Digraphs and Inclusion Intervals of Brualdi-type for Singular Values

A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.     

On lie algebras of affine vector fields of ideal realizations of holomorphic linear connections

We study the properties of real realizations of holomorphic linear connections over associative commutative algebras \(\mathbb{A}\) _m with unity. The following statements are proved.If a holomorphic linear connection ? on M _n over \(\mathbb{A}\) _m (m ≥ 2) is torsion-free and R ≠ 0, then the dimension over ? of the Lie algebra of all affine vector fields of the space (M _mn ^? , ?^?) is no greater than (mn)² ? 2mn + 5, where m = dim_? \(\mathbb{A}\), \(n = dim_\mathbb{A} \) M _n , and ?^? is the real realization of the connection ?.Let ?^? =¹ ? ײ ? be the real realization of a holomorphic linear connection ? over the algebra of double numbers. If the Weyl tensor W = 0 and the components of the curvature tensor ¹ R ≠ 0, ² R ≠ 0, then the Lie algebra of infinitesimal affine transformations of the space (M _2n ^? , ?^?) is isomorphic to the direct sum of the Lie algebras of infinitesimal affine transformations of the spaces ( ^a M _n , ^a ?) (a = 1, 2).     

Categorical Realizations of Quivers

We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9 Gothen, P. B., King, Alastair D. (2005). Homological algebra of twisted quiver bundles. J. London Math. Soc. (2) 71(1):85–99.[Crossref], [Web of Science ®] , [Google Scholar]]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.     

Linear system identification via an asymptotically stable observer

This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero corresponding to a deadbeat observer. In this formulation, the Markov parameters of the observer are first identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to realize a state space model of the system. The basic mathematical formulation is derived, and numerical examples are presented to illustrate the proposed method.     

Polyhedral hyperbolic metrics on surfaces

Let S be a topologically finite surface, and g be a hyperbolic metric on S with a finite number of conical singularities of positive singular curvature, cusps and complete ends of infinite area. We prove that there exists a convex polyhedral surface P in hyperbolic space and a group G of isometries of such that the induced metric on the quotient P/G is isometric to g. Moreover, the pair (P, G) is unique among a particular class of convex polyhedra.      

定向可图的度偶序列

n为非负整数序列，若存在以该序列为度序列的图，则称n为可图的，特别的，若此图是一个定向图，该序列则称为是定向可图的，本提出了一个判断序列是否为定向可图的充分必要条件，并且在定理的证明过程中给出了一个在定理条件下构造所求定向图的有效算法。     

Realization and Smoothness Related to the Laplacian

For f L _n (T ^d ) and , the modulus of smoothness

Theory of semidefinite programming for Sensor Network Localization

We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub-networks in the input network. A preliminary version of this paper has appeared in the Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2005.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

超声动态向量血流成像的产品化实现

传统超声彩色多普勒成像测量的是血流沿超声传播方向上的速度分量,故无法得到垂直于超声传播方向的血流。向量血流成像是一种更加先进的超声血流成像技术。它不受角度限制,可以直接计算出血流速度的大小和方向。本文总结了现有多种超声向量血流成像技术的特点和发展情况,并从产品化实现的角度分析了各项技术的优缺点。从超声系统发射接收、血流成像、向量速度方向合成、显示等几个方面详述了迈瑞超声向量血流成像技术产品化实现过程中遇到的主要问题及解决方案。实验采用了中科院声学所研制的超声多普勒仿血流体模,通过向量血流成像和脉冲多普勒成像分别测量体模的仿血流速度。将向量血流成像直接计算出来的速度值与脉冲多普勒经过角度校正得到的速度进行对比。在不同条件下,经过多次测量,二者的平均相对误差均在10%以内。