2012年中考专题复习(1)——“数与式”

中考内容要求实数与代数式所考查的知识有:有理数,倒数,相反数,绝对值,数轴的运用,实数的大小比较,乘方,科学记数法,有效数字,二次根式,实数的估算,列代数式,解释代数式,求代数式的值,探求数与式的规律.     

借形解题应防止片面引起的失误

在中学,乃至大学的数学,都应该提倡“形数结合”,解析几何的诞生正是形数结合的光辉范例,在解析几何中,我们都知道,通过量(坐标)的演算,给许多几何问题提供了准确而又普遍的解法;反过来,给数与算式赋以适当的几何意义,又可借助图形的几何性质和直观形象,使困难的问题迎刃而解,同时,图形生动鲜明的形象,既便于理解又易于记忆,因此,这借几何直观解决问题的方法,倍受广大师生的青睐,近年来,出现了不少这方面的好文章,对数学的教学和传播起了很大的推动作用,然而,图形的描绘,显然不可能达到100％的精确,特别是较为复杂的图形;图形的多     

我与珠心算

提起珠心算,我想说的太多了。刚进一年级实验班,第一件让我傻眼的事就是珠心算了。当老师将小小的算盘轻轻放在我的面前时,我吓坏了,我的爸爸、妈妈都是会计,这可是大人们用的东西呀,我的天,我才几岁呀。刚开始练的时候,我的手不听话,不是多带珠就是少拨珠,我手用力,脚用力,浑身上下都用力,都不行,急得我眼里那些不争气的小水滴一个劲儿往下掉。这时,一只温暖的手轻轻地抚在我的头上,睁眼一看,一双慈爱的目光,温和地看着我,是张老师。她不慌不忙地对我说:“眼泪只会让你丧失信心,珠心算不是一两天就能练好的,只要你天天认真去练,就像你练钢琴一样,你一定会学好的。今天你为它流泪,明天你会为能应用它而骄傲的。”老师的话使我平静了。在以后的日子里,我不再急躁,而是跟在老师的后面一步一步地练,老师布置的作业我总是多练几遍,功夫不负有心人,经过半年时间的苦练,我的珠算水平已经突飞猛进了,手像在算盘上飞舞一样,连做会计的爸爸、妈妈也比不上我的速度,心算的速度快得令爸爸、妈妈、爷爷、奶奶刮目相看,终于,被老师选为小选手。又经过半年的苦练,我终于和其他三名同学代表如皋去南通参加比赛,我获得了听心算满分,个人全能三等奖好成绩。当登上领奖台,捧着金灿...     

境由心生

在现实生活中,有人总是企盼没有的,却忘了现成的,追求遥远的,却无视身边的永无止境的物质追求,让人变得贪婪;盲目的攀比,让人抱怨生活的不公境由心生,心情不好,就会失去一次次微笑着感受人生的喜悦,就会失去不少在情绪乐观时可以获得成功的机会……其实,在这个纷繁复杂、充满诱惑的社会,不羡慕别人,不轻贱目己,过自己喜欢过的日子,就是最好的日子,活自己喜欢的活法,就是最好的活法,按自己的天性度过自己的时日,就是天堂般的日子!     

换种思路求解一道高考题并探究

求最值,一直是高考的重点,求解的方法很多,有配方法,判别式法,不等式法,换元法,导数法等等,对于特定的题目选择合适的方法,有利于解题速度的提高,有利于解题结论正确性的提高．     

“创新”可从“论文”始

作为高中生 ,要想具备科学精神和创新思维习惯 ,可能有很多途径 ,其中有一条重要途径 ,成为众多成功的经验之谈 ,那就是论文写作 .一篇论文 ,或者介绍自己的学习心得 ,或者阐述自己的学习成果 ,或者归纳自己的解题经验 ,或者表达自己的某种想法 ,或者解答别人提出的问题 ,或者提出问题引发同仁讨论 ,你都必须有自己的思考 :首先是价值判断 ,认为你的所思所写有自己的东西 ,能够反映自己的水平 ,别人读后可以从中获益 ;其次 ,你必须把要写的东西弄明白 ,这就要广泛地收集材料 ,进行必要的推理 ,还要向老师请教与同学磋商 ;其三 ,论点清楚了 ,…     

推广应用优选法的体会

优选法是一种科学方法,特别是它的思想方法——重实践,抓主要矛盾,以辩证唯物主义的哲学思想为指南,用理论联系实际的内容,深入浅出地引出既简单又通俗易懂的多种计算方法,使工农兵易于掌握,因此,优选法的推广和应用,深受广大工农兵的欢迎,取得了可喜的成果.但是,任何新生事物都是在斗争中产生、在斗争中发展的.所以,努力学习马列主义、毛泽东思想,提高路线斗争觉悟,在实践中分析各种矛盾的内在联系,抓准主要矛盾,是推广应用优选法的根本.     

