查询词典 decomposition into linear factors

In the one half part, according to the strontium nature, thermodynamic calculation of correlative reaction and the principle of the vacuum aluminothermy reduction process, with the laboratory findings of preparation strontium by vacuum aluminothermy reduction compared and analyzed in different parameter conditions, a variety of factors which effect the decomposition rate of SrCO_3 and the percent reduction of strontia are gotten out. The factors include that the decomposition rate of SrCO_3 is influenced by different addition and pressure. They also include that the percent reduction of strontia is influenced by excess coefficient of reducing agent aluminium powder, the particle size of raw material or reducing agent, the pressure of barbecuing, temperature and reduction time. According to those, we can draw the conclusion as follows:(1) Decomposition temperature of SrCO_3 is decreased by adding carbon and alumina in different degree.(2) With quantitative carbon added under the vacuum condition, the decomposition temperature of SrCO_3 is decreased obviously, which can fall 150℃ compared with atmospheric pressure.(3) In keeping 1150℃ of 2.5h, under the 5Pa vacuum condition, the decomposition rate of SrCO_3 nearly keeps in 99% steadily.

在前半部分的真空铝热还原法中，根据锶的性质、相关反应的热力学计算及真空铝热还原法原理，通过对不同参数条件下的真空铝热还原法生产金属锶的实验结果的分析比较，得出了影响SrCO_3的分解率和氧化锶的还原率的种种因素，具体因素包括不同添加剂、不同气压对SrCO_3分解率的影响，还原剂铝粉的过量系数、原料与还原剂的粒度、制团压力、温度和还原时间等对氧化锶还原率的影响，得出具体结论如下：(1)添加碳和Al_2O_3能不同程度的降低SrCO_3的分解温度；(2)真空条件下加入一定量的碳可显著降低SrCO_3的分解温度，比之常压下可降低150℃之多；(3)在1150℃恒温2.5h、真空度达到5Pa的条件下，SrCO_3的分解率几乎保持稳定在99％；(4)氧化锶的还原率随还原剂过量系数的增大而增大，但是趋势越来越小，当过量系数超过25％后，氧化锶的还原率几乎不再增加；(5)氧化锶的还原率随原料与还原剂的粒度的变细而增加；(6)氧化锶的还原率随制团压力的增加而增加，但超过一定值后，氧化锶的还原率反而会下降；(7)氧化锶的还原率随还原温度的升高而增加；(8)氧化锶的还原率随还原时间延长而增加，在本实验条件下，超过2.5h趋于稳定。

The linear function applicable scope is broad, when the reservoir turnover water volume and the time, the student leaves the staircase mouth population and the time and the time and the motion communication speech spends the comparison and so on the relational question has the important application;The study linear function, may deepen in the life the linear question understanding and the understanding, is helpful in solves some simple function problem; The linear function some problem solving method has the universality in mathematics, the linear function related theory may use for to solve some other mathematics problem, For instance the dual linear equation group, a Yuan inequality, a Yuan quadratic equation most value question and some complex mathematics question, the light is studies the linear function the theory is insufficient, the key is can utilize actual the linear function goes is our final goal.

一次函数的适用范围广，在蓄水池的进出水量与时间、学生出楼梯口人数与时间与时间和移动通讯的话费比较等的关系问题时均有重要的应用；学习一次函数，可以加深生活中线性问题的认识与理解，有助于解决一些简单的函数问题；一次函数的一些解题方法在数学中具有普遍性，一次函数的有关理论可以用来解决一些其它的数学问题，比如二元一次方程组、一元一次不等式、一元二次方程的最值问题及一些复杂的数学问题，光是学习一次函数的理论是不够的，关键是能把一次函数运用到实际中去才是我们最终的目的。

Modeling and stability analysis problem of linear switched system are emphasized in this part and main results include:(1) Through investigation in the projection of 〓 on x, where x denotes continuous state vector, a series of sufficient conditions for stability, asymptotic stability and unstability of linear switched system's equilibrium in the sense of Lyapunov are achieved. And also, a sufficient and necessary condition for state bounded stability of linear switched system is received.(2) For a class of periodical linear switched system whose switching sets are a group of ordinal lines starting from the original point, it's proved that state bounded stability can be defined by the running characteristic in a single period (3) Based on linear switched system, the concept of linear switched system network is put forward. Linear switched system network is a complex network interconnected by many linear switched systems.

