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1.
On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis 下载免费PDF全文
Subhankar Mondal & M. Thamban Nair 《偏微分方程(英文版)》2021,34(3):240-257
We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation. 相似文献
2.
Frank Nielsen 《Entropy (Basel, Switzerland)》2021,23(4)
We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures. 相似文献
3.
We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor at a 68% confidence level. 相似文献
4.
SHEN Yi-jun YANG Zi-chen WANG Ting-yu WANG Cheng-wei LI Lei CHEN Guo-qing 《光谱学与光谱分析》2021,41(9):2665-2669
人们消费方式的变化促使电商崛起,美妆市场呈爆发式增长,口红产品的安全成为关注焦点。面对品牌口红真伪问题,市场检测化妆品方法单一,对品牌口红的特征无针对性。采用三维荧光技术和共聚焦拉曼技术对某品牌真假口红的光谱性质进行了研究。三维荧光光谱显示五组口红均存在激发光峰值波长为320 nm左右,发射峰波长在372 nm附近的荧光(Ⅰ区)。A1,A2,A3,B1,B2和B3这6个样品中,激发光峰值波长为230 nm时会发出中心波长在400 nm左右的荧光,而在A4,A5,B4和B5这4个样品中,激发光峰值波长红移到250 nm左右,其荧光发射峰也发生了相应的红移,到450~470 nm(Ⅱ区)。此外,A5还存在激发光峰值波长550 nm,发射峰在590 nm附近的荧光;B1还存在270 nm激发,292 nm左右发射的荧光峰(Ⅲ区)。采用荧光强度相对法来定量分析,若都以Ⅰ区的荧光强度为1,口红不同色号间、同色号真假口红间的Ⅱ区和Ⅲ区的相对荧光强度显著不同。拉曼光谱显示正品口红中存在TiO2的振动峰,也还存在大量的C-C,C-N,-CH2和-NH2等有机化官能团的振动特征峰。相比于正品口红,部分假口红中还存在四个特异性的振动峰,分别是228,447,609和1 090 cm-1,这与Fe2O3的拉曼峰位吻合。实验结果表明口红不同色号间、同色号真假口红之间均存在着明显的光谱差异,利用口红光谱的指纹特性可实现对真假口红的鉴别。 相似文献
5.
6.
利用裂纹诱导弦挠度函数,建立了悬臂Euler-Bernoulli 中开闭裂纹位置、深度、初始张开角等损伤参数的识别方法.为此,首先将梁中开闭裂纹等效为单向扭转弹簧,给出了考虑裂纹缝隙效应的裂纹梁等效抗弯刚度,并得到悬臂Euler-Bernoulli 开闭裂纹梁弯曲挠度的显式闭合解及裂纹诱导弦挠度函数,证明了裂纹诱导弦挠度的分段线性函数.其次,基于单向扭转弹簧的性质,建立了通过多步加载进行梁中开闭裂纹参数及其上下侧属性的识别方法.最后,通过数值算例验证了本文所建立的开闭裂纹损伤识别方法的适用性和可靠性,考察了裂纹分布位置、深度和初始张开角以及裂纹识别区间和挠度测量误差等参数对识别结果的影响,结果表明:当裂纹处于张开状态时,裂纹处裂纹诱导弦挠度斜率改变量随着施加荷载的增加而增加;当裂纹闭合时,其裂纹诱导弦挠度斜率改变量将保持为常量;裂纹损伤参数的识别误差随测量误差的增加而增加,但整体识别结果具有较高的精度,较好的鲁棒性. 相似文献
7.
为了通过植被指数(VI)准确、可靠的获取不同施肥梯度、不同品种的水稻叶面积指数(LAI),提出了一种基于改进的QGA-ELM算法应用于水稻LAI反演。首先通过8折交叉验证确定极限学习机(ELM)最佳的隐含层神经元个数与隐含层激活函数类型,再通过引入组合动态旋转角策略、单点混沌交叉操作、混沌变异操作、确定性选择策略、量子灾变操作对量子遗传算法(QGA)进行改进,最后使用改进后的QGA算法优化ELM神经网络输入层到隐含层的连接权值和隐含层的阈值。为了验证该模型普适性和有效性,依次建立多元线性回归、BP、ELM、QGA-ELM、改进的QGA-ELM算法5种模型,并在不同数据集上进行反演效果比较,结果表明:(1)对比QGA-ELM算法和改进的QGA-ELM算法进化过程,改进的算法能有效提升模型寻优能力,避免算法早熟,且能寻得更优结果。(2)对比五种算法在不同数据集上的反演效果,验证了NDVI,RVI与LAI之间主要为非线性关系,且ELM神经网络模型反演效果要优于BP神经网络模型和多元线性回归模型。(3)对比五种算法在不同数据集上的反演效果,改进的QGA-ELM算法绝大部分情况下拥有最高的反演精度和最低的误差,改进后的算法反演精度得到了明显提升,泛化性能也得到了增强。(4)改进的QGA-ELM算法在各种施肥梯度上均具有最高反演精度和最低误差,且精度较高,能为不同生长状况水稻LAI反演提供依据。(5)五种模型对庆和香LAI反演精度均要高于龙稻18,而改进的QGA-ELM算法在不同水稻品种上依然具有较高的反演精度,且在不同水稻品种上反演精度相差极小,远低于其他四种模型,能很好适应不同水稻品种LAI反演要求,极大提升模型的稳定性性,为不同水稻品种反演提供参考意义。 相似文献
8.
《Particuology》2022
The coaxial mixers enhance the suspension of concentrated slurries in an agitated reactor. In this research work, the complex slurry suspension and dissemination behavior in a coaxial slurry mixing system (comprised of a close clearance anchor rotating with a low speed and an inner axial impeller rotating with a high speed) was analyzed employing ERT (electrical resistance tomography, a non-intrusive flow visualization technique), and computational fluid dynamics (CFD). The numerical models were validated by comparing the axial solid concentration profiles generated using the ERT data and the CFD simulation results. The influences of various important parameters such as the diameter of the inner axial impeller, the inner impeller type, and the inner impeller spacing on the hydrodynamic characteristics of the slurry suspensions in a coaxial mixing vessel were thoroughly analyzed. The radial and axial velocity profiles of solid particles were generated using the validated mathematical models. The assessment of energy loss due to the solid–solid collisions, the particle–fluid frictions, and the particle–vessel wall collisions was conducted. The evaluation of optimum inner impeller clearance and inner impeller diameter is essential to attain a high degree of solids suspension and dissemination in a coaxial slurry mixing system. 相似文献
9.
James E. Castle 《Surface and interface analysis : SIA》2022,54(4):455-464
The Auger parameter (AP) is a value extracted from the X-ray photoelectron spectrum (XPS) by addition of the binding energy of a photoelectron, for a given element in the spectrum, to the kinetic energy of the Auger electron emitted as the resulting hole in the electronic structure is filled by an electron from one of the outer orbitals. The value of the AP is sensitive to the polarization of electrons in the orbitals of neighbouring ions towards the photo-ionized atom and is thus related to other opto-electronic properties of the material. A correlation had been shown between the refractive index and the AP of aluminosilicates and thus the ability to compare, on a single chart, the AP's of the Al and Si ions gave important structural information. This comparison was made possible by normalising the individual APs to a common zero-point. In this contribution, the methodology employed is extended to a wider range of elements. The resulting ability, to compare and contrast the normalised AP, thus generated, greatly enhances the information available from XPS and thus relates it directly to the polarizability of the material's structure. 相似文献
10.