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A Few Remarks on Milburn Equation

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Communications in Theoretical Physics 2009年第7期52卷 85-87页

作者： chen jun-Hua fan Hong-Yi Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

After presenting the infinite operator-sum form solution to the Milburn equation dp/dt=γ（UρU^f - ρ）=γU[p, Uf], where U=e^-iH/hγ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the yon Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then theproduct AB obeys （d/dt）（AB） = γU[AB, U^f]-（1/γ）（dA/dt）（dB/dt）, which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general

关键词： Milburn equation density operator evolution von Neumann entropy

Some Normality Criteria for Families of Meromorphic Functions

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Communications in Mathematical Research 2018年第2期34卷 125-132页

作者： chen jun-fan Cai Xiao-hua Department of Mathematics Fujian Normal University

Let κ be a positive integer and F be a family of meromorphic functions in a domain D such that for each f ∈ F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least κ + 1. Let α and b be two distinct finite complex numbers. If for each f ∈ F, all zeros of f;-α are of multiplicity at least 2,and for each pair of functions f, g ∈ F, f;and g;share b in D, then F is normal in D.

关键词： meromorphic function normal family multiple value shared value

Shared Values of Certain Nonlinear Differential Polynomials of Meromorphic Functions

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Communications in Mathematical Research 2017年第4期33卷 347-358页

作者： chen jun-fan CAI XIAO-HUA Ji You-qing Department of Mathematics Fujian Normal University

In this paper, by using the idea of truncated counting functions of meromorphic functions, we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one... 详细信息

关键词： meromorphic function shared value differential polynomial uniqueness

Partial or Truncated Sharing Values of Meromorphic Functions with Their Shifts

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Communications in Mathematical Research 2018年第4期34卷 343-350页

作者： lian gui chen jun-fan cai xiao-hua ji you-qing Department of Mathematics Fujian Normal UniversityFuzhou350117 不详

We mainly study the periodicity theorems of meromorphic functions having truncated or partial sharing values with their shifts, where meromorphic functions are of hyper order less than 1 and N（r, f） aT（r; f） for s... 详细信息

关键词： meromorphic function periodicity truncated sharing value partial sharing value

Molecular Dynamics of Ultra-thin Lubricating Films under Confined Shear

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Journal of Wuhan University of Technology(Materials Science) 2004年第B10期19卷 76-78页

作者：丁建宁 Jiangsu University

The molecular dynamics simulation of ultra-thin films under confined shear was performed to investigate the relation between dynamic properties of ultra-thin films and their microstructure. The solid walls were modelled using an Au crystal and the fluid molecules were modeled using decane. The simulation results indicate that the microstructure of ultra-thin films is a kind of solid-like layering structure. The density and velocity profiles of the fluid molecules are symmetric. The slip and shear thinning behavior was founded and interpreted.A mathematic model was set up according to the results of the simulation and experiments.

关键词： ultra-thin lubricating films micro-structure molecular dynamics mathematical model

与例外函数和分担函数相关的亚纯函数的正规族

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数学学报（中文版） 2010年第4期53卷 655-662页

作者：陈俊凡福建师范大学数学与计算机科学学院数学系福州350108

设F为区域D内的一族亚纯函数,对于每个f∈F,f的所有极点重数至少是2,a(z)和b(z)为两个在D内满足a(z)■b(z)的全纯函数.若对于每个f∈F,f(z)≠a(z)和f(z)≠b(z),则F在D内正规.这个结果改进了经典的Montel定则.此外,我们也讨论了亚纯函数... 详细信息

设F为区域D内的一族亚纯函数,对于每个f∈F,f的所有极点重数至少是2,a(z)和b(z)为两个在D内满足a(z)■b(z)的全纯函数.若对于每个f∈F,f(z)≠a(z)和f(z)≠b(z),则F在D内正规.这个结果改进了经典的Montel定则.此外,我们也讨论了亚纯函数族中每个函数与其导函数分担两个全纯函数的正规性.

关键词：亚纯函数正规族例外函数与分担函数

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一类非线性复微分方程的超越亚纯解

数学学报（中文版） 2022年第2期65卷 371-386页

作者：李铮陈俊凡福建师范大学数学与统计学院福州350117

本文主要研究非线性复微分方程f^(4)+a(z)ff^((k))=p_(1)(z)e^(α_(1)(z))+p_(2)(z)e^(α_(2)(z))的超越亚纯解,其中a,p_(1),p_(2)是非零的有理函数,α_(1),α_(2)是非常数的多项式.进一步地,考虑当亚纯解存在时,α_(1),α_(2),p_(1)和p_(2)所满足的条件.另外,还讨论了非线性复微分方程f^(3)+a(z)f’=p_(1)(z)e^(ν(z))+p_(2)(z)e^(-ν(z))的亚纯解的存在性,其中a,p_(1),p_(2)是非零的有理函数,ν是非常数的多项式.所得的结果直接推广了一些已知的结果.

