几个非线性偏微分方程的非古典对称及相似解

研究了一些非线性偏微分方程的非古典势对称和非古典对称,得到了某些方程的新的势对称和新的对称,同时也得到了其伴随系统的新的对称,并求出了一些相似解．这些解对进一步研究这些非线性偏微分方程所描述的物理现象具有广泛的应用价值．     

无线传感网络安全定位和位置检测

无线传感网络的基本功能是检测和报告事件发生的位置,所以位置发现很重要。在以前的定位协议设计过程中,只注重能耗和精度问题而忽略安全,近来定位过程中的安全问题引起了关注。分析了定位过程中可能存在的威胁,对传统的定位算法进行了安全分析,介绍了已有的安全定位算法和检测方法,并对将来的研究提出了初步的设想。     

Benney方程的势对称和不变解

利用微分形式的吴方法计算了Benney方程的势对称及其不变解．由于Benney方程中包含不稳定项和耗散项,使得直接求其不变解较为困难,利用吴一微分特征列算法可大大降低其中确定方程组的计算难度．本文全面讨论了Benney方程不同系数情况下的对称,并且得到了新的势对称,同时利用这些对称求得了相应的不变解,这些解对进一步研究Benney方程所描述的物理现象具有广泛的应用价值．文章表明,对于守恒形式的偏微分方程,可通过其辅助系统求得的势对称来构造其不变解．     

Lie point symmetries and conservation laws in microstretch and micromorphic elasticity

In this paper, following Noether’s theorem we investigate Lie point symmetries of linear theories of microstretch elasticity and micromorphic elasticity. We restrict our consideration to isotropic, compatible and homogeneous materials. Conservation and balance laws are derived, thereby extending results from micropolar elasticity.     

用FPGA实现高冲击过程中的加速度数据回收

FPGA(现场可编程逻辑门阵列)用做高速数据采集系统的主控制器具有单片机、DSP等通用CPU所不具备的特点:并行执行、速度快、低功耗等。基于FPGA的数据回收系统可以对高冲击过程中的加速度值进行实时采集回收。数据回收系统的设计采用自顶向下的模块化设计方法,对每个功能模块的设计进行了说明,最后对系统进行了实验验证。     

Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers

The inherent dynamics of bipedal, passive mechanisms are studiedto investigate the relation between motions constrained to two-dimensional (2D)planes and those free to move in a three-dimensional (3D) environment. Inparticular, we develop numerical and analytical techniques usingdynamical-systems methodology to address the persistence and stabilitychanges of periodic, gait-like motions due to the relaxation ofconfiguration constraints and the breaking of problem symmetries. Theresults indicate the limitations of a 2D analysis to predictthe dynamics in the 3D environment. For example, it is shownhow the loss of constraints may introduce characteristically non-2Dinstability mechanisms, and how small symmetry-breaking terms may result inthe termination of solution branches.     

A New Batch Verifying Scheme for Identifying Illegal Signatures

The concept of batch verifying multiple digital signatures is to find a method by which multiple digital signatures can be verified simultaneously in a lower time complexity than separately verifying all the signatures.In this article,we analyze the complexity of the batch verifying schemes defined by Li,Hwang and Chen in 2010,and propose a new batch verifying multiple digital signature scheme,in two variants:one for RSA-by completing the Harn’s schema with an identifying illegal signatures algorithm,and the other adapted for a modified Elliptic Curve Digital Signature Algorithm protocol.     

Linearization through state immersion of nonlinear systems admitting Lie symmetries

In this paper, it is shown that if a nonlinear system admits a Lie symmetry that can be transformed into its Poincaré-Dulac normal form by a state diffeomorphism, then, under some technical conditions, such a nonlinear system can be immersed into a linear one. This allows us to compute in closed-form the flow, all algebraic invariant curves (through semi-invariants) of the nonlinear system, and Lyapunov functions to study stability properties.     

李白、崔颢《黄鹤楼》诗案考辨

分析了李白、崔颢《黄鹤楼》诗案本末,认为肯定诗案的观点缺乏有力的依据,质疑诗案的观点值得重视。提出否定诗案的5个视点及澄清诗案的4点意义。     

一类非线性偏微分方程的对称研究

利用待定系数法研究了一类任意阶偏微分方程的对称，并将此方法应用到Rosenau—Hyman方程，得到了该方程的对称，从而证明此方法对于一维偏微分方程的可行性。