The space of non-extendable quasimorphisms

For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov hyperbolic groups. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length for certain pairs of a group and its normal subgroup.Comment: 58 pages, 1 figure. Major revision. Theorem 1.12 in v3 has been generalized to Theorem 1.2 in the current version: this new theorem treats hyperbolic mapping tori in general cases, and it serves as a leading application of our main theore

Survey on invariant quasimorphisms and stable mixed commutator length

In this survey, we review the history and recent developments of invariant quasimorphisms and stable mixed commutator length.Comment: 26 pages, 1 figure; minor revisio

A thermal immersed boundary-lattice Boltzmann method for moving-boundary flows with Dirichlet and Neumann conditions

We construct a simple immersed boundary-lattice Boltzmann method for moving-boundary flows with heat transfer. On the basis of the immersed boundary-lattice Boltzmann method for calculating the fluid velocity and the pressure fields presented in the previous work by Suzuki and Inamuro (2011), the present method incorporates a lattice Boltzmann method for the temperature field combined with immersed boundary methods for satisfying thermal boundary conditions, i.e., the Dirichlet (iso-thermal) and Neumann (iso-heat-flux) conditions. We validate the present method through many benchmark problems including stationary and moving boundaries with iso-thermal and iso-heat-flux conditions, and we find that the present results have good agreement with other numerical results. Also, we investigate the internal heat effect through simulations of moving-boundary flows with heat transfer by using the present method. In addition, we apply the method to an interesting example of a moving-boundary flow with heat transfer, i.e., a two-dimensional thermal flow in a heated channel with moving cold particles, which is a simplified model of ice slurry flow. (C) 2018 Elsevier Ltd. All rights reserved.ArticleINTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER.121: 1099-1117(2018)journal articl

Coarse group theoretic study on stable mixed commutator length

Let $G$ be a group and $N$ a normal subgroup of $G$. We study the large scale behavior, not the exact values themselves, of the stable mixed commutator length $scl_{G,N}$ on the mixed commutator subgroup $[G,N]$; when $N=G$, $scl_{G,N}$ equals the stable commutator length $scl_G$ on the commutator subgroup $[G,G]$. For this purpose, we regard $scl_{G,N}$ not only as a function from $[G,N]$ to $\mathbb{R}_{\geq 0}$, but as a bi-invariant metric function $d^+_{scl_{G,N}}$ from $[G,N]\times [G,N]$ to $\mathbb{R}_{\geq 0}$. Our main focus is coarse group theoretic structures of $([G,N],d^+_{scl_{G,N}})$. Our preliminary result (the absolute version) connects, via the Bavard duality, $([G,N],d^+_{scl_{G,N}})$ and the quotient vector space of the space of $G$-invariant quasimorphisms on $N$ over one of such homomorphisms. In particular, we prove that the dimension of this vector space equals the asymptotic dimension of $([G,N],d^+_{scl_{G,N}})$. Our main result is the comparative version: we connect the coarse kernel, formulated by Leitner and Vigolo, of the coarse homomorphism $\iota_{G,N}\colon ([G,N],d^+_{scl_{G,N}})\to ([G,N],d^+_{scl_{G}})$; $y\mapsto y$, and a certain quotient vector space $W(G,N)$ of the space of invariant quasimorphisms. Assume that $N=[G,G]$ and that $W(G,N)$ is finite dimensional with dimension $\ell$. Then we prove that the coarse kernel of $\iota_{G,N}$ is isomorphic to $\mathbb{Z}^{\ell}$ as a coarse group. In contrast to the absolute version, the space $W(G,N)$ is finite dimensional in many cases, including all $(G,N)$ with finitely generated $G$ and nilpotent $G/N$. As an application of our result, given a group homomorphism $\varphi\colon G\to H$ between finitely generated groups, we define an $\mathbb{R}$-linear map `inside' the groups, which is dual to the naturally defined $\mathbb{R}$-linear map from $W(H,[H,H])$ to $W(G,[G,G])$ induced by $\varphi$.Comment: 69 pages, no figure. Minor revision (v2): some symbols change

Effects of Imipramine and Lithium on the Suppression of Cell Proliferation in the Dentate Gyrus of the Hippocampus in Adrenocorticotropic Hormone-treated Rats

We examined the influence of chronic adrenocorticotropic hormone (ACTH) treatment on the number of Ki-67-positive cells in the dentate gyrus of the hippocampus in rats. ACTH treatment for 14 days decreased the number of such cells. The administration of imipramine or lithium alone for 14 days had no effect in saline-treated rats. The effect of ACTH was blocked by the administration of imipramine. Furthermore, the coadministration of imipramine and lithium for 14 days significantly increased the number of Ki-67-positive cells in both the saline and ACTH-treated rats. The coadministration of imipramine and lithium normalized the cell proliferation in the dentate gyrus of the hippocampus in rats treated with ACTH

Affleck-Dine leptogenesis via multiscalar evolution in a supersymmetric seesaw model

A leptogenesis scenario in a supersymmetric standard model extended with introducing right-handed neutrinos is reconsidered. Lepton asymmetry is produced in the condensate of a right-handed sneutrino via the Affleck-Dine mechanism. The LH_u direction develops large value due to a negative effective mass induced by the right-handed sneutrino condensate through the Yukawa coupling of the right-handed neutrino, even if the minimum during the inflation is fixed at the origin. The lepton asymmetry is nonperturbatively transfered to the LH_u direction by this Yukawa coupling.Comment: 19 pages, 3 figures. Revised version for publication. The model was modified to fix some problem