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双语推荐：离散性

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NURBS曲线广泛应用于工业产品复杂曲线曲面设计中,但在实际应用中常遇到曲线离散的几何处理问题。针对NURBS曲线离散问题,提出了一种按等弧长原则对NURBS曲线进行离散的方法。该方法引入步长函数控制离散曲线段的弧长,采用积分法和迭代法调整步长函数以控制曲线的离散精度,通过误差检验方法校验曲线离散的逼近精度。通过实际算例,验证了NURBS曲线等弧长离散算法的合理性和有效性。
NURBS curves are widely used in complex curves and curved surfaces of industrial product design, but geometry processing problems of curve discrete are found in practical applications. According to the NURBS curve discrete problems, a method of curve discrete based on equal arc-length principle is put forward. Step function is introduced to control the length of the discrete curve, and the precision of curve discrete can be controlled by adjusting step function through integration and itera-tive methods. The approximation accuracy of curve division is checked by error checking algorithm. The rationality and validity of the NURBS curve discrete based on equal arc-length principle are verified by practical calculation example.

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本文从离散系数的定义出发，提出离散系数在实际应用中存在的问题以供大家探讨，同时试图对存在的问题进行改进与完善，使离散系数更具有严密性。
This article starts from the definition of discrete coef icient, and puts forward the existing issues in the actual application of discrete coef icient for discus ion, also tried to improve and perfect the existing problems so that the dispersion coef icient is more rigor.

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研究灰色离散性微分边界条件下的稳定性分析,灰色离散性对于许多数学模型具有很好的映射分析效果,而微分边界条件下的灰色离散性分析对于数学模型的稳定性具有很好的代表性,连续边界分析方法,推导出稳定性条件下的稳定误差分析结果,指导稳定性分析,并通过引理论证和推导方法,给出灰色离散性微分边界条件下的稳定性分析结果,并推导出稳定性的充分条件,为数学模型的稳定性分析提供指导。
The stability analysis in gray discrete differential boundary conditions was analyzed, the gray discrete mathemati-cal model had good mapping analysis for many actual models, while the gray discrete differential analysis under boundary conditions had good representation for the stability of the mathematical model in continuous boundary, the error analysis re-sults derived stable under the stability condition was studied, the guiding stability analysis was taken out, and by Lemma demonstration and derivation methods, the stability analysis results are given in gray discrete differential boundary condi-tions, and deduced sufficient condition for stability, which provide guidance for the stability analysis of mathematical mod-els.

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通常具有非因果性的离散广义系统在物理上是无法实现的，但实际系统中往往存在这种情况。本文首先讨论离散广义系统具有因果性的充要条件。然后针对不具有因果性的离散广义系统，证明存在状态反馈控制器和输出反馈控制器使闭环离散广义系统具有因果性的充要条件，并采用构造性方法分别针对 rank（B）= r 和不限制矩阵 B 秩的两种情况，给出状态反馈控制器和输出反馈控制器的设计方案，确保闭环离散广义系统具有因果性。
In generally,discrete-time singular systems with non-causality are considered impossible in physics, which often exist in the practical systems. First,this paper discusses a necessary and sufficient condition of discrete-time singular systems with causality. Then for discrete-time singular systems with non-causality,the necessary and sufficient conditions for existences of state feedback controller and output feedback controller are proved to guarantee causality of the closed-loop systems. And state feedback controller and output feedback controller are designed respectively by constructive method for two cases of rank(B)= r and no requirement for the rank of matrix B which ensure the causality of the closed-loop discrete-time singular systems.

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利用线性系统的耗散性对线性系统的输入输出稳定性进行分析.将重置控制的概念引入奇异离散型系统中,给出了奇异离散型重置控制系统的定义,并运用线性矩阵不等式对奇异离散型重置控制系统的耗散性进行分析,得到其稳定性的判定方法.
Abstact:The intput and ouput stability of linear system is analyzed via dissipativity properties .By intro-ducing definition of reset control to singular discrete-time system ,the definition of singular discrete-time reset control system is proposed .And by using linear matrix inequality (LMI) to analysis dissipativity ,a method to judge the stability of a singular discrete-time reset control systems is obtained .

