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摘要： 一、结构统一,构造函数例1 （2022届深圳市实验学校月考）已知函数f（x）=1/2x2,g（x）=aln x。（1）若曲线y=f（x）-g（x）在x=2处的切线与直线x+3y-7=0垂直,求实数a的值;（2）设h（x）=f（x）+g（x）,若对任意两个不等的正数x1,x2,都有(h（x1）-h（x2）)/（x1-x2）>2恒成立,求实数a的取值范围。

关键词： Survival Analysis   Ordinary Differential Equation   Neural Networks  

摘要： In this paper, we propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. One key technical challenge for directly applying maximum likelihood estimation (MLE) to censored data is that evaluating the objective function and its gradients with respect to model parameters requires the calculation of integrals. To address this challenge, we recognize from a novel perspective that the MLE for censored data can be viewed as a differential-equation constrained optimization problem. Following this connection, we model the distribution of event time through an ordinary differential equation and utilize efficient ODE solvers and adjoint sensitivity analysis to numerically evaluate the likelihood and the gradients. Using this approach, we are able to 1) provide a broad family of continuous-time survival distributions without strong structural assumptions, 2) obtain powerful feature representations using neural networks, and 3) allow efficient estimation of the model in large-scale applications using stochastic gradient descent. Through both simulation studies and real-world data examples, we demonstrate the effectiveness of the proposed method in comparison to existing state-of-theart deep learning survival analysis models. The implementation of the proposed SODEN approach has been made publicly available at https://***/jiaqima/SODEN.

关键词： Batteries   Feature extraction   Degradation   Predictive models   Discharges (electric)   Bayes methods   Voltage   Battery life   feature extraction   lithium-ion batteries   regression analysis   remaining useful life (RUL) prediction   sparse Bayesian learning (SBL)  

摘要： Accurate prediction of the remaining useful life (RUL) of batteries is of great importance for the health management of different equipment and machines, such as electric vehicles and smartphones. It gives operators information about when the battery should be replaced. Predicting the batteries' RUL using the data only from early cycles can also be beneficial for manufacturers. For example, it can reduce the batteries' testing costs during the research and development phase. This article focuses on batteries' RUL early prediction using data-driven methods. The differential capacity (dV/d Q) curves can reveal the potential capacity and voltage of a battery, respectively, and they are known to be indicators of the batteries' degradation. We will present a practical method for batteries' RUL early prediction using features extracted from those two curves. Accordingly, 19 features generated from the d Q/dV and dV/d Q curves are analyzed and extracted. The Sparse Bayesian Learning (SBL) method is a popular machine learning method in the field of RUL prediction, and it is used to achieve an RUL early prediction for batteries. In the end, the training and test errors are investigated to evaluate the presented method's efficiency. Moreover, we compared our results with two other methods (lasso and elastic net), which have been recognized as best performing methods in this field so far, and the comparisons showed our proposed method outperforms those two methods in the term of accuracy. The presented method is generic and can be used for RUL early prediction of different batteries.

关键词： 数学分析   一题多解   创新能力  

摘要： 创新能力的源泉和发展的基础是对数学概念和原理的透彻理解以及数学思想方法的掌握,本文结合多元函数微分学应用实例,引导学生从多个角度去分析和解决问题。

关键词： Mathematics  

ISBN: (数字)9789811248108 ISBN: (纸本)9789811248092

摘要： This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding *** researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.

关键词： 分数阶微分方程   混合单调算子   奇异项   解的存在唯一性  

摘要： 文章研究了一类具有奇异项的Caputo型分数阶微分方程边值问题。首先利用非线性算子理论及相关性质给出了算子方程A(x,x)=x存在唯一解的条件，由此获得了该边值问题存在唯一解的若干充分条件。最后，通过应用举例，对主要结果做了进一步验证。

关键词： 常微分方程   课程思政   案例教学  

摘要： 探索常微分方程教学过程中进行课程思政建设的方法，以“变量分离方程”的教学为切入点，进行课堂教学设计，将思想政治教育资源因素有机融入，落实立德树人的根本任务。同时挖掘常微分方程这门课中的思政元素，以期为该课程的课程思政建设提供一些参考。

关键词： Location awareness   Endoscopes   Magnetic analysis   Sensor arrays   Planar arrays   Permanent magnets   Permeability   Capsule endoscopy   geomagnetic compensation   magnetic localization   wearable system   wireless capsule endoscopy  

摘要： Static magnetic localization is widely employed to localize capsule endoscopes. A permanent magnet is integrated into the capsule, and a sensor array outside the body measures its magnetic field. However, the geomagnetic flux density distorts the localization when no compensation method is applied. In this study, an optimized differential geomagnetic compensation method is proposed. A sensor array adapted to the typical abdomen size with 12 equally oriented sensors was used. The sensors are grouped into 26 pairs, and by subtracting the measured values of those, the geomagnetic field cancels out. This method was experimentally evaluated within a localization region of the size of a typical gastrointestinal tract. Static and dynamic scenarios in domestic environments were applied to evaluate the system in daily life situations. Moreover, the magnet was continuously moved, while the traveled distance was recorded. The mean position and orientation errors for the static and dynamic scenarios did not exceed 4 mm and 2 degrees, respectively. Furthermore, the traveled distance of the magnet was tracked with an accuracy of 3.4 mm. Therefore, it was revealed that the proposed system is applicable in daily life scenarios and capable of precisely tracking the traveled distance of the capsule inside the intestine to locate abnormalities. Overall, the results significantly outperform state-of-the-art methods.