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Stability of Functional Equations in Several Variables

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Acta Mathematica Sinica,English Series 2007年第2期23卷 321-326页

作者： Deng Hua ZHANG huai xin cao College of Mathematics and Information Science Shaanxi Normal University

We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.

关键词： stability functional equation, Jordan homomorphism, Lie homomorphism

Characterizations and Extensions of Lipschitz-α Operators

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Acta Mathematica Sinica,English Series 2006年第3期22卷 671-678页

作者： huai xin cao Jian Hua ZHANG Zong Ben XU College of Mathematics and Information Science Shaanxi Normal University Faculty of Science Xi'an Jiaotong University

In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^＊ the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ （σ o f）＇ is a bounded linear operator from X^＊ into L^∞（[a, b]）. When K is a compact subset of a finite interval （a, b） and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα（f） ≤ Lα（F） ≤ 3^1-α Lα（f）. A similar extension theorem for a little Lipschitz-α operator is also obtained.

关键词： Characterization Extension Lipschitz-α operator

Local Lipschitz-α Mappings and Applications to Sublinear Expectations

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Acta Mathematica Sinica,English Series 2014年第5期30卷 844-860页

作者： huai xin cao Jun Cheng YIN Zhi Hua GUO Zheng Li CHEN College of Mathematics and Information Science Shaanxi Normal University

The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α opera... 详细信息

关键词： Local Lipschitz-α mapping random variable sublinear expectation

Stability of (p,Y)-Operator Frames

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Journal of Mathematical Research and Exposition 2011年第3期31卷 535-544页

作者： Zhi Hua GUO huai xin cao Jun Cheng YIN College of Mathematics and Information Science Shaan.vi Normal University Shaanxi 710062 P. R. China College of Science China Jiliang University Zhejiang 310018 P. R. China

In this paper we study the stability of（p,Y）-operator *** firstly discuss the relations between p-Bessel sequences（or p-frames） and（p,Y）-operator Bessel sequences（or（p,Y）-operator frames）.Through defining a new union,we prove that adding some elements to a given（p,Y）-operator frame,the resulted sequence will be still a（p,Y）-operator *** obtain a necessary and sufficient condition for a sequence of compound operators to be a（p,Y）operator ***,we show that（p,Y）-operator frames for X are stable under some small perturbations.

关键词： p-frame (p Y)-operator Bessel sequence (p Y)-operator frame perturbation Banach space.

Dysfunction of synaptic endocytic trafficking in Parkinson's disease

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Neural Regeneration Research 2024年第12期19卷 2649-2660页

作者： xin Yi Ng Mian cao Programme in Neuroscience and Behavioural Disorders Duke-NUS Medical SchoolSingaporeSingapore Department of Physiology National University of SingaporeSingaporeSingapore

Parkinson's disease is characterized by the selective degeneration of dopamine neurons in the nigrostriatal pathway and dopamine deficiency in the *** precise reasons behind the specific degeneration of these dopamine neurons remain largely *** investigations have identified over 20 causative PARK genes and 90 genomic risk loci associated with both familial and sporadic Parkinson's ***,several of these genes are linked to the synaptic vesicle recycling process,particularly the clathrinmediated endocytosis *** suggests that impaired synaptic vesicle recycling might represent an early feature of Parkinson's disease,followed by axonal degeneration and the eventual loss of dopamine cell bodies in the midbrain via a"dying back"***,several new animal and cellular models with Parkinson's disease-linked mutations affecting the endocytic pathway have been created and extensively *** models faithfully recapitulate certain Parkinson's disease-like features at the animal,circuit,and cellular levels,and exhibit defects in synaptic membrane trafficking,further supporting the findings from human genetics and clinical *** this review,we will first summarize the cellular and molecular findings from the models of two Parkinson's disease-linked clathrin uncoating proteins:auxilin(DNAJC6/PARK19)and synaptojanin 1(SYNJ1/PARK20).The mouse models carrying these two PARK gene mutations phenocopy each other with specific dopamine terminal pathology and display a potent synergistic ***,we will delve into the involvement of several clathrin-mediated endocytosis-related proteins(GAK,endophilin A1,SAC2/INPP5 F,synaptotagmin-11),identified as Parkinson's disease risk factors through genome-wide association studies,in Parkinson's disease *** will also explore the direct or indirect roles of some common Parkinson's disease-linked proteins(alpha-synuclein(PARK1/4),Parkin(PARK2),and LRRK2(PARK

关键词： autophagy auxilin/PARK19 clathrin-mediated endocytosis dopamine neurons neurodegeneration nigrostriatal pathway Parkinson's disease synaptic vesicle recycling synaptojanin1/PARK20

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ε-近似保正交映射的稳定性与扰动

数学学报（中文版） 2010年第1期53卷 61-66页

作者：孔亮曹怀信陕西师范大学数学与信息科学学院西安710062

对于Hilbert空间之间的ε-近似保正交线性映射T,给出了｜〈T（x）,T（y）〉-｜｜T｜｜^2〈x,y〉｜的一个估计,得到了ε-近似保正交线性映射的充分条件,研究了ε-近似保正交线性映射的稳定性,并获得了ε-近似保正交线性映射的扰动定理.

