四极透镜的三阶像差分析

用Lie代数方法推导了四极透镜的三阶像差.像差源于四极透镜场在轴向的有限分布.在一阶焦距不变的条件下,增加透镜的长度或增加透镜的孔径可以减小三阶像差     

Imaging of the H NMR Second Moment with C Chemical-Shift Resolution

A method of ¹³C chemical-shift-resolved ¹H second moment imaging is proposed for molecular mobility imaging of heterogeneous materials. For evaluating the ¹H second moment, the method relies on the curve fitting procedure using spin-echo shapes indirectly: The information of ¹H echo shapes is transferred to the ¹³C signal amplitude through ¹H–¹³C cross polarization and then the curve fitting is made using the ¹³C signal amplitude. The ¹³C signal is detected under ¹H dipolar decoupling and magic angle spinning, resulting in the incorporation of ¹³C chemical-shift resolution. Imaging information is included in the ¹³C signal by application of phase-encoding gradients. The second moment images obtained can reflect the molecular mobility at every molecular site separated by ¹³C chemical shifts, yielding detailed information on the molecular mobility. The method is demonstrated by spatially 1D experiments performed on a model sample.     

Splitting of the isovector Giant Quadrupole Resonances in12C and16O

The isovector Giant Quadrupole Resonances (GQR) of¹²C and¹⁶O have been investigated in a (1p1h) and (2p2h) modelspace using bound state wavefunctions. The results indicate a strong splitting of the (1p1h) E2 strength in both nuclei due to the coupling to the (2p2h) configurations. Such an effect has not been found in the case of the Giant Dipole resonance. This qualitatively different behaviour can be understood from the unperturbed particle hole energies of the 1 and E2 Giant Resonances, respectively.     

基于二阶滤波器的消光起伏谱颗粒测量结果

消光起伏频谱法是一种新的测量两相流系统中颗粒粒径分布和浓度的方法,装置简单,操作方便,适合实时、在线测量。采用二阶低通滤波器对起伏的透射率信号分析,得到消光起伏频谱实验数据,并利用改进的Chahine循环方法计算得到颗粒的粒径分布和浓度信息。重点讨论高浓度情况,包括对特征函数频率响应的修正和对其阶高修正两个方面,得到修正参量并运用到反演算法中从而得到正确的测量结果。测量结果表明,通过高浓度修正,消光起伏频谱法可以在很大的颗粒浓度动态范围得到合理的测量结果,其可测颗粒最大体积分数视颗粒的大小而定。     

Selective Detection of 1H NMR Resonances of 13CHn Groups Using Two-Dimensional Maximum-Quantum Correlation Spectroscopy

Methods for editing spectra based upon maximum-quantum filtering in two-dimensional ¹H NMR are presented (MAXY NMR). Separation of ¹H resonances from ¹³CH, ¹³CH₂, and ¹³CH₃ groups is demonstrated, using the coherence of the attached natural-abundance ¹³C spin. Two-dimensional correlation pulse sequences based on J connectivity (MAXY-COSY), total J connectivity (MAXY-TOCSY), and NOE and exchange processes (MAXY-NOESY) are given and exemplified using dexamethasone as a model compound. In addition, an improved form of a ¹³CH₂ only COSY spectrum (gem-COSY) is shown, and the application of z magnetic-field gradients is demonstrated as an alternative to phase cycling. The approach should have utility in the assignment of complex ¹H NMR spectra which arise from peptides or complex mixtures such as biofluids.     

蛋白质分子核磁共振谱峰的特性及其化学位移归属

尽可能完全、准确地归属蛋白质分子的核磁共振（Nuclear Magnetic Resonance,NMR）谱峰,是解析可信赖、高质量的蛋白质三维空间溶液结构的首要条件．自动归属软件的开发和应用,已经方便并加快了蛋白质分子核磁共振谱峰的归属进程．然而,对蛋白质核磁共振研究领域的新手来说,因为缺乏对蛋白质分子的核磁共振谱峰特性的系统认识而可能发生对自动归属结果的错误指认或指认不完全,从而导致蛋白质结构解析的错误或偏差．该文针对蛋白质分子中的核磁共振谱峰特性,比如同位素效应和立体异构等,结合具体的蛋白质分子的核磁共振实验图谱,进行了较为详尽的论述,期望对从事蛋白质核磁共振的研究者在理解蛋白质分子的核磁共振谱峰特性及其归属方面有所裨益．     

