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The purpose of this paper is to exploit the multiple-Toeplitz matrices reconstruction method combined with quadratic spatial smoothing processing to improve the direction-of-arrival (DOA) estimation performance of coherent signals at low signal-to-noise ratio (SNRs).

An improved multiple-Toeplitz matrices reconstruction method is proposed via quadratic spatial smoothing processing. Our proposed method takes advantage of the available information contained in the auto-covariance matrices of individual Toeplitz matrices and the cross-covariance matrices of different Toeplitz matrices, which results in a higher noise suppression ability.

Theoretical analysis and simulation results show that, compared with the existing Toeplitz matrix processing methods, the proposed method improves the DOA estimation performance in cases with a low SNR. Especially for the cases with a low SNR and small snapshot number as well as with closely spaced sources, the proposed method can achieve much better performance on estimation accuracy and resolution probability.

The study investigates the possibility of reusing pre-existing designs for the DOA estimation of the coherent signals. The proposed technique enables achieve good estimation performance at low SNRs.

The paper includes implications for the DOA problem at low SNRs in communication systems.

The proposed method proved to be useful for the DOA estimation at low SNR.

The purpose of this paper is to enhance the method developed by previous researchers. In addition to using the combined interference matrix, the combined connection matrix and the combined contact matrix of product components, the disassembly sequence matrix and the combined instability matrix with platform to evaluate instability of sub‐assemblies are built, and effects of changes of sub‐assembly disassembly directions or tools and the effect of gravity are considered to obtain the best disassembly sequence for a product with many components. A computer program is generated and results of two cases are compared with those of the available studies.

The methodology includes the combined interference matrix, the combined contact matrix and the combined connection matrix of components for a product. The combined instability matrix of sub‐assemblies, changes of sub‐assembly disassembly direction or tools, and the effect of gravity during operation are considered. The binary number system is used to simplify relations among components of a product.

This methodology enhances the existing method and software is generated. Results of two cases are compared and show the same optimum disassembly processes as those obtained from other researchers.

All matrices are defined by the directions of x, y and z with three axes perpendicular to each other. The computer program generated cannot be used for a product with components that must be disassembled in the directions different from the axes.

Two cases are used to investigate feasibility of the proposed methodology with the computer program generated. The first one is an electric drill, and the second one is a flash lighter.

The methodology described in this paper is feasible for study of disassembly processes of products. The software generated can be used to obtain the optimum disassembly process of products.

The linear matrix equations have wide applications in engineering, physics, economics and statistics. The purpose of this paper is to introduce iterative methods for solving the systems of linear matrix equations.

According to the hierarchical identification principle, the authors construct alternating direction gradient-based iterative (ADGI) methods to solve systems of linear matrix equations.

The authors propose efficient ADGI methods to solve the systems of linear matrix equations. It is proven that the ADGI methods consistently converge to the solution for any initial matrix. Moreover, the constructed methods are extended for finding the reflexive solution to the systems of linear matrix equations.

This paper proposes efficient iterative methods without computing any matrix inverses, vec operator and Kronecker product for finding the solution of the systems of linear matrix equations.

The Semiloof shell element stiffness and mass matrices are analysed. Various integration rules for the stiffness matrix are used, and the influence of these rules on the existence of mechanisms and on the element spectra is studied. Some methods for lumping the mass matrix are attempted with special reference to a method imposing a given behaviour of the spectra of eigenvalues.

In the present study we introduce a new recursive matrix inversion (RMI) algorithm for a distributed memory computer. The RMI algorithm was designed to meet the requirements of high performance flexible software for implementing different parallel optimization algorithms. Special consideration has been taken to ensure the usability and portability of the algorithm. The results we present show that a significant improvement in performance is attainable over the LU‐factorization algorithm included in the LAPACK library.

The purpose of this paper is to model the particle capture of elliptic magnetic matrices for parallel stream type high magnetic separation, which can be a guidance for the development of novel elliptic cylinder matrices for high-gradient magnetic separation (HGMS).

