We prove in this paper a noncommutative version of Leray Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with E 2 terms as E 2 p,q = HP p (A; HP q (B, A)) =⇒ HP p+q (B) and E 2 p,q = HP p (A; Kq(B, A)) =⇒ Kp+q(B).

We construct an analogue of the Lyndon-HochschildSerre spectral sequence in the context of polynomially bounded cohomology. For G an extension of Q by H, this spectral sequences converges to the polynomially bounded cohomology of G, HP ∗(G). If the extension is a polynomial extension in the sense of Noskov with H and Q isocohomological and Q of type HF∞, the spectral sequence has E 2 -term HP (...

The Hodrick-Prescott (HP) filter is widely used in the field of economics to estimate trends and cycles from time series data. For certain applications – such as deriving implied trend and cycle models and obtaining filter weights – it is desirable to express the frequency response of the HP as the spectral density of an ARMA model; in other words, to accomplish the spectral factorization of th...

The harmonic projection (HP), which is implicit in the numerous harmonic transforms between physical and spectral spaces, is responsible for the reliability of the spectral method for modeling geophysical phenomena. As currently configured, the HP consists of a forward transform from physical to spectral space (harmonic analysis) immediately followed by a harmonic synthesis back to physical spa...

Abstract As the use of spectral/ hp element methods, and high-order finite methods in general, continues to spread, community efforts create efficient, optimized algorithms associated with fundamental operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness mass matrix generation, assembly received tremendous attention. With types problems which ar...

When a numerical simulation has to handle physics problem with wide range of time-dependent length scales, dynamically adaptive discretizations can be the method choice. We present major upgrade relativity code bamps in form fully adaptive, physics-agnostic hp refinement. describe foundations mesh refinement context spectral element methods, precise algorithm used perform bamps, as well several...