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We investigate the one-dimensional cutting-stock problem integrated with the lot-sizing problem in the context of paper industries. The production process in paper mill industries consists of producing raw materials characterized by rolls of paper and cutting them into smaller rolls according to customer requirements. Typically, both problems are dealt with in sequence, but if the decisions concerning the cutting patterns and the production of rolls are made together, it can result in better resource management. We investigate Dantzig–Wolfe decompositions and develop column generation techniques to obtain upper and lower bounds for the integrated problem. First, we analyze the classical column generation method for the cutting-stock problem embedded in the integrated problem. Second, we propose the machine decomposition that is compared with the classical period decomposition for the lot-sizing problem. The machine decomposition model and the period decomposition model provide the same lower bound, which is recognized as being better than the linear relaxation of the classical lot-sizing model. To obtain feasible solutions, a rounding heuristic is applied after the column generation method. In addition, we propose a method that combines an adaptive large neighborhood search and column generation method, which is performed on the machine decomposition model. We carried out computational experiments on instances from the literature and on instances adapted from real-world data. The rounding heuristic applied to the first column generation method and the adaptive large neighborhood search combined with the column generation method are efficient and competitive. [ABSTRACT FROM AUTHOR]

We model the folding of ordinary paper via piecewise isometries R2→R3. The collection of crease lines and vertices in the unfolded paper is called the crease pattern. Our results generalize the previously known necessity conditions from the more restrictive case of folding paper flat (into R2); if the crease pattern is foldable, then the product (in a non-intuitive order) of the associated rotational matrices is the identity matrix. This condition holds locally in a multiple vertex crease pattern and can be adapted to a global condition. Sufficiency conditions are significantly harder, and are not known except in the two-dimensional single-vertex case. [Copyright &y& Elsevier]

Complex systems in the real world often can be modeled as network structures, and community discovery algorithms for complex networks enable researchers to understand the internal structure and implicit information of networks. Existing community discovery algorithms are usually designed for single-layer networks or single-interaction relationships and do not consider the attribute information of nodes. However, many real-world networks consist of multiple types of nodes and edges, and there may be rich semantic information on nodes and edges. The methods for single-layer networks cannot effectively tackle multi-layer information, multi-relationship information, and attribute information. This paper proposes a community discovery algorithm based on multi-relationship embedding. The proposed algorithm first models the nodes in the network to obtain the embedding matrix for each node relationship type and generates the node embedding matrix for each specific relationship type in the network by node encoder. The node embedding matrix is provided as input for aggregating the node embedding matrix of each specific relationship type using a Graph Convolutional Network (GCN) to obtain the final node embedding matrix. This strategy allows capturing of rich structural and attributes information in multi-relational networks. Experiments were conducted on different datasets with baselines, and the results show that the proposed algorithm obtains significant performance improvement in community discovery, node clustering, and similarity search tasks, and compared to the baseline with the best performance, the proposed algorithm achieves an average improvement of 3.1% on Macro-F1 and 4.7% on Micro-F1, which proves the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive assessment procedure for evaluating Ensemble-based Machine Learning algorithms in the context of exoplanet classification. Each of the algorithm hyperparameter values were tuned. Deployments were carried out using the cross-validation method. Performance metrics, including accuracy, sensitivity, specificity, precision, and F1 score, were evaluated using confusion matrices generated from each implementation. Machine Learning (ML) algorithms were trained and used to identify exoplanet data. Most of the current research deals with traditional ML algorithms for this purpose. The Ensemble algorithm is another type of ML technique that combines the prediction performance of two or more algorithms to obtain an improved final prediction. Few studies have applied Ensemble algorithms to predict exoplanets. To the best of our knowledge, no paper that has exclusively assessed Ensemble algorithms exists, highlighting a significant gap in the literature about the potential of Ensemble methods. Five Ensemble algorithms were evaluated in this paper: Adaboost, Random Forest, Stacking, Random Subspace Method, and Extremely Randomized Trees. They achieved an average performance of more than 80% in all metrics. The results underscore the substantial benefits of fine tuning hyperparameters to enhance predictive performance. The Stacking algorithm achieved a higher performance than the other algorithms. This aspect is discussed in this paper. The results of this work show that it is worth increasing the use of Ensemble algorithms to improve exoplanet identification. [ABSTRACT FROM AUTHOR]

