查询词典 reduced equation

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

When the gas flux is constant, the ratio of reduced resistance is improved with the increase of the water stream velocity. However, the relationship between the gas flux and the ratio of reduced resistance is more complex. When the water stream velocity is constant, if the gas flux is small in contrast, the effectiveness of reduced resistance is not obvious. But when the gas flux increased, the jetted gas will form """"archform"""" which will augment the shape resistance. In this condition, resistance could not be reduced and could even be increased, if the gas flux continues to be increased. So that there needs setting a baffle called step, which introduces the jetted gas into the turbulence boundary layer. In this case, the shape resistance may be fairly great. Besides, the waterline of model has also some effect on the ratio of reduced resistance, which acts on the size of wave. If waterline is deep, the wave could not affect the deployment of microbubble layer, so there is almost no effect on ratio of reduced resistance. However, the wave would affect distributing of microbubble layer under the model so that the gas could leak out from the two sides of model and directly affect the ratio of reduce resistance if the waterline is very small. Whether installing the dashplate or not has also the great influence on the effectiveness the ratio of reduced resistance. From the results of experiment, conclusion is that adding dashplate will greatly improve the effectiveness of reduced resistance.

当喷气量一定时，水流速度增大，减阻率提高；喷气量与减阻率之间的关系比较复杂，速度一定时，如果喷气量较小，减阻效果就比较差，但当喷气量增大的话，喷射出的气体就会形成一个&拱度&，增加了船模的形状阻力，在这种情况下最好采取断阶喷气，把气体引入到湍流边界层中，在这种情况下，船模的形状阻力比较大；船模的吃水对减阻率也有一定的影响，主要表现在波浪大小上，如果吃水较深，波浪影响不到微气泡层的分布，对减阻率不会造成太大影响，如果吃水较浅，波浪就会影响到微气泡层在船模底部的覆盖情况，可能会有部分微气泡从船模两侧泄漏，这样就直接影响到了减阻效果；是否安装压浪板，对减阻率也有较大的影响，从试验结果可以看出，在船模尾部加设了压浪板时，减阻效果明显得到改善。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

Kg(p.01).stamina index,healthy index,appetite index,sleep index,sleep time,the total count of sex arousing people and the degree concerning about the health of oneself were all reduced gradually(p.01).the counts of ailing people and using medicine people were higher in 1～3 weeks.later,the counts were reduced wavily and touched bottom in the 6th week and the 10th week respectively.the count of ailing people was reduced more obviously(p.01～0.001).the trend of disease variety among persons was that the proportion of respiratory system disease was reduced and alimentary system disease was increased gradually,the proportion of skin disease was higher at the 7th week and locomotor system disease was higher at the 8th week,the proportion of diarrhea was reduced and constipation was increased gradually.conclusion working on the reef for 3 months,the physical health status and the degree concerning about health of self of the personnel was reduced gradually.the count of ailing people and using medicine people were reduced wavily.

kg(p.01)。体能指数、健康指数、食欲指数及睡眠指数逐渐降低，睡眠时间逐渐减少，性唤起总人数比例逐渐降低，对自身健康的关心程度也逐渐降低(p.01)。患病及用药人次数以上礁后的前3周较多，此后呈波浪式逐渐减少，第6周和第10周分别降至低谷，减少幅度尤以患病人次数明显(p.01)。疾病变化趋势为呼吸系统疾病所占比例逐渐降低，消化系统疾病所占比例逐渐增加，皮肤疾病和运动系统疾病分别于第7，8周时较多；腹泻比例逐渐减少，便秘比例则逐渐增多。结论在礁3个月期间，作业人员身体状况和对自身健康的关心程度逐渐降低，患病和用药人次数呈波浪式逐渐减少。南海群礁；身体健康；患病；动态变化；医疗卫生保障

Establish the steady-state and transient model using the three hydrodynamics equations (Continuity equation, Momentum equation and Energy equation). By comparing different state equation, it selects the BWRS state equation which is considered the most accurate state equation in current natural gas measurement. It calculates compression factor, density and other Thermal parameters based on BWRS state equation. In Numerical solution of the steady-state and transient model, compression factor, friction coefficient and all the other Thermal parameters are recalculated in each small time step to reduce the numerical calculation error.

在稳态模型的建立上，利用流体力学三大方程(连续性方程、运动方程和能量方程)，通过比较不同的状态方程选用了目前被认为最精确的用于天然气计量的BWRS状态方程，并以此方程为基础进行压缩因子、密度等热物性参数的计算；在稳态模型的求解上，选用容易计算，精度较高的标准型龙格—库塔(Runge-Kutta)法进行数值求解，并且在迭代过程的每一小步都重新计算燃气的压缩因子，摩阻系数等所有的计算参数，以减少数值计算的误差。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

It was found that PLZT was easily reduced and the thickness of reduced layer had a linear relationship with the reduction time; The optimal conditions for PLZT were determined to be 950℃ for 1~5 hours; Reduced PLZT was composed of reduced and unreduced layer obviously and the reduced layer was transgranularly fractured while the unreduced ceramic was intergranularly fractured; Metallic lead and refractor oxides (PbO, ZrO2, TiO2, etc.) were found in the reduced layer, however, the crystal structure of PLZT was not found.

研究表明，PLZT具有较好的还原性能，还原层厚度与时间有线性关係，理想的还原条件为：950℃保温1~1.5h；还原样品有明显的分层结构，还原层表现出穿晶断裂而未还原层则是沿晶断裂的特徵；还原层主要由金属Pb及PbO， ZrO2， TiO2等氧化物组成，原先的晶体结构已不存在。

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。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。