Bilateral polynomial matrix equations in two indeterminates

Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.     

Quadratic polynomial guided fuzzy C-means and dual attention mechanism for medical image segmentation

Medical image segmentation is the most complex and important task in the field of medical image processing and analysis, as it is linked to disease diagnosis accuracy. However, due to the medical image's high complexity and noise, segmentation performance is limited. We propose a novel quadratic polynomial guided fuzzy C-means and dual attention mechanism composite network model architecture to address the aforementioned issues (QPFC-DA). It has mechanisms for channel and spatial edge attention, which guide the content and edge segmentation branches, respectively. The bi-directional long short-term memory network was added after the two content segmentation branches to better integrate multi-scale features and prevent the loss of important features. Furthermore, the fuzzy C-means algorithm guided by the quadratic polynomial can better distinguish the image's weak edge regions and has a degree of noise resistance, resulting in a membership matrix with less ambiguity and a more reliable segmentation result. We also conducted comparison and ablation experiments on three medical data sets. The experimental results show that this method is superior to several other well-known methods.     

一种基于多项式的代理保护代理签名体制研究

文章首先分析了张青坡等人中提出的多项式形式的E1Gamal签名体制的安全缺陷,然后基于有限域上多项式的性质,提出了有限域上多项式形式代理保护代理签名方案;新的签名方案中,利用多项式进行签名权利的委托,并由改进的有限域上的多项式形式的E1Gamal签名体制生成代理签名。新方案的安全性基于离散对数的难解性。     

一种改进的基于多项式滤波的稳态检测方法

化工过程的数据中常常含有较多的随机误差和粗差干扰,导致传统的稳态检测方法无法得到准确的结果,从而降低系统故障诊断的可靠性。针对实际的工业过程数据,提出一种融合自适应平滑技术的稳态检测方法,该方法首先以基于导数分析的自适应平滑算法进行降噪处理,消除随机误差的影响,然后引入阈值拟合技术进一步抑制粗差干扰,以多项式滤波方法对数据进行稳态检测,根据测量信号的趋势特征确定过程是否处于稳态。仿真实验研究表明:融合自适应平滑技术的稳态检测方法能够克服传统稳态检测方法中随机误差和粗差干扰对检测结果的影响,进而显著提高稳态检测处理的准确性,检测结果明显优于传统的基于多项式滤波的检测方法。     

Single-machine parallel-batching scheduling with family jobs to minimize weighted number of tardy jobs

We consider the problem of scheduling n jobs in batches on a single parallel-batching machine, where the jobs are partitioned into jobs families and the jobs in each family have the same due date. The objective is to minimize the weighted number of tardy jobs. We first devise an efficient pseudo-polynomial time and a fully polynomial time approximation scheme for the weighted problem. Then we present $O(n^2)$-time and $O(n\log n)$-time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time, respectively.     

On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus

In Winkel (2001) a generalization of Bernstein polynomials and Bézier curves based on umbral calculus has been introduced. In the present paper we describe new geometric and algorithmic properties of this generalization including: (1) families of polynomials introduced by Stancu (1968) and Goldman (1985), i.e., families that include both Bernstein and Lagrange polynomial, are generalized in a new way, (2) a generalized de Casteljau algorithm is discussed, (3) an efficient evaluation of generalized Bézier curves through a linear transformation of the control polygon is described, (4) a simple criterion for endpoint tangentiality is established.     

基于CPLD的光电编码器角位移拟合测速法

针对常用的M法和T法无法满足增量式光电编码器整个测速范围内误差要求的问题,提出了对码盘信号进行角位移拟合求采样时刻即时速度的新方法,在匀加速条件下对这3种方法进行了仿真实验,比较了测速误差。实验结果表明,角位移拟合法在整个速度范围内都能获得很高的测速精度和误差一致性。最后用CPLD对该方法加以实现,给出了Verilog硬件描述语言的设计程序和3种方法的实验结果比较。基于CPLD的实现方法电路简单,运行稳定可靠,处理速度快,为角位移拟合法提供了一种非常好的实现方法。     

平行梁式电容传感器力学性能的仿真与分析

针对S型平行梁式电容称重传感器参数结构设计问题,运用有限元软件ANSYS Workbench对平行梁式弹性体结构进行参数化模拟仿真,基于二次多项式曲面拟合建立其结构力学性能与主要结构参数的函数关系,并通过算例分析验证了拟合公式的有效性。研究表明,拟合公式对复杂仿真计算后的结果有很好的近似,能更好的反应实际情况,公式结构更加简洁,具有较快的收敛速度、较高的精度和较好的推广能力,有利于准确实现平行梁式电容称重传感器结构参数设计。     

Polynomial time approximation algorithms for proportionate open‐shop scheduling

This paper deals with the presentation of polynomial time (approximation) algorithms for a variant of open‐shop scheduling, where the processing times are only machine‐dependent. This variant of scheduling is called proportionate scheduling and its applications are used in many real‐world environments. This paper develops three polynomial time algorithms for the problem. First, we present a polynomial time algorithm that solves the problem optimally if , where n and m denote the numbers of jobs and machines, respectively. If, on the other hand, , we develop a polynomial time approximation algorithm with a worst‐case performance ratio of that improves the bound existing for general open‐shops. Next, in the case of , we take into account the problem under consideration as a master problem and convert it into a simpler secondary approximation problem. Furthermore, we formulate both the master and secondary problems, and compare their complexity sizes. We finally present another polynomial time algorithm that provides optimal solution for a special case of the problem where .     

基于量子克隆的二面体群隐含子群问题量子算法的研究

基于最短向量问题的格公钥密码体制是典型的抗量子计算密码体制。格的唯一最短向量问题可转化为二面体群的隐含子群问题。有效地求解二面体群的隐含子群问题可攻破基于格的唯一最短向量问题的公钥密码体制。Kuperberg提出了二面体群隐含子群问题的半指数级量子算法。通过研究Kuperberg量子算法,利用概率量子克隆,文中提出了二面体群隐含子群问题的多项式时间量子算法。