正的

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

This article takes the teaching of conic sections as an example. By designing worksheets, teachers can introduce the historical material about conic sections to students. By way of using Apollonius' definition of parabola, ellipse and hyperbola, teachers can introduce the geometric aspect of "conic section" to students. By using the concept of " latus rectum " in Conics , we can connect "conic sections"-- representation of geometrical aspect, with "the equation of conic sections"-- representation of algebraic aspect to improving insufficiency of text books.

同时本文也试著从历史文本中寻找材料，简单举例说明数学教师可以如何应用这些史料在几何单元教学上，例如三角函数的正余弦定理，最后再以圆锥曲线的正焦弦为例，说明如何利用数学史料於此单元的教学，尤其是阿波罗尼斯的《锥线论》中对圆锥曲线的3个命题，将此3个命题的内容与意涵，尤其是正焦弦在圆锥曲线的几何意义上所扮演的角色，将其适当地融入教学中，将可使学生真正学习圆锥曲线的几何知识，而不再只是代数形式的几何知识。

Based on the information taken from the subcompartmental records a comparison between the actual and normal forests was made and a new point of view was proposed in the article: in the case of cultivating timber-forest which is different in cutover age, age class and growing speed within the range of the whole forest station, the forest age class distribution showing the opposite shape of "J" is of more benefit to keeping the relative stability of all the age class area than the age class distribution of th...

本文在统计森林资源小班档案卡片有关资料的基础上，把现实林分与法正林相比较，用法正林学说来指导全场森林的调查。并提出了一个新的观点：在整个经营单位内，培育不同生长速度，不同主伐年龄，龄级期不同的用材树种，森林的龄级结构呈反"J"形分布此法正分布更有利于维持各龄级面积的相对稳定，并且，年伐量的波动不大，有利于森林的永续利用。

Then the finite element software ANSYS is used to simulate the orthotropic flattened Brazilian disc specimen subjected to diametrical compression, the accuracy of the approximate formula of compression displacement is checked. The formula is further modified with a semi-empirical and semi-analytical approach, and it is shown to have better accuracy than the original formula covering the whole range of orthotropic anisotropic index of rock, the error is less than 6%.

用有限元分析软件ANSYS模拟正交异性岩石的巴西圆盘试样的对径压缩实验；利用有限元分析结果对正交异性平台位移压缩公式进行精度检验，并用半经验半解析的方法，对该公式进行局部的修改，修改后的公式在岩石材料的正交异性指数的整个范围的总体评价上，误差小于6%，具有更好的计算精度。

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

It realizes the global optimal computation via the local interacting agents with abilities of local perceptivity, competition and cooperation, self-learning etc. Then orthogonal design is introduced to generate an initial population of points that are scattered uniformly over the feasible solution space and to generate a crossover operator. As a result, the resulting algorithm is more robust and statistically sound. For high dimensional functions, a large memory is needed in generating an initial population with orthogonal design. To overcome this problem, a method called subspace partition is proposed, so that the memory is one tenth that of original one.

它以Multi-Agent系统为基础，通过Agent间的相互作用与每个Agent所具有的知识和自学习功能来提高算法的全局优化能力和收敛速度；同时利用正交试验设计方法产生较好的初始种群和设计正交交叉算子以获得更好的后代；针对正交试验设计产生初始化种群在函数维数很高时需很大存贮空间的缺点，提出了子空间分割法来产生所需的初始化种群，它只需要原来存贮空间的十分之一。

The T; LH and FSH level of serum of male schizophrenia were lower than that of normal control, but the PRL level of serum of male were significant higher than that of normal control, f There wsa a significant relationship between psychiatric symptoms and sex hormones level. There was a positive correlation between extreme and pugnacity factor of PANSS and T level of serum in male schizophrenic patients, There was a negative correlation between psychopathological scores and 〓level of serum in female schizophrenic patients, g There was a significant correlation between neuropsychological tests scores and sex hormones level of serum. There was a significant positive correlation between cognitive function and T level of serum in male schizophrenic patients. There was a significant positive correlation between cognitive function and 〓 in female schizophrenic patients.

治疗后病人的PRL较治疗前有显著提高；6）精神分裂症病人的精神症状与其性激素水平的相关有统计学意义，其中男性病人的T与PANSS中的偏激/好斗呈正相关，女性病人的〓与PANSS中的一般精神病理量表分呈负相关；7）精神分裂症病人的认知功能与其性激素水平的相关有统计学意义，男性病人的神经心理测验成绩与T呈正相关，女性病人的神经心理测验成绩与〓呈正相关。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！