具有转向点的二阶拟线性系统奇摄动边值问题解的渐近展开

本证明了一类具有转向点的二阶拟线性系统奇摄动边值问题解的存在性，给出摄动解及其导数按分量一致有效渐近估计。     

从光电效应现象看光的本性

以光的波粒二象性与量子光学理论和经典光学理论的内在联系为基础对光电效应进行研究，纠正了教学中存在的一些错误的认识，为今后的有关光的本性的教学研究工作的建立一个正确的观点．     

Dragin逆对于条件数在某些扰动问题中的极小性

设A∈Cnxn,条件数KD（A）＝‖A‖‖AD‖,其中AD是A的Dragin逆。本文指出在一定条件假设下,KD（A）在求矩阵扰动Dragin逆（A＋E）D时的相对误差界中的极小性质,在某些条件假设下,KD（A）在约束问题AX＝b（X∈R（AD））求解的误差估计中的极小性。     

平方阻尼Josephson结的混沌探讨

用Melnikov函数法和微扰法讨论了平方阻尼Josephson结存在Smale马蹄变换意义下的混沌,结果揭示了异宿混沌在经常性扰动下的稳定性．     

伴有边界摄动的三阶微分方程边值问题解的多重边界层现象

本研究一类伴有边界摄动的三阶半线性微分方程边值问题解的多重边界层现象,在适当的假设条件下,利用微分不等式的方法,证明解的一致有效展开式及有关余项估计。     

Efficient federated item similarity model for privacy-preserving recommendation

Previous federated recommender systems are based on traditional matrix factorization, which can improve personalized service but are vulnerable to gradient inference attacks. Most of them adopt model averaging to fit the data heterogeneity of federated recommender systems, requiring more training costs. To address privacy and efficiency, we propose an efficient federated item similarity model for the heterogeneous recommendation, called FedIS, which can train a global item-based collaborative filtering model to eliminate user feature dependencies. Specifically, we extend the neural item similarity model to the federated model, where each client only locally optimizes the shared item feature matrix. We then propose a fast-convergent federated aggregation method inspired by meta-learning to address heterogeneous user updates and accelerate the convergence of global training. Furthermore, we propose a two-stage perturbation method to protect both local training and transmission while reducing communication costs. Finally, extensive experiments on four real-world datasets validate that FedIS can provide more competitive performance on federated recommendations. Our proposed method also shows significant training efficiency with less performance degradation.     

Recent progress in study of singular perturbation problems

Some results for the singular perturbation theory, methods and applications in the new century are reviewed in this paper. It could be found that in the recent decade, many approximate methods have been developed and refined, including the method of averaging, boundary layer methods, methods of matched asymptotic expansion and methods of multiple scales. An overview is given on the new work about various problems, such as the reaction diffusion, turning points, boundary layers, shock waves, stability problem, solitons, attractors, canard solution, scattering light wave and neuron network, etc. And then, a great number of applied problems are solved in applied mathematics, computational mathematics, fluid mechanics, elastic mechanics, optics, thermophysics, quantum mechanics, plasm physics, physical chemistry, analytical chemistry, epidemiology, neurology, engineering science, environment science, bionomics, atmosphere physics, ocean climate, aeronautics and astrnatics and so on, from which only some examples are extracted and described in this review.     

Singular perturbation of a second-order three-point boundary value problem for nonlinear systems

This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.     

一类高次非线性奇摄动问题的匹配解法

在适当的条件下,利用奇摄动理论中的收缩变换以及匹配技巧,讨论了一类高次非线性奇摄动两点边值问题.相应于边界条件.构造了原同题的外部解和内部解.按ε的增幂展开非线性项、比较同次幂的系数.再利用特异极限,由匹配原问题的内、外部解得出了相应于参数k=0、k=1、k<0、k>1和0相似文献   

氢原子第四激发态（n=5）能级简并的解除

用简并微扰论研究氢原子第四激发态（n=5）在正交非均匀外电场中的能级分裂情况.并介绍高阶方阵本征问题的Jacobi解法.