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运用知识存量理论、知识网络理论的分析方法，提出知识网络中知识存量离散性问题。通过模型假设和案例分析，构建知识存量离散性演化机理模型。认为在知识聚集度、知识转移速度和知识共振度的影响作用下，知识存量离散性经历四个阶段，沿着非线性S型路径演化。
Analyzing from the theories of knowledge stock and knowledge network, the article proposes the issue of knowl-edge discreteness in knowledge network. By model hypothesis and case study, the evolutional mechanism of discreteness of knowledge stock is build up. It thinks that the discreteness of knowledge stock is experienced four stages along with nonlin-ear S type path, which is influenced by knowledge aggregation, knowledge transfer speed and knowledge resonance.

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针对公共重点区域的智能监视问题,提出了一种新的徘徊行为异常检测方法。该方法利用视频目标跟踪算法得到可疑行人的运动轨迹,通过曲线拟合对运动目标的离散点轨迹进行平滑,计算离散点的离散曲率,计算感兴趣区域内运动目标轨迹点的离散曲率的熵及方差,通过离散熵阈值比较进行徘徊行为判断,该方法只需计算运动目标的轨迹,无需建立样本库,实验证明了该方法的有效性、实时性。
In order to solve the intelligent monitoring problem, a novel method is introduced for loitering detection. Moving object is detected and tracked using tracking algorithm. This mothod gets the trajectory of moving object, smoothes the trajectory using curve fitting, and gets the discrete curvature and the entropy. Loitering detection is accomplished by judging threshold value. The method has no database for samples. Experiments demonstrate the efficiency of the proposed method.

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通过对已有离散零空间矩阵计算方法的改进,构造了改进的离散零空间等效变换公式,该公式可不依赖于特定的积分方法,能简洁、方便的与多种数值积分方法相结合。基于改进公式,提出了改进的离散零空间算法框架,并将该框架与一般变分积分法结合,构造了约束多体系统动力学分析的改进的离散零空间算法。通过曲柄滑块机构的数值实验,验证了改进的离散零空间等效变换公式的正确性,示例了其与数值积分算法的良好结合性,说明了改进算法的可行性和有效性。
T hrough improving the calculation method of the discrete null space matrix ,an improved dis-crete null space equivalent transformation formula is constructed .T he proposed formula is not depended upon special integral method ,and thus can easily and flexibly be combined with many kinds of integral methods .Based on the improved formula ,an improved discrete null space scheme is proposed ,applying for dynamics analysis constrained multiboby systems .Then by the combination of the scheme and general variational integral ,an improved discrete null space method for constrained multiboby systems is con-structed .By the numerical experiment of the mechanism of slider-crank ,it is demonstrated that the im-proved discrete null space equivalent transformation formula is correct and can smoothly be combined with integral methods ,and that the improved discrete null space method is feasible and effective .

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该文首先定义了多离散对数问题,给出了现有隐含子群问题量子计算算法不适用于求解该问题的必要条件,且该问题在经典计算模式下,其困难性比离散对数问题难,用于求解有限域上离散对数问题的数域筛法不适用于求解多离散对数问题。然后设计了基于多离散对数问题的公钥密码,其安全性依赖于多离散对数问题,且公私钥的数据量小,分析了算法参数的选取原则,证明了算法脱密原理的正确性,算法在每次加密时需要随机选取一个数,使得算法对同一个明文加密所得的密文不一定相同。
In this paper, the multi-discrete logarithm problem is formally defined, and the necessary conditions of resistance to the quantum algorithm for the hidden subgroup problem are given. It is more difficult than the discrete logarithm problem. And the number field sieve for the discrete logarithm problem is not suitable for addressing it. Furthermore, the public-key cryptograph is designed against the problem, of which the key amount is small. This paper analyses the principles of parameter selection and proves the correctness of the decryption works. It is critical that different random integers are received to the encrypt different messages.

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为提高Buck系统的快速跟踪性能,提出了一种改进的离散PID控制策略。在建立Buck电路数学模型的基础上,设计了基于离散PID控制算法的Buck变换器,并对PID控制参数进行了整定,提高了系统效率。仿真结果表明,与常规PID控制相比,利用离散PID控制算法系统在快速性、稳定性、准确性得到显著提高,系统具有较强的鲁棒性。
In order to improve the tracking performance of the Buck system,an improved discrete PID control strategy is proposed. Based on the mathematical model of the Buck circuit,a Buck converter based on discrete PID control algorithm was designed and the PID control parameters are set. The system efficiency was improved. The simulation results show that,com-pared with the conventional PID control algorithm,rapidity,stability and accuracy of the system using discrete PID control algo-rithm is improved more significantly,and the system has stronger robustness.

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