一类数论函数均值的误差项

设n为任意的正整数，σ(n)为n的除数和函数，E(x)表示和式∑n=x σ（n）/n渐近公式中的误差项。研究了E(x)的性质，给出∑n=xE（n）和∫1^xE(t)dt的两个有趣的渐近公式。     

数学竞赛与等幂和的整除性

等幂和最Sm(n)=1^m 2^m … n^m及Fm(n）=1^m-2^m… (-1)^m-1n^m是一个古老而有趣的难题，曾有许多人进行了研究，它们在数论中有着重要的作用本文运用配时原理和数论的方法来研究等幂和的整除性问题，证明了当n为自然数m为奇数时必有n(n 1)|2Sm(n),n 2xSm(n)；当m与n奇偶相异时．必有n 2xfm(n),n|2fm(n)；当m与n奇偶相同时，必有n 1|2fm(n)。     

关于三角形数补数及其渐近性质

对任意正整数n，设a(n)表示n的三角形数补数，即就是a(n)是最小的非负整数使得n a(n)为一三角形数m(m 1)/2．用初等和解析的方法研究了三角形数补数列{a(n)｝(n=1，2，3，…)的渐近性质，给出了两种不同类型的渐近公式．     

二项展开式系数最大（小）项的求法

一、(x y)^n型展开式中系数最大项的求法 在(x n)^n的展开式中，二项式系数就是项的系数，展开式的中间项就是系数最大项．当n为偶数时，中间项是第(n/2 1)项；当n为奇数时，中间两项是第(n 1/2)项和第((n 1/2) 1)项(注意：此两项虽然系数相同，但字母的次数并不相同)．     

例说数学解题时信息的获取和运用

题目已知函数y=f(x)的图象是自原点出发的折线．当n≤y≤n 1(n=0，1，2，…)时，该图象是斜率为6n的线段(其中正常数b≠1)，设数列{xn}由f(xn)=n(n=1，2，…)定义.     

智能篮球

我家楼(lóu)下有一个大操(cāo)场(chǎng)，每天都有好多大哥哥在那里打篮(lán)球(qiǘ)。他们投(tòu)得很(hěn)准(zhǔn)，我好羡(xiàn)慕(mù)他们呀!我也很喜欢打篮球，但(dàn)因(yīn)为(wèi)我还小，总(zǒng)是投不进篮筐(kuāng)，有时球掉(diào)到我身(shēn)上，还很疼(téng)。我想，如     

分拆函数p(n)的下界

设n为正整数,p(n)是正整数n的分析函数，改进了[4]的结果，得到了 一个关于p(n)的新下界。     

自然数方幂和的求法

∑i=1^n i^m(n，m是正整数)叫做自然数的m次方幂和。如何把∑i=1^n i^m表示成n的多项式Fm(n)，是历代数学家们不断探求的内容。从古代的欧几里德到现代的陈景润等，大多走离散的路子，所以过程较繁，也仅给了m在20以内的Fm(n)的表达式，本文把这个问题转化为研究∑i=1^n(i x)^n(x∈R)的表达式，化离散为连续，从而求得Fm(n)的递推表达式，使这个问题得到彻底的解决。     

关于一类p叶解析函数的性质

设Ap(n)为在单位圆盘内形如f(z)=z^p ∑k=n^∞αp k^Zp k的解析函数类。Hp(n,λ，α，b）为Ap(n)的一个子类。在这篇文章中，我们得到了类Hp(n,λ，α，b）中函数的偏差定理，系数不等式及卷积性质。     

一道对数比较大小题目的多种解法

扭匆对于n>1，n〔N’，试比较109。(n 1)与109。 ;(n十2)的大小.解法1:作差比较法. 109。(n 1)一109。一 ，(n 2)= l 109。 一n一109。 1(n 2)一竺卫丝遍塑口里遍述二上丝> 109。 1刀109， In 109。 In > 109。 In 109二(n l)>109。 1(n 2).解法2:作商比较法.由已知得109。(n l)>o，logn ，(n 2)>0. 109。 1(n 2) 109。(n 1)一「109， ，(n 2) 109。 ，n]’一‘09· ’、”卞‘少’‘。g” ’儿\L—-一了—一—」一厂109。 ，(nZ Zn)]2一「109。 ，(n 1)2]2_1—l—l、、、l—l—工L乙」L乙J 109。(”十1)>109。 一(n 2).点评:以上两种解…     

Semantic and Pragmatic Approaches to Presupposition

Presupposition is widely studied in the field of linguistics nowadays while it was firstly put forward in philosophy.Early study ex amined it from semantic approach,which treated it as the relation between two propositions.In 1970s,it was found presupposition was also a pragmatic concept,which held that presupposition varied with context.The author holds that semantic approach can’t solve all the com plex problems while it’s the basic part about the issue.Only through the pragmatic approach can we study it dynamically.     

The Cost of Higher Education Cannot Continue to Rise Unchecked

A system of restricted admission to certain faculties has been in operation in Netherlands universities for the past two or three years. Limiting the number of first-year students admitted to certain faculties was found necessary in order to ensure the maintenance of teaching standards, which could otherwise not be guaranteed. For financial reasons it is practically impossible to create the additional educational facilities which would be necessary if all applicants were to be admitted; and for this reason it was decided to institute a "student freeze" in some subjects which, it was hoped, would be of a temporary nature.     

