关于含参变量函数求导的注记

对于由参变量方程决定的平面曲线C:x=ψ(t),y=Ψ(t),在求曲线的切线时,一般教材中要求x'(t),y'(t)中至少一个不为零.本文对于x'(t)与y'(t)公共零点处的切线进行了讨论,以在教学中加强知识间的联系.     

分部积分法在重积分中的应用

本文通过对重积分计算的分析,认为可以不用交换积分的次序来计算,从而得到用分部积分法计算重积分的结论:∫Df(x,y)dxdy=x[x∫y2(x)y1(x)F(x,y)dy]ba-∫bax,[F(x,y2(x))y'2(x)-F(x,y'1(x))Y'1(x)]dx同时将结论予以推广,并通过具体例题说明其应用.     

一类非线性摄动问题解的渐近性态及其精度分析

在适当的条件下,应用摄动理论与渐近展开方法,讨论一类较广泛的非线性摄动问题y'+f(y';t;ε)=0,y(t0)=A(ε),y'(t0)=B(ε).证明了其解的存在性并得出了解的渐近表达式,再将结果应用于原物理模型,得出的结论与相应参考文献中的结果是一致的.通过对渐近解进行精确度分析,说明采用的渐近展开法为解决相关类型的摄动问题提供了一种较为有效的方法.     

一类二阶微分方程的振动性

二阶微分方程y'+p(t)y＝0(其中p(t)＞0)在闭区间[2nt.,2n+1t.]上的振动与非振动的充分条件已得到证明,在更一般意义上,此方程在[lnt.,ln+1t.]上振动与非振动的充分条件同样成立.     

一类二阶微分方程解的渐进性质

本研究了一类二阶非线性微分方程。[p(5)h(x(t)x'(t))]' q(t)e(x(t))c(x'(t)) r(t)f(x(g))t))))=0的解的性质，证明了若干最终单调解的渐近性质。     

一类二阶微分方程解的渐近性质

本文研究了一类二阶非线性微分方程。 [p(t)h(x(t)x'(t))]' q(t)e(x(t))c(x'(t)) r(t)f(x(g((t)))=0的解的性质,证明了若干最终单调解的渐近性质。     

一类中立型变时滞微分方程的零解全局吸引的充分条件

利用构造Liapunov泛函的方法，给出了中立型变时滞微分方程d/dt[x(t) ax(t-τ（t))]=bx(t) cx(t-τ1(t))和d/dt[x(t) ax(t-τ（t））]=bx(t-τ（t)) cx(t-τ2(t))零解全局吸引的一个充分条件。     

具有多重时滞的一类积分微分方程周期解的存在与稳定性

文章考虑如下周期系统ddt(x(t)-∫t-∞B(t,s)x(s)ds)=A(t,x(t))x(t) ∫t-∞C(t,s)x(s)ds g(t,x(t-τ)) b(t)的周期解存在性与稳定性问题,给出其周期解存在和一致稳定的充分条件。     

一类具时滞和比率依赖的捕食-食饵模型2个周期解存在性

研究一类带有Holling III型反应函数的捕食-食饵模型{ì?dx(t)t?)[r1(t)-a(t)x(t-τ1(t))-b(t)íd=xt(∫t-∞k(t-s)x(s)d]c-1(t)x(t)y2(ts)m2y2τ(t)+x2(t),?dy(t)d=y2(t))y(t-τt(t)[-r2(t)c+2(t)x(t-))2(t?))m2y2(t-τ2(t+x2(t-τ2(t))].运用重合度拓展定理,证明其存在2个正周期解.并举一个实例验证结论的可行性.     

一类带有p-Lapcaian算子Liénard型泛函微分方程周期解的存在性

主要利用Mawhin连续性定理,讨论了一类具有多个变时滞的p-Lapcaian型中立型Liénard泛函微分方程:(φp(x(t)-cx(t-σ))’)’+f(x(t))x’(t)+∑ni=1gi(t,x(t-τi(t)))=e(t)周期解的存在性并举例说明结果的有效性。     

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!     

胡主席在印度,我却在中国

Today, Sunday morning, I sit thinking and typing at my computer. My thoughts are in my homeland, India and my body is in China. The body is here and mind there for a good reason. Mr. Hu is president and I am resident and both are in each other's countries (what a difference the absence of one small letter makes!). Mr. Hu will return in a few days and I will stay on longer.