电商平台产品共同购买网络的影响因素研究

共同购买网络的推荐系统应用越加广泛，仅基于网络内生结构变量研究其共同购买链接的经济意义已有局限，故加入网络口碑这一外生变量，进行更全面的分析。采用了社会网络方法中指数随机图模型进行建模，主要围绕产品销售量、产品入度、差评率和评论数4个方面因素，探究其对共同购买网络中共同购买链接形成的影响。结果显示，销售量、产品入度和评论数对共同购买链接形成的影响呈正比关系，而差评率则会显著地降低产品共同购买的几率。该指数随机图构建出的共同购买网络为在线电商平台管理网络口碑和推荐系统优化设计提供有益参考。     

Melting heat transfer analysis of electrically conducting nanofluid flow over an exponentially shrinking/stretching porous sheet with radiative heat flux under a magnetic field

Modern magnetic nanomaterial processing operations are progressing rapidly and require increasingly sophisticated mathematical models for their optimization. Stimulated by such developments, in this paper, a theoretical and computational study of a steady magnetohydrodynamic nanofluid over an exponentially stretching/shrinking permeable sheet with melting (phase change) and radiative heat transfer is presented. Besides, wall transpiration, that is, suction and blowing (injection), is included. This study deploys Buongiorno's nanofluid model, which simulates the effects of the Brownian motion and thermophoresis. The transport equations and boundary conditions are normalized via similarity transformations and appropriate variables, and the similarity solutions are shown to depend on the transpiration parameter. The emerging dimensionless nonlinear coupled ordinary differential boundary value problem is solved numerically with the Newton-Fehlberg iteration technique. Validation with special cases from the literature is included. The increase in the magnetic field, that is, the Hartmann number, is observed to elevate nanoparticle concentration and temperature, whereas it dampens the velocity. Higher values of the melting parameter consistently decelerate the boundary layer flow and suppress temperature and nanoparticle concentration. A higher radiative parameter strongly increases temperature (and thermal boundary layer thickness) and weakly accelerates the flow. The increase in the Brownian motion reduces nanoparticle concentrations, whereas a greater thermophoretic body force strongly enhances them. The Nusselt number and Sherwood number are observed to be decreased with an increasing Hartmann number, whereas they are elevated with a stronger wall suction and melting parameter.     

Pinning exponential synchronisation and passivity of coupled delayed reaction–diffusion neural networks with and without parametric uncertainties

In this paper, we focus on the pinning exponential synchronisation and passivity of coupled reaction–diffusion neural networks (CRDNNs) with and without parametric uncertainties, respectively. On the one hand, with the help of designed nonlinear pinning controllers and Lyapunov functional method, sufficient conditions are established to let the CRDNNs with hybrid coupling and mixed time-varying delays realise exponential synchronisation and passivity. On the other hand, considering that the external perturbations may lead the reaction–diffusion neural networks (RDNNs) parameters to containing uncertainties, the robust pinning exponential synchronisation and robust pinning passivity for coupled delayed RDNNs with parametric uncertainties are investigated by designing appropriate pinning control strategies. Finally, the effectiveness of the theoretical results are substantiated by the two given numerical examples.     

An enhanced state estimation for linear parabolic PDE systems with mobile sensors

This paper studies an enhanced state estimation problem of distributed parameter processes modeled by a linear parabolic partial differential equation using mobile sensors. The proposed estimation scheme contains a state estimator and the guidance of mobile sensors, where the spatial domain is decomposed into multiple subdomains according to the number of sensors and each sensor is capable of moving within the respective subdomain. The state estimator is desired to make the state estimation error system exponentially stable while providing an performance bound. The mobile sensor guidance is used to enhance the transient performance of the error system. By the Lyapunov direct technique, an integrated design of state estimator and mobile sensor guidance laws is developed in the form of bilinear matrix inequalities (BMIs) to meet the desired design objectives. Moreover, to make the performance bound as small as possible, a suboptimal enhanced state estimation problem is formulated as a BMI optimization one, which can be solved via an iterative linear matrix inequality algorithm. Finally, numerical simulations are given to show the effectiveness of the proposed method.     

Stabilisation of stochastic differential equations driven by G-Brownian motion via aperiodically intermittent control

ABSTRACT

As an emerging field, the G-Itô stochastic calculus plays an important role in describing the model uncertainty. Many interesting works have been done on stochastic differential equations driven by G-Brownian motion (G-SDEs). Among the theories and applications of G-SDEs, the stability is the vital important one. In this paper, we investigate the stabilisation for G-SDEs based on G-Lyapunov function and aperiodically adaptive intermittent controller. As an application, the sufficient conditions are established for the stabilisation of stochastic Cohen–Grossberg neural networks driven by G-Brownian motion (G-SCGNNs). Finally, an example is provided to illustrate the obtained results.     

Controller design for distributed parameter systems with time delays in the boundary feedbacks via the backstepping method

For a distributed parameter system with an input delay in the boundary, a feedback control law is presented by means of the backstepping method. The square integrability of input signal is verified based on the target system. Then, the boundedness and invertibility of the corresponding backstepping transformation are proved under the regularity of system and the admissibility of feedback operator. Thus, the resulting closed-loop system is shown to be exponentially stable. Finally, as an application, a numerical simulation of a one-dimensional Schrödinger equation with a delay input is carried out, and the simulation results demonstrate the effectiveness of the suggested control law.     

An inventory model with truncated exponential replenishment intervals and special sale offer

In this study, we develop an inventory model with stochastic replenishment intervals and special sale offer from a supplier. The replenishment interval is assumed to obey a truncated exponential distribution and shortage is partially backordered. Our goal in this research is to maximize the total profit of cost savings due to special sale offer from supplier. A closed-form solution of the model and its convexity condition is developed. A numerical example with real world data is provided to illustrate the theory.     

Robust method to provide exponential convergence of model parameters solving linear time-invariant plant identification problem

The scope of this research is a problem of parameters identification of a linear time-invariant plant, which (1) input signal is not frequency-rich, (2) is subjected to initial conditions and external disturbances. The memory regressor extension (MRE) scheme, in which a specially derived differential equation is used as a filter, is applied to solve the above-stated problem. Such a filter allows us to obtain a bounded regressor value, for which a condition of the initial excitation (IE) is met. Using the MRE scheme, the recursive least-squares method with the forgetting factor is used to derive an adaptation law. The following properties have been proved for the proposed approach. If the IE condition is met, then: (1) the parameter error of identification is bounded and converges to zero exponentially (if there are no external disturbances) or to a set (in the case of them) with an adjustable rate, (2) the parameters adaptation rate is a finite value. The above-mentioned properties are mathematically proved and demonstrated via simulation experiments.     

基于时间序列汽车轮毂尺寸偏差趋势预测

文章选用指数平滑法和ARIMA法两种典型的时间序列算法作为预测模型,对流水线生产的汽车轮毂倒锥大尺寸值偏差趋势进行预测。以MATLAB作为工具进行实验计算,依据预测数据和实际观察值的RMSE和期望误差的对比来比较这两种模型的预测效果,得出在预测汽车轮毂倒锥大尺寸值偏差趋势时,二次指数平滑法的预测效果更好,所以最终采用此模型,从而为宏观调控刀具补偿值提供有力的依据。