The 1925 paper "On quantum mechanics" by M. Born and P. Jordan, and the sequel "On quantum mechanics II" by M. Born, W. Heisenberg, and P. Jordan, developed Heisenberg's pioneering theory into the first complete formulation of quantum mechanics. The Born and Jordan paper is the subject of the present article. This paper introduced matrices to physicists. We discuss the original postulates of quantum mechanics, present the two-part discovery of the law of commutation, and clarify the origin of Heisenberg's equation. We show how the 1925 proof of energy conservation and Bohr's frequency condition served as the gold standard with which to measure the validity of the new quantum mechanics. [ABSTRACT FROM AUTHOR]

Computer-assisted photometric determination of chemical compounds in paper matrices (chromatographic paper circles 10 mm in diameter) is described. A device with a video camera attached to a computer was developed for image density measurements. Matrices containing certified neutral-density glass filters and Congo Red in different concentrations were used. It was shown that the digital recording and computer-assisted photometric analysis of matrix images can be used for determining analyte concentrations in the matrices and assessing the optical homogeneity of these matrices. The advantages and areas of application the method were discussed. [ABSTRACT FROM AUTHOR]

We use Regev's double centralizer theorem from [7] to study invariants of matrices with group actions. This theory then has applications to trace identities and Poincaré series. [ABSTRACT FROM AUTHOR]

Abstract: An integrated model for ranking scientific publications together with authors and journals recently presented in [Bini, Del Corso, Romani, ETNA 2008] is closely analyzed. The model, which relies on certain adjacency matrices and obtained from the relations of citation, authorship and publication, provides the ranking by means of the Perron vector of a stochastic matrix obtained by combining and . Some perturbation theorems concerning the Perron vector previously introduced by the authors are extended to more general cases and a counterexample to a property previously addressed by the authors is presented. The theoretical results confirm the consistency and effectiveness of our model. Some paradigmatic examples are reported together with some results obtained on a real set of data. [Copyright &y& Elsevier]

Let k be a field of characteristic 0, and let f : kn→kn be a polynomial map with components of the form fi=xi+hi, where the hi are monomials. If the Jacobian determinant of the map f is a nonzero constant, then f is a tame automorphism. If, in addition, each hi is either constant or of degree 2 or more, then f is linearly triangularizable. [Copyright &y& Elsevier]

In this study, we introduce a system called Matrix Researcher2vec (MResearcher2vec) which generates researcher embedding vectors from their papers and research projects in researchmap and KAKENHI databases. The system includes data on 276,841 researchers, 6,161,592 papers, and research projects. Utilizing natural language processing techniques, the MResearcher2vec model extracts researcher vectors from the papers and research project summaries of KAKENHI grant recipients. The similarity between reseachers is then computed to visualize inter-researcher relationships. The machine learning results have been integrated into a web service, providing a novel approach for academic relationship mining. It can be applied in the matching of research contents and researchers in evaluation of industry-government-academia collaboration and joint research. It contributes in four aspects: (1) exchanges between researchers, (2) creation of opportunities for researchers and companies to connect, (3) further promotion of interdisciplinary research, and (4) reduction of lost opportunities for research institutions to acquire talents. [ABSTRACT FROM AUTHOR]

The present review paper examines the use of different types of polymeric matrix composites in hard tissue replacement applications. The review presents the actual state of the art in the fields of bioinert composites for permanent applications, biodegradable matrix composites for temporary applications and the emerging area of injectable composites. In all cases some recent developments are also discussed. The paper starts with an introduction to locate the reader. Bone–analogue composites are then extensively discussed. Several other systems based on an inert polymeric matrix are described, focusing on their proposed applications. A great emphasis is afterwards given to biodegradable matrix systems. The most widely used synthetic bioresorbable systems are analysed and compared with an example of natural origin degradable composites–starch based composites. Finally, composite systems that are non-processable by melt based routes and in many cases injectable are discussed in detail, including several recent developments on this emerging area of research. [Copyright &y& Elsevier]

