也谈函数单调性的几种运算法则

文[1]给出了函数单调,陛的四种运算法则,即线性法则、倒数法则、和差法则和根式法则,读后颇受启发．本文将探讨函数单调性的另外几种运算法则．     

工科高等数学中洛必达法则的教学思考

从教学法的角度对高等数学中洛必达法则的教学给出了我们的看法,剖析了洛必达法则的实质,对各种形式下的洛必达法则给出了一致性的简明证明,并探讨了在这部分知识的教学过程中的教学设计思路     

关于∞/∞型的L''''Hospital法则的一个改进

本文对现行的数学分析、微积分及其高等数学的教材中的∞/∞型的L'Hospital法则进行了一个改进,论证了该法则在无须考虑分子是否趋于∞的条件时,仍旧成立,利用了这个减弱了的∞/∞型的L'Hospital法则给出了一大类的极限问题的简单解法.     

带有讨厌参数的multi-armed bandit问题

这篇文章讨论了带有讨厌参数的multi-armed bandit问题。给出了关于该问题的所有ISS法则(不变的序贯抽样法则)之“遗憾”的渐近下界;找出了渐近最优的法则,即使“遗憾”达到上述下界的法则;并给出了构造渐近最优法则中要求的点估计和置信序列的一般性方法。还着重考虑了讨厌参数为刻度参数的情形。最后用一些技巧对几个常见的总体进行了具体计算。     

关于型的L′Hospital法则的一个改进

本文对现行的数学分析、微积分及其高等数学的教材中的 ∞∞ 型的 L′Hospital法则进行了一个改进 ,论证了该法则在无须考虑分子是否趋于∞的条件时 ,仍旧成立 ,利用了这个减弱了的 ∞∞ 型的 L′Hospital法则给出了一大类的极限问题的简单解法     

洛必达法则应用两则

指出洛必达法则在证明二重极限不存在时的一个应用,并指出了洛必达法则的一个推广。     

向量加法的“多边形法则”

我们可利用三角形法则对两个向量进行加减运算,但要是用三角形法则对平面上多个向量做加减运算,就显得太麻烦了．而改用多边形法则就十分方便．     

运算法则中条件的非必要性

微积分运算是通过运算法则实现的.极限、连续导教的四则运算法则,罗必达法则等等,都是高等数学中重要的运算法则.这些运算法则中的条件对结论的成立都是充分而非必要的,这同法则的使用条件有着严格的区别.教学中,如能加强对法则条件的非必要性的认识,帮助学生划清法则的使用条件同结论成立条件的界限.这对于深化概念,提高学生的逻     

Leibniz法则的推广

本文导出n=-1时的Leibniz法则,从而推广了原来的法则。利用推广后的法则,为计算Fourier级数展开时常碰到的分部积分,提供了简便的方法,从而节省了工程技术人员不可繁杂的计算。同时,利用推广后的法则,还很容易导出具有积分余项的Taylor展开式,从而为改革这部分内容的教学提供了新的材料。     

关于一些数值求积公式的渐近性

该文给出了一些数值求积公式的渐近性质,这些公式包括求积分的矩形法则、梯形法则和抛物线法则,包含于余项中的中介点的位置当积分区间的长度趋于零时被确定,对应于该法则的校正公式被得到,它们具有较高的代数精度,我们也进行了一些数值试验,得到较满意的数值结果。     

基于中介逻辑的时序逻辑系统

本文基于中介逻辑建立了一种中介时序逻辑系统ＭＴＬ（Ｍｅｄｉｕｍ Ｔｅｍｐｏｒａｌ Ｌｏｇｉｃ），文中着重讨论了ＭＴＬ的形式系统并给出了它的语义解释，证明了ＭＴＬ系统的可靠性．最后对ＭＴＬ系统和经典时序命题逻辑系统进行对比，指出经典时序命题逻辑系统是ＭＴＬ的子系统     

On triangular norm based axiomatic extensions of the weak nilpotent minimum logic

In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic (WNM) and its t‐norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM‐algebras (?????) and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM‐chains, in particular varieties generated by standard WNM‐chains, or equivalently t‐norm based axiomatic extensions of WNM, and we study their standard completeness properties. We also characterize the generic WNM‐chains, i. e. those that generate the variety ?????, and we give finite axiomatizations for some t‐norm based extensions of WNM. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preservativity logic: An analogue of interpretability logic for constructive theories

In this paper we study the modal behavior of Σ‐preservativity, an extension of provability which is equivalent to interpretability for classical superarithmetical theories. We explain the connection between the principles of this logic and some well‐known properties of HA, like the disjunction property and its admissible rules. We show that the intuitionistic modal logic given by the preservativity principles of HA known so far, is complete with respect to a certain class of frames.     

Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property

We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2^No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90.     

The Operators of Vector Logic

Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. Mathematics Subject Classification: 03B05, 03B50.     

扰动模糊命题逻辑的代数结构及其广义重言式性质

着眼于扰动模糊命题逻辑的代数结构,为研究二维扰动模糊命题逻辑最大子代数I2R及其广义重言式提供了一些代数理论基础,最后研究了子代数间广义重言式的关系.     

FLAGG AND FRIEDMAN'S TRANSLATION IS NOT FAITHFUL

We prove that Flagg and Friedman's translation from epistemic to intuitionistic predicate (propositional) logics is not faithful.     

对偶定理在三角教与学中的应用

数理逻辑中的对偶定理在计算中已经有广泛的应用，笔用对偶定理作为指导思想在三角证明题的构造，在条件等式的证明和三角化简求值中都有广泛的应用。可见对定理可以开拓研究领域，还可以使研究的三角题扩大一倍，更可以创造更多的三角题。     

On the infinite-valued Łukasiewicz logic that preserves degrees of truth

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens.While writing this paper, the authors were partially supported by grants MTM2004-03101 and TIN2004-07933-C03-02 of the Spanish Ministry of Education and Science, including FEDER funds of the European Union.