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1.
利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.  相似文献   
2.
为提高K9光学玻璃在一些特殊应用领域(如高压、温度变化剧烈等)的力学性能,并保证其光学性能符合精密光学仪器要求,对K9光学玻璃进行了化学钢化技术研究。以脆性材料断裂过程微裂纹扩展理论为基础,导出化学钢化玻璃强度应力因子计算模型,分析化学钢化表面应力与表面微裂纹深度、韧性之间的关系,指出化学钢化工艺应注意的事项。通过实验研究,分析化学钢化温度和钢化时间对K9光学玻璃抗弯强度、表面应力及应力层厚度的影响,优化得出K9光学玻璃化学钢化温度为400 ℃、钢化时间为40 h。采用优化工艺,获得了表面应力为500 MPa、应力层厚度为50 μm量级及规格为220 mm×110 mm×22 mm的化学钢化K9光学玻璃样件。钢化后,样件抗弯强度提高了3.5倍以上,且表面疵病、光学鉴别率、透过率等光学性能指标未见明显变化。  相似文献   
3.
When applying a diagnostic technique to complex systems, whose dynamics, constraints, and environment evolve over time, being able to re-evaluate the residuals that are capable of detecting defaults and proposing the most appropriate ones can quickly prove to make sense. For this purpose, the concept of adaptive diagnosis is introduced. In this work, the contributions of information theory are investigated in order to propose a Fault-Tolerant multi-sensor data fusion framework. This work is part of studies proposing an architecture combining a stochastic filter for state estimation with a diagnostic layer with the aim of proposing a safe and accurate state estimation from potentially inconsistent or erroneous sensors measurements. From the design of the residuals, using α-Rényi Divergence (α-RD), to the optimization of the decision threshold, through the establishment of a function that is dedicated to the choice of α at each moment, we detail each step of the proposed automated decision-support framework. We also dwell on: (1) the consequences of the degree of freedom provided by this α parameter and on (2) the application-dictated policy to design the α tuning function playing on the overall performance of the system (detection rate, false alarms, and missed detection rates). Finally, we present a real application case on which this framework has been tested. The problem of multi-sensor localization, integrating sensors whose operating range is variable according to the environment crossed, is a case study to illustrate the contributions of such an approach and show the performance.  相似文献   
4.
We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.  相似文献   
5.
In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.  相似文献   
6.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.  相似文献   
7.
8.
Ying Yang 《中国物理 B》2021,30(11):110202-110202
The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics, physics, biological fluid mechanics, oceanography, etc. Using the reductive perturbation theory and long wave approximation, the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrödinger (NLS) equations with variable coefficients. The third-order nonlinear Schrödinger equation is degenerated into a completely integrable Sasa-Satsuma equation (SSE) whose solutions can be used to approximately simulate the real rogue waves in the vessels. For the first time, we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves. Based on the traveling wave solutions of the fourth-order nonlinear Schrödinger equation, we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall. Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube. The high-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.  相似文献   
9.
Much research has been devoted to two problems, Yi yuancai fang (From a circular timber [find] a square) and Yi fangcai yuan (From a square timber [find] a circle), both of which appear in the Suanshu shu, an early Han dynasty mathematical work written on bamboo slips, excavated from tomb 247 at Zhangjiashan in Hubei Province, China. In this article, the geometric relations between circles and squares and the methods for determining their mutual relations in these two problems are interpreted in a different way, and an alternative approach is offered for reconciling these two problems.  相似文献   
10.
为提高生鲜羊肉储存期内(4,8和20 ℃环境)挥发性盐基氮(TVB-N)的近红外光谱(NIR)检测的稳定性和准确性,选取特征光谱和预测模型是关键步骤。以121个羊肉样品为实验对象,采集生鲜羊肉680~2 600 nm波段的近红外光谱。以多元散射校正(MSC)、标准正态变换(SNV)等散射校正方法,Savitzky-Golay卷积平滑(SGS)、移动平均平滑(MAS)等平滑处理方法,以及归一化(Normalization)、中心化(Centering)、标准化(Autoscaling)等尺度缩放方法分别预处理光谱数据后建立偏最小二乘法(PLS)预测模型。比较发现SGS处理的光谱建模效果最好。利用蒙特卡洛采样(MCS)法及马氏距离法(MD)消除了羊肉光谱的5个异常数据。运用光谱-理化值共生距离(SPXY)算法划分总样本的75%(87个)为校正集样本,剩余29个为验证集样本,利用竞争性自适应重加权法(CARS)、无信息变量消除法(UVE)、改进的无信息变量消除法(IUVE)和连续投影算法(SPA)提取特征光谱得到的波长个数分别为14,713,144和15。将全光谱和4种方法提取的特征波长作为输入变量建立预测模型,CARS提取的波长所建立模型的性能优于UVE、IUVE和SPA提取的波长所建立模型的性能,表明CARS方法可以有效简化输入变量并提高预测模型的性能。改进后得到的IUVE法相比于UVE法,筛选出的波长数更少且模型性能有所提升。以提取的特征波长建立PLS,支持向量机(SVM)和最小二乘支持向量机(LS-SVM)预测模型,SVM模型得到最优的校正集预测结果,其中CARS-SVM预测模型的校正决定系数(R2C)和校正均方根误差(RMSEC)分别为0.939 1和1.426 7,最优的验证集预测效果为LS-SVM预测模型得到,其中IUVE-LS-SVM预测模型的验证决定系数(R2V)和验证均方根误差(RMSEV)分别为0.856 8和1.886 2。基于近红外特征光谱建立简化、优化的生鲜羊肉储存期TVB-N预测模型,为实现快速无损检测生鲜羊肉中的TVB-N浓度提供技术支持。  相似文献   
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