高等师范院校计算机专业离散数学的教学改革与实践

根据当前高等师范院校计算机专业人才培养的特点和离散数学的教学现状,从离散数学的教学内容、教学手段和实验教学等方面探讨了计算机专业离散数学的教学改革。通过这几年的改革实践,离散数学的教学效果得到了明显提高。     

线性逻辑方程组的解

软件设计和硬件设计中经常遇见用逻辑方程或逻辑方程组表示的数学模型,讨论这类数学模型的求解问题是非常必要的.给出了AX=0,AX=1,AX=B,AY=1(X中不含逻辑非变量,Y中含逻辑非变量)等类型的线性逻辑方程组有解,有惟一解的充分必要条件,讨论了解的个数并给出了求解公式或解集表示式,阐明了任何形式的逻辑方程或逻辑方程组都可转化为线性逻辑方程组求解,采用置换矩阵和极大项两种方法,系统全面地解决了线性逻辑方程组、一般逻辑方程和一般逻辑方程组的求解问题.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

基于击键特征的手机用户身份认证系统

针对目前手机的高普及、高智能和安全性差的问题,统计并研究了不同手机用户使用手机的击键特征。依据数理统计知识发现其符合正态分布,进而设计和实现了基于击键特征的手机用户身份认证系统。经测试表明,该系统能显著提高手机安全性。     

带折痕的Loop细分曲面等距面处理算法

Loop细分曲面不同细分层次的网格面可作为不同加工工序的加工模型.现有等距面生成算法因未考虑折痕和边界的特殊情况,当折痕或边界存在时将会生成与预期结果有较大差别的等距面.给出了折痕等尖锐特征处极限等距位置的计算方法,以及根据尖锐特征点极限位置反求初始网格等距位置的Gauss-Jacobi迭代公式,并证明了其迭代收敛性.采用文中算法得到的等距网格面令人满意.     

A realistic theory for the “normal state” and pairing mechanism in the high-tc cuprates

The electronic structure of the high-T _c cuprates is studied on the basis of large-U and smallU orbitals. Two types of charge carriers are predicted: (i) spinless polarons with a very small bandwidth; (ii) anomalous carriers of both charge and spin. The results are consistent with many anomalous properties of the cuprates. The spinless polarons undergo a CDW transition, and transitions between pair states of the two types of carriers provide the pairing mechanism.The author acknowledges stimulating discussions with participants of the workshop. Some numerical work was performed at the Florida State University Computing Center.     

Bending-stretching analysis of thick functionally graded micro-plates using higher-order shear and normal deformable plate theory

In the present article, higher-order shear and normal deformable plate theory together with modified couple stress theory are developed to study the bending analysis of thick functionally graded rectangular micro-plates. One material length scale parameter is used for capturing the size effects. Utilizing the variational approach and also a principle of virtual displacement, a new form of equilibrium equations and the corresponding boundary conditions are derived. It is assumed that material properties vary through the thickness according to the power law function. Finally, an analytical solution for the bending problem of a simply supported FG rectangular micro-plate is presented.     

Optimization of correlated multi-response quality engineering by the upside-down normal loss function

Most of the published literature on robust design is basically concerned with a single response. However, the reality is that common industrial problems usually involve several quality characteristics, which are often correlated. Traditional approaches to multidimensional quality do not offer much information on how much better or worse a process is when finding optimal settings. Köksoy and Fan [Engineering Optimization 44 (8): 935–945] pointed out that the upside-down normal loss function provides a more reasonable risk assessment to the losses of being off-target in product engineering research. However, they only consider the single-response case. This article generalizes their idea to more than one response under possible correlations and co-movement effects of responses on the process loss. The response surface methodology has been adapted, estimating the expected multivariate upside-down normal loss function of a multidimensional system to find the optimal control factor settings of a given problem. The procedure and its merits are illustrated through an example.     

Modal Pure Type Systems

We present a framework for intensional reasoning in typed -calculus. In this family of calculi, called Modal Pure Type Systems (MPTSs), a propositions-as-types-interpretation can be given for normal modal logics. MPTSs are an extension of the Pure Type Systems (PTSs) of Barendregt (1992). We show that they retain the desirable meta-theoretical properties of PTSs, and briefly discuss applications in the area of knowledge representation.