Complete set of periodic solutions of a discontinuous recurrence equation

A nonlinear three-term recurrence relation arising from seeking the steady states of a cellular neural network with bang‐bang control is studied. We show that each solution is periodic and its prime period can be determined by three of its consecutive terms. By means of this periodicity property, we may then solve the steady state problem which to our knowledge is not solved by other means.     

具有四次轨道的二次可积系统的周期函数

利用Picard-Fuchs方程法,研究了一般Lotka-Volterra可逆系统周期函数的单调性问题,证明了一般Lotka-Volterra可逆系统在四次轨道条件下的周期函数是单调的。     

Periodic Solutions of Classical Hamiltonian Systems without Palais-Smale Condition

In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.     

Multi-separation, centrifugality and centripetality imply chaos

Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.

     

Aurifeuillian factorizations and the period of the Bell numbers modulo a prime

We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.

     

同步动态随机存储器辐射效应测试系统研制

在分析同步动态随机存储器(SDRAM)辐射效应主要失效现象的基础上,研制了具备了读写功能测试、刷新周期测试及功耗电流测试三种功能的SDRAM辐射效应在线测试系统,并开展了SDRAM的总剂量效应实验研究。结果表明,总剂量效应会导致SDRAM器件的数据保持时间不断减小,功耗电流不断增大以及读写功能失效。实验样品MT48LC8M32B2的功能失效主要由外围控制电路造成,而非存储单元翻转。数据保持时间虽然随着辐照剂量的累积不断减小,但不是造成该器件功能失效的直接原因。     

单摆周期的系统误差分析

文章逐个分析计算了单摆的摆角、摆球的自转、摆线质量、空气浮力以及空气阻力对于单摆周期的影响,以1 m长5°小幅单摆为例,得到这5种因素带来的系统相对误差分别为+0.45‰、+0.02‰、-0.45‰、+0.07‰、-0.14‰,合计仅为-0.05‰,即这5种误差因素几乎相互抵消,小幅单摆实验在理论上的系统误差极小.文章给出了较为详细的推理、计算和分析过程,尤其空气阻力矩的推理过程以及图、表等,意在提供较为完整和准确的认识.文末,针对人们在空气阻力认识上可能存在的某些不足,文章给出了几点必要的说明.     

基于氧化石墨烯的长周期光纤光栅的全光控制

实验验证了一种通过将氧化石墨烯分散液沉积在长周期光纤光栅的全光控制的相关研究。通过外加的垂直泵浦光的作用,氧化石墨烯吸收泵浦光产生热量,改变长周期光纤光栅的包层模式的相位差,由于热膨胀的作用改变了氧化石墨烯所覆盖部分的光栅周期,使得谐振谱发生了移动,其最大调制深度可达10.6 dB,谐振谱最大可红移12.8 nm。通过实验发现,沉积相同浓度氧化石墨烯分散液的次数影响实验结果,通过在相同光栅的相同位置分别沉积三次,发现沉积三次可以在光纤表面获得更加均匀的氧化石墨烯膜,进行了时间响应的测试,其中沉积三次后的长周期光纤光栅的响应速度可达0.61 ms,沉积多次氧化石墨烯分散液可以在光纤表面沉积得更加平整均匀,从而获得更大的导热性能。     

对称面形光栅TE模的衍射特性

本文采用耦合波方法计算了对称面形光栅的衍射效率,分析了光栅截面面形为正弦、三角形、矩形、梯形光栅衍射效率与光栅周期、沟槽深度的关系,计算了光栅的峰值衍射效率。理论计算表明:合理地选择光栅周期、沟槽深度,对称面形光栅都可以达到很高衍射效率,接近100%;光栅的峰值衍射效率基本出现在Bragg衍射且光栅的周期等于衍射波长时。