Sharp estimates for Hübner’s upper bound function with applications

New better estimates, which are given in terms of elementary functions, for the function r → (2/π)(1 - r2)K(r)K (r) + log r appearing in Hübner's sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.     

Minimal distortion morphs generated by time-dependent vector fields

A morph between two Riemannian n-manifolds is an isotopy between them together with the set of all intermediate manifolds equipped with Riemannian metrics. We propose measures of the distortion produced by some classes of morphs and diffeomorphisms between two isotopic Riemannian n-manifolds and, with respect to these classes, prove the existence of minimal distortion morphs and diffeomorphisms. In particular, we consider the class of time-dependent vector fields (on an open subset Ω of Rn+1 in which the manifolds are embedded) that generate morphs between two manifolds M and N via an evolution equation, define the bending and the morphing distortion energies for these morphs, and prove the existence of minimizers of the corresponding functionals in the set of time-dependent vector fields that generate morphs between M and N and are L² functions from [0,1] to the Sobolev space .     

CEV模型下时滞最优投资与再保险问题

在常方差弹性（constant elasticity of variance,CEV）模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

Calculated spectroscopic properties for C12H and HC11N, molecules of astrochemical interest

A comparative theoretical study of the (potential) interstellar molecules C₁₂H⁻ and HC₁₁N has been carried out, making use of the coupled cluster variant CCSD(T) in conjunction with large basis sets comprising up to 715 contracted Gaussian-type orbitals. The ground-state rotational constants of C₁₂H⁻ and C₁₂D⁻ are predicted to be 174.11 and 170.32 MHz, respectively. The corresponding quartic centrifugal distortion constant of C₁₂H⁻ is estimated to be 0.26 Hz, to be compared with an experimental value of 0.24 Hz for HC₁₁N. Most of the total infrared intensity of C₁₂H⁻ isotopomers concentrates in one or two bands around 2000 cm⁻¹. The total IR intensity exceeds 13 000 km mol⁻¹ and is thus about 20 times larger than for HC₁₁ N isotopomers. The bending vibrations of C₁₂H⁻, HC₁₁N and their deuterated species are analysed by means of mass plots.     

Influence of mode distortion on the transverse mode competition in large-mode-area amplifiers

In large mode area fiber amplifier, it is difficult to avoid the bend induced mode distortion. With the existence of mode distortion taken into account, a previous transverse mode competition model has been improved. Based on this model and the finite element difference-beam propagation method, the behaviors of bent mode competition are demonstrated and compared with the straight mode competition where the mode distortion is neglected, the comparison and quantitative results show that serious mode distortion can change the appearance of transverse mode competition in bent fiber amplifiers and even drastically degrade the amplifier performance.     

Semianalytical analysis of thermal effect in LD double-side-pumped rectangular laser crystal

A semianalytical method to analyze the thermal effect in a LD double-side-pumped rectangular laser crystal is put forward. Through the analysis of working characteristics of the laser crystal, a thermal model that matches actual situations of the laser crystal is established. General expressions of temperature field and thermal distortion field in the laser crystal can be obtained by a novel method to solve the heat conduction equation of orthotropic material. This semianalytical method can be used to calculate the temperature field and thermal distortion field in other LD double-side-pumped laser crystals and is applied to Nd:YVO₄ crystal in detail in this paper, and two methods of effectively reducing thermal distortion in the laser crystal are offered. Results show that a maximum temperature rise of 362.2 °C and a maximum thermal distortion of 5.55 μm are obtained in Nd:YVO₄ crystal when the output power of the two laser diodes are both 30 W. When the off-center distance is 0.6 mm, the maximum thermal distortion is reduced by 37.7%; when the thickness of the crystal is reduced from 2.0 mm to 1.4 mm, the maximum thermal distortion is reduced by 31.7%. Results in this paper can offer theoretical base for better solving thermal problems in laser system.     

Radial and spiral distortion of magnetic lenses with fields of the form B(z)αz

Both radial and spiral distortion of magnetic lens with the field distribution in the form B(z)αzⁿ are analyzed by means of Scherzer's formula. To estimate the performance of the image in electron microscope the dimensionless quality factors (F.Z. Marai, T. Mulvey, Sherzer's formula and the correction of spiral distortion in the electron microscope, Ultramicroscopy 2 (1977) 187–192.), for both radial and spiral distortion is calculated. The results have been compared with different projector lenses.     

阵形畸变条件下双线阵左右舷分辨性能分析

研究了双线阵在两种阵形畸变(轴向滑移和航向偏差)条件下的左右舷分辨性能,根据双线阵指向性函数的背瓣特性分析了阵形畸变对左右舷分辨性能的影响。理论分析表明,在无阵形畸变的理想阵形情况下,窄带信号的左右舷分辨能力取决于阵间距和信噪比,而对宽带信号,左右舷分辨能力不仅与阵间距和信噪比有关,而且还与接收信号的功率谱密度、处理频段有关。在阵形发生轴向滑移和航向不一致的情况下,在正横方向附近,左右舷分辨性能主要受双线阵的航向差影响,偏离正横方向,较大的轴向滑移会导致左右舷误判。     

Pr0.7(Sr1-xCax)0.3MnO3多晶体系中的小极化子性质

采用基于柠檬酸体系的溶胶-凝胶法制备了Pr_0.7（Sr_1-xCa_x）_0.3MnO₃系列的多晶块材, 同时还用脉冲激光沉积技术（PLD）在SrTiO₃（100）衬底上外延生长了同一系列的薄膜, 系统研究了它们的晶格结构和电输运行为. 多晶和薄膜样品都具有正交晶格结构, 电输运行为在居里温度T_Ｃ以上的高温顺磁相都很好 关键词： 0.7（Sr_1-xCa_x）_0.3MnO₃')" href="#">Pr_0.7（Sr_1-xCa_x）_0.3MnO₃ 绝热小极化子模型 双交换作用 Jahn-Teller晶格畸变     

大型短脉冲激光装置中脉冲前沿畸变效应的研究

阐述了短脉冲激光装置中脉冲前沿畸变效应的产生机理和可能的畸变源.利用Fourier光学方法,建立了一个基于单程压缩构型的研究脉冲前沿畸变效应的理论模型,分析不同种脉冲前沿畸变效应对于压缩器输出脉冲的近场时空特性的影响.基于此,对一个在建的大口径（300 mm）短脉冲装置中的各种畸变源（包括可编程声光光谱色散滤波器、透镜色差以及劈板等元件）进行了数值计算.研究表明：近场输出脉冲宽度显著加宽,输出脉冲前沿形状不同于输入时的畸变形状,只有中心部分区域的脉冲前沿形状与输入类似,该区域的大小由系统带宽决定. 关键词： 脉冲前沿畸变 角色散 单程压缩 透镜