A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method.     

基于红外测温的试件内部缺陷的识别算法研究

内部缺陷形状位置的识别是传热逆问题的重要研究课题.本文对带有内部缺陷的试件建立了二维传热模型,通过有限元法求解了在一定加热条件下试件表面的温度分布;并通过共轭梯度法,提出了根据表面所测温度分布识别试件内部缺陷形状、位置的计算方法.数值实验证明了算法的有效性.     

透平叶栅三维粘性气动反问题的控制理论方法

将基于控制理论的形状优化设计方法应用于粘性可压流动条件下的透平叶栅三维气动反设计,详细推导了三维N-S方程伴随系统的偏微分方程组及其各类边界条件.讨论了伴随系统的解的适定性条件,并由此给出应用N-S方程进行气动优化的目标函数的选取限制.研究了伴随方程的数值求解技术,给出敏感性导数的最终计算式,结合拟牛顿算法发展了三维透平叶栅粘性反问题的气动设计方法.     

The Use of Constituent Spectra and Weighting in Extended Multiplicative Signal Correction in Infrared Spectroscopy

Extended multiplicative signal correction (EMSC) is a widely used preprocessing technique in infrared spectroscopy. EMSC is a model-based method favored for its flexibility and versatility. The model can be extended by adding constituent spectra to explicitly model-known analytes or interferents. This paper addresses the use of constituent spectra and demonstrates common pitfalls. It clarifies the difference between analyte and interferent spectra, and the importance of orthogonality between model spectra. Different normalization approaches are discussed, and the importance of weighting in the EMSC is demonstrated. The paper illustrates how constituent analyte spectra can be estimated, and how they can be used to extract additional information from spectral features. It is shown that the EMSC parameters can be used in both regression tasks and segmentation tasks.     

高铁锻钢制动盘热疲劳裂纹扩展仿真及寿命评价

巨大的制动热能导致高铁制动盘面出现热斑或热点,形成沿径向扩展的热疲劳裂纹,严重危及行车安全.通过仿真获得热疲劳裂纹扩展规律,据此制定出合适、经济的检测周期,具有重要意义.基于断裂力学理论,采用扩展有限单元法和自主研发的裂尖网格加密技术,得到热点形成规律,植入半椭圆形裂纹进行热疲劳断裂仿真,得到制动速度为400 km/h...     

石墨消解-原子荧光光谱法测定土壤中的总硒

为准确定量土壤硒总量,提出以逆王水(1+1)-石墨消解法消解土壤,氢化物原子荧光光谱法(HG-AFS)测定土壤总硒含量的方法.其中,对消解方式、消解时间和仪器条件进行了探讨,确定最优检测条件.称取0.2 g土壤样品加入5 mL逆王水(1+1),于石墨消解仪120℃消解1.5 h,冷却至室温后用超纯水定容至25 m L,...     

求解参数识别反问题的同伦正则化方法

提出了求解参数识别反问题的同伦正则化方法,给出了相应的收敛性定理.数值结果表明该方法是一种快速的大范围收敛方法.     

锥形透镜光纤聚焦特性研究

锥形透镜光纤(TLF)是实现光纤与平面光波光路(PLC)芯片高效耦合的核心元件。了解和掌握其聚焦特性是指导平面光波光路尾纤封装技术的关键。给出了表征锥形透镜光纤聚焦特性的两个参量出射光斑直径和远场发散角的理论分析模型,其误差小于1.14%;采用光束传播法数值模拟了锥形透镜光纤中的光波传输和模斑的演化,确定了锥形透镜光纤端面出射光斑的大小;优化锥形透镜光纤结构参量为:拉锥长度300μm,锥角0.733°,透镜曲率半径13.485μm;建立了基于数字摄像机的锥形透镜光纤出射光场测试系统,提出了物理光学反向推演法,计算出锥形透镜光纤聚焦光斑尺寸和远场发散角。理论与实验结果有着良好的一致:对于相同结构参量的锥形透镜光纤,实验反推法得到的出射光斑尺寸与理论值相比误差为3.15%,远场发散角误差为3.67%。     

逆极限空间上渐近伪轨跟踪性质

The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP.     

Tumor Hypoxia Heterogeneity Affects Radiotherapy: Inverse-Percolation Shell-Model Monte Carlo Simulations

Tumor hypoxia was discovered a century ago, and the interference of hypoxia with all radiotherapies is well known. Here, we demonstrate the potentially extreme effects of hypoxia heterogeneity on radiotherapy and combination radiochemotherapy. We observe that there is a decrease in hypoxia from tumor periphery to tumor center, due to oxygen diffusion, resulting in a gradient of radiative cell-kill probability, mathematically expressed as a probability gradient of occupied space removal. The radiotherapy-induced break-up of the tumor/TME network is modeled by the physics model of inverse percolation in a shell-like medium, using Monte Carlo simulations. The different shells now have different probabilities of space removal, spanning from higher probability in the periphery to lower probability in the center of the tumor. Mathematical results regarding the variability of the critical percolation concentration show an increase in the critical threshold with the applied increase in the probability of space removal. Such an observation will have an important medical implication: a much larger than expected radiation dose is needed for a tumor breakup enabling successful follow-up chemotherapy. Information on the TME’s hypoxia heterogeneity, as shown here with the numerical percolation model, may enable personalized precision radiation oncology therapy.