‎Let $p$ be a prime with $pgeq 7$ and $q=2(p-1)$‎. ‎In this paper‎ ‎we prove the existence of a nontrivial product of‎ ‎filtration $s+4$ in the stable homotopy groups of spheres‎. ‎This nontrivial‎ ‎product is shown to be represented up to a nonzero scalar by‎ ‎the product element $widetilde{gamma}_{s}b_{n-1}g_{0}in‎ ‎{Ext}_{mathcal{A}}^{s+4,(p^n+sp^2+sp+s)q+s-3}(mathbb{Z}/p,mathbb{Z}/p)$‎ ‎in ...

We have investigated some statistical properties of integrated spectra of galaxies from Kennicutt (1992a) spectrophotometric atlas. The input for the analysis are galaxy spectra sampled in 1300 bins between 3750 Å and 6500 Å. We make use of Principal Component Analysis (PCA) to analyse the 1300-dimensional space spanned by the spectra. Their projection onto the plane defined by the first two pr...

abutting to the stable homotopy of X. It has long been recognized that a map A +B of ring-spectra gives rise to information about the differentials in this spectral sequence. The main purpose of this paper is to prove a systematic theorem in this direction, and give some applications. To fix ideas, let p be a prime number, and take B to be the modp EilenbergMacLane spectrum H and A to be the Br...

Humans have an excellent ability to select a particular sound source from a noisy environment, called the \Cocktail-Party E ect" and to compensate for physically missing sound, called the \Illusion of Continuity." This paper proposes a spectral peak tracker as a model of the illusion of continuity (or phonemic restoration) and a spectral sequence prediction method using a spectral peak tracker....