M-纤维式纤维化的特征与诱导M-纤维式纤维化

本文研究了M-纤维式纤维化的问题,利用M-纤维式升腾函数获得了M-纤维式纤维化的特征,以及证明了M-纤维式上纤维化诱导的映射空间之间的M-纤维式映射在一定条件下也是M-纤维式纤维化.     

新课标视角下的变式教学

变式教学不仅仅是教师设计变式,学生应付变式,教师应该让学生也加入到变式的行列,并培养学生主动对问题进行变式思考,让学生充分认识变式的自然性,变式的可行性,变式前后问题的关联性,从哪些方面去进行变式,只有这样,变式教学才更为有效和深入.     

善用习题变式教学 促进学生认知发展

习题变式教学是高中数学教师经常应用的一种教学手段.变式教学能帮助辨析正误,从而达到举一反三的教学效果;变式教学能有效内化知识,从而形成知识网络;变式教学能提升数学思维能力,从而提高、升华数学思想方法;变式教学能有效节约时间,从而提高教学效率…….但在实施变式教学时,切忌随意、盲目地进行变式,要结合教学内容和教学目标,适时适度地进行.那么,在何处进行变式教学更加适宜呢?下面以几个案例浅谈如何把握变式教学     

新授课概念性变式教学的三个环节

顾泠沅等学者把变式教学分为概念性变式和过程性变式教学两类.概念性变式教学突出对概念内涵的理解,注重概念的情景引入、语言转换等,逐步从概念的"标准变式"转向概念的"非标准变式",使学生获得对概念的多角度的理解;过程     

对称弧式连通凸多目标半无限规划的最优性

以弧式连通函数和对称梯度为基础,研究新函数在多目标半无限规划下的最优性理论.定义了一类新的弧式连通函数,对称弧式连通函数、对称拟弧式连通函数、对称弱拟弧式连通函数、对称伪弧式连通函数、对称严格伪弧式连通函数,讨论了这些函数在多目标半无限规划下的最优性.给出更加广义的弧式连通函数,将它们运用到多目标半无限规划.     

弱空间式Locale

空间式locale范畴SLoc是locale范畴Loc的余反射满子范畴,但对locale乘积不封闭．本文引入弱空间式locale,证明弱空间式locale范畴WSloc为范畴Loc的余反射满子范畴,且对locale秉积封闭．还证明了一个locale A是空间式的当且仅当它的枝映射localeN(A)是弱空间式的;一个空问式locale的每一个子locale都是空间式的当且仅当它的每一个子locale是弱空间式的．最后,证明了弱空间式性在定向函子下保持不变．     

初中数学教学中的变式教学

在初中数学教学中,变式教学是一个重要的环节.通过变式教学,可以帮助学生提高对知识的理解与认识,促进思维的深度发展,增强解决问题的能力.因此,教师需要重视变式教学,不断提升变式教学水平.本文中主要探讨了初中数学变式教学的常用方法,给出了对变式教学的几点思考.     

Radon不等式的新推广

利用Ho。lder不等式、Young不等式、Chebyshev不等式、幂平均不等式建立Radon不等式的指数推广形式,得到一个具有广泛应用价值的不等式.指出文[7]中给出的关于Radon不等式的推广结果是错误的,并在本文中作了修正.     

优化递进式变式题组应用的几点思考

何谓递进式变式题组?递进式变式题组是指在课堂教学中,为了达到某一教学目的,根据学生的认知规律,合理有效地设计一组数学问题,且这组数学问题又有一定的内在逻辑联系,即前一个问题是后一个问题的特殊情况,后一个问题是前一个问题的一般的情况,这样由特殊到一般的题目组合称为递进式变式     

巧设过一个定点的直线方程

关于直线方程的形式,教材中给出了斜截式、点斜式、截距式、两点式和一般式．学生根据具体题目选择相应的直线形式．当直线过一定点（x0,Y0）时,学生一般会用点斜式将直线设为y-Y0=k（x-x0）,     

The complexity of recursive constraint satisfaction problems

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem.     

集合上的递归函数

本文在Ｊｅｎｓｅｎ和Ｋａｒｐ工作的基础上引进了集合上的递归函数的概念．研究了递归集函数的初步性质，讨论了递归集函数与Ｊｅｎｓｅｎ和Ｋａｒｐ定义的原始递归集函数及递归数论函数之间的关系，并给出了ＺＦＣ的可定义集模型上递归集函数的范式定理．     

Recursive computational formulas of the least squares criterion functions for scalar system identification

The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided.     

Provably total functions of Basic Arithmetic

It is shown that all the provably total functions of Basic Arithmetic BA, a theory introduced by Ruitenburg based on Predicate Basic Calculus, are primitive recursive. Along the proof a new kind of primitive recursive realizability to which BA is sound, is introduced. This realizability is similar to Kleene's recursive realizability, except that recursive functions are restricted to primitive recursives.     

Endomorphisms of the group of all recursive permutations

We describe all endomorphisms of the group Aut_T ɛ of all recursive permutations. It is proved that the family of these endomorphisms is countable, and that they all are continuous and may be defined by some natural recursive operators. Orbits relative to the image of Aut_Tω prove to be recursive, and there exists a recursive model M such that this image is exactly its recursive automorphism group. There exists a universal endomorphism which contains, in a sense, all endomorphisms of that group. The universal endomorphism is unique with respect to some natural recursive equivalence. Supported by RFFR grant No. 093-01-01525. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 54–76, January–February, 1997.     

Asymptotic Normality of the Recursive M-estimators of the Scale Parameters

In this paper, the limit distributions of the recursive M-estimators of scatter parameters in a multivariate linear model setting are studied. Under some mild conditions, the asymptotic normality of the recursive M-esimtators is established. Some Monte Carlo simulation results are presented to illustrate the performance of the recursive M-estimators.     

并行准高斯高阶递归滤波算法研究

三维变分同化系统中一个重要的问题是背景误差协方差矩阵B及其逆的求解.背景误差协方差矩阵的水平变换部分采用递归滤波运算,可以简化矩阵的求解,解决了背景误差协方差矩阵B及其逆难以求解的问题.本文对准高斯高阶递归滤波的算法原理和过程进行了深入研究.因为递归滤波并行的低可扩展性制约了高阶递归滤波算法在三维变分同化系统中的应用,所以本文提出了阶段二维区域剖分并行化方法,实现了并行准高斯高阶递归滤波算法库.数值试验表明,四阶递归滤波1次的效果明显优于一阶4次的滤波效果;并且高阶递归滤波并行算法64核时能达到大约50倍的加速,并行效率高达78%,具有良好的加速效果和较强的可扩展性.     

Extension of partial recursive functions and functions with a recursive graph

It is proved that every degree of complexity of mass problems, containing the decision problem of a recursive enumerable set, contains also the problem of extension of a partial recursive function, the graph of which is recursive. Some properties of functions with a recursive graph are considered.Translated from Matematicheskie Zametki, Vol. 5, No. 2, pp. 261–267, February, 1969.The author is deeply indebted to V. A. Uspenskii for discussion of the results.     

Recursive automorphisms of recursive linear orderings

We characterize by classical order type those recursive linear orderings L such that every classically isomorphic recursive copy R of L has a non-identity recursive automorphism.