In the present paper, we introduce the concept of idempotent-aided factorization (I.-A. factorization) of a regular element of a semigroup, which can be understood as a semigroup-theoretical extension of full-rank factorization of matrices over a field. I.-A. factorization of a regular element d is defined by means of an idempotent e from its Green's D -class as decomposition into the product d = u v , so that the element u belongs to the Green's R -class of the element d and the Green's L -class of the idempotent e, while the element v belongs to the Green's L -class of the element d and the Green's R -class of the idempotent e. The main result of the paper is a theorem which states that each regular element of a semigroup possesses an I.-A. factorization with respect to each idempotent from its Green's D -class. In addition, we prove that when one of the factors is given, then the other factor is uniquely determined. I.-A. factorizations are then used to provide new existence conditions and characterizations of group inverses and (b , c) -inverses in a semigroup. In our further research, these factorizations will be applied to matrices with entries in a field, and efficient algorithms for realization of such factorizations will be provided. [ABSTRACT FROM AUTHOR]

This paper focuses on addressing the linear quadratic (LQ) optimal control problem on an infinite time horizon for stochastic systems controlled by impulses. No constraint regarding the sign of the quadratic functional is applied. That is why our first concern is to find conditions which guarantee that the considered optimal control problem is well posed. Then, when the optimal control problem is well posed, it is natural to look for conditions which guarantee the attainability of the optimal control problem that is being evaluated. The main tool involved in the solution of the problems stated before is a backward jump matrix linear differential equation (BJMLDE) with a Riccati-type jumping operator. This is formulated using the matrix coefficients of the controlled system and the weight matrices of the performance criterion. We show that the well posedness of the optimal control problem under investigation is guaranteed by the existence of the maximal and bounded solution of the associated BJMLDE with a Riccati-type jumping operator. Further, we show that when the associated BJMLDE with a Riccati-type jumping operator has a maximal solution which satisfies a suitable sign condition, then the optimal control problem is attainable if and only if it has an optimal control in a state feedback form, or if and only if the maximal solution of the BJMLDE with a Riccati-type jumping operator is a stabilizing solution. In order to make the paper more self-contained, we present a set of conditions that correspond to the existence of the maximal solution of the BJMLDE satisfying the desired sign condition. [ABSTRACT FROM AUTHOR]

In response to the challenges of path planning in complex scenarios, to overcome the influence of optimal path determination by the precision of grid map sizes, and to escape the uncertainty in solving by intelligent algorithms, this paper designs a method for obtaining an adjacency matrix based on node planning of shortest path diagrams with polygonal obstacles and then uses the Dijkstra algorithm to get the shortest path. For irregular curved obstacles, an edge straightening method is proposed. To enhance the applicability of the path, this paper introduces the constraint of minimum turning radius. It researches path smoothing under obstacle conditions based on arcs and straight lines, providing practical solutions for different scenarios. Considering the need to maintain a safe distance due to the size of the moving carrier and the deviation in trajectory tracking, this paper conducts an expansion analysis of obstacles. It obtains the trajectory on the arc after edge straight line fitting, followed by further smoothing treatment. The method proposed in this paper demonstrates excellent accuracy and robustness in path planning through simulation verification, proving its practicality and effectiveness in complex environments. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear model is developed for a SEFFFE system employed for concentrating weak black liquor in an Indian Kraft Paper Mill. The system incorporates different operating strategies such as condensate-, feed- and product-flashing, and steam- and feed-splitting. This model is capable of simulating a MEE system by accounting variations in τ, U, Q loss, physico-thermal properties of the liquor, F and operating strategies. The developed model is used to analyze six different F including backward as well as mixed flow sequences. For these F, the effects of variations of input parameters, T 0 and F, on output parameters such as SC and SE have been studied to select the optimal F for the complete range of operating parameters. Thus, this model is used as a screening tool for the selection of an optimal F amongst the different F. An advantage of the present model is that a F is represented using an input Boolean matrix and to change the F this input matrix needs to be changed rather than modifying the complete set of model equations for each F. It is found that for the SEFFFE system, backward feed flow sequence is the best as far as SE is concerned. [Copyright &y& Elsevier]

