Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

FINITE GROUPS WHOSE AUTOMORPHISM GROUP HAS ORDER CUBEFREE

ＦＩＮＩＴＥＧＲＯＵＰＳＷＨＯＳＥＡＵＴＯＭＯＲＰＨＩＳＭＧＲＯＵＰＨＡＳＯＲＤＥＲＣＵＢＥＦＲＥＥＬＩＳＨＩＲＯＮＧＡｂｓｔｒａｃｔＬｅｔＧｄｅｎｏｔｅａｆｉｎｉｔｅｇｒｏｕｐ．Ｉｔｉｓｓｈｏｗｎｔｈａｔｉｆ｜Ａｕｔ（Ｇ）｜ｉｓｃｕｂｅｆｒｅ...     

C^n中子空间之间极端主角的一些应用

本文给出了Ｃ＾ｎ中子空间之间最大和最小主角在矩阵逼近，投影算子的扰动分析，群逆以及Ｏｒａｘｉｎ逆的扰动估计，条件数理论，Ｂｏｔｔ－Ｄｕｆｆｉｎ系统扰动分析中一些应用。     

应力对M-Z型InP/InGaAsP-EAM偏振

采用Agilent 81910A光子全参量测试仪,首次实验研究了InP/In1－xGaxAs1－yPy-MQW（Multiple-Quantum-Well,MQW）材料与衬底间因应力而产生的M-Z型光调制器的PDL影响以及由此引起的由差分群时延(Differential Group Delay,DGD)表征的偏振模色散(Polarization Mode Dispersion,PMD).研究结果表明,半导体MQW光调制器的PDL与DGD是一致的.因此在半导体光器件的制作过程中,应尽可能地减小衬底与波导芯层之间的因残存应力的存在造成对光器件的高速性能的不利影响.     

Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory