In this paper, we study the Ricci flow on higher dimensional compact manifolds. We prove that nonnegative isotropic curvature is preserved by the Ricci flow in dimensions greater than or equal to four. In order to do so, we introduce a new technique to prove that curvature functions defined on the orthonormal frame bundle are preserved by the Ricci flow. At a minimum of such a function, we comp...

The concept of pulled fronts with a cutoff epsilon has been introduced to model the effects of the discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (pulled fronts are the fronts that propagate into an unstable state, and have an asymptotic front speed equal to the linear spreading speed v* of small linear perturbations around the unst...

We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the ...

In this note we investigate the operators associated with frame sequences in a Hilbert space H, i.e., the synthesis operator T : l (N) → H , the analysis operator T ∗ : H → l (N) and the associated frame operator S = TT ∗ as operators defined on (or to) the whole space rather than on subspaces. Furthermore, the projection P onto the range of T , the projection Q onto the range of T ∗ and the Gr...

‎Frames generalize orthonormal bases and allow representation of all the elements of the space‎. ‎Frames play significant role in signal and image processing‎, ‎which leads to many applications in informatics‎, ‎engineering‎, ‎medicine‎, ‎and probability‎. ‎In this paper‎, ‎we introduce the concepts of operator frame for the space $End_{mathcal{A}}^{ast}(mathcal{H})$ of all adjointable operator...