926 research outputs found

    Mutually-orthogonal unitary and orthogonal matrices

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    We introduce the concept of n-OU and n-OO matrix sets, a collection of n mutually-orthogonal unitary and real orthogonal matrices under Hilbert-Schmidt inner product. We give a detailed characterization of order-three n-OO matrix sets under orthogonal equivalence. As an application in quantum information theory, we show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively. Further, we propose a new matrix decomposition approach, defining an n-OU (resp. n-OO) decomposition for a matrix as a linear combination of n matrices from an n-OU (resp. n-OO) matrix set. We show that any order-d matrix has a d-OU decomposition. As a contrast, we provide criteria for an order-three real matrix to possess an n-OO decomposition.Comment: 16 pages, no figur

    Taraxerol exerts potent anticancer effects via induction of apoptosis and inhibition of Nf-kB signalling pathway in human middle ear epithelial cholesteatoma cells

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    Purpose: To investigate the effect of taraxerol on the proliferation of middle ear epithelial cholesteatoma cells.Methods: The anti-proliferative effect of taraxerol was investigated by cell counting kit-8 (CCK8) and clonogenic assays. Apoptosis was measured using DAPI, while mitochondrial membrane potential was determined with the aid of rhodamine 123 staining. Protein expression was studied by western blotting.Results: Taraxerol induced concentration-dependent anti-proliferative effects on the middle ear epithelial cholesteatoma cells, and also inhibited their colony formation potential. The drug induced apoptosis in the middle ear epithelial cholesteatoma cells by reducing mitochondrial membrane potential, and also triggered sub-G1 cell cycle arrest in these cells. Moreover, taraxerol inhibited the expression of Nf-kB.Conclusion: These findings reveal that taraxerol may be a potential lead compound for the treatment of middle ear cholesteatoma.Keywords: Cholesteatoma, Epithelial tissues, Taraxerol, Apoptosis, Cell cycle arres