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Chapter one has introduced the background and classification of minimax theorems; Chapter two summarizes several proof method of minimax theorems, which are illustrated with examples; Chapter three has explained the development general situation of minimax theorems for a function and for two functions with chapter four respectively, and according to the classification of the theorem, has illustrated some important conclusionses in quantitative minimax theorems, topological minimax theorems and quantitative-topological minimax theorems separately.

第一章介绍了极大极小定理的背景及其分类；第二章总结了极大极小定理的几种证明方法，并举出例子进行说明；第三章和第四章分别阐述了单函数的极大极小定理和两个函数的极大极小定理的发展概况，在第三章中，按照极大极小定理的分类，分别对数量极大极小定理，拓扑极大极小定理和数量拓扑极大极小定理的一些重要结论作了介绍。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesn't calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesnt calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

The uniform approximation of normal wavelet neural network and the robust analysis of wavelet neural networks of the combination of Sigmoid function are detailedly introduction; Multiple model failure detection based on wavelet neural network is demonstrated detailedly; At last, the failure diagnosis results of aerocraft is present seperately by employing wavelet neural network and BP neural network, and the fault diagnosis of areocraft system by wavelet neural network is achieved.

论文以小波神经网络为研究对象，提出了一类新的加权小波基，分析证明了加权小波基的诸多良好特性；对于常见小波神经网络的一致逼近特性、S型函数组合小波神经网络的鲁棒性分析、多模型小波神经网络的故障检测等问题给出了详细的论证；最后，针对歼击机的常见故障问题，分别给出了应用小波神经网络和BP神经网络的故障诊断结果，实现了小波神经网络对飞机系统的故障诊断。

Spikelets with 1 floret, small, often gaping, without rachilla extension; rachilla disarticulating above glumes; glumes persistent, longer than floret, subequal or lower a little longer, membranous, 1-veined, apex subacute to acuminate; floret callus glabrous or shortly pilose; lemma oblong to elliptic, thinner than glumes, often hyaline, 5-veined, rounded on back, glabrous or hairy, lateral veins sometimes excurrent, awnless or awned from back, apex truncate or toothed; awn usually geniculate, sometimes weakly so or straight when short; palea shorter than lemma, sometimes very small.

小穗具1小花，小，张口的通常，没有小穗轴扩展；高于颖片脱节的小穗轴；宿存的颖片，长于小花，下部的近等长的或稍长些，膜质，1脉，先端近尖的到渐尖；无毛的小花结茧或者具短柔毛；外稃长方形到椭圆形，比颖片瘦，经常透明，5脉，通常膝曲，有时身体虚弱的芒或者直接，缺乏；内稃短于外稃，有时很小。

Spikelets with 1 floret; rachilla disarticulating above glumes, extension beyond floret absent or small and glabrous, rarely better developed and penicillate; glumes persistent, subequal or unequal with lower longer, narrowly lanceolate, much exceeding floret, lower glume 1-veined, upper glume 3-veined at base, apex finely acuminate or subulate; floret callus conspicuously bearded, hairs much exceeding floret; lemma ca. 1/2 as long as glumes, hyaline, 3–5-veined, awned, apex erose, denticulate or deeply 2-lobed; awn very slender, straight or almost so, arising from lemma back, apex or between teeth; palea 1/2 as long to slightly shorter than lemma.

小穗具1小花；在缺席或者小和无毛小花以外高于颖片脱节的小穗轴，扩展，很少很好地发展，具毛撮；颖片宿存，近等长或不等长用低长时间，狭披针形，很多超过小花，小花结茧显著公然反对，头发很多超过小花；外稃大约1/2的倍于颖片，透明，3-5－脉，具芒，啮蚀状的顶，或者深深2裂的具小齿；返回的芒非常细长，直的或几乎如此，生于外稃，或者在牙齿之间的顶；作为稍短于外稃的长时期的内稃1/2。

Inflorescence a raceme with 2 or 3(–6) spikelets, rarely a panicle with many spikelets, peduncle, axis, branches, and pedicels slender, glabrous, scabrous or pubescent along longitudinal angles, branches usually subtended by a scaly bract at base. Spikelets ± compressed at maturity, several to many florets; rachilla disarticulating below fertile florets, extended beyond palea of uppermost floret, internodes flattened or concave on side facing floret.