论苏轼的豪放词

苏轼的豪放词,在中国词史上有着十分重要的意义。本文认为:苏轼豪放词的形成,首先取决于他的独特的个性性情,其次与他的词学理念及他的词的创作主张有关系,同时也是北宋诗文革新运动的必然产物。苏轼豪放词的总体风貌特征,可以用“豪放”、“旷达”概括。苏轼豪放词的文学史意义,首先是打破了“诗庄词媚”界限,“以诗为词”,扩大了词的表现功能,提高了词的境界;其次突破了词的声律的束缚,真正实现了词体的大解放,使词从音乐的附属品转变为一种独立的抒情诗体;第三,对词的语言进行了革新,“一洗绮罗香泽之态”,以清新韶秀见长;第四是抒情言志,自我形象超逸,个性分明。     

明代科考复试述略

科举考试的复试起于唐宋,明代沿袭其旧,而未形成制度,系偶一为之。明代科考复试类别,约略有三：一是处于政治考量,二是出于党派斗争和纠正弊端,三是出于表明清白而自请。同时,明代科考复试有一定的程式,如考试官选任、试题的选取、以及考试地点、时间、监考、阅卷、裁定等,都是临时决定,与乡会试程式不同。复试之举虽有一定的威慑力,但也很难以从根本上杜绝科考弊端的产生和蔓延。     

赞扬与批判:现代性的选择和失落——重读萧也牧《我们夫妇之间》

萧也牧《我们夫妇之间》是新中国成立后最早发表的小说之一。发表之初,受到了当时文坛的重视和赞扬,不久,旋即受到了批判,对它的批判构成了当代文学史的一次重要事件。从现代性的角度解读这一事件,认为这是革命现实主义文学对启蒙现实主义文学消除的开端,在当代文学史上产生了广泛而又深刻的影响。     

叶燮正变观的形成

叶燮的正变观是在继承以《诗大序》为代表的儒家文艺正变思想的基础上，同时借鉴了钱谦益、黄宗羲等人的主变思想，并在与汪琬等崇正排变的观点的论争中提出来的。叶燮的正变观表现出主变而崇正的特点。“主变”是主艺术形式之变，强调艺术形式风格发展的独创性和多样性；“崇正”是崇尚儒家温柔敦厚的诗教传统，要求文学艺术要充分发挥其政教功能。同时它也强调温柔敦厚不受形式风格的制约，温柔敦厚为体，形式风格为用，任何艺术形式风格都是为温柔敦厚的本质服务的，这就充分肯定了多种多样的艺术风格存在的合理性，在一定程度上补充和完善了儒家一向主和平之音而排怨愤之调的诗教传统，在理论上发展了儒家温柔敦厚的诗教思想，具有积极的进步意义和价值。     

Challenging behaviour: the perceptions of teachers of children and young people with severe learning disabilities

This paper reports the findings of a study which aimed to elicit teachers' perceptions of pupils' challenging behaviour. Teachers were asked to indicate: which aspects of challenging behaviour concerned them; their responses to it; which strategies they found effective; what they believed to be the causes of it; how stressed they felt; and how effective they felt when dealing with it. They were also asked to identify sources of information, advice and help and to rate different types of challenging behaviour in terms of severity of challenge. Results indicate that teachers are concerned about challenging behaviour and find it stressful. Whilst considering themselves to be effective in dealing with it, a proportion report feeling frustrated by it, angry, upset and/or at a loss. The most frequently cited challenging behaviour was aggression, although self-injury was found to be the most challenging. Whilst recognising the communicative basis of many forms of challenging behaviour teachers nevertheless tended to select strategies which were concerned with diffusion rather than prevention. The most likely source of information, advice and help was other teachers. Some differences in responses were noted according to experience and whether or not additional qualifications were held.     

The Moment of 1963: Reflections and the new English

Reflections is the name of an English course book for pupils aged 14 to 18 which was published in 1963. Widely praised at the time of publication, it is now regarded as one of the most important English books in the post‐war period, representing as it did a ‘new English’. This article looks at what was ‘new’ about the type of pedagogy embodied in the book, contrasting it with English, a series of course books which was popular during the late 1950s and early 1960s. The author then traces the factors‐‐institutional and intellectual‐‐which made Reflections possible, before going on to examine the influence the book had.     

《岳阳楼记》写于岳阳

范仲淹《岳阳楼记》写于岳阳，其理由有三：一是，求记与撰记间隔时间之长、记成后转递书刻紧张的时间问题和滕子京对所求之《岳阳楼记》的要求，及当时严峻的现实情况的需要，是范仲淹亲临实地作记的主要原因；二是，范仲淹的《岳阳楼记》是此记写于岳阳的内证；三是，范仲淹在岳阳市云溪区置有田庄，乃其亲赴岳州作记的重要旁证。     

论国民政府分期禁绝毒品政策的弊端——以甘肃省的禁政为中心

关于国民政府分期禁绝毒品政策的弊端,学术界有所论述,但泛泛而谈者居多,鲜有用实例论证者。笔者拟以甘肃省为例,论证国民政府不采取断禁措施,而是着眼于鸦片的巨额利润,致使在执行此政策的过程中,禁绝与烟亩罚款常常纠缠不清,执行者难以遽断;禁绝县份与未禁绝县份之间纠葛纷出,弊端丛生,影响禁政效果至巨,给后续的禁烟带来了诸多掣肘。总体上,从成本、收益和政策的可操作性方面看,该政策弊大于利。