富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

New progress in active immunotherapy targeting to amyloid beta

Alzheimer's disease(AD) is one of the most common types of dementia whose hallmarks include neurofibrillary tangles and senile plaques. The latter are mainly composed of amyloid-β proteins(Aβ), and it's suggested that Aβ may be the causative factor in AD pathogenesis. Immunotherapy targeting Aβ for preventing aggregation of Aβ and mildly clearing amyloid plaques has been a hot topic since 1999. Although the first clinical trial of Aβ vaccine, AN-1792, failed in phase II, its results suggested some key points in the design of Aβ vaccines. Avoiding the possible toxic Aβ specific T cell response and inducing a Th2 type cellular immune response may be beneficial for Aβ immunotherapy. Many associations and research groups are working on Aβ vaccine and some progress has been made in recent years. In this review, we have provided a detailed summary of past Aβ vaccines, which have been sorted by the immunogen, and we also discuss some recent progress and future perspectives.     

广义Khasminskii条件下自变量分段连续型带Poisson随机测度随机微分方程Euler方法的依概率收敛性

针对满足广义Khasminskii条件的由维纳过程和泊松随机测度驱动的自变量分段连续型随机微分方程(EPCASDEs),给出了Euler方法,广义Khasminskii条件比经典条件包容了更多的EPC.ASDEs.现有文献对该类方程的研究成果较少.针对EPCASDEs在广义Khasminskii条件下证明了全局解的存在唯一性,并研究了Euler方法的依概率收敛性.给出了数值算例支持主要结论.     

EFK方程一个新的低阶非协调混合有限元方法的高精度分析

对Extended Fisher-Kolmogorov(EFK)方程,利用EQ_1~(rot)元和零阶RaviartThomas(R-T)元建立了一个新的非协调混合元逼近格式.首先,证明了半离散格式逼近解的一个先验估计并证明了逼近解的存在唯一性.在半离散格式下,利用上述两种元的高精度分析结果以及这个先验估计,在不需要有限元解u_h属于L~∞的条件下,得到了原始变量u和中间变量v=-?u的H~1-模以及流量p=u的(L~2)~2-模意义下O(h~2)阶的超逼近性质.同时,借助插值后处理技术,证明了上述变量的具有O(h~2)阶的整体超收敛结果.其次,建立了一个新的线性化向后Euler全离散格式并证明了其逼近解的存在唯一性.另一方面,通过对相容误差和非线性项采取与传统误差分析不同的新的分裂技巧,分别导出了以往文献中尚未涉及的关于u和v在H~1-模以及p在(L~2)~2-模意义下具有O(h~2+τ)阶的超逼近性质,进一步地,借助插值后处理技术,得到了上述变量的整体超收敛结果.这里h和τ分别表示空间剖分参数和时间步长.最后,给出了一个数值算例,计算结果验证了理论分析的正确性.     

一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.     

Besov空间中双参数Volterra型重分数过程的弱逼近

In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes{B_n(s,t)},n∈N defined by B_n(s,t)=∫_0~s ∫_0~tk_(a(s))(s,u)K_(β(t))(t,u)θ_(n(u,v))dudv,here {θ_n(u, v)}n∈N is a family of processes, converging in law to a Brownian sheet as n→∞,based on the well known Donsker's theorem.     

State-crossing from a Locally Excited to an Electron Transfer State(SLEET) Model Rationalizing the Aggregation-induced Emission Mechanism of (Bi)piperidylanthracenes

Luminogens with aggregation-induced emission(AIE)characteristics(or AIEgens)have been widely used in various applications due to their excellent luminescent properties in molecular aggregates and the solid state.A deep understanding of the AIE mechanism is critical for the rational development of AIEgens.In this work,the“state-crossing from a locally excited to an electron transfer state”(SLEET)model is employed to rationalize the AIE phenomenon of two(bi)piperidylanthracenes.According to the SLEET model,an electron transfer(ET)state is formed along with the rotation of the piperidyl group in the excited state of(bi)piperidylan-thracene monomers,leading to fluorescence quenching.In contrast,a bright state exists in the crystal and molecular aggregates of these compounds,as the intermolecular interactions restrict the formation of the dark ET state.This mechanistic understanding could inspire the deployment of the SLEET model in the rational designs of various functional AIEgens.     

钯催化二溴代化合物自偶联环化合成二苯并[a,e]环辛四烯

由于独特的结构和广泛的应用,多取代环辛四烯及其苯并稠环衍生物的合成方法研究具有重要意义.本文报道了一种钯催化烯基溴化物与芳基溴化物的偶联反应.利用此钯催化的环化自偶联反应,以中等至较好的收率高选择性地从双溴代芳基或烯基化合物合成了多种二苯并[a,e]环辛四烯衍生物.     

浊度对荧光光谱法测定水体中叶绿素a的影响

研究了浊度对荧光光谱法测定水体中叶绿素a的影响。采用荧光分光光度计分别测定了不同浊度的叶绿素a提取液和铜绿微囊藻液的荧光强度,使用海水叶绿素现场检测仪测定了不同浊度的铜绿微囊藻液和实际水样的叶绿素a浓度值。结果表明:当水体浊度较大时,由于悬浮颗粒物的强烈散射作用会使叶绿素a的测定结果偏高。当水体透明度较高时,浊度对测定的影响基本可以忽略。