可证明的

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

Motivated by Baker\'s result, we introduce a functional index‖E‖_∞to prove that if a mapping f which is from a normed space to a normed algebra satisfying‖ab‖=‖a‖‖b‖satisfies that‖E‖_∞is bounded,then either f is bounded or f is exponential.

受到Baker的结论启发，通过引入一个泛函指标‖E‖∞，证明了从赋范空间到满足范数可乘性的赋范代数的映射f，只要满足‖E‖∞是有界的，则f要么是有界的，要么是指数的。

Granted that the presence of these elements need not argue anauthorial awareness of novelistic construction comparable to that of Henry James,their presence does(15) encourage attempts to unify the novel's heterogeneous parts.

诚然，这些因素的存在并不能证明作者对88架构的意识可与亨利。詹姆斯的那种意识相比拟；然则，任何力图将88所有形形色色的因素统一起来的做法，在某种程度上注定是无法令人信服的。

When treat-ing the spectra, transition, scattering problems, we must use the semi-microscopicapproach. The main new conclusions in this thesis are following:We found the different shrinking effect in ∧ hypernuclei and 〓 hypernuclei, the shrink-ing effect in ∧ hypernuclei are confirmed in a recent experiment;We also found a new approach to treat the configuration mixing of ∧∧ hypernuclei and〓 hypernuclei and that the conversion process may change the spectra and widths of〓 hypernuclei;For the first time, we investigate the neutron star matter without the ∑ hyperon butwith the new meson 〓(975) and φ(1020), we found the contribution of 〓 and φ canmake the equation of state of neutron star soften, and the maximum mass of neutronstar reduces;we extract a set of optimum parameters of the optical potential for the scattering of 〓with nucleus, we found that the 〓 nucleus optical potential need a bigger imaginarypart.

本论文所取得的主要新成果是：独立揭示∧超核和〓超核的不同的收缩效应，其中∧超核的收缩效应被最新实验证实；提出了处理∧∧超核与〓超核混合态的新方法，并发现conversion过程使〓超核能谱和宽度改变；首次在中子星研究中在不包含∑超子的同时考虑新介子〓(975)和φ(1020)，并发现这可使中子星物质的状态方程变软、中子星半径变大、质量变小；独立提取了〓核光学势的一组最佳参数，并证明〓+核光学势要求一个较大的虚部。

The solvability of quadratic matrix inequalities of singular H∞ control problems with infinite zeros is studied in this paper. It is proved that the quadratic matrix inequality can be solved directly via the generalized eigenvalue problems. The previous method of solving the quadratic matrix inequality involving complicated decompositions and transformations of the systems is avoided.

摘要研究具有无穷远零点的奇异H∞控制问题的二次矩阵不等式的可解性，证明了通过求解广义特征值问题，可以直接求得二次矩阵不等式的解，从而简化了原需通过复杂的系统分解和变换来求解二次矩阵不等式的方法。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Summarily, our research showed that HMFS had important effects on beings process and activity, such as embryo development, the framework and function of CNS, and that was can't be negligible; the effect of HMFS is an result of long-term exposure; the effect of short-term exposure may be partial and revertible, or helpful to the organism at some time; long-term HMFS exposure may lead to serious negative influence.

综上所述，本研究证明，亚磁空间对生命过程和生命活动具有不可忽视的重要影响，这些影响可涉及胚胎发育、神经系统结构和功能的改变；亚磁空间的效应是长期效应；短期的影响可能是局部的和易恢复的，有的甚至可能是有益的；但长期作用有可能导致严重的负面作用。

Formal transaction model of its transaction system is given and its property of supporting dynamic security attributes revocation and serializability of the history of well-formed transactions is proven.

对系统框架中的关键组件进行了伪码描述，并通过形式化的事务模型证明了事务系统对动态安全属性撤销的支持和良构事务构成的历史的可串行化的性质。

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。