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In the first part an solver for a semiseparable matrix of semiseparability rank p is derived, and in a second part we derive an solver for a band matrix with bandwidth . Both solvers are constructed in a similar way: firstly a Yule–Walker-like equation needs to be solved, and secondly this solution is used for solving a linear equation with an arbitrary right-hand side. Finally, a combination of the above methods is presented to solve linear systems with semiseparable plus band coefficient matrices. The overall complexity of this solver is plus lower order terms. In the final section numerical experiments are performed. Attention is paid to the timing and the accuracy of the described methods. [Copyright &y& Elsevier]

In this paper, we compute paradeterminants and parapermanents of some triangular matrices that give bihyperbolic numbers of the Fibonacci type. Using connections between the paradeterminant of triangular matrix and the lower Hessenberg determinant, we also obtain the general term of these sequences. [ABSTRACT FROM AUTHOR]

The paper addresses the issue of classification machine learning algorithm performance based on a novel probabilistic confusion matrix concept. The paper develops a theoretical framework which associates the proposed confusion matrix and the resulting performance metrics with the regular confusion matrix. The theoretical results are verified based on a wide variety of real-world classification problems and state-of-the-art machine learning algorithms. Based on the properties of the probabilistic confusion matrix, the paper then highlights the benefits of using the proposed concept both during the training phase and the application phase of a classification machine learning algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some additive results on gp-Hirano invertibility in Banach algebras. By applying our results, some new results for operator matrices are obtained. This extends the main results of [H. Zou, T. Li and Y. Wei, arXiv:2302.06080v1]. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that if H is the real quaternion division ring and n is an integer greater than 1, then every matrix in the special linear group SLn(H) can be expressed as a product of at most three commutators of unipotent matrices of index 2. [ABSTRACT FROM AUTHOR]

The class of generalized S D D 1 (G S D D 1 ) matrices is a new subclass of H -matrices. In this paper, we focus on the subdirect sum of G S D D 1 matrices, and some sufficient conditions to ensure that the subdirect sum of G S D D 1 matrices with strictly diagonally dominant (S D D) matrices is in the class of G S D D 1 matrices are given. Moreover, corresponding examples are given to illustrate our results. The class of generalized matrices is a new subclass of -matrices. In this paper, we focus on the subdirect sum of matrices, and some sufficient conditions to ensure that the subdirect sum of matrices with strictly diagonally dominant matrices is in the class of matrices are given. Moreover, corresponding examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In the field of radar target detection, the conventional approach is to employ the range profile energy accumulation method for detecting extended targets. However, this method becomes ineffective when dealing with non-stationary and non-uniform radar clutter scenarios, as well as long-distance targets with weak radar cross sections (RCSs). In such cases, the signal-to-noise ratio (SNR) of the target echo is severely degraded, rendering the energy accumulation detection algorithm unreliable. To address this issue, this paper presents a new extended target detection method based on the maximum eigenvalue of the Hermitian matrix. This method utilizes a detection model that incorporates observed data and employs the likelihood ratio test (LRT) theory to derive the maximum eigenvalue detector at low SNR. Specifically, the detector constructs a matrix using a sliding window block with the available data and then computes the maximum eigenvalue of the covariance matrix. Subsequently, the maximum eigenvalue matrix is transformed into a one-dimensional eigenvalue image, enabling extended target detection through analogy with the energy accumulation detection method. Furthermore, this paper analyzes the proposed extended target detection method from both theoretical and experimental perspectives, validating it through field-measured data. The results obtained from the measured data demonstrate that the method effectively enhances the SNR in low SNR conditions, thereby improving target detection performance. Additionally, the method exhibits robustness across different scattering center targets. [ABSTRACT FROM AUTHOR]

In this paper, we give a simple sufficient condition for the eigenvalue-separation properties of real tridiagonal matrices T. This result is much more than the statement that the pertinent eigenvalues are distinct. Its derivation is based on recurrence formulae satisfied by the polynomials made up by the minors of the characteristic polynomial det(xE - T) that are proven to form a Sturm sequence. This is a new result, and it proves the simple spectrum property of a symmetric tridiagonal matrix studied in a Grünbaum paper. Two numerical examples underpin the theoretical findings. The style of the paper is expository in order to address a large readership. [ABSTRACT FROM AUTHOR]

Accurate evaluation of the critical nodes in the system is essential work for a multiplatform avionics system (MPAS) for resource allocation and other works. However, current evaluation methods are either limited to the aircraft level or the function module level. There is a lack of research on the evaluation using the information of these two levels. In view of this situation, this paper researches the two-level iterative method of evaluating the importance of aircraft function modules. The influence matrix was constructed by using the node access probability calculated by the PageRank algorithm and the function module weight calculated based on centrality. In addition, the importance of aircraft nodes was used to carry out two-level iteration, and finally, the importance of aircraft function modules was obtained. The experimental results show that this method can comprehensively utilize the information on aircraft cooperative network and function module cooperative network, solve the key problems of two-level iterative evaluation, and meet the requirement of evaluating critical nodes in a system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the mixed solution of reduced biquaternion matrix equation Σni=1 AiXiBi=Ewith sub-matrix constraints. With the help of LC-representation and the properties of vector operator based on semi-tensor product of reduced biquaternion matrices, the reduced biquaternion matrix equation (1.1) can be transformed into linear equations. A systematic method, GH-representation, is proposed to decrease the number of variables of a special unknown reduced biquaternion matrix and applied to solve the least squares problem of linear equations. Meanwhile, we give the necessary and suficient conditions for the compatibility of reduced biquaternion matrix equation (1.1) under sub-matrix constraints. Numerical examples are given to demonstrate the results. The method proposed in this paper is applied to color image restoration. [ABSTRACT FROM AUTHOR]

The article presents a study which investigates the improvement of retrieval quality for airborne limb-sounders. The study used horizontal regularisation technique, cross-sectional method, and a precision matrix. Results show that a cross-section retrievals has the ability to produce finer vertical structures while maintaining the same noise level.

This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is \ssr NP-hard. As a consequence of our result, it is impossible to efficiently test for RIP provided \ssr P\ne\ssr NP. [ABSTRACT FROM PUBLISHER]

Real-time process data are the foundation for the successful implementation of intelligent manufacturing in the chemical industry. However, in the actual production process, process data may randomly be missing due to various reasons, thus affecting the practical application of intelligent manufacturing technology. Therefore, this paper proposes the application of appropriate matrix completion algorithms to impute the missing values of real-time process data. Considering the characteristics of online missing value imputation problems, this paper proposes an improved method for a matrix completion algorithm that is suitable for real-time missing data imputation. By utilizing real device data, this paper studies the impact of algorithm parameters on the effect of missing value imputing and compares it with several classical missing value imputing methods. The results show that the introduced method achieves higher accuracy in data imputation compared to the baseline method. Furthermore, the proposed enhancement significantly improves the speed performance of algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation A X B   =   C , and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations A X   =   C and X B   =   C . Finally, we provide a numerical example to demonstrate the findings of this paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the reversibility of multidimensional linear cellular automata with an intermediate boundary condition. We begin by addressing the matrix representation of these automata, and the question of reversibility boils down to the invertibility of this matrix representation. We introduce a decomposition method that factorizes the matrix representation into a Kronecker sum of significantly smaller matrices. The invertibility of the matrix hinges on determining whether zero can be expressed as the sum of eigenvalues of these smaller matrices, which happen to be tridiagonal Toeplitz matrices. Notably, each of these smaller matrices represents a one-dimensional cellular automaton. Leveraging the rich body of research on the eigenvalue problem of Toeplitz matrices, our result provides an efficient algorithm for addressing the reversibility problem. As an application, we show that there is no reversible nontrivial linear cellular automaton over Z 2 . This paper focuses on the reversibility of multidimensional linear cellular automata with an intermediate boundary condition. We begin by addressing the matrix representation of these automata, and the question of reversibility boils down to the invertibility of this matrix representation. We introduce a decomposition method that factorizes the matrix representation into a Kronecker sum of significantly smaller matrices. The invertibility of the matrix hinges on determining whether zero can be expressed as the sum of eigenvalues of these smaller matrices, which happen to be tridiagonal Toeplitz matrices. Notably, each of these smaller matrices represents a one-dimensional cellular automaton. Leveraging the rich body of research on the eigenvalue problem of Toeplitz matrices, our result provides an efficient algorithm for addressing the reversibility problem. As an application, we show that there is no reversible nontrivial linear cellular automaton over . [ABSTRACT FROM AUTHOR]

