让思维插上“联想”的翅膀

<正>数学解题与联想是分不开的.在数学解题中,同学们应该通过各种大胆联想,如在形式、结构、方法、特征上等,寻求解题的适当途径、方法探索新的结论,促使思维向多层次、多方位发散,从而使自己分析问题、解决问题的能力不断提高.一、形式上的联想     

Measuring Carrier-Envelope Phase of Few-Cycle Laser Pulses Using High-Order Above-Threshold Ionization Photoelectrons

We experimentally demonstrate the measurement of carrier-envelope phase of few-cycle laser pulses. We have built a stereo above-threshold ionization setup. The photoelectron energy spectra of high-order above-threshold ionization are measured in both the left and right directions in the linearly polarized laser fields. It is shown that the left-right asymmetry of the spectra is dependent on carrier-envelope phase of few-cycle laser pulses. Two asymmetry parameters from the low-energy and high-energy regions at the above-threshold ionization plateau map a phase ellipse, in which the points indicate the absolute value of carrier-envelope phase. We have calibrated the phase ellipse by comparison with the semiclassical calculation. This setup allows us to determine the value of the absolute phase of few-cycle laser pulses.     

一类亚半正定矩阵的左右逆特征值问题

1．引言在工程技术中常常遇到这样一类逆特征值问题：要求在一个矩阵集合S中，找具有给定的部分右特征对（特征值及相应的特征向量）和给定的部分左特征对（特征值及相应的特征向量）的矩阵．文［2］，［3］讨论了S为。x。实矩阵集合的情形．文［4］－［7］对S为nxn实对称矩阵．对称正定矩阵，对称半正定矩阵集合的情形进行了讨论．文【川讨论了S为亚正定阵集合的情形．并提到了对于亚半正定矩阵的情形目下无人涉及，有待进一步研究．本文将对S为nxn亚半正定矩阵集合的情形进行讨论．给出了亚半正定矩阵的左右逆特征值问题有解的充要条件…     

The time-delay estimation method of resolving left-right target ambiguity for twin-line array and its realization

The directivity function of twin-line array sonar can be used to identify left/right target. But the performance is limited by the distance between two lines and also exists the blind area for target identification. A method, which is based on the time-delay estimation between two line arrays, is proposed to identify left/right target. The method is robust with the variation of distance between two line array, the blind area is considerable decreased. The theoretical analysis results and realization method is described. An algorithm base on interpolation method for precisely estimating tune-delay of two line array are derived, therefore the left-right ambiguity problem is solved.     

Cauchy积分中值定理逆问题的注记

使用函数严格单调性,获得了定积分的若干性质.应用这些性质,解决了Cauchy积分中值定理中值点的唯一性,并得到了该定理及其逆定理的较弱表述,进一步解决了其逆定理中积分区间端点的唯一性.     

Versal unfolding of smooth map germs under a subgroup of the left-right equivalence group

定义了左右等价群的一个子群,给出了在这个子群下映射芽的等价及其开折的同构等概念.利用乘积积分理论,讨论在该子群下映射芽的通用开折,证明了相应开折的平凡性引理,几何引理和代数引理,给出了映射茅的开折是通用开折的充要条件.     

带有不完全信息随机截尾试验下总体均值型参数的经验似然

本文考虑带有不完全信息随机截尾试验模型,当模型中寿命随机变量的总体分布类型完全未知时,针对总体均值型参数进行统计推断,构造经验对数似然比统计量,模拟表明该统计量的分布与标准卡方分布拟合得很好,由于数据是不完全数据,借鉴[11]采用广义EM算法计算该统计量,数值模拟表明这是个行之有效的方法.     

激光辐射控制化学反应

 很多年以来,化学家们总试图借助于激光来控制化学反应过程,可是一直没能成功。但是利用激光照射物质时产生的精细量子效应,就可以达到这一目的。     

Single Production of Charged Gauge Boson WH^- from Left-Right Twin Higgs Model in Association with Top Quark at LHC

The twin Higgs mechanism has recently been proposed to solve the little hierarchy problem. In the context of the left-right twin Higgs （LRTH） model, we discuss single production of the new charged gauge boson WH^- , which is predicted by the left-right twin Higgs model, in association with top quark at the CERN Large Hadron Collider （LHC）. It is found that, for a typical nonzero value of mass mixing parameter M = 150 GeV in the LRTH model, the production cross section is in the range of 3 ×10^-2 - 6.07×10^3 fb at the LHC. As long as the WH^- is not too heavy, the possible signatures of the heavy charged gauge boson might be detected at the LHC experiments.