248 research outputs found
The space of non-extendable quasimorphisms
For a pair of a group and its normal subgroup , we consider
the space of quasimorphisms and quasi-cocycles on non-extendable to . 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 be a group and a normal subgroup of . We study the large scale
behavior, not the exact values themselves, of the stable mixed commutator
length on the mixed commutator subgroup ; when ,
equals the stable commutator length on the commutator
subgroup . For this purpose, we regard not only as a
function from to , but as a bi-invariant metric
function from to .
Our main focus is coarse group theoretic structures of
. Our preliminary result (the absolute version)
connects, via the Bavard duality, and the quotient
vector space of the space of -invariant quasimorphisms on over one of
such homomorphisms. In particular, we prove that the dimension of this vector
space equals the asymptotic dimension of .
Our main result is the comparative version: we connect the coarse kernel,
formulated by Leitner and Vigolo, of the coarse homomorphism ; , and a certain
quotient vector space of the space of invariant quasimorphisms. Assume
that and that is finite dimensional with dimension .
Then we prove that the coarse kernel of is isomorphic to
as a coarse group. In contrast to the absolute version, the
space is finite dimensional in many cases, including all with
finitely generated and nilpotent . As an application of our result,
given a group homomorphism between finitely generated
groups, we define an -linear map `inside' the groups, which is dual
to the naturally defined -linear map from to
induced by .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
- …