非正交小波的收敛性

研究非正交小波的收敛性.从尺度函数构造出的一组Riesz基出发,通过对函数f在不同序列处取值,构造两种不同形式的部分和序列,并证明这两种部分和序列与函数f的差都以无穷限反常积分收敛于0.     

绝对值函数的常见类型及求解策略

<正>一、常见的含绝对值的函数类型及其图象常见的含绝对值的函数主要包括y=|f(x)|和y=f(|x|)两种类型.由于自变量x的取值被分成若干不同的区间,因此,这些函数在不同的区间有不同的表达式:f(x),f(x)0,y=|f(x)≥|={-f(x),f(x)<0,{f(x),x 0,y=f(|x|)≥=f(-x),x<0.     

构造可导函数在解不等式中的巧妙应用

<正>构造函数法是一种常用的解题方法,比如函数与方程、不等式问题,小题中构造可导函数解不等式是常见题型,如果巧妙地构造函数,进而研究函数的性质,问题就会迎刃而解,下面就几种题型和大家一起交流一下。一、构造f(x)±g(x)型例1定义在R上的函数f(x),其导函数f'(x)满足f'(x)>1,且f(2)=3,则关于x的不等式f(x)相似文献   

由Leibniz公式得到的组合恒等式

对函数f(x)=exsinx和f(x)=exconx用两种不同的方法求高阶导数,得到结构优美的组合恒等式．     

用几个特殊函数构造零点问题中的辅助函数

在高等数学的很多问题,特别是中值命题中,常通过构造辅助函数的方法达到解决问题的目的,而辅助函数往往与题设中的已知函数密切相关,也就是说,辅助函数的构造离不开已知函数,如拉格朗日定理证明中的辅助函数φ(x)=f(α)f(b)b--fα(α)(x-α)与柯西定理中的辅助函数F(x)=-f(α)-gf((bb))--fg((αα))[b(x)-g(α)]均由题设中函数f(x)或g(x)及其端点的函数值构成。在中值命题中,还有较广泛一类零点问题需用已知函数的导数f‘(x)、ex等特殊函数去构造辅助函数,使命题的假设与结论之间搭建更为便捷的桥梁,从而达到化难为易的目的。本文就几个常用特殊函数对辅助函数的构造予举例说明。1用已知函数f(x)的导数f‘(x)构造辅助函数例1若函数f(x)在区间[α,b]上具有二阶导数,f(x)与f‘‘(x)同号,且f(x)在任何小区间上不恒为零,则f(x)或f‘(x)在[α,b]上至多有一个零点。分析:由结论,可考虑构造辅助函数F(x)=f(x)f‘(x),对其求导,便有f‘2(x)+f‘‘(x)f(x)。由已知条件知,f(x)在[α,b]可导,且x∈[α,b],F‘(x)=f‘2(x)+...     

外尔斯特拉斯逼近定理的概率证明

在外尔斯特拉斯逼近定理的各种证明中,伯恩斯坦的证明谅必最普通。它特别有感染力,因为它是构造证明。如果f是区间[0,1]上的连续实值函数,伯恩斯坦多项式序列     

函数图象的两种对称性

本文分析函数图象的两种不同类型的对称性:函数图象自身的对称性及两个函数图象的对称性。 1 问题的提出 题1 如果函数f(x)=x~2 bx c对任意的实数t都有f(2 t)=f(2-t),那么( ) (A)f(2)相似文献   

演好用导数证不等式的前奏——构造辅助函数

用导数证明不等式是证不等式的一种重要方法,证明过程往往简捷、明快,特别是证明超越不等式,更是如鱼得水.证明的第一步要考虑如何构造函数,是证明的关键.若函数构造恰当,把不等式的证明转化为利用导数研究函数的单调性或求最值,从而证得不等式.本文谈谈在用导数证明不等式时,构造辅助函数的几种常用途径.途径一构造差函数直接作差,即构造差函数,是构造辅助函数的最主要方法.例1求证:不等式x-x22<1n(1+x)0,所以y=f(x)在(0,+∞)上单调递增,因为x>0,且f(x)在…     

