特殊类型函数高阶导数与原函数的统一公式

本文通过研究几种特殊类型函数的高阶导数与原函数的求法 ,获得了由该类函数自身及其一阶导数的特征 ,即可快速写出该类函数的 n阶导数 y( n) 与原函数 y( - 1 ) 的统一公式 y( n) ( n=-1 ,1 ,2 ,3 ,… ) .该公式可给实际运算带来许多简化与方便 .     

一类高阶非线性泛函微分方程的振动性

给出了一类高阶非线性泛函微分方程的若干振动定理,推广了文献中的一些振动结果.     

高稳定度大视场大气风场测量新方法

提出了一种利用广角迈克耳孙干涉仪在动镜固定的情况下,依靠视场角的变化以调制光程差来测量大气风场的新方法以及探测模式和装置设想;采用干涉成像光谱技术对被探测源谱线为高斯轮廓时风扬的速度、温度的测量进行了分析和计算,这种方法具有稳定度高、实时性好,精确度高、大视场和高通量等优点。     

兰姆移位的一种半定量计算方法

考虑一个自由电子以动量p运动时因吸放虚光子而引起自能的辐射修正,用非协变形式的量子微扰论算出它有b₂p⁴的形式.在此基础上加上真空极化修正和核有限半径引起的修正,算得氢原子2S_1/2–2P_1/2态的兰姆移位为1056.522MHz,比实验值1057.845MHz仅小0.13%. 用Dirac方程作相对论性修正后,还计算了氢原子4D_5/2–4S_1/2态的能级差,所谓“超兰姆移位”和1S态的“绝对”兰姆移位.误差最大达6.7%,并分析了原因.     

Manifestation of nuclear spin dependent P odd electron–nucleon interaction in atomic ytterbium

P odd effects caused by the nuclear spin dependent electron-nucleon interaction are considered. P-odd amplitudes are calculated for ¹S₀ → ³D_1,2 transitions in atomic ytterbium. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamics of ion-acoustic rogue waves in electron-positron-ion magneto-plasmas

A more general and realistic four-component magnetized plasma medium consisting of opposite polarity ions and nonthermal distributed positrons and electrons is considered to investigate the stable/unstable frequency regimes of modulated ion-acoustic waves (IAWs) in the D-F regions of Earth's ionosphere. A (3 + 1) -dimensional nonlinear Schrödinger equation, which leads to the modulation instability (MI) of IAWs, is derived. The parametric regimes for the existence of the MI, first- and second-order rogue waves, and also their basic features (viz., amplitude, width, and speed) are found to be significantly modified by the effect of physical plasma parameters and external magnetic field. It is found that the nonlinearity of the different types of electronegative plasma system depends on the positive to negative ion mass ratio. It is also shown that the presence of nonthermal distributed electrons and positrons modifies the nature of the MI of the modulated IAWs. The implication of our results for the laboratory plasma [e.g., (Ar⁺, F⁻ ) electronegative plasma] and space plasma [e.g., (H⁺, H⁻ ), () electronegative plasma in D-F regions of Earth's ionosphere] are briefly discussed.     

Error and work estimates for high‐order elements

Error and work estimates for high‐order elements are derived. The comparison of error and work estimates shows that for relative accuracy in the 1% range, which is typical of engineering interest, it may prove very difficult to improve on linear elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. Copyright © 2011 John Wiley & Sons, Ltd.     

AUTOMORPHISMS OF CURVES

The article deals with local symmetries of the infinite-order jet space of C^∞-smooth curves in ?^m+1 (m ≥ 1). Transformations under consideration are the most general possible: they need not preserve the distinction between dependent and independent variables and the order of derivatives may be arbitrarily changed. Unlike the common prolonged point and Lie's contact transformations, they destroy the finite-order jet spaces.     

PbnSn(n=1-19)合金团簇电偶极矩和极化率的研究

利用基于密度泛函理论的有限电场方法对PbnSn(n=1-19)团簇的电偶极矩和极化率进行研究。PbnSn(n=1-19)合金团簇的高对称性抑制其电偶极矩的产生。在团簇原子总数N＜14时，团簇的电偶极矩与能隙表现出相反的变化趋势（同一尺寸下，高能隙与低电偶极矩相对应），然而在14≤N≤19范围内，由于构型生长方式的转变，能隙与电偶极矩展现出相同的演化趋势。研究所得的极化率与实验值在部分尺寸相符合较好，但总体上与实验值还有一定的差别，这可能是实验中包含混合态或激发态的缘故。     

Collisional depolarization of rotational angular momentum: what are the observables and how can they be measured?

The destruction and transfer of polarization of the rotational angular momentum of small molecules in an isotropic collisional environment is reviewed. Several recent independent treatments are drawn together, including unpublished details from the authors' own work, of the formal kinetics in terms of moments of the density matrix. The final results are shown to be equivalent and directly amenable to comparison with results of exact quantum scattering calculations. In passing, some differences in nomenclature are noted and a self-consistent version is presented that might usefully be adopted. The existing experimental approaches are surveyed, within the common theme of laser-based creation of the initial rotational anisotropy of relatively low rank, K, combined with a spectroscopic probe, also sensitive to restricted K. Those formally defined quantities that may be measured are identified, either individually or in some combination, with each method. In particular, an attempt is made to distinguish between measurements of individual tensor moments of the density matrix, or ‘bulk polarizations’, and alignment moments, which are normalized to the population. Some cases are noted where experimental procedures have compromised the results, or where the analysis has been similarly approximate or carried out on a less rigorous empirical basis.