这部分着重研究线性切换系统的建模与稳定性分析问题，主要成果包括：（1）通过考察〓在x上的投影，得到线性切换系统的平衡点在Lyapunov意义下稳定、渐近稳定及不稳定的一系列充分条件，并得到了线性切换系统状态有界稳定的一个充要条件；（2）证明了对于一类切换集为从原点出发的一组射线的周期线性切换系统，其状态有界稳定可根据一个周期内的系统运行特性来判定；（3）在线性切换系统的基础上提出了线性切换系统网络的概念，线性切换系统网络是由多个线性切换系统交互作用而形成的复杂网络。

The effects and mechanism of GABAergic neurons, NOergic neurons, opioid peptide and cyclic adenosine monophosphate in the nucleus reticularis thalami on sleep-wakefulness cycle of rats and the effects and mechanism of the 5-HTergic nerve fibers project from the nucleus raphes dorsalis to RT on sleep-wakefulness cycle of rats were investigated with the methods of brain stereotaxic, nucleus spile, microinjection and polysomngraphy.1. The effects of GABAergic neurons in RT on sleep-wakefulness cycle of rats1.1 Microinjection of 3-mercaptopropionic acid (3-MP, a kind of glutamate decarboxylase inhibitor) into RT. On the day of microinjection, sleep only decreased a litter. On the second day, sleep marked decreased and wakefulness marked increased. On the third and fourth day, sleep and wakefulness stages resumed to normal.1.2 Microinjection of gamma-amino butyric acid (GABA 1.0μg) into RT enhanced sleep and reduced wakefulness compared with control; while microinjection of L-glutamate (L-Glu, 0.2μg) decreased sleep and increased wakefulness; microinjection of bicuculline (BIC, 1.0μg), a GABAA receptor antagonist, enhanced wakefulness and reduced sleep; microinjection of baclofen (BAC, 1.0μg), GABAB receptor agonist, had the same effects as GABA.2. The effects of NOergic neurons in RT on sleep-wakefulness cycle of rats2.1 Microinjection of L-arginine (L-Arg, 0.5μg) into RT decreased sleep compared with control, but there were on statistaical difference between L-Arg group and control; while microinjection of sodium nitroprusside (SNP, 0.2μg), a NO donor into RT, sleep marked decreased and wakefulness marked increased. Microinjection of nitric oxide synthase inhibitor, N-nitro-L-arginine (L-NNA, 2.0μg) into RT enhanced sleep and reduced wakefulness.2.2 After simultaneous microinjection of L-NNA (2.0μg) and SNP (0.2μg) into RT, SNP abolished the sleep-promoting effect of L-NNA compared with L-NNA group; after simultaneous microinjection of L-NNA (2.0μg) and L-Arg(0.5μg) into RT, we found that L-NNA could not blocked the wakefulness-promoting effect of L-Arg.3. The effects of opioid peptide in RT on sleep-wakefulness cycle of rats3.1 Microinjection of morphine sulfate (MOR, 1.0μg) into RT increased wakefulness and decreased sleep compared with control; while microinjection of naloxone hydrochloride (NAL, 1.0μg), the antagonist of opiate receptors, into RT, enhanced sleep and reduced wakefulness.3.2 After simultaneous microinjection of MOR (1.0μg) and NAL (1.0μg) into RT, the wakefulness-promoting effect of MOR and the sleep-promoting effect of NAL were not observed compared with control.4. The effects of cAMP in RT on sleep-wakefulness cycle of rats Microinjection of cAMP (1.0μg) into RT increased sleep and decreased wakefulness compared with control; microinjection of methylene blue (MB,1.0μg) into RT enhanced sleep and reduced wakefulness compared with control.5. The effects of the 5-HTergic nerve fibers project from DRN to RT on sleep-wakefulness cycle of rats5.1 When L-Glu (0.2μg) was microinjected into DRN and normal sodium (NS,1.0μg) was microinjected into bilateral RT. We found that sleep was decreased and wakefulness was increased compared with control; when L-Glu (0.2μg) was microinjected into DRN and methysergide (MS,1.0μg), a non-selective 5-HT antagonist, was microinjected into bilateral RT, We found that sleep was enhanced and wakefulness was reduced compared with L-Glu group.5.2 When p-chlorophenylalanine (PCPA, 10μg) was microinjected into DRN and NS (1.0μg) was microinjected into bilateral RT, We found that sleep was increased and wakefulness was decreased compared with control; microinjection of 5-hydroxytryptaphan (5-HTP, 1.0μg), which can convert to 5-HT by the enzyme tryptophane hydroxylase and enhance 5-HT into bilateral RT, could block the effect of microinjection of PCPA into DRN on sleep-wakefulness cycle.