巧构函数求解含参数不等式问题

<正>构造函数法是高中解题中一种重要的解题方法.其基本思想是:通过构造适当的函数来转化问题,以利用所作函数的性质帮助论证或求解.比如,已知函数f(x)的定义域是R,f(0)=2,对任意的x∈R,f(x)+f'(x)>1恒成立,求不等式exf(x)>ex+1的解集.从已知"条件x∈R,f(x)+f'(x)>1恒成立"来看,自然想到依托f(x)来构造一个函数,然     

由两个已知bent序列构造bent序列

文献[1-5]都讨论了由给定的bent函数（或序列）构造新的bent函数（序列）的方法,本文证明文献[5]中的方法实际上可以通过结合文献[1]和文献[3]的方法而得到的,从而对给定的两个bent序列可以得到比文献[5]中构造出的序列更多的bent序列。     

果蝇DNA和基因间序列的两个信息参数沿染色体分布

以果蝇染色体的全序列和基因间序列作为研究对象.分别用描述序列构成的两个信息参数X和F分析两类序列沿着染色体分布特征,并着重讨论染色体着丝粒及其周围区域的分布规律,用线性拟合和多项式拟合分析染色体各类序列沿染色体的统计分布特征(学生t检验),分析各个参数的平均值在染色体不同区域的分布.     

On the construction of cryptographically strong Boolean functions with desirable trade-off

INTRODUCTION A variety of desirable criteria for functions have been identified: balancedness, local and global ava-lanche characteristics, high nonlinearity, etc. These properties are also very important for cryptographic purpose. Obtaining optimal tradeoffs among so many properties is hard. If we take into account more crite-ria, it is more difficult to generate Boolean functions satisfying those properties purely by constructive algebraic methods. How to construct Boolean func-tions …     

Banach空间中k-次增生算子方程带误差的迭代序列的收敛性

在实Banach空间中,研究了L ipsch itz的k-次增生算子方程x＋Tx=f和k-次散逸算子方程x-λTx=f的解的带误差的收敛性和稳定性问题,并给出了收敛率的估计式,从而在很大程度上统一和发展了有关文献中的相应结果.     

哲学思维方式总体演变初析

哲学的发展、不同哲学形态的衍生，都源于哲学思维方式的改变。目前对哲学发展的总体性研究，多以哲学研究重心的转移为尺度，把哲学总体划分为本体论哲学、认识论哲学、方法论哲学的演化序列，而未涉及这种演变中所含的哲学思维方式的演变及其规律性。必须对此发展过程进行考察，并发掘出其内在规律，明确实践思维方式的历史土壤、产生的历史必然性，从而确立其应有的历史地位。     

Iteration sequences and their representations

Given a function f and an initial value a ₁, we consider properties and representations of the iteration sequence a ₁ , f(a ₁ ), f(f(a ₁ )),.... Because iteration sequences often cannot be expressed in explicit algebraic terms, there is an emphasis on using various graphical and numerical representations. An empirical investigation examined the influence of representations on the discovery of properties and on problem solving abilities for iteration sequences. A total of 79 students (11th graders) and 22 secondary mathematics teachers participated. The empirical study was implemented with a computer program, developed by the author.     

果蝇基因组中两类序列的信息参数沿染色体的分布

由于真核生物基因组染色体上各种序列的组织和安排复杂,所以我们把果蝇染色体上顺次排列的DNA序列分成内含子和编码序列两类.分别用描述序列构成的四个信息参数,分析各类序列沿着染色体分布特征,并着重讨论染色体着丝粒及其周围区域的分布规律,并解释引起这些特征的原因.用线性拟合和多项式拟合分析染色体各类序列沿染色体的统计分布特征(学生t检验),分析各个参数的平均值在染色体不同区域的差别.果蝇染色体参数X值是由D1(碱基偏置)和D2(碱基关联)值共同决定的,但果蝇染色体的编码序列参数X分内含子序列相比,分布没有趋同性.显示出编码序列跟内含子序列染色体的分布不同.     

