查询词典 first derivative

For the first-order ordinary differential equation system, the coefficient matrix of variables with derivative is decomposed into the triangular factor form and transformed into unit matrix.

对于一阶常微分方程组，将具有导数变量的系数矩阵作三角化分解，使其简化成单位矩阵。

The suspended sediment exponent model and quadratic inversion model solving spectrum reflectance, spectrum reflectance mean value and reflectance first-order derivative are established respectively, based on the analysis of spectrum characteristics. The results showed that the 900 nm wavelength exponent model can accurately quantitatively inverse the suspended sediment concentrations.

在对其光谱特性进行分析的基础上，分别建立了悬浮泥沙光谱反射率、光谱反射率均值和反射率一阶微分的指数反演模型和二次反演模型，结果显示 900 nm 波长的指数模型可以较准确地定量反演出悬浮泥沙浓度。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

However, the pseudo-triaxial strengths of several rocks from the best fitting solutions have great scatterness from the real magnitudes. Also, it does not correspond to the experimental results that rock has the same strength under conventional triaxial compression and tension; the maximum increase of strength from intermediate principal stress has a linear relation with the minor principal stress; and the first-order derivative of strength has an interruption at the peak point.

此外，统一强度理论认为岩石三轴伸长强度与常规三轴压缩强度相同，在最小主应力恒定时中间主应力引起的强度最大增加值随最小主应力线性增加，且强度关于中间主应力的一阶导数在峰值点是不连续的，这些都与试验结果不能完全协调。

At first, this thesis gives right calaculation results of derivative of Daubechies scaling function, the determine fashion of continuity is rendered.

本论文首先推导了Daubechies尺度函数导数或高阶导数的正确计算结果，给出了它的连续性的判定方式。

First of all, modeling image by fractional-order derivative and negative Sobolev space, this paper presents a fractional-order multi-scale variation PDE model, and the proposes the adaptive parameter selection method and obtains the field and scale adaptively algorithm for SAR image denoising.

首先利用分数阶导数以及负指数Sobolev 空间对图像进行建模，建立了分数阶多尺度变分PDE 模型，然后给出了模型参数自适应选择方法，并在此基础上提出了区域、尺度自适应的SAR 图像去噪算法。

What is unique about Australia is not its sun-baked, derivative society, clinging to the sea, but its first people, the oldest on earth, whose skill and courage in surviving invasion, of which the current onslaught is merely the latest, deserves humanity's support.

什麼是澳大利亚独特之处不是它的太阳烤，衍生的社会，抱住大海，但它的第一人，最古老的地球上，他们的技能和勇气，幸存的入侵，而目前的攻击仅仅是最新的，值得人类的支持。

It is proved by using the function approximation theory and martrix theory that for a degenerate elliptic equation of the first class, if the third boundary value condition is satisfied at its nondegenerate boundary and the given derivative values are satisfied at its degenerate boundary, then its solution is existent and unique.

摘 要 运用逼近理论及矩阵理论证明：如果一类退化椭圆型方程在非退化边界上满足第三边界条件，在退化边界上满足给定微商值，那么它的解是存在且唯一的。

METHODS:AsOR was conjugated to PL by EDC; The active ester of PEG derivative was reacted with the amino groups in PEI to form PEG-PEI conjugate; DNA was first complexed with PEG-PEI and then with AsOR-PL. In vitro transfection experiment was conducted in the galactose receptor positive Huh-7 cells.

