解空间

What differ from that of the researchers in the past is the consideration of the direction of Hopf bifurcation with Dirichlet boundary condition , that is, the conditions when the Hopf bifurcation periodic solutions are orbitally asymptotically stable with asymptotic phase.Our basic idea come from the results given by Tang[30]. We adopt the method used by Hassard in the Hopf bifurcation theorem in [24], which is to judge the existence and the direction of Hopf bifurcation, and the stability of the Hopf bifurcation periodic solutions.

与以前的研究者不同的是，本文不仅讨论了在Dirichlet边界条件下系统的Hopf分支在以扩散系数为分支参数的情况下的存在性和分支周期解的空间非齐次性，而且更多的关注了系统在Dirichlet边界条件下Hopf分支解的稳定性及Hopf分支的方向，也即系统定态解在何种条件下，当分支参数如何变化时产生Hopf分支且分支周期解是带渐近位相轨道渐近稳定的。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

The second section: Under the conditions of nonlinear boundary controbility, we consider the initial boundary value problem of Camassa—Holm equations with dissipative. By using the contractive mapping fixed point theorem and a priori estimates, the existence of global smooth solution, global attractor in H〓, time periodic solution or almost-periodic solution and the global exponential stability are proved.

第二部分：在非线性控制边界条件之下，对于带耗散项的Camassa—Holm方程的初边值问题，用压缩映射不动点原理及先验估计方法，证明了整体光滑解的存在性、整体解的指数稳定性、H〓空间中整体吸引子的存在性以及时间周期解和殆时间周期解的存在性。

In western painting it came from the primitive society when a few space factors appeared in the mural paintings sketched out by single line, the Greek bottle picture with the simple perspectivity, the Rome mural painting in which the perspectivity was originated, the Middle Ages when the perspectivity develop relatively slowly, the Renaissauce when the perspectivity highly developed, the Post Impressionism when Cezanne reformed the structure of space subjectively and orderly to open the gate of Modern Art, the 21 Century when the space was des-constructed and the idea of space developed pluratislically, at last the beginning of Actionism , to reach the end of the development of the space in painting, so to achieve the return from the three-dimensional illusion to the reality.

西方绘画由原始社会单线勾勒的壁画中极少的空间因素的运用，继而希腊瓶画中简单的透视。罗马时期透视法的萌芽，中世纪的相对滞缓的发展，文艺复兴时期对自然完善的表现至塞尚，则开启了现代艺术中空间主观化、秩序化的先河，进而出现二十世纪绘画空间解构、重组、多元化发展的状况，行为艺术的产生，实现了绘画空间由三维幻象到真实的还原，成为西方绘画的空间发展历程的终结点。

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

The result showed that there existed spatial variability of soil nutrients. N, P and K had medium variability, which were mainly affected by routine fertilization measures. On the contrary, Organic matter has a smaller spatial variability; Soil nutrient had semi-variance structure, and model best fit included Circular, Pentaspherical and Exponential. There existed medium spatial correlation in N, P, K and OM.

结果表明，土壤养分性质均存在着空间变异性，受常规施肥措施影响较大的碱解氮、速效磷、速效钾变异相对较大；常规施肥有机质投放较少，变异相对较小；土壤养分性质均存在半方差结构，分别拟合Circular、Pentaspherical、Exponential模型，碱解氮、速效磷、速效钾和有机质均显示中等的空间相关性。

Via basic and descriptor adverse transformation of matrix, an equivalent standard linear system is derived. Sufficient and necessary conditions are established for observers with disturbance decoupling and LTR in systems. Analysis showed that the necessary and sufficient condition for observers with LTR is disturbance decoupling to any undnown inputs. So it is con verted to the problem that observers are designed with disturbance decoupling.

通过矩阵的初等变换和广义逆变换，将非方广义系统等价地转化为正常状态空间的广义线性系统，并运用有关定理给出观测器具有干扰解耦和环路复现特性的充要条件，经分析可知，系统具有环路复现特性的充要条件是系统对于任何未知输入干扰解耦，则具有环路复现特性的干扰解耦观测器的设计问题转化为系统关于任何扰动都是解耦的。

In order to help for evaluating properties of soil in interaction more precisely, the paper applies elastic theory solution on different modulus in tension and compression for vertical load into semi-infinite elastic body. Through quoting Heaviside function, the solution of elasticity theory with different modulus in tension and compression is established founded on the solution of elasticity theory for the material incapable in tension and Mindlinsolution for equal modulus.

为使地基土在共同作用中的行为特征评价更为合理，本文应用了半空间问题竖向荷载下地基土的拉压模量不同弹性理论解，该理论解是通过引入Heaviside函数，利用不能承受拉应力材料的弹性理论解并结合拉压模量相等的经典Mindlin解而获得。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

在适当的条件下，我们建立了Hestenes-Powell 增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失