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples. [ABSTRACT FROM AUTHOR]

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation A X B = C has been extensively studied. However, there is currently limited information on matrix equation A X B = C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation A X B = C , and present the expression for the general solution when it is solvable. As an application, we derive the ϕ -Hermitian solutions for dual quaternion matrix equation A X A ϕ = C , where the ϕ -Hermitian extends the concepts of Hermiticity and η -Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the minimum eigenvalue involving the Fan product. By utilizing the Hölder inequality and the classic eigenvalue inclusion theorem, we introduce two novel lower bounds for τ (A 1 ⋆ A 2) , representing the minimum eigenvalue involving the Fan product of two M-matrices A 1 , A 2 . The newly derived lower bounds are then compared with the traditional findings. Numerical tests are presented to illustrate that the new lower bound formulas significantly enhance Johnson and Horn's results in certain scenarios and are more precise than other existing findings. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel four-dimensional (4D) parameter estimation method to localize the mixed far-field (FF) and near-field (NF) targets using bistatic MIMO arrays and higher-order singular value decomposition (HOSVD). The estimated four parameters include the angle-of-departure (AOD), angle-of-arrival (AOA), range-of-departure (ROD), and range-of-arrival (ROA). In the method, we store array data in a tensor form to preserve the inherent multidimensional properties of the array data. First, the observation data are arranged into a third-order tensor and its covariance tensor is calculated. Then, the HOSVD of the covariance tensor is performed. From the left singular vector matrices of the corresponding module expansion of the covariance tensor, the subspaces with respect to transmit and receive arrays are obtained, respectively. The AOD and AOA of the mixed FF and NF targets are estimated with signal-subspace, and the ROD and ROA of the NF targets are achieved using noise-subspace. Finally, the estimated four parameters are matched via a pairing method. The Cramér–Rao lower bound (CRLB) of the mixed target parameters is also derived. The numerical simulations demonstrate the superiority of the tensor-based method. [ABSTRACT FROM AUTHOR]

With the increasing demand for the refined management of residential loads, the study of the non-invasive load monitoring (NILM) technologies has attracted much attention in recent years. This paper proposes a novel method of residential load identification based on load feature matrix and improved neural networks. Firstly, it constructs a unified scale bitmap format gray image consisted of multiple load feature matrix including: V-I characteristic curve, 1-16 harmonic currents, 1- cycle steady-state current waveform, maximum and minimum current values, active and reactive power. Secondly, it adopts a convolutional layer to extract image features and performs further feature extraction through a convolutional block attention module (CBAM). Thirdly, the feature matrix is converted and input to a bidirectional long short-term memory (BiLSTM) for training and identification. Furthermore, the identification results are optimized with dynamic time warping (DTW). The effectiveness of the proposed method is verified by the commonly used PLAID database. [ABSTRACT FROM AUTHOR]

