The Energy-Delay product or ED product was proposed as a metric to gauge design effectiveness. This metric is widely used in the area of low-power architecture research, however it is also often improperly used when reporting a new architecture design that addresses energy-performance effectiveness. In this paper, we discuss two common fallacies from the literature: (1) the way the ED product i...

Suppose M is an n-dimensional Kähler manifold and L is an ample line bundle over M . Let the Kähler form of M be ωg and the Hermitian metric of L be H. We assume that ωg is the curvature of H, that is, ωg = Ric(H). The Kähler metric of ωg is called a polarized Kähler metric on M . Using H and ωg, for any positive integer m, H 0(M,Lm) becomes a Hermitian inner product space. We use the following...

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...

C onstructing a distance that is invariant under a given class of mappings is one of the fundamental tools for the geometric approach in mathematics. The idea goes back to Klein and even to Riemann. In this article we will consider distances invariant under biholomorphic mappings of complex manifolds. There will be many such distances. A number of these will come from functions on the tangent s...

The metric-adjusted skew information establishes a connection between the geometrical formulation of quantum statistics and measures information. We study uncertainty relations in product summation forms present lower bounds on inequalities based via operator representation observables. Explicit examples are provided to back our claims.

Let (Xi, di), i = 1, 2, be proper geodesic hyperbolic metric spaces. We give a general construction for a " hyperbolic product " X1× h X2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.