Complemented Brunn–Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures

Homogeneous and Non Homogeneous Algorithms

Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non-homogeneous algorithms.1 Although both classes contain algorithms with worst and best cases, homogeneous algorithms behave uniformly on all instances. This partition clarifies in a completely mathematical way the previously ment...

Symmetric Homogeneous Triangle Inequalities

A brief scan through the problem columns of various mathematical journals shows a continual outpouring of proposed problems involving what can be roughly described as “triangle inequalities”. A few examples will suffice to indicate the flavor of these perennial favorites: Let the sides of a triangle be a, b, c and let the angles be A, B, C. Let r and R be the inradius and circumradius, respecti...

On Bezout Inequalities for non-homogeneous Polynomial Ideals

We introduce a “workable” notion of degree for non-homogeneous polynomial ideals and formulate and prove ideal theoretic Bézout Inequalities for the sum of two ideals in terms of this notion of degree and the degree of generators. We compute probabilistically the degree of an equidimensional ideal.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces