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The measurement matrix which plays an important role in compressed sensing has got a lot of attention. However, the existing measurement matrices ignore the energy concentration characteristic of the natural images in the sparse domain, which can help to improve the sensing efficiency and the construction efficiency. Here, the authors propose a simple but efficient measurement matrix based on the Hadamard matrix, named Hadamard-diagonal matrix (HDM). In HDM, the energy conservation in the sparse domain is maximised. In addition, considering the reconstruction performance can be further improved by decreasing the mutual coherence of the measurement matrix, an effective optimisation strategy is adopted in order to reducing the mutual coherence for better reconstruction quality. The authors conduct several experiments to evaluate the performance of HDM and the effectiveness of optimisation algorithm. The experimental results show that HDM performs better than other popular measurement matrices, and the optimisation algorithm can improve the performance of not only the HDM but also the other popular measurement matrices.

This research proposed a new approach to recognize face image under various lighting expression. The Proposed method is started by generating of the Left Diagonal Matrix (LDM) and the Right Diagonal Matrix (RDM). Subsequently, the dimensionality reduction is conducted by using Two- Dimensional Eigenface of the LDM and the RDM. The results of dimensionality reduction are selected the maximum value based on the corresponding features. Finally, the geometric similarity measurement model is carried out to obtain the recognition rate. The proposed method was evaluated using three different facial image databases, which are the YALE, the ORL and the UoB face image databases. Two until six column features were used to measure the similarity between the training and the testing sets. Experimental results revealed that the proposed method produced 92.2%, 94%, and 94.7% recognition rate for the YALE, the ORL, and the UoB face image databases respectively. The proposed method was also compared to the other methods. On the ORL face image database, the comparison results show that the proposed method outperformed to the Eigenface, the Fisherface, and the Laplacianfaces but not for O-Laplacianfaces and Two-Dimensional Principal Component Analysis method. On the YALE and the UoB face image databases, the proposed method outperformed to the other appearance methods which are the Eigenface, the Fisherface, the Laplacianfaces, the O-Laplacianfaces and Two-Dimensional Principal Component Analysis methods.

Freeze drying is a highly advanced dehydration technique used for preserving pharmaceuticals, human organs transplanted to others and highly heat sensitive food products. During the freeze drying, there are two layers formed namely dried region and frozen region. In this present work, a numerical model is developed to estimate the temperature distribution of both regions. The sample object considered is skimmed milk. The transient heat conduction equations are solved for both regions of dried and frozen region. The interface layer between the two region is considered as moving sublimation front as same as the realistic case. Radiative boundary condition at the top and convective boundary condition at the bottom are considered. The model has been solved by finite difference method and the scheme used is backward difference in time and central difference in space (implicit scheme), which generates set of finite difference equations forming a Tri-Diagonal Matrix. A computer program is developed in MATLAB to solve the tri-diagonal matrix. The temperature distribution along the length of the product with varying chamber pressures and the sublimation front temperature with time are estimated. The transient effect of sublimation front movement was estimated with different applied chamber pressure. It was noticed that at lower pressure the sublimation rate is very fast.

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA

We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

Inaccurate mass estimates have been recognized as an important source of uncertainty in structural identification, especially for large-scale structures with old ages. Over the past decades, some identification algorithms for structural states and unknown parameters, including unknown mass, have been proposed by researchers. However, most of these identification algorithms are based on the simplified mechanical model of chain-like structures. For a chain-like structure, the mass matrix and its inverse matrix are diagonal matrices, which simplify the difficulty of identifying the structure with unknown mass. However, a structure with a non-diagonal mass matrix is not of such a simple characteristic. In this paper, an online joint state-parameter identification algorithm based on an Unscented Kalman filter (UKF) is proposed for a structure with a non-diagonal mass matrix under unknown mass using only partial acceleration measurements. The effectiveness of the proposed algorithm is verified by numerical examples of a beam excited by wide-band white noise excitation and a two-story one-span plane frame structure excited by filtered white noise excitation generated according to the Kanai–Tajimi power spectrum. The identification results show that the proposed algorithm can effectively identify the structural state, unknown stiffness, damping and mass parameters of the structures.

In this article, we study the boundedness of matrix operators acting on weighted sequence Besov spaces b ˙ p , w α , q . First we obtain the necessary and sufficient condition for the boundedness of diagonal matrices acting on weighted sequence Besov space b ˙ p , w α , q , and investigate the duals of b ˙ p , w α , q , where the weight is nonnegative and locally integrable. In particular, when 0

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