本研究采用脑立体定位、核团插管、微量注射、多导睡眠描记等方法，研究丘脑网状核(nucleus reticularis thalami，RT)中γ-氨基丁酸(gamma-amino butyric acid ，GABA)能神经元、一氧化氮(nitrogen monoxidum，NO)能神经元、阿片肽类神经递质、环一磷酸腺苷(cyclic adenosine monophosphate，cAMP)及中缝背核(nucleus raphes dorsalis，DRN)至RT的5-羟色胺(5-hydroxytryptamine，5-HT)能神经纤维投射对大鼠睡眠-觉醒周期的影响及其作用机制。1 RT内GABA能神经元对大鼠睡眠-觉醒周期的影响1.1大鼠RT内微量注射GABA合成关键酶抑制剂3-巯基丙酸(3-MP，5μg)，注射当天睡眠时间略有减少，第二日睡眠时间显著减少，觉醒时间明显增多，第三、四日睡眠和觉醒时间逐渐恢复至正常。1.2大鼠RT内微量注射GABA受体激动剂GABA( 1.0μg)后，与生理盐水组比较，睡眠时间增加，觉醒时间减少；而RT内微量注射L-谷氨酸(glutamic acid， L-Glu， 0.2μg)后，睡眠时间减少，觉醒时间增加；RT内微量注射GABAA受体阻断剂荷包牡丹碱(bicuculline，BIC，1.0μg)后，睡眠时间减少，觉醒时间增加；RT内微量注射GABAB受体激动剂氯苯氨丁酸(baclofen，BAC，1.0μg)后，产生了与GABA相似的促睡眠效果。2 RT内NO能神经元对大鼠睡眠-觉醒周期的影响2.1大鼠RT内微量注射NO的前体L-精氨酸(L-Arg，0.5μg)后，与生理盐水组对比，睡眠时间略有减少，但无显著性意义；而RT内微量注射NO的供体硝普钠(Sodium Nitroprusside，SNP，0.2μg)后可明显增加觉醒时间，缩短睡眠时间；微量注射一氧化氮合酶抑制剂L-硝基精氨酸(L-arginine，L-NNA，2.0μg)后，引起睡眠时间增多，觉醒时间减少。2.2大鼠RT内同时微量注射L-NNA(2.0μg)和SNP(0.2μg)后与L-NNA组比较发现SNP逆转了L-NNA的促睡眠作用；RT内同时微量注射L-NNA(2.0μg)和L-Arg(0.5μg)后，与L-NNA(2.0μg)组比较发现L-Arg可以增加觉醒而缩短睡眠，其促觉醒作用未能被NOS的抑制剂L-NNA所逆转。3 RT内阿片肽对大鼠睡眠-觉醒周期的影响3.1大鼠RT内微量注射硫酸吗啡(morphine sulfate，MOR，1.0μg)后与生理盐水组对比，睡眠时间减少而觉醒时间增加； RT内微量注射阿片肽受体拮抗剂盐酸纳洛酮(naloxone hydrochloride，NAL，1.0μg)后与生理盐水组比较，睡眠时间增加而觉醒时间减少。3.2大鼠RT内同时微量注射MOR(1.0μg)和NAL(1.0μg)后，与生理盐水组对比，原有的MOR促觉醒效果和NAL的促睡眠效果都没有表现。4 RT内环一磷酸腺苷信使对大鼠睡眠-觉醒周期的影响大鼠RT内微量注射cAMP(1.0μg)后与NS(1.0μg)组比较，睡眠时间增多而觉醒时间减少；RT内微量注射亚甲蓝(methylene blue，MB，1.0μg)后，与NS组比较，睡眠时间增多而觉醒时间减少。5中缝背核投射到丘脑网状核的5-羟色胺能神经纤维对大鼠睡眠-觉醒周期的影响5.1大鼠DRN内微量注射L-Glu(0.2μg)，同时在双侧RT内微量注射NS (1.0μg)后，与对照组(DRN和双侧RT注射NS， 0.2μg)比较，睡眠时间减少，觉醒时间增多；大鼠DRN内微量注射L-Glu(0.2μg)，同时在双侧RT内微量注射二甲基麦角新碱(methysergide， MS， 1.0μg )后，与对照组(DRN注射L-Glu 0.2μg，双侧RT注射NS 1.0μg)比较，睡眠时间增多，觉醒时间减少。5.2大鼠DRN内微量注射对氯苯丙氨酸(p-chlorophenylalanine，PCPA，10μg)，同时在双侧RT内微量注射NS (1.0μg)后，与对照组(DRN和双侧RT注射NS， 1.0μg)比较，睡眠时间增多，觉醒时间减少；大鼠DRN内微量注射PCPA(10μg)，产生睡眠增多效应后，在双侧RT内微量注射5-羟色胺酸(5-hydroxytryptaphan ， 5-HTP， 1.0μg )后，与对照组(DRN注射PCPA 10μg，双侧RT注射NS 1.0μg)比较，睡眠时间减少，觉醒时间增多。

