格值上下文无关文法的范式

给出了格值上下文无关文法（LCFG）,Chomsky范式文法,Greibach范式文法的定义.证明了对任意的LCFG存在与之等价的Chomsky范式文法;给出了对任意的LCFG,存在与之等价的Greibach范式文法的条件.文中结论表明了LCFG的特性与其取值格的代数性质密切相关.     

非半简分叉问题的范式

根据文[1]给出了求解非半简分叉问题范式的方法．作为应用实例分析了一般非线性系统的非半简双零特征值问题的范式，给出用原系统系数表达的范式系数．     

中间逻辑中的良构范式

本文在中间逻辑中引入了良构范式的概念,为该类范式的研究提出了一个通用方法,并应用该方法证明了HT逻辑是存在一般蕴含范式的最弱中间逻辑,经典命题逻辑CPL是存在限制蕴含范式的仅有中间逻辑.     

基于学情分析的初中数学复习课教学范式研究——以“整式乘法”复习课为例

数据技术应用在教育领域能帮助教师分析学生的学情,使教师的教学更具有针对性.笔者在教育云平台的支持下,充分了解学生学情,根据学情调整教学,从而形成了一定的教学范式,优化了课堂的教学效果.     

关于如何利用Maple软件进行平面几何命题的验证的补充说明

文 [1 ]中通过定理 :设G是理想I的Gr bner基 ,f是k[x1 ,…xn]中的多项式 ,则f∈I的充分必要条件是f模G的范式为 0 .即通过对理想成员的判定 ,得出了验证几何命题是否成立的下述方法 :1、首先建立坐标系 ,将命题的条件和结论实行代数化 ,即转化成多项式的形式 ;2、求命题的所有条件 (用多项式表示 )所形成的理想I的Gr bner基Gs;3、求命题的结论f模Gs 的范式conc ;4、对范式进行判断 ,若范式为 0 ,说明命题结论成立 (或对 ) ;若范式不为 0 ,则说明命题结论不成立(或错 ) .但笔者认为该方法欠妥 ,还不够完善 ,有时会使我们得到错误的结论 ,…     

博奕论范式中的科层失灵

交易费用经济学范式中的科层失灵难以表述个人理性与集体理性的矛盾和冲突。本在博奕论范式中重新定义了科层失灵的概念，区分了科层横向失灵和科层纵向失灵，并分析了它们产生的原因——团队生产的外部性和不对称信息。     

基于混合fuzzy entropy-TOPSIS法的供应链范式选择

针对精益、敏捷、精敏供应链范式选择决策涉及到多种定性指标和定量指标这一特点,提出一种基于模糊集理论、熵和TOPSIS的混合型多属性决策模型。为了避免主观赋权法无法反映客观条件变化,或客观赋权法无法反映专家经验的双重弊端,在对定量指标赋权时,采用主观赋权的三角模糊数法和客观赋权的熵权法对定量指标进行组合赋权。对于定性指标仅依靠三角模糊数法确定其权重。然后,运用fuzzy TOPSIS法选择出最佳的供应链范式。最后通过实例对模型进行验证以及对评价指标权重进行敏感性分析,证实了该模型能为企业选择适用自身运作的供应链范式提供高效方法。     

中介逻辑的命题演算系统（MP^＊）的一些特征

本文证明了MP~*中的完全析取范式定理及其两个推论。文中也给出了判别Γ(?)A在MP~*中是否成立的算法。由此MP~*是可判定的。文中推论2说明了MP~*与经典逻辑的命题演算系统(P~*)的关系。     

用范式理论研究常微分方程焦点量问题*

利用范式与焦点量之间关系的一个定理并拓展了矩阵表示法,借助于计算机代数语言Mathe-matica的帮助,本文给出了一种计算常微分方程焦点量问题的新方法,利用这种方法可以计算常微分方程的任意阶焦点量,并通过一个算例验证了本文所提出的方法的正确性。这种方法的优点是简捷、方便、只进行简单的代数运算。     

旋转摆的周期单调性

考虑了一类旋转摆系统.该系统拥有至多5个周期轨族,通过计算椭圆积分得到了参数在不同取值范围内该系统各个周期轨族的周期单调性.该文的分析过程也为讨论这类周期单调性问题提供了一个比Abel积分更基本的方法.最后给出的数值仿真结果映证了文中的结论.     

Inexact restoration method for minimization problems arising in electronic structure calculations

An inexact restoration (IR) approach is presented to solve a matricial optimization problem arising in electronic structure calculations. The solution of the problem is the closed-shell density matrix and the constraints are represented by a Grassmann manifold. One of the mathematical and computational challenges in this area is to develop methods for solving the problem not using eigenvalue calculations and having the possibility of preserving sparsity of iterates and gradients. The inexact restoration approach enjoys local quadratic convergence and global convergence to stationary points and does not use spectral matrix decompositions, so that, in principle, large-scale implementations may preserve sparsity. Numerical experiments show that IR algorithms are competitive with current algorithms for solving closed-shell Hartree-Fock equations and similar mathematical problems, thus being a promising alternative for problems where eigenvalue calculations are a limiting factor.     

