Two linear subpattern dimensionality reduction algorithms

This paper presents two novel algorithms for feature extraction-Subpattern Complete Two Dimensional Linear Discriminant Principal Component Analysis (SpC2DLDPCA) and Subpattern Complete Two Dimensional Locality Preserving Principal Component Analysis (SpC2DLPPCA). The modified SpC2DLDPCA and SpC2DLPPCA algorithm over their non-subpattern version and Subpattern Complete Two Dimensional Principal Component Analysis (SpC2DPCA) methods benefit greatly in the following four points: (1) SpC2DLDPCA and SpC2DLPPCA can avoid the failure that the larger dimension matrix may bring about more consuming time on computing their eigenvalues and eigenvectors. (2) SpC2DLDPCA and SpC2DLPPCA can extract local information to implement recognition. (3)The idea of subblock is introduced into Two Dimensional Principal Component Analysis (2DPCA) and Two Dimensional Linear Discriminant Analysis (2DLDA). SpC2DLDPCA combines a discriminant analysis and a compression technique with low energy loss. (4) The idea is also introduced into 2DPCA and Two Dimensional Locality Preserving projections (2DLPP), so SpC2DLPPCA can preserve local neighbor graph structure and compact feature expressions. Finally, the experiments on the CASIA(B) gait database show that SpC2DLDPCA and SpC2DLPPCA have higher recognition accuracies than their non-subpattern versions and SpC2DPCA.

Establishment of infinite dimensional Hamiltonian system of multilayer quasi-geostrophic flow & study on its linear stability

A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.

Gravity effect calculation of threedimensional linear density distribution andits application

An algorithm for calculating gravity effect of three-dimensional (3D) linear density distribution is presented in this paper. The linear continuous density distribution is represented with 3D grid model, which has a resemblance to the velocity model used in some seismic tomography codes. The consensus in representation method of density model and velocity model facilitates the seismic-gravity-integrated interpretation or simultaneous inversion. The numerical test of synthetic data shows that although the analytical gravity formula for linear density distribution is more complex than that for piecewise constant density distribution, it takes less time to calculate the gravity effect with linear density model than that with piecewise constant density model. In addition, this method is used in the integrated interpretation of 3D seismological tomography and gravity data in Dabie Mountain area.

Certain Algebraic Test for Analyzing Aperiodic Stability of Two-Dimensional Linear Discrete Systems

This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.

Exact solutions and linear stability analysis for two-dimensional Ablowitz Ladik equation

The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the （GI/G）-expansion method, and the effects of the parameters （including the coupling constant and other parameters） on the linear stability of the exact solutions are analysed and numerically simulated.

k-MAJOR ORDER IN REAL INFINITE-DIMENSIONAL LINEAR SPACE AND ITS APPLICATION

In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.

A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled Approach

This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach.

A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle

This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.

Review of Dimension Reduction Methods

Purpose: This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various Dimension Reduction techniques. Methodology: The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where 341 papers were reviewed. Results: The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that have complex non-linear structures considered were Kernel Principal Component Analysis (KPCA), Multi-dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. Conclusion: The various application areas, strengths, weaknesses and variants of the DR techniques were explored. The different data types that have been applied on the various DR techniques were also explored.

Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE

It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation （3D- LPSE） approach, a 3D extension of the two-dimensional LPSE （2D-LPSE）, is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation （DNS） rather than a 2D-eigenvalue problem （EVP） procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.

Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

This paper presents a novel design method for discrete-time repetitive control systems （RCS） based on two-dimensional （2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality （LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

Instability in Three-Dimensional Magnetohydrodynamic Flows of an Electrically Conducting Fluid

The three-dimensional instability of an electrically conducting fluid between two parallel plates affected by an imposed transversal magnetic field is numerically investigated by a Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. The details of instability are analyzed by solving the generalized Orr-Sommerfeld equation. The critical Reynolds number Rec, the stream-wise and span-wise critical wave numbers αc and βc are obtained for a wide range of Hartmann number Ha. The effects of Lorentz force and span-wise perturbation on three-dimensional instability are investigated. The results show that magnetic field would suppress the instability and critical Reynolds number tends to be larger than that for two-dimensional instability.