分别制备AsOR-PL偶合物及PEG-PEI偶合物，然后按照不同的比例先后与报告基因DNA形成复合物，再进行Huh-7细胞的体外转染试验和静脉给药后小鼠体内的表达试验。

In this thesis,the AM1,MNDO,MINDO/3(mainly AM1)and INDO/S-CI semiempirical MO methods were used toinvestigate the excited-state intramolecular protontransfer reactions of salicylic acid derivatives—salicylic acid,methyl salicylate,salicylaldehyde,o-hydroxyaceto-phenone,salicylamide and 3-hydroxy-picolinamide (6 conformers and 2-3 anion species);2-(2'-hydroxy-5' methylphenyl) benzotriazole(4 conformers),2-(2' hydroxyphenyl) benzimidazole (3 conformers and 3anion species),Bis-2,5-(2-benzoxazolyl)hydroquinone(3 conformers),2-(2'-hydroxyphenyl)benzothiazole(2conformers) and 7-azaindole dimer (2 conformers).Theinvestigations were described as follows.Geometry optimization,relative stability andhydrogen bonding energy First,for sylicylic acid derivative molecules,the AM1,MNDO and MINDO/3 methods were used toinvestigate ground-state geometry optimization,energies,relative stabilities and hydrogen-bondingenergies on the five kinds of the molecules(designing 6 conformers and 2-3 anion species).Comparing with experimental data,the optimizedgeometry,the order of stability,the hydrogen-bonding energies and the distances between O-O in O-H..O hydrogen bonds by AM1 method were in agreementwith the experimental data,however,the C-C bondlengths optimized by MNDO and MINDO/3 were longer,C-O and O-H bond lengths were shorter;for C-N bondlengths,the results opitimized by MNDO method werethe same as those by AM1 method,nevertheless the C-Nbond lengths given by MINDO/3 method were muchshorter.For some sylicylic acid derivatives(e.g.methyl salicylate,salicylamide),the order ofstabilities on the conformers given by MNDO andMINDO/3 methods were not in agreement with theexisting conformers deduced by experimental methods,and the hydrogen bonding energies calculated by MNDO.and MINDO/3 methods were smaller.Second,the studyon the other systems found that the optimizedgeometry of the proton-transfered product with INDOmethod could not be obtained,only could theoptimized geometry of reactant be obtained,and thecalculated hydrogen bonding energies were greater.Many results of calculation indicated that the studyon the excited-state intramolecular proton transferreaction system using AM1 method was suitable andreliable.

本论文用AM1、MNDO、MINDO/3（主要是AM1）和INDO/S-CI半经验分子轨道方法对水杨酸衍生物系列——水杨酸、水杨酸甲酯、水杨醛、O-羟基乙酰苯酮、水杨酰胺和3-羟基吡啶酰胺（6种异构体和2-3种阴离子）；2-（2'-羟基-5'-甲基苯基）苯并三〓唑（4种异构体）；2-（2'-羟基苯基）苯并咪唑（3种异构体和3种阴离子）；2，5-二间氮杂氧茚氢醌（3种异构体）；2-（2'-羟基苯基）间〓杂硫茚（2种异构体）和7-〓吲哚二体（2种异构体）的激发态分子内质子转移反应在以下几个方面进行了较系统的理论研究：几何构型优化和相对稳定性及氢键能首先以水杨酸衍生物系列分子为例，用AM1、MNDO和MINDO/3方法考察了5种分子（每种分子设计6种异构体和2-3种阴离子）的基态几何构型优化，能量、相对稳定性和氢键能计算，通过和实验数据进行比较，AM1方法给出的优化几何构型、稳定性次序、氢键能和O—H。。。O氢键的0—0距离与实验数据吻合最好，MNDO和MINDO/3方法优化的C-C键长偏长，C-O键和O-H键长偏短；对于C-N键长，MNDO和AM1优化结果差别不大，而MINDO/3给出了过短的C-N键长，MNDO和MINDO/3方法给出的有些水杨酸衍生物分子（如水杨酸甲酯和水杨酰胺）异构体的稳定性次序和实验上推测的可存在异构体结果不一致，MNDO和MINDO/3方法给出的氢键能偏低，对其他体系的研究发现INDO方法常常不能得到质子转移产物的优化几何构型，只能得到反应物的优化构型，并且估算的氢键能偏高，大量的计算结果表明AM1方法对本论文研究的激发态分子内质子转移反应体系是适宜和可靠的。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。