Numerical solution of high-order differential equations by using periodized Shannon wavelets

In this paper, periodized Shannon wavelets are applied as basis functions in solution of the high-order ordinary differential equations and eigenvalue problem. The first periodized Shannon wavelets are defined. The second the connection coefficients of periodized Shannon wavelets are related by a simple variable transformation to the Cattani connection coefficients. Finally, collocation method is used for solving the high-order ordinary differential equations and eigenvalue problem. Some equations are solved in order to find out advantage of such choice of the basis functions.     

B-Splines with Arbitrary Connection Matrices

We consider a space of Chebyshev splines whose left and right derivatives satisfy linear constraints that are given by arbitrary nonsingular connection matrices. We show that for almost all knot sequences such spline spaces have basis functions whose support is equal to the support of the ordinary B-splines with the same knots. Consequently, there are knot insertion and evaluation algorithms analogous to de Boors algorithm for ordinary splines.     

Calderón problem for connections

In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9 Dos Santos Ferreira, D., Kenig, C., Salo, M., Uhlmann, G. (2009). Limiting Carleman weights and anisotropic inverse problems. Invent. Math. 178:119–171.[Crossref], [Web of Science ®] , [Google Scholar]] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11 Dos Santos Ferreira, D., Kurylev, Y., Lassas, M., Salo, M. (2016). The Calderón problem in transversally anisotropic geometries. J. Eur. Math. Soc., 18:2579–2626.[Crossref], [Web of Science ®] , [Google Scholar]]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy.     

On the double commutant of Cowen-Douglas operators

Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V^?(T) consisting of operators commuting with both T and T^? from a geometric viewpoint. We identify operators in V^?(T) with connection-preserving bundle maps on E(T), the holomorphic Hermitian vector bundle associated to T. By studying such bundle maps, the structure of V^?(T) as well as information on reducing subspaces of T can be determined.     

Connection coefficients between Boas-Buck polynomial sets

In this paper, a general method to express explicitly connection coefficients between two Boas-Buck polynomial sets is presented. As application, we consider some generalized hypergeometric polynomials, from which we derive some well-known results including duplication and inversion formulas.     

基于联系数不确定性分析的区间数多属性决策

区间数多属性决策通常是在某一算法下得到方案的排序,很少考虑区间数不确定性的影响,通过区间数转换成联系数,可以客观地反映区间数的不确定性,在此基础上,建立基于联系数的多属性决策模型,从而对不确定性进行较全面的取值分西,使决策结果更为合理.     

子孔径光学检测拼接准确度实验研究

实验研究了子孔径光学检测的拼接准确度.实验选取9个子孔径进行拼接,同时利用ZYGO干涉仪来测量子孔径和整个被检面的表面面形.实验发现,测量基准子孔径和整个被检面的时间间隔对子孔径拼接准确度的评价存在严重影响.为此,重点研究了产生影响的原因并提出了消除测量基准子孔径和整个被测面时间间隙影响的方法.最后,利用该方法研究了子孔径重叠面积对拼接准确度的影响.结果显示,当重叠面积比为7%时,PV和RMS的拼接误差分别为0.03λ(λ=632.8 nm) 和 0.01λ,并且重叠面积比和拼接准确度呈近似线性关系.     

Design Optimization of Connection Section for Concentrated Force Diffusion

In many load carrying thin shell structures, a connection section is arranged to transfer concentrated external forces to its main section. It is very important for the concentrated external forces to diffuse as uniformly as possible. Nevertheless the traditional design of uniform radial rib is not optimized. The present paper studies an integrated optimization procedure for design optimization of connection section. Variance constraint of node forces at the interface between the main section and connection section is firstly proposed as the evaluation criterion of concentrated force diffusion efficiency and introduced into the topology optimization formulation. Afterwards, for improving the manufacturability of the final design the topology optimization results are interpreted and further optimized by size or shape optimization. Two strategies of interpretation are examined. The first strategy is called strategy of making holes, which inserts a number of internal holes of regular geometric features and smooth boundary with B-spline curves in the continuum based on the topology optimization result. In the second strategy, an initial truss-like design is extracted from the characteristic of topology optimization result. Then a further shape and sizing optimization is followed to obtain the final optimal design. An example of design optimization of plane connection section is presented. The effectiveness of the present approach is demonstrated. The respective advantages and disadvantages of the two strategies are discussed.     

源端网络检测与抑制DDoS方法设计与实现

提出了一种源端网络DDoS攻击检测的方法。本方法基于BPF包过滤在源端网络的网关上监控数据包,通过计算网络报文的目的IP地址的信息熵进行可疑流量的检测,最终进一步使用连接跟踪的技术对可疑流量进行判别。本方法可以有效的鉴别出SYN Flood的流量,并在源端网络中直接拦截,节省计算资源。