The Existence of Positive Bounded Entire Solutions of Second Order Quasilinear Elliptic Equations

Ｉｎｔｈｉｓｐａｐｅｒｗｅａｒｅｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｅｎｔｉｒｅｓｏｌｕｔｉｏｎｓｏｆｓｅｃｏｎｄｏｒｄｅｒｑｕａｓｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅ ｑｕａｔｉｏｎｓｏｆｔｈｅｔｙｐｅｄｉｖ(｜Ｄｕ｜ｐ- 2 Ｄｕ) +ｆ(ｘ ,ｕ) =0 ,ｘ∈ＲＮ,(1 )ｗｈｅｒｅｆ(ｘ,ｕ)ｉｓａｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｏｎＲＮ× (0 ,∞ ) .Ｔｈｉｓｐｒｏｂｌｅｍａｐｐｅａｒｓｉｎｔｈｅｓｔｕｄｙｏｆｎｏｎ -Ｎｅｗｔｏｎｉａｎｆｌｕｉｄｓａｎｄｎｏｎ -Ｎｅｗｔｏｎｉａ…     

The Equivalence Forms of Random Kolmogorov Forward（Backward） Equations

The concepts of Markov process in random environment, q-matrix in random environment and q-process in random environment are introduced. Three forms of random Kolmoogrov farward （or backward） equations are introduced and the equivalence of these three forms are also proved. Moreover any conservative q-process in random environment satisfies random Kolmogrov backward equation.     

求解矩阵方程组AX=C,XB=D的迭代法

给出了求解矩阵方程组ＡＸ＝Ｃ,ＸＢ＝Ｄ的迭代法,迭代收敛到它的极小Ｆ－范数解,并给出了此极小Ｆ－范数解的显式．     

多项式恒等式d^HM（AX）=d^HM（XA）成立的条件

讨论Ａ∈ＧＬ（ｎ，ｃ）时ＶＸ∈Ｍｎ（Ｃ），多项式恒等式ｄ＾ＨＭ（ＡＸ）＝ｄ＾ＨＭ（ＸＡ）成立的充要条件，这里Ｈ是ｎ次对称群Ｓ的子群，而ｄＨＭ表示由群Ｈ的酉表示Ｍ诱导的矩阵函数。     

Wavelet Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind

Daubechies interval wavelet is used to solve numerically weakly singular Fredholm integral equations of the second kind. Utilizing the orthogonality of the wavelet basis,the integral equation is reduced into a linear system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse,while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally,numerical example is presented to show the application of the wavelet method.     

The Features of the Ecological Environment and Protective Solutions along the Qinghai-Tibet Railway

On29June,2001aninaugurationceremonyfortheQuinghai TibetRailway,aprojectattractingworldwideattention,washeldsimultaneouslyattheCityofGolmudinQinghaiprovince,andtheCityofLhasainTibetAutonomousRegion,indicatingthattheconstructionofthesectionfromGolmudtoLhasaoftheQinghai TibetRailwaywasfullytocarryout.ThePlateauofQinghai Tibethasaveryfragileecologicalenvironment.ThestategaveprioritytotheissueoftheecologicalenvironmentalprotectionintheconstructionoftheQinghai TibetRailway.PresidentJiangZh…     

The Effect of Cyclic Stretching on Matrix Production, Mineralization and Differentiation of Osteoblasts

A four-point bending apparatus is used to investigate the effects of stretching on collagen synthesis, mineralization and differentiation of osteoblasts. Cells are stretched at 1500με for 24 hours. The responses of osteoblasts to mechanical signal of physiological stretching are evaluatedfrom three aspects: collagen production, extracellular inorganic calcium secretion and ALP activity. The results show that osteoblasts decrease the collagen synthesis, calcium secretion and ALP activity compared to the control cells (65.82 %, 73.51%, 48.10 96 respectively ), confirming that cyclic stretching at 1500με inhabits the ohvsiological activity of osteoblasts.     

Theoretical study on photophysical property of C60M（CO）5 （M=Cr,Mo and W）

Configurations of three η2 models of transition-metal [60]fullerene derivatives C60M（CO）5（M=Cr, Mo and W） have been optimized at B3LYP/LanL2DZ level. On the basis of the optimized geometrical structures, their electronic spectra and the frequency dependence of third-order nonlinear optical polarizabilities γ in different optical processes of third-harmonic generation （THG）, electric-field-induced second-harmonic generation （EFISHG） and degenerate four-wave mixing （DFWM） are calculated by using TDB3LYP model based on LanL2DZ level coupled with the SOS （sum-over-state） method. The obtained results show that their electronic spectra have a red shift compared with that of [60]fullerene and different transition-metal functional groups added to C60 cage may result in different spectrum properties. For the three studied species, （η^2-C60）Mo（CO）5 has the largest third-order nonlinear optical polarizability.     

