Off‐grid DoA estimation method of wideband signals

In this paper, an off‐grid direction of arrival (DoA) estimation method is proposed for wideband signals. This method is based on the sparse representation (SR) of the array covariance matrix. Similar to the time domain DoA estimation methods, the correlation function of the sources was assumed to be the same and known. A new measurement vector is obtained using the lower‐left triangular elements of the covariance matrix. The DoAs are estimated by quantizing the entire range of continuous angle space into discrete grid points. However, the exact DoAs may be located between two grid points; therefore, this estimation has errors. The accuracy of DoA estimation is improved by the minimization of the difference between the new measurement vector and its estimated values. Simulation results revealed that the proposed method can enhance the DoA estimation accuracy of wideband signals.     

Prime divisors of sparse integers

We obtain a lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits. This revised version was published online in August 2006 with corrections to the Cover Date.     

Prefiltration technique via aggregation for constructing low‐density high‐quality factorized sparse approximate inverse preconditionings

This paper considers a new approach to a priori sparsification of the sparsity pattern of the factorized approximate inverses (FSAI) preconditioner using the so‐called vector aggregation technique. The suggested approach consists in construction of the FSAI preconditioner to the aggregated matrix with a prescribed sparsity pattern. Then small entries of the computed ‘aggregated’ FSAI preconditioning matrix are dropped, and the resulting pointwise sparsity pattern is used to construct the low‐density block sparsity pattern of the FSAI preconditioning matrix to the original matrix. This approach allows to minimize (sometimes significantly) the construction costs of low‐density high‐quality FSAI preconditioners. Numerical results with sample matrices from structural mechanics and thin shell problems are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

在线滤波技术在光纤马赫-德尔交叉复用器中的应用

为构造出与理想梯形滤波器接近的滤波形状，在单级光纤马赫-德尔交叉复用器的基础上，引入在线滤波技术；通过增加干涉级数和调整2对干涉臂的干涉长度和耦合器的耦合比，实现了逼近宽带陡沿的滤波输出。通过与梯形滤波器傅里叶展开式的比较，计算得到了器件的最佳参数，器件的滤波性能以及温度稳定性相对于单级结构得到了明显提高。根据理论计算，成功制作出通道间隔为50GHz的样品器件。其输出为-0.5dB，带宽大于0.185nm，相邻通道隔离度大于30dB，满足了DWDM系统指标要求。     

Linear Ramsey numbers of sparse graphs

The Ramsey number R(G₁,G₂) of two graphs G₁ and G₂ is the least integer p so that either a graph G of order p contains a copy of G₁ or its complement G^c contains a copy of G₂. In 1973, Burr and Erd?s offered a total of $25 for settling the conjecture that there is a constant c = c(d) so that R(G,G)≤ c|V(G)| for all d‐degenerate graphs G, i.e., the Ramsey numbers grow linearly for d‐degenerate graphs. We show in this paper that the Ramsey numbers grow linearly for degenerate graphs versus some sparser graphs, arrangeable graphs, and crowns for example. This implies that the Ramsey numbers grow linearly for degenerate graphs versus graphs with bounded maximum degree, planar graphs, or graphs without containing any topological minor of a fixed clique, etc. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Infinite classes of anti‐mitre and 5‐sparse Steiner triple systems

In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class modulo 36. The third construction generates many infinite classes of anti‐mitre STSs in the remaining possible orders. As a consequence of these three constructions we can construct anti‐mitre systems for at least 13/14 of the admissible orders. For 5‐sparse STS(υ), we give a construction for υ ≡ 1, 19 (mod 54) and υ ≠ 109. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 237–250, 2006     

一些稀疏图的强边染色（英文）

图G的强边染色是指对图G进行正常边染色使得任意长度为3的路的三条边染不同的颜色.图G的强边色数,记为χ’_s(G),是使得图G是强k边着色的最小正整数kk.2015年,Zang [arXiv:1510.00785]证明了:最大度△(G)=5的图G,χ’_s(G)≤37.本文证明了:最大度△(G)=5且最大平均度小于8/3(或者14/5)的图G,χ’_s(G)≤13 (或者14).另外,本文证明了:最大度△(G)≥3的不含K_2,3-图子式的图G,χ’_s(G)≤4△(G)-6,这个界是紧的.     

“模式识别”课程线上线下混合教学模式探索与实践

在模式识别课程教学中,针对传统线下课程短板,开展线上与线下相结合的混合教学模式教学改革探索。阐述了本课程教学改革的教学环节设计、教学实施方法、考核方式等,以思维导图和综合案例串联庞杂知识点,采用多样化手段,加强对学生创新思维和能力的培养。教学实践证明,该课程教学改革调动了学生主动性,培育了其创新能力与科学精神,丰富了线上线下混合教学改革的理论研究。     

基于问题导向的在线教学研究

本文以“电力电子技术基础”的在线教学为例,开展以学生为中心的基于问题导向的教学方法优化实践。教学过程中,结合学校教师教学发展中心组织的EMI教师培训,对教学计划、教学重点进行了大力度的改进;同时,结合过程中与学生的交互、期末学生的反馈以及同行专家的建议,对本次的优化改进进行了教学分析、分析、反思和总结,以期不断提升本课程的教学质量,并为其它工科类课程的教学优化提供借鉴。