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关键词： 导数非线性Schr dinger方程   爆破解   修正的virial等式  

摘要： 研究下述导数非线性Schrodinger方程的初边值问题:iφ_(t)+αφ_(xx)=iβ|φ|^(2σ)φx-g(|φ|^(2))φ,σ1,x∈[a,b],其中α,β为实数,g(·)是实值函数.当α,β,φ0及g(s)满足一定条件时,利用守恒律和修正的virial等式,证明了爆破解的存在性.最后,得到了爆破解的渐近行为等一些性质.

关键词： 导数与函数   构造函数   核心素养  

摘要： 2021年全国乙卷第20题是以函数与导数知识为载体的不等式的证明问题,重点考查导数的工具性的同时,也考查了逻辑推理与数学运算、数学建模等核心素养.本文谈其第(2)问的几种解题方法,这一方法与2011年高考题的导数有异曲同工之妙,由此总结高中数学"构造函数"方法的巧妙运用.

关键词： Lighting   Estimation   Rendering (computer graphics)   Light sources   Augmented reality   Visualization   Cameras   Augmented reality   specular and transparent objects   global illumination   light estimation   material estimation   joint optimization  

摘要： In augmented reality, it is important to achieve visual consistency between inserted virtual objects and the real scene. As specular and transparent objects can produce caustics, which affect the appearance of inserted virtual objects, we herein propose a framework for differential rendering beyond the Lambertian-world assumption. Our key idea is to jointly optimize illumination and parameters of specular and transparent objects. To estimate the parameters of transparent objects efficiently, the psychophysical scaling method is introduced while considering visual characteristics of the human eye to obtain the step size for estimating the refractive index. We verify our technique on multiple real scenes, and the experimental results show that the fusion effects are visually consistent.

关键词： 导数   双变量   一题多解   解题分析  

摘要： 作为高考题的风向标,广州一模总能引起广大师生的高度关注.本文对本次考试的导数压轴题进行深入的探究,通过几种不同的解法来展示不同的思维构成,从而提高学生一题多解的能力,促进学生数学核心素养的形成.

关键词： Damage evolution   Periodic ultrasonic testing   Differential imaging   Discontinuous material interfaces   Inverse scattering  

摘要： The differential evolution indicators, recently introduced Pourahmadian and Haddar (2020) [1] for imaging mechanical evolution in highly scattering solids, is examined in a laboratory setting with the focus on spatiotemporal tracking of an advancing damage zone in an elastic specimen. To this end, a prismatic slab of charcoal granite is quasi-statically fractured in the three-pointbending (3 PB) configuration, while ultrasonic shear waves are periodically generated in the sample at certain time steps t kappa, kappa = circle, 1, 2, ..., 4. The interaction of probing waves with the propagating damage give rise to transient velocity responses measured on the plate's boundary by a 3D scanning laser Doppler vibrometer. Thus obtained sensory data are then carefully processed to retrieve the associated spectra of scattered displacement fields v kappa at every t kappa. On deploying consecutive pairs of multifrequency data (v kappa, v kappa+1), the differential indicators are computed exposing the progress of 3 PB-induced damage in the specimen. Verified with in situ observations, each indicator map successfully reconstructs (a) the support of newborn fractures, and (b) the loci of discontinuities in the process zone that undergo interfacial evolution in the designated timeframe [t kappa t kappa+1]. Further, it is shown that the evolution indicators help better understand the damage mechanism e.g., by shining light on the fragmented nature of induced cracks and their coalescence. For completeness, data inversion via reduced and partial-aperture data is investigated, including the one-sided reconstruction.

关键词： Mobile robot   Sliding mode control   Trajectory tracking  

摘要： Differential drive wheeled mobile robots (DDWMRs) have been widely used in various applications due to their maneuverability and energy-saving characteristics. Tracking control of such mechanical systems with nonholonomic constraints in the presence of uncertainties and disturbances has attracted much attention. In this paper, a robust control scheme is developed for trajectory tracking control of a DDWMR in the presence of parametric uncertainties and disturbances. To fulfill the controller design, an inner-outer loop control structure is adopted for the DDWMR. For the inner-loop controller, a fast nonsingular terminal sliding mode (FNTSM) control law is applied for robust disturbance rejection in a finite time. Based on the kinematic model of the DDWMR, the outer-loop controller is designed for accurate trajectory tracking control. Finally, experiments are carried out to validate that the proposed control scheme has more robust tracking accuracy and faster response than an existing robust method.

关键词： shape memory alloy   antagonistic actuator   phase dependent differential resistance   constant heating current   PWM  

摘要： This work presents the development of a precise, constant current heating mechanism for an antagonistic shape memory alloy (SMA) actuator. The actuator was developed using a pair of SMA wires arranged in an antagonistic configuration. SMA possesses a unique phase-dependent, resistance variation property which is called self-sensing. This phenomenon is observed during thermal phase transition. A constant heating current was employed to measure combined differential resistance (Delta R) which provides insignificant hysteresis and linear relationship with displacement. Delta R eventually helps to determine the present position of the actuator for sensorless feedback control. The aim is to remove additional external sensors, reducing actuator footprint and interface complexity using the proposed study. The performance analysis of the actuator was evaluated under constant current by the tracking trajectory of reference signals. The tracking results confirmed the improvement in operating bandwidth by a reduction in displacement. The heating module mainly consisted of a low pass filter, operational amplifier with a current sense feedback mechanism that regulates the heating current in proportion to PWM signals. The result shows a significant 21% variation in the observed value of Delta R (1.200-0.254 omega) between the major-minor loops. The study confirms linearity and maintains similarity by highest correlation 0.9508 during open-loop, which further improves to 0.9891 in close feedback reference tracking with an error band +/- 0.05 mm.

关键词： advertising   differential game   general demand and cost functions   oligopoly  

摘要： We present an analysis of advertising activities in a dynamic oligopoly with differentiated goods using a differential game approach under general demand and cost functions. The main conclusion is that the memoryless closed-loop solution and the feedback solution are equivalent when there is no spillover effect of advertising activities. We also show that the comparison of the open-loop solution and the memoryless closed-loop solution depends on whether the firms' outputs are strategic substitutes or strategic complements.

关键词： Control system analysis and synthesis methods   Stability in control theory   Optimal control   Discrete control systems   Linear control systems  

摘要： A quasi-differential type event-triggered model predictive control (ET-MPC) framework for continuous-time linear systems with additional disturbances is constructed. Different from the existing ET-MPC, the triggering condition of the proposed method is focused on the differences of the errors between the actual states and the best prediction sequence at two consecutive sampling moments. Its advantage is that the dynamic characteristics of state changes can be better considered, which will achieve a more effective balance between communication load and system control performance. Then, to deal with persistent disturbances, a time-varying tightening robustness state constraint is utilized in this scheme, instead of conventional state constraints. Finally, the new ET-MPC algorithm is designed based on the dual-mode control framework, and its feasibility, the system closed-loop stability, as well as avoidance of Zeno behaviour are rigorously verified. Simulations and comparisons are provided to demonstrate the algorithm effectiveness.