关键词：保正交映射 ε-近似保正交映射稳定性扰动

Numerical study of the influence of the atmospheric pressure on the thermal environment in the passenger cabin

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Building Simulation 2024年第2期17卷 253-265页

作者： xin Su Yu Guo Zhengwei Long Yi cao Tianjin Key Lab.of Indoor Air Environmental Quality Control School of Environmental Science and EngineeringTianjin UniversityTianjin300072China Shanghai Aircraft Design and Research Institute Jinke RoadPudong DistrictShanghai201210China

The cabin air pressure remains lower than the horizontal atmospheric pressure when the airplane is in *** pressure is one of the parameters that must be taken into consideration while studying the thermal environment of an airplane *** are still no reference values for aircraft cabins despite the fact that numerous studies on low pressure heat transfer have demonstrated the connection between convective heat transfer coefficient(CHTC)and air *** this paper,a correction method for CHTC under low pressure conditions was established by using the dummy heat dissipation in the low-pressure cabin *** this basis,a thermal environment simulation model was developed,then was applied to the simulation of a seven-row aircraft cabin containing 42 passengers,and the CHTC and heat loss of dummy surface in the cabin were ***,the results of PMV calculated by using heat dissipation and air parameters at sampling points were *** results show that the modified CHTC can accurately reflect the cabin thermal environment under low pressure conditions,and the correction of CHTC can be realized by adjusting the turbulent Prandtl number,which is nonlinear correlated with the *** simulation results of the thermal environment in the seven-row cabin show that the CHTC changes by about 42%before and after *** air pressure decreases during take-off,which reduces the average CHTC of the crew surface from 5.09 W/(m^(2)·K)to 4.56 W/(m^(2)·K),but the air temperature rises by about 0.2°C as a *** deviation of PMV results calculated by using simulated heat loss data and using air parameters of measuring points in space is up to 0.5,but the latter is representative for calculating the thermal comfort level of the whole cabin.

关键词： low pressure aircraft cabin simulation heat dissipation convective heat transfer coefficient

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两类可观测量的Bell不等式

数学学报（中文版） 2014年第3期57卷 473-484页

作者：杨莹曹怀信李静运城学院应用数学系运城044000 陕西师范大学数学与信息科学学院西安710062 陕西铁路工程职业技术学院渭南714000

引入了可观量a和ab关于密度矩阵ρ的平均值E_ρ(a)=Tr(aρ)与E_ρ(a,b)=Tr((ab)ρ),给出了一系列性质,建立了相应的Bell不等式|E_ρ(a,b)+E_ρ(a,c)+E_ρ(d,b)-E_ρ(d,c)|≤2(‖Pρn1‖2+‖Pρn2‖2)～(1/2)≤22^(1/2).

关键词： Bell不等式平均值可因子化可分性纠缠性

Theoretical understanding of correlation between magnetic phase transition and the superconducting dome in high-Tc cuprates

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Science China(Physics,Mechanics & Astronomy) 2024年第2期67卷 167-173页

作者： Chen Zhang Cai-xin Zhang Su-huai Wei Haiqing Lin Hui-Xiong Deng State Key Laboratory of Superlattices and Microstructures Institute of SemiconductorsChinese Academy of SciencesBeijing 100083China Center of Materials Science and Optoelectronics Engineering University of Chinese Academy of SciencesBeijing 100049China Beijing Computational Science Research Center Beijing 100193China

Many issues concerning the origin of high-temperature superconductivity(HTS)are still under *** example,how the magnetic order varies with doping and its relationship with the superconducting temperature(Tc);and why Tcalways peaks near the quantum critical *** this paper,taking hole-doped La_(2)CuO_(4)as a classical example,we employ the first-principles band structure and total energy calculations with Monte Carlo simulations to explore how the symmetry-breaking magnetic ground state evolves with hole doping and the origin of a dome-shaped superconductivity region in the phase *** demonstrate that the local antiferromagnetic order and doping play key roles in determining the electron-phonon coupling,thus ***,the La_(2)CuO_(4)possesses a checkerboard local antiferromagnetic ground *** the hole doping increases,Tcincreases with the enhanced electron-phonon coupling *** as the doping increases further,the strength of the antiferromagnetic interaction weakens and spin fluctuation *** the critical doping level,a magnetic phase transition occurs that reduces the local antiferromagnetism-assisted electron-phonon coupling,thus diminishing the *** superconductivity disappears in the heavily overdoped region when the ferromagnetic order *** observations could account for why cuprates have a dome-shaped superconductivity region in the phase *** study,thus,contributes to a fundamental understanding of the correlation between doping,local magnetic order,and superconductivity of HTS.

关键词： high-temperature superconductivity antiferromagnetic order electron-phonon coupling doping effect cuprates