This paper studies the extension of the Hofer metric and general Finsler metrics on the Hamiltonian symplectomorphism group Ham(M,ω) to the identity component Symp0(M,ω) of the symplectomorphism group. In particular, we prove that the Hofer metric on Ham(M,ω) does not extend to a bi-invariant metric on Symp0(M,ω) for many symplectic manifolds. We also show that for the torus T2n with the standa...

Let M be a compact connected m-dimensional manifold. We denote by Diff(M) the space of all C1-diffeomorphisms from M to itself endowed with C1-topology. For a collection of diffeomorphisms L = {f1, . . . , fn} ⊂ Diff(M), the iterated function system (abbrivately IFS) G(M ; f1, . . . , fn) on M generated by L is given by iterates fi1o · · · ofik with ij ∈ {1, . . . , n}. Recall that an IFS G(M ;...

Reply to comment on: Dietary yeasts reduce inflammation in central nervous system via microflora Kazushiro Takata, Takayuki Tomita, Tatsusada Okuno, Makoto Kinoshita, Toru Koda, Josephe A. Honorat, Masaya Takei, Kouichiro Hagihara, Tomoyuki Sugimoto, Hideki Mochizuki, Saburo Sakoda & Yuji Nakatsuji* Department of Neurology, Osaka University Graduate School of Medicine D4, 2-2 Yamada-oka, Suita,...

This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N -determined and conclud...

The paper presents a morphological analysis of the palatine torus of the Cracovian skull dated from XV-XVIIIth century. The cranial collection analysed comprised 98 skulls with the hard palate preserved but only 27 male and 28 female skulls showed the palatine torus. The length, breadth and height of the palatine torus were measured, and a visual inspection of the position and form of the torus...

Petersen-Gaussian (PG) networks are a broad family of interconnection networks for multi processor systems proposed recently. In this paper, a special case of PG networks, called PetersenTwisted-Torus (PTT) network, is considered. We analyze the diameter of PTT network, and find that PTT has smaller diameter and lower costing requirement than the well-known honeycomb mesh, diagonal mesh, torus,...

In [8] we introduced the notion of a local torus actions modeled on the standard representation (we call it a local torus action for simplicity), which is a generalization of a locally standard torus action. In this note we define a lifting of a local torus action to a principal torus bundle, and show that there is an obstruction class for the existence of liftings in the first cohomology of th...