THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

基于Matrix Profile的时间序列分割技术改进

时间序列分割是数据挖掘领域中的一个重要研究方向.目前基于矩阵轮廓(matrix profile,MP)的时间序列分割技术得到了越来越多研究人员的关注,并且取得了不错的研究成果.不过该技术及其衍生算法仍然存在不足:首先,基于矩阵轮廓的快速低代价语义分割算法中对给定活动状态的时间序列分割时,最近邻之间通过弧进行连接,会出现弧跨越非目标活动状态匹配相似子序列问题;其次,现有提取分割点算法在提取分割点时采用给定长度窗口,容易得到与真实值偏差较大的分割点,降低准确性.针对以上问题,提出一种限制弧跨越的时间序列分割算法(limit arc curve cross-FLOSS,LAC-FLOSS),该算法给弧添加权重,形成一种带权弧,并通过设置匹配距离阈值解决弧的跨状态子序列误匹配问题.此外,提出一种改进的提取分割点算法(improved extract regimes,IER),它通过纠正弧跨越(corrected arc crossings,CAC)序列的形状特性,从波谷中提取极值,避免直接使用窗口在非拐点处取到分割点的问题.在公开数据集datasets_seg和MobiAct上面进行对比实验,验证以上两种解决方案的可行性和有效性.

BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX

Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).

Applications of Lodrigues Matrix in 3D Coordinate Transformation

三个转变模型(囊狼， Molodensky，和 WTUSM ) 通常在二数据系统转变之间被使用。当旋转角度是小的时，线性模型被使用；然而，当旋转角度变得更大时，模型错误将被生产。在这篇论文，我们在场有三个主要术语的一个方法：传统的旋转 angles0,0,1/s 被代替与一， b，是三各自的价值在的 c 反对称或 Lodrigues 矩阵；(2 ) 直接并且精确地在旋转角度的任何价值计算七个参数的公式；并且一个相应调整模型被建立。这个方法不使用三角功能。相反它使用增加，减法，增加和分割，和方程的复杂性被减少，使计算容易、快。

Inverse Transformation of Elliptical Relative State Transition Matrix

A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.

Determination of Transmission Routing of OXC Nodes Based on AWG Multiplexer by Matrix Transformation

The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relation between the input and output wavelengths of the AWG multiplexer, the wavelength transmission routings of the space switching and wavelength switching OXC nodes are determined.

Matrix transformations of l^q(X) to l^p(Y )

Let X and Y be Banach spaces, 0 〈 q 〈 ＋∞, i ≤ p 〈 ＋∞. In this paper, we characterize matrix transformations of lq （ X ） to lp （ Y ）.

A Direct Transformation of a Matrix Spectrum

A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.

Orthogonalization of unified and extended Bézier basis and its transformation matrix

UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.

A Note on the Spectral Radius of Weighted Signless Laplacian Matrix

A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.

MATHEMATICAL ANALYSIS OF DRUG RELEASE FROM A MONOLITHIC MATRIX WITH AN INITIALLY LINEAR CONCENTRATION DISTRIBUTION

将化学工程学原理应用到药物释放这一多学科领域，研究了初始浓度分布为线性的平板混合药膜体系释放动力学模型，该模型可用来描述高装填量平板混合药膜的释放后期，并可简化为无限渗阱时的特定情况．根据该模型，计算了混合药膜内的浓度－距离分布和浓度－时间分布曲线，研究了释放介质体积对释放过程的影响．

Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations

The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of metamorphic mechanisms because it can only be used in the topological representation of mechanisms with single joints.In order to overcome the drawback of the adjacency matrix,a kind of new matrix named as extended adjacency matrix is proposed to express topological structures of all mechanisms.The extended adjacency matrix is not only suitable for the topological representation of mechanisms with single joints,but also can be used in that of mechanisms with multiple joints.On this basis,a method of matrix operations based on the extended adjacency matrix is proposed to analyze the configuration transformation of metamorphic mechanisms.The method is not only suitable for configuration analysis of metamorphic mechanisms with single joints as well as metamorphic mechanisms with multiple joints.The method is evaluated by calculating two examples representing metamorphic mechanisms with single joint and multiple joints respectively.It can be concluded that the method is effective and correct for analysis of configuration transformation of all metamorphic mechanisms.The proposed method is simple and easy to be achieved by computer programming.It provides a basis for structural synthesis of all metamorphic mechanisms.

An iterative algorithm of NWTLS-EC for three dimensional-datum transformation with large rotation angle

The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.

Low Co-Cultivation Temperature at 20°C Resulted in the Reproducible Maximum Increase in Both the Fresh Weight Yield and Stable Expression of GUS Activity after <i>Agrobacterium tumefaciens</i>-Mediated Transformation of Tobacco Leaf Disks

The importance of controlled temperature during the four-days co-cultivation period was evaluated under the most physiologically relevant conditions for Agrobacterium tumefaciens-mediated transformation of tobacco (Nicotiana tabacum L. cv. Xanthi (nn, Smith)) leaf disks. We compared the effect of temperatures ranging from 15°C, 18°C, 20°C, 22°C to 25°C on the stable expression of β-glucuronidase (GUS) activity of 14 days old hygromycin-selected leaf disks, and on the increase in the fresh weight yield of 28 days old kanamycin-selected calli. The highest average of GUS activity was obtained at 20°C among the five temperatures tested although the difference between the 18°C and 20°C treatment was not statistically significant. The GUS activity at 15°C was statistically lower than those at 18°C and 20°C. The GUS activity in 22°C treatment was an intermediate between the highest (18/20°C) and second highest averages (15°C), and was not statistically significantly different. The lowest average of GUS activity was observed at 25°C. The highest increase in the plate average of fresh weight yield was obtained at 20°C among the five temperature tested. The 20°C treatment was statistically significantly better than the 15°C and 18°C treatments. The 20°C co-cultivation treatment resulted in the higher FW yield than 22°C and 25°C even though the differences were not statistically significant. In conclusion, low co-cultivation temperature at 20°C resulted in the reproducible maximum increase in both the fresh weight yield and stable expression of GUS activity after transformation of tobacco leaf disks.

Drawing Weighted Directed Graph from It's Adjacency Matrix

This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

Effects of transforming growth factor β2 and connective tissue growth factor on induction of epithelial mesenchymal transition and extracellular matrix synthesis in human lens epithelial cells

AIM:To Investigate the effects of transforming growth factorβ2(TGF-β2)and connective tissue growth factor(CTGF)on transdifferentiation of human lens epithelial cells(HLECs)cultured in vitro and synthesis of extracellular matrix(ECM).METHODS:HLECs were treated with TGF-β2(0,0.5,1.0,5,10μg/L)and CTGF(0,15,30,60,100μg/L)for different times(0,24,48,72h)in vitro and the expression ofα-smooth muscle actin(α-SMA),the main component of the extracellular matrix typeⅠcollagen(Col-1)and fibronectin(Fn)were measured by using real-time polymerase chain reaction(PCR)and western-blot.RESULTS:TGF-β2 and CTGF significantly increased expression ofα-SMA mRNA and protein(P【0.05,P【0.001),Fn mRNA and protein(P【0.001),Col-1 mRNA and protein(P【0.001).TGF-β2 could induce HLECs expression of CTGF mRNA and protein in dosedependent manner(P【0.05,P【0.001).TGF-β2 and CTGF could induce HLECs to expressα-SMA,Fn and Col-1 in time-dependent manner.Each time of TGF-β2and CTGF induced HELCs expression ofα-SMA,Fn,Col-1 mRNA and protein was significant increase compared with control(P【0.05,P【0.001).CONCLUSION:TGF-β2 and CTGF could induce HLECs epithelial mesenchymal transition and ECM synthesis.

CHARACTERIZATIONS OF SOME MATRIX CLASSES OF QUASI-HOMOGENEOUS OPERATORS

In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.

Modulation of Matrix Metalloproteinase and TIMP-1 Expression by TGF-β_1 in Cultured Human RPE Cells

In order to investigate the effects of TGF-β1 on the expression of MMP-2, -9 and TIMP- 1 in human retinal pigment epithelial （RPE） cells, the third-sixth passage cultured RPE cells were treated with TGF-β1 at different concentrations （0.01, 0. 1, 1.0, 10 ng/mL）, the expression of MMP-2, -9 and TIMP-1 mRNA was detected by semi-qudntitative RT-PCR assays. MMP-2, -9 and TIMP-1 mRNA were expressed in the cultured RPE cells. The values of MMP-2/β-actin in the cells treated with 0.1, 1.0, 10 ng/mL TGF-β1 were 1.04±0.04, 1.07±0.02 and 1.11±0.03, respectively, significantly higher than in the control group （0.96±0.03, P〈0. 05-0.01）. The expression of MMP-2 mRNA could be up-regulated by TGF-β, , in a dose-dependent manner. The expression of MMP-9 mRNA in the cultured RPE cells was slightly up-regulated by various TGF-β1 concentrations treatment. The values of TIMP-1/β-actin in the cells treated with 0.01 and 0.1 ng/ mL TGF-β1 were 0.85 ±0.01 and 0.97 ± 0.02 respectively, significantly lower than in the control group （1.07±0.04, P〈0.01）, indicating that the expression of TIMP-1 mRNA was down-regulated by TGF-β1 at low concentrations. But along with the increase of TGF-β1 concentrations （1.0 and 10 ng/mL）, the expression of TIMP-1 mRNA was slightly up-regulated, not significantly different from that in the control group （P〉0.05）. It was concluded that TGF-β1 might play an important role in the up-regulation of the expression of MMP-2 in RPE cells and result in a directional shift in the balance between MMP and TIMP. This may be facilitated for RPE cells to migrate in the pathogenesis of vitreoretinopathy.