An identity involving binomial coefficients that appeared in the evaluation of a definite integral is established by a variety of methods.
ASPP2 is a pro-apoptotic member of the p53 binding protein family. ASPP2 has been shown to inhibit autophagy, which maintains energy balance in nutritional deprivation. We attempted to identify the role of ASPP2 in the pathogenesis of non-alcoholic fatty liver disease (NAFLD). In a NAFLD cell model, control treated and untreated HepG2 cells were… (More)
Let H = M K K * N be a Hermitian matrix. It is known that the vector of diagonal elements of H, diag(H), is majorized by the vector of the eigenvalues of H, λ(H), and that this majorization can be extended to the eigenvalues of diagonal blocks of H. Reverse majorization results for the eigenvalues are our goal. Under the additional assumptions that H is… (More)
Let T = X Y 0 Z be an n-square matrix, where X,Z are r-square and (n − r)-square, respectively. Among other determinantal inequalities, it is proved that det (I n + T * T) det (I r + X * X) · det (I n−r + Z * Z) with equality if and only if Y = 0 .
As a complement to Olkin's extension of Anderson-Taylor's trace inequality, the following inequality is proved:
We present a very general Hua-type matrix equality. Among several applications of the proposed equality, we give a matrix version of the Aczél inequality. 1 Hua-type matrix equality Let M m×n be the set of all complex matrices of size m × n with M n = M n×n. For A ∈ M m×n , we denote the conjugate transpose of A by A * and call A strictly contractive if I −… (More)
A new notion of coneigenvalue was introduced by Ikramov in [Kh.D. Ikramov. On pseudo-eigenvalues and singular numbers of a complex square matrix (in Russian). Zap. Nauchn. This paper presents some majorization inequalities for coneigen-values, which extend some classical majorization relations for eigenvalues and singular values, and may serve as a basis… (More)