Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type

In order to further study the dynamical behavior of nonconservative systems,we study the conserved quantities and the adiabatic invariants of fractional Brikhoffian systems with four kinds of different fractional derivatives based on Herglotz differential variational principle.Firstly,the conserved quantities of Herglotz type for the fractional Brikhoffian systems based on Riemann-Liouville derivatives and their existence conditions are established by using the fractional Pfaff-Birkhoff-d Alembert principle of Herglotz type.Secondly,the effects of small perturbations on fractional Birkhoffian systems are studied,the conditions for the existence of adiabatic invariants for the Birkhoffian systems of Herglotz type based on Riemann-Liouville derivatives are established,and the adiabatic invariants of Herglotz type are obtained.Thirdly,the conserved quantities and adiabatic invariants for the fractional Birkhoffian systems of Herglotz type under other three kinds of fractional derivatives are established,namely Caputo derivative,Riesz-Riemann-Liouville derivative and Riesz-Caputo derivative.Finally,an example is given to illustrate the application of the results.     

HADAR实验对活动星系核伽马射线辐射观测的预期研究

HADAR (High Altitude Detection of Astronomical Radiation)是一个基于大气切伦科夫成像技术的地面望远镜阵列,其采用大口径折射式水透镜系统来收集大气切伦科夫光,以实现对10 GeV—10 TeV能量段的伽马射线和宇宙线的探测.HADAR具有低阈能和大视场的优势,因此可以对天区进行连续扫描和观测,在观测活动星系核(Active Galactic Nuclei,AGN)等银河系外伽马射线源方面具有明显优势.本文研究了HADAR实验对AGN的探测能力.基于费米望远镜(Fermi Large Area Telescope,Fermi-LAT)的AGN源能谱信息,将观测能量外推至甚高能能段,同时加入河外背景光的吸收效应,以计算HADAR对AGN源观测的统计显著性.研究结果显示,HADAR运行一年时间,预计将有31个Fermi-LAT AGN源以高于5倍显著性被观测到,其中大部分为蝎虎状天体类型.     

哌啶并[2,3-b]哌嗪类衍生物的设计、合成及其抗血小板聚集活性研究

以2,3-二氨基吡啶和2,3-丁二酮为起始原料,经环化、催化氢化和亲核取代反应合成了10个新型哌啶并[2,3-b]哌嗪类衍生物(3a~3j),其结构经¹H NMR、¹³C NMR和HR-MS确证。体外抗血小板聚集活性研究表明,化合物3d、3e、3g、3h和3j具有一定的抗血小板聚集作用,其中化合物3h(IC₅₀=1.24mmol/L)的活性显著优于母体化合物川芎嗪(IC₅₀=3.96mmol/L)和阳性药物阿司匹林(IC₅₀=2.41mmol/L)。     

新型低共熔溶剂的制备及其在分散液-液微萃取水样中臧红T和胭脂红的应用EI北大核心CSCD

建立了一种基于低共熔溶剂的旋涡辅助分散液-液微萃取和高效液相色谱连用检测水样中臧红T和胭脂红染料的方法。制备了一类分别由苄基三乙基溴化铵、苄基三丁基溴化铵、苄基三乙基氯化铵或苄基三丁基氯化铵(氢键受体)和正辛酸(氢键供体)组成的新型疏水性低共熔溶剂。最佳萃取条件为:选取苄基三丁基氯化铵和正辛酸(摩尔比为1∶2)制备的低共熔溶剂为萃取剂,萃取剂用量为75μL,萃取时间为1 min,溶液pH=7,NaCl浓度为3 mg/mL。在最优化条件下,检测臧红T和胭脂红的线性范围为4.8~1000 ng/mL;相关系数(R^(2))分别为0.9981和0.9987;检出限分别为1.5和1.8 ng/mL;定量限均为4.8 ng/mL。将该方法应用于实际水样中臧红T和胭脂红的测定,加标回收率为88.5%~113.6%,相对标准偏差均低于8.8%。     

Birkhoff系统的积分因子与守恒定理

本文提出了构造Birkhoff系统守恒律的积分因子方法。首先，给出了Birkhoff方程的积分因子的定义，研究了Birkhoff系统的守恒量存在必要条件；其次，建立了系统的积分因子与守恒律的对应关系，并给出了用于确定积分因子的广义Killing方程，最后，建立了守恒定理的逆定理。文末，举例说明结果的应用。     

面向5G多波束应用的紧凑宽带Rotman透镜设计

提出了一种基于等光程差原理设计的紧凑宽带Rotman透镜波束赋形网络,用于5G毫米波通信的天线阵列多波束实现。首先,详细介绍了Rotman透镜的基本原理;然后,利用二等分功分器替代传统的单端口馈电模式,产生高定向波束,降低相邻端口处的能量损失以及透镜内部能量的散射;最后利用切比雪夫多枝节匹配变换器,优化原有的锥形阵列输出端口,在保证宽频带的条件下,缩短原有匹配端口尺寸,使得透镜整体尺寸减少20%,实现了Rotman透镜的紧凑性。改进模型的实测结果表明,该透镜工作频带为16.5～33.8 GHz,其中在17.2～32 GHz,S₁₁优于15 dB,扫描角度为±30°。该透镜结构简单紧凑,能够有效地为相邻阵元提供稳定的相位差信号,很好地实现5G毫米波阵列多波束的目标。     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

基于场放大进样富集的微流控芯片-激光诱导荧光法检测奶制品中的β-酪啡肽

基于微流控芯片-激光诱导荧光分析技术,探讨了奶酪中两种β-酪啡肽(β-CM-5和β-CM-7)的场放大进样富集和检测。采用10 mmol/L硼酸-硼砂溶液(pH8.7)作为衍生缓冲液,5 mmol/L硼砂溶液(pH8.9)作为样品缓冲液,进样10s,60 mmol/L硼砂溶液(pH8.9)作为运行缓冲液,分离电压1500V,在120s内成功分离检测了两种β-酪啡肽。实验结果表明,β-CM-5和β-CM-7的富集倍数是16倍和21倍,检出限分别是8.2 nmol/L和3.6 nmol/L,线性范围分别是0.05~2μmol/L和0.02~1μmol/L,加标回收率在86.9%~107.5%,该方法可应用于奶制品中β-CM-5和β-CM-7的含量测定。     

预制层溅射气压对CIGS薄膜结构及器件的影响

研究了金属预制层制备过程中溅射气压对Cu(In_1-xGa_x)Se₂(CIGS)薄膜及电池器件性能的影响.通过调节溅射气压改变预制层的结晶状态及疏松度与粗糙度,在合适的预制层结构下,活性硒化热处理过程中,可使Ga有效地掺入到薄膜中形成优质的CIGS固溶体.高溅射气压会使预制层过于致密,呈现非晶态趋势.经活性硒化热处理后,CIGS薄膜容易产生CIS与CGS"两相分离"现象,从而导致CIGS薄膜太阳电池的开路电压和填充因子降低,电池转换效率由10.03%降低到5.02%.