花序为一总状花序具2或3(-6)小穗，一圆锥花序具很多小穗，花序梗，轴，分枝和花梗纤细，沿着纵向的有棱的无毛，粗糙的或短柔毛的很少，成熟时的小穗多少压扁，数枚到多数小花；在肥沃的小花下面脱节的小穗轴，在最重要的小花的内稃以外延长，在边面对小花上节间被变平或者凹。

Spikelets laterally compressed, lanceolate-oblong, florets several, contiguous; rachilla scaberulous, disarticulating above glumes and between florets; glumes slightly unequal, upper nearly as long as spikelet, firmly membranous, keel scaberulous, apex abruptly acuminate, lower glume 1–3-veined, upper glume 3–5-veined; lemmas broadly lanceolate, thinly leathery, rounded on back, 5–7-veined, veins smooth, not raised, scabrid above middle, apex scarious, usually 3-denticulate, sometimes mucronate; floret callus subacute, bearded laterally with stiff hairs; palea subequal to lemma, narrow, flat, apex sharply 2-denticulate.

小穗侧面压扁，披针形长圆形，小花数个，邻接；小穗轴高于颖片微糙，脱节和在小花之间；颖片稍不等长，上面近等长小穗，坚定膜质，龙骨状，先端突然渐尖，下部颖片1-3，上面颖片3-5－脉；宽披针形的外稃，在背面上薄革质，圆形，5-7－脉，平滑的脉，不凸起，在中部以上，先端，通常3－具小齿，小花结茧稍尖，用硬的头发侧面公然反对；内稃近等长于外稃，缩小，平，顶明显2－具小齿。

It was a Sunday afternoon, I was window homework, I suddenly saw the big cocks and small cocks actually playing up: big cock, small cock crest directed at a peck, but a small cock leisurely side of the head , no other large cock his head to go back, it will ramp lips a peck, just peck at the eyes on the big cock, big cock, cried, launching the anger, a pair of swollen eyes watching a small cock, small cock also milli do not show weakness, neck Yishenyishen's ready for battle, suddenly big cock sky dive jump out sharp claws, small cock was throwing herself to the ground, big cock, taking advantage of this time back down the small cock small cock look at the neck, blood from small rooster's neck and upper class down, I was taken aback, was about to help it in the past.

那是一个星期天的下午，我正在窗前做作业，忽然看见大公鸡和小公鸡竟打了起来：大公鸡冲着小公鸡的冠子一啄，可是小公鸡不慌不忙的把头一侧，还没等大公鸡把头收回去，它就斜着嘴一啄，正好啄在了大公鸡眼睛上，大公鸡叫了一声，发起怒来，一双红肿的眼睛注视着小公鸡，小公鸡也毫不示弱，脖子一伸一伸的做好战斗准备，突然大公鸡腾空而起伸出锋利的爪子纵身一跳，小公鸡被扑到了地上，大公鸡趁这时压在小公鸡的背上了小公鸡的脖子一下，血从小公鸡的脖子上流了下来，我吃了一惊，刚想过去帮它。

Four little human run over. They talk loudly and nosey .One little human surprisingly catch Little Sheep. Little Sheep struggle and try to run away. He kick with his two legs in the back. That little human fell down. He hurt his knee and cry. The other three start to throw stone to Little Sheep. Little Sheep run and run.

四个小人类跑过，讲话的声音大声且刺耳，他们朝小羊跑来，一个小人类冷不防的将小羊给抓住，小羊挣扎著，后腿一踢，那小人类被跌倒在地上，他擦破膝盖，痛哭起来，其他三人开始朝小羊丢石头，小羊一路跑著，三个小人类在后头紧追不舍。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。