耦合矩阵方程AX+XB=C,DX+X~TE=F的递度迭代算法

通过应用递阶辨识原理和推广求解矩阵方程AX=b的递度迭代算法,本文给出了求解耦合矩阵方程AX+XB=C,DX+XTE=F的递度迭代算法。分析表明,只要矩阵方程有唯一解,则对任何初始值此算法给出的迭代解都快速收敛到其真实解。一个数值例子表明了此算法的有效性。     

The Further Results of the Chromatic Uniqueness of Certain Bipartite Graphs K （m,n）- A

With its comprehensive application in network information engineering （e. g. dynamic spectrum allocation under different distance constraints ） and in network combination optimization （e. g. safe storage of deleterious materials）, the graphs＇ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K （ m, n） - A （A belong to E（K （m, n） ） and ｜ A ｜≥ 2） is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K（m, n） - A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.     

求矩阵方程AXB+CYD=E自反最佳逼近解的迭代算法

利用复合最速下降法的迭代算法对基于自反矩阵(或反自反矩阵)下广义Sylvester矩阵方程AXB+CYD=E最佳逼近解进行了研究,证明了无论矩阵方程AXB+CYD=E是否相容,该算法都可以用于计算其最佳逼近解.最后,通过2个数值实验证明了该算法的可行性.     

矩阵方程的反Hermite自反矩阵问题的解

通过广义奇异值分解定理,得到了矩阵方程AHXA=B的反Hermite-自反解存在的一个充要条件,并导出了这个矩阵方程的与已知矩阵最佳逼近的反Hermite-自反解,最后相应地获得了方程的最小范数解.     

矩阵方程AHXA=B的自反解及其最佳逼近

通过广义奇异值分解定理,得到了矩阵方程AHXA=B的自反解存在的一个充要条件,并导出了这个矩阵方程的与已知矩阵最佳逼近的自反解.     

线性矩阵方程的埃尔米特自反半正定解

利用埃尔米特自反正半定矩阵的表示定理,建立了线性矩阵方程在埃尔米特自反半正定矩阵集合中可解的充分必要条件,得到了解的一般表达式。最后对任意一个给定的复矩阵,推导出了相关的最佳逼近问题解的表达式。     

一类矩阵方程组AX=B,XD=E的对称解与反对称解

考虑矩阵方程组AX=B,XD=E的对称解与反对称解, 利用对称(反对称)矩阵的性质和矩阵对的标准相关分解(CCD), 给出了矩阵方程组对称解(反对称解)存在的充分必要条件及解的一般表达式, 并讨论了对任意给定矩阵的最佳逼近问题.     

矩阵方程组(AX=B,XC=D)的Hermitian反自反（反Hermitian反自反）最小二乘解及其最佳逼近

研究矩阵方程组(AX=B, XC=D)的Hermitian反自反(反Hermitian反自反)最小二乘解. 利用分块矩阵和Hermitian反自反(反Hermitian反自反)矩阵的性质, 得到了解的一般表达式, 并研究了与其相关的任意给定矩阵的最佳逼近问题.     

矩阵方程组AX=B,CXD=E的广义自反解及其最佳逼近

对于给定的A∈Ct×m,B∈Ct×n,C∈Cp×m,D∈Cn×q,E∈Cp×q,通过奇异值分解和广义奇异值分解,我们得到了AX=B,XCD=E有广义自反解的充要条件,给出了一般解的表达式,在此基础上我们给出了最佳逼近解的表达式。     

矩阵方程A^HXA=B的反自反解及其最佳逼近

利用广义奇异值分解定理，得到了矩阵方程A^HXA=B的反自反解存在的一个充要条件，并获得了相应的通解表达式和最佳逼近解，最后获得了最小范数解。     

实四元数矩阵方程的广义反对称酉反对称解

利用广义反对称酉反对称矩阵的性质和矩阵的自反逆的理论,得到了实四元数矩阵方程AX=C和矩阵方程组[A1X=C1,A2X=C2]的广义反对称酉反对称解的存在条件及其通解表达式．     

矩阵方程ATXA=D的广义双对称最小二乘解

本文利用矩阵的标准相关分解给出了矩阵方程A^TXA=D在SRp^nxn上最小二乘解的通式。