四维Clifford代数的相似与合相似

两四元数相似当且仅当它们有相同的实部和模,两四元数合相似当且仅当它们有相同的模.应用四维Clifford代数的矩阵表示,得到了四维Clifford代数中两元素相似或合相似的充分必要条件.     

基于应变模态和稀疏贝叶斯学习的网架结构损伤识别

传统稀疏贝叶斯学习算法进行损伤识别时需要对每个单元进行刚度损伤系数的迭代更新,当结构单元众多时,存在计算效率低和对振型的完备性要求高等问题.本文提出了损伤识别两步法,首先利用应变模态差指标进行疑似损伤单元的判断;接着以单元刚度损伤系数为目标参数,建立结构损伤识别的多层次稀疏贝叶斯学习模型,利用稀疏贝叶斯学习算法进一步识...     

Coarse-Grained Pruning of Neural Network Models Based on Blocky Sparse Structure

Deep neural networks may achieve excellent performance in many research fields. However, many deep neural network models are over-parameterized. The computation of weight matrices often consumes a lot of time, which requires plenty of computing resources. In order to solve these problems, a novel block-based division method and a special coarse-grained block pruning strategy are proposed in this paper to simplify and compress the fully connected structure, and the pruned weight matrices with a blocky structure are then stored in the format of Block Sparse Row (BSR) to accelerate the calculation of the weight matrices. First, the weight matrices are divided into square sub-blocks based on spatial aggregation. Second, a coarse-grained block pruning procedure is utilized to scale down the model parameters. Finally, the BSR storage format, which is much more friendly to block sparse matrix storage and computation, is employed to store these pruned dense weight blocks to speed up the calculation. In the following experiments on MNIST and Fashion-MNIST datasets, the trend of accuracies with different pruning granularities and different sparsity is explored in order to analyze our method. The experimental results show that our coarse-grained block pruning method can compress the network and can reduce the computational cost without greatly degrading the classification accuracy. The experiment on the CIFAR-10 dataset shows that our block pruning strategy can combine well with the convolutional networks.     

Body‐based activities in secondary geometry: An analysis of learning and viewpoint

Body‐based activities have the potential to support mathematics learning, but we know little about the impact they have in the classroom. This study compares high school geometry students learning through either body‐based or analogous non‐body‐based activities over the course of a two‐week unit on similarity. Pre‐ and post‐tests revealed that while students in both conditions showed gains in content area comprehension over the course of the study, the body‐based condition showed significantly greater gains. Further, there were differences in the language students used to describe the learning activities at the end of the unit that may have contributed to the differences in learning gains. The students in the body‐based condition included more mathematical and nonmathematical details in their recollections. Additionally, students in the body‐based condition were more likely to recall their experiences from a first‐person perspective, while students in the control condition were more likely to use a third‐person perspective.     

On the connection between the representation type of an algebra and its lattice of preradicals

In this paper, we study lattices of preradicals which are not small classes (in which case we say that the corresponding rings are p-large), and specially we consider some infinite representation type algebras. We construct an injective assignment between lattices of preradicals, using a full functor between the corresponding categories of modules, that satisfies certain conditions. We show that the polynomial ring over any field is p-large, and we use this fact to provide examples and some classes of algebras (both tame and wild) which are p-large.     

Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory

This paper aims to present, in a unified manner, algebraic techniques for least squares problem in quaternionic and split quaternionic mechanics. This paper, by means of a complex representation and a real representation of a generalized quaternion matrix, studies generalized quaternion least squares (GQLS) problem, and derives two algebraic methods for solving the GQLS problem. This paper gives not only algebraic techniques for least squares problem over generalized quaternion algebras, but also a unification of algebraic techniques for least squares problem in quaternionic and split quaternionic theory.     

差分吸收激光雷达回波信号统计模型的研究

差分吸收激光雷达回波信号统计模型是研究差分吸收激光雷达系统的基础,但是现有的统计模型中均没有考虑大气湍流导致的激光闪烁对回波信号的影响。针对已有统计模型的缺陷和应用需要,综合考虑了大气湍流导致的激光闪烁、目标反射斑纹、接收噪声以及发射功率波动对回波信号统计特性的影响,提出了一种改进的长程差分吸收激光雷达回波信号统计模型,分析了该模型的统计特性。仿真结果表明大气湍流导致的激光闪烁对回波信号统计特性的影响十分显著,同时也验证了该统计模型比已有统计模型更精确、更符合实际。     

The generalized quaternion matrix equation AXB+CX⋆D=E

In this paper, we discuss the generalized quaternion matrix equation AXB+CX^⋆D=E, where X^⋆ is one of X, X^*, the η-conjugate or the η-conjugate transpose of X with η∈{i,j,k}. Two new real representations of a generalized quaternion matrix are proposed. By using this method, the criteria for the existence and uniqueness of solutions to the mentioned matrix equation as well as the existence of X=± X^⋆ solutions to the generalized quaternion matrix equation AXB+CXD=E are derived in a unified way.     

The GLM representation of the two-component nonlinear Schrödinger equation on the half-line

The Gelfand-Levitan-Marchenko representation is used to analyze the initialboundary value problem of two-component nonlinear Schr¨odinger equation on the half-line.It has shown that the global relation can be effectively analyzed by the Gelfand-LevitanMarchenko representation. we also derive expressions for the Dirichlet-to-Neumann map to characterize the unknown boundary values.     

Representations of max-stable processes via exponential tilting

The recent contribution (Dieker and Mikosch, 2015) obtained representations of max-stable stationary Brown–Resnick process ${\zeta }_Z\left(t\right),t\in {\mathbb{R}}^d$ with spectral process $Z$ being Gaussian. With motivations from Dieker and Mikosch (2015) we derive for general $Z$, representations for ${\zeta }_Z$ via exponential tilting of $Z$. Our findings concern Dieker–Mikosch representations of max-stable processes, two-sided extensions of stationary max-stable processes, inf-argmax representation of max-stable distributions, and new formulas for generalised Pickands constants. Our applications include conditions for the stationarity of ${\zeta }_Z$, a characterisation of Gaussian distributions and an alternative proof of Kabluchko’s characterisation of Gaussian processes with stationary increments.