5 Mathematics eBooks (3)

Tetsu Mizumachi, "Stability of Line Solitons for the KP-II Equation in R"
Volodymyr Nekrashevych, "Hyperbolic Groupoids and Duality"
Bob Oliver, "Reduced Fusion Systems Over 2-Groups of Sectional Rank at Most 4"
U. Meierfrankenfeld and B. Stellmacher, "The Local Structure for Finite Groups With a Large $p$-Subgroup"
Toshihiko Masuda and Reiji Tomatsu, "Rohlin Flows on von Neumann Algebras"

Tetsu Mizumachi, "Stability of Line Solitons for the KP-II Equation in R"
English | ISBN: 1470414244 | 2015 | 95 pages | PDF | 1 MB
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as y→∞. He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y=±∞. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

Volodymyr Nekrashevych, "Hyperbolic Groupoids and Duality"
English | ISBN: 1470415445 | 2015 | 108 pages | PDF | 1 MB
The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc.
The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid $\mathfrak{G}$ there is a naturally defined dual groupoid $\mathfrak{G}^\top$ acting on the Gromov boundary of a Cayley graph of $\mathfrak{G}$. The groupoid $\mathfrak{G}^\top$ is also hyperbolic and such that $(\mathfrak{G}^\top)^\top$ is equivalent to $\mathfrak{G}$. Several classes of examples of hyperbolic groupoids and their applications are discussed.

Bob Oliver, "Reduced Fusion Systems Over 2-Groups of Sectional Rank at Most 4"
English | ISBN: 1470415488 | 2016 | 100 pages | PDF | 1 MB
The author classifies all reduced, indecomposable fusion systems over finite $2$-groups of sectional rank at most $4$. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional $2$-rank at most $4$. But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

U. Meierfrankenfeld and B. Stellmacher, "The Local Structure for Finite Groups With a Large $p$-Subgroup"
English | ISBN: 1470418770 | 2016 | 342 pages | PDF | 4 MB
Let $p$ be a prime, $G$ a finite $\mathcal{K}_p$-group $S$ a Sylow $p$-subgroup of $G$ and $Q$ a large subgroup of $G$ in $S$ (i.e., $C_G(Q) \leq Q$ and $N_G(U) \leq N_G(Q)$ for $1 \ne U \leq C_G(Q)$). Let $L$ be any subgroup of $G$ with $S\leq L$, $O_p(L)\neq 1$ and $Q\ntrianglelefteq L$. In this paper the authors determine the action of $L$ on the largest elementary abelian normal $p$-reduced $p$-subgroup $Y_L$ of $L$.

Toshihiko Masuda and Reiji Tomatsu, "Rohlin Flows on von Neumann Algebras"
English | ISBN: 1470420163 | 2016 | 111 pages | PDF | 1 MB
The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II$_1$ factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III$_0$ factors. Several concrete examples are also studied.