Relations in the 24-th homotopy groups of spheres

The main purpose of this note is to give a proof of the fact that the Toda brackets $$and$$ are not trivial. This is an affirmative answer of the second author's Conjecture (Determination of the $P$-image by Toda brackets, Geometry and Topology Monographs 13(2008), 355-383). The second purpose is to show the relation $\bar{\nu}_7\omega_{15}=\nu_7\sigma_{10}\kappa_{17}$ in $\pi^7_{31}$.Comment: 27 page

Self-homotopy of the Double Suspension of the Real 7-projective Space

We determine the group structure of the self-homotopy set of the double suspension of the real 7-dimensionnal projective space.</p

An optimization method for designing high rate and high performance SCTCM systems with in-line interleavers

We present a method for designing high-rate, high-performance SCTCM systems with in-line interleavers. Using in-line EXIT charts and ML performance analysis, we develop criteria for choosing constituent codes and optimization methods for selecting the best ones. To illustrate our methods, we show that an optimized SCTCM system with an in-line interleaver for rate r = 5/6 and 64QAM has better performance than other turbo-like TCMs with the same parameters

The 2-components of the 31-stem homotopy groups of the 9 and 10-spheres

Group structures of the 2-primary components of the 31-stem homotopy groups of spheres were studied by Oda in 1979. There are,however, two incompletely determined ｇroups. In this paper,our investigation with Toda's composition method gives structures of them.ArticleJournal of the Faculty of Science Shinshu University 46: 1-19(2015)departmental bulletin pape

Homotopy commutativity in symmetric spaces

We extend the former results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric spaces such that the loop spaces of all irreducible symmetric spaces but $\mathbb{C}P^3$ are not homotopy commutative.Comment: 11page