The main goal of this article is to present new inequalities for the recently defined generalized numerical radius block operators.

I report on recent progress in our understanding of the structure of CDM halos, and in particular of the inner mass profile of galaxysized systems. Numerical simulations have consistently shown that the density profiles of CDM halos steepen monotonically from the center outwards, with slopes shallower than isothermal near the center and steeper than isothermal near the virial radius. Ongoing de...

In this paper we find new estimate for the numerical radius of a given matrix, and we prove that, this estimate is better than any estimate for the numerical radius. We present also new bounds for the zero of polynomials by using new estimate for the numerical radius of a companion matrix of a given polynomial and matrix inequalities.

1. Consider a circle. It has both a radius and a circumference. There is obviously a real distinction between the properties having a radius and having a circumference. This is not because, when confining ourselves to circles, having a radius can ever exist apart from having a circumference. A real distinction does not depend on that. Descartes thought that a real distinction between x and y me...