On the cone eigenvalue complementarity problem for higher-order tensors

In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we given an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing an upper bound of cone eigenvalues of tensors. Moreover, some new results concerning the bounds of number of eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least, an implementable projection algorithm for solving TGEiCP is also developed for the problem under consideration. As an illustration of our theoretical results, preliminary computational results are reported.Comment: 26 pages, 2 figures, 3 table

Effect of Roucongrong (Herba Cistanches Deserticolae) on reproductive toxicity in mice induced by glycoside of Leigongteng (Radix et Rhizoma Tripterygii)

AbstractObjectiveThe purpose of this research is to study the effect of Roucongrong (Herba Cistanches Deserticolae) on reproductive toxicity in mice induced by a glycoside extracted from Leigongteng (Radix et Rhizoma Tripterygii) (GRT).MethodsForty-eight BALB/c mice were randomly divided into two groups in the ratio of 1: 3, 12 in one group and 36 in the other. The 12-mouse group was the control group that was intragastrically administered physiological saline for 3 weeks. The 36 mice in the other group were given 30 mg · kg−1 · d −1 GRT for 3 weeks, then randomly divided into 3 subgroups: the model group, GRT group and Roucongrong (Herba Cistanches Deserticolae) group, with 12 mice in each group. In the model group, 0.25 mL physiological saline was intragastrically administered; in the GRT group, GRT, 0.25 mL at 30 mg · kg−1 · d−1 was intragastrically administered once a day; in the Roucongrong (Herba Cistanches Deserticolae) group, mice were administered Roucongrong (Herba Cistanches Deserticolae) decoction equivalent to 0.25 mL at a final dose of 10 g · kg−1 · d−1 crude drug (calculated as per 20 times of 0.5 g · kg−1 · d−1 for adults), and GRT 0.25 mL at 30 mg · kg−1 · d−1 daily. After another 3 weeks of exposure, expression levels of the reproduction-related genes DEAD (Asp-Glu-Ala-Asp) box polypeptide 3, Y-linked, B-cell CLL/lymphoma 6 and Signal transducer and activator of transcription 3 were evaluated.ResultsAfter 6 weeks of GRT treatment, the spermatogenic cell population in the convoluted tubule of testis was in disorder and the tubule cavity expanded. Sertoli cell and Leydig cells exhibited atrophy or disappeared. The number of sperm decreased. The spermatogenic cell level of testis for male mice was ranked in order and sperm was produced in the cavity of the spermatogenic cell. The expression levels of DDX3Y, BCL6 and STAT3 were up-regulated.ConclusionGRT affected reproduction-related genes. Roucongrong (Herba Cistanches Deserticolae) reversed reproductive toxicity in mice induced by GRT

von Neumann type trace inequality for dual quaternion matrices

As a powerful tool to represent rigid body motion in 3D spaces, dual quaternions have been successfully applied to robotics, 3D motion modelling and control, and computer graphics. Due to the important applications in multi-agent formation control, this paper addresses the concept of spectral norm of dual quaternion matrices. We introduce a von Neumann type trace inequality and a Hoffman-Wielandt type inequality for general dual quaternion matrices, where the latter characterizes a simultaneous perturbation bound on all singular values of a dual quaternion matrix. In particular, we also present two variants of the above two inequalities expressed by eigenvalues of dual quaternion Hermitian matrices. Our results are helpful for the further study of dual quaternion matrix theory, algorithmic design, and applications