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We propose a class of iterative algorithms to solve some tensor equations via Einstein product. These algorithms use tensor computations with no matricizations involved. For any (special) initial tensor, a solution (the minimal Frobenius norm solution) of related problems can be obtained within finite iteration steps in the absence of roundoff errors. Numerical examples are provided to confirm the theoretical results, which demonstrate that this kind of iterative methods are effective and feasible for solving some tensor equations. [ABSTRACT FROM AUTHOR]

We study the system of quaternion generalized Sylvester matrix equations , and . We establish necessary and sufficient conditions for the system to be solvable, and when such conditions are met, we present the general solution to the system. We also investigate the number of solutions a solvable system could have. Our techniques entail the investigation of the quaternion matrix system and in X and Y with the constraint that X and Y have a common submatrix. For such systems, we establish a characterization of solvable systems and provide their general solution. We also study in detail the number of solutions a solvable system could have and present necessary and sufficient conditions for a solvable system to have a unique solution. We finally illustrate our techniques in solving the generalized Sylvester matrix equations by providing an example. [ABSTRACT FROM AUTHOR]

We characterize linear transformations on matrices over commutative antinegative semirings that are monotone with respect to minus, star, and sharp partial orders. [ABSTRACT FROM AUTHOR]

Several inequalities are presented for sector matrices. First, an analogue of the AM-GM inequality is established. As applications of this inequality, similar inequalities are presented for singular values and norms. Finally, some unitarily invariant norm inequalities are obtained for sector matrices. [ABSTRACT FROM AUTHOR]

In this paper, we prove that some recent Rotfel’d theorem extensions are equivalent. [ABSTRACT FROM AUTHOR]

The low surface free energy makes wood plastic composites difficult to bond with traditional adhesives, such as urea formaldehyde resin (UF). This study investigates the decoration of wood flour/high‐density‐polyethylene composite (WF/HDPE) board with poplar wood veneers. High‐density polyethylene (HDPE) or maleic anhydride grafted polyethylene (MAPE) film was introduced between the veneer and the WF/HDPE composite board as an intermediate component to strengthen the bond. Surface bonding strength, hot water resistance, and bending performance of the composites were then evaluated. Contact angle, Attenuated total reflection‐Fourier transform infrared (ATR‐FTIR) spectroscopy, and scanning electron microscopy (SEM) were used to analyze the interface of the wood veneer and the WF/HDPE composites. The addition of MAPE film enhanced the polar characteristic of the WF/HDPE composite surface and increased the number of functional groups reacting with the –OH groups present in the wood veneer. A MAPE intermediate film increased the surface bonding strength of the wood veneer to WF/HDPE composite surface, and also endured boiling water without delimitation failure. After being covered with the wood veneer, the flexural strength and modulus of WF/HDPE composite panels increased four times comparing to that of the uncovered composites. POLYM. COMPOS., 39:1144–1151, 2018. © 2016 Society of Plastics Engineers [ABSTRACT FROM AUTHOR]

In this paper, we give the complete structures of the equivalence canonical form of four matrices over an arbitrary division ring. As applications, we derive some practical necessary and sufficient conditions for the solvability to some systems of generalized Sylvester matrix equations using the ranks of their coefficient matrices. The results of this paper are new and available over the real number field, the complex number field, and the quaternion algebra. [ABSTRACT FROM PUBLISHER]

By keeping in mind the great number of applications of generalized Sylvester matrix equations in systems and control theory, in this paper we establish some necessary and sufficient conditions for the solvability to a system of eight generalized Sylvester matrix equations over the quaternion algebra. The general solution to this system is also constructed when it is solvable. Moreover, an algorithm and a numerical example are also given to make the results of this paper more practical in various fields of engineering. The findings of this paper generalize previous results in the literature. [ABSTRACT FROM AUTHOR]

We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number, positive semi-definite matrices,, and generalized matrix functionssuch as the determinant and permanent, etc., we have A general scheme is introduced to prove more general inequalities involvingmpositive semi-definite matrices forthat extend the results of other authors. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a class of tensor least squares problem with an invertible linear transform, which arises in image restoration. Based on the operator-bidiagonal procedure, two Paige’s algorithms are designed to solve it. The convergence theorems of the new methods are derived. Numerical experiments are performed to illustrate the feasibility and efficiency of the new methods, including when the algorithm is tested with the synthetic data and on some image restoration problems. Comparisons with some previous methods are also given. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to present a better bound than the recent result given by Zhang [Linear Multilinear Algebra. 2015;63:2511–2517]. [ABSTRACT FROM AUTHOR]

In this paper, we first define a generalized ( f, g)-skew information $\left |I_{ \rho }^{(f, g)}\right |(A)$ and two related quantity $\left |J_{ \rho }^{(f, g)}\right |(A)$ and $\left |U_{ \rho }^{(f, g)}\right |(A)$ for any non-Hermitian Hilbert-Schmidt operator A and a density operator ρ on a Hilbert space H and discuss some properties of them. And then, we obtain the following uncertainty relation in terms of $\left |U_{ \rho }^{(f, g)}\right |(A)$ : which is a generalization of a known uncertainty relation in Ko and Yoo (J. Math. Anal. Appl. 383, 208-214, 11). [ABSTRACT FROM AUTHOR]