用数学方法学语文——语文教学法初论

叶老曾在一九八0年说过这样句意味深长的话:“语文教学殊难乐观。上海北京为人才荟萃之区,亦复各分派别,各自以为道在干我,而不甚顾及学生之实益,则彼此正同,至干他地,更难言矣。”语文教了廿年,纵观教坛,除了命题有了较大变化,似乎在教法上与自己读书时的老师所用变化不大(不是一点没有变化,这里指的是“大面积”上,教改先驱者除外),至少在教学应“顾及学生之实益”上点子还不多,教学思路还不宽,怎样让学生学得方便一些,获得的“实益”多一些(尤其在教法上)。

超数学——一种新的数学方法学与计算机科学

超数学作为一种新的数学方法学不同于经典数学的“定义—定理—证明”模型,而是基于“说明—断言—辩明”模型工作的,其基础是“操作逻辑”。它的理论与实现既为计算机科学提供基础。同时又借助于计算机科学的有关理论、技术和方法学,本文就这些方面概要地讨论超数学及其计算机科学的联系。

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

Fuzzy MP-filters Lattice on a Given FI-algebra

In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.

Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables

In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.

On Reverses of the Blaschke-Santalo Inequality for Convex Bodies

Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty＇s conjecture for projection bodies, respectively.

Simplicities and Automorphisms of a Special Infinite Dimensional Lie Algebra

In this paper, a special infinite dimensional Lie algebra is studied. The infinite dimensional Lie algebra appears in the fields of conformal theory, mathematical physics, statistic mechanics and Hamilton operator. The infinite dimensional Lie algebras is pop ularized Virasoro-like Lie algebra. Isomorphisms, homomorphisms, ideals of the infinite dimensional Lie algebra are studied.

Solution of ODE u″+p(u)(u′)2+q(u)=0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.

On Fair Prices of a Contingent Claim with Random Interval Payoff

In order to get the price of a contingent claim with random interval payoff, a concept of fair price was proposed based on weighted expected utility maximization. After setting up a programming model of maximizing the weighted expected utility involving basic securities and contingent claim,and using techniques in optimization analysis,explicit expressions of the fair price interval for a contingent claim were derived. Relations between acceptable price interval and fair price interval were discussed. It is shown that all fair prices fit the demand for acceptability of a market.

Form Invariant Sommerfeld Electrical Conductivity in Generalised d Dimensions

The Sommerfeld electrical conductivity is calculated in d dimensions following Boltzmann kinetic approach.At T = 0,the mathematical form of the electrical conductivity is found to remain invariant in any generalised spatial(d)dimensions.

Research on the fully fuzzy time-cost trade-off based on genetic algorithms

It is very difficult to estimate exact values of time and cost of an activity in project scheduling process because many uncertain factors, such as weather, productivity level, human factors etc. , dynamically affect them during project implementation process. A GAs-based fully fuzzy optimal time-cost trade-off model is presented based on fuzzy sets and genetic algorithms (GAs). In tihs model all parameters and variables are characteristics by fuzzy numbers. And then GAs is adopted to search for the optimal solution to this model. The method solves the time-cost trade-off problems under an uncertain environment and is proved practicable through a giving example in ship building scheduling.

An integrated model for predicting the flame propagation in crimped ribbon flame arresters

Crimped ribbon flame arresters are important safety devices in the chemical industry, especially for the danger- ous situations. Although proper design of arresters by the numerical simulation method is promising, its reliabil- ity and accuracy are dependent upon the mathematical model. In this work, an integrated mathematical model for the microchannel in the crimped ribbon flame attesters was set up; the fluid flow behavior and the sensitiv- ities of four chemical kinetics mechanisms of propane-air on the accuracy were analysed. It is shown that turbu- lence is predominant in the microchannel of the crimped ribbon flame arresters under the defiagration and detonation conditions, and a new quenching criterion for the numerical simulation is proposed. The kinetics mechanism of Mansouri et al. among the four ones is the most accurate due to the best agreement of the pre- dicted outlet temperature at the experimental flameproof velocity with the autoignition temperature of propane-air. The species mass fraction profiles and the temperature distribution, which are too difficult to mea- sure due to the tiny dimension of the microchannel in experiments, are captured. The fundamental insights into chemical reactions and heat loss are well portrayed. It can be concluded that the integrated mathematical model established in this work can be used as a reliable tool for modeling, selecting and designing such type of crimped ribbon flame attesters with the propane-air medium in the future.

Concurrence of Quantum States: Algebraic Dynamical Method Study XXX Models in a Time-Depending Random External Field

Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.

Prolongation Structure of Semi-discrete Nonlinear Evolution Equations

Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.

Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gompertz Model

A delayed predator-prey Gompertz model is investigated. The stability is analyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.

The Relations between Discrete Frames and Continuous Frames with Respect to （N, μ）

The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.

Nonfactorizable B→xcoK Decay and QCD Factorization

We study the unexpectedly large rate for the factorization-forbidden decay B →xcoK within the QCD factorization approach. We use a non-zero gluon mass to regularize the infrared divergences in vertex corrections. The end-point singularities arising from spectator corrections are regularized and carefully estimated by the off-shellness of quarks. We find that the contributions arising from the vertex and leading-twist spectator corrections are numerically small, and the twist-3 spectator contribution with chiral enhancement and linear end-point singularity becomes dominant. With reasonable choices for the parameters, the branching ratio for B → XcoK decay is estimated to be in the range （2 ～ 4）× 10^-4, which is compatible with the Belle and BaBar data.

On Pseudo Small Injective Modules

The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.