The magnetic field distribution around the elliptic matrices is investigated quantitatively and the magnetic field and gradient were calculated. The motion equations of the magnetic particles around the matrices were derived and the particle capture cross-section of elliptic matrices was studied and was compared with that of the conventional circular matrices.

Elliptic matrices can present larger particle capture cross-section than the conventional circular matrices and can be a kind of promising matrices to be applied to HGMS.

There is little literature investigating the magnetic characteristics and the particle capture of the elliptic matrices in HGMS, the study is of great significance for the development of novel elliptic magnetic matrices in HGMS.

Carbon nanotubes (CNTs) with exceptional mechanical, thermal and electrical properties are considered to be ideal for reinforcing high-performance structures. The interfacial stresses between the CNTs and surrounding matrix are important phenomena which critically govern the mechanical properties of CNTs-reinforced nanocomposites. A number of methods have been proposed to investigate the stress transfer across the CNT/matrix interface, such as experimental measurement and molecular dynamics (MDs). Experimental tests are difficulty and expensive. MDs simulations, on the other hand, are computationally inefficient. The purpose of this paper is to present a reasonably simplified model. Incorporating the simplified model, the analytical expressions of the interface stresses including the shear stress and longitudinal normal stress are obtained.

The analytical model consists of two concentric cylinders, namely a single-walled carbon nanotube (SWCNT) cylinder and a matrix cylinder, as the representative volume element (RVE). The interfacial stress analysis is performed using the shear lag model for the axisymmetric RVE. Analytical solutions for the normal stresses in the SWCNT and matrix, and the interfacial shear stress across the SWCNT/matrix interface are obtained. The proposed model has a great ability to theoretical prediction of the stress transfer between the matrix and CNTs.

In order to demonstrate the simulation capabilities of the proposed model, parametric studies are conducted to investigate the effects of the volume fraction of SWCNT and matrix modulus on the stress transfer. The axial stress in the matrix is decreasing with the increase of the volume fraction and decrease of the matrix modulus. As a result of more loads can be transferred to the SWCNT for a large volume fraction and small matrix modulus. These results show that using a large volume fraction and a small matrix modulus improves the efficiency of the stress transfer from the matrix to the CNTs.

A simple but accurate model using a simplified 2D RVE for characterizing the stress transfer in CNT-reinforced nanocomposites is presented. The predictions from the current method compare favourably with those by existing experimental, analytical and computational studies. The simple and explicit expressions of the interfacial stresses provide valuable analysis tools accessible to practical users.

A computer program, CALFEM, is presented. This interactive computer program is designed as a tool for teaching of the finite element method. No programming knowledge is needed. The program is well suited to solve problems in structural mechanics and for solution of field problems. A variety of finite elements is available. One objective when designing CALFEM was that the user shall understand every part of the computational procedure. The program is based on a command language. All information is stored in user‐defined matrices created by usage of commands. Required input to matrices are given on request from the program. The contents of the matrices can be looked upon at any time and new decisions can be made in the course of the run. The user of the program determines in which way he wants to proceed with the calculation process by choosing proper commands. This means that everything in the computational procedure is under the direct control of the user. This is in contrast to many conventional ‘black box’ finite element programs. Commands can be stored on user‐defined secondary storage files. The files can be edited in CALFEM and be used further on in the calculation procedure. The program is written in FORTRAN 77 and all calculations are performed in double precision.

A quantitative method for the estimation of the discrete transition matrix is developed for the periodic time‐varying system of state differential equations governing electrical synchronous machine behaviour. The approach allows the eigensystem of this transition matrix to be calculated to an arbitrary accuracy without significant added computational burden by using modal structural properties of the state‐space equations.

This paper describes the use of preset and programme parameters with the matrix interpretive scheme (which was considered in Part I) for the preparation of general purpose programmes for an electronic digital computer. The implications of partitioning the matrices when using the force method of analysis are considered in detail and the above techniques are applied to develop general purpose programmes for the calculations encountered when using this method of structural analysis. The general case, when all matrices are partitioned; the displacement method of structural analysis, and the use of magnetic tape storage, are considered in Part III.