查询词典 solutions

The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

Chapter 2 discuss firstly the local existence of solutions for a class of abstract functionalintegro-differential equations with unbounded delay by Schauder's fixed point theorem, then byintroducing an inequality condition and applying the continuity property of solutions it obtainsthe global existence of the solutions.

第二章先利用Schauder不动点定理讨论一类具有无限时滞抽象泛函积分微分方程解的局部存在性，然后引入一不等式条件并利用解的延拓性质获得了解的整体存在性

In the first part, we discuss the properties of solutions of (0.1) system with dif-ferent diffusion coefficient and the second boundary condition. The stability of non-negative constant solutions is given, some prior-estimate of the positive steaystateare proved by using the maximum principle and lower-upper solutions, the non-existence of non-constant positive solution, the global exitence of non-constant pos-itive solution and bifurcation solution of non-constant positive steady-states areobtained.

第一章讨论了系统(0.1)在扩散系数不相同的情况下非负常数解的稳定性，运用极值原理，上下解方法确定了系统(0.1)正平衡态解的一些先验估计，然后讨论了非常数解的不存在性，非常数正平衡态解的全局存在性及非常数正平衡态的分歧解。

This thesis is concerned with the existence of solutions of semilinear evolution impulsive equations as well as the existence of positive solutions of them. And the existence of solutions for terminal problems of impulsive differential equations is also concerned in this thesis.

本文主要研究半线性发展脉冲微分方程解和正解的存在性，以及脉冲微分方程终值问题解的存在性。

By adopting its complex variable solutions, the stress solutions of dislocation in bi-material on the whole plane were worked out, integration of which along the crack line would lead to the basic stress solutions in Cartesian and polar coordinates system of an bi-material incline crack.

应用两相材料中点位错在全平面的复势函数解，导出了两相材料中点位错在全平面的应力场解，进而将该解沿裂纹线积分得到倾斜裂纹的直角坐标及极坐标应力场基本解，同时利用该基本解退化出单根界面裂纹的直角坐标及极坐标应力场基本解。

At present,the rate laws and reaction mechanisms of pyrite oxidation,pyrite and chalcopyrite formation,uraninite and magnetite dissolution in aqueous solutions are mainly studied,and it is discovered that (1)oxidation rate of pyrite controlled by surface reaction assume fractional dependence on Fe3+ and O2 molalities in acid solutions;(2)Pyrite cannot nucleate directly from solutions below 300 ℃,it can only form initially through sulfidation of a FeS precursor. The rate equation of reaction between FeS and H2S to form pyrite is of the second order;(3)Chalcopyrite is formed by reactions of pyrrhotite or pyrite with Cu2+,the former proceeds via a series of mediate metastable phases of Cu-Fe sulfide,whereas the rate equation of the latter is apparently of the first order which is controlled by surface reaction;(4)The nonlinear behavior of magnetite dissolution at acid pH can be represented by a shrinking core model coupling with surface reaction and diffusion transport.

目前主要研究了水溶液中黄铁矿氧化、黄铁矿和黄铜矿形成、晶质铀矿和磁铁矿溶解的速率定律和反应机理，发现：(1)酸性溶液中黄铁矿的氧化速率对Fe3+和O2浓度呈分数依赖并受表面反应的控制；(2)低于300 ℃时黄铁矿不能从溶液中直接成核，而需初始地通过FeS先驱物的硫化生成，FeS与H2S反应形成黄铁矿的速率方程为二级；(3)磁黄铁矿或黄铁矿与Cu2+反应均可形成黄铜矿，前者经历了一系列准稳的Cu-Fe硫化物的中间物，后者的速率方程为表观一级并受表面反应的控制；(4)酸性pH时磁铁矿的非线性溶解行为可采用表面反应扩散输运耦合的收缩核模型来描述。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

Analyses for well posed characteristic and boundedness of the solutions to the models, especially for existence and stability of the corresponding cyclic steady-state solutions and other large time behavior of the solutions to the models have much meaning to assure that the models are practical and to understand the processes of this kind reactors.

分析模型解的适定性和有界性，特别是循环定态解的存在唯一性和稳定性以及其它解的大时间性态，对保证模型的实用，深刻了解此类反应器的过程特性有重要的意义。

The solutions we provide include natural gas and biogas purification, natural gas dehydration, hydrogen purification for fuel cell and industrial applications, and specialized solutions for other gases. Xebec also offers compressed air treatment solutions.

我们为客户提供的解决方案包括：天然气和生物气净化、天然气脱水、氢气净化、压缩空气净化处理，应用于燃料电池以及工业应用以及其他气体的特殊解决方案。

Nonnegativity of solutions, state stability, existence and uniqueness, asymptotical behavior of stable solutions, and existence of periodic solutions are studied.

研究了该问题解的非负性，稳态解的存在唯一性和渐近性以及周期解的存在性。

Aquatic or marsh-growing fern allies; known to have existed since the Cenozoic; sometimes included in Lycopodiales.

生活于水中或湿地的蕨类；从新生代生存至今；有时归于石松目之中。

The engine was uprated from a 90hp Franklin to a 125hp Lycoming.

改良过的引擎是从90hp到125hp莱康明富兰克林。