联想让思维展翅飞翔

美国数学家波利亚在《怎样解题》一书中,提出了一个解题计划表,其中有一个重要的环节是联想.联想是我们能否顺利解决问题的桥梁,它是一种重要的思维形式.包括两种情况:一种“横向联系”,把处于不同知识块的知识联系在一起,这种思维形式有利于提高我们的思维的灵活性,也有利于我们把不同的数学知识融会贯通.联想的另一种形式,是“纵向联系”.以逻辑推理能力和运算能力为基础,将一个数学问题多次转化成另一个容易解决的数学问题,这种思维形式有利于提高思维的深刻性.横向联想,让我们的思维插上飞翔的翅膀,我们能飞得更高更远更轻盈灵活;纵向联想,能让我们的思维更加深刻,让我们的数学素养更加深厚.     

基于有限非阿贝尔群的密钥交换

从一般线性群GL（n,F）和对称群Sn上的困难问题出发,构造了几个密钥交换算法,新算法具有更高的效率.同时,指出基于一般线性群的密钥交换算法的安全性直接依赖于广义矩阵覆盖问题,基于对称群的密钥交换协议的安全性直接依赖于置换群上的共轭问题.     

并列双圆柱流致振动的不对称振动和对称性迟滞研究

对雷诺数Re = 100 间距比s/D = 2.5 和5.0 的并列双圆柱流致振动进行了数值模拟研究, 其中圆柱质量比m = 2.0, 折合流速U_r 在2.0~10.0 之间, 两圆柱仅能做横流向振动. 研究发现, 当间距比s/D = 2.5 时, 在折合流速4.4 < U_r< 4.8区间内, 两圆柱流致振动响应出现不对称振动现象, 在折合流速4.4 < U_r< 4.8 区间内, 两圆柱流致振动响应出现对称性迟滞现象; 而当间距比s/D = 2.5时, 圆柱流致振动响应与单圆柱涡激振动响应相似, 没有出现不对称振动和对称性迟滞现象. 在不对称振动区间内, 两圆柱的升、阻力参数也出现了不相等的情况. 此外, 当两圆柱不对称振动时, 圆柱间隙流稳定地偏斜向其中的一个圆柱; 相应地, 尾涡也出现了宽窄不等的模式. 窄尾流圆柱的振幅和升、阻力均较宽尾流圆柱的大. 通过对比不对称振动现象发生前后的尾涡模式, 对新现象的产生机制进行了阐述.      

平面弹性方程的非协调有限元分析

针对纯位移平面弹性问题,构造了两个无闭锁非协调有限元,单元对于Lamé常数λ一致收敛,证明了能量模和L2模误差分别为O(h2)和O(h3)．最后给出了数值试验验证了理论分析的正确性．     

苯并寡聚乙二氧链螺旋体的合成

以对甲氧基苯酚、对苄氧基苯酚、对苯二酚和四乙二醇二磺酸酯这些简单化合物为原料,通过磺酸酯与酚的亲核取代反应及苄基保护、钯碳氢化去保护策略制备得到了4种新颖的苯并寡聚乙二氧链螺旋体化合物.     

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple onedimensional, symmetric periodic potentials under the influence of both a time periodic and a static biasing force. The physical system employed contains a friction coefficient that is speed-dependent. Within the tailored parameter regime, the absolute negative mobility, in which a particle can travel in the direction opposite to a constant applied force, is observed.This behavior is robust and can be maximized at two regimes upon variation of the characteristic factor of friction coefficient. Further analysis reveals that this uphill motion is subdiffusion in terms of localization(diffusion coefficient with the form D(t) ~t~(-1) at long times). We also have observed the non-trivially anomalous subdiffusion which is significantly deviated from the localization; whereas most of the downhill motion evolves chaotically, with the normal diffusion.     

Stress-induced leakage current characteristics of PMOS fabricated by a new multi-deposition multi-annealing technique with full gate last process

In the process of high-k films fabrication, a novel multi deposition multi annealing(MDMA) technique is introduced to replace simple post deposition annealing. The leakage current decreases with the increase of the post deposition annealing(PDA) times. The equivalent oxide thickness(EOT) decreases when the annealing time(s) change from 1 to 2. Furthermore,the characteristics of SILC(stress-induced leakage current) for an ultra-thin SiO_2/HfO_2 gate dielectric stack are studied systematically. The increase of the PDA time(s) from 1 to 2 can decrease the defect and defect generation rate in the HK layer. However, increasing the PDA times to 4 and 7 may introduce too much oxygen, therefore the type of oxygen vacancy changes.     

硅探测器的数字化脉冲形状甄别

介绍了利用硅探测器的脉冲形状甄别进行粒子鉴别的原理。详细叙述了基于数字化方法的脉冲形状甄别的实现。采样频率和位数是数字化方法的两个重要参数。对于硅探测器信号,采用100 MS/s,12 bit的Digitizer可以满足脉冲形状甄别法对时间分辨的要求。同时对该方法粒子鉴别的特征和能量阈值做了简要的分析和对比。粒子背面入射硅探测器的所得的阈值低于正面入射的情况。例如对于氖周围的同位素,背面入射情况的阈值约为100 MeV,为正面入射情况下鉴别阈值的二分之一,相当与ΔE-E方法中ΔE探测器厚度约为60 μm情况下的阈值。最后定性讨论了硅探测器的电阻率不均匀性和沟道效应对粒子鉴别性能的影响。In this paper Pulse Shape Discrimination(PSD) for silicon detector has been briefly introduced. The emerging digital method successfully applied to detector signal processing makes digital PSD method one of the most promising particle identification methods. Sampling frequency and the number of bits are two key parameters of digital method. For silicon detector signal, adopting 100 Ms/s, 12 bit Digitizer can satisfy the time resolution requirement of PSD method. The identification characteristic and energy threshold of this method have been discussed and compared with both front injection and rear injection cases. Energy threshold with rear injection usually is much lower than that with front injection. For example, around for Neon isotope energy threshold with rear injection is about 100 MeV which is only half of the threshold with front injection, also equivalent to thickness of about 60 μm silicon detector threshold in ΔE-E method. At the end the impact of silicon detector's resistivity nonuniformity and channel effect on the identification capacity of PSD method has been discussed in detail.     

基于生活实践的工程流体力学启发性教学初探

工程流体力学教学中需要强调理论与实践的有机结合.本文提出基于生活实践案例以问题链形式进行启发性工程流体力学教学.以总流能量方程及水头损失计算教学为例,设计了"自来水水龙头堵住一部分出口后水流喷射的距离和流量如何变化"这一简单生活实践问题,将重要知识点贯穿其中.教学应用效果表明,启发性、开放性的生活实践问题,能够很好地引导学生综合运用理论知识,解决实际问题,同时能够培养学生的生活观察和独立思考能力.