Oscillation Criteria for Two-dimensional Differential Systems

This paper is concerned with the oscillation behavior of solution of the second order linear differential system u'= p(t)v,v'=-q(t)u,some sufficient conditions are given to improve some results in [1] where{p},{q} :[0,+∞) → [0+∞) are locally summable functions.

Fault Detection Based on Incremental Locally Linear Embedding for Satellite TX-I

A fault detection method based on incremental locally linear embedding(LLE)is presented to improve fault detecting accuracy for satellites with telemetry data.Since conventional LLE algorithm cannot handle incremental learning,an incremental LLE method is proposed to acquire low-dimensional feature embedded in high-dimensional space.Then,telemetry data of Satellite TX-I are analyzed.Therefore,fault detection are performed by analyzing feature information extracted from the telemetry data with the statistical indexes T2 and squared prediction error(SPE)and SPE.Simulation results verify the fault detection scheme.

Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry＇s theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.

Two-dimensional equations for thin-films of ionic conductors

A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.

DOWNWARD LOOKING SPARSE LINEAR ARRAY 3D SAR IMAGING ALGORITHM BASED ON BACK-PROJECTION AND CONVEX OPTIMIZATION

Downward Looking Sparse Linear Array Three Dimensional SAR(DLSLA 3D SAR) is an important form of 3D SAR imaging, which has a widespread application field. Since its practical equivalent phase centers are usually distributed sparsely and nonuniformly, traditional 3D SAR algorithms suffer from low resolution and high sidelobes in cross-track dimension. To deal with this problem, this paper introduces a method based on back-projection and convex optimization to achieve 3D high accuracy imaging reconstruction. Compared with traditional SAR algorithms, the proposed method sufficiently utilizes the sparsity of the 3D SAR imaging scene and can achieve lower sidelobes and higher resolution in cross-track dimension. In the simulated experiments, the reconstructed results of both simple and complex imaging scene verify that the proposed method outperforms 3D back-projection algorithm and shows satisfying cross-track dimensional resolution and good robustness to noise.

基于一元线性回归模型的供水网络中水表读数虚高问题研究

为了定量研究供水网络中总表漏水程度和分表读数虚高程度,根据水量平衡分析法的原理,结合大数据分析技术,建立了一元线性回归方程,回归常数代表总表漏水量程度,回归系数代表分表读数虚高程度。通过针对2021年某高校供水管网的实证研究表明,总表日均漏水量为15.5958吨,分表读数虚高率为1.07%。该方法对供水管网漏损率的精准评估等问题的解决提供了新的思路和方法。

一种三维混沌系统的混沌同步研究

混沌同步在保密通信领域有着广阔的应用前景,但要实现混沌保密通信,位于接收端和发送端的两个混沌系统必须达到混沌同步。为此,采用简单的线性反馈控制实现了一个新三维混沌系统的混沌同步控制,并应用Lyapunov稳定性理论,证明了两个混沌系统在线性反馈控制下实现混沌同步的条件。根据这些同步条件,只要给定系统参数值,就能够判断两个混沌系统是否能够达到混沌同步;另一方面,也可以根据这些判据来选取实现混沌同步的系统参数。最后,进行了计算机仿真,验证了所得到的同步条件是有效的。

昆都仑泄洪冲沙洞结构静动力三维有限元配筋计算

昆都仑水库是一座以防洪、供水为主的综合利用的中型水库。为改善水库泄洪条件,新建泄洪冲沙洞并布置于库区右岸山体内。首先,构建了泄洪冲沙洞三维有限元模型,模拟了各结构的精细构造部位;然后,采用三维线性有限单元法对泄洪冲沙洞开展静动力工况下变形、应力分析计算,基于有限元内力法进行内力计算并提出相应配筋方案;最后,进行结构限裂复核验算。选取的配筋计算方案实用可靠,为工程设计提供指导、验证复核作用并成功付诸实施。