鬼成像中一些数学问题

鬼成像是一种与传统成像方式不同的通过光场涨落的高阶关联获得图像信息的新型成像方式。近年来,相比传统成像方式,鬼成像所拥有的一些优点如高灵敏度、超分辨能力、抗散射等,使其在遥感、多光谱成像、热X射线衍射成像等领域得到广泛研究。随着对鬼成像的广泛研究,数学理论和方法在其中发挥的作用愈显突出。例如,基于压缩感知理论,可以进行鬼成像系统采样方式优化、图像重构算法设计及图像重构质量分析等研究工作。本文旨在探索鬼成像中的一些有趣的数学问题,主要包括:系统预处理方法、光场优化及相位恢复问题。对这些问题的研究既可以丰富鬼成像理论,又能推动它在实际应用中的发展。     

一种超导重力仪磁悬浮力的等效计算

为实现超导重力仪磁悬浮力的精确计算,以GWR型超导重力仪为模型基础,采用有限元的思想,将超导球表面电流理想化为多个等高共轴电流环,计算出各个电流环与超导线圈的作用力,求和得到线圈与超导球间的磁悬浮力。利用MATLAB完成计算程序实现,通过改变下线圈电流和上、下线圈电流比,获得满足一定条件的磁悬浮力及其梯度。选取合适的模型参数,计算出线圈对质量为m=4.069 g超导球的磁悬浮力大小为:Ftotal=3.988×10^-2N,磁悬浮力梯度为:-9.699×10^-3N/m,此时悬浮力梯度合适,满足系统稳定性和灵敏度的要求。     

OH+C2H3F的反应机理及产物支化比反应的理论研究

本文对HOC₂H₃F可能解离通道的势能面进行从头算CCSD(T)/CBS//B3LYP/6-311G(d,p)计算,同时对速率常数进行Rice-Ramsperger-Kassel-Marcus计算. 生成主要产物CH₂CHO+HF最有利的反应途径是OHC₂H₃F→i2→TS14→i6→TS9→i3→TS3→CH₂CHO+HF,其中速率决定步骤是HF通过TS11从CO桥接位置解离,能量比反应物高3.8 kcal/mol. 借助中间态TS14,F原子从C_α迁移到C_β位置生成CH₂O+CH₂F,然后通过中间态TS16,H从O迁移到C_α位置;通过中间态TS5,C-C键断裂生成产物,其能量比反应物低1.8 kcal/mol,比TS11低4.0 kcal/mol.     

HL-2A装置上边界间歇性事件与湍流粒子输运的统计学研究

通过对粒子概率分布函数的计算,发现在高等离子体密度下边界间歇性事件的爆发频率有所增加。通过条件平均的手段,正负间歇性事件得以区分,并发现了二者在空间上的不同特征。不同密度梯度下的湍流粒子输运计算表明,间歇性事件与湍流粒子输运之间存在密切联系,间歇性事件的存在能够大大增加湍流粒子输运的大小。在高等离子体密度时,间歇性事件的强度有所增加,而与之相应地,湍流粒子输运的大小也有所增强。     

羟基对界面水分子的扰动与其对非离子型氢氟烃杂化表面活性剂聚集行为的改变

本文合成并比较了具有和不具有羟基的两种非离子型氢氟烃杂化表面活性剂,它们均表现出良好的热稳定性和优异的表面活性. 实验观察到羟基对改变其溶液的表面张力和所形成胶束的形态具有较大的影响. 该作用可归因于烷烃基团从空气/水表面上方到其下方的重排以及由羟基诱导的界面水结构的扰动. 本工作提供了一种通过修改界面处的取向结构来弱化碳氢链和碳氟链之间的不混溶性,从而利于设计具有不同界面性质表面活性剂的策略.     

Magnetic resonance imaging of bone after radiation

Magnetic resonance imaging (MRI) was performed in 22 patients at various times (0-3) years) following radiation therapy to the spine. T1 and T2 weighted images were obtained at 0.5 Tesla. Increased signal was seen after 800-6000 rads (8-60 Gy). Marrow effects corresponded to radiation ports. Recurrent tumor was clearly separated from fatty replacement. This was much better seen on T1 weighted images. Five patients that had MRI during their course of radiotherapy (XRT) did not have increased signal on T1 images of the bone marrow. The earliest fatty marrow change was seen nine days following completion of 3000 rads (30 Gy) XRT over one month's duration. One patient who received 800 rads (8 Gy) to the upper thoracic spine for eosinophilic granuloma had no radiation effects on MRI when imaged 16 days following completion of XRT given over five days. Fatty marrow change was seen in this patient on MRI six months later. MRI was particularly useful in defining the extent of prior radiation effects when repeat therapy was needed.     

Frozen strain moiré used in the analysis of impact loading

This paper presents a solution to the problem of the displacement fields and strains in a semi-infinite plate with two half-circular holes during the propagation of a stress wave. The solution was realized experimentally by means of the method of the frozen strain moiré using a double-pulse ruby laser. The load of impact was applied by a pendulum hammer. Two suitable external-trigger mechanisms were used to fire the ruby laser at predetermined intervals. The moiré fringe patterns of the U and V displacement fields were recorded on a holographic film adhered to the specimen at different time delays after impact.     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

Numerical study of the effect of gas flow in low pressure inductively coupled Ar/N<Subscript>2</Subscript> plasmas

The effect of gas flow in low pressure inductively coupled Ar/N₂ plasmas operating at the rf frequency of 13.56 MHz and the total gas pressure of 20 mTorr is studied at the gas flows of 5–700 sccm by coupling the plasma simulation with the calculation of flow dynamics. The gas temperature is 300 K and input power is 300 W. The Ar fractions are varied from 0% to 95%. The species taken into account include electrons, Ar atoms and their excited levels, N₂ molecules and their seven different excited levels, N atoms, and Ar⁺, N⁺, N₂ ⁺, N₄ ⁺ ions. 51 chemical reactions are considered. It is found that the electron densities increase and electron temperatures decrease with a rise in gas flow rate for the different Ar fractions. The densities of all the plasma species for the different Ar fractions and gas flow rates are obtained. The collisional power losses in plasma discharges are presented and the effect of gas flow is investigated.     

蝙蝠听觉神经系统如何在复杂环境中识别昆虫

生物声纳的高灵敏度和高可靠性一直是仿生设计所追求的目标, 然而至今仍没有一个令人信服的物理模型能很好得解释生物声纳优越性能的原因, 其主要是缺乏对动物听觉系统神经信息编码的认识. 本文从蝙蝠听觉神经系统的生理结构出发, 用圆映射和符号动力学方法讨论了蝙蝠听觉神经系统在复杂环境中处理多普勒信号的一种可能性方案, 并通过计算机仿真证明了其合理性. 针对蝙蝠神经系统的不稳定性, 用符号动力学的方法分析神经系统信息处理的机理具有良好的鲁棒性和高灵敏度. 这种新的信号处理方法的研究, 为生物声纳信号的处理过程的进一步认识提供了一种新的解释.