一个加强的Hardy不等式

要：通过精确估算，建立如下权系数的不等式，W（k)=1/√kk∑n=1∞∑j=n1/j3/2≤4(1-η/√k)(k∈N, η=0.3469^ )，从而导出Hardy不等式的一个加强式(p=2)．     

一个Hilbert型不等式的加强

引入如下权系数的不等式：ω（n）=∑k=1^∞1/max{k,n}√n/k≤4-θ/√n（θ=1.3876^＋）.从而得到一个Hilbert型不等式的一个加强式．     

p=5的Hardy不等式的一个加强改进

对P=5的Hardy不等式，建立如下的加强不等式∞∑n=1（1/nn∑k=1ak）^9〈（5/4）%5∞∑n=1（1-1/[（5n^4/5）/2＋0.624]＋1/[（5n^4/5）^3＋（5n^4/5）^2/24]）ak^5其中an≥0（n∈N）,1〈∞∑n=1an^5〈∞.     

一个加强不等式的推广

将哈代不等式的加强型改进∞∑n=1(1/nn∑k=1αk)^p＜q^p∞∑n=1(1-1/38n^1/q)α^p/n成立的参数p的范围，由2≤p≤5推广到9/7≤p≤5(1/p 1/q=1).     

自然数平方倒数和的一个改进不等式

得到了不等式：（1/n＋α≤π^2/6-n∑k=1 1/k^2）,其中（α=12-π^2/π^2-6）=0.5505460967^＋;当且仅当n=1时,等号成立.且证明了不等式：（1/n＋α≤π^2/6-n∑k=1 1/k^2 1/n＋1/2）两端的常数1/2、α均为最付佳值.     

重尾随机变量的随机加权和

本文讨论了当X1,X2…,Xn（-∞,∞）上分布函数分别为F1,F2,…,Fn的n个随机变量,其中Fk∈S（r）,k=1,2…n,{θk,1≤k≤n}是与{Xk,1≤k≤n}独立的n个相互独立随机变量情形下,重尾随机变量的随机加权和,证明了当→∞时渐近关系式p（^n∑i=1θiXi〉x）-∑i≠jFi（γ）^-Fi（x/θi）成立     

Vander Corput不等式的新加强

对VanderCorput不等式进行研究,并将其进一步改进如下：设aa≥0,n=1,2,∧,Sn=k=1∑n 1/k,∞∑n=1（k=1∏n ak 1/k）^1/sn≤e^1＋y ∞∑n=1e-1/25n（n-17/50n logn）an,则其中为Euler常数．     

一类级数的敛散性问题

本文通过建立离散不等式 （1/2√n）^s≤[（2n-1）!!/（2n）!!]^s≤（1/√2n）^s,讨论级数∑^∞ n=1[（2n-1）!!/（2n）!!]^s（s〉0）的敛散性。     

利用导数解决不等式问题

笔者在解决一些不等式问题时,经常遇到题目条件难以放缩或不等关系等,而应用导数常可以使问题简单许多. 1用导数降低原不等式次幂 例1设x为非负实数,n为正整数证明:n∑k=1xk2/k≥xn(n+1)/2. 证明 设f(x)=n∑k=1xk2/k-xn(n+1)/2.则f'(x)=n∑k=1kxk2-1-n(n+1)/...     

一类级数的求和问题

从f(x)=x在（-ππ）内的傅立叶级数展开式出发，导出形如∑n=1^∞ （-1）^n 1sin nx/n^2k-1及∑n=1^∞ (-1)^n 1con nx/n^2k的三角级数的和函数特点及函数的递推求法，从而解决形如∑n=1^∞ 1/n^2k、∑n=1^∞（-1）^n 1/N^2k、∑n=1^∞ 1/（2n-1)^2k-1（其中k∈N）等级数的求和问题。     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.     

Improvement of one-cycle controller by use of proportional integral differential controller

1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec…     

库克斯顿城堡

城堡, 是欧洲典型的建筑之一, 每个城堡都有一个美丽的传说或是一段历史。从本期开始, 我们将推出“城堡之旅”, 带各位读者去浏览、观赏欧洲各地的城堡, 开始一段文化与历史的旅途!     

The Reader Response Approach to Teaching of English Literature

During interview with English majors, it was found that a majority of students expressed disappointment with their experience of English literature classes. Students' dislike of learning English literature appears to be the major problem of teaching English literature in China. Reader response approach is a good way to solve this problem. In this paper, I explain the rationale behind the reader response approach, such as its origin, definition, features, assumptions, and strategies. Then I illustrate how reader response approach works as a teaching strategy by presenting several teaching models. At last I evaluate its usefuiness for teachers and present the advantages of reader response approach in Chinese context.