This paper introduces a nonconvex ℓ 1 − 2 -analysis model: min x (∥ D ∗ x ∥ 1 − ∥ D ∗ x ∥ 2) s.t.  A x = y , where A is a measurement matrix and D is a tight frame. Our main motivation is to generalize the sparse recovery via ℓ 1 − ℓ 2 minimization to this new model. As a nonconvex model, it is well known that its global minimizer and local minimizer are usually inconsistent. This paper provides a type of null space property (NSP) characterization which are necessary and sufficient conditions for the measurement matrix A such that a vector x can be recovered from A x with a tight frame D via ℓ 1 − 2 -analysis local minimization, or any vector x can be uniformly recovered from A x with a tight frame D via ℓ 1 − 2 -analysis minimization locally and globally. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph with n vertices. Denote by L+ (G) = D(G)-1/2 Q(G) D(G)-1/2 the normalized signless Laplacian matrix of graph G, where Q(G) and D(G) are the signless Laplacian and diagonal degree matrices of G, respectively. The eigenvalues of matrix L+ (G), 2 = γ1+ ≥ γ2+ > … ≥ γn+ ≥ 0, are normalized signless Laplacian eigenvalues of G. In this paper, we introduce the normalized signless Laplacian resolvent energy of G as ERNS (G) = ∑i=1n 1/3-γ4+. We also obtain some lower and upper bounds for ERNS (G) as well as its relationships with other energies and signless Kemeny's constant. [ABSTRACT FROM AUTHOR]

This paper explores geometric circulant matrices whose entries are Chebyshev polynomials of the first or second kind. Motivated by our previous research on r − circulant matrices and Chebyshev polynomials, we focus on calculating the Frobenius norm and deriving estimates for the spectral norm bounds of these matrices. Our analysis reveals that this approach yields notably improved results compared to previous methods. To validate the practical significance of our research, we apply it to existing studies on geometric circulant matrices involving the generalized k − Horadam numbers. The obtained results confirm the effectiveness and utility of our proposed approach. [ABSTRACT FROM AUTHOR]

Non-Tarskian interpretations of many-valued logics have been widely explored in the logic literature. The development of non-tarskian conceptions of logical consequence set the theoretical foundations for rediscovering well-known (Tarskian) many-valued logics. One may find in distinct authors many novel interpretations of many-valued systems. They are produced through a type of procedure which consists in altering the semantic structure of Tarskian many-valued logics in order to output a non-Tarskian interpretation of these logics. Through this type of transformation the paper explores a uniform way of transforming finitely many-valued Tarskian logics into their non-Tarskian interpretation. Some general properties of carrying out this type of procedure are studied, namely the dualities between these logics and the conditions under which negation-explosive and negation-complete Tarskian logics become non-explosive. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs are reported. Examples are provided to illustrate the applications of this product in some growing graphs and complex networks. [ABSTRACT FROM AUTHOR]

Let un = un(k) denote the generalized Leonardo number defined recursively by un = un−1 + un−2 + k for n ≥ 2, where u0 = u1 = 1. Terms of the sequence un(1) are referred to simply as Leonardo numbers. In this paper, we find expressions for the determinants of several Toeplitz–Hessenberg matrices having generalized Leonardo number entries. These results are obtained as special cases of more general formulas for the generating function of the corresponding sequence of determinants. Special attention is paid to the cases 1 ≤ k ≤ 7, where several connections are made to entries in the On-Line Encyclopedia of Integer Sequences. By Trudi's formula, one obtains equivalent multi-sum identities involving sums of products of generalized Leonardo numbers. Finally, in the case k = 1, we also provide combinatorial proofs of the determinant formulas, where we make extensive use of sign-changing involutions on the related structures. [ABSTRACT FROM AUTHOR]