关键词： Nevanlinna理论亚纯解复微分方程零点极点

Moxibustion treatment for knee osteoarthritis： cumulative meta-analysis and trial sequential analysis

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TMR Integrative Nursing 2018年第3期2卷 115-122页

作者： jun-chen fan Hui-Min Zhang Miao Zhang fan-Mei Kong Wen-Rui Wang Yu-Ling Wang Tianjin University of Traditional Chinese Medicine Tianjin 300100 China Nan Kai Hospital of Tianjin Tianjin 300100China

Objective： To evaluate the effect of moxibustion on knee osteoarthritis patients with cumulative meta-analysis, and trial sequential analysis was applied to test the authenticity of results. Methods： We searched PubMed, EMbase, The Cochrane Library, CNKI and CBM to collect RCTs about moxibustion on knee osteoarthritis patients. The selection of literature, data extraction and evaluation of eligible literature were carried out independently by two reviewers. Then Stata11.0 software was used for data analysis. Result： Totally 11 RCTs involved 1005 patients were recruited. The results of meta-analysis showed that no significant differences were found between the two groups in VAS, moxibustion is better than drug therapy in effective rate [OR = 0.40, 95%CI （0.27, 0.60）] and knee score [SMD = -0.70, 95%CI （-1.22, -0.19）]. The result of trial sequential analysis indicated that the sample size didn＇t reach the TSA Boundary on VAS, the sample size of effectiveness achieved Require Information Size. In the indicator of knee score has obtained certain re- sult before reaching the Require Information Size. Conclusion： moxibustion is superior to drug therapy on treatment knee osteoarthritis. However, large sample size and high-quality studies are still needed.

关键词： Moxibustion Knee osteoarthritis Cumulative meta-analysis Trial sequential analysis

纳米结构表面形貌成型机理及其对石墨烯拉曼光谱的影响

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光谱学与光谱分析 2021年第6期41卷 1821-1827页

作者：孙宁陈俊帆张洁朱永重庆大学光电技术及系统教育部重点实验室重庆400044

通过真空热蒸镀和高温退火法制备的金属纳米复结构SERS基底因其具有良好的灵敏度,稳定性和均匀性而广泛应用于各种检测领域。石墨烯具有优良的光学特性,化学惰性以及荧光猝灭效应,自被发现以后一直是光学微纳器件中的一大热门材料。石... 详细信息

通过真空热蒸镀和高温退火法制备的金属纳米复结构SERS基底因其具有良好的灵敏度,稳定性和均匀性而广泛应用于各种检测领域。石墨烯具有优良的光学特性,化学惰性以及荧光猝灭效应,自被发现以后一直是光学微纳器件中的一大热门材料。石墨烯还可以有效分离探针分子与基底,优化拉曼光谱质量,因此广泛应用于SERS研究领域。同时石墨烯可以有效隔绝金属纳米结构与空气的直接接触防止金属纳米结构被氧化而失效,也可以催化氧化银的脱氧反应提升SERS基底的稳定性。在石墨烯/金属纳米复合结构SERS基底在制备过程中,受到金属膜的种类、厚度参数、气体种类、退火时间、温度和气压等因素的影响,制备的金属纳米结构形貌存在很大差异。石墨烯的拉曼光谱会因为应力和掺杂导致其拉曼特征峰出现不同程度的增强,移动以及展宽。(1)采用真空热蒸镀法和高温退火法制备石墨烯/银纳米复合结构SERS基底,建立了金属纳米颗粒成型机理的模型,从孔洞形成、孔洞生长、金属纳米岛形成三个阶段分析了金属纳米粒子的成型过程,实验沉积5,10,15以及20 nm的银薄膜,退火后银纳米结构的覆盖率分别为~35.1%,~24.4%,~30%以及~96.0%,在沉积银薄膜样品上使用湿法转移石墨烯,退火处理后发现石墨烯阻止了银纳米岛的形成过程;(2)理论分析了银薄膜厚度、石墨烯覆盖对复合结构的几何形貌、拉曼增强特性的影响,石墨烯由于其具有较高的杨氏模量和表面张力,可以有效抑制退火过程中银薄膜向纳米粒子转变的过程,从而实现对复合结构表面形貌的调控;(3)实验研究了银纳米粒结构形貌对石墨烯拉曼光谱的影响,并理论分析了蒸镀不同银薄膜厚度的样品对石墨烯的拉曼光谱增强,移动以及展宽影响的具体原因。

关键词：表面增强拉曼散射石墨烯退火厚度