To one quaternion matrix, according to its normal form, into which a quaternion matrix is transformed after decomposed, the types of decomposition of a quaternion matrix are divided into three large classes: diagonalized decomposition, triangular decomposition and triangular-diagonalized decomposition.

对单个四元数矩阵，以分解后的四元数矩阵的标准型作为分类的标准，将四元数矩阵的分解分为三大类：对角化分解、三角化分解、三角一对角化分解。

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

The results show that the decalescence of catalyst bed affects the process of hydrogen peroxide catalytic decomposition greatly. If the catalyst bed is preheated or made up of materials with low thermal conductivity, that influence can be depressed. At the same time, the response characteristic of catalyst bed and the efficiency of catalytic decomposition can be improved. The low frequency pressure instability of catalyst bed occurs because of the coupling of catalytic decomposition and supplying. The decomposition plane pushes all the way through the catalyst bed during pressure oscillations, causing unreacted liquid hydrogen peroxide to be exhausted from the bed and leading to the appearance of liquid hydrogen peroxide channeling. Consequently, how to prevent or at least limit this channeling is the key to eliminate the pressure instability of catalyst bed. It was found that adding clapboard to the catalyst bed can depress the pressure instability efficiently.

结果表明催化剂床及催化剂的吸热对过氧化氢分解过程影响很大，对催化剂床进行预热或采用热导率低的材料制造催化剂床等措施，可以降低催化剂床壁面吸热对催化分解过程的影响，提高催化剂床的响应特性和催化分解效率；催化剂床的低频不稳定是催化分解过程与供应系统耦合产生的，催化剂床气体界面的波动过程中，液体过氧化氢穿透催化剂床形成过氧化氢液体通道，过氧化氢液体通道的产生和扩大是催化剂床不稳定的主要原因，也是消除催化剂床不稳定的关键，试验中在催化剂床内加入分流板成功地抑制了催化剂床的低频不稳定。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

The solvable Lie algebra is corresponding to a cascade decomposition of the system and the semisimple Lie algebra is corresponding to a qasi-parallel decomposition such that the system has a parallel form of a cascade decomposition and a qasi-parallel decomposition.

任一李代数都可分解为一可解李代数与一半单李代数的半直和，可解李代数对应于系统的级联分解，半单李代数对应的是系统的准平行分解，将二者合并起来，就得到一般李群下的非线性系统的结构分解，这是一级联形式与一准平行形式的并联形式分解。

In this article, several common matrix decomposition theory and its applications was put forward, such as triangular decomposition, QR decomposition, the full rank decomposition, SVD and so on.

本文给出了几种较常见的矩阵分解理论及其应用。如三角分解，QR分解，满秩分解，奇异值分解等。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。