An algebraic approach for obtaining nilpotent normal forms in dimension 4

In this paper, an algebraic approach is presented for determiningthe normal forms of four-dimensional systems with a nilpotentlinear part. Certain transformations introduced in this caseresult in a simplified procedure for the calculation of normalforms. Thus, one does not need to solve a series of partialdifferential equations as usually required by the normal-formtheory; indeed, algebraic calculations are sufficient. The approachcan be applied to higher-order systems with a nilpotent linearpart as well. To illustrate the new approach, five examplesare presented. Normal forms and the associated coefficientsof two physical systems, an electric network and a mechanicalsystem, are fully analyzed.     

A numerical-analytical solution of multi-term fractional-order differential equations

In this paper, a solution to initial value problems for fractional-order linear commensurate multi-term differential equations with Caputo derivatives is presented. The solution is obtained in the form of a finite sum of the Mittag-Leffler–type functions and the meta-trigonometric cosine function by using a numerical-analytical method. The results of presented numerical experiments show that for high accuracy calculations of these functions, the multi-precision arithmetic must be applied. The approach for solving of the initial value problems for generalized Basset equation, generalized Bagley-Torvik equation, and multi-term fractional equation is demonstrated.     

Higher-Order Convex Approximations of Young Measures in Optimal Control

The general theory of approximation of (possibly generalized) Young measures is presented, and concrete cases are investigated. An adjoint-operator approach, combined with quasi-interpolation of test integrands, is systematically used. Applicability is demonstrated on an optimal control problem for an elliptic system, together with one-dimensional illustrative calculations of various options.     

The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations

The weakly dissipative version of the Kolmogorov-Arnold-Moser theory deals with the dynamics of systems that are a weakly dissipative perturbation of Hamiltonian systems. In the framework of this approach, both regular (asymptotically stable (unstable) periodic motions) and stochastic (Arnold’s web) dynamic properties are combined in the phase space. In this case, computer calculations are considerably simplified for the regular dynamics, which makes it possible to estimate physical parameters for stochastic components. A simple example of this approach is presented.     

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.     

Bessel,sine and cosine functions and extrapolation methods for computing molecular multi-center integrals

In this work, we present an extremely efficient approach for a fast numerical evaluation of highly oscillatory spherical Bessel integrals occurring in the analytic expressions of the so-called molecular multi-center integrals over exponential type functions. The approach is based on the Slevinsky-Safouhi formulae for higher derivatives applied to spherical Bessel functions and on extrapolation methods combined with practical properties of sine and cosine functions. Recurrence relations are used for computing the approximations of the spherical Bessel integrals, allowing for a control of accuracy and the stability of the algorithm. The computer algebra system Maple was used in our development, mainly to prove the applicability of the extrapolation methods. Among molecular multi-center integrals, the three-center nuclear attraction and four-center two-electron Coulomb and exchange integrals are undoubtedly the most difficult ones to evaluate rapidly to a high pre-determined accuracy. These integrals are required for both density functional and ab initio calculations. Already for small molecules, many millions of them have to be computed. As the molecular system gets larger, the computation of these integrals becomes one of the most laborious and time consuming steps in molecular electronic structure calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. Convergence properties are analyzed to show that the approach presented in this work is a valuable contribution to the existing literature on molecular integral calculations as well as on spherical Bessel integral calculations.     

Micromechanical modeling of twinning

There exist material models that incorporate mechanical twinning in a homogenized sense, or consider specific aspects, like grain refinement or texture evolution. However, since the RVE-technique became a standard method, it is possible to obtain more detailed predictions based on micromechanical models. In this work, an approach based on a nonconvex elastic potential and the corresponding results of FE calculations are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于超曲面的切面公式及其应用

本文给出任意ｎ维超曲面上任意一点的超切面方程的简洁的统一求法，将曲面方程微分即得切面方程．此法侧重对微分本质的理解，不需死记任何公式，计算简便．本文还讨论了此方法的理论意义，分别列举了到各种类型曲面的应用．     

Approximation procedures for the optimal control of bilinear and nonlinear systems

Optimal control problems for bilinear systems are studied and solved with a view to approximating analogous problems for general nonlinear systems. For a given bilinear optimal control problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. Also, the direct solution to the Hamilton-Jacobi equation is analyzed. A power-series approach is presented which requires offline calculations as in the linear case (Riccati equation). The methods are compared and illustrated. Relations to classical linear systems theory are discussed.