Focal distributions and Hertz potentials

The three-dimensional (3D) pupil function for a high-aperture focusing system can be expressed in terms of Hertz or Debye potentials. The electromagnetic field in the focal region can be calculated directly from these. The Debye potential pupil function is given for optical systems obeying different conditions.     

Lagrange系统的共形不变性与Hojman守恒量

研究了一般完整Lagrange系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,并且找到在特殊无限小变换下的共形不变性并且是Lie对称性的共形因子,接下来导出Lagrange系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例. 关键词： Lagrange系统 共形不变性 Hojman守恒量 确定方程     

Conformal invariance and Hojman conservedquantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

温度对长焦距测量精度的影响

 基于Ronchi光栅的泰伯效应,在理论上分析了温度场的波动对长焦距测量系统稳定性的影响。通过大量实验研究验证了在长焦距测量系统中内部和外部温度场的波动引起空气折射率的随机变化,进而影响到测量系统焦距测量值的稳定性。在对测量系统He-Ne激光源采取水循环降温、切断系统外部冷热源、对测量系统中光栅对采取隔热封装等有效措施后,使长焦距测量系统的重复性测量精度提高了5～8倍,标准差达到了0.1‰左右,测量数据波动范围在5 mm左右,其测量精度及其稳定性均达到了实际测量的要求。     

Preliminary observations on magnetic resonance imaging in refractory epilepsy

We are studying the use of magnetic resonance (MR) imaging in localization of epileptogenic foci in patients with medically refractory partial epilepsy. Imaging is performed using a prototype resistive unit operating at 0.15 T. All studies include 7 mm axial sections obtained with a partial saturation sequence (TR = 200 msec) in which signals are recovered with a spin echo (TE = 11 msec) and images reconstructed using a modified 2D Fourier transform technique. Since the temporal lobe and limbic system are the commonest site of seizure foci in this group of patients, examinations were performed with the plane of section parallel to the temporal horns of the lateral ventricles.

Consensus interpretations by a radiologist, neurologist and neurosurgeon have recognized findings considered possibly abnormal in six of 11 epilepsy patients and none of six normal volunteers.

These preliminary results indicate that further study is warranted in this group of patients. Critical evaluation of such findings must be carried out in a larger group including normals and patients with a variety of neurologic disorders.     

Noether＇s theorem and one-step corrections method for holonomic system

In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.     

M/G1/1型可修排队的强度守恒律分析

用从平稳点过程和Palm分布理论推得的强度守恒律尝试研究了寿命为一般分布的M／G1／1型可修排队系统,在求得模型稳态工作量和拟虚等待时间表达式的基础上,得到了服务台的首次故障前时间,系统可用度,平均失效概率,服务台平均失效次数和系统故障频度等．有趣的是,当寿命分布取其特例指数分布时,与文选中已知的结果完全一致．     

Bifurcation of limit cycles at the equator

This paper studies center conditions and bifurcation of limit cycles from the equator for a class of polynomial differential system of order seven. By converting real planar system into complex system, we established the relation of focal values of a real system with singular point quantities of its concomitant system, and the recursion formula for the computation of singular point quantities of a complex system at the infinity. Therefore, the first 14 singular point quantities of a complex system at the infinity are deduced by using computer algebra system Mathematica. What’s more, the conditions for the infinity of the real system to be a center or 14 degree fine focus are derived, respectively. A system of order seven that bifurcates 12 limit cycles from the infinity is constructed for the first time.     

On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations

In this paper we generalize some results in the literature concerning the structure of numerical approximations to solitary wave solutions of some nonlinear, dispersive equations is studied. We prove that those time discretizations with the property of preserving, exactly or approximately up to certain order, some invariants of the problems, have a better propagation of the error and provide a more suitable simulation of the solitary waves. The generalization involves the treatment of nonlocal operators and two different kinds of equations.     

Projected explicit lawson methods for the integration of Schrödinger equation

In this article, it is proved that explicit Lawson methods, when projected onto one of the invariants of nonlinear Schrödinger equation (norm) are also automatically projected onto another invariant (momentum) for many solutions. As this procedure is very cheap and geometric because two invariants are conserved, it offers an efficient tool to integrate some solutions of this equation till long times. On the other hand, we show a detailed study on the numerical performance of these methods against splitting ones, with fixed and variable stepsize implementation. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq31: 78–104, 2015