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．     

一种改进的范式方法的应用

对ZHANG Wei-yi和K.Huseyin等人提出的改进的范式方法作了进一步发展，引进了不同的分析过程，使其更适合于符合推导语言（如MAPLE）的应用，与过去的方法相比，在实际计算范式时，文中介绍了分析过程更简便，实用，具有更多的优越性，文中3个范例说明了此结论。     

MP中的析取范式和合取范式

本文讨论了中介逻辑命题演算(MP)的形式系统。它可主要分成三个部份。第一部份是析合范式(合析范式)的普遍存在性证明,即对任何一个MP中的合式公式,恒存在至少一个析合范式(合析范式)与它等价(?)。第二部份是关于指派及逻辑永真性、可满足性的一点讨论。主要结果是:任何逻辑永真公式,当且仅当满足在任何指派下恒取真值,也当且仅当满足它可由空集推导出来,正巧了分别属于语义和语法的范畴。最后,应用范式我们得到一些很有意义的结果,特别是用了全范式这个概念之后。其中重要的就是:任何一个合式公式,如果取到真值,也取到假值,则它必也能取到中值,这正体现了贯串整个中介逻辑的形式系统的中介原则,给出了中介原则在MP中的一个形式证明。     

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 ,…     

模糊逻辑中的一些问题研究

本文讨论了模糊逻辑中存在的一些问题。特别地，对与、或、非和蕴含作了更深入的讨论。     

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。     

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。     

一种带压缩和动量步的联邦学习算法CSCD

1引言联邦学习(Federated Learning)是一种分布式学习范式,这一概念自2016年被谷歌研究院提出以来就一直受到广泛的关注和研究;.本文研究的是联邦学习中存在的一类优化问题,该优化问题可以抽象成。     

错误系统结构分析与置换变换研究北大核心

为了研究具有基本结构的系统错误和错误的避免或消除的方法,在简单分析模糊错误系统和一般系统存在的六种静态基本结构,串联、并联、扩缩、蕴含、反馈和其它基本型后,研究用基本结构中的其中一种或多种结构去置换其它一种或多种基本结构时模糊错误系统的错误变化的逻辑规律,并以系统结构图,错误函数和逻辑命题去形式化描述,接着还研究了模糊错误系统的动态的结构变化的几种形式.     

Normal forms for fuzzy logics: a proof-theoretic approach

A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In particular, a normal form with simple McNaughton functions as literals is generated for ?ukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic.     

Implicational (semilinear) logics I: a new hierarchy

In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of logics expanding Leibniz hierarchy: the hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field.     

双霍普夫分叉规范型的计算

研究了一般四维系统的双霍普夫分叉的规范型,提出计算这类规范型的一种方法.作为应用,最后给出了一个例子.     

A logic of implications in algebra and coalgebra

Implications in a category can be presented as epimorphisms: an object satisfies the implication iff it is injective with respect to that epimorphism. G. Ro?u formulated a logic for deriving an implication from other implications. We present two versions of implicational logics: a general one and a finitary one (for epimorphisms with finitely presentable domains and codomains). In categories Alg Σ of algebras on a given signature our logic specializes to the implicational logic of R. Quackenbush. In categories Coalg H of coalgebras for a given accessible endofunctor H of sets we derive a logic for implications in the sense of P. Gumm.     

Symmetric implicational method of fuzzy reasoning

Fuzzy reasoning should take into account the factors of both the logic system and the reasoning model, thus a new fuzzy reasoning method called the symmetric implicational method is proposed, which contains the full implication inference method as its particular case. The previous full implication inference principles are improved, and unified forms of the new method are respectively established for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) to let different fuzzy implications be used under the same way. Furthermore, reversibility properties of the new method are analyzed from some conditions that many fuzzy implications satisfy, and it is found that its reversibility properties seem fine. Lastly, the more general α-symmetric implicational method is put forward, and its unified forms are achieved.     

Normal forms for differentiable maps near a fixed point

We propose in this paper a significant refinement of normal forms for differentiable maps near a fixed point. We give a method to obtain further reduction of classical normal forms with concrete and interesting applications. Our method leads to unique normal forms either with respect to general diffeomorphisms in certain cases or with respect to near identity diffeomorphisms in other cases. Our approach is rational in the sense that if the coefficients of a map are in a field K, so is its normal form. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stanley decomposition of the joint covariants of three quadratics

The Stanley decomposition of the joint covariants of three quadratics is computed using a new transvectant algorithm and computer algebra. This is sufficient to compute the general form of the normal form with respect to a nilpotent with three 3-dimensional irreducible blocks.      

线性规划的教学

作者给出了线性规划的一个更为一般的表现形式 ,明确定义了具有标准型形式的线性规划的等价变换 ,使得单纯形法的讲解更清晰简洁 ,便于学生掌握 ,且兼顾了数学形式美和逻辑美的学科特点 ;文中也体现了重视实例式教学的想法 .     

Proof complexity of intuitionistic implicational formulas

We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of intuitionistic extended Frege (EF) or substitution Frege (SF) proofs up to a polynomial. On the other hand, EF proofs in the implicational fragment of IPC polynomially simulate full intuitionistic logic for implicational tautologies. The results also apply to other fragments of other superintuitionistic logics under certain conditions.In particular, the exponential lower bounds on the length of intuitionistic EF proofs by Hrube? (2007), generalized to exponential separation between EF and SF systems in superintuitionistic logics of unbounded branching by Je?ábek (2009), can be realized by implicational tautologies.