A method for sequencing instructional objectives which minimizes memory load

A Gagné-style learning hierarchy often permits a large number of alternate linear arrangements (sequences) of instructional objectives. An alternative is described here to traditional methods of choosing between sequences. Its premise is that, for every sequence, a value temed thememory load can be calculated which is theoretically related to the probability that students will fail to recall prerequisite objectives. A graph theoretic approach is taken in presenting an algorithm which generates a minimal memory load sequence from a learning tree, a restricted but frequently encountered type of learning hierarchy. In order to assess the effectiveness of the algorithm in generating low memory load sequences when given hierarchies which are not trees, it was applied to several published examples of learning hierarchies. The results indicated that the algorithm is effective as an heuristic, especially when combined with a hill-descending procedure which attempts to incrementally improve the generated sequence.     

语料库驱动的语义序列研究——以搭配框架为例

Hunston(2008)提出了语义序列的概念、构成及其研究方法。语义序列指在语料库中有规则地出现的一系列意义成分。本文以Hunston(2008)所论为方法框架,以英语搭配框架"the*of"为研究焦点,以语料库驱动的方法探讨语料库证据显示的不同语类如医学英语和传记英语的语义序列。结果显示,医学英语形成与医疗、疾病、变化等有关的语义序列,而传记英语形成与生平、经历、时间等有关的语义序列。因此,语义序列能够反映语篇特征,对语类区分和预测具有重要意义。     

A Longitudinal Investigation of Siblings’ and Friends’ Features of Connectedness and Interaction Quality During Play

The present study examined features of sibling and friend dyads’ connectedness (e.g., length and emotional tone of connected sequences) and the quality of the dyads’ interactions during play from early to middle childhood. Forty-four families with a 4-year-old focal child were observed at Time 1 (T1) and again at Time 2 (T2) at age 7 in two separate play sessions (i.e., sibling and friend). Play sessions were coded for interaction quality (i.e., conflict, cooperation). Based on previous research, features of the sequences (i.e., emotional tone, length of sequence) were compared across relationship and time. Research Findings: Findings revealed similarities in the dyads’ interaction quality, with both siblings and friends increasing in cooperation over time. Similarly, the emotional tone of siblings’ and friends’ connected sequences was more likely to be positive than negative; however, siblings’ sequences were short rather than long, whereas friends’ sequences were more likely to be long than short. Practice or Policy: These findings provide new insights into children’s connectedness in child-child relationships and changes in connectedness across development from early to middle childhood. The study highlights the importance of observing the dyad when using a relationships theory framework to examine children’s interactions.     

Increasing Steps in Recall of Events: Factors Facilitating Immediate and Long-Term Memory in 13.5- and 16.5-Month-Old Children

Children late in the second year of life show patterns of event recall similar to those of older children: (a) well-ordered immediate and delayed recall, and (b) facilitation of recall by familiarity and by enabling relations. We used elicited imitation to test whether the patterns extend to children early in the second year. In Experiment 1, 13.5- and 16.5-month-olds accurately recalled familiar and novel 2-act sequences immediately and after a 1-week delay. For 16.5-month-olds, recall was facilitated by familiarity and by enabling relations; for 13.5-month-olds, only enabling relations facilitated recall. In Experiment 2, verbal cues were used to test immediate and 1-week delayed recall of 3-act sequences. For both ages, recall was facilitated by familiarity and by enabling relations. Experiment 3 verified that the verbal information served to cue recall of previously experienced events, not to "suggest" sequences that could be performed. Together the results demonstrate that children as young as 13 months can recall specific events after a delay. They also suggest development in sensitivity to factors that facilitate recall.