Quadrupole effects in63Cu NMR spectroscopy of copper nanocrystals

Quadrupole effects in room-temperature continuous-wave (CW)⁶³Cu nuclear magnetic resonance (NMR) spectra, “π/2” pulse length shortening and amplitudes of two-pulse generated echoes were investigated on nanocrystalline copper powders produced by cryogenic melting and by ball milling techniques. Systematic measurements on the parent polycrystalline copper and on copper-based copper-palladium dilute alloys on the basis of the same experimental techniques were also made and the results were compared to that of the nanophase samples. Fractions of Cu nuclei contributing to the specific NMR responses and average field gradients coming from noncubic neighborhoods were estimated in all the investigated cases. The satellite and/or central component origins of NMR spectra of the samples are not a priori trivial even in the simplest case. Comparative analysis of CW and pulsed experiments allowed a surprising technological conclusion to be drawn by finding a smaller chemical impurity content inside the nanograins than the value characteristic of the entire sample. The measured decrease of the impurity concentration in the inner region of the copper nanoparticles is the consequence of the applied technologies: cryogenic melting and ball milling. These preparation methods cause grain-boundary segregation and result in a cleaner inside of copper nanoparticles.     

利用核四极矩共振技术探测炸药

介绍了用核四极矩共振的原理进行爆炸危险物品检测的方法及实验测试系统. 该系统运用特殊的激励信号来激发被检测样品中所含的特殊元素¹⁴N（炸药的主要成分）,使其产生核四极矩共振,并产生辐射,从而达到检测的目的. 由于该辐射信号的能量非常小(10 nV量级）,在通常的环境中很难检测该信号, 这就对此弱信号的检测和提取提出了很高的要求. 本测试系统使用了一系列有效的组合激励信号及弱信号采集、处理技术,在通常环境中成功地检测到了RDX（黑索金）信号.     

飞秒互相关时间选通技术用于光学层析成像的实验研究

利用飞秒互相关二次谐波信号时间选通技术。实现了对埋藏在高度散射介质中物体的透射成像和反射以析成像。互相关选通门有效地选出携带物体信息的弹道光子和蛇行光子，排除了给成像带来背景噪声的温射光子，分别获得了散射介质中物体的二次谐波一维和二维图像。     

Higher Derivative versus Second Order Field Equations

The first part of this work reviews problems of (particle and field) theories with higher than second time derivatives. The second part gives an overview about the known results concerning the structure of bosonic field theories with at most second order equations.     

Second Order Perturbation Theory for Embedded Eigenvalues

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.     

二阶偏振模色散测量分析

在庞加莱球的基础上,对原偏振模色散的测量方法进行了理论分析.研究表明,原方法属于间接测量,在测量二阶偏振模色散中存在明显不足.一阶偏振模色散测量的误差影响二阶偏振模色散的测量,间接测量降低了二阶偏振模色散的测量准确度.提出了一种二阶偏振模色散测量的新方法,保证了测量准确度,并通过实验中的统计结果得到证实.     

Second Order Correction of Relativistic Optical Potential

The imaginary part of the off-energy shell optical potential of a nucleon in nuclear matter, where the polarization and correlation contribution of the exchanges of the σ and ω mesons are taken into account, is derived in the framework of the relativistic meson-nucleon field theory. The second order correction of the real part of the optical potential is calculated in terms of the dispersion relation and the effective mass of a nucleon in the nuclear medium is also investigated in this paper.     

Percolation Phase Transitions from Second Order to First Order in Random Networks

We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 qc 0.25 separating the two phase transition types.     

Resonances of the Spatial Distribution of Dislocations upon Interaction with the Structural Order Parameter

The interaction of a structural subsystem with dislocations under the superposition of an elastic torsion strain and an additional uniaxial spatially nonuniform time-constant pressure is studied. The analysis is carried out within of Landau’s phenomenological theory with refusal of the approximation of constant magnitudes of irreducible vectors. The rise of spatial resonances of the dislocation density in these conditions is shown.     

二阶总广义变分图像放大

为了在图像放大中获得更好的视觉效果,提出了一种基于总广义变分性质的变分放大模型.该模型将原始低分辨图像作为被估计的高分辨放大图像到所在空间的某个子空间的投影,利用二阶总广义变分正则化迭代处理得到被估计放大图像.通过分析新模型的性质,给出了一种有效的原始对偶放大算法.实验结果表明:该方法能去除总变分放大方法产生的图像阶梯块效应,恢复更多的细节边缘及纹理信息,从而重构出高质量的图像;相比于总变分图像放大方法和小波图像放大方法,该方法具有更高的峰值信噪比和更小的均方误差.     

Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.     

Why Fundamental Physical Equations Are of Second Order

We use a deep mathematical result (namely, aminor modification of Kolmogorov's solution to Hilbert's13th problem) to explain why fundamental physicalequations are of second order. This same result explain why all these fundamental equations naturallylead to nonsmooth solutions likesingularities.