Slow escaping points of quasiregular mappings

This article concerns the iteration of quasiregular mappings on \(\mathbb {R}^d\) and entire functions on \(\mathbb {C}\). It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let \(f:\mathbb {R}^d\rightarrow \mathbb {R}^d\) be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates \(f^n\) tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of \(|f^n(x)|\) is asymptotic to the iterated maximum modulus \(M^{n}(R,f)\).     

专业化与研究性——面向工科专业开设的专业研究教学实验

本文针对国内高校尤其是工科院校学生培养中普遍存在的教学环节设置低年级专业渗透不够、高年级研究性不足的问题,提出开设贯穿于四年的工科学生培养专业研究实践教学模式。文章阐述了工科大学专业研究实验的研究性与专业化思想,在此基础上提出应根据学生在学习过程中所处的不同学习阶段有侧重的选择实验项目,以期帮助学生理解基础课程与专业课程之间的知识关联、形成统一的学科知识体系,满足后续工作、科研的需求的同时培养他们对于专业的感情。文章在此基础上,依据所提出的教学模式给出了相应的教学实验示例。旨在为应用工程类专业学生培养提供一种新的教学思路和教学模式,调动学生主观能动性的同时推进学研结合。     

Double-slit diffraction of terahertz wave generated by tilted-pulse-front pumping

We propose a spatial diffraction diagnostic method via inserting a millimeter-gap double slit into the collimated terahertz beam to monitor the minute variation of the terahertz beam in strong-field terahertz sources, which is difficult to be resolved in conventional terahertz imaging systems. To verify the method, we intentionally fabricate tiny variations of the terahertz beam through tuning the iris for the infrared pumping beam before the tilted-pulse-front pumping setups.The phenomena can be well explained by the theory based on the tilted-pulse-front technique and terahertz diffraction.     

Some Remarks on p-Adic Analytic Groups

A theorem of Maranda [1, Section 30] states that if F is a finitegroup, p is a prime and p^e exactly divides |F|, then a Z_pF-latticeM is determined up to isomorphism by its finite quotient M/p^e+1M.If M is a free Z_p-module of rank d, this is equivalent to sayingthat representations of F in GL_d(Z_p) are determined up to equivalenceby their images modulo p^e+1. 1991 Mathematics Subject Classification20E18, 22E20.     

样品温度和空间约束两种方法相结合对激光诱导击穿光谱的影响

升高样品温度和采用空间约束能提高激光诱导击穿光谱的信号强度,两种技术的结合可以进一步提高激光诱导击穿光谱的光谱强度.本文在空气环境中研究了升高样品温度和空间约束效应两种方法相结合对激光诱导击穿光谱的影响,测量了激光诱导铝等离子体的时间分辨光谱.实验结果表明:升高样品温度能增加激光诱导击穿光谱的信号强度,高温样品能耦合更...     

Moduli of twisted spin curves

In this note we give a new, natural construction of a compactification of the stack of smooth -spin curves, which we call the stack of stable twisted -spin curves. This stack is identified with a special case of a stack of twisted stable maps of Abramovich and Vistoli. Realizations in terms of admissible -spaces and -line bundles are given as well. The infinitesimal structure of this stack is described in a relatively straightforward manner, similar to that of usual stable curves.

We construct representable morphisms from the stacks of stable twisted -spin curves to the stacks of stable -spin curves and show that they are isomorphisms. Many delicate features of -spin curves, including torsion free sheaves with power maps, arise as simple by-products of twisted spin curves. Various constructions, such as the -operator of Seeley and Singer and Witten's cohomology class go through without complications in the setting of twisted spin curves.

     

Crystal structure,dielectric and piezoelectric properties of Ta/W codoped Bi3TiNbO9 Aurivillius phase ceramics

Aurivillius phase Bi₃Ti_1−xTa_xNb_1−xW_xO₁₂ high temperature piezoceramics were prepared by a conventional solid state reaction method. The crystal structure, dielectric, electrical conduction and piezoelectric properties were systematically studied. Pure or modified Bi₃TiNbO₉ ceramics revealed the presence of only two-layered Aurivillius phase, indicating that Ta/W doping entered into the B-site of pseudo-perovskite structure and formed solid solutions. The Curie temperature had a strong reliance on the structural distortion. Furthermore, Ta/W dopants act as a donor doping, decrease the number of oxygen vacancies and facilitate the domain wall motion. As a result, Ta/W modifications significantly increase the DC resistivity and piezoelectric properties. Bi₃Ti_0.98Ta_0.02Nb_0.98W_0.02O₁₂ ceramics possess the optimum d₃₃ value (∼12.5 pC/N) together with a high T_C point (∼893 °C). Moreover, the resonance–antiresonance spectra demonstrate that the Ta/W-BTN ceramics are indeed piezoelectric in nature at 600 °C. The d₃₃ value of BTTNW-2 ceramic remains ∼12.2 pC/N after annealing at 700 °C. These factors suggest that the BTTNW-based ceramic is a promising candidate for ultra-high temperature sensor applications.     

大气激光通信中的偏振调制性能

为充分证明偏振移位键控可有效抑制大气湍流等因素的影响这一观点,对目前大气激光通信系统中广泛采用的几种强度调制和偏振移位键控技术进行详细的分析研究,从各调制方式的功率利用率、带宽需求、传输容量以及差错性能几个方面进行对比。研究结果表明,各调制方式各有千秋,不能一概而论。综合各方面性能考虑,偏振移位键控较其他几种强度调制方式更具优越性,其具有最大传输容量、最小的带宽需求和接收误码率。由此可见,偏振调制方式更适合应用于大气激光通信。     

高功率激光系统nm宽带激光脉冲传输特性

对高功率激光系统采用宽带激光消除菲涅耳衍射问题进行了研究,指出只有数百nm的宽带啁啾光脉冲才对近场衍射有一定的平滑作用,数nm的宽带啁啾光脉冲对近场衍射几乎没有平滑作用;同时,还对宽带啁啾光的B积分表征方式和最快增长频率问题进行了研究,并与原型装置上开展的窄带脉冲、宽带啁啾堆积脉冲的非线性实验结果进行了对比研究,指出以最大B积分或加权B积分反映非线性自聚焦更为准确。研究还表明,在数nm,ns情况下最快增长频率与窄带激光脉冲的差别不大。     

Convergence and Stability of Locally ℝ N -Invariant Solutions of Ricci Flow

Valuable models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally $\mathcal{G}Valuable models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G\mathcal{G} -invariant solutions on bundles G^N\hookrightarrowM \oversetp? Bⁿ\mathcal{G}^{N}\hookrightarrow\mathcal{M}\,\overset{\pi }{\mathcal{\longrightarrow}}\,\mathcal{B}^{n} , with G\mathcal{G} a nilpotent Lie group. In this paper, we establish convergence and asymptotic stability, modulo smooth finite-dimensional center manifolds, of certain ℝ ^N -invariant model solutions. In case N+n=3, our results are relevant to work of Lott classifying the asymptotic behavior of all 3-dimensional Ricci flow solutions whose sectional curvatures and diameters are respectively O(t^-1)\mathcal{O}(t^{-1}) and O(t^1/2)\mathcal{O}(t^{1/2}) as t→∞.