Norm inequalities related to the arithmetic–geometric mean inequalities for positive semidefinite matrices

In this paper, we propose three new matrix versions of the arithmetic–geometric mean inequality for unitarily invariant norms, which stem from the fact that the Heinz mean of two positive real numbers interpolates between the geometric and arithmetic means of these numbers. Related trace inequalities are also presented.     

The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra

Propositions 24 and 25 of Book I of Euclid??s Elements state the fairly obvious fact that if an angle in a triangle is increased (without changing the lengths of its arms), then the length of the opposite side increases. In less technical terms, the wider you open your mouth, the farther apart your lips are. In this paper, we see that this has a very satisfactory analogue for orthocentric (but not for general) tetrahedra.     

More Characterizations of Certain Special Families of Simplices

This paper is about various characterizations of orthocentric, and other special types of, d-dimensional simplices and related issues. It puts together several three-dimensional results that are scattered in the literature, and establishes stronger versions and extensions to higher dimensions. These compactly organized results, which are mostly new for higher dimensions, are expected to be very useful tools for further research. Several open problems are posed.     

Mechanical performance,thermal stability and morphological analysis of date palm fiber reinforced polypropylene composites toward functional bio-products

Cellulose - Sustainable bio-materials are now potential alternatives for synthetic composites to achieve more functional green products. However, the microstructure-performance synergy is critical...