高考专题复习系列讲座——直线、平面和简单几何体

[考试内容及考试要求]考试内容:平面及其基本性质,平面图形直观图的画法,平行直线,直线和平面平行的判定与性质,直线和平面垂直的判定,三垂线定理及其逆定理,两个平面的位置关系,空间向量及其加法、减法与数乘.空间向量的坐标表示,空间向量的数量积,直线的方向向量,异面直线所成的角,异面直线的公垂线,异面直线的距离,直线和平面垂直的性质,平面的法向量,点到平面的距离,直线和平面所成的角,向量在平面内的射影,平行平面的判定和性质,平行平面间的距离,二面角及其平面角,两个平面垂直的判定和性质,多面体、正多面体、棱柱、棱锥、球.考试要…     

过程参数未知时的连续检验问题

对连续检验问题,Page(Page,1954）提出的累积和控制图（CUSUM）已被证明在检测小的漂移时效果很好,然而,当受控过程的参数未知时,CUSUM的应用受到限制,Quensenberyy（1991）提出用变换的方法将观测值中的未知参数消去,在原假设“过程保持一致”成立的条件下,变换得到的Q统计量为独立同分布的标准正态变量,这里有二个问题：问题之一是,如果过程中有一漂移发生,变换得到的Q统计量的分布就很复杂,漂移对Q统计量的均值的影响是非时间齐次的,随着过程的推移,漂移对Q的均值的影响越来越小,因此,基于Q统计量的检验问题与一般的连续检验问题是不同的,好的检验方法应将这种不同反映出来,因此,基一种基于Q的新的累积和检验统计量,模拟结果显示,这种统计量的效果是不错的,问题之二是,当过程方差未知时,Q统计量的值的计算很难,它需要计算t分布的分布函数和正态分布函数的逆函数,这在实际使用中几乎是做不到的,本文提出一种近似方法,它不需计算复杂的分布函数,而是给出近拟服从标准正态分布的统计量为作为检验统计量,模拟研究的结果显示,这种近似的效果很好,它的各项指标与精确方法的相应指标非常接近。     

共同探究,享受数学

众所周知,数学很重要,这很大层面上是由高考指挥棒决定的,学生在沉重的数学作业负担下,大多是疲于应付,很少有人真正体验到数学内在的美,学会享受数学.笔者从事高中数学多年,做了一点有益的尝试,让学生从多种角度理解数学,师生平等,教师做好组织、引领工作,充分调动学生学习数学积极性,各抒己见,经常是一个平淡的问题,往往出现多种漂亮的解法,碰撞出思维的火花,师生乐在其中,一同享受数学带给我们的快乐.现举两个案例,供大家分享.     

信用传染违约Aalen加性风险模型

本文考虑了基于加性风险模型的信用风险违约预报模型,不但考虑了宏观因素和公司个体因素,并且通过引入行业因素来刻画公司间可能存在的不同于宏观因素的信用传染效应,由此克服了以往模型对违约相关性的低估.本文在参数加性风险模型下给出极大似然估计及渐近性,提出两种估计方法并比较二者表现,得到最优权估计更加有效.同时本文还考虑了半参数的风险模型,并基于鞅的估计方程得到其估计及渐近性,均得到不错的结果.     

Exploring an unknown graph

We wish to explore all edges of an unknown directed, strongly connected graph. At each point, we have a map of all nodes and edges we have visited, we can recognize these nodes and edges if we see them again, and we know how many unexplored edges emanate from each node we have visited, but we cannot tell where each leads until we traverse it. We wish to minimize the ratio of the total number of edges traversed divided by the optimum number of traversals, had we known the graph. For Eulerian graphs, this ratio cannot be better than two, and two is achievable by a simple algorithm. In contrast, the ratio is unbounded when the deficiency of the graph (the number of edges that have to be added to make it Eulerian) is unbounded. Our main result is an algorithm that achieves a bounded ratio when the deficiency is bounded. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 265–297, 1999     

Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

Estimation of error variance in ANOVA model and order restricted scale parameters

We consider the estimation of error variance in the analysis of experiments using two level orthogonal arrays. We address the estimator which is the minimum of all the estimators which we obtain by pooling some sums of squares for factorial effects. Under squared error loss, we discuss whether or not this estimator uniformly improves upon the best positive multiple of error sum of squares. We show that when we have two factorial effects, we obtain uniform improvement. However, we show that when we have more than two factorial effects, we cannot necessarily obtain uniform improvement. Further, the above results are applied to the problem of estimating the smallest scale parameter of chi-square distributions.     

Asymptotic behaviour of a closed‐loop thermosyphon with linear friction and viscoelastic binary fluid

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed‐loop thermosyphons even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions.     

The value of foresight

Suppose you have one unit of stock, currently worth 1, which you must sell before time $T$. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see $a$ units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight.     

Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Hereditary atomicity in integral domains

If every subring of an integral domain is atomic, we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in terms of atomic overrings. Then we use this characterization to determine the fields that are hereditarily atomic. On the other hand, we investigate hereditary atomicity in the context of rings of polynomials and rings of Laurent polynomials, characterizing the fields and rings whose rings of polynomials and rings of Laurent polynomials, respectively, are hereditarily atomic. As a result, we obtain two classes of hereditarily atomic domains that cannot be embedded into any hereditarily atomic field. By contrast, we show that rings of power series are never hereditarily atomic. Finally, we make some progress on the still open question of whether every subring of a hereditarily atomic domain satisfies ACCP.     

基于跳扩散过程的可转换债券的定价

本文标的股票的方程采用跳扩散方程,首先规定一个跳跃的涨跌区间,这样就可以很快的找出跳跃点,我们根据跳跃点将股价聚类,然后把各个类看成是总体中抽取出来的一个样本,我们就可以估计出跳扩散方程中的所有参数.由于我们的标的股票的方程是含跳过程,因此无法找出完全保值的自融资策略,但我们可以根据风险最小化的原理给出可转换债券的价格,最后运用Monte Carlo模拟计算出了南京水运转债在0时刻的价格。     

Classification of quintic eutactic forms

From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.