In this paper, a novel measurement matrix construction method based on adaptive cross-approximation (ACA) is proposed to improve the performance of the compressive sensing-based method of moments (CS-MoM) for analyzing electromagnetic scattering problems. ACA is based on a weight scheme and is able to recognize the rows and columns that contribute significantly to the matrix. Thus, the object is divided into multiple blocks, and the impedance matrix is partitioned into near-field and far-field groups to establish the condition for applying ACA. Then, the row indexes are extracted from the group with the highest number of ACA recognized rows in the far-field groups of each block. Finally, by combining all row indexes to extract the impedance matrix, a lower-dimensional and deterministic measurement matrix is constructed, thereby improving computational efficiency. Numerical simulation results validate the accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article explores the mathematical and statistical performances and connections of the two well-known ordinary least-squares estimators (OLSEs) and best linear unbiased estimators (BLUEs) of unknown parameter matrices in the context of a multivariate general linear model (MGLM) for regression, both of which are defined under two different optimality criteria. Tian and Zhang [38] once collected a series of existing and novel identifying conditions for OLSEs to be BLUEs under general linear models: On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model, Stat. Probabil. Lett., 112 (2016), 105–112. In this paper, we show how to extend this kind of results to multivariate general linear models. We shall give a direct algebraic procedure to derive explicit formulas for calculating the OLSEs and BLUEs of parameter spaces in a given MGLM, discuss the relationships between OLSEs and BLUEs of parameter matrices in the MGLM, establish many algebraic equalities related to the equivalence of OLSEs and BLUEs, and give various intrinsic statistical interpretations about the equivalence of OLSEs and BLUEs of parameter matrices in a given MGLM using some matrix analysis tools concerning ranks, ranges, and generalized inverses of matrices. [ABSTRACT FROM AUTHOR]

This paper attempts to demystify the stability of CoCoSo ranking method via a comprehensive simulation experiment. In the experiment, matrices of different dimensions are generated via Python with fuzzy data. Stability is investigated via adequacy and partial adequacy tests. The test passes if the ranking order does not change even after changes are made to entities, and the partial pass signifies that the top ranked alternative remains intact. Results infer that CoCoSo method has better stability with respect to change of alternatives compared to criteria; and CoCoSo method shows better stability with respect to partial adequacy test for criteria. [ABSTRACT FROM AUTHOR]

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation A X B + C Y D ≈ E , where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH -representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation A X B + C Y D ≈ E . The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an inexact Noda iteration method featuring inner and outer iterations for computing the smallest eigenvalue and corresponding eigenvector of an irreducible monotone matrix. The proposed method includes two primary relaxation steps designed to compute the smallest eigenvalue and its associated eigenvector. These steps are influenced by specific relaxation factors, and we examine how these factors impact the convergence of the outer iterations. By applying two distinct relaxation factors to solve the inner linear systems, we demonstrate that the convergence can be globally linear or superlinear, contingent upon the relaxation factor used. Additionally, the relaxation factor affects the rate of convergence. The inexact Noda iterations we propose are structure-preserving and ensure the positivity of the approximate eigenvectors. Numerical examples are provided to demonstrate the practicality of the proposed method, consistently preserving the positivity of approximate eigenvectors. [ABSTRACT FROM AUTHOR]

This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge–Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step, and thus, the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed s-sub-step implicit method with s ≤ 6 can reach sth-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present s-sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors' previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the computational advantages of the spherical parametrisation for correlation matrices in the context of Maximum Likelihood estimation via numerical optimisation. By using the special structure of correlation matrices, it is possible to define a bijective transformation of an n × n correlation matrix R into a vector of n (n - 1) / 2 angles between 0 and π . After discussing the algebraic aspects of the problem, we provide examples of the use of the technique we propose in popular econometric models: the multivariate DCC-GARCH model, widely used in applied finance for large-scale problems, and the multivariate probit model, for which the computation of the likelihood is typically accomplished by simulated Maximum Likelihood. Our analysis reveals the conditions when the spherical parametrisation is advantageous; numerical optimisation algorithms are often more robust and efficient, especially when R is large and near-singular. [ABSTRACT FROM AUTHOR]