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Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of mathematics, Chinese Academy of Sciences, beijing 100080,{2. 2. department of mathematics, beijing normal university, beijing 100875,{2. Institute of mathematics Chinese Academy of Sciences Beijing China department of mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

单位球面上Hardy空间中Cesàro平均的逼近及几乎处处收敛问题

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武汉大学学报（理学版） 2002年第3期48卷 257-260页

作者：余纯武陈莘萌戴峰武汉大学计算机学院湖北武汉430072 北京师范大学数学系北京100875

利用球面上Cesaro平均的性质,通过对各种乘子的估计,讨论了单位球面上Hardy空间Hp(Ωn)(0

关键词：单位球面 Hardy空间 Cesaro平均逼近几乎处处收敛

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几何教学改革展望

数学教育学报 2000年第4期9卷 95-99页

作者：王家铧王申怀沈阳师范学院数学与计算机系辽宁沈阳110031 北京师范大学数学系新数运动问题解决

阐述了几何教学改革的历史以及给予我们的启迪，并对新世纪的几何教学改革的前景作出展望与设想．

关键词： “新数运动” 几何教学改革数学教育课程标准中学

SINGLE BIRTH PROCESSES

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Chinese Annals of mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of mathematics,{2. normal university,{2. 100875,china) beijing normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2.(this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

Recommendation Method for Contrastive Enhancement of Neighborhood Information

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Computers, Materials & Continua 2024年第1期78卷 453-472页

作者： Hairong Wang beijing Zhou Lisi Zhang He Ma School of Computer Science and Engineering North Minzu UniversityNingxia750021China

Knowledge graph can assist in improving recommendation performance and is widely applied in various person-alized recommendation ***,existing knowledge-aware recommendation methods face challenges such as weak user-item interaction supervisory signals and noise in the knowledge *** tackle these issues,this paper proposes a neighbor information contrast-enhanced recommendation method by adding subtle noise to construct contrast views and employing contrastive learning to strengthen supervisory signals and reduce knowledge ***,first,this paper adopts heterogeneous propagation and knowledge-aware attention networks to obtain multi-order neighbor embedding of users and items,mining the high-order neighbor informa-tion of users and ***,in the neighbor information,this paper introduces weak noise following a uniform distribution to construct neighbor contrast views,effectively reducing the time overhead of view *** paper then performs contrastive learning between neighbor views to promote the uniformity of view information,adjusting the neighbor structure,and achieving the goal of reducing the knowledge noise in the knowledge ***,this paper introduces multi-task learning to mitigate the problem of weak supervisory *** validate the effectiveness of our method,experiments are conducted on theMovieLens-1M,MovieLens-2.M,Book-Crossing,and Last-FM *** results showthat compared to the best baselines,our method shows significant improvements in AUC and F1.

关键词： Contrastive learning knowledge graph recommendation method

维普期刊数据库评论

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong department of mathematics,{2., beijing 100875, china department of mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun department of mathematics,{2., beijing 100875, china department of mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.

Functional central limit theorem for super α-stable processes

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Science china mathematics 2004年第6期47卷 874-881页

作者： HONG Wenmingdepartment of mathematics,{2., beijing 100875, china 1. department of mathematics Beijing Normal University 100875 Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α 2. (0 2., the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2. and higher dimensions d 2., the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

On asymptotics of t-type regression estimation in multiple linear model

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Science china mathematics 2004年第4期47卷 628-639页

作者： GUI Hengjiandepartment of mathematics,{2., beijing 100875, china 1. department of